Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.10 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.a.1187.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.03699 | + | 0.598709i | 0.463758 | + | 0.267751i | 0.713623 | − | 0.700530i | \(-0.247053\pi\) |
−0.249865 | + | 0.968281i | \(0.580386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52745 | − | 0.782297i | 0.955287 | − | 0.295681i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.03699 | + | 0.598709i | −0.327926 | + | 0.189328i | ||||
\(11\) | −2.65352 | − | 1.98969i | −0.800065 | − | 0.599913i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.26196i | − | 0.904706i | −0.891839 | − | 0.452353i | \(-0.850585\pi\) | ||
0.891839 | − | 0.452353i | \(-0.149415\pi\) | |||||||
\(14\) | −0.586237 | + | 2.57999i | −0.156678 | + | 0.689530i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.21006 | + | 3.82794i | 0.536019 | + | 0.928412i | 0.999113 | + | 0.0421028i | \(0.0134057\pi\) |
−0.463095 | + | 0.886309i | \(0.653261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73468 | + | 3.88827i | 1.54504 | + | 0.892030i | 0.998509 | + | 0.0545917i | \(0.0173857\pi\) |
0.546532 | + | 0.837438i | \(0.315948\pi\) | |||||||
\(20\) | − | 1.19742i | − | 0.267751i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.04988 | − | 1.30317i | 0.650236 | − | 0.277836i | ||||
\(23\) | −5.94749 | − | 3.43378i | −1.24014 | − | 0.715993i | −0.271015 | − | 0.962575i | \(-0.587359\pi\) |
−0.969122 | + | 0.246582i | \(0.920693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.78309 | − | 3.08841i | −0.356619 | − | 0.617682i | ||||
\(26\) | 2.82494 | + | 1.63098i | 0.554017 | + | 0.319862i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.94121 | − | 1.79769i | −0.366855 | − | 0.339731i | ||||
\(29\) | 7.85827 | 1.45924 | 0.729622 | − | 0.683850i | \(-0.239696\pi\) | ||||
0.729622 | + | 0.683850i | \(0.239696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.103382 | − | 0.179063i | −0.0185680 | − | 0.0321607i | 0.856592 | − | 0.515994i | \(-0.172577\pi\) |
−0.875160 | + | 0.483833i | \(0.839244\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.42012 | −0.758045 | ||||||||
\(35\) | 3.08932 | + | 0.701970i | 0.522191 | + | 0.118655i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.83230 | − | 6.63773i | 0.630026 | − | 1.09124i | −0.357520 | − | 0.933905i | \(-0.616378\pi\) |
0.987546 | − | 0.157331i | \(-0.0502891\pi\) | |||||||
\(38\) | −6.73468 | + | 3.88827i | −1.09251 | + | 0.630760i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.03699 | + | 0.598709i | 0.163963 | + | 0.0946642i | ||||
\(41\) | 3.15304 | 0.492422 | 0.246211 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246211 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00258i | − | 1.22038i | −0.792254 | − | 0.610191i | \(-0.791093\pi\) | ||
0.792254 | − | 0.610191i | \(-0.208907\pi\) | |||||||
\(44\) | −0.396361 | + | 3.29286i | −0.0597537 | + | 0.496417i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.94749 | − | 3.43378i | 0.876909 | − | 0.506284i | ||||
\(47\) | 0.355926 | + | 0.205494i | 0.0519172 | + | 0.0299744i | 0.525734 | − | 0.850649i | \(-0.323791\pi\) |
−0.473817 | + | 0.880623i | \(0.657124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.77602 | − | 3.95444i | 0.825146 | − | 0.564919i | ||||
\(50\) | 3.56619 | 0.504335 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.82494 | + | 1.63098i | −0.391749 | + | 0.226177i | ||||
\(53\) | −5.02547 | + | 2.90146i | −0.690302 | + | 0.398546i | −0.803725 | − | 0.595001i | \(-0.797152\pi\) |
0.113423 | + | 0.993547i | \(0.463818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.56044 | − | 3.65198i | −0.210409 | − | 0.492433i | ||||
\(56\) | 2.52745 | − | 0.782297i | 0.337745 | − | 0.104539i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.92914 | + | 6.80547i | −0.515921 | + | 0.893601i | ||||
\(59\) | −3.66888 | + | 2.11823i | −0.477647 | + | 0.275770i | −0.719436 | − | 0.694559i | \(-0.755599\pi\) |
0.241788 | + | 0.970329i | \(0.422266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.94695 | − | 5.74287i | −1.27358 | − | 0.735300i | −0.297917 | − | 0.954592i | \(-0.596292\pi\) |
−0.975659 | + | 0.219292i | \(0.929625\pi\) | |||||||
\(62\) | 0.206764 | 0.0262591 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.95297 | − | 3.38264i | 0.242236 | − | 0.419565i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.61793 | + | 9.73055i | 0.686340 | + | 1.18878i | 0.973014 | + | 0.230747i | \(0.0741170\pi\) |
−0.286674 | + | 0.958028i | \(0.592550\pi\) | |||||||
\(68\) | 2.21006 | − | 3.82794i | 0.268009 | − | 0.464206i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.15258 | + | 2.32445i | −0.257283 | + | 0.277824i | ||||
\(71\) | 3.80688i | 0.451793i | 0.974151 | + | 0.225897i | \(0.0725312\pi\) | ||||
−0.974151 | + | 0.225897i | \(0.927469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.195764 | − | 0.113024i | 0.0229124 | − | 0.0132285i | −0.488500 | − | 0.872564i | \(-0.662456\pi\) |
0.511412 | + | 0.859335i | \(0.329122\pi\) | |||||||
\(74\) | 3.83230 | + | 6.63773i | 0.445496 | + | 0.771621i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.77654i | − | 0.892030i | ||||||
\(77\) | −8.26316 | − | 2.95300i | −0.941674 | − | 0.336525i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00851 | + | 1.15961i | 0.225975 | + | 0.130466i | 0.608714 | − | 0.793390i | \(-0.291686\pi\) |
−0.382739 | + | 0.923856i | \(0.625019\pi\) | |||||||
\(80\) | −1.03699 | + | 0.598709i | −0.115940 | + | 0.0669377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.57652 | + | 2.73061i | −0.174098 | + | 0.301546i | ||||
\(83\) | 10.8698 | 1.19311 | 0.596557 | − | 0.802571i | \(-0.296535\pi\) | ||||
0.596557 | + | 0.802571i | \(0.296535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.29274i | 0.574078i | ||||||||
\(86\) | 6.93044 | + | 4.00129i | 0.747329 | + | 0.431470i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.65352 | − | 1.98969i | −0.282866 | − | 0.212101i | ||||
\(89\) | 11.4053 | + | 6.58488i | 1.20896 | + | 0.697996i | 0.962533 | − | 0.271165i | \(-0.0874087\pi\) |
0.246431 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.55183 | − | 8.24446i | −0.267504 | − | 0.864254i | ||||
\(92\) | 6.86757i | 0.715993i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.355926 | + | 0.205494i | −0.0367110 | + | 0.0211951i | ||||
\(95\) | 4.65588 | + | 8.06422i | 0.477683 | + | 0.827372i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1097 | 1.33109 | 0.665545 | − | 0.746357i | \(-0.268199\pi\) | ||||
0.665545 | + | 0.746357i | \(0.268199\pi\) | |||||||
\(98\) | 0.536631 | + | 6.97940i | 0.0542079 | + | 0.705026i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.78309 | + | 3.08841i | −0.178309 | + | 0.308841i | ||||
\(101\) | 4.82575 | + | 8.35845i | 0.480181 | + | 0.831697i | 0.999741 | − | 0.0227363i | \(-0.00723780\pi\) |
−0.519561 | + | 0.854433i | \(0.673904\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.95521 | − | 8.58267i | 0.488251 | − | 0.845676i | −0.511658 | − | 0.859189i | \(-0.670968\pi\) |
0.999909 | + | 0.0135137i | \(0.00430167\pi\) | |||||||
\(104\) | − | 3.26196i | − | 0.319862i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 5.80291i | − | 0.563629i | ||||||
\(107\) | 4.82669 | − | 8.36007i | 0.466614 | − | 0.808199i | −0.532659 | − | 0.846330i | \(-0.678807\pi\) |
0.999273 | + | 0.0381312i | \(0.0121405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.34796 | − | 3.66500i | 0.608024 | − | 0.351043i | −0.164168 | − | 0.986432i | \(-0.552494\pi\) |
0.772192 | + | 0.635390i | \(0.219160\pi\) | |||||||
\(110\) | 3.94292 | + | 0.474610i | 0.375943 | + | 0.0452523i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.586237 | + | 2.57999i | −0.0553941 | + | 0.243786i | ||||
\(113\) | − | 12.0213i | − | 1.13087i | −0.824792 | − | 0.565436i | \(-0.808708\pi\) | ||
0.824792 | − | 0.565436i | \(-0.191292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.11168 | − | 7.12163i | −0.383416 | − | 0.664095i | ||||
\(116\) | −3.92914 | − | 6.80547i | −0.364811 | − | 0.631872i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.23646i | − | 0.389997i | ||||||
\(119\) | 8.58041 | + | 7.94601i | 0.786565 | + | 0.728409i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.08229 | + | 10.5593i | 0.280208 | + | 0.959939i | ||||
\(122\) | 9.94695 | − | 5.74287i | 0.900555 | − | 0.519935i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.103382 | + | 0.179063i | −0.00928400 | + | 0.0160804i | ||||
\(125\) | − | 10.2573i | − | 0.917442i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1862i | 1.61376i | 0.590715 | + | 0.806880i | \(0.298846\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.95297 | + | 3.38264i | 0.171287 | + | 0.296677i | ||||
\(131\) | −0.397483 | + | 0.688460i | −0.0347282 | + | 0.0601511i | −0.882867 | − | 0.469623i | \(-0.844390\pi\) |
0.848139 | + | 0.529774i | \(0.177723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.0634 | + | 4.55889i | 1.73971 | + | 0.395306i | ||||
\(134\) | −11.2359 | −0.970631 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.21006 | + | 3.82794i | 0.189511 | + | 0.328243i | ||||
\(137\) | −5.20922 | + | 3.00754i | −0.445053 | + | 0.256952i | −0.705739 | − | 0.708472i | \(-0.749385\pi\) |
0.260685 | + | 0.965424i | \(0.416051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.8585i | − | 1.00583i | −0.864337 | − | 0.502913i | \(-0.832262\pi\) | ||
0.864337 | − | 0.502913i | \(-0.167738\pi\) | |||||||
\(140\) | −0.936737 | − | 3.02642i | −0.0791687 | − | 0.255779i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.29685 | − | 1.90344i | −0.276666 | − | 0.159733i | ||||
\(143\) | −6.49029 | + | 8.65567i | −0.542745 | + | 0.723824i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.14899 | + | 4.70482i | 0.676737 | + | 0.390714i | ||||
\(146\) | 0.226048i | 0.0187079i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.66460 | −0.630026 | ||||||||
\(149\) | 9.00137 | − | 15.5908i | 0.737421 | − | 1.27725i | −0.216232 | − | 0.976342i | \(-0.569377\pi\) |
0.953653 | − | 0.300908i | \(-0.0972898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.49066 | + | 2.59269i | −0.365445 | + | 0.210990i | −0.671467 | − | 0.741035i | \(-0.734335\pi\) |
0.306022 | + | 0.952025i | \(0.401002\pi\) | |||||||
\(152\) | 6.73468 | + | 3.88827i | 0.546254 | + | 0.315380i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.68895 | − | 5.67961i | 0.539011 | − | 0.457676i | ||||
\(155\) | − | 0.247583i | − | 0.0198864i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.83949 | + | 17.0425i | 0.785277 | + | 1.36014i | 0.928834 | + | 0.370497i | \(0.120813\pi\) |
−0.143557 | + | 0.989642i | \(0.545854\pi\) | |||||||
\(158\) | −2.00851 | + | 1.15961i | −0.159788 | + | 0.0922537i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.19742i | − | 0.0946642i | ||||||
\(161\) | −17.7182 | − | 4.02602i | −1.39639 | − | 0.317295i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0169 | + | 20.8138i | −0.941234 | + | 1.63026i | −0.178111 | + | 0.984010i | \(0.556999\pi\) |
−0.763122 | + | 0.646254i | \(0.776335\pi\) | |||||||
\(164\) | −1.57652 | − | 2.73061i | −0.123106 | − | 0.213225i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.43489 | + | 9.41350i | −0.421829 | + | 0.730630i | ||||
\(167\) | −13.3713 | −1.03471 | −0.517353 | − | 0.855772i | \(-0.673082\pi\) | ||||
−0.517353 | + | 0.855772i | \(0.673082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.35959 | 0.181507 | ||||||||
\(170\) | −4.58364 | − | 2.64637i | −0.351549 | − | 0.202967i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.93044 | + | 4.00129i | −0.528441 | + | 0.305096i | ||||
\(173\) | −11.9348 | + | 20.6717i | −0.907385 | + | 1.57164i | −0.0897011 | + | 0.995969i | \(0.528591\pi\) |
−0.817684 | + | 0.575668i | \(0.804742\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.92274 | − | 6.41090i | −0.523310 | − | 0.484618i | ||||
\(176\) | 3.04988 | − | 1.30317i | 0.229893 | − | 0.0982300i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4053 | + | 6.58488i | −0.854867 | + | 0.493558i | ||||
\(179\) | −17.6015 | + | 10.1622i | −1.31560 | + | 0.759560i | −0.983017 | − | 0.183515i | \(-0.941252\pi\) |
−0.332580 | + | 0.943075i | \(0.607919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4560 | −1.44616 | −0.723078 | − | 0.690766i | \(-0.757273\pi\) | ||||
−0.723078 | + | 0.690766i | \(0.757273\pi\) | |||||||
\(182\) | 8.41582 | + | 1.91228i | 0.623822 | + | 0.141748i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.94749 | − | 3.43378i | −0.438455 | − | 0.253142i | ||||
\(185\) | 7.94814 | − | 4.58886i | 0.584359 | − | 0.337380i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.75197 | − | 14.5548i | 0.128116 | − | 1.06435i | ||||
\(188\) | − | 0.410988i | − | 0.0299744i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.31176 | −0.675546 | ||||||||
\(191\) | −8.14743 | − | 4.70392i | −0.589527 | − | 0.340364i | 0.175383 | − | 0.984500i | \(-0.443884\pi\) |
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.92081 | − | 1.68633i | 0.210245 | − | 0.121385i | −0.391180 | − | 0.920314i | \(-0.627933\pi\) |
0.601425 | + | 0.798929i | \(0.294600\pi\) | |||||||
\(194\) | −6.55486 | + | 11.3534i | −0.470612 | + | 0.815123i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.31265 | − | 3.02496i | −0.450904 | − | 0.216069i | ||||
\(197\) | 6.33128 | 0.451085 | 0.225543 | − | 0.974233i | \(-0.427585\pi\) | ||||
0.225543 | + | 0.974233i | \(0.427585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.331375 | + | 0.573958i | 0.0234905 | + | 0.0406868i | 0.877532 | − | 0.479519i | \(-0.159189\pi\) |
−0.854041 | + | 0.520205i | \(0.825855\pi\) | |||||||
\(200\) | −1.78309 | − | 3.08841i | −0.126084 | − | 0.218384i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.65151 | −0.679078 | ||||||||
\(203\) | 19.8614 | − | 6.14751i | 1.39400 | − | 0.431470i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.26969 | + | 1.88775i | 0.228365 | + | 0.131846i | ||||
\(206\) | 4.95521 | + | 8.58267i | 0.345246 | + | 0.597983i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.82494 | + | 1.63098i | 0.195875 | + | 0.113088i | ||||
\(209\) | −10.1341 | − | 23.7175i | −0.700993 | − | 1.64057i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9427i | 1.02870i | 0.857580 | + | 0.514350i | \(0.171967\pi\) | ||||
−0.857580 | + | 0.514350i | \(0.828033\pi\) | |||||||
\(212\) | 5.02547 | + | 2.90146i | 0.345151 | + | 0.199273i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.82669 | + | 8.36007i | 0.329946 | + | 0.571483i | ||||
\(215\) | 4.79122 | − | 8.29864i | 0.326758 | − | 0.565962i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.401374 | − | 0.371698i | −0.0272471 | − | 0.0252325i | ||||
\(218\) | 7.32999i | 0.496450i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.38249 | + | 3.17737i | −0.160627 | + | 0.214218i | ||||
\(221\) | 12.4866 | − | 7.20914i | 0.839940 | − | 0.484939i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0313 | −1.14050 | −0.570250 | − | 0.821471i | \(-0.693154\pi\) | ||||
−0.570250 | + | 0.821471i | \(0.693154\pi\) | |||||||
\(224\) | −1.94121 | − | 1.79769i | −0.129703 | − | 0.120113i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4108 | + | 6.01066i | 0.692514 | + | 0.399823i | ||||
\(227\) | −9.58521 | − | 16.6021i | −0.636193 | − | 1.10192i | −0.986261 | − | 0.165194i | \(-0.947175\pi\) |
0.350068 | − | 0.936724i | \(-0.386158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.51023 | − | 11.2760i | 0.430208 | − | 0.745142i | −0.566683 | − | 0.823936i | \(-0.691774\pi\) |
0.996891 | + | 0.0787938i | \(0.0251069\pi\) | |||||||
\(230\) | 8.22335 | 0.542232 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.85827 | 0.515921 | ||||||||
\(233\) | 2.04857 | − | 3.54823i | 0.134206 | − | 0.232452i | −0.791088 | − | 0.611703i | \(-0.790485\pi\) |
0.925294 | + | 0.379251i | \(0.123818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.246063 | + | 0.426193i | 0.0160513 | + | 0.0278018i | ||||
\(236\) | 3.66888 | + | 2.11823i | 0.238824 | + | 0.137885i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.1716 | + | 3.45785i | −0.724150 | + | 0.224139i | ||||
\(239\) | −4.68979 | −0.303357 | −0.151679 | − | 0.988430i | \(-0.548468\pi\) | ||||
−0.151679 | + | 0.988430i | \(0.548468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0323 | + | 6.36950i | −0.710652 | + | 0.410295i | −0.811303 | − | 0.584627i | \(-0.801241\pi\) |
0.100650 | + | 0.994922i | \(0.467908\pi\) | |||||||
\(242\) | −10.6858 | − | 2.61032i | −0.686909 | − | 0.167798i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4857i | 0.735300i | ||||||||
\(245\) | 8.35726 | − | 0.642572i | 0.533926 | − | 0.0410524i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6834 | − | 21.9683i | 0.807025 | − | 1.39781i | ||||
\(248\) | −0.103382 | − | 0.179063i | −0.00656478 | − | 0.0113705i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.88309 | + | 5.12866i | 0.561816 | + | 0.324365i | ||||
\(251\) | − | 25.6272i | − | 1.61758i | −0.588100 | − | 0.808788i | \(-0.700124\pi\) | ||
0.588100 | − | 0.808788i | \(-0.299876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.94960 | + | 20.9452i | 0.562657 | + | 1.31682i | ||||
\(254\) | −15.7497 | − | 9.09308i | −0.988222 | − | 0.570550i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.92122 | − | 2.84127i | −0.306978 | − | 0.177234i | 0.338596 | − | 0.940932i | \(-0.390048\pi\) |
−0.645573 | + | 0.763698i | \(0.723381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.49327 | − | 19.7745i | 0.279198 | − | 1.22873i | ||||
\(260\) | −3.90594 | −0.242236 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.397483 | − | 0.688460i | −0.0245566 | − | 0.0425332i | ||||
\(263\) | −14.4242 | − | 24.9835i | −0.889436 | − | 1.54055i | −0.840544 | − | 0.541744i | \(-0.817764\pi\) |
−0.0488920 | − | 0.998804i | \(-0.515569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.94852 | −0.426844 | ||||||||
\(266\) | −13.9798 | + | 15.0959i | −0.857156 | + | 0.925591i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.61793 | − | 9.73055i | 0.343170 | − | 0.594388i | ||||
\(269\) | −15.8208 | + | 9.13413i | −0.964610 | + | 0.556918i | −0.897589 | − | 0.440834i | \(-0.854683\pi\) |
−0.0670210 | + | 0.997752i | \(0.521349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.05904 | + | 2.92084i | 0.307315 | + | 0.177428i | 0.645724 | − | 0.763571i | \(-0.276556\pi\) |
−0.338410 | + | 0.940999i | \(0.609889\pi\) | |||||||
\(272\) | −4.42012 | −0.268009 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.01509i | − | 0.363385i | ||||||
\(275\) | −1.41350 | + | 11.7429i | −0.0852373 | + | 0.708126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0938 | + | 7.55973i | −0.786732 | + | 0.454220i | −0.838811 | − | 0.544423i | \(-0.816749\pi\) |
0.0520786 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(278\) | 10.2698 | + | 5.92926i | 0.615940 | + | 0.355613i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.08932 | + | 0.701970i | 0.184622 | + | 0.0419507i | ||||
\(281\) | −7.22799 | −0.431186 | −0.215593 | − | 0.976483i | \(-0.569168\pi\) | ||||
−0.215593 | + | 0.976483i | \(0.569168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0575633 | − | 0.0332342i | 0.00342179 | − | 0.00197557i | −0.498288 | − | 0.867011i | \(-0.666038\pi\) |
0.501710 | + | 0.865036i | \(0.332704\pi\) | |||||||
\(284\) | 3.29685 | − | 1.90344i | 0.195632 | − | 0.112948i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.25089 | − | 9.94859i | −0.251360 | − | 0.588272i | ||||
\(287\) | 7.96916 | − | 2.46662i | 0.470405 | − | 0.145600i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.26875 | + | 2.19753i | −0.0746322 | + | 0.129267i | ||||
\(290\) | −8.14899 | + | 4.70482i | −0.478525 | + | 0.276277i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.195764 | − | 0.113024i | −0.0114562 | − | 0.00661424i | ||||
\(293\) | 22.1095 | 1.29165 | 0.645824 | − | 0.763486i | \(-0.276514\pi\) | ||||
0.645824 | + | 0.763486i | \(0.276514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.07281 | −0.295350 | ||||||||
\(296\) | 3.83230 | − | 6.63773i | 0.222748 | − | 0.385810i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.00137 | + | 15.5908i | 0.521435 | + | 0.903152i | ||||
\(299\) | −11.2009 | + | 19.4005i | −0.647764 | + | 1.12196i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.26040 | − | 20.2261i | −0.360843 | − | 1.16582i | ||||
\(302\) | − | 5.18537i | − | 0.298385i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.73468 | + | 3.88827i | −0.386260 | + | 0.223007i | ||||
\(305\) | −6.87662 | − | 11.9107i | −0.393754 | − | 0.682002i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0987i | 1.14710i | 0.819172 | + | 0.573548i | \(0.194433\pi\) | ||||
−0.819172 | + | 0.573548i | \(0.805567\pi\) | |||||||
\(308\) | 1.57421 | + | 8.63261i | 0.0896988 | + | 0.491888i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.214414 | + | 0.123792i | 0.0121779 | + | 0.00703090i | ||||
\(311\) | −13.7708 | + | 7.95055i | −0.780868 | + | 0.450834i | −0.836738 | − | 0.547604i | \(-0.815540\pi\) |
0.0558698 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.27538 | − | 14.3334i | 0.467752 | − | 0.810170i | −0.531569 | − | 0.847015i | \(-0.678397\pi\) |
0.999321 | + | 0.0368447i | \(0.0117307\pi\) | |||||||
\(314\) | −19.6790 | −1.11055 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 2.31922i | − | 0.130466i | ||||||
\(317\) | 8.65990 | + | 4.99980i | 0.486389 | + | 0.280817i | 0.723075 | − | 0.690770i | \(-0.242728\pi\) |
−0.236686 | + | 0.971586i | \(0.576061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.8521 | − | 15.6355i | −1.16749 | − | 0.875420i | ||||
\(320\) | 1.03699 | + | 0.598709i | 0.0579698 | + | 0.0334689i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.3457 | − | 13.3314i | 0.688002 | − | 0.742931i | ||||
\(323\) | 34.3733i | 1.91258i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0743 | + | 5.81639i | −0.558821 | + | 0.322635i | ||||
\(326\) | −12.0169 | − | 20.8138i | −0.665553 | − | 1.15277i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.15304 | 0.174098 | ||||||||
\(329\) | 1.06034 | + | 0.240936i | 0.0584587 | + | 0.0132833i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5068 | + | 28.5906i | −0.907294 | + | 1.57148i | −0.0894857 | + | 0.995988i | \(0.528522\pi\) |
−0.817808 | + | 0.575491i | \(0.804811\pi\) | |||||||
\(332\) | −5.43489 | − | 9.41350i | −0.298278 | − | 0.516633i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.68567 | − | 11.5799i | 0.365824 | − | 0.633625i | ||||
\(335\) | 13.4540i | 0.735072i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.870822i | − | 0.0474367i | −0.999719 | − | 0.0237184i | \(-0.992450\pi\) | ||
0.999719 | − | 0.0237184i | \(-0.00755050\pi\) | |||||||
\(338\) | −1.17979 | + | 2.04346i | −0.0641724 | + | 0.111150i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.58364 | − | 2.64637i | 0.248583 | − | 0.143519i | ||||
\(341\) | −0.0819535 | + | 0.680845i | −0.00443803 | + | 0.0368698i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5051 | − | 14.5132i | 0.621215 | − | 0.783640i | ||||
\(344\) | − | 8.00258i | − | 0.431470i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.9348 | − | 20.6717i | −0.641618 | − | 1.11131i | ||||
\(347\) | −3.92630 | − | 6.80054i | −0.210775 | − | 0.365072i | 0.741183 | − | 0.671304i | \(-0.234265\pi\) |
−0.951957 | + | 0.306231i | \(0.900932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6953i | 1.10779i | 0.832586 | + | 0.553896i | \(0.186860\pi\) | ||||
−0.832586 | + | 0.553896i | \(0.813140\pi\) | |||||||
\(350\) | 9.01337 | − | 2.78982i | 0.481785 | − | 0.149122i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.396361 | + | 3.29286i | −0.0211261 | + | 0.175510i | ||||
\(353\) | 23.0277 | − | 13.2951i | 1.22564 | − | 0.707625i | 0.259527 | − | 0.965736i | \(-0.416433\pi\) |
0.966115 | + | 0.258111i | \(0.0831001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.27921 | + | 3.94771i | −0.120968 | + | 0.209523i | ||||
\(356\) | − | 13.1698i | − | 0.697996i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 20.3244i | − | 1.07418i | ||||||
\(359\) | 0.0346521 | − | 0.0600191i | 0.00182887 | − | 0.00316769i | −0.865110 | − | 0.501583i | \(-0.832751\pi\) |
0.866938 | + | 0.498415i | \(0.166085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7373 | + | 35.9180i | 1.09143 | + | 1.89042i | ||||
\(362\) | 9.72802 | − | 16.8494i | 0.511293 | − | 0.885586i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.86400 | + | 6.33217i | −0.307357 | + | 0.331896i | ||||
\(365\) | 0.270674 | 0.0141677 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5149 | − | 32.0687i | −0.966469 | − | 1.67397i | −0.705615 | − | 0.708595i | \(-0.749329\pi\) |
−0.260854 | − | 0.965378i | \(-0.584004\pi\) | |||||||
\(368\) | 5.94749 | − | 3.43378i | 0.310034 | − | 0.178998i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.17773i | 0.477127i | ||||||||
\(371\) | −10.4318 | + | 11.2647i | −0.541594 | + | 0.584834i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9206 | + | 6.30501i | 0.565447 | + | 0.326461i | 0.755329 | − | 0.655346i | \(-0.227477\pi\) |
−0.189882 | + | 0.981807i | \(0.560810\pi\) | |||||||
\(374\) | 11.7289 | + | 8.79466i | 0.606485 | + | 0.454761i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.355926 | + | 0.205494i | 0.0183555 | + | 0.0105976i | ||||
\(377\) | − | 25.6334i | − | 1.32019i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.45725 | −0.228954 | −0.114477 | − | 0.993426i | \(-0.536519\pi\) | ||||
−0.114477 | + | 0.993426i | \(0.536519\pi\) | |||||||
\(380\) | 4.65588 | − | 8.06422i | 0.238842 | − | 0.413686i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.14743 | − | 4.70392i | 0.416859 | − | 0.240674i | ||||
\(383\) | −11.0167 | − | 6.36051i | −0.562928 | − | 0.325007i | 0.191392 | − | 0.981514i | \(-0.438700\pi\) |
−0.754320 | + | 0.656507i | \(0.772033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.80086 | − | 8.00947i | −0.346604 | − | 0.408200i | ||||
\(386\) | 3.37267i | 0.171664i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.55486 | − | 11.3534i | −0.332773 | − | 0.576379i | ||||
\(389\) | −18.7691 | + | 10.8364i | −0.951633 | + | 0.549426i | −0.893588 | − | 0.448888i | \(-0.851820\pi\) |
−0.0580454 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.3555i | − | 1.53514i | ||||||
\(392\) | 5.77602 | − | 3.95444i | 0.291733 | − | 0.199729i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.16564 | + | 5.48305i | −0.159483 | + | 0.276232i | ||||
\(395\) | 1.38854 | + | 2.40502i | 0.0698650 | + | 0.121010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.77259 | + | 11.7305i | −0.339907 | + | 0.588736i | −0.984415 | − | 0.175862i | \(-0.943729\pi\) |
0.644508 | + | 0.764597i | \(0.277062\pi\) | |||||||
\(398\) | −0.662749 | −0.0332206 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.56619 | 0.178309 | ||||||||
\(401\) | −23.0277 | − | 13.2951i | −1.14995 | − | 0.663924i | −0.201075 | − | 0.979576i | \(-0.564443\pi\) |
−0.948875 | + | 0.315652i | \(0.897777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.584098 | + | 0.337229i | −0.0290960 | + | 0.0167986i | ||||
\(404\) | 4.82575 | − | 8.35845i | 0.240090 | − | 0.415849i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.60681 | + | 20.2742i | −0.228632 | + | 1.00619i | ||||
\(407\) | −23.3761 | + | 9.98826i | −1.15871 | + | 0.495100i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.51290 | − | 3.18288i | 0.272596 | − | 0.157383i | −0.357471 | − | 0.933924i | \(-0.616361\pi\) |
0.630067 | + | 0.776541i | \(0.283028\pi\) | |||||||
\(410\) | −3.26969 | + | 1.88775i | −0.161478 | + | 0.0932296i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.91042 | −0.488251 | ||||||||
\(413\) | −7.61583 | + | 8.22387i | −0.374751 | + | 0.404670i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2719 | + | 6.50783i | 0.553316 | + | 0.319457i | ||||
\(416\) | −2.82494 | + | 1.63098i | −0.138504 | + | 0.0799655i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.6070 | + | 3.08232i | 1.25248 | + | 0.150761i | ||||
\(419\) | − | 21.1161i | − | 1.03159i | −0.856713 | − | 0.515794i | \(-0.827497\pi\) | ||
0.856713 | − | 0.515794i | \(-0.172503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.94131 | −0.435773 | −0.217886 | − | 0.975974i | \(-0.569916\pi\) | ||||
−0.217886 | + | 0.975974i | \(0.569916\pi\) | |||||||
\(422\) | −12.9408 | − | 7.47137i | −0.629948 | − | 0.363701i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.02547 | + | 2.90146i | −0.244058 | + | 0.140907i | ||||
\(425\) | 7.88150 | − | 13.6512i | 0.382309 | − | 0.662178i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.6331 | − | 6.73337i | −1.43404 | − | 0.325850i | ||||
\(428\) | −9.65338 | −0.466614 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.79122 | + | 8.29864i | 0.231053 | + | 0.400196i | ||||
\(431\) | 4.16534 | + | 7.21459i | 0.200638 | + | 0.347514i | 0.948734 | − | 0.316076i | \(-0.102365\pi\) |
−0.748096 | + | 0.663590i | \(0.769032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.288704 | 0.0138742 | 0.00693711 | − | 0.999976i | \(-0.497792\pi\) | ||||
0.00693711 | + | 0.999976i | \(0.497792\pi\) | |||||||
\(434\) | 0.522587 | − | 0.161751i | 0.0250850 | − | 0.00776431i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.34796 | − | 3.66500i | −0.304012 | − | 0.175521i | ||||
\(437\) | −26.7029 | − | 46.2509i | −1.27738 | − | 2.21248i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0491 | − | 5.80186i | −0.479618 | − | 0.276908i | 0.240639 | − | 0.970615i | \(-0.422643\pi\) |
−0.720257 | + | 0.693707i | \(0.755976\pi\) | |||||||
\(440\) | −1.56044 | − | 3.65198i | −0.0743910 | − | 0.174101i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.4183i | 0.685808i | ||||||||
\(443\) | 4.34544 | + | 2.50884i | 0.206458 | + | 0.119199i | 0.599664 | − | 0.800252i | \(-0.295301\pi\) |
−0.393206 | + | 0.919450i | \(0.628634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.88485 | + | 13.6570i | 0.373778 | + | 0.647402i | ||||
\(446\) | 8.51565 | − | 14.7495i | 0.403228 | − | 0.698411i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.52745 | − | 0.782297i | 0.119411 | − | 0.0369601i | ||||
\(449\) | 14.7868i | 0.697835i | 0.937154 | + | 0.348917i | \(0.113451\pi\) | ||||
−0.937154 | + | 0.348917i | \(0.886549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.36665 | − | 6.27357i | −0.393970 | − | 0.295411i | ||||
\(452\) | −10.4108 | + | 6.01066i | −0.489682 | + | 0.282718i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.1704 | 0.899712 | ||||||||
\(455\) | 2.28980 | − | 10.0773i | 0.107348 | − | 0.472429i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.4805 | − | 17.0205i | −1.37904 | − | 0.796188i | −0.386994 | − | 0.922082i | \(-0.626487\pi\) |
−0.992044 | + | 0.125895i | \(0.959820\pi\) | |||||||
\(458\) | 6.51023 | + | 11.2760i | 0.304203 | + | 0.526895i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.11168 | + | 7.12163i | −0.191708 | + | 0.332048i | ||||
\(461\) | 31.2127 | 1.45372 | 0.726861 | − | 0.686785i | \(-0.240979\pi\) | ||||
0.726861 | + | 0.686785i | \(0.240979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.66544 | 0.309769 | 0.154885 | − | 0.987933i | \(-0.450499\pi\) | ||||
0.154885 | + | 0.987933i | \(0.450499\pi\) | |||||||
\(464\) | −3.92914 | + | 6.80547i | −0.182406 | + | 0.315936i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.04857 | + | 3.54823i | 0.0948983 | + | 0.164369i | ||||
\(467\) | −6.58720 | − | 3.80312i | −0.304819 | − | 0.175987i | 0.339787 | − | 0.940503i | \(-0.389645\pi\) |
−0.644606 | + | 0.764515i | \(0.722978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.8112 | + | 20.1986i | 1.00715 | + | 0.932684i | ||||
\(470\) | −0.492125 | −0.0227000 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.66888 | + | 2.11823i | −0.168874 | + | 0.0974994i | ||||
\(473\) | −15.9226 | + | 21.2350i | −0.732124 | + | 0.976386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 27.7326i | − | 1.27246i | ||||||
\(476\) | 2.59124 | − | 11.4039i | 0.118769 | − | 0.522695i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.34489 | − | 4.06147i | 0.107253 | − | 0.185767i | ||||
\(479\) | 7.64294 | + | 13.2380i | 0.349215 | + | 0.604858i | 0.986110 | − | 0.166092i | \(-0.0531150\pi\) |
−0.636895 | + | 0.770950i | \(0.719782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.6521 | − | 12.5008i | −0.987249 | − | 0.569988i | ||||
\(482\) | − | 12.7390i | − | 0.580245i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.60350 | − | 7.94901i | 0.345614 | − | 0.361319i | ||||
\(485\) | 13.5947 | + | 7.84891i | 0.617304 | + | 0.356401i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.790493 | + | 1.36917i | 0.0358206 | + | 0.0620432i | 0.883380 | − | 0.468658i | \(-0.155262\pi\) |
−0.847559 | + | 0.530701i | \(0.821929\pi\) | |||||||
\(488\) | −9.94695 | − | 5.74287i | −0.450277 | − | 0.259968i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.62215 | + | 7.55889i | −0.163632 | + | 0.341476i | ||||
\(491\) | 6.90788 | 0.311748 | 0.155874 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155874 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3673 | + | 30.0810i | 0.782183 | + | 1.35478i | ||||
\(494\) | 12.6834 | + | 21.9683i | 0.570653 | + | 0.988400i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.206764 | 0.00928400 | ||||||||
\(497\) | 2.97811 | + | 9.62170i | 0.133587 | + | 0.431592i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.474107 | + | 0.821178i | −0.0212240 | + | 0.0367610i | −0.876442 | − | 0.481507i | \(-0.840090\pi\) |
0.855218 | + | 0.518268i | \(0.173423\pi\) | |||||||
\(500\) | −8.88309 | + | 5.12866i | −0.397264 | + | 0.229360i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.1938 | + | 12.8136i | 0.990559 | + | 0.571900i | ||||
\(503\) | −30.8752 | −1.37666 | −0.688328 | − | 0.725400i | \(-0.741655\pi\) | ||||
−0.688328 | + | 0.725400i | \(0.741655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5569i | 0.514275i | ||||||||
\(506\) | −22.6139 | − | 2.72204i | −1.00531 | − | 0.121009i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.7497 | − | 9.09308i | 0.698779 | − | 0.403440i | ||||
\(509\) | 31.6394 | + | 18.2670i | 1.40239 | + | 0.809670i | 0.994638 | − | 0.103422i | \(-0.0329794\pi\) |
0.407752 | + | 0.913093i | \(0.366313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.406364 | − | 0.438808i | 0.0179765 | − | 0.0194117i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.92122 | − | 2.84127i | 0.217066 | − | 0.125323i | ||||
\(515\) | 10.2770 | − | 5.93346i | 0.452861 | − | 0.261459i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.535587 | − | 1.25346i | −0.0235551 | − | 0.0551273i | ||||
\(518\) | 14.8786 | + | 13.7786i | 0.653729 | + | 0.605395i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.95297 | − | 3.38264i | 0.0856433 | − | 0.148339i | ||||
\(521\) | 0.780812 | − | 0.450802i | 0.0342080 | − | 0.0197500i | −0.482798 | − | 0.875731i | \(-0.660380\pi\) |
0.517006 | + | 0.855981i | \(0.327046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.65582 | + | 4.99744i | 0.378492 | + | 0.218523i | 0.677162 | − | 0.735834i | \(-0.263210\pi\) |
−0.298670 | + | 0.954357i | \(0.596543\pi\) | |||||||
\(524\) | 0.794965 | 0.0347282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.8484 | 1.25785 | ||||||||
\(527\) | 0.456962 | − | 0.791482i | 0.0199056 | − | 0.0344775i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0817 | + | 20.9262i | 0.525293 | + | 0.909835i | ||||
\(530\) | 3.47426 | − | 6.01759i | 0.150912 | − | 0.261387i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.08356 | − | 19.6548i | −0.263756 | − | 0.852144i | ||||
\(533\) | − | 10.2851i | − | 0.445498i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0105 | − | 5.77957i | 0.432792 | − | 0.249872i | ||||
\(536\) | 5.61793 | + | 9.73055i | 0.242658 | + | 0.420296i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 18.2683i | − | 0.787601i | ||||||
\(539\) | −23.1949 | − | 0.999316i | −0.999073 | − | 0.0430436i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8485 | + | 17.8104i | 1.32628 | + | 0.765727i | 0.984722 | − | 0.174134i | \(-0.0557126\pi\) |
0.341557 | + | 0.939861i | \(0.389046\pi\) | |||||||
\(542\) | −5.05904 | + | 2.92084i | −0.217304 | + | 0.125461i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.21006 | − | 3.82794i | 0.0947556 | − | 0.164122i | ||||
\(545\) | 8.77706 | 0.375968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.11968i | − | 0.304416i | −0.988349 | − | 0.152208i | \(-0.951362\pi\) | ||
0.988349 | − | 0.152208i | \(-0.0486383\pi\) | |||||||
\(548\) | 5.20922 | + | 3.00754i | 0.222527 | + | 0.128476i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.46294 | − | 7.09560i | −0.403501 | − | 0.302557i | ||||
\(551\) | 52.9229 | + | 30.5551i | 2.25459 | + | 1.30169i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.98356 | + | 1.35961i | 0.254447 | + | 0.0578166i | ||||
\(554\) | − | 15.1195i | − | 0.642364i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.2698 | + | 5.92926i | −0.435535 | + | 0.251457i | ||||
\(557\) | 9.08485 | + | 15.7354i | 0.384938 | + | 0.666731i | 0.991761 | − | 0.128106i | \(-0.0408896\pi\) |
−0.606823 | + | 0.794837i | \(0.707556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.1041 | −1.10409 | ||||||||
\(560\) | −2.15258 | + | 2.32445i | −0.0909633 | + | 0.0982258i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.61399 | − | 6.25962i | 0.152447 | − | 0.264046i | ||||
\(563\) | 6.69275 | + | 11.5922i | 0.282066 | + | 0.488552i | 0.971893 | − | 0.235422i | \(-0.0756471\pi\) |
−0.689828 | + | 0.723974i | \(0.742314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.19728 | − | 12.4660i | 0.302792 | − | 0.524451i | ||||
\(566\) | 0.0664684i | 0.00279388i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.80688i | 0.159733i | ||||||||
\(569\) | −0.774915 | + | 1.34219i | −0.0324861 | + | 0.0562676i | −0.881811 | − | 0.471602i | \(-0.843676\pi\) |
0.849325 | + | 0.527870i | \(0.177009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9067 | + | 21.3081i | −1.54450 | + | 0.891715i | −0.545949 | + | 0.837819i | \(0.683831\pi\) |
−0.998547 | + | 0.0538962i | \(0.982836\pi\) | |||||||
\(572\) | 10.7412 | + | 1.29292i | 0.449111 | + | 0.0540596i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.84843 | + | 8.13480i | −0.0771519 | + | 0.339540i | ||||
\(575\) | 24.4911i | 1.02135i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.303156 | + | 0.525081i | 0.0126205 | + | 0.0218594i | 0.872267 | − | 0.489030i | \(-0.162649\pi\) |
−0.859646 | + | 0.510890i | \(0.829316\pi\) | |||||||
\(578\) | −1.26875 | − | 2.19753i | −0.0527729 | − | 0.0914054i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 9.40964i | − | 0.390714i | ||||||
\(581\) | 27.4728 | − | 8.50340i | 1.13977 | − | 0.352780i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1082 | + | 2.30005i | 0.791379 | + | 0.0952584i | ||||
\(584\) | 0.195764 | − | 0.113024i | 0.00810075 | − | 0.00467697i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0547 | + | 19.1474i | −0.456667 | + | 0.790970i | ||||
\(587\) | − | 2.21478i | − | 0.0914137i | −0.998955 | − | 0.0457069i | \(-0.985446\pi\) | ||
0.998955 | − | 0.0457069i | \(-0.0145540\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.60791i | − | 0.0662528i | ||||||
\(590\) | 2.53641 | − | 4.39318i | 0.104422 | − | 0.180864i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.83230 | + | 6.63773i | 0.157506 | + | 0.272809i | ||||
\(593\) | −16.2190 | + | 28.0922i | −0.666036 | + | 1.15361i | 0.312967 | + | 0.949764i | \(0.398677\pi\) |
−0.979003 | + | 0.203844i | \(0.934656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.14049 | + | 13.3771i | 0.169744 | + | 0.548409i | ||||
\(596\) | −18.0027 | −0.737421 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.2009 | − | 19.4005i | −0.458038 | − | 0.793345i | ||||
\(599\) | −39.3780 | + | 22.7349i | −1.60894 | + | 0.928922i | −0.619333 | + | 0.785128i | \(0.712597\pi\) |
−0.989608 | + | 0.143794i | \(0.954070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.7080i | − | 0.967069i | −0.875325 | − | 0.483535i | \(-0.839353\pi\) | ||
0.875325 | − | 0.483535i | \(-0.160647\pi\) | |||||||
\(602\) | 20.6466 | + | 4.69141i | 0.841491 | + | 0.191207i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.49066 | + | 2.59269i | 0.182723 | + | 0.105495i | ||||
\(605\) | −3.12565 | + | 12.7954i | −0.127076 | + | 0.520206i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5637 | − | 9.56306i | −0.672300 | − | 0.388153i | 0.124648 | − | 0.992201i | \(-0.460220\pi\) |
−0.796948 | + | 0.604049i | \(0.793553\pi\) | |||||||
\(608\) | − | 7.77654i | − | 0.315380i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.7532 | 0.556853 | ||||||||
\(611\) | 0.670315 | − | 1.16102i | 0.0271180 | − | 0.0469698i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.26599 | + | 1.88562i | −0.131912 | + | 0.0761595i | −0.564504 | − | 0.825430i | \(-0.690932\pi\) |
0.432592 | + | 0.901590i | \(0.357599\pi\) | |||||||
\(614\) | −17.4060 | − | 10.0494i | −0.702450 | − | 0.405560i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.26316 | − | 2.95300i | −0.332932 | − | 0.118980i | ||||
\(617\) | 13.0431i | 0.525096i | 0.964919 | + | 0.262548i | \(0.0845628\pi\) | ||||
−0.964919 | + | 0.262548i | \(0.915437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6271 | + | 35.7272i | 0.829074 | + | 1.43600i | 0.898766 | + | 0.438429i | \(0.144465\pi\) |
−0.0696922 | + | 0.997569i | \(0.522202\pi\) | |||||||
\(620\) | −0.214414 | + | 0.123792i | −0.00861106 | + | 0.00497160i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 15.9011i | − | 0.637576i | ||||||
\(623\) | 33.9778 | + | 7.72059i | 1.36129 | + | 0.309319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.77433 | + | 4.80528i | −0.110973 | + | 0.192211i | ||||
\(626\) | 8.27538 | + | 14.3334i | 0.330751 | + | 0.572877i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.83949 | − | 17.0425i | 0.392638 | − | 0.680070i | ||||
\(629\) | 33.8785 | 1.35082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.4512 | −1.41129 | −0.705645 | − | 0.708566i | \(-0.749343\pi\) | ||||
−0.705645 | + | 0.708566i | \(0.749343\pi\) | |||||||
\(632\) | 2.00851 | + | 1.15961i | 0.0798941 | + | 0.0461269i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.65990 | + | 4.99980i | −0.343929 | + | 0.198567i | ||||
\(635\) | −10.8882 | + | 18.8589i | −0.432086 | + | 0.748394i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.8992 | − | 18.8412i | −0.511086 | − | 0.746515i | ||||
\(638\) | 23.9668 | − | 10.2407i | 0.948854 | − | 0.405431i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.03699 | + | 0.598709i | −0.0409908 | + | 0.0236661i | ||||
\(641\) | 14.8938 | − | 8.59891i | 0.588268 | − | 0.339637i | −0.176144 | − | 0.984364i | \(-0.556363\pi\) |
0.764412 | + | 0.644728i | \(0.223029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.9068 | −0.587869 | −0.293934 | − | 0.955826i | \(-0.594965\pi\) | ||||
−0.293934 | + | 0.955826i | \(0.594965\pi\) | |||||||
\(644\) | 5.37248 | + | 17.3574i | 0.211705 | + | 0.683979i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.7681 | − | 17.1866i | −1.17121 | − | 0.676199i | ||||
\(647\) | 8.06855 | − | 4.65838i | 0.317208 | − | 0.183140i | −0.332940 | − | 0.942948i | \(-0.608041\pi\) |
0.650147 | + | 0.759808i | \(0.274707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.9500 | + | 1.67917i | 0.547587 | + | 0.0659131i | ||||
\(650\) | − | 11.6328i | − | 0.456275i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.0337 | 0.941234 | ||||||||
\(653\) | −16.4127 | − | 9.47591i | −0.642281 | − | 0.370821i | 0.143212 | − | 0.989692i | \(-0.454257\pi\) |
−0.785492 | + | 0.618871i | \(0.787590\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.824375 | + | 0.475953i | −0.0322110 | + | 0.0185970i | ||||
\(656\) | −1.57652 | + | 2.73061i | −0.0615528 | + | 0.106613i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.738829 | + | 0.797817i | −0.0288026 | + | 0.0311021i | ||||
\(659\) | 22.1801 | 0.864016 | 0.432008 | − | 0.901870i | \(-0.357805\pi\) | ||||
0.432008 | + | 0.901870i | \(0.357805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8342 | + | 30.8897i | 0.693670 | + | 1.20147i | 0.970627 | + | 0.240589i | \(0.0773406\pi\) |
−0.276957 | + | 0.960882i | \(0.589326\pi\) | |||||||
\(662\) | −16.5068 | − | 28.5906i | −0.641554 | − | 1.11120i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.8698 | 0.421829 | ||||||||
\(665\) | 18.0761 | + | 16.7397i | 0.700963 | + | 0.649136i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.7370 | − | 26.9836i | −1.80966 | − | 1.04481i | ||||
\(668\) | 6.68567 | + | 11.5799i | 0.258676 | + | 0.448041i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.6515 | − | 6.72702i | −0.450138 | − | 0.259887i | ||||
\(671\) | 14.9679 | + | 35.0301i | 0.577828 | + | 1.35232i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.5749i | − | 0.716010i | −0.933720 | − | 0.358005i | \(-0.883457\pi\) | ||
0.933720 | − | 0.358005i | \(-0.116543\pi\) | |||||||
\(674\) | 0.754154 | + | 0.435411i | 0.0290489 | + | 0.0167714i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.17979 | − | 2.04346i | −0.0453767 | − | 0.0785948i | ||||
\(677\) | 0.0528202 | − | 0.0914873i | 0.00203005 | − | 0.00351614i | −0.865009 | − | 0.501757i | \(-0.832687\pi\) |
0.867039 | + | 0.498241i | \(0.166020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1342 | − | 10.2557i | 1.27157 | − | 0.393578i | ||||
\(680\) | 5.29274i | 0.202967i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.548653 | − | 0.411397i | −0.0210090 | − | 0.0157532i | ||||
\(683\) | −6.42302 | + | 3.70833i | −0.245770 | + | 0.141895i | −0.617826 | − | 0.786315i | \(-0.711986\pi\) |
0.372056 | + | 0.928210i | \(0.378653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.20257 | −0.275196 | ||||||||
\(686\) | 6.81627 | + | 17.2203i | 0.260247 | + | 0.657474i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.93044 | + | 4.00129i | 0.264221 | + | 0.152548i | ||||
\(689\) | 9.46445 | + | 16.3929i | 0.360567 | + | 0.624520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5227 | + | 18.2258i | −0.400302 | + | 0.693343i | −0.993762 | − | 0.111520i | \(-0.964428\pi\) |
0.593460 | + | 0.804863i | \(0.297761\pi\) | |||||||
\(692\) | 23.8696 | 0.907385 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.85259 | 0.298080 | ||||||||
\(695\) | 7.09980 | − | 12.2972i | 0.269311 | − | 0.466460i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.96842 | + | 12.0697i | 0.263948 | + | 0.457171i | ||||
\(698\) | −17.9226 | − | 10.3476i | −0.678382 | − | 0.391664i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.09063 | + | 9.20072i | −0.0790184 | + | 0.347755i | ||||
\(701\) | −2.71470 | −0.102533 | −0.0512663 | − | 0.998685i | \(-0.516326\pi\) | ||||
−0.0512663 | + | 0.998685i | \(0.516326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.6186 | − | 29.8020i | 1.94683 | − | 1.12400i | ||||
\(704\) | −2.65352 | − | 1.98969i | −0.100008 | − | 0.0749891i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.5901i | 1.00073i | ||||||||
\(707\) | 18.7357 | + | 17.3504i | 0.704627 | + | 0.652529i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.7895 | + | 20.4200i | −0.442763 | + | 0.766888i | −0.997893 | − | 0.0648754i | \(-0.979335\pi\) |
0.555130 | + | 0.831763i | \(0.312668\pi\) | |||||||
\(710\) | −2.27921 | − | 3.94771i | −0.0855373 | − | 0.148155i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.4053 | + | 6.58488i | 0.427433 | + | 0.246779i | ||||
\(713\) | 1.41997i | 0.0531783i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9126 | + | 5.09009i | −0.445507 | + | 0.190359i | ||||
\(716\) | 17.6015 | + | 10.1622i | 0.657798 | + | 0.379780i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.0346521 | + | 0.0600191i | 0.00129320 | + | 0.00223989i | ||||
\(719\) | −39.6365 | − | 22.8842i | −1.47819 | − | 0.853435i | −0.478497 | − | 0.878089i | \(-0.658818\pi\) |
−0.999696 | + | 0.0246536i | \(0.992152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.80985 | − | 25.5687i | 0.216370 | − | 0.952229i | ||||
\(722\) | −41.4745 | −1.54352 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.72802 | + | 16.8494i | 0.361539 | + | 0.626204i | ||||
\(725\) | −14.0120 | − | 24.2696i | −0.520394 | − | 0.901350i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.07152 | −0.225180 | −0.112590 | − | 0.993642i | \(-0.535915\pi\) | ||||
−0.112590 | + | 0.993642i | \(0.535915\pi\) | |||||||
\(728\) | −2.55183 | − | 8.24446i | −0.0945769 | − | 0.305560i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.135337 | + | 0.234411i | −0.00500905 | + | 0.00867593i | ||||
\(731\) | 30.6334 | − | 17.6862i | 1.13302 | − | 0.654148i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.1021 | − | 20.8436i | −1.33346 | − | 0.769875i | −0.347634 | − | 0.937630i | \(-0.613015\pi\) |
−0.985829 | + | 0.167755i | \(0.946348\pi\) | |||||||
\(734\) | 37.0298 | 1.36679 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.86757i | 0.253142i | ||||||||
\(737\) | 4.45346 | − | 36.9981i | 0.164045 | − | 1.36284i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.62892 | − | 4.40456i | 0.280635 | − | 0.162024i | −0.353076 | − | 0.935595i | \(-0.614864\pi\) |
0.633711 | + | 0.773570i | \(0.281531\pi\) | |||||||
\(740\) | −7.94814 | − | 4.58886i | −0.292180 | − | 0.168690i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.53960 | − | 14.6666i | −0.166654 | − | 0.538427i | ||||
\(743\) | 45.0818 | 1.65389 | 0.826945 | − | 0.562283i | \(-0.190077\pi\) | ||||
0.826945 | + | 0.562283i | \(0.190077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6687 | − | 10.7784i | 0.683970 | − | 0.394890i | ||||
\(746\) | −10.9206 | + | 6.30501i | −0.399831 | + | 0.230843i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.4808 | + | 5.76017i | −0.492908 | + | 0.210613i | ||||
\(749\) | 5.65916 | − | 24.9056i | 0.206781 | − | 0.910030i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.739343 | − | 1.28058i | 0.0269790 | − | 0.0467290i | −0.852221 | − | 0.523183i | \(-0.824745\pi\) |
0.879200 | + | 0.476453i | \(0.158078\pi\) | |||||||
\(752\) | −0.355926 | + | 0.205494i | −0.0129793 | + | 0.00749360i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.1992 | + | 12.8167i | 0.808447 | + | 0.466757i | ||||
\(755\) | −6.20906 | −0.225971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5239 | 0.709608 | 0.354804 | − | 0.934941i | \(-0.384548\pi\) | ||||
0.354804 | + | 0.934941i | \(0.384548\pi\) | |||||||
\(758\) | 2.22863 | − | 3.86010i | 0.0809474 | − | 0.140205i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.65588 | + | 8.06422i | 0.168887 | + | 0.292520i | ||||
\(761\) | −14.9359 | + | 25.8697i | −0.541426 | + | 0.937777i | 0.457396 | + | 0.889263i | \(0.348782\pi\) |
−0.998822 | + | 0.0485145i | \(0.984551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1770 | − | 14.2291i | 0.477041 | − | 0.515128i | ||||
\(764\) | 9.40784i | 0.340364i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.0167 | − | 6.36051i | 0.398050 | − | 0.229815i | ||||
\(767\) | 6.90959 | + | 11.9678i | 0.249491 | + | 0.432131i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.72669i | − | 0.0983268i | −0.998791 | − | 0.0491634i | \(-0.984344\pi\) | ||
0.998791 | − | 0.0491634i | \(-0.0156555\pi\) | |||||||
\(770\) | 10.3368 | − | 1.88498i | 0.372514 | − | 0.0679301i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.92081 | − | 1.68633i | −0.105122 | − | 0.0606925i | ||||
\(773\) | 9.27880 | − | 5.35712i | 0.333735 | − | 0.192682i | −0.323763 | − | 0.946138i | \(-0.604948\pi\) |
0.657498 | + | 0.753456i | \(0.271615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.368681 | + | 0.638574i | −0.0132434 | + | 0.0229382i | ||||
\(776\) | 13.1097 | 0.470612 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 21.6727i | − | 0.777005i | ||||||
\(779\) | 21.2347 | + | 12.2599i | 0.760813 | + | 0.439255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.57450 | − | 10.1016i | 0.271037 | − | 0.361464i | ||||
\(782\) | 26.2886 | + | 15.1778i | 0.940080 | + | 0.542755i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.536631 | + | 6.97940i | 0.0191654 | + | 0.249264i | ||||
\(785\) | 23.5640i | 0.841034i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.6208 | + | 7.86396i | −0.485529 | + | 0.280320i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.237189 | + | 0.971464i | \(0.423774\pi\) | |||||||
\(788\) | −3.16564 | − | 5.48305i | −0.112771 | − | 0.195326i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.77708 | −0.0988040 | ||||||||
\(791\) | −9.40425 | − | 30.3833i | −0.334377 | − | 1.08031i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7331 | + | 32.4466i | −0.665230 | + | 1.15221i | ||||
\(794\) | −6.77259 | − | 11.7305i | −0.240350 | − | 0.416299i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.331375 | − | 0.573958i | 0.0117453 | − | 0.0203434i | ||||
\(797\) | − | 22.1018i | − | 0.782884i | −0.920203 | − | 0.391442i | \(-0.871976\pi\) | ||
0.920203 | − | 0.391442i | \(-0.128024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.81662i | 0.0642674i | ||||||||
\(800\) | −1.78309 | + | 3.08841i | −0.0630419 | + | 0.109192i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.0277 | − | 13.2951i | 0.813137 | − | 0.469465i | ||||
\(803\) | −0.744344 | − | 0.0895968i | −0.0262673 | − | 0.00316180i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.9633 | − | 14.7830i | −0.562632 | − | 0.521033i | ||||
\(806\) | − | 0.674458i | − | 0.0237568i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.82575 | + | 8.35845i | 0.169769 | + | 0.294049i | ||||
\(809\) | 22.1026 | + | 38.2828i | 0.777086 | + | 1.34595i | 0.933614 | + | 0.358280i | \(0.116637\pi\) |
−0.156528 | + | 0.987674i | \(0.550030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.1956i | 0.674048i | 0.941496 | + | 0.337024i | \(0.109420\pi\) | ||||
−0.941496 | + | 0.337024i | \(0.890580\pi\) | |||||||
\(812\) | −15.2546 | − | 14.1267i | −0.535332 | − | 0.495751i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.03795 | − | 25.2384i | 0.106480 | − | 0.884606i | ||||
\(815\) | −24.9228 | + | 14.3892i | −0.873009 | + | 0.504032i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.1162 | − | 53.8948i | 1.08862 | − | 1.88554i | ||||
\(818\) | 6.36575i | 0.222573i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 3.77551i | − | 0.131846i | ||||||
\(821\) | −23.2612 | + | 40.2895i | −0.811821 | + | 1.40611i | 0.0997680 | + | 0.995011i | \(0.468190\pi\) |
−0.911589 | + | 0.411104i | \(0.865143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0487 | + | 20.8689i | 0.419990 | + | 0.727444i | 0.995938 | − | 0.0900423i | \(-0.0287002\pi\) |
−0.575948 | + | 0.817486i | \(0.695367\pi\) | |||||||
\(824\) | 4.95521 | − | 8.58267i | 0.172623 | − | 0.298992i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.31417 | − | 10.7074i | −0.115315 | − | 0.372559i | ||||
\(827\) | 39.8140 | 1.38447 | 0.692235 | − | 0.721673i | \(-0.256626\pi\) | ||||
0.692235 | + | 0.721673i | \(0.256626\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4410 | − | 26.7447i | −0.536289 | − | 0.928880i | −0.999100 | − | 0.0424231i | \(-0.986492\pi\) |
0.462810 | − | 0.886457i | \(-0.346841\pi\) | |||||||
\(830\) | −11.2719 | + | 6.50783i | −0.391253 | + | 0.225890i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 3.26196i | − | 0.113088i | ||||||
\(833\) | 27.9027 | + | 13.3707i | 0.966772 | + | 0.463268i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8660 | − | 8.00554i | −0.479853 | − | 0.277043i | ||||
\(836\) | −15.4729 | + | 20.6352i | −0.535140 | + | 0.713682i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.2871 | + | 10.5580i | 0.631716 | + | 0.364721i | ||||
\(839\) | − | 11.6938i | − | 0.403716i | −0.979415 | − | 0.201858i | \(-0.935302\pi\) | ||
0.979415 | − | 0.201858i | \(-0.0646980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.7525 | 1.12940 | ||||||||
\(842\) | 4.47066 | − | 7.74340i | 0.154069 | − | 0.266855i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.9408 | − | 7.47137i | 0.445440 | − | 0.257175i | ||||
\(845\) | 2.44688 | + | 1.41271i | 0.0841753 | + | 0.0485986i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.0509 | + | 24.2769i | 0.551515 | + | 0.834165i | ||||
\(848\) | − | 5.80291i | − | 0.199273i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.88150 | + | 13.6512i | 0.270333 | + | 0.468231i | ||||
\(851\) | −45.5851 | + | 26.3186i | −1.56264 | + | 0.902189i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.8586i | 0.988098i | 0.869434 | + | 0.494049i | \(0.164484\pi\) | ||||
−0.869434 | + | 0.494049i | \(0.835516\pi\) | |||||||
\(854\) | 20.6478 | − | 22.2963i | 0.706553 | − | 0.762964i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.82669 | − | 8.36007i | 0.164973 | − | 0.285741i | ||||
\(857\) | −5.00247 | − | 8.66454i | −0.170881 | − | 0.295975i | 0.767847 | − | 0.640633i | \(-0.221328\pi\) |
−0.938728 | + | 0.344658i | \(0.887995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.4504 | + | 31.9570i | −0.629519 | + | 1.09036i | 0.358129 | + | 0.933672i | \(0.383415\pi\) |
−0.987648 | + | 0.156687i | \(0.949919\pi\) | |||||||
\(860\) | −9.58244 | −0.326758 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.33069 | −0.283744 | ||||||||
\(863\) | −8.29145 | − | 4.78707i | −0.282244 | − | 0.162954i | 0.352195 | − | 0.935927i | \(-0.385435\pi\) |
−0.634439 | + | 0.772973i | \(0.718769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.7526 | + | 14.2909i | −0.841614 | + | 0.485906i | ||||
\(866\) | −0.144352 | + | 0.250025i | −0.00490528 | + | 0.00849619i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.121213 | + | 0.533449i | −0.00411423 | + | 0.0181065i | ||||
\(869\) | −3.02234 | − | 7.07334i | −0.102526 | − | 0.239947i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.7407 | − | 18.3255i | 1.07549 | − | 0.620936i | ||||
\(872\) | 6.34796 | − | 3.66500i | 0.214969 | − | 0.124112i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 53.4059 | 1.80648 | ||||||||
\(875\) | −8.02427 | − | 25.9249i | −0.271270 | − | 0.876420i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9020 | − | 13.7998i | −0.807114 | − | 0.465987i | 0.0388390 | − | 0.999245i | \(-0.487634\pi\) |
−0.845952 | + | 0.533258i | \(0.820967\pi\) | |||||||
\(878\) | 10.0491 | − | 5.80186i | 0.339141 | − | 0.195803i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.94292 | + | 0.474610i | 0.132916 | + | 0.0159991i | ||||
\(881\) | 12.0483i | 0.405916i | 0.979187 | + | 0.202958i | \(0.0650555\pi\) | ||||
−0.979187 | + | 0.202958i | \(0.934944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1451 | 0.375061 | 0.187531 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187531 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(884\) | −12.4866 | − | 7.20914i | −0.419970 | − | 0.242470i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.34544 | + | 2.50884i | −0.145988 | + | 0.0842862i | ||||
\(887\) | 9.43091 | − | 16.3348i | 0.316659 | − | 0.548469i | −0.663130 | − | 0.748504i | \(-0.730772\pi\) |
0.979789 | + | 0.200035i | \(0.0641056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.2270 | + | 45.9646i | 0.477158 | + | 1.54160i | ||||
\(890\) | −15.7697 | −0.528602 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.51565 | + | 14.7495i | 0.285125 | + | 0.493851i | ||||
\(893\) | 1.59803 | + | 2.76787i | 0.0534761 | + | 0.0926234i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.3369 | −0.813491 | ||||||||
\(896\) | −0.586237 | + | 2.57999i | −0.0195848 | + | 0.0861913i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8058 | − | 7.39342i | −0.427335 | − | 0.246722i | ||||
\(899\) | −0.812406 | − | 1.40713i | −0.0270953 | − | 0.0469304i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.2132 | − | 12.8248i | −0.740029 | − | 0.427256i | ||||
\(902\) | 9.61639 | − | 4.10895i | 0.320191 | − | 0.136813i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 12.0213i | − | 0.399823i | ||||||
\(905\) | −20.1758 | − | 11.6485i | −0.670666 | − | 0.387209i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.2003 | − | 45.3802i | −0.869965 | − | 1.50682i | −0.862031 | − | 0.506855i | \(-0.830808\pi\) |
−0.00793394 | − | 0.999969i | \(-0.502525\pi\) | |||||||
\(908\) | −9.58521 | + | 16.6021i | −0.318096 | + | 0.550959i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.58226 | + | 7.02165i | 0.251349 | + | 0.232766i | ||||
\(911\) | 36.2035i | 1.19948i | 0.800197 | + | 0.599738i | \(0.204728\pi\) | ||||
−0.800197 | + | 0.599738i | \(0.795272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8431 | − | 21.6275i | −0.954568 | − | 0.715764i | ||||
\(914\) | 29.4805 | − | 17.0205i | 0.975127 | − | 0.562990i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.0205 | −0.430208 | ||||||||
\(917\) | −0.466038 | + | 2.05100i | −0.0153899 | + | 0.0677300i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.5266 | + | 17.0472i | 0.973991 | + | 0.562334i | 0.900451 | − | 0.434958i | \(-0.143237\pi\) |
0.0735407 | + | 0.997292i | \(0.476570\pi\) | |||||||
\(920\) | −4.11168 | − | 7.12163i | −0.135558 | − | 0.234793i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.6064 | + | 27.0310i | −0.513968 | + | 0.890219i | ||||
\(923\) | 12.4179 | 0.408740 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.3334 | −0.898717 | ||||||||
\(926\) | −3.33272 | + | 5.77244i | −0.109520 | + | 0.189694i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.92914 | − | 6.80547i | −0.128980 | − | 0.223400i | ||||
\(929\) | 5.38330 | + | 3.10805i | 0.176620 | + | 0.101972i | 0.585704 | − | 0.810525i | \(-0.300818\pi\) |
−0.409083 | + | 0.912497i | \(0.634152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.2756 | − | 4.17313i | 1.77881 | − | 0.136769i | ||||
\(932\) | −4.09714 | −0.134206 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.58720 | − | 3.80312i | 0.215540 | − | 0.124442i | ||||
\(935\) | 10.5309 | − | 14.0444i | 0.344397 | − | 0.459300i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.8415i | 1.20356i | 0.798662 | + | 0.601780i | \(0.205542\pi\) | ||||
−0.798662 | + | 0.601780i | \(0.794458\pi\) | |||||||
\(938\) | −28.3981 | + | 8.78979i | −0.927231 | + | 0.286997i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.246063 | − | 0.426193i | 0.00802567 | − | 0.0139009i | ||||
\(941\) | −18.3238 | − | 31.7377i | −0.597337 | − | 1.03462i | −0.993212 | − | 0.116314i | \(-0.962892\pi\) |
0.395875 | − | 0.918304i | \(-0.370441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.7527 | − | 10.8269i | −0.610671 | − | 0.352571i | ||||
\(944\) | − | 4.23646i | − | 0.137885i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4287 | − | 24.4069i | −0.339067 | − | 0.793537i | ||||
\(947\) | 25.5002 | + | 14.7226i | 0.828646 | + | 0.478419i | 0.853389 | − | 0.521275i | \(-0.174543\pi\) |
−0.0247427 | + | 0.999694i | \(0.507877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.368681 | − | 0.638574i | −0.0119679 | − | 0.0207290i | ||||
\(950\) | 24.0171 | + | 13.8663i | 0.779219 | + | 0.449882i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.58041 | + | 7.94601i | 0.278093 | + | 0.257532i | ||||
\(953\) | 10.3535 | 0.335384 | 0.167692 | − | 0.985839i | \(-0.446369\pi\) | ||||
0.167692 | + | 0.985839i | \(0.446369\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.63256 | − | 9.75588i | −0.182265 | − | 0.315693i | ||||
\(956\) | 2.34489 | + | 4.06147i | 0.0758393 | + | 0.131357i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.2859 | −0.493864 | ||||||||
\(959\) | −10.8133 | + | 11.6766i | −0.349178 | + | 0.377056i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4786 | − | 26.8098i | 0.499310 | − | 0.864831i | ||||
\(962\) | 21.6521 | − | 12.5008i | 0.698090 | − | 0.403043i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.0323 | + | 6.36950i | 0.355326 | + | 0.205148i | ||||
\(965\) | 4.03849 | 0.130004 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.804904i | 0.0258840i | 0.999916 | + | 0.0129420i | \(0.00411968\pi\) | ||||
−0.999916 | + | 0.0129420i | \(0.995880\pi\) | |||||||
\(968\) | 3.08229 | + | 10.5593i | 0.0990686 | + | 0.339390i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.5947 | + | 7.84891i | −0.436500 | + | 0.252013i | ||||
\(971\) | 34.1340 | + | 19.7073i | 1.09541 | + | 0.632436i | 0.935012 | − | 0.354616i | \(-0.115388\pi\) |
0.160399 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.27688 | − | 29.9718i | −0.297403 | − | 0.960852i | ||||
\(974\) | −1.58099 | −0.0506580 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.94695 | − | 5.74287i | 0.318394 | − | 0.183825i | ||||
\(977\) | 21.2420 | − | 12.2641i | 0.679592 | − | 0.392363i | −0.120109 | − | 0.992761i | \(-0.538324\pi\) |
0.799701 | + | 0.600398i | \(0.204991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.1624 | − | 40.1661i | −0.548513 | − | 1.28372i | ||||
\(980\) | −4.73511 | − | 6.91631i | −0.151258 | − | 0.220934i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.45394 | + | 5.98240i | −0.110220 | + | 0.190906i | ||||
\(983\) | 3.94538 | − | 2.27787i | 0.125838 | − | 0.0726526i | −0.435760 | − | 0.900063i | \(-0.643520\pi\) |
0.561598 | + | 0.827410i | \(0.310187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.56550 | + | 3.79060i | 0.209194 | + | 0.120778i | ||||
\(986\) | −34.7345 | −1.10617 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.3668 | −0.807025 | ||||||||
\(989\) | −27.4791 | + | 47.5953i | −0.873786 | + | 1.51344i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.66468 | − | 13.2756i | −0.243477 | − | 0.421714i | 0.718226 | − | 0.695810i | \(-0.244955\pi\) |
−0.961702 | + | 0.274096i | \(0.911621\pi\) | |||||||
\(992\) | −0.103382 | + | 0.179063i | −0.00328239 | + | 0.00568526i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.82169 | − | 2.23173i | −0.311525 | − | 0.0707862i | ||||
\(995\) | 0.793588i | 0.0251584i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.8972 | − | 28.8082i | 1.58026 | − | 0.912364i | 0.585441 | − | 0.810715i | \(-0.300921\pi\) |
0.994820 | − | 0.101649i | \(-0.0324119\pi\) | |||||||
\(998\) | −0.474107 | − | 0.821178i | −0.0150076 | − | 0.0259939i | ||||
\(999\) | 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 | 1386.2.ba.a.989.10 | yes | 32 | |
3.2 | odd | 2 | 1386.2.ba.b.989.7 | yes | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.a.1187.7 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.b.989.10 | yes | 32 | ||
21.11 | odd | 6 | 1386.2.ba.b.1187.10 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.a.989.7 | ✓ | 32 | |
77.32 | odd | 6 | 1386.2.ba.b.1187.7 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.a.1187.10 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.7 | ✓ | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.a.989.10 | yes | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.a.1187.7 | yes | 32 | 7.4 | even | 3 | inner | |
1386.2.ba.a.1187.10 | yes | 32 | 231.32 | even | 6 | inner | |
1386.2.ba.b.989.7 | yes | 32 | 3.2 | odd | 2 | ||
1386.2.ba.b.989.10 | yes | 32 | 11.10 | odd | 2 | ||
1386.2.ba.b.1187.7 | yes | 32 | 77.32 | odd | 6 | ||
1386.2.ba.b.1187.10 | yes | 32 | 21.11 | odd | 6 |