Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 24.5 | ||
Character | \(\chi\) | \(=\) | 475.24 |
Dual form | 475.2.u.c.99.5 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.575828 | + | 1.58207i | 0.407172 | + | 1.11869i | 0.958670 | + | 0.284519i | \(0.0918339\pi\) |
−0.551499 | + | 0.834176i | \(0.685944\pi\) | |||||||
\(3\) | −3.20261 | − | 0.564707i | −1.84903 | − | 0.326034i | −0.864688 | − | 0.502309i | \(-0.832484\pi\) |
−0.984341 | + | 0.176275i | \(0.943595\pi\) | |||||||
\(4\) | −0.639290 | + | 0.536428i | −0.319645 | + | 0.268214i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.950745 | − | 5.39194i | −0.388140 | − | 2.20125i | ||||
\(7\) | 0.474919 | − | 0.274194i | 0.179502 | − | 0.103636i | −0.407556 | − | 0.913180i | \(-0.633619\pi\) |
0.587059 | + | 0.809544i | \(0.300286\pi\) | |||||||
\(8\) | 1.69930 | + | 0.981094i | 0.600795 | + | 0.346869i | ||||
\(9\) | 7.11876 | + | 2.59101i | 2.37292 | + | 0.863672i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.165601 | + | 0.286829i | −0.0499306 | + | 0.0864823i | −0.889910 | − | 0.456135i | \(-0.849233\pi\) |
0.839980 | + | 0.542617i | \(0.182567\pi\) | |||||||
\(12\) | 2.35032 | − | 1.35696i | 0.678480 | − | 0.391720i | ||||
\(13\) | −4.74830 | + | 0.837254i | −1.31694 | + | 0.232212i | −0.787595 | − | 0.616193i | \(-0.788674\pi\) |
−0.529347 | + | 0.848406i | \(0.677563\pi\) | |||||||
\(14\) | 0.707267 | + | 0.593468i | 0.189025 | + | 0.158611i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.863487 | + | 4.89708i | −0.215872 | + | 1.22427i | ||||
\(17\) | 1.80612 | + | 4.96227i | 0.438048 | + | 1.20353i | 0.940760 | + | 0.339074i | \(0.110114\pi\) |
−0.502711 | + | 0.864454i | \(0.667664\pi\) | |||||||
\(18\) | 12.7544i | 3.00623i | ||||||||
\(19\) | −4.30704 | + | 0.670409i | −0.988102 | + | 0.153802i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.67582 | + | 0.609949i | −0.365694 | + | 0.133102i | ||||
\(22\) | −0.549142 | − | 0.0968286i | −0.117078 | − | 0.0206439i | ||||
\(23\) | −0.713529 | − | 0.850350i | −0.148781 | − | 0.177310i | 0.686507 | − | 0.727124i | \(-0.259143\pi\) |
−0.835288 | + | 0.549813i | \(0.814699\pi\) | |||||||
\(24\) | −4.88818 | − | 4.10167i | −0.997796 | − | 0.837250i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.05880 | − | 7.03005i | −0.795996 | − | 1.37871i | ||||
\(27\) | −12.8865 | − | 7.44000i | −2.48000 | − | 1.43183i | ||||
\(28\) | −0.156525 | + | 0.430050i | −0.0295805 | + | 0.0812717i | ||||
\(29\) | −3.01199 | − | 1.09627i | −0.559312 | − | 0.203573i | 0.0468671 | − | 0.998901i | \(-0.485076\pi\) |
−0.606179 | + | 0.795328i | \(0.707298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.01060 | + | 5.21452i | 0.540720 | + | 0.936555i | 0.998863 | + | 0.0476765i | \(0.0151816\pi\) |
−0.458142 | + | 0.888879i | \(0.651485\pi\) | |||||||
\(32\) | −4.38000 | + | 0.772312i | −0.774282 | + | 0.136527i | ||||
\(33\) | 0.692330 | − | 0.825087i | 0.120519 | − | 0.143629i | ||||
\(34\) | −6.81067 | + | 5.71483i | −1.16802 | + | 0.980085i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.94084 | + | 2.16229i | −0.990140 | + | 0.360382i | ||||
\(37\) | 6.67261i | 1.09697i | 0.836161 | + | 0.548485i | \(0.184795\pi\) | ||||
−0.836161 | + | 0.548485i | \(0.815205\pi\) | |||||||
\(38\) | −3.54075 | − | 6.42801i | −0.574385 | − | 1.04276i | ||||
\(39\) | 15.6798 | 2.51077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.37380 | + | 7.79121i | −0.214552 | + | 1.21678i | 0.667131 | + | 0.744940i | \(0.267522\pi\) |
−0.881683 | + | 0.471842i | \(0.843589\pi\) | |||||||
\(42\) | −1.92997 | − | 2.30005i | −0.297800 | − | 0.354905i | ||||
\(43\) | −1.05356 | + | 1.25559i | −0.160667 | + | 0.191475i | −0.840372 | − | 0.542010i | \(-0.817663\pi\) |
0.679705 | + | 0.733486i | \(0.262108\pi\) | |||||||
\(44\) | −0.0479962 | − | 0.272200i | −0.00723570 | − | 0.0410357i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.934447 | − | 1.61851i | 0.137777 | − | 0.238636i | ||||
\(47\) | 1.57373 | − | 4.32380i | 0.229553 | − | 0.630691i | −0.770424 | − | 0.637532i | \(-0.779955\pi\) |
0.999977 | + | 0.00684117i | \(0.00217763\pi\) | |||||||
\(48\) | 5.53083 | − | 15.1958i | 0.798306 | − | 2.19333i | ||||
\(49\) | −3.34963 | + | 5.80174i | −0.478519 | + | 0.828820i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.98207 | − | 16.9122i | −0.417574 | − | 2.36818i | ||||
\(52\) | 2.58642 | − | 3.08237i | 0.358671 | − | 0.427448i | ||||
\(53\) | 4.32352 | + | 5.15257i | 0.593881 | + | 0.707759i | 0.976347 | − | 0.216210i | \(-0.0693696\pi\) |
−0.382466 | + | 0.923970i | \(0.624925\pi\) | |||||||
\(54\) | 4.35025 | − | 24.6715i | 0.591994 | − | 3.35736i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.07604 | 0.143792 | ||||||||
\(57\) | 14.1723 | + | 0.285152i | 1.87717 | + | 0.0377693i | ||||
\(58\) | − | 5.39645i | − | 0.708588i | ||||||
\(59\) | −6.39331 | + | 2.32697i | −0.832338 | + | 0.302946i | −0.722818 | − | 0.691038i | \(-0.757154\pi\) |
−0.109520 | + | 0.993985i | \(0.534931\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.520640 | − | 0.436869i | 0.0666612 | − | 0.0559354i | −0.608848 | − | 0.793287i | \(-0.708368\pi\) |
0.675509 | + | 0.737351i | \(0.263924\pi\) | |||||||
\(62\) | −6.51616 | + | 7.76566i | −0.827554 | + | 0.986240i | ||||
\(63\) | 4.09127 | − | 0.721402i | 0.515452 | − | 0.0908881i | ||||
\(64\) | 1.22864 | + | 2.12807i | 0.153580 | + | 0.266009i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.70401 | + | 0.620209i | 0.209749 | + | 0.0763425i | ||||
\(67\) | 2.65816 | − | 7.30324i | 0.324746 | − | 0.892232i | −0.664672 | − | 0.747136i | \(-0.731429\pi\) |
0.989418 | − | 0.145097i | \(-0.0463493\pi\) | |||||||
\(68\) | −3.81654 | − | 2.20348i | −0.462823 | − | 0.267211i | ||||
\(69\) | 1.80496 | + | 3.12628i | 0.217291 | + | 0.376360i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.832574 | − | 0.698612i | −0.0988083 | − | 0.0829101i | 0.592045 | − | 0.805905i | \(-0.298321\pi\) |
−0.690854 | + | 0.722995i | \(0.742765\pi\) | |||||||
\(72\) | 9.55490 | + | 11.3871i | 1.12606 | + | 1.34198i | ||||
\(73\) | 13.7393 | + | 2.42261i | 1.60806 | + | 0.283545i | 0.904302 | − | 0.426892i | \(-0.140392\pi\) |
0.703761 | + | 0.710437i | \(0.251503\pi\) | |||||||
\(74\) | −10.5566 | + | 3.84227i | −1.22717 | + | 0.446655i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.39382 | − | 2.73900i | 0.274590 | − | 0.314185i | ||||
\(77\) | 0.181627i | 0.0206984i | ||||||||
\(78\) | 9.02885 | + | 24.8065i | 1.02232 | + | 2.80879i | ||||
\(79\) | 0.243868 | − | 1.38304i | 0.0274373 | − | 0.155605i | −0.968011 | − | 0.250908i | \(-0.919271\pi\) |
0.995448 | + | 0.0953032i | \(0.0303821\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19.6591 | + | 16.4960i | 2.18435 | + | 1.83289i | ||||
\(82\) | −13.1173 | + | 2.31294i | −1.44857 | + | 0.255422i | ||||
\(83\) | −0.740346 | + | 0.427439i | −0.0812636 | + | 0.0469176i | −0.540081 | − | 0.841613i | \(-0.681606\pi\) |
0.458818 | + | 0.888530i | \(0.348273\pi\) | |||||||
\(84\) | 0.744142 | − | 1.28889i | 0.0811925 | − | 0.140630i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.59310 | − | 0.943812i | −0.279621 | − | 0.101774i | ||||
\(87\) | 9.02715 | + | 5.21183i | 0.967812 | + | 0.558767i | ||||
\(88\) | −0.562813 | + | 0.324940i | −0.0599960 | + | 0.0346387i | ||||
\(89\) | −2.52694 | − | 14.3310i | −0.267855 | − | 1.51908i | −0.760781 | − | 0.649009i | \(-0.775184\pi\) |
0.492926 | − | 0.870071i | \(-0.335927\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02549 | + | 1.69959i | −0.212329 | + | 0.178165i | ||||
\(92\) | 0.912304 | + | 0.160864i | 0.0951142 | + | 0.0167712i | ||||
\(93\) | −6.69712 | − | 18.4002i | −0.694459 | − | 1.90801i | ||||
\(94\) | 7.74677 | 0.799018 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.4636 | 1.47618 | ||||||||
\(97\) | −2.40147 | − | 6.59799i | −0.243832 | − | 0.669924i | −0.999881 | − | 0.0154088i | \(-0.995095\pi\) |
0.756049 | − | 0.654515i | \(-0.227127\pi\) | |||||||
\(98\) | −11.1076 | − | 1.95857i | −1.12204 | − | 0.197845i | ||||
\(99\) | −1.92205 | + | 1.61279i | −0.193173 | + | 0.162092i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25144 | − | 7.09728i | −0.124523 | − | 0.706206i | −0.981590 | − | 0.191000i | \(-0.938827\pi\) |
0.857067 | − | 0.515205i | \(-0.172284\pi\) | |||||||
\(102\) | 25.0391 | − | 14.4563i | 2.47924 | − | 1.43139i | ||||
\(103\) | −6.12729 | − | 3.53759i | −0.603739 | − | 0.348569i | 0.166772 | − | 0.985996i | \(-0.446666\pi\) |
−0.770511 | + | 0.637426i | \(0.779999\pi\) | |||||||
\(104\) | −8.89023 | − | 3.23578i | −0.871759 | − | 0.317294i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.66214 | + | 9.80711i | −0.549956 | + | 0.952551i | ||||
\(107\) | 5.63008 | − | 3.25053i | 0.544281 | − | 0.314241i | −0.202531 | − | 0.979276i | \(-0.564917\pi\) |
0.746812 | + | 0.665035i | \(0.231583\pi\) | |||||||
\(108\) | 12.2292 | − | 2.15634i | 1.17676 | − | 0.207494i | ||||
\(109\) | 13.5289 | + | 11.3521i | 1.29583 | + | 1.08733i | 0.990850 | + | 0.134971i | \(0.0430942\pi\) |
0.304980 | + | 0.952359i | \(0.401350\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.76807 | − | 21.3698i | 0.357649 | − | 2.02833i | ||||
\(112\) | 0.932665 | + | 2.56248i | 0.0881286 | + | 0.242131i | ||||
\(113\) | − | 4.86487i | − | 0.457649i | −0.973468 | − | 0.228824i | \(-0.926512\pi\) | ||
0.973468 | − | 0.228824i | \(-0.0734882\pi\) | |||||||
\(114\) | 7.70970 | + | 22.5859i | 0.722079 | + | 2.11536i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.51360 | − | 0.914877i | 0.233382 | − | 0.0849442i | ||||
\(117\) | −35.9713 | − | 6.34272i | −3.32555 | − | 0.586384i | ||||
\(118\) | −7.36289 | − | 8.77475i | −0.677809 | − | 0.807781i | ||||
\(119\) | 2.21839 | + | 1.86145i | 0.203359 | + | 0.170639i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.44515 | + | 9.43128i | 0.495014 | + | 0.857389i | ||||
\(122\) | 0.990958 | + | 0.572130i | 0.0897171 | + | 0.0517982i | ||||
\(123\) | 8.79950 | − | 24.1764i | 0.793424 | − | 2.17992i | ||||
\(124\) | −4.72186 | − | 1.71862i | −0.424036 | − | 0.154336i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.49718 | + | 6.05729i | 0.311553 | + | 0.539626i | ||||
\(127\) | −2.92418 | + | 0.515613i | −0.259479 | + | 0.0457532i | −0.301874 | − | 0.953348i | \(-0.597612\pi\) |
0.0423950 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(128\) | −8.37696 | + | 9.98327i | −0.740426 | + | 0.882405i | ||||
\(129\) | 4.08319 | − | 3.42620i | 0.359505 | − | 0.301660i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.51285 | − | 2.73445i | 0.656400 | − | 0.238910i | 0.00771895 | − | 0.999970i | \(-0.497543\pi\) |
0.648682 | + | 0.761060i | \(0.275321\pi\) | |||||||
\(132\) | 0.898855i | 0.0782353i | ||||||||
\(133\) | −1.86167 | + | 1.49936i | −0.161427 | + | 0.130011i | ||||
\(134\) | 13.0849 | 1.13036 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.79931 | + | 10.2044i | −0.154289 | + | 0.875019i | ||||
\(137\) | −0.591862 | − | 0.705354i | −0.0505662 | − | 0.0602625i | 0.740169 | − | 0.672421i | \(-0.234746\pi\) |
−0.790735 | + | 0.612159i | \(0.790301\pi\) | |||||||
\(138\) | −3.90666 | + | 4.65577i | −0.332557 | + | 0.396326i | ||||
\(139\) | 0.0173742 | + | 0.0985339i | 0.00147366 | + | 0.00835754i | 0.985536 | − | 0.169468i | \(-0.0542049\pi\) |
−0.984062 | + | 0.177825i | \(0.943094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.48174 | + | 12.9588i | −0.630076 | + | 1.09132i | ||||
\(142\) | 0.625837 | − | 1.71947i | 0.0525191 | − | 0.144295i | ||||
\(143\) | 0.546174 | − | 1.50060i | 0.0456734 | − | 0.125487i | ||||
\(144\) | −18.8353 | + | 32.6238i | −1.56961 | + | 2.71865i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.07872 | + | 23.1316i | 0.337557 | + | 1.91438i | ||||
\(147\) | 14.0039 | − | 16.6892i | 1.15502 | − | 1.37650i | ||||
\(148\) | −3.57937 | − | 4.26573i | −0.294223 | − | 0.350641i | ||||
\(149\) | 3.00368 | − | 17.0347i | 0.246071 | − | 1.39554i | −0.571922 | − | 0.820308i | \(-0.693802\pi\) |
0.817992 | − | 0.575229i | \(-0.195087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2178 | −1.56393 | −0.781963 | − | 0.623325i | \(-0.785781\pi\) | ||||
−0.781963 | + | 0.623325i | \(0.785781\pi\) | |||||||
\(152\) | −7.97670 | − | 3.08638i | −0.646996 | − | 0.250338i | ||||
\(153\) | 40.0049i | 3.23420i | ||||||||
\(154\) | −0.287348 | + | 0.104586i | −0.0231552 | + | 0.00842779i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.0239 | + | 8.41107i | −0.802556 | + | 0.673424i | ||||
\(157\) | −4.23125 | + | 5.04261i | −0.337690 | + | 0.402444i | −0.907989 | − | 0.418994i | \(-0.862383\pi\) |
0.570299 | + | 0.821437i | \(0.306827\pi\) | |||||||
\(158\) | 2.32850 | − | 0.410578i | 0.185246 | − | 0.0326638i | ||||
\(159\) | −10.9369 | − | 18.9432i | −0.867349 | − | 1.50229i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.572030 | − | 0.208202i | −0.0450822 | − | 0.0164086i | ||||
\(162\) | −14.7776 | + | 40.6010i | −1.16104 | + | 3.18992i | ||||
\(163\) | 12.6377 | + | 7.29637i | 0.989860 | + | 0.571496i | 0.905232 | − | 0.424917i | \(-0.139697\pi\) |
0.0846275 | + | 0.996413i | \(0.473030\pi\) | |||||||
\(164\) | −3.30117 | − | 5.71779i | −0.257778 | − | 0.446484i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.10255 | − | 0.925151i | −0.0855746 | − | 0.0718057i | ||||
\(167\) | −2.25595 | − | 2.68854i | −0.174571 | − | 0.208045i | 0.671664 | − | 0.740856i | \(-0.265580\pi\) |
−0.846234 | + | 0.532811i | \(0.821136\pi\) | |||||||
\(168\) | −3.44615 | − | 0.607648i | −0.265876 | − | 0.0468811i | ||||
\(169\) | 9.62936 | − | 3.50480i | 0.740720 | − | 0.269600i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −32.3978 | − | 6.38711i | −2.47752 | − | 0.488435i | ||||
\(172\) | − | 1.36784i | − | 0.104297i | ||||||
\(173\) | −0.856059 | − | 2.35200i | −0.0650849 | − | 0.178819i | 0.902887 | − | 0.429878i | \(-0.141443\pi\) |
−0.967972 | + | 0.251059i | \(0.919221\pi\) | |||||||
\(174\) | −3.04741 | + | 17.2827i | −0.231024 | + | 1.31020i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.26163 | − | 1.05863i | −0.0950990 | − | 0.0797975i | ||||
\(177\) | 21.7894 | − | 3.84205i | 1.63779 | − | 0.288786i | ||||
\(178\) | 21.2176 | − | 12.2500i | 1.59032 | − | 0.918174i | ||||
\(179\) | −2.51029 | + | 4.34795i | −0.187628 | + | 0.324981i | −0.944459 | − | 0.328630i | \(-0.893413\pi\) |
0.756831 | + | 0.653610i | \(0.226747\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.09429 | + | 1.85417i | 0.378656 | + | 0.137819i | 0.524334 | − | 0.851513i | \(-0.324314\pi\) |
−0.145678 | + | 0.989332i | \(0.546536\pi\) | |||||||
\(182\) | −3.85520 | − | 2.22580i | −0.285766 | − | 0.164987i | ||||
\(183\) | −1.91411 | + | 1.10511i | −0.141495 | + | 0.0816923i | ||||
\(184\) | −0.378229 | − | 2.14504i | −0.0278834 | − | 0.158135i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 25.2541 | − | 21.1907i | 1.85172 | − | 1.55378i | ||||
\(187\) | −1.72242 | − | 0.303709i | −0.125956 | − | 0.0222094i | ||||
\(188\) | 1.31333 | + | 3.60836i | 0.0957847 | + | 0.263166i | ||||
\(189\) | −8.16003 | −0.593555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.98517 | 0.433071 | 0.216536 | − | 0.976275i | \(-0.430524\pi\) | ||||
0.216536 | + | 0.976275i | \(0.430524\pi\) | |||||||
\(192\) | −2.73313 | − | 7.50921i | −0.197247 | − | 0.541931i | ||||
\(193\) | 2.13565 | + | 0.376572i | 0.153727 | + | 0.0271063i | 0.249982 | − | 0.968250i | \(-0.419575\pi\) |
−0.0962548 | + | 0.995357i | \(0.530686\pi\) | |||||||
\(194\) | 9.05567 | − | 7.59861i | 0.650159 | − | 0.545548i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.970827 | − | 5.50583i | −0.0693448 | − | 0.393274i | ||||
\(197\) | −14.3471 | + | 8.28327i | −1.02219 | + | 0.590159i | −0.914736 | − | 0.404052i | \(-0.867602\pi\) |
−0.107449 | + | 0.994211i | \(0.534268\pi\) | |||||||
\(198\) | −3.65833 | − | 2.11214i | −0.259986 | − | 0.150103i | ||||
\(199\) | 13.1370 | + | 4.78149i | 0.931259 | + | 0.338951i | 0.762709 | − | 0.646742i | \(-0.223869\pi\) |
0.168551 | + | 0.985693i | \(0.446091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.6372 | + | 21.8884i | −0.891363 | + | 1.54389i | ||||
\(202\) | 10.5078 | − | 6.06668i | 0.739327 | − | 0.426850i | ||||
\(203\) | −1.73104 | + | 0.305229i | −0.121495 | + | 0.0214229i | ||||
\(204\) | 10.9786 | + | 9.21211i | 0.768654 | + | 0.644977i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.06847 | − | 11.7309i | 0.144117 | − | 0.817328i | ||||
\(207\) | −2.87617 | − | 7.90220i | −0.199907 | − | 0.549241i | ||||
\(208\) | − | 23.9757i | − | 1.66242i | ||||||
\(209\) | 0.520956 | − | 1.34640i | 0.0360353 | − | 0.0931327i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9908 | − | 6.18415i | 1.16970 | − | 0.425735i | 0.317145 | − | 0.948377i | \(-0.397276\pi\) |
0.852552 | + | 0.522643i | \(0.175054\pi\) | |||||||
\(212\) | −5.52796 | − | 0.974729i | −0.379662 | − | 0.0669447i | ||||
\(213\) | 2.27190 | + | 2.70755i | 0.155668 | + | 0.185518i | ||||
\(214\) | 8.38453 | + | 7.03546i | 0.573155 | + | 0.480934i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.5987 | − | 25.2856i | −0.993314 | − | 1.72047i | ||||
\(217\) | 2.85958 | + | 1.65098i | 0.194121 | + | 0.112076i | ||||
\(218\) | −10.1695 | + | 27.9405i | −0.688766 | + | 1.89237i | ||||
\(219\) | −42.6336 | − | 15.5174i | −2.88091 | − | 1.04857i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.7307 | − | 22.0502i | −0.856358 | − | 1.48326i | ||||
\(222\) | 35.9783 | − | 6.34395i | 2.41471 | − | 0.425778i | ||||
\(223\) | −16.8838 | + | 20.1214i | −1.13062 | + | 1.34743i | −0.200710 | + | 0.979651i | \(0.564325\pi\) |
−0.929915 | + | 0.367775i | \(0.880119\pi\) | |||||||
\(224\) | −1.86838 | + | 1.56776i | −0.124836 | + | 0.104750i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.69659 | − | 2.80133i | 0.511969 | − | 0.186342i | ||||
\(227\) | − | 6.97401i | − | 0.462881i | −0.972849 | − | 0.231441i | \(-0.925656\pi\) | ||
0.972849 | − | 0.231441i | \(-0.0743439\pi\) | |||||||
\(228\) | −9.21321 | + | 7.42015i | −0.610159 | + | 0.491411i | ||||
\(229\) | −2.62489 | −0.173458 | −0.0867288 | − | 0.996232i | \(-0.527641\pi\) | ||||
−0.0867288 | + | 0.996232i | \(0.527641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.102566 | − | 0.581682i | 0.00674837 | − | 0.0382719i | ||||
\(232\) | −4.04273 | − | 4.81794i | −0.265419 | − | 0.316313i | ||||
\(233\) | 17.1358 | − | 20.4217i | 1.12260 | − | 1.33787i | 0.188004 | − | 0.982168i | \(-0.439798\pi\) |
0.934600 | − | 0.355700i | \(-0.115757\pi\) | |||||||
\(234\) | −10.6786 | − | 60.5616i | −0.698085 | − | 3.95904i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.83892 | − | 4.91716i | 0.184798 | − | 0.320080i | ||||
\(237\) | −1.56203 | + | 4.29164i | −0.101465 | + | 0.278772i | ||||
\(238\) | −1.66754 | + | 4.58153i | −0.108091 | + | 0.296976i | ||||
\(239\) | 6.55369 | − | 11.3513i | 0.423923 | − | 0.734256i | −0.572396 | − | 0.819977i | \(-0.693986\pi\) |
0.996319 | + | 0.0857211i | \(0.0273194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.63284 | − | 14.9316i | −0.169596 | − | 0.961828i | −0.944198 | − | 0.329379i | \(-0.893161\pi\) |
0.774602 | − | 0.632449i | \(-0.217950\pi\) | |||||||
\(242\) | −11.7855 | + | 14.0454i | −0.757601 | + | 0.902874i | ||||
\(243\) | −24.9511 | − | 29.7356i | −1.60062 | − | 1.90754i | ||||
\(244\) | −0.0984913 | + | 0.558572i | −0.00630526 | + | 0.0357589i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 43.3159 | 2.76172 | ||||||||
\(247\) | 19.8898 | − | 6.78939i | 1.26556 | − | 0.431998i | ||||
\(248\) | 11.8147i | 0.750237i | ||||||||
\(249\) | 2.61242 | − | 0.950843i | 0.165555 | − | 0.0602573i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5597 | − | 12.2170i | 0.919001 | − | 0.771133i | −0.0548090 | − | 0.998497i | \(-0.517455\pi\) |
0.973810 | + | 0.227364i | \(0.0730106\pi\) | |||||||
\(252\) | −2.22853 | + | 2.65586i | −0.140384 | + | 0.167303i | ||||
\(253\) | 0.362066 | − | 0.0638421i | 0.0227629 | − | 0.00401372i | ||||
\(254\) | −2.49956 | − | 4.32937i | −0.156837 | − | 0.271649i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9998 | − | 5.82344i | −0.999986 | − | 0.363965i | ||||
\(257\) | −7.46911 | + | 20.5212i | −0.465910 | + | 1.28008i | 0.455066 | + | 0.890458i | \(0.349616\pi\) |
−0.920976 | + | 0.389620i | \(0.872606\pi\) | |||||||
\(258\) | 7.77172 | + | 4.48701i | 0.483846 | + | 0.279349i | ||||
\(259\) | 1.82959 | + | 3.16895i | 0.113685 | + | 0.196909i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.6011 | − | 15.6082i | −1.15138 | − | 0.966124i | ||||
\(262\) | 8.65221 | + | 10.3113i | 0.534535 | + | 0.637034i | ||||
\(263\) | −19.3231 | − | 3.40719i | −1.19152 | − | 0.210096i | −0.457488 | − | 0.889216i | \(-0.651251\pi\) |
−0.734028 | + | 0.679119i | \(0.762362\pi\) | |||||||
\(264\) | 1.98597 | − | 0.722833i | 0.122228 | − | 0.0444873i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.44409 | − | 2.08193i | −0.211171 | − | 0.127651i | ||||
\(267\) | 47.3235i | 2.89615i | ||||||||
\(268\) | 2.21832 | + | 6.09480i | 0.135506 | + | 0.372299i | ||||
\(269\) | 0.293697 | − | 1.66564i | 0.0179070 | − | 0.101556i | −0.974544 | − | 0.224195i | \(-0.928025\pi\) |
0.992451 | + | 0.122639i | \(0.0391359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.08215 | − | 5.10353i | −0.369465 | − | 0.310018i | 0.439085 | − | 0.898445i | \(-0.355303\pi\) |
−0.808550 | + | 0.588428i | \(0.799747\pi\) | |||||||
\(272\) | −25.8602 | + | 4.55985i | −1.56800 | + | 0.276481i | ||||
\(273\) | 7.44662 | − | 4.29931i | 0.450690 | − | 0.260206i | ||||
\(274\) | 0.775111 | − | 1.34253i | 0.0468262 | − | 0.0811053i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.83091 | − | 1.03037i | −0.170401 | − | 0.0620209i | ||||
\(277\) | −8.20468 | − | 4.73698i | −0.492972 | − | 0.284617i | 0.232835 | − | 0.972516i | \(-0.425200\pi\) |
−0.725806 | + | 0.687899i | \(0.758533\pi\) | |||||||
\(278\) | −0.145883 | + | 0.0842258i | −0.00874950 | + | 0.00505153i | ||||
\(279\) | 7.92086 | + | 44.9214i | 0.474209 | + | 2.68937i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.62922 | + | 8.07988i | −0.574431 | + | 0.482005i | −0.883113 | − | 0.469160i | \(-0.844557\pi\) |
0.308682 | + | 0.951165i | \(0.400112\pi\) | |||||||
\(282\) | −24.8099 | − | 4.37465i | −1.47741 | − | 0.260507i | ||||
\(283\) | 6.35609 | + | 17.4632i | 0.377830 | + | 1.03808i | 0.972254 | + | 0.233928i | \(0.0751580\pi\) |
−0.594424 | + | 0.804152i | \(0.702620\pi\) | |||||||
\(284\) | 0.907012 | 0.0538212 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.68856 | 0.158978 | ||||||||
\(287\) | 1.48386 | + | 4.07688i | 0.0875897 | + | 0.240651i | ||||
\(288\) | −33.1812 | − | 5.85074i | −1.95522 | − | 0.344758i | ||||
\(289\) | −8.33933 | + | 6.99753i | −0.490549 | + | 0.411619i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.96505 | + | 22.4869i | 0.232435 | + | 1.31821i | ||||
\(292\) | −10.0830 | + | 5.82139i | −0.590060 | + | 0.340671i | ||||
\(293\) | 15.0386 | + | 8.68253i | 0.878563 | + | 0.507239i | 0.870184 | − | 0.492726i | \(-0.164000\pi\) |
0.00837865 | + | 0.999965i | \(0.497333\pi\) | |||||||
\(294\) | 34.4673 | + | 12.5451i | 2.01017 | + | 0.731643i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.54645 | + | 11.3388i | −0.380505 | + | 0.659054i | ||||
\(297\) | 4.26802 | − | 2.46414i | 0.247656 | − | 0.142984i | ||||
\(298\) | 28.6798 | − | 5.05701i | 1.66137 | − | 0.292945i | ||||
\(299\) | 4.10001 | + | 3.44032i | 0.237110 | + | 0.198959i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.156082 | + | 0.885183i | −0.00899639 | + | 0.0510211i | ||||
\(302\) | −11.0662 | − | 30.4040i | −0.636786 | − | 1.74956i | ||||
\(303\) | 23.4365i | 1.34639i | ||||||||
\(304\) | 0.436022 | − | 21.6708i | 0.0250076 | − | 1.24290i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −63.2907 | + | 23.0359i | −3.61809 | + | 1.31688i | ||||
\(307\) | 24.6698 | + | 4.34996i | 1.40798 | + | 0.248265i | 0.825419 | − | 0.564521i | \(-0.190939\pi\) |
0.582563 | + | 0.812786i | \(0.302050\pi\) | |||||||
\(308\) | −0.0974301 | − | 0.116113i | −0.00555159 | − | 0.00661613i | ||||
\(309\) | 17.6256 | + | 14.7897i | 1.00269 | + | 0.841354i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.79206 | + | 4.83598i | 0.158323 | + | 0.274223i | 0.934264 | − | 0.356582i | \(-0.116058\pi\) |
−0.775941 | + | 0.630805i | \(0.782725\pi\) | |||||||
\(312\) | 26.6447 | + | 15.3833i | 1.50846 | + | 0.870909i | ||||
\(313\) | −0.280835 | + | 0.771588i | −0.0158737 | + | 0.0436127i | −0.947376 | − | 0.320122i | \(-0.896276\pi\) |
0.931503 | + | 0.363734i | \(0.118498\pi\) | |||||||
\(314\) | −10.4142 | − | 3.79048i | −0.587710 | − | 0.213909i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.586001 | + | 1.01498i | 0.0329651 | + | 0.0570973i | ||||
\(317\) | 33.0230 | − | 5.82285i | 1.85476 | − | 0.327044i | 0.868948 | − | 0.494904i | \(-0.164797\pi\) |
0.985811 | + | 0.167860i | \(0.0536857\pi\) | |||||||
\(318\) | 23.6718 | − | 28.2109i | 1.32745 | − | 1.58199i | ||||
\(319\) | 0.813231 | − | 0.682382i | 0.0455322 | − | 0.0382061i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.8666 | + | 7.23084i | −1.10884 | + | 0.403586i | ||||
\(322\) | − | 1.02488i | − | 0.0571144i | ||||||
\(323\) | −11.1058 | − | 20.1618i | −0.617942 | − | 1.12184i | ||||
\(324\) | −21.4168 | −1.18982 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.26627 | + | 24.1952i | −0.236287 | + | 1.34005i | ||||
\(327\) | −36.9171 | − | 43.9961i | −2.04152 | − | 2.43299i | ||||
\(328\) | −9.97841 | + | 11.8918i | −0.550966 | + | 0.656615i | ||||
\(329\) | −0.438166 | − | 2.48496i | −0.0241569 | − | 0.137000i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.63364 | + | 9.75775i | −0.309653 | + | 0.536334i | −0.978286 | − | 0.207258i | \(-0.933546\pi\) |
0.668634 | + | 0.743592i | \(0.266879\pi\) | |||||||
\(332\) | 0.244006 | − | 0.670400i | 0.0133916 | − | 0.0367930i | ||||
\(333\) | −17.2888 | + | 47.5006i | −0.947421 | + | 2.60302i | ||||
\(334\) | 2.95442 | − | 5.11721i | 0.161659 | − | 0.280001i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.53992 | − | 8.73330i | −0.0840093 | − | 0.476441i | ||||
\(337\) | 4.04684 | − | 4.82284i | 0.220445 | − | 0.262717i | −0.644475 | − | 0.764625i | \(-0.722924\pi\) |
0.864921 | + | 0.501909i | \(0.167369\pi\) | |||||||
\(338\) | 11.0897 | + | 13.2162i | 0.603201 | + | 0.718866i | ||||
\(339\) | −2.74723 | + | 15.5803i | −0.149209 | + | 0.846206i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.99424 | −0.107994 | ||||||||
\(342\) | −8.55065 | − | 54.9335i | −0.462366 | − | 2.97046i | ||||
\(343\) | 7.51253i | 0.405638i | ||||||||
\(344\) | −3.02217 | + | 1.09998i | −0.162945 | + | 0.0593070i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.22810 | − | 2.70870i | 0.173544 | − | 0.145620i | ||||
\(347\) | −11.2851 | + | 13.4490i | −0.605814 | + | 0.721981i | −0.978562 | − | 0.205952i | \(-0.933971\pi\) |
0.372749 | + | 0.927932i | \(0.378415\pi\) | |||||||
\(348\) | −8.56674 | + | 1.51055i | −0.459225 | + | 0.0809738i | ||||
\(349\) | 6.25844 | + | 10.8399i | 0.335007 | + | 0.580248i | 0.983486 | − | 0.180984i | \(-0.0579281\pi\) |
−0.648480 | + | 0.761232i | \(0.724595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 67.4180 | + | 24.5381i | 3.59850 | + | 1.30975i | ||||
\(352\) | 0.503810 | − | 1.38421i | 0.0268532 | − | 0.0737785i | ||||
\(353\) | −5.04735 | − | 2.91409i | −0.268643 | − | 0.155101i | 0.359628 | − | 0.933096i | \(-0.382904\pi\) |
−0.628271 | + | 0.777995i | \(0.716237\pi\) | |||||||
\(354\) | 18.6253 | + | 32.2600i | 0.989924 | + | 1.71460i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.30298 | + | 7.80613i | 0.493057 | + | 0.413724i | ||||
\(357\) | −6.05346 | − | 7.21424i | −0.320383 | − | 0.381818i | ||||
\(358\) | −8.32426 | − | 1.46779i | −0.439951 | − | 0.0775752i | ||||
\(359\) | 0.544588 | − | 0.198214i | 0.0287423 | − | 0.0104613i | −0.327609 | − | 0.944813i | \(-0.606243\pi\) |
0.356351 | + | 0.934352i | \(0.384021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1011 | − | 5.77495i | 0.952690 | − | 0.303945i | ||||
\(362\) | 9.12723i | 0.479717i | ||||||||
\(363\) | −12.1128 | − | 33.2797i | −0.635757 | − | 1.74673i | ||||
\(364\) | 0.383168 | − | 2.17306i | 0.0200835 | − | 0.113899i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.85057 | − | 2.39191i | −0.149002 | − | 0.125027i | ||||
\(367\) | −7.78614 | + | 1.37291i | −0.406433 | + | 0.0716651i | −0.373127 | − | 0.927780i | \(-0.621715\pi\) |
−0.0333057 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(368\) | 4.78035 | − | 2.75994i | 0.249193 | − | 0.143872i | ||||
\(369\) | −29.9669 | + | 51.9042i | −1.56001 | + | 2.70202i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.46613 | + | 1.26157i | 0.179952 | + | 0.0654973i | ||||
\(372\) | 14.1518 | + | 8.17054i | 0.733736 | + | 0.423623i | ||||
\(373\) | −7.19338 | + | 4.15310i | −0.372459 | + | 0.215039i | −0.674532 | − | 0.738245i | \(-0.735655\pi\) |
0.302073 | + | 0.953285i | \(0.402321\pi\) | |||||||
\(374\) | −0.511327 | − | 2.89988i | −0.0264401 | − | 0.149949i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.91630 | − | 5.80347i | 0.356681 | − | 0.299291i | ||||
\(377\) | 15.2197 | + | 2.68364i | 0.783853 | + | 0.138214i | ||||
\(378\) | −4.69877 | − | 12.9098i | −0.241679 | − | 0.664007i | ||||
\(379\) | −10.2928 | −0.528707 | −0.264354 | − | 0.964426i | \(-0.585159\pi\) | ||||
−0.264354 | + | 0.964426i | \(0.585159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.65620 | 0.494702 | ||||||||
\(382\) | 3.44642 | + | 9.46897i | 0.176334 | + | 0.484475i | ||||
\(383\) | 31.5418 | + | 5.56168i | 1.61171 | + | 0.284188i | 0.905671 | − | 0.423981i | \(-0.139368\pi\) |
0.706042 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(384\) | 32.4658 | − | 27.2420i | 1.65676 | − | 1.39019i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.634000 | + | 3.59559i | 0.0322698 | + | 0.183011i | ||||
\(387\) | −10.7533 | + | 6.20842i | −0.546621 | + | 0.315592i | ||||
\(388\) | 5.07458 | + | 2.92981i | 0.257623 | + | 0.148739i | ||||
\(389\) | −28.7624 | − | 10.4686i | −1.45831 | − | 0.530781i | −0.513411 | − | 0.858143i | \(-0.671618\pi\) |
−0.944899 | + | 0.327362i | \(0.893840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.93095 | − | 5.07656i | 0.148225 | − | 0.256733i | ||||
\(392\) | −11.3841 | + | 6.57261i | −0.574984 | + | 0.331967i | ||||
\(393\) | −25.6049 | + | 4.51483i | −1.29160 | + | 0.227743i | ||||
\(394\) | −21.3662 | − | 17.9284i | −1.07641 | − | 0.903217i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.363601 | − | 2.06208i | 0.0182716 | − | 0.103624i | ||||
\(397\) | 3.63241 | + | 9.97995i | 0.182305 | + | 0.500880i | 0.996858 | − | 0.0792100i | \(-0.0252398\pi\) |
−0.814553 | + | 0.580090i | \(0.803018\pi\) | |||||||
\(398\) | 23.5371i | 1.17981i | ||||||||
\(399\) | 6.80890 | − | 3.75056i | 0.340871 | − | 0.187763i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.3159 | − | 5.21056i | 0.714901 | − | 0.260203i | 0.0411417 | − | 0.999153i | \(-0.486901\pi\) |
0.673760 | + | 0.738950i | \(0.264678\pi\) | |||||||
\(402\) | −41.9059 | − | 7.38913i | −2.09007 | − | 0.368536i | ||||
\(403\) | −18.6611 | − | 22.2395i | −0.929577 | − | 1.10783i | ||||
\(404\) | 4.60721 | + | 3.86591i | 0.229217 | + | 0.192336i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.47968 | − | 2.56287i | −0.0734351 | − | 0.127193i | ||||
\(407\) | −1.91390 | − | 1.10499i | −0.0948684 | − | 0.0547723i | ||||
\(408\) | 11.5250 | − | 31.6646i | 0.570571 | − | 1.56763i | ||||
\(409\) | −10.9607 | − | 3.98936i | −0.541971 | − | 0.197261i | 0.0565046 | − | 0.998402i | \(-0.482004\pi\) |
−0.598476 | + | 0.801141i | \(0.704227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.49719 | + | 2.59320i | 0.0738508 | + | 0.127913i | ||||
\(412\) | 5.81478 | − | 1.02530i | 0.286473 | − | 0.0505130i | ||||
\(413\) | −2.39826 | + | 2.85813i | −0.118011 | + | 0.140640i | ||||
\(414\) | 10.8457 | − | 9.10061i | 0.533036 | − | 0.447271i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.1509 | − | 7.33434i | 0.987981 | − | 0.359595i | ||||
\(417\) | − | 0.325377i | − | 0.0159338i | ||||||
\(418\) | 2.43009 | + | 0.0488942i | 0.118860 | + | 0.00239149i | ||||
\(419\) | −17.7028 | −0.864840 | −0.432420 | − | 0.901672i | \(-0.642340\pi\) | ||||
−0.432420 | + | 0.901672i | \(0.642340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.57756 | − | 20.2893i | 0.174359 | − | 0.988841i | −0.764521 | − | 0.644599i | \(-0.777025\pi\) |
0.938881 | − | 0.344243i | \(-0.111864\pi\) | |||||||
\(422\) | 19.5676 | + | 23.3197i | 0.952534 | + | 1.13519i | ||||
\(423\) | 22.4061 | − | 26.7025i | 1.08942 | − | 1.29832i | ||||
\(424\) | 2.29182 | + | 12.9976i | 0.111301 | + | 0.631217i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.97531 | + | 5.15339i | −0.144154 | + | 0.249683i | ||||
\(427\) | 0.127475 | − | 0.350234i | 0.00616894 | − | 0.0169490i | ||||
\(428\) | −1.85558 | + | 5.09817i | −0.0896929 | + | 0.246429i | ||||
\(429\) | −2.59658 | + | 4.49742i | −0.125364 | + | 0.217137i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.44676 | + | 8.20498i | 0.0696879 | + | 0.395220i | 0.999622 | + | 0.0274936i | \(0.00875258\pi\) |
−0.929934 | + | 0.367726i | \(0.880136\pi\) | |||||||
\(432\) | 47.5615 | − | 56.6816i | 2.28831 | − | 2.72710i | ||||
\(433\) | 18.1228 | + | 21.5979i | 0.870926 | + | 1.03793i | 0.998934 | + | 0.0461560i | \(0.0146971\pi\) |
−0.128008 | + | 0.991773i | \(0.540858\pi\) | |||||||
\(434\) | −0.965347 | + | 5.47475i | −0.0463381 | + | 0.262797i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.7384 | −0.705843 | ||||||||
\(437\) | 3.64328 | + | 3.18413i | 0.174282 | + | 0.152318i | ||||
\(438\) | − | 76.3848i | − | 3.64981i | ||||||
\(439\) | 28.5501 | − | 10.3914i | 1.36262 | − | 0.495954i | 0.445759 | − | 0.895153i | \(-0.352934\pi\) |
0.916864 | + | 0.399199i | \(0.130712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.8776 | + | 32.6222i | −1.85132 | + | 1.55344i | ||||
\(442\) | 27.5543 | − | 32.8380i | 1.31063 | − | 1.56194i | ||||
\(443\) | −24.1482 | + | 4.25799i | −1.14732 | + | 0.202303i | −0.714804 | − | 0.699325i | \(-0.753484\pi\) |
−0.432513 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(444\) | 9.05446 | + | 15.6828i | 0.429705 | + | 0.744272i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −41.5556 | − | 15.1250i | −1.96772 | − | 0.716190i | ||||
\(447\) | −19.2392 | + | 52.8594i | −0.909984 | + | 2.50016i | ||||
\(448\) | 1.16701 | + | 0.673774i | 0.0551361 | + | 0.0318328i | ||||
\(449\) | 12.3444 | + | 21.3812i | 0.582570 | + | 1.00904i | 0.995174 | + | 0.0981300i | \(0.0312861\pi\) |
−0.412604 | + | 0.910911i | \(0.635381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00724 | − | 1.68428i | −0.0945174 | − | 0.0793095i | ||||
\(452\) | 2.60965 | + | 3.11007i | 0.122748 | + | 0.146285i | ||||
\(453\) | 61.5473 | + | 10.8525i | 2.89175 | + | 0.509893i | ||||
\(454\) | 11.0334 | − | 4.01583i | 0.517823 | − | 0.188472i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 23.8034 | + | 14.3890i | 1.11469 | + | 0.673825i | ||||
\(457\) | − | 7.16480i | − | 0.335155i | −0.985859 | − | 0.167578i | \(-0.946406\pi\) | ||
0.985859 | − | 0.167578i | \(-0.0535945\pi\) | |||||||
\(458\) | −1.51148 | − | 4.15277i | −0.0706270 | − | 0.194046i | ||||
\(459\) | 13.6448 | − | 77.3837i | 0.636886 | − | 3.61196i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6388 | + | 13.9616i | 0.774947 | + | 0.650258i | 0.941971 | − | 0.335695i | \(-0.108971\pi\) |
−0.167024 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(462\) | 0.979325 | − | 0.172681i | 0.0455623 | − | 0.00803386i | ||||
\(463\) | −27.6508 | + | 15.9642i | −1.28504 | + | 0.741918i | −0.977765 | − | 0.209703i | \(-0.932750\pi\) |
−0.307274 | + | 0.951621i | \(0.599417\pi\) | |||||||
\(464\) | 7.96934 | − | 13.8033i | 0.369968 | − | 0.640803i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 42.1759 | + | 15.3508i | 1.95376 | + | 0.711110i | ||||
\(467\) | −16.9206 | − | 9.76911i | −0.782992 | − | 0.452061i | 0.0544977 | − | 0.998514i | \(-0.482644\pi\) |
−0.837490 | + | 0.546453i | \(0.815978\pi\) | |||||||
\(468\) | 26.3985 | − | 15.2412i | 1.22027 | − | 0.704524i | ||||
\(469\) | −0.740097 | − | 4.19730i | −0.0341745 | − | 0.193813i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.3986 | − | 13.7601i | 0.755610 | − | 0.634032i | ||||
\(472\) | −13.1472 | − | 2.31820i | −0.605147 | − | 0.106704i | ||||
\(473\) | −0.185668 | − | 0.510119i | −0.00853703 | − | 0.0234553i | ||||
\(474\) | −7.68914 | −0.353174 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.41673 | −0.110770 | ||||||||
\(477\) | 17.4277 | + | 47.8822i | 0.797959 | + | 2.19237i | ||||
\(478\) | 21.7324 | + | 3.83201i | 0.994018 | + | 0.175272i | ||||
\(479\) | 9.37543 | − | 7.86692i | 0.428374 | − | 0.359449i | −0.402964 | − | 0.915216i | \(-0.632020\pi\) |
0.831338 | + | 0.555767i | \(0.187575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.58666 | − | 31.6835i | −0.254730 | − | 1.44464i | ||||
\(482\) | 22.1068 | − | 12.7634i | 1.00694 | − | 0.581356i | ||||
\(483\) | 1.71442 | + | 0.989819i | 0.0780086 | + | 0.0450383i | ||||
\(484\) | −8.54024 | − | 3.10839i | −0.388193 | − | 0.141291i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 32.6764 | − | 56.5971i | 1.48223 | − | 2.56730i | ||||
\(487\) | 12.2125 | − | 7.05086i | 0.553399 | − | 0.319505i | −0.197093 | − | 0.980385i | \(-0.563150\pi\) |
0.750492 | + | 0.660880i | \(0.229817\pi\) | |||||||
\(488\) | 1.31334 | − | 0.231577i | 0.0594519 | − | 0.0104830i | ||||
\(489\) | −36.3533 | − | 30.5040i | −1.64395 | − | 1.37944i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.45329 | + | 19.5846i | −0.155845 | + | 0.883839i | 0.802165 | + | 0.597103i | \(0.203682\pi\) |
−0.958009 | + | 0.286737i | \(0.907430\pi\) | |||||||
\(492\) | 7.34348 | + | 20.1761i | 0.331070 | + | 0.909607i | ||||
\(493\) | − | 16.9263i | − | 0.762322i | ||||||
\(494\) | 22.1944 | + | 27.5576i | 0.998573 | + | 1.23988i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.1355 | + | 10.2405i | −1.26332 | + | 0.459812i | ||||
\(497\) | −0.586961 | − | 0.103497i | −0.0263288 | − | 0.00464248i | ||||
\(498\) | 3.00861 | + | 3.58552i | 0.134819 | + | 0.160671i | ||||
\(499\) | 5.69739 | + | 4.78068i | 0.255050 | + | 0.214013i | 0.761343 | − | 0.648349i | \(-0.224540\pi\) |
−0.506293 | + | 0.862362i | \(0.668985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.70670 | + | 9.88429i | 0.254956 | + | 0.441598i | ||||
\(502\) | 27.7122 | + | 15.9996i | 1.23685 | + | 0.714098i | ||||
\(503\) | −4.62141 | + | 12.6972i | −0.206059 | + | 0.566141i | −0.999072 | − | 0.0430624i | \(-0.986289\pi\) |
0.793014 | + | 0.609204i | \(0.208511\pi\) | |||||||
\(504\) | 7.66008 | + | 2.78804i | 0.341207 | + | 0.124189i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.309491 | + | 0.536054i | 0.0137585 | + | 0.0238305i | ||||
\(507\) | −32.8183 | + | 5.78675i | −1.45751 | + | 0.256999i | ||||
\(508\) | 1.59281 | − | 1.89824i | 0.0706696 | − | 0.0842208i | ||||
\(509\) | 26.9446 | − | 22.6092i | 1.19430 | − | 1.00214i | 0.194525 | − | 0.980898i | \(-0.437684\pi\) |
0.999774 | − | 0.0212383i | \(-0.00676087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.18932 | − | 2.61670i | 0.318037 | − | 0.115756i | ||||
\(512\) | − | 2.60163i | − | 0.114977i | ||||||
\(513\) | 60.4903 | + | 23.4051i | 2.67071 | + | 1.03336i | ||||
\(514\) | −36.7670 | −1.62172 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.772431 | + | 4.38068i | −0.0340044 | + | 0.192849i | ||||
\(517\) | 0.979580 | + | 1.16742i | 0.0430819 | + | 0.0513430i | ||||
\(518\) | −3.95998 | + | 4.71931i | −0.173991 | + | 0.207355i | ||||
\(519\) | 1.41343 | + | 8.01597i | 0.0620428 | + | 0.351862i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.92797 | − | 5.07140i | 0.128277 | − | 0.222182i | −0.794732 | − | 0.606960i | \(-0.792389\pi\) |
0.923009 | + | 0.384778i | \(0.125722\pi\) | |||||||
\(522\) | 13.9823 | − | 38.4160i | 0.611988 | − | 1.68142i | ||||
\(523\) | 3.95014 | − | 10.8529i | 0.172727 | − | 0.474565i | −0.822877 | − | 0.568219i | \(-0.807633\pi\) |
0.995605 | + | 0.0936543i | \(0.0298548\pi\) | |||||||
\(524\) | −3.33605 | + | 5.77821i | −0.145736 | + | 0.252422i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.73637 | − | 32.5326i | −0.250118 | − | 1.41849i | ||||
\(527\) | −20.4384 | + | 24.3575i | −0.890309 | + | 1.06103i | ||||
\(528\) | 3.44270 | + | 4.10284i | 0.149824 | + | 0.178553i | ||||
\(529\) | 3.77994 | − | 21.4371i | 0.164345 | − | 0.932047i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −51.5416 | −2.23672 | ||||||||
\(532\) | 0.385851 | − | 1.95717i | 0.0167287 | − | 0.0848543i | ||||
\(533\) | − | 38.1452i | − | 1.65225i | ||||||
\(534\) | −74.8693 | + | 27.2502i | −3.23991 | + | 1.17923i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.6822 | − | 9.80251i | 0.504593 | − | 0.423404i | ||||
\(537\) | 10.4948 | − | 12.5072i | 0.452884 | − | 0.539726i | ||||
\(538\) | 2.80428 | − | 0.494470i | 0.120901 | − | 0.0213181i | ||||
\(539\) | −1.10941 | − | 1.92155i | −0.0477855 | − | 0.0827669i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0424 | − | 4.01909i | −0.474748 | − | 0.172794i | 0.0935540 | − | 0.995614i | \(-0.470177\pi\) |
−0.568302 | + | 0.822820i | \(0.692399\pi\) | |||||||
\(542\) | 4.57189 | − | 12.5612i | 0.196380 | − | 0.539548i | ||||
\(543\) | −15.2680 | − | 8.81497i | −0.655212 | − | 0.378287i | ||||
\(544\) | −11.7432 | − | 20.3399i | −0.503487 | − | 0.872064i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.0898 | + | 9.30544i | 0.474599 | + | 0.398236i | ||||
\(547\) | 18.6150 | + | 22.1845i | 0.795920 | + | 0.948541i | 0.999534 | − | 0.0305106i | \(-0.00971334\pi\) |
−0.203614 | + | 0.979051i | \(0.565269\pi\) | |||||||
\(548\) | 0.756743 | + | 0.133434i | 0.0323265 | + | 0.00570003i | ||||
\(549\) | 4.83825 | − | 1.76098i | 0.206491 | − | 0.0751567i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.7077 | + | 2.70242i | 0.583967 | + | 0.115127i | ||||
\(552\) | 7.08333i | 0.301486i | ||||||||
\(553\) | −0.263405 | − | 0.723700i | −0.0112011 | − | 0.0307749i | ||||
\(554\) | 2.76976 | − | 15.7081i | 0.117676 | − | 0.667373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0639635 | − | 0.0536718i | −0.00271266 | − | 0.00227619i | ||||
\(557\) | −23.8476 | + | 4.20497i | −1.01045 | + | 0.178170i | −0.654282 | − | 0.756250i | \(-0.727029\pi\) |
−0.356171 | + | 0.934421i | \(0.615918\pi\) | |||||||
\(558\) | −66.5079 | + | 38.3984i | −2.81550 | + | 1.62553i | ||||
\(559\) | 3.95139 | − | 6.84400i | 0.167126 | − | 0.289470i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.34474 | + | 1.94533i | 0.225655 | + | 0.0821317i | ||||
\(562\) | −18.3277 | − | 10.5815i | −0.773109 | − | 0.446355i | ||||
\(563\) | 39.3578 | − | 22.7232i | 1.65873 | − | 0.957669i | 0.685431 | − | 0.728138i | \(-0.259614\pi\) |
0.973301 | − | 0.229531i | \(-0.0737194\pi\) | |||||||
\(564\) | −2.16844 | − | 12.2978i | −0.0913076 | − | 0.517831i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.9681 | + | 20.1116i | −1.00745 | + | 0.845354i | ||||
\(567\) | 13.8596 | + | 2.44382i | 0.582048 | + | 0.102631i | ||||
\(568\) | −0.729392 | − | 2.00399i | −0.0306046 | − | 0.0840855i | ||||
\(569\) | −28.1695 | −1.18093 | −0.590463 | − | 0.807065i | \(-0.701055\pi\) | ||||
−0.590463 | + | 0.807065i | \(0.701055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2742 | 0.764752 | 0.382376 | − | 0.924007i | \(-0.375106\pi\) | ||||
0.382376 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(572\) | 0.455801 | + | 1.25230i | 0.0190580 | + | 0.0523614i | ||||
\(573\) | −19.1682 | − | 3.37987i | −0.800762 | − | 0.141196i | ||||
\(574\) | −5.59547 | + | 4.69516i | −0.233551 | + | 0.195972i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.23254 | + | 18.3327i | 0.134689 | + | 0.763861i | ||||
\(577\) | 17.4797 | − | 10.0919i | 0.727689 | − | 0.420132i | −0.0898868 | − | 0.995952i | \(-0.528651\pi\) |
0.817576 | + | 0.575820i | \(0.195317\pi\) | |||||||
\(578\) | −15.8726 | − | 9.16406i | −0.660214 | − | 0.381175i | ||||
\(579\) | −6.62700 | − | 2.41203i | −0.275409 | − | 0.100241i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.234403 | + | 0.405998i | −0.00972467 | + | 0.0168436i | ||||
\(582\) | −33.2928 | + | 19.2216i | −1.38003 | + | 0.796761i | ||||
\(583\) | −2.19389 | + | 0.386841i | −0.0908614 | + | 0.0160213i | ||||
\(584\) | 20.9704 | + | 17.5963i | 0.867763 | + | 0.728140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.07677 | + | 28.7918i | −0.209719 | + | 1.18938i | ||||
\(587\) | −6.32474 | − | 17.3771i | −0.261050 | − | 0.717229i | −0.999097 | − | 0.0424803i | \(-0.986474\pi\) |
0.738047 | − | 0.674749i | \(-0.235748\pi\) | |||||||
\(588\) | 18.1813i | 0.749783i | ||||||||
\(589\) | −16.4626 | − | 20.4408i | −0.678331 | − | 0.842248i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.6257 | − | 18.4262i | 2.08246 | − | 0.757954i | ||||
\(592\) | −32.6763 | − | 5.76170i | −1.34299 | − | 0.236805i | ||||
\(593\) | −3.28098 | − | 3.91012i | −0.134734 | − | 0.160569i | 0.694459 | − | 0.719532i | \(-0.255644\pi\) |
−0.829193 | + | 0.558963i | \(0.811199\pi\) | |||||||
\(594\) | 6.35610 | + | 5.33340i | 0.260794 | + | 0.218832i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.21767 | + | 12.5014i | 0.295647 | + | 0.512076i | ||||
\(597\) | −39.3727 | − | 22.7318i | −1.61142 | − | 0.930352i | ||||
\(598\) | −3.08193 | + | 8.46754i | −0.126030 | + | 0.346264i | ||||
\(599\) | 33.6127 | + | 12.2340i | 1.37338 | + | 0.499869i | 0.920164 | − | 0.391532i | \(-0.128055\pi\) |
0.453215 | + | 0.891401i | \(0.350277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1676 | − | 29.7352i | −0.700281 | − | 1.21292i | −0.968368 | − | 0.249528i | \(-0.919725\pi\) |
0.268087 | − | 0.963395i | \(-0.413609\pi\) | |||||||
\(602\) | −1.49030 | + | 0.262780i | −0.0607401 | + | 0.0107101i | ||||
\(603\) | 37.8456 | − | 45.1026i | 1.54119 | − | 1.83672i | ||||
\(604\) | 12.2858 | − | 10.3090i | 0.499901 | − | 0.419467i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −37.0783 | + | 13.4954i | −1.50620 | + | 0.548213i | ||||
\(607\) | 3.43239i | 0.139316i | 0.997571 | + | 0.0696582i | \(0.0221909\pi\) | ||||
−0.997571 | + | 0.0696582i | \(0.977809\pi\) | |||||||
\(608\) | 18.3470 | − | 6.26277i | 0.744071 | − | 0.253989i | ||||
\(609\) | 5.71622 | 0.231633 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.85245 | + | 21.8483i | −0.155853 | + | 0.883888i | ||||
\(612\) | −21.4597 | − | 25.5747i | −0.867459 | − | 1.03380i | ||||
\(613\) | −18.0630 | + | 21.5266i | −0.729556 | + | 0.869451i | −0.995522 | − | 0.0945313i | \(-0.969865\pi\) |
0.265966 | + | 0.963982i | \(0.414309\pi\) | |||||||
\(614\) | 7.32362 | + | 41.5343i | 0.295557 | + | 1.67619i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.178194 | + | 0.308640i | −0.00717962 | + | 0.0124355i | ||||
\(617\) | 4.07805 | − | 11.2044i | 0.164176 | − | 0.451070i | −0.830138 | − | 0.557558i | \(-0.811738\pi\) |
0.994314 | + | 0.106488i | \(0.0339606\pi\) | |||||||
\(618\) | −13.2490 | + | 36.4013i | −0.532953 | + | 1.46428i | ||||
\(619\) | −13.9457 | + | 24.1547i | −0.560525 | + | 0.970858i | 0.436926 | + | 0.899498i | \(0.356067\pi\) |
−0.997451 | + | 0.0713602i | \(0.977266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.86825 | + | 16.2667i | 0.115099 | + | 0.652759i | ||||
\(622\) | −6.04314 | + | 7.20193i | −0.242308 | + | 0.288771i | ||||
\(623\) | −5.12956 | − | 6.11318i | −0.205512 | − | 0.244919i | ||||
\(624\) | −13.5393 | + | 76.7850i | −0.542005 | + | 3.07386i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.38242 | −0.0552527 | ||||||||
\(627\) | −2.42874 | + | 4.01782i | −0.0969947 | + | 0.160456i | ||||
\(628\) | − | 5.49345i | − | 0.219212i | ||||||
\(629\) | −33.1113 | + | 12.0515i | −1.32023 | + | 0.480526i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3666 | − | 12.0550i | 0.571927 | − | 0.479904i | −0.310358 | − | 0.950620i | \(-0.600449\pi\) |
0.882285 | + | 0.470716i | \(0.156004\pi\) | |||||||
\(632\) | 1.77130 | − | 2.11095i | 0.0704586 | − | 0.0839692i | ||||
\(633\) | −57.9073 | + | 10.2106i | −2.30161 | + | 0.405835i | ||||
\(634\) | 28.2278 | + | 48.8919i | 1.12107 | + | 1.94175i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 17.1535 | + | 6.24336i | 0.680180 | + | 0.247565i | ||||
\(637\) | 11.0475 | − | 30.3529i | 0.437720 | − | 1.20263i | ||||
\(638\) | 1.54786 | + | 0.893657i | 0.0612803 | + | 0.0353802i | ||||
\(639\) | −4.11677 | − | 7.13046i | −0.162857 | − | 0.282077i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.7076 | − | 14.0193i | −0.659909 | − | 0.553729i | 0.250151 | − | 0.968207i | \(-0.419520\pi\) |
−0.910059 | + | 0.414478i | \(0.863964\pi\) | |||||||
\(642\) | −22.8794 | − | 27.2667i | −0.902980 | − | 1.07613i | ||||
\(643\) | −46.7686 | − | 8.24656i | −1.84437 | − | 0.325213i | −0.861253 | − | 0.508176i | \(-0.830320\pi\) |
−0.983120 | + | 0.182964i | \(0.941431\pi\) | |||||||
\(644\) | 0.477378 | − | 0.173751i | 0.0188113 | − | 0.00684676i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.5025 | − | 29.1799i | 1.00338 | − | 1.14807i | ||||
\(647\) | − | 35.0985i | − | 1.37986i | −0.723874 | − | 0.689932i | \(-0.757640\pi\) | ||
0.723874 | − | 0.689932i | \(-0.242360\pi\) | |||||||
\(648\) | 17.2227 | + | 47.3191i | 0.676573 | + | 1.85887i | ||||
\(649\) | 0.391294 | − | 2.21914i | 0.0153596 | − | 0.0871087i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.22582 | − | 6.90228i | −0.322395 | − | 0.270522i | ||||
\(652\) | −11.9931 | + | 2.11471i | −0.469687 | + | 0.0828185i | ||||
\(653\) | 40.2844 | − | 23.2582i | 1.57645 | − | 0.910163i | 0.581099 | − | 0.813833i | \(-0.302623\pi\) |
0.995349 | − | 0.0963305i | \(-0.0307106\pi\) | |||||||
\(654\) | 48.3472 | − | 83.7397i | 1.89052 | − | 3.27448i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.9679 | − | 13.4552i | −1.44335 | − | 0.525338i | ||||
\(657\) | 91.5297 | + | 52.8447i | 3.57091 | + | 2.06167i | ||||
\(658\) | 3.67908 | − | 2.12412i | 0.143426 | − | 0.0828068i | ||||
\(659\) | 7.50737 | + | 42.5764i | 0.292445 | + | 1.65854i | 0.677407 | + | 0.735608i | \(0.263103\pi\) |
−0.384962 | + | 0.922932i | \(0.625785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9309 | + | 30.1496i | −1.39755 | + | 1.17268i | −0.435376 | + | 0.900249i | \(0.643385\pi\) |
−0.962174 | + | 0.272436i | \(0.912171\pi\) | |||||||
\(662\) | −18.6815 | − | 3.29405i | −0.726076 | − | 0.128027i | ||||
\(663\) | 28.3195 | + | 77.8073i | 1.09984 | + | 3.02179i | ||||
\(664\) | −1.67743 | −0.0650970 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −85.1049 | −3.29775 | ||||||||
\(667\) | 1.21692 | + | 3.34347i | 0.0471194 | + | 0.129460i | ||||
\(668\) | 2.88441 | + | 0.508600i | 0.111601 | + | 0.0196783i | ||||
\(669\) | 65.4350 | − | 54.9065i | 2.52986 | − | 2.12281i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0390883 | + | 0.221681i | 0.00150899 | + | 0.00855789i | ||||
\(672\) | 6.86902 | − | 3.96583i | 0.264978 | − | 0.152985i | ||||
\(673\) | −12.3944 | − | 7.15589i | −0.477768 | − | 0.275839i | 0.241718 | − | 0.970347i | \(-0.422289\pi\) |
−0.719486 | + | 0.694507i | \(0.755622\pi\) | |||||||
\(674\) | 9.96036 | + | 3.62528i | 0.383659 | + | 0.139640i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.27588 | + | 7.40605i | −0.164457 | + | 0.284848i | ||||
\(677\) | 23.9767 | − | 13.8430i | 0.921501 | − | 0.532029i | 0.0373874 | − | 0.999301i | \(-0.488096\pi\) |
0.884114 | + | 0.467272i | \(0.154763\pi\) | |||||||
\(678\) | −26.2311 | + | 4.62525i | −1.00740 | + | 0.177632i | ||||
\(679\) | −2.94963 | − | 2.47504i | −0.113197 | − | 0.0949832i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.93827 | + | 22.3350i | −0.150915 | + | 0.855881i | ||||
\(682\) | −1.14834 | − | 3.15503i | −0.0439721 | − | 0.120812i | ||||
\(683\) | 20.0771i | 0.768228i | 0.923286 | + | 0.384114i | \(0.125493\pi\) | ||||
−0.923286 | + | 0.384114i | \(0.874507\pi\) | |||||||
\(684\) | 24.1378 | − | 13.2959i | 0.922932 | − | 0.508380i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.8854 | + | 4.32592i | −0.453786 | + | 0.165164i | ||||
\(687\) | 8.40651 | + | 1.48229i | 0.320728 | + | 0.0565531i | ||||
\(688\) | −5.23897 | − | 6.24356i | −0.199734 | − | 0.238033i | ||||
\(689\) | −24.8434 | − | 20.8461i | −0.946457 | − | 0.794172i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3678 | + | 24.8857i | 0.546577 | + | 0.946698i | 0.998506 | + | 0.0546446i | \(0.0174026\pi\) |
−0.451929 | + | 0.892054i | \(0.649264\pi\) | |||||||
\(692\) | 1.80895 | + | 1.04440i | 0.0687659 | + | 0.0397020i | ||||
\(693\) | −0.470599 | + | 1.29296i | −0.0178766 | + | 0.0491155i | ||||
\(694\) | −27.7756 | − | 10.1095i | −1.05435 | − | 0.383751i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.2266 | + | 17.7130i | 0.387638 | + | 0.671408i | ||||
\(697\) | −41.1434 | + | 7.25468i | −1.55842 | + | 0.274791i | ||||
\(698\) | −13.5458 | + | 16.1432i | −0.512716 | + | 0.611031i | ||||
\(699\) | −66.4116 | + | 55.7260i | −2.51192 | + | 2.10775i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.2861 | − | 9.20337i | 0.955041 | − | 0.347607i | 0.182953 | − | 0.983122i | \(-0.441434\pi\) |
0.772089 | + | 0.635515i | \(0.219212\pi\) | |||||||
\(702\) | 120.790i | 4.55892i | ||||||||
\(703\) | −4.47338 | − | 28.7391i | −0.168717 | − | 1.08392i | ||||
\(704\) | −0.813858 | −0.0306734 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.70390 | − | 9.66329i | 0.0641271 | − | 0.363683i | ||||
\(707\) | −2.54037 | − | 3.02749i | −0.0955404 | − | 0.113861i | ||||
\(708\) | −11.8687 | + | 14.1446i | −0.446054 | + | 0.531587i | ||||
\(709\) | 1.74216 | + | 9.88027i | 0.0654281 | + | 0.371061i | 0.999888 | + | 0.0149918i | \(0.00477223\pi\) |
−0.934460 | + | 0.356069i | \(0.884117\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.31952 | − | 9.21368i | 0.199498 | − | 0.345540i | ||||
\(712\) | 9.76599 | − | 26.8318i | 0.365996 | − | 1.00557i | ||||
\(713\) | 2.28602 | − | 6.28078i | 0.0856120 | − | 0.235217i | ||||
\(714\) | 7.92770 | − | 13.7312i | 0.296687 | − | 0.513877i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.727558 | − | 4.12619i | −0.0271901 | − | 0.154203i | ||||
\(717\) | −27.3991 | + | 32.6530i | −1.02324 | + | 1.21945i | ||||
\(718\) | 0.627178 | + | 0.747441i | 0.0234061 | + | 0.0278943i | ||||
\(719\) | −4.57974 | + | 25.9730i | −0.170796 | + | 0.968630i | 0.772090 | + | 0.635513i | \(0.219211\pi\) |
−0.942886 | + | 0.333117i | \(0.891900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.87995 | −0.144497 | ||||||||
\(722\) | 19.5595 | + | 25.3119i | 0.727930 | + | 0.942011i | ||||
\(723\) | 49.3069i | 1.83374i | ||||||||
\(724\) | −4.25136 | + | 1.54737i | −0.158001 | + | 0.0575075i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 45.6760 | − | 38.3267i | 1.69519 | − | 1.42244i | ||||
\(727\) | −31.1191 | + | 37.0863i | −1.15414 | + | 1.37546i | −0.239648 | + | 0.970860i | \(0.577032\pi\) |
−0.914496 | + | 0.404595i | \(0.867412\pi\) | |||||||
\(728\) | −5.10937 | + | 0.900920i | −0.189366 | + | 0.0333903i | ||||
\(729\) | 24.6222 | + | 42.6469i | 0.911932 | + | 1.57951i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.13342 | − | 2.96032i | −0.300826 | − | 0.109492i | ||||
\(732\) | 0.630859 | − | 1.73327i | 0.0233172 | − | 0.0640636i | ||||
\(733\) | 30.6031 | + | 17.6687i | 1.13035 | + | 0.652610i | 0.944024 | − | 0.329878i | \(-0.107008\pi\) |
0.186329 | + | 0.982487i | \(0.440341\pi\) | |||||||
\(734\) | −6.65551 | − | 11.5277i | −0.245659 | − | 0.425495i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.78199 | + | 3.17347i | 0.139406 | + | 0.116976i | ||||
\(737\) | 1.65459 | + | 1.97186i | 0.0609475 | + | 0.0726344i | ||||
\(738\) | −99.3720 | − | 17.5220i | −3.65793 | − | 0.644992i | ||||
\(739\) | 18.2924 | − | 6.65787i | 0.672895 | − | 0.244914i | 0.0171013 | − | 0.999854i | \(-0.494556\pi\) |
0.655794 | + | 0.754940i | \(0.272334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −67.5333 | + | 10.5119i | −2.48090 | + | 0.386163i | ||||
\(742\) | 6.21011i | 0.227980i | ||||||||
\(743\) | −9.78221 | − | 26.8764i | −0.358875 | − | 0.986000i | −0.979421 | − | 0.201830i | \(-0.935311\pi\) |
0.620546 | − | 0.784170i | \(-0.286911\pi\) | |||||||
\(744\) | 6.67187 | − | 37.8380i | 0.244602 | − | 1.38721i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.7127 | − | 8.98899i | −0.392218 | − | 0.329110i | ||||
\(747\) | −6.37785 | + | 1.12459i | −0.233353 | + | 0.0411465i | ||||
\(748\) | 1.26404 | − | 0.729796i | 0.0462180 | − | 0.0266840i | ||||
\(749\) | 1.78255 | − | 3.08748i | 0.0651331 | − | 0.112814i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.7071 | − | 16.2721i | −1.63139 | − | 0.593776i | −0.645883 | − | 0.763436i | \(-0.723511\pi\) |
−0.985503 | + | 0.169660i | \(0.945733\pi\) | |||||||
\(752\) | 19.8151 | + | 11.4402i | 0.722581 | + | 0.417182i | ||||
\(753\) | −53.5282 | + | 30.9045i | −1.95068 | + | 1.12622i | ||||
\(754\) | 4.51820 | + | 25.6240i | 0.164543 | + | 0.933170i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.21663 | − | 4.37727i | 0.189727 | − | 0.159200i | ||||
\(757\) | −11.6962 | − | 2.06236i | −0.425107 | − | 0.0749578i | −0.0429980 | − | 0.999075i | \(-0.513691\pi\) |
−0.382109 | + | 0.924117i | \(0.624802\pi\) | |||||||
\(758\) | −5.92689 | − | 16.2840i | −0.215274 | − | 0.591462i | ||||
\(759\) | −1.19561 | −0.0433979 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.1049 | 1.01880 | 0.509401 | − | 0.860530i | \(-0.329867\pi\) | ||||
0.509401 | + | 0.860530i | \(0.329867\pi\) | |||||||
\(762\) | 5.56031 | + | 15.2768i | 0.201429 | + | 0.553421i | ||||
\(763\) | 9.53778 | + | 1.68177i | 0.345291 | + | 0.0608841i | ||||
\(764\) | −3.82626 | + | 3.21061i | −0.138429 | + | 0.116156i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.36368 | + | 53.1041i | 0.338324 | + | 1.91873i | ||||
\(767\) | 28.4091 | − | 16.4020i | 1.02579 | − | 0.592242i | ||||
\(768\) | 47.9525 | + | 27.6854i | 1.73034 | + | 0.999011i | ||||
\(769\) | 52.0340 | + | 18.9388i | 1.87639 | + | 0.682952i | 0.957486 | + | 0.288481i | \(0.0931502\pi\) |
0.918909 | + | 0.394471i | \(0.129072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5091 | − | 61.5036i | 1.27883 | − | 2.21500i | ||||
\(772\) | −1.56730 | + | 0.904883i | −0.0564085 | + | 0.0325674i | ||||
\(773\) | −17.6165 | + | 3.10626i | −0.633621 | + | 0.111725i | −0.481228 | − | 0.876595i | \(-0.659809\pi\) |
−0.152393 | + | 0.988320i | \(0.548698\pi\) | |||||||
\(774\) | −16.0142 | − | 13.4375i | −0.575619 | − | 0.483002i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.39241 | − | 13.5681i | 0.0858826 | − | 0.487065i | ||||
\(777\) | −4.06995 | − | 11.1821i | −0.146009 | − | 0.401155i | ||||
\(778\) | − | 51.5323i | − | 1.84752i | ||||||
\(779\) | 0.693708 | − | 34.4780i | 0.0248547 | − | 1.23530i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.338258 | − | 0.123116i | 0.0121038 | − | 0.00440542i | ||||
\(782\) | 9.71921 | + | 1.71376i | 0.347558 | + | 0.0612839i | ||||
\(783\) | 30.6576 | + | 36.5363i | 1.09561 | + | 1.30570i | ||||
\(784\) | −25.5192 | − | 21.4131i | −0.911399 | − | 0.764755i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.8868 | − | 37.9091i | −0.780677 | − | 1.35217i | ||||
\(787\) | 6.41114 | + | 3.70147i | 0.228532 | + | 0.131943i | 0.609895 | − | 0.792482i | \(-0.291212\pi\) |
−0.381362 | + | 0.924426i | \(0.624545\pi\) | |||||||
\(788\) | 4.72855 | − | 12.9916i | 0.168448 | − | 0.462806i | ||||
\(789\) | 59.9605 | + | 21.8238i | 2.13465 | + | 0.776949i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.33392 | − | 2.31042i | −0.0474288 | − | 0.0821491i | ||||
\(792\) | −4.84845 | + | 0.854913i | −0.172282 | + | 0.0303780i | ||||
\(793\) | −2.10639 | + | 2.51029i | −0.0748000 | + | 0.0891432i | ||||
\(794\) | −13.6974 | + | 11.4935i | −0.486102 | + | 0.407888i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9633 | + | 3.99031i | −0.388584 | + | 0.141433i | ||||
\(797\) | − | 45.6568i | − | 1.61725i | −0.588326 | − | 0.808624i | \(-0.700213\pi\) | ||
0.588326 | − | 0.808624i | \(-0.299787\pi\) | |||||||
\(798\) | 9.85441 | + | 8.61251i | 0.348842 | + | 0.304880i | ||||
\(799\) | 24.2982 | 0.859609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.1431 | − | 108.566i | 0.676389 | − | 3.83599i | ||||
\(802\) | 16.4870 | + | 19.6484i | 0.582175 | + | 0.693809i | ||||
\(803\) | −2.97012 | + | 3.53965i | −0.104813 | + | 0.124911i | ||||
\(804\) | −3.66266 | − | 20.7720i | −0.129172 | − | 0.732571i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.4389 | − | 42.3294i | 0.860823 | − | 1.49099i | ||||
\(807\) | −1.88119 | + | 5.16853i | −0.0662211 | + | 0.181941i | ||||
\(808\) | 4.83652 | − | 13.2882i | 0.170148 | − | 0.467478i | ||||
\(809\) | −9.67626 | + | 16.7598i | −0.340199 | + | 0.589242i | −0.984469 | − | 0.175556i | \(-0.943828\pi\) |
0.644270 | + | 0.764798i | \(0.277161\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.61818 | + | 20.5197i | 0.127052 | + | 0.720546i | 0.980068 | + | 0.198662i | \(0.0636595\pi\) |
−0.853016 | + | 0.521884i | \(0.825229\pi\) | |||||||
\(812\) | 0.942904 | − | 1.12371i | 0.0330894 | − | 0.0394345i | ||||
\(813\) | 16.5968 | + | 19.7793i | 0.582075 | + | 0.693689i | ||||
\(814\) | 0.646099 | − | 3.66421i | 0.0226458 | − | 0.128431i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 85.3951 | 2.98943 | ||||||||
\(817\) | 3.69597 | − | 6.11417i | 0.129306 | − | 0.213908i | ||||
\(818\) | − | 19.6378i | − | 0.686619i | ||||||
\(819\) | −18.8226 | + | 6.85087i | −0.657715 | + | 0.239389i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4739 | + | 19.6969i | −0.819244 | + | 0.687427i | −0.952795 | − | 0.303615i | \(-0.901806\pi\) |
0.133551 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(822\) | −3.24052 | + | 3.86190i | −0.113026 | + | 0.134699i | ||||
\(823\) | −7.95277 | + | 1.40229i | −0.277216 | + | 0.0488807i | −0.310528 | − | 0.950564i | \(-0.600506\pi\) |
0.0333116 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(824\) | −6.94142 | − | 12.0229i | −0.241816 | − | 0.418837i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.90276 | − | 2.14843i | −0.205383 | − | 0.0747534i | ||||
\(827\) | 12.4978 | − | 34.3375i | 0.434593 | − | 1.19403i | −0.508371 | − | 0.861138i | \(-0.669752\pi\) |
0.942964 | − | 0.332895i | \(-0.108026\pi\) | |||||||
\(828\) | 6.07767 | + | 3.50894i | 0.211213 | + | 0.121944i | ||||
\(829\) | −21.3514 | − | 36.9817i | −0.741564 | − | 1.28443i | −0.951783 | − | 0.306773i | \(-0.900751\pi\) |
0.210218 | − | 0.977654i | \(-0.432582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.6014 | + | 19.8039i | 0.818724 | + | 0.686991i | ||||
\(832\) | −7.61570 | − | 9.07604i | −0.264027 | − | 0.314655i | ||||
\(833\) | −34.8396 | − | 6.14317i | −1.20712 | − | 0.212848i | ||||
\(834\) | 0.514771 | − | 0.187361i | 0.0178251 | − | 0.00648779i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.389207 | + | 1.14020i | 0.0134610 | + | 0.0394346i | ||||
\(837\) | − | 89.5956i | − | 3.09688i | ||||||
\(838\) | −10.1938 | − | 28.0072i | −0.352138 | − | 0.967492i | ||||
\(839\) | −8.35614 | + | 47.3900i | −0.288486 | + | 1.63609i | 0.404075 | + | 0.914726i | \(0.367594\pi\) |
−0.692561 | + | 0.721360i | \(0.743518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3450 | − | 12.0369i | −0.494657 | − | 0.415066i | ||||
\(842\) | 34.1593 | − | 6.02320i | 1.17721 | − | 0.207573i | ||||
\(843\) | 35.4014 | − | 20.4390i | 1.21929 | − | 0.703958i | ||||
\(844\) | −7.54471 | + | 13.0678i | −0.259700 | + | 0.449813i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 55.1473 | + | 20.0720i | 1.89600 | + | 0.690089i | ||||
\(847\) | 5.17201 | + | 2.98606i | 0.177712 | + | 0.102602i | ||||
\(848\) | −28.9658 | + | 16.7234i | −0.994690 | + | 0.574285i | ||||
\(849\) | −10.4945 | − | 59.5172i | −0.360170 | − | 2.04263i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.67405 | − | 4.76110i | 0.194504 | − | 0.163208i | ||||
\(852\) | −2.90481 | − | 0.512196i | −0.0995170 | − | 0.0175475i | ||||
\(853\) | −11.0981 | − | 30.4917i | −0.379991 | − | 1.04402i | −0.971359 | − | 0.237615i | \(-0.923634\pi\) |
0.591368 | − | 0.806402i | \(-0.298588\pi\) | |||||||
\(854\) | 0.627500 | 0.0214726 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.7563 | 0.436001 | ||||||||
\(857\) | 10.3213 | + | 28.3576i | 0.352569 | + | 0.968677i | 0.981542 | + | 0.191249i | \(0.0612537\pi\) |
−0.628972 | + | 0.777428i | \(0.716524\pi\) | |||||||
\(858\) | −8.61043 | − | 1.51825i | −0.293955 | − | 0.0518322i | ||||
\(859\) | −20.3519 | + | 17.0772i | −0.694396 | + | 0.582668i | −0.920173 | − | 0.391511i | \(-0.871952\pi\) |
0.225777 | + | 0.974179i | \(0.427508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.45000 | − | 13.8946i | −0.0834956 | − | 0.473527i | ||||
\(862\) | −12.1478 | + | 7.01353i | −0.413756 | + | 0.238882i | ||||
\(863\) | −10.0083 | − | 5.77830i | −0.340687 | − | 0.196696i | 0.319889 | − | 0.947455i | \(-0.396354\pi\) |
−0.660576 | + | 0.750759i | \(0.729688\pi\) | |||||||
\(864\) | 62.1887 | + | 22.6348i | 2.11570 | + | 0.770052i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7339 | + | 41.1083i | −0.806510 | + | 1.39692i | ||||
\(867\) | 30.6592 | − | 17.7011i | 1.04124 | − | 0.601161i | ||||
\(868\) | −2.71374 | + | 0.478505i | −0.0921102 | + | 0.0162415i | ||||
\(869\) | 0.356312 | + | 0.298982i | 0.0120871 | + | 0.0101423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.50709 | + | 36.9035i | −0.220484 | + | 1.25043i | ||||
\(872\) | 11.8522 | + | 32.5637i | 0.401366 | + | 1.10275i | ||||
\(873\) | − | 53.1917i | − | 1.80027i | ||||||
\(874\) | −2.93963 | + | 7.59744i | −0.0994346 | + | 0.256987i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.5792 | − | 12.9498i | 1.20211 | − | 0.437532i | ||||
\(877\) | −17.8905 | − | 3.15457i | −0.604118 | − | 0.106522i | −0.136781 | − | 0.990601i | \(-0.543676\pi\) |
−0.467338 | + | 0.884079i | \(0.654787\pi\) | |||||||
\(878\) | 32.8799 | + | 39.1847i | 1.10964 | + | 1.32242i | ||||
\(879\) | −43.2596 | − | 36.2992i | −1.45911 | − | 1.22434i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9306 | + | 34.5209i | 0.671480 | + | 1.16304i | 0.977484 | + | 0.211008i | \(0.0676745\pi\) |
−0.306004 | + | 0.952030i | \(0.598992\pi\) | |||||||
\(882\) | −73.9975 | − | 42.7225i | −2.49163 | − | 1.43854i | ||||
\(883\) | −9.01286 | + | 24.7626i | −0.303307 | + | 0.833329i | 0.690613 | + | 0.723224i | \(0.257341\pi\) |
−0.993920 | + | 0.110104i | \(0.964882\pi\) | |||||||
\(884\) | 19.9669 | + | 7.26737i | 0.671561 | + | 0.244428i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.6417 | − | 35.7524i | −0.693470 | − | 1.20113i | ||||
\(887\) | 55.1080 | − | 9.71703i | 1.85035 | − | 0.326266i | 0.865664 | − | 0.500626i | \(-0.166897\pi\) |
0.984682 | + | 0.174360i | \(0.0557857\pi\) | |||||||
\(888\) | 27.3688 | − | 32.6169i | 0.918438 | − | 1.09455i | ||||
\(889\) | −1.24737 | + | 1.04667i | −0.0418355 | + | 0.0351042i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.98710 | + | 2.90707i | −0.267578 | + | 0.0973903i | ||||
\(892\) | − | 21.9203i | − | 0.733947i | ||||||
\(893\) | −3.87941 | + | 19.6778i | −0.129820 | + | 0.658492i | ||||
\(894\) | −94.7059 | −3.16744 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.24102 | + | 7.03816i | −0.0414595 | + | 0.235128i | ||||
\(897\) | −11.1880 | − | 13.3333i | −0.373555 | − | 0.445186i | ||||
\(898\) | −26.7183 | + | 31.8417i | −0.891603 | + | 1.06257i | ||||
\(899\) | −3.35136 | − | 19.0065i | −0.111774 | − | 0.633903i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.7597 | + | 30.7606i | −0.591660 | + | 1.02479i | ||||
\(902\) | 1.50882 | − | 4.14546i | 0.0502384 | − | 0.138029i | ||||
\(903\) | 0.999738 | − | 2.74676i | 0.0332692 | − | 0.0914064i | ||||
\(904\) | 4.77290 | − | 8.26690i | 0.158744 | − | 0.274953i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.2713 | + | 103.622i | 0.607022 | + | 3.44259i | ||||
\(907\) | −29.6403 | + | 35.3239i | −0.984188 | + | 1.17291i | 0.000749224 | 1.00000i | \(0.499762\pi\) | |
−0.984938 | + | 0.172910i | \(0.944683\pi\) | |||||||
\(908\) | 3.74105 | + | 4.45841i | 0.124151 | + | 0.147958i | ||||
\(909\) | 9.48045 | − | 53.7663i | 0.314447 | − | 1.78332i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.40625 | 0.0465912 | 0.0232956 | − | 0.999729i | \(-0.492584\pi\) | ||||
0.0232956 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(912\) | −13.6340 | + | 69.1568i | −0.451468 | + | 2.29001i | ||||
\(913\) | − | 0.283137i | − | 0.00937048i | ||||||
\(914\) | 11.3352 | − | 4.12569i | 0.374936 | − | 0.136466i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.67807 | − | 1.40807i | 0.0554449 | − | 0.0465238i | ||||
\(917\) | 2.81822 | − | 3.35862i | 0.0930658 | − | 0.110912i | ||||
\(918\) | 130.284 | − | 22.9725i | 4.30000 | − | 0.758207i | ||||
\(919\) | 23.5177 | + | 40.7338i | 0.775777 | + | 1.34369i | 0.934357 | + | 0.356339i | \(0.115975\pi\) |
−0.158579 | + | 0.987346i | \(0.550691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76.5515 | − | 27.8625i | −2.52246 | − | 0.918099i | ||||
\(922\) | −12.5072 | + | 34.3633i | −0.411903 | + | 1.13170i | ||||
\(923\) | 4.53823 | + | 2.62015i | 0.149378 | + | 0.0862432i | ||||
\(924\) | 0.246461 | + | 0.426883i | 0.00810798 | + | 0.0140434i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −41.1786 | − | 34.5529i | −1.35321 | − | 1.13548i | ||||
\(927\) | −34.4527 | − | 41.0591i | −1.13158 | − | 1.34856i | ||||
\(928\) | 14.0392 | + | 2.47548i | 0.460858 | + | 0.0812617i | ||||
\(929\) | −0.927569 | + | 0.337607i | −0.0304325 | + | 0.0110765i | −0.357192 | − | 0.934031i | \(-0.616266\pi\) |
0.326759 | + | 0.945108i | \(0.394043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5375 | − | 27.2339i | 0.345351 | − | 0.892555i | ||||
\(932\) | 22.2475i | 0.728741i | ||||||||
\(933\) | −6.21096 | − | 17.0645i | −0.203338 | − | 0.558666i | ||||
\(934\) | 5.71210 | − | 32.3950i | 0.186906 | − | 1.06000i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.9034 | − | 46.0694i | −1.79457 | − | 1.50583i | ||||
\(937\) | −10.4614 | + | 1.84463i | −0.341760 | + | 0.0602615i | −0.341894 | − | 0.939739i | \(-0.611068\pi\) |
0.000134284 | 1.00000i | \(0.499957\pi\) | ||||||||
\(938\) | 6.21426 | − | 3.58781i | 0.202903 | − | 0.117146i | ||||
\(939\) | 1.33513 | − | 2.31251i | 0.0435702 | − | 0.0754659i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.88893 | + | 3.59928i | 0.322370 | + | 0.117333i | 0.498136 | − | 0.867099i | \(-0.334018\pi\) |
−0.175766 | + | 0.984432i | \(0.556240\pi\) | |||||||
\(942\) | 31.2123 | + | 18.0204i | 1.01695 | + | 0.587137i | ||||
\(943\) | 7.60550 | − | 4.39104i | 0.247669 | − | 0.142992i | ||||
\(944\) | −5.87483 | − | 33.3178i | −0.191210 | − | 1.08440i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.700133 | − | 0.587481i | 0.0227633 | − | 0.0191007i | ||||
\(947\) | −34.5779 | − | 6.09701i | −1.12363 | − | 0.198126i | −0.419196 | − | 0.907896i | \(-0.637688\pi\) |
−0.704434 | + | 0.709770i | \(0.748799\pi\) | |||||||
\(948\) | −1.30357 | − | 3.58152i | −0.0423378 | − | 0.116322i | ||||
\(949\) | −67.2667 | −2.18357 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −109.048 | −3.53613 | ||||||||
\(952\) | 1.94346 | + | 5.33961i | 0.0629879 | + | 0.173058i | ||||
\(953\) | 20.7575 | + | 3.66011i | 0.672402 | + | 0.118563i | 0.499417 | − | 0.866362i | \(-0.333548\pi\) |
0.172985 | + | 0.984924i | \(0.444659\pi\) | |||||||
\(954\) | −65.7178 | + | 55.1437i | −2.12769 | + | 1.78534i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.89946 | + | 10.7724i | 0.0614329 | + | 0.348403i | ||||
\(957\) | −2.98981 | + | 1.72617i | −0.0966468 | + | 0.0557991i | ||||
\(958\) | 17.8447 | + | 10.3026i | 0.576535 | + | 0.332863i | ||||
\(959\) | −0.474491 | − | 0.172701i | −0.0153221 | − | 0.00557679i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62747 | + | 4.55092i | −0.0847572 | + | 0.146804i | ||||
\(962\) | 46.9087 | − | 27.0828i | 1.51240 | − | 0.873183i | ||||
\(963\) | 48.5014 | − | 8.55210i | 1.56293 | − | 0.275587i | ||||
\(964\) | 9.69287 | + | 8.13329i | 0.312186 | + | 0.261956i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.578758 | + | 3.28230i | −0.0186212 | + | 0.105606i | ||||
\(967\) | 16.2138 | + | 44.5471i | 0.521401 | + | 1.43254i | 0.868961 | + | 0.494881i | \(0.164788\pi\) |
−0.347560 | + | 0.937658i | \(0.612990\pi\) | |||||||
\(968\) | 21.3688i | 0.686820i | ||||||||
\(969\) | 24.1820 | + | 70.8421i | 0.776836 | + | 2.27578i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.6348 | − | 11.1502i | 0.983117 | − | 0.357825i | 0.200066 | − | 0.979782i | \(-0.435884\pi\) |
0.783051 | + | 0.621957i | \(0.213662\pi\) | |||||||
\(972\) | 31.9020 | + | 5.62519i | 1.02326 | + | 0.180428i | ||||
\(973\) | 0.0352688 | + | 0.0420317i | 0.00113067 | + | 0.00134747i | ||||
\(974\) | 18.1873 | + | 15.2609i | 0.582757 | + | 0.488991i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.68982 | + | 2.92685i | 0.0540897 | + | 0.0936861i | ||||
\(977\) | −20.7772 | − | 11.9957i | −0.664721 | − | 0.383777i | 0.129353 | − | 0.991599i | \(-0.458710\pi\) |
−0.794073 | + | 0.607822i | \(0.792043\pi\) | |||||||
\(978\) | 27.3264 | − | 75.0787i | 0.873802 | − | 2.40075i | ||||
\(979\) | 4.52900 | + | 1.64842i | 0.144748 | + | 0.0526838i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.8953 | + | 115.866i | 2.13580 | + | 3.69932i | ||||
\(982\) | −32.9727 | + | 5.81398i | −1.05220 | + | 0.185532i | ||||
\(983\) | −2.75592 | + | 3.28438i | −0.0879003 | + | 0.104756i | −0.808202 | − | 0.588906i | \(-0.799559\pi\) |
0.720302 | + | 0.693661i | \(0.244003\pi\) | |||||||
\(984\) | 38.6724 | − | 32.4500i | 1.23283 | − | 1.03447i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.7787 | − | 9.74663i | 0.852806 | − | 0.310396i | ||||
\(987\) | 8.20581i | 0.261194i | ||||||||
\(988\) | −9.07333 | + | 15.0098i | −0.288661 | + | 0.477526i | ||||
\(989\) | 1.81944 | 0.0578547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.94255 | + | 45.0444i | −0.252303 | + | 1.43088i | 0.550597 | + | 0.834771i | \(0.314400\pi\) |
−0.802901 | + | 0.596113i | \(0.796711\pi\) | |||||||
\(992\) | −17.2137 | − | 20.5145i | −0.546535 | − | 0.651335i | ||||
\(993\) | 23.5526 | − | 28.0689i | 0.747420 | − | 0.890741i | ||||
\(994\) | −0.174248 | − | 0.988211i | −0.00552682 | − | 0.0313442i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.16004 | + | 2.00924i | −0.0367571 | + | 0.0636652i | ||||
\(997\) | −4.09478 | + | 11.2503i | −0.129683 | + | 0.356301i | −0.987492 | − | 0.157667i | \(-0.949603\pi\) |
0.857809 | + | 0.513968i | \(0.171825\pi\) | |||||||
\(998\) | −4.28267 | + | 11.7665i | −0.135566 | + | 0.372463i | ||||
\(999\) | 49.6442 | − | 85.9863i | 1.57067 | − | 2.72048i |
(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 | 475.2.u.c.24.5 | 36 | ||
5.2 | odd | 4 | 95.2.k.b.81.1 | yes | 18 | ||
5.3 | odd | 4 | 475.2.l.b.176.3 | 18 | |||
5.4 | even | 2 | inner | 475.2.u.c.24.2 | 36 | ||
15.2 | even | 4 | 855.2.bs.b.271.3 | 18 | |||
19.4 | even | 9 | inner | 475.2.u.c.99.2 | 36 | ||
95.2 | even | 36 | 1805.2.a.u.1.3 | 9 | |||
95.4 | even | 18 | inner | 475.2.u.c.99.5 | 36 | ||
95.17 | odd | 36 | 1805.2.a.t.1.7 | 9 | |||
95.23 | odd | 36 | 475.2.l.b.251.3 | 18 | |||
95.42 | odd | 36 | 95.2.k.b.61.1 | ✓ | 18 | ||
95.78 | even | 36 | 9025.2.a.cd.1.7 | 9 | |||
95.93 | odd | 36 | 9025.2.a.ce.1.3 | 9 | |||
285.137 | even | 36 | 855.2.bs.b.631.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.61.1 | ✓ | 18 | 95.42 | odd | 36 | ||
95.2.k.b.81.1 | yes | 18 | 5.2 | odd | 4 | ||
475.2.l.b.176.3 | 18 | 5.3 | odd | 4 | |||
475.2.l.b.251.3 | 18 | 95.23 | odd | 36 | |||
475.2.u.c.24.2 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.c.24.5 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.c.99.2 | 36 | 19.4 | even | 9 | inner | ||
475.2.u.c.99.5 | 36 | 95.4 | even | 18 | inner | ||
855.2.bs.b.271.3 | 18 | 15.2 | even | 4 | |||
855.2.bs.b.631.3 | 18 | 285.137 | even | 36 | |||
1805.2.a.t.1.7 | 9 | 95.17 | odd | 36 | |||
1805.2.a.u.1.3 | 9 | 95.2 | even | 36 | |||
9025.2.a.cd.1.7 | 9 | 95.78 | even | 36 | |||
9025.2.a.ce.1.3 | 9 | 95.93 | odd | 36 |