Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,3,Mod(8,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.8");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.f (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: | \(2.20709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Character | \(\chi\) | \(=\) | 81.8 |
Dual form | 81.3.f.a.71.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14332 | − | 0.201599i | −0.571662 | − | 0.100799i | −0.119658 | − | 0.992815i | \(-0.538180\pi\) |
−0.452004 | + | 0.892016i | \(0.649291\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.49222 | − | 0.907094i | −0.623055 | − | 0.226774i | ||||
\(5\) | 3.46013 | + | 4.12362i | 0.692026 | + | 0.824724i | 0.991599 | − | 0.129349i | \(-0.0412889\pi\) |
−0.299574 | + | 0.954073i | \(0.596844\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.89907 | − | 3.60297i | 1.41415 | − | 0.514709i | 0.481807 | − | 0.876278i | \(-0.339981\pi\) |
0.932346 | + | 0.361568i | \(0.117759\pi\) | |||||||
\(8\) | 6.68824 | + | 3.86146i | 0.836030 | + | 0.482682i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.12473 | − | 5.41219i | −0.312473 | − | 0.541219i | ||||
\(11\) | 7.54888 | − | 8.99640i | 0.686262 | − | 0.817855i | −0.304636 | − | 0.952469i | \(-0.598535\pi\) |
0.990898 | + | 0.134614i | \(0.0429794\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95057 | + | 11.0622i | 0.150044 | + | 0.850940i | 0.963178 | + | 0.268864i | \(0.0866482\pi\) |
−0.813134 | + | 0.582076i | \(0.802241\pi\) | |||||||
\(14\) | −12.0442 | + | 2.12372i | −0.860300 | + | 0.151694i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.25834 | + | 1.05588i | 0.0786465 | + | 0.0659923i | ||||
\(17\) | −2.73630 | + | 1.57980i | −0.160959 | + | 0.0929296i | −0.578316 | − | 0.815813i | \(-0.696290\pi\) |
0.417357 | + | 0.908743i | \(0.362956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.26051 | − | 3.91532i | 0.118974 | − | 0.206069i | −0.800387 | − | 0.599483i | \(-0.795373\pi\) |
0.919361 | + | 0.393414i | \(0.128706\pi\) | |||||||
\(20\) | −4.88289 | − | 13.4156i | −0.244145 | − | 0.670782i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.4445 | + | 8.76396i | −0.474749 | + | 0.398362i | ||||
\(23\) | −6.80880 | + | 18.7070i | −0.296035 | + | 0.813349i | 0.699118 | + | 0.715007i | \(0.253576\pi\) |
−0.995153 | + | 0.0983427i | \(0.968646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.690550 | + | 3.91630i | −0.0276220 | + | 0.156652i | ||||
\(26\) | − | 13.0409i | − | 0.501575i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −27.9389 | −0.997818 | ||||||||
\(29\) | −24.9744 | − | 4.40366i | −0.861187 | − | 0.151851i | −0.274424 | − | 0.961609i | \(-0.588487\pi\) |
−0.586763 | + | 0.809758i | \(0.699598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.7874 | − | 7.56598i | −0.670560 | − | 0.244064i | −0.0157712 | − | 0.999876i | \(-0.505020\pi\) |
−0.654789 | + | 0.755812i | \(0.727243\pi\) | |||||||
\(32\) | −21.0826 | − | 25.1253i | −0.658832 | − | 0.785165i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.44696 | − | 1.25459i | 0.101381 | − | 0.0368998i | ||||
\(35\) | 49.1093 | + | 28.3533i | 1.40312 | + | 0.810093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.82807 | − | 15.2907i | −0.238596 | − | 0.413261i | 0.721715 | − | 0.692190i | \(-0.243354\pi\) |
−0.960312 | + | 0.278929i | \(0.910021\pi\) | |||||||
\(38\) | −3.37382 | + | 4.02076i | −0.0887847 | + | 0.105810i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.21898 | + | 40.9409i | 0.180475 | + | 1.02352i | ||||
\(41\) | 12.2557 | − | 2.16101i | 0.298920 | − | 0.0527076i | −0.0221770 | − | 0.999754i | \(-0.507060\pi\) |
0.321096 | + | 0.947046i | \(0.395949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.9211 | + | 23.4286i | 0.649329 | + | 0.544851i | 0.906867 | − | 0.421417i | \(-0.138467\pi\) |
−0.257539 | + | 0.966268i | \(0.582911\pi\) | |||||||
\(44\) | −26.9741 | + | 15.5735i | −0.613047 | + | 0.353943i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.5560 | − | 20.0156i | 0.251217 | − | 0.435121i | ||||
\(47\) | 4.24091 | + | 11.6518i | 0.0902320 | + | 0.247910i | 0.976597 | − | 0.215076i | \(-0.0690000\pi\) |
−0.886365 | + | 0.462987i | \(0.846778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.4740 | − | 39.8354i | 0.968857 | − | 0.812967i | ||||
\(50\) | 1.57905 | − | 4.33839i | 0.0315809 | − | 0.0867679i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.17323 | − | 29.3388i | 0.0994852 | − | 0.564209i | ||||
\(53\) | − | 84.6210i | − | 1.59662i | −0.602245 | − | 0.798311i | \(-0.705727\pi\) | ||
0.602245 | − | 0.798311i | \(-0.294273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.2178 | 1.14942 | ||||||||
\(56\) | 80.1200 | + | 14.1273i | 1.43071 | + | 0.252274i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 27.6661 | + | 10.0696i | 0.477002 | + | 0.173614i | ||||
\(59\) | 43.8854 | + | 52.3006i | 0.743820 | + | 0.886451i | 0.996711 | − | 0.0810443i | \(-0.0258255\pi\) |
−0.252890 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −73.3637 | + | 26.7022i | −1.20268 | + | 0.437741i | −0.864160 | − | 0.503217i | \(-0.832150\pi\) |
−0.338523 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(62\) | 22.2414 | + | 12.8411i | 0.358733 | + | 0.207114i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 15.7537 | + | 27.2863i | 0.246152 | + | 0.426348i | ||||
\(65\) | −38.8672 | + | 46.3201i | −0.597956 | + | 0.712617i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.8654 | − | 95.6483i | −0.251722 | − | 1.42759i | −0.804349 | − | 0.594157i | \(-0.797486\pi\) |
0.552627 | − | 0.833429i | \(-0.313625\pi\) | |||||||
\(68\) | 8.25249 | − | 1.45514i | 0.121360 | − | 0.0213991i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −50.4319 | − | 42.3174i | −0.720455 | − | 0.604534i | ||||
\(71\) | −105.364 | + | 60.8322i | −1.48401 | + | 0.856791i | −0.999835 | − | 0.0181820i | \(-0.994212\pi\) |
−0.484171 | + | 0.874973i | \(0.660879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.5705 | + | 78.9304i | −0.624254 | + | 1.08124i | 0.364431 | + | 0.931230i | \(0.381263\pi\) |
−0.988685 | + | 0.150009i | \(0.952070\pi\) | |||||||
\(74\) | 7.01076 | + | 19.2619i | 0.0947401 | + | 0.260296i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.18525 | + | 7.70734i | −0.120859 | + | 0.101412i | ||||
\(77\) | 42.3131 | − | 116.254i | 0.549521 | − | 1.50980i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.54032 | + | 20.0781i | −0.0448142 | + | 0.254154i | −0.998982 | − | 0.0451196i | \(-0.985633\pi\) |
0.954167 | + | 0.299273i | \(0.0967442\pi\) | |||||||
\(80\) | 8.84240i | 0.110530i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.4479 | −0.176194 | ||||||||
\(83\) | −31.1219 | − | 5.48763i | −0.374963 | − | 0.0661161i | −0.0170090 | − | 0.999855i | \(-0.505414\pi\) |
−0.357954 | + | 0.933739i | \(0.616526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9824 | − | 5.81713i | −0.188029 | − | 0.0684369i | ||||
\(86\) | −27.1997 | − | 32.4154i | −0.316276 | − | 0.376923i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 85.2279 | − | 31.0204i | 0.968499 | − | 0.352505i | ||||
\(89\) | −59.7756 | − | 34.5114i | −0.671636 | − | 0.387769i | 0.125060 | − | 0.992149i | \(-0.460088\pi\) |
−0.796696 | + | 0.604380i | \(0.793421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 59.1656 | + | 102.478i | 0.650171 | + | 1.12613i | ||||
\(92\) | 33.9381 | − | 40.4458i | 0.368892 | − | 0.439629i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.49974 | − | 14.1767i | −0.0265930 | − | 0.150816i | ||||
\(95\) | 23.9669 | − | 4.22602i | 0.252283 | − | 0.0444844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −61.1335 | − | 51.2971i | −0.630243 | − | 0.528836i | 0.270762 | − | 0.962646i | \(-0.412724\pi\) |
−0.901004 | + | 0.433810i | \(0.857169\pi\) | |||||||
\(98\) | −62.3089 | + | 35.9741i | −0.635806 | + | 0.367083i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.27346 | − | 9.13390i | 0.0527346 | − | 0.0913390i | ||||
\(101\) | 1.63372 | + | 4.48862i | 0.0161755 | + | 0.0444417i | 0.947518 | − | 0.319704i | \(-0.103583\pi\) |
−0.931342 | + | 0.364145i | \(0.881361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −55.3795 | + | 46.4689i | −0.537665 | + | 0.451154i | −0.870738 | − | 0.491746i | \(-0.836359\pi\) |
0.333074 | + | 0.942901i | \(0.391914\pi\) | |||||||
\(104\) | −29.6704 | + | 81.5188i | −0.285293 | + | 0.783835i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.0595 | + | 96.7493i | −0.160939 | + | 0.912729i | ||||
\(107\) | − | 158.133i | − | 1.47788i | −0.673773 | − | 0.738938i | \(-0.735328\pi\) | ||
0.673773 | − | 0.738938i | \(-0.264672\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.5788 | −0.170448 | −0.0852240 | − | 0.996362i | \(-0.527161\pi\) | ||||
−0.0852240 | + | 0.996362i | \(0.527161\pi\) | |||||||
\(110\) | −72.2785 | − | 12.7447i | −0.657077 | − | 0.115860i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.2607 | + | 5.91842i | 0.145185 | + | 0.0528430i | ||||
\(113\) | 11.5806 | + | 13.8012i | 0.102483 | + | 0.122134i | 0.814848 | − | 0.579675i | \(-0.196820\pi\) |
−0.712365 | + | 0.701809i | \(0.752376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −100.700 | + | 36.6518i | −0.875652 | + | 0.318711i | ||||
\(116\) | 58.2473 | + | 33.6291i | 0.502131 | + | 0.289906i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −39.6315 | − | 68.6438i | −0.335860 | − | 0.581727i | ||||
\(119\) | −21.3948 | + | 25.4974i | −0.179788 | + | 0.214264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.93828 | − | 16.6638i | −0.0242833 | − | 0.137717i | ||||
\(122\) | 89.2617 | − | 15.7392i | 0.731653 | − | 0.129010i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 44.9437 | + | 37.7122i | 0.362449 | + | 0.304131i | ||||
\(125\) | 98.0067 | − | 56.5842i | 0.784054 | − | 0.452674i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 78.1067 | − | 135.285i | 0.615013 | − | 1.06523i | −0.375369 | − | 0.926876i | \(-0.622484\pi\) |
0.990382 | − | 0.138359i | \(-0.0441827\pi\) | |||||||
\(128\) | 32.3605 | + | 88.9098i | 0.252817 | + | 0.694608i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 53.7759 | − | 45.1233i | 0.413661 | − | 0.347102i | ||||
\(131\) | −33.6955 | + | 92.5776i | −0.257217 | + | 0.706699i | 0.742119 | + | 0.670268i | \(0.233821\pi\) |
−0.999336 | + | 0.0364307i | \(0.988401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.27018 | − | 46.9025i | 0.0621818 | − | 0.352651i | ||||
\(134\) | 112.757i | 0.841471i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.4014 | −0.179422 | ||||||||
\(137\) | 64.6590 | + | 11.4011i | 0.471963 | + | 0.0832199i | 0.404571 | − | 0.914507i | \(-0.367421\pi\) |
0.0673925 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 117.744 | + | 42.8553i | 0.847080 | + | 0.308312i | 0.728849 | − | 0.684674i | \(-0.240056\pi\) |
0.118231 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(140\) | −96.6721 | − | 115.209i | −0.690515 | − | 0.822924i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 132.729 | − | 48.3096i | 0.934714 | − | 0.340208i | ||||
\(143\) | 114.245 | + | 65.9593i | 0.798915 | + | 0.461254i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.2557 | − | 118.222i | −0.470729 | − | 0.815326i | ||||
\(146\) | 68.0142 | − | 81.0562i | 0.465851 | − | 0.555179i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.13142 | + | 46.1156i | 0.0549420 | + | 0.311592i | ||||
\(149\) | −198.691 | + | 35.0346i | −1.33350 | + | 0.235132i | −0.794546 | − | 0.607204i | \(-0.792291\pi\) |
−0.538953 | + | 0.842336i | \(0.681180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 98.1613 | + | 82.3671i | 0.650075 | + | 0.545478i | 0.907094 | − | 0.420929i | \(-0.138296\pi\) |
−0.257019 | + | 0.966406i | \(0.582740\pi\) | |||||||
\(152\) | 30.2377 | − | 17.4577i | 0.198932 | − | 0.114853i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −71.8144 | + | 124.386i | −0.466327 | + | 0.807703i | ||||
\(155\) | −40.7277 | − | 111.898i | −0.262759 | − | 0.721926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −106.439 | + | 89.3129i | −0.677955 | + | 0.568872i | −0.915408 | − | 0.402527i | \(-0.868132\pi\) |
0.237453 | + | 0.971399i | \(0.423687\pi\) | |||||||
\(158\) | 8.09547 | − | 22.2421i | 0.0512371 | − | 0.140773i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 30.6586 | − | 173.873i | 0.191616 | − | 1.08671i | ||||
\(161\) | 209.714i | 1.30257i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 39.8569 | 0.244521 | 0.122261 | − | 0.992498i | \(-0.460986\pi\) | ||||
0.122261 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(164\) | −32.5042 | − | 5.73136i | −0.198196 | − | 0.0349473i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34.4762 | + | 12.5483i | 0.207688 | + | 0.0755921i | ||||
\(167\) | 106.672 | + | 127.127i | 0.638757 | + | 0.761241i | 0.984173 | − | 0.177208i | \(-0.0567067\pi\) |
−0.345416 | + | 0.938450i | \(0.612262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 40.2401 | − | 14.6462i | 0.238107 | − | 0.0866639i | ||||
\(170\) | 17.1004 | + | 9.87292i | 0.100591 | + | 0.0580760i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −48.3337 | − | 83.7164i | −0.281010 | − | 0.486723i | ||||
\(173\) | 7.00006 | − | 8.34234i | 0.0404628 | − | 0.0482216i | −0.745434 | − | 0.666580i | \(-0.767757\pi\) |
0.785896 | + | 0.618358i | \(0.212202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.27451 | + | 41.2558i | 0.0415686 | + | 0.235747i | ||||
\(176\) | 18.9982 | − | 3.34989i | 0.107944 | − | 0.0190335i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 61.3854 | + | 51.5085i | 0.344862 | + | 0.289374i | ||||
\(179\) | 244.720 | − | 141.289i | 1.36715 | − | 0.789326i | 0.376590 | − | 0.926380i | \(-0.377097\pi\) |
0.990564 | + | 0.137054i | \(0.0437633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 54.3996 | − | 94.2228i | 0.300550 | − | 0.520568i | −0.675711 | − | 0.737167i | \(-0.736163\pi\) |
0.976261 | + | 0.216599i | \(0.0694964\pi\) | |||||||
\(182\) | −46.9861 | − | 129.093i | −0.258165 | − | 0.709303i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −117.775 | + | 98.8252i | −0.640083 | + | 0.537094i | ||||
\(185\) | 32.5066 | − | 89.3112i | 0.175711 | − | 0.482763i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.44344 | + | 36.5426i | −0.0344569 | + | 0.195415i | ||||
\(188\) | − | 32.8857i | − | 0.174924i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −28.2539 | −0.148705 | ||||||||
\(191\) | −106.979 | − | 18.8633i | −0.560100 | − | 0.0987607i | −0.113571 | − | 0.993530i | \(-0.536229\pi\) |
−0.446529 | + | 0.894769i | \(0.647340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −188.040 | − | 68.4410i | −0.974301 | − | 0.354617i | −0.194679 | − | 0.980867i | \(-0.562367\pi\) |
−0.779622 | + | 0.626250i | \(0.784589\pi\) | |||||||
\(194\) | 59.5540 | + | 70.9737i | 0.306980 | + | 0.365844i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −154.450 | + | 56.2152i | −0.788011 | + | 0.286812i | ||||
\(197\) | −253.494 | − | 146.355i | −1.28677 | − | 0.742918i | −0.308694 | − | 0.951161i | \(-0.599892\pi\) |
−0.978077 | + | 0.208243i | \(0.933225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 41.1548 | + | 71.2822i | 0.206808 | + | 0.358202i | 0.950707 | − | 0.310090i | \(-0.100359\pi\) |
−0.743899 | + | 0.668292i | \(0.767026\pi\) | |||||||
\(200\) | −19.7412 | + | 23.5267i | −0.0987060 | + | 0.117633i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.962975 | − | 5.46130i | −0.00476720 | − | 0.0270361i | ||||
\(203\) | −263.090 | + | 46.3898i | −1.29601 | + | 0.228521i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 51.3175 | + | 43.0605i | 0.250329 | + | 0.210051i | ||||
\(206\) | 72.6848 | − | 41.9646i | 0.352839 | − | 0.203712i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.22585 | + | 15.9796i | −0.0443550 | + | 0.0768252i | ||||
\(209\) | −18.1595 | − | 49.8927i | −0.0868874 | − | 0.238721i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 88.7425 | − | 74.4638i | 0.420581 | − | 0.352909i | −0.407803 | − | 0.913070i | \(-0.633705\pi\) |
0.828384 | + | 0.560161i | \(0.189261\pi\) | |||||||
\(212\) | −76.7592 | + | 210.894i | −0.362072 | + | 0.994784i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31.8794 | + | 180.797i | −0.148969 | + | 0.844846i | ||||
\(215\) | 196.202i | 0.912568i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233.036 | −1.07390 | ||||||||
\(218\) | 21.2416 | + | 3.74547i | 0.0974387 | + | 0.0171811i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −157.553 | − | 57.3445i | −0.716149 | − | 0.260657i | ||||
\(221\) | −22.8135 | − | 27.1880i | −0.103228 | − | 0.123023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 186.281 | − | 67.8007i | 0.835341 | − | 0.304039i | 0.111292 | − | 0.993788i | \(-0.464501\pi\) |
0.724049 | + | 0.689749i | \(0.242279\pi\) | |||||||
\(224\) | −299.224 | − | 172.757i | −1.33582 | − | 0.771236i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4580 | − | 18.1138i | −0.0462745 | − | 0.0801498i | ||||
\(227\) | 3.31155 | − | 3.94655i | 0.0145883 | − | 0.0173857i | −0.758701 | − | 0.651439i | \(-0.774166\pi\) |
0.773289 | + | 0.634053i | \(0.218610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 61.3581 | + | 347.979i | 0.267939 | + | 1.51956i | 0.760533 | + | 0.649299i | \(0.224938\pi\) |
−0.492594 | + | 0.870259i | \(0.663951\pi\) | |||||||
\(230\) | 122.522 | − | 21.6039i | 0.532703 | − | 0.0939300i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −150.030 | − | 125.890i | −0.646683 | − | 0.542631i | ||||
\(233\) | −121.729 | + | 70.2803i | −0.522442 | + | 0.301632i | −0.737933 | − | 0.674874i | \(-0.764198\pi\) |
0.215491 | + | 0.976506i | \(0.430865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −33.3735 | + | 57.8046i | −0.142015 | + | 0.245977i | ||||
\(236\) | −61.9306 | − | 170.153i | −0.262418 | − | 0.720987i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 29.6015 | − | 24.8386i | 0.124376 | − | 0.104364i | ||||
\(239\) | 50.5074 | − | 138.768i | 0.211328 | − | 0.580619i | −0.788060 | − | 0.615598i | \(-0.788914\pi\) |
0.999388 | + | 0.0349794i | \(0.0111366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 52.8609 | − | 299.789i | 0.219340 | − | 1.24394i | −0.653875 | − | 0.756602i | \(-0.726858\pi\) |
0.873215 | − | 0.487335i | \(-0.162031\pi\) | |||||||
\(242\) | 19.6445i | 0.0811755i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 207.060 | 0.848606 | ||||||||
\(245\) | 328.532 | + | 57.9291i | 1.34095 | + | 0.236445i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 47.7214 | + | 17.3692i | 0.193204 | + | 0.0703205i | ||||
\(248\) | −109.815 | − | 130.873i | −0.442803 | − | 0.527712i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −123.461 | + | 44.9361i | −0.493843 | + | 0.179744i | ||||
\(251\) | 108.072 | + | 62.3955i | 0.430567 | + | 0.248588i | 0.699588 | − | 0.714546i | \(-0.253367\pi\) |
−0.269021 | + | 0.963134i | \(0.586700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 116.897 | + | 202.472i | 0.462044 | + | 0.800284i | ||||
\(254\) | −116.575 | + | 138.928i | −0.458955 | + | 0.546961i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −40.9593 | − | 232.292i | −0.159997 | − | 0.907390i | ||||
\(257\) | 450.088 | − | 79.3627i | 1.75132 | − | 0.308804i | 0.796199 | − | 0.605035i | \(-0.206841\pi\) |
0.955116 | + | 0.296231i | \(0.0957298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −142.481 | − | 119.556i | −0.550121 | − | 0.461606i | ||||
\(260\) | 138.882 | − | 80.1837i | 0.534163 | − | 0.308399i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 57.1884 | − | 99.0533i | 0.218276 | − | 0.378066i | ||||
\(263\) | 160.047 | + | 439.726i | 0.608545 | + | 1.67196i | 0.733408 | + | 0.679789i | \(0.237929\pi\) |
−0.124863 | + | 0.992174i | \(0.539849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 348.945 | − | 292.799i | 1.31677 | − | 1.10490i | ||||
\(266\) | −18.9110 | + | 51.9576i | −0.0710940 | + | 0.195329i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −44.7298 | + | 253.675i | −0.166902 | + | 0.946549i | ||||
\(269\) | 317.049i | 1.17862i | 0.807907 | + | 0.589310i | \(0.200601\pi\) | ||||
−0.807907 | + | 0.589310i | \(0.799399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 115.698 | 0.426931 | 0.213465 | − | 0.976951i | \(-0.431525\pi\) | ||||
0.213465 | + | 0.976951i | \(0.431525\pi\) | |||||||
\(272\) | −5.11128 | − | 0.901257i | −0.0187915 | − | 0.00331344i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −71.6277 | − | 26.0704i | −0.261415 | − | 0.0951473i | ||||
\(275\) | 30.0198 | + | 35.7762i | 0.109163 | + | 0.130095i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 108.352 | − | 39.4370i | 0.391163 | − | 0.142372i | −0.138949 | − | 0.990300i | \(-0.544372\pi\) |
0.530112 | + | 0.847928i | \(0.322150\pi\) | |||||||
\(278\) | −125.980 | − | 72.7347i | −0.453166 | − | 0.261635i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 218.970 | + | 379.267i | 0.782035 | + | 1.35452i | ||||
\(281\) | 52.4463 | − | 62.5031i | 0.186642 | − | 0.222431i | −0.664607 | − | 0.747193i | \(-0.731401\pi\) |
0.851249 | + | 0.524762i | \(0.175846\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −72.4355 | − | 410.802i | −0.255956 | − | 1.45160i | −0.793608 | − | 0.608430i | \(-0.791800\pi\) |
0.537652 | − | 0.843167i | \(-0.319311\pi\) | |||||||
\(284\) | 317.772 | − | 56.0318i | 1.11892 | − | 0.197295i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −117.322 | − | 98.4445i | −0.410215 | − | 0.344211i | ||||
\(287\) | 113.534 | − | 65.5489i | 0.395589 | − | 0.228393i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −139.508 | + | 241.636i | −0.482728 | + | 0.836110i | ||||
\(290\) | 54.2049 | + | 148.927i | 0.186913 | + | 0.513540i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 185.169 | − | 155.375i | 0.634141 | − | 0.532107i | ||||
\(293\) | 118.282 | − | 324.977i | 0.403693 | − | 1.10914i | −0.556755 | − | 0.830676i | \(-0.687954\pi\) |
0.960448 | − | 0.278460i | \(-0.0898238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −63.8186 | + | 361.933i | −0.216334 | + | 1.22689i | ||||
\(296\) | − | 136.357i | − | 0.460665i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 234.232 | 0.786012 | ||||||||
\(299\) | −220.222 | − | 38.8311i | −0.736529 | − | 0.129870i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 360.806 | + | 131.323i | 1.19869 | + | 0.436287i | ||||
\(302\) | −95.6252 | − | 113.962i | −0.316640 | − | 0.377356i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.97859 | − | 2.54000i | 0.0229559 | − | 0.00835526i | ||||
\(305\) | −363.957 | − | 210.131i | −1.19330 | − | 0.688954i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −288.668 | − | 499.988i | −0.940286 | − | 1.62862i | −0.764925 | − | 0.644120i | \(-0.777224\pi\) |
−0.175362 | − | 0.984504i | \(-0.556110\pi\) | |||||||
\(308\) | −210.907 | + | 251.350i | −0.684764 | + | 0.816070i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.0064 | + | 136.147i | 0.0774399 | + | 0.439184i | ||||
\(311\) | −442.280 | + | 77.9859i | −1.42212 | + | 0.250759i | −0.831202 | − | 0.555971i | \(-0.812347\pi\) |
−0.590921 | + | 0.806730i | \(0.701235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.30206 | + | 6.96625i | 0.0265241 | + | 0.0222564i | 0.655953 | − | 0.754801i | \(-0.272267\pi\) |
−0.629429 | + | 0.777058i | \(0.716711\pi\) | |||||||
\(314\) | 139.700 | − | 80.6557i | 0.444904 | − | 0.256865i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.0360 | − | 46.8278i | 0.0855570 | − | 0.148189i | ||||
\(317\) | 74.6402 | + | 205.072i | 0.235458 | + | 0.646916i | 0.999997 | + | 0.00233841i | \(0.000744341\pi\) |
−0.764539 | + | 0.644577i | \(0.777033\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −228.146 | + | 191.437i | −0.715191 | + | 0.600117i | ||||
\(320\) | −58.0083 | + | 159.376i | −0.181276 | + | 0.498051i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.2781 | − | 239.771i | 0.131299 | − | 0.744631i | ||||
\(323\) | 14.2846i | 0.0442249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.6700 | −0.137446 | ||||||||
\(326\) | −45.5694 | − | 8.03512i | −0.139784 | − | 0.0246476i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 90.3137 | + | 32.8715i | 0.275347 | + | 0.100218i | ||||
\(329\) | 83.9620 | + | 100.062i | 0.255204 | + | 0.304140i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −564.453 | + | 205.444i | −1.70530 | + | 0.620677i | −0.996411 | − | 0.0846470i | \(-0.973024\pi\) |
−0.708885 | + | 0.705324i | \(0.750802\pi\) | |||||||
\(332\) | 72.5849 | + | 41.9069i | 0.218629 | + | 0.126226i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −96.3325 | − | 166.853i | −0.288421 | − | 0.499559i | ||||
\(335\) | 336.061 | − | 400.502i | 1.00317 | − | 1.19553i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 78.0147 | + | 442.443i | 0.231498 | + | 1.31289i | 0.849865 | + | 0.527000i | \(0.176683\pi\) |
−0.618368 | + | 0.785889i | \(0.712206\pi\) | |||||||
\(338\) | −48.9602 | + | 8.63300i | −0.144853 | + | 0.0255414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 34.5551 | + | 28.9952i | 0.101633 | + | 0.0852799i | ||||
\(341\) | −224.988 | + | 129.897i | −0.659789 | + | 0.380929i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 68.3305 | − | 118.352i | 0.199214 | − | 0.345049i | ||||
\(344\) | 96.2747 | + | 264.512i | 0.279868 | + | 0.768932i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.68515 | + | 8.12680i | −0.0279918 | + | 0.0234879i | ||||
\(347\) | 80.7717 | − | 221.918i | 0.232771 | − | 0.639534i | −0.767227 | − | 0.641376i | \(-0.778364\pi\) |
0.999998 | + | 0.00184170i | \(0.000586231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 41.6381 | − | 236.141i | 0.119307 | − | 0.676622i | −0.865221 | − | 0.501391i | \(-0.832822\pi\) |
0.984527 | − | 0.175231i | \(-0.0560672\pi\) | |||||||
\(350\) | − | 48.6353i | − | 0.138958i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −385.187 | −1.09428 | ||||||||
\(353\) | −25.2020 | − | 4.44379i | −0.0713937 | − | 0.0125886i | 0.137837 | − | 0.990455i | \(-0.455985\pi\) |
−0.209231 | + | 0.977866i | \(0.567096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −615.423 | − | 223.996i | −1.73359 | − | 0.630974i | ||||
\(356\) | 117.669 | + | 140.232i | 0.330530 | + | 0.393911i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −308.279 | + | 112.204i | −0.861114 | + | 0.313420i | ||||
\(359\) | −16.7796 | − | 9.68773i | −0.0467399 | − | 0.0269853i | 0.476448 | − | 0.879203i | \(-0.341924\pi\) |
−0.523188 | + | 0.852217i | \(0.675257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 170.280 | + | 294.934i | 0.471690 | + | 0.816992i | ||||
\(362\) | −81.1916 | + | 96.7604i | −0.224286 | + | 0.267294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −54.4967 | − | 309.066i | −0.149716 | − | 0.849083i | ||||
\(365\) | −483.159 | + | 85.1939i | −1.32372 | + | 0.233408i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 299.305 | + | 251.147i | 0.815545 | + | 0.684324i | 0.951924 | − | 0.306333i | \(-0.0991021\pi\) |
−0.136379 | + | 0.990657i | \(0.543547\pi\) | |||||||
\(368\) | −28.3201 | + | 16.3506i | −0.0769569 | + | 0.0444311i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −55.1707 | + | 95.5584i | −0.149110 | + | 0.258266i | ||||
\(371\) | −304.886 | − | 837.669i | −0.821796 | − | 2.25787i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −136.986 | + | 114.945i | −0.367255 | + | 0.308164i | −0.807675 | − | 0.589628i | \(-0.799274\pi\) |
0.440419 | + | 0.897792i | \(0.354830\pi\) | |||||||
\(374\) | 14.7339 | − | 40.4810i | 0.0393954 | − | 0.108238i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.6287 | + | 94.3061i | −0.0442253 | + | 0.250814i | ||||
\(377\) | − | 284.862i | − | 0.755603i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.48118 | 0.00918518 | 0.00459259 | − | 0.999989i | \(-0.498538\pi\) | ||||
0.00459259 | + | 0.999989i | \(0.498538\pi\) | |||||||
\(380\) | −63.5643 | − | 11.2081i | −0.167274 | − | 0.0294950i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 118.509 | + | 43.1337i | 0.310233 | + | 0.112916i | ||||
\(383\) | −11.0730 | − | 13.1963i | −0.0289112 | − | 0.0344550i | 0.751395 | − | 0.659853i | \(-0.229381\pi\) |
−0.780306 | + | 0.625398i | \(0.784937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 625.797 | − | 227.772i | 1.62545 | − | 0.591615i | ||||
\(386\) | 201.193 | + | 116.159i | 0.521226 | + | 0.300930i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 105.827 | + | 183.298i | 0.272750 | + | 0.472417i | ||||
\(389\) | −203.618 | + | 242.662i | −0.523439 | + | 0.623810i | −0.961390 | − | 0.275189i | \(-0.911260\pi\) |
0.437952 | + | 0.898999i | \(0.355704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.9225 | − | 61.9446i | −0.0279348 | − | 0.158426i | ||||
\(392\) | 471.340 | − | 83.1100i | 1.20240 | − | 0.212015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 260.321 | + | 218.435i | 0.660713 | + | 0.554404i | ||||
\(395\) | −95.0446 | + | 54.8740i | −0.240619 | + | 0.138922i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −134.041 | + | 232.165i | −0.337634 | + | 0.584800i | −0.983987 | − | 0.178239i | \(-0.942960\pi\) |
0.646353 | + | 0.763039i | \(0.276293\pi\) | |||||||
\(398\) | −32.6829 | − | 89.7955i | −0.0821178 | − | 0.225617i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00408 | + | 4.19892i | −0.0125102 | + | 0.0104973i | ||||
\(401\) | −33.3356 | + | 91.5887i | −0.0831311 | + | 0.228401i | −0.974293 | − | 0.225285i | \(-0.927669\pi\) |
0.891162 | + | 0.453685i | \(0.149891\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.1494 | − | 244.712i | 0.107070 | − | 0.607227i | ||||
\(404\) | − | 12.6686i | − | 0.0313578i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 310.149 | 0.763914 | ||||||||
\(407\) | −204.203 | − | 36.0065i | −0.501727 | − | 0.0884680i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 380.898 | + | 138.636i | 0.931292 | + | 0.338962i | 0.762721 | − | 0.646727i | \(-0.223863\pi\) |
0.168570 | + | 0.985690i | \(0.446085\pi\) | |||||||
\(410\) | −49.9916 | − | 59.5777i | −0.121931 | − | 0.145311i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 180.170 | − | 65.5764i | 0.437305 | − | 0.159166i | ||||
\(413\) | 622.862 | + | 359.609i | 1.50814 | + | 0.870725i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −85.0569 | − | 147.323i | −0.204956 | − | 0.354995i | ||||
\(416\) | 236.818 | − | 282.229i | 0.569275 | − | 0.678435i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.7038 | + | 60.7045i | 0.0256073 | + | 0.145226i | ||||
\(419\) | −115.552 | + | 20.3750i | −0.275781 | + | 0.0486277i | −0.309828 | − | 0.950793i | \(-0.600272\pi\) |
0.0340470 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −399.365 | − | 335.107i | −0.948610 | − | 0.795979i | 0.0304527 | − | 0.999536i | \(-0.490305\pi\) |
−0.979063 | + | 0.203558i | \(0.934750\pi\) | |||||||
\(422\) | −116.473 | + | 67.2459i | −0.276003 | + | 0.159351i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 326.760 | − | 565.966i | 0.770661 | − | 1.33482i | ||||
\(425\) | −4.29744 | − | 11.8071i | −0.0101116 | − | 0.0277814i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −630.025 | + | 528.654i | −1.47547 | + | 1.23806i | ||||
\(428\) | −143.441 | + | 394.102i | −0.335143 | + | 0.920799i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.5541 | − | 224.323i | 0.0919864 | − | 0.521681i | ||||
\(431\) | 263.580i | 0.611555i | 0.952103 | + | 0.305777i | \(0.0989163\pi\) | ||||
−0.952103 | + | 0.305777i | \(0.901084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −702.013 | −1.62128 | −0.810639 | − | 0.585547i | \(-0.800880\pi\) | ||||
−0.810639 | + | 0.585547i | \(0.800880\pi\) | |||||||
\(434\) | 266.435 | + | 46.9797i | 0.613906 | + | 0.108248i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 46.3025 | + | 16.8527i | 0.106198 | + | 0.0386531i | ||||
\(437\) | 57.8526 | + | 68.9461i | 0.132386 | + | 0.157771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 416.204 | − | 151.486i | 0.948073 | − | 0.345070i | 0.178724 | − | 0.983899i | \(-0.442803\pi\) |
0.769349 | + | 0.638829i | \(0.220581\pi\) | |||||||
\(440\) | 422.816 | + | 244.113i | 0.960946 | + | 0.554802i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.6021 | + | 35.6839i | 0.0466111 | + | 0.0807328i | ||||
\(443\) | 390.071 | − | 464.868i | 0.880520 | − | 1.04936i | −0.117891 | − | 0.993026i | \(-0.537613\pi\) |
0.998412 | − | 0.0563369i | \(-0.0179421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −64.5191 | − | 365.906i | −0.144987 | − | 0.822260i | ||||
\(446\) | −226.648 | + | 39.9642i | −0.508180 | + | 0.0896058i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 254.259 | + | 213.348i | 0.567542 | + | 0.476224i | ||||
\(449\) | −347.745 | + | 200.771i | −0.774488 | + | 0.447151i | −0.834473 | − | 0.551048i | \(-0.814228\pi\) |
0.0599853 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 73.0755 | − | 126.570i | 0.162030 | − | 0.280644i | ||||
\(452\) | −16.3423 | − | 44.9002i | −0.0361556 | − | 0.0993368i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.58180 | + | 3.84458i | −0.0100921 | + | 0.00846825i | ||||
\(455\) | −217.859 | + | 598.563i | −0.478811 | + | 1.31552i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.5458 | + | 144.878i | −0.0558990 | + | 0.317019i | −0.999917 | − | 0.0128747i | \(-0.995902\pi\) |
0.944018 | + | 0.329894i | \(0.107013\pi\) | |||||||
\(458\) | − | 410.223i | − | 0.895683i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 284.213 | 0.617855 | ||||||||
\(461\) | 773.480 | + | 136.385i | 1.67783 | + | 0.295847i | 0.929868 | − | 0.367893i | \(-0.119921\pi\) |
0.747963 | + | 0.663740i | \(0.231032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 336.835 | + | 122.598i | 0.727506 | + | 0.264791i | 0.679109 | − | 0.734037i | \(-0.262366\pi\) |
0.0483975 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(464\) | −26.7767 | − | 31.9112i | −0.0577084 | − | 0.0687742i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 153.344 | − | 55.8128i | 0.329065 | − | 0.119770i | ||||
\(467\) | 88.2727 | + | 50.9643i | 0.189021 | + | 0.109131i | 0.591524 | − | 0.806287i | \(-0.298526\pi\) |
−0.402503 | + | 0.915419i | \(0.631860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −511.569 | − | 886.063i | −1.09077 | − | 1.88926i | ||||
\(470\) | 49.8101 | − | 59.3613i | 0.105979 | − | 0.126301i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 91.5597 | + | 519.261i | 0.193982 | + | 1.10013i | ||||
\(473\) | 421.547 | − | 74.3300i | 0.891219 | − | 0.157146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7726 | + | 11.5566i | 0.0289949 | + | 0.0243296i | ||||
\(476\) | 76.4491 | − | 44.1379i | 0.160607 | − | 0.0927267i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −85.7219 | + | 148.475i | −0.179334 | + | 0.310616i | ||||
\(479\) | −43.2210 | − | 118.749i | −0.0902318 | − | 0.247910i | 0.886365 | − | 0.462986i | \(-0.153222\pi\) |
−0.976597 | + | 0.215077i | \(0.931000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 151.929 | − | 127.483i | 0.315860 | − | 0.265038i | ||||
\(482\) | −120.874 | + | 332.099i | −0.250776 | + | 0.689003i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.79280 | + | 44.1952i | −0.0161008 | + | 0.0913123i | ||||
\(485\) | − | 429.586i | − | 0.885745i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 454.010 | 0.932258 | 0.466129 | − | 0.884717i | \(-0.345648\pi\) | ||||
0.466129 | + | 0.884717i | \(0.345648\pi\) | |||||||
\(488\) | −593.783 | − | 104.700i | −1.21677 | − | 0.214549i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −363.940 | − | 132.463i | −0.742735 | − | 0.270334i | ||||
\(491\) | −203.177 | − | 242.137i | −0.413803 | − | 0.493151i | 0.518374 | − | 0.855154i | \(-0.326537\pi\) |
−0.932177 | + | 0.362003i | \(0.882093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 75.2944 | − | 27.4049i | 0.152727 | − | 0.0555881i | ||||
\(494\) | −51.0594 | − | 29.4792i | −0.103359 | − | 0.0596744i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.1689 | − | 31.4695i | −0.0366309 | − | 0.0634466i | ||||
\(497\) | −823.833 | + | 981.806i | −1.65761 | + | 1.97547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2323 | + | 120.414i | 0.0425497 | + | 0.241312i | 0.998663 | − | 0.0516842i | \(-0.0164589\pi\) |
−0.956114 | + | 0.292996i | \(0.905348\pi\) | |||||||
\(500\) | −295.582 | + | 52.1190i | −0.591163 | + | 0.104238i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −110.983 | − | 93.1256i | −0.221081 | − | 0.185509i | ||||
\(503\) | 391.041 | − | 225.768i | 0.777418 | − | 0.448843i | −0.0580963 | − | 0.998311i | \(-0.518503\pi\) |
0.835515 | + | 0.549468i | \(0.185170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8565 | + | 22.2680i | −0.0254583 | + | 0.0440951i | ||||
\(506\) | −92.8333 | − | 255.057i | −0.183465 | − | 0.504066i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −317.375 | + | 266.309i | −0.624754 | + | 0.524231i | ||||
\(509\) | 170.911 | − | 469.573i | 0.335778 | − | 0.922541i | −0.650800 | − | 0.759249i | \(-0.725566\pi\) |
0.986578 | − | 0.163292i | \(-0.0522113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −166.722 | + | 945.527i | −0.326266 | + | 1.85035i | ||||
\(512\) | − | 104.621i | − | 0.204338i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −530.596 | −1.03229 | ||||||||
\(515\) | −383.240 | − | 67.5756i | −0.744156 | − | 0.131215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 136.838 | + | 49.8051i | 0.264678 | + | 0.0963348i | ||||
\(518\) | 138.800 | + | 165.415i | 0.267954 | + | 0.319335i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −438.816 | + | 159.716i | −0.843877 | + | 0.307146i | ||||
\(521\) | 595.632 | + | 343.888i | 1.14325 | + | 0.660054i | 0.947233 | − | 0.320546i | \(-0.103867\pi\) |
0.196015 | + | 0.980601i | \(0.437200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 260.218 | + | 450.711i | 0.497549 | + | 0.861780i | 0.999996 | − | 0.00282784i | \(-0.000900130\pi\) |
−0.502447 | + | 0.864608i | \(0.667567\pi\) | |||||||
\(524\) | 167.953 | − | 200.159i | 0.320521 | − | 0.381983i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −94.3376 | − | 535.015i | −0.179349 | − | 1.01714i | ||||
\(527\) | 68.8332 | − | 12.1372i | 0.130613 | − | 0.0230306i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 101.644 | + | 85.2896i | 0.192144 | + | 0.161228i | ||||
\(530\) | −457.985 | + | 264.418i | −0.864123 | + | 0.498902i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −63.1561 | + | 109.390i | −0.118715 | + | 0.205620i | ||||
\(533\) | 47.8111 | + | 131.360i | 0.0897020 | + | 0.246454i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 652.079 | − | 547.160i | 1.21884 | − | 1.02273i | ||||
\(536\) | 256.542 | − | 704.844i | 0.478623 | − | 1.31501i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 63.9168 | − | 362.490i | 0.118804 | − | 0.673773i | ||||
\(539\) | − | 727.808i | − | 1.35029i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 803.120 | 1.48451 | 0.742255 | − | 0.670117i | \(-0.233756\pi\) | ||||
0.742255 | + | 0.670117i | \(0.233756\pi\) | |||||||
\(542\) | −132.281 | − | 23.3247i | −0.244060 | − | 0.0430344i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 97.3813 | + | 35.4439i | 0.179010 | + | 0.0651542i | ||||
\(545\) | −64.2851 | − | 76.6120i | −0.117954 | − | 0.140572i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 64.5461 | − | 23.4929i | 0.118000 | − | 0.0429486i | −0.282345 | − | 0.959313i | \(-0.591112\pi\) |
0.400345 | + | 0.916364i | \(0.368890\pi\) | |||||||
\(548\) | −150.803 | − | 87.0659i | −0.275187 | − | 0.158879i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −27.1099 | − | 46.9557i | −0.0492907 | − | 0.0853741i | ||||
\(551\) | −73.6967 | + | 87.8283i | −0.133751 | + | 0.159398i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.2950 | + | 211.511i | 0.0674412 | + | 0.382478i | ||||
\(554\) | −131.832 | + | 23.2456i | −0.237964 | + | 0.0419595i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −254.570 | − | 213.610i | −0.457861 | − | 0.384191i | ||||
\(557\) | −575.120 | + | 332.045i | −1.03253 | + | 0.596132i | −0.917709 | − | 0.397254i | \(-0.869963\pi\) |
−0.114822 | + | 0.993386i | \(0.536630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −204.710 | + | 354.569i | −0.366208 | + | 0.634291i | ||||
\(560\) | 31.8589 | + | 87.5315i | 0.0568908 | + | 0.156306i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −72.5637 | + | 60.8882i | −0.129117 | + | 0.108342i | ||||
\(563\) | 118.905 | − | 326.689i | 0.211199 | − | 0.580264i | −0.788182 | − | 0.615442i | \(-0.788978\pi\) |
0.999381 | + | 0.0351778i | \(0.0111997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8406 | + | 95.5076i | −0.0298063 | + | 0.169040i | ||||
\(566\) | 484.283i | 0.855623i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −939.603 | −1.65423 | ||||||||
\(569\) | 385.078 | + | 67.8997i | 0.676763 | + | 0.119332i | 0.501457 | − | 0.865182i | \(-0.332797\pi\) |
0.175306 | + | 0.984514i | \(0.443909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −804.118 | − | 292.675i | −1.40826 | − | 0.512566i | −0.477644 | − | 0.878554i | \(-0.658509\pi\) |
−0.930620 | + | 0.365988i | \(0.880731\pi\) | |||||||
\(572\) | −224.892 | − | 268.016i | −0.393168 | − | 0.468559i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −143.021 | + | 52.0553i | −0.249165 | + | 0.0906887i | ||||
\(575\) | −68.5606 | − | 39.5835i | −0.119236 | − | 0.0688408i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 313.746 | + | 543.423i | 0.543753 | + | 0.941808i | 0.998684 | + | 0.0512815i | \(0.0163306\pi\) |
−0.454931 | + | 0.890527i | \(0.650336\pi\) | |||||||
\(578\) | 208.217 | − | 248.143i | 0.360237 | − | 0.429314i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 62.8694 | + | 356.550i | 0.108396 | + | 0.614742i | ||||
\(581\) | −327.850 | + | 57.8088i | −0.564285 | + | 0.0994987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −761.285 | − | 638.794i | −1.30581 | − | 1.09570i | ||||
\(584\) | −609.573 | + | 351.937i | −1.04379 | + | 0.602632i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −200.750 | + | 347.709i | −0.342576 | + | 0.593359i | ||||
\(587\) | 254.654 | + | 699.655i | 0.433822 | + | 1.19192i | 0.943448 | + | 0.331520i | \(0.107561\pi\) |
−0.509626 | + | 0.860396i | \(0.670216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −76.6133 | + | 64.2862i | −0.130073 | + | 0.109145i | ||||
\(590\) | 145.931 | − | 400.942i | 0.247340 | − | 0.679562i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.03630 | − | 28.5623i | 0.00850726 | − | 0.0482471i | ||||
\(593\) | − | 625.722i | − | 1.05518i | −0.849499 | − | 0.527591i | \(-0.823096\pi\) | ||
0.849499 | − | 0.527591i | \(-0.176904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −179.170 | −0.301126 | ||||||||
\(596\) | 526.963 | + | 92.9177i | 0.884165 | + | 0.155902i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 243.957 | + | 88.7932i | 0.407955 | + | 0.148484i | ||||
\(599\) | 368.344 | + | 438.975i | 0.614932 | + | 0.732847i | 0.980190 | − | 0.198059i | \(-0.0634638\pi\) |
−0.365258 | + | 0.930906i | \(0.619019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1063.24 | + | 386.989i | −1.76912 | + | 0.643908i | −0.769134 | + | 0.639088i | \(0.779312\pi\) |
−0.999988 | + | 0.00482034i | \(0.998466\pi\) | |||||||
\(602\) | −386.043 | − | 222.882i | −0.641268 | − | 0.370236i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −169.925 | − | 294.319i | −0.281333 | − | 0.487283i | ||||
\(605\) | 58.5483 | − | 69.7752i | 0.0967741 | − | 0.115331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.3687 | − | 228.942i | −0.0665052 | − | 0.377170i | −0.999835 | − | 0.0181503i | \(-0.994222\pi\) |
0.933330 | − | 0.359019i | \(-0.116889\pi\) | |||||||
\(608\) | −146.031 | + | 25.7492i | −0.240182 | + | 0.0423506i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 373.759 | + | 313.621i | 0.612720 | + | 0.514133i | ||||
\(611\) | −120.623 | + | 69.6414i | −0.197418 | + | 0.113979i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 533.889 | − | 924.724i | 0.870945 | − | 1.50852i | 0.00992514 | − | 0.999951i | \(-0.496841\pi\) |
0.861020 | − | 0.508571i | \(-0.169826\pi\) | |||||||
\(614\) | 229.244 | + | 629.843i | 0.373362 | + | 1.02580i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 731.912 | − | 614.147i | 1.18817 | − | 0.996991i | ||||
\(617\) | −144.247 | + | 396.317i | −0.233788 | + | 0.642328i | −1.00000 | 0.000260046i | \(-0.999917\pi\) | |
0.766212 | + | 0.642588i | \(0.222139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 104.335 | − | 591.711i | 0.168554 | − | 0.955915i | −0.776771 | − | 0.629783i | \(-0.783144\pi\) |
0.945324 | − | 0.326131i | \(-0.105745\pi\) | |||||||
\(620\) | 315.820i | 0.509386i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 521.392 | 0.838250 | ||||||||
\(623\) | −716.066 | − | 126.262i | −1.14938 | − | 0.202667i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 665.870 | + | 242.357i | 1.06539 | + | 0.387771i | ||||
\(626\) | −8.08756 | − | 9.63837i | −0.0129194 | − | 0.0153968i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 346.285 | − | 126.037i | 0.551409 | − | 0.200696i | ||||
\(629\) | 48.3124 | + | 27.8932i | 0.0768083 | + | 0.0443453i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 554.621 | + | 960.632i | 0.878956 | + | 1.52240i | 0.852488 | + | 0.522747i | \(0.175093\pi\) |
0.0264679 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(632\) | −101.209 | + | 120.617i | −0.160141 | + | 0.190849i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −43.9956 | − | 249.512i | −0.0693937 | − | 0.393551i | ||||
\(635\) | 828.122 | − | 146.020i | 1.30413 | − | 0.229953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 533.269 | + | 447.466i | 0.837157 | + | 0.702458i | ||||
\(638\) | 299.439 | − | 172.881i | 0.469340 | − | 0.270973i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −254.659 | + | 441.082i | −0.397904 | + | 0.689191i | ||||
\(641\) | 56.5257 | + | 155.303i | 0.0881837 | + | 0.242283i | 0.975943 | − | 0.218025i | \(-0.0699614\pi\) |
−0.887760 | + | 0.460308i | \(0.847739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 608.717 | − | 510.774i | 0.946683 | − | 0.794361i | −0.0320527 | − | 0.999486i | \(-0.510204\pi\) |
0.978736 | + | 0.205125i | \(0.0657600\pi\) | |||||||
\(644\) | 190.230 | − | 522.654i | 0.295389 | − | 0.811574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.87977 | − | 16.3320i | 0.00445785 | − | 0.0252817i | ||||
\(647\) | − | 222.504i | − | 0.343900i | −0.985106 | − | 0.171950i | \(-0.944993\pi\) | ||
0.985106 | − | 0.171950i | \(-0.0550068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 801.803 | 1.23544 | ||||||||
\(650\) | 51.0723 | + | 9.00542i | 0.0785728 | + | 0.0138545i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −99.3323 | − | 36.1540i | −0.152350 | − | 0.0554509i | ||||
\(653\) | 299.851 | + | 357.348i | 0.459190 | + | 0.547241i | 0.945106 | − | 0.326764i | \(-0.105958\pi\) |
−0.485916 | + | 0.874006i | \(0.661514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −498.345 | + | 181.383i | −0.760833 | + | 0.276920i | ||||
\(656\) | 17.7037 | + | 10.2212i | 0.0269873 | + | 0.0155811i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −75.8234 | − | 131.330i | −0.115233 | − | 0.199590i | ||||
\(659\) | 133.876 | − | 159.547i | 0.203150 | − | 0.242104i | −0.654845 | − | 0.755764i | \(-0.727266\pi\) |
0.857994 | + | 0.513659i | \(0.171710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −110.055 | − | 624.153i | −0.166498 | − | 0.944256i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.781009 | − | 0.624520i | \(-0.214705\pi\) | |||||||
\(662\) | 686.770 | − | 121.096i | 1.03742 | − | 0.182925i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −186.961 | − | 156.879i | −0.281567 | − | 0.236263i | ||||
\(665\) | 222.024 | − | 128.186i | 0.333871 | − | 0.192760i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 252.425 | − | 437.214i | 0.378449 | − | 0.655493i | ||||
\(668\) | −150.535 | − | 413.591i | −0.225352 | − | 0.619149i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −464.967 | + | 390.154i | −0.693981 | + | 0.582319i | ||||
\(671\) | −313.590 | + | 861.581i | −0.467347 | + | 1.28403i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1049 | − | 108.349i | 0.0283877 | − | 0.160994i | −0.967319 | − | 0.253564i | \(-0.918397\pi\) |
0.995706 | + | 0.0925699i | \(0.0295082\pi\) | |||||||
\(674\) | − | 521.584i | − | 0.773864i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −113.573 | −0.168007 | ||||||||
\(677\) | 140.866 | + | 24.8384i | 0.208073 | + | 0.0366890i | 0.276713 | − | 0.960953i | \(-0.410755\pi\) |
−0.0686398 | + | 0.997642i | \(0.521866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −789.987 | − | 287.532i | −1.16346 | − | 0.423463i | ||||
\(680\) | −84.4318 | − | 100.622i | −0.124164 | − | 0.147973i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 283.421 | − | 103.157i | 0.415574 | − | 0.151257i | ||||
\(683\) | −784.050 | − | 452.671i | −1.14795 | − | 0.662769i | −0.199563 | − | 0.979885i | \(-0.563952\pi\) |
−0.948387 | + | 0.317116i | \(0.897286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 176.714 | + | 306.078i | 0.257977 | + | 0.446830i | ||||
\(686\) | −101.984 | + | 121.539i | −0.148664 | + | 0.177171i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.3967 | + | 58.9625i | 0.0151115 | + | 0.0857013i | ||||
\(689\) | 936.096 | − | 165.059i | 1.35863 | − | 0.239563i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 407.543 | + | 341.969i | 0.589788 | + | 0.494891i | 0.888145 | − | 0.459564i | \(-0.151994\pi\) |
−0.298357 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(692\) | −25.0130 | + | 14.4413i | −0.0361459 | + | 0.0208689i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −137.087 | + | 237.441i | −0.197531 | + | 0.342134i | ||||
\(695\) | 230.690 | + | 633.817i | 0.331929 | + | 0.911967i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.1213 | + | 25.2748i | −0.0432156 | + | 0.0362622i | ||||
\(698\) | −95.2117 | + | 261.592i | −0.136406 | + | 0.374773i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 19.2932 | − | 109.417i | 0.0275617 | − | 0.156310i | ||||
\(701\) | 905.026i | 1.29105i | 0.763739 | + | 0.645525i | \(0.223361\pi\) | ||||
−0.763739 | + | 0.645525i | \(0.776639\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −79.8237 | −0.113547 | ||||||||
\(704\) | 364.401 | + | 64.2538i | 0.517616 | + | 0.0912696i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.9182 | + | 10.1614i | 0.0395442 | + | 0.0143929i | ||||
\(707\) | 32.3447 | + | 38.5469i | 0.0457492 | + | 0.0545217i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 341.922 | − | 124.450i | 0.482260 | − | 0.175528i | −0.0894380 | − | 0.995992i | \(-0.528507\pi\) |
0.571698 | + | 0.820464i | \(0.306285\pi\) | |||||||
\(710\) | 658.471 | + | 380.168i | 0.927424 | + | 0.535449i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −266.529 | − | 461.642i | −0.374338 | − | 0.648373i | ||||
\(713\) | 283.074 | − | 337.355i | 0.397019 | − | 0.473148i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 123.311 | + | 699.329i | 0.172462 | + | 0.978083i | ||||
\(716\) | −738.060 | + | 130.140i | −1.03081 | + | 0.181760i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.2315 | + | 14.4590i | 0.0239994 | + | 0.0201379i | ||||
\(719\) | 389.328 | − | 224.778i | 0.541485 | − | 0.312626i | −0.204196 | − | 0.978930i | \(-0.565458\pi\) |
0.745680 | + | 0.666304i | \(0.232125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −380.779 | + | 659.529i | −0.528127 | + | 0.914742i | ||||
\(722\) | −135.227 | − | 371.534i | −0.187295 | − | 0.514589i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −221.045 | + | 185.479i | −0.305310 | + | 0.256186i | ||||
\(725\) | 34.4922 | − | 94.7665i | 0.0475754 | − | 0.130712i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 100.606 | − | 570.564i | 0.138385 | − | 0.784820i | −0.834058 | − | 0.551677i | \(-0.813988\pi\) |
0.972443 | − | 0.233142i | \(-0.0749009\pi\) | |||||||
\(728\) | 913.862i | 1.25530i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 569.582 | 0.780250 | ||||||||
\(731\) | −113.413 | − | 19.9978i | −0.155148 | − | 0.0273568i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −879.854 | − | 320.241i | −1.20035 | − | 0.436891i | −0.337002 | − | 0.941504i | \(-0.609413\pi\) |
−0.863345 | + | 0.504613i | \(0.831635\pi\) | |||||||
\(734\) | −291.572 | − | 347.482i | −0.397237 | − | 0.473409i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 613.567 | − | 223.320i | 0.833650 | − | 0.303424i | ||||
\(737\) | −987.805 | − | 570.310i | −1.34031 | − | 0.773826i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −263.918 | − | 457.119i | −0.357128 | − | 0.618564i | 0.630352 | − | 0.776310i | \(-0.282911\pi\) |
−0.987480 | + | 0.157746i | \(0.949577\pi\) | |||||||
\(740\) | −162.027 | + | 193.097i | −0.218956 | + | 0.260942i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 179.711 | + | 1019.19i | 0.242198 | + | 1.37357i | ||||
\(743\) | 36.2725 | − | 6.39582i | 0.0488190 | − | 0.00860811i | −0.149185 | − | 0.988809i | \(-0.547665\pi\) |
0.198004 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −831.967 | − | 698.103i | −1.11673 | − | 0.937051i | ||||
\(746\) | 179.793 | − | 103.803i | 0.241009 | − | 0.139146i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 49.2061 | − | 85.2274i | 0.0657835 | − | 0.113940i | ||||
\(749\) | −569.747 | − | 1565.37i | −0.760677 | − | 2.08994i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 75.4565 | − | 63.3155i | 0.100475 | − | 0.0843082i | −0.591167 | − | 0.806550i | \(-0.701332\pi\) |
0.691641 | + | 0.722241i | \(0.256888\pi\) | |||||||
\(752\) | −6.96633 | + | 19.1398i | −0.00926374 | + | 0.0254519i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −57.4279 | + | 325.690i | −0.0761644 | + | 0.431950i | ||||
\(755\) | 689.781i | 0.913617i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1385.09 | −1.82971 | −0.914857 | − | 0.403779i | \(-0.867697\pi\) | ||||
−0.914857 | + | 0.403779i | \(0.867697\pi\) | |||||||
\(758\) | −3.98012 | − | 0.701803i | −0.00525082 | − | 0.000925861i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 176.615 | + | 64.2827i | 0.232388 | + | 0.0845825i | ||||
\(761\) | −935.204 | − | 1114.53i | −1.22891 | − | 1.46456i | −0.839374 | − | 0.543555i | \(-0.817078\pi\) |
−0.389541 | − | 0.921009i | \(-0.627366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −183.913 | + | 66.9389i | −0.241039 | + | 0.0877312i | ||||
\(764\) | 249.505 | + | 144.052i | 0.326577 | + | 0.188549i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.99966 | + | 17.3199i | 0.0130544 | + | 0.0226109i | ||||
\(767\) | −492.959 | + | 587.486i | −0.642711 | + | 0.765953i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.3763 | − | 98.5458i | −0.0225959 | − | 0.128148i | 0.971423 | − | 0.237354i | \(-0.0762802\pi\) |
−0.994019 | + | 0.109206i | \(0.965169\pi\) | |||||||
\(770\) | −761.408 | + | 134.257i | −0.988842 | + | 0.174360i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 406.555 | + | 341.140i | 0.526626 | + | 0.441891i | ||||
\(773\) | 547.928 | − | 316.347i | 0.708834 | − | 0.409245i | −0.101795 | − | 0.994805i | \(-0.532459\pi\) |
0.810629 | + | 0.585560i | \(0.199125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.9854 | − | 76.1850i | 0.0567554 | − | 0.0983032i | ||||
\(776\) | −210.794 | − | 579.152i | −0.271642 | − | 0.746330i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 281.722 | − | 236.392i | 0.362110 | − | 0.303846i | ||||
\(779\) | 19.2431 | − | 52.8699i | 0.0247023 | − | 0.0678690i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −248.112 | + | 1407.12i | −0.317686 | + | 1.80168i | ||||
\(782\) | 73.0247i | 0.0933820i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 101.800 | 0.129847 | ||||||||
\(785\) | −736.585 | − | 129.880i | −0.938325 | − | 0.165452i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 766.476 | + | 278.974i | 0.973921 | + | 0.354478i | 0.779474 | − | 0.626435i | \(-0.215487\pi\) |
0.194447 | + | 0.980913i | \(0.437709\pi\) | |||||||
\(788\) | 499.005 | + | 594.691i | 0.633256 | + | 0.754685i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 119.729 | − | 43.5779i | 0.151556 | − | 0.0551619i | ||||
\(791\) | 164.362 | + | 94.8944i | 0.207790 | + | 0.119968i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −438.486 | − | 759.481i | −0.552946 | − | 0.957731i | ||||
\(794\) | 200.056 | − | 238.418i | 0.251960 | − | 0.300275i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37.9072 | − | 214.982i | −0.0476221 | − | 0.270078i | ||||
\(797\) | −1233.67 | + | 217.529i | −1.54789 | + | 0.272934i | −0.881323 | − | 0.472514i | \(-0.843347\pi\) |
−0.666564 | + | 0.745448i | \(0.732236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.0119 | − | 25.1830i | −0.0375618 | − | 0.0315181i | ||||
\(800\) | 112.957 | − | 65.2156i | 0.141196 | − | 0.0815196i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 56.5776 | − | 97.9952i | 0.0705456 | − | 0.122189i | ||||
\(803\) | 366.084 | + | 1005.81i | 0.455895 | + | 1.25256i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −864.781 | + | 725.637i | −1.07426 | + | 0.901413i | ||||
\(806\) | −98.6675 | + | 271.087i | −0.122416 | + | 0.336336i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.40587 | + | 36.3295i | −0.00792806 | + | 0.0449622i | ||||
\(809\) | − | 1021.88i | − | 1.26313i | −0.775321 | − | 0.631567i | \(-0.782412\pi\) | ||
0.775321 | − | 0.631567i | \(-0.217588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −365.788 | −0.451034 | −0.225517 | − | 0.974239i | \(-0.572407\pi\) | ||||
−0.225517 | + | 0.974239i | \(0.572407\pi\) | |||||||
\(812\) | 697.758 | + | 123.034i | 0.859308 | + | 0.151519i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 226.211 | + | 82.3342i | 0.277901 | + | 0.101148i | ||||
\(815\) | 137.910 | + | 164.355i | 0.169215 | + | 0.201662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 154.846 | − | 56.3595i | 0.189531 | − | 0.0689835i | ||||
\(818\) | −407.542 | − | 235.294i | −0.498217 | − | 0.287646i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −88.8346 | − | 153.866i | −0.108335 | − | 0.187641i | ||||
\(821\) | 6.23245 | − | 7.42755i | 0.00759129 | − | 0.00904695i | −0.762235 | − | 0.647300i | \(-0.775898\pi\) |
0.769827 | + | 0.638253i | \(0.220343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.155222 | + | 0.880308i | 0.000188605 | + | 0.00106963i | 0.984902 | − | 0.173113i | \(-0.0553827\pi\) |
−0.984713 | + | 0.174183i | \(0.944272\pi\) | |||||||
\(824\) | −549.829 | + | 96.9497i | −0.667268 | + | 0.117657i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −639.636 | − | 536.719i | −0.774378 | − | 0.649780i | ||||
\(827\) | 583.611 | − | 336.948i | 0.705696 | − | 0.407434i | −0.103769 | − | 0.994601i | \(-0.533090\pi\) |
0.809465 | + | 0.587168i | \(0.199757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4804 | + | 25.0808i | −0.0174673 | + | 0.0302542i | −0.874627 | − | 0.484797i | \(-0.838894\pi\) |
0.857160 | + | 0.515051i | \(0.172227\pi\) | |||||||
\(830\) | 67.5475 | + | 185.585i | 0.0813825 | + | 0.223597i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −271.118 | + | 227.495i | −0.325863 | + | 0.273431i | ||||
\(833\) | −66.9709 | + | 184.001i | −0.0803972 | + | 0.220890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −155.124 | + | 879.753i | −0.185778 | + | 1.05360i | ||||
\(836\) | 140.816i | 0.168440i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 136.221 | 0.162555 | ||||||||
\(839\) | −629.012 | − | 110.912i | −0.749716 | − | 0.132195i | −0.214282 | − | 0.976772i | \(-0.568741\pi\) |
−0.535434 | + | 0.844577i | \(0.679852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −185.952 | − | 67.6809i | −0.221108 | − | 0.0804767i | ||||
\(842\) | 389.047 | + | 463.648i | 0.462051 | + | 0.550650i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −288.712 | + | 105.082i | −0.342075 | + | 0.124505i | ||||
\(845\) | 199.631 | + | 115.257i | 0.236250 | + | 0.136399i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −89.1253 | − | 154.370i | −0.105225 | − | 0.182254i | ||||
\(848\) | 89.3493 | − | 106.482i | 0.105365 | − | 0.125569i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.53306 | + | 14.3657i | 0.00298008 | + | 0.0169008i | ||||
\(851\) | 346.151 | − | 61.0358i | 0.406758 | − | 0.0717225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 595.279 | + | 499.498i | 0.697865 | + | 0.585578i | 0.921165 | − | 0.389171i | \(-0.127239\pi\) |
−0.223300 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(854\) | 826.899 | − | 477.410i | 0.968266 | − | 0.559029i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 610.623 | − | 1057.63i | 0.713345 | − | 1.23555i | ||||
\(857\) | −368.296 | − | 1011.88i | −0.429750 | − | 1.18073i | −0.945965 | − | 0.324269i | \(-0.894882\pi\) |
0.516215 | − | 0.856459i | \(-0.327341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −62.0374 | + | 52.0556i | −0.0722205 | + | 0.0606002i | −0.678183 | − | 0.734893i | \(-0.737232\pi\) |
0.605963 | + | 0.795493i | \(0.292788\pi\) | |||||||
\(860\) | 177.974 | − | 488.979i | 0.206946 | − | 0.568580i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 53.1375 | − | 301.358i | 0.0616444 | − | 0.349603i | ||||
\(863\) | 1599.17i | 1.85304i | 0.376244 | + | 0.926520i | \(0.377215\pi\) | ||||
−0.376244 | + | 0.926520i | \(0.622785\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.6217 | 0.0677708 | ||||||||
\(866\) | 802.629 | + | 141.525i | 0.926823 | + | 0.163424i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 580.776 | + | 211.385i | 0.669097 | + | 0.243531i | ||||
\(869\) | 153.906 | + | 183.418i | 0.177107 | + | 0.211067i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1025.19 | − | 373.137i | 1.17702 | − | 0.428400i | ||||
\(872\) | −124.260 | − | 71.7413i | −0.142500 | − | 0.0822722i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52.2449 | − | 90.4908i | −0.0597767 | − | 0.103536i | ||||
\(875\) | 766.304 | − | 913.245i | 0.875776 | − | 1.04371i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −65.7402 | − | 372.831i | −0.0749603 | − | 0.425121i | −0.999075 | − | 0.0430055i | \(-0.986307\pi\) |
0.924115 | − | 0.382116i | \(-0.124804\pi\) | |||||||
\(878\) | −506.396 | + | 89.2913i | −0.576761 | + | 0.101698i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 79.5498 | + | 66.7502i | 0.0903975 | + | 0.0758525i | ||||
\(881\) | 1046.81 | − | 604.374i | 1.18820 | − | 0.686009i | 0.230305 | − | 0.973119i | \(-0.426028\pi\) |
0.957898 | + | 0.287109i | \(0.0926943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 298.144 | − | 516.401i | 0.337649 | − | 0.584826i | −0.646341 | − | 0.763049i | \(-0.723702\pi\) |
0.983990 | + | 0.178223i | \(0.0570349\pi\) | |||||||
\(884\) | 32.1941 | + | 88.4525i | 0.0364186 | + | 0.100059i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −539.694 | + | 452.857i | −0.609136 | + | 0.511126i | ||||
\(887\) | −34.7360 | + | 95.4364i | −0.0391612 | + | 0.107595i | −0.957732 | − | 0.287662i | \(-0.907122\pi\) |
0.918571 | + | 0.395256i | \(0.129344\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 285.757 | − | 1620.61i | 0.321436 | − | 1.82296i | ||||
\(890\) | 431.356i | 0.484670i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −525.755 | −0.589412 | ||||||||
\(893\) | 55.2071 | + | 9.73450i | 0.0618220 | + | 0.0109009i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1429.39 | + | 520.255i | 1.59708 | + | 0.581290i | ||||
\(896\) | 640.678 | + | 763.531i | 0.715043 | + | 0.852155i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 438.061 | − | 159.441i | 0.487818 | − | 0.177551i | ||||
\(899\) | 485.835 | + | 280.497i | 0.540417 | + | 0.312010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 133.684 | + | 231.548i | 0.148373 | + | 0.256990i | ||||
\(902\) | −109.065 | + | 129.979i | −0.120915 | + | 0.144101i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.1609 | + | 137.023i | 0.0267267 | + | 0.151575i | ||||
\(905\) | 576.769 | − | 101.700i | 0.637313 | − | 0.112376i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1321.91 | + | 1109.21i | 1.45745 | + | 1.22295i | 0.926906 | + | 0.375293i | \(0.122458\pi\) |
0.530547 | + | 0.847656i | \(0.321987\pi\) | |||||||
\(908\) | −11.8330 | + | 6.83179i | −0.0130319 | + | 0.00752400i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 369.753 | − | 640.431i | 0.406322 | − | 0.703771i | ||||
\(911\) | −106.953 | − | 293.850i | −0.117401 | − | 0.322558i | 0.867048 | − | 0.498224i | \(-0.166014\pi\) |
−0.984450 | + | 0.175666i | \(0.943792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −284.305 | + | 238.560i | −0.311396 | + | 0.261292i | ||||
\(914\) | 58.4144 | − | 160.492i | 0.0639107 | − | 0.175593i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 162.732 | − | 922.898i | 0.177655 | − | 1.00753i | ||||
\(917\) | 1037.84i | 1.13177i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 198.504 | 0.216000 | 0.108000 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108000 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(920\) | −815.035 | − | 143.713i | −0.885908 | − | 0.156209i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −856.844 | − | 311.866i | −0.929332 | − | 0.338249i | ||||
\(923\) | −878.459 | − | 1046.91i | −0.951743 | − | 1.13424i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.9791 | − | 24.0144i | 0.0713287 | − | 0.0259615i | ||||
\(926\) | −360.397 | − | 208.075i | −0.389197 | − | 0.224703i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 415.883 | + | 720.330i | 0.448149 | + | 0.776218i | ||||
\(929\) | −854.746 | + | 1018.65i | −0.920071 | + | 1.09650i | 0.0749849 | + | 0.997185i | \(0.476109\pi\) |
−0.995056 | + | 0.0993136i | \(0.968335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.6528 | − | 275.924i | −0.0522587 | − | 0.296374i | ||||
\(932\) | 367.127 | − | 64.7343i | 0.393913 | − | 0.0694574i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −90.6501 | − | 76.0644i | −0.0970557 | − | 0.0814394i | ||||
\(935\) | −172.983 | + | 99.8717i | −0.185008 | + | 0.106815i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −675.671 | + | 1170.30i | −0.721100 | + | 1.24898i | 0.239459 | + | 0.970906i | \(0.423030\pi\) |
−0.960559 | + | 0.278076i | \(0.910303\pi\) | |||||||
\(938\) | 406.260 | + | 1116.19i | 0.433113 | + | 1.18997i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 135.608 | − | 113.789i | 0.144264 | − | 0.121052i | ||||
\(941\) | −265.840 | + | 730.391i | −0.282508 | + | 0.776186i | 0.714553 | + | 0.699581i | \(0.246630\pi\) |
−0.997062 | + | 0.0766044i | \(0.975592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.0206 | + | 243.982i | −0.0456210 | + | 0.258729i | ||||
\(944\) | 112.150i | 0.118803i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −496.949 | −0.525316 | ||||||||
\(947\) | 270.124 | + | 47.6301i | 0.285242 | + | 0.0502958i | 0.314438 | − | 0.949278i | \(-0.398184\pi\) |
−0.0291967 | + | 0.999574i | \(0.509295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −962.034 | − | 350.152i | −1.01373 | − | 0.368969i | ||||
\(950\) | −13.4167 | − | 15.9894i | −0.0141229 | − | 0.0168310i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −241.551 | + | 87.9173i | −0.253730 | + | 0.0923501i | ||||
\(953\) | −858.313 | − | 495.548i | −0.900644 | − | 0.519987i | −0.0232347 | − | 0.999730i | \(-0.507397\pi\) |
−0.877409 | + | 0.479743i | \(0.840730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −292.376 | − | 506.410i | −0.306153 | − | 0.530272i | ||||
\(956\) | −251.751 | + | 300.025i | −0.263338 | + | 0.313834i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.4760 | + | 144.482i | 0.0265929 | + | 0.150816i | ||||
\(959\) | 681.141 | − | 120.104i | 0.710262 | − | 0.125238i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −361.298 | − | 303.165i | −0.375961 | − | 0.315468i | ||||
\(962\) | −199.405 | + | 115.126i | −0.207281 | + | 0.119674i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −403.678 | + | 699.190i | −0.418753 | + | 0.725301i | ||||
\(965\) | −368.418 | − | 1012.22i | −0.381780 | − | 1.04893i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 239.352 | − | 200.840i | 0.247520 | − | 0.207694i | −0.510583 | − | 0.859828i | \(-0.670571\pi\) |
0.758104 | + | 0.652134i | \(0.226126\pi\) | |||||||
\(968\) | 44.6946 | − | 122.797i | 0.0461721 | − | 0.126857i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −86.6041 | + | 491.156i | −0.0892826 | + | 0.506347i | ||||
\(971\) | − | 487.838i | − | 0.502407i | −0.967934 | − | 0.251204i | \(-0.919174\pi\) | ||
0.967934 | − | 0.251204i | \(-0.0808264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1319.96 | 1.35659 | ||||||||
\(974\) | −519.080 | − | 91.5279i | −0.532937 | − | 0.0939711i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −120.511 | − | 43.8624i | −0.123474 | − | 0.0449410i | ||||
\(977\) | 413.839 | + | 493.194i | 0.423582 | + | 0.504805i | 0.935059 | − | 0.354492i | \(-0.115346\pi\) |
−0.511478 | + | 0.859297i | \(0.670902\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −761.718 | + | 277.243i | −0.778057 | + | 0.283190i | ||||
\(980\) | −766.227 | − | 442.382i | −0.781865 | − | 0.451410i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 183.483 | + | 317.802i | 0.186846 | + | 0.323627i | ||||
\(983\) | 989.779 | − | 1179.57i | 1.00690 | − | 1.19997i | 0.0271699 | − | 0.999631i | \(-0.491350\pi\) |
0.979726 | − | 0.200341i | \(-0.0642051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −273.610 | − | 1551.72i | −0.277777 | − | 1.57535i | ||||
\(986\) | −91.6108 | + | 16.1534i | −0.0929115 | + | 0.0163828i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −103.177 | − | 86.5756i | −0.104430 | − | 0.0876271i | ||||
\(989\) | −628.389 | + | 362.801i | −0.635378 | + | 0.366836i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −155.571 | + | 269.456i | −0.156984 | + | 0.271903i | −0.933780 | − | 0.357849i | \(-0.883510\pi\) |
0.776796 | + | 0.629752i | \(0.216844\pi\) | |||||||
\(992\) | 248.155 | + | 681.799i | 0.250156 | + | 0.687297i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1139.84 | − | 956.439i | 1.14672 | − | 0.962213i | ||||
\(995\) | −151.540 | + | 416.352i | −0.152301 | + | 0.418445i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.37502 | + | 47.4971i | −0.00840022 | + | 0.0476400i | −0.988720 | − | 0.149777i | \(-0.952144\pi\) |
0.980320 | + | 0.197417i | \(0.0632554\pi\) | |||||||
\(998\) | − | 141.953i | − | 0.142238i | ||||||
\(999\) | 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 | 81.3.f.a.8.2 | 30 | ||
3.2 | odd | 2 | 27.3.f.a.2.4 | ✓ | 30 | ||
9.2 | odd | 6 | 243.3.f.c.188.2 | 30 | |||
9.4 | even | 3 | 243.3.f.a.107.4 | 30 | |||
9.5 | odd | 6 | 243.3.f.d.107.2 | 30 | |||
9.7 | even | 3 | 243.3.f.b.188.4 | 30 | |||
12.11 | even | 2 | 432.3.bc.a.353.3 | 30 | |||
27.4 | even | 9 | 243.3.f.d.134.2 | 30 | |||
27.5 | odd | 18 | 243.3.f.b.53.4 | 30 | |||
27.11 | odd | 18 | 729.3.b.a.728.19 | 30 | |||
27.13 | even | 9 | 27.3.f.a.14.4 | yes | 30 | ||
27.14 | odd | 18 | inner | 81.3.f.a.71.2 | 30 | ||
27.16 | even | 9 | 729.3.b.a.728.12 | 30 | |||
27.22 | even | 9 | 243.3.f.c.53.2 | 30 | |||
27.23 | odd | 18 | 243.3.f.a.134.4 | 30 | |||
108.67 | odd | 18 | 432.3.bc.a.257.3 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.2.4 | ✓ | 30 | 3.2 | odd | 2 | ||
27.3.f.a.14.4 | yes | 30 | 27.13 | even | 9 | ||
81.3.f.a.8.2 | 30 | 1.1 | even | 1 | trivial | ||
81.3.f.a.71.2 | 30 | 27.14 | odd | 18 | inner | ||
243.3.f.a.107.4 | 30 | 9.4 | even | 3 | |||
243.3.f.a.134.4 | 30 | 27.23 | odd | 18 | |||
243.3.f.b.53.4 | 30 | 27.5 | odd | 18 | |||
243.3.f.b.188.4 | 30 | 9.7 | even | 3 | |||
243.3.f.c.53.2 | 30 | 27.22 | even | 9 | |||
243.3.f.c.188.2 | 30 | 9.2 | odd | 6 | |||
243.3.f.d.107.2 | 30 | 9.5 | odd | 6 | |||
243.3.f.d.134.2 | 30 | 27.4 | even | 9 | |||
432.3.bc.a.257.3 | 30 | 108.67 | odd | 18 | |||
432.3.bc.a.353.3 | 30 | 12.11 | even | 2 | |||
729.3.b.a.728.12 | 30 | 27.16 | even | 9 | |||
729.3.b.a.728.19 | 30 | 27.11 | odd | 18 |