Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,3,Mod(2,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, 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("27.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.f (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.735696713773\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Character | \(\chi\) | \(=\) | 27.2 |
Dual form | 27.3.f.a.14.4 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
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 | 0.452004 | − | 0.892016i | \(-0.350709\pi\) |
0.119658 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(3\) | 1.10490 | + | 2.78912i | 0.368300 | + | 0.929707i | ||||
\(4\) | −2.49222 | − | 0.907094i | −0.623055 | − | 0.226774i | ||||
\(5\) | −3.46013 | − | 4.12362i | −0.692026 | − | 0.824724i | 0.299574 | − | 0.954073i | \(-0.403156\pi\) |
−0.991599 | + | 0.129349i | \(0.958711\pi\) | |||||||
\(6\) | 0.700975 | + | 3.41162i | 0.116829 | + | 0.568603i | ||||
\(7\) | 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 | ||||
\(9\) | −6.55839 | + | 6.16340i | −0.728710 | + | 0.684822i | ||||
\(10\) | −3.12473 | − | 5.41219i | −0.312473 | − | 0.541219i | ||||
\(11\) | −7.54888 | + | 8.99640i | −0.686262 | + | 0.817855i | −0.990898 | − | 0.134614i | \(-0.957021\pi\) |
0.304636 | + | 0.952469i | \(0.401465\pi\) | |||||||
\(12\) | −0.223658 | − | 7.95335i | −0.0186382 | − | 0.662780i | ||||
\(13\) | 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 | ||||
\(15\) | 7.67818 | − | 14.2069i | 0.511879 | − | 0.947127i | ||||
\(16\) | 1.25834 | + | 1.05588i | 0.0786465 | + | 0.0659923i | ||||
\(17\) | 2.73630 | − | 1.57980i | 0.160959 | − | 0.0929296i | −0.417357 | − | 0.908743i | \(-0.637044\pi\) |
0.578316 | + | 0.815813i | \(0.303710\pi\) | |||||||
\(18\) | −8.74091 | + | 5.72460i | −0.485606 | + | 0.318033i | ||||
\(19\) | 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 | ||||
\(21\) | 20.9866 | + | 23.6288i | 0.999361 | + | 1.12518i | ||||
\(22\) | −10.4445 | + | 8.76396i | −0.474749 | + | 0.398362i | ||||
\(23\) | 6.80880 | − | 18.7070i | 0.296035 | − | 0.813349i | −0.699118 | − | 0.715007i | \(-0.746424\pi\) |
0.995153 | − | 0.0983427i | \(-0.0313541\pi\) | |||||||
\(24\) | 3.38024 | − | 22.9208i | 0.140843 | − | 0.955035i | ||||
\(25\) | −0.690550 | + | 3.91630i | −0.0276220 | + | 0.156652i | ||||
\(26\) | 13.0409i | 0.501575i | ||||||||
\(27\) | −24.4368 | − | 11.4822i | −0.905068 | − | 0.425267i | ||||
\(28\) | −27.9389 | −0.997818 | ||||||||
\(29\) | 24.9744 | + | 4.40366i | 0.861187 | + | 0.151851i | 0.586763 | − | 0.809758i | \(-0.300402\pi\) |
0.274424 | + | 0.961609i | \(0.411513\pi\) | |||||||
\(30\) | 11.6428 | − | 14.6952i | 0.388092 | − | 0.489840i | ||||
\(31\) | −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 | ||||
\(33\) | −33.4328 | − | 11.1146i | −1.01312 | − | 0.336807i | ||||
\(34\) | 3.44696 | − | 1.25459i | 0.101381 | − | 0.0368998i | ||||
\(35\) | −49.1093 | − | 28.3533i | −1.40312 | − | 0.810093i | ||||
\(36\) | 21.9358 | − | 9.41147i | 0.609326 | − | 0.261430i | ||||
\(37\) | −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 | ||||
\(39\) | −28.6987 | + | 17.6630i | −0.735864 | + | 0.452898i | ||||
\(40\) | 7.21898 | + | 40.9409i | 0.180475 | + | 1.02352i | ||||
\(41\) | −12.2557 | + | 2.16101i | −0.298920 | + | 0.0527076i | −0.321096 | − | 0.947046i | \(-0.604051\pi\) |
0.0221770 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(42\) | 19.2309 | + | 31.2462i | 0.457880 | + | 0.743958i | ||||
\(43\) | 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 | ||||
\(45\) | 48.1084 | + | 5.71818i | 1.06908 | + | 0.127071i | ||||
\(46\) | 11.5560 | − | 20.0156i | 0.251217 | − | 0.435121i | ||||
\(47\) | −4.24091 | − | 11.6518i | −0.0902320 | − | 0.247910i | 0.886365 | − | 0.462987i | \(-0.153222\pi\) |
−0.976597 | + | 0.215076i | \(0.931000\pi\) | |||||||
\(48\) | −1.55462 | + | 4.67631i | −0.0323880 | + | 0.0974232i | ||||
\(49\) | 47.4740 | − | 39.8354i | 0.968857 | − | 0.812967i | ||||
\(50\) | −1.57905 | + | 4.33839i | −0.0315809 | + | 0.0867679i | ||||
\(51\) | 7.42960 | + | 5.88634i | 0.145678 | + | 0.115419i | ||||
\(52\) | 5.17323 | − | 29.3388i | 0.0994852 | − | 0.564209i | ||||
\(53\) | 84.6210i | 1.59662i | 0.602245 | + | 0.798311i | \(0.294273\pi\) | ||||
−0.602245 | + | 0.798311i | \(0.705727\pi\) | |||||||
\(54\) | −25.6244 | − | 18.0543i | −0.474526 | − | 0.334340i | ||||
\(55\) | 63.2178 | 1.14942 | ||||||||
\(56\) | −80.1200 | − | 14.1273i | −1.43071 | − | 0.252274i | ||||
\(57\) | 13.4179 | + | 1.97880i | 0.235402 | + | 0.0347158i | ||||
\(58\) | 27.6661 | + | 10.0696i | 0.477002 | + | 0.173614i | ||||
\(59\) | −43.8854 | − | 52.3006i | −0.743820 | − | 0.886451i | 0.252890 | − | 0.967495i | \(-0.418619\pi\) |
−0.996711 | + | 0.0810443i | \(0.974174\pi\) | |||||||
\(60\) | −32.0227 | + | 28.4419i | −0.533712 | + | 0.474032i | ||||
\(61\) | −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 | ||||
\(63\) | −42.7155 | + | 84.6415i | −0.678023 | + | 1.34352i | ||||
\(64\) | 15.7537 | + | 27.2863i | 0.246152 | + | 0.426348i | ||||
\(65\) | 38.8672 | − | 46.3201i | 0.597956 | − | 0.712617i | ||||
\(66\) | −35.9839 | − | 19.4476i | −0.545210 | − | 0.294661i | ||||
\(67\) | −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 | ||||
\(69\) | 59.6992 | − | 1.67882i | 0.865206 | − | 0.0243307i | ||||
\(70\) | −50.4319 | − | 42.3174i | −0.720455 | − | 0.604534i | ||||
\(71\) | 105.364 | − | 60.8322i | 1.48401 | − | 0.856791i | 0.484171 | − | 0.874973i | \(-0.339121\pi\) |
0.999835 | + | 0.0181820i | \(0.00578784\pi\) | |||||||
\(72\) | 67.6638 | − | 15.8973i | 0.939775 | − | 0.220796i | ||||
\(73\) | −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 | ||||
\(75\) | −11.6860 | + | 2.40109i | −0.155814 | + | 0.0320146i | ||||
\(76\) | −9.18525 | + | 7.70734i | −0.120859 | + | 0.101412i | ||||
\(77\) | −42.3131 | + | 116.254i | −0.549521 | + | 1.50980i | ||||
\(78\) | −36.3728 | + | 14.4089i | −0.466317 | + | 0.184730i | ||||
\(79\) | −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 | ||||||
\(81\) | 5.02506 | − | 80.8440i | 0.0620378 | − | 0.998074i | ||||
\(82\) | −14.4479 | −0.176194 | ||||||||
\(83\) | 31.1219 | + | 5.48763i | 0.374963 | + | 0.0661161i | 0.357954 | − | 0.933739i | \(-0.383474\pi\) |
0.0170090 | + | 0.999855i | \(0.494586\pi\) | |||||||
\(84\) | −30.8697 | − | 77.9250i | −0.367496 | − | 0.927678i | ||||
\(85\) | −15.9824 | − | 5.81713i | −0.188029 | − | 0.0684369i | ||||
\(86\) | 27.1997 | + | 32.4154i | 0.316276 | + | 0.376923i | ||||
\(87\) | 15.3119 | + | 74.5223i | 0.175999 | + | 0.856578i | ||||
\(88\) | 85.2279 | − | 31.0204i | 0.968499 | − | 0.352505i | ||||
\(89\) | 59.7756 | + | 34.5114i | 0.671636 | + | 0.387769i | 0.796696 | − | 0.604380i | \(-0.206579\pi\) |
−0.125060 | + | 0.992149i | \(0.539912\pi\) | |||||||
\(90\) | 53.8507 | + | 16.2363i | 0.598341 | + | 0.180404i | ||||
\(91\) | 59.1656 | + | 102.478i | 0.650171 | + | 1.12613i | ||||
\(92\) | −33.9381 | + | 40.4458i | −0.368892 | + | 0.439629i | ||||
\(93\) | −1.86551 | − | 66.3381i | −0.0200592 | − | 0.713313i | ||||
\(94\) | −2.49974 | − | 14.1767i | −0.0265930 | − | 0.150816i | ||||
\(95\) | −23.9669 | + | 4.22602i | −0.252283 | + | 0.0444844i | ||||
\(96\) | −46.7833 | + | 86.5629i | −0.487326 | + | 0.901696i | ||||
\(97\) | −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 | ||||
\(99\) | −5.93989 | − | 105.529i | −0.0599989 | − | 1.06595i | ||||
\(100\) | 5.27346 | − | 9.13390i | 0.0527346 | − | 0.0913390i | ||||
\(101\) | −1.63372 | − | 4.48862i | −0.0161755 | − | 0.0444417i | 0.931342 | − | 0.364145i | \(-0.118639\pi\) |
−0.947518 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(102\) | 7.30776 | + | 8.22780i | 0.0716447 | + | 0.0806647i | ||||
\(103\) | −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 | ||||
\(105\) | 24.8199 | − | 168.299i | 0.236380 | − | 1.60285i | ||||
\(106\) | −17.0595 | + | 96.7493i | −0.160939 | + | 0.912729i | ||||
\(107\) | 158.133i | 1.47788i | 0.673773 | + | 0.738938i | \(0.264672\pi\) | ||||
−0.673773 | + | 0.738938i | \(0.735328\pi\) | |||||||
\(108\) | 50.4865 | + | 50.7827i | 0.467468 | + | 0.470211i | ||||
\(109\) | −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 | ||||
\(111\) | 32.8934 | − | 41.5172i | 0.296337 | − | 0.374029i | ||||
\(112\) | 16.2607 | + | 5.91842i | 0.145185 | + | 0.0528430i | ||||
\(113\) | −11.5806 | − | 13.8012i | −0.102483 | − | 0.122134i | 0.712365 | − | 0.701809i | \(-0.247624\pi\) |
−0.814848 | + | 0.579675i | \(0.803180\pi\) | |||||||
\(114\) | 14.9421 | + | 4.96746i | 0.131071 | + | 0.0435742i | ||||
\(115\) | −100.700 | + | 36.6518i | −0.875652 | + | 0.318711i | ||||
\(116\) | −58.2473 | − | 33.6291i | −0.502131 | − | 0.289906i | ||||
\(117\) | −80.9734 | − | 60.5283i | −0.692081 | − | 0.517336i | ||||
\(118\) | −39.6315 | − | 68.6438i | −0.335860 | − | 0.581727i | ||||
\(119\) | 21.3948 | − | 25.4974i | 0.179788 | − | 0.214264i | ||||
\(120\) | −106.213 | + | 65.3702i | −0.885107 | + | 0.544752i | ||||
\(121\) | −2.93828 | − | 16.6638i | −0.0242833 | − | 0.137717i | ||||
\(122\) | −89.2617 | + | 15.7392i | −0.731653 | + | 0.129010i | ||||
\(123\) | −19.5686 | − | 31.7949i | −0.159095 | − | 0.258495i | ||||
\(124\) | 44.9437 | + | 37.7122i | 0.362449 | + | 0.304131i | ||||
\(125\) | −98.0067 | + | 56.5842i | −0.784054 | + | 0.452674i | ||||
\(126\) | −65.9013 | + | 88.1614i | −0.523026 | + | 0.699693i | ||||
\(127\) | 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 | ||||
\(129\) | −34.4952 | + | 103.762i | −0.267405 | + | 0.804354i | ||||
\(130\) | 53.7759 | − | 45.1233i | 0.413661 | − | 0.347102i | ||||
\(131\) | 33.6955 | − | 92.5776i | 0.257217 | − | 0.706699i | −0.742119 | − | 0.670268i | \(-0.766179\pi\) |
0.999336 | − | 0.0364307i | \(-0.0115988\pi\) | |||||||
\(132\) | 73.2400 | + | 58.0268i | 0.554848 | + | 0.439597i | ||||
\(133\) | 8.27018 | − | 46.9025i | 0.0621818 | − | 0.352651i | ||||
\(134\) | − | 112.757i | − | 0.841471i | ||||||
\(135\) | 37.2062 | + | 140.498i | 0.275602 | + | 1.04073i | ||||
\(136\) | −24.4014 | −0.179422 | ||||||||
\(137\) | −64.6590 | − | 11.4011i | −0.471963 | − | 0.0832199i | −0.0673925 | − | 0.997727i | \(-0.521468\pi\) |
−0.404571 | + | 0.914507i | \(0.632579\pi\) | |||||||
\(138\) | 68.5941 | + | 10.1159i | 0.497058 | + | 0.0733034i | ||||
\(139\) | 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 | ||||
\(141\) | 27.8125 | − | 24.7025i | 0.197252 | − | 0.175195i | ||||
\(142\) | 132.729 | − | 48.3096i | 0.934714 | − | 0.340208i | ||||
\(143\) | −114.245 | − | 65.9593i | −0.798915 | − | 0.461254i | ||||
\(144\) | −14.7605 | + | 0.830824i | −0.102503 | + | 0.00576961i | ||||
\(145\) | −68.2557 | − | 118.222i | −0.470729 | − | 0.815326i | ||||
\(146\) | −68.0142 | + | 81.0562i | −0.465851 | + | 0.555179i | ||||
\(147\) | 163.560 | + | 88.3966i | 1.11265 | + | 0.601337i | ||||
\(148\) | 8.13142 | + | 46.1156i | 0.0549420 | + | 0.311592i | ||||
\(149\) | 198.691 | − | 35.0346i | 1.33350 | − | 0.235132i | 0.538953 | − | 0.842336i | \(-0.318820\pi\) |
0.794546 | + | 0.607204i | \(0.207709\pi\) | |||||||
\(150\) | −13.8450 | + | 0.389338i | −0.0922999 | + | 0.00259559i | ||||
\(151\) | 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 | ||||
\(153\) | −8.20877 | + | 27.2259i | −0.0536521 | + | 0.177947i | ||||
\(154\) | −71.8144 | + | 124.386i | −0.466327 | + | 0.807703i | ||||
\(155\) | 40.7277 | + | 111.898i | 0.262759 | + | 0.721926i | ||||
\(156\) | 87.5455 | − | 17.9877i | 0.561189 | − | 0.115306i | ||||
\(157\) | −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 | ||||
\(159\) | −236.018 | + | 93.4977i | −1.48439 | + | 0.588036i | ||||
\(160\) | 30.6586 | − | 173.873i | 0.191616 | − | 1.08671i | ||||
\(161\) | − | 209.714i | − | 1.30257i | ||||||
\(162\) | 22.0433 | − | 91.4179i | 0.136070 | − | 0.564308i | ||||
\(163\) | 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 | ||||
\(165\) | 69.8494 | + | 176.322i | 0.423329 | + | 1.06862i | ||||
\(166\) | 34.4762 | + | 12.5483i | 0.207688 | + | 0.0755921i | ||||
\(167\) | −106.672 | − | 127.127i | −0.638757 | − | 0.761241i | 0.345416 | − | 0.938450i | \(-0.387738\pi\) |
−0.984173 | + | 0.177208i | \(0.943293\pi\) | |||||||
\(168\) | −49.1218 | − | 239.074i | −0.292391 | − | 1.42306i | ||||
\(169\) | 40.2401 | − | 14.6462i | 0.238107 | − | 0.0866639i | ||||
\(170\) | −17.1004 | − | 9.87292i | −0.100591 | − | 0.0580760i | ||||
\(171\) | 9.30634 | + | 39.6106i | 0.0544231 | + | 0.231641i | ||||
\(172\) | −48.3337 | − | 83.7164i | −0.281010 | − | 0.486723i | ||||
\(173\) | −7.00006 | + | 8.34234i | −0.0404628 | + | 0.0482216i | −0.785896 | − | 0.618358i | \(-0.787798\pi\) |
0.745434 | + | 0.666580i | \(0.232243\pi\) | |||||||
\(174\) | 2.48282 | + | 88.2901i | 0.0142691 | + | 0.507414i | ||||
\(175\) | 7.27451 | + | 41.2558i | 0.0415686 | + | 0.235747i | ||||
\(176\) | −18.9982 | + | 3.34989i | −0.107944 | + | 0.0190335i | ||||
\(177\) | 97.3837 | − | 180.189i | 0.550191 | − | 1.01801i | ||||
\(178\) | 61.3854 | + | 51.5085i | 0.344862 | + | 0.289374i | ||||
\(179\) | −244.720 | + | 141.289i | −1.36715 | + | 0.789326i | −0.990564 | − | 0.137054i | \(-0.956237\pi\) |
−0.376590 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(180\) | −114.710 | − | 57.8898i | −0.637277 | − | 0.321610i | ||||
\(181\) | 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 | ||||
\(183\) | −155.535 | − | 175.117i | −0.849919 | − | 0.956923i | ||||
\(184\) | −117.775 | + | 98.8252i | −0.640083 | + | 0.537094i | ||||
\(185\) | −32.5066 | + | 89.3112i | −0.175711 | + | 0.482763i | ||||
\(186\) | 11.2408 | − | 76.2221i | 0.0604345 | − | 0.409796i | ||||
\(187\) | −6.44344 | + | 36.5426i | −0.0344569 | + | 0.195415i | ||||
\(188\) | 32.8857i | 0.174924i | ||||||||
\(189\) | −283.272 | − | 25.6182i | −1.49879 | − | 0.135546i | ||||
\(190\) | −28.2539 | −0.148705 | ||||||||
\(191\) | 106.979 | + | 18.8633i | 0.560100 | + | 0.0987607i | 0.446529 | − | 0.894769i | \(-0.352660\pi\) |
0.113571 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(192\) | −58.6984 | + | 74.0877i | −0.305721 | + | 0.385873i | ||||
\(193\) | −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 | ||||
\(195\) | 172.137 | + | 57.2262i | 0.882752 | + | 0.293468i | ||||
\(196\) | −154.450 | + | 56.2152i | −0.788011 | + | 0.286812i | ||||
\(197\) | 253.494 | + | 146.355i | 1.28677 | + | 0.742918i | 0.978077 | − | 0.208243i | \(-0.0667746\pi\) |
0.308694 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(198\) | 14.4833 | − | 121.851i | 0.0731478 | − | 0.615409i | ||||
\(199\) | 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 | ||||
\(201\) | 248.140 | − | 152.721i | 1.23453 | − | 0.759807i | ||||
\(202\) | −0.962975 | − | 5.46130i | −0.00476720 | − | 0.0270361i | ||||
\(203\) | 263.090 | − | 46.3898i | 1.29601 | − | 0.228521i | ||||
\(204\) | −13.1767 | − | 21.4094i | −0.0645918 | − | 0.104948i | ||||
\(205\) | 51.3175 | + | 43.0605i | 0.250329 | + | 0.210051i | ||||
\(206\) | −72.6848 | + | 41.9646i | −0.352839 | + | 0.203712i | ||||
\(207\) | 70.6441 | + | 164.653i | 0.341276 | + | 0.795427i | ||||
\(208\) | −9.22585 | + | 15.9796i | −0.0443550 | + | 0.0768252i | ||||
\(209\) | 18.1595 | + | 49.8927i | 0.0868874 | + | 0.238721i | ||||
\(210\) | 62.3061 | − | 187.417i | 0.296696 | − | 0.892462i | ||||
\(211\) | 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 | ||||
\(213\) | 286.085 | + | 226.661i | 1.34312 | + | 1.06413i | ||||
\(214\) | −31.8794 | + | 180.797i | −0.148969 | + | 0.844846i | ||||
\(215\) | − | 196.202i | − | 0.912568i | ||||||
\(216\) | 119.101 | + | 171.158i | 0.551395 | + | 0.792396i | ||||
\(217\) | −233.036 | −1.07390 | ||||||||
\(218\) | −21.2416 | − | 3.74547i | −0.0974387 | − | 0.0171811i | ||||
\(219\) | −270.497 | − | 39.8915i | −1.23515 | − | 0.182153i | ||||
\(220\) | −157.553 | − | 57.3445i | −0.716149 | − | 0.260657i | ||||
\(221\) | 22.8135 | + | 27.1880i | 0.103228 | + | 0.123023i | ||||
\(222\) | 45.9776 | − | 40.8364i | 0.207106 | − | 0.183948i | ||||
\(223\) | 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 | ||||
\(225\) | −19.6088 | − | 29.9408i | −0.0871504 | − | 0.133070i | ||||
\(226\) | −10.4580 | − | 18.1138i | −0.0462745 | − | 0.0801498i | ||||
\(227\) | −3.31155 | + | 3.94655i | −0.0145883 | + | 0.0173857i | −0.773289 | − | 0.634053i | \(-0.781390\pi\) |
0.758701 | + | 0.651439i | \(0.225834\pi\) | |||||||
\(228\) | −31.6455 | − | 17.1029i | −0.138796 | − | 0.0750129i | ||||
\(229\) | 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 | ||||
\(231\) | −370.999 | + | 10.4330i | −1.60606 | + | 0.0451643i | ||||
\(232\) | −150.030 | − | 125.890i | −0.646683 | − | 0.542631i | ||||
\(233\) | 121.729 | − | 70.2803i | 0.522442 | − | 0.301632i | −0.215491 | − | 0.976506i | \(-0.569135\pi\) |
0.737933 | + | 0.674874i | \(0.235802\pi\) | |||||||
\(234\) | −80.3765 | − | 85.5276i | −0.343489 | − | 0.365503i | ||||
\(235\) | −33.3735 | + | 57.8046i | −0.142015 | + | 0.245977i | ||||
\(236\) | 61.9306 | + | 170.153i | 0.262418 | + | 0.720987i | ||||
\(237\) | −59.9121 | + | 12.3100i | −0.252794 | + | 0.0519407i | ||||
\(238\) | 29.6015 | − | 24.8386i | 0.124376 | − | 0.104364i | ||||
\(239\) | −50.5074 | + | 138.768i | −0.211328 | + | 0.580619i | −0.999388 | − | 0.0349794i | \(-0.988863\pi\) |
0.788060 | + | 0.615598i | \(0.211086\pi\) | |||||||
\(240\) | 24.6625 | − | 9.76996i | 0.102761 | − | 0.0407082i | ||||
\(241\) | 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 | ||||||
\(243\) | 231.036 | − | 75.3090i | 0.950765 | − | 0.309913i | ||||
\(244\) | 207.060 | 0.848606 | ||||||||
\(245\) | −328.532 | − | 57.9291i | −1.34095 | − | 0.236445i | ||||
\(246\) | −15.9635 | − | 40.2970i | −0.0648922 | − | 0.163809i | ||||
\(247\) | 47.7214 | + | 17.3692i | 0.193204 | + | 0.0703205i | ||||
\(248\) | 109.815 | + | 130.873i | 0.442803 | + | 0.527712i | ||||
\(249\) | 19.0809 | + | 92.8661i | 0.0766302 | + | 0.372956i | ||||
\(250\) | −123.461 | + | 44.9361i | −0.493843 | + | 0.179744i | ||||
\(251\) | −108.072 | − | 62.3955i | −0.430567 | − | 0.248588i | 0.269021 | − | 0.963134i | \(-0.413300\pi\) |
−0.699588 | + | 0.714546i | \(0.746633\pi\) | |||||||
\(252\) | 183.234 | − | 172.198i | 0.727120 | − | 0.683327i | ||||
\(253\) | 116.897 | + | 202.472i | 0.462044 | + | 0.800284i | ||||
\(254\) | 116.575 | − | 138.928i | 0.458955 | − | 0.546961i | ||||
\(255\) | −1.43430 | − | 51.0043i | −0.00562472 | − | 0.200017i | ||||
\(256\) | −40.9593 | − | 232.292i | −0.159997 | − | 0.907390i | ||||
\(257\) | −450.088 | + | 79.3627i | −1.75132 | + | 0.308804i | −0.955116 | − | 0.296231i | \(-0.904270\pi\) |
−0.796199 | + | 0.605035i | \(0.793159\pi\) | |||||||
\(258\) | −60.3575 | + | 111.679i | −0.233944 | + | 0.432865i | ||||
\(259\) | −142.481 | − | 119.556i | −0.550121 | − | 0.461606i | ||||
\(260\) | −138.882 | + | 80.1837i | −0.534163 | + | 0.308399i | ||||
\(261\) | −190.934 | + | 125.046i | −0.731547 | + | 0.479105i | ||||
\(262\) | 57.1884 | − | 99.0533i | 0.218276 | − | 0.378066i | ||||
\(263\) | −160.047 | − | 439.726i | −0.608545 | − | 1.67196i | −0.733408 | − | 0.679789i | \(-0.762071\pi\) |
0.124863 | − | 0.992174i | \(-0.460151\pi\) | |||||||
\(264\) | 180.688 | + | 203.437i | 0.684425 | + | 0.770593i | ||||
\(265\) | 348.945 | − | 292.799i | 1.31677 | − | 1.10490i | ||||
\(266\) | 18.9110 | − | 51.9576i | 0.0710940 | − | 0.195329i | ||||
\(267\) | −30.2106 | + | 204.853i | −0.113148 | + | 0.767240i | ||||
\(268\) | −44.7298 | + | 253.675i | −0.166902 | + | 0.946549i | ||||
\(269\) | − | 317.049i | − | 1.17862i | −0.807907 | − | 0.589310i | \(-0.799399\pi\) | ||
0.807907 | − | 0.589310i | \(-0.200601\pi\) | |||||||
\(270\) | 14.2145 | + | 168.136i | 0.0526464 | + | 0.622725i | ||||
\(271\) | 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 | ||||
\(273\) | −220.451 | + | 278.248i | −0.807513 | + | 1.01922i | ||||
\(274\) | −71.6277 | − | 26.0704i | −0.261415 | − | 0.0951473i | ||||
\(275\) | −30.0198 | − | 35.7762i | −0.109163 | − | 0.130095i | ||||
\(276\) | −150.307 | − | 49.9689i | −0.544589 | − | 0.181047i | ||||
\(277\) | 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 | ||||
\(279\) | 182.964 | − | 78.5001i | 0.655785 | − | 0.281362i | ||||
\(280\) | 218.970 | + | 379.267i | 0.782035 | + | 1.35452i | ||||
\(281\) | −52.4463 | + | 62.5031i | −0.186642 | + | 0.222431i | −0.851249 | − | 0.524762i | \(-0.824154\pi\) |
0.664607 | + | 0.747193i | \(0.268599\pi\) | |||||||
\(282\) | 36.7787 | − | 22.6360i | 0.130421 | − | 0.0802694i | ||||
\(283\) | −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 | ||||
\(285\) | −38.2679 | − | 62.1773i | −0.134273 | − | 0.218166i | ||||
\(286\) | −117.322 | − | 98.4445i | −0.410215 | − | 0.344211i | ||||
\(287\) | −113.534 | + | 65.5489i | −0.395589 | + | 0.228393i | ||||
\(288\) | −293.125 | − | 34.8410i | −1.01780 | − | 0.120976i | ||||
\(289\) | −139.508 | + | 241.636i | −0.482728 | + | 0.836110i | ||||
\(290\) | −54.2049 | − | 148.927i | −0.186913 | − | 0.513540i | ||||
\(291\) | 75.5275 | − | 227.187i | 0.259545 | − | 0.780712i | ||||
\(292\) | 185.169 | − | 155.375i | 0.634141 | − | 0.532107i | ||||
\(293\) | −118.282 | + | 324.977i | −0.403693 | + | 1.10914i | 0.556755 | + | 0.830676i | \(0.312046\pi\) |
−0.960448 | + | 0.278460i | \(0.910176\pi\) | |||||||
\(294\) | 169.181 | + | 134.039i | 0.575446 | + | 0.455917i | ||||
\(295\) | −63.8186 | + | 361.933i | −0.216334 | + | 1.22689i | ||||
\(296\) | 136.357i | 0.460665i | ||||||||
\(297\) | 287.769 | − | 133.166i | 0.968920 | − | 0.448369i | ||||
\(298\) | 234.232 | 0.786012 | ||||||||
\(299\) | 220.222 | + | 38.8311i | 0.736529 | + | 0.129870i | ||||
\(300\) | 31.3022 | + | 4.61628i | 0.104341 | + | 0.0153876i | ||||
\(301\) | 360.806 | + | 131.323i | 1.19869 | + | 0.436287i | ||||
\(302\) | 95.6252 | + | 113.962i | 0.316640 | + | 0.377356i | ||||
\(303\) | 10.7142 | − | 9.51612i | 0.0353604 | − | 0.0314063i | ||||
\(304\) | 6.97859 | − | 2.54000i | 0.0229559 | − | 0.00835526i | ||||
\(305\) | 363.957 | + | 210.131i | 1.19330 | + | 0.688954i | ||||
\(306\) | −14.8740 | + | 29.4731i | −0.0486078 | + | 0.0963174i | ||||
\(307\) | −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 | ||||
\(309\) | −190.796 | − | 103.117i | −0.617463 | − | 0.333711i | ||||
\(310\) | 24.0064 | + | 136.147i | 0.0774399 | + | 0.439184i | ||||
\(311\) | 442.280 | − | 77.9859i | 1.42212 | − | 0.250759i | 0.590921 | − | 0.806730i | \(-0.298765\pi\) |
0.831202 | + | 0.555971i | \(0.187653\pi\) | |||||||
\(312\) | 260.149 | − | 7.31570i | 0.833810 | − | 0.0234478i | ||||
\(313\) | 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 | ||||
\(315\) | 496.830 | − | 116.728i | 1.57724 | − | 0.370566i | ||||
\(316\) | 27.0360 | − | 46.8278i | 0.0855570 | − | 0.148189i | ||||
\(317\) | −74.6402 | − | 205.072i | −0.235458 | − | 0.646916i | −0.999997 | − | 0.00233841i | \(-0.999256\pi\) |
0.764539 | − | 0.644577i | \(-0.222967\pi\) | |||||||
\(318\) | −288.694 | + | 59.3172i | −0.907844 | + | 0.186532i | ||||
\(319\) | −228.146 | + | 191.437i | −0.715191 | + | 0.600117i | ||||
\(320\) | 58.0083 | − | 159.376i | 0.181276 | − | 0.498051i | ||||
\(321\) | −441.051 | + | 174.721i | −1.37399 | + | 0.544302i | ||||
\(322\) | 42.2781 | − | 239.771i | 0.131299 | − | 0.744631i | ||||
\(323\) | − | 14.2846i | − | 0.0442249i | ||||||
\(324\) | −85.8567 | + | 196.923i | −0.264990 | + | 0.607787i | ||||
\(325\) | −44.6700 | −0.137446 | ||||||||
\(326\) | 45.5694 | + | 8.03512i | 0.139784 | + | 0.0246476i | ||||
\(327\) | −20.5277 | − | 51.8186i | −0.0627760 | − | 0.158467i | ||||
\(328\) | 90.3137 | + | 32.8715i | 0.275347 | + | 0.100218i | ||||
\(329\) | −83.9620 | − | 100.062i | −0.255204 | − | 0.304140i | ||||
\(330\) | 44.3141 | + | 215.675i | 0.134285 | + | 0.653561i | ||||
\(331\) | −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 | ||||
\(333\) | 152.140 | + | 45.8713i | 0.456878 | + | 0.137752i | ||||
\(334\) | −96.3325 | − | 166.853i | −0.288421 | − | 0.499559i | ||||
\(335\) | −336.061 | + | 400.502i | −1.00317 | + | 1.19553i | ||||
\(336\) | 1.45928 | + | 51.8924i | 0.00434309 | + | 0.154442i | ||||
\(337\) | 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 | ||||
\(339\) | 25.6978 | − | 47.5485i | 0.0758047 | − | 0.140261i | ||||
\(340\) | 34.5551 | + | 28.9952i | 0.101633 | + | 0.0852799i | ||||
\(341\) | 224.988 | − | 129.897i | 0.659789 | − | 0.380929i | ||||
\(342\) | 2.65471 | + | 47.1639i | 0.00776232 | + | 0.137906i | ||||
\(343\) | 68.3305 | − | 118.352i | 0.199214 | − | 0.345049i | ||||
\(344\) | −96.2747 | − | 264.512i | −0.279868 | − | 0.768932i | ||||
\(345\) | −213.490 | − | 240.368i | −0.618811 | − | 0.696719i | ||||
\(346\) | −9.68515 | + | 8.12680i | −0.0279918 | + | 0.0234879i | ||||
\(347\) | −80.7717 | + | 221.918i | −0.232771 | + | 0.639534i | −0.999998 | − | 0.00184170i | \(-0.999414\pi\) |
0.767227 | + | 0.641376i | \(0.221636\pi\) | |||||||
\(348\) | 29.4382 | − | 199.615i | 0.0845925 | − | 0.573607i | ||||
\(349\) | 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 | ||||||||
\(351\) | 79.3531 | − | 292.722i | 0.226077 | − | 0.833967i | ||||
\(352\) | −385.187 | −1.09428 | ||||||||
\(353\) | 25.2020 | + | 4.44379i | 0.0713937 | + | 0.0125886i | 0.209231 | − | 0.977866i | \(-0.432904\pi\) |
−0.137837 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(354\) | 147.667 | − | 186.382i | 0.417139 | − | 0.526502i | ||||
\(355\) | −615.423 | − | 223.996i | −1.73359 | − | 0.630974i | ||||
\(356\) | −117.669 | − | 140.232i | −0.330530 | − | 0.393911i | ||||
\(357\) | 94.7544 | + | 31.5007i | 0.265418 | + | 0.0882374i | ||||
\(358\) | −308.279 | + | 112.204i | −0.861114 | + | 0.313420i | ||||
\(359\) | 16.7796 | + | 9.68773i | 0.0467399 | + | 0.0269853i | 0.523188 | − | 0.852217i | \(-0.324743\pi\) |
−0.476448 | + | 0.879203i | \(0.658076\pi\) | |||||||
\(360\) | −299.680 | − | 224.013i | −0.832444 | − | 0.622258i | ||||
\(361\) | 170.280 | + | 294.934i | 0.471690 | + | 0.816992i | ||||
\(362\) | 81.1916 | − | 96.7604i | 0.224286 | − | 0.267294i | ||||
\(363\) | 43.2308 | − | 26.6070i | 0.119093 | − | 0.0732976i | ||||
\(364\) | −54.4967 | − | 309.066i | −0.149716 | − | 0.849083i | ||||
\(365\) | 483.159 | − | 85.1939i | 1.32372 | − | 0.233408i | ||||
\(366\) | −142.524 | − | 231.571i | −0.389409 | − | 0.632709i | ||||
\(367\) | 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 | ||||
\(369\) | 67.0585 | − | 89.7095i | 0.181730 | − | 0.243115i | ||||
\(370\) | −55.1707 | + | 95.5584i | −0.149110 | + | 0.258266i | ||||
\(371\) | 304.886 | + | 837.669i | 0.821796 | + | 2.25787i | ||||
\(372\) | −55.5257 | + | 167.022i | −0.149263 | + | 0.448983i | ||||
\(373\) | −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 | ||||
\(375\) | −266.108 | − | 210.833i | −0.709621 | − | 0.562221i | ||||
\(376\) | −16.6287 | + | 94.3061i | −0.0442253 | + | 0.250814i | ||||
\(377\) | 284.862i | 0.755603i | ||||||||
\(378\) | −318.707 | − | 86.3973i | −0.843140 | − | 0.228564i | ||||
\(379\) | 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 | ||||
\(381\) | 463.626 | + | 68.3730i | 1.21687 | + | 0.179457i | ||||
\(382\) | 118.509 | + | 43.1337i | 0.310233 | + | 0.112916i | ||||
\(383\) | 11.0730 | + | 13.1963i | 0.0289112 | + | 0.0344550i | 0.780306 | − | 0.625398i | \(-0.215063\pi\) |
−0.751395 | + | 0.659853i | \(0.770619\pi\) | |||||||
\(384\) | 212.225 | − | 188.494i | 0.552670 | − | 0.490870i | ||||
\(385\) | 625.797 | − | 227.772i | 1.62545 | − | 0.591615i | ||||
\(386\) | −201.193 | − | 116.159i | −0.521226 | − | 0.300930i | ||||
\(387\) | −327.518 | + | 18.4350i | −0.846299 | + | 0.0476356i | ||||
\(388\) | 105.827 | + | 183.298i | 0.272750 | + | 0.472417i | ||||
\(389\) | 203.618 | − | 242.662i | 0.523439 | − | 0.623810i | −0.437952 | − | 0.898999i | \(-0.644296\pi\) |
0.961390 | + | 0.275189i | \(0.0887403\pi\) | |||||||
\(390\) | 185.271 | + | 100.131i | 0.475055 | + | 0.256745i | ||||
\(391\) | −10.9225 | − | 61.9446i | −0.0279348 | − | 0.158426i | ||||
\(392\) | −471.340 | + | 83.1100i | −1.20240 | + | 0.212015i | ||||
\(393\) | 295.440 | − | 8.30814i | 0.751756 | − | 0.0211403i | ||||
\(394\) | 260.321 | + | 218.435i | 0.660713 | + | 0.554404i | ||||
\(395\) | 95.0446 | − | 54.8740i | 0.240619 | − | 0.138922i | ||||
\(396\) | −80.9210 | + | 268.389i | −0.204346 | + | 0.677750i | ||||
\(397\) | −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 | ||||
\(399\) | 139.955 | − | 28.7560i | 0.350763 | − | 0.0720703i | ||||
\(400\) | −5.00408 | + | 4.19892i | −0.0125102 | + | 0.0104973i | ||||
\(401\) | 33.3356 | − | 91.5887i | 0.0831311 | − | 0.228401i | −0.891162 | − | 0.453685i | \(-0.850109\pi\) |
0.974293 | + | 0.225285i | \(0.0723312\pi\) | |||||||
\(402\) | 314.493 | − | 124.585i | 0.782321 | − | 0.309914i | ||||
\(403\) | 43.1494 | − | 244.712i | 0.107070 | − | 0.607227i | ||||
\(404\) | 12.6686i | 0.0313578i | ||||||||
\(405\) | −350.757 | + | 259.009i | −0.866067 | + | 0.639528i | ||||
\(406\) | 310.149 | 0.763914 | ||||||||
\(407\) | 204.203 | + | 36.0065i | 0.501727 | + | 0.0884680i | ||||
\(408\) | −26.9611 | − | 68.0584i | −0.0660810 | − | 0.166810i | ||||
\(409\) | 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 | ||||
\(411\) | −39.6426 | − | 192.939i | −0.0964539 | − | 0.469437i | ||||
\(412\) | 180.170 | − | 65.5764i | 0.437305 | − | 0.159166i | ||||
\(413\) | −622.862 | − | 359.609i | −1.50814 | − | 0.870725i | ||||
\(414\) | 47.5751 | + | 202.494i | 0.114916 | + | 0.489116i | ||||
\(415\) | −85.0569 | − | 147.323i | −0.204956 | − | 0.354995i | ||||
\(416\) | −236.818 | + | 282.229i | −0.569275 | + | 0.678435i | ||||
\(417\) | 10.5666 | + | 375.753i | 0.0253397 | + | 0.901087i | ||||
\(418\) | 10.7038 | + | 60.7045i | 0.0256073 | + | 0.145226i | ||||
\(419\) | 115.552 | − | 20.3750i | 0.275781 | − | 0.0486277i | −0.0340470 | − | 0.999420i | \(-0.510840\pi\) |
0.309828 | + | 0.950793i | \(0.399728\pi\) | |||||||
\(420\) | −214.520 | + | 396.925i | −0.510762 | + | 0.945060i | ||||
\(421\) | −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 | ||||
\(423\) | 99.6282 | + | 50.2787i | 0.235528 | + | 0.118862i | ||||
\(424\) | 326.760 | − | 565.966i | 0.770661 | − | 1.33482i | ||||
\(425\) | 4.29744 | + | 11.8071i | 0.0101116 | + | 0.0277814i | ||||
\(426\) | 281.394 | + | 316.821i | 0.660549 | + | 0.743712i | ||||
\(427\) | −630.025 | + | 528.654i | −1.47547 | + | 1.23806i | ||||
\(428\) | 143.441 | − | 394.102i | 0.335143 | − | 0.920799i | ||||
\(429\) | 57.7393 | − | 391.521i | 0.134591 | − | 0.912636i | ||||
\(430\) | 39.5541 | − | 224.323i | 0.0919864 | − | 0.521681i | ||||
\(431\) | − | 263.580i | − | 0.611555i | −0.952103 | − | 0.305777i | \(-0.901084\pi\) | ||
0.952103 | − | 0.305777i | \(-0.0989163\pi\) | |||||||
\(432\) | −18.6261 | − | 40.2509i | −0.0431161 | − | 0.0931733i | ||||
\(433\) | −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 | ||||
\(435\) | 254.321 | − | 320.997i | 0.584645 | − | 0.737924i | ||||
\(436\) | 46.3025 | + | 16.8527i | 0.106198 | + | 0.0386531i | ||||
\(437\) | −57.8526 | − | 68.9461i | −0.132386 | − | 0.157771i | ||||
\(438\) | −301.224 | − | 100.141i | −0.687727 | − | 0.228632i | ||||
\(439\) | 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 | ||||
\(441\) | −65.8317 | + | 553.857i | −0.149278 | + | 1.25591i | ||||
\(442\) | 20.6021 | + | 35.6839i | 0.0466111 | + | 0.0807328i | ||||
\(443\) | −390.071 | + | 464.868i | −0.880520 | + | 1.04936i | 0.117891 | + | 0.993026i | \(0.462387\pi\) |
−0.998412 | + | 0.0563369i | \(0.982058\pi\) | |||||||
\(444\) | −119.638 | + | 73.6326i | −0.269454 | + | 0.165839i | ||||
\(445\) | −64.5191 | − | 365.906i | −0.144987 | − | 0.822260i | ||||
\(446\) | 226.648 | − | 39.9642i | 0.508180 | − | 0.0896058i | ||||
\(447\) | 317.250 | + | 515.464i | 0.709731 | + | 1.15316i | ||||
\(448\) | 254.259 | + | 213.348i | 0.567542 | + | 0.476224i | ||||
\(449\) | 347.745 | − | 200.771i | 0.774488 | − | 0.447151i | −0.0599853 | − | 0.998199i | \(-0.519105\pi\) |
0.834473 | + | 0.551048i | \(0.185772\pi\) | |||||||
\(450\) | −16.3832 | − | 38.1852i | −0.0364072 | − | 0.0848560i | ||||
\(451\) | 73.0755 | − | 126.570i | 0.162030 | − | 0.280644i | ||||
\(452\) | 16.3423 | + | 44.9002i | 0.0361556 | + | 0.0993368i | ||||
\(453\) | −121.274 | + | 364.791i | −0.267712 | + | 0.805279i | ||||
\(454\) | −4.58180 | + | 3.84458i | −0.0100921 | + | 0.00846825i | ||||
\(455\) | 217.859 | − | 598.563i | 0.478811 | − | 1.31552i | ||||
\(456\) | −82.1013 | − | 65.0475i | −0.180047 | − | 0.142648i | ||||
\(457\) | −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 | ||||||||
\(459\) | −85.0061 | + | 7.18658i | −0.185198 | + | 0.0156570i | ||||
\(460\) | 284.213 | 0.617855 | ||||||||
\(461\) | −773.480 | − | 136.385i | −1.67783 | − | 0.295847i | −0.747963 | − | 0.663740i | \(-0.768968\pi\) |
−0.929868 | + | 0.367893i | \(0.880079\pi\) | |||||||
\(462\) | −426.276 | − | 62.8648i | −0.922675 | − | 0.136071i | ||||
\(463\) | 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 | ||||
\(465\) | −267.098 | + | 237.231i | −0.574405 | + | 0.510174i | ||||
\(466\) | 153.344 | − | 55.8128i | 0.329065 | − | 0.119770i | ||||
\(467\) | −88.2727 | − | 50.9643i | −0.189021 | − | 0.109131i | 0.402503 | − | 0.915419i | \(-0.368140\pi\) |
−0.591524 | + | 0.806287i | \(0.701474\pi\) | |||||||
\(468\) | 146.899 | + | 224.300i | 0.313886 | + | 0.479274i | ||||
\(469\) | −511.569 | − | 886.063i | −1.09077 | − | 1.88926i | ||||
\(470\) | −49.8101 | + | 59.3613i | −0.105979 | + | 0.126301i | ||||
\(471\) | −366.709 | − | 198.189i | −0.778575 | − | 0.420784i | ||||
\(472\) | 91.5597 | + | 519.261i | 0.193982 | + | 1.10013i | ||||
\(473\) | −421.547 | + | 74.3300i | −0.891219 | + | 0.157146i | ||||
\(474\) | −70.9806 | + | 1.99606i | −0.149748 | + | 0.00421110i | ||||
\(475\) | 13.7726 | + | 11.5566i | 0.0289949 | + | 0.0243296i | ||||
\(476\) | −76.4491 | + | 44.1379i | −0.160607 | + | 0.0927267i | ||||
\(477\) | −521.553 | − | 554.978i | −1.09340 | − | 1.16348i | ||||
\(478\) | −85.7219 | + | 148.475i | −0.179334 | + | 0.310616i | ||||
\(479\) | 43.2210 | + | 118.749i | 0.0902318 | + | 0.247910i | 0.976597 | − | 0.215077i | \(-0.0690001\pi\) |
−0.886365 | + | 0.462986i | \(0.846778\pi\) | |||||||
\(480\) | 518.828 | − | 106.602i | 1.08089 | − | 0.222088i | ||||
\(481\) | 151.929 | − | 127.483i | 0.315860 | − | 0.265038i | ||||
\(482\) | 120.874 | − | 332.099i | 0.250776 | − | 0.689003i | ||||
\(483\) | 584.918 | − | 231.713i | 1.21101 | − | 0.479737i | ||||
\(484\) | −7.79280 | + | 44.1952i | −0.0161008 | + | 0.0913123i | ||||
\(485\) | 429.586i | 0.885745i | ||||||||
\(486\) | 279.331 | − | 39.5260i | 0.574756 | − | 0.0813292i | ||||
\(487\) | 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 | ||||
\(489\) | 44.0379 | + | 111.166i | 0.0900571 | + | 0.227333i | ||||
\(490\) | −363.940 | − | 132.463i | −0.742735 | − | 0.270334i | ||||
\(491\) | 203.177 | + | 242.137i | 0.413803 | + | 0.493151i | 0.932177 | − | 0.362003i | \(-0.117907\pi\) |
−0.518374 | + | 0.855154i | \(0.673463\pi\) | |||||||
\(492\) | 19.9284 | + | 96.9906i | 0.0405048 | + | 0.197135i | ||||
\(493\) | 75.2944 | − | 27.4049i | 0.152727 | − | 0.0555881i | ||||
\(494\) | 51.0594 | + | 29.4792i | 0.103359 | + | 0.0596744i | ||||
\(495\) | −414.607 | + | 389.637i | −0.837591 | + | 0.787145i | ||||
\(496\) | −18.1689 | − | 31.4695i | −0.0366309 | − | 0.0634466i | ||||
\(497\) | 823.833 | − | 981.806i | 1.65761 | − | 1.97547i | ||||
\(498\) | 3.09398 | + | 110.023i | 0.00621280 | + | 0.220929i | ||||
\(499\) | 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 | ||||
\(501\) | 236.711 | − | 437.985i | 0.472477 | − | 0.874222i | ||||
\(502\) | −110.983 | − | 93.1256i | −0.221081 | − | 0.185509i | ||||
\(503\) | −391.041 | + | 225.768i | −0.777418 | + | 0.448843i | −0.835515 | − | 0.549468i | \(-0.814830\pi\) |
0.0580963 | + | 0.998311i | \(0.481497\pi\) | |||||||
\(504\) | 612.531 | − | 401.159i | 1.21534 | − | 0.795951i | ||||
\(505\) | −12.8565 | + | 22.2680i | −0.0254583 | + | 0.0440951i | ||||
\(506\) | 92.8333 | + | 255.057i | 0.183465 | + | 0.504066i | ||||
\(507\) | 85.3113 | + | 96.0519i | 0.168267 | + | 0.189452i | ||||
\(508\) | −317.375 | + | 266.309i | −0.624754 | + | 0.524231i | ||||
\(509\) | −170.911 | + | 469.573i | −0.335778 | + | 0.922541i | 0.650800 | + | 0.759249i | \(0.274434\pi\) |
−0.986578 | + | 0.163292i | \(0.947789\pi\) | |||||||
\(510\) | 8.64255 | − | 58.6037i | 0.0169462 | − | 0.114909i | ||||
\(511\) | −166.722 | + | 945.527i | −0.326266 | + | 1.85035i | ||||
\(512\) | 104.621i | 0.204338i | ||||||||
\(513\) | −100.196 | + | 69.7223i | −0.195314 | + | 0.135911i | ||||
\(514\) | −530.596 | −1.03229 | ||||||||
\(515\) | 383.240 | + | 67.5756i | 0.744156 | + | 0.131215i | ||||
\(516\) | 180.091 | − | 227.307i | 0.349014 | − | 0.440517i | ||||
\(517\) | 136.838 | + | 49.8051i | 0.264678 | + | 0.0963348i | ||||
\(518\) | −138.800 | − | 165.415i | −0.267954 | − | 0.319335i | ||||
\(519\) | −31.0022 | − | 10.3066i | −0.0597344 | − | 0.0198585i | ||||
\(520\) | −438.816 | + | 159.716i | −0.843877 | + | 0.307146i | ||||
\(521\) | −595.632 | − | 343.888i | −1.14325 | − | 0.660054i | −0.196015 | − | 0.980601i | \(-0.562800\pi\) |
−0.947233 | + | 0.320546i | \(0.896133\pi\) | |||||||
\(522\) | −243.508 | + | 104.477i | −0.466491 | + | 0.200147i | ||||
\(523\) | 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 | ||||
\(525\) | −107.030 | + | 65.8730i | −0.203866 | + | 0.125472i | ||||
\(526\) | −94.3376 | − | 535.015i | −0.179349 | − | 1.01714i | ||||
\(527\) | −68.8332 | + | 12.1372i | −0.130613 | + | 0.0230306i | ||||
\(528\) | −30.3343 | − | 49.2869i | −0.0574514 | − | 0.0933465i | ||||
\(529\) | 101.644 | + | 85.2896i | 0.192144 | + | 0.161228i | ||||
\(530\) | 457.985 | − | 264.418i | 0.864123 | − | 0.498902i | ||||
\(531\) | 610.167 | + | 72.5247i | 1.14909 | + | 0.136581i | ||||
\(532\) | −63.1561 | + | 109.390i | −0.118715 | + | 0.205620i | ||||
\(533\) | −47.8111 | − | 131.360i | −0.0897020 | − | 0.246454i | ||||
\(534\) | −75.8387 | + | 228.123i | −0.142020 | + | 0.427197i | ||||
\(535\) | 652.079 | − | 547.160i | 1.21884 | − | 1.02273i | ||||
\(536\) | −256.542 | + | 704.844i | −0.478623 | + | 1.31501i | ||||
\(537\) | −664.465 | − | 526.444i | −1.23736 | − | 0.980343i | ||||
\(538\) | 63.9168 | − | 362.490i | 0.118804 | − | 0.673773i | ||||
\(539\) | 727.808i | 1.35029i | ||||||||
\(540\) | 34.7189 | − | 383.902i | 0.0642942 | − | 0.710930i | ||||
\(541\) | 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 | ||||
\(543\) | 322.905 | + | 47.6203i | 0.594668 | + | 0.0876984i | ||||
\(544\) | 97.3813 | + | 35.4439i | 0.179010 | + | 0.0651542i | ||||
\(545\) | 64.2851 | + | 76.6120i | 0.117954 | + | 0.140572i | ||||
\(546\) | −308.142 | + | 273.685i | −0.564362 | + | 0.501254i | ||||
\(547\) | 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 | ||||
\(549\) | 316.572 | − | 627.293i | 0.576633 | − | 1.14261i | ||||
\(550\) | −27.1099 | − | 46.9557i | −0.0492907 | − | 0.0853741i | ||||
\(551\) | 73.6967 | − | 87.8283i | 0.133751 | − | 0.159398i | ||||
\(552\) | −405.765 | − | 219.298i | −0.735082 | − | 0.397278i | ||||
\(553\) | 37.2950 | + | 211.511i | 0.0674412 | + | 0.382478i | ||||
\(554\) | 131.832 | − | 23.2456i | 0.237964 | − | 0.0419595i | ||||
\(555\) | −285.016 | + | 8.01501i | −0.513543 | + | 0.0144415i | ||||
\(556\) | −254.570 | − | 213.610i | −0.457861 | − | 0.384191i | ||||
\(557\) | 575.120 | − | 332.045i | 1.03253 | − | 0.596132i | 0.114822 | − | 0.993386i | \(-0.463370\pi\) |
0.917709 | + | 0.397254i | \(0.130037\pi\) | |||||||
\(558\) | 225.013 | − | 52.8658i | 0.403249 | − | 0.0947415i | ||||
\(559\) | −204.710 | + | 354.569i | −0.366208 | + | 0.634291i | ||||
\(560\) | −31.8589 | − | 87.5315i | −0.0568908 | − | 0.156306i | ||||
\(561\) | −109.041 | + | 22.4043i | −0.194369 | + | 0.0399364i | ||||
\(562\) | −72.5637 | + | 60.8882i | −0.129117 | + | 0.108342i | ||||
\(563\) | −118.905 | + | 326.689i | −0.211199 | + | 0.580264i | −0.999381 | − | 0.0351778i | \(-0.988800\pi\) |
0.788182 | + | 0.615442i | \(0.211022\pi\) | |||||||
\(564\) | −91.7223 | + | 36.3354i | −0.162628 | + | 0.0644246i | ||||
\(565\) | −16.8406 | + | 95.5076i | −0.0298063 | + | 0.169040i | ||||
\(566\) | − | 484.283i | − | 0.855623i | ||||||
\(567\) | −241.535 | − | 818.385i | −0.425987 | − | 1.44336i | ||||
\(568\) | −939.603 | −1.65423 | ||||||||
\(569\) | −385.078 | − | 67.8997i | −0.676763 | − | 0.119332i | −0.175306 | − | 0.984514i | \(-0.556091\pi\) |
−0.501457 | + | 0.865182i | \(0.667203\pi\) | |||||||
\(570\) | −31.2178 | − | 78.8037i | −0.0547680 | − | 0.138252i | ||||
\(571\) | −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 | ||||
\(573\) | 65.5891 | + | 319.219i | 0.114466 | + | 0.557102i | ||||
\(574\) | −143.021 | + | 52.0553i | −0.249165 | + | 0.0906887i | ||||
\(575\) | 68.5606 | + | 39.5835i | 0.119236 | + | 0.0688408i | ||||
\(576\) | −271.495 | − | 81.8576i | −0.471346 | − | 0.142114i | ||||
\(577\) | 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 | ||||
\(579\) | −16.8752 | − | 600.087i | −0.0291454 | − | 1.03642i | ||||
\(580\) | 62.8694 | + | 356.550i | 0.108396 | + | 0.614742i | ||||
\(581\) | 327.850 | − | 57.8088i | 0.564285 | − | 0.0994987i | ||||
\(582\) | 132.153 | − | 244.522i | 0.227067 | − | 0.420141i | ||||
\(583\) | −761.285 | − | 638.794i | −1.30581 | − | 1.09570i | ||||
\(584\) | 609.573 | − | 351.937i | 1.04379 | − | 0.602632i | ||||
\(585\) | 30.5829 | + | 543.339i | 0.0522785 | + | 0.928785i | ||||
\(586\) | −200.750 | + | 347.709i | −0.342576 | + | 0.593359i | ||||
\(587\) | −254.654 | − | 699.655i | −0.433822 | − | 1.19192i | −0.943448 | − | 0.331520i | \(-0.892439\pi\) |
0.509626 | − | 0.860396i | \(-0.329784\pi\) | |||||||
\(588\) | −327.443 | − | 368.668i | −0.556876 | − | 0.626986i | ||||
\(589\) | −76.6133 | + | 64.2862i | −0.130073 | + | 0.109145i | ||||
\(590\) | −145.931 | + | 400.942i | −0.247340 | + | 0.679562i | ||||
\(591\) | −128.116 | + | 868.733i | −0.216778 | + | 1.46994i | ||||
\(592\) | 5.03630 | − | 28.5623i | 0.00850726 | − | 0.0482471i | ||||
\(593\) | 625.722i | 1.05518i | 0.849499 | + | 0.527591i | \(0.176904\pi\) | ||||
−0.849499 | + | 0.527591i | \(0.823096\pi\) | |||||||
\(594\) | 355.860 | − | 94.2376i | 0.599091 | − | 0.158649i | ||||
\(595\) | −179.170 | −0.301126 | ||||||||
\(596\) | −526.963 | − | 92.9177i | −0.884165 | − | 0.155902i | ||||
\(597\) | −153.343 | + | 193.546i | −0.256856 | + | 0.324197i | ||||
\(598\) | 243.957 | + | 88.7932i | 0.407955 | + | 0.148484i | ||||
\(599\) | −368.344 | − | 438.975i | −0.614932 | − | 0.732847i | 0.365258 | − | 0.930906i | \(-0.380981\pi\) |
−0.980190 | + | 0.198059i | \(0.936536\pi\) | |||||||
\(600\) | 87.4307 | + | 29.0660i | 0.145718 | + | 0.0484434i | ||||
\(601\) | −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 | ||||
\(603\) | 700.128 | + | 523.351i | 1.16107 | + | 0.867912i | ||||
\(604\) | −169.925 | − | 294.319i | −0.281333 | − | 0.487283i | ||||
\(605\) | −58.5483 | + | 69.7752i | −0.0967741 | + | 0.115331i | ||||
\(606\) | 14.1682 | − | 8.72004i | 0.0233799 | − | 0.0143895i | ||||
\(607\) | −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 | ||||
\(609\) | 420.075 | + | 682.533i | 0.689778 | + | 1.12074i | ||||
\(610\) | 373.759 | + | 313.621i | 0.612720 | + | 0.514133i | ||||
\(611\) | 120.623 | − | 69.6414i | 0.197418 | − | 0.113979i | ||||
\(612\) | 45.1545 | − | 60.4067i | 0.0737819 | − | 0.0987038i | ||||
\(613\) | 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 | ||||
\(615\) | −63.4002 | + | 190.708i | −0.103090 | + | 0.310095i | ||||
\(616\) | 731.912 | − | 614.147i | 1.18817 | − | 0.996991i | ||||
\(617\) | 144.247 | − | 396.317i | 0.233788 | − | 0.642328i | −0.766212 | − | 0.642588i | \(-0.777861\pi\) |
1.00000 | 0.000260046i | \(8.27751e-5\pi\) | ||||||||
\(618\) | −197.354 | − | 156.360i | −0.319343 | − | 0.253010i | ||||
\(619\) | 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 | ||||||
\(621\) | −381.184 | + | 378.960i | −0.613823 | + | 0.610242i | ||||
\(622\) | 521.392 | 0.838250 | ||||||||
\(623\) | 716.066 | + | 126.262i | 1.14938 | + | 0.202667i | ||||
\(624\) | −54.7628 | − | 8.07611i | −0.0877609 | − | 0.0129425i | ||||
\(625\) | 665.870 | + | 242.357i | 1.06539 | + | 0.387771i | ||||
\(626\) | 8.08756 | + | 9.63837i | 0.0129194 | + | 0.0153968i | ||||
\(627\) | −119.092 | + | 105.775i | −0.189940 | + | 0.168701i | ||||
\(628\) | 346.285 | − | 126.037i | 0.551409 | − | 0.200696i | ||||
\(629\) | −48.3124 | − | 27.8932i | −0.0768083 | − | 0.0443453i | ||||
\(630\) | 591.571 | − | 33.2977i | 0.939001 | − | 0.0528535i | ||||
\(631\) | 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 | ||||
\(633\) | 305.740 | + | 165.239i | 0.483002 | + | 0.261040i | ||||
\(634\) | −43.9956 | − | 249.512i | −0.0693937 | − | 0.393551i | ||||
\(635\) | −828.122 | + | 146.020i | −1.30413 | + | 0.229953i | ||||
\(636\) | 673.021 | − | 18.9262i | 1.05821 | − | 0.0297581i | ||||
\(637\) | 533.269 | + | 447.466i | 0.837157 | + | 0.702458i | ||||
\(638\) | −299.439 | + | 172.881i | −0.469340 | + | 0.270973i | ||||
\(639\) | −316.089 | + | 1048.36i | −0.494661 | + | 1.64063i | ||||
\(640\) | −254.659 | + | 441.082i | −0.397904 | + | 0.689191i | ||||
\(641\) | −56.5257 | − | 155.303i | −0.0881837 | − | 0.242283i | 0.887760 | − | 0.460308i | \(-0.152261\pi\) |
−0.975943 | + | 0.218025i | \(0.930039\pi\) | |||||||
\(642\) | −539.489 | + | 110.847i | −0.840325 | + | 0.172659i | ||||
\(643\) | 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 | ||||
\(645\) | 547.231 | − | 216.784i | 0.848421 | − | 0.336099i | ||||
\(646\) | 2.87977 | − | 16.3320i | 0.00445785 | − | 0.0252817i | ||||
\(647\) | 222.504i | 0.343900i | 0.985106 | + | 0.171950i | \(0.0550068\pi\) | ||||
−0.985106 | + | 0.171950i | \(0.944993\pi\) | |||||||
\(648\) | −345.784 | + | 521.300i | −0.533618 | + | 0.804475i | ||||
\(649\) | 801.803 | 1.23544 | ||||||||
\(650\) | −51.0723 | − | 9.00542i | −0.0785728 | − | 0.0138545i | ||||
\(651\) | −257.481 | − | 649.964i | −0.395516 | − | 0.998409i | ||||
\(652\) | −99.3323 | − | 36.1540i | −0.152350 | − | 0.0554509i | ||||
\(653\) | −299.851 | − | 357.348i | −0.459190 | − | 0.547241i | 0.485916 | − | 0.874006i | \(-0.338486\pi\) |
−0.945106 | + | 0.326764i | \(0.894042\pi\) | |||||||
\(654\) | −13.0233 | − | 63.3839i | −0.0199133 | − | 0.0969172i | ||||
\(655\) | −498.345 | + | 181.383i | −0.760833 | + | 0.276920i | ||||
\(656\) | −17.7037 | − | 10.2212i | −0.0269873 | − | 0.0155811i | ||||
\(657\) | −187.610 | − | 798.526i | −0.285556 | − | 1.21541i | ||||
\(658\) | −75.8234 | − | 131.330i | −0.115233 | − | 0.199590i | ||||
\(659\) | −133.876 | + | 159.547i | −0.203150 | + | 0.242104i | −0.857994 | − | 0.513659i | \(-0.828290\pi\) |
0.654845 | + | 0.755764i | \(0.272734\pi\) | |||||||
\(660\) | −14.1392 | − | 502.794i | −0.0214230 | − | 0.761809i | ||||
\(661\) | −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 | ||||
\(663\) | −50.6241 | + | 93.6695i | −0.0763561 | + | 0.141281i | ||||
\(664\) | −186.961 | − | 156.879i | −0.281567 | − | 0.236263i | ||||
\(665\) | −222.024 | + | 128.186i | −0.333871 | + | 0.192760i | ||||
\(666\) | 164.698 | + | 83.1171i | 0.247295 | + | 0.124800i | ||||
\(667\) | 252.425 | − | 437.214i | 0.378449 | − | 0.655493i | ||||
\(668\) | 150.535 | + | 413.591i | 0.225352 | + | 0.619149i | ||||
\(669\) | 394.926 | + | 444.647i | 0.590323 | + | 0.664645i | ||||
\(670\) | −464.967 | + | 390.154i | −0.693981 | + | 0.582319i | ||||
\(671\) | 313.590 | − | 861.581i | 0.467347 | − | 1.28403i | ||||
\(672\) | −151.228 | + | 1025.45i | −0.225041 | + | 1.52597i | ||||
\(673\) | 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 | ||||||||
\(675\) | 61.8427 | − | 87.7730i | 0.0916188 | − | 0.130034i | ||||
\(676\) | −113.573 | −0.168007 | ||||||||
\(677\) | −140.866 | − | 24.8384i | −0.208073 | − | 0.0366890i | 0.0686398 | − | 0.997642i | \(-0.478134\pi\) |
−0.276713 | + | 0.960953i | \(0.589245\pi\) | |||||||
\(678\) | 38.9666 | − | 49.1827i | 0.0574729 | − | 0.0725409i | ||||
\(679\) | −789.987 | − | 287.532i | −1.16346 | − | 0.423463i | ||||
\(680\) | 84.4318 | + | 100.622i | 0.124164 | + | 0.147973i | ||||
\(681\) | −14.6663 | − | 4.87577i | −0.0215365 | − | 0.00715972i | ||||
\(682\) | 283.421 | − | 103.157i | 0.415574 | − | 0.151257i | ||||
\(683\) | 784.050 | + | 452.671i | 1.14795 | + | 0.662769i | 0.948387 | − | 0.317116i | \(-0.102714\pi\) |
0.199563 | + | 0.979885i | \(0.436048\pi\) | |||||||
\(684\) | 12.7371 | − | 107.160i | 0.0186215 | − | 0.156667i | ||||
\(685\) | 176.714 | + | 306.078i | 0.257977 | + | 0.446830i | ||||
\(686\) | 101.984 | − | 121.539i | 0.148664 | − | 0.177171i | ||||
\(687\) | −902.761 | + | 555.617i | −1.31406 | + | 0.808758i | ||||
\(688\) | 10.3967 | + | 58.9625i | 0.0151115 | + | 0.0857013i | ||||
\(689\) | −936.096 | + | 165.059i | −1.35863 | + | 0.239563i | ||||
\(690\) | −195.630 | − | 317.858i | −0.283522 | − | 0.460664i | ||||
\(691\) | 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 | ||||
\(693\) | −439.016 | − | 1023.23i | −0.633500 | − | 1.47653i | ||||
\(694\) | −137.087 | + | 237.441i | −0.197531 | + | 0.342134i | ||||
\(695\) | −230.690 | − | 633.817i | −0.331929 | − | 0.911967i | ||||
\(696\) | 185.355 | − | 557.549i | 0.266315 | − | 0.801077i | ||||
\(697\) | −30.1213 | + | 25.2748i | −0.0432156 | + | 0.0362622i | ||||
\(698\) | 95.2117 | − | 261.592i | 0.136406 | − | 0.374773i | ||||
\(699\) | 330.519 | + | 261.864i | 0.472845 | + | 0.374627i | ||||
\(700\) | 19.2932 | − | 109.417i | 0.0275617 | − | 0.156310i | ||||
\(701\) | − | 905.026i | − | 1.29105i | −0.763739 | − | 0.645525i | \(-0.776639\pi\) | ||
0.763739 | − | 0.645525i | \(-0.223361\pi\) | |||||||
\(702\) | 149.739 | − | 318.679i | 0.213303 | − | 0.453959i | ||||
\(703\) | −79.8237 | −0.113547 | ||||||||
\(704\) | −364.401 | − | 64.2538i | −0.517616 | − | 0.0912696i | ||||
\(705\) | −198.098 | − | 29.2144i | −0.280991 | − | 0.0414389i | ||||
\(706\) | 27.9182 | + | 10.1614i | 0.0395442 | + | 0.0143929i | ||||
\(707\) | −32.3447 | − | 38.5469i | −0.0457492 | − | 0.0545217i | ||||
\(708\) | −406.150 | + | 360.734i | −0.573658 | + | 0.509511i | ||||
\(709\) | 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 | ||||
\(711\) | −100.531 | − | 153.501i | −0.141393 | − | 0.215894i | ||||
\(712\) | −266.529 | − | 461.642i | −0.374338 | − | 0.648373i | ||||
\(713\) | −283.074 | + | 337.355i | −0.397019 | + | 0.473148i | ||||
\(714\) | 101.984 | + | 55.1180i | 0.142835 | + | 0.0771960i | ||||
\(715\) | 123.311 | + | 699.329i | 0.172462 | + | 0.978083i | ||||
\(716\) | 738.060 | − | 130.140i | 1.03081 | − | 0.181760i | ||||
\(717\) | −442.846 | + | 12.4534i | −0.617638 | + | 0.0173687i | ||||
\(718\) | 17.2315 | + | 14.4590i | 0.0239994 | + | 0.0201379i | ||||
\(719\) | −389.328 | + | 224.778i | −0.541485 | + | 0.312626i | −0.745680 | − | 0.666304i | \(-0.767875\pi\) |
0.204196 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(720\) | 54.4992 | + | 57.9919i | 0.0756934 | + | 0.0805444i | ||||
\(721\) | −380.779 | + | 659.529i | −0.528127 | + | 0.914742i | ||||
\(722\) | 135.227 | + | 371.534i | 0.187295 | + | 0.514589i | ||||
\(723\) | 894.553 | − | 183.801i | 1.23728 | − | 0.254220i | ||||
\(724\) | −221.045 | + | 185.479i | −0.305310 | + | 0.256186i | ||||
\(725\) | −34.4922 | + | 94.7665i | −0.0475754 | + | 0.130712i | ||||
\(726\) | 54.7908 | − | 21.7052i | 0.0754695 | − | 0.0298969i | ||||
\(727\) | 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 | ||||||
\(729\) | 465.317 | + | 561.178i | 0.638295 | + | 0.769792i | ||||
\(730\) | 569.582 | 0.780250 | ||||||||
\(731\) | 113.413 | + | 19.9978i | 0.155148 | + | 0.0273568i | ||||
\(732\) | 228.780 | + | 577.515i | 0.312542 | + | 0.788955i | ||||
\(733\) | −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 | ||||
\(735\) | −201.424 | − | 980.321i | −0.274046 | − | 1.33377i | ||||
\(736\) | 613.567 | − | 223.320i | 0.833650 | − | 0.303424i | ||||
\(737\) | 987.805 | + | 570.310i | 1.34031 | + | 0.773826i | ||||
\(738\) | 94.7550 | − | 89.0482i | 0.128394 | − | 0.120661i | ||||
\(739\) | −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 | ||||
\(741\) | 4.28263 | + | 152.292i | 0.00577953 | + | 0.205522i | ||||
\(742\) | 179.711 | + | 1019.19i | 0.242198 | + | 1.37357i | ||||
\(743\) | −36.2725 | + | 6.39582i | −0.0488190 | + | 0.00860811i | −0.198004 | − | 0.980201i | \(-0.563446\pi\) |
0.149185 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(744\) | −243.685 | + | 450.889i | −0.327534 | + | 0.606034i | ||||
\(745\) | −831.967 | − | 698.103i | −1.11673 | − | 0.937051i | ||||
\(746\) | −179.793 | + | 103.803i | −0.241009 | + | 0.139146i | ||||
\(747\) | −237.932 | + | 155.827i | −0.318517 | + | 0.208603i | ||||
\(748\) | 49.2061 | − | 85.2274i | 0.0657835 | − | 0.113940i | ||||
\(749\) | 569.747 | + | 1565.37i | 0.760677 | + | 2.08994i | ||||
\(750\) | −261.744 | − | 294.697i | −0.348992 | − | 0.392930i | ||||
\(751\) | 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 | ||||
\(753\) | 54.6197 | − | 370.367i | 0.0725362 | − | 0.491856i | ||||
\(754\) | −57.4279 | + | 325.690i | −0.0761644 | + | 0.431950i | ||||
\(755\) | − | 689.781i | − | 0.913617i | ||||||
\(756\) | 682.738 | + | 320.801i | 0.903093 | + | 0.424339i | ||||
\(757\) | −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 | ||||
\(759\) | −435.559 | + | 549.752i | −0.573859 | + | 0.724310i | ||||
\(760\) | 176.615 | + | 64.2827i | 0.232388 | + | 0.0845825i | ||||
\(761\) | 935.204 | + | 1114.53i | 1.22891 | + | 1.46456i | 0.839374 | + | 0.543555i | \(0.182922\pi\) |
0.389541 | + | 0.921009i | \(0.372634\pi\) | |||||||
\(762\) | 516.291 | + | 171.639i | 0.677547 | + | 0.225248i | ||||
\(763\) | −183.913 | + | 66.9389i | −0.241039 | + | 0.0877312i | ||||
\(764\) | −249.505 | − | 144.052i | −0.326577 | − | 0.188549i | ||||
\(765\) | 140.672 | − | 60.3551i | 0.183886 | − | 0.0788956i | ||||
\(766\) | 9.99966 | + | 17.3199i | 0.0130544 | + | 0.0226109i | ||||
\(767\) | 492.959 | − | 587.486i | 0.642711 | − | 0.765953i | ||||
\(768\) | 602.634 | − | 370.900i | 0.784680 | − | 0.482942i | ||||
\(769\) | −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 | ||||
\(771\) | −718.654 | − | 1167.66i | −0.932106 | − | 1.51448i | ||||
\(772\) | 406.555 | + | 341.140i | 0.526626 | + | 0.441891i | ||||
\(773\) | −547.928 | + | 316.347i | −0.708834 | + | 0.409245i | −0.810629 | − | 0.585560i | \(-0.800875\pi\) |
0.101795 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(774\) | −378.175 | − | 44.9501i | −0.488599 | − | 0.0580750i | ||||
\(775\) | 43.9854 | − | 76.1850i | 0.0567554 | − | 0.0983032i | ||||
\(776\) | 210.794 | + | 579.152i | 0.271642 | + | 0.746330i | ||||
\(777\) | 176.029 | − | 529.495i | 0.226549 | − | 0.681461i | ||||
\(778\) | 281.722 | − | 236.392i | 0.362110 | − | 0.303846i | ||||
\(779\) | −19.2431 | + | 52.8699i | −0.0247023 | + | 0.0678690i | ||||
\(780\) | −377.093 | − | 298.765i | −0.483453 | − | 0.383031i | ||||
\(781\) | −248.112 | + | 1407.12i | −0.317686 | + | 1.80168i | ||||
\(782\) | − | 73.0247i | − | 0.0933820i | ||||||
\(783\) | −559.732 | − | 394.373i | −0.714856 | − | 0.503670i | ||||
\(784\) | 101.800 | 0.129847 | ||||||||
\(785\) | 736.585 | + | 129.880i | 0.938325 | + | 0.165452i | ||||
\(786\) | 339.459 | + | 50.0616i | 0.431882 | + | 0.0636915i | ||||
\(787\) | 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 | ||||
\(789\) | 1049.61 | − | 932.244i | 1.33031 | − | 1.18155i | ||||
\(790\) | 119.729 | − | 43.5779i | 0.151556 | − | 0.0551619i | ||||
\(791\) | −164.362 | − | 94.8944i | −0.207790 | − | 0.119968i | ||||
\(792\) | −367.767 | + | 728.738i | −0.464353 | + | 0.920124i | ||||
\(793\) | −438.486 | − | 759.481i | −0.552946 | − | 0.957731i | ||||
\(794\) | −200.056 | + | 238.418i | −0.251960 | + | 0.300275i | ||||
\(795\) | 1202.20 | + | 649.735i | 1.51220 | + | 0.817277i | ||||
\(796\) | −37.9072 | − | 214.982i | −0.0476221 | − | 0.270078i | ||||
\(797\) | 1233.67 | − | 217.529i | 1.54789 | − | 0.272934i | 0.666564 | − | 0.745448i | \(-0.267764\pi\) |
0.881323 | + | 0.472514i | \(0.156653\pi\) | |||||||
\(798\) | 165.811 | − | 4.66280i | 0.207783 | − | 0.00584311i | ||||
\(799\) | −30.0119 | − | 25.1830i | −0.0375618 | − | 0.0315181i | ||||
\(800\) | −112.957 | + | 65.2156i | −0.141196 | + | 0.0815196i | ||||
\(801\) | −604.740 | + | 142.081i | −0.754981 | + | 0.177380i | ||||
\(802\) | 56.5776 | − | 97.9952i | 0.0705456 | − | 0.122189i | ||||
\(803\) | −366.084 | − | 1005.81i | −0.455895 | − | 1.25256i | ||||
\(804\) | −756.953 | + | 155.529i | −0.941483 | + | 0.193444i | ||||
\(805\) | −864.781 | + | 725.637i | −1.07426 | + | 0.901413i | ||||
\(806\) | 98.6675 | − | 271.087i | 0.122416 | − | 0.336336i | ||||
\(807\) | 884.288 | − | 350.307i | 1.09577 | − | 0.434086i | ||||
\(808\) | −6.40587 | + | 36.3295i | −0.00792806 | + | 0.0449622i | ||||
\(809\) | 1021.88i | 1.26313i | 0.775321 | + | 0.631567i | \(0.217588\pi\) | ||||
−0.775321 | + | 0.631567i | \(0.782412\pi\) | |||||||
\(810\) | −453.245 | + | 225.419i | −0.559562 | + | 0.278295i | ||||
\(811\) | −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 | ||||
\(813\) | 127.835 | + | 322.696i | 0.157239 | + | 0.396921i | ||||
\(814\) | 226.211 | + | 82.3342i | 0.277901 | + | 0.101148i | ||||
\(815\) | −137.910 | − | 164.355i | −0.169215 | − | 0.201662i | ||||
\(816\) | 3.13374 | + | 15.2518i | 0.00384037 | + | 0.0186909i | ||||
\(817\) | 154.846 | − | 56.3595i | 0.189531 | − | 0.0689835i | ||||
\(818\) | 407.542 | + | 235.294i | 0.498217 | + | 0.287646i | ||||
\(819\) | −1019.64 | − | 307.429i | −1.24498 | − | 0.375371i | ||||
\(820\) | −88.8346 | − | 153.866i | −0.108335 | − | 0.187641i | ||||
\(821\) | −6.23245 | + | 7.42755i | −0.00759129 | + | 0.00904695i | −0.769827 | − | 0.638253i | \(-0.779657\pi\) |
0.762235 | + | 0.647300i | \(0.224102\pi\) | |||||||
\(822\) | −6.42805 | − | 228.584i | −0.00782001 | − | 0.278082i | ||||
\(823\) | 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 | ||||
\(825\) | 66.6153 | − | 123.258i | 0.0807458 | − | 0.149403i | ||||
\(826\) | −639.636 | − | 536.719i | −0.774378 | − | 0.649780i | ||||
\(827\) | −583.611 | + | 336.948i | −0.705696 | + | 0.407434i | −0.809465 | − | 0.587168i | \(-0.800243\pi\) |
0.103769 | + | 0.994601i | \(0.466910\pi\) | |||||||
\(828\) | −26.7044 | − | 474.434i | −0.0322517 | − | 0.572988i | ||||
\(829\) | −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 | ||||
\(831\) | 229.713 | + | 258.633i | 0.276429 | + | 0.311231i | ||||
\(832\) | −271.118 | + | 227.495i | −0.325863 | + | 0.273431i | ||||
\(833\) | 66.9709 | − | 184.001i | 0.0803972 | − | 0.220890i | ||||
\(834\) | −63.6704 | + | 431.738i | −0.0763434 | + | 0.517672i | ||||
\(835\) | −155.124 | + | 879.753i | −0.185778 | + | 1.05360i | ||||
\(836\) | − | 140.816i | − | 0.168440i | ||||||
\(837\) | 421.103 | + | 423.574i | 0.503110 | + | 0.506062i | ||||
\(838\) | 136.221 | 0.162555 | ||||||||
\(839\) | 629.012 | + | 110.912i | 0.749716 | + | 0.132195i | 0.535434 | − | 0.844577i | \(-0.320148\pi\) |
0.214282 | + | 0.976772i | \(0.431259\pi\) | |||||||
\(840\) | −815.882 | + | 1029.79i | −0.971288 | + | 1.22593i | ||||
\(841\) | −185.952 | − | 67.6809i | −0.221108 | − | 0.0804767i | ||||
\(842\) | −389.047 | − | 463.648i | −0.462051 | − | 0.550650i | ||||
\(843\) | −232.277 | − | 77.2195i | −0.275536 | − | 0.0916008i | ||||
\(844\) | −288.712 | + | 105.082i | −0.342075 | + | 0.124505i | ||||
\(845\) | −199.631 | − | 115.257i | −0.236250 | − | 0.136399i | ||||
\(846\) | 103.771 | + | 77.5698i | 0.122661 | + | 0.0916900i | ||||
\(847\) | −89.1253 | − | 154.370i | −0.105225 | − | 0.182254i | ||||
\(848\) | −89.3493 | + | 106.482i | −0.105365 | + | 0.125569i | ||||
\(849\) | 1065.74 | − | 655.926i | 1.25529 | − | 0.772587i | ||||
\(850\) | 2.53306 | + | 14.3657i | 0.00298008 | + | 0.0169008i | ||||
\(851\) | −346.151 | + | 61.0358i | −0.406758 | + | 0.0717225i | ||||
\(852\) | −507.386 | − | 824.395i | −0.595523 | − | 0.967600i | ||||
\(853\) | 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 | ||||
\(855\) | 131.138 | − | 175.434i | 0.153378 | − | 0.205185i | ||||
\(856\) | 610.623 | − | 1057.63i | 0.713345 | − | 1.23555i | ||||
\(857\) | 368.296 | + | 1011.88i | 0.429750 | + | 1.18073i | 0.945965 | + | 0.324269i | \(0.105118\pi\) |
−0.516215 | + | 0.856459i | \(0.672659\pi\) | |||||||
\(858\) | 144.945 | − | 435.995i | 0.168934 | − | 0.508153i | ||||
\(859\) | −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 | ||||
\(861\) | −308.267 | − | 244.235i | −0.358034 | − | 0.283664i | ||||
\(862\) | 53.1375 | − | 301.358i | 0.0616444 | − | 0.349603i | ||||
\(863\) | − | 1599.17i | − | 1.85304i | −0.376244 | − | 0.926520i | \(-0.622785\pi\) | ||
0.376244 | − | 0.926520i | \(-0.377215\pi\) | |||||||
\(864\) | −226.698 | − | 856.057i | −0.262382 | − | 0.990807i | ||||
\(865\) | 58.6217 | 0.0677708 | ||||||||
\(866\) | −802.629 | − | 141.525i | −0.926823 | − | 0.163424i | ||||
\(867\) | −828.094 | − | 122.123i | −0.955126 | − | 0.140857i | ||||
\(868\) | 580.776 | + | 211.385i | 0.669097 | + | 0.243531i | ||||
\(869\) | −153.906 | − | 183.418i | −0.177107 | − | 0.211067i | ||||
\(870\) | 355.484 | − | 315.733i | 0.408602 | − | 0.362912i | ||||
\(871\) | 1025.19 | − | 373.137i | 1.17702 | − | 0.428400i | ||||
\(872\) | 124.260 | + | 71.7413i | 0.142500 | + | 0.0822722i | ||||
\(873\) | 717.103 | − | 40.3635i | 0.821423 | − | 0.0462354i | ||||
\(874\) | −52.2449 | − | 90.4908i | −0.0597767 | − | 0.103536i | ||||
\(875\) | −766.304 | + | 913.245i | −0.875776 | + | 1.04371i | ||||
\(876\) | 637.954 | + | 344.785i | 0.728258 | + | 0.393590i | ||||
\(877\) | −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 | ||||
\(879\) | −1037.09 | + | 29.1642i | −1.17985 | + | 0.0331789i | ||||
\(880\) | 79.5498 | + | 66.7502i | 0.0903975 | + | 0.0758525i | ||||
\(881\) | −1046.81 | + | 604.374i | −1.18820 | + | 0.686009i | −0.957898 | − | 0.287109i | \(-0.907306\pi\) |
−0.230305 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(882\) | −186.924 | + | 619.967i | −0.211932 | + | 0.702910i | ||||
\(883\) | 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 | ||||
\(885\) | −1079.99 | + | 221.902i | −1.22033 | + | 0.250737i | ||||
\(886\) | −539.694 | + | 452.857i | −0.609136 | + | 0.511126i | ||||
\(887\) | 34.7360 | − | 95.4364i | 0.0391612 | − | 0.107595i | −0.918571 | − | 0.395256i | \(-0.870656\pi\) |
0.957732 | + | 0.287662i | \(0.0928779\pi\) | |||||||
\(888\) | −380.316 | + | 150.661i | −0.428283 | + | 0.169663i | ||||
\(889\) | 285.757 | − | 1620.61i | 0.321436 | − | 1.82296i | ||||
\(890\) | − | 431.356i | − | 0.484670i | ||||||
\(891\) | 689.371 | + | 655.489i | 0.773705 | + | 0.735678i | ||||
\(892\) | −525.755 | −0.589412 | ||||||||
\(893\) | −55.2071 | − | 9.73450i | −0.0618220 | − | 0.0109009i | ||||
\(894\) | 258.802 | + | 653.301i | 0.289488 | + | 0.730761i | ||||
\(895\) | 1429.39 | + | 520.255i | 1.59708 | + | 0.581290i | ||||
\(896\) | −640.678 | − | 763.531i | −0.715043 | − | 0.852155i | ||||
\(897\) | 135.019 | + | 657.131i | 0.150523 | + | 0.732588i | ||||
\(898\) | 438.061 | − | 159.441i | 0.487818 | − | 0.177551i | ||||
\(899\) | −485.835 | − | 280.497i | −0.540417 | − | 0.312010i | ||||
\(900\) | 21.7104 | + | 92.4062i | 0.0241227 | + | 0.102674i | ||||
\(901\) | 133.684 | + | 231.548i | 0.148373 | + | 0.256990i | ||||
\(902\) | 109.065 | − | 129.979i | 0.120915 | − | 0.144101i | ||||
\(903\) | 32.3796 | + | 1151.43i | 0.0358578 | + | 1.27511i | ||||
\(904\) | 24.1609 | + | 137.023i | 0.0267267 | + | 0.151575i | ||||
\(905\) | −576.769 | + | 101.700i | −0.637313 | + | 0.112376i | ||||
\(906\) | −212.197 | + | 392.626i | −0.234213 | + | 0.433362i | ||||
\(907\) | 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 | ||||
\(909\) | 38.3797 | + | 19.3688i | 0.0422219 | + | 0.0213078i | ||||
\(910\) | 369.753 | − | 640.431i | 0.406322 | − | 0.703771i | ||||
\(911\) | 106.953 | + | 293.850i | 0.117401 | + | 0.322558i | 0.984450 | − | 0.175666i | \(-0.0562080\pi\) |
−0.867048 | + | 0.498224i | \(0.833986\pi\) | |||||||
\(912\) | 14.7950 | + | 16.6577i | 0.0162226 | + | 0.0182650i | ||||
\(913\) | −284.305 | + | 238.560i | −0.311396 | + | 0.261292i | ||||
\(914\) | −58.4144 | + | 160.492i | −0.0639107 | + | 0.175593i | ||||
\(915\) | −183.944 | + | 1247.30i | −0.201032 | + | 1.36316i | ||||
\(916\) | 162.732 | − | 922.898i | 0.177655 | − | 1.00753i | ||||
\(917\) | − | 1037.84i | − | 1.13177i | ||||||
\(918\) | −98.6384 | − | 8.92054i | −0.107449 | − | 0.00971737i | ||||
\(919\) | 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 | ||||
\(921\) | 1075.58 | − | 1357.57i | 1.16784 | − | 1.47401i | ||||
\(922\) | −856.844 | − | 311.866i | −0.929332 | − | 0.338249i | ||||
\(923\) | 878.459 | + | 1046.91i | 0.951743 | + | 1.13424i | ||||
\(924\) | 934.076 | + | 310.530i | 1.01090 | + | 0.336072i | ||||
\(925\) | 65.9791 | − | 24.0144i | 0.0713287 | − | 0.0259615i | ||||
\(926\) | 360.397 | + | 208.075i | 0.389197 | + | 0.224703i | ||||
\(927\) | 76.7941 | − | 646.087i | 0.0828416 | − | 0.696966i | ||||
\(928\) | 415.883 | + | 720.330i | 0.448149 | + | 0.776218i | ||||
\(929\) | 854.746 | − | 1018.65i | 0.920071 | − | 1.09650i | −0.0749849 | − | 0.997185i | \(-0.523891\pi\) |
0.995056 | − | 0.0993136i | \(-0.0316647\pi\) | |||||||
\(930\) | −353.206 | + | 217.385i | −0.379791 | + | 0.233748i | ||||
\(931\) | −48.6528 | − | 275.924i | −0.0522587 | − | 0.296374i | ||||
\(932\) | −367.127 | + | 64.7343i | −0.393913 | + | 0.0694574i | ||||
\(933\) | 706.187 | + | 1147.41i | 0.756899 | + | 1.22980i | ||||
\(934\) | −90.6501 | − | 76.0644i | −0.0970557 | − | 0.0814394i | ||||
\(935\) | 172.983 | − | 99.8717i | 0.185008 | − | 0.106815i | ||||
\(936\) | 307.843 | + | 717.503i | 0.328892 | + | 0.766563i | ||||
\(937\) | −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 | ||||
\(939\) | −10.2568 | + | 30.8524i | −0.0109231 | + | 0.0328567i | ||||
\(940\) | 135.608 | − | 113.789i | 0.144264 | − | 0.121052i | ||||
\(941\) | 265.840 | − | 730.391i | 0.282508 | − | 0.776186i | −0.714553 | − | 0.699581i | \(-0.753370\pi\) |
0.997062 | − | 0.0766044i | \(-0.0244078\pi\) | |||||||
\(942\) | −379.313 | − | 300.523i | −0.402667 | − | 0.319027i | ||||
\(943\) | −43.0206 | + | 243.982i | −0.0456210 | + | 0.258729i | ||||
\(944\) | − | 112.150i | − | 0.118803i | ||||||
\(945\) | 874.517 | + | 1256.75i | 0.925415 | + | 1.32989i | ||||
\(946\) | −496.949 | −0.525316 | ||||||||
\(947\) | −270.124 | − | 47.6301i | −0.285242 | − | 0.0502958i | 0.0291967 | − | 0.999574i | \(-0.490705\pi\) |
−0.314438 | + | 0.949278i | \(0.601816\pi\) | |||||||
\(948\) | 160.480 | + | 23.6668i | 0.169283 | + | 0.0249649i | ||||
\(949\) | −962.034 | − | 350.152i | −1.01373 | − | 0.368969i | ||||
\(950\) | 13.4167 | + | 15.9894i | 0.0141229 | + | 0.0168310i | ||||
\(951\) | 489.501 | − | 434.765i | 0.514723 | − | 0.457166i | ||||
\(952\) | −241.551 | + | 87.9173i | −0.253730 | + | 0.0923501i | ||||
\(953\) | 858.313 | + | 495.548i | 0.900644 | + | 0.519987i | 0.877409 | − | 0.479743i | \(-0.159270\pi\) |
0.0232347 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(954\) | −484.421 | − | 739.664i | −0.507779 | − | 0.775329i | ||||
\(955\) | −292.376 | − | 506.410i | −0.306153 | − | 0.530272i | ||||
\(956\) | 251.751 | − | 300.025i | 0.263338 | − | 0.313834i | ||||
\(957\) | −786.020 | − | 424.808i | −0.821338 | − | 0.443896i | ||||
\(958\) | 25.4760 | + | 144.482i | 0.0265929 | + | 0.150816i | ||||
\(959\) | −681.141 | + | 120.104i | −0.710262 | + | 0.125238i | ||||
\(960\) | 508.613 | − | 14.3028i | 0.529806 | − | 0.0148988i | ||||
\(961\) | −361.298 | − | 303.165i | −0.375961 | − | 0.315468i | ||||
\(962\) | 199.405 | − | 115.126i | 0.207281 | − | 0.119674i | ||||
\(963\) | −974.635 | − | 1037.10i | −1.01208 | − | 1.07694i | ||||
\(964\) | −403.678 | + | 699.190i | −0.418753 | + | 0.725301i | ||||
\(965\) | 368.418 | + | 1012.22i | 0.381780 | + | 1.04893i | ||||
\(966\) | 715.464 | − | 147.004i | 0.740646 | − | 0.152178i | ||||
\(967\) | 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 | ||||
\(969\) | 39.8416 | − | 15.7831i | 0.0411162 | − | 0.0162880i | ||||
\(970\) | −86.6041 | + | 491.156i | −0.0892826 | + | 0.506347i | ||||
\(971\) | 487.838i | 0.502407i | 0.967934 | + | 0.251204i | \(0.0808264\pi\) | ||||
−0.967934 | + | 0.251204i | \(0.919174\pi\) | |||||||
\(972\) | −644.105 | − | 21.8847i | −0.662659 | − | 0.0225151i | ||||
\(973\) | 1319.96 | 1.35659 | ||||||||
\(974\) | 519.080 | + | 91.5279i | 0.532937 | + | 0.0939711i | ||||
\(975\) | −49.3558 | − | 124.590i | −0.0506214 | − | 0.127785i | ||||
\(976\) | −120.511 | − | 43.8624i | −0.123474 | − | 0.0449410i | ||||
\(977\) | −413.839 | − | 493.194i | −0.423582 | − | 0.504805i | 0.511478 | − | 0.859297i | \(-0.329098\pi\) |
−0.935059 | + | 0.354492i | \(0.884654\pi\) | |||||||
\(978\) | 27.9387 | + | 135.977i | 0.0285672 | + | 0.139035i | ||||
\(979\) | −761.718 | + | 277.243i | −0.778057 | + | 0.283190i | ||||
\(980\) | 766.227 | + | 442.382i | 0.781865 | + | 0.451410i | ||||
\(981\) | 121.847 | − | 114.509i | 0.124207 | − | 0.116726i | ||||
\(982\) | 183.483 | + | 317.802i | 0.186846 | + | 0.323627i | ||||
\(983\) | −989.779 | + | 1179.57i | −1.00690 | + | 1.19997i | −0.0271699 | + | 0.999631i | \(0.508650\pi\) |
−0.979726 | + | 0.200341i | \(0.935795\pi\) | |||||||
\(984\) | 8.10498 | + | 288.216i | 0.00823676 | + | 0.292902i | ||||
\(985\) | −273.610 | − | 1551.72i | −0.277777 | − | 1.57535i | ||||
\(986\) | 91.6108 | − | 16.1534i | 0.0929115 | − | 0.0163828i | ||||
\(987\) | 186.316 | − | 344.739i | 0.188770 | − | 0.349279i | ||||
\(988\) | −103.177 | − | 86.5756i | −0.104430 | − | 0.0876271i | ||||
\(989\) | 628.389 | − | 362.801i | 0.635378 | − | 0.366836i | ||||
\(990\) | −552.581 | + | 361.897i | −0.558163 | + | 0.365552i | ||||
\(991\) | −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 | ||||
\(993\) | −1196.67 | − | 1347.33i | −1.20511 | − | 1.35683i | ||||
\(994\) | 1139.84 | − | 956.439i | 1.14672 | − | 0.962213i | ||||
\(995\) | 151.540 | − | 416.352i | 0.152301 | − | 0.418445i | ||||
\(996\) | 36.6844 | − | 248.751i | 0.0368318 | − | 0.249750i | ||||
\(997\) | −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 | ||||||||
\(999\) | 40.1592 | + | 475.021i | 0.0401994 | + | 0.475496i |
(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 | 27.3.f.a.2.4 | ✓ | 30 | |
3.2 | odd | 2 | 81.3.f.a.8.2 | 30 | |||
4.3 | odd | 2 | 432.3.bc.a.353.3 | 30 | |||
9.2 | odd | 6 | 243.3.f.b.188.4 | 30 | |||
9.4 | even | 3 | 243.3.f.d.107.2 | 30 | |||
9.5 | odd | 6 | 243.3.f.a.107.4 | 30 | |||
9.7 | even | 3 | 243.3.f.c.188.2 | 30 | |||
27.4 | even | 9 | 243.3.f.a.134.4 | 30 | |||
27.5 | odd | 18 | 243.3.f.c.53.2 | 30 | |||
27.11 | odd | 18 | 729.3.b.a.728.12 | 30 | |||
27.13 | even | 9 | 81.3.f.a.71.2 | 30 | |||
27.14 | odd | 18 | inner | 27.3.f.a.14.4 | yes | 30 | |
27.16 | even | 9 | 729.3.b.a.728.19 | 30 | |||
27.22 | even | 9 | 243.3.f.b.53.4 | 30 | |||
27.23 | odd | 18 | 243.3.f.d.134.2 | 30 | |||
108.95 | even | 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 | 1.1 | even | 1 | trivial | |
27.3.f.a.14.4 | yes | 30 | 27.14 | odd | 18 | inner | |
81.3.f.a.8.2 | 30 | 3.2 | odd | 2 | |||
81.3.f.a.71.2 | 30 | 27.13 | even | 9 | |||
243.3.f.a.107.4 | 30 | 9.5 | odd | 6 | |||
243.3.f.a.134.4 | 30 | 27.4 | even | 9 | |||
243.3.f.b.53.4 | 30 | 27.22 | even | 9 | |||
243.3.f.b.188.4 | 30 | 9.2 | odd | 6 | |||
243.3.f.c.53.2 | 30 | 27.5 | odd | 18 | |||
243.3.f.c.188.2 | 30 | 9.7 | even | 3 | |||
243.3.f.d.107.2 | 30 | 9.4 | even | 3 | |||
243.3.f.d.134.2 | 30 | 27.23 | odd | 18 | |||
432.3.bc.a.257.3 | 30 | 108.95 | even | 18 | |||
432.3.bc.a.353.3 | 30 | 4.3 | odd | 2 | |||
729.3.b.a.728.12 | 30 | 27.11 | odd | 18 | |||
729.3.b.a.728.19 | 30 | 27.16 | even | 9 |