Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(272,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.272");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.g (of order \(2\), degree \(1\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 272.15 | ||
Character | \(\chi\) | \(=\) | 273.272 |
Dual form | 273.2.g.a.272.16 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.305902 | −0.216305 | −0.108153 | − | 0.994134i | \(-0.534493\pi\) | ||||
−0.108153 | + | 0.994134i | \(0.534493\pi\) | |||||||
\(3\) | 1.47187 | − | 0.913018i | 0.849784 | − | 0.527131i | ||||
\(4\) | −1.90642 | −0.953212 | ||||||||
\(5\) | 2.05385i | 0.918509i | 0.888305 | + | 0.459254i | \(0.151883\pi\) | ||||
−0.888305 | + | 0.459254i | \(0.848117\pi\) | |||||||
\(6\) | −0.450247 | + | 0.279294i | −0.183813 | + | 0.114021i | ||||
\(7\) | 0.946976 | + | 2.47047i | 0.357923 | + | 0.933751i | ||||
\(8\) | 1.19498 | 0.422490 | ||||||||
\(9\) | 1.33280 | − | 2.68769i | 0.444266 | − | 0.895895i | ||||
\(10\) | − | 0.628276i | − | 0.198678i | ||||||
\(11\) | 5.03717 | 1.51876 | 0.759381 | − | 0.650646i | \(-0.225502\pi\) | ||||
0.759381 | + | 0.650646i | \(0.225502\pi\) | |||||||
\(12\) | −2.80601 | + | 1.74060i | −0.810024 | + | 0.502468i | ||||
\(13\) | −1.75886 | + | 3.14745i | −0.487819 | + | 0.872945i | ||||
\(14\) | −0.289682 | − | 0.755722i | −0.0774206 | − | 0.201975i | ||||
\(15\) | 1.87520 | + | 3.02300i | 0.484175 | + | 0.780534i | ||||
\(16\) | 3.44730 | 0.861825 | ||||||||
\(17\) | 3.24764 | 0.787668 | 0.393834 | − | 0.919182i | \(-0.371148\pi\) | ||||
0.393834 | + | 0.919182i | \(0.371148\pi\) | |||||||
\(18\) | −0.407705 | + | 0.822167i | −0.0960970 | + | 0.193787i | ||||
\(19\) | −4.21149 | −0.966182 | −0.483091 | − | 0.875570i | \(-0.660486\pi\) | ||||
−0.483091 | + | 0.875570i | \(0.660486\pi\) | |||||||
\(20\) | − | 3.91551i | − | 0.875534i | ||||||
\(21\) | 3.64941 | + | 2.77161i | 0.796367 | + | 0.604814i | ||||
\(22\) | −1.54088 | −0.328516 | ||||||||
\(23\) | − | 5.65284i | − | 1.17870i | −0.807879 | − | 0.589349i | \(-0.799384\pi\) | ||
0.807879 | − | 0.589349i | \(-0.200616\pi\) | |||||||
\(24\) | 1.75886 | − | 1.09104i | 0.359025 | − | 0.222707i | ||||
\(25\) | 0.781707 | 0.156341 | ||||||||
\(26\) | 0.538037 | − | 0.962809i | 0.105518 | − | 0.188822i | ||||
\(27\) | −0.492200 | − | 5.17279i | −0.0947240 | − | 0.995504i | ||||
\(28\) | −1.80534 | − | 4.70977i | −0.341177 | − | 0.890063i | ||||
\(29\) | 5.12387i | 0.951478i | 0.879586 | + | 0.475739i | \(0.157819\pi\) | ||||
−0.879586 | + | 0.475739i | \(0.842181\pi\) | |||||||
\(30\) | −0.573627 | − | 0.924739i | −0.104729 | − | 0.168834i | ||||
\(31\) | −5.11198 | −0.918139 | −0.459070 | − | 0.888400i | \(-0.651817\pi\) | ||||
−0.459070 | + | 0.888400i | \(0.651817\pi\) | |||||||
\(32\) | −3.44450 | −0.608907 | ||||||||
\(33\) | 7.41405 | − | 4.59902i | 1.29062 | − | 0.800587i | ||||
\(34\) | −0.993458 | −0.170377 | ||||||||
\(35\) | −5.07398 | + | 1.94495i | −0.857659 | + | 0.328756i | ||||
\(36\) | −2.54088 | + | 5.12387i | −0.423480 | + | 0.853978i | ||||
\(37\) | − | 4.85607i | − | 0.798333i | −0.916879 | − | 0.399166i | \(-0.869300\pi\) | ||
0.916879 | − | 0.399166i | \(-0.130700\pi\) | |||||||
\(38\) | 1.28830 | 0.208990 | ||||||||
\(39\) | 0.284868 | + | 6.23850i | 0.0456155 | + | 0.998959i | ||||
\(40\) | 2.45431i | 0.388061i | ||||||||
\(41\) | 3.35692i | 0.524263i | 0.965032 | + | 0.262131i | \(0.0844254\pi\) | ||||
−0.965032 | + | 0.262131i | \(0.915575\pi\) | |||||||
\(42\) | −1.11636 | − | 0.847839i | −0.172258 | − | 0.130824i | ||||
\(43\) | −2.44730 | −0.373210 | −0.186605 | − | 0.982435i | \(-0.559748\pi\) | ||||
−0.186605 | + | 0.982435i | \(0.559748\pi\) | |||||||
\(44\) | −9.60298 | −1.44770 | ||||||||
\(45\) | 5.52010 | + | 2.73736i | 0.822888 | + | 0.408062i | ||||
\(46\) | 1.72921i | 0.254958i | ||||||||
\(47\) | 7.14420i | 1.04209i | 0.853530 | + | 0.521044i | \(0.174457\pi\) | ||||
−0.853530 | + | 0.521044i | \(0.825543\pi\) | |||||||
\(48\) | 5.07398 | − | 3.14745i | 0.732365 | − | 0.454295i | ||||
\(49\) | −5.20647 | + | 4.67896i | −0.743782 | + | 0.668423i | ||||
\(50\) | −0.239125 | −0.0338174 | ||||||||
\(51\) | 4.78010 | − | 2.96515i | 0.669348 | − | 0.415204i | ||||
\(52\) | 3.35313 | − | 6.00037i | 0.464995 | − | 0.832102i | ||||
\(53\) | − | 3.08346i | − | 0.423545i | −0.977319 | − | 0.211773i | \(-0.932076\pi\) | ||
0.977319 | − | 0.211773i | \(-0.0679236\pi\) | |||||||
\(54\) | 0.150565 | + | 1.58236i | 0.0204893 | + | 0.215333i | ||||
\(55\) | 10.3456i | 1.39500i | ||||||||
\(56\) | 1.13162 | + | 2.95217i | 0.151219 | + | 0.394500i | ||||
\(57\) | −6.19876 | + | 3.84516i | −0.821046 | + | 0.509304i | ||||
\(58\) | − | 1.56740i | − | 0.205810i | ||||||
\(59\) | − | 12.5550i | − | 1.63452i | −0.576271 | − | 0.817258i | \(-0.695493\pi\) | ||
0.576271 | − | 0.817258i | \(-0.304507\pi\) | |||||||
\(60\) | −3.57493 | − | 5.76311i | −0.461521 | − | 0.744015i | ||||
\(61\) | − | 3.48120i | − | 0.445722i | −0.974850 | − | 0.222861i | \(-0.928460\pi\) | ||
0.974850 | − | 0.222861i | \(-0.0715396\pi\) | |||||||
\(62\) | 1.56376 | 0.198598 | ||||||||
\(63\) | 7.90198 | + | 0.747467i | 0.995556 | + | 0.0941719i | ||||
\(64\) | −5.84093 | −0.730116 | ||||||||
\(65\) | −6.46438 | − | 3.61242i | −0.801808 | − | 0.448066i | ||||
\(66\) | −2.26797 | + | 1.40685i | −0.279168 | + | 0.173171i | ||||
\(67\) | − | 7.77520i | − | 0.949892i | −0.880015 | − | 0.474946i | \(-0.842468\pi\) | ||
0.880015 | − | 0.474946i | \(-0.157532\pi\) | |||||||
\(68\) | −6.19138 | −0.750815 | ||||||||
\(69\) | −5.16114 | − | 8.32024i | −0.621328 | − | 1.00164i | ||||
\(70\) | 1.55214 | − | 0.594962i | 0.185516 | − | 0.0711116i | ||||
\(71\) | 6.61172 | 0.784667 | 0.392333 | − | 0.919823i | \(-0.371668\pi\) | ||||
0.392333 | + | 0.919823i | \(0.371668\pi\) | |||||||
\(72\) | 1.59267 | − | 3.21173i | 0.187698 | − | 0.378506i | ||||
\(73\) | −15.1278 | −1.77057 | −0.885286 | − | 0.465046i | \(-0.846038\pi\) | ||||
−0.885286 | + | 0.465046i | \(0.846038\pi\) | |||||||
\(74\) | 1.48548i | 0.172683i | ||||||||
\(75\) | 1.15057 | − | 0.713712i | 0.132856 | − | 0.0824124i | ||||
\(76\) | 8.02888 | 0.920976 | ||||||||
\(77\) | 4.77008 | + | 12.4442i | 0.543601 | + | 1.41815i | ||||
\(78\) | −0.0871417 | − | 1.90837i | −0.00986686 | − | 0.216080i | ||||
\(79\) | 2.15279 | 0.242208 | 0.121104 | − | 0.992640i | \(-0.461356\pi\) | ||||
0.121104 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(80\) | 7.08024i | 0.791594i | ||||||||
\(81\) | −5.44730 | − | 7.16428i | −0.605256 | − | 0.796031i | ||||
\(82\) | − | 1.02689i | − | 0.113401i | ||||||
\(83\) | − | 0.936674i | − | 0.102813i | −0.998678 | − | 0.0514067i | \(-0.983630\pi\) | ||
0.998678 | − | 0.0514067i | \(-0.0163705\pi\) | |||||||
\(84\) | −6.95732 | − | 5.28386i | −0.759106 | − | 0.576516i | ||||
\(85\) | 6.67016i | 0.723480i | ||||||||
\(86\) | 0.748634 | 0.0807272 | ||||||||
\(87\) | 4.67818 | + | 7.54166i | 0.501554 | + | 0.808551i | ||||
\(88\) | 6.01932 | 0.641662 | ||||||||
\(89\) | − | 11.5084i | − | 1.21988i | −0.792446 | − | 0.609941i | \(-0.791193\pi\) | ||
0.792446 | − | 0.609941i | \(-0.208807\pi\) | |||||||
\(90\) | −1.68861 | − | 0.837364i | −0.177995 | − | 0.0882659i | ||||
\(91\) | −9.44128 | − | 1.36465i | −0.989715 | − | 0.143054i | ||||
\(92\) | 10.7767i | 1.12355i | ||||||||
\(93\) | −7.52417 | + | 4.66733i | −0.780220 | + | 0.483980i | ||||
\(94\) | − | 2.18542i | − | 0.225409i | ||||||
\(95\) | − | 8.64976i | − | 0.887447i | ||||||
\(96\) | −5.06985 | + | 3.14489i | −0.517439 | + | 0.320974i | ||||
\(97\) | 11.4241 | 1.15995 | 0.579973 | − | 0.814636i | \(-0.303063\pi\) | ||||
0.579973 | + | 0.814636i | \(0.303063\pi\) | |||||||
\(98\) | 1.59267 | − | 1.43130i | 0.160884 | − | 0.144583i | ||||
\(99\) | 6.71352 | − | 13.5383i | 0.674734 | − | 1.36065i | ||||
\(100\) | −1.49026 | −0.149026 | ||||||||
\(101\) | −13.5884 | −1.35210 | −0.676048 | − | 0.736857i | \(-0.736309\pi\) | ||||
−0.676048 | + | 0.736857i | \(0.736309\pi\) | |||||||
\(102\) | −1.46224 | + | 0.907045i | −0.144783 | + | 0.0898108i | ||||
\(103\) | − | 4.90862i | − | 0.483661i | −0.970319 | − | 0.241830i | \(-0.922252\pi\) | ||
0.970319 | − | 0.241830i | \(-0.0777478\pi\) | |||||||
\(104\) | −2.10180 | + | 3.76114i | −0.206099 | + | 0.368810i | ||||
\(105\) | −5.69246 | + | 7.49534i | −0.555527 | + | 0.731470i | ||||
\(106\) | 0.943234i | 0.0916150i | ||||||||
\(107\) | − | 7.75382i | − | 0.749590i | −0.927108 | − | 0.374795i | \(-0.877713\pi\) | ||
0.927108 | − | 0.374795i | \(-0.122287\pi\) | |||||||
\(108\) | 0.938343 | + | 9.86153i | 0.0902921 | + | 0.948926i | ||||
\(109\) | − | 7.69033i | − | 0.736600i | −0.929707 | − | 0.368300i | \(-0.879940\pi\) | ||
0.929707 | − | 0.368300i | \(-0.120060\pi\) | |||||||
\(110\) | − | 3.16473i | − | 0.301745i | ||||||
\(111\) | −4.43368 | − | 7.14750i | −0.420826 | − | 0.678410i | ||||
\(112\) | 3.26451 | + | 8.51647i | 0.308467 | + | 0.804730i | ||||
\(113\) | 0.251502i | 0.0236593i | 0.999930 | + | 0.0118297i | \(0.00376559\pi\) | ||||
−0.999930 | + | 0.0118297i | \(0.996234\pi\) | |||||||
\(114\) | 1.89621 | − | 1.17624i | 0.177596 | − | 0.110165i | ||||
\(115\) | 11.6101 | 1.08264 | ||||||||
\(116\) | − | 9.76827i | − | 0.906961i | ||||||
\(117\) | 6.11515 | + | 8.92216i | 0.565346 | + | 0.824854i | ||||
\(118\) | 3.84058i | 0.353554i | ||||||||
\(119\) | 3.07544 | + | 8.02320i | 0.281925 | + | 0.735486i | ||||
\(120\) | 2.24083 | + | 3.61242i | 0.204559 | + | 0.329768i | ||||
\(121\) | 14.3730 | 1.30664 | ||||||||
\(122\) | 1.06490i | 0.0964119i | ||||||||
\(123\) | 3.06493 | + | 4.94095i | 0.276355 | + | 0.445510i | ||||
\(124\) | 9.74561 | 0.875181 | ||||||||
\(125\) | 11.8747i | 1.06211i | ||||||||
\(126\) | −2.41723 | − | 0.228651i | −0.215344 | − | 0.0203699i | ||||
\(127\) | 6.22901 | 0.552735 | 0.276368 | − | 0.961052i | \(-0.410869\pi\) | ||||
0.276368 | + | 0.961052i | \(0.410869\pi\) | |||||||
\(128\) | 8.67574 | 0.766835 | ||||||||
\(129\) | −3.60211 | + | 2.23443i | −0.317148 | + | 0.196731i | ||||
\(130\) | 1.97746 | + | 1.10505i | 0.173435 | + | 0.0969190i | ||||
\(131\) | 19.0708 | 1.66623 | 0.833114 | − | 0.553102i | \(-0.186556\pi\) | ||||
0.833114 | + | 0.553102i | \(0.186556\pi\) | |||||||
\(132\) | −14.1343 | + | 8.76769i | −1.23024 | + | 0.763129i | ||||
\(133\) | −3.98818 | − | 10.4044i | −0.345819 | − | 0.902173i | ||||
\(134\) | 2.37845i | 0.205467i | ||||||||
\(135\) | 10.6241 | − | 1.01090i | 0.914379 | − | 0.0870048i | ||||
\(136\) | 3.88087 | 0.332782 | ||||||||
\(137\) | −1.85183 | −0.158212 | −0.0791062 | − | 0.996866i | \(-0.525207\pi\) | ||||
−0.0791062 | + | 0.996866i | \(0.525207\pi\) | |||||||
\(138\) | 1.57880 | + | 2.54517i | 0.134396 | + | 0.216660i | ||||
\(139\) | 5.72541i | 0.485623i | 0.970073 | + | 0.242811i | \(0.0780696\pi\) | ||||
−0.970073 | + | 0.242811i | \(0.921930\pi\) | |||||||
\(140\) | 9.67315 | − | 3.70789i | 0.817531 | − | 0.313374i | ||||
\(141\) | 6.52278 | + | 10.5153i | 0.549317 | + | 0.885550i | ||||
\(142\) | −2.02254 | −0.169727 | ||||||||
\(143\) | −8.85965 | + | 15.8542i | −0.740881 | + | 1.32580i | ||||
\(144\) | 4.59455 | − | 9.26526i | 0.382880 | − | 0.772105i | ||||
\(145\) | −10.5236 | −0.873941 | ||||||||
\(146\) | 4.62761 | 0.382984 | ||||||||
\(147\) | −3.39128 | + | 11.6404i | −0.279708 | + | 0.960085i | ||||
\(148\) | 9.25773i | 0.760980i | ||||||||
\(149\) | 0.129937 | 0.0106448 | 0.00532241 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532241 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(150\) | −0.351961 | + | 0.218326i | −0.0287375 | + | 0.0178262i | ||||
\(151\) | 21.8890i | 1.78130i | 0.454688 | + | 0.890651i | \(0.349751\pi\) | ||||
−0.454688 | + | 0.890651i | \(0.650249\pi\) | |||||||
\(152\) | −5.03265 | −0.408202 | ||||||||
\(153\) | 4.32844 | − | 8.72863i | 0.349934 | − | 0.705668i | ||||
\(154\) | −1.45917 | − | 3.80670i | −0.117584 | − | 0.306752i | ||||
\(155\) | − | 10.4992i | − | 0.843319i | ||||||
\(156\) | −0.543080 | − | 11.8932i | −0.0434812 | − | 0.952220i | ||||
\(157\) | − | 10.1747i | − | 0.812030i | −0.913866 | − | 0.406015i | \(-0.866918\pi\) | ||
0.913866 | − | 0.406015i | \(-0.133082\pi\) | |||||||
\(158\) | −0.658543 | −0.0523909 | ||||||||
\(159\) | −2.81525 | − | 4.53844i | −0.223264 | − | 0.359922i | ||||
\(160\) | − | 7.07448i | − | 0.559287i | ||||||
\(161\) | 13.9652 | − | 5.35310i | 1.10061 | − | 0.421883i | ||||
\(162\) | 1.66634 | + | 2.19156i | 0.130920 | + | 0.172186i | ||||
\(163\) | 10.0437i | 0.786684i | 0.919392 | + | 0.393342i | \(0.128681\pi\) | ||||
−0.919392 | + | 0.393342i | \(0.871319\pi\) | |||||||
\(164\) | − | 6.39971i | − | 0.499734i | ||||||
\(165\) | 9.44569 | + | 15.2273i | 0.735346 | + | 1.18545i | ||||
\(166\) | 0.286530i | 0.0222391i | ||||||||
\(167\) | − | 10.8675i | − | 0.840953i | −0.907303 | − | 0.420477i | \(-0.861863\pi\) | ||
0.907303 | − | 0.420477i | \(-0.138137\pi\) | |||||||
\(168\) | 4.36098 | + | 3.31202i | 0.336457 | + | 0.255528i | ||||
\(169\) | −6.81285 | − | 11.0718i | −0.524065 | − | 0.851678i | ||||
\(170\) | − | 2.04041i | − | 0.156492i | ||||||
\(171\) | −5.61306 | + | 11.3192i | −0.429242 | + | 0.865597i | ||||
\(172\) | 4.66560 | 0.355748 | ||||||||
\(173\) | 2.91530 | 0.221646 | 0.110823 | − | 0.993840i | \(-0.464651\pi\) | ||||
0.110823 | + | 0.993840i | \(0.464651\pi\) | |||||||
\(174\) | −1.43106 | − | 2.30701i | −0.108489 | − | 0.174894i | ||||
\(175\) | 0.740257 | + | 1.93118i | 0.0559582 | + | 0.145984i | ||||
\(176\) | 17.3646 | 1.30891 | ||||||||
\(177\) | −11.4629 | − | 18.4793i | −0.861605 | − | 1.38899i | ||||
\(178\) | 3.52042i | 0.263867i | ||||||||
\(179\) | 14.3632i | 1.07355i | 0.843724 | + | 0.536777i | \(0.180358\pi\) | ||||
−0.843724 | + | 0.536777i | \(0.819642\pi\) | |||||||
\(180\) | −10.5236 | − | 5.21858i | −0.784386 | − | 0.388970i | ||||
\(181\) | 21.5491i | 1.60173i | 0.598844 | + | 0.800866i | \(0.295627\pi\) | ||||
−0.598844 | + | 0.800866i | \(0.704373\pi\) | |||||||
\(182\) | 2.88810 | + | 0.417449i | 0.214080 | + | 0.0309433i | ||||
\(183\) | −3.17840 | − | 5.12387i | −0.234954 | − | 0.378767i | ||||
\(184\) | − | 6.75504i | − | 0.497988i | ||||||
\(185\) | 9.97363 | 0.733276 | ||||||||
\(186\) | 2.30166 | − | 1.42774i | 0.168766 | − | 0.104687i | ||||
\(187\) | 16.3589 | 1.19628 | ||||||||
\(188\) | − | 13.6199i | − | 0.993331i | ||||||
\(189\) | 12.3131 | − | 6.11447i | 0.895649 | − | 0.444763i | ||||
\(190\) | 2.64598i | 0.191959i | ||||||||
\(191\) | − | 17.6376i | − | 1.27621i | −0.769950 | − | 0.638104i | \(-0.779719\pi\) | ||
0.769950 | − | 0.638104i | \(-0.220281\pi\) | |||||||
\(192\) | −8.59708 | + | 5.33287i | −0.620441 | + | 0.384867i | ||||
\(193\) | − | 9.25773i | − | 0.666386i | −0.942859 | − | 0.333193i | \(-0.891874\pi\) | ||
0.942859 | − | 0.333193i | \(-0.108126\pi\) | |||||||
\(194\) | −3.49466 | −0.250902 | ||||||||
\(195\) | −12.8129 | + | 0.585077i | −0.917553 | + | 0.0418982i | ||||
\(196\) | 9.92575 | − | 8.92008i | 0.708982 | − | 0.637148i | ||||
\(197\) | −27.4590 | −1.95637 | −0.978186 | − | 0.207729i | \(-0.933393\pi\) | ||||
−0.978186 | + | 0.207729i | \(0.933393\pi\) | |||||||
\(198\) | −2.05368 | + | 4.14139i | −0.145949 | + | 0.294316i | ||||
\(199\) | 7.53188i | 0.533921i | 0.963707 | + | 0.266960i | \(0.0860193\pi\) | ||||
−0.963707 | + | 0.266960i | \(0.913981\pi\) | |||||||
\(200\) | 0.934125 | 0.0660526 | ||||||||
\(201\) | −7.09890 | − | 11.4441i | −0.500718 | − | 0.807203i | ||||
\(202\) | 4.15671 | 0.292465 | ||||||||
\(203\) | −12.6584 | + | 4.85218i | −0.888444 | + | 0.340556i | ||||
\(204\) | −9.11290 | + | 5.65284i | −0.638030 | + | 0.395778i | ||||
\(205\) | −6.89460 | −0.481540 | ||||||||
\(206\) | 1.50156i | 0.104618i | ||||||||
\(207\) | −15.1930 | − | 7.53409i | −1.05599 | − | 0.523655i | ||||
\(208\) | −6.06331 | + | 10.8502i | −0.420415 | + | 0.752326i | ||||
\(209\) | −21.2140 | −1.46740 | ||||||||
\(210\) | 1.74133 | − | 2.29284i | 0.120163 | − | 0.158221i | ||||
\(211\) | −6.51280 | −0.448360 | −0.224180 | − | 0.974548i | \(-0.571970\pi\) | ||||
−0.224180 | + | 0.974548i | \(0.571970\pi\) | |||||||
\(212\) | 5.87837i | 0.403728i | ||||||||
\(213\) | 9.73159 | − | 6.03662i | 0.666797 | − | 0.413622i | ||||
\(214\) | 2.37191i | 0.162140i | ||||||||
\(215\) | − | 5.02639i | − | 0.342797i | ||||||
\(216\) | −0.588170 | − | 6.18139i | −0.0400199 | − | 0.420590i | ||||
\(217\) | −4.84093 | − | 12.6290i | −0.328623 | − | 0.857313i | ||||
\(218\) | 2.35248i | 0.159330i | ||||||||
\(219\) | −22.2661 | + | 13.8119i | −1.50460 | + | 0.933324i | ||||
\(220\) | − | 19.7231i | − | 1.32973i | ||||||
\(221\) | −5.71213 | + | 10.2218i | −0.384239 | + | 0.687591i | ||||
\(222\) | 1.35627 | + | 2.18643i | 0.0910268 | + | 0.146744i | ||||
\(223\) | 5.02772 | 0.336681 | 0.168340 | − | 0.985729i | \(-0.446159\pi\) | ||||
0.168340 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(224\) | −3.26186 | − | 8.50954i | −0.217942 | − | 0.568568i | ||||
\(225\) | 1.04186 | − | 2.10098i | 0.0694571 | − | 0.140065i | ||||
\(226\) | − | 0.0769350i | − | 0.00511764i | ||||||
\(227\) | − | 10.0833i | − | 0.669255i | −0.942350 | − | 0.334628i | \(-0.891389\pi\) | ||
0.942350 | − | 0.334628i | \(-0.108611\pi\) | |||||||
\(228\) | 11.8175 | − | 7.33051i | 0.782631 | − | 0.485475i | ||||
\(229\) | −7.00449 | −0.462870 | −0.231435 | − | 0.972850i | \(-0.574342\pi\) | ||||
−0.231435 | + | 0.972850i | \(0.574342\pi\) | |||||||
\(230\) | −3.55154 | −0.234182 | ||||||||
\(231\) | 18.3827 | + | 13.9610i | 1.20949 | + | 0.918569i | ||||
\(232\) | 6.12293i | 0.401990i | ||||||||
\(233\) | 23.2904i | 1.52580i | 0.646514 | + | 0.762902i | \(0.276226\pi\) | ||||
−0.646514 | + | 0.762902i | \(0.723774\pi\) | |||||||
\(234\) | −1.87063 | − | 2.72930i | −0.122287 | − | 0.178420i | ||||
\(235\) | −14.6731 | −0.957167 | ||||||||
\(236\) | 23.9351i | 1.55804i | ||||||||
\(237\) | 3.16863 | − | 1.96554i | 0.205825 | − | 0.127676i | ||||
\(238\) | −0.940781 | − | 2.45431i | −0.0609818 | − | 0.159089i | ||||
\(239\) | 9.99015 | 0.646209 | 0.323105 | − | 0.946363i | \(-0.395273\pi\) | ||||
0.323105 | + | 0.946363i | \(0.395273\pi\) | |||||||
\(240\) | 6.46438 | + | 10.4212i | 0.417274 | + | 0.672684i | ||||
\(241\) | 6.73574 | 0.433887 | 0.216944 | − | 0.976184i | \(-0.430391\pi\) | ||||
0.216944 | + | 0.976184i | \(0.430391\pi\) | |||||||
\(242\) | −4.39674 | −0.282633 | ||||||||
\(243\) | −14.5588 | − | 5.57140i | −0.933949 | − | 0.357405i | ||||
\(244\) | 6.63664i | 0.424867i | ||||||||
\(245\) | −9.60987 | − | 10.6933i | −0.613952 | − | 0.683170i | ||||
\(246\) | −0.937566 | − | 1.51144i | −0.0597770 | − | 0.0963661i | ||||
\(247\) | 7.40740 | − | 13.2554i | 0.471322 | − | 0.843423i | ||||
\(248\) | −6.10872 | −0.387904 | ||||||||
\(249\) | −0.855200 | − | 1.37866i | −0.0541961 | − | 0.0873691i | ||||
\(250\) | − | 3.63251i | − | 0.229740i | ||||||
\(251\) | 7.28687 | 0.459943 | 0.229971 | − | 0.973197i | \(-0.426137\pi\) | ||||
0.229971 | + | 0.973197i | \(0.426137\pi\) | |||||||
\(252\) | −15.0645 | − | 1.42499i | −0.948976 | − | 0.0897658i | ||||
\(253\) | − | 28.4743i | − | 1.79016i | ||||||
\(254\) | −1.90546 | −0.119559 | ||||||||
\(255\) | 6.08997 | + | 9.81760i | 0.381369 | + | 0.614802i | ||||
\(256\) | 9.02793 | 0.564245 | ||||||||
\(257\) | −13.3387 | −0.832046 | −0.416023 | − | 0.909354i | \(-0.636576\pi\) | ||||
−0.416023 | + | 0.909354i | \(0.636576\pi\) | |||||||
\(258\) | 1.10189 | − | 0.683516i | 0.0686007 | − | 0.0425538i | ||||
\(259\) | 11.9968 | − | 4.59858i | 0.745444 | − | 0.285742i | ||||
\(260\) | 12.3238 | + | 6.88681i | 0.764293 | + | 0.427102i | ||||
\(261\) | 13.7713 | + | 6.82908i | 0.852425 | + | 0.422709i | ||||
\(262\) | −5.83380 | −0.360413 | ||||||||
\(263\) | 17.9410i | 1.10629i | 0.833086 | + | 0.553144i | \(0.186572\pi\) | ||||
−0.833086 | + | 0.553144i | \(0.813428\pi\) | |||||||
\(264\) | 8.85965 | − | 5.49575i | 0.545274 | − | 0.338240i | ||||
\(265\) | 6.33295 | 0.389030 | ||||||||
\(266\) | 1.21999 | + | 3.18271i | 0.0748024 | + | 0.195145i | ||||
\(267\) | −10.5073 | − | 16.9388i | −0.643038 | − | 1.03664i | ||||
\(268\) | 14.8228i | 0.905449i | ||||||||
\(269\) | 29.5227 | 1.80003 | 0.900015 | − | 0.435858i | \(-0.143555\pi\) | ||||
0.900015 | + | 0.435858i | \(0.143555\pi\) | |||||||
\(270\) | −3.24994 | + | 0.309237i | −0.197785 | + | 0.0188196i | ||||
\(271\) | 11.1865 | 0.679531 | 0.339765 | − | 0.940510i | \(-0.389652\pi\) | ||||
0.339765 | + | 0.940510i | \(0.389652\pi\) | |||||||
\(272\) | 11.1956 | 0.678832 | ||||||||
\(273\) | −15.1423 | + | 6.61147i | −0.916452 | + | 0.400144i | ||||
\(274\) | 0.566478 | 0.0342222 | ||||||||
\(275\) | 3.93759 | 0.237445 | ||||||||
\(276\) | 9.83932 | + | 15.8619i | 0.592258 | + | 0.954774i | ||||
\(277\) | −17.2968 | −1.03927 | −0.519633 | − | 0.854390i | \(-0.673931\pi\) | ||||
−0.519633 | + | 0.854390i | \(0.673931\pi\) | |||||||
\(278\) | − | 1.75141i | − | 0.105043i | ||||||
\(279\) | −6.81324 | + | 13.7394i | −0.407898 | + | 0.822556i | ||||
\(280\) | −6.06331 | + | 2.32417i | −0.362352 | + | 0.138896i | ||||
\(281\) | −14.6332 | −0.872946 | −0.436473 | − | 0.899717i | \(-0.643773\pi\) | ||||
−0.436473 | + | 0.899717i | \(0.643773\pi\) | |||||||
\(282\) | −1.99533 | − | 3.21665i | −0.118820 | − | 0.191549i | ||||
\(283\) | − | 22.6152i | − | 1.34433i | −0.740399 | − | 0.672167i | \(-0.765364\pi\) | ||
0.740399 | − | 0.672167i | \(-0.234636\pi\) | |||||||
\(284\) | −12.6047 | −0.747954 | ||||||||
\(285\) | −7.89738 | − | 12.7313i | −0.467801 | − | 0.754138i | ||||
\(286\) | 2.71018 | − | 4.84983i | 0.160256 | − | 0.286776i | ||||
\(287\) | −8.29318 | + | 3.17892i | −0.489531 | + | 0.187646i | ||||
\(288\) | −4.59082 | + | 9.25773i | −0.270517 | + | 0.545517i | ||||
\(289\) | −6.45284 | −0.379579 | ||||||||
\(290\) | 3.21920 | 0.189038 | ||||||||
\(291\) | 16.8148 | − | 10.4304i | 0.985704 | − | 0.611443i | ||||
\(292\) | 28.8400 | 1.68773 | ||||||||
\(293\) | − | 7.02886i | − | 0.410631i | −0.978696 | − | 0.205315i | \(-0.934178\pi\) | ||
0.978696 | − | 0.205315i | \(-0.0658220\pi\) | |||||||
\(294\) | 1.03740 | − | 3.56082i | 0.0605022 | − | 0.207671i | ||||
\(295\) | 25.7860 | 1.50132 | ||||||||
\(296\) | − | 5.80291i | − | 0.337287i | ||||||
\(297\) | −2.47930 | − | 26.0562i | −0.143863 | − | 1.51193i | ||||
\(298\) | −0.0397478 | −0.00230253 | ||||||||
\(299\) | 17.7920 | + | 9.94253i | 1.02894 | + | 0.574991i | ||||
\(300\) | −2.19347 | + | 1.36064i | −0.126640 | + | 0.0785565i | ||||
\(301\) | −2.31754 | − | 6.04599i | −0.133581 | − | 0.348485i | ||||
\(302\) | − | 6.69588i | − | 0.385305i | ||||||
\(303\) | −20.0004 | + | 12.4065i | −1.14899 | + | 0.712732i | ||||
\(304\) | −14.5183 | −0.832680 | ||||||||
\(305\) | 7.14985 | 0.409399 | ||||||||
\(306\) | −1.32408 | + | 2.67010i | −0.0756925 | + | 0.152640i | ||||
\(307\) | −5.56810 | −0.317788 | −0.158894 | − | 0.987296i | \(-0.550793\pi\) | ||||
−0.158894 | + | 0.987296i | \(0.550793\pi\) | |||||||
\(308\) | −9.09379 | − | 23.7239i | −0.518167 | − | 1.35179i | ||||
\(309\) | −4.48166 | − | 7.22485i | −0.254953 | − | 0.411007i | ||||
\(310\) | 3.21173i | 0.182414i | ||||||||
\(311\) | −11.4078 | −0.646878 | −0.323439 | − | 0.946249i | \(-0.604839\pi\) | ||||
−0.323439 | + | 0.946249i | \(0.604839\pi\) | |||||||
\(312\) | 0.340413 | + | 7.45489i | 0.0192721 | + | 0.422050i | ||||
\(313\) | 30.7773i | 1.73964i | 0.493374 | + | 0.869818i | \(0.335764\pi\) | ||||
−0.493374 | + | 0.869818i | \(0.664236\pi\) | |||||||
\(314\) | 3.11246i | 0.175646i | ||||||||
\(315\) | −1.53518 | + | 16.2295i | −0.0864978 | + | 0.914427i | ||||
\(316\) | −4.10414 | −0.230876 | ||||||||
\(317\) | −2.17223 | −0.122005 | −0.0610023 | − | 0.998138i | \(-0.519430\pi\) | ||||
−0.0610023 | + | 0.998138i | \(0.519430\pi\) | |||||||
\(318\) | 0.861189 | + | 1.38832i | 0.0482931 | + | 0.0778530i | ||||
\(319\) | 25.8098i | 1.44507i | ||||||||
\(320\) | − | 11.9964i | − | 0.670618i | ||||||
\(321\) | −7.07937 | − | 11.4126i | −0.395132 | − | 0.636989i | ||||
\(322\) | −4.27197 | + | 1.63752i | −0.238068 | + | 0.0912556i | ||||
\(323\) | −13.6774 | −0.761030 | ||||||||
\(324\) | 10.3849 | + | 13.6582i | 0.576937 | + | 0.758786i | ||||
\(325\) | −1.37491 | + | 2.46038i | −0.0762663 | + | 0.136477i | ||||
\(326\) | − | 3.07239i | − | 0.170164i | ||||||
\(327\) | −7.02140 | − | 11.3192i | −0.388285 | − | 0.625951i | ||||
\(328\) | 4.01146i | 0.221496i | ||||||||
\(329\) | −17.6495 | + | 6.76538i | −0.973051 | + | 0.372988i | ||||
\(330\) | −2.88945 | − | 4.65807i | −0.159059 | − | 0.256418i | ||||
\(331\) | − | 6.75504i | − | 0.371290i | −0.982617 | − | 0.185645i | \(-0.940563\pi\) | ||
0.982617 | − | 0.185645i | \(-0.0594375\pi\) | |||||||
\(332\) | 1.78570i | 0.0980029i | ||||||||
\(333\) | −13.0516 | − | 6.47216i | −0.715222 | − | 0.354672i | ||||
\(334\) | 3.32439i | 0.181902i | ||||||||
\(335\) | 15.9691 | 0.872485 | ||||||||
\(336\) | 12.5806 | + | 9.55456i | 0.686329 | + | 0.521244i | ||||
\(337\) | 9.27641 | 0.505318 | 0.252659 | − | 0.967555i | \(-0.418695\pi\) | ||||
0.252659 | + | 0.967555i | \(0.418695\pi\) | |||||||
\(338\) | 2.08406 | + | 3.38689i | 0.113358 | + | 0.184222i | ||||
\(339\) | 0.229626 | + | 0.370178i | 0.0124716 | + | 0.0201053i | ||||
\(340\) | − | 12.7161i | − | 0.689630i | ||||||
\(341\) | −25.7499 | −1.39444 | ||||||||
\(342\) | 1.71704 | − | 3.46255i | 0.0928471 | − | 0.187233i | ||||
\(343\) | −16.4896 | − | 8.43159i | −0.890357 | − | 0.455263i | ||||
\(344\) | −2.92448 | −0.157677 | ||||||||
\(345\) | 17.0885 | − | 10.6002i | 0.920014 | − | 0.570695i | ||||
\(346\) | −0.891795 | −0.0479432 | ||||||||
\(347\) | 27.7698i | 1.49076i | 0.666639 | + | 0.745381i | \(0.267732\pi\) | ||||
−0.666639 | + | 0.745381i | \(0.732268\pi\) | |||||||
\(348\) | −8.91860 | − | 14.3776i | −0.478087 | − | 0.770721i | ||||
\(349\) | 3.18709 | 0.170601 | 0.0853006 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0853006 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(350\) | −0.226446 | − | 0.590753i | −0.0121040 | − | 0.0315771i | ||||
\(351\) | 17.1468 | + | 7.54902i | 0.915228 | + | 0.402937i | ||||
\(352\) | −17.3505 | −0.924785 | ||||||||
\(353\) | − | 22.2593i | − | 1.18474i | −0.805664 | − | 0.592372i | \(-0.798192\pi\) | ||
0.805664 | − | 0.592372i | \(-0.201808\pi\) | |||||||
\(354\) | 3.50652 | + | 5.65284i | 0.186369 | + | 0.300445i | ||||
\(355\) | 13.5795i | 0.720723i | ||||||||
\(356\) | 21.9398i | 1.16281i | ||||||||
\(357\) | 11.8520 | + | 9.00118i | 0.627273 | + | 0.476393i | ||||
\(358\) | − | 4.39372i | − | 0.232215i | ||||||
\(359\) | 21.3887 | 1.12885 | 0.564426 | − | 0.825484i | \(-0.309098\pi\) | ||||
0.564426 | + | 0.825484i | \(0.309098\pi\) | |||||||
\(360\) | 6.59641 | + | 3.27110i | 0.347662 | + | 0.172402i | ||||
\(361\) | −1.26336 | −0.0664929 | ||||||||
\(362\) | − | 6.59190i | − | 0.346463i | ||||||
\(363\) | 21.1552 | − | 13.1228i | 1.11036 | − | 0.688771i | ||||
\(364\) | 17.9991 | + | 2.60160i | 0.943408 | + | 0.136361i | ||||
\(365\) | − | 31.0702i | − | 1.62629i | ||||||
\(366\) | 0.972276 | + | 1.56740i | 0.0508217 | + | 0.0819293i | ||||
\(367\) | − | 0.740357i | − | 0.0386463i | −0.999813 | − | 0.0193232i | \(-0.993849\pi\) | ||
0.999813 | − | 0.0193232i | \(-0.00615113\pi\) | |||||||
\(368\) | − | 19.4870i | − | 1.01583i | ||||||
\(369\) | 9.02234 | + | 4.47409i | 0.469684 | + | 0.232912i | ||||
\(370\) | −3.05095 | −0.158611 | ||||||||
\(371\) | 7.61759 | − | 2.91996i | 0.395486 | − | 0.151597i | ||||
\(372\) | 14.3443 | − | 8.89791i | 0.743715 | − | 0.461335i | ||||
\(373\) | −32.7429 | −1.69536 | −0.847681 | − | 0.530506i | \(-0.822002\pi\) | ||||
−0.847681 | + | 0.530506i | \(0.822002\pi\) | |||||||
\(374\) | −5.00421 | −0.258762 | ||||||||
\(375\) | 10.8419 | + | 17.4781i | 0.559871 | + | 0.902564i | ||||
\(376\) | 8.53718i | 0.440272i | ||||||||
\(377\) | −16.1271 | − | 9.01215i | −0.830588 | − | 0.464149i | ||||
\(378\) | −3.76661 | + | 1.87043i | −0.193733 | + | 0.0962044i | ||||
\(379\) | 17.2796i | 0.887594i | 0.896127 | + | 0.443797i | \(0.146369\pi\) | ||||
−0.896127 | + | 0.443797i | \(0.853631\pi\) | |||||||
\(380\) | 16.4901i | 0.845925i | ||||||||
\(381\) | 9.16828 | − | 5.68719i | 0.469705 | − | 0.291364i | ||||
\(382\) | 5.39536i | 0.276050i | ||||||||
\(383\) | 20.5205i | 1.04855i | 0.851549 | + | 0.524274i | \(0.175663\pi\) | ||||
−0.851549 | + | 0.524274i | \(0.824337\pi\) | |||||||
\(384\) | 12.7696 | − | 7.92111i | 0.651644 | − | 0.404222i | ||||
\(385\) | −25.5585 | + | 9.79701i | −1.30258 | + | 0.499302i | ||||
\(386\) | 2.83195i | 0.144143i | ||||||||
\(387\) | −3.26176 | + | 6.57758i | −0.165804 | + | 0.334357i | ||||
\(388\) | −21.7793 | −1.10567 | ||||||||
\(389\) | − | 32.7317i | − | 1.65956i | −0.558089 | − | 0.829781i | \(-0.688465\pi\) | ||
0.558089 | − | 0.829781i | \(-0.311535\pi\) | |||||||
\(390\) | 3.91950 | − | 0.178976i | 0.198471 | − | 0.00906280i | ||||
\(391\) | − | 18.3584i | − | 0.928423i | ||||||
\(392\) | −6.22164 | + | 5.59127i | −0.314240 | + | 0.282402i | ||||
\(393\) | 28.0698 | − | 17.4120i | 1.41593 | − | 0.878320i | ||||
\(394\) | 8.39975 | 0.423173 | ||||||||
\(395\) | 4.42151i | 0.222471i | ||||||||
\(396\) | −12.7988 | + | 25.8098i | −0.643165 | + | 1.29699i | ||||
\(397\) | −32.5731 | −1.63480 | −0.817399 | − | 0.576073i | \(-0.804585\pi\) | ||||
−0.817399 | + | 0.576073i | \(0.804585\pi\) | |||||||
\(398\) | − | 2.30401i | − | 0.115490i | ||||||
\(399\) | −15.3694 | − | 11.6726i | −0.769435 | − | 0.584360i | ||||
\(400\) | 2.69478 | 0.134739 | ||||||||
\(401\) | 26.8272 | 1.33968 | 0.669842 | − | 0.742503i | \(-0.266362\pi\) | ||||
0.669842 | + | 0.742503i | \(0.266362\pi\) | |||||||
\(402\) | 2.17156 | + | 3.50076i | 0.108308 | + | 0.174602i | ||||
\(403\) | 8.99124 | − | 16.0897i | 0.447886 | − | 0.801485i | ||||
\(404\) | 25.9053 | 1.28883 | ||||||||
\(405\) | 14.7143 | − | 11.1879i | 0.731162 | − | 0.555933i | ||||
\(406\) | 3.87222 | − | 1.48429i | 0.192175 | − | 0.0736641i | ||||
\(407\) | − | 24.4608i | − | 1.21248i | ||||||
\(408\) | 5.71213 | − | 3.54330i | 0.282793 | − | 0.175420i | ||||
\(409\) | −21.6481 | −1.07043 | −0.535215 | − | 0.844716i | \(-0.679769\pi\) | ||||
−0.535215 | + | 0.844716i | \(0.679769\pi\) | |||||||
\(410\) | 2.10907 | 0.104160 | ||||||||
\(411\) | −2.72565 | + | 1.69075i | −0.134446 | + | 0.0833987i | ||||
\(412\) | 9.35792i | 0.461031i | ||||||||
\(413\) | 31.0167 | − | 11.8893i | 1.52623 | − | 0.585032i | ||||
\(414\) | 4.64758 | + | 2.30469i | 0.228416 | + | 0.113269i | ||||
\(415\) | 1.92379 | 0.0944350 | ||||||||
\(416\) | 6.05838 | − | 10.8414i | 0.297036 | − | 0.531542i | ||||
\(417\) | 5.22740 | + | 8.42705i | 0.255987 | + | 0.412675i | ||||
\(418\) | 6.48939 | 0.317406 | ||||||||
\(419\) | 15.2533 | 0.745173 | 0.372586 | − | 0.927998i | \(-0.378471\pi\) | ||||
0.372586 | + | 0.927998i | \(0.378471\pi\) | |||||||
\(420\) | 10.8522 | − | 14.2893i | 0.529535 | − | 0.697246i | ||||
\(421\) | 15.6273i | 0.761630i | 0.924651 | + | 0.380815i | \(0.124357\pi\) | ||||
−0.924651 | + | 0.380815i | \(0.875643\pi\) | |||||||
\(422\) | 1.99228 | 0.0969825 | ||||||||
\(423\) | 19.2013 | + | 9.52177i | 0.933601 | + | 0.462964i | ||||
\(424\) | − | 3.68467i | − | 0.178944i | ||||||
\(425\) | 2.53870 | 0.123145 | ||||||||
\(426\) | −2.97691 | + | 1.84661i | −0.144232 | + | 0.0894686i | ||||
\(427\) | 8.60021 | − | 3.29661i | 0.416193 | − | 0.159534i | ||||
\(428\) | 14.7821i | 0.714518i | ||||||||
\(429\) | 1.43493 | + | 31.4244i | 0.0692791 | + | 1.51718i | ||||
\(430\) | 1.53758i | 0.0741487i | ||||||||
\(431\) | 26.9735 | 1.29927 | 0.649634 | − | 0.760247i | \(-0.274922\pi\) | ||||
0.649634 | + | 0.760247i | \(0.274922\pi\) | |||||||
\(432\) | −1.69676 | − | 17.8322i | −0.0816356 | − | 0.857950i | ||||
\(433\) | 22.0774i | 1.06097i | 0.847693 | + | 0.530487i | \(0.177991\pi\) | ||||
−0.847693 | + | 0.530487i | \(0.822009\pi\) | |||||||
\(434\) | 1.48085 | + | 3.86324i | 0.0710829 | + | 0.185441i | ||||
\(435\) | −15.4894 | + | 9.60828i | −0.742661 | + | 0.460682i | ||||
\(436\) | 14.6610i | 0.702136i | ||||||||
\(437\) | 23.8069i | 1.13884i | ||||||||
\(438\) | 6.81124 | − | 4.22509i | 0.325454 | − | 0.201883i | ||||
\(439\) | − | 14.1901i | − | 0.677257i | −0.940920 | − | 0.338628i | \(-0.890037\pi\) | ||
0.940920 | − | 0.338628i | \(-0.109963\pi\) | |||||||
\(440\) | 12.3628i | 0.589372i | ||||||||
\(441\) | 5.63639 | + | 20.2295i | 0.268400 | + | 0.963308i | ||||
\(442\) | 1.74735 | − | 3.12686i | 0.0831130 | − | 0.148729i | ||||
\(443\) | 26.8422i | 1.27531i | 0.770321 | + | 0.637657i | \(0.220096\pi\) | ||||
−0.770321 | + | 0.637657i | \(0.779904\pi\) | |||||||
\(444\) | 8.45247 | + | 13.6262i | 0.401136 | + | 0.646669i | ||||
\(445\) | 23.6364 | 1.12047 | ||||||||
\(446\) | −1.53799 | −0.0728258 | ||||||||
\(447\) | 0.191250 | − | 0.118634i | 0.00904580 | − | 0.00561121i | ||||
\(448\) | −5.53122 | − | 14.4298i | −0.261325 | − | 0.681746i | ||||
\(449\) | −2.49034 | −0.117526 | −0.0587631 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587631 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(450\) | −0.318706 | + | 0.642694i | −0.0150239 | + | 0.0302969i | ||||
\(451\) | 16.9094i | 0.796231i | ||||||||
\(452\) | − | 0.479470i | − | 0.0225524i | ||||||
\(453\) | 19.9850 | + | 32.2177i | 0.938979 | + | 1.51372i | ||||
\(454\) | 3.08451i | 0.144763i | ||||||||
\(455\) | 2.80278 | − | 19.3910i | 0.131397 | − | 0.909062i | ||||
\(456\) | −7.40740 | + | 4.59490i | −0.346883 | + | 0.215176i | ||||
\(457\) | 19.3863i | 0.906853i | 0.891294 | + | 0.453427i | \(0.149799\pi\) | ||||
−0.891294 | + | 0.453427i | \(0.850201\pi\) | |||||||
\(458\) | 2.14268 | 0.100121 | ||||||||
\(459\) | −1.59849 | − | 16.7993i | −0.0746111 | − | 0.784126i | ||||
\(460\) | −22.1337 | −1.03199 | ||||||||
\(461\) | 17.5300i | 0.816452i | 0.912881 | + | 0.408226i | \(0.133853\pi\) | ||||
−0.912881 | + | 0.408226i | \(0.866147\pi\) | |||||||
\(462\) | −5.62329 | − | 4.27071i | −0.261619 | − | 0.198691i | ||||
\(463\) | − | 1.55946i | − | 0.0724741i | −0.999343 | − | 0.0362371i | \(-0.988463\pi\) | ||
0.999343 | − | 0.0362371i | \(-0.0115371\pi\) | |||||||
\(464\) | 17.6635i | 0.820008i | ||||||||
\(465\) | −9.58599 | − | 15.4535i | −0.444540 | − | 0.716639i | ||||
\(466\) | − | 7.12457i | − | 0.330039i | ||||||
\(467\) | −36.3661 | −1.68282 | −0.841412 | − | 0.540394i | \(-0.818275\pi\) | ||||
−0.841412 | + | 0.540394i | \(0.818275\pi\) | |||||||
\(468\) | −11.6581 | − | 17.0094i | −0.538894 | − | 0.786261i | ||||
\(469\) | 19.2084 | − | 7.36293i | 0.886963 | − | 0.339989i | ||||
\(470\) | 4.48852 | 0.207040 | ||||||||
\(471\) | −9.28968 | − | 14.9758i | −0.428046 | − | 0.690050i | ||||
\(472\) | − | 15.0029i | − | 0.690567i | ||||||
\(473\) | −12.3275 | −0.566817 | ||||||||
\(474\) | −0.969290 | + | 0.601262i | −0.0445210 | + | 0.0276169i | ||||
\(475\) | −3.29215 | −0.151054 | ||||||||
\(476\) | −5.86309 | − | 15.2956i | −0.268734 | − | 0.701074i | ||||
\(477\) | −8.28736 | − | 4.10962i | −0.379452 | − | 0.188167i | ||||
\(478\) | −3.05600 | −0.139778 | ||||||||
\(479\) | 21.0908i | 0.963662i | 0.876264 | + | 0.481831i | \(0.160028\pi\) | ||||
−0.876264 | + | 0.481831i | \(0.839972\pi\) | |||||||
\(480\) | −6.45912 | − | 10.4127i | −0.294817 | − | 0.475273i | ||||
\(481\) | 15.2842 | + | 8.54113i | 0.696900 | + | 0.389442i | ||||
\(482\) | −2.06047 | −0.0938521 | ||||||||
\(483\) | 15.6674 | − | 20.6295i | 0.712893 | − | 0.938676i | ||||
\(484\) | −27.4011 | −1.24551 | ||||||||
\(485\) | 23.4635i | 1.06542i | ||||||||
\(486\) | 4.45357 | + | 1.70430i | 0.202018 | + | 0.0773086i | ||||
\(487\) | − | 28.4284i | − | 1.28821i | −0.764936 | − | 0.644106i | \(-0.777229\pi\) | ||
0.764936 | − | 0.644106i | \(-0.222771\pi\) | |||||||
\(488\) | − | 4.15997i | − | 0.188313i | ||||||
\(489\) | 9.17008 | + | 14.7830i | 0.414685 | + | 0.668511i | ||||
\(490\) | 2.93967 | + | 3.27110i | 0.132801 | + | 0.147773i | ||||
\(491\) | − | 11.0888i | − | 0.500429i | −0.968190 | − | 0.250215i | \(-0.919499\pi\) | ||
0.968190 | − | 0.250215i | \(-0.0805012\pi\) | |||||||
\(492\) | −5.84305 | − | 9.41954i | −0.263425 | − | 0.424666i | ||||
\(493\) | 16.6405i | 0.749449i | ||||||||
\(494\) | −2.26594 | + | 4.05486i | −0.101949 | + | 0.182437i | ||||
\(495\) | 27.8057 | + | 13.7886i | 1.24977 | + | 0.619750i | ||||
\(496\) | −17.6225 | −0.791276 | ||||||||
\(497\) | 6.26114 | + | 16.3341i | 0.280851 | + | 0.732683i | ||||
\(498\) | 0.261607 | + | 0.421735i | 0.0117229 | + | 0.0188984i | ||||
\(499\) | 17.7340i | 0.793884i | 0.917844 | + | 0.396942i | \(0.129929\pi\) | ||||
−0.917844 | + | 0.396942i | \(0.870071\pi\) | |||||||
\(500\) | − | 22.6383i | − | 1.01242i | ||||||
\(501\) | −9.92223 | − | 15.9956i | −0.443293 | − | 0.714629i | ||||
\(502\) | −2.22906 | −0.0994880 | ||||||||
\(503\) | 5.75154 | 0.256449 | 0.128224 | − | 0.991745i | \(-0.459072\pi\) | ||||
0.128224 | + | 0.991745i | \(0.459072\pi\) | |||||||
\(504\) | 9.44272 | + | 0.893209i | 0.420612 | + | 0.0397867i | ||||
\(505\) | − | 27.9085i | − | 1.24191i | ||||||
\(506\) | 8.71033i | 0.387221i | ||||||||
\(507\) | −20.1364 | − | 10.0760i | −0.894288 | − | 0.447491i | ||||
\(508\) | −11.8751 | −0.526874 | ||||||||
\(509\) | − | 22.4218i | − | 0.993831i | −0.867799 | − | 0.496915i | \(-0.834466\pi\) | ||
0.867799 | − | 0.496915i | \(-0.165534\pi\) | |||||||
\(510\) | −1.86293 | − | 3.00322i | −0.0824920 | − | 0.132985i | ||||
\(511\) | −14.3256 | − | 37.3728i | −0.633729 | − | 1.65327i | ||||
\(512\) | −20.1131 | −0.888884 | ||||||||
\(513\) | 2.07290 | + | 21.7851i | 0.0915206 | + | 0.961837i | ||||
\(514\) | 4.08034 | 0.179976 | ||||||||
\(515\) | 10.0816 | 0.444247 | ||||||||
\(516\) | 6.86715 | − | 4.25977i | 0.302309 | − | 0.187526i | ||||
\(517\) | 35.9865i | 1.58268i | ||||||||
\(518\) | −3.66984 | + | 1.40671i | −0.161243 | + | 0.0618074i | ||||
\(519\) | 4.29094 | − | 2.66172i | 0.188351 | − | 0.116837i | ||||
\(520\) | −7.72481 | − | 4.31678i | −0.338756 | − | 0.189303i | ||||
\(521\) | 1.51591 | 0.0664132 | 0.0332066 | − | 0.999449i | \(-0.489428\pi\) | ||||
0.0332066 | + | 0.999449i | \(0.489428\pi\) | |||||||
\(522\) | −4.21268 | − | 2.08903i | −0.184384 | − | 0.0914342i | ||||
\(523\) | − | 10.9151i | − | 0.477282i | −0.971108 | − | 0.238641i | \(-0.923298\pi\) | ||
0.971108 | − | 0.238641i | \(-0.0767020\pi\) | |||||||
\(524\) | −36.3571 | −1.58827 | ||||||||
\(525\) | 2.85277 | + | 2.16658i | 0.124505 | + | 0.0945575i | ||||
\(526\) | − | 5.48818i | − | 0.239296i | ||||||
\(527\) | −16.6019 | −0.723189 | ||||||||
\(528\) | 25.5585 | − | 15.8542i | 1.11229 | − | 0.689966i | ||||
\(529\) | −8.95456 | −0.389329 | ||||||||
\(530\) | −1.93726 | −0.0841492 | ||||||||
\(531\) | −33.7438 | − | 16.7332i | −1.46436 | − | 0.726160i | ||||
\(532\) | 7.60316 | + | 19.8351i | 0.329639 | + | 0.859962i | ||||
\(533\) | −10.5657 | − | 5.90434i | −0.457652 | − | 0.255745i | ||||
\(534\) | 3.21421 | + | 5.18160i | 0.139092 | + | 0.224230i | ||||
\(535\) | 15.9252 | 0.688505 | ||||||||
\(536\) | − | 9.29123i | − | 0.401320i | ||||||
\(537\) | 13.1138 | + | 21.1407i | 0.565903 | + | 0.912288i | ||||
\(538\) | −9.03104 | −0.389356 | ||||||||
\(539\) | −26.2259 | + | 23.5687i | −1.12963 | + | 1.01518i | ||||
\(540\) | −20.2541 | + | 1.92721i | −0.871597 | + | 0.0829341i | ||||
\(541\) | 7.42511i | 0.319230i | 0.987179 | + | 0.159615i | \(0.0510253\pi\) | ||||
−0.987179 | + | 0.159615i | \(0.948975\pi\) | |||||||
\(542\) | −3.42196 | −0.146986 | ||||||||
\(543\) | 19.6747 | + | 31.7174i | 0.844322 | + | 1.36113i | ||||
\(544\) | −11.1865 | −0.479617 | ||||||||
\(545\) | 15.7948 | 0.676573 | ||||||||
\(546\) | 4.63205 | − | 2.02246i | 0.198233 | − | 0.0865532i | ||||
\(547\) | 16.0698 | 0.687094 | 0.343547 | − | 0.939135i | \(-0.388371\pi\) | ||||
0.343547 | + | 0.939135i | \(0.388371\pi\) | |||||||
\(548\) | 3.53037 | 0.150810 | ||||||||
\(549\) | −9.35636 | − | 4.63973i | −0.399320 | − | 0.198019i | ||||
\(550\) | −1.20451 | −0.0513607 | ||||||||
\(551\) | − | 21.5791i | − | 0.919301i | ||||||
\(552\) | −6.16747 | − | 9.94253i | −0.262505 | − | 0.423182i | ||||
\(553\) | 2.03865 | + | 5.31842i | 0.0866920 | + | 0.226162i | ||||
\(554\) | 5.29113 | 0.224799 | ||||||||
\(555\) | 14.6799 | − | 9.10610i | 0.623126 | − | 0.386532i | ||||
\(556\) | − | 10.9151i | − | 0.462902i | ||||||
\(557\) | 16.8791 | 0.715193 | 0.357596 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357596 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(558\) | 2.08418 | − | 4.20290i | 0.0882304 | − | 0.177923i | ||||
\(559\) | 4.30445 | − | 7.70275i | 0.182059 | − | 0.325792i | ||||
\(560\) | −17.4915 | + | 6.70481i | −0.739152 | + | 0.283330i | ||||
\(561\) | 24.0782 | − | 14.9360i | 1.01658 | − | 0.630597i | ||||
\(562\) | 4.47633 | 0.188823 | ||||||||
\(563\) | −0.607801 | −0.0256157 | −0.0128079 | − | 0.999918i | \(-0.504077\pi\) | ||||
−0.0128079 | + | 0.999918i | \(0.504077\pi\) | |||||||
\(564\) | −12.4352 | − | 20.0467i | −0.523616 | − | 0.844117i | ||||
\(565\) | −0.516548 | −0.0217313 | ||||||||
\(566\) | 6.91803i | 0.290786i | ||||||||
\(567\) | 12.5407 | − | 20.2418i | 0.526660 | − | 0.850076i | ||||
\(568\) | 7.90088 | 0.331514 | ||||||||
\(569\) | 5.43594i | 0.227886i | 0.993487 | + | 0.113943i | \(0.0363482\pi\) | ||||
−0.993487 | + | 0.113943i | \(0.963652\pi\) | |||||||
\(570\) | 2.41582 | + | 3.89453i | 0.101188 | + | 0.163124i | ||||
\(571\) | −25.0656 | −1.04896 | −0.524482 | − | 0.851422i | \(-0.675741\pi\) | ||||
−0.524482 | + | 0.851422i | \(0.675741\pi\) | |||||||
\(572\) | 16.8903 | − | 30.2249i | 0.706217 | − | 1.26376i | ||||
\(573\) | −16.1034 | − | 25.9602i | −0.672729 | − | 1.08450i | ||||
\(574\) | 2.53690 | − | 0.972438i | 0.105888 | − | 0.0405888i | ||||
\(575\) | − | 4.41886i | − | 0.184279i | ||||||
\(576\) | −7.78477 | + | 15.6986i | −0.324365 | + | 0.654107i | ||||
\(577\) | 15.8303 | 0.659022 | 0.329511 | − | 0.944152i | \(-0.393116\pi\) | ||||
0.329511 | + | 0.944152i | \(0.393116\pi\) | |||||||
\(578\) | 1.97394 | 0.0821049 | ||||||||
\(579\) | −8.45247 | − | 13.6262i | −0.351273 | − | 0.566284i | ||||
\(580\) | 20.0625 | 0.833051 | ||||||||
\(581\) | 2.31403 | − | 0.887008i | 0.0960021 | − | 0.0367993i | ||||
\(582\) | −5.14369 | + | 3.19069i | −0.213213 | + | 0.132258i | ||||
\(583\) | − | 15.5319i | − | 0.643265i | ||||||
\(584\) | −18.0774 | −0.748049 | ||||||||
\(585\) | −18.3248 | + | 12.5596i | −0.757636 | + | 0.519275i | ||||
\(586\) | 2.15014i | 0.0888215i | ||||||||
\(587\) | − | 34.0187i | − | 1.40410i | −0.712126 | − | 0.702052i | \(-0.752267\pi\) | ||
0.712126 | − | 0.702052i | \(-0.247733\pi\) | |||||||
\(588\) | 6.46521 | − | 22.1916i | 0.266621 | − | 0.915165i | ||||
\(589\) | 21.5291 | 0.887089 | ||||||||
\(590\) | −7.88798 | −0.324743 | ||||||||
\(591\) | −40.4161 | + | 25.0706i | −1.66249 | + | 1.03126i | ||||
\(592\) | − | 16.7403i | − | 0.688023i | ||||||
\(593\) | 0.808753i | 0.0332115i | 0.999862 | + | 0.0166058i | \(0.00528602\pi\) | ||||
−0.999862 | + | 0.0166058i | \(0.994714\pi\) | |||||||
\(594\) | 0.758420 | + | 7.97063i | 0.0311184 | + | 0.327039i | ||||
\(595\) | −16.4784 | + | 6.31648i | −0.675550 | + | 0.258950i | ||||
\(596\) | −0.247714 | −0.0101468 | ||||||||
\(597\) | 6.87674 | + | 11.0859i | 0.281446 | + | 0.453717i | ||||
\(598\) | −5.44260 | − | 3.04144i | −0.222565 | − | 0.124374i | ||||
\(599\) | 0.0865332i | 0.00353565i | 0.999998 | + | 0.00176783i | \(0.000562717\pi\) | ||||
−0.999998 | + | 0.00176783i | \(0.999437\pi\) | |||||||
\(600\) | 1.37491 | − | 0.852873i | 0.0561305 | − | 0.0348184i | ||||
\(601\) | − | 11.1624i | − | 0.455322i | −0.973740 | − | 0.227661i | \(-0.926892\pi\) | ||
0.973740 | − | 0.227661i | \(-0.0731079\pi\) | |||||||
\(602\) | 0.708938 | + | 1.84948i | 0.0288942 | + | 0.0753791i | ||||
\(603\) | −20.8973 | − | 10.3628i | −0.851004 | − | 0.422005i | ||||
\(604\) | − | 41.7297i | − | 1.69796i | ||||||
\(605\) | 29.5201i | 1.20016i | ||||||||
\(606\) | 6.11814 | − | 3.79515i | 0.248532 | − | 0.154168i | ||||
\(607\) | − | 16.6405i | − | 0.675416i | −0.941251 | − | 0.337708i | \(-0.890348\pi\) | ||
0.941251 | − | 0.337708i | \(-0.109652\pi\) | |||||||
\(608\) | 14.5065 | 0.588315 | ||||||||
\(609\) | −14.2013 | + | 18.6991i | −0.575468 | + | 0.757726i | ||||
\(610\) | −2.18715 | −0.0885552 | ||||||||
\(611\) | −22.4860 | − | 12.5656i | −0.909685 | − | 0.508350i | ||||
\(612\) | −8.25185 | + | 16.6405i | −0.333561 | + | 0.672651i | ||||
\(613\) | 33.9935i | 1.37298i | 0.727137 | + | 0.686492i | \(0.240850\pi\) | ||||
−0.727137 | + | 0.686492i | \(0.759150\pi\) | |||||||
\(614\) | 1.70329 | 0.0687392 | ||||||||
\(615\) | −10.1480 | + | 6.29489i | −0.409205 | + | 0.253835i | ||||
\(616\) | 5.70015 | + | 14.8706i | 0.229666 | + | 0.599152i | ||||
\(617\) | 8.17576 | 0.329144 | 0.164572 | − | 0.986365i | \(-0.447376\pi\) | ||||
0.164572 | + | 0.986365i | \(0.447376\pi\) | |||||||
\(618\) | 1.37095 | + | 2.21009i | 0.0551476 | + | 0.0889030i | ||||
\(619\) | 35.7291 | 1.43607 | 0.718037 | − | 0.696005i | \(-0.245041\pi\) | ||||
0.718037 | + | 0.696005i | \(0.245041\pi\) | |||||||
\(620\) | 20.0160i | 0.803862i | ||||||||
\(621\) | −29.2409 | + | 2.78233i | −1.17340 | + | 0.111651i | ||||
\(622\) | 3.48967 | 0.139923 | ||||||||
\(623\) | 28.4311 | − | 10.8981i | 1.13907 | − | 0.436625i | ||||
\(624\) | 0.982028 | + | 21.5060i | 0.0393126 | + | 0.860928i | ||||
\(625\) | −20.4804 | −0.819216 | ||||||||
\(626\) | − | 9.41482i | − | 0.376292i | ||||||
\(627\) | −31.2242 | + | 19.3687i | −1.24697 | + | 0.773512i | ||||
\(628\) | 19.3973i | 0.774037i | ||||||||
\(629\) | − | 15.7708i | − | 0.628821i | ||||||
\(630\) | 0.469615 | − | 4.96462i | 0.0187099 | − | 0.197795i | ||||
\(631\) | 31.6781i | 1.26108i | 0.776155 | + | 0.630542i | \(0.217167\pi\) | ||||
−0.776155 | + | 0.630542i | \(0.782833\pi\) | |||||||
\(632\) | 2.57255 | 0.102331 | ||||||||
\(633\) | −9.58599 | + | 5.94630i | −0.381009 | + | 0.236344i | ||||
\(634\) | 0.664489 | 0.0263902 | ||||||||
\(635\) | 12.7934i | 0.507692i | ||||||||
\(636\) | 5.36706 | + | 8.65220i | 0.212818 | + | 0.343082i | ||||
\(637\) | −5.56934 | − | 24.6167i | −0.220665 | − | 0.975350i | ||||
\(638\) | − | 7.89525i | − | 0.312576i | ||||||
\(639\) | 8.81208 | − | 17.7702i | 0.348601 | − | 0.702979i | ||||
\(640\) | 17.8187i | 0.704345i | ||||||||
\(641\) | 0.921906i | 0.0364131i | 0.999834 | + | 0.0182065i | \(0.00579564\pi\) | ||||
−0.999834 | + | 0.0182065i | \(0.994204\pi\) | |||||||
\(642\) | 2.16559 | + | 3.49113i | 0.0854691 | + | 0.137784i | ||||
\(643\) | 10.1310 | 0.399528 | 0.199764 | − | 0.979844i | \(-0.435982\pi\) | ||||
0.199764 | + | 0.979844i | \(0.435982\pi\) | |||||||
\(644\) | −26.6236 | + | 10.2053i | −1.04912 | + | 0.402144i | ||||
\(645\) | −4.58918 | − | 7.39818i | −0.180699 | − | 0.291303i | ||||
\(646\) | 4.18394 | 0.164615 | ||||||||
\(647\) | −17.9763 | −0.706721 | −0.353360 | − | 0.935487i | \(-0.614961\pi\) | ||||
−0.353360 | + | 0.935487i | \(0.614961\pi\) | |||||||
\(648\) | −6.50942 | − | 8.56118i | −0.255714 | − | 0.336315i | ||||
\(649\) | − | 63.2414i | − | 2.48244i | ||||||
\(650\) | 0.420587 | − | 0.752634i | 0.0164968 | − | 0.0295207i | ||||
\(651\) | −18.6557 | − | 14.1684i | −0.731175 | − | 0.555304i | ||||
\(652\) | − | 19.1476i | − | 0.749876i | ||||||
\(653\) | − | 2.78003i | − | 0.108791i | −0.998519 | − | 0.0543954i | \(-0.982677\pi\) | ||
0.998519 | − | 0.0543954i | \(-0.0173231\pi\) | |||||||
\(654\) | 2.14786 | + | 3.46255i | 0.0839879 | + | 0.135396i | ||||
\(655\) | 39.1686i | 1.53044i | ||||||||
\(656\) | 11.5723i | 0.451823i | ||||||||
\(657\) | −20.1623 | + | 40.6587i | −0.786605 | + | 1.58625i | ||||
\(658\) | 5.39902 | − | 2.06954i | 0.210476 | − | 0.0806791i | ||||
\(659\) | 27.7092i | 1.07940i | 0.841858 | + | 0.539700i | \(0.181462\pi\) | ||||
−0.841858 | + | 0.539700i | \(0.818538\pi\) | |||||||
\(660\) | −18.0075 | − | 29.0298i | −0.700941 | − | 1.12998i | ||||
\(661\) | 0.0294905 | 0.00114705 | 0.000573524 | − | 1.00000i | \(-0.499817\pi\) | ||||
0.000573524 | 1.00000i | \(0.499817\pi\) | ||||||||
\(662\) | 2.06638i | 0.0803120i | ||||||||
\(663\) | 0.925150 | + | 20.2604i | 0.0359298 | + | 0.786848i | ||||
\(664\) | − | 1.11931i | − | 0.0434376i | ||||||
\(665\) | 21.3690 | − | 8.19112i | 0.828654 | − | 0.317638i | ||||
\(666\) | 3.99250 | + | 1.97984i | 0.154706 | + | 0.0767174i | ||||
\(667\) | 28.9644 | 1.12151 | ||||||||
\(668\) | 20.7181i | 0.801607i | ||||||||
\(669\) | 7.40014 | − | 4.59040i | 0.286106 | − | 0.177475i | ||||
\(670\) | −4.88497 | −0.188723 | ||||||||
\(671\) | − | 17.5354i | − | 0.676946i | ||||||
\(672\) | −12.5704 | − | 9.54679i | −0.484913 | − | 0.368276i | ||||
\(673\) | 23.4074 | 0.902289 | 0.451145 | − | 0.892451i | \(-0.351016\pi\) | ||||
0.451145 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(674\) | −2.83767 | −0.109303 | ||||||||
\(675\) | −0.384756 | − | 4.04360i | −0.0148093 | − | 0.155638i | ||||
\(676\) | 12.9882 | + | 21.1076i | 0.499545 | + | 0.811830i | ||||
\(677\) | 24.9484 | 0.958844 | 0.479422 | − | 0.877585i | \(-0.340846\pi\) | ||||
0.479422 | + | 0.877585i | \(0.340846\pi\) | |||||||
\(678\) | −0.0702430 | − | 0.113238i | −0.00269767 | − | 0.00434889i | ||||
\(679\) | 10.8184 | + | 28.2230i | 0.415172 | + | 1.08310i | ||||
\(680\) | 7.97071i | 0.305663i | ||||||||
\(681\) | −9.20627 | − | 14.8414i | −0.352785 | − | 0.568722i | ||||
\(682\) | 7.87694 | 0.301624 | ||||||||
\(683\) | −20.8437 | −0.797561 | −0.398780 | − | 0.917046i | \(-0.630566\pi\) | ||||
−0.398780 | + | 0.917046i | \(0.630566\pi\) | |||||||
\(684\) | 10.7009 | − | 21.5791i | 0.409158 | − | 0.825098i | ||||
\(685\) | − | 3.80338i | − | 0.145320i | ||||||
\(686\) | 5.04421 | + | 2.57924i | 0.192589 | + | 0.0984757i | ||||
\(687\) | −10.3097 | + | 6.39522i | −0.393339 | + | 0.243993i | ||||
\(688\) | −8.43659 | −0.321642 | ||||||||
\(689\) | 9.70501 | + | 5.42336i | 0.369732 | + | 0.206613i | ||||
\(690\) | −5.22740 | + | 3.24262i | −0.199004 | + | 0.123444i | ||||
\(691\) | 35.0440 | 1.33314 | 0.666569 | − | 0.745443i | \(-0.267762\pi\) | ||||
0.666569 | + | 0.745443i | \(0.267762\pi\) | |||||||
\(692\) | −5.55780 | −0.211276 | ||||||||
\(693\) | 39.8036 | + | 3.76511i | 1.51201 | + | 0.143025i | ||||
\(694\) | − | 8.49483i | − | 0.322459i | ||||||
\(695\) | −11.7591 | −0.446049 | ||||||||
\(696\) | 5.59034 | + | 9.01215i | 0.211901 | + | 0.341605i | ||||
\(697\) | 10.9021i | 0.412945i | ||||||||
\(698\) | −0.974937 | −0.0369019 | ||||||||
\(699\) | 21.2645 | + | 34.2804i | 0.804299 | + | 1.29660i | ||||
\(700\) | −1.41124 | − | 3.68166i | −0.0533400 | − | 0.139154i | ||||
\(701\) | − | 9.20469i | − | 0.347656i | −0.984776 | − | 0.173828i | \(-0.944386\pi\) | ||
0.984776 | − | 0.173828i | \(-0.0556137\pi\) | |||||||
\(702\) | −5.24523 | − | 2.30926i | −0.197968 | − | 0.0871573i | ||||
\(703\) | 20.4513i | 0.771334i | ||||||||
\(704\) | −29.4217 | −1.10887 | ||||||||
\(705\) | −21.5969 | + | 13.3968i | −0.813385 | + | 0.504552i | ||||
\(706\) | 6.80916i | 0.256266i | ||||||||
\(707\) | −12.8679 | − | 33.5698i | −0.483947 | − | 1.26252i | ||||
\(708\) | 21.8532 | + | 35.2293i | 0.821292 | + | 1.32400i | ||||
\(709\) | − | 16.2515i | − | 0.610338i | −0.952298 | − | 0.305169i | \(-0.901287\pi\) | ||
0.952298 | − | 0.305169i | \(-0.0987130\pi\) | |||||||
\(710\) | − | 4.15398i | − | 0.155896i | ||||||
\(711\) | 2.86924 | − | 5.78603i | 0.107605 | − | 0.216993i | ||||
\(712\) | − | 13.7523i | − | 0.515388i | ||||||
\(713\) | 28.8972i | 1.08221i | ||||||||
\(714\) | −3.62554 | − | 2.75347i | −0.135682 | − | 0.103046i | ||||
\(715\) | −32.5622 | − | 18.1964i | −1.21776 | − | 0.680506i | ||||
\(716\) | − | 27.3823i | − | 1.02332i | ||||||
\(717\) | 14.7042 | − | 9.12119i | 0.549138 | − | 0.340637i | ||||
\(718\) | −6.54284 | −0.244176 | ||||||||
\(719\) | 50.1573 | 1.87055 | 0.935276 | − | 0.353920i | \(-0.115151\pi\) | ||||
0.935276 | + | 0.353920i | \(0.115151\pi\) | |||||||
\(720\) | 19.0294 | + | 9.43652i | 0.709185 | + | 0.351678i | ||||
\(721\) | 12.1266 | − | 4.64835i | 0.451619 | − | 0.173114i | ||||
\(722\) | 0.386465 | 0.0143828 | ||||||||
\(723\) | 9.91413 | − | 6.14985i | 0.368711 | − | 0.228715i | ||||
\(724\) | − | 41.0817i | − | 1.52679i | ||||||
\(725\) | 4.00536i | 0.148755i | ||||||||
\(726\) | −6.47142 | + | 4.01430i | −0.240177 | + | 0.148985i | ||||
\(727\) | − | 19.3029i | − | 0.715903i | −0.933740 | − | 0.357952i | \(-0.883475\pi\) | ||
0.933740 | − | 0.357952i | \(-0.116525\pi\) | |||||||
\(728\) | −11.2822 | − | 1.63073i | −0.418144 | − | 0.0604389i | ||||
\(729\) | −26.5155 | + | 5.09210i | −0.982055 | + | 0.188596i | ||||
\(730\) | 9.50442i | 0.351774i | ||||||||
\(731\) | −7.94795 | −0.293966 | ||||||||
\(732\) | 6.05937 | + | 9.76827i | 0.223961 | + | 0.361045i | ||||
\(733\) | −23.6407 | −0.873188 | −0.436594 | − | 0.899659i | \(-0.643815\pi\) | ||||
−0.436594 | + | 0.899659i | \(0.643815\pi\) | |||||||
\(734\) | 0.226476i | 0.00835940i | ||||||||
\(735\) | −23.9076 | − | 6.96517i | −0.881847 | − | 0.256914i | ||||
\(736\) | 19.4712i | 0.717717i | ||||||||
\(737\) | − | 39.1650i | − | 1.44266i | ||||||
\(738\) | −2.75995 | − | 1.36863i | −0.101595 | − | 0.0503801i | ||||
\(739\) | − | 20.0184i | − | 0.736389i | −0.929749 | − | 0.368195i | \(-0.879976\pi\) | ||
0.929749 | − | 0.368195i | \(-0.120024\pi\) | |||||||
\(740\) | −19.0140 | −0.698967 | ||||||||
\(741\) | −1.19972 | − | 26.2734i | −0.0440728 | − | 0.965176i | ||||
\(742\) | −2.33023 | + | 0.893220i | −0.0855456 | + | 0.0327911i | ||||
\(743\) | 27.2916 | 1.00123 | 0.500616 | − | 0.865669i | \(-0.333107\pi\) | ||||
0.500616 | + | 0.865669i | \(0.333107\pi\) | |||||||
\(744\) | −8.99124 | + | 5.57737i | −0.329635 | + | 0.204476i | ||||
\(745\) | 0.266870i | 0.00977736i | ||||||||
\(746\) | 10.0161 | 0.366715 | ||||||||
\(747\) | −2.51748 | − | 1.24840i | −0.0921100 | − | 0.0456765i | ||||
\(748\) | −31.1870 | −1.14031 | ||||||||
\(749\) | 19.1556 | − | 7.34268i | 0.699930 | − | 0.268296i | ||||
\(750\) | −3.31654 | − | 5.34657i | −0.121103 | − | 0.195229i | ||||
\(751\) | 26.4623 | 0.965623 | 0.482812 | − | 0.875724i | \(-0.339616\pi\) | ||||
0.482812 | + | 0.875724i | \(0.339616\pi\) | |||||||
\(752\) | 24.6282i | 0.898098i | ||||||||
\(753\) | 10.7253 | − | 6.65304i | 0.390852 | − | 0.242450i | ||||
\(754\) | 4.93331 | + | 2.75683i | 0.179660 | + | 0.100398i | ||||
\(755\) | −44.9567 | −1.63614 | ||||||||
\(756\) | −23.4741 | + | 11.6568i | −0.853743 | + | 0.423953i | ||||
\(757\) | −20.3911 | −0.741129 | −0.370564 | − | 0.928807i | \(-0.620836\pi\) | ||||
−0.370564 | + | 0.928807i | \(0.620836\pi\) | |||||||
\(758\) | − | 5.28586i | − | 0.191991i | ||||||
\(759\) | −25.9975 | − | 41.9104i | −0.943650 | − | 1.52125i | ||||
\(760\) | − | 10.3363i | − | 0.374937i | ||||||
\(761\) | 47.6663i | 1.72790i | 0.503576 | + | 0.863951i | \(0.332017\pi\) | ||||
−0.503576 | + | 0.863951i | \(0.667983\pi\) | |||||||
\(762\) | −2.80459 | + | 1.73972i | −0.101600 | + | 0.0630235i | ||||
\(763\) | 18.9987 | − | 7.28256i | 0.687801 | − | 0.263646i | ||||
\(764\) | 33.6247i | 1.21650i | ||||||||
\(765\) | 17.9273 | + | 8.88997i | 0.648162 | + | 0.321418i | ||||
\(766\) | − | 6.27725i | − | 0.226806i | ||||||
\(767\) | 39.5161 | + | 22.0824i | 1.42684 | + | 0.797348i | ||||
\(768\) | 13.2879 | − | 8.24266i | 0.479487 | − | 0.297431i | ||||
\(769\) | 16.8136 | 0.606313 | 0.303156 | − | 0.952941i | \(-0.401960\pi\) | ||||
0.303156 | + | 0.952941i | \(0.401960\pi\) | |||||||
\(770\) | 7.81838 | − | 2.99692i | 0.281755 | − | 0.108002i | ||||
\(771\) | −19.6328 | + | 12.1785i | −0.707060 | + | 0.438597i | ||||
\(772\) | 17.6492i | 0.635207i | ||||||||
\(773\) | − | 23.0113i | − | 0.827659i | −0.910354 | − | 0.413830i | \(-0.864191\pi\) | ||
0.910354 | − | 0.413830i | \(-0.135809\pi\) | |||||||
\(774\) | 0.997777 | − | 2.01209i | 0.0358644 | − | 0.0723231i | ||||
\(775\) | −3.99607 | −0.143543 | ||||||||
\(776\) | 13.6516 | 0.490065 | ||||||||
\(777\) | 13.4591 | − | 17.7218i | 0.482843 | − | 0.635766i | ||||
\(778\) | 10.0127i | 0.358972i | ||||||||
\(779\) | − | 14.1376i | − | 0.506533i | ||||||
\(780\) | 24.4269 | − | 1.11540i | 0.874622 | − | 0.0399379i | ||||
\(781\) | 33.3043 | 1.19172 | ||||||||
\(782\) | 5.61586i | 0.200823i | ||||||||
\(783\) | 26.5047 | − | 2.52197i | 0.947200 | − | 0.0901278i | ||||
\(784\) | −17.9483 | + | 16.1298i | −0.641010 | + | 0.576064i | ||||
\(785\) | 20.8973 | 0.745857 | ||||||||
\(786\) | −8.58659 | + | 5.32636i | −0.306274 | + | 0.189985i | ||||
\(787\) | −37.1096 | −1.32281 | −0.661406 | − | 0.750028i | \(-0.730040\pi\) | ||||
−0.661406 | + | 0.750028i | \(0.730040\pi\) | |||||||
\(788\) | 52.3485 | 1.86484 | ||||||||
\(789\) | 16.3804 | + | 26.4068i | 0.583159 | + | 0.940106i | ||||
\(790\) | − | 1.35255i | − | 0.0481215i | ||||||
\(791\) | −0.621330 | + | 0.238167i | −0.0220919 | + | 0.00846823i | ||||
\(792\) | 8.02254 | − | 16.1780i | 0.285068 | − | 0.574862i | ||||
\(793\) | 10.9569 | + | 6.12293i | 0.389090 | + | 0.217432i | ||||
\(794\) | 9.96416 | 0.353615 | ||||||||
\(795\) | 9.32127 | − | 5.78210i | 0.330592 | − | 0.205070i | ||||
\(796\) | − | 14.3590i | − | 0.508940i | ||||||
\(797\) | −18.3081 | −0.648507 | −0.324254 | − | 0.945970i | \(-0.605113\pi\) | ||||
−0.324254 | + | 0.945970i | \(0.605113\pi\) | |||||||
\(798\) | 4.70154 | + | 3.57066i | 0.166433 | + | 0.126400i | ||||
\(799\) | 23.2018i | 0.820819i | ||||||||
\(800\) | −2.69259 | −0.0951973 | ||||||||
\(801\) | −30.9308 | − | 15.3383i | −1.09289 | − | 0.541952i | ||||
\(802\) | −8.20647 | −0.289781 | ||||||||
\(803\) | −76.2012 | −2.68908 | ||||||||
\(804\) | 13.5335 | + | 21.8173i | 0.477290 | + | 0.769436i | ||||
\(805\) | 10.9945 | + | 28.6824i | 0.387504 | + | 1.01092i | ||||
\(806\) | −2.75044 | + | 4.92186i | −0.0968800 | + | 0.173365i | ||||
\(807\) | 43.4535 | − | 26.9547i | 1.52964 | − | 0.948852i | ||||
\(808\) | −16.2379 | −0.571247 | ||||||||
\(809\) | − | 36.0180i | − | 1.26633i | −0.774019 | − | 0.633163i | \(-0.781756\pi\) | ||
0.774019 | − | 0.633163i | \(-0.218244\pi\) | |||||||
\(810\) | −4.50114 | + | 3.42241i | −0.158154 | + | 0.120251i | ||||
\(811\) | 52.3273 | 1.83746 | 0.918729 | − | 0.394888i | \(-0.129217\pi\) | ||||
0.918729 | + | 0.394888i | \(0.129217\pi\) | |||||||
\(812\) | 24.1322 | − | 9.25031i | 0.846875 | − | 0.324622i | ||||
\(813\) | 16.4650 | − | 10.2135i | 0.577454 | − | 0.358202i | ||||
\(814\) | 7.48261i | 0.262265i | ||||||||
\(815\) | −20.6282 | −0.722576 | ||||||||
\(816\) | 16.4784 | − | 10.2218i | 0.576861 | − | 0.357834i | ||||
\(817\) | 10.3068 | 0.360589 | ||||||||
\(818\) | 6.62219 | 0.231539 | ||||||||
\(819\) | −16.2511 | + | 23.5564i | −0.567858 | + | 0.823127i | ||||
\(820\) | 13.1440 | 0.459010 | ||||||||
\(821\) | 15.7911 | 0.551112 | 0.275556 | − | 0.961285i | \(-0.411138\pi\) | ||||
0.275556 | + | 0.961285i | \(0.411138\pi\) | |||||||
\(822\) | 0.833781 | − | 0.517204i | 0.0290815 | − | 0.0180396i | ||||
\(823\) | −16.2290 | −0.565708 | −0.282854 | − | 0.959163i | \(-0.591281\pi\) | ||||
−0.282854 | + | 0.959163i | \(0.591281\pi\) | |||||||
\(824\) | − | 5.86571i | − | 0.204342i | ||||||
\(825\) | 5.79561 | − | 3.59509i | 0.201777 | − | 0.125165i | ||||
\(826\) | −9.48806 | + | 3.63694i | −0.330132 | + | 0.126545i | ||||
\(827\) | 3.50935 | 0.122032 | 0.0610161 | − | 0.998137i | \(-0.480566\pi\) | ||||
0.0610161 | + | 0.998137i | \(0.480566\pi\) | |||||||
\(828\) | 28.9644 | + | 14.3632i | 1.00658 | + | 0.499154i | ||||
\(829\) | 13.6148i | 0.472860i | 0.971649 | + | 0.236430i | \(0.0759774\pi\) | ||||
−0.971649 | + | 0.236430i | \(0.924023\pi\) | |||||||
\(830\) | −0.588489 | −0.0204268 | ||||||||
\(831\) | −25.4587 | + | 15.7923i | −0.883152 | + | 0.547829i | ||||
\(832\) | 10.2733 | − | 18.3840i | 0.356164 | − | 0.637351i | ||||
\(833\) | −16.9087 | + | 15.1956i | −0.585853 | + | 0.526495i | ||||
\(834\) | −1.59907 | − | 2.57785i | −0.0553713 | − | 0.0892636i | ||||
\(835\) | 22.3202 | 0.772423 | ||||||||
\(836\) | 40.4428 | 1.39874 | ||||||||
\(837\) | 2.51612 | + | 26.4432i | 0.0869698 | + | 0.914011i | ||||
\(838\) | −4.66601 | −0.161185 | ||||||||
\(839\) | 11.6876i | 0.403502i | 0.979437 | + | 0.201751i | \(0.0646632\pi\) | ||||
−0.979437 | + | 0.201751i | \(0.935337\pi\) | |||||||
\(840\) | −6.80238 | + | 8.95679i | −0.234705 | + | 0.309039i | ||||
\(841\) | 2.74598 | 0.0946889 | ||||||||
\(842\) | − | 4.78043i | − | 0.164744i | ||||||
\(843\) | −21.5382 | + | 13.3604i | −0.741816 | + | 0.460157i | ||||
\(844\) | 12.4162 | 0.427382 | ||||||||
\(845\) | 22.7398 | − | 13.9926i | 0.782274 | − | 0.481359i | ||||
\(846\) | −5.87372 | − | 2.91272i | −0.201943 | − | 0.100142i | ||||
\(847\) | 13.6109 | + | 35.5082i | 0.467677 | + | 1.22008i | ||||
\(848\) | − | 10.6296i | − | 0.365022i | ||||||
\(849\) | −20.6481 | − | 33.2866i | −0.708640 | − | 1.14239i | ||||
\(850\) | −0.776593 | −0.0266369 | ||||||||
\(851\) | −27.4506 | −0.940993 | ||||||||
\(852\) | −18.5525 | + | 11.5084i | −0.635599 | + | 0.394270i | ||||
\(853\) | −14.5565 | −0.498404 | −0.249202 | − | 0.968452i | \(-0.580168\pi\) | ||||
−0.249202 | + | 0.968452i | \(0.580168\pi\) | |||||||
\(854\) | −2.63082 | + | 1.00844i | −0.0900247 | + | 0.0345081i | ||||
\(855\) | −23.2478 | − | 11.5284i | −0.795059 | − | 0.394262i | ||||
\(856\) | − | 9.26567i | − | 0.316694i | ||||||
\(857\) | 24.0760 | 0.822420 | 0.411210 | − | 0.911541i | \(-0.365106\pi\) | ||||
0.411210 | + | 0.911541i | \(0.365106\pi\) | |||||||
\(858\) | −0.438947 | − | 9.61276i | −0.0149854 | − | 0.328174i | ||||
\(859\) | 9.15176i | 0.312254i | 0.987737 | + | 0.156127i | \(0.0499009\pi\) | ||||
−0.987737 | + | 0.156127i | \(0.950099\pi\) | |||||||
\(860\) | 9.58243i | 0.326758i | ||||||||
\(861\) | −9.30406 | + | 12.2508i | −0.317082 | + | 0.417505i | ||||
\(862\) | −8.25124 | −0.281038 | ||||||||
\(863\) | 14.6037 | 0.497115 | 0.248558 | − | 0.968617i | \(-0.420043\pi\) | ||||
0.248558 | + | 0.968617i | \(0.420043\pi\) | |||||||
\(864\) | 1.69538 | + | 17.8177i | 0.0576781 | + | 0.606169i | ||||
\(865\) | 5.98759i | 0.203584i | ||||||||
\(866\) | − | 6.75352i | − | 0.229494i | ||||||
\(867\) | −9.49774 | + | 5.89156i | −0.322560 | + | 0.200088i | ||||
\(868\) | 9.22886 | + | 24.0763i | 0.313248 | + | 0.817201i | ||||
\(869\) | 10.8440 | 0.367857 | ||||||||
\(870\) | 4.73824 | − | 2.93919i | 0.160641 | − | 0.0996478i | ||||
\(871\) | 24.4720 | + | 13.6755i | 0.829204 | + | 0.463376i | ||||
\(872\) | − | 9.18980i | − | 0.311206i | ||||||
\(873\) | 15.2261 | − | 30.7045i | 0.515324 | − | 1.03919i | ||||
\(874\) | − | 7.28256i | − | 0.246336i | ||||||
\(875\) | −29.3362 | + | 11.2451i | −0.991746 | + | 0.380154i | ||||
\(876\) | 42.4487 | − | 26.3314i | 1.43421 | − | 0.889656i | ||||
\(877\) | 23.0869i | 0.779588i | 0.920902 | + | 0.389794i | \(0.127454\pi\) | ||||
−0.920902 | + | 0.389794i | \(0.872546\pi\) | |||||||
\(878\) | 4.34078i | 0.146494i | ||||||||
\(879\) | −6.41748 | − | 10.3456i | −0.216456 | − | 0.348947i | ||||
\(880\) | 35.6643i | 1.20224i | ||||||||
\(881\) | 49.4957 | 1.66755 | 0.833777 | − | 0.552102i | \(-0.186174\pi\) | ||||
0.833777 | + | 0.552102i | \(0.186174\pi\) | |||||||
\(882\) | −1.72418 | − | 6.18822i | −0.0580562 | − | 0.208368i | ||||
\(883\) | −43.4915 | −1.46360 | −0.731802 | − | 0.681517i | \(-0.761321\pi\) | ||||
−0.731802 | + | 0.681517i | \(0.761321\pi\) | |||||||
\(884\) | 10.8897 | − | 19.4870i | 0.366262 | − | 0.655420i | ||||
\(885\) | 37.9536 | − | 23.5431i | 1.27580 | − | 0.791391i | ||||
\(886\) | − | 8.21109i | − | 0.275857i | ||||||
\(887\) | 6.21981 | 0.208841 | 0.104420 | − | 0.994533i | \(-0.466701\pi\) | ||||
0.104420 | + | 0.994533i | \(0.466701\pi\) | |||||||
\(888\) | −5.29816 | − | 8.54113i | −0.177795 | − | 0.286621i | ||||
\(889\) | 5.89872 | + | 15.3886i | 0.197837 | + | 0.516117i | ||||
\(890\) | −7.23042 | −0.242364 | ||||||||
\(891\) | −27.4390 | − | 36.0877i | −0.919240 | − | 1.20898i | ||||
\(892\) | −9.58496 | −0.320928 | ||||||||
\(893\) | − | 30.0877i | − | 1.00685i | ||||||
\(894\) | −0.0585036 | + | 0.0362904i | −0.00195665 | + | 0.00121373i | ||||
\(895\) | −29.4998 | −0.986068 | ||||||||
\(896\) | 8.21572 | + | 21.4332i | 0.274468 | + | 0.716033i | ||||
\(897\) | 35.2652 | − | 1.61031i | 1.17747 | − | 0.0537669i | ||||
\(898\) | 0.761798 | 0.0254215 | ||||||||
\(899\) | − | 26.1931i | − | 0.873590i | ||||||
\(900\) | −1.98622 | + | 4.00536i | −0.0662074 | + | 0.133512i | ||||
\(901\) | − | 10.0140i | − | 0.333613i | ||||||
\(902\) | − | 5.17260i | − | 0.172229i | ||||||
\(903\) | −8.93121 | − | 6.78296i | −0.297212 | − | 0.225723i | ||||
\(904\) | 0.300541i | 0.00999583i | ||||||||
\(905\) | −44.2586 | −1.47120 | ||||||||
\(906\) | −6.11346 | − | 9.85546i | −0.203106 | − | 0.327426i | ||||
\(907\) | −19.2141 | −0.637994 | −0.318997 | − | 0.947756i | \(-0.603346\pi\) | ||||
−0.318997 | + | 0.947756i | \(0.603346\pi\) | |||||||
\(908\) | 19.2231i | 0.637942i | ||||||||
\(909\) | −18.1106 | + | 36.5213i | −0.600690 | + | 1.21134i | ||||
\(910\) | −0.857376 | + | 5.93172i | −0.0284217 | + | 0.196635i | ||||
\(911\) | 47.4651i | 1.57259i | 0.617852 | + | 0.786295i | \(0.288003\pi\) | ||||
−0.617852 | + | 0.786295i | \(0.711997\pi\) | |||||||
\(912\) | −21.3690 | + | 13.2554i | −0.707598 | + | 0.438931i | ||||
\(913\) | − | 4.71818i | − | 0.156149i | ||||||
\(914\) | − | 5.93030i | − | 0.196157i | ||||||
\(915\) | 10.5236 | − | 6.52794i | 0.347901 | − | 0.215807i | ||||
\(916\) | 13.3535 | 0.441213 | ||||||||
\(917\) | 18.0596 | + | 47.1140i | 0.596382 | + | 1.55584i | ||||
\(918\) | 0.488980 | + | 5.13895i | 0.0161388 | + | 0.169611i | ||||
\(919\) | −15.5459 | −0.512812 | −0.256406 | − | 0.966569i | \(-0.582538\pi\) | ||||
−0.256406 | + | 0.966569i | \(0.582538\pi\) | |||||||
\(920\) | 13.8738 | 0.457406 | ||||||||
\(921\) | −8.19552 | + | 5.08378i | −0.270051 | + | 0.167516i | ||||
\(922\) | − | 5.36245i | − | 0.176603i | ||||||
\(923\) | −11.6291 | + | 20.8100i | −0.382775 | + | 0.684971i | ||||
\(924\) | −35.0452 | − | 26.6157i | −1.15290 | − | 0.875591i | ||||
\(925\) | − | 3.79602i | − | 0.124812i | ||||||
\(926\) | 0.477040i | 0.0156765i | ||||||||
\(927\) | −13.1928 | − | 6.54220i | −0.433309 | − | 0.214874i | ||||
\(928\) | − | 17.6492i | − | 0.579362i | ||||||
\(929\) | 15.4941i | 0.508345i | 0.967159 | + | 0.254173i | \(0.0818032\pi\) | ||||
−0.967159 | + | 0.254173i | \(0.918197\pi\) | |||||||
\(930\) | 2.93237 | + | 4.72725i | 0.0961562 | + | 0.155013i | ||||
\(931\) | 21.9270 | − | 19.7054i | 0.718628 | − | 0.645818i | ||||
\(932\) | − | 44.4014i | − | 1.45442i | ||||||
\(933\) | −16.7908 | + | 10.4155i | −0.549707 | + | 0.340989i | ||||
\(934\) | 11.1245 | 0.364003 | ||||||||
\(935\) | 33.5987i | 1.09879i | ||||||||
\(936\) | 7.30749 | + | 10.6618i | 0.238853 | + | 0.348492i | ||||
\(937\) | − | 29.4443i | − | 0.961903i | −0.876747 | − | 0.480952i | \(-0.840291\pi\) | ||
0.876747 | − | 0.480952i | \(-0.159709\pi\) | |||||||
\(938\) | −5.87589 | + | 2.25233i | −0.191855 | + | 0.0735413i | ||||
\(939\) | 28.1002 | + | 45.3001i | 0.917016 | + | 1.47831i | ||||
\(940\) | 27.9731 | 0.912383 | ||||||||
\(941\) | − | 9.88486i | − | 0.322237i | −0.986935 | − | 0.161119i | \(-0.948490\pi\) | ||
0.986935 | − | 0.161119i | \(-0.0515102\pi\) | |||||||
\(942\) | 2.84173 | + | 4.58113i | 0.0925886 | + | 0.149261i | ||||
\(943\) | 18.9761 | 0.617947 | ||||||||
\(944\) | − | 43.2807i | − | 1.40867i | ||||||
\(945\) | 12.5582 | + | 25.2893i | 0.408518 | + | 0.822661i | ||||
\(946\) | 3.77099 | 0.122606 | ||||||||
\(947\) | −51.5722 | −1.67587 | −0.837935 | − | 0.545769i | \(-0.816237\pi\) | ||||
−0.837935 | + | 0.545769i | \(0.816237\pi\) | |||||||
\(948\) | −6.04076 | + | 3.74715i | −0.196195 | + | 0.121702i | ||||
\(949\) | 26.6076 | − | 47.6139i | 0.863719 | − | 1.54561i | ||||
\(950\) | 1.00707 | 0.0326738 | ||||||||
\(951\) | −3.19724 | + | 1.98328i | −0.103678 | + | 0.0643124i | ||||
\(952\) | 3.67509 | + | 9.58758i | 0.119110 | + | 0.310735i | ||||
\(953\) | 21.3774i | 0.692481i | 0.938146 | + | 0.346240i | \(0.112542\pi\) | ||||
−0.938146 | + | 0.346240i | \(0.887458\pi\) | |||||||
\(954\) | 2.53512 | + | 1.25714i | 0.0820774 | + | 0.0407014i | ||||
\(955\) | 36.2249 | 1.17221 | ||||||||
\(956\) | −19.0455 | −0.615975 | ||||||||
\(957\) | 23.5648 | + | 37.9886i | 0.761741 | + | 1.22800i | ||||
\(958\) | − | 6.45170i | − | 0.208445i | ||||||
\(959\) | −1.75364 | − | 4.57490i | −0.0566279 | − | 0.147731i | ||||
\(960\) | −10.9529 | − | 17.6571i | −0.353503 | − | 0.569880i | ||||
\(961\) | −4.86763 | −0.157020 | ||||||||
\(962\) | −4.67547 | − | 2.61274i | −0.150743 | − | 0.0842383i | ||||
\(963\) | −20.8398 | − | 10.3343i | −0.671554 | − | 0.333017i | ||||
\(964\) | −12.8412 | −0.413587 | ||||||||
\(965\) | 19.0140 | 0.612081 | ||||||||
\(966\) | −4.79270 | + | 6.31060i | −0.154202 | + | 0.203040i | ||||
\(967\) | − | 19.6205i | − | 0.630953i | −0.948933 | − | 0.315476i | \(-0.897836\pi\) | ||
0.948933 | − | 0.315476i | \(-0.102164\pi\) | |||||||
\(968\) | 17.1755 | 0.552042 | ||||||||
\(969\) | −20.1313 | + | 12.4877i | −0.646712 | + | 0.401163i | ||||
\(970\) | − | 7.17751i | − | 0.230456i | ||||||
\(971\) | 5.81429 | 0.186589 | 0.0932947 | − | 0.995639i | \(-0.470260\pi\) | ||||
0.0932947 | + | 0.995639i | \(0.470260\pi\) | |||||||
\(972\) | 27.7553 | + | 10.6215i | 0.890252 | + | 0.340683i | ||||
\(973\) | −14.1445 | + | 5.42183i | −0.453451 | + | 0.173816i | ||||
\(974\) | 8.69628i | 0.278647i | ||||||||
\(975\) | 0.222684 | + | 4.87667i | 0.00713158 | + | 0.156179i | ||||
\(976\) | − | 12.0007i | − | 0.384134i | ||||||
\(977\) | −29.0313 | −0.928792 | −0.464396 | − | 0.885628i | \(-0.653729\pi\) | ||||
−0.464396 | + | 0.885628i | \(0.653729\pi\) | |||||||
\(978\) | −2.80514 | − | 4.52215i | −0.0896986 | − | 0.144602i | ||||
\(979\) | − | 57.9695i | − | 1.85271i | ||||||
\(980\) | 18.3205 | + | 20.3860i | 0.585227 | + | 0.651206i | ||||
\(981\) | −20.6692 | − | 10.2496i | −0.659916 | − | 0.327246i | ||||
\(982\) | 3.39207i | 0.108245i | ||||||||
\(983\) | − | 27.7980i | − | 0.886619i | −0.896369 | − | 0.443309i | \(-0.853804\pi\) | ||
0.896369 | − | 0.443309i | \(-0.146196\pi\) | |||||||
\(984\) | 3.66253 | + | 5.90434i | 0.116757 | + | 0.188223i | ||||
\(985\) | − | 56.3966i | − | 1.79695i | ||||||
\(986\) | − | 5.09035i | − | 0.162110i | ||||||
\(987\) | −19.8009 | + | 26.0721i | −0.630270 | + | 0.829884i | ||||
\(988\) | −14.1217 | + | 25.2705i | −0.449270 | + | 0.803961i | ||||
\(989\) | 13.8342i | 0.439902i | ||||||||
\(990\) | −8.50579 | − | 4.21794i | −0.270332 | − | 0.134055i | ||||
\(991\) | 22.5644 | 0.716781 | 0.358390 | − | 0.933572i | \(-0.383326\pi\) | ||||
0.358390 | + | 0.933572i | \(0.383326\pi\) | |||||||
\(992\) | 17.6082 | 0.559061 | ||||||||
\(993\) | −6.16747 | − | 9.94253i | −0.195719 | − | 0.315517i | ||||
\(994\) | −1.91529 | − | 4.99662i | −0.0607494 | − | 0.158483i | ||||
\(995\) | −15.4693 | −0.490411 | ||||||||
\(996\) | 1.63037 | + | 2.62831i | 0.0516604 | + | 0.0832813i | ||||
\(997\) | 20.4951i | 0.649087i | 0.945871 | + | 0.324543i | \(0.105211\pi\) | ||||
−0.945871 | + | 0.324543i | \(0.894789\pi\) | |||||||
\(998\) | − | 5.42487i | − | 0.171721i | ||||||
\(999\) | −25.1194 | + | 2.39016i | −0.794743 | + | 0.0756213i |
(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 | 273.2.g.a.272.15 | yes | 32 | |
3.2 | odd | 2 | inner | 273.2.g.a.272.17 | yes | 32 | |
7.6 | odd | 2 | inner | 273.2.g.a.272.14 | yes | 32 | |
13.12 | even | 2 | inner | 273.2.g.a.272.19 | yes | 32 | |
21.20 | even | 2 | inner | 273.2.g.a.272.20 | yes | 32 | |
39.38 | odd | 2 | inner | 273.2.g.a.272.13 | ✓ | 32 | |
91.90 | odd | 2 | inner | 273.2.g.a.272.18 | yes | 32 | |
273.272 | even | 2 | inner | 273.2.g.a.272.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.g.a.272.13 | ✓ | 32 | 39.38 | odd | 2 | inner | |
273.2.g.a.272.14 | yes | 32 | 7.6 | odd | 2 | inner | |
273.2.g.a.272.15 | yes | 32 | 1.1 | even | 1 | trivial | |
273.2.g.a.272.16 | yes | 32 | 273.272 | even | 2 | inner | |
273.2.g.a.272.17 | yes | 32 | 3.2 | odd | 2 | inner | |
273.2.g.a.272.18 | yes | 32 | 91.90 | odd | 2 | inner | |
273.2.g.a.272.19 | yes | 32 | 13.12 | even | 2 | inner | |
273.2.g.a.272.20 | yes | 32 | 21.20 | even | 2 | inner |