Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(68,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 68.16 | ||
Character | \(\chi\) | \(=\) | 441.68 |
Dual form | 441.2.i.d.227.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.664297i | 0.469729i | 0.972028 | + | 0.234864i | \(0.0754646\pi\) | ||||
−0.972028 | + | 0.234864i | \(0.924535\pi\) | |||||||
\(3\) | 1.15747 | + | 1.28852i | 0.668263 | + | 0.743925i | ||||
\(4\) | 1.55871 | 0.779355 | ||||||||
\(5\) | 0.0141520 | + | 0.0245119i | 0.00632895 | + | 0.0109621i | 0.869173 | − | 0.494509i | \(-0.164652\pi\) |
−0.862844 | + | 0.505471i | \(0.831319\pi\) | |||||||
\(6\) | −0.855956 | + | 0.768901i | −0.349443 | + | 0.313903i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.36404i | 0.835814i | ||||||||
\(9\) | −0.320544 | + | 2.98283i | −0.106848 | + | 0.994275i | ||||
\(10\) | −0.0162832 | + | 0.00940110i | −0.00514919 | + | 0.00297289i | ||||
\(11\) | 0.885324 | + | 0.511142i | 0.266935 | + | 0.154115i | 0.627494 | − | 0.778621i | \(-0.284081\pi\) |
−0.360559 | + | 0.932736i | \(0.617414\pi\) | |||||||
\(12\) | 1.80415 | + | 2.00842i | 0.520814 | + | 0.579781i | ||||
\(13\) | −4.87844 | − | 2.81657i | −1.35304 | − | 0.781176i | −0.364363 | − | 0.931257i | \(-0.618713\pi\) |
−0.988674 | + | 0.150081i | \(0.952047\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0152036 | + | 0.0466067i | −0.00392554 | + | 0.0120338i | ||||
\(16\) | 1.54700 | 0.386749 | ||||||||
\(17\) | 2.83940 | + | 4.91798i | 0.688656 | + | 1.19279i | 0.972273 | + | 0.233849i | \(0.0751321\pi\) |
−0.283617 | + | 0.958938i | \(0.591535\pi\) | |||||||
\(18\) | −1.98148 | − | 0.212936i | −0.467040 | − | 0.0501895i | ||||
\(19\) | −1.81237 | − | 1.04637i | −0.415786 | − | 0.240054i | 0.277487 | − | 0.960729i | \(-0.410498\pi\) |
−0.693273 | + | 0.720675i | \(0.743832\pi\) | |||||||
\(20\) | 0.0220588 | + | 0.0382070i | 0.00493250 | + | 0.00854334i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.339550 | + | 0.588118i | −0.0723923 | + | 0.125387i | ||||
\(23\) | 6.28849 | − | 3.63066i | 1.31124 | − | 0.757046i | 0.328940 | − | 0.944351i | \(-0.393309\pi\) |
0.982302 | + | 0.187305i | \(0.0599754\pi\) | |||||||
\(24\) | −3.04610 | + | 2.73630i | −0.621783 | + | 0.558544i | ||||
\(25\) | 2.49960 | − | 4.32943i | 0.499920 | − | 0.865887i | ||||
\(26\) | 1.87104 | − | 3.24073i | 0.366941 | − | 0.635560i | ||||
\(27\) | −4.21444 | + | 3.03949i | −0.811069 | + | 0.584951i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.52577 | + | 2.03560i | −0.654718 | + | 0.378002i | −0.790262 | − | 0.612770i | \(-0.790055\pi\) |
0.135543 | + | 0.990771i | \(0.456722\pi\) | |||||||
\(30\) | −0.0309607 | − | 0.0100997i | −0.00565262 | − | 0.00184394i | ||||
\(31\) | − | 3.31820i | − | 0.595966i | −0.954571 | − | 0.297983i | \(-0.903686\pi\) | ||
0.954571 | − | 0.297983i | \(-0.0963139\pi\) | |||||||
\(32\) | 5.75574i | 1.01748i | ||||||||
\(33\) | 0.366118 | + | 1.73238i | 0.0637330 | + | 0.301569i | ||||
\(34\) | −3.26700 | + | 1.88620i | −0.560286 | + | 0.323481i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.499635 | + | 4.64936i | −0.0832725 | + | 0.774893i | ||||
\(37\) | 1.23632 | − | 2.14137i | 0.203250 | − | 0.352040i | −0.746324 | − | 0.665583i | \(-0.768183\pi\) |
0.949574 | + | 0.313543i | \(0.101516\pi\) | |||||||
\(38\) | 0.695101 | − | 1.20395i | 0.112760 | − | 0.195306i | ||||
\(39\) | −2.01744 | − | 9.54604i | −0.323049 | − | 1.52859i | ||||
\(40\) | −0.0579471 | + | 0.0334558i | −0.00916224 | + | 0.00528982i | ||||
\(41\) | 3.52867 | − | 6.11183i | 0.551085 | − | 0.954508i | −0.447111 | − | 0.894478i | \(-0.647547\pi\) |
0.998197 | − | 0.0600295i | \(-0.0191195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.15994 | − | 2.00908i | −0.176890 | − | 0.306382i | 0.763924 | − | 0.645306i | \(-0.223270\pi\) |
−0.940814 | + | 0.338924i | \(0.889937\pi\) | |||||||
\(44\) | 1.37996 | + | 0.796722i | 0.208037 | + | 0.120110i | ||||
\(45\) | −0.0776511 | + | 0.0343557i | −0.0115755 | + | 0.00512144i | ||||
\(46\) | 2.41184 | + | 4.17742i | 0.355606 | + | 0.615928i | ||||
\(47\) | −10.8799 | −1.58700 | −0.793502 | − | 0.608568i | \(-0.791744\pi\) | ||||
−0.793502 | + | 0.608568i | \(0.791744\pi\) | |||||||
\(48\) | 1.79060 | + | 1.99333i | 0.258450 | + | 0.287712i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.87603 | + | 1.66048i | 0.406732 | + | 0.234827i | ||||
\(51\) | −3.05039 | + | 9.35101i | −0.427140 | + | 1.30940i | ||||
\(52\) | −7.60408 | − | 4.39022i | −1.05450 | − | 0.608814i | ||||
\(53\) | −10.0454 | + | 5.79973i | −1.37985 | + | 0.796655i | −0.992141 | − | 0.125128i | \(-0.960066\pi\) |
−0.387706 | + | 0.921783i | \(0.626732\pi\) | |||||||
\(54\) | −2.01913 | − | 2.79964i | −0.274768 | − | 0.380982i | ||||
\(55\) | 0.0289346i | 0.00390155i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.749489 | − | 3.54640i | −0.0992723 | − | 0.469733i | ||||
\(58\) | −1.35224 | − | 2.34215i | −0.177558 | − | 0.307540i | ||||
\(59\) | 6.02222 | 0.784027 | 0.392013 | − | 0.919960i | \(-0.371779\pi\) | ||||
0.392013 | + | 0.919960i | \(0.371779\pi\) | |||||||
\(60\) | −0.0236979 | + | 0.0726464i | −0.00305939 | + | 0.00937861i | ||||
\(61\) | 2.36968i | 0.303406i | 0.988426 | + | 0.151703i | \(0.0484757\pi\) | ||||
−0.988426 | + | 0.151703i | \(0.951524\pi\) | |||||||
\(62\) | 2.20427 | 0.279942 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.729528 | −0.0911909 | ||||||||
\(65\) | − | 0.159440i | − | 0.0197761i | ||||||
\(66\) | −1.15082 | + | 0.243211i | −0.141656 | + | 0.0299372i | ||||
\(67\) | 12.7799 | 1.56131 | 0.780656 | − | 0.624960i | \(-0.214885\pi\) | ||||
0.780656 | + | 0.624960i | \(0.214885\pi\) | |||||||
\(68\) | 4.42580 | + | 7.66571i | 0.536707 | + | 0.929604i | ||||
\(69\) | 11.9569 | + | 3.90045i | 1.43944 | + | 0.469559i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.93415i | − | 0.941610i | −0.882237 | − | 0.470805i | \(-0.843964\pi\) | ||
0.882237 | − | 0.470805i | \(-0.156036\pi\) | |||||||
\(72\) | −7.05152 | − | 0.757778i | −0.831029 | − | 0.0893050i | ||||
\(73\) | 9.43889 | − | 5.44955i | 1.10474 | − | 0.637821i | 0.167277 | − | 0.985910i | \(-0.446503\pi\) |
0.937462 | + | 0.348089i | \(0.113169\pi\) | |||||||
\(74\) | 1.42251 | + | 0.821285i | 0.165363 | + | 0.0954725i | ||||
\(75\) | 8.47174 | − | 1.79040i | 0.978233 | − | 0.206738i | ||||
\(76\) | −2.82496 | − | 1.63099i | −0.324045 | − | 0.187087i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.34140 | − | 1.34018i | 0.718022 | − | 0.151745i | ||||
\(79\) | −15.6004 | −1.75518 | −0.877588 | − | 0.479415i | \(-0.840849\pi\) | ||||
−0.877588 | + | 0.479415i | \(0.840849\pi\) | |||||||
\(80\) | 0.0218930 | + | 0.0379198i | 0.00244772 | + | 0.00423957i | ||||
\(81\) | −8.79450 | − | 1.91225i | −0.977167 | − | 0.212473i | ||||
\(82\) | 4.06007 | + | 2.34408i | 0.448360 | + | 0.258861i | ||||
\(83\) | 3.07406 | + | 5.32442i | 0.337421 | + | 0.584431i | 0.983947 | − | 0.178461i | \(-0.0571119\pi\) |
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0803661 | + | 0.139198i | −0.00871693 | + | 0.0150982i | ||||
\(86\) | 1.33463 | − | 0.770546i | 0.143916 | − | 0.0830902i | ||||
\(87\) | −6.70386 | − | 2.18686i | −0.718729 | − | 0.234456i | ||||
\(88\) | −1.20836 | + | 2.09294i | −0.128812 | + | 0.223108i | ||||
\(89\) | 6.02582 | − | 10.4370i | 0.638736 | − | 1.10632i | −0.346975 | − | 0.937874i | \(-0.612791\pi\) |
0.985711 | − | 0.168448i | \(-0.0538756\pi\) | |||||||
\(90\) | −0.0228224 | − | 0.0515834i | −0.00240569 | − | 0.00543736i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.80194 | − | 5.65915i | 1.02192 | − | 0.590007i | ||||
\(93\) | 4.27555 | − | 3.84070i | 0.443354 | − | 0.398262i | ||||
\(94\) | − | 7.22751i | − | 0.745461i | ||||||
\(95\) | − | 0.0592328i | − | 0.00607716i | ||||||
\(96\) | −7.41636 | + | 6.66208i | −0.756929 | + | 0.679946i | ||||
\(97\) | 6.77565 | − | 3.91192i | 0.687963 | − | 0.397196i | −0.114885 | − | 0.993379i | \(-0.536650\pi\) |
0.802848 | + | 0.596183i | \(0.203317\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.80843 | + | 2.47692i | −0.181754 | + | 0.248940i | ||||
\(100\) | 3.89615 | − | 6.74833i | 0.389615 | − | 0.674833i | ||||
\(101\) | −0.226924 | + | 0.393043i | −0.0225797 | + | 0.0391093i | −0.877094 | − | 0.480318i | \(-0.840521\pi\) |
0.854515 | + | 0.519427i | \(0.173855\pi\) | |||||||
\(102\) | −6.21185 | − | 2.02636i | −0.615064 | − | 0.200640i | ||||
\(103\) | −4.58316 | + | 2.64609i | −0.451592 | + | 0.260727i | −0.708502 | − | 0.705708i | \(-0.750629\pi\) |
0.256910 | + | 0.966435i | \(0.417296\pi\) | |||||||
\(104\) | 6.65848 | − | 11.5328i | 0.652918 | − | 1.13089i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.85274 | − | 6.67315i | −0.374212 | − | 0.648153i | ||||
\(107\) | −7.85273 | − | 4.53377i | −0.759152 | − | 0.438296i | 0.0698394 | − | 0.997558i | \(-0.477751\pi\) |
−0.828991 | + | 0.559262i | \(0.811085\pi\) | |||||||
\(108\) | −6.56908 | + | 4.73769i | −0.632110 | + | 0.455885i | ||||
\(109\) | −2.36514 | − | 4.09654i | −0.226539 | − | 0.392377i | 0.730241 | − | 0.683190i | \(-0.239408\pi\) |
−0.956780 | + | 0.290812i | \(0.906074\pi\) | |||||||
\(110\) | −0.0192212 | −0.00183267 | ||||||||
\(111\) | 4.19020 | − | 0.885547i | 0.397716 | − | 0.0840524i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.21108 | − | 4.74067i | −0.772433 | − | 0.445965i | 0.0613086 | − | 0.998119i | \(-0.480473\pi\) |
−0.833742 | + | 0.552154i | \(0.813806\pi\) | |||||||
\(114\) | 2.35586 | − | 0.497883i | 0.220647 | − | 0.0466310i | ||||
\(115\) | 0.177989 | + | 0.102762i | 0.0165976 | + | 0.00958261i | ||||
\(116\) | −5.49565 | + | 3.17291i | −0.510258 | + | 0.294598i | ||||
\(117\) | 9.96510 | − | 13.6487i | 0.921273 | − | 1.26182i | ||||
\(118\) | 4.00054i | 0.368280i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.110180 | − | 0.0359418i | −0.0100580 | − | 0.00328102i | ||||
\(121\) | −4.97747 | − | 8.62123i | −0.452497 | − | 0.783748i | ||||
\(122\) | −1.57417 | −0.142519 | ||||||||
\(123\) | 11.9595 | − | 2.52750i | 1.07835 | − | 0.227897i | ||||
\(124\) | − | 5.17211i | − | 0.464469i | ||||||
\(125\) | 0.283017 | 0.0253138 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37297 | 0.388039 | 0.194019 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(128\) | 11.0269i | 0.974646i | ||||||||
\(129\) | 1.24614 | − | 3.82005i | 0.109716 | − | 0.336336i | ||||
\(130\) | 0.105915 | 0.00928940 | ||||||||
\(131\) | 1.27231 | + | 2.20371i | 0.111162 | + | 0.192539i | 0.916239 | − | 0.400632i | \(-0.131209\pi\) |
−0.805077 | + | 0.593171i | \(0.797876\pi\) | |||||||
\(132\) | 0.570672 | + | 2.70028i | 0.0496706 | + | 0.235029i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.48964i | 0.733393i | ||||||||
\(135\) | −0.134146 | − | 0.0602891i | −0.0115455 | − | 0.00518886i | ||||
\(136\) | −11.6263 | + | 6.71245i | −0.996948 | + | 0.575588i | ||||
\(137\) | 9.82536 | + | 5.67267i | 0.839437 | + | 0.484649i | 0.857073 | − | 0.515195i | \(-0.172281\pi\) |
−0.0176357 | + | 0.999844i | \(0.505614\pi\) | |||||||
\(138\) | −2.59106 | + | 7.94292i | −0.220565 | + | 0.676146i | ||||
\(139\) | 3.04891 | + | 1.76029i | 0.258605 | + | 0.149306i | 0.623698 | − | 0.781665i | \(-0.285629\pi\) |
−0.365093 | + | 0.930971i | \(0.618963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.5932 | − | 14.0190i | −1.06054 | − | 1.18061i | ||||
\(142\) | 5.27063 | 0.442301 | ||||||||
\(143\) | −2.87933 | − | 4.98715i | −0.240782 | − | 0.417047i | ||||
\(144\) | −0.495880 | + | 4.61442i | −0.0413233 | + | 0.384535i | ||||
\(145\) | −0.0997930 | − | 0.0576155i | −0.00828736 | − | 0.00478471i | ||||
\(146\) | 3.62012 | + | 6.27022i | 0.299603 | + | 0.518927i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.92707 | − | 3.33778i | 0.158404 | − | 0.274364i | ||||
\(149\) | 13.7806 | − | 7.95623i | 1.12895 | − | 0.651800i | 0.185279 | − | 0.982686i | \(-0.440681\pi\) |
0.943671 | + | 0.330886i | \(0.107348\pi\) | |||||||
\(150\) | 1.18936 | + | 5.62775i | 0.0971106 | + | 0.459504i | ||||
\(151\) | −1.73008 | + | 2.99659i | −0.140792 | + | 0.243859i | −0.927795 | − | 0.373090i | \(-0.878298\pi\) |
0.787003 | + | 0.616949i | \(0.211632\pi\) | |||||||
\(152\) | 2.47366 | − | 4.28451i | 0.200640 | − | 0.347520i | ||||
\(153\) | −15.5796 | + | 6.89301i | −1.25954 | + | 0.557267i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0813354 | − | 0.0469590i | 0.00653302 | − | 0.00377184i | ||||
\(156\) | −3.14460 | − | 14.8795i | −0.251770 | − | 1.19131i | ||||
\(157\) | 16.3488i | 1.30478i | 0.757883 | + | 0.652390i | \(0.226234\pi\) | ||||
−0.757883 | + | 0.652390i | \(0.773766\pi\) | |||||||
\(158\) | − | 10.3633i | − | 0.824457i | ||||||
\(159\) | −19.1003 | − | 6.23070i | −1.51475 | − | 0.494127i | ||||
\(160\) | −0.141084 | + | 0.0814550i | −0.0111537 | + | 0.00643959i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.27030 | − | 5.84216i | 0.0998044 | − | 0.459003i | ||||
\(163\) | −5.17782 | + | 8.96824i | −0.405558 | + | 0.702447i | −0.994386 | − | 0.105811i | \(-0.966256\pi\) |
0.588828 | + | 0.808258i | \(0.299589\pi\) | |||||||
\(164\) | 5.50017 | − | 9.52657i | 0.429491 | − | 0.743900i | ||||
\(165\) | −0.0372827 | + | 0.0334909i | −0.00290246 | + | 0.00260726i | ||||
\(166\) | −3.53699 | + | 2.04208i | −0.274524 | + | 0.158497i | ||||
\(167\) | −2.94297 | + | 5.09738i | −0.227734 | + | 0.394447i | −0.957136 | − | 0.289638i | \(-0.906465\pi\) |
0.729402 | + | 0.684085i | \(0.239798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.36614 | + | 16.2226i | 0.720473 | + | 1.24790i | ||||
\(170\) | −0.0924689 | − | 0.0533870i | −0.00709204 | − | 0.00409459i | ||||
\(171\) | 3.70209 | − | 5.07057i | 0.283106 | − | 0.387756i | ||||
\(172\) | −1.80802 | − | 3.13157i | −0.137860 | − | 0.238780i | ||||
\(173\) | −4.86551 | −0.369918 | −0.184959 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184959 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(174\) | 1.45273 | − | 4.45335i | 0.110131 | − | 0.337608i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.36959 | + | 0.790735i | 0.103237 | + | 0.0596039i | ||||
\(177\) | 6.97052 | + | 7.75973i | 0.523936 | + | 0.583257i | ||||
\(178\) | 6.93328 | + | 4.00293i | 0.519671 | + | 0.300032i | ||||
\(179\) | −0.175495 | + | 0.101322i | −0.0131171 | + | 0.00757319i | −0.506544 | − | 0.862214i | \(-0.669077\pi\) |
0.493427 | + | 0.869787i | \(0.335744\pi\) | |||||||
\(180\) | −0.121036 | + | 0.0535506i | −0.00902146 | + | 0.00399142i | ||||
\(181\) | − | 6.26273i | − | 0.465505i | −0.972536 | − | 0.232753i | \(-0.925227\pi\) | ||
0.972536 | − | 0.232753i | \(-0.0747732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.05337 | + | 2.74282i | −0.225711 | + | 0.202755i | ||||
\(184\) | 8.58303 | + | 14.8662i | 0.632749 | + | 1.09595i | ||||
\(185\) | 0.0699856 | 0.00514544 | ||||||||
\(186\) | 2.55137 | + | 2.84023i | 0.187075 | + | 0.208256i | ||||
\(187\) | 5.80534i | 0.424529i | ||||||||
\(188\) | −16.9587 | −1.23684 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0393482 | 0.00285462 | ||||||||
\(191\) | 13.8034i | 0.998776i | 0.866379 | + | 0.499388i | \(0.166442\pi\) | ||||
−0.866379 | + | 0.499388i | \(0.833558\pi\) | |||||||
\(192\) | −0.844404 | − | 0.940007i | −0.0609396 | − | 0.0678392i | ||||
\(193\) | −21.0774 | −1.51719 | −0.758593 | − | 0.651565i | \(-0.774113\pi\) | ||||
−0.758593 | + | 0.651565i | \(0.774113\pi\) | |||||||
\(194\) | 2.59868 | + | 4.50104i | 0.186574 | + | 0.323156i | ||||
\(195\) | 0.205441 | − | 0.184546i | 0.0147119 | − | 0.0132156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1679i | 1.08067i | 0.841451 | + | 0.540334i | \(0.181702\pi\) | ||||
−0.841451 | + | 0.540334i | \(0.818298\pi\) | |||||||
\(198\) | −1.64541 | − | 1.20134i | −0.116934 | − | 0.0853752i | ||||
\(199\) | 8.38940 | − | 4.84362i | 0.594709 | − | 0.343355i | −0.172249 | − | 0.985054i | \(-0.555103\pi\) |
0.766957 | + | 0.641698i | \(0.221770\pi\) | |||||||
\(200\) | 10.2349 | + | 5.90915i | 0.723720 | + | 0.417840i | ||||
\(201\) | 14.7923 | + | 16.4671i | 1.04337 | + | 1.16150i | ||||
\(202\) | −0.261097 | − | 0.150745i | −0.0183707 | − | 0.0106064i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.75467 | + | 14.5755i | −0.332894 | + | 1.02049i | ||||
\(205\) | 0.199750 | 0.0139512 | ||||||||
\(206\) | −1.75779 | − | 3.04458i | −0.122471 | − | 0.212126i | ||||
\(207\) | 8.81390 | + | 19.9213i | 0.612608 | + | 1.38462i | ||||
\(208\) | −7.54694 | − | 4.35723i | −0.523286 | − | 0.302119i | ||||
\(209\) | −1.06969 | − | 1.85275i | −0.0739919 | − | 0.128158i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.05942 | + | 12.2273i | −0.485991 | + | 0.841761i | −0.999870 | − | 0.0161017i | \(-0.994874\pi\) |
0.513880 | + | 0.857862i | \(0.328208\pi\) | |||||||
\(212\) | −15.6579 | + | 9.04010i | −1.07539 | + | 0.620877i | ||||
\(213\) | 10.2233 | − | 9.18351i | 0.700487 | − | 0.629243i | ||||
\(214\) | 3.01177 | − | 5.21654i | 0.205880 | − | 0.356595i | ||||
\(215\) | 0.0328309 | − | 0.0568649i | 0.00223905 | − | 0.00387815i | ||||
\(216\) | −7.18549 | − | 9.96309i | −0.488910 | − | 0.677903i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.72132 | − | 1.57115i | 0.184311 | − | 0.106412i | ||||
\(219\) | 17.9470 | + | 5.85449i | 1.21275 | + | 0.395610i | ||||
\(220\) | 0.0451007i | 0.00304069i | ||||||||
\(221\) | − | 31.9895i | − | 2.15185i | ||||||
\(222\) | 0.588266 | + | 2.78353i | 0.0394818 | + | 0.186819i | ||||
\(223\) | −2.58777 | + | 1.49405i | −0.173290 | + | 0.100049i | −0.584136 | − | 0.811656i | \(-0.698567\pi\) |
0.410846 | + | 0.911705i | \(0.365233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.1127 | + | 8.84364i | 0.807514 | + | 0.589576i | ||||
\(226\) | 3.14921 | − | 5.45459i | 0.209482 | − | 0.362834i | ||||
\(227\) | −14.3867 | + | 24.9184i | −0.954876 | + | 1.65389i | −0.220224 | + | 0.975449i | \(0.570679\pi\) |
−0.734652 | + | 0.678444i | \(0.762654\pi\) | |||||||
\(228\) | −1.16824 | − | 5.52781i | −0.0773684 | − | 0.366088i | ||||
\(229\) | 7.67401 | − | 4.43059i | 0.507113 | − | 0.292782i | −0.224533 | − | 0.974466i | \(-0.572086\pi\) |
0.731646 | + | 0.681685i | \(0.238752\pi\) | |||||||
\(230\) | −0.0682645 | + | 0.118238i | −0.00450122 | + | 0.00779635i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.81224 | − | 8.33505i | −0.315939 | − | 0.547223i | ||||
\(233\) | −11.1789 | − | 6.45412i | −0.732351 | − | 0.422823i | 0.0869305 | − | 0.996214i | \(-0.472294\pi\) |
−0.819282 | + | 0.573391i | \(0.805628\pi\) | |||||||
\(234\) | 9.06680 | + | 6.61978i | 0.592715 | + | 0.432749i | ||||
\(235\) | −0.153973 | − | 0.266688i | −0.0100441 | − | 0.0173968i | ||||
\(236\) | 9.38690 | 0.611035 | ||||||||
\(237\) | −18.0569 | − | 20.1013i | −1.17292 | − | 1.30572i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.85712 | − | 2.80426i | −0.314181 | − | 0.181392i | 0.334615 | − | 0.942355i | \(-0.391394\pi\) |
−0.648796 | + | 0.760963i | \(0.724727\pi\) | |||||||
\(240\) | −0.0235199 | + | 0.0721005i | −0.00151820 | + | 0.00465406i | ||||
\(241\) | 9.51481 | + | 5.49338i | 0.612903 | + | 0.353860i | 0.774101 | − | 0.633063i | \(-0.218202\pi\) |
−0.161198 | + | 0.986922i | \(0.551536\pi\) | |||||||
\(242\) | 5.72705 | − | 3.30652i | 0.368149 | − | 0.212551i | ||||
\(243\) | −7.71537 | − | 13.5452i | −0.494941 | − | 0.868926i | ||||
\(244\) | 3.69364i | 0.236461i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.67901 | + | 7.94466i | 0.107050 | + | 0.506533i | ||||
\(247\) | 5.89436 | + | 10.2093i | 0.375049 | + | 0.649604i | ||||
\(248\) | 7.84435 | 0.498117 | ||||||||
\(249\) | −3.30248 | + | 10.1238i | −0.209286 | + | 0.641570i | ||||
\(250\) | 0.188007i | 0.0118906i | ||||||||
\(251\) | −24.2241 | −1.52901 | −0.764505 | − | 0.644618i | \(-0.777016\pi\) | ||||
−0.764505 | + | 0.644618i | \(0.777016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.42314 | 0.466689 | ||||||||
\(254\) | 2.90495i | 0.182273i | ||||||||
\(255\) | −0.272380 | + | 0.0575643i | −0.0170571 | + | 0.00360481i | ||||
\(256\) | −8.78416 | −0.549010 | ||||||||
\(257\) | 8.86142 | + | 15.3484i | 0.552760 | + | 0.957409i | 0.998074 | + | 0.0620341i | \(0.0197588\pi\) |
−0.445314 | + | 0.895375i | \(0.646908\pi\) | |||||||
\(258\) | 2.53765 | + | 0.827804i | 0.157987 | + | 0.0515368i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 0.248521i | − | 0.0154126i | ||||||
\(261\) | −4.94168 | − | 11.1692i | −0.305883 | − | 0.691359i | ||||
\(262\) | −1.46392 | + | 0.845193i | −0.0904411 | + | 0.0522162i | ||||
\(263\) | −2.51031 | − | 1.44933i | −0.154793 | − | 0.0893695i | 0.420603 | − | 0.907245i | \(-0.361819\pi\) |
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(264\) | −4.09542 | + | 0.865518i | −0.252056 | + | 0.0532689i | ||||
\(265\) | −0.284325 | − | 0.164155i | −0.0174660 | − | 0.0100840i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.4230 | − | 4.31614i | 1.24986 | − | 0.264144i | ||||
\(268\) | 19.9202 | 1.21682 | ||||||||
\(269\) | −10.9469 | − | 18.9606i | −0.667444 | − | 1.15605i | −0.978616 | − | 0.205694i | \(-0.934055\pi\) |
0.311172 | − | 0.950354i | \(-0.399278\pi\) | |||||||
\(270\) | 0.0400498 | − | 0.0891130i | 0.00243736 | − | 0.00542324i | ||||
\(271\) | 7.77992 | + | 4.49174i | 0.472596 | + | 0.272854i | 0.717326 | − | 0.696738i | \(-0.245366\pi\) |
−0.244730 | + | 0.969591i | \(0.578699\pi\) | |||||||
\(272\) | 4.39254 | + | 7.60811i | 0.266337 | + | 0.461309i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.76834 | + | 6.52695i | −0.227654 | + | 0.394308i | ||||
\(275\) | 4.42591 | − | 2.55530i | 0.266892 | − | 0.154090i | ||||
\(276\) | 18.6373 | + | 6.07967i | 1.12183 | + | 0.365953i | ||||
\(277\) | −7.95091 | + | 13.7714i | −0.477724 | + | 0.827442i | −0.999674 | − | 0.0255339i | \(-0.991871\pi\) |
0.521950 | + | 0.852976i | \(0.325205\pi\) | |||||||
\(278\) | −1.16936 | + | 2.02538i | −0.0701333 | + | 0.121474i | ||||
\(279\) | 9.89761 | + | 1.06363i | 0.592554 | + | 0.0636777i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.50324 | + | 2.59995i | −0.268641 | + | 0.155100i | −0.628270 | − | 0.777996i | \(-0.716237\pi\) |
0.359629 | + | 0.933095i | \(0.382903\pi\) | |||||||
\(282\) | 9.31276 | − | 8.36560i | 0.554567 | − | 0.498164i | ||||
\(283\) | 18.7739i | 1.11599i | 0.829844 | + | 0.557995i | \(0.188429\pi\) | ||||
−0.829844 | + | 0.557995i | \(0.811571\pi\) | |||||||
\(284\) | − | 12.3670i | − | 0.733848i | ||||||
\(285\) | 0.0763224 | − | 0.0685600i | 0.00452095 | − | 0.00406114i | ||||
\(286\) | 3.31295 | − | 1.91273i | 0.195899 | − | 0.113102i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −17.1684 | − | 1.84497i | −1.01166 | − | 0.108716i | ||||
\(289\) | −7.62438 | + | 13.2058i | −0.448493 | + | 0.776813i | ||||
\(290\) | 0.0382738 | − | 0.0662922i | 0.00224751 | − | 0.00389281i | ||||
\(291\) | 12.8832 | + | 4.20261i | 0.755224 | + | 0.246361i | ||||
\(292\) | 14.7125 | − | 8.49426i | 0.860983 | − | 0.497089i | ||||
\(293\) | −11.4201 | + | 19.7802i | −0.667169 | + | 1.15557i | 0.311523 | + | 0.950238i | \(0.399161\pi\) |
−0.978692 | + | 0.205332i | \(0.934173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0852263 | + | 0.147616i | 0.00496206 | + | 0.00859455i | ||||
\(296\) | 5.06229 | + | 2.92272i | 0.294240 | + | 0.169879i | ||||
\(297\) | −5.28475 | + | 0.536762i | −0.306652 | + | 0.0311461i | ||||
\(298\) | 5.28530 | + | 9.15440i | 0.306169 | + | 0.530300i | ||||
\(299\) | −40.9041 | −2.36554 | ||||||||
\(300\) | 13.2050 | − | 2.79072i | 0.762390 | − | 0.161122i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.99062 | − | 1.14929i | −0.114548 | − | 0.0661341i | ||||
\(303\) | −0.769099 | + | 0.162540i | −0.0441836 | + | 0.00933766i | ||||
\(304\) | −2.80373 | − | 1.61873i | −0.160805 | − | 0.0928407i | ||||
\(305\) | −0.0580853 | + | 0.0335356i | −0.00332596 | + | 0.00192024i | ||||
\(306\) | −4.57900 | − | 10.3495i | −0.261764 | − | 0.591642i | ||||
\(307\) | 18.6325i | 1.06341i | 0.846928 | + | 0.531707i | \(0.178449\pi\) | ||||
−0.846928 | + | 0.531707i | \(0.821551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.71438 | − | 2.84271i | −0.495744 | − | 0.161716i | ||||
\(310\) | 0.0311947 | + | 0.0540308i | 0.00177174 | + | 0.00306875i | ||||
\(311\) | −20.5495 | −1.16526 | −0.582628 | − | 0.812739i | \(-0.697975\pi\) | ||||
−0.582628 | + | 0.812739i | \(0.697975\pi\) | |||||||
\(312\) | 22.5672 | − | 4.76931i | 1.27762 | − | 0.270009i | ||||
\(313\) | 0.721071i | 0.0407574i | 0.999792 | + | 0.0203787i | \(0.00648718\pi\) | ||||
−0.999792 | + | 0.0203787i | \(0.993513\pi\) | |||||||
\(314\) | −10.8605 | −0.612893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3164 | −1.36791 | ||||||||
\(317\) | − | 21.9295i | − | 1.23168i | −0.787871 | − | 0.615841i | \(-0.788816\pi\) | ||
0.787871 | − | 0.615841i | \(-0.211184\pi\) | |||||||
\(318\) | 4.13903 | − | 12.6883i | 0.232105 | − | 0.711523i | ||||
\(319\) | −4.16193 | −0.233023 | ||||||||
\(320\) | −0.0103242 | − | 0.0178821i | −0.000577143 | − | 0.000999641i | ||||
\(321\) | −3.24743 | − | 15.3660i | −0.181254 | − | 0.857649i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.8843i | − | 0.661258i | ||||||
\(324\) | −13.7081 | − | 2.98065i | −0.761560 | − | 0.165592i | ||||
\(325\) | −24.3883 | + | 14.0806i | −1.35282 | + | 0.781051i | ||||
\(326\) | −5.95757 | − | 3.43961i | −0.329959 | − | 0.190502i | ||||
\(327\) | 2.54089 | − | 7.78912i | 0.140511 | − | 0.430739i | ||||
\(328\) | 14.4486 | + | 8.34191i | 0.797791 | + | 0.460605i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0222479 | − | 0.0247668i | −0.00122470 | − | 0.00136337i | ||||
\(331\) | 21.6676 | 1.19096 | 0.595480 | − | 0.803370i | \(-0.296962\pi\) | ||||
0.595480 | + | 0.803370i | \(0.296962\pi\) | |||||||
\(332\) | 4.79156 | + | 8.29923i | 0.262971 | + | 0.455479i | ||||
\(333\) | 5.99105 | + | 4.37414i | 0.328308 | + | 0.239701i | ||||
\(334\) | −3.38617 | − | 1.95501i | −0.185283 | − | 0.106973i | ||||
\(335\) | 0.180861 | + | 0.313260i | 0.00988147 | + | 0.0171152i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6455 | − | 21.9026i | 0.688844 | − | 1.19311i | −0.283369 | − | 0.959011i | \(-0.591452\pi\) |
0.972212 | − | 0.234101i | \(-0.0752147\pi\) | |||||||
\(338\) | −10.7766 | + | 6.22190i | −0.586172 | + | 0.338427i | ||||
\(339\) | −3.39562 | − | 16.0673i | −0.184425 | − | 0.872654i | ||||
\(340\) | −0.125268 | + | 0.216970i | −0.00679358 | + | 0.0117668i | ||||
\(341\) | 1.69607 | − | 2.93768i | 0.0918474 | − | 0.159084i | ||||
\(342\) | 3.36836 | + | 2.45928i | 0.182140 | + | 0.132983i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.74955 | − | 2.74215i | 0.256078 | − | 0.147847i | ||||
\(345\) | 0.0736058 | + | 0.348285i | 0.00396281 | + | 0.0187510i | ||||
\(346\) | − | 3.23215i | − | 0.173761i | ||||||
\(347\) | 5.68598i | 0.305239i | 0.988285 | + | 0.152620i | \(0.0487709\pi\) | ||||
−0.988285 | + | 0.152620i | \(0.951229\pi\) | |||||||
\(348\) | −10.4494 | − | 3.40869i | −0.560145 | − | 0.182725i | ||||
\(349\) | 9.68412 | − | 5.59113i | 0.518379 | − | 0.299286i | −0.217892 | − | 0.975973i | \(-0.569918\pi\) |
0.736271 | + | 0.676687i | \(0.236585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.1208 | − | 2.95775i | 1.55436 | − | 0.157873i | ||||
\(352\) | −2.94200 | + | 5.09570i | −0.156809 | + | 0.271601i | ||||
\(353\) | −7.02111 | + | 12.1609i | −0.373696 | + | 0.647260i | −0.990131 | − | 0.140146i | \(-0.955243\pi\) |
0.616435 | + | 0.787406i | \(0.288576\pi\) | |||||||
\(354\) | −5.15476 | + | 4.63049i | −0.273972 | + | 0.246108i | ||||
\(355\) | 0.194481 | − | 0.112284i | 0.0103220 | − | 0.00595940i | ||||
\(356\) | 9.39250 | − | 16.2683i | 0.497802 | − | 0.862218i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0673081 | − | 0.116581i | −0.00355734 | − | 0.00616150i | ||||
\(359\) | −23.5052 | − | 13.5707i | −1.24056 | − | 0.716235i | −0.271348 | − | 0.962481i | \(-0.587469\pi\) |
−0.969207 | + | 0.246246i | \(0.920803\pi\) | |||||||
\(360\) | −0.0812182 | − | 0.183570i | −0.00428058 | − | 0.00967500i | ||||
\(361\) | −7.31022 | − | 12.6617i | −0.384748 | − | 0.666403i | ||||
\(362\) | 4.16031 | 0.218661 | ||||||||
\(363\) | 5.34733 | − | 16.3923i | 0.280662 | − | 0.860374i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.267158 | + | 0.154244i | 0.0139837 | + | 0.00807347i | ||||
\(366\) | −1.82205 | − | 2.02834i | −0.0952399 | − | 0.106023i | ||||
\(367\) | 5.95891 | + | 3.44038i | 0.311053 | + | 0.179586i | 0.647397 | − | 0.762153i | \(-0.275857\pi\) |
−0.336345 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(368\) | 9.72828 | − | 5.61662i | 0.507122 | − | 0.292787i | ||||
\(369\) | 17.0994 | + | 12.4845i | 0.890161 | + | 0.649918i | ||||
\(370\) | 0.0464912i | 0.00241696i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.66434 | − | 5.98654i | 0.345530 | − | 0.310388i | ||||
\(373\) | 0.123926 | + | 0.214645i | 0.00641662 | + | 0.0111139i | 0.869216 | − | 0.494433i | \(-0.164624\pi\) |
−0.862799 | + | 0.505547i | \(0.831291\pi\) | |||||||
\(374\) | −3.85647 | −0.199413 | ||||||||
\(375\) | 0.327582 | + | 0.364671i | 0.0169163 | + | 0.0188315i | ||||
\(376\) | − | 25.7206i | − | 1.32644i | ||||||
\(377\) | 22.9337 | 1.18114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.91863 | −0.458119 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(380\) | − | 0.0923268i | − | 0.00473626i | ||||||
\(381\) | 5.06157 | + | 5.63465i | 0.259312 | + | 0.288672i | ||||
\(382\) | −9.16952 | −0.469154 | ||||||||
\(383\) | −0.163545 | − | 0.283268i | −0.00835675 | − | 0.0144743i | 0.861817 | − | 0.507220i | \(-0.169327\pi\) |
−0.870174 | + | 0.492745i | \(0.835993\pi\) | |||||||
\(384\) | −14.2083 | + | 12.7632i | −0.725063 | + | 0.651320i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 14.0017i | − | 0.712665i | ||||||
\(387\) | 6.36455 | − | 2.81591i | 0.323528 | − | 0.143141i | ||||
\(388\) | 10.5613 | − | 6.09755i | 0.536167 | − | 0.309556i | ||||
\(389\) | 5.72348 | + | 3.30445i | 0.290192 | + | 0.167542i | 0.638028 | − | 0.770013i | \(-0.279750\pi\) |
−0.347837 | + | 0.937555i | \(0.613084\pi\) | |||||||
\(390\) | 0.122594 | + | 0.136474i | 0.00620777 | + | 0.00691061i | ||||
\(391\) | 35.7111 | + | 20.6178i | 1.80599 | + | 1.04269i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36686 | + | 4.19011i | −0.0689487 | + | 0.211363i | ||||
\(394\) | −10.0760 | −0.507621 | ||||||||
\(395\) | −0.220776 | − | 0.382394i | −0.0111084 | − | 0.0192404i | ||||
\(396\) | −2.81882 | + | 3.86080i | −0.141651 | + | 0.194013i | ||||
\(397\) | 6.50435 | + | 3.75529i | 0.326444 | + | 0.188472i | 0.654261 | − | 0.756269i | \(-0.272980\pi\) |
−0.327817 | + | 0.944741i | \(0.606313\pi\) | |||||||
\(398\) | 3.21760 | + | 5.57305i | 0.161284 | + | 0.279352i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.86687 | − | 6.69762i | 0.193344 | − | 0.334881i | ||||
\(401\) | 5.48595 | − | 3.16732i | 0.273956 | − | 0.158168i | −0.356728 | − | 0.934208i | \(-0.616108\pi\) |
0.630684 | + | 0.776040i | \(0.282774\pi\) | |||||||
\(402\) | −10.9390 | + | 9.82647i | −0.545589 | + | 0.490100i | ||||
\(403\) | −9.34594 | + | 16.1876i | −0.465555 | + | 0.806364i | ||||
\(404\) | −0.353708 | + | 0.612640i | −0.0175976 | + | 0.0304800i | ||||
\(405\) | −0.0775865 | − | 0.242632i | −0.00385530 | − | 0.0120565i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.18909 | − | 1.26387i | 0.108509 | − | 0.0626479i | ||||
\(408\) | −22.1062 | − | 7.21124i | −1.09442 | − | 0.357010i | ||||
\(409\) | − | 33.4915i | − | 1.65605i | −0.560693 | − | 0.828024i | \(-0.689465\pi\) | ||
0.560693 | − | 0.828024i | \(-0.310535\pi\) | |||||||
\(410\) | 0.132693i | 0.00655326i | ||||||||
\(411\) | 4.06319 | + | 19.2261i | 0.200423 | + | 0.948351i | ||||
\(412\) | −7.14382 | + | 4.12448i | −0.351951 | + | 0.203199i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.2336 | + | 5.85504i | −0.650398 | + | 0.287760i | ||||
\(415\) | −0.0870078 | + | 0.150702i | −0.00427105 | + | 0.00739767i | ||||
\(416\) | 16.2115 | − | 28.0791i | 0.794832 | − | 1.37669i | ||||
\(417\) | 1.26085 | + | 5.96605i | 0.0617442 | + | 0.292159i | ||||
\(418\) | 1.23078 | − | 0.710590i | 0.0601993 | − | 0.0347561i | ||||
\(419\) | −0.896459 | + | 1.55271i | −0.0437949 | + | 0.0758550i | −0.887092 | − | 0.461593i | \(-0.847278\pi\) |
0.843297 | + | 0.537448i | \(0.180611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90262 | + | 3.29543i | 0.0927278 | + | 0.160609i | 0.908658 | − | 0.417541i | \(-0.137108\pi\) |
−0.815930 | + | 0.578150i | \(0.803775\pi\) | |||||||
\(422\) | −8.12254 | − | 4.68955i | −0.395399 | − | 0.228284i | ||||
\(423\) | 3.48750 | − | 32.4530i | 0.169568 | − | 1.57792i | ||||
\(424\) | −13.7108 | − | 23.7478i | −0.665855 | − | 1.15330i | ||||
\(425\) | 28.3894 | 1.37709 | ||||||||
\(426\) | 6.10057 | + | 6.79128i | 0.295574 | + | 0.329039i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.2401 | − | 7.06684i | −0.591649 | − | 0.341589i | ||||
\(429\) | 3.09329 | − | 9.48253i | 0.149346 | − | 0.457821i | ||||
\(430\) | 0.0377751 | + | 0.0218095i | 0.00182168 | + | 0.00105175i | ||||
\(431\) | −1.15145 | + | 0.664787i | −0.0554632 | + | 0.0320217i | −0.527475 | − | 0.849570i | \(-0.676861\pi\) |
0.472012 | + | 0.881592i | \(0.343528\pi\) | |||||||
\(432\) | −6.51972 | + | 4.70209i | −0.313680 | + | 0.226229i | ||||
\(433\) | − | 37.4292i | − | 1.79873i | −0.437194 | − | 0.899367i | \(-0.644028\pi\) | ||
0.437194 | − | 0.899367i | \(-0.355972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0412686 | − | 0.195273i | −0.00197868 | − | 0.00936262i | ||||
\(436\) | −3.68656 | − | 6.38531i | −0.176554 | − | 0.305801i | ||||
\(437\) | −15.1961 | −0.726927 | ||||||||
\(438\) | −3.88912 | + | 11.9221i | −0.185829 | + | 0.569662i | ||||
\(439\) | 23.7388i | 1.13299i | 0.824064 | + | 0.566496i | \(0.191702\pi\) | ||||
−0.824064 | + | 0.566496i | \(0.808298\pi\) | |||||||
\(440\) | −0.0684026 | −0.00326097 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.2505 | 1.01078 | ||||||||
\(443\) | 11.2504i | 0.534525i | 0.963624 | + | 0.267262i | \(0.0861191\pi\) | ||||
−0.963624 | + | 0.267262i | \(0.913881\pi\) | |||||||
\(444\) | 6.53130 | − | 1.38031i | 0.309962 | − | 0.0655067i | ||||
\(445\) | 0.341109 | 0.0161701 | ||||||||
\(446\) | −0.992491 | − | 1.71904i | −0.0469958 | − | 0.0813991i | ||||
\(447\) | 26.2023 | + | 8.54744i | 1.23933 | + | 0.404280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3953i | 0.679357i | 0.940542 | + | 0.339679i | \(0.110318\pi\) | ||||
−0.940542 | + | 0.339679i | \(0.889682\pi\) | |||||||
\(450\) | −5.87480 | + | 8.04644i | −0.276941 | + | 0.379313i | ||||
\(451\) | 6.24803 | − | 3.60730i | 0.294208 | − | 0.169861i | ||||
\(452\) | −12.7987 | − | 7.38933i | −0.602000 | − | 0.347565i | ||||
\(453\) | −5.86366 | + | 1.23921i | −0.275499 | + | 0.0582234i | ||||
\(454\) | −16.5532 | − | 9.55701i | −0.776881 | − | 0.448533i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.38384 | − | 1.77182i | 0.392609 | − | 0.0829732i | ||||
\(457\) | −20.6269 | −0.964888 | −0.482444 | − | 0.875927i | \(-0.660251\pi\) | ||||
−0.482444 | + | 0.875927i | \(0.660251\pi\) | |||||||
\(458\) | 2.94323 | + | 5.09782i | 0.137528 | + | 0.238206i | ||||
\(459\) | −26.9147 | − | 12.0962i | −1.25627 | − | 0.564602i | ||||
\(460\) | 0.277433 | + | 0.160176i | 0.0129354 | + | 0.00746825i | ||||
\(461\) | 0.832511 | + | 1.44195i | 0.0387739 | + | 0.0671584i | 0.884761 | − | 0.466045i | \(-0.154321\pi\) |
−0.845987 | + | 0.533203i | \(0.820988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.604175 | − | 1.04646i | 0.0280784 | − | 0.0486332i | −0.851645 | − | 0.524119i | \(-0.824395\pi\) |
0.879723 | + | 0.475486i | \(0.157728\pi\) | |||||||
\(464\) | −5.45435 | + | 3.14907i | −0.253212 | + | 0.146192i | ||||
\(465\) | 0.154650 | + | 0.0504484i | 0.00717174 | + | 0.00233949i | ||||
\(466\) | 4.28745 | − | 7.42608i | 0.198612 | − | 0.344006i | ||||
\(467\) | −4.61994 | + | 8.00197i | −0.213785 | + | 0.370287i | −0.952896 | − | 0.303297i | \(-0.901913\pi\) |
0.739111 | + | 0.673584i | \(0.235246\pi\) | |||||||
\(468\) | 15.5327 | − | 21.2744i | 0.717999 | − | 0.983409i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.177160 | − | 0.102283i | 0.00817179 | − | 0.00471798i | ||||
\(471\) | −21.0657 | + | 18.9232i | −0.970658 | + | 0.871937i | ||||
\(472\) | 14.2368i | 0.655300i | ||||||||
\(473\) | − | 2.37158i | − | 0.109045i | ||||||
\(474\) | 13.3532 | − | 11.9951i | 0.613334 | − | 0.550954i | ||||
\(475\) | −9.06039 | + | 5.23102i | −0.415719 | + | 0.240016i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0796 | − | 31.8229i | −0.644660 | − | 1.45707i | ||||
\(478\) | 1.86286 | − | 3.22657i | 0.0852052 | − | 0.147580i | ||||
\(479\) | 8.77241 | − | 15.1943i | 0.400822 | − | 0.694243i | −0.593004 | − | 0.805200i | \(-0.702058\pi\) |
0.993825 | + | 0.110956i | \(0.0353914\pi\) | |||||||
\(480\) | −0.268256 | − | 0.0875078i | −0.0122442 | − | 0.00399417i | ||||
\(481\) | −12.0627 | + | 6.96438i | −0.550010 | + | 0.317549i | ||||
\(482\) | −3.64923 | + | 6.32066i | −0.166218 | + | 0.287898i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.75843 | − | 13.4380i | −0.352656 | − | 0.610818i | ||||
\(485\) | 0.191777 | + | 0.110723i | 0.00870817 | + | 0.00502766i | ||||
\(486\) | 8.99804 | − | 5.12530i | 0.408160 | − | 0.232488i | ||||
\(487\) | 21.5949 | + | 37.4034i | 0.978558 | + | 1.69491i | 0.667657 | + | 0.744469i | \(0.267297\pi\) |
0.310900 | + | 0.950442i | \(0.399369\pi\) | |||||||
\(488\) | −5.60201 | −0.253591 | ||||||||
\(489\) | −17.5489 | + | 3.70874i | −0.793587 | + | 0.167715i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0046 | + | 13.2817i | 1.03818 | + | 0.599396i | 0.919319 | − | 0.393514i | \(-0.128741\pi\) |
0.118866 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(492\) | 18.6414 | − | 3.93963i | 0.840419 | − | 0.177612i | ||||
\(493\) | −20.0221 | − | 11.5598i | −0.901751 | − | 0.520626i | ||||
\(494\) | −6.78202 | + | 3.91560i | −0.305138 | + | 0.176171i | ||||
\(495\) | −0.0863070 | − | 0.00927482i | −0.00387921 | − | 0.000416872i | ||||
\(496\) | − | 5.13324i | − | 0.230489i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.72521 | − | 2.19383i | −0.301364 | − | 0.0983078i | ||||
\(499\) | −2.65759 | − | 4.60308i | −0.118970 | − | 0.206062i | 0.800390 | − | 0.599480i | \(-0.204626\pi\) |
−0.919360 | + | 0.393418i | \(0.871293\pi\) | |||||||
\(500\) | 0.441141 | 0.0197284 | ||||||||
\(501\) | −9.97445 | + | 2.10798i | −0.445625 | + | 0.0941776i | ||||
\(502\) | − | 16.0920i | − | 0.718220i | ||||||
\(503\) | 35.5334 | 1.58436 | 0.792178 | − | 0.610290i | \(-0.208947\pi\) | ||||
0.792178 | + | 0.610290i | \(0.208947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0128457 | −0.000571624 | ||||||||
\(506\) | 4.93116i | 0.219217i | ||||||||
\(507\) | −10.0621 | + | 30.8456i | −0.446874 | + | 1.36990i | ||||
\(508\) | 6.81620 | 0.302420 | ||||||||
\(509\) | −6.81654 | − | 11.8066i | −0.302138 | − | 0.523318i | 0.674482 | − | 0.738291i | \(-0.264367\pi\) |
−0.976620 | + | 0.214973i | \(0.931034\pi\) | |||||||
\(510\) | −0.0382397 | − | 0.180941i | −0.00169328 | − | 0.00801221i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.2184i | 0.716760i | ||||||||
\(513\) | 10.8185 | − | 1.09882i | 0.477651 | − | 0.0485141i | ||||
\(514\) | −10.1959 | + | 5.88661i | −0.449722 | + | 0.259647i | ||||
\(515\) | −0.129721 | − | 0.0748947i | −0.00571621 | − | 0.00330025i | ||||
\(516\) | 1.94236 | − | 5.95435i | 0.0855078 | − | 0.262125i | ||||
\(517\) | −9.63227 | − | 5.56120i | −0.423627 | − | 0.244581i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.63167 | − | 6.26929i | −0.247203 | − | 0.275191i | ||||
\(520\) | 0.376922 | 0.0165291 | ||||||||
\(521\) | −5.11259 | − | 8.85526i | −0.223987 | − | 0.387956i | 0.732028 | − | 0.681274i | \(-0.238574\pi\) |
−0.956015 | + | 0.293318i | \(0.905241\pi\) | |||||||
\(522\) | 7.41969 | − | 3.28274i | 0.324751 | − | 0.143682i | ||||
\(523\) | −4.48150 | − | 2.58740i | −0.195962 | − | 0.113139i | 0.398808 | − | 0.917034i | \(-0.369424\pi\) |
−0.594771 | + | 0.803895i | \(0.702757\pi\) | |||||||
\(524\) | 1.98317 | + | 3.43495i | 0.0866350 | + | 0.150056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.962785 | − | 1.66759i | 0.0419794 | − | 0.0727105i | ||||
\(527\) | 16.3189 | − | 9.42169i | 0.710860 | − | 0.410415i | ||||
\(528\) | 0.566383 | + | 2.67999i | 0.0246487 | + | 0.116632i | ||||
\(529\) | 14.8634 | − | 25.7442i | 0.646236 | − | 1.11931i | ||||
\(530\) | 0.109048 | − | 0.188876i | 0.00473673 | − | 0.00820426i | ||||
\(531\) | −1.93039 | + | 17.9632i | −0.0837716 | + | 0.779538i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.4288 | + | 19.8775i | −1.49128 | + | 0.860990i | ||||
\(534\) | 2.86720 | + | 13.5669i | 0.124076 | + | 0.587097i | ||||
\(535\) | − | 0.256647i | − | 0.0110958i | ||||||
\(536\) | 30.2122i | 1.30497i | ||||||||
\(537\) | −0.333685 | − | 0.108851i | −0.0143996 | − | 0.00469728i | ||||
\(538\) | 12.5955 | − | 7.27199i | 0.543029 | − | 0.313518i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.209095 | − | 0.0939732i | −0.00899803 | − | 0.00404396i | ||||
\(541\) | 12.7197 | − | 22.0312i | 0.546864 | − | 0.947196i | −0.451623 | − | 0.892209i | \(-0.649155\pi\) |
0.998487 | − | 0.0549871i | \(-0.0175118\pi\) | |||||||
\(542\) | −2.98385 | + | 5.16817i | −0.128167 | + | 0.221992i | ||||
\(543\) | 8.06963 | − | 7.24890i | 0.346301 | − | 0.311080i | ||||
\(544\) | −28.3067 | + | 16.3429i | −1.21364 | + | 0.700694i | ||||
\(545\) | 0.0669427 | − | 0.115948i | 0.00286751 | − | 0.00496667i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7771 | + | 25.5947i | 0.631824 | + | 1.09435i | 0.987179 | + | 0.159620i | \(0.0510267\pi\) |
−0.355355 | + | 0.934732i | \(0.615640\pi\) | |||||||
\(548\) | 15.3149 | + | 8.84205i | 0.654219 | + | 0.377714i | ||||
\(549\) | −7.06833 | − | 0.759585i | −0.301669 | − | 0.0324183i | ||||
\(550\) | 1.69748 | + | 2.94012i | 0.0723807 | + | 0.125367i | ||||
\(551\) | 8.51998 | 0.362963 | ||||||||
\(552\) | −9.22082 | + | 28.2665i | −0.392464 | + | 1.20310i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.14828 | − | 5.28176i | −0.388673 | − | 0.224401i | ||||
\(555\) | 0.0810060 | + | 0.0901775i | 0.00343851 | + | 0.00382782i | ||||
\(556\) | 4.75237 | + | 2.74378i | 0.201545 | + | 0.116362i | ||||
\(557\) | 16.9788 | − | 9.80269i | 0.719413 | − | 0.415353i | −0.0951237 | − | 0.995465i | \(-0.530325\pi\) |
0.814537 | + | 0.580112i | \(0.196991\pi\) | |||||||
\(558\) | −0.706565 | + | 6.57495i | −0.0299113 | + | 0.278340i | ||||
\(559\) | 13.0683i | 0.552728i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.48028 | + | 6.71949i | −0.315817 | + | 0.283697i | ||||
\(562\) | −1.72714 | − | 2.99149i | −0.0728548 | − | 0.126188i | ||||
\(563\) | 14.4759 | 0.610087 | 0.305044 | − | 0.952338i | \(-0.401329\pi\) | ||||
0.305044 | + | 0.952338i | \(0.401329\pi\) | |||||||
\(564\) | −19.6291 | − | 21.8515i | −0.826534 | − | 0.920115i | ||||
\(565\) | − | 0.268359i | − | 0.0112899i | ||||||
\(566\) | −12.4714 | −0.524213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.7566 | 0.787011 | ||||||||
\(569\) | 7.74769i | 0.324800i | 0.986725 | + | 0.162400i | \(0.0519235\pi\) | ||||
−0.986725 | + | 0.162400i | \(0.948076\pi\) | |||||||
\(570\) | 0.0455442 | + | 0.0507007i | 0.00190764 | + | 0.00212362i | ||||
\(571\) | 16.1371 | 0.675318 | 0.337659 | − | 0.941269i | \(-0.390365\pi\) | ||||
0.337659 | + | 0.941269i | \(0.390365\pi\) | |||||||
\(572\) | −4.48805 | − | 7.77353i | −0.187655 | − | 0.325027i | ||||
\(573\) | −17.7858 | + | 15.9769i | −0.743014 | + | 0.667445i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 36.3008i | − | 1.51385i | ||||||
\(576\) | 0.233846 | − | 2.17605i | 0.00974356 | − | 0.0906689i | ||||
\(577\) | 10.5403 | − | 6.08542i | 0.438797 | − | 0.253339i | −0.264290 | − | 0.964443i | \(-0.585138\pi\) |
0.703087 | + | 0.711104i | \(0.251804\pi\) | |||||||
\(578\) | −8.77258 | − | 5.06485i | −0.364891 | − | 0.210670i | ||||
\(579\) | −24.3964 | − | 27.1586i | −1.01388 | − | 1.12867i | ||||
\(580\) | −0.155548 | − | 0.0898059i | −0.00645879 | − | 0.00372899i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.79178 | + | 8.55824i | −0.115723 | + | 0.354750i | ||||
\(583\) | −11.8579 | −0.491106 | ||||||||
\(584\) | 12.8829 | + | 22.3139i | 0.533100 | + | 0.923356i | ||||
\(585\) | 0.475582 | + | 0.0511075i | 0.0196629 | + | 0.00211304i | ||||
\(586\) | −13.1399 | − | 7.58633i | −0.542805 | − | 0.313388i | ||||
\(587\) | −16.8761 | − | 29.2302i | −0.696550 | − | 1.20646i | −0.969655 | − | 0.244476i | \(-0.921384\pi\) |
0.273106 | − | 0.961984i | \(-0.411949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.47207 | + | 6.01380i | −0.143064 | + | 0.247794i | ||||
\(590\) | −0.0980610 | + | 0.0566155i | −0.00403711 | + | 0.00233082i | ||||
\(591\) | −19.5441 | + | 17.5563i | −0.803936 | + | 0.722171i | ||||
\(592\) | 1.91259 | − | 3.31270i | 0.0786069 | − | 0.136151i | ||||
\(593\) | 9.15123 | − | 15.8504i | 0.375796 | − | 0.650897i | −0.614650 | − | 0.788800i | \(-0.710703\pi\) |
0.990446 | + | 0.137903i | \(0.0440361\pi\) | |||||||
\(594\) | −0.356569 | − | 3.51064i | −0.0146302 | − | 0.144043i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.4799 | − | 12.4015i | 0.879853 | − | 0.507983i | ||||
\(597\) | 15.9515 | + | 5.20354i | 0.652852 | + | 0.212967i | ||||
\(598\) | − | 27.1724i | − | 1.11116i | ||||||
\(599\) | 39.4798i | 1.61310i | 0.591165 | + | 0.806551i | \(0.298668\pi\) | ||||
−0.591165 | + | 0.806551i | \(0.701332\pi\) | |||||||
\(600\) | 4.23258 | + | 20.0275i | 0.172794 | + | 0.817621i | ||||
\(601\) | −34.4865 | + | 19.9108i | −1.40673 | + | 0.812177i | −0.995072 | − | 0.0991600i | \(-0.968384\pi\) |
−0.411661 | + | 0.911337i | \(0.635051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.09652 | + | 38.1202i | −0.166823 | + | 1.55237i | ||||
\(604\) | −2.69670 | + | 4.67082i | −0.109727 | + | 0.190053i | ||||
\(605\) | 0.140882 | − | 0.244015i | 0.00572766 | − | 0.00992060i | ||||
\(606\) | −0.107975 | − | 0.510910i | −0.00438617 | − | 0.0207543i | ||||
\(607\) | 21.6104 | − | 12.4768i | 0.877140 | − | 0.506417i | 0.00742570 | − | 0.999972i | \(-0.497636\pi\) |
0.869714 | + | 0.493555i | \(0.164303\pi\) | |||||||
\(608\) | 6.02264 | − | 10.4315i | 0.244250 | − | 0.423054i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0222776 | − | 0.0385859i | −0.000901992 | − | 0.00156230i | ||||
\(611\) | 53.0772 | + | 30.6441i | 2.14727 | + | 1.23973i | ||||
\(612\) | −24.2841 | + | 10.7442i | −0.981628 | + | 0.434308i | ||||
\(613\) | −14.0285 | − | 24.2980i | −0.566605 | − | 0.981388i | −0.996898 | − | 0.0786994i | \(-0.974923\pi\) |
0.430294 | − | 0.902689i | \(-0.358410\pi\) | |||||||
\(614\) | −12.3775 | −0.499516 | ||||||||
\(615\) | 0.231204 | + | 0.257381i | 0.00932305 | + | 0.0103786i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.8093 | + | 17.2104i | 1.20008 | + | 0.692865i | 0.960573 | − | 0.278030i | \(-0.0896813\pi\) |
0.239506 | + | 0.970895i | \(0.423015\pi\) | |||||||
\(618\) | 1.88841 | − | 5.78893i | 0.0759628 | − | 0.232865i | ||||
\(619\) | 17.2889 | + | 9.98173i | 0.694898 | + | 0.401200i | 0.805444 | − | 0.592671i | \(-0.201927\pi\) |
−0.110546 | + | 0.993871i | \(0.535260\pi\) | |||||||
\(620\) | 0.126778 | − | 0.0731955i | 0.00509154 | − | 0.00293960i | ||||
\(621\) | −15.4671 | + | 34.4150i | −0.620672 | + | 1.38103i | ||||
\(622\) | − | 13.6510i | − | 0.547354i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.12097 | − | 14.7677i | −0.124939 | − | 0.591181i | ||||
\(625\) | −12.4940 | − | 21.6402i | −0.499760 | − | 0.865609i | ||||
\(626\) | −0.479005 | −0.0191449 | ||||||||
\(627\) | 1.14917 | − | 3.52281i | 0.0458936 | − | 0.140687i | ||||
\(628\) | 25.4831i | 1.01689i | ||||||||
\(629\) | 14.0417 | 0.559878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.8447 | −1.86486 | −0.932429 | − | 0.361354i | \(-0.882314\pi\) | ||||
−0.932429 | + | 0.361354i | \(0.882314\pi\) | |||||||
\(632\) | − | 36.8798i | − | 1.46700i | ||||||
\(633\) | −23.9261 | + | 5.05649i | −0.950976 | + | 0.200977i | ||||
\(634\) | 14.5677 | 0.578556 | ||||||||
\(635\) | 0.0618862 | + | 0.107190i | 0.00245588 | + | 0.00425370i | ||||
\(636\) | −29.7718 | − | 9.71185i | −1.18053 | − | 0.385100i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.76475i | − | 0.109458i | ||||||
\(639\) | 23.6662 | + | 2.54324i | 0.936220 | + | 0.100609i | ||||
\(640\) | −0.270290 | + | 0.156052i | −0.0106841 | + | 0.00616849i | ||||
\(641\) | 3.34281 | + | 1.92997i | 0.132033 | + | 0.0762293i | 0.564562 | − | 0.825391i | \(-0.309045\pi\) |
−0.432529 | + | 0.901620i | \(0.642379\pi\) | |||||||
\(642\) | 10.2076 | − | 2.15726i | 0.402862 | − | 0.0851401i | ||||
\(643\) | −31.0233 | − | 17.9113i | −1.22344 | − | 0.706352i | −0.257789 | − | 0.966201i | \(-0.582994\pi\) |
−0.965649 | + | 0.259849i | \(0.916327\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.111272 | − | 0.0235160i | 0.00438133 | − | 0.000925941i | ||||
\(646\) | 7.89468 | 0.310612 | ||||||||
\(647\) | 21.8246 | + | 37.8013i | 0.858013 | + | 1.48612i | 0.873821 | + | 0.486248i | \(0.161635\pi\) |
−0.0158075 | + | 0.999875i | \(0.505032\pi\) | |||||||
\(648\) | 4.52064 | − | 20.7906i | 0.177588 | − | 0.816730i | ||||
\(649\) | 5.33162 | + | 3.07821i | 0.209284 | + | 0.120830i | ||||
\(650\) | −9.35369 | − | 16.2011i | −0.366882 | − | 0.635458i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.07072 | + | 13.9789i | −0.316074 | + | 0.547456i | ||||
\(653\) | −6.45191 | + | 3.72501i | −0.252483 | + | 0.145771i | −0.620901 | − | 0.783889i | \(-0.713233\pi\) |
0.368418 | + | 0.929660i | \(0.379900\pi\) | |||||||
\(654\) | 5.17429 | + | 1.68790i | 0.202331 | + | 0.0660022i | ||||
\(655\) | −0.0360114 | + | 0.0623736i | −0.00140708 | + | 0.00243714i | ||||
\(656\) | 5.45884 | − | 9.45498i | 0.213132 | − | 0.369155i | ||||
\(657\) | 13.2295 | + | 29.9014i | 0.516131 | + | 1.16656i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.52607 | + | 4.34518i | −0.293174 | + | 0.169264i | −0.639372 | − | 0.768897i | \(-0.720806\pi\) |
0.346198 | + | 0.938161i | \(0.387472\pi\) | |||||||
\(660\) | −0.0581130 | + | 0.0522025i | −0.00226204 | + | 0.00203198i | ||||
\(661\) | 28.8505i | 1.12215i | 0.827763 | + | 0.561077i | \(0.189613\pi\) | ||||
−0.827763 | + | 0.561077i | \(0.810387\pi\) | |||||||
\(662\) | 14.3937i | 0.559428i | ||||||||
\(663\) | 41.2189 | − | 37.0267i | 1.60081 | − | 1.43800i | ||||
\(664\) | −12.5871 | + | 7.26719i | −0.488476 | + | 0.282022i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.90573 | + | 3.97984i | −0.112595 | + | 0.154216i | ||||
\(667\) | −14.7812 | + | 25.6017i | −0.572329 | + | 0.991303i | ||||
\(668\) | −4.58724 | + | 7.94534i | −0.177486 | + | 0.307414i | ||||
\(669\) | −4.92036 | − | 1.60507i | −0.190232 | − | 0.0620555i | ||||
\(670\) | −0.208097 | + | 0.120145i | −0.00803950 | + | 0.00464161i | ||||
\(671\) | −1.21124 | + | 2.09793i | −0.0467594 | + | 0.0809897i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.60695 | − | 6.24742i | −0.139038 | − | 0.240820i | 0.788095 | − | 0.615554i | \(-0.211068\pi\) |
−0.927133 | + | 0.374733i | \(0.877734\pi\) | |||||||
\(674\) | 14.5498 | + | 8.40036i | 0.560439 | + | 0.323570i | ||||
\(675\) | 2.62489 | + | 25.8436i | 0.101032 | + | 0.994722i | ||||
\(676\) | 14.5991 | + | 25.2864i | 0.561504 | + | 0.972553i | ||||
\(677\) | 36.3821 | 1.39828 | 0.699140 | − | 0.714985i | \(-0.253567\pi\) | ||||
0.699140 | + | 0.714985i | \(0.253567\pi\) | |||||||
\(678\) | 10.6734 | − | 2.25570i | 0.409911 | − | 0.0866297i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.329070 | − | 0.189989i | −0.0126193 | − | 0.00728573i | ||||
\(681\) | −48.7598 | + | 10.3048i | −1.86848 | + | 0.394881i | ||||
\(682\) | 1.95149 | + | 1.12669i | 0.0747265 | + | 0.0431433i | ||||
\(683\) | −20.5530 | + | 11.8663i | −0.786438 | + | 0.454050i | −0.838707 | − | 0.544583i | \(-0.816688\pi\) |
0.0522688 | + | 0.998633i | \(0.483355\pi\) | |||||||
\(684\) | 5.77048 | − | 7.90355i | 0.220640 | − | 0.302200i | ||||
\(685\) | 0.321118i | 0.0122693i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.5913 | + | 4.75982i | 0.556693 | + | 0.181599i | ||||
\(688\) | −1.79443 | − | 3.10804i | −0.0684119 | − | 0.118493i | ||||
\(689\) | 65.3415 | 2.48931 | ||||||||
\(690\) | −0.231365 | + | 0.0488961i | −0.00880790 | + | 0.00186144i | ||||
\(691\) | 3.30391i | 0.125687i | 0.998023 | + | 0.0628433i | \(0.0200168\pi\) | ||||
−0.998023 | + | 0.0628433i | \(0.979983\pi\) | |||||||
\(692\) | −7.58393 | −0.288298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.77718 | −0.143380 | ||||||||
\(695\) | 0.0996463i | 0.00377980i | ||||||||
\(696\) | 5.16983 | − | 15.8482i | 0.195962 | − | 0.600724i | ||||
\(697\) | 40.0772 | 1.51803 | ||||||||
\(698\) | 3.71417 | + | 6.43313i | 0.140583 | + | 0.243498i | ||||
\(699\) | −4.62292 | − | 21.8746i | −0.174855 | − | 0.827371i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.873603i | 0.0329955i | 0.999864 | + | 0.0164978i | \(0.00525164\pi\) | ||||
−0.999864 | + | 0.0164978i | \(0.994748\pi\) | |||||||
\(702\) | 1.96482 | + | 19.3449i | 0.0741574 | + | 0.730125i | ||||
\(703\) | −4.48135 | + | 2.58731i | −0.169017 | + | 0.0975821i | ||||
\(704\) | −0.645868 | − | 0.372892i | −0.0243421 | − | 0.0140539i | ||||
\(705\) | 0.165414 | − | 0.507079i | 0.00622985 | − | 0.0190977i | ||||
\(706\) | −8.07845 | − | 4.66410i | −0.304037 | − | 0.175536i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.8650 | + | 12.0952i | 0.408332 | + | 0.454564i | ||||
\(709\) | 16.1553 | 0.606727 | 0.303363 | − | 0.952875i | \(-0.401890\pi\) | ||||
0.303363 | + | 0.952875i | \(0.401890\pi\) | |||||||
\(710\) | 0.0745897 | + | 0.129193i | 0.00279930 | + | 0.00484853i | ||||
\(711\) | 5.00060 | − | 46.5331i | 0.187537 | − | 1.74513i | ||||
\(712\) | 24.6735 | + | 14.2453i | 0.924680 | + | 0.533864i | ||||
\(713\) | −12.0473 | − | 20.8665i | −0.451174 | − | 0.781456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0814965 | − | 0.141156i | 0.00304779 | − | 0.00527894i | ||||
\(716\) | −0.273546 | + | 0.157932i | −0.0102229 | + | 0.00590220i | ||||
\(717\) | −2.00862 | − | 9.50430i | −0.0750133 | − | 0.354945i | ||||
\(718\) | 9.01498 | − | 15.6144i | 0.336436 | − | 0.582724i | ||||
\(719\) | −22.5953 | + | 39.1361i | −0.842661 | + | 1.45953i | 0.0449767 | + | 0.998988i | \(0.485679\pi\) |
−0.887637 | + | 0.460543i | \(0.847655\pi\) | |||||||
\(720\) | −0.120126 | + | 0.0531481i | −0.00447683 | + | 0.00198071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.41110 | − | 4.85615i | 0.313029 | − | 0.180727i | ||||
\(723\) | 3.93477 | + | 18.6184i | 0.146336 | + | 0.692425i | ||||
\(724\) | − | 9.76178i | − | 0.362794i | ||||||
\(725\) | 20.3528i | 0.755883i | ||||||||
\(726\) | 10.8894 | + | 3.55222i | 0.404142 | + | 0.131835i | ||||
\(727\) | 7.15775 | − | 4.13253i | 0.265466 | − | 0.153267i | −0.361359 | − | 0.932427i | \(-0.617687\pi\) |
0.626826 | + | 0.779160i | \(0.284354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.52294 | − | 25.6195i | 0.315664 | − | 0.948871i | ||||
\(730\) | −0.102463 | + | 0.177472i | −0.00379234 | + | 0.00656853i | ||||
\(731\) | 6.58709 | − | 11.4092i | 0.243632 | − | 0.421983i | ||||
\(732\) | −4.75931 | + | 4.27526i | −0.175909 | + | 0.158018i | ||||
\(733\) | −10.5799 | + | 6.10830i | −0.390777 | + | 0.225615i | −0.682497 | − | 0.730889i | \(-0.739106\pi\) |
0.291720 | + | 0.956504i | \(0.405773\pi\) | |||||||
\(734\) | −2.28543 | + | 3.95849i | −0.0843569 | + | 0.146110i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8972 | + | 36.1949i | 0.770280 | + | 1.33416i | ||||
\(737\) | 11.3143 | + | 6.53234i | 0.416769 | + | 0.240622i | ||||
\(738\) | −8.29342 | + | 11.3591i | −0.305285 | + | 0.418134i | ||||
\(739\) | 10.3536 | + | 17.9330i | 0.380863 | + | 0.659674i | 0.991186 | − | 0.132478i | \(-0.0422935\pi\) |
−0.610323 | + | 0.792153i | \(0.708960\pi\) | |||||||
\(740\) | 0.109087 | 0.00401013 | ||||||||
\(741\) | −6.33235 | + | 19.4119i | −0.232625 | + | 0.713115i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2862 | + | 5.93873i | 0.377363 | + | 0.217871i | 0.676670 | − | 0.736286i | \(-0.263422\pi\) |
−0.299307 | + | 0.954157i | \(0.596756\pi\) | |||||||
\(744\) | 9.07957 | + | 10.1076i | 0.332873 | + | 0.370561i | ||||
\(745\) | 0.390045 | + | 0.225192i | 0.0142901 | + | 0.00825041i | ||||
\(746\) | −0.142588 | + | 0.0823233i | −0.00522053 | + | 0.00301407i | ||||
\(747\) | −16.8672 | + | 7.46266i | −0.617138 | + | 0.273045i | ||||
\(748\) | 9.04885i | 0.330859i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.242250 | + | 0.217612i | −0.00884571 | + | 0.00794606i | ||||
\(751\) | −11.8554 | − | 20.5342i | −0.432610 | − | 0.749303i | 0.564487 | − | 0.825442i | \(-0.309074\pi\) |
−0.997097 | + | 0.0761390i | \(0.975741\pi\) | |||||||
\(752\) | −16.8312 | −0.613772 | ||||||||
\(753\) | −28.0385 | − | 31.2131i | −1.02178 | − | 1.13747i | ||||
\(754\) | 15.2348i | 0.554817i | ||||||||
\(755\) | −0.0979362 | −0.00356426 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2494 | 1.60827 | 0.804136 | − | 0.594446i | \(-0.202628\pi\) | ||||
0.804136 | + | 0.594446i | \(0.202628\pi\) | |||||||
\(758\) | − | 5.92462i | − | 0.215192i | ||||||
\(759\) | 8.59203 | + | 9.56482i | 0.311871 | + | 0.347181i | ||||
\(760\) | 0.140029 | 0.00507937 | ||||||||
\(761\) | −24.3767 | − | 42.2217i | −0.883656 | − | 1.53054i | −0.847246 | − | 0.531200i | \(-0.821741\pi\) |
−0.0364098 | − | 0.999337i | \(-0.511592\pi\) | |||||||
\(762\) | −3.74308 | + | 3.36238i | −0.135597 | + | 0.121806i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.5154i | 0.778401i | ||||||||
\(765\) | −0.389443 | − | 0.284337i | −0.0140804 | − | 0.0102802i | ||||
\(766\) | 0.188174 | − | 0.108642i | 0.00679900 | − | 0.00392540i | ||||
\(767\) | −29.3791 | − | 16.9620i | −1.06082 | − | 0.612463i | ||||
\(768\) | −10.1674 | − | 11.3185i | −0.366883 | − | 0.408422i | ||||
\(769\) | −23.3870 | − | 13.5025i | −0.843357 | − | 0.486912i | 0.0150472 | − | 0.999887i | \(-0.495210\pi\) |
−0.858404 | + | 0.512975i | \(0.828543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.51989 | + | 29.1834i | −0.342851 | + | 1.05101i | ||||
\(772\) | −32.8536 | −1.18243 | ||||||||
\(773\) | −13.3567 | − | 23.1345i | −0.480408 | − | 0.832092i | 0.519339 | − | 0.854568i | \(-0.326178\pi\) |
−0.999747 | + | 0.0224765i | \(0.992845\pi\) | |||||||
\(774\) | 1.87060 | + | 4.22795i | 0.0672373 | + | 0.151971i | ||||
\(775\) | −14.3659 | − | 8.29417i | −0.516039 | − | 0.297935i | ||||
\(776\) | 9.24794 | + | 16.0179i | 0.331982 | + | 0.575009i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.19514 | + | 3.80209i | −0.0786994 | + | 0.136311i | ||||
\(779\) | −12.7905 | + | 7.38459i | −0.458267 | + | 0.264580i | ||||
\(780\) | 0.320223 | − | 0.287654i | 0.0114658 | − | 0.0102997i | ||||
\(781\) | 4.05547 | − | 7.02429i | 0.145116 | − | 0.251349i | ||||
\(782\) | −13.6963 | + | 23.7228i | −0.489780 | + | 0.848324i | ||||
\(783\) | 8.67191 | − | 19.2955i | 0.309909 | − | 0.689564i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.400742 | + | 0.231368i | −0.0143031 | + | 0.00825789i | ||||
\(786\) | −2.78348 | − | 0.907998i | −0.0992834 | − | 0.0323872i | ||||
\(787\) | − | 47.3534i | − | 1.68797i | −0.536369 | − | 0.843983i | \(-0.680205\pi\) | ||
0.536369 | − | 0.843983i | \(-0.319795\pi\) | |||||||
\(788\) | 23.6424i | 0.842224i | ||||||||
\(789\) | −1.03812 | − | 4.91213i | −0.0369580 | − | 0.174876i | ||||
\(790\) | 0.254023 | − | 0.146660i | 0.00903775 | − | 0.00521795i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.85554 | − | 4.27520i | −0.208068 | − | 0.151913i | ||||
\(793\) | 6.67436 | − | 11.5603i | 0.237014 | − | 0.410520i | ||||
\(794\) | −2.49462 | + | 4.32082i | −0.0885309 | + | 0.153340i | ||||
\(795\) | −0.117580 | − | 0.556362i | −0.00417014 | − | 0.0197321i | ||||
\(796\) | 13.0766 | − | 7.54980i | 0.463489 | − | 0.267596i | ||||
\(797\) | 4.42781 | − | 7.66919i | 0.156841 | − | 0.271657i | −0.776887 | − | 0.629640i | \(-0.783202\pi\) |
0.933728 | + | 0.357984i | \(0.116536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8925 | − | 53.5074i | −1.09290 | − | 1.89296i | ||||
\(800\) | 24.9191 | + | 14.3871i | 0.881023 | + | 0.508659i | ||||
\(801\) | 29.2003 | + | 21.3195i | 1.03174 | + | 0.753287i | ||||
\(802\) | 2.10404 | + | 3.64430i | 0.0742962 | + | 0.128685i | ||||
\(803\) | 11.1420 | 0.393191 | ||||||||
\(804\) | 23.0569 | + | 25.6674i | 0.813154 | + | 0.905220i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.7534 | − | 6.20848i | −0.378772 | − | 0.218684i | ||||
\(807\) | 11.7603 | − | 36.0515i | 0.413984 | − | 1.26907i | ||||
\(808\) | −0.929170 | − | 0.536456i | −0.0326881 | − | 0.0188725i | ||||
\(809\) | −6.40871 | + | 3.70007i | −0.225318 | + | 0.130087i | −0.608410 | − | 0.793623i | \(-0.708192\pi\) |
0.383092 | + | 0.923710i | \(0.374859\pi\) | |||||||
\(810\) | 0.161180 | − | 0.0515404i | 0.00566328 | − | 0.00181095i | ||||
\(811\) | 25.0843i | 0.880829i | 0.897794 | + | 0.440415i | \(0.145169\pi\) | ||||
−0.897794 | + | 0.440415i | \(0.854831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.21732 | + | 15.2236i | 0.112836 | + | 0.533914i | ||||
\(814\) | 0.839587 | + | 1.45421i | 0.0294275 | + | 0.0509699i | ||||
\(815\) | −0.293105 | −0.0102670 | ||||||||
\(816\) | −4.71894 | + | 14.4660i | −0.165196 | + | 0.506411i | ||||
\(817\) | 4.85492i | 0.169852i | ||||||||
\(818\) | 22.2483 | 0.777893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.311353 | 0.0108729 | ||||||||
\(821\) | 21.2212i | 0.740627i | 0.928907 | + | 0.370313i | \(0.120750\pi\) | ||||
−0.928907 | + | 0.370313i | \(0.879250\pi\) | |||||||
\(822\) | −12.7718 | + | 2.69917i | −0.445468 | + | 0.0941442i | ||||
\(823\) | 16.9538 | 0.590972 | 0.295486 | − | 0.955347i | \(-0.404518\pi\) | ||||
0.295486 | + | 0.955347i | \(0.404518\pi\) | |||||||
\(824\) | −6.25546 | − | 10.8348i | −0.217919 | − | 0.377447i | ||||
\(825\) | 8.41538 | + | 2.74518i | 0.292986 | + | 0.0955749i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.3052i | − | 0.879949i | −0.898010 | − | 0.439975i | \(-0.854987\pi\) | ||
0.898010 | − | 0.439975i | \(-0.145013\pi\) | |||||||
\(828\) | 13.7383 | + | 31.0515i | 0.477439 | + | 1.07911i | ||||
\(829\) | 35.9640 | − | 20.7638i | 1.24908 | − | 0.721158i | 0.278156 | − | 0.960536i | \(-0.410277\pi\) |
0.970927 | + | 0.239378i | \(0.0769434\pi\) | |||||||
\(830\) | −0.100111 | − | 0.0577990i | −0.00347490 | − | 0.00200623i | ||||
\(831\) | −26.9475 | + | 5.69504i | −0.934800 | + | 0.197559i | ||||
\(832\) | 3.55896 | + | 2.05477i | 0.123385 | + | 0.0712362i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.96323 | + | 0.837580i | −0.137235 | + | 0.0290030i | ||||
\(835\) | −0.166595 | −0.00576527 | ||||||||
\(836\) | −1.66733 | − | 2.88791i | −0.0576659 | − | 0.0998803i | ||||
\(837\) | 10.0856 | + | 13.9843i | 0.348611 | + | 0.483369i | ||||
\(838\) | −1.03146 | − | 0.595515i | −0.0356312 | − | 0.0205717i | ||||
\(839\) | −6.61780 | − | 11.4624i | −0.228472 | − | 0.395725i | 0.728884 | − | 0.684638i | \(-0.240040\pi\) |
−0.957355 | + | 0.288913i | \(0.906706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.21265 | + | 10.7606i | −0.214229 | + | 0.371056i | ||||
\(842\) | −2.18914 | + | 1.26390i | −0.0754428 | + | 0.0435569i | ||||
\(843\) | −8.56242 | − | 2.79314i | −0.294905 | − | 0.0962009i | ||||
\(844\) | −11.0036 | + | 19.0588i | −0.378759 | + | 0.656030i | ||||
\(845\) | −0.265099 | + | 0.459164i | −0.00911967 | + | 0.0157957i | ||||
\(846\) | 21.5584 | + | 2.31673i | 0.741193 | + | 0.0796509i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.5403 | + | 8.97217i | −0.533654 | + | 0.308106i | ||||
\(849\) | −24.1904 | + | 21.7301i | −0.830213 | + | 0.745776i | ||||
\(850\) | 18.8590i | 0.646859i | ||||||||
\(851\) | − | 17.9547i | − | 0.615479i | ||||||
\(852\) | 15.9351 | − | 14.3144i | 0.545928 | − | 0.490404i | ||||
\(853\) | 15.3814 | − | 8.88048i | 0.526651 | − | 0.304062i | −0.213001 | − | 0.977052i | \(-0.568324\pi\) |
0.739651 | + | 0.672990i | \(0.234990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.176681 | + | 0.0189867i | 0.00604237 | + | 0.000649332i | ||||
\(856\) | 10.7180 | − | 18.5642i | 0.366334 | − | 0.634510i | ||||
\(857\) | −9.17157 | + | 15.8856i | −0.313295 | + | 0.542643i | −0.979074 | − | 0.203507i | \(-0.934766\pi\) |
0.665779 | + | 0.746149i | \(0.268100\pi\) | |||||||
\(858\) | 6.29921 | + | 2.05486i | 0.215052 | + | 0.0701519i | ||||
\(859\) | −2.69126 | + | 1.55380i | −0.0918246 | + | 0.0530150i | −0.545209 | − | 0.838300i | \(-0.683550\pi\) |
0.453385 | + | 0.891315i | \(0.350216\pi\) | |||||||
\(860\) | 0.0511739 | − | 0.0886358i | 0.00174502 | − | 0.00302246i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.441616 | − | 0.764902i | −0.0150415 | − | 0.0260527i | ||||
\(863\) | −35.8587 | − | 20.7030i | −1.22064 | − | 0.704739i | −0.255589 | − | 0.966786i | \(-0.582269\pi\) |
−0.965055 | + | 0.262047i | \(0.915603\pi\) | |||||||
\(864\) | −17.4946 | − | 24.2572i | −0.595177 | − | 0.825247i | ||||
\(865\) | −0.0688566 | − | 0.119263i | −0.00234119 | − | 0.00405507i | ||||
\(866\) | 24.8641 | 0.844917 | ||||||||
\(867\) | −25.8409 | + | 5.46115i | −0.877602 | + | 0.185471i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8114 | − | 7.97399i | −0.468518 | − | 0.270499i | ||||
\(870\) | 0.129719 | − | 0.0274146i | 0.00439789 | − | 0.000929441i | ||||
\(871\) | −62.3460 | − | 35.9955i | −2.11251 | − | 1.21966i | ||||
\(872\) | 9.68438 | − | 5.59128i | 0.327954 | − | 0.189345i | ||||
\(873\) | 9.49669 | + | 21.4645i | 0.321414 | + | 0.726464i | ||||
\(874\) | − | 10.0947i | − | 0.341459i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.9742 | + | 9.12545i | 0.945161 | + | 0.308320i | ||||
\(877\) | 11.3979 | + | 19.7417i | 0.384878 | + | 0.666628i | 0.991752 | − | 0.128170i | \(-0.0409102\pi\) |
−0.606874 | + | 0.794798i | \(0.707577\pi\) | |||||||
\(878\) | −15.7696 | −0.532199 | ||||||||
\(879\) | −38.7054 | + | 8.17993i | −1.30550 | + | 0.275902i | ||||
\(880\) | 0.0447618i | 0.00150892i | ||||||||
\(881\) | 43.4050 | 1.46235 | 0.731175 | − | 0.682190i | \(-0.238972\pi\) | ||||
0.731175 | + | 0.682190i | \(0.238972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9309 | −1.00725 | −0.503627 | − | 0.863921i | \(-0.668001\pi\) | ||||
−0.503627 | + | 0.863921i | \(0.668001\pi\) | |||||||
\(884\) | − | 49.8623i | − | 1.67705i | ||||||
\(885\) | −0.0915592 | + | 0.280676i | −0.00307773 | + | 0.00943483i | ||||
\(886\) | −7.47363 | −0.251082 | ||||||||
\(887\) | −19.4788 | − | 33.7382i | −0.654033 | − | 1.13282i | −0.982135 | − | 0.188176i | \(-0.939742\pi\) |
0.328102 | − | 0.944642i | \(-0.393591\pi\) | |||||||
\(888\) | 2.09347 | + | 9.90579i | 0.0702522 | + | 0.332417i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.226597i | 0.00759556i | ||||||||
\(891\) | −6.80855 | − | 6.18820i | −0.228095 | − | 0.207313i | ||||
\(892\) | −4.03358 | + | 2.32879i | −0.135054 | + | 0.0779736i | ||||
\(893\) | 19.7185 | + | 11.3845i | 0.659853 | + | 0.380966i | ||||
\(894\) | −5.67803 | + | 17.4061i | −0.189902 | + | 0.582147i | ||||
\(895\) | −0.00496721 | − | 0.00286782i | −0.000166035 | − | 9.58606e-5i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.3451 | − | 52.7055i | −1.58081 | − | 1.75979i | ||||
\(898\) | −9.56277 | −0.319114 | ||||||||
\(899\) | 6.75453 | + | 11.6992i | 0.225276 | + | 0.390190i | ||||
\(900\) | 18.8802 | + | 13.7847i | 0.629340 | + | 0.459489i | ||||
\(901\) | −57.0460 | − | 32.9355i | −1.90048 | − | 1.09724i | ||||
\(902\) | 2.39632 | + | 4.15054i | 0.0797886 | + | 0.138198i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2071 | − | 19.4113i | 0.372743 | − | 0.645611i | ||||
\(905\) | 0.153512 | − | 0.0886299i | 0.00510290 | − | 0.00294616i | ||||
\(906\) | −0.823206 | − | 3.89521i | −0.0273492 | − | 0.129410i | ||||
\(907\) | 14.0526 | − | 24.3399i | 0.466610 | − | 0.808192i | −0.532663 | − | 0.846328i | \(-0.678809\pi\) |
0.999273 | + | 0.0381355i | \(0.0121419\pi\) | |||||||
\(908\) | −22.4246 | + | 38.8406i | −0.744187 | + | 1.28897i | ||||
\(909\) | −1.09964 | − | 0.802861i | −0.0364728 | − | 0.0266292i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3883 | − | 18.6994i | 1.07307 | − | 0.619538i | 0.144052 | − | 0.989570i | \(-0.453987\pi\) |
0.929019 | + | 0.370032i | \(0.120653\pi\) | |||||||
\(912\) | −1.15946 | − | 5.48627i | −0.0383935 | − | 0.181669i | ||||
\(913\) | 6.28511i | 0.208007i | ||||||||
\(914\) | − | 13.7024i | − | 0.453235i | ||||||
\(915\) | −0.110443 | − | 0.0360275i | −0.00365113 | − | 0.00119103i | ||||
\(916\) | 11.9616 | − | 6.90601i | 0.395221 | − | 0.228181i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.03546 | − | 17.8793i | 0.265210 | − | 0.590105i | ||||
\(919\) | 12.9115 | − | 22.3634i | 0.425911 | − | 0.737699i | −0.570594 | − | 0.821232i | \(-0.693287\pi\) |
0.996505 | + | 0.0835328i | \(0.0266203\pi\) | |||||||
\(920\) | −0.242933 | + | 0.420773i | −0.00800928 | + | 0.0138725i | ||||
\(921\) | −24.0083 | + | 21.5665i | −0.791100 | + | 0.710641i | ||||
\(922\) | −0.957884 | + | 0.553034i | −0.0315462 | + | 0.0182132i | ||||
\(923\) | −22.3471 | + | 38.7063i | −0.735563 | + | 1.27403i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.18063 | − | 10.7052i | −0.203218 | − | 0.351983i | ||||
\(926\) | 0.695162 | + | 0.401352i | 0.0228444 | + | 0.0131892i | ||||
\(927\) | −6.42372 | − | 14.5190i | −0.210983 | − | 0.476865i | ||||
\(928\) | −11.7164 | − | 20.2934i | −0.384610 | − | 0.666164i | ||||
\(929\) | 15.9419 | 0.523036 | 0.261518 | − | 0.965199i | \(-0.415777\pi\) | ||||
0.261518 | + | 0.965199i | \(0.415777\pi\) | |||||||
\(930\) | −0.0335127 | + | 0.102734i | −0.00109893 | + | 0.00336877i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.4246 | − | 10.0601i | −0.570762 | − | 0.329529i | ||||
\(933\) | −23.7854 | − | 26.4783i | −0.778697 | − | 0.866862i | ||||
\(934\) | −5.31568 | − | 3.06901i | −0.173934 | − | 0.100421i | ||||
\(935\) | −0.142300 | + | 0.0821570i | −0.00465371 | + | 0.00268682i | ||||
\(936\) | 32.2661 | + | 23.5579i | 1.05465 | + | 0.770013i | ||||
\(937\) | − | 15.0698i | − | 0.492308i | −0.969231 | − | 0.246154i | \(-0.920833\pi\) | ||
0.969231 | − | 0.246154i | \(-0.0791668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.929112 | + | 0.834616i | −0.0303204 | + | 0.0272367i | ||||
\(940\) | −0.239999 | − | 0.415690i | −0.00782789 | − | 0.0135583i | ||||
\(941\) | 11.5372 | 0.376102 | 0.188051 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188051 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(942\) | −12.5706 | − | 13.9939i | −0.409574 | − | 0.455946i | ||||
\(943\) | − | 51.2456i | − | 1.66879i | ||||||
\(944\) | 9.31636 | 0.303222 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.57543 | 0.0512218 | ||||||||
\(947\) | − | 28.3321i | − | 0.920671i | −0.887745 | − | 0.460336i | \(-0.847729\pi\) | ||
0.887745 | − | 0.460336i | \(-0.152271\pi\) | |||||||
\(948\) | −28.1454 | − | 31.3321i | −0.914121 | − | 1.01762i | ||||
\(949\) | −61.3961 | −1.99300 | ||||||||
\(950\) | −3.47495 | − | 6.01879i | −0.112742 | − | 0.195275i | ||||
\(951\) | 28.2565 | − | 25.3826i | 0.916278 | − | 0.823088i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.8498i | 0.966931i | 0.875364 | + | 0.483465i | \(0.160622\pi\) | ||||
−0.875364 | + | 0.483465i | \(0.839378\pi\) | |||||||
\(954\) | 21.1398 | − | 9.35303i | 0.684427 | − | 0.302816i | ||||
\(955\) | −0.338347 | + | 0.195345i | −0.0109486 | + | 0.00632120i | ||||
\(956\) | −7.57084 | − | 4.37102i | −0.244858 | − | 0.141369i | ||||
\(957\) | −4.81729 | − | 5.36271i | −0.155721 | − | 0.173352i | ||||
\(958\) | 10.0935 | + | 5.82748i | 0.326106 | + | 0.188277i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0110914 | − | 0.0340009i | 0.000357974 | − | 0.00109737i | ||||
\(961\) | 19.9896 | 0.644824 | ||||||||
\(962\) | −4.62642 | − | 8.01319i | −0.149162 | − | 0.258356i | ||||
\(963\) | 16.0406 | − | 21.9700i | 0.516901 | − | 0.707975i | ||||
\(964\) | 14.8308 | + | 8.56258i | 0.477669 | + | 0.275782i | ||||
\(965\) | −0.298287 | − | 0.516648i | −0.00960219 | − | 0.0166315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.17864 | − | 14.1658i | 0.263007 | − | 0.455542i | −0.704032 | − | 0.710168i | \(-0.748619\pi\) |
0.967040 | + | 0.254626i | \(0.0819523\pi\) | |||||||
\(968\) | 20.3809 | − | 11.7669i | 0.655068 | − | 0.378203i | ||||
\(969\) | 15.3131 | − | 13.7556i | 0.491926 | − | 0.441895i | ||||
\(970\) | −0.0735528 | + | 0.127397i | −0.00236164 | + | 0.00409048i | ||||
\(971\) | 10.7315 | − | 18.5875i | 0.344390 | − | 0.596500i | −0.640853 | − | 0.767663i | \(-0.721419\pi\) |
0.985243 | + | 0.171163i | \(0.0547526\pi\) | |||||||
\(972\) | −12.0260 | − | 21.1131i | −0.385735 | − | 0.677202i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.8470 | + | 14.3454i | −0.796148 | + | 0.459657i | ||||
\(975\) | −46.3717 | − | 15.1269i | −1.48508 | − | 0.484448i | ||||
\(976\) | 3.66588i | 0.117342i | ||||||||
\(977\) | 21.5027i | 0.687932i | 0.938982 | + | 0.343966i | \(0.111770\pi\) | ||||
−0.938982 | + | 0.343966i | \(0.888230\pi\) | |||||||
\(978\) | −2.46370 | − | 11.6577i | −0.0787806 | − | 0.372771i | ||||
\(979\) | 10.6696 | − | 6.16010i | 0.341002 | − | 0.196878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9774 | − | 5.74167i | 0.414336 | − | 0.183318i | ||||
\(982\) | −8.82301 | + | 15.2819i | −0.281554 | + | 0.487665i | ||||
\(983\) | 12.7097 | − | 22.0138i | 0.405376 | − | 0.702131i | −0.588989 | − | 0.808141i | \(-0.700474\pi\) |
0.994365 | + | 0.106009i | \(0.0338073\pi\) | |||||||
\(984\) | 5.97510 | + | 28.2727i | 0.190479 | + | 0.901302i | ||||
\(985\) | −0.371794 | + | 0.214656i | −0.0118464 | + | 0.00683949i | ||||
\(986\) | 7.67912 | − | 13.3006i | 0.244553 | − | 0.423578i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.18759 | + | 15.9134i | 0.292296 | + | 0.506272i | ||||
\(989\) | −14.5886 | − | 8.42273i | −0.463890 | − | 0.267827i | ||||
\(990\) | 0.00616123 | − | 0.0573334i | 0.000195817 | − | 0.00182218i | ||||
\(991\) | −11.8768 | − | 20.5713i | −0.377280 | − | 0.653468i | 0.613385 | − | 0.789784i | \(-0.289807\pi\) |
−0.990665 | + | 0.136315i | \(0.956474\pi\) | |||||||
\(992\) | 19.0987 | 0.606384 | ||||||||
\(993\) | 25.0795 | + | 27.9191i | 0.795875 | + | 0.885985i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.237453 | + | 0.137093i | 0.00752776 | + | 0.00434615i | ||||
\(996\) | −5.14761 | + | 15.7801i | −0.163108 | + | 0.500011i | ||||
\(997\) | 10.5366 | + | 6.08329i | 0.333697 | + | 0.192660i | 0.657481 | − | 0.753471i | \(-0.271622\pi\) |
−0.323785 | + | 0.946131i | \(0.604955\pi\) | |||||||
\(998\) | 3.05781 | − | 1.76543i | 0.0967934 | − | 0.0558837i | ||||
\(999\) | 1.29829 | + | 12.7825i | 0.0410762 | + | 0.404420i |
(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 | 441.2.i.d.68.16 | 48 | ||
3.2 | odd | 2 | 1323.2.i.d.1097.9 | 48 | |||
7.2 | even | 3 | 441.2.o.e.293.15 | yes | 48 | ||
7.3 | odd | 6 | 441.2.s.d.374.9 | 48 | |||
7.4 | even | 3 | 441.2.s.d.374.10 | 48 | |||
7.5 | odd | 6 | 441.2.o.e.293.16 | yes | 48 | ||
7.6 | odd | 2 | inner | 441.2.i.d.68.15 | 48 | ||
9.2 | odd | 6 | 441.2.s.d.362.9 | 48 | |||
9.7 | even | 3 | 1323.2.s.d.656.16 | 48 | |||
21.2 | odd | 6 | 1323.2.o.e.881.9 | 48 | |||
21.5 | even | 6 | 1323.2.o.e.881.10 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.962.15 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.962.16 | 48 | |||
21.20 | even | 2 | 1323.2.i.d.1097.10 | 48 | |||
63.2 | odd | 6 | 441.2.o.e.146.16 | yes | 48 | ||
63.11 | odd | 6 | inner | 441.2.i.d.227.9 | 48 | ||
63.16 | even | 3 | 1323.2.o.e.440.10 | 48 | |||
63.20 | even | 6 | 441.2.s.d.362.10 | 48 | |||
63.25 | even | 3 | 1323.2.i.d.521.10 | 48 | |||
63.34 | odd | 6 | 1323.2.s.d.656.15 | 48 | |||
63.38 | even | 6 | inner | 441.2.i.d.227.10 | 48 | ||
63.47 | even | 6 | 441.2.o.e.146.15 | ✓ | 48 | ||
63.52 | odd | 6 | 1323.2.i.d.521.9 | 48 | |||
63.61 | odd | 6 | 1323.2.o.e.440.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.15 | 48 | 7.6 | odd | 2 | inner | ||
441.2.i.d.68.16 | 48 | 1.1 | even | 1 | trivial | ||
441.2.i.d.227.9 | 48 | 63.11 | odd | 6 | inner | ||
441.2.i.d.227.10 | 48 | 63.38 | even | 6 | inner | ||
441.2.o.e.146.15 | ✓ | 48 | 63.47 | even | 6 | ||
441.2.o.e.146.16 | yes | 48 | 63.2 | odd | 6 | ||
441.2.o.e.293.15 | yes | 48 | 7.2 | even | 3 | ||
441.2.o.e.293.16 | yes | 48 | 7.5 | odd | 6 | ||
441.2.s.d.362.9 | 48 | 9.2 | odd | 6 | |||
441.2.s.d.362.10 | 48 | 63.20 | even | 6 | |||
441.2.s.d.374.9 | 48 | 7.3 | odd | 6 | |||
441.2.s.d.374.10 | 48 | 7.4 | even | 3 | |||
1323.2.i.d.521.9 | 48 | 63.52 | odd | 6 | |||
1323.2.i.d.521.10 | 48 | 63.25 | even | 3 | |||
1323.2.i.d.1097.9 | 48 | 3.2 | odd | 2 | |||
1323.2.i.d.1097.10 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.440.9 | 48 | 63.61 | odd | 6 | |||
1323.2.o.e.440.10 | 48 | 63.16 | even | 3 | |||
1323.2.o.e.881.9 | 48 | 21.2 | odd | 6 | |||
1323.2.o.e.881.10 | 48 | 21.5 | even | 6 | |||
1323.2.s.d.656.15 | 48 | 63.34 | odd | 6 | |||
1323.2.s.d.656.16 | 48 | 9.7 | even | 3 | |||
1323.2.s.d.962.15 | 48 | 21.11 | odd | 6 | |||
1323.2.s.d.962.16 | 48 | 21.17 | even | 6 |