Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(214,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.q (of order \(15\), degree \(8\), 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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 410.3 | ||
Character | \(\chi\) | \(=\) | 539.410 |
Dual form | 539.2.q.f.422.3 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.01812 | + | 0.453294i | 0.719917 | + | 0.320528i | 0.733790 | − | 0.679376i | \(-0.237750\pi\) |
−0.0138735 | + | 0.999904i | \(0.504416\pi\) | |||||||
\(3\) | −2.79635 | − | 0.594382i | −1.61447 | − | 0.343166i | −0.689820 | − | 0.723981i | \(-0.742310\pi\) |
−0.924651 | + | 0.380815i | \(0.875644\pi\) | |||||||
\(4\) | −0.507177 | − | 0.563277i | −0.253589 | − | 0.281639i | ||||
\(5\) | 0.361259 | − | 3.43715i | 0.161560 | − | 1.53714i | −0.550390 | − | 0.834908i | \(-0.685521\pi\) |
0.711950 | − | 0.702230i | \(-0.247812\pi\) | |||||||
\(6\) | −2.57757 | − | 1.87272i | −1.05229 | − | 0.764534i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.949813 | − | 2.92322i | −0.335810 | − | 1.03352i | ||||
\(9\) | 4.72563 | + | 2.10398i | 1.57521 | + | 0.701328i | ||||
\(10\) | 1.92584 | − | 3.33566i | 0.609005 | − | 1.05483i | ||||
\(11\) | −1.73896 | + | 2.82418i | −0.524318 | + | 0.851523i | ||||
\(12\) | 1.08344 | + | 1.87657i | 0.312762 | + | 0.541720i | ||||
\(13\) | −1.66629 | + | 1.21063i | −0.462147 | + | 0.335769i | −0.794373 | − | 0.607430i | \(-0.792200\pi\) |
0.332226 | + | 0.943200i | \(0.392200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.05318 | + | 9.39672i | −0.788328 | + | 2.42622i | ||||
\(16\) | 0.199604 | − | 1.89910i | 0.0499009 | − | 0.474775i | ||||
\(17\) | −1.76655 | + | 0.786518i | −0.428451 | + | 0.190759i | −0.609621 | − | 0.792693i | \(-0.708678\pi\) |
0.181170 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(18\) | 3.85751 | + | 4.28420i | 0.909224 | + | 1.00980i | ||||
\(19\) | −1.08597 | + | 1.20609i | −0.249139 | + | 0.276697i | −0.854723 | − | 0.519085i | \(-0.826273\pi\) |
0.605584 | + | 0.795782i | \(0.292940\pi\) | |||||||
\(20\) | −2.11929 | + | 1.53975i | −0.473887 | + | 0.344299i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.05065 | + | 2.08708i | −0.650401 | + | 0.444967i | ||||
\(23\) | 0.403568 | + | 0.699000i | 0.0841497 | + | 0.145752i | 0.905029 | − | 0.425351i | \(-0.139849\pi\) |
−0.820879 | + | 0.571102i | \(0.806516\pi\) | |||||||
\(24\) | 0.918495 | + | 8.73890i | 0.187487 | + | 1.78382i | ||||
\(25\) | −6.79272 | − | 1.44384i | −1.35854 | − | 0.288767i | ||||
\(26\) | −2.24525 | + | 0.477243i | −0.440331 | + | 0.0935951i | ||||
\(27\) | −5.02542 | − | 3.65118i | −0.967142 | − | 0.702670i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46400 | − | 7.58342i | 0.457554 | − | 1.40821i | −0.410557 | − | 0.911835i | \(-0.634666\pi\) |
0.868111 | − | 0.496371i | \(-0.165334\pi\) | |||||||
\(30\) | −7.36797 | + | 8.18296i | −1.34520 | + | 1.49400i | ||||
\(31\) | 0.0824123 | + | 0.784101i | 0.0148017 | + | 0.140829i | 0.999427 | − | 0.0338518i | \(-0.0107774\pi\) |
−0.984625 | + | 0.174680i | \(0.944111\pi\) | |||||||
\(32\) | −2.00959 | + | 3.48071i | −0.355248 | + | 0.615308i | ||||
\(33\) | 6.54139 | − | 6.86378i | 1.13871 | − | 1.19483i | ||||
\(34\) | −2.15508 | −0.369592 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.21160 | − | 3.72893i | −0.201934 | − | 0.621488i | ||||
\(37\) | −9.84189 | + | 2.09196i | −1.61800 | + | 0.343916i | −0.925865 | − | 0.377854i | \(-0.876662\pi\) |
−0.692133 | + | 0.721770i | \(0.743329\pi\) | |||||||
\(38\) | −1.65236 | + | 0.735679i | −0.268048 | + | 0.119343i | ||||
\(39\) | 5.37911 | − | 2.39494i | 0.861347 | − | 0.383497i | ||||
\(40\) | −10.3907 | + | 2.20861i | −1.64291 | + | 0.349211i | ||||
\(41\) | 0.657011 | + | 2.02207i | 0.102608 | + | 0.315795i | 0.989162 | − | 0.146831i | \(-0.0469074\pi\) |
−0.886554 | + | 0.462626i | \(0.846907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08043 | 0.469761 | 0.234880 | − | 0.972024i | \(-0.424530\pi\) | ||||
0.234880 | + | 0.972024i | \(0.424530\pi\) | |||||||
\(44\) | 2.47276 | − | 0.452841i | 0.372783 | − | 0.0682683i | ||||
\(45\) | 8.93887 | − | 15.4826i | 1.33253 | − | 2.30801i | ||||
\(46\) | 0.0940260 | + | 0.894598i | 0.0138634 | + | 0.131901i | ||||
\(47\) | −5.06286 | + | 5.62287i | −0.738493 | + | 0.820180i | −0.988997 | − | 0.147936i | \(-0.952737\pi\) |
0.250504 | + | 0.968116i | \(0.419404\pi\) | |||||||
\(48\) | −1.68695 | + | 5.19190i | −0.243490 | + | 0.749387i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.26129 | − | 4.54910i | −0.885481 | − | 0.643339i | ||||
\(51\) | 5.40737 | − | 1.14937i | 0.757184 | − | 0.160944i | ||||
\(52\) | 1.52703 | + | 0.324580i | 0.211761 | + | 0.0450111i | ||||
\(53\) | −1.13125 | − | 10.7632i | −0.155390 | − | 1.47843i | −0.743001 | − | 0.669290i | \(-0.766598\pi\) |
0.587611 | − | 0.809143i | \(-0.300068\pi\) | |||||||
\(54\) | −3.46140 | − | 5.99532i | −0.471037 | − | 0.815859i | ||||
\(55\) | 9.07891 | + | 6.99733i | 1.22420 | + | 0.943520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.75363 | − | 2.72717i | 0.497181 | − | 0.361223i | ||||
\(58\) | 5.94616 | − | 6.60388i | 0.780769 | − | 0.867132i | ||||
\(59\) | 2.20588 | + | 2.44988i | 0.287181 | + | 0.318947i | 0.869423 | − | 0.494069i | \(-0.164491\pi\) |
−0.582242 | + | 0.813016i | \(0.697824\pi\) | |||||||
\(60\) | 6.84146 | − | 3.04602i | 0.883229 | − | 0.393239i | ||||
\(61\) | −0.112538 | + | 1.07073i | −0.0144090 | + | 0.137093i | −0.999361 | − | 0.0357334i | \(-0.988623\pi\) |
0.984952 | + | 0.172826i | \(0.0552899\pi\) | |||||||
\(62\) | −0.271523 | + | 0.835662i | −0.0344835 | + | 0.106129i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.71351 | + | 4.87765i | −0.839189 | + | 0.609707i | ||||
\(65\) | 3.55916 | + | 6.16465i | 0.441459 | + | 0.764630i | ||||
\(66\) | 9.77121 | − | 4.02295i | 1.20275 | − | 0.495191i | ||||
\(67\) | −1.20157 | + | 2.08118i | −0.146795 | + | 0.254257i | −0.930041 | − | 0.367455i | \(-0.880229\pi\) |
0.783246 | + | 0.621712i | \(0.213562\pi\) | |||||||
\(68\) | 1.33898 | + | 0.596153i | 0.162375 | + | 0.0722941i | ||||
\(69\) | −0.713042 | − | 2.19452i | −0.0858402 | − | 0.264189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.57963 | + | 1.87421i | 0.306145 | + | 0.222428i | 0.730241 | − | 0.683190i | \(-0.239408\pi\) |
−0.424095 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(72\) | 1.66196 | − | 15.8124i | 0.195863 | − | 1.86352i | ||||
\(73\) | −0.820539 | − | 0.911300i | −0.0960368 | − | 0.106660i | 0.693210 | − | 0.720735i | \(-0.256196\pi\) |
−0.789247 | + | 0.614076i | \(0.789529\pi\) | |||||||
\(74\) | −10.9685 | − | 2.33142i | −1.27506 | − | 0.271022i | ||||
\(75\) | 18.1366 | + | 8.07494i | 2.09424 | + | 0.932414i | ||||
\(76\) | 1.23015 | 0.141107 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.56217 | 0.743020 | ||||||||
\(79\) | −8.66208 | − | 3.85660i | −0.974560 | − | 0.433902i | −0.143235 | − | 0.989689i | \(-0.545750\pi\) |
−0.831325 | + | 0.555787i | \(0.812417\pi\) | |||||||
\(80\) | −6.45538 | − | 1.37213i | −0.721733 | − | 0.153409i | ||||
\(81\) | 1.49869 | + | 1.66447i | 0.166521 | + | 0.184941i | ||||
\(82\) | −0.247681 | + | 2.35652i | −0.0273518 | + | 0.260235i | ||||
\(83\) | −13.0004 | − | 9.44536i | −1.42698 | − | 1.03676i | −0.990569 | − | 0.137016i | \(-0.956249\pi\) |
−0.436412 | − | 0.899747i | \(-0.643751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.06520 | + | 6.35602i | 0.224002 | + | 0.689407i | ||||
\(86\) | 3.13623 | + | 1.39634i | 0.338189 | + | 0.150571i | ||||
\(87\) | −11.3976 | + | 19.7413i | −1.22196 | + | 2.11649i | ||||
\(88\) | 9.90740 | + | 2.40094i | 1.05613 | + | 0.255941i | ||||
\(89\) | −2.21915 | − | 3.84368i | −0.235230 | − | 0.407430i | 0.724110 | − | 0.689685i | \(-0.242251\pi\) |
−0.959339 | + | 0.282255i | \(0.908918\pi\) | |||||||
\(90\) | 16.1190 | − | 11.7111i | 1.69909 | − | 1.23446i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.189050 | − | 0.581837i | 0.0197099 | − | 0.0606607i | ||||
\(93\) | 0.235602 | − | 2.24160i | 0.0244308 | − | 0.232443i | ||||
\(94\) | −7.70339 | + | 3.42977i | −0.794544 | + | 0.353754i | ||||
\(95\) | 3.75320 | + | 4.16836i | 0.385071 | + | 0.427664i | ||||
\(96\) | 7.68837 | − | 8.53880i | 0.784691 | − | 0.871488i | ||||
\(97\) | 5.23278 | − | 3.80184i | 0.531308 | − | 0.386018i | −0.289539 | − | 0.957166i | \(-0.593502\pi\) |
0.820847 | + | 0.571148i | \(0.193502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.1597 | + | 9.68727i | −1.42311 | + | 0.973607i | ||||
\(100\) | 2.63183 | + | 4.55847i | 0.263183 | + | 0.455847i | ||||
\(101\) | −1.61443 | − | 15.3603i | −0.160642 | − | 1.52841i | −0.716770 | − | 0.697310i | \(-0.754380\pi\) |
0.556128 | − | 0.831097i | \(-0.312286\pi\) | |||||||
\(102\) | 6.02634 | + | 1.28094i | 0.596696 | + | 0.126832i | ||||
\(103\) | 8.71346 | − | 1.85210i | 0.858563 | − | 0.182493i | 0.242462 | − | 0.970161i | \(-0.422045\pi\) |
0.616100 | + | 0.787668i | \(0.288712\pi\) | |||||||
\(104\) | 5.12162 | + | 3.72107i | 0.502216 | + | 0.364881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.72713 | − | 11.4709i | 0.362011 | − | 1.11416i | ||||
\(107\) | 2.35011 | − | 2.61007i | 0.227194 | − | 0.252325i | −0.618760 | − | 0.785580i | \(-0.712365\pi\) |
0.845954 | + | 0.533255i | \(0.179031\pi\) | |||||||
\(108\) | 0.492150 | + | 4.68250i | 0.0473572 | + | 0.450574i | ||||
\(109\) | −1.93827 | + | 3.35719i | −0.185653 | + | 0.321560i | −0.943796 | − | 0.330527i | \(-0.892773\pi\) |
0.758143 | + | 0.652088i | \(0.226107\pi\) | |||||||
\(110\) | 6.07153 | + | 11.2395i | 0.578897 | + | 1.07165i | ||||
\(111\) | 28.7648 | 2.73023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.29224 | + | 10.1325i | 0.309708 | + | 0.953183i | 0.977878 | + | 0.209175i | \(0.0670777\pi\) |
−0.668170 | + | 0.744008i | \(0.732922\pi\) | |||||||
\(114\) | 5.05785 | − | 1.07508i | 0.473711 | − | 0.100690i | ||||
\(115\) | 2.54836 | − | 1.13460i | 0.237635 | − | 0.105802i | ||||
\(116\) | −5.52125 | + | 2.45822i | −0.512635 | + | 0.228240i | ||||
\(117\) | −10.4214 | + | 2.21514i | −0.963462 | + | 0.204790i | ||||
\(118\) | 1.13533 | + | 3.49417i | 0.104515 | + | 0.321665i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 30.3687 | 2.77227 | ||||||||
\(121\) | −4.95200 | − | 9.82230i | −0.450182 | − | 0.892937i | ||||
\(122\) | −0.599933 | + | 1.03911i | −0.0543154 | + | 0.0940769i | ||||
\(123\) | −0.635348 | − | 6.04493i | −0.0572874 | − | 0.545053i | ||||
\(124\) | 0.399868 | − | 0.444099i | 0.0359092 | − | 0.0398813i | ||||
\(125\) | −2.07667 | + | 6.39134i | −0.185743 | + | 0.571659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7361 | − | 11.4330i | −1.39635 | − | 1.01451i | −0.995134 | − | 0.0985289i | \(-0.968586\pi\) |
−0.401220 | − | 0.915982i | \(-0.631414\pi\) | |||||||
\(128\) | −1.18346 | + | 0.251551i | −0.104604 | + | 0.0222342i | ||||
\(129\) | −8.61394 | − | 1.83095i | −0.758415 | − | 0.161206i | ||||
\(130\) | 0.829238 | + | 7.88967i | 0.0727290 | + | 0.691970i | ||||
\(131\) | 2.55642 | + | 4.42785i | 0.223355 | + | 0.386863i | 0.955825 | − | 0.293937i | \(-0.0949657\pi\) |
−0.732469 | + | 0.680800i | \(0.761632\pi\) | |||||||
\(132\) | −7.18385 | − | 0.203464i | −0.625274 | − | 0.0177092i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.16672 | + | 1.57422i | −0.187176 | + | 0.135992i | ||||
\(135\) | −14.3651 | + | 15.9541i | −1.23635 | + | 1.37311i | ||||
\(136\) | 3.97706 | + | 4.41697i | 0.341030 | + | 0.378752i | ||||
\(137\) | 8.31374 | − | 3.70151i | 0.710290 | − | 0.316242i | −0.0195980 | − | 0.999808i | \(-0.506239\pi\) |
0.729888 | + | 0.683566i | \(0.239572\pi\) | |||||||
\(138\) | 0.268803 | − | 2.55749i | 0.0228821 | − | 0.217708i | ||||
\(139\) | 4.02234 | − | 12.3795i | 0.341171 | − | 1.05002i | −0.622431 | − | 0.782675i | \(-0.713855\pi\) |
0.963602 | − | 0.267341i | \(-0.0861450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4996 | − | 12.7142i | 1.47373 | − | 1.07073i | ||||
\(142\) | 1.77679 | + | 3.07749i | 0.149105 | + | 0.258257i | ||||
\(143\) | −0.521422 | − | 6.81117i | −0.0436035 | − | 0.569578i | ||||
\(144\) | 4.93893 | − | 8.55448i | 0.411577 | − | 0.712873i | ||||
\(145\) | −25.1752 | − | 11.2087i | −2.09068 | − | 0.930832i | ||||
\(146\) | −0.422316 | − | 1.29975i | −0.0349511 | − | 0.107568i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.16994 | + | 4.48272i | 0.507166 | + | 0.368477i | ||||
\(149\) | 0.328899 | − | 3.12926i | 0.0269444 | − | 0.256359i | −0.972755 | − | 0.231836i | \(-0.925527\pi\) |
0.999699 | − | 0.0245229i | \(-0.00780666\pi\) | |||||||
\(150\) | 14.8048 | + | 16.4424i | 1.20881 | + | 1.34252i | ||||
\(151\) | −2.80431 | − | 0.596075i | −0.228212 | − | 0.0485079i | 0.0923863 | − | 0.995723i | \(-0.470551\pi\) |
−0.320598 | + | 0.947215i | \(0.603884\pi\) | |||||||
\(152\) | 4.55715 | + | 2.02898i | 0.369634 | + | 0.164572i | ||||
\(153\) | −10.0029 | −0.808684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72484 | 0.218864 | ||||||||
\(156\) | −4.07718 | − | 1.81528i | −0.326435 | − | 0.145338i | ||||
\(157\) | −21.0199 | − | 4.46792i | −1.67757 | − | 0.356579i | −0.731827 | − | 0.681491i | \(-0.761332\pi\) |
−0.945744 | + | 0.324912i | \(0.894665\pi\) | |||||||
\(158\) | −7.07082 | − | 7.85294i | −0.562524 | − | 0.624746i | ||||
\(159\) | −3.23405 | + | 30.7699i | −0.256477 | + | 2.44021i | ||||
\(160\) | 11.2377 | + | 8.16468i | 0.888420 | + | 0.645475i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.771349 | + | 2.37397i | 0.0606029 | + | 0.186517i | ||||
\(163\) | −7.51158 | − | 3.34437i | −0.588353 | − | 0.261951i | 0.0908952 | − | 0.995860i | \(-0.471027\pi\) |
−0.679248 | + | 0.733909i | \(0.737694\pi\) | |||||||
\(164\) | 0.805767 | − | 1.39563i | 0.0629198 | − | 0.108980i | ||||
\(165\) | −21.2287 | − | 24.9633i | −1.65265 | − | 1.94339i | ||||
\(166\) | −8.95440 | − | 15.5095i | −0.694997 | − | 1.20377i | ||||
\(167\) | −17.5626 | + | 12.7600i | −1.35904 | + | 0.987397i | −0.360529 | + | 0.932748i | \(0.617404\pi\) |
−0.998506 | + | 0.0546489i | \(0.982596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70632 | + | 8.32919i | −0.208178 | + | 0.640707i | ||||
\(170\) | −0.778540 | + | 7.40731i | −0.0597113 | + | 0.568115i | ||||
\(171\) | −7.66950 | + | 3.41468i | −0.586501 | + | 0.261127i | ||||
\(172\) | −1.56232 | − | 1.73513i | −0.119126 | − | 0.132303i | ||||
\(173\) | 5.38358 | − | 5.97907i | 0.409306 | − | 0.454580i | −0.502880 | − | 0.864356i | \(-0.667726\pi\) |
0.912186 | + | 0.409776i | \(0.134393\pi\) | |||||||
\(174\) | −20.5527 | + | 14.9324i | −1.55810 | + | 1.13203i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.01630 | + | 3.86619i | 0.378118 | + | 0.291425i | ||||
\(177\) | −4.71224 | − | 8.16184i | −0.354194 | − | 0.613482i | ||||
\(178\) | −0.517033 | − | 4.91924i | −0.0387533 | − | 0.368713i | ||||
\(179\) | 3.54178 | + | 0.752829i | 0.264725 | + | 0.0562691i | 0.338362 | − | 0.941016i | \(-0.390127\pi\) |
−0.0736366 | + | 0.997285i | \(0.523460\pi\) | |||||||
\(180\) | −13.2546 | + | 2.81735i | −0.987938 | + | 0.209993i | ||||
\(181\) | 12.7970 | + | 9.29753i | 0.951190 | + | 0.691080i | 0.951088 | − | 0.308920i | \(-0.0999675\pi\) |
0.000102207 | 1.00000i | \(0.499967\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.951118 | − | 2.92724i | 0.0703087 | − | 0.216388i | ||||
\(184\) | 1.66002 | − | 1.84364i | 0.122378 | − | 0.135915i | ||||
\(185\) | 3.63490 | + | 34.5838i | 0.267243 | + | 2.54265i | ||||
\(186\) | 1.25598 | − | 2.17541i | 0.0920926 | − | 0.159509i | ||||
\(187\) | 0.850696 | − | 6.35678i | 0.0622091 | − | 0.464854i | ||||
\(188\) | 5.73500 | 0.418268 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.93170 | + | 5.94518i | 0.140141 | + | 0.431308i | ||||
\(191\) | −0.419704 | + | 0.0892109i | −0.0303687 | + | 0.00645508i | −0.223071 | − | 0.974802i | \(-0.571608\pi\) |
0.192702 | + | 0.981257i | \(0.438275\pi\) | |||||||
\(192\) | 21.6725 | − | 9.64922i | 1.56408 | − | 0.696372i | ||||
\(193\) | −13.8629 | + | 6.17216i | −0.997873 | + | 0.444282i | −0.839654 | − | 0.543122i | \(-0.817242\pi\) |
−0.158219 | + | 0.987404i | \(0.550575\pi\) | |||||||
\(194\) | 7.05092 | − | 1.49872i | 0.506227 | − | 0.107602i | ||||
\(195\) | −6.28849 | − | 19.3540i | −0.450328 | − | 1.38597i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.8082 | −1.48252 | −0.741262 | − | 0.671216i | \(-0.765772\pi\) | ||||
−0.741262 | + | 0.671216i | \(0.765772\pi\) | |||||||
\(198\) | −18.8074 | + | 3.44424i | −1.33659 | + | 0.244771i | ||||
\(199\) | 4.22284 | − | 7.31417i | 0.299349 | − | 0.518488i | −0.676638 | − | 0.736316i | \(-0.736564\pi\) |
0.975987 | + | 0.217828i | \(0.0698972\pi\) | |||||||
\(200\) | 2.23115 | + | 21.2280i | 0.157766 | + | 1.50105i | ||||
\(201\) | 4.59702 | − | 5.10551i | 0.324249 | − | 0.360115i | ||||
\(202\) | 5.31906 | − | 16.3704i | 0.374247 | − | 1.15182i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.38991 | − | 2.46292i | −0.237341 | − | 0.172439i | ||||
\(205\) | 7.18751 | − | 1.52775i | 0.501998 | − | 0.106703i | ||||
\(206\) | 9.71086 | + | 2.06411i | 0.676588 | + | 0.143813i | ||||
\(207\) | 0.436426 | + | 4.15231i | 0.0303337 | + | 0.288606i | ||||
\(208\) | 1.96652 | + | 3.40611i | 0.136353 | + | 0.236171i | ||||
\(209\) | −1.51776 | − | 5.16434i | −0.104986 | − | 0.357225i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97632 | − | 5.79513i | 0.549112 | − | 0.398953i | −0.278346 | − | 0.960481i | \(-0.589786\pi\) |
0.827458 | + | 0.561528i | \(0.189786\pi\) | |||||||
\(212\) | −5.48890 | + | 6.09604i | −0.376979 | + | 0.418678i | ||||
\(213\) | −6.09954 | − | 6.77422i | −0.417933 | − | 0.464162i | ||||
\(214\) | 3.57582 | − | 1.59206i | 0.244438 | − | 0.108831i | ||||
\(215\) | 1.11283 | − | 10.5879i | 0.0758944 | − | 0.722087i | ||||
\(216\) | −5.90001 | + | 18.1584i | −0.401445 | + | 1.23552i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.49518 | + | 2.53940i | −0.236724 | + | 0.171990i | ||||
\(219\) | 1.75285 | + | 3.03602i | 0.118447 | + | 0.205156i | ||||
\(220\) | −0.663174 | − | 8.66283i | −0.0447112 | − | 0.584048i | ||||
\(221\) | 1.99140 | − | 3.44921i | 0.133956 | − | 0.232019i | ||||
\(222\) | 29.2859 | + | 13.0389i | 1.96554 | + | 0.875114i | ||||
\(223\) | −5.37562 | − | 16.5445i | −0.359978 | − | 1.10790i | −0.953066 | − | 0.302762i | \(-0.902091\pi\) |
0.593088 | − | 0.805138i | \(-0.297909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.0620 | − | 21.1148i | −1.93747 | − | 1.40765i | ||||
\(226\) | −1.24111 | + | 11.8084i | −0.0825575 | + | 0.785482i | ||||
\(227\) | 8.45211 | + | 9.38702i | 0.560986 | + | 0.623038i | 0.955193 | − | 0.295983i | \(-0.0956473\pi\) |
−0.394207 | + | 0.919022i | \(0.628981\pi\) | |||||||
\(228\) | −3.43991 | − | 0.731176i | −0.227814 | − | 0.0484233i | ||||
\(229\) | −4.17802 | − | 1.86018i | −0.276091 | − | 0.122924i | 0.264020 | − | 0.964517i | \(-0.414951\pi\) |
−0.540112 | + | 0.841593i | \(0.681618\pi\) | |||||||
\(230\) | 3.10883 | 0.204990 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5084 | −1.60905 | ||||||||
\(233\) | 21.7944 | + | 9.70347i | 1.42780 | + | 0.635696i | 0.967684 | − | 0.252166i | \(-0.0811428\pi\) |
0.460111 | + | 0.887861i | \(0.347809\pi\) | |||||||
\(234\) | −11.6143 | − | 2.46870i | −0.759253 | − | 0.161384i | ||||
\(235\) | 17.4976 | + | 19.4331i | 1.14142 | + | 1.26767i | ||||
\(236\) | 0.261189 | − | 2.48504i | 0.0170019 | − | 0.161763i | ||||
\(237\) | 21.9299 | + | 15.9330i | 1.42450 | + | 1.03496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.73114 | + | 8.40558i | 0.176663 | + | 0.543711i | 0.999705 | − | 0.0242677i | \(-0.00772541\pi\) |
−0.823043 | + | 0.567979i | \(0.807725\pi\) | |||||||
\(240\) | 17.2359 | + | 7.67392i | 1.11257 | + | 0.495349i | ||||
\(241\) | 9.47322 | − | 16.4081i | 0.610224 | − | 1.05694i | −0.380978 | − | 0.924584i | \(-0.624413\pi\) |
0.991202 | − | 0.132355i | \(-0.0422539\pi\) | |||||||
\(242\) | −0.589317 | − | 12.2450i | −0.0378827 | − | 0.787136i | ||||
\(243\) | 6.11610 | + | 10.5934i | 0.392348 | + | 0.679567i | ||||
\(244\) | 0.660194 | − | 0.479659i | 0.0422646 | − | 0.0307070i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.09328 | − | 6.44244i | 0.133462 | − | 0.410755i | ||||
\(247\) | 0.349411 | − | 3.32442i | 0.0222325 | − | 0.211528i | ||||
\(248\) | 2.21383 | − | 0.985658i | 0.140578 | − | 0.0625894i | ||||
\(249\) | 30.7395 | + | 34.1397i | 1.94804 | + | 2.16352i | ||||
\(250\) | −5.01145 | + | 5.56578i | −0.316952 | + | 0.352011i | ||||
\(251\) | −2.31938 | + | 1.68513i | −0.146398 | + | 0.106364i | −0.658573 | − | 0.752516i | \(-0.728840\pi\) |
0.512175 | + | 0.858881i | \(0.328840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67589 | − | 0.0757876i | −0.168232 | − | 0.00476473i | ||||
\(254\) | −10.8387 | − | 18.7732i | −0.680080 | − | 1.17793i | ||||
\(255\) | −1.99710 | − | 19.0012i | −0.125063 | − | 1.18990i | ||||
\(256\) | 14.9151 | + | 3.17031i | 0.932195 | + | 0.198144i | ||||
\(257\) | 21.9260 | − | 4.66052i | 1.36771 | − | 0.290715i | 0.535199 | − | 0.844726i | \(-0.320237\pi\) |
0.832510 | + | 0.554011i | \(0.186903\pi\) | |||||||
\(258\) | −7.94003 | − | 5.76877i | −0.494325 | − | 0.359148i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.66728 | − | 5.13136i | 0.103400 | − | 0.318234i | ||||
\(261\) | 27.5993 | − | 30.6522i | 1.70836 | − | 1.89732i | ||||
\(262\) | 0.595612 | + | 5.66687i | 0.0367970 | + | 0.350100i | ||||
\(263\) | −0.495353 | + | 0.857976i | −0.0305448 | + | 0.0529051i | −0.880894 | − | 0.473314i | \(-0.843058\pi\) |
0.850349 | + | 0.526219i | \(0.176391\pi\) | |||||||
\(264\) | −26.2775 | − | 12.6026i | −1.61727 | − | 0.775639i | ||||
\(265\) | −37.4032 | −2.29766 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.92090 | + | 12.0673i | 0.239955 | + | 0.738506i | ||||
\(268\) | 1.78169 | − | 0.378710i | 0.108834 | − | 0.0231334i | ||||
\(269\) | 6.56873 | − | 2.92458i | 0.400502 | − | 0.178315i | −0.196593 | − | 0.980485i | \(-0.562988\pi\) |
0.597096 | + | 0.802170i | \(0.296321\pi\) | |||||||
\(270\) | −21.8572 | + | 9.73147i | −1.33019 | + | 0.592238i | ||||
\(271\) | −26.5707 | + | 5.64777i | −1.61405 | + | 0.343078i | −0.924508 | − | 0.381164i | \(-0.875523\pi\) |
−0.689546 | + | 0.724241i | \(0.742190\pi\) | |||||||
\(272\) | 1.14107 | + | 3.51185i | 0.0691874 | + | 0.212937i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1422 | 0.612714 | ||||||||
\(275\) | 15.8900 | − | 16.6731i | 0.958201 | − | 1.00543i | ||||
\(276\) | −0.874484 | + | 1.51465i | −0.0526377 | + | 0.0911712i | ||||
\(277\) | −2.19359 | − | 20.8706i | −0.131800 | − | 1.25400i | −0.837877 | − | 0.545860i | \(-0.816203\pi\) |
0.706076 | − | 0.708136i | \(-0.250464\pi\) | |||||||
\(278\) | 9.70677 | − | 10.7805i | 0.582173 | − | 0.646569i | ||||
\(279\) | −1.26029 | + | 3.87876i | −0.0754513 | + | 0.232215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7803 | + | 16.5509i | 1.35896 | + | 0.987341i | 0.998510 | + | 0.0545621i | \(0.0173763\pi\) |
0.360448 | + | 0.932779i | \(0.382624\pi\) | |||||||
\(282\) | 23.5799 | − | 5.01207i | 1.40416 | − | 0.298464i | ||||
\(283\) | −25.6194 | − | 5.44557i | −1.52291 | − | 0.323705i | −0.630954 | − | 0.775820i | \(-0.717336\pi\) |
−0.891960 | + | 0.452115i | \(0.850670\pi\) | |||||||
\(284\) | −0.252629 | − | 2.40360i | −0.0149908 | − | 0.142627i | ||||
\(285\) | −8.01766 | − | 13.8870i | −0.474925 | − | 0.822595i | ||||
\(286\) | 2.55660 | − | 7.17091i | 0.151175 | − | 0.424025i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.8199 | + | 12.2204i | −0.991123 | + | 0.720093i | ||||
\(289\) | −8.87314 | + | 9.85462i | −0.521949 | + | 0.579683i | ||||
\(290\) | −20.5504 | − | 22.8235i | −1.20676 | − | 1.34024i | ||||
\(291\) | −16.8924 | + | 7.52098i | −0.990250 | + | 0.440888i | ||||
\(292\) | −0.0971564 | + | 0.924381i | −0.00568565 | + | 0.0540953i | ||||
\(293\) | 1.37941 | − | 4.24538i | 0.0805858 | − | 0.248017i | −0.902644 | − | 0.430388i | \(-0.858377\pi\) |
0.983230 | + | 0.182370i | \(0.0583769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.21748 | − | 6.69689i | 0.536663 | − | 0.389908i | ||||
\(296\) | 15.4632 | + | 26.7831i | 0.898782 | + | 1.55674i | ||||
\(297\) | 19.0506 | − | 7.84342i | 1.10543 | − | 0.455121i | ||||
\(298\) | 1.75333 | − | 3.03686i | 0.101568 | − | 0.175921i | ||||
\(299\) | −1.51870 | − | 0.676167i | −0.0878284 | − | 0.0391037i | ||||
\(300\) | −4.65004 | − | 14.3114i | −0.268470 | − | 0.826267i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.58492 | − | 1.87805i | −0.148745 | − | 0.108070i | ||||
\(303\) | −4.61537 | + | 43.9123i | −0.265146 | + | 2.52269i | ||||
\(304\) | 2.07373 | + | 2.30311i | 0.118937 | + | 0.132092i | ||||
\(305\) | 3.63960 | + | 0.773620i | 0.208403 | + | 0.0442974i | ||||
\(306\) | −10.1841 | − | 4.53425i | −0.582185 | − | 0.259206i | ||||
\(307\) | −12.8841 | −0.735334 | −0.367667 | − | 0.929957i | \(-0.619843\pi\) | ||||
−0.367667 | + | 0.929957i | \(0.619843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4667 | −1.44875 | ||||||||
\(310\) | 2.77420 | + | 1.23515i | 0.157564 | + | 0.0701521i | ||||
\(311\) | 26.2338 | + | 5.57616i | 1.48758 | + | 0.316195i | 0.878818 | − | 0.477157i | \(-0.158333\pi\) |
0.608763 | + | 0.793352i | \(0.291666\pi\) | |||||||
\(312\) | −12.1101 | − | 13.4496i | −0.685598 | − | 0.761434i | ||||
\(313\) | 0.375120 | − | 3.56903i | 0.0212030 | − | 0.201733i | −0.978792 | − | 0.204856i | \(-0.934327\pi\) |
0.999995 | + | 0.00312281i | \(0.000994021\pi\) | |||||||
\(314\) | −19.3754 | − | 14.0771i | −1.09342 | − | 0.794415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.22087 | + | 6.83513i | 0.124934 | + | 0.384506i | ||||
\(317\) | −15.4554 | − | 6.88119i | −0.868062 | − | 0.386486i | −0.0761321 | − | 0.997098i | \(-0.524257\pi\) |
−0.791930 | + | 0.610611i | \(0.790924\pi\) | |||||||
\(318\) | −17.2405 | + | 29.8614i | −0.966797 | + | 1.67454i | ||||
\(319\) | 17.1321 | + | 20.1461i | 0.959216 | + | 1.12796i | ||||
\(320\) | 14.3399 | + | 24.8374i | 0.801624 | + | 1.38845i | ||||
\(321\) | −8.12311 | + | 5.90178i | −0.453388 | + | 0.329405i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.969808 | − | 2.98476i | 0.0539616 | − | 0.166077i | ||||
\(324\) | 0.177454 | − | 1.68836i | 0.00985854 | − | 0.0937977i | ||||
\(325\) | 13.0666 | − | 5.81764i | 0.724806 | − | 0.322704i | ||||
\(326\) | −6.13168 | − | 6.80992i | −0.339602 | − | 0.377166i | ||||
\(327\) | 7.41554 | − | 8.23579i | 0.410080 | − | 0.455440i | ||||
\(328\) | 5.28693 | − | 3.84118i | 0.291922 | − | 0.212094i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.2975 | − | 35.0384i | −0.566860 | − | 1.92880i | ||||
\(331\) | 0.619131 | + | 1.07237i | 0.0340305 | + | 0.0589426i | 0.882539 | − | 0.470239i | \(-0.155832\pi\) |
−0.848509 | + | 0.529182i | \(0.822499\pi\) | |||||||
\(332\) | 1.27316 | + | 12.1133i | 0.0698737 | + | 0.664804i | ||||
\(333\) | −50.9106 | − | 10.8214i | −2.78988 | − | 0.593008i | ||||
\(334\) | −23.6648 | + | 5.03011i | −1.29488 | + | 0.275235i | ||||
\(335\) | 6.71924 | + | 4.88181i | 0.367111 | + | 0.266722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.32885 | + | 19.4782i | −0.344754 | + | 1.06104i | 0.616961 | + | 0.786994i | \(0.288364\pi\) |
−0.961715 | + | 0.274051i | \(0.911636\pi\) | |||||||
\(338\) | −6.53092 | + | 7.25332i | −0.355235 | + | 0.394529i | ||||
\(339\) | −3.18369 | − | 30.2908i | −0.172914 | − | 1.64517i | ||||
\(340\) | 2.53278 | − | 4.38691i | 0.137359 | − | 0.237913i | ||||
\(341\) | −2.35775 | − | 1.13078i | −0.127680 | − | 0.0612350i | ||||
\(342\) | −9.35630 | −0.505931 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.92583 | − | 9.00478i | −0.157750 | − | 0.485505i | ||||
\(345\) | −7.80047 | + | 1.65804i | −0.419963 | + | 0.0892660i | ||||
\(346\) | 8.19139 | − | 3.64704i | 0.440372 | − | 0.196066i | ||||
\(347\) | 24.9122 | − | 11.0916i | 1.33736 | − | 0.595431i | 0.391551 | − | 0.920156i | \(-0.371939\pi\) |
0.945808 | + | 0.324725i | \(0.105272\pi\) | |||||||
\(348\) | 16.9005 | − | 3.59230i | 0.905959 | − | 0.192568i | ||||
\(349\) | −2.46730 | − | 7.59356i | −0.132071 | − | 0.406474i | 0.863052 | − | 0.505116i | \(-0.168550\pi\) |
−0.995123 | + | 0.0986418i | \(0.968550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7941 | 0.682897 | ||||||||
\(352\) | −6.33555 | − | 11.7283i | −0.337686 | − | 0.625119i | ||||
\(353\) | 2.96736 | − | 5.13961i | 0.157937 | − | 0.273554i | −0.776188 | − | 0.630502i | \(-0.782849\pi\) |
0.934124 | + | 0.356948i | \(0.116183\pi\) | |||||||
\(354\) | −1.09789 | − | 10.4457i | −0.0583523 | − | 0.555185i | ||||
\(355\) | 7.37384 | − | 8.18948i | 0.391363 | − | 0.434652i | ||||
\(356\) | −1.03956 | + | 3.19942i | −0.0550964 | + | 0.169569i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26469 | + | 2.37194i | 0.172544 | + | 0.125361i | ||||
\(359\) | −27.7992 | + | 5.90891i | −1.46719 | + | 0.311860i | −0.871118 | − | 0.491073i | \(-0.836605\pi\) |
−0.596069 | + | 0.802933i | \(0.703271\pi\) | |||||||
\(360\) | −53.7493 | − | 11.4248i | −2.83284 | − | 0.602138i | ||||
\(361\) | 1.71071 | + | 16.2763i | 0.0900375 | + | 0.856650i | ||||
\(362\) | 8.81427 | + | 15.2668i | 0.463267 | + | 0.802403i | ||||
\(363\) | 8.00931 | + | 30.4099i | 0.420380 | + | 1.59611i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.42870 | + | 2.49109i | −0.179466 | + | 0.130390i | ||||
\(366\) | 2.29525 | − | 2.54913i | 0.119975 | − | 0.133245i | ||||
\(367\) | 20.3425 | + | 22.5927i | 1.06187 | + | 1.17933i | 0.983220 | + | 0.182425i | \(0.0583948\pi\) |
0.0786515 | + | 0.996902i | \(0.474939\pi\) | |||||||
\(368\) | 1.40802 | − | 0.626893i | 0.0733984 | − | 0.0326791i | ||||
\(369\) | −1.14962 | + | 10.9379i | −0.0598468 | + | 0.569404i | ||||
\(370\) | −11.9759 | + | 36.8580i | −0.622596 | + | 1.91615i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38213 | + | 1.00418i | −0.0716603 | + | 0.0520643i | ||||
\(373\) | −7.21128 | − | 12.4903i | −0.373386 | − | 0.646723i | 0.616698 | − | 0.787200i | \(-0.288470\pi\) |
−0.990084 | + | 0.140476i | \(0.955137\pi\) | |||||||
\(374\) | 3.74760 | − | 6.08633i | 0.193784 | − | 0.314716i | ||||
\(375\) | 9.60599 | − | 16.6381i | 0.496051 | − | 0.859186i | ||||
\(376\) | 21.2457 | + | 9.45918i | 1.09566 | + | 0.487820i | ||||
\(377\) | 5.07499 | + | 15.6192i | 0.261375 | + | 0.804430i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1278 | + | 13.1706i | 0.931163 | + | 0.676529i | 0.946277 | − | 0.323356i | \(-0.104811\pi\) |
−0.0151144 | + | 0.999886i | \(0.504811\pi\) | |||||||
\(380\) | 0.444401 | − | 4.22819i | 0.0227973 | − | 0.216902i | ||||
\(381\) | 37.2081 | + | 41.3238i | 1.90623 | + | 2.11708i | ||||
\(382\) | −0.467747 | − | 0.0994226i | −0.0239320 | − | 0.00508690i | ||||
\(383\) | −30.7669 | − | 13.6983i | −1.57211 | − | 0.699950i | −0.578808 | − | 0.815464i | \(-0.696482\pi\) |
−0.993306 | + | 0.115514i | \(0.963149\pi\) | |||||||
\(384\) | 3.45887 | 0.176510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9118 | −0.860790 | ||||||||
\(387\) | 14.5569 | + | 6.48117i | 0.739971 | + | 0.329456i | ||||
\(388\) | −4.79543 | − | 1.01930i | −0.243451 | − | 0.0517471i | ||||
\(389\) | 1.62454 | + | 1.80423i | 0.0823672 | + | 0.0914780i | 0.782920 | − | 0.622123i | \(-0.213730\pi\) |
−0.700552 | + | 0.713601i | \(0.747063\pi\) | |||||||
\(390\) | 2.37064 | − | 22.5551i | 0.120042 | − | 1.14212i | ||||
\(391\) | −1.26270 | − | 0.917404i | −0.0638574 | − | 0.0463951i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.51680 | − | 13.9013i | −0.227842 | − | 0.701227i | ||||
\(394\) | −21.1852 | − | 9.43224i | −1.06729 | − | 0.475190i | ||||
\(395\) | −16.3850 | + | 28.3796i | −0.824417 | + | 1.42793i | ||||
\(396\) | 12.6381 | + | 3.06269i | 0.635089 | + | 0.153906i | ||||
\(397\) | −2.94848 | − | 5.10692i | −0.147980 | − | 0.256309i | 0.782501 | − | 0.622650i | \(-0.213944\pi\) |
−0.930481 | + | 0.366341i | \(0.880610\pi\) | |||||||
\(398\) | 7.61481 | − | 5.53248i | 0.381696 | − | 0.277318i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.09784 | + | 12.6119i | −0.204892 | + | 0.630593i | ||||
\(401\) | −1.17486 | + | 11.1780i | −0.0586696 | + | 0.558203i | 0.925221 | + | 0.379430i | \(0.123880\pi\) |
−0.983890 | + | 0.178774i | \(0.942787\pi\) | |||||||
\(402\) | 6.99460 | − | 3.11420i | 0.348859 | − | 0.155322i | ||||
\(403\) | −1.08658 | − | 1.20677i | −0.0541265 | − | 0.0601136i | ||||
\(404\) | −7.83330 | + | 8.69976i | −0.389721 | + | 0.432829i | ||||
\(405\) | 6.26243 | − | 4.54992i | 0.311183 | − | 0.226087i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2066 | − | 31.4331i | 0.555492 | − | 1.55808i | ||||
\(408\) | −8.49587 | − | 14.7153i | −0.420608 | − | 0.728515i | ||||
\(409\) | 3.06628 | + | 29.1737i | 0.151618 | + | 1.44255i | 0.760527 | + | 0.649306i | \(0.224941\pi\) |
−0.608909 | + | 0.793240i | \(0.708393\pi\) | |||||||
\(410\) | 8.01024 | + | 1.70263i | 0.395598 | + | 0.0840869i | ||||
\(411\) | −25.4482 | + | 5.40918i | −1.25527 | + | 0.266815i | ||||
\(412\) | −5.46251 | − | 3.96875i | −0.269119 | − | 0.195526i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.43789 | + | 4.42536i | −0.0706683 | + | 0.217495i | ||||
\(415\) | −37.1616 | + | 41.2721i | −1.82419 | + | 2.02597i | ||||
\(416\) | −0.865298 | − | 8.23276i | −0.0424247 | − | 0.403644i | ||||
\(417\) | −18.6060 | + | 32.2266i | −0.911140 | + | 1.57814i | ||||
\(418\) | 0.795708 | − | 5.94589i | 0.0389194 | − | 0.290823i | ||||
\(419\) | 20.2858 | 0.991027 | 0.495514 | − | 0.868600i | \(-0.334980\pi\) | ||||
0.495514 | + | 0.868600i | \(0.334980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.945600 | − | 2.91026i | −0.0460857 | − | 0.141837i | 0.925366 | − | 0.379075i | \(-0.123758\pi\) |
−0.971452 | + | 0.237238i | \(0.923758\pi\) | |||||||
\(422\) | 10.7477 | − | 2.28450i | 0.523191 | − | 0.111208i | ||||
\(423\) | −35.7556 | + | 15.9194i | −1.73850 | + | 0.774028i | ||||
\(424\) | −30.3886 | + | 13.5299i | −1.47580 | + | 0.657070i | ||||
\(425\) | 13.1353 | − | 2.79199i | 0.637155 | − | 0.135431i | ||||
\(426\) | −3.13932 | − | 9.66183i | −0.152100 | − | 0.468117i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.66211 | −0.128678 | ||||||||
\(429\) | −2.59036 | + | 19.3563i | −0.125064 | + | 0.934531i | ||||
\(430\) | 5.93241 | − | 10.2752i | 0.286086 | − | 0.495516i | ||||
\(431\) | −0.788350 | − | 7.50065i | −0.0379735 | − | 0.361294i | −0.996965 | − | 0.0778572i | \(-0.975192\pi\) |
0.958991 | − | 0.283436i | \(-0.0914745\pi\) | |||||||
\(432\) | −7.93705 | + | 8.81499i | −0.381871 | + | 0.424111i | ||||
\(433\) | 9.93848 | − | 30.5875i | 0.477613 | − | 1.46994i | −0.364788 | − | 0.931091i | \(-0.618859\pi\) |
0.842401 | − | 0.538851i | \(-0.181141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 63.7362 | + | 46.3071i | 3.05592 | + | 2.22025i | ||||
\(436\) | 2.87408 | − | 0.610904i | 0.137643 | − | 0.0292570i | ||||
\(437\) | −1.28132 | − | 0.272354i | −0.0612940 | − | 0.0130284i | ||||
\(438\) | 0.408391 | + | 3.88558i | 0.0195137 | + | 0.185660i | ||||
\(439\) | −2.33363 | − | 4.04196i | −0.111378 | − | 0.192912i | 0.804948 | − | 0.593345i | \(-0.202193\pi\) |
−0.916326 | + | 0.400433i | \(0.868860\pi\) | |||||||
\(440\) | 11.8315 | − | 33.1858i | 0.564045 | − | 1.58207i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.59099 | − | 2.60901i | 0.170806 | − | 0.124098i | ||||
\(443\) | 11.5607 | − | 12.8394i | 0.549264 | − | 0.610020i | −0.403036 | − | 0.915184i | \(-0.632045\pi\) |
0.952300 | + | 0.305165i | \(0.0987116\pi\) | |||||||
\(444\) | −14.5888 | − | 16.2025i | −0.692355 | − | 0.768938i | ||||
\(445\) | −14.0130 | + | 6.23898i | −0.664279 | + | 0.295756i | ||||
\(446\) | 2.02651 | − | 19.2809i | 0.0959579 | − | 0.912979i | ||||
\(447\) | −2.77969 | + | 8.55501i | −0.131475 | + | 0.404638i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.5430 | − | 9.83957i | 0.639134 | − | 0.464358i | −0.220418 | − | 0.975405i | \(-0.570742\pi\) |
0.859553 | + | 0.511047i | \(0.170742\pi\) | |||||||
\(450\) | −20.0173 | − | 34.6710i | −0.943625 | − | 1.63441i | ||||
\(451\) | −6.85322 | − | 1.66079i | −0.322706 | − | 0.0782038i | ||||
\(452\) | 4.03764 | − | 6.99340i | 0.189915 | − | 0.328942i | ||||
\(453\) | 7.48753 | + | 3.33366i | 0.351795 | + | 0.156629i | ||||
\(454\) | 4.35015 | + | 13.3884i | 0.204162 | + | 0.628347i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.5374 | − | 8.38241i | −0.540288 | − | 0.392542i | ||||
\(457\) | 2.26800 | − | 21.5785i | 0.106092 | − | 1.00940i | −0.803897 | − | 0.594769i | \(-0.797243\pi\) |
0.909989 | − | 0.414633i | \(-0.136090\pi\) | |||||||
\(458\) | −3.41050 | − | 3.78775i | −0.159362 | − | 0.176990i | ||||
\(459\) | 11.7494 | + | 2.49740i | 0.548413 | + | 0.116569i | ||||
\(460\) | −1.93156 | − | 0.859987i | −0.0900596 | − | 0.0400971i | ||||
\(461\) | 6.07778 | 0.283070 | 0.141535 | − | 0.989933i | \(-0.454796\pi\) | ||||
0.141535 | + | 0.989933i | \(0.454796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14719 | −0.239210 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(464\) | −13.9099 | − | 6.19307i | −0.645749 | − | 0.287506i | ||||
\(465\) | −7.61960 | − | 1.61959i | −0.353350 | − | 0.0751069i | ||||
\(466\) | 17.7906 | + | 19.7585i | 0.824136 | + | 0.915296i | ||||
\(467\) | −0.409676 | + | 3.89780i | −0.0189575 | + | 0.180369i | −0.999903 | − | 0.0139134i | \(-0.995571\pi\) |
0.980946 | + | 0.194282i | \(0.0622378\pi\) | |||||||
\(468\) | 6.53325 | + | 4.74669i | 0.302000 | + | 0.219416i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.00570 | + | 27.7167i | 0.415402 | + | 1.27848i | ||||
\(471\) | 56.1233 | + | 24.9877i | 2.58602 | + | 1.15137i | ||||
\(472\) | 5.06637 | − | 8.77521i | 0.233199 | − | 0.403912i | ||||
\(473\) | −5.35675 | + | 8.69968i | −0.246304 | + | 0.400012i | ||||
\(474\) | 15.1048 | + | 26.1623i | 0.693787 | + | 1.20167i | ||||
\(475\) | 9.11811 | − | 6.62469i | 0.418368 | − | 0.303962i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.2996 | − | 53.2428i | 0.792096 | − | 2.43782i | ||||
\(478\) | −1.02959 | + | 9.79586i | −0.0470922 | + | 0.448052i | ||||
\(479\) | 13.8063 | − | 6.14698i | 0.630828 | − | 0.280863i | −0.0663109 | − | 0.997799i | \(-0.521123\pi\) |
0.697139 | + | 0.716936i | \(0.254456\pi\) | |||||||
\(480\) | −26.5716 | − | 29.5108i | −1.21282 | − | 1.34698i | ||||
\(481\) | 13.8669 | − | 15.4007i | 0.632276 | − | 0.702214i | ||||
\(482\) | 17.0825 | − | 12.4112i | 0.778088 | − | 0.565314i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.02114 | + | 7.77100i | −0.137324 | + | 0.353227i | ||||
\(485\) | −11.1771 | − | 19.3593i | −0.507525 | − | 0.879059i | ||||
\(486\) | 1.42497 | + | 13.5577i | 0.0646380 | + | 0.614990i | ||||
\(487\) | −24.5288 | − | 5.21376i | −1.11151 | − | 0.236258i | −0.384660 | − | 0.923058i | \(-0.625681\pi\) |
−0.726846 | + | 0.686800i | \(0.759015\pi\) | |||||||
\(488\) | 3.23687 | − | 0.688018i | 0.146526 | − | 0.0311451i | ||||
\(489\) | 19.0172 | + | 13.8168i | 0.859985 | + | 0.624816i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5019 | − | 35.3991i | 0.519071 | − | 1.59754i | −0.256679 | − | 0.966497i | \(-0.582628\pi\) |
0.775750 | − | 0.631040i | \(-0.217372\pi\) | |||||||
\(492\) | −3.08274 | + | 3.42373i | −0.138981 | + | 0.154354i | ||||
\(493\) | 1.61172 | + | 15.3345i | 0.0725881 | + | 0.690630i | ||||
\(494\) | 1.86268 | − | 3.22626i | 0.0838060 | − | 0.145156i | ||||
\(495\) | 28.1812 | + | 52.1687i | 1.26665 | + | 2.34481i | ||||
\(496\) | 1.50554 | 0.0676006 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.8211 | + | 48.6922i | 0.708959 | + | 2.18195i | ||||
\(499\) | 31.1182 | − | 6.61437i | 1.39304 | − | 0.296100i | 0.550546 | − | 0.834805i | \(-0.314420\pi\) |
0.842494 | + | 0.538705i | \(0.181086\pi\) | |||||||
\(500\) | 4.65334 | − | 2.07180i | 0.208104 | − | 0.0926537i | ||||
\(501\) | 56.6954 | − | 25.2424i | 2.53296 | − | 1.12775i | ||||
\(502\) | −3.12526 | + | 0.664294i | −0.139487 | + | 0.0296489i | ||||
\(503\) | 5.93493 | + | 18.2658i | 0.264626 | + | 0.814434i | 0.991779 | + | 0.127959i | \(0.0408426\pi\) |
−0.727154 | + | 0.686474i | \(0.759157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.3788 | −2.37532 | ||||||||
\(506\) | −2.69001 | − | 1.29013i | −0.119586 | − | 0.0573532i | ||||
\(507\) | 12.5185 | − | 21.6827i | 0.555967 | − | 0.962963i | ||||
\(508\) | 1.54107 | + | 14.6623i | 0.0683740 | + | 0.650536i | ||||
\(509\) | −1.68319 | + | 1.86937i | −0.0746060 | + | 0.0828584i | −0.779292 | − | 0.626661i | \(-0.784421\pi\) |
0.704686 | + | 0.709519i | \(0.251088\pi\) | |||||||
\(510\) | 6.57984 | − | 20.2506i | 0.291360 | − | 0.896714i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.7059 | + | 11.4110i | 0.694109 | + | 0.504300i | ||||
\(513\) | 9.86113 | − | 2.09605i | 0.435379 | − | 0.0925428i | ||||
\(514\) | 24.4358 | + | 5.19400i | 1.07782 | + | 0.229097i | ||||
\(515\) | −3.21814 | − | 30.6185i | −0.141808 | − | 1.34921i | ||||
\(516\) | 3.33746 | + | 5.78065i | 0.146924 | + | 0.254479i | ||||
\(517\) | −7.07588 | − | 24.0764i | −0.311197 | − | 1.05888i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.6082 | + | 13.5196i | −0.816809 | + | 0.593447i | ||||
\(520\) | 14.6401 | − | 16.2595i | 0.642011 | − | 0.713025i | ||||
\(521\) | −9.96788 | − | 11.0705i | −0.436701 | − | 0.485005i | 0.484114 | − | 0.875005i | \(-0.339142\pi\) |
−0.920815 | + | 0.389999i | \(0.872475\pi\) | |||||||
\(522\) | 41.9938 | − | 18.6968i | 1.83802 | − | 0.818338i | ||||
\(523\) | −1.03536 | + | 9.85076i | −0.0452730 | + | 0.430744i | 0.948285 | + | 0.317420i | \(0.102816\pi\) |
−0.993558 | + | 0.113324i | \(0.963850\pi\) | |||||||
\(524\) | 1.19755 | − | 3.68567i | 0.0523151 | − | 0.161009i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.893242 | + | 0.648979i | −0.0389472 | + | 0.0282968i | ||||
\(527\) | −0.762295 | − | 1.32033i | −0.0332061 | − | 0.0575146i | ||||
\(528\) | −11.7293 | − | 13.7928i | −0.510453 | − | 0.600254i | ||||
\(529\) | 11.1743 | − | 19.3544i | 0.485838 | − | 0.841496i | ||||
\(530\) | −38.0808 | − | 16.9547i | −1.65412 | − | 0.736464i | ||||
\(531\) | 5.26966 | + | 16.2183i | 0.228684 | + | 0.703816i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.54276 | − | 2.57397i | −0.153454 | − | 0.111491i | ||||
\(534\) | −1.47810 | + | 14.0632i | −0.0639638 | + | 0.608575i | ||||
\(535\) | −8.12218 | − | 9.02059i | −0.351152 | − | 0.389994i | ||||
\(536\) | 7.22502 | + | 1.53573i | 0.312073 | + | 0.0663332i | ||||
\(537\) | −9.45659 | − | 4.21034i | −0.408082 | − | 0.181690i | ||||
\(538\) | 8.01342 | 0.345483 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.2722 | 0.700245 | ||||||||
\(541\) | −20.1057 | − | 8.95161i | −0.864409 | − | 0.384860i | −0.0738677 | − | 0.997268i | \(-0.523534\pi\) |
−0.790542 | + | 0.612408i | \(0.790201\pi\) | |||||||
\(542\) | −29.6121 | − | 6.29425i | −1.27195 | − | 0.270361i | ||||
\(543\) | −30.2584 | − | 33.6054i | −1.29851 | − | 1.44215i | ||||
\(544\) | 0.812395 | − | 7.72942i | 0.0348311 | − | 0.331396i | ||||
\(545\) | 10.8389 | + | 7.87494i | 0.464289 | + | 0.337325i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.35724 | − | 10.3325i | −0.143545 | − | 0.441787i | 0.853276 | − | 0.521460i | \(-0.174612\pi\) |
−0.996821 | + | 0.0796728i | \(0.974612\pi\) | |||||||
\(548\) | −6.30152 | − | 2.80562i | −0.269187 | − | 0.119850i | ||||
\(549\) | −2.78461 | + | 4.82309i | −0.118844 | + | 0.205844i | ||||
\(550\) | 23.7356 | − | 9.77231i | 1.01209 | − | 0.416693i | ||||
\(551\) | 6.47048 | + | 11.2072i | 0.275652 | + | 0.477443i | ||||
\(552\) | −5.73781 | + | 4.16876i | −0.244218 | + | 0.177434i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.22721 | − | 22.2431i | 0.307055 | − | 0.945018i | ||||
\(555\) | 10.3915 | − | 98.8687i | 0.441095 | − | 4.19674i | ||||
\(556\) | −9.01313 | + | 4.01290i | −0.382242 | + | 0.170185i | ||||
\(557\) | 22.4912 | + | 24.9790i | 0.952983 | + | 1.05840i | 0.998233 | + | 0.0594193i | \(0.0189249\pi\) |
−0.0452499 | + | 0.998976i | \(0.514408\pi\) | |||||||
\(558\) | −3.04134 | + | 3.37775i | −0.128750 | + | 0.142991i | ||||
\(559\) | −5.13290 | + | 3.72927i | −0.217098 | + | 0.157731i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.15720 | + | 17.2701i | −0.259957 | + | 0.729145i | ||||
\(562\) | 15.6906 | + | 27.1769i | 0.661867 | + | 1.14639i | ||||
\(563\) | −0.214647 | − | 2.04223i | −0.00904631 | − | 0.0860699i | 0.989067 | − | 0.147465i | \(-0.0471115\pi\) |
−0.998114 | + | 0.0613956i | \(0.980445\pi\) | |||||||
\(564\) | −16.0370 | − | 3.40878i | −0.675281 | − | 0.143535i | ||||
\(565\) | 36.0161 | − | 7.65547i | 1.51521 | − | 0.322068i | ||||
\(566\) | −23.6151 | − | 17.1573i | −0.992615 | − | 0.721177i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.02857 | − | 9.32098i | 0.127076 | − | 0.391099i | ||||
\(569\) | 2.19084 | − | 2.43317i | 0.0918448 | − | 0.102004i | −0.695470 | − | 0.718555i | \(-0.744804\pi\) |
0.787315 | + | 0.616551i | \(0.211471\pi\) | |||||||
\(570\) | −1.86801 | − | 17.7729i | −0.0782424 | − | 0.744426i | ||||
\(571\) | 21.9448 | − | 38.0096i | 0.918363 | − | 1.59065i | 0.116462 | − | 0.993195i | \(-0.462845\pi\) |
0.801901 | − | 0.597457i | \(-0.203822\pi\) | |||||||
\(572\) | −3.57212 | + | 3.74817i | −0.149358 | + | 0.156719i | ||||
\(573\) | 1.22666 | 0.0512446 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.73208 | − | 5.33080i | −0.0722328 | − | 0.222310i | ||||
\(576\) | −41.9881 | + | 8.92484i | −1.74950 | + | 0.371868i | ||||
\(577\) | 40.0959 | − | 17.8518i | 1.66921 | − | 0.743181i | 0.669213 | − | 0.743071i | \(-0.266631\pi\) |
1.00000 | 0.000110759i | \(-3.52556e-5\pi\) | ||||||||
\(578\) | −13.5009 | + | 6.01100i | −0.561564 | + | 0.250025i | ||||
\(579\) | 42.4341 | − | 9.01964i | 1.76350 | − | 0.374843i | ||||
\(580\) | 6.45466 | + | 19.8654i | 0.268015 | + | 0.824866i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −20.6076 | −0.854214 | ||||||||
\(583\) | 32.3643 | + | 15.5219i | 1.34039 | + | 0.642851i | ||||
\(584\) | −1.88458 | + | 3.26418i | −0.0779843 | + | 0.135073i | ||||
\(585\) | 3.84894 | + | 36.6202i | 0.159134 | + | 1.51406i | ||||
\(586\) | 3.32880 | − | 3.69701i | 0.137511 | − | 0.152722i | ||||
\(587\) | −0.862670 | + | 2.65503i | −0.0356062 | + | 0.109585i | −0.967280 | − | 0.253711i | \(-0.918349\pi\) |
0.931674 | + | 0.363296i | \(0.118349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03520 | − | 0.752114i | −0.0426545 | − | 0.0309903i | ||||
\(590\) | 12.4201 | − | 2.63998i | 0.511329 | − | 0.108686i | ||||
\(591\) | 58.1869 | + | 12.3680i | 2.39349 | + | 0.508752i | ||||
\(592\) | 2.00836 | + | 19.1083i | 0.0825433 | + | 0.785347i | ||||
\(593\) | 11.6263 | + | 20.1374i | 0.477435 | + | 0.826942i | 0.999666 | − | 0.0258622i | \(-0.00823311\pi\) |
−0.522230 | + | 0.852805i | \(0.674900\pi\) | |||||||
\(594\) | 22.9511 | + | 0.650030i | 0.941696 | + | 0.0266710i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.92945 | + | 1.40183i | −0.0790334 | + | 0.0574211i | ||||
\(597\) | −16.1559 | + | 17.9430i | −0.661218 | + | 0.734357i | ||||
\(598\) | −1.23971 | − | 1.37683i | −0.0506953 | − | 0.0563029i | ||||
\(599\) | 9.55519 | − | 4.25424i | 0.390414 | − | 0.173824i | −0.202135 | − | 0.979358i | \(-0.564788\pi\) |
0.592550 | + | 0.805534i | \(0.298121\pi\) | |||||||
\(600\) | 6.37846 | − | 60.6870i | 0.260400 | − | 2.47754i | ||||
\(601\) | −6.89406 | + | 21.2177i | −0.281215 | + | 0.865489i | 0.706293 | + | 0.707919i | \(0.250366\pi\) |
−0.987508 | + | 0.157570i | \(0.949634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0569 | + | 7.30679i | −0.409550 | + | 0.297556i | ||||
\(604\) | 1.08653 | + | 1.88192i | 0.0442102 | + | 0.0765743i | ||||
\(605\) | −35.5496 | + | 13.4724i | −1.44530 | + | 0.547729i | ||||
\(606\) | −24.6042 | + | 42.6157i | −0.999476 | + | 1.73114i | ||||
\(607\) | −17.3468 | − | 7.72328i | −0.704084 | − | 0.313478i | 0.0232812 | − | 0.999729i | \(-0.492589\pi\) |
−0.727365 | + | 0.686251i | \(0.759255\pi\) | |||||||
\(608\) | −2.01571 | − | 6.20370i | −0.0817477 | − | 0.251593i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.35485 | + | 2.43744i | 0.135834 | + | 0.0986892i | ||||
\(611\) | 1.62897 | − | 15.4986i | 0.0659011 | − | 0.627007i | ||||
\(612\) | 5.07323 | + | 5.63439i | 0.205073 | + | 0.227757i | ||||
\(613\) | −19.7211 | − | 4.19185i | −0.796528 | − | 0.169307i | −0.208366 | − | 0.978051i | \(-0.566815\pi\) |
−0.588161 | + | 0.808744i | \(0.700148\pi\) | |||||||
\(614\) | −13.1175 | − | 5.84029i | −0.529379 | − | 0.235695i | ||||
\(615\) | −21.0068 | −0.847077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03919 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(618\) | −25.9281 | − | 11.5439i | −1.04298 | − | 0.464364i | ||||
\(619\) | −30.4038 | − | 6.46254i | −1.22203 | − | 0.259751i | −0.448660 | − | 0.893702i | \(-0.648099\pi\) |
−0.773373 | + | 0.633951i | \(0.781432\pi\) | |||||||
\(620\) | −1.38198 | − | 1.53484i | −0.0555015 | − | 0.0616407i | ||||
\(621\) | 0.524078 | − | 4.98626i | 0.0210305 | − | 0.200092i | ||||
\(622\) | 24.1814 | + | 17.5688i | 0.969585 | + | 0.704445i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.47453 | − | 10.6935i | −0.139093 | − | 0.428083i | ||||
\(625\) | −10.5027 | − | 4.67611i | −0.420108 | − | 0.187044i | ||||
\(626\) | 1.99974 | − | 3.46364i | 0.0799255 | − | 0.138435i | ||||
\(627\) | 1.17460 | + | 15.3434i | 0.0469090 | + | 0.612757i | ||||
\(628\) | 8.14414 | + | 14.1061i | 0.324986 | + | 0.562893i | ||||
\(629\) | 15.7408 | − | 11.4364i | 0.627628 | − | 0.455998i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.78971 | − | 20.8966i | 0.270294 | − | 0.831880i | −0.720132 | − | 0.693837i | \(-0.755919\pi\) |
0.990426 | − | 0.138043i | \(-0.0440812\pi\) | |||||||
\(632\) | −3.04637 | + | 28.9842i | −0.121178 | + | 1.15293i | ||||
\(633\) | −25.7491 | + | 11.4642i | −1.02343 | + | 0.455662i | ||||
\(634\) | −12.6162 | − | 14.0117i | −0.501053 | − | 0.556476i | ||||
\(635\) | −44.9815 | + | 49.9570i | −1.78504 | + | 1.98248i | ||||
\(636\) | 18.9722 | − | 13.7841i | 0.752298 | − | 0.546576i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.31039 | + | 28.2770i | 0.329012 | + | 1.11950i | ||||
\(639\) | 8.24705 | + | 14.2843i | 0.326248 | + | 0.565078i | ||||
\(640\) | 0.437085 | + | 4.15858i | 0.0172773 | + | 0.164382i | ||||
\(641\) | 13.0005 | + | 2.76334i | 0.513489 | + | 0.109145i | 0.457366 | − | 0.889278i | \(-0.348793\pi\) |
0.0561227 | + | 0.998424i | \(0.482126\pi\) | |||||||
\(642\) | −10.9455 | + | 2.32654i | −0.431985 | + | 0.0918212i | ||||
\(643\) | 11.8848 | + | 8.63480i | 0.468690 | + | 0.340523i | 0.796930 | − | 0.604071i | \(-0.206456\pi\) |
−0.328241 | + | 0.944594i | \(0.606456\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.40510 | + | 28.9459i | −0.370325 | + | 1.13974i | ||||
\(646\) | 2.34035 | − | 2.59922i | 0.0920799 | − | 0.102265i | ||||
\(647\) | −0.642352 | − | 6.11157i | −0.0252534 | − | 0.240271i | −0.999866 | − | 0.0163722i | \(-0.994788\pi\) |
0.974613 | − | 0.223898i | \(-0.0718783\pi\) | |||||||
\(648\) | 3.44213 | − | 5.96195i | 0.135220 | − | 0.234207i | ||||
\(649\) | −10.7549 | + | 1.96955i | −0.422165 | + | 0.0773118i | ||||
\(650\) | 15.9404 | 0.625236 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.92589 | + | 5.92729i | 0.0754238 | + | 0.232131i | ||||
\(653\) | 39.7804 | − | 8.45558i | 1.55673 | − | 0.330893i | 0.652448 | − | 0.757834i | \(-0.273742\pi\) |
0.904279 | + | 0.426941i | \(0.140409\pi\) | |||||||
\(654\) | 11.2831 | − | 5.02357i | 0.441205 | − | 0.196437i | ||||
\(655\) | 16.1427 | − | 7.18718i | 0.630746 | − | 0.280826i | ||||
\(656\) | 3.97126 | − | 0.844118i | 0.155052 | − | 0.0329573i | ||||
\(657\) | −1.96020 | − | 6.03286i | −0.0764745 | − | 0.235364i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0090 | 0.701531 | 0.350765 | − | 0.936463i | \(-0.385921\pi\) | ||||
0.350765 | + | 0.936463i | \(0.385921\pi\) | |||||||
\(660\) | −3.29456 | + | 24.6184i | −0.128241 | + | 0.958272i | ||||
\(661\) | −8.57098 | + | 14.8454i | −0.333373 | + | 0.577418i | −0.983171 | − | 0.182689i | \(-0.941520\pi\) |
0.649798 | + | 0.760107i | \(0.274853\pi\) | |||||||
\(662\) | 0.144249 | + | 1.37244i | 0.00560641 | + | 0.0533415i | ||||
\(663\) | −7.61881 | + | 8.46154i | −0.295890 | + | 0.328619i | ||||
\(664\) | −15.2629 | + | 46.9744i | −0.592316 | + | 1.82296i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −46.9276 | − | 34.0949i | −1.81841 | − | 1.32115i | ||||
\(667\) | 6.29520 | − | 1.33809i | 0.243751 | − | 0.0518109i | ||||
\(668\) | 16.0948 | + | 3.42105i | 0.622725 | + | 0.132364i | ||||
\(669\) | 5.19838 | + | 49.4592i | 0.200981 | + | 1.91220i | ||||
\(670\) | 4.62807 | + | 8.01605i | 0.178798 | + | 0.309687i | ||||
\(671\) | −2.82823 | − | 2.17979i | −0.109183 | − | 0.0841498i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7632 | − | 13.6322i | 0.723268 | − | 0.525485i | −0.164159 | − | 0.986434i | \(-0.552491\pi\) |
0.887426 | + | 0.460949i | \(0.152491\pi\) | |||||||
\(674\) | −15.2729 | + | 16.9622i | −0.588288 | + | 0.653361i | ||||
\(675\) | 28.8645 | + | 32.0573i | 1.11100 | + | 1.23389i | ||||
\(676\) | 6.06423 | − | 2.69997i | 0.233239 | − | 0.103845i | ||||
\(677\) | −2.88191 | + | 27.4195i | −0.110761 | + | 1.05382i | 0.788089 | + | 0.615561i | \(0.211070\pi\) |
−0.898850 | + | 0.438256i | \(0.855596\pi\) | |||||||
\(678\) | 10.4893 | − | 32.2826i | 0.402838 | − | 1.23981i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.6185 | − | 12.0741i | 0.637291 | − | 0.463019i | ||||
\(681\) | −18.0556 | − | 31.2731i | −0.691890 | − | 1.19839i | ||||
\(682\) | −1.88789 | − | 2.22002i | −0.0722912 | − | 0.0850089i | ||||
\(683\) | −10.9675 | + | 18.9963i | −0.419661 | + | 0.726874i | −0.995905 | − | 0.0904032i | \(-0.971184\pi\) |
0.576244 | + | 0.817278i | \(0.304518\pi\) | |||||||
\(684\) | 5.81321 | + | 2.58821i | 0.222274 | + | 0.0989626i | ||||
\(685\) | −9.71923 | − | 29.9127i | −0.371353 | − | 1.14291i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.5775 | + | 7.68503i | 0.403558 | + | 0.293202i | ||||
\(688\) | 0.614864 | − | 5.85004i | 0.0234415 | − | 0.223031i | ||||
\(689\) | 14.9152 | + | 16.5651i | 0.568226 | + | 0.631078i | ||||
\(690\) | −8.69337 | − | 1.84783i | −0.330951 | − | 0.0703458i | ||||
\(691\) | 23.4476 | + | 10.4396i | 0.891990 | + | 0.397139i | 0.800966 | − | 0.598709i | \(-0.204320\pi\) |
0.0910234 | + | 0.995849i | \(0.470986\pi\) | |||||||
\(692\) | −6.09830 | −0.231823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3913 | 1.15364 | ||||||||
\(695\) | −41.0970 | − | 18.2976i | −1.55890 | − | 0.694067i | ||||
\(696\) | 68.5339 | + | 14.5673i | 2.59777 | + | 0.552173i | ||||
\(697\) | −2.75104 | − | 3.05534i | −0.104203 | − | 0.115729i | ||||
\(698\) | 0.930124 | − | 8.84954i | 0.0352057 | − | 0.334960i | ||||
\(699\) | −55.1770 | − | 40.0884i | −2.08699 | − | 1.51628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.69007 | − | 17.5122i | −0.214911 | − | 0.661428i | −0.999160 | − | 0.0409817i | \(-0.986951\pi\) |
0.784249 | − | 0.620446i | \(-0.213049\pi\) | |||||||
\(702\) | 13.0258 | + | 5.79948i | 0.491629 | + | 0.218887i | ||||
\(703\) | 8.16492 | − | 14.1421i | 0.307946 | − | 0.533378i | ||||
\(704\) | −2.10081 | − | 27.4423i | −0.0791774 | − | 1.03427i | ||||
\(705\) | −37.3787 | − | 64.7419i | −1.40776 | − | 2.43832i | ||||
\(706\) | 5.35087 | − | 3.88764i | 0.201383 | − | 0.146313i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.20744 | + | 6.79380i | −0.0829607 | + | 0.255327i | ||||
\(709\) | −2.47336 | + | 23.5324i | −0.0928889 | + | 0.883779i | 0.844514 | + | 0.535533i | \(0.179889\pi\) |
−0.937403 | + | 0.348246i | \(0.886777\pi\) | |||||||
\(710\) | 11.2197 | − | 4.99532i | 0.421067 | − | 0.187471i | ||||
\(711\) | −32.8195 | − | 36.4497i | −1.23083 | − | 1.36697i | ||||
\(712\) | −9.12816 | + | 10.1379i | −0.342092 | + | 0.379932i | ||||
\(713\) | −0.514827 | + | 0.374044i | −0.0192804 | + | 0.0140081i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5993 | − | 0.668389i | −0.882565 | − | 0.0249963i | ||||
\(716\) | −1.37226 | − | 2.37682i | −0.0512838 | − | 0.0888261i | ||||
\(717\) | −2.64108 | − | 25.1282i | −0.0986331 | − | 0.938431i | ||||
\(718\) | −30.9813 | − | 6.58528i | −1.15621 | − | 0.245760i | ||||
\(719\) | 10.8792 | − | 2.31244i | 0.405726 | − | 0.0862396i | −0.000528360 | − | 1.00000i | \(-0.500168\pi\) |
0.406254 | + | 0.913760i | \(0.366835\pi\) | |||||||
\(720\) | −27.6187 | − | 20.0662i | −1.02929 | − | 0.747823i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.63627 | + | 17.3467i | −0.209760 | + | 0.645576i | ||||
\(723\) | −36.2431 | + | 40.2520i | −1.34790 | + | 1.49699i | ||||
\(724\) | −1.25323 | − | 11.9237i | −0.0465761 | − | 0.443142i | ||||
\(725\) | −27.6865 | + | 47.9544i | −1.02825 | + | 1.78098i | ||||
\(726\) | −5.63025 | + | 34.5914i | −0.208958 | + | 1.28381i | ||||
\(727\) | −42.4803 | −1.57551 | −0.787753 | − | 0.615991i | \(-0.788756\pi\) | ||||
−0.787753 | + | 0.615991i | \(0.788756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.8826 | − | 39.6485i | −0.477133 | − | 1.46846i | ||||
\(730\) | −4.62001 | + | 0.982014i | −0.170994 | + | 0.0363460i | ||||
\(731\) | −5.44173 | + | 2.42281i | −0.201269 | + | 0.0896109i | ||||
\(732\) | −2.13123 | + | 0.948886i | −0.0787726 | + | 0.0350718i | ||||
\(733\) | 21.7036 | − | 4.61323i | 0.801639 | − | 0.170394i | 0.211165 | − | 0.977450i | \(-0.432274\pi\) |
0.590474 | + | 0.807057i | \(0.298941\pi\) | |||||||
\(734\) | 10.4699 | + | 32.2231i | 0.386452 | + | 1.18938i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.24402 | −0.119576 | ||||||||
\(737\) | −3.78814 | − | 7.01255i | −0.139538 | − | 0.258311i | ||||
\(738\) | −6.12854 | + | 10.6149i | −0.225595 | + | 0.390741i | ||||
\(739\) | −3.07817 | − | 29.2868i | −0.113232 | − | 1.07733i | −0.892626 | − | 0.450798i | \(-0.851140\pi\) |
0.779394 | − | 0.626534i | \(-0.215527\pi\) | |||||||
\(740\) | 17.6367 | − | 19.5875i | 0.648338 | − | 0.720053i | ||||
\(741\) | −2.95305 | + | 9.08855i | −0.108483 | + | 0.333876i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6772 | − | 9.93704i | −0.501766 | − | 0.364555i | 0.307925 | − | 0.951411i | \(-0.400365\pi\) |
−0.809691 | + | 0.586856i | \(0.800365\pi\) | |||||||
\(744\) | −6.77648 | + | 1.44038i | −0.248438 | + | 0.0528071i | ||||
\(745\) | −10.6369 | − | 2.26094i | −0.389706 | − | 0.0828346i | ||||
\(746\) | −1.68013 | − | 15.9854i | −0.0615141 | − | 0.585267i | ||||
\(747\) | −41.5622 | − | 71.9879i | −1.52068 | − | 2.63390i | ||||
\(748\) | −4.01208 | + | 2.74484i | −0.146696 | + | 0.100361i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.3220 | − | 12.5851i | 0.632508 | − | 0.459544i | ||||
\(751\) | −1.03813 | + | 1.15296i | −0.0378820 | + | 0.0420722i | −0.761788 | − | 0.647826i | \(-0.775678\pi\) |
0.723906 | + | 0.689899i | \(0.242345\pi\) | |||||||
\(752\) | 9.66783 | + | 10.7372i | 0.352550 | + | 0.391546i | ||||
\(753\) | 7.48740 | − | 3.33361i | 0.272856 | − | 0.121483i | ||||
\(754\) | −1.91317 | + | 18.2026i | −0.0696737 | + | 0.662901i | ||||
\(755\) | −3.06188 | + | 9.42349i | −0.111433 | + | 0.342956i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1505 | + | 7.37474i | −0.368925 | + | 0.268040i | −0.756765 | − | 0.653687i | \(-0.773221\pi\) |
0.387840 | + | 0.921727i | \(0.373221\pi\) | |||||||
\(758\) | 12.4860 | + | 21.6265i | 0.453513 | + | 0.785508i | ||||
\(759\) | 7.43768 | + | 1.80243i | 0.269971 | + | 0.0654241i | ||||
\(760\) | 8.62019 | − | 14.9306i | 0.312687 | − | 0.541590i | ||||
\(761\) | 8.25330 | + | 3.67460i | 0.299182 | + | 0.133204i | 0.550837 | − | 0.834613i | \(-0.314308\pi\) |
−0.251656 | + | 0.967817i | \(0.580975\pi\) | |||||||
\(762\) | 19.1503 | + | 58.9386i | 0.693742 | + | 2.13512i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.263115 | + | 0.191164i | 0.00951916 | + | 0.00691608i | ||||
\(765\) | −3.61362 | + | 34.3813i | −0.130651 | + | 1.24306i | ||||
\(766\) | −25.1149 | − | 27.8929i | −0.907438 | − | 1.00781i | ||||
\(767\) | −6.64155 | − | 1.41171i | −0.239813 | − | 0.0509737i | ||||
\(768\) | −39.8235 | − | 17.7305i | −1.43701 | − | 0.639796i | ||||
\(769\) | 16.1383 | 0.581963 | 0.290981 | − | 0.956729i | \(-0.406018\pi\) | ||||
0.290981 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.0829 | −2.30789 | ||||||||
\(772\) | 10.5076 | + | 4.67827i | 0.378176 | + | 0.168375i | ||||
\(773\) | −18.0111 | − | 3.82837i | −0.647813 | − | 0.137697i | −0.127725 | − | 0.991810i | \(-0.540767\pi\) |
−0.520088 | + | 0.854113i | \(0.674101\pi\) | |||||||
\(774\) | 11.8828 | + | 13.1972i | 0.427118 | + | 0.474362i | ||||
\(775\) | 0.572310 | − | 5.44517i | 0.0205580 | − | 0.195596i | ||||
\(776\) | −16.0838 | − | 11.6855i | −0.577374 | − | 0.419487i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.836118 | + | 2.57331i | 0.0299763 | + | 0.0922575i | ||||
\(779\) | −3.15231 | − | 1.40350i | −0.112943 | − | 0.0502855i | ||||
\(780\) | −7.71228 | + | 13.3581i | −0.276144 | + | 0.478295i | ||||
\(781\) | −9.77899 | + | 4.02615i | −0.349920 | + | 0.144067i | ||||
\(782\) | −0.869719 | − | 1.50640i | −0.0311011 | − | 0.0538687i | ||||
\(783\) | −40.0711 | + | 29.1133i | −1.43202 | + | 1.04043i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9505 | + | 70.6344i | −0.819139 | + | 2.52105i | ||||
\(786\) | 1.70275 | − | 16.2005i | 0.0607349 | − | 0.577854i | ||||
\(787\) | −42.9248 | + | 19.1113i | −1.53010 | + | 0.681246i | −0.987337 | − | 0.158638i | \(-0.949290\pi\) |
−0.542767 | + | 0.839884i | \(0.682623\pi\) | |||||||
\(788\) | 10.5534 | + | 11.7208i | 0.375951 | + | 0.417536i | ||||
\(789\) | 1.89514 | − | 2.10477i | 0.0674689 | − | 0.0749318i | ||||
\(790\) | −29.5461 | + | 21.4665i | −1.05120 | + | 0.763744i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 41.7671 | + | 32.1910i | 1.48413 | + | 1.14386i | ||||
\(793\) | −1.10874 | − | 1.92039i | −0.0393725 | − | 0.0681952i | ||||
\(794\) | −0.686958 | − | 6.53597i | −0.0243792 | − | 0.231953i | ||||
\(795\) | 104.592 | + | 22.2318i | 3.70951 | + | 0.788480i | ||||
\(796\) | −6.26163 | + | 1.33095i | −0.221938 | + | 0.0471743i | ||||
\(797\) | −2.52781 | − | 1.83656i | −0.0895395 | − | 0.0650543i | 0.542115 | − | 0.840304i | \(-0.317624\pi\) |
−0.631654 | + | 0.775250i | \(0.717624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.52129 | − | 13.9151i | 0.159952 | − | 0.492281i | ||||
\(800\) | 18.6761 | − | 20.7420i | 0.660301 | − | 0.733339i | ||||
\(801\) | −2.39983 | − | 22.8329i | −0.0847938 | − | 0.806760i | ||||
\(802\) | −6.26307 | + | 10.8480i | −0.221157 | + | 0.383055i | ||||
\(803\) | 4.00057 | − | 0.732630i | 0.141177 | − | 0.0258540i | ||||
\(804\) | −5.20732 | −0.183648 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.559243 | − | 1.72117i | −0.0196985 | − | 0.0606258i | ||||
\(807\) | −20.1067 | + | 4.27382i | −0.707791 | + | 0.150446i | ||||
\(808\) | −43.3682 | + | 19.3087i | −1.52569 | + | 0.679279i | ||||
\(809\) | −29.8964 | + | 13.3107i | −1.05110 | + | 0.467980i | −0.858241 | − | 0.513246i | \(-0.828443\pi\) |
−0.192859 | + | 0.981226i | \(0.561776\pi\) | |||||||
\(810\) | 8.43833 | − | 1.79362i | 0.296493 | − | 0.0630215i | ||||
\(811\) | −10.0929 | − | 31.0627i | −0.354410 | − | 1.09076i | −0.956351 | − | 0.292220i | \(-0.905606\pi\) |
0.601941 | − | 0.798540i | \(-0.294394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.6578 | 2.72358 | ||||||||
\(814\) | 25.6581 | − | 26.9227i | 0.899317 | − | 0.943639i | ||||
\(815\) | −14.2087 | + | 24.6102i | −0.497710 | + | 0.862058i | ||||
\(816\) | −1.10344 | − | 10.4986i | −0.0386283 | − | 0.367523i | ||||
\(817\) | −3.34526 | + | 3.71529i | −0.117036 | + | 0.129981i | ||||
\(818\) | −10.1024 | + | 31.0921i | −0.353224 | + | 1.08711i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.50589 | − | 3.27372i | −0.157352 | − | 0.114323i | ||||
\(821\) | 7.26903 | − | 1.54508i | 0.253691 | − | 0.0539236i | −0.0793107 | − | 0.996850i | \(-0.525272\pi\) |
0.333001 | + | 0.942926i | \(0.391939\pi\) | |||||||
\(822\) | −28.3612 | − | 6.02835i | −0.989209 | − | 0.210263i | ||||
\(823\) | −0.685567 | − | 6.52273i | −0.0238974 | − | 0.227368i | −0.999952 | − | 0.00984082i | \(-0.996868\pi\) |
0.976054 | − | 0.217527i | \(-0.0697991\pi\) | |||||||
\(824\) | −13.6903 | − | 23.7122i | −0.476923 | − | 0.826055i | ||||
\(825\) | −54.3440 | + | 37.1790i | −1.89202 | + | 1.29441i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.2982 | + | 14.0209i | −0.671063 | + | 0.487556i | −0.870381 | − | 0.492379i | \(-0.836127\pi\) |
0.199318 | + | 0.979935i | \(0.436127\pi\) | |||||||
\(828\) | 2.11756 | − | 2.35179i | 0.0735902 | − | 0.0817302i | ||||
\(829\) | 17.4932 | + | 19.4281i | 0.607563 | + | 0.674767i | 0.965927 | − | 0.258815i | \(-0.0833320\pi\) |
−0.358364 | + | 0.933582i | \(0.616665\pi\) | |||||||
\(830\) | −56.5432 | + | 25.1747i | −1.96264 | + | 0.873825i | ||||
\(831\) | −6.27108 | + | 59.6654i | −0.217541 | + | 2.06977i | ||||
\(832\) | 5.28164 | − | 16.2552i | 0.183108 | − | 0.563548i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −33.5512 | + | 24.3764i | −1.16178 | + | 0.844085i | ||||
\(835\) | 37.5133 | + | 64.9749i | 1.29820 | + | 2.24855i | ||||
\(836\) | −2.13918 | + | 3.47415i | −0.0739851 | + | 0.120156i | ||||
\(837\) | 2.44874 | − | 4.24133i | 0.0846407 | − | 0.146602i | ||||
\(838\) | 20.6533 | + | 9.19545i | 0.713457 | + | 0.317651i | ||||
\(839\) | −10.5959 | − | 32.6107i | −0.365810 | − | 1.12585i | −0.949472 | − | 0.313851i | \(-0.898381\pi\) |
0.583662 | − | 0.811997i | \(-0.301619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9754 | − | 20.3253i | −0.964670 | − | 0.700874i | ||||
\(842\) | 0.356473 | − | 3.39162i | 0.0122849 | − | 0.116883i | ||||
\(843\) | −53.8641 | − | 59.8221i | −1.85518 | − | 2.06038i | ||||
\(844\) | −7.30967 | − | 1.55372i | −0.251609 | − | 0.0534812i | ||||
\(845\) | 27.6510 | + | 12.3110i | 0.951222 | + | 0.423511i | ||||
\(846\) | −43.6195 | −1.49967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6661 | −0.709678 | ||||||||
\(849\) | 68.4039 | + | 30.4554i | 2.34762 | + | 1.04523i | ||||
\(850\) | 14.6388 | + | 3.11158i | 0.502108 | + | 0.106726i | ||||
\(851\) | −5.43415 | − | 6.03524i | −0.186280 | − | 0.206885i | ||||
\(852\) | −0.722219 | + | 6.87146i | −0.0247428 | + | 0.235412i | ||||
\(853\) | 17.3002 | + | 12.5693i | 0.592347 | + | 0.430365i | 0.843154 | − | 0.537672i | \(-0.180696\pi\) |
−0.250807 | + | 0.968037i | \(0.580696\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.96608 | + | 27.5948i | 0.306634 | + | 0.943721i | ||||
\(856\) | −9.86197 | − | 4.39083i | −0.337075 | − | 0.150076i | ||||
\(857\) | 21.4348 | − | 37.1262i | 0.732200 | − | 1.26821i | −0.223741 | − | 0.974649i | \(-0.571827\pi\) |
0.955941 | − | 0.293559i | \(-0.0948396\pi\) | |||||||
\(858\) | −11.4114 | + | 18.5328i | −0.389578 | + | 0.632698i | ||||
\(859\) | −15.1958 | − | 26.3198i | −0.518473 | − | 0.898022i | −0.999770 | − | 0.0214638i | \(-0.993167\pi\) |
0.481297 | − | 0.876558i | \(-0.340166\pi\) | |||||||
\(860\) | −6.52831 | + | 4.74310i | −0.222614 | + | 0.161738i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59737 | − | 7.99389i | 0.0884668 | − | 0.272273i | ||||
\(863\) | −1.23536 | + | 11.7537i | −0.0420522 | + | 0.400100i | 0.953168 | + | 0.302442i | \(0.0978018\pi\) |
−0.995220 | + | 0.0976580i | \(0.968865\pi\) | |||||||
\(864\) | 22.8077 | − | 10.1546i | 0.775934 | − | 0.345468i | ||||
\(865\) | −18.6061 | − | 20.6641i | −0.632625 | − | 0.702602i | ||||
\(866\) | 23.9837 | − | 26.6366i | 0.814998 | − | 0.905147i | ||||
\(867\) | 30.6698 | − | 22.2829i | 1.04160 | − | 0.756766i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9548 | − | 17.7568i | 0.880456 | − | 0.602357i | ||||
\(870\) | 43.9001 | + | 76.0373i | 1.48835 | + | 2.57790i | ||||
\(871\) | −0.517377 | − | 4.92252i | −0.0175307 | − | 0.166793i | ||||
\(872\) | 11.6548 | + | 2.47731i | 0.394682 | + | 0.0838922i | ||||
\(873\) | 32.7271 | − | 6.95637i | 1.10765 | − | 0.235437i | ||||
\(874\) | −1.18108 | − | 0.858104i | −0.0399506 | − | 0.0290258i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.821118 | − | 2.52714i | 0.0277430 | − | 0.0853842i | ||||
\(877\) | −6.15927 | + | 6.84056i | −0.207984 | + | 0.230989i | −0.838107 | − | 0.545506i | \(-0.816338\pi\) |
0.630123 | + | 0.776495i | \(0.283004\pi\) | |||||||
\(878\) | −0.543704 | − | 5.17300i | −0.0183491 | − | 0.174580i | ||||
\(879\) | −6.38067 | + | 11.0516i | −0.215215 | + | 0.372763i | ||||
\(880\) | 15.1008 | − | 15.8451i | 0.509049 | − | 0.534137i | ||||
\(881\) | 41.9030 | 1.41175 | 0.705874 | − | 0.708338i | \(-0.250555\pi\) | ||||
0.705874 | + | 0.708338i | \(0.250555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.95906 | − | 15.2624i | −0.166886 | − | 0.513621i | 0.832285 | − | 0.554348i | \(-0.187032\pi\) |
−0.999170 | + | 0.0407275i | \(0.987032\pi\) | |||||||
\(884\) | −2.95286 | + | 0.627649i | −0.0993154 | + | 0.0211101i | ||||
\(885\) | −29.7558 | + | 13.2481i | −1.00023 | + | 0.445331i | ||||
\(886\) | 17.5901 | − | 7.83164i | 0.590952 | − | 0.263109i | ||||
\(887\) | −33.1087 | + | 7.03747i | −1.11168 | + | 0.236295i | −0.726921 | − | 0.686722i | \(-0.759049\pi\) |
−0.384760 | + | 0.923017i | \(0.625716\pi\) | |||||||
\(888\) | −27.3211 | − | 84.0858i | −0.916838 | − | 2.82174i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17.0949 | −0.573024 | ||||||||
\(891\) | −7.30693 | + | 1.33813i | −0.244791 | + | 0.0448291i | ||||
\(892\) | −6.59273 | + | 11.4189i | −0.220741 | + | 0.382335i | ||||
\(893\) | −1.28359 | − | 12.2126i | −0.0429538 | − | 0.408678i | ||||
\(894\) | −6.70798 | + | 7.44997i | −0.224349 | + | 0.249164i | ||||
\(895\) | 3.86708 | − | 11.9017i | 0.129262 | − | 0.397829i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.84490 | + | 2.79348i | 0.128377 | + | 0.0932716i | ||||
\(898\) | 18.2486 | − | 3.87886i | 0.608963 | − | 0.129439i | ||||
\(899\) | 6.14923 | + | 1.30706i | 0.205088 | + | 0.0435928i | ||||
\(900\) | 2.84611 | + | 27.0789i | 0.0948704 | + | 0.902631i | ||||
\(901\) | 10.4638 | + | 18.1239i | 0.348601 | + | 0.603795i | ||||
\(902\) | −6.22455 | − | 4.79741i | −0.207255 | − | 0.159736i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4925 | − | 19.2479i | 0.881127 | − | 0.640176i | ||||
\(905\) | 36.5800 | − | 40.6262i | 1.21596 | − | 1.35046i | ||||
\(906\) | 6.11204 | + | 6.78811i | 0.203059 | + | 0.225520i | ||||
\(907\) | −40.2886 | + | 17.9376i | −1.33776 | + | 0.595609i | −0.945913 | − | 0.324421i | \(-0.894831\pi\) |
−0.391848 | + | 0.920030i | \(0.628164\pi\) | |||||||
\(908\) | 1.00078 | − | 9.52176i | 0.0332120 | − | 0.315991i | ||||
\(909\) | 24.6886 | − | 75.9837i | 0.818869 | − | 2.52022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.1075 | + | 29.1398i | −1.32882 | + | 0.965446i | −0.329045 | + | 0.944314i | \(0.606727\pi\) |
−0.999777 | + | 0.0211316i | \(0.993273\pi\) | |||||||
\(912\) | −4.42994 | − | 7.67288i | −0.146690 | − | 0.254075i | ||||
\(913\) | 49.2827 | − | 20.2904i | 1.63102 | − | 0.671514i | ||||
\(914\) | 12.0905 | − | 20.9414i | 0.399919 | − | 0.692680i | ||||
\(915\) | −9.71775 | − | 4.32662i | −0.321259 | − | 0.143034i | ||||
\(916\) | 1.07120 | + | 3.29682i | 0.0353935 | + | 0.108930i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.8302 | + | 7.86857i | 0.357448 | + | 0.259701i | ||||
\(919\) | 4.26399 | − | 40.5692i | 0.140656 | − | 1.33825i | −0.665432 | − | 0.746458i | \(-0.731753\pi\) |
0.806088 | − | 0.591795i | \(-0.201581\pi\) | |||||||
\(920\) | −5.73715 | − | 6.37176i | −0.189148 | − | 0.210071i | ||||
\(921\) | 36.0284 | + | 7.65807i | 1.18718 | + | 0.252342i | ||||
\(922\) | 6.18788 | + | 2.75502i | 0.203787 | + | 0.0907319i | ||||
\(923\) | −6.56740 | −0.216169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.8737 | 2.29743 | ||||||||
\(926\) | −5.24044 | − | 2.33319i | −0.172211 | − | 0.0766735i | ||||
\(927\) | 45.0733 | + | 9.58063i | 1.48040 | + | 0.314669i | ||||
\(928\) | 21.4440 | + | 23.8160i | 0.703935 | + | 0.781799i | ||||
\(929\) | 4.32674 | − | 41.1662i | 0.141956 | − | 1.35062i | −0.659112 | − | 0.752044i | \(-0.729068\pi\) |
0.801068 | − | 0.598573i | \(-0.204265\pi\) | |||||||
\(930\) | −7.02348 | − | 5.10286i | −0.230309 | − | 0.167329i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.58785 | − | 17.1976i | −0.183036 | − | 0.563327i | ||||
\(933\) | −70.0443 | − | 31.1857i | −2.29315 | − | 1.02098i | ||||
\(934\) | −2.18395 | + | 3.78271i | −0.0714610 | + | 0.123774i | ||||
\(935\) | −21.5419 | − | 5.22041i | −0.704494 | − | 0.170726i | ||||
\(936\) | 16.3738 | + | 28.3602i | 0.535194 | + | 0.926982i | ||||
\(937\) | 1.29155 | − | 0.938364i | 0.0421930 | − | 0.0306550i | −0.566489 | − | 0.824069i | \(-0.691699\pi\) |
0.608682 | + | 0.793414i | \(0.291699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.17033 | + | 9.75727i | −0.103460 | + | 0.318416i | ||||
\(940\) | 2.07182 | − | 19.7120i | 0.0675752 | − | 0.642935i | ||||
\(941\) | −6.49336 | + | 2.89103i | −0.211678 | + | 0.0942449i | −0.509836 | − | 0.860271i | \(-0.670294\pi\) |
0.298159 | + | 0.954516i | \(0.403627\pi\) | |||||||
\(942\) | 45.8132 | + | 50.8807i | 1.49268 | + | 1.65778i | ||||
\(943\) | −1.14828 | + | 1.27529i | −0.0373932 | + | 0.0415293i | ||||
\(944\) | 5.09287 | − | 3.70019i | 0.165759 | − | 0.120431i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.39731 | + | 6.42910i | −0.305533 | + | 0.209028i | ||||
\(947\) | 1.22993 | + | 2.13030i | 0.0399674 | + | 0.0692255i | 0.885317 | − | 0.464988i | \(-0.153941\pi\) |
−0.845350 | + | 0.534213i | \(0.820608\pi\) | |||||||
\(948\) | −2.14764 | − | 20.4334i | −0.0697521 | − | 0.663647i | ||||
\(949\) | 2.47051 | + | 0.525123i | 0.0801961 | + | 0.0170462i | ||||
\(950\) | 12.2862 | − | 2.61152i | 0.398618 | − | 0.0847288i | ||||
\(951\) | 39.1286 | + | 28.4286i | 1.26883 | + | 0.921861i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.83790 | + | 27.2003i | −0.286288 | + | 0.881103i | 0.699722 | + | 0.714415i | \(0.253307\pi\) |
−0.986010 | + | 0.166688i | \(0.946693\pi\) | |||||||
\(954\) | 41.7477 | − | 46.3655i | 1.35163 | − | 1.50114i | ||||
\(955\) | 0.155009 | + | 1.47481i | 0.00501598 | + | 0.0477238i | ||||
\(956\) | 3.34950 | − | 5.80150i | 0.108331 | − | 0.187634i | ||||
\(957\) | −35.9329 | − | 66.5185i | −1.16155 | − | 2.15024i | ||||
\(958\) | 16.8428 | 0.544168 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25.3364 | − | 77.9774i | −0.817728 | − | 2.51671i | ||||
\(961\) | 29.7146 | − | 6.31602i | 0.958534 | − | 0.203743i | ||||
\(962\) | 21.0992 | − | 9.39396i | 0.680265 | − | 0.302873i | ||||
\(963\) | 16.5973 | − | 7.38959i | 0.534840 | − | 0.238126i | ||||
\(964\) | −14.0469 | + | 2.98576i | −0.452421 | + | 0.0961650i | ||||
\(965\) | 16.2065 | + | 49.8785i | 0.521706 | + | 1.60565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.213338 | −0.00686047 | −0.00343024 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343024 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(968\) | −24.0093 | + | 23.8052i | −0.771689 | + | 0.765127i | ||||
\(969\) | −4.48601 | + | 7.76999i | −0.144111 | + | 0.249608i | ||||
\(970\) | −2.60411 | − | 24.7765i | −0.0836130 | − | 0.795525i | ||||
\(971\) | 0.554173 | − | 0.615471i | 0.0177843 | − | 0.0197514i | −0.734187 | − | 0.678947i | \(-0.762436\pi\) |
0.751971 | + | 0.659196i | \(0.229103\pi\) | |||||||
\(972\) | 2.86507 | − | 8.81779i | 0.0918973 | − | 0.282831i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.6098 | − | 16.4270i | −0.724465 | − | 0.526354i | ||||
\(975\) | −39.9967 | + | 8.50156i | −1.28092 | + | 0.272268i | ||||
\(976\) | 2.01096 | + | 0.427443i | 0.0643693 | + | 0.0136821i | ||||
\(977\) | −1.01990 | − | 9.70369i | −0.0326295 | − | 0.310449i | −0.998648 | − | 0.0519768i | \(-0.983448\pi\) |
0.966019 | − | 0.258472i | \(-0.0832189\pi\) | |||||||
\(978\) | 13.0986 | + | 22.6874i | 0.418847 | + | 0.725464i | ||||
\(979\) | 14.7143 | + | 0.416743i | 0.470271 | + | 0.0133192i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.2230 | + | 11.7867i | −0.517961 | + | 0.376321i | ||||
\(982\) | 27.7564 | − | 30.8266i | 0.885743 | − | 0.983717i | ||||
\(983\) | −30.1910 | − | 33.5305i | −0.962944 | − | 1.06946i | −0.997543 | − | 0.0700562i | \(-0.977682\pi\) |
0.0345993 | − | 0.999401i | \(-0.488985\pi\) | |||||||
\(984\) | −17.0672 | + | 7.59882i | −0.544083 | + | 0.242241i | ||||
\(985\) | −7.51714 | + | 71.5208i | −0.239516 | + | 2.27884i | ||||
\(986\) | −5.31011 | + | 16.3428i | −0.169108 | + | 0.520462i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.04978 | + | 1.48926i | −0.0652123 | + | 0.0473795i | ||||
\(989\) | 1.24316 | + | 2.15322i | 0.0395302 | + | 0.0684684i | ||||
\(990\) | 5.04400 | + | 65.8881i | 0.160309 | + | 2.09406i | ||||
\(991\) | −26.7702 | + | 46.3674i | −0.850384 | + | 1.47291i | 0.0304776 | + | 0.999535i | \(0.490297\pi\) |
−0.880862 | + | 0.473373i | \(0.843036\pi\) | |||||||
\(992\) | −2.89484 | − | 1.28887i | −0.0919113 | − | 0.0409215i | ||||
\(993\) | −1.09391 | − | 3.36671i | −0.0347142 | − | 0.106839i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6143 | − | 17.1568i | −0.748624 | − | 0.543907i | ||||
\(996\) | 3.63973 | − | 34.6297i | 0.115329 | − | 1.09729i | ||||
\(997\) | 20.8506 | + | 23.1569i | 0.660344 | + | 0.733387i | 0.976547 | − | 0.215305i | \(-0.0690746\pi\) |
−0.316203 | + | 0.948692i | \(0.602408\pi\) | |||||||
\(998\) | 34.6801 | + | 7.37149i | 1.09778 | + | 0.233341i | ||||
\(999\) | 57.0977 | + | 25.4216i | 1.80649 | + | 0.804302i |
(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 | 539.2.q.f.410.3 | 32 | ||
7.2 | even | 3 | inner | 539.2.q.f.520.2 | 32 | ||
7.3 | odd | 6 | 77.2.f.b.36.2 | yes | 16 | ||
7.4 | even | 3 | 539.2.f.e.344.2 | 16 | |||
7.5 | odd | 6 | 539.2.q.g.520.2 | 32 | |||
7.6 | odd | 2 | 539.2.q.g.410.3 | 32 | |||
11.4 | even | 5 | inner | 539.2.q.f.312.2 | 32 | ||
21.17 | even | 6 | 693.2.m.i.190.3 | 16 | |||
77.3 | odd | 30 | 847.2.f.w.148.3 | 16 | |||
77.4 | even | 15 | 539.2.f.e.246.2 | 16 | |||
77.10 | even | 6 | 847.2.f.x.729.3 | 16 | |||
77.17 | even | 30 | 847.2.f.v.372.2 | 16 | |||
77.24 | even | 30 | 847.2.a.o.1.3 | 8 | |||
77.26 | odd | 30 | 539.2.q.g.422.3 | 32 | |||
77.31 | odd | 30 | 847.2.a.p.1.6 | 8 | |||
77.37 | even | 15 | inner | 539.2.q.f.422.3 | 32 | ||
77.38 | odd | 30 | 847.2.f.w.372.3 | 16 | |||
77.46 | odd | 30 | 5929.2.a.bs.1.3 | 8 | |||
77.48 | odd | 10 | 539.2.q.g.312.2 | 32 | |||
77.52 | even | 30 | 847.2.f.v.148.2 | 16 | |||
77.53 | even | 15 | 5929.2.a.bt.1.6 | 8 | |||
77.59 | odd | 30 | 77.2.f.b.15.2 | ✓ | 16 | ||
77.73 | even | 30 | 847.2.f.x.323.3 | 16 | |||
231.59 | even | 30 | 693.2.m.i.631.3 | 16 | |||
231.101 | odd | 30 | 7623.2.a.cw.1.6 | 8 | |||
231.185 | even | 30 | 7623.2.a.ct.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 77.59 | odd | 30 | ||
77.2.f.b.36.2 | yes | 16 | 7.3 | odd | 6 | ||
539.2.f.e.246.2 | 16 | 77.4 | even | 15 | |||
539.2.f.e.344.2 | 16 | 7.4 | even | 3 | |||
539.2.q.f.312.2 | 32 | 11.4 | even | 5 | inner | ||
539.2.q.f.410.3 | 32 | 1.1 | even | 1 | trivial | ||
539.2.q.f.422.3 | 32 | 77.37 | even | 15 | inner | ||
539.2.q.f.520.2 | 32 | 7.2 | even | 3 | inner | ||
539.2.q.g.312.2 | 32 | 77.48 | odd | 10 | |||
539.2.q.g.410.3 | 32 | 7.6 | odd | 2 | |||
539.2.q.g.422.3 | 32 | 77.26 | odd | 30 | |||
539.2.q.g.520.2 | 32 | 7.5 | odd | 6 | |||
693.2.m.i.190.3 | 16 | 21.17 | even | 6 | |||
693.2.m.i.631.3 | 16 | 231.59 | even | 30 | |||
847.2.a.o.1.3 | 8 | 77.24 | even | 30 | |||
847.2.a.p.1.6 | 8 | 77.31 | odd | 30 | |||
847.2.f.v.148.2 | 16 | 77.52 | even | 30 | |||
847.2.f.v.372.2 | 16 | 77.17 | even | 30 | |||
847.2.f.w.148.3 | 16 | 77.3 | odd | 30 | |||
847.2.f.w.372.3 | 16 | 77.38 | odd | 30 | |||
847.2.f.x.323.3 | 16 | 77.73 | even | 30 | |||
847.2.f.x.729.3 | 16 | 77.10 | even | 6 | |||
5929.2.a.bs.1.3 | 8 | 77.46 | odd | 30 | |||
5929.2.a.bt.1.6 | 8 | 77.53 | even | 15 | |||
7623.2.a.ct.1.3 | 8 | 231.185 | even | 30 | |||
7623.2.a.cw.1.6 | 8 | 231.101 | odd | 30 |