Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 496.8 | ||
Character | \(\chi\) | \(=\) | 819.496 |
Dual form | 819.2.fm.f.748.8 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16866 | + | 0.581092i | 1.53348 | + | 0.410894i | 0.924152 | − | 0.382026i | \(-0.124774\pi\) |
0.609326 | + | 0.792920i | \(0.291440\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.63339 | + | 1.52039i | 1.31669 | + | 0.760193i | ||||
\(5\) | 1.87790 | + | 1.87790i | 0.839823 | + | 0.839823i | 0.988835 | − | 0.149013i | \(-0.0476095\pi\) |
−0.149013 | + | 0.988835i | \(0.547610\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.25300 | + | 1.38707i | 0.851556 | + | 0.524264i | ||||
\(8\) | 1.65230 | + | 1.65230i | 0.584177 | + | 0.584177i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.98130 | + | 5.16377i | 0.942771 | + | 1.63293i | ||||
\(11\) | 1.20979 | − | 4.51499i | 0.364764 | − | 1.36132i | −0.502975 | − | 0.864301i | \(-0.667761\pi\) |
0.867740 | − | 0.497019i | \(-0.165572\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52548 | − | 3.26694i | −0.423092 | − | 0.906087i | ||||
\(14\) | 4.07999 | + | 4.31730i | 1.09042 | + | 1.15385i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.417624 | − | 0.723346i | −0.104406 | − | 0.180836i | ||||
\(17\) | −2.18729 | + | 3.78849i | −0.530495 | + | 0.918845i | 0.468872 | + | 0.883266i | \(0.344661\pi\) |
−0.999367 | + | 0.0355783i | \(0.988673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.194491 | + | 0.0521138i | −0.0446194 | + | 0.0119557i | −0.281060 | − | 0.959690i | \(-0.590686\pi\) |
0.236440 | + | 0.971646i | \(0.424019\pi\) | |||||||
\(20\) | 2.09010 | + | 7.80037i | 0.467361 | + | 1.74422i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.24724 | − | 9.08849i | 1.11872 | − | 1.93767i | ||||
\(23\) | −7.20237 | + | 4.15829i | −1.50180 | + | 0.867064i | −0.501801 | + | 0.864983i | \(0.667329\pi\) |
−0.999998 | + | 0.00208060i | \(0.999338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.05302i | 0.410604i | ||||||||
\(26\) | −1.40986 | − | 7.97134i | −0.276497 | − | 1.56331i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.82414 | + | 7.07814i | 0.722695 | + | 1.33764i | ||||
\(29\) | 5.20380 | + | 9.01325i | 0.966322 | + | 1.67372i | 0.706022 | + | 0.708190i | \(0.250488\pi\) |
0.260300 | + | 0.965528i | \(0.416179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.75799 | − | 6.75799i | −1.21377 | − | 1.21377i | −0.969777 | − | 0.243995i | \(-0.921542\pi\) |
−0.243995 | − | 0.969777i | \(-0.578458\pi\) | |||||||
\(32\) | −1.69492 | − | 6.32554i | −0.299623 | − | 1.11821i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.94495 | + | 6.94495i | −1.19105 | + | 1.19105i | ||||
\(35\) | 1.62613 | + | 6.83570i | 0.274866 | + | 1.15544i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.22755 | − | 4.58128i | 0.201808 | − | 0.753158i | −0.788591 | − | 0.614919i | \(-0.789189\pi\) |
0.990399 | − | 0.138240i | \(-0.0441444\pi\) | |||||||
\(38\) | −0.452070 | −0.0733354 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.20572i | 0.981210i | ||||||||
\(41\) | −0.136339 | + | 0.508825i | −0.0212926 | + | 0.0794651i | −0.975755 | − | 0.218867i | \(-0.929764\pi\) |
0.954462 | + | 0.298333i | \(0.0964304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.49507 | + | 1.44053i | 0.380494 | + | 0.219678i | 0.678033 | − | 0.735031i | \(-0.262832\pi\) |
−0.297539 | + | 0.954710i | \(0.596166\pi\) | |||||||
\(44\) | 10.0504 | − | 10.0504i | 1.51515 | − | 1.51515i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −18.0359 | + | 4.83270i | −2.65925 | + | 0.712543i | ||||
\(47\) | −0.928461 | + | 0.928461i | −0.135430 | + | 0.135430i | −0.771572 | − | 0.636142i | \(-0.780529\pi\) |
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.15206 | + | 6.25016i | 0.450294 | + | 0.892881i | ||||
\(50\) | −1.19299 | + | 4.45231i | −0.168715 | + | 0.629651i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.949833 | − | 10.9224i | 0.131718 | − | 1.51467i | ||||
\(53\) | −1.95082 | −0.267966 | −0.133983 | − | 0.990984i | \(-0.542777\pi\) | ||||
−0.133983 | + | 0.990984i | \(0.542777\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7506 | − | 6.20683i | 1.44960 | − | 0.836929i | ||||
\(56\) | 1.43078 | + | 6.01451i | 0.191196 | + | 0.803722i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.04777 | + | 22.5706i | 0.794111 | + | 2.96366i | ||||
\(59\) | −1.76081 | − | 6.57142i | −0.229237 | − | 0.855526i | −0.980662 | − | 0.195707i | \(-0.937300\pi\) |
0.751425 | − | 0.659819i | \(-0.229367\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.13306 | + | 1.23152i | 0.273111 | + | 0.157681i | 0.630300 | − | 0.776351i | \(-0.282932\pi\) |
−0.357190 | + | 0.934032i | \(0.616265\pi\) | |||||||
\(62\) | −10.7288 | − | 18.5828i | −1.36256 | − | 2.36002i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 13.0324i | − | 1.62905i | ||||||
\(65\) | 3.27029 | − | 8.99969i | 0.405630 | − | 1.11627i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.40878 | − | 0.377482i | −0.172110 | − | 0.0461168i | 0.171735 | − | 0.985143i | \(-0.445063\pi\) |
−0.343845 | + | 0.939026i | \(0.611729\pi\) | |||||||
\(68\) | −11.5199 | + | 6.65104i | −1.39700 | + | 0.806558i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.445637 | + | 15.7693i | −0.0532638 | + | 1.88479i | ||||
\(71\) | 1.44014 | + | 5.37468i | 0.170913 | + | 0.637857i | 0.997212 | + | 0.0746244i | \(0.0237758\pi\) |
−0.826299 | + | 0.563232i | \(0.809558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.75032 | − | 8.75032i | 1.02415 | − | 1.02415i | 0.0244465 | − | 0.999701i | \(-0.492218\pi\) |
0.999701 | − | 0.0244465i | \(-0.00778234\pi\) | |||||||
\(74\) | 5.32429 | − | 9.22194i | 0.618936 | − | 1.07203i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.591404 | − | 0.158466i | −0.0678387 | − | 0.0181773i | ||||
\(77\) | 8.98827 | − | 8.49422i | 1.02431 | − | 0.968006i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.46495 | −0.502346 | −0.251173 | − | 0.967942i | \(-0.580816\pi\) | ||||
−0.251173 | + | 0.967942i | \(0.580816\pi\) | |||||||
\(80\) | 0.574115 | − | 2.14263i | 0.0641880 | − | 0.239553i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.591348 | + | 1.02425i | −0.0653035 | + | 0.113109i | ||||
\(83\) | 5.42187 | + | 5.42187i | 0.595128 | + | 0.595128i | 0.939012 | − | 0.343884i | \(-0.111743\pi\) |
−0.343884 | + | 0.939012i | \(0.611743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2219 | + | 3.00690i | −1.21719 | + | 0.326145i | ||||
\(86\) | 4.57389 | + | 4.57389i | 0.493215 | + | 0.493215i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.45905 | − | 5.46119i | 1.00834 | − | 0.582164i | ||||
\(89\) | −15.0461 | − | 4.03159i | −1.59488 | − | 0.427347i | −0.651390 | − | 0.758743i | \(-0.725814\pi\) |
−0.943492 | + | 0.331396i | \(0.892480\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.09457 | − | 9.47639i | 0.114742 | − | 0.993395i | ||||
\(92\) | −25.2888 | −2.63654 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.55304 | + | 1.47400i | −0.263326 | + | 0.152031i | ||||
\(95\) | −0.463100 | − | 0.267371i | −0.0475131 | − | 0.0274317i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.84925 | + | 0.763454i | −0.289297 | + | 0.0775170i | −0.400549 | − | 0.916275i | \(-0.631181\pi\) |
0.111252 | + | 0.993792i | \(0.464514\pi\) | |||||||
\(98\) | 3.20383 | + | 15.3861i | 0.323636 | + | 1.55423i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.12138 | + | 5.40639i | −0.312138 | + | 0.540639i | ||||
\(101\) | −0.316767 | − | 0.548657i | −0.0315195 | − | 0.0545934i | 0.849835 | − | 0.527048i | \(-0.176701\pi\) |
−0.881355 | + | 0.472455i | \(0.843368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.95716 | 0.192845 | 0.0964223 | − | 0.995341i | \(-0.469260\pi\) | ||||
0.0964223 | + | 0.995341i | \(0.469260\pi\) | |||||||
\(104\) | 2.87742 | − | 7.91853i | 0.282154 | − | 0.776475i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.23068 | − | 1.13361i | −0.410920 | − | 0.110106i | ||||
\(107\) | 3.59988 | + | 6.23517i | 0.348013 | + | 0.602777i | 0.985896 | − | 0.167357i | \(-0.0535231\pi\) |
−0.637883 | + | 0.770133i | \(0.720190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.42207 | + | 2.42207i | −0.231992 | + | 0.231992i | −0.813524 | − | 0.581531i | \(-0.802454\pi\) |
0.581531 | + | 0.813524i | \(0.302454\pi\) | |||||||
\(110\) | 26.9211 | − | 7.21348i | 2.56682 | − | 0.687778i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0624252 | − | 2.20898i | 0.00589863 | − | 0.208729i | ||||
\(113\) | −0.379755 | + | 0.657754i | −0.0357243 | + | 0.0618763i | −0.883335 | − | 0.468743i | \(-0.844707\pi\) |
0.847610 | + | 0.530619i | \(0.178040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.3342 | − | 5.71648i | −1.98942 | − | 0.533065i | ||||
\(116\) | 31.6471i | 2.93836i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 15.2744i | − | 1.40612i | ||||||
\(119\) | −10.1829 | + | 5.50156i | −0.933464 | + | 0.504327i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39523 | − | 5.42434i | −0.854112 | − | 0.493122i | ||||
\(122\) | 3.91027 | + | 3.91027i | 0.354019 | + | 0.354019i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.52164 | − | 28.0712i | −0.675464 | − | 2.52086i | ||||
\(125\) | 5.53414 | − | 5.53414i | 0.494988 | − | 0.494988i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.04032 | + | 0.600626i | −0.0923131 | + | 0.0532970i | −0.545446 | − | 0.838146i | \(-0.683640\pi\) |
0.453133 | + | 0.891443i | \(0.350306\pi\) | |||||||
\(128\) | 4.18317 | − | 15.6118i | 0.369743 | − | 1.37990i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.3218 | − | 17.6170i | 1.08069 | − | 1.54511i | ||||
\(131\) | − | 3.03417i | − | 0.265097i | −0.991177 | − | 0.132548i | \(-0.957684\pi\) | ||
0.991177 | − | 0.132548i | \(-0.0423160\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.510476 | − | 0.152361i | −0.0442639 | − | 0.0132114i | ||||
\(134\) | −2.83582 | − | 1.63726i | −0.244978 | − | 0.141438i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.87379 | + | 2.64567i | −0.846671 | + | 0.226865i | ||||
\(137\) | 11.2793 | − | 3.02227i | 0.963654 | − | 0.258210i | 0.257508 | − | 0.966276i | \(-0.417099\pi\) |
0.706146 | + | 0.708066i | \(0.250432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.80746 | + | 3.35294i | 0.492582 | + | 0.284393i | 0.725645 | − | 0.688069i | \(-0.241541\pi\) |
−0.233063 | + | 0.972462i | \(0.574875\pi\) | |||||||
\(140\) | −6.11067 | + | 20.4734i | −0.516446 | + | 1.73032i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.4927i | 1.04837i | ||||||||
\(143\) | −16.5957 | + | 2.93522i | −1.38780 | + | 0.245455i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.15376 | + | 26.6982i | −0.594087 | + | 2.21716i | ||||
\(146\) | 24.0612 | − | 13.8918i | 1.99132 | − | 1.14969i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.1979 | − | 10.1979i | 0.838265 | − | 0.838265i | ||||
\(149\) | 1.23932 | + | 4.62521i | 0.101529 | + | 0.378912i | 0.997928 | − | 0.0643356i | \(-0.0204928\pi\) |
−0.896399 | + | 0.443248i | \(0.853826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.66300 | − | 7.66300i | −0.623606 | − | 0.623606i | 0.322845 | − | 0.946452i | \(-0.395361\pi\) |
−0.946452 | + | 0.322845i | \(0.895361\pi\) | |||||||
\(152\) | −0.407466 | − | 0.235251i | −0.0330499 | − | 0.0190814i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 24.4285 | − | 13.1981i | 1.96850 | − | 1.06353i | ||||
\(155\) | − | 25.3817i | − | 2.03870i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00601i | 0.638949i | 0.947595 | + | 0.319475i | \(0.103506\pi\) | ||||
−0.947595 | + | 0.319475i | \(0.896494\pi\) | |||||||
\(158\) | −9.68297 | − | 2.59455i | −0.770336 | − | 0.206411i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.69584 | − | 15.0616i | 0.687467 | − | 1.19073i | ||||
\(161\) | −21.9948 | − | 0.621570i | −1.73344 | − | 0.0489865i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3794 | − | 4.92475i | 1.43959 | − | 0.385736i | 0.547199 | − | 0.837003i | \(-0.315694\pi\) |
0.892389 | + | 0.451266i | \(0.149028\pi\) | |||||||
\(164\) | −1.13264 | + | 1.13264i | −0.0884447 | + | 0.0884447i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.60761 | + | 14.9088i | 0.668080 | + | 1.15715i | ||||
\(167\) | −10.5127 | − | 2.81688i | −0.813500 | − | 0.217977i | −0.171997 | − | 0.985097i | \(-0.555022\pi\) |
−0.641503 | + | 0.767121i | \(0.721689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.34582 | + | 9.96731i | −0.641986 | + | 0.766716i | ||||
\(170\) | −26.0839 | −2.00054 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.38032 | + | 7.58693i | 0.333996 | + | 0.578498i | ||||
\(173\) | −4.07283 | + | 7.05435i | −0.309651 | + | 0.536332i | −0.978286 | − | 0.207259i | \(-0.933546\pi\) |
0.668635 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.84769 | + | 4.62546i | −0.215265 | + | 0.349652i | ||||
\(176\) | −3.77113 | + | 1.01047i | −0.284260 | + | 0.0761672i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −30.2872 | − | 17.4863i | −2.27012 | − | 1.31065i | ||||
\(179\) | −10.2340 | + | 5.90863i | −0.764928 | + | 0.441631i | −0.831062 | − | 0.556179i | \(-0.812267\pi\) |
0.0661342 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4995 | −0.780423 | −0.390212 | − | 0.920725i | \(-0.627598\pi\) | ||||
−0.390212 | + | 0.920725i | \(0.627598\pi\) | |||||||
\(182\) | 7.88041 | − | 19.9151i | 0.584135 | − | 1.47620i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.7712 | − | 5.02974i | −1.38383 | − | 0.370797i | ||||
\(185\) | 10.9084 | − | 6.29797i | 0.802002 | − | 0.463036i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4588 | + | 14.4588i | 1.05734 | + | 1.05734i | ||||
\(188\) | −3.85661 | + | 1.03338i | −0.281272 | + | 0.0753667i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.848942 | − | 0.848942i | −0.0615887 | − | 0.0615887i | ||||
\(191\) | 6.67464 | − | 11.5608i | 0.482960 | − | 0.836511i | −0.516849 | − | 0.856077i | \(-0.672895\pi\) |
0.999809 | + | 0.0195655i | \(0.00622830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.08783 | + | 7.79189i | −0.150285 | + | 0.560872i | 0.849178 | + | 0.528107i | \(0.177098\pi\) |
−0.999463 | + | 0.0327652i | \(0.989569\pi\) | |||||||
\(194\) | −6.62270 | −0.475482 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.20208 | + | 21.2514i | −0.0858631 | + | 1.51796i | ||||
\(197\) | 12.2629 | + | 3.28585i | 0.873699 | + | 0.234107i | 0.667686 | − | 0.744443i | \(-0.267285\pi\) |
0.206012 | + | 0.978549i | \(0.433951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.8366 | − | 18.7696i | 0.768188 | − | 1.33054i | −0.170356 | − | 0.985383i | \(-0.554492\pi\) |
0.938544 | − | 0.345158i | \(-0.112175\pi\) | |||||||
\(200\) | −3.39221 | + | 3.39221i | −0.239865 | + | 0.239865i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.368142 | − | 1.37392i | −0.0259024 | − | 0.0966689i | ||||
\(203\) | −0.777849 | + | 27.5249i | −0.0545943 | + | 1.93187i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.21155 | + | 0.699491i | −0.0846186 | + | 0.0488546i | ||||
\(206\) | 4.24442 | + | 1.13729i | 0.295723 | + | 0.0792387i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.72605 | + | 2.46780i | −0.119680 | + | 0.171111i | ||||
\(209\) | 0.941173i | 0.0651023i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50914 | + | 11.2742i | 0.448108 | + | 0.776145i | 0.998263 | − | 0.0589170i | \(-0.0187647\pi\) |
−0.550155 | + | 0.835062i | \(0.685431\pi\) | |||||||
\(212\) | −5.13727 | − | 2.96601i | −0.352829 | − | 0.203706i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.18372 | + | 15.6138i | 0.285993 | + | 1.06734i | ||||
\(215\) | 1.98032 | + | 7.39066i | 0.135057 | + | 0.504039i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.85195 | − | 24.5996i | −0.397257 | − | 1.66993i | ||||
\(218\) | −6.66011 | + | 3.84521i | −0.451079 | + | 0.260431i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 37.7471 | 2.54491 | ||||||||
\(221\) | 15.7135 | + | 1.36647i | 1.05700 | + | 0.0919186i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.38178 | − | 16.3530i | 0.293426 | − | 1.09508i | −0.649034 | − | 0.760759i | \(-0.724827\pi\) |
0.942460 | − | 0.334320i | \(-0.108507\pi\) | |||||||
\(224\) | 4.95532 | − | 16.6025i | 0.331091 | − | 1.10930i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.20578 | + | 1.20578i | −0.0802070 | + | 0.0802070i | ||||
\(227\) | 18.2910 | − | 4.90106i | 1.21402 | − | 0.325295i | 0.405679 | − | 0.914015i | \(-0.367035\pi\) |
0.808336 | + | 0.588721i | \(0.200368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.181433 | + | 0.181433i | −0.0119894 | + | 0.0119894i | −0.713076 | − | 0.701087i | \(-0.752699\pi\) |
0.701087 | + | 0.713076i | \(0.252699\pi\) | |||||||
\(230\) | −42.9449 | − | 24.7943i | −2.83170 | − | 1.63488i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.29435 | + | 23.4909i | −0.413245 | + | 1.54225i | ||||
\(233\) | 11.3848i | 0.745842i | 0.927863 | + | 0.372921i | \(0.121644\pi\) | ||||
−0.927863 | + | 0.372921i | \(0.878356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.48711 | −0.227474 | ||||||||
\(236\) | 5.35421 | − | 19.9822i | 0.348529 | − | 1.30073i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.2802 | + | 6.01385i | −1.63867 | + | 0.389820i | ||||
\(239\) | 12.2181 | − | 12.2181i | 0.790322 | − | 0.790322i | −0.191224 | − | 0.981546i | \(-0.561246\pi\) |
0.981546 | + | 0.191224i | \(0.0612458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.89185 | + | 29.4528i | 0.508359 | + | 1.89722i | 0.436254 | + | 0.899824i | \(0.356305\pi\) |
0.0721047 | + | 0.997397i | \(0.477028\pi\) | |||||||
\(242\) | −17.2231 | − | 17.2231i | −1.10714 | − | 1.10714i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.74479 | + | 6.48616i | 0.239735 | + | 0.415234i | ||||
\(245\) | −5.81794 | + | 17.6564i | −0.371694 | + | 1.12803i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.466946 | + | 0.555894i | 0.0297111 | + | 0.0353707i | ||||
\(248\) | − | 22.3325i | − | 1.41811i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.2175 | − | 8.78584i | 0.962441 | − | 0.555666i | ||||
\(251\) | 5.46171 | − | 9.45996i | 0.344740 | − | 0.597107i | −0.640566 | − | 0.767903i | \(-0.721300\pi\) |
0.985307 | + | 0.170795i | \(0.0546337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0613 | + | 37.5493i | 0.632548 | + | 2.36070i | ||||
\(254\) | −2.60511 | + | 0.698038i | −0.163459 | + | 0.0437988i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.11138 | − | 8.85317i | 0.319461 | − | 0.553323i | ||||
\(257\) | 14.2035 | + | 24.6012i | 0.885991 | + | 1.53458i | 0.844574 | + | 0.535439i | \(0.179854\pi\) |
0.0414174 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.12025 | − | 8.61895i | 0.566705 | − | 0.535555i | ||||
\(260\) | 22.2949 | − | 18.7276i | 1.38267 | − | 1.16143i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.76313 | − | 6.58009i | 0.108927 | − | 0.406520i | ||||
\(263\) | −10.8579 | − | 18.8064i | −0.669526 | − | 1.15965i | −0.978037 | − | 0.208433i | \(-0.933164\pi\) |
0.308510 | − | 0.951221i | \(-0.400170\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.66345 | − | 3.66345i | −0.225044 | − | 0.225044i | ||||
\(266\) | −1.01851 | − | 0.627054i | −0.0624491 | − | 0.0384471i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.13595 | − | 3.13595i | −0.191559 | − | 0.191559i | ||||
\(269\) | −10.7149 | − | 6.18625i | −0.653298 | − | 0.377182i | 0.136420 | − | 0.990651i | \(-0.456440\pi\) |
−0.789719 | + | 0.613469i | \(0.789774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.64449 | − | 2.04834i | −0.464370 | − | 0.124427i | 0.0190456 | − | 0.999819i | \(-0.493937\pi\) |
−0.483415 | + | 0.875391i | \(0.660604\pi\) | |||||||
\(272\) | 3.65385 | 0.221547 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.2172 | 1.58384 | ||||||||
\(275\) | 9.26935 | + | 2.48371i | 0.558963 | + | 0.149774i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.70888 | + | 5.60543i | 0.583350 | + | 0.336797i | 0.762464 | − | 0.647031i | \(-0.223990\pi\) |
−0.179113 | + | 0.983828i | \(0.557323\pi\) | |||||||
\(278\) | 10.6461 | + | 10.6461i | 0.638509 | + | 0.638509i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.60778 | + | 13.9815i | −0.514413 | + | 0.835555i | ||||
\(281\) | 15.1948 | + | 15.1948i | 0.906448 | + | 0.906448i | 0.995984 | − | 0.0895355i | \(-0.0285383\pi\) |
−0.0895355 | + | 0.995984i | \(0.528538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.64747 | + | 13.2458i | 0.454595 | + | 0.787382i | 0.998665 | − | 0.0516583i | \(-0.0164507\pi\) |
−0.544070 | + | 0.839040i | \(0.683117\pi\) | |||||||
\(284\) | −4.37914 | + | 16.3432i | −0.259854 | + | 0.969789i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −37.6961 | − | 3.27812i | −2.22902 | − | 0.193839i | ||||
\(287\) | −1.01295 | + | 0.957272i | −0.0597926 | + | 0.0565060i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06845 | − | 1.85062i | −0.0628502 | − | 0.108860i | ||||
\(290\) | −31.0282 | + | 53.7424i | −1.82204 | + | 3.15586i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 36.3468 | − | 9.73911i | 2.12704 | − | 0.569938i | ||||
\(293\) | −5.44000 | − | 20.3023i | −0.317808 | − | 1.18608i | −0.921347 | − | 0.388742i | \(-0.872910\pi\) |
0.603539 | − | 0.797334i | \(-0.293757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.03385 | − | 15.6471i | 0.525971 | − | 0.911009i | ||||
\(296\) | 9.59795 | − | 5.54138i | 0.557869 | − | 0.322086i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.7507i | 0.622771i | ||||||||
\(299\) | 24.5720 | + | 17.1863i | 1.42103 | + | 0.993912i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.62328 | + | 6.70636i | 0.208842 | + | 0.386548i | ||||
\(302\) | −12.1656 | − | 21.0714i | −0.700050 | − | 1.21252i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.118921 | + | 0.118921i | 0.00682057 | + | 0.00682057i | ||||
\(305\) | 1.69300 | + | 6.31836i | 0.0969409 | + | 0.361788i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7905 | + | 12.7905i | −0.729995 | + | 0.729995i | −0.970618 | − | 0.240624i | \(-0.922648\pi\) |
0.240624 | + | 0.970618i | \(0.422648\pi\) | |||||||
\(308\) | 36.5841 | − | 8.70292i | 2.08457 | − | 0.495895i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.7491 | − | 55.0443i | 0.837692 | − | 3.12631i | ||||
\(311\) | 19.5517 | 1.10868 | 0.554338 | − | 0.832292i | \(-0.312972\pi\) | ||||
0.554338 | + | 0.832292i | \(0.312972\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2495i | 0.748904i | 0.927246 | + | 0.374452i | \(0.122169\pi\) | ||||
−0.927246 | + | 0.374452i | \(0.877831\pi\) | |||||||
\(314\) | −4.65223 | + | 17.3624i | −0.262540 | + | 0.979814i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7579 | − | 6.78845i | −0.661435 | − | 0.381880i | ||||
\(317\) | −17.8861 | + | 17.8861i | −1.00458 | + | 1.00458i | −0.00459262 | + | 0.999989i | \(0.501462\pi\) |
−0.999989 | + | 0.00459262i | \(0.998538\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.9902 | − | 12.5910i | 2.63094 | − | 0.704959i | ||||
\(320\) | 24.4735 | − | 24.4735i | 1.36811 | − | 1.36811i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −47.3382 | − | 14.1290i | −2.63806 | − | 0.787378i | ||||
\(323\) | 0.227976 | − | 0.850818i | 0.0126849 | − | 0.0473408i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.70709 | − | 3.13184i | 0.372043 | − | 0.173723i | ||||
\(326\) | 42.7206 | 2.36607 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.06601 | + | 0.615459i | −0.0588603 | + | 0.0339830i | ||||
\(329\) | −3.37967 | + | 0.803983i | −0.186327 | + | 0.0443250i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.51837 | − | 13.1307i | −0.193387 | − | 0.721731i | −0.992678 | − | 0.120787i | \(-0.961458\pi\) |
0.799291 | − | 0.600944i | \(-0.205208\pi\) | |||||||
\(332\) | 6.03454 | + | 22.5212i | 0.331189 | + | 1.23601i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.1617 | − | 12.2177i | −1.15792 | − | 0.668524i | ||||
\(335\) | −1.93668 | − | 3.35443i | −0.105812 | − | 0.183272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.75678i | 0.0956980i | 0.998855 | + | 0.0478490i | \(0.0152366\pi\) | ||||
−0.998855 | + | 0.0478490i | \(0.984763\pi\) | |||||||
\(338\) | −23.8912 | + | 16.7661i | −1.29951 | + | 0.911954i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.1233 | − | 9.14331i | −1.85060 | − | 0.495866i | ||||
\(341\) | −38.6880 | + | 22.3365i | −2.09507 | + | 1.20959i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.56784 | + | 18.4538i | −0.0846554 | + | 0.996410i | ||||
\(344\) | 1.74242 | + | 6.50279i | 0.0939449 | + | 0.350607i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9318 | + | 12.9318i | −0.695219 | + | 0.695219i | ||||
\(347\) | −5.43920 | + | 9.42098i | −0.291992 | + | 0.505744i | −0.974281 | − | 0.225338i | \(-0.927651\pi\) |
0.682289 | + | 0.731083i | \(0.260985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9450 | − | 3.20064i | −0.639399 | − | 0.171326i | −0.0754676 | − | 0.997148i | \(-0.524045\pi\) |
−0.563931 | + | 0.825822i | \(0.690712\pi\) | |||||||
\(350\) | −8.86349 | + | 8.37630i | −0.473774 | + | 0.447732i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.6102 | −1.63153 | ||||||||
\(353\) | −4.55715 | + | 17.0075i | −0.242552 | + | 0.905218i | 0.732045 | + | 0.681256i | \(0.238566\pi\) |
−0.974598 | + | 0.223962i | \(0.928101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.38867 | + | 12.7975i | −0.392150 | + | 0.679223i | ||||
\(356\) | −33.4926 | − | 33.4926i | −1.77510 | − | 1.77510i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.6277 | + | 6.86691i | −1.35446 | + | 0.362927i | ||||
\(359\) | −11.4993 | − | 11.4993i | −0.606911 | − | 0.606911i | 0.335227 | − | 0.942137i | \(-0.391187\pi\) |
−0.942137 | + | 0.335227i | \(0.891187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4194 | + | 9.47973i | −0.864177 | + | 0.498933i | ||||
\(362\) | −22.7699 | − | 6.10119i | −1.19676 | − | 0.320671i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.2902 | − | 23.2908i | 0.906253 | − | 1.22077i | ||||
\(365\) | 32.8645 | 1.72020 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3884 | + | 6.57510i | −0.594470 | + | 0.343217i | −0.766863 | − | 0.641811i | \(-0.778183\pi\) |
0.172393 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(368\) | 6.01577 | + | 3.47320i | 0.313594 | + | 0.181053i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.3164 | − | 7.31940i | 1.42011 | − | 0.380518i | ||||
\(371\) | −4.39522 | − | 2.70594i | −0.228188 | − | 0.140485i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.81532 | − | 8.34037i | 0.249328 | − | 0.431848i | −0.714012 | − | 0.700134i | \(-0.753124\pi\) |
0.963339 | + | 0.268286i | \(0.0864571\pi\) | |||||||
\(374\) | 22.9545 | + | 39.7583i | 1.18695 | + | 2.05585i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.06819 | −0.158230 | ||||||||
\(377\) | 21.5075 | − | 30.7500i | 1.10769 | − | 1.58371i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.1516 | − | 8.61500i | −1.65152 | − | 0.442523i | −0.691481 | − | 0.722395i | \(-0.743041\pi\) |
−0.960037 | + | 0.279872i | \(0.909708\pi\) | |||||||
\(380\) | −0.813014 | − | 1.40818i | −0.0417068 | − | 0.0722382i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.1930 | − | 21.1930i | 1.08433 | − | 1.08433i | ||||
\(383\) | 3.73221 | − | 1.00004i | 0.190707 | − | 0.0510998i | −0.162201 | − | 0.986758i | \(-0.551859\pi\) |
0.352908 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.8304 | + | 0.927780i | 1.67319 | + | 0.0472840i | ||||
\(386\) | −9.05560 | + | 15.6848i | −0.460918 | + | 0.798334i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.66392 | − | 2.32149i | −0.439844 | − | 0.117856i | ||||
\(389\) | 12.5816i | 0.637911i | 0.947770 | + | 0.318955i | \(0.103332\pi\) | ||||
−0.947770 | + | 0.318955i | \(0.896668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 36.3815i | − | 1.83989i | ||||||
\(392\) | −5.11901 | + | 15.5353i | −0.258549 | + | 0.784651i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.6848 | + | 14.2518i | 1.24360 | + | 0.717995i | ||||
\(395\) | −8.38473 | − | 8.38473i | −0.421881 | − | 0.421881i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.87160 | − | 25.6452i | −0.344876 | − | 1.28709i | −0.892757 | − | 0.450538i | \(-0.851232\pi\) |
0.547882 | − | 0.836556i | \(-0.315434\pi\) | |||||||
\(398\) | 34.4079 | − | 34.4079i | 1.72471 | − | 1.72471i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.48504 | − | 0.857390i | 0.0742521 | − | 0.0428695i | ||||
\(401\) | 3.89519 | − | 14.5370i | 0.194517 | − | 0.725946i | −0.797875 | − | 0.602823i | \(-0.794043\pi\) |
0.992391 | − | 0.123123i | \(-0.0392908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.7688 | + | 32.3872i | −0.586245 | + | 1.61332i | ||||
\(404\) | − | 1.92643i | − | 0.0958437i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.6814 | + | 59.2403i | −0.877514 | + | 2.94005i | ||||
\(407\) | −19.1994 | − | 11.0848i | −0.951676 | − | 0.549451i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9970 | − | 6.42996i | 1.18657 | − | 0.317941i | 0.389042 | − | 0.921220i | \(-0.372806\pi\) |
0.797531 | + | 0.603279i | \(0.206139\pi\) | |||||||
\(410\) | −3.03392 | + | 0.812937i | −0.149835 | + | 0.0401481i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.15395 | + | 2.97564i | 0.253917 | + | 0.146599i | ||||
\(413\) | 5.14793 | − | 17.2478i | 0.253313 | − | 0.848709i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.3635i | 0.999603i | ||||||||
\(416\) | −18.0796 | + | 15.1867i | −0.886426 | + | 0.744590i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.546908 | + | 2.04109i | −0.0267501 | + | 0.0998329i | ||||
\(419\) | −15.5289 | + | 8.96562i | −0.758637 | + | 0.437999i | −0.828806 | − | 0.559536i | \(-0.810979\pi\) |
0.0701691 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.833811 | − | 0.833811i | 0.0406375 | − | 0.0406375i | −0.686496 | − | 0.727134i | \(-0.740852\pi\) |
0.727134 | + | 0.686496i | \(0.240852\pi\) | |||||||
\(422\) | 7.56482 | + | 28.2323i | 0.368250 | + | 1.37433i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.22335 | − | 3.22335i | −0.156540 | − | 0.156540i | ||||
\(425\) | −7.77785 | − | 4.49054i | −0.377281 | − | 0.217823i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.09758 | + | 5.73334i | 0.149903 | + | 0.277456i | ||||
\(428\) | 21.8928i | 1.05823i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.1786i | 0.828426i | ||||||||
\(431\) | −13.4572 | − | 3.60584i | −0.648209 | − | 0.173687i | −0.0802899 | − | 0.996772i | \(-0.525585\pi\) |
−0.567919 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.380141 | + | 0.658423i | −0.0182684 | + | 0.0316418i | −0.875015 | − | 0.484096i | \(-0.839149\pi\) |
0.856747 | + | 0.515737i | \(0.172482\pi\) | |||||||
\(434\) | 1.60371 | − | 56.7488i | 0.0769806 | − | 2.72403i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0607 | + | 2.69577i | −0.481822 | + | 0.129104i | ||||
\(437\) | 1.18410 | − | 1.18410i | 0.0566430 | − | 0.0566430i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9560 | + | 27.6366i | 0.761539 | + | 1.31902i | 0.942057 | + | 0.335453i | \(0.108889\pi\) |
−0.180518 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(440\) | 28.0187 | + | 7.50759i | 1.33574 | + | 0.357910i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 33.2832 | + | 12.0944i | 1.58312 | + | 0.575270i | ||||
\(443\) | −13.9082 | −0.660799 | −0.330399 | − | 0.943841i | \(-0.607183\pi\) | ||||
−0.330399 | + | 0.943841i | \(0.607183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.6841 | − | 35.8260i | −0.980522 | − | 1.69831i | ||||
\(446\) | 19.0052 | − | 32.9180i | 0.899923 | − | 1.55871i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.0769 | − | 29.3620i | 0.854052 | − | 1.38723i | ||||
\(449\) | −37.3413 | + | 10.0056i | −1.76224 | + | 0.472192i | −0.987169 | − | 0.159677i | \(-0.948955\pi\) |
−0.775075 | + | 0.631869i | \(0.782288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.13240 | + | 1.23114i | 0.100411 | + | 0.0579721i | ||||
\(452\) | −2.00008 | + | 1.15475i | −0.0940759 | + | 0.0543148i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 42.5150 | 1.99533 | ||||||||
\(455\) | 19.8512 | − | 15.7402i | 0.930639 | − | 0.737912i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2913 | − | 3.02549i | −0.528183 | − | 0.141526i | −0.0151341 | − | 0.999885i | \(-0.504818\pi\) |
−0.513049 | + | 0.858359i | \(0.671484\pi\) | |||||||
\(458\) | −0.498897 | + | 0.288038i | −0.0233119 | + | 0.0134591i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −47.4899 | − | 47.4899i | −2.21423 | − | 2.21423i | ||||
\(461\) | −33.0727 | + | 8.86180i | −1.54035 | + | 0.412735i | −0.926379 | − | 0.376594i | \(-0.877095\pi\) |
−0.613971 | + | 0.789329i | \(0.710429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.1263 | − | 18.1263i | −0.842399 | − | 0.842399i | 0.146772 | − | 0.989170i | \(-0.453112\pi\) |
−0.989170 | + | 0.146772i | \(0.953112\pi\) | |||||||
\(464\) | 4.34646 | − | 7.52830i | 0.201780 | − | 0.349492i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.61561 | + | 24.6898i | −0.306462 | + | 1.14373i | ||||
\(467\) | 20.4427 | 0.945975 | 0.472988 | − | 0.881069i | \(-0.343176\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.65040 | − | 2.80455i | −0.122384 | − | 0.129502i | ||||
\(470\) | −7.56238 | − | 2.02633i | −0.348826 | − | 0.0934678i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.94858 | − | 13.7673i | 0.365863 | − | 0.633694i | ||||
\(473\) | 9.52246 | − | 9.52246i | 0.437843 | − | 0.437843i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.106991 | − | 0.399295i | −0.00490907 | − | 0.0183209i | ||||
\(476\) | −35.1800 | − | 0.994179i | −1.61247 | − | 0.0455681i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 33.5967 | − | 19.3971i | 1.53668 | − | 0.887202i | ||||
\(479\) | 11.4241 | + | 3.06108i | 0.521980 | + | 0.139864i | 0.510182 | − | 0.860066i | \(-0.329578\pi\) |
0.0117979 | + | 0.999930i | \(0.496245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8394 | + | 2.97832i | −0.767810 | + | 0.135800i | ||||
\(482\) | 68.4591i | 3.11823i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.4942 | − | 28.5688i | −0.749736 | − | 1.29858i | ||||
\(485\) | −6.78430 | − | 3.91692i | −0.308059 | − | 0.177858i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.0483236 | + | 0.180346i | 0.00218975 | + | 0.00817226i | 0.967012 | − | 0.254731i | \(-0.0819868\pi\) |
−0.964822 | + | 0.262903i | \(0.915320\pi\) | |||||||
\(488\) | 1.48961 | + | 5.55931i | 0.0674316 | + | 0.251658i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.8772 | + | 34.9101i | −1.03348 | + | 1.57708i | ||||
\(491\) | 2.43785 | − | 1.40749i | 0.110019 | − | 0.0635193i | −0.443981 | − | 0.896036i | \(-0.646434\pi\) |
0.554000 | + | 0.832517i | \(0.313101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.5288 | −2.05052 | ||||||||
\(494\) | 0.689624 | + | 1.47689i | 0.0310276 | + | 0.0664482i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.06607 | + | 7.71067i | −0.0927691 | + | 0.346219i | ||||
\(497\) | −4.21043 | + | 14.1067i | −0.188864 | + | 0.632774i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.80207 | − | 1.80207i | 0.0806719 | − | 0.0806719i | −0.665619 | − | 0.746291i | \(-0.731833\pi\) |
0.746291 | + | 0.665619i | \(0.231833\pi\) | |||||||
\(500\) | 22.9875 | − | 6.15949i | 1.02803 | − | 0.275461i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.3417 | − | 17.3417i | 0.773999 | − | 0.773999i | ||||
\(503\) | −6.33177 | − | 3.65565i | −0.282320 | − | 0.162997i | 0.352153 | − | 0.935942i | \(-0.385450\pi\) |
−0.634473 | + | 0.772945i | \(0.718783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.435466 | − | 1.62518i | 0.0193780 | − | 0.0723196i | ||||
\(506\) | 87.2783i | 3.87999i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.65274 | −0.162064 | ||||||||
\(509\) | −6.75398 | + | 25.2062i | −0.299365 | + | 1.11724i | 0.638324 | + | 0.769768i | \(0.279628\pi\) |
−0.937689 | + | 0.347477i | \(0.887039\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.8518 | − | 7.57717i | 1.40904 | − | 0.335194i | ||||
\(512\) | −6.62788 | + | 6.62788i | −0.292914 | + | 0.292914i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.5071 | + | 61.6053i | 0.728097 | + | 2.71729i | ||||
\(515\) | 3.67535 | + | 3.67535i | 0.161955 | + | 0.161955i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.06875 | + | 5.31523i | 0.134963 | + | 0.233763i | ||||
\(518\) | 24.7872 | − | 13.3919i | 1.08909 | − | 0.588406i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 20.2737 | − | 9.46670i | 0.889061 | − | 0.415142i | ||||
\(521\) | 5.50223i | 0.241057i | 0.992710 | + | 0.120529i | \(0.0384589\pi\) | ||||
−0.992710 | + | 0.120529i | \(0.961541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.0507 | + | 20.2365i | −1.53266 | + | 0.884882i | −0.533423 | + | 0.845849i | \(0.679095\pi\) |
−0.999238 | + | 0.0390336i | \(0.987572\pi\) | |||||||
\(524\) | 4.61311 | − | 7.99014i | 0.201525 | − | 0.349051i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6189 | − | 47.0943i | −0.550209 | − | 2.05341i | ||||
\(527\) | 40.3843 | − | 10.8209i | 1.75917 | − | 0.471367i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0828 | − | 39.9806i | 1.00360 | − | 1.73829i | ||||
\(530\) | −5.81600 | − | 10.0736i | −0.252631 | − | 0.437569i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.11263 | − | 1.17735i | −0.0482387 | − | 0.0510444i | ||||
\(533\) | 1.87028 | − | 0.330790i | 0.0810110 | − | 0.0143281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.94882 | + | 18.4692i | −0.213956 | + | 0.798495i | ||||
\(536\) | −1.70402 | − | 2.95145i | −0.0736024 | − | 0.127483i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.6422 | − | 19.6422i | −0.846836 | − | 0.846836i | ||||
\(539\) | 32.0327 | − | 6.67012i | 1.37975 | − | 0.287302i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7367 | + | 25.7367i | 1.10651 | + | 1.10651i | 0.993606 | + | 0.112900i | \(0.0360139\pi\) |
0.112900 | + | 0.993606i | \(0.463986\pi\) | |||||||
\(542\) | −15.3881 | − | 8.88430i | −0.660974 | − | 0.381613i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27.6716 | + | 7.41457i | 1.18641 | + | 0.317897i | ||||
\(545\) | −9.09682 | −0.389665 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.3852 | 1.34193 | 0.670967 | − | 0.741487i | \(-0.265879\pi\) | ||||
0.670967 | + | 0.741487i | \(0.265879\pi\) | |||||||
\(548\) | 34.2977 | + | 9.19005i | 1.46513 | + | 0.392579i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.6588 | + | 10.7727i | 0.795616 | + | 0.459349i | ||||
\(551\) | −1.48181 | − | 1.48181i | −0.0631272 | − | 0.0631272i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0595 | − | 6.19321i | −0.427775 | − | 0.263362i | ||||
\(554\) | 17.7980 | + | 17.7980i | 0.756166 | + | 0.756166i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.1955 | + | 17.6592i | 0.432387 | + | 0.748916i | ||||
\(557\) | 0.169733 | − | 0.633453i | 0.00719183 | − | 0.0268403i | −0.962237 | − | 0.272214i | \(-0.912244\pi\) |
0.969429 | + | 0.245374i | \(0.0789107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.899944 | − | 10.3487i | 0.0380636 | − | 0.437705i | ||||
\(560\) | 4.26547 | − | 4.03101i | 0.180249 | − | 0.170341i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.1229 | + | 41.7821i | 1.01756 | + | 1.76247i | ||||
\(563\) | 12.5830 | − | 21.7944i | 0.530309 | − | 0.918523i | −0.469065 | − | 0.883164i | \(-0.655409\pi\) |
0.999375 | − | 0.0353593i | \(-0.0112576\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94834 | + | 0.522056i | −0.0819672 | + | 0.0219630i | ||||
\(566\) | 8.88777 | + | 33.1696i | 0.373581 | + | 1.39422i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.50104 | + | 11.2601i | −0.272778 | + | 0.472465i | ||||
\(569\) | 3.46005 | − | 1.99766i | 0.145053 | − | 0.0837463i | −0.425717 | − | 0.904856i | \(-0.639978\pi\) |
0.570770 | + | 0.821110i | \(0.306645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9370i | 0.750640i | 0.926895 | + | 0.375320i | \(0.122467\pi\) | ||||
−0.926895 | + | 0.375320i | \(0.877533\pi\) | |||||||
\(572\) | −48.1656 | − | 17.5023i | −2.01390 | − | 0.731808i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.75301 | + | 1.48739i | −0.114909 | + | 0.0620823i | ||||
\(575\) | −8.53705 | − | 14.7866i | −0.356020 | − | 0.616644i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6210 | + | 29.6210i | 1.23314 | + | 1.23314i | 0.962751 | + | 0.270389i | \(0.0871524\pi\) |
0.270389 | + | 0.962751i | \(0.412848\pi\) | |||||||
\(578\) | −1.24174 | − | 4.63424i | −0.0516496 | − | 0.192759i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −59.4302 | + | 59.4302i | −2.46770 | + | 2.46770i | ||||
\(581\) | 4.69497 | + | 19.7360i | 0.194780 | + | 0.818789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.36008 | + | 8.80794i | −0.0977446 | + | 0.364788i | ||||
\(584\) | 28.9163 | 1.19657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 47.1901i | − | 1.94941i | ||||||
\(587\) | 0.571868 | − | 2.13424i | 0.0236035 | − | 0.0880895i | −0.953119 | − | 0.302595i | \(-0.902147\pi\) |
0.976723 | + | 0.214505i | \(0.0688138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.66656 | + | 0.962187i | 0.0686693 | + | 0.0396462i | ||||
\(590\) | 28.6838 | − | 28.6838i | 1.18089 | − | 1.18089i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.82651 | + | 1.02531i | −0.157268 | + | 0.0421400i | ||||
\(593\) | −1.48928 | + | 1.48928i | −0.0611573 | + | 0.0611573i | −0.737024 | − | 0.675867i | \(-0.763770\pi\) |
0.675867 | + | 0.737024i | \(0.263770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.4538 | − | 8.79106i | −1.20749 | − | 0.360398i | ||||
\(596\) | −3.76850 | + | 14.0642i | −0.154364 | + | 0.576093i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 43.3015 | + | 51.5500i | 1.77073 | + | 2.10804i | ||||
\(599\) | −13.9002 | −0.567945 | −0.283973 | − | 0.958832i | \(-0.591653\pi\) | ||||
−0.283973 | + | 0.958832i | \(0.591653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.59776 | + | 4.96392i | −0.350710 | + | 0.202482i | −0.664998 | − | 0.746845i | \(-0.731568\pi\) |
0.314288 | + | 0.949328i | \(0.398234\pi\) | |||||||
\(602\) | 3.96067 | + | 16.6493i | 0.161425 | + | 0.678575i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.52892 | − | 31.8304i | −0.347037 | − | 1.29516i | ||||
\(605\) | −7.45694 | − | 27.8297i | −0.303168 | − | 1.13144i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.6015 | + | 15.3584i | 1.07972 | + | 0.623378i | 0.930821 | − | 0.365475i | \(-0.119093\pi\) |
0.148900 | + | 0.988852i | \(0.452427\pi\) | |||||||
\(608\) | 0.659297 | + | 1.14194i | 0.0267380 | + | 0.0463116i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.6862i | 0.594626i | ||||||||
\(611\) | 4.44958 | + | 1.61688i | 0.180011 | + | 0.0654119i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.42794 | + | 2.52621i | 0.380791 | + | 0.102033i | 0.444137 | − | 0.895959i | \(-0.353510\pi\) |
−0.0633459 | + | 0.997992i | \(0.520177\pi\) | |||||||
\(614\) | −35.1709 | + | 20.3059i | −1.41938 | + | 0.819480i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.8863 | + | 0.816322i | 1.16386 | + | 0.0328906i | ||||
\(617\) | −6.69956 | − | 25.0031i | −0.269714 | − | 1.00659i | −0.959301 | − | 0.282384i | \(-0.908875\pi\) |
0.689587 | − | 0.724203i | \(-0.257792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5525 | − | 25.5525i | 1.02704 | − | 1.02704i | 0.0274172 | − | 0.999624i | \(-0.491272\pi\) |
0.999624 | − | 0.0274172i | \(-0.00872826\pi\) | |||||||
\(620\) | 38.5899 | − | 66.8397i | 1.54981 | − | 2.68435i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.4011 | + | 11.3613i | 1.70013 | + | 0.455548i | ||||
\(623\) | −28.3068 | − | 29.9532i | −1.13409 | − | 1.20005i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0502 | 1.24201 | ||||||||
\(626\) | −7.69915 | + | 28.7336i | −0.307720 | + | 1.14843i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.1722 | + | 21.0829i | −0.485725 | + | 0.841300i | ||||
\(629\) | 14.6712 | + | 14.6712i | 0.584977 | + | 0.584977i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.92759 | − | 2.66009i | 0.395211 | − | 0.105897i | −0.0557396 | − | 0.998445i | \(-0.517752\pi\) |
0.450951 | + | 0.892549i | \(0.351085\pi\) | |||||||
\(632\) | −7.37744 | − | 7.37744i | −0.293459 | − | 0.293459i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −49.1823 | + | 28.3954i | −1.95328 | + | 1.12773i | ||||
\(635\) | −3.08153 | − | 0.825692i | −0.122287 | − | 0.0327666i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.6105 | − | 19.8321i | 0.618511 | − | 0.785776i | ||||
\(638\) | 109.222 | 4.32416 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37.1730 | − | 21.4618i | 1.46939 | − | 0.848353i | ||||
\(641\) | 26.2509 | + | 15.1559i | 1.03685 | + | 0.598624i | 0.918939 | − | 0.394401i | \(-0.129048\pi\) |
0.117908 | + | 0.993025i | \(0.462381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.0393 | − | 9.38876i | 1.38182 | − | 0.370256i | 0.510035 | − | 0.860153i | \(-0.329632\pi\) |
0.871780 | + | 0.489897i | \(0.162966\pi\) | |||||||
\(644\) | −56.9759 | − | 35.0775i | −2.24516 | − | 1.38225i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.988806 | − | 1.71266i | 0.0389041 | − | 0.0673838i | ||||
\(647\) | 9.62979 | + | 16.6793i | 0.378586 | + | 0.655730i | 0.990857 | − | 0.134918i | \(-0.0430771\pi\) |
−0.612271 | + | 0.790648i | \(0.709744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.8001 | −1.24826 | ||||||||
\(650\) | 16.3653 | − | 2.89447i | 0.641901 | − | 0.113531i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 55.8877 | + | 14.9751i | 2.18873 | + | 0.586468i | ||||
\(653\) | 0.0312823 | + | 0.0541825i | 0.00122417 | + | 0.00212033i | 0.866637 | − | 0.498939i | \(-0.166277\pi\) |
−0.865413 | + | 0.501060i | \(0.832944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.69787 | − | 5.69787i | 0.222634 | − | 0.222634i | ||||
\(656\) | 0.424995 | − | 0.113877i | 0.0165933 | − | 0.00444615i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.79655 | − | 0.220329i | −0.303941 | − | 0.00858932i | ||||
\(659\) | −3.09067 | + | 5.35320i | −0.120395 | + | 0.208531i | −0.919924 | − | 0.392098i | \(-0.871750\pi\) |
0.799528 | + | 0.600628i | \(0.205083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.90812 | − | 1.85103i | −0.268695 | − | 0.0719965i | 0.121956 | − | 0.992536i | \(-0.461083\pi\) |
−0.390651 | + | 0.920539i | \(0.627750\pi\) | |||||||
\(662\) | − | 30.5207i | − | 1.18622i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.9171i | 0.695320i | ||||||||
\(665\) | −0.672503 | − | 1.24474i | −0.0260786 | − | 0.0482690i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −74.9594 | − | 43.2778i | −2.90244 | − | 1.67572i | ||||
\(668\) | −23.4013 | − | 23.4013i | −0.905425 | − | 0.905425i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.25078 | − | 8.40001i | −0.0869551 | − | 0.324521i | ||||
\(671\) | 8.14087 | − | 8.14087i | 0.314275 | − | 0.314275i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.05354 | + | 2.34031i | −0.156253 | + | 0.0902125i | −0.576088 | − | 0.817388i | \(-0.695421\pi\) |
0.419835 | + | 0.907600i | \(0.362088\pi\) | |||||||
\(674\) | −1.02085 | + | 3.80987i | −0.0393217 | + | 0.146751i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.1319 | + | 13.5589i | −1.42815 | + | 0.521497i | ||||
\(677\) | − | 31.1590i | − | 1.19754i | −0.800922 | − | 0.598769i | \(-0.795657\pi\) | ||
0.800922 | − | 0.598769i | \(-0.204343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.47834 | − | 2.23205i | −0.286992 | − | 0.0856583i | ||||
\(680\) | −23.5103 | − | 13.5737i | −0.901579 | − | 0.520527i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −96.8808 | + | 25.9591i | −3.70976 | + | 0.994026i | ||||
\(683\) | −41.3109 | + | 11.0692i | −1.58072 | + | 0.423552i | −0.939148 | − | 0.343512i | \(-0.888383\pi\) |
−0.641570 | + | 0.767064i | \(0.721717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.8569 | + | 15.5058i | 1.02615 | + | 0.592447i | ||||
\(686\) | −14.1235 | + | 39.1090i | −0.539236 | + | 1.49319i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 2.40640i | − | 0.0917430i | ||||||
\(689\) | 2.97595 | + | 6.37323i | 0.113374 | + | 0.242801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.65384 | − | 17.3684i | 0.177040 | − | 0.660724i | −0.819155 | − | 0.573573i | \(-0.805557\pi\) |
0.996195 | − | 0.0871512i | \(-0.0277763\pi\) | |||||||
\(692\) | −21.4507 | + | 12.3845i | −0.815432 | + | 0.470790i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.2703 | + | 17.2703i | −0.655570 | + | 0.655570i | ||||
\(695\) | 4.60935 | + | 17.2023i | 0.174843 | + | 0.652521i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.62947 | − | 1.62947i | −0.0617205 | − | 0.0617205i | ||||
\(698\) | −24.0447 | − | 13.8822i | −0.910106 | − | 0.525450i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.5315 | + | 7.85104i | −0.549241 | + | 0.296741i | ||||
\(701\) | − | 34.0110i | − | 1.28458i | −0.766462 | − | 0.642290i | \(-0.777985\pi\) | ||
0.766462 | − | 0.642290i | \(-0.222015\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.954993i | 0.0360182i | ||||||||
\(704\) | −58.8411 | − | 15.7664i | −2.21766 | − | 0.594219i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.7658 | + | 34.2354i | −0.743897 | + | 1.28847i | ||||
\(707\) | 0.0473495 | − | 1.67551i | 0.00178076 | − | 0.0630139i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.70932 | + | 0.725960i | −0.101751 | + | 0.0272640i | −0.309335 | − | 0.950953i | \(-0.600106\pi\) |
0.207584 | + | 0.978217i | \(0.433440\pi\) | |||||||
\(710\) | −23.4601 | + | 23.4601i | −0.880441 | + | 0.880441i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.1993 | − | 31.5221i | −0.682047 | − | 1.18134i | ||||
\(713\) | 76.7753 | + | 20.5719i | 2.87526 | + | 0.770423i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.6771 | − | 25.6530i | −1.37165 | − | 0.959369i | ||||
\(716\) | −35.9336 | −1.34290 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.2560 | − | 31.6203i | −0.681308 | − | 1.18006i | ||||
\(719\) | 10.7719 | − | 18.6575i | 0.401725 | − | 0.695809i | −0.592209 | − | 0.805784i | \(-0.701744\pi\) |
0.993934 | + | 0.109976i | \(0.0350773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.40949 | + | 2.71472i | 0.164218 | + | 0.101102i | ||||
\(722\) | −41.1167 | + | 11.0172i | −1.53021 | + | 0.410017i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.6493 | − | 15.9633i | −1.02758 | − | 0.593272i | ||||
\(725\) | −18.5044 | + | 10.6835i | −0.687235 | + | 0.396775i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2656 | 0.937048 | 0.468524 | − | 0.883451i | \(-0.344786\pi\) | ||||
0.468524 | + | 0.883451i | \(0.344786\pi\) | |||||||
\(728\) | 17.4664 | − | 13.8493i | 0.647348 | − | 0.513289i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 71.2720 | + | 19.0973i | 2.63789 | + | 0.706822i | ||||
\(731\) | −10.9149 | + | 6.30170i | −0.403701 | + | 0.233077i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8545 | − | 22.8545i | −0.844152 | − | 0.844152i | 0.145244 | − | 0.989396i | \(-0.453603\pi\) |
−0.989396 | + | 0.145244i | \(0.953603\pi\) | |||||||
\(734\) | −28.5184 | + | 7.64147i | −1.05263 | + | 0.282052i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.5109 | + | 38.5109i | 1.41953 | + | 1.41953i | ||||
\(737\) | −3.40865 | + | 5.90396i | −0.125559 | + | 0.217475i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.35655 | − | 12.5268i | 0.123473 | − | 0.460806i | −0.876308 | − | 0.481751i | \(-0.840001\pi\) |
0.999781 | + | 0.0209450i | \(0.00666750\pi\) | |||||||
\(740\) | 38.3014 | 1.40799 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.95935 | − | 8.42229i | −0.292197 | − | 0.309192i | ||||
\(743\) | −31.0606 | − | 8.32266i | −1.13950 | − | 0.305329i | −0.360751 | − | 0.932662i | \(-0.617480\pi\) |
−0.778751 | + | 0.627333i | \(0.784146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.35837 | + | 11.0130i | −0.232953 | + | 0.403486i | ||||
\(746\) | 15.2893 | − | 15.2893i | 0.559782 | − | 0.559782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0927 | + | 60.0587i | 0.588407 | + | 2.19596i | ||||
\(749\) | −0.538099 | + | 19.0412i | −0.0196617 | + | 0.695749i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1305 | + | 7.58091i | −0.479140 | + | 0.276631i | −0.720058 | − | 0.693914i | \(-0.755885\pi\) |
0.240918 | + | 0.970545i | \(0.422551\pi\) | |||||||
\(752\) | 1.05935 | + | 0.283851i | 0.0386304 | + | 0.0103510i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 64.5111 | − | 54.1887i | 2.34935 | − | 1.97344i | ||||
\(755\) | − | 28.7807i | − | 1.04744i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8529 | − | 30.9221i | −0.648875 | − | 1.12388i | −0.983392 | − | 0.181494i | \(-0.941907\pi\) |
0.334517 | − | 0.942390i | \(-0.391427\pi\) | |||||||
\(758\) | −64.7200 | − | 37.3661i | −2.35074 | − | 1.35720i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.323404 | − | 1.20696i | −0.0117311 | − | 0.0437810i | ||||
\(761\) | 0.802382 | + | 2.99453i | 0.0290863 | + | 0.108552i | 0.978943 | − | 0.204134i | \(-0.0654379\pi\) |
−0.949857 | + | 0.312686i | \(0.898771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.81653 | + | 2.09735i | −0.319180 | + | 0.0759291i | ||||
\(764\) | 35.1538 | − | 20.2961i | 1.27182 | − | 0.734286i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.67503 | 0.313442 | ||||||||
\(767\) | −18.7824 | + | 15.7770i | −0.678192 | + | 0.569675i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.07284 | − | 30.1282i | 0.291114 | − | 1.08645i | −0.653141 | − | 0.757237i | \(-0.726549\pi\) |
0.944255 | − | 0.329216i | \(-0.106784\pi\) | |||||||
\(770\) | 70.6589 | + | 21.0895i | 2.54637 | + | 0.760013i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.3447 | + | 17.3447i | −0.624251 | + | 0.624251i | ||||
\(773\) | −5.18000 | + | 1.38798i | −0.186312 | + | 0.0499220i | −0.350768 | − | 0.936462i | \(-0.614080\pi\) |
0.164457 | + | 0.986384i | \(0.447413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8743 | − | 13.8743i | 0.498379 | − | 0.498379i | ||||
\(776\) | −5.96928 | − | 3.44636i | −0.214284 | − | 0.123717i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.31105 | + | 27.2852i | −0.262114 | + | 0.978222i | ||||
\(779\) | − | 0.106067i | − | 0.00380026i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.0089 | 0.930670 | ||||||||
\(782\) | 21.1410 | − | 78.8993i | 0.756001 | − | 2.82143i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.20466 | − | 4.89024i | 0.114452 | − | 0.174652i | ||||
\(785\) | −15.0345 | + | 15.0345i | −0.536604 | + | 0.536604i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.63938 | − | 13.5824i | −0.129730 | − | 0.484159i | 0.870234 | − | 0.492638i | \(-0.163967\pi\) |
−0.999964 | + | 0.00847973i | \(0.997301\pi\) | |||||||
\(788\) | 27.2973 | + | 27.2973i | 0.972426 | + | 0.972426i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.3114 | − | 23.0560i | −0.473597 | − | 0.820294i | ||||
\(791\) | −1.76794 | + | 0.955176i | −0.0628608 | + | 0.0339621i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.769372 | − | 8.84726i | 0.0273212 | − | 0.314175i | ||||
\(794\) | − | 59.6088i | − | 2.11544i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 57.0740 | − | 32.9517i | 2.02294 | − | 1.16794i | ||||
\(797\) | −14.0098 | + | 24.2657i | −0.496252 | + | 0.859534i | −0.999991 | − | 0.00432247i | \(-0.998624\pi\) |
0.503739 | + | 0.863856i | \(0.331957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.48666 | − | 5.54828i | −0.0525941 | − | 0.196284i | ||||
\(800\) | 12.9865 | − | 3.47971i | 0.459141 | − | 0.123026i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.8947 | − | 29.2625i | 0.596573 | − | 1.03330i | ||||
\(803\) | −28.9216 | − | 50.0936i | −1.02062 | − | 1.76776i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.1369 | − | 42.4713i | −1.41464 | − | 1.49692i | ||||
\(806\) | −44.3424 | + | 63.3981i | −1.56190 | + | 2.23310i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.383152 | − | 1.42994i | 0.0134792 | − | 0.0503052i | ||||
\(809\) | −22.8429 | − | 39.5651i | −0.803115 | − | 1.39104i | −0.917556 | − | 0.397606i | \(-0.869841\pi\) |
0.114441 | − | 0.993430i | \(-0.463492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.85623 | − | 7.85623i | −0.275870 | − | 0.275870i | 0.555588 | − | 0.831458i | \(-0.312493\pi\) |
−0.831458 | + | 0.555588i | \(0.812493\pi\) | |||||||
\(812\) | −43.8969 | + | 71.3012i | −1.54048 | + | 2.50218i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.1957 | − | 35.1957i | −1.23361 | − | 1.23361i | ||||
\(815\) | 43.7629 | + | 25.2665i | 1.53295 | + | 0.885048i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.560341 | − | 0.150143i | −0.0196038 | − | 0.00525284i | ||||
\(818\) | 55.7777 | 1.95022 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.25399 | −0.148556 | ||||||||
\(821\) | −25.7120 | − | 6.88952i | −0.897356 | − | 0.240446i | −0.219476 | − | 0.975618i | \(-0.570435\pi\) |
−0.677881 | + | 0.735172i | \(0.737101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5488 | + | 22.2561i | 1.34373 | + | 0.775800i | 0.987352 | − | 0.158543i | \(-0.0506798\pi\) |
0.356373 | + | 0.934344i | \(0.384013\pi\) | |||||||
\(824\) | 3.23382 | + | 3.23382i | 0.112655 | + | 0.112655i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.1867 | − | 34.4133i | 0.737179 | − | 1.19739i | ||||
\(827\) | 10.7544 | + | 10.7544i | 0.373966 | + | 0.373966i | 0.868920 | − | 0.494953i | \(-0.164815\pi\) |
−0.494953 | + | 0.868920i | \(0.664815\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.8384 | − | 39.5572i | −0.793209 | − | 1.37388i | −0.923970 | − | 0.382464i | \(-0.875076\pi\) |
0.130761 | − | 0.991414i | \(-0.458258\pi\) | |||||||
\(830\) | −11.8330 | + | 44.1615i | −0.410731 | + | 1.53287i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −42.5761 | + | 19.8807i | −1.47606 | + | 0.689238i | ||||
\(833\) | −30.5732 | − | 1.72936i | −1.05930 | − | 0.0599189i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4521 | − | 25.0317i | −0.500134 | − | 0.866257i | ||||
\(836\) | −1.43095 | + | 2.47847i | −0.0494903 | + | 0.0857197i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −38.8869 | + | 10.4197i | −1.34332 | + | 0.359943i | ||||
\(839\) | 0.546041 | + | 2.03785i | 0.0188514 | + | 0.0703546i | 0.974711 | − | 0.223470i | \(-0.0717385\pi\) |
−0.955859 | + | 0.293825i | \(0.905072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.6591 | + | 68.6916i | −1.36755 | + | 2.36867i | ||||
\(842\) | 2.29278 | − | 1.32374i | 0.0790144 | − | 0.0456190i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 39.5856i | 1.36259i | ||||||||
\(845\) | −34.3902 | + | 3.04501i | −1.18306 | + | 0.104751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6435 | − | 25.2529i | −0.468798 | − | 0.867701i | ||||
\(848\) | 0.814711 | + | 1.41112i | 0.0279773 | + | 0.0484581i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.2581 | − | 14.2581i | −0.489050 | − | 0.489050i | ||||
\(851\) | 10.2090 | + | 38.1006i | 0.349961 | + | 1.30607i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.7998 | − | 31.7998i | 1.08881 | − | 1.08881i | 0.0931541 | − | 0.995652i | \(-0.470305\pi\) |
0.995652 | − | 0.0931541i | \(-0.0296949\pi\) | |||||||
\(854\) | 3.38602 | + | 14.2337i | 0.115867 | + | 0.487066i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.35430 | + | 16.2505i | −0.148827 | + | 0.555429i | ||||
\(857\) | 0.314991 | 0.0107599 | 0.00537994 | − | 0.999986i | \(-0.498288\pi\) | ||||
0.00537994 | + | 0.999986i | \(0.498288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6151i | 0.396303i | 0.980171 | + | 0.198151i | \(0.0634938\pi\) | ||||
−0.980171 | + | 0.198151i | \(0.936506\pi\) | |||||||
\(860\) | −6.02170 | + | 22.4733i | −0.205338 | + | 0.766333i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.0887 | − | 15.6397i | −0.922646 | − | 0.532690i | ||||
\(863\) | 10.5474 | − | 10.5474i | 0.359038 | − | 0.359038i | −0.504420 | − | 0.863458i | \(-0.668294\pi\) |
0.863458 | + | 0.504420i | \(0.168294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.8957 | + | 5.59899i | −0.710476 | + | 0.190371i | ||||
\(866\) | −1.20700 | + | 1.20700i | −0.0410156 | + | 0.0410156i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.9905 | − | 73.6775i | 0.746405 | − | 2.50078i | ||||
\(869\) | −5.40164 | + | 20.1592i | −0.183238 | + | 0.683853i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.915858 | + | 5.17825i | 0.0310327 | + | 0.175458i | ||||
\(872\) | −8.00399 | −0.271049 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.25597 | − | 1.87984i | 0.110135 | − | 0.0635865i | ||||
\(875\) | 20.1447 | − | 4.79218i | 0.681015 | − | 0.162005i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5647 | + | 50.6241i | 0.458047 | + | 1.70945i | 0.678972 | + | 0.734164i | \(0.262426\pi\) |
−0.220925 | + | 0.975291i | \(0.570908\pi\) | |||||||
\(878\) | 18.5438 | + | 69.2065i | 0.625824 | + | 2.33561i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.97938 | − | 5.18425i | −0.302695 | − | 0.174761i | ||||
\(881\) | 2.13878 | + | 3.70447i | 0.0720572 | + | 0.124807i | 0.899803 | − | 0.436297i | \(-0.143710\pi\) |
−0.827746 | + | 0.561104i | \(0.810377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.8768i | − | 1.14004i | −0.821630 | − | 0.570022i | \(-0.806935\pi\) | ||
0.821630 | − | 0.570022i | \(-0.193065\pi\) | |||||||
\(884\) | 39.3020 | + | 27.4890i | 1.32187 | + | 0.924554i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.1622 | − | 8.08195i | −1.01332 | − | 0.271518i | ||||
\(887\) | −3.88879 | + | 2.24520i | −0.130573 | + | 0.0753863i | −0.563864 | − | 0.825868i | \(-0.690686\pi\) |
0.433291 | + | 0.901254i | \(0.357352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.17695 | − | 0.0897799i | −0.106551 | − | 0.00301112i | ||||
\(890\) | −24.0388 | − | 89.7139i | −0.805781 | − | 3.00722i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.4018 | − | 36.4018i | 1.21882 | − | 1.21882i | ||||
\(893\) | 0.132192 | − | 0.228963i | 0.00442364 | − | 0.00766197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.3143 | − | 8.12270i | −1.01330 | − | 0.271512i | ||||
\(896\) | 31.0794 | − | 29.3711i | 1.03829 | − | 0.981219i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −86.7949 | −2.89638 | ||||||||
\(899\) | 25.7442 | − | 96.0787i | 0.858617 | − | 3.20440i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.26701 | − | 7.39069i | 0.142155 | − | 0.246219i | ||||
\(902\) | 3.90905 | + | 3.90905i | 0.130157 | + | 0.130157i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.71428 | + | 0.459339i | −0.0570160 | + | 0.0152774i | ||||
\(905\) | −19.7171 | − | 19.7171i | −0.655417 | − | 0.655417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.2542 | − | 7.65232i | 0.440099 | − | 0.254091i | −0.263541 | − | 0.964648i | \(-0.584890\pi\) |
0.703640 | + | 0.710557i | \(0.251557\pi\) | |||||||
\(908\) | 55.6187 | + | 14.9030i | 1.84577 | + | 0.494573i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 52.1971 | − | 22.5999i | 1.73032 | − | 0.749178i | ||||
\(911\) | −15.6790 | −0.519470 | −0.259735 | − | 0.965680i | \(-0.583635\pi\) | ||||
−0.259735 | + | 0.965680i | \(0.583635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.0390 | − | 17.9204i | 1.02724 | − | 0.593077i | ||||
\(914\) | −22.7289 | − | 13.1225i | −0.751805 | − | 0.434055i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.753632 | + | 0.201935i | −0.0249007 | + | 0.00667212i | ||||
\(917\) | 4.20861 | − | 6.83600i | 0.138981 | − | 0.225744i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.1402 | + | 45.2762i | −0.862287 | + | 1.49352i | 0.00742976 | + | 0.999972i | \(0.497635\pi\) |
−0.869716 | + | 0.493552i | \(0.835698\pi\) | |||||||
\(920\) | −25.8052 | − | 44.6959i | −0.850771 | − | 1.47358i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −76.8731 | −2.53168 | ||||||||
\(923\) | 15.3619 | − | 12.9038i | 0.505641 | − | 0.424734i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.40546 | + | 2.52019i | 0.309250 | + | 0.0828632i | ||||
\(926\) | −28.7768 | − | 49.8428i | −0.945663 | − | 1.63794i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 48.1936 | − | 48.1936i | 1.58203 | − | 1.58203i | ||||
\(929\) | 19.0687 | − | 5.10945i | 0.625625 | − | 0.167636i | 0.0679414 | − | 0.997689i | \(-0.478357\pi\) |
0.557684 | + | 0.830054i | \(0.311690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.938768 | − | 1.05134i | −0.0307669 | − | 0.0344562i | ||||
\(932\) | −17.3093 | + | 29.9806i | −0.566984 | + | 0.982046i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44.3333 | + | 11.8791i | 1.45063 | + | 0.388696i | ||||
\(935\) | 54.3045i | 1.77595i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.0301i | − | 1.04638i | −0.852217 | − | 0.523189i | \(-0.824742\pi\) | ||
0.852217 | − | 0.523189i | \(-0.175258\pi\) | |||||||
\(938\) | −4.11812 | − | 7.62226i | −0.134461 | − | 0.248875i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.18291 | − | 5.30176i | −0.299514 | − | 0.172924i | ||||
\(941\) | −16.4141 | − | 16.4141i | −0.535083 | − | 0.535083i | 0.386998 | − | 0.922081i | \(-0.373512\pi\) |
−0.922081 | + | 0.386998i | \(0.873512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.13388 | − | 4.23169i | −0.0369241 | − | 0.137803i | ||||
\(944\) | −4.01805 | + | 4.01805i | −0.130777 | + | 0.130777i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.1845 | − | 15.1176i | 0.851330 | − | 0.491516i | ||||
\(947\) | 11.1001 | − | 41.4261i | 0.360704 | − | 1.34617i | −0.512447 | − | 0.858719i | \(-0.671261\pi\) |
0.873152 | − | 0.487449i | \(-0.162072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.9352 | − | 15.2383i | −1.36128 | − | 0.494658i | ||||
\(950\) | − | 0.928107i | − | 0.0301118i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.9154 | − | 7.73496i | −0.839924 | − | 0.250691i | ||||
\(953\) | 10.3745 | + | 5.98973i | 0.336064 | + | 0.194026i | 0.658530 | − | 0.752554i | \(-0.271179\pi\) |
−0.322466 | + | 0.946581i | \(0.604512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.2444 | − | 9.17575i | 1.10812 | − | 0.296920i | ||||
\(956\) | 50.7511 | − | 13.5987i | 1.64141 | − | 0.439814i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.9963 | + | 13.2769i | 0.742976 | + | 0.428957i | ||||
\(959\) | 29.6044 | + | 8.83599i | 0.955975 | + | 0.285329i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.3409i | 1.94648i | ||||||||
\(962\) | −38.2497 | − | 3.32625i | −1.23322 | − | 0.107243i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.9973 | + | 89.5592i | −0.772902 | + | 2.88451i | ||||
\(965\) | −18.5531 | + | 10.7117i | −0.597246 | + | 0.344820i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.08553 | − | 3.08553i | 0.0992241 | − | 0.0992241i | −0.655752 | − | 0.754976i | \(-0.727648\pi\) |
0.754976 | + | 0.655752i | \(0.227648\pi\) | |||||||
\(968\) | −6.56111 | − | 24.4864i | −0.210882 | − | 0.787023i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.4368 | − | 12.4368i | −0.399321 | − | 0.399321i | ||||
\(971\) | 25.8972 | + | 14.9518i | 0.831081 | + | 0.479825i | 0.854223 | − | 0.519907i | \(-0.174033\pi\) |
−0.0231414 | + | 0.999732i | \(0.507367\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.43346 | + | 15.6096i | 0.270364 | + | 0.500420i | ||||
\(974\) | 0.419190i | 0.0134317i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 2.05726i | − | 0.0658512i | ||||||
\(977\) | 9.78075 | + | 2.62074i | 0.312914 | + | 0.0838450i | 0.411858 | − | 0.911248i | \(-0.364880\pi\) |
−0.0989443 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.4051 | + | 63.0555i | −1.16351 | + | 2.01526i | ||||
\(980\) | −42.1655 | + | 37.6507i | −1.34693 | + | 1.20271i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.10476 | − | 1.63577i | 0.194811 | − | 0.0521994i | ||||
\(983\) | −5.97019 | + | 5.97019i | −0.190419 | + | 0.190419i | −0.795877 | − | 0.605458i | \(-0.792990\pi\) |
0.605458 | + | 0.795877i | \(0.292990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8581 | + | 29.1991i | 0.537144 | + | 0.930360i | ||||
\(986\) | −98.7368 | − | 26.4564i | −3.14442 | − | 0.842545i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.384476 | + | 2.17382i | 0.0122318 | + | 0.0691585i | ||||
\(989\) | −23.9605 | −0.761901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.8012 | − | 48.1532i | −0.883136 | − | 1.52964i | −0.847836 | − | 0.530259i | \(-0.822095\pi\) |
−0.0353002 | − | 0.999377i | \(-0.511239\pi\) | |||||||
\(992\) | −31.2937 | + | 54.2023i | −0.993576 | + | 1.72092i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.3283 | + | 28.1462i | −0.549621 | + | 0.892742i | ||||
\(995\) | 55.5975 | − | 14.8973i | 1.76256 | − | 0.472277i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.66852 | − | 5.58213i | −0.306205 | − | 0.176788i | 0.339022 | − | 0.940778i | \(-0.389904\pi\) |
−0.645227 | + | 0.763991i | \(0.723237\pi\) | |||||||
\(998\) | 4.95526 | − | 2.86092i | 0.156856 | − | 0.0905609i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.fm.f.496.8 | 32 | ||
3.2 | odd | 2 | 273.2.by.c.223.1 | yes | 32 | ||
7.6 | odd | 2 | 819.2.fm.e.496.8 | 32 | |||
13.7 | odd | 12 | 819.2.fm.e.748.8 | 32 | |||
21.20 | even | 2 | 273.2.by.d.223.1 | yes | 32 | ||
39.20 | even | 12 | 273.2.by.d.202.1 | yes | 32 | ||
91.20 | even | 12 | inner | 819.2.fm.f.748.8 | 32 | ||
273.20 | odd | 12 | 273.2.by.c.202.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.by.c.202.1 | ✓ | 32 | 273.20 | odd | 12 | ||
273.2.by.c.223.1 | yes | 32 | 3.2 | odd | 2 | ||
273.2.by.d.202.1 | yes | 32 | 39.20 | even | 12 | ||
273.2.by.d.223.1 | yes | 32 | 21.20 | even | 2 | ||
819.2.fm.e.496.8 | 32 | 7.6 | odd | 2 | |||
819.2.fm.e.748.8 | 32 | 13.7 | odd | 12 | |||
819.2.fm.f.496.8 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fm.f.748.8 | 32 | 91.20 | even | 12 | inner |