Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,3,Mod(7,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.f (of order \(20\), 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: | \(6.81200660901\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(-1.64599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.143 |
Dual form | 250.3.f.a.7.2 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26007 | + | 0.642040i | 0.630037 | + | 0.321020i | ||||
\(3\) | 3.59668 | + | 0.569657i | 1.19889 | + | 0.189886i | 0.723774 | − | 0.690037i | \(-0.242406\pi\) |
0.475117 | + | 0.879922i | \(0.342406\pi\) | |||||||
\(4\) | 1.17557 | + | 1.61803i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.16633 | + | 3.02702i | 0.694389 | + | 0.504503i | ||||
\(7\) | 0.635779 | − | 0.635779i | 0.0908256 | − | 0.0908256i | −0.660234 | − | 0.751060i | \(-0.729543\pi\) |
0.751060 | + | 0.660234i | \(0.229543\pi\) | |||||||
\(8\) | 0.442463 | + | 2.79360i | 0.0553079 | + | 0.349201i | ||||
\(9\) | 4.05206 | + | 1.31659i | 0.450229 | + | 0.146288i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24327 | + | 13.0594i | 0.385751 | + | 1.18722i | 0.935934 | + | 0.352176i | \(0.114558\pi\) |
−0.550182 | + | 0.835045i | \(0.685442\pi\) | |||||||
\(12\) | 3.30642 | + | 6.48922i | 0.275535 | + | 0.540768i | ||||
\(13\) | 8.13219 | − | 4.14356i | 0.625553 | − | 0.318735i | −0.112323 | − | 0.993672i | \(-0.535829\pi\) |
0.737876 | + | 0.674936i | \(0.235829\pi\) | |||||||
\(14\) | 1.20932 | − | 0.392933i | 0.0863803 | − | 0.0280667i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.23607 | + | 3.80423i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −5.81218 | + | 0.920559i | −0.341893 | + | 0.0541505i | −0.325020 | − | 0.945707i | \(-0.605371\pi\) |
−0.0168729 | + | 0.999858i | \(0.505371\pi\) | |||||||
\(18\) | 4.26058 | + | 4.26058i | 0.236699 | + | 0.236699i | ||||
\(19\) | 18.5227 | − | 25.4943i | 0.974878 | − | 1.34180i | 0.0353349 | − | 0.999376i | \(-0.488750\pi\) |
0.939544 | − | 0.342429i | \(-0.111250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.64887 | − | 1.92451i | 0.126137 | − | 0.0916436i | ||||
\(22\) | −3.03784 | + | 19.1802i | −0.138084 | + | 0.871827i | ||||
\(23\) | −14.0070 | + | 27.4902i | −0.608999 | + | 1.19523i | 0.356372 | + | 0.934344i | \(0.384014\pi\) |
−0.965370 | + | 0.260883i | \(0.915986\pi\) | |||||||
\(24\) | 10.2997i | 0.429156i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.9075 | 0.496442 | ||||||||
\(27\) | −15.3775 | − | 7.83525i | −0.569539 | − | 0.290194i | ||||
\(28\) | 1.77612 | + | 0.281309i | 0.0634327 | + | 0.0100468i | ||||
\(29\) | −33.4337 | − | 46.0176i | −1.15289 | − | 1.58681i | −0.734604 | − | 0.678496i | \(-0.762632\pi\) |
−0.418282 | − | 0.908317i | \(-0.637368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.57058 | − | 1.14109i | −0.0506637 | − | 0.0368093i | 0.562165 | − | 0.827025i | \(-0.309969\pi\) |
−0.612829 | + | 0.790216i | \(0.709969\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 7.82225 | + | 49.3877i | 0.237038 | + | 1.49660i | ||||
\(34\) | −7.91481 | − | 2.57168i | −0.232788 | − | 0.0756376i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.63319 | + | 8.10411i | 0.0731441 | + | 0.225114i | ||||
\(37\) | 5.33922 | + | 10.4788i | 0.144303 | + | 0.283211i | 0.951834 | − | 0.306615i | \(-0.0991964\pi\) |
−0.807530 | + | 0.589826i | \(0.799196\pi\) | |||||||
\(38\) | 39.7083 | − | 20.2324i | 1.04496 | − | 0.532431i | ||||
\(39\) | 31.6093 | − | 10.2705i | 0.810494 | − | 0.263345i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.6793 | − | 63.6443i | 0.504373 | − | 1.55230i | −0.297449 | − | 0.954738i | \(-0.596136\pi\) |
0.801822 | − | 0.597563i | \(-0.203864\pi\) | |||||||
\(42\) | 4.57338 | − | 0.724353i | 0.108890 | − | 0.0172465i | ||||
\(43\) | −38.8107 | − | 38.8107i | −0.902573 | − | 0.902573i | 0.0930849 | − | 0.995658i | \(-0.470327\pi\) |
−0.995658 | + | 0.0930849i | \(0.970327\pi\) | |||||||
\(44\) | −16.1423 | + | 22.2180i | −0.366871 | + | 0.504955i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −35.2996 | + | 25.6467i | −0.767383 | + | 0.557537i | ||||
\(47\) | −7.80337 | + | 49.2685i | −0.166029 | + | 1.04827i | 0.754131 | + | 0.656724i | \(0.228058\pi\) |
−0.920160 | + | 0.391542i | \(0.871942\pi\) | |||||||
\(48\) | −6.61284 | + | 12.9784i | −0.137768 | + | 0.270384i | ||||
\(49\) | 48.1916i | 0.983501i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.4289 | −0.420175 | ||||||||
\(52\) | 16.2644 | + | 8.28712i | 0.312777 | + | 0.159368i | ||||
\(53\) | −35.9841 | − | 5.69932i | −0.678945 | − | 0.107534i | −0.192568 | − | 0.981284i | \(-0.561682\pi\) |
−0.486377 | + | 0.873749i | \(0.661682\pi\) | |||||||
\(54\) | −14.3463 | − | 19.7460i | −0.265672 | − | 0.365666i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.05742 | + | 1.49481i | 0.0367397 | + | 0.0266930i | ||||
\(57\) | 81.1431 | − | 81.1431i | 1.42356 | − | 1.42356i | ||||
\(58\) | −12.5838 | − | 79.4513i | −0.216963 | − | 1.36985i | ||||
\(59\) | 57.8198 | + | 18.7868i | 0.979997 | + | 0.318420i | 0.754845 | − | 0.655904i | \(-0.227712\pi\) |
0.225152 | + | 0.974324i | \(0.427712\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.37780 | + | 13.4735i | 0.0717672 | + | 0.220877i | 0.980506 | − | 0.196488i | \(-0.0629537\pi\) |
−0.908739 | + | 0.417365i | \(0.862954\pi\) | |||||||
\(62\) | −1.24642 | − | 2.44623i | −0.0201035 | − | 0.0394553i | ||||
\(63\) | 3.41328 | − | 1.73915i | 0.0541790 | − | 0.0276056i | ||||
\(64\) | −7.60845 | + | 2.47214i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −21.8523 | + | 67.2544i | −0.331095 | + | 1.01901i | ||||
\(67\) | −63.8194 | + | 10.1080i | −0.952528 | + | 0.150866i | −0.613310 | − | 0.789842i | \(-0.710162\pi\) |
−0.339218 | + | 0.940708i | \(0.610162\pi\) | |||||||
\(68\) | −8.32212 | − | 8.32212i | −0.122384 | − | 0.122384i | ||||
\(69\) | −66.0385 | + | 90.8943i | −0.957080 | + | 1.31731i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 25.4392 | − | 18.4826i | 0.358298 | − | 0.260319i | −0.394044 | − | 0.919092i | \(-0.628924\pi\) |
0.752342 | + | 0.658773i | \(0.228924\pi\) | |||||||
\(72\) | −1.88515 | + | 11.9024i | −0.0261827 | + | 0.165311i | ||||
\(73\) | 31.4489 | − | 61.7220i | 0.430807 | − | 0.845506i | −0.568926 | − | 0.822389i | \(-0.692641\pi\) |
0.999733 | − | 0.0231175i | \(-0.00735918\pi\) | |||||||
\(74\) | 16.6321i | 0.224757i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 63.0254 | 0.829281 | ||||||||
\(77\) | 11.0007 | + | 5.60513i | 0.142866 | + | 0.0727939i | ||||
\(78\) | 46.4241 | + | 7.35285i | 0.595180 | + | 0.0942673i | ||||
\(79\) | −33.4082 | − | 45.9825i | −0.422889 | − | 0.582057i | 0.543414 | − | 0.839465i | \(-0.317132\pi\) |
−0.966303 | + | 0.257408i | \(0.917132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −81.8666 | − | 59.4796i | −1.01070 | − | 0.734316i | ||||
\(82\) | 66.9196 | − | 66.9196i | 0.816093 | − | 0.816093i | ||||
\(83\) | 6.33607 | + | 40.0044i | 0.0763382 | + | 0.481981i | 0.996006 | + | 0.0892838i | \(0.0284578\pi\) |
−0.919668 | + | 0.392697i | \(0.871542\pi\) | |||||||
\(84\) | 6.22786 | + | 2.02355i | 0.0741412 | + | 0.0240899i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23.9863 | − | 73.8222i | −0.278910 | − | 0.858398i | ||||
\(87\) | −94.0360 | − | 184.556i | −1.08087 | − | 2.12133i | ||||
\(88\) | −34.6054 | + | 17.6323i | −0.393243 | + | 0.200367i | ||||
\(89\) | 57.1826 | − | 18.5798i | 0.642501 | − | 0.208761i | 0.0303965 | − | 0.999538i | \(-0.490323\pi\) |
0.612105 | + | 0.790777i | \(0.290323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.53589 | − | 7.80467i | 0.0278669 | − | 0.0857656i | ||||
\(92\) | −60.9463 | + | 9.65295i | −0.662460 | + | 0.104923i | ||||
\(93\) | −4.99882 | − | 4.99882i | −0.0537507 | − | 0.0537507i | ||||
\(94\) | −41.4652 | + | 57.0719i | −0.441119 | + | 0.607148i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.6653 | + | 12.1081i | −0.173597 | + | 0.126126i | ||||
\(97\) | 1.94856 | − | 12.3027i | 0.0200882 | − | 0.126832i | −0.975606 | − | 0.219528i | \(-0.929548\pi\) |
0.995694 | + | 0.0926957i | \(0.0295484\pi\) | |||||||
\(98\) | −30.9409 | + | 60.7249i | −0.315723 | + | 0.619642i | ||||
\(99\) | 58.5042i | 0.590952i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −66.0665 | −0.654124 | −0.327062 | − | 0.945003i | \(-0.606059\pi\) | ||||
−0.327062 | + | 0.945003i | \(0.606059\pi\) | |||||||
\(102\) | −27.0020 | − | 13.7582i | −0.264726 | − | 0.134884i | ||||
\(103\) | −10.0920 | − | 1.59842i | −0.0979807 | − | 0.0155186i | 0.107252 | − | 0.994232i | \(-0.465795\pi\) |
−0.205232 | + | 0.978713i | \(0.565795\pi\) | |||||||
\(104\) | 15.1737 | + | 20.8848i | 0.145901 | + | 0.200815i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −41.6834 | − | 30.2848i | −0.393240 | − | 0.285705i | ||||
\(107\) | 28.4807 | − | 28.4807i | 0.266175 | − | 0.266175i | −0.561382 | − | 0.827557i | \(-0.689730\pi\) |
0.827557 | + | 0.561382i | \(0.189730\pi\) | |||||||
\(108\) | −5.39969 | − | 34.0923i | −0.0499971 | − | 0.315669i | ||||
\(109\) | −50.7034 | − | 16.4745i | −0.465169 | − | 0.151142i | 0.0670496 | − | 0.997750i | \(-0.478641\pi\) |
−0.532218 | + | 0.846607i | \(0.678641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.2341 | + | 40.7304i | 0.119226 | + | 0.366940i | ||||
\(112\) | 1.63278 | + | 3.20451i | 0.0145784 | + | 0.0286117i | ||||
\(113\) | −95.9600 | + | 48.8940i | −0.849203 | + | 0.432691i | −0.823728 | − | 0.566985i | \(-0.808110\pi\) |
−0.0254749 | + | 0.999675i | \(0.508110\pi\) | |||||||
\(114\) | 154.343 | − | 50.1492i | 1.35389 | − | 0.439905i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 35.1543 | − | 108.194i | 0.303054 | − | 0.932705i | ||||
\(117\) | 38.4075 | − | 6.08315i | 0.328269 | − | 0.0519927i | ||||
\(118\) | 60.7953 | + | 60.7953i | 0.515215 | + | 0.515215i | ||||
\(119\) | −3.10999 | + | 4.28053i | −0.0261344 | + | 0.0359709i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.6524 | + | 39.7073i | −0.451672 | + | 0.328159i | ||||
\(122\) | −3.13416 | + | 19.7883i | −0.0256898 | + | 0.162199i | ||||
\(123\) | 110.632 | − | 217.128i | 0.899449 | − | 1.76527i | ||||
\(124\) | − | 3.88268i | − | 0.0313119i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.41758 | 0.0429967 | ||||||||
\(127\) | 78.6966 | + | 40.0979i | 0.619658 | + | 0.315732i | 0.735488 | − | 0.677537i | \(-0.236953\pi\) |
−0.115830 | + | 0.993269i | \(0.536953\pi\) | |||||||
\(128\) | −11.1744 | − | 1.76985i | −0.0873001 | − | 0.0138270i | ||||
\(129\) | −117.481 | − | 161.698i | −0.910702 | − | 1.25347i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 77.7492 | + | 56.4881i | 0.593505 | + | 0.431207i | 0.843568 | − | 0.537023i | \(-0.180451\pi\) |
−0.250062 | + | 0.968230i | \(0.580451\pi\) | |||||||
\(132\) | −70.7154 | + | 70.7154i | −0.535723 | + | 0.535723i | ||||
\(133\) | −4.43240 | − | 27.9851i | −0.0333263 | − | 0.210414i | ||||
\(134\) | −86.9069 | − | 28.2377i | −0.648559 | − | 0.210729i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.14335 | − | 15.8296i | −0.0378188 | − | 0.116394i | ||||
\(137\) | 108.715 | + | 213.366i | 0.793542 | + | 1.55741i | 0.829793 | + | 0.558071i | \(0.188458\pi\) |
−0.0362512 | + | 0.999343i | \(0.511542\pi\) | |||||||
\(138\) | −141.571 | + | 72.1341i | −1.02588 | + | 0.522711i | ||||
\(139\) | 132.664 | − | 43.1053i | 0.954420 | − | 0.310110i | 0.209910 | − | 0.977721i | \(-0.432683\pi\) |
0.744510 | + | 0.667611i | \(0.232683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −56.1324 | + | 172.758i | −0.398102 | + | 1.22523i | ||||
\(142\) | 43.9218 | − | 6.95653i | 0.309308 | − | 0.0489896i | ||||
\(143\) | 88.6196 | + | 88.6196i | 0.619717 | + | 0.619717i | ||||
\(144\) | −10.0172 | + | 13.7875i | −0.0695641 | + | 0.0957468i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 79.2559 | − | 57.5828i | 0.542849 | − | 0.394403i | ||||
\(147\) | −27.4527 | + | 173.329i | −0.186753 | + | 1.17911i | ||||
\(148\) | −10.6784 | + | 20.9576i | −0.0721516 | + | 0.141605i | ||||
\(149\) | 187.994i | 1.26170i | 0.775903 | + | 0.630852i | \(0.217295\pi\) | ||||
−0.775903 | + | 0.630852i | \(0.782705\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 160.259 | 1.06132 | 0.530660 | − | 0.847585i | \(-0.321944\pi\) | ||||
0.530660 | + | 0.847585i | \(0.321944\pi\) | |||||||
\(152\) | 79.4166 | + | 40.4648i | 0.522478 | + | 0.266216i | ||||
\(153\) | −24.7633 | − | 3.92212i | −0.161852 | − | 0.0256348i | ||||
\(154\) | 10.2630 | + | 14.1258i | 0.0666426 | + | 0.0917257i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 53.7769 | + | 39.0712i | 0.344724 | + | 0.250456i | ||||
\(157\) | −88.0051 | + | 88.0051i | −0.560542 | + | 0.560542i | −0.929461 | − | 0.368919i | \(-0.879728\pi\) |
0.368919 | + | 0.929461i | \(0.379728\pi\) | |||||||
\(158\) | −12.5743 | − | 79.3907i | −0.0795839 | − | 0.502473i | ||||
\(159\) | −126.176 | − | 40.9972i | −0.793562 | − | 0.257844i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.57237 | + | 26.3831i | 0.0532446 | + | 0.163870i | ||||
\(162\) | −64.9697 | − | 127.510i | −0.401048 | − | 0.787100i | ||||
\(163\) | 162.119 | − | 82.6039i | 0.994597 | − | 0.506772i | 0.120599 | − | 0.992701i | \(-0.461519\pi\) |
0.873998 | + | 0.485929i | \(0.161519\pi\) | |||||||
\(164\) | 127.289 | − | 41.3586i | 0.776150 | − | 0.252186i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.7005 | + | 54.4765i | −0.106629 | + | 0.328172i | ||||
\(167\) | −179.271 | + | 28.3937i | −1.07348 | + | 0.170022i | −0.668059 | − | 0.744109i | \(-0.732874\pi\) |
−0.405419 | + | 0.914131i | \(0.632874\pi\) | |||||||
\(168\) | 6.54836 | + | 6.54836i | 0.0389783 | + | 0.0389783i | ||||
\(169\) | −50.3722 | + | 69.3314i | −0.298061 | + | 0.410245i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 108.621 | − | 78.9175i | 0.635208 | − | 0.461506i | ||||
\(172\) | 17.1723 | − | 108.422i | 0.0998389 | − | 0.630358i | ||||
\(173\) | −100.701 | + | 197.637i | −0.582086 | + | 1.14241i | 0.392783 | + | 0.919631i | \(0.371512\pi\) |
−0.974869 | + | 0.222777i | \(0.928488\pi\) | |||||||
\(174\) | − | 292.929i | − | 1.68350i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −54.9260 | −0.312079 | ||||||||
\(177\) | 197.257 | + | 100.507i | 1.11445 | + | 0.567839i | ||||
\(178\) | 83.9833 | + | 13.3016i | 0.471816 | + | 0.0747283i | ||||
\(179\) | 38.1969 | + | 52.5735i | 0.213391 | + | 0.293707i | 0.902272 | − | 0.431167i | \(-0.141898\pi\) |
−0.688882 | + | 0.724874i | \(0.741898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 171.558 | + | 124.644i | 0.947832 | + | 0.688641i | 0.950293 | − | 0.311356i | \(-0.100783\pi\) |
−0.00246082 | + | 0.999997i | \(0.500783\pi\) | |||||||
\(182\) | 8.20631 | − | 8.20631i | 0.0450896 | − | 0.0450896i | ||||
\(183\) | 8.07025 | + | 50.9536i | 0.0440997 | + | 0.278435i | ||||
\(184\) | −82.9944 | − | 26.9665i | −0.451057 | − | 0.146557i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.08944 | − | 9.50832i | −0.0166099 | − | 0.0511200i | ||||
\(187\) | −36.6846 | − | 71.9976i | −0.196174 | − | 0.385014i | ||||
\(188\) | −88.8916 | + | 45.2925i | −0.472827 | + | 0.240918i | ||||
\(189\) | −14.7582 | + | 4.79523i | −0.0780858 | + | 0.0253716i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 28.5061 | − | 87.7327i | 0.149247 | − | 0.459334i | −0.848286 | − | 0.529538i | \(-0.822365\pi\) |
0.997533 | + | 0.0702046i | \(0.0223652\pi\) | |||||||
\(192\) | −28.7734 | + | 4.55726i | −0.149861 | + | 0.0237357i | ||||
\(193\) | 151.113 | + | 151.113i | 0.782967 | + | 0.782967i | 0.980330 | − | 0.197363i | \(-0.0632378\pi\) |
−0.197363 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(194\) | 10.3541 | − | 14.2513i | 0.0533719 | − | 0.0734601i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −77.9756 | + | 56.6526i | −0.397835 | + | 0.289044i | ||||
\(197\) | −10.5979 | + | 66.9124i | −0.0537964 | + | 0.339657i | 0.946080 | + | 0.323933i | \(0.105005\pi\) |
−0.999876 | + | 0.0157239i | \(0.994995\pi\) | |||||||
\(198\) | −37.5620 | + | 73.7196i | −0.189707 | + | 0.372321i | ||||
\(199\) | − | 113.482i | − | 0.570260i | −0.958489 | − | 0.285130i | \(-0.907963\pi\) | ||
0.958489 | − | 0.285130i | \(-0.0920368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −235.296 | −1.17063 | ||||||||
\(202\) | −83.2487 | − | 42.4173i | −0.412122 | − | 0.209987i | ||||
\(203\) | −50.5135 | − | 8.00055i | −0.248835 | − | 0.0394116i | ||||
\(204\) | −25.1912 | − | 34.6727i | −0.123486 | − | 0.169964i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.6904 | − | 8.49360i | −0.0567497 | − | 0.0412311i | ||||
\(207\) | −92.9505 | + | 92.9505i | −0.449036 | + | 0.449036i | ||||
\(208\) | 5.71109 | + | 36.0584i | 0.0274572 | + | 0.173358i | ||||
\(209\) | 411.538 | + | 133.717i | 1.96908 | + | 0.639793i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50834 | − | 10.7976i | −0.0166272 | − | 0.0511733i | 0.942399 | − | 0.334492i | \(-0.108565\pi\) |
−0.959026 | + | 0.283319i | \(0.908565\pi\) | |||||||
\(212\) | −33.0801 | − | 64.9234i | −0.156038 | − | 0.306243i | ||||
\(213\) | 102.025 | − | 51.9844i | 0.478991 | − | 0.244058i | ||||
\(214\) | 54.1736 | − | 17.6021i | 0.253148 | − | 0.0822526i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.0846 | − | 46.4256i | 0.0698361 | − | 0.214933i | ||||
\(217\) | −1.72402 | + | 0.273058i | −0.00794479 | + | 0.00125833i | ||||
\(218\) | −53.3127 | − | 53.3127i | −0.244554 | − | 0.244554i | ||||
\(219\) | 148.272 | − | 204.079i | 0.677041 | − | 0.931867i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −43.4514 | + | 31.5693i | −0.196613 | + | 0.142847i | ||||
\(222\) | −9.47457 | + | 59.8201i | −0.0426783 | + | 0.269460i | ||||
\(223\) | 66.5421 | − | 130.596i | 0.298395 | − | 0.585633i | −0.692320 | − | 0.721591i | \(-0.743411\pi\) |
0.990715 | + | 0.135958i | \(0.0434111\pi\) | |||||||
\(224\) | 5.08623i | 0.0227064i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −152.309 | −0.673931 | ||||||||
\(227\) | 187.668 | + | 95.6214i | 0.826729 | + | 0.421240i | 0.815542 | − | 0.578698i | \(-0.196439\pi\) |
0.0111872 | + | 0.999937i | \(0.496439\pi\) | |||||||
\(228\) | 226.682 | + | 35.9029i | 0.994218 | + | 0.157469i | ||||
\(229\) | −111.799 | − | 153.877i | −0.488203 | − | 0.671954i | 0.491852 | − | 0.870679i | \(-0.336320\pi\) |
−0.980055 | + | 0.198725i | \(0.936320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 36.3729 | + | 26.4265i | 0.157459 | + | 0.114400i | ||||
\(232\) | 113.762 | − | 113.762i | 0.490352 | − | 0.490352i | ||||
\(233\) | 69.4571 | + | 438.535i | 0.298099 | + | 1.88212i | 0.448935 | + | 0.893565i | \(0.351804\pi\) |
−0.150836 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(234\) | 52.3019 | + | 16.9939i | 0.223512 | + | 0.0726236i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 37.5736 | + | 115.640i | 0.159210 | + | 0.489998i | ||||
\(237\) | −93.9643 | − | 184.415i | −0.396474 | − | 0.778124i | ||||
\(238\) | −6.66709 | + | 3.39705i | −0.0280130 | + | 0.0142733i | ||||
\(239\) | −245.647 | + | 79.8157i | −1.02781 | + | 0.333957i | −0.773925 | − | 0.633277i | \(-0.781710\pi\) |
−0.253888 | + | 0.967234i | \(0.581710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −50.4176 | + | 155.169i | −0.209202 | + | 0.643857i | 0.790313 | + | 0.612703i | \(0.209918\pi\) |
−0.999515 | + | 0.0311532i | \(0.990082\pi\) | |||||||
\(242\) | −94.3596 | + | 14.9451i | −0.389916 | + | 0.0617566i | ||||
\(243\) | −150.731 | − | 150.731i | −0.620294 | − | 0.620294i | ||||
\(244\) | −16.6541 | + | 22.9224i | −0.0682546 | + | 0.0939444i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 278.809 | − | 202.567i | 1.13337 | − | 0.823442i | ||||
\(247\) | 44.9930 | − | 284.074i | 0.182158 | − | 1.15010i | ||||
\(248\) | 2.49283 | − | 4.89246i | 0.0100517 | − | 0.0197276i | ||||
\(249\) | 147.492i | 0.592338i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 269.305 | 1.07293 | 0.536463 | − | 0.843924i | \(-0.319760\pi\) | ||||
0.536463 | + | 0.843924i | \(0.319760\pi\) | |||||||
\(252\) | 6.82655 | + | 3.47830i | 0.0270895 | + | 0.0138028i | ||||
\(253\) | −418.442 | − | 66.2747i | −1.65392 | − | 0.261955i | ||||
\(254\) | 73.4191 | + | 101.053i | 0.289051 | + | 0.397845i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 61.4130 | − | 61.4130i | 0.238961 | − | 0.238961i | −0.577459 | − | 0.816420i | \(-0.695956\pi\) |
0.816420 | + | 0.577459i | \(0.195956\pi\) | |||||||
\(258\) | −44.2176 | − | 279.179i | −0.171386 | − | 1.08209i | ||||
\(259\) | 10.0568 | + | 3.26764i | 0.0388292 | + | 0.0126164i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −74.8889 | − | 230.484i | −0.286931 | − | 0.883082i | ||||
\(262\) | 61.7021 | + | 121.097i | 0.235504 | + | 0.462203i | ||||
\(263\) | 324.035 | − | 165.104i | 1.23207 | − | 0.627773i | 0.288039 | − | 0.957619i | \(-0.406997\pi\) |
0.944035 | + | 0.329846i | \(0.106997\pi\) | |||||||
\(264\) | −134.509 | + | 43.7045i | −0.509503 | + | 0.165548i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.3824 | − | 38.1090i | 0.0465503 | − | 0.143267i | ||||
\(267\) | 216.251 | − | 34.2509i | 0.809931 | − | 0.128280i | ||||
\(268\) | −91.3793 | − | 91.3793i | −0.340967 | − | 0.340967i | ||||
\(269\) | −184.825 | + | 254.390i | −0.687082 | + | 0.945687i | −0.999992 | − | 0.00409606i | \(-0.998696\pi\) |
0.312910 | + | 0.949783i | \(0.398696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −196.495 | + | 142.762i | −0.725073 | + | 0.526797i | −0.888001 | − | 0.459841i | \(-0.847906\pi\) |
0.162928 | + | 0.986638i | \(0.447906\pi\) | |||||||
\(272\) | 3.68224 | − | 23.2487i | 0.0135376 | − | 0.0854732i | ||||
\(273\) | 13.5668 | − | 26.6263i | 0.0496951 | − | 0.0975321i | ||||
\(274\) | 338.656i | 1.23597i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −224.703 | −0.814141 | ||||||||
\(277\) | −382.219 | − | 194.750i | −1.37985 | − | 0.703070i | −0.402646 | − | 0.915356i | \(-0.631909\pi\) |
−0.977208 | + | 0.212286i | \(0.931909\pi\) | |||||||
\(278\) | 194.842 | + | 30.8600i | 0.700871 | + | 0.111007i | ||||
\(279\) | −4.86171 | − | 6.69157i | −0.0174255 | − | 0.0239841i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −180.948 | − | 131.467i | −0.643944 | − | 0.467852i | 0.217259 | − | 0.976114i | \(-0.430288\pi\) |
−0.861203 | + | 0.508262i | \(0.830288\pi\) | |||||||
\(282\) | −181.648 | + | 181.648i | −0.644142 | + | 0.644142i | ||||
\(283\) | −55.7689 | − | 352.111i | −0.197063 | − | 1.24421i | −0.865679 | − | 0.500600i | \(-0.833113\pi\) |
0.668615 | − | 0.743608i | \(-0.266887\pi\) | |||||||
\(284\) | 59.8111 | + | 19.4338i | 0.210602 | + | 0.0684288i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 54.7699 | + | 168.564i | 0.191503 | + | 0.589386i | ||||
\(287\) | −27.3163 | − | 53.6112i | −0.0951786 | − | 0.186799i | ||||
\(288\) | −21.4746 | + | 10.9419i | −0.0745646 | + | 0.0379926i | ||||
\(289\) | −241.921 | + | 78.6050i | −0.837098 | + | 0.271990i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0166 | − | 43.1388i | 0.0481672 | − | 0.148243i | ||||
\(292\) | 136.839 | − | 21.6731i | 0.468626 | − | 0.0742230i | ||||
\(293\) | −331.758 | − | 331.758i | −1.13228 | − | 1.13228i | −0.989797 | − | 0.142481i | \(-0.954492\pi\) |
−0.142481 | − | 0.989797i | \(-0.545508\pi\) | |||||||
\(294\) | −145.877 | + | 200.782i | −0.496179 | + | 0.682932i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −26.9112 | + | 19.5522i | −0.0909163 | + | 0.0660546i | ||||
\(297\) | 37.0729 | − | 234.069i | 0.124825 | − | 0.788111i | ||||
\(298\) | −120.700 | + | 236.886i | −0.405032 | + | 0.794920i | ||||
\(299\) | 281.595i | 0.941788i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.3500 | −0.163954 | ||||||||
\(302\) | 201.938 | + | 102.893i | 0.668670 | + | 0.340705i | ||||
\(303\) | −237.620 | − | 37.6353i | −0.784224 | − | 0.124209i | ||||
\(304\) | 74.0908 | + | 101.977i | 0.243720 | + | 0.335451i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −28.6854 | − | 20.8412i | −0.0937431 | − | 0.0681084i | ||||
\(307\) | 5.33327 | − | 5.33327i | 0.0173722 | − | 0.0173722i | −0.698367 | − | 0.715740i | \(-0.746090\pi\) |
0.715740 | + | 0.698367i | \(0.246090\pi\) | |||||||
\(308\) | 3.86279 | + | 24.3887i | 0.0125415 | + | 0.0791842i | ||||
\(309\) | −35.3872 | − | 11.4980i | −0.114522 | − | 0.0372103i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −78.3745 | − | 241.212i | −0.252008 | − | 0.775601i | −0.994404 | − | 0.105640i | \(-0.966311\pi\) |
0.742396 | − | 0.669961i | \(-0.233689\pi\) | |||||||
\(312\) | 42.6776 | + | 83.7595i | 0.136787 | + | 0.268460i | ||||
\(313\) | 118.104 | − | 60.1772i | 0.377330 | − | 0.192259i | −0.255031 | − | 0.966933i | \(-0.582086\pi\) |
0.632362 | + | 0.774673i | \(0.282086\pi\) | |||||||
\(314\) | −167.396 | + | 54.3901i | −0.533107 | + | 0.173217i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 35.1275 | − | 108.111i | 0.111163 | − | 0.342125i | ||||
\(317\) | 222.037 | − | 35.1671i | 0.700431 | − | 0.110937i | 0.203945 | − | 0.978982i | \(-0.434624\pi\) |
0.496486 | + | 0.868045i | \(0.334624\pi\) | |||||||
\(318\) | −132.670 | − | 132.670i | −0.417200 | − | 0.417200i | ||||
\(319\) | 459.095 | − | 631.890i | 1.43917 | − | 1.98085i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 118.660 | − | 86.2117i | 0.369658 | − | 0.268572i | ||||
\(322\) | −6.13714 | + | 38.7484i | −0.0190594 | + | 0.120337i | ||||
\(323\) | −84.1882 | + | 165.229i | −0.260645 | + | 0.511544i | ||||
\(324\) | − | 202.385i | − | 0.624646i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 257.317 | 0.789317 | ||||||||
\(327\) | −172.979 | − | 88.1371i | −0.528987 | − | 0.269532i | ||||
\(328\) | 186.947 | + | 29.6095i | 0.569960 | + | 0.0902728i | ||||
\(329\) | 26.3627 | + | 36.2851i | 0.0801297 | + | 0.110289i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −340.878 | − | 247.662i | −1.02984 | − | 0.748225i | −0.0615656 | − | 0.998103i | \(-0.519609\pi\) |
−0.968277 | + | 0.249878i | \(0.919609\pi\) | |||||||
\(332\) | −57.2800 | + | 57.2800i | −0.172530 | + | 0.172530i | ||||
\(333\) | 7.83849 | + | 49.4903i | 0.0235390 | + | 0.148619i | ||||
\(334\) | −244.124 | − | 79.3208i | −0.730911 | − | 0.237487i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.04711 | + | 12.4557i | 0.0120450 | + | 0.0370706i | ||||
\(337\) | 158.905 | + | 311.868i | 0.471527 | + | 0.925423i | 0.997203 | + | 0.0747388i | \(0.0238123\pi\) |
−0.525676 | + | 0.850685i | \(0.676188\pi\) | |||||||
\(338\) | −107.986 | + | 55.0217i | −0.319486 | + | 0.162786i | ||||
\(339\) | −372.990 | + | 121.192i | −1.10026 | + | 0.357498i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.23761 | − | 25.3528i | 0.0241572 | − | 0.0743483i | ||||
\(342\) | 187.538 | − | 29.7031i | 0.548357 | − | 0.0868512i | ||||
\(343\) | 61.7924 | + | 61.7924i | 0.180153 | + | 0.180153i | ||||
\(344\) | 91.2493 | − | 125.594i | 0.265260 | − | 0.365099i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −253.781 | + | 184.383i | −0.733471 | + | 0.532898i | ||||
\(347\) | 25.8523 | − | 163.225i | 0.0745022 | − | 0.470388i | −0.922026 | − | 0.387129i | \(-0.873467\pi\) |
0.996528 | − | 0.0832597i | \(-0.0265331\pi\) | |||||||
\(348\) | 188.072 | − | 369.112i | 0.540437 | − | 1.06067i | ||||
\(349\) | − | 541.612i | − | 1.55190i | −0.630796 | − | 0.775949i | \(-0.717272\pi\) | ||
0.630796 | − | 0.775949i | \(-0.282728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −157.519 | −0.448772 | ||||||||
\(352\) | −69.2108 | − | 35.2647i | −0.196622 | − | 0.100184i | ||||
\(353\) | −5.62039 | − | 0.890182i | −0.0159218 | − | 0.00252176i | 0.148468 | − | 0.988917i | \(-0.452566\pi\) |
−0.164390 | + | 0.986395i | \(0.552566\pi\) | |||||||
\(354\) | 184.029 | + | 253.294i | 0.519855 | + | 0.715519i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 97.2849 | + | 70.6816i | 0.273272 | + | 0.198544i | ||||
\(357\) | −13.6241 | + | 13.6241i | −0.0381626 | + | 0.0381626i | ||||
\(358\) | 14.3766 | + | 90.7704i | 0.0401582 | + | 0.253549i | ||||
\(359\) | 46.7523 | + | 15.1908i | 0.130229 | + | 0.0423141i | 0.373407 | − | 0.927668i | \(-0.378190\pi\) |
−0.243177 | + | 0.969982i | \(0.578190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −195.314 | − | 601.114i | −0.541036 | − | 1.66514i | ||||
\(362\) | 136.149 | + | 267.207i | 0.376102 | + | 0.738142i | ||||
\(363\) | −219.186 | + | 111.681i | −0.603819 | + | 0.307661i | ||||
\(364\) | 15.6093 | − | 5.07178i | 0.0428828 | − | 0.0139335i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.5451 | + | 69.3866i | −0.0615986 | + | 0.189581i | ||||
\(367\) | −353.395 | + | 55.9723i | −0.962929 | + | 0.152513i | −0.618054 | − | 0.786136i | \(-0.712079\pi\) |
−0.344875 | + | 0.938649i | \(0.612079\pi\) | |||||||
\(368\) | −87.2655 | − | 87.2655i | −0.237134 | − | 0.237134i | ||||
\(369\) | 167.587 | − | 230.664i | 0.454166 | − | 0.625106i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.5014 | + | 19.2544i | −0.0714324 | + | 0.0518987i | ||||
\(372\) | 2.21180 | − | 13.9647i | 0.00594569 | − | 0.0375396i | ||||
\(373\) | −75.0714 | + | 147.336i | −0.201264 | + | 0.395003i | −0.969474 | − | 0.245196i | \(-0.921148\pi\) |
0.768210 | + | 0.640198i | \(0.221148\pi\) | |||||||
\(374\) | − | 114.275i | − | 0.305549i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −141.089 | −0.375238 | ||||||||
\(377\) | −462.566 | − | 235.689i | −1.22697 | − | 0.625170i | ||||
\(378\) | −21.6752 | − | 3.43301i | −0.0573417 | − | 0.00908203i | ||||
\(379\) | 346.461 | + | 476.863i | 0.914145 | + | 1.25821i | 0.965731 | + | 0.259544i | \(0.0835723\pi\) |
−0.0515863 | + | 0.998669i | \(0.516428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 260.204 | + | 189.049i | 0.682950 | + | 0.496193i | ||||
\(382\) | 92.2477 | − | 92.2477i | 0.241486 | − | 0.241486i | ||||
\(383\) | 106.883 | + | 674.830i | 0.279067 | + | 1.76196i | 0.586080 | + | 0.810253i | \(0.300670\pi\) |
−0.307013 | + | 0.951705i | \(0.599330\pi\) | |||||||
\(384\) | −39.1825 | − | 12.7312i | −0.102038 | − | 0.0331541i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 93.3928 | + | 287.433i | 0.241950 | + | 0.744646i | ||||
\(387\) | −106.165 | − | 208.361i | −0.274329 | − | 0.538400i | ||||
\(388\) | 22.1968 | − | 11.3099i | 0.0572084 | − | 0.0291491i | ||||
\(389\) | −149.313 | + | 48.5147i | −0.383837 | + | 0.124716i | −0.494579 | − | 0.869133i | \(-0.664678\pi\) |
0.110741 | + | 0.993849i | \(0.464678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 56.1047 | − | 172.672i | 0.143490 | − | 0.441617i | ||||
\(392\) | −134.628 | + | 21.3230i | −0.343439 | + | 0.0543954i | ||||
\(393\) | 247.460 | + | 247.460i | 0.629669 | + | 0.629669i | ||||
\(394\) | −56.3145 | + | 77.5103i | −0.142930 | + | 0.196727i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −94.6618 | + | 68.7758i | −0.239045 | + | 0.173676i | ||||
\(397\) | 27.1282 | − | 171.281i | 0.0683331 | − | 0.431438i | −0.929677 | − | 0.368377i | \(-0.879914\pi\) |
0.998010 | − | 0.0630614i | \(-0.0200864\pi\) | |||||||
\(398\) | 72.8598 | − | 142.995i | 0.183065 | − | 0.359285i | ||||
\(399\) | − | 103.178i | − | 0.258592i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 410.229 | 1.02302 | 0.511508 | − | 0.859278i | \(-0.329087\pi\) | ||||
0.511508 | + | 0.859278i | \(0.329087\pi\) | |||||||
\(402\) | −296.490 | − | 151.069i | −0.737537 | − | 0.375794i | ||||
\(403\) | −17.5004 | − | 2.77179i | −0.0434253 | − | 0.00687789i | ||||
\(404\) | −77.6659 | − | 106.898i | −0.192242 | − | 0.264599i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −58.5140 | − | 42.5129i | −0.144123 | − | 0.104712i | ||||
\(407\) | −114.191 | + | 114.191i | −0.280569 | + | 0.280569i | ||||
\(408\) | −9.48152 | − | 59.8639i | −0.0232390 | − | 0.146725i | ||||
\(409\) | −38.3159 | − | 12.4496i | −0.0936820 | − | 0.0304391i | 0.261801 | − | 0.965122i | \(-0.415684\pi\) |
−0.355483 | + | 0.934683i | \(0.615684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 269.468 | + | 829.338i | 0.655640 | + | 2.01785i | ||||
\(412\) | −9.27758 | − | 18.2083i | −0.0225184 | − | 0.0441948i | ||||
\(413\) | 48.7049 | − | 24.8164i | 0.117929 | − | 0.0600881i | ||||
\(414\) | −176.802 | + | 57.4466i | −0.427059 | + | 0.138760i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.9545 | + | 49.1030i | −0.0383522 | + | 0.118036i | ||||
\(417\) | 501.706 | − | 79.4624i | 1.20313 | − | 0.190557i | ||||
\(418\) | 432.716 | + | 432.716i | 1.03521 | + | 1.03521i | ||||
\(419\) | 256.242 | − | 352.687i | 0.611556 | − | 0.841735i | −0.385148 | − | 0.922855i | \(-0.625850\pi\) |
0.996704 | + | 0.0811197i | \(0.0258496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 140.600 | − | 102.152i | 0.333967 | − | 0.242641i | −0.408145 | − | 0.912917i | \(-0.633824\pi\) |
0.742112 | + | 0.670276i | \(0.233824\pi\) | |||||||
\(422\) | 2.51169 | − | 15.8582i | 0.00595188 | − | 0.0375787i | ||||
\(423\) | −96.4863 | + | 189.365i | −0.228100 | + | 0.447671i | ||||
\(424\) | − | 103.047i | − | 0.243035i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 161.935 | 0.380130 | ||||||||
\(427\) | 11.3495 | + | 5.78284i | 0.0265795 | + | 0.0135430i | ||||
\(428\) | 79.5639 | + | 12.6017i | 0.185897 | + | 0.0294432i | ||||
\(429\) | 268.253 | + | 369.219i | 0.625299 | + | 0.860650i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −98.9485 | − | 71.8903i | −0.229579 | − | 0.166799i | 0.467049 | − | 0.884231i | \(-0.345317\pi\) |
−0.696628 | + | 0.717433i | \(0.745317\pi\) | |||||||
\(432\) | 48.8148 | − | 48.8148i | 0.112997 | − | 0.112997i | ||||
\(433\) | −46.0011 | − | 290.440i | −0.106238 | − | 0.670761i | −0.982123 | − | 0.188241i | \(-0.939721\pi\) |
0.875885 | − | 0.482520i | \(-0.160279\pi\) | |||||||
\(434\) | −2.34771 | − | 0.762816i | −0.00540946 | − | 0.00175764i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.9491 | − | 101.407i | −0.0755712 | − | 0.232584i | ||||
\(437\) | 441.397 | + | 866.291i | 1.01006 | + | 1.98236i | ||||
\(438\) | 317.860 | − | 161.958i | 0.725708 | − | 0.369767i | ||||
\(439\) | −135.892 | + | 44.1541i | −0.309550 | + | 0.100579i | −0.459672 | − | 0.888089i | \(-0.652033\pi\) |
0.150123 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −63.4487 | + | 195.275i | −0.143875 | + | 0.442800i | ||||
\(442\) | −75.0206 | + | 11.8821i | −0.169730 | + | 0.0268826i | ||||
\(443\) | 13.7393 | + | 13.7393i | 0.0310143 | + | 0.0310143i | 0.722444 | − | 0.691430i | \(-0.243019\pi\) |
−0.691430 | + | 0.722444i | \(0.743019\pi\) | |||||||
\(444\) | −50.3455 | + | 69.2947i | −0.113391 | + | 0.156069i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 167.696 | − | 121.838i | 0.376000 | − | 0.273180i | ||||
\(447\) | −107.092 | + | 676.154i | −0.239580 | + | 1.51265i | ||||
\(448\) | −3.26556 | + | 6.40903i | −0.00728920 | + | 0.0143059i | ||||
\(449\) | − | 313.808i | − | 0.698904i | −0.936954 | − | 0.349452i | \(-0.886368\pi\) | ||
0.936954 | − | 0.349452i | \(-0.113632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 918.906 | 2.03749 | ||||||||
\(452\) | −191.920 | − | 97.7881i | −0.424602 | − | 0.216345i | ||||
\(453\) | 576.401 | + | 91.2929i | 1.27241 | + | 0.201530i | ||||
\(454\) | 175.082 | + | 240.980i | 0.385644 | + | 0.530793i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 262.585 | + | 190.779i | 0.575844 | + | 0.418375i | ||||
\(457\) | −36.5102 | + | 36.5102i | −0.0798911 | + | 0.0798911i | −0.745923 | − | 0.666032i | \(-0.767991\pi\) |
0.666032 | + | 0.745923i | \(0.267991\pi\) | |||||||
\(458\) | −42.0789 | − | 265.676i | −0.0918754 | − | 0.580079i | ||||
\(459\) | 96.5899 | + | 31.3839i | 0.210435 | + | 0.0683746i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 252.310 | + | 776.530i | 0.547310 | + | 1.68445i | 0.715434 | + | 0.698680i | \(0.246229\pi\) |
−0.168124 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(462\) | 28.8657 | + | 56.6522i | 0.0624799 | + | 0.122624i | ||||
\(463\) | −490.040 | + | 249.688i | −1.05840 | + | 0.539283i | −0.894442 | − | 0.447184i | \(-0.852427\pi\) |
−0.163960 | + | 0.986467i | \(0.552427\pi\) | |||||||
\(464\) | 216.388 | − | 70.3086i | 0.466353 | − | 0.151527i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −194.036 | + | 597.180i | −0.416385 | + | 1.28150i | ||||
\(467\) | 581.328 | − | 92.0733i | 1.24481 | − | 0.197159i | 0.500941 | − | 0.865481i | \(-0.332987\pi\) |
0.743872 | + | 0.668322i | \(0.232987\pi\) | |||||||
\(468\) | 54.9935 | + | 54.9935i | 0.117507 | + | 0.117507i | ||||
\(469\) | −34.1486 | + | 47.0015i | −0.0728115 | + | 0.100216i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −366.659 | + | 266.393i | −0.778468 | + | 0.565590i | ||||
\(472\) | −26.8997 | + | 169.838i | −0.0569909 | + | 0.359827i | ||||
\(473\) | 342.161 | − | 671.529i | 0.723385 | − | 1.41972i | ||||
\(474\) | − | 292.706i | − | 0.617523i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.5821 | −0.0222312 | ||||||||
\(477\) | −138.306 | − | 70.4704i | −0.289949 | − | 0.147737i | ||||
\(478\) | −360.779 | − | 57.1417i | −0.754767 | − | 0.119543i | ||||
\(479\) | 122.812 | + | 169.037i | 0.256393 | + | 0.352895i | 0.917737 | − | 0.397188i | \(-0.130014\pi\) |
−0.661344 | + | 0.750083i | \(0.730014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 86.8391 | + | 63.0923i | 0.180539 | + | 0.131169i | ||||
\(482\) | −163.155 | + | 163.155i | −0.338495 | + | 0.338495i | ||||
\(483\) | 15.8027 | + | 99.7746i | 0.0327179 | + | 0.206573i | ||||
\(484\) | −128.495 | − | 41.7507i | −0.265486 | − | 0.0862617i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −93.1571 | − | 286.708i | −0.191681 | − | 0.589935i | ||||
\(487\) | 75.5860 | + | 148.346i | 0.155207 | + | 0.304611i | 0.955496 | − | 0.295003i | \(-0.0953206\pi\) |
−0.800289 | + | 0.599614i | \(0.795321\pi\) | |||||||
\(488\) | −35.7025 | + | 18.1914i | −0.0731609 | + | 0.0372774i | ||||
\(489\) | 630.146 | − | 204.747i | 1.28864 | − | 0.418705i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 91.4686 | − | 281.511i | 0.186290 | − | 0.573343i | −0.813678 | − | 0.581316i | \(-0.802538\pi\) |
0.999968 | + | 0.00797308i | \(0.00253794\pi\) | |||||||
\(492\) | 481.376 | − | 76.2425i | 0.978407 | − | 0.154964i | ||||
\(493\) | 236.685 | + | 236.685i | 0.480091 | + | 0.480091i | ||||
\(494\) | 239.081 | − | 329.067i | 0.483970 | − | 0.666128i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.28230 | − | 4.56436i | 0.0126659 | − | 0.00920234i | ||||
\(497\) | 4.42282 | − | 27.9246i | 0.00889903 | − | 0.0561862i | ||||
\(498\) | −94.6958 | + | 185.851i | −0.190152 | + | 0.373195i | ||||
\(499\) | − | 459.459i | − | 0.920759i | −0.887722 | − | 0.460380i | \(-0.847713\pi\) | ||
0.887722 | − | 0.460380i | \(-0.152287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −660.954 | −1.31927 | ||||||||
\(502\) | 339.344 | + | 172.904i | 0.675983 | + | 0.344431i | ||||
\(503\) | 230.666 | + | 36.5339i | 0.458580 | + | 0.0726319i | 0.381451 | − | 0.924389i | \(-0.375425\pi\) |
0.0771293 | + | 0.997021i | \(0.475425\pi\) | |||||||
\(504\) | 6.36875 | + | 8.76583i | 0.0126364 | + | 0.0173925i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −484.717 | − | 352.167i | −0.957938 | − | 0.695983i | ||||
\(507\) | −220.668 | + | 220.668i | −0.435242 | + | 0.435242i | ||||
\(508\) | 27.6336 | + | 174.472i | 0.0543969 | + | 0.343448i | ||||
\(509\) | −241.356 | − | 78.4213i | −0.474177 | − | 0.154069i | 0.0621728 | − | 0.998065i | \(-0.480197\pi\) |
−0.536349 | + | 0.843996i | \(0.680197\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.2470 | − | 59.2361i | −0.0376653 | − | 0.115922i | ||||
\(512\) | −10.2726 | − | 20.1612i | −0.0200637 | − | 0.0393773i | ||||
\(513\) | −484.588 | + | 246.910i | −0.944615 | + | 0.481306i | ||||
\(514\) | 116.815 | − | 37.9553i | 0.227266 | − | 0.0738431i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 123.526 | − | 380.175i | 0.239392 | − | 0.736773i | ||||
\(517\) | −676.531 | + | 107.152i | −1.30857 | + | 0.207257i | ||||
\(518\) | 10.5743 | + | 10.5743i | 0.0204137 | + | 0.0204137i | ||||
\(519\) | −474.774 | + | 653.470i | −0.914785 | + | 1.25909i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 260.762 | − | 189.454i | 0.500502 | − | 0.363636i | −0.308707 | − | 0.951157i | \(-0.599896\pi\) |
0.809209 | + | 0.587521i | \(0.199896\pi\) | |||||||
\(522\) | 53.6146 | − | 338.509i | 0.102710 | − | 0.648485i | ||||
\(523\) | 62.4913 | − | 122.646i | 0.119486 | − | 0.234505i | −0.823515 | − | 0.567295i | \(-0.807990\pi\) |
0.943001 | + | 0.332790i | \(0.107990\pi\) | |||||||
\(524\) | 192.207i | 0.366806i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 514.312 | 0.977780 | ||||||||
\(527\) | 10.1789 | + | 5.18641i | 0.0193148 | + | 0.00984139i | ||||
\(528\) | −197.551 | − | 31.2890i | −0.374150 | − | 0.0592595i | ||||
\(529\) | −248.579 | − | 342.140i | −0.469904 | − | 0.646767i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 209.555 | + | 152.250i | 0.394641 | + | 0.286724i | ||||
\(532\) | 40.0702 | − | 40.0702i | 0.0753199 | − | 0.0753199i | ||||
\(533\) | −95.5460 | − | 603.254i | −0.179261 | − | 1.13181i | ||||
\(534\) | 294.483 | + | 95.6834i | 0.551467 | + | 0.179182i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −56.4755 | − | 173.814i | −0.105365 | − | 0.324279i | ||||
\(537\) | 107.433 | + | 210.849i | 0.200061 | + | 0.392643i | ||||
\(538\) | −396.221 | + | 201.885i | −0.736471 | + | 0.375251i | ||||
\(539\) | −629.354 | + | 204.490i | −1.16763 | + | 0.379387i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 195.153 | − | 600.618i | 0.360726 | − | 1.11020i | −0.591889 | − | 0.806020i | \(-0.701617\pi\) |
0.952614 | − | 0.304180i | \(-0.0983825\pi\) | |||||||
\(542\) | −339.257 | + | 53.7330i | −0.625935 | + | 0.0991383i | ||||
\(543\) | 546.033 | + | 546.033i | 1.00559 | + | 1.00559i | ||||
\(544\) | 19.5665 | − | 26.9310i | 0.0359678 | − | 0.0495054i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 34.1902 | − | 24.8407i | 0.0626195 | − | 0.0454957i | ||||
\(547\) | 15.5855 | − | 98.4028i | 0.0284926 | − | 0.179895i | −0.969338 | − | 0.245732i | \(-0.920972\pi\) |
0.997830 | + | 0.0658367i | \(0.0209717\pi\) | |||||||
\(548\) | −217.430 | + | 426.731i | −0.396771 | + | 0.778707i | ||||
\(549\) | 60.3591i | 0.109944i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1792.47 | −3.25312 | ||||||||
\(552\) | −283.142 | − | 144.268i | −0.512939 | − | 0.261355i | ||||
\(553\) | −50.4750 | − | 7.99445i | −0.0912748 | − | 0.0144565i | ||||
\(554\) | −356.587 | − | 490.800i | −0.643659 | − | 0.885920i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 225.702 | + | 163.982i | 0.405939 | + | 0.294932i | ||||
\(557\) | 557.960 | − | 557.960i | 1.00172 | − | 1.00172i | 0.00172416 | − | 0.999999i | \(-0.499451\pi\) |
0.999999 | − | 0.00172416i | \(-0.000548818\pi\) | |||||||
\(558\) | −1.82986 | − | 11.5533i | −0.00327932 | − | 0.0207048i | ||||
\(559\) | −476.430 | − | 154.801i | −0.852290 | − | 0.276926i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −90.9286 | − | 279.850i | −0.162083 | − | 0.498841i | ||||
\(562\) | −143.601 | − | 281.833i | −0.255518 | − | 0.501483i | ||||
\(563\) | −99.2730 | + | 50.5821i | −0.176329 | + | 0.0898439i | −0.539927 | − | 0.841712i | \(-0.681548\pi\) |
0.363598 | + | 0.931556i | \(0.381548\pi\) | |||||||
\(564\) | −345.515 | + | 112.265i | −0.612616 | + | 0.199051i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 155.796 | − | 479.492i | 0.275258 | − | 0.847158i | ||||
\(567\) | −89.8649 | + | 14.2332i | −0.158492 | + | 0.0251027i | ||||
\(568\) | 62.8891 | + | 62.8891i | 0.110720 | + | 0.110720i | ||||
\(569\) | −1.68455 | + | 2.31858i | −0.00296054 | + | 0.00407483i | −0.810495 | − | 0.585746i | \(-0.800802\pi\) |
0.807534 | + | 0.589821i | \(0.200802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −144.753 | + | 105.169i | −0.253507 | + | 0.184184i | −0.707280 | − | 0.706934i | \(-0.750078\pi\) |
0.453773 | + | 0.891118i | \(0.350078\pi\) | |||||||
\(572\) | −39.2109 | + | 247.568i | −0.0685506 | + | 0.432811i | ||||
\(573\) | 152.505 | − | 299.308i | 0.266151 | − | 0.522352i | ||||
\(574\) | − | 85.0922i | − | 0.148244i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −34.0847 | −0.0591748 | ||||||||
\(577\) | −426.909 | − | 217.521i | −0.739878 | − | 0.376987i | 0.0430716 | − | 0.999072i | \(-0.486286\pi\) |
−0.782949 | + | 0.622085i | \(0.786286\pi\) | |||||||
\(578\) | −355.306 | − | 56.2750i | −0.614717 | − | 0.0973615i | ||||
\(579\) | 457.421 | + | 629.586i | 0.790019 | + | 1.08737i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.4623 | + | 21.4056i | 0.0507096 | + | 0.0368427i | ||||
\(582\) | 45.3588 | − | 45.3588i | 0.0779361 | − | 0.0779361i | ||||
\(583\) | −78.2602 | − | 494.115i | −0.134237 | − | 0.847539i | ||||
\(584\) | 186.342 | + | 60.5461i | 0.319078 | + | 0.103675i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −205.038 | − | 631.041i | −0.349893 | − | 1.07686i | ||||
\(587\) | −390.539 | − | 766.476i | −0.665313 | − | 1.30575i | −0.938995 | − | 0.343931i | \(-0.888241\pi\) |
0.273682 | − | 0.961820i | \(-0.411759\pi\) | |||||||
\(588\) | −312.725 | + | 159.342i | −0.531846 | + | 0.270989i | ||||
\(589\) | −58.1826 | + | 18.9047i | −0.0987819 | + | 0.0320962i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −76.2343 | + | 234.625i | −0.128992 | + | 0.396997i | ||||
\(592\) | −46.4634 | + | 7.35908i | −0.0784854 | + | 0.0124309i | ||||
\(593\) | −735.093 | − | 735.093i | −1.23962 | − | 1.23962i | −0.960158 | − | 0.279459i | \(-0.909845\pi\) |
−0.279459 | − | 0.960158i | \(-0.590155\pi\) | |||||||
\(594\) | 196.996 | − | 271.142i | 0.331643 | − | 0.456468i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −304.181 | + | 221.000i | −0.510370 | + | 0.370806i | ||||
\(597\) | 64.6457 | − | 408.157i | 0.108284 | − | 0.683680i | ||||
\(598\) | −180.795 | + | 354.830i | −0.302332 | + | 0.593361i | ||||
\(599\) | − | 515.872i | − | 0.861222i | −0.902538 | − | 0.430611i | \(-0.858298\pi\) | ||
0.902538 | − | 0.430611i | \(-0.141702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 707.544 | 1.17728 | 0.588639 | − | 0.808396i | \(-0.299664\pi\) | ||||
0.588639 | + | 0.808396i | \(0.299664\pi\) | |||||||
\(602\) | −62.1846 | − | 31.6847i | −0.103297 | − | 0.0526323i | ||||
\(603\) | −271.908 | − | 43.0660i | −0.450925 | − | 0.0714195i | ||||
\(604\) | 188.396 | + | 259.305i | 0.311914 | + | 0.429313i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −275.255 | − | 199.985i | −0.454217 | − | 0.330008i | ||||
\(607\) | −422.828 | + | 422.828i | −0.696587 | + | 0.696587i | −0.963673 | − | 0.267086i | \(-0.913939\pi\) |
0.267086 | + | 0.963673i | \(0.413939\pi\) | |||||||
\(608\) | 27.8864 | + | 176.068i | 0.0458658 | + | 0.289585i | ||||
\(609\) | −177.123 | − | 57.5507i | −0.290842 | − | 0.0945004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 140.689 | + | 432.995i | 0.230259 | + | 0.708666i | ||||
\(612\) | −22.7649 | − | 44.6786i | −0.0371975 | − | 0.0730042i | ||||
\(613\) | 879.227 | − | 447.989i | 1.43430 | − | 0.730813i | 0.447734 | − | 0.894167i | \(-0.352231\pi\) |
0.986568 | + | 0.163353i | \(0.0522310\pi\) | |||||||
\(614\) | 10.1445 | − | 3.29614i | 0.0165219 | − | 0.00536831i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.7911 | + | 33.2117i | −0.0175181 | + | 0.0539150i | ||||
\(617\) | −601.071 | + | 95.2002i | −0.974182 | + | 0.154295i | −0.623179 | − | 0.782079i | \(-0.714159\pi\) |
−0.351003 | + | 0.936374i | \(0.614159\pi\) | |||||||
\(618\) | −37.2083 | − | 37.2083i | −0.0602075 | − | 0.0602075i | ||||
\(619\) | −716.320 | + | 985.930i | −1.15722 | + | 1.59278i | −0.436227 | + | 0.899836i | \(0.643686\pi\) |
−0.720994 | + | 0.692942i | \(0.756314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 430.786 | − | 312.984i | 0.693697 | − | 0.504000i | ||||
\(622\) | 56.1099 | − | 354.264i | 0.0902089 | − | 0.569557i | ||||
\(623\) | 24.5429 | − | 48.1681i | 0.0393947 | − | 0.0773164i | ||||
\(624\) | 132.944i | 0.213051i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 187.456 | 0.299451 | ||||||||
\(627\) | 1403.99 | + | 715.371i | 2.23923 | + | 1.14094i | ||||
\(628\) | −245.851 | − | 38.9390i | −0.391483 | − | 0.0620048i | ||||
\(629\) | −40.6788 | − | 55.9896i | −0.0646723 | − | 0.0890137i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −694.007 | − | 504.226i | −1.09985 | − | 0.799090i | −0.118817 | − | 0.992916i | \(-0.537910\pi\) |
−0.981036 | + | 0.193827i | \(0.937910\pi\) | |||||||
\(632\) | 113.675 | − | 113.675i | 0.179865 | − | 0.179865i | ||||
\(633\) | −6.46745 | − | 40.8339i | −0.0102171 | − | 0.0645085i | ||||
\(634\) | 302.361 | + | 98.2430i | 0.476910 | + | 0.154957i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −81.9944 | − | 252.353i | −0.128922 | − | 0.396781i | ||||
\(637\) | 199.685 | + | 391.903i | 0.313477 | + | 0.615233i | ||||
\(638\) | 984.192 | − | 501.471i | 1.54262 | − | 0.786004i | ||||
\(639\) | 127.415 | − | 41.3997i | 0.199398 | − | 0.0647882i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −263.656 | + | 811.451i | −0.411321 | + | 1.26591i | 0.504180 | + | 0.863598i | \(0.331795\pi\) |
−0.915501 | + | 0.402316i | \(0.868205\pi\) | |||||||
\(642\) | 204.872 | − | 32.4485i | 0.319115 | − | 0.0505429i | ||||
\(643\) | −382.594 | − | 382.594i | −0.595015 | − | 0.595015i | 0.343967 | − | 0.938982i | \(-0.388229\pi\) |
−0.938982 | + | 0.343967i | \(0.888229\pi\) | |||||||
\(644\) | −32.6112 | + | 44.8855i | −0.0506386 | + | 0.0696980i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −212.167 | + | 154.148i | −0.328431 | + | 0.238619i | ||||
\(647\) | 36.6956 | − | 231.687i | 0.0567165 | − | 0.358094i | −0.942966 | − | 0.332890i | \(-0.891976\pi\) |
0.999682 | − | 0.0252045i | \(-0.00802368\pi\) | |||||||
\(648\) | 129.939 | − | 255.020i | 0.200524 | − | 0.393550i | ||||
\(649\) | 834.811i | 1.28630i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.35629 | −0.00976389 | ||||||||
\(652\) | 324.239 | + | 165.208i | 0.497298 | + | 0.253386i | ||||
\(653\) | 344.513 | + | 54.5654i | 0.527584 | + | 0.0835612i | 0.414544 | − | 0.910029i | \(-0.363941\pi\) |
0.113040 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(654\) | −161.379 | − | 222.118i | −0.246756 | − | 0.339631i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 216.556 | + | 157.337i | 0.330116 | + | 0.239844i | ||||
\(657\) | 208.696 | − | 208.696i | 0.317649 | − | 0.317649i | ||||
\(658\) | 9.92244 | + | 62.6478i | 0.0150797 | + | 0.0952094i | ||||
\(659\) | 130.784 | + | 42.4942i | 0.198458 | + | 0.0644829i | 0.406559 | − | 0.913624i | \(-0.366728\pi\) |
−0.208101 | + | 0.978107i | \(0.566728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 60.3829 | + | 185.840i | 0.0913509 | + | 0.281149i | 0.986286 | − | 0.165048i | \(-0.0527780\pi\) |
−0.894935 | + | 0.446197i | \(0.852778\pi\) | |||||||
\(662\) | −270.522 | − | 530.930i | −0.408644 | − | 0.802009i | ||||
\(663\) | −174.264 | + | 88.7920i | −0.262842 | + | 0.133925i | ||||
\(664\) | −108.953 | + | 35.4010i | −0.164086 | + | 0.0533147i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.8976 | + | 67.3940i | −0.0328793 | + | 0.101192i | ||||
\(667\) | 1733.34 | − | 274.534i | 2.59871 | − | 0.411595i | ||||
\(668\) | −256.687 | − | 256.687i | −0.384263 | − | 0.384263i | ||||
\(669\) | 313.726 | − | 431.806i | 0.468947 | − | 0.645450i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −157.380 | + | 114.343i | −0.234545 | + | 0.170407i | ||||
\(672\) | −2.89741 | + | 18.2935i | −0.00431162 | + | 0.0272225i | ||||
\(673\) | −79.6810 | + | 156.383i | −0.118397 | + | 0.232367i | −0.942598 | − | 0.333931i | \(-0.891625\pi\) |
0.824201 | + | 0.566298i | \(0.191625\pi\) | |||||||
\(674\) | 494.999i | 0.734420i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −171.397 | −0.253545 | ||||||||
\(677\) | −430.607 | − | 219.405i | −0.636051 | − | 0.324084i | 0.106061 | − | 0.994360i | \(-0.466176\pi\) |
−0.742112 | + | 0.670275i | \(0.766176\pi\) | |||||||
\(678\) | −547.804 | − | 86.7637i | −0.807971 | − | 0.127970i | ||||
\(679\) | −6.58295 | − | 9.06065i | −0.00969506 | − | 0.0133441i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 620.508 | + | 450.825i | 0.911172 | + | 0.662005i | ||||
\(682\) | 26.6575 | − | 26.6575i | 0.0390872 | − | 0.0390872i | ||||
\(683\) | −42.2070 | − | 266.484i | −0.0617964 | − | 0.390167i | −0.999129 | − | 0.0417309i | \(-0.986713\pi\) |
0.937332 | − | 0.348436i | \(-0.113287\pi\) | |||||||
\(684\) | 255.382 | + | 82.9788i | 0.373366 | + | 0.121314i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 38.1898 | + | 117.536i | 0.0556702 | + | 0.171335i | ||||
\(687\) | −314.446 | − | 617.134i | −0.457708 | − | 0.898303i | ||||
\(688\) | 195.617 | − | 99.6719i | 0.284327 | − | 0.144872i | ||||
\(689\) | −316.245 | + | 102.754i | −0.458991 | + | 0.149135i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.1934 | + | 120.625i | −0.0567198 | + | 0.174565i | −0.975403 | − | 0.220430i | \(-0.929254\pi\) |
0.918683 | + | 0.394996i | \(0.129254\pi\) | |||||||
\(692\) | −438.164 | + | 69.3983i | −0.633185 | + | 0.100287i | ||||
\(693\) | 37.1958 | + | 37.1958i | 0.0536735 | + | 0.0536735i | ||||
\(694\) | 137.373 | − | 189.077i | 0.197943 | − | 0.272445i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 473.969 | − | 344.359i | 0.680990 | − | 0.494768i | ||||
\(697\) | −61.6034 | + | 388.949i | −0.0883837 | + | 0.558033i | ||||
\(698\) | 347.736 | − | 682.471i | 0.498190 | − | 0.977752i | ||||
\(699\) | 1616.83i | 2.31307i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −988.792 | −1.41054 | −0.705272 | − | 0.708937i | \(-0.749175\pi\) | ||||
−0.705272 | + | 0.708937i | \(0.749175\pi\) | |||||||
\(702\) | −198.485 | − | 101.133i | −0.282743 | − | 0.144065i | ||||
\(703\) | 366.046 | + | 57.9761i | 0.520692 | + | 0.0824695i | ||||
\(704\) | −64.5694 | − | 88.8721i | −0.0917179 | − | 0.126239i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.51057 | − | 4.73020i | −0.00922177 | − | 0.00670001i | ||||
\(707\) | −42.0037 | + | 42.0037i | −0.0594112 | + | 0.0594112i | ||||
\(708\) | 69.2650 | + | 437.322i | 0.0978320 | + | 0.617687i | ||||
\(709\) | 1071.72 | + | 348.224i | 1.51160 | + | 0.491148i | 0.943375 | − | 0.331728i | \(-0.107631\pi\) |
0.568222 | + | 0.822875i | \(0.307631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −74.8319 | − | 230.309i | −0.105249 | − | 0.323922i | ||||
\(712\) | 77.2057 | + | 151.525i | 0.108435 | + | 0.212816i | ||||
\(713\) | 53.3678 | − | 27.1923i | 0.0748497 | − | 0.0381378i | ||||
\(714\) | −25.9145 | + | 8.42014i | −0.0362948 | + | 0.0117929i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −40.1626 | + | 123.608i | −0.0560930 | + | 0.172637i | ||||
\(717\) | −928.982 | + | 147.136i | −1.29565 | + | 0.205211i | ||||
\(718\) | 49.1583 | + | 49.1583i | 0.0684656 | + | 0.0684656i | ||||
\(719\) | 52.6231 | − | 72.4294i | 0.0731892 | − | 0.100736i | −0.770853 | − | 0.637013i | \(-0.780170\pi\) |
0.844042 | + | 0.536277i | \(0.180170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.43253 | + | 5.40005i | −0.0103086 | + | 0.00748967i | ||||
\(722\) | 139.829 | − | 882.848i | 0.193669 | − | 1.22278i | ||||
\(723\) | −269.729 | + | 529.373i | −0.373069 | + | 0.732190i | ||||
\(724\) | 424.114i | 0.585793i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −347.895 | −0.479194 | ||||||||
\(727\) | 596.168 | + | 303.763i | 0.820038 | + | 0.417830i | 0.813085 | − | 0.582145i | \(-0.197787\pi\) |
0.00695359 | + | 0.999976i | \(0.497787\pi\) | |||||||
\(728\) | 22.9252 | + | 3.63099i | 0.0314906 | + | 0.00498763i | ||||
\(729\) | 79.0493 | + | 108.802i | 0.108435 | + | 0.149248i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 261.302 | + | 189.847i | 0.357458 | + | 0.259709i | ||||
\(732\) | −72.9574 | + | 72.9574i | −0.0996686 | + | 0.0996686i | ||||
\(733\) | 38.0021 | + | 239.936i | 0.0518446 | + | 0.327334i | 0.999956 | + | 0.00939532i | \(0.00299067\pi\) |
−0.948111 | + | 0.317939i | \(0.897009\pi\) | |||||||
\(734\) | −481.240 | − | 156.364i | −0.655641 | − | 0.213031i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.9330 | − | 165.989i | −0.0732786 | − | 0.225528i | ||||
\(737\) | −402.807 | − | 790.554i | −0.546550 | − | 1.07266i | ||||
\(738\) | 359.268 | − | 183.056i | 0.486813 | − | 0.248044i | ||||
\(739\) | 1232.20 | − | 400.367i | 1.66739 | − | 0.541769i | 0.684993 | − | 0.728550i | \(-0.259805\pi\) |
0.982402 | + | 0.186781i | \(0.0598054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 323.650 | − | 996.093i | 0.436775 | − | 1.34425i | ||||
\(742\) | −45.7559 | + | 7.24702i | −0.0616656 | + | 0.00976687i | ||||
\(743\) | −560.204 | − | 560.204i | −0.753976 | − | 0.753976i | 0.221243 | − | 0.975219i | \(-0.428989\pi\) |
−0.975219 | + | 0.221243i | \(0.928989\pi\) | |||||||
\(744\) | 11.7529 | − | 16.1765i | 0.0157969 | − | 0.0217426i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −189.191 | + | 137.455i | −0.253607 | + | 0.184257i | ||||
\(747\) | −26.9954 | + | 170.442i | −0.0361384 | + | 0.228169i | ||||
\(748\) | 73.3692 | − | 143.995i | 0.0980872 | − | 0.192507i | ||||
\(749\) | − | 36.2149i | − | 0.0483510i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1236.03 | 1.64585 | 0.822926 | − | 0.568149i | \(-0.192340\pi\) | ||||
0.822926 | + | 0.568149i | \(0.192340\pi\) | |||||||
\(752\) | −177.783 | − | 90.5850i | −0.236414 | − | 0.120459i | ||||
\(753\) | 968.601 | + | 153.411i | 1.28632 | + | 0.203734i | ||||
\(754\) | −431.545 | − | 593.971i | −0.572341 | − | 0.787760i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −25.1082 | − | 18.2422i | −0.0332119 | − | 0.0241298i | ||||
\(757\) | −212.988 | + | 212.988i | −0.281358 | + | 0.281358i | −0.833650 | − | 0.552293i | \(-0.813753\pi\) |
0.552293 | + | 0.833650i | \(0.313753\pi\) | |||||||
\(758\) | 130.402 | + | 823.324i | 0.172034 | + | 1.08618i | ||||
\(759\) | −1467.25 | − | 476.737i | −1.93313 | − | 0.628112i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −93.0421 | − | 286.354i | −0.122263 | − | 0.376287i | 0.871129 | − | 0.491053i | \(-0.163388\pi\) |
−0.993392 | + | 0.114767i | \(0.963388\pi\) | |||||||
\(762\) | 206.499 | + | 405.277i | 0.270996 | + | 0.531860i | ||||
\(763\) | −42.7103 | + | 21.7620i | −0.0559768 | + | 0.0285216i | ||||
\(764\) | 175.465 | − | 57.0122i | 0.229667 | − | 0.0746233i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −298.588 | + | 918.958i | −0.389801 | + | 1.19968i | ||||
\(767\) | 548.046 | − | 86.8019i | 0.714532 | − | 0.113171i | ||||
\(768\) | −41.1990 | − | 41.1990i | −0.0536445 | − | 0.0536445i | ||||
\(769\) | −191.979 | + | 264.237i | −0.249648 | + | 0.343611i | −0.915388 | − | 0.402573i | \(-0.868116\pi\) |
0.665740 | + | 0.746184i | \(0.268116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 255.867 | − | 185.898i | 0.331864 | − | 0.241113i | ||||
\(772\) | −66.8618 | + | 422.149i | −0.0866086 | + | 0.546825i | ||||
\(773\) | −484.917 | + | 951.703i | −0.627318 | + | 1.23118i | 0.330500 | + | 0.943806i | \(0.392783\pi\) |
−0.957818 | + | 0.287375i | \(0.907217\pi\) | |||||||
\(774\) | − | 330.712i | − | 0.427277i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35.2310 | 0.0454008 | ||||||||
\(777\) | 34.3095 | + | 17.4816i | 0.0441564 | + | 0.0224988i | ||||
\(778\) | −219.293 | − | 34.7327i | −0.281868 | − | 0.0446435i | ||||
\(779\) | −1239.53 | − | 1706.07i | −1.59118 | − | 2.19007i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 349.318 | + | 253.794i | 0.447270 | + | 0.324961i | ||||
\(782\) | 181.558 | − | 181.558i | 0.232172 | − | 0.232172i | ||||
\(783\) | 153.569 | + | 969.599i | 0.196129 | + | 1.23831i | ||||
\(784\) | −183.332 | − | 59.5681i | −0.233841 | − | 0.0759797i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 152.939 | + | 470.696i | 0.194578 | + | 0.598850i | ||||
\(787\) | 205.111 | + | 402.553i | 0.260624 | + | 0.511503i | 0.983825 | − | 0.179135i | \(-0.0573298\pi\) |
−0.723201 | + | 0.690638i | \(0.757330\pi\) | |||||||
\(788\) | −120.725 | + | 61.5125i | −0.153205 | + | 0.0780616i | ||||
\(789\) | 1259.50 | − | 409.237i | 1.59633 | − | 0.518679i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.9235 | + | 92.0952i | −0.0378300 | + | 0.116429i | ||||
\(792\) | −163.438 | + | 25.8860i | −0.206361 | + | 0.0326843i | ||||
\(793\) | 91.4292 | + | 91.4292i | 0.115295 | + | 0.115295i | ||||
\(794\) | 144.153 | − | 198.409i | 0.181553 | − | 0.249886i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 183.617 | − | 133.406i | 0.230675 | − | 0.167595i | ||||
\(797\) | −8.61487 | + | 54.3922i | −0.0108091 | + | 0.0682461i | −0.992503 | − | 0.122218i | \(-0.960999\pi\) |
0.981694 | + | 0.190464i | \(0.0609993\pi\) | |||||||
\(798\) | 66.2445 | − | 130.012i | 0.0830131 | − | 0.162922i | ||||
\(799\) | − | 293.541i | − | 0.367385i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 256.169 | 0.319812 | ||||||||
\(802\) | 516.919 | + | 263.384i | 0.644538 | + | 0.328408i | ||||
\(803\) | 939.500 | + | 148.802i | 1.16999 | + | 0.185308i | ||||
\(804\) | −276.607 | − | 380.716i | −0.344038 | − | 0.473528i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.2722 | − | 14.7286i | −0.0251516 | − | 0.0182737i | ||||
\(807\) | −809.670 | + | 809.670i | −1.00331 | + | 1.00331i | ||||
\(808\) | −29.2320 | − | 184.564i | −0.0361783 | − | 0.228421i | ||||
\(809\) | −33.7918 | − | 10.9796i | −0.0417698 | − | 0.0135718i | 0.288058 | − | 0.957613i | \(-0.406991\pi\) |
−0.329827 | + | 0.944041i | \(0.606991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −392.037 | − | 1206.57i | −0.483400 | − | 1.48775i | −0.834285 | − | 0.551333i | \(-0.814119\pi\) |
0.350885 | − | 0.936419i | \(-0.385881\pi\) | |||||||
\(812\) | −46.4370 | − | 91.1377i | −0.0571884 | − | 0.112239i | ||||
\(813\) | −788.054 | + | 401.533i | −0.969316 | + | 0.493891i | ||||
\(814\) | −217.205 | + | 70.5742i | −0.266837 | + | 0.0867005i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 26.4876 | − | 81.5205i | 0.0324603 | − | 0.0999026i | ||||
\(817\) | −1708.33 | + | 270.573i | −2.09098 | + | 0.331178i | ||||
\(818\) | −40.2878 | − | 40.2878i | −0.0492515 | − | 0.0492515i | ||||
\(819\) | 20.5511 | − | 28.2862i | 0.0250930 | − | 0.0345375i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 739.680 | − | 537.409i | 0.900950 | − | 0.654578i | −0.0377601 | − | 0.999287i | \(-0.512022\pi\) |
0.938710 | + | 0.344709i | \(0.112022\pi\) | |||||||
\(822\) | −192.918 | + | 1218.04i | −0.234693 | + | 1.48180i | ||||
\(823\) | −464.929 | + | 912.475i | −0.564920 | + | 1.10872i | 0.415091 | + | 0.909780i | \(0.363750\pi\) |
−0.980012 | + | 0.198939i | \(0.936250\pi\) | |||||||
\(824\) | − | 28.9003i | − | 0.0350732i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 77.3048 | 0.0935894 | ||||||||
\(827\) | 311.391 | + | 158.662i | 0.376531 | + | 0.191852i | 0.632006 | − | 0.774963i | \(-0.282232\pi\) |
−0.255475 | + | 0.966816i | \(0.582232\pi\) | |||||||
\(828\) | −259.667 | − | 41.1272i | −0.313607 | − | 0.0496705i | ||||
\(829\) | −46.1567 | − | 63.5292i | −0.0556775 | − | 0.0766336i | 0.780270 | − | 0.625442i | \(-0.215081\pi\) |
−0.835948 | + | 0.548809i | \(0.815081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1263.78 | − | 918.188i | −1.52079 | − | 1.10492i | ||||
\(832\) | −51.6300 | + | 51.6300i | −0.0620552 | + | 0.0620552i | ||||
\(833\) | −44.3632 | − | 280.098i | −0.0532571 | − | 0.336252i | ||||
\(834\) | 683.204 | + | 221.987i | 0.819190 | + | 0.266171i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 267.433 | + | 823.075i | 0.319896 | + | 0.984540i | ||||
\(837\) | 15.2109 | + | 29.8530i | 0.0181731 | + | 0.0356667i | ||||
\(838\) | 549.323 | − | 279.894i | 0.655517 | − | 0.334002i | ||||
\(839\) | 251.975 | − | 81.8717i | 0.300328 | − | 0.0975824i | −0.154977 | − | 0.987918i | \(-0.549530\pi\) |
0.455305 | + | 0.890336i | \(0.349530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −739.920 | + | 2277.24i | −0.879809 | + | 2.70777i | ||||
\(842\) | 242.752 | − | 38.4482i | 0.288304 | − | 0.0456629i | ||||
\(843\) | −575.921 | − | 575.921i | −0.683180 | − | 0.683180i | ||||
\(844\) | 13.3465 | − | 18.3699i | 0.0158134 | − | 0.0217653i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −243.160 | + | 176.666i | −0.287423 | + | 0.208825i | ||||
\(847\) | −9.50178 | + | 59.9919i | −0.0112182 | + | 0.0708287i | ||||
\(848\) | 66.1603 | − | 129.847i | 0.0780192 | − | 0.153121i | ||||
\(849\) | − | 1298.20i | − | 1.52909i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −362.851 | −0.426382 | ||||||||
\(852\) | 204.050 | + | 103.969i | 0.239496 | + | 0.122029i | ||||
\(853\) | −753.921 | − | 119.409i | −0.883846 | − | 0.139987i | −0.302021 | − | 0.953301i | \(-0.597661\pi\) |
−0.581825 | + | 0.813314i | \(0.697661\pi\) | |||||||
\(854\) | 10.5883 | + | 14.5736i | 0.0123985 | + | 0.0170651i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 92.1656 | + | 66.9622i | 0.107670 | + | 0.0782269i | ||||
\(857\) | 326.208 | − | 326.208i | 0.380639 | − | 0.380639i | −0.490693 | − | 0.871332i | \(-0.663256\pi\) |
0.871332 | + | 0.490693i | \(0.163256\pi\) | |||||||
\(858\) | 100.966 | + | 637.472i | 0.117676 | + | 0.742974i | ||||
\(859\) | 1286.41 | + | 417.979i | 1.49756 | + | 0.486588i | 0.939306 | − | 0.343080i | \(-0.111470\pi\) |
0.558257 | + | 0.829668i | \(0.311470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −67.7077 | − | 208.383i | −0.0786385 | − | 0.242024i | ||||
\(862\) | −78.5260 | − | 154.116i | −0.0910974 | − | 0.178789i | ||||
\(863\) | 295.874 | − | 150.755i | 0.342843 | − | 0.174687i | −0.274088 | − | 0.961705i | \(-0.588376\pi\) |
0.616931 | + | 0.787017i | \(0.288376\pi\) | |||||||
\(864\) | 92.8512 | − | 30.1692i | 0.107467 | − | 0.0349180i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 128.509 | − | 395.510i | 0.148394 | − | 0.456709i | ||||
\(867\) | −914.890 | + | 144.904i | −1.05524 | + | 0.167133i | ||||
\(868\) | −2.46852 | − | 2.46852i | −0.00284392 | − | 0.00284392i | ||||
\(869\) | 458.745 | − | 631.409i | 0.527900 | − | 0.726592i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −477.108 | + | 346.640i | −0.547771 | + | 0.397979i | ||||
\(872\) | 23.5889 | − | 148.935i | 0.0270515 | − | 0.170797i | ||||
\(873\) | 24.0933 | − | 47.2858i | 0.0275983 | − | 0.0541647i | ||||
\(874\) | 1374.98i | 1.57321i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 504.511 | 0.575925 | ||||||||
\(877\) | 973.819 | + | 496.185i | 1.11040 | + | 0.565776i | 0.910279 | − | 0.413996i | \(-0.135867\pi\) |
0.200119 | + | 0.979772i | \(0.435867\pi\) | |||||||
\(878\) | −199.583 | − | 31.6108i | −0.227316 | − | 0.0360032i | ||||
\(879\) | −1004.24 | − | 1382.21i | −1.14248 | − | 1.57248i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 489.612 | + | 355.724i | 0.555745 | + | 0.403773i | 0.829899 | − | 0.557913i | \(-0.188398\pi\) |
−0.274154 | + | 0.961686i | \(0.588398\pi\) | |||||||
\(882\) | −205.324 | + | 205.324i | −0.232794 | + | 0.232794i | ||||
\(883\) | −181.570 | − | 1146.39i | −0.205628 | − | 1.29829i | −0.847221 | − | 0.531241i | \(-0.821726\pi\) |
0.641592 | − | 0.767046i | \(-0.278274\pi\) | |||||||
\(884\) | −102.160 | − | 33.1939i | −0.115566 | − | 0.0375497i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.49138 | + | 26.1338i | 0.00958395 | + | 0.0294964i | ||||
\(887\) | −309.274 | − | 606.984i | −0.348674 | − | 0.684311i | 0.648355 | − | 0.761338i | \(-0.275457\pi\) |
−0.997029 | + | 0.0770268i | \(0.975457\pi\) | |||||||
\(888\) | −107.929 | + | 54.9926i | −0.121542 | + | 0.0619286i | ||||
\(889\) | 75.5271 | − | 24.5402i | 0.0849574 | − | 0.0276043i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 429.387 | − | 1321.52i | 0.481916 | − | 1.48319i | ||||
\(892\) | 289.534 | − | 45.8577i | 0.324590 | − | 0.0514100i | ||||
\(893\) | 1111.53 | + | 1111.53i | 1.24471 | + | 1.24471i | ||||
\(894\) | −569.061 | + | 783.246i | −0.636534 | + | 0.876114i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.22970 | + | 5.97923i | −0.00918493 | + | 0.00667324i | ||||
\(897\) | −160.412 | + | 1012.80i | −0.178832 | + | 1.12910i | ||||
\(898\) | 201.477 | − | 395.421i | 0.224362 | − | 0.440335i | ||||
\(899\) | 110.425i | 0.122831i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 214.393 | 0.237950 | ||||||||
\(902\) | 1157.89 | + | 589.974i | 1.28369 | + | 0.654073i | ||||
\(903\) | −177.496 | − | 28.1126i | −0.196563 | − | 0.0311324i | ||||
\(904\) | −179.049 | − | 246.440i | −0.198063 | − | 0.272611i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 667.693 | + | 485.108i | 0.736968 | + | 0.535439i | ||||
\(907\) | 911.088 | − | 911.088i | 1.00451 | − | 1.00451i | 0.00451769 | − | 0.999990i | \(-0.498562\pi\) |
0.999990 | − | 0.00451769i | \(-0.00143803\pi\) | |||||||
\(908\) | 65.8978 | + | 416.062i | 0.0725746 | + | 0.458218i | ||||
\(909\) | −267.705 | − | 86.9828i | −0.294505 | − | 0.0956906i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 315.739 | + | 971.745i | 0.346585 | + | 1.06668i | 0.960730 | + | 0.277486i | \(0.0895011\pi\) |
−0.614145 | + | 0.789193i | \(0.710499\pi\) | |||||||
\(912\) | 208.388 | + | 408.985i | 0.228496 | + | 0.448449i | ||||
\(913\) | −495.549 | + | 252.495i | −0.542770 | + | 0.276555i | ||||
\(914\) | −69.4466 | + | 22.5646i | −0.0759810 | + | 0.0246877i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 117.552 | − | 361.788i | 0.128332 | − | 0.394965i | ||||
\(917\) | 85.3453 | − | 13.5174i | 0.0930701 | − | 0.0147409i | ||||
\(918\) | 101.561 | + | 101.561i | 0.110632 | + | 0.110632i | ||||
\(919\) | −713.919 | + | 982.625i | −0.776843 | + | 1.06923i | 0.218780 | + | 0.975774i | \(0.429792\pi\) |
−0.995623 | + | 0.0934584i | \(0.970208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.2202 | − | 16.1439i | 0.0241261 | − | 0.0175287i | ||||
\(922\) | −180.634 | + | 1140.48i | −0.195915 | + | 1.23696i | ||||
\(923\) | 130.292 | − | 255.713i | 0.141162 | − | 0.277045i | ||||
\(924\) | 89.9188i | 0.0973147i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −777.796 | −0.839953 | ||||||||
\(927\) | −38.7890 | − | 19.7640i | −0.0418435 | − | 0.0213203i | ||||
\(928\) | 317.805 | + | 50.3354i | 0.342462 | + | 0.0542407i | ||||
\(929\) | 317.570 | + | 437.097i | 0.341840 | + | 0.470503i | 0.944978 | − | 0.327134i | \(-0.106083\pi\) |
−0.603137 | + | 0.797637i | \(0.706083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1228.61 | + | 892.637i | 1.31967 | + | 0.958794i | ||||
\(932\) | −627.912 | + | 627.912i | −0.673726 | + | 0.673726i | ||||
\(933\) | −144.479 | − | 912.208i | −0.154855 | − | 0.977714i | ||||
\(934\) | 791.630 | + | 257.216i | 0.847570 | + | 0.275392i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.9878 | + | 104.604i | 0.0363118 | + | 0.111756i | ||||
\(937\) | −300.755 | − | 590.265i | −0.320976 | − | 0.629952i | 0.672988 | − | 0.739653i | \(-0.265011\pi\) |
−0.993965 | + | 0.109701i | \(0.965011\pi\) | |||||||
\(938\) | −73.2065 | + | 37.3006i | −0.0780453 | + | 0.0397661i | ||||
\(939\) | 459.064 | − | 149.159i | 0.488886 | − | 0.158849i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.8066 | − | 54.8030i | 0.0189230 | − | 0.0582391i | −0.941149 | − | 0.337992i | \(-0.890252\pi\) |
0.960072 | + | 0.279753i | \(0.0902524\pi\) | |||||||
\(942\) | −633.052 | + | 100.266i | −0.672029 | + | 0.106439i | ||||
\(943\) | 1459.94 | + | 1459.94i | 1.54819 | + | 1.54819i | ||||
\(944\) | −142.938 | + | 196.738i | −0.151418 | + | 0.208409i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 862.296 | − | 626.495i | 0.911518 | − | 0.662257i | ||||
\(947\) | 16.9962 | − | 107.310i | 0.0179474 | − | 0.113316i | −0.977088 | − | 0.212835i | \(-0.931730\pi\) |
0.995036 | + | 0.0995191i | \(0.0317304\pi\) | |||||||
\(948\) | 187.929 | − | 368.831i | 0.198237 | − | 0.389062i | ||||
\(949\) | − | 632.245i | − | 0.666223i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 818.627 | 0.860806 | ||||||||
\(952\) | −13.3342 | − | 6.79410i | −0.0140065 | − | 0.00713666i | ||||
\(953\) | 69.0176 | + | 10.9313i | 0.0724214 | + | 0.0114704i | 0.192540 | − | 0.981289i | \(-0.438327\pi\) |
−0.120119 | + | 0.992760i | \(0.538327\pi\) | |||||||
\(954\) | −129.031 | − | 177.596i | −0.135252 | − | 0.186159i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −417.920 | − | 303.637i | −0.437155 | − | 0.317612i | ||||
\(957\) | 2011.18 | − | 2011.18i | 2.10154 | − | 2.10154i | ||||
\(958\) | 46.2244 | + | 291.849i | 0.0482509 | + | 0.304644i | ||||
\(959\) | 204.772 | + | 66.5346i | 0.213527 | + | 0.0693791i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −295.801 | − | 910.381i | −0.307805 | − | 0.947327i | ||||
\(962\) | 68.9159 | + | 135.255i | 0.0716381 | + | 0.140598i | ||||
\(963\) | 152.903 | − | 77.9080i | 0.158778 | − | 0.0809014i | ||||
\(964\) | −310.339 | + | 100.835i | −0.321928 | + | 0.104601i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −44.1466 | + | 135.869i | −0.0457004 | + | 0.140651i | ||||
\(967\) | 382.375 | − | 60.5623i | 0.395424 | − | 0.0626290i | 0.0444438 | − | 0.999012i | \(-0.485848\pi\) |
0.350980 | + | 0.936383i | \(0.385848\pi\) | |||||||
\(968\) | −135.108 | − | 135.108i | −0.139574 | − | 0.139574i | ||||
\(969\) | −396.921 | + | 546.315i | −0.409620 | + | 0.563793i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −801.968 | + | 582.664i | −0.825920 | + | 0.600066i | −0.918402 | − | 0.395648i | \(-0.870520\pi\) |
0.0924822 | + | 0.995714i | \(0.470520\pi\) | |||||||
\(972\) | 66.6932 | − | 421.084i | 0.0686144 | − | 0.433214i | ||||
\(973\) | 56.9398 | − | 111.751i | 0.0585198 | − | 0.114852i | ||||
\(974\) | 235.456i | 0.241741i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −56.6674 | −0.0580608 | ||||||||
\(977\) | −813.120 | − | 414.305i | −0.832262 | − | 0.424059i | −0.0146951 | − | 0.999892i | \(-0.504678\pi\) |
−0.817567 | + | 0.575833i | \(0.804678\pi\) | |||||||
\(978\) | 925.486 | + | 146.583i | 0.946305 | + | 0.149880i | ||||
\(979\) | 485.282 | + | 667.934i | 0.495692 | + | 0.682261i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −183.763 | − | 133.511i | −0.187322 | − | 0.136097i | ||||
\(982\) | 295.999 | − | 295.999i | 0.301424 | − | 0.301424i | ||||
\(983\) | 93.2715 | + | 588.893i | 0.0948846 | + | 0.599078i | 0.988614 | + | 0.150472i | \(0.0480793\pi\) |
−0.893730 | + | 0.448606i | \(0.851921\pi\) | |||||||
\(984\) | 655.520 | + | 212.991i | 0.666179 | + | 0.216455i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 146.279 | + | 450.201i | 0.148356 | + | 0.456593i | ||||
\(987\) | 74.1479 | + | 145.523i | 0.0751245 | + | 0.147440i | ||||
\(988\) | 512.534 | − | 261.149i | 0.518759 | − | 0.264321i | ||||
\(989\) | 1610.53 | − | 523.294i | 1.62845 | − | 0.529114i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 146.456 | − | 450.746i | 0.147786 | − | 0.454840i | −0.849572 | − | 0.527472i | \(-0.823140\pi\) |
0.997359 | + | 0.0726323i | \(0.0231400\pi\) | |||||||
\(992\) | 10.8467 | − | 1.71794i | 0.0109341 | − | 0.00173180i | ||||
\(993\) | −1084.94 | − | 1084.94i | −1.09259 | − | 1.09259i | ||||
\(994\) | 23.5017 | − | 32.3474i | 0.0236436 | − | 0.0325426i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −238.647 | + | 173.387i | −0.239606 | + | 0.174084i | ||||
\(997\) | −162.004 | + | 1022.85i | −0.162492 | + | 1.02593i | 0.762789 | + | 0.646648i | \(0.223830\pi\) |
−0.925280 | + | 0.379284i | \(0.876170\pi\) | |||||||
\(998\) | 294.991 | − | 578.952i | 0.295582 | − | 0.580112i | ||||
\(999\) | − | 202.972i | − | 0.203176i |
(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 | 250.3.f.a.143.2 | 16 | ||
5.2 | odd | 4 | 50.3.f.a.17.2 | yes | 16 | ||
5.3 | odd | 4 | 250.3.f.b.107.1 | 16 | |||
5.4 | even | 2 | 250.3.f.c.143.1 | 16 | |||
20.7 | even | 4 | 400.3.bg.a.17.1 | 16 | |||
25.3 | odd | 20 | 250.3.f.c.7.1 | 16 | |||
25.4 | even | 10 | 250.3.f.b.243.1 | 16 | |||
25.21 | even | 5 | 50.3.f.a.3.2 | ✓ | 16 | ||
25.22 | odd | 20 | inner | 250.3.f.a.7.2 | 16 | ||
100.71 | odd | 10 | 400.3.bg.a.353.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.3.f.a.3.2 | ✓ | 16 | 25.21 | even | 5 | ||
50.3.f.a.17.2 | yes | 16 | 5.2 | odd | 4 | ||
250.3.f.a.7.2 | 16 | 25.22 | odd | 20 | inner | ||
250.3.f.a.143.2 | 16 | 1.1 | even | 1 | trivial | ||
250.3.f.b.107.1 | 16 | 5.3 | odd | 4 | |||
250.3.f.b.243.1 | 16 | 25.4 | even | 10 | |||
250.3.f.c.7.1 | 16 | 25.3 | odd | 20 | |||
250.3.f.c.143.1 | 16 | 5.4 | even | 2 | |||
400.3.bg.a.17.1 | 16 | 20.7 | even | 4 | |||
400.3.bg.a.353.1 | 16 | 100.71 | odd | 10 |