Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 324.3 | ||
Root | \(1.98293 - 0.531325i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.324 |
Dual form | 637.2.r.e.116.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.596598 | − | 0.344446i | −0.421859 | − | 0.243560i | 0.274014 | − | 0.961726i | \(-0.411649\pi\) |
−0.695872 | + | 0.718166i | \(0.744982\pi\) | |||||||
\(3\) | 1.10716 | + | 1.91766i | 0.639219 | + | 1.10716i | 0.985604 | + | 0.169068i | \(0.0540756\pi\) |
−0.346385 | + | 0.938092i | \(0.612591\pi\) | |||||||
\(4\) | −0.762714 | − | 1.32106i | −0.381357 | − | 0.660530i | ||||
\(5\) | −2.78368 | − | 1.60716i | −1.24490 | − | 0.718744i | −0.274813 | − | 0.961498i | \(-0.588616\pi\) |
−0.970088 | + | 0.242754i | \(0.921949\pi\) | |||||||
\(6\) | − | 1.52543i | − | 0.622753i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.42864i | 0.858654i | ||||||||
\(9\) | −0.951606 | + | 1.64823i | −0.317202 | + | 0.549410i | ||||
\(10\) | 1.10716 | + | 1.91766i | 0.350115 | + | 0.606416i | ||||
\(11\) | −2.32865 | + | 1.34445i | −0.702114 | + | 0.405366i | −0.808134 | − | 0.588998i | \(-0.799522\pi\) |
0.106020 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(12\) | 1.68889 | − | 2.92525i | 0.487541 | − | 0.844446i | ||||
\(13\) | 3.59210 | + | 0.311108i | 0.996270 | + | 0.0862858i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.11753i | − | 1.83774i | ||||||
\(16\) | −0.688892 | + | 1.19320i | −0.172223 | + | 0.298299i | ||||
\(17\) | 1.79605 | + | 3.11085i | 0.435607 | + | 0.754493i | 0.997345 | − | 0.0728222i | \(-0.0232006\pi\) |
−0.561738 | + | 0.827315i | \(0.689867\pi\) | |||||||
\(18\) | 1.13545 | − | 0.655554i | 0.267629 | − | 0.154516i | ||||
\(19\) | 7.40120 | + | 4.27309i | 1.69795 | + | 0.980313i | 0.947701 | + | 0.319160i | \(0.103401\pi\) |
0.750251 | + | 0.661153i | \(0.229933\pi\) | |||||||
\(20\) | 4.90321i | 1.09639i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.85236 | 0.394924 | ||||||||
\(23\) | −1.64050 | + | 2.84143i | −0.342068 | + | 0.592478i | −0.984817 | − | 0.173599i | \(-0.944460\pi\) |
0.642749 | + | 0.766077i | \(0.277794\pi\) | |||||||
\(24\) | −4.65730 | + | 2.68889i | −0.950667 | + | 0.548868i | ||||
\(25\) | 2.66593 | + | 4.61752i | 0.533185 | + | 0.923504i | ||||
\(26\) | −2.03588 | − | 1.42289i | −0.399269 | − | 0.279052i | ||||
\(27\) | 2.42864 | 0.467392 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05086 | 0.380834 | 0.190417 | − | 0.981703i | \(-0.439016\pi\) | ||||
0.190417 | + | 0.981703i | \(0.439016\pi\) | |||||||
\(30\) | −2.45161 | + | 4.24631i | −0.447600 | + | 0.775266i | ||||
\(31\) | 5.05459 | − | 2.91827i | 0.907831 | − | 0.524136i | 0.0280982 | − | 0.999605i | \(-0.491055\pi\) |
0.879733 | + | 0.475469i | \(0.157722\pi\) | |||||||
\(32\) | 5.02851 | − | 2.90321i | 0.888923 | − | 0.513220i | ||||
\(33\) | −5.15637 | − | 2.97703i | −0.897609 | − | 0.518235i | ||||
\(34\) | − | 2.47457i | − | 0.424386i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.90321 | 0.483869 | ||||||||
\(37\) | 3.40636 | + | 1.96666i | 0.560002 | + | 0.323317i | 0.753146 | − | 0.657853i | \(-0.228535\pi\) |
−0.193144 | + | 0.981170i | \(0.561869\pi\) | |||||||
\(38\) | −2.94370 | − | 5.09863i | −0.477530 | − | 0.827107i | ||||
\(39\) | 3.38044 | + | 7.23287i | 0.541303 | + | 1.15819i | ||||
\(40\) | 3.90321 | − | 6.76056i | 0.617152 | − | 1.06894i | ||||
\(41\) | 0.755569i | 0.118000i | 0.998258 | + | 0.0590000i | \(0.0187912\pi\) | ||||
−0.998258 | + | 0.0590000i | \(0.981209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.80642 | −1.34297 | −0.671484 | − | 0.741019i | \(-0.734343\pi\) | ||||
−0.671484 | + | 0.741019i | \(0.734343\pi\) | |||||||
\(44\) | 3.55219 | + | 2.05086i | 0.535512 | + | 0.309178i | ||||
\(45\) | 5.29794 | − | 3.05877i | 0.789770 | − | 0.455974i | ||||
\(46\) | 1.95744 | − | 1.13013i | 0.288608 | − | 0.166628i | ||||
\(47\) | 1.63027 | + | 0.941234i | 0.237799 | + | 0.137293i | 0.614165 | − | 0.789178i | \(-0.289493\pi\) |
−0.376366 | + | 0.926471i | \(0.622826\pi\) | |||||||
\(48\) | −3.05086 | −0.440353 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 3.67307i | − | 0.519451i | ||||||
\(51\) | −3.97703 | + | 6.88842i | −0.556896 | + | 0.964572i | ||||
\(52\) | −2.32876 | − | 4.98267i | −0.322940 | − | 0.690972i | ||||
\(53\) | −1.26271 | − | 2.18708i | −0.173447 | − | 0.300419i | 0.766176 | − | 0.642631i | \(-0.222157\pi\) |
−0.939623 | + | 0.342212i | \(0.888824\pi\) | |||||||
\(54\) | −1.44892 | − | 0.836535i | −0.197173 | − | 0.113838i | ||||
\(55\) | 8.64296 | 1.16542 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.9240i | 2.50654i | ||||||||
\(58\) | −1.22354 | − | 0.706409i | −0.160658 | − | 0.0927560i | ||||
\(59\) | −6.34957 | + | 3.66593i | −0.826644 | + | 0.477263i | −0.852702 | − | 0.522398i | \(-0.825038\pi\) |
0.0260585 | + | 0.999660i | \(0.491704\pi\) | |||||||
\(60\) | −9.40268 | + | 5.42864i | −1.21388 | + | 0.700834i | ||||
\(61\) | −4.52543 | + | 7.83827i | −0.579422 | + | 1.00359i | 0.416124 | + | 0.909308i | \(0.363388\pi\) |
−0.995546 | + | 0.0942799i | \(0.969945\pi\) | |||||||
\(62\) | −4.02074 | −0.510635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.24443 | −0.155554 | ||||||||
\(65\) | −9.49928 | − | 6.63911i | −1.17824 | − | 0.823480i | ||||
\(66\) | 2.05086 | + | 3.55219i | 0.252443 | + | 0.437244i | ||||
\(67\) | 0.371213 | − | 0.214320i | 0.0453508 | − | 0.0261833i | −0.477153 | − | 0.878820i | \(-0.658331\pi\) |
0.522504 | + | 0.852637i | \(0.324998\pi\) | |||||||
\(68\) | 2.73975 | − | 4.74538i | 0.332243 | − | 0.575462i | ||||
\(69\) | −7.26517 | −0.874624 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.98418i | 1.06623i | 0.846044 | + | 0.533113i | \(0.178978\pi\) | ||||
−0.846044 | + | 0.533113i | \(0.821022\pi\) | |||||||
\(72\) | −4.00296 | − | 2.31111i | −0.471753 | − | 0.272367i | ||||
\(73\) | −5.01481 | + | 2.89530i | −0.586939 | + | 0.338869i | −0.763886 | − | 0.645351i | \(-0.776711\pi\) |
0.176947 | + | 0.984220i | \(0.443378\pi\) | |||||||
\(74\) | −1.35482 | − | 2.34661i | −0.157494 | − | 0.272788i | ||||
\(75\) | −5.90321 | + | 10.2247i | −0.681644 | + | 1.18064i | ||||
\(76\) | − | 13.0366i | − | 1.49540i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.474572 | − | 5.47949i | 0.0537347 | − | 0.620431i | ||||
\(79\) | 2.23975 | − | 3.87936i | 0.251991 | − | 0.436462i | −0.712083 | − | 0.702096i | \(-0.752248\pi\) |
0.964074 | + | 0.265634i | \(0.0855812\pi\) | |||||||
\(80\) | 3.83531 | − | 2.21432i | 0.428801 | − | 0.247568i | ||||
\(81\) | 5.54371 | + | 9.60199i | 0.615968 | + | 1.06689i | ||||
\(82\) | 0.260253 | − | 0.450771i | 0.0287401 | − | 0.0497793i | ||||
\(83\) | − | 10.8272i | − | 1.18844i | −0.804304 | − | 0.594218i | \(-0.797462\pi\) | ||
0.804304 | − | 0.594218i | \(-0.202538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.5462i | − | 1.25236i | ||||||
\(86\) | 5.25390 | + | 3.03334i | 0.566542 | + | 0.327093i | ||||
\(87\) | 2.27062 | + | 3.93284i | 0.243436 | + | 0.421644i | ||||
\(88\) | −3.26517 | − | 5.65545i | −0.348069 | − | 0.602873i | ||||
\(89\) | 4.64360 | + | 2.68098i | 0.492220 | + | 0.284183i | 0.725495 | − | 0.688227i | \(-0.241611\pi\) |
−0.233275 | + | 0.972411i | \(0.574944\pi\) | |||||||
\(90\) | −4.21432 | −0.444228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.00492 | 0.521799 | ||||||||
\(93\) | 11.1925 | + | 6.46198i | 1.16061 | + | 0.670076i | ||||
\(94\) | −0.648409 | − | 1.12308i | −0.0668783 | − | 0.115837i | ||||
\(95\) | −13.7351 | − | 23.7898i | −1.40919 | − | 2.44078i | ||||
\(96\) | 11.1347 | + | 6.42864i | 1.13643 | + | 0.656120i | ||||
\(97\) | 9.62867i | 0.977643i | 0.872384 | + | 0.488822i | \(0.162573\pi\) | ||||
−0.872384 | + | 0.488822i | \(0.837427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.11753i | − | 0.514331i | ||||||
\(100\) | 4.06668 | − | 7.04369i | 0.406668 | − | 0.704369i | ||||
\(101\) | 6.84691 | + | 11.8592i | 0.681293 | + | 1.18003i | 0.974587 | + | 0.224011i | \(0.0719152\pi\) |
−0.293294 | + | 0.956022i | \(0.594751\pi\) | |||||||
\(102\) | 4.74538 | − | 2.73975i | 0.469863 | − | 0.271275i | ||||
\(103\) | 6.14764 | − | 10.6480i | 0.605745 | − | 1.04918i | −0.386188 | − | 0.922420i | \(-0.626208\pi\) |
0.991933 | − | 0.126761i | \(-0.0404583\pi\) | |||||||
\(104\) | −0.755569 | + | 8.72393i | −0.0740896 | + | 0.855451i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73975i | 0.168979i | ||||||||
\(107\) | 9.09457 | − | 15.7522i | 0.879205 | − | 1.52283i | 0.0269898 | − | 0.999636i | \(-0.491408\pi\) |
0.852215 | − | 0.523192i | \(-0.175259\pi\) | |||||||
\(108\) | −1.85236 | − | 3.20838i | −0.178243 | − | 0.308726i | ||||
\(109\) | 7.24167 | − | 4.18098i | 0.693626 | − | 0.400465i | −0.111343 | − | 0.993782i | \(-0.535515\pi\) |
0.804969 | + | 0.593317i | \(0.202182\pi\) | |||||||
\(110\) | −5.15637 | − | 2.97703i | −0.491641 | − | 0.283849i | ||||
\(111\) | 8.70964i | 0.826682i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.46520 | −0.796339 | −0.398170 | − | 0.917312i | \(-0.630354\pi\) | ||||
−0.398170 | + | 0.917312i | \(0.630354\pi\) | |||||||
\(114\) | 6.51828 | − | 11.2900i | 0.610493 | − | 1.05741i | ||||
\(115\) | 9.13325 | − | 5.27309i | 0.851680 | − | 0.491718i | ||||
\(116\) | −1.56422 | − | 2.70930i | −0.145234 | − | 0.251552i | ||||
\(117\) | −3.93104 | + | 5.62456i | −0.363425 | + | 0.519991i | ||||
\(118\) | 5.05086 | 0.464969 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.2859 | 1.57798 | ||||||||
\(121\) | −1.88493 | + | 3.26479i | −0.171357 | + | 0.296799i | ||||
\(122\) | 5.39972 | − | 3.11753i | 0.488868 | − | 0.282248i | ||||
\(123\) | −1.44892 | + | 0.836535i | −0.130645 | + | 0.0754279i | ||||
\(124\) | −7.71041 | − | 4.45161i | −0.692415 | − | 0.399766i | ||||
\(125\) | − | 1.06668i | − | 0.0954065i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.08742 | −0.362700 | −0.181350 | − | 0.983419i | \(-0.558047\pi\) | ||||
−0.181350 | + | 0.983419i | \(0.558047\pi\) | |||||||
\(128\) | −9.31460 | − | 5.37778i | −0.823302 | − | 0.475333i | ||||
\(129\) | −9.75012 | − | 16.8877i | −0.858450 | − | 1.48688i | ||||
\(130\) | 3.38044 | + | 7.23287i | 0.296484 | + | 0.634365i | ||||
\(131\) | −2.96989 | + | 5.14400i | −0.259480 | + | 0.449433i | −0.966103 | − | 0.258158i | \(-0.916885\pi\) |
0.706622 | + | 0.707591i | \(0.250218\pi\) | |||||||
\(132\) | 9.08250i | 0.790530i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.295286 | −0.0255089 | ||||||||
\(135\) | −6.76056 | − | 3.90321i | −0.581856 | − | 0.335935i | ||||
\(136\) | −7.55514 | + | 4.36196i | −0.647848 | + | 0.374035i | ||||
\(137\) | −14.1699 | + | 8.18098i | −1.21061 | + | 0.698948i | −0.962893 | − | 0.269883i | \(-0.913015\pi\) |
−0.247721 | + | 0.968831i | \(0.579682\pi\) | |||||||
\(138\) | 4.33439 | + | 2.50246i | 0.368968 | + | 0.213024i | ||||
\(139\) | 3.03011 | 0.257011 | 0.128505 | − | 0.991709i | \(-0.458982\pi\) | ||||
0.128505 | + | 0.991709i | \(0.458982\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.16839i | 0.351041i | ||||||||
\(142\) | 3.09457 | − | 5.35994i | 0.259690 | − | 0.449797i | ||||
\(143\) | −8.78302 | + | 4.10493i | −0.734473 | + | 0.343271i | ||||
\(144\) | −1.31111 | − | 2.27091i | −0.109259 | − | 0.189242i | ||||
\(145\) | −5.70893 | − | 3.29605i | −0.474101 | − | 0.273722i | ||||
\(146\) | 3.98910 | 0.330140 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 12.5892 | + | 7.26840i | 1.03135 | + | 0.595451i | 0.917371 | − | 0.398032i | \(-0.130307\pi\) |
0.113979 | + | 0.993483i | \(0.463640\pi\) | |||||||
\(150\) | 7.04369 | − | 4.06668i | 0.575115 | − | 0.332043i | ||||
\(151\) | 17.2987 | − | 9.98741i | 1.40775 | − | 0.812764i | 0.412577 | − | 0.910923i | \(-0.364629\pi\) |
0.995171 | + | 0.0981592i | \(0.0312954\pi\) | |||||||
\(152\) | −10.3778 | + | 17.9748i | −0.841749 | + | 1.45795i | ||||
\(153\) | −6.83654 | −0.552701 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.7605 | −1.50688 | ||||||||
\(156\) | 6.97674 | − | 9.98236i | 0.558587 | − | 0.799229i | ||||
\(157\) | −3.69926 | − | 6.40731i | −0.295233 | − | 0.511359i | 0.679806 | − | 0.733392i | \(-0.262064\pi\) |
−0.975039 | + | 0.222033i | \(0.928731\pi\) | |||||||
\(158\) | −2.67246 | + | 1.54294i | −0.212609 | + | 0.122750i | ||||
\(159\) | 2.79605 | − | 4.84290i | 0.221741 | − | 0.384067i | ||||
\(160\) | −18.6637 | −1.47550 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 7.63804i | − | 0.600101i | ||||||
\(163\) | 2.01518 | + | 1.16346i | 0.157841 | + | 0.0911296i | 0.576840 | − | 0.816857i | \(-0.304286\pi\) |
−0.418999 | + | 0.907987i | \(0.637619\pi\) | |||||||
\(164\) | 0.998151 | − | 0.576283i | 0.0779425 | − | 0.0450001i | ||||
\(165\) | 9.56914 | + | 16.5742i | 0.744956 | + | 1.29030i | ||||
\(166\) | −3.72938 | + | 6.45947i | −0.289456 | + | 0.501352i | ||||
\(167\) | 3.42219i | 0.264817i | 0.991195 | + | 0.132408i | \(0.0422710\pi\) | ||||
−0.991195 | + | 0.132408i | \(0.957729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8064 | + | 2.23506i | 0.985110 | + | 0.171928i | ||||
\(170\) | −3.97703 | + | 6.88842i | −0.305025 | + | 0.528318i | ||||
\(171\) | −14.0861 | + | 8.13259i | −1.07719 | + | 0.621915i | ||||
\(172\) | 6.71678 | + | 11.6338i | 0.512150 | + | 0.887069i | ||||
\(173\) | 4.13727 | − | 7.16596i | 0.314551 | − | 0.544818i | −0.664791 | − | 0.747029i | \(-0.731479\pi\) |
0.979342 | + | 0.202211i | \(0.0648127\pi\) | |||||||
\(174\) | − | 3.12843i | − | 0.237166i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.70471i | − | 0.279253i | ||||||
\(177\) | −14.0600 | − | 8.11753i | −1.05681 | − | 0.610151i | ||||
\(178\) | −1.84691 | − | 3.19894i | −0.138432 | − | 0.239770i | ||||
\(179\) | −8.11285 | − | 14.0519i | −0.606383 | − | 1.05029i | −0.991831 | − | 0.127556i | \(-0.959287\pi\) |
0.385449 | − | 0.922729i | \(-0.374047\pi\) | |||||||
\(180\) | −8.08162 | − | 4.66593i | −0.602368 | − | 0.347778i | ||||
\(181\) | 9.20495 | 0.684199 | 0.342099 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342099 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0415 | −1.48151 | ||||||||
\(184\) | −6.90080 | − | 3.98418i | −0.508734 | − | 0.293718i | ||||
\(185\) | −6.32148 | − | 10.9491i | −0.464764 | − | 0.804996i | ||||
\(186\) | −4.45161 | − | 7.71041i | −0.326408 | − | 0.565355i | ||||
\(187\) | −8.36475 | − | 4.82939i | −0.611691 | − | 0.353160i | ||||
\(188\) | − | 2.87157i | − | 0.209431i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.9240i | 1.37289i | ||||||||
\(191\) | 3.33407 | − | 5.77479i | 0.241245 | − | 0.417849i | −0.719824 | − | 0.694157i | \(-0.755778\pi\) |
0.961069 | + | 0.276308i | \(0.0891109\pi\) | |||||||
\(192\) | −1.37778 | − | 2.38639i | −0.0994330 | − | 0.172223i | ||||
\(193\) | −17.8431 | + | 10.3017i | −1.28438 | + | 0.741535i | −0.977645 | − | 0.210261i | \(-0.932569\pi\) |
−0.306732 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(194\) | 3.31656 | − | 5.74445i | 0.238115 | − | 0.412427i | ||||
\(195\) | 2.21432 | − | 25.5669i | 0.158571 | − | 1.83088i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.36842i | − | 0.596225i | −0.954531 | − | 0.298112i | \(-0.903643\pi\) | ||
0.954531 | − | 0.298112i | \(-0.0963571\pi\) | |||||||
\(198\) | −1.76271 | + | 3.05311i | −0.125271 | + | 0.216975i | ||||
\(199\) | −0.300736 | − | 0.520890i | −0.0213186 | − | 0.0369249i | 0.855169 | − | 0.518349i | \(-0.173453\pi\) |
−0.876488 | + | 0.481424i | \(0.840120\pi\) | |||||||
\(200\) | −11.2143 | + | 6.47457i | −0.792970 | + | 0.457821i | ||||
\(201\) | 0.821984 | + | 0.474572i | 0.0579783 | + | 0.0334738i | ||||
\(202\) | − | 9.43356i | − | 0.663743i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.1334 | 0.849505 | ||||||||
\(205\) | 1.21432 | − | 2.10326i | 0.0848118 | − | 0.146898i | ||||
\(206\) | −7.33534 | + | 4.23506i | −0.511078 | + | 0.295071i | ||||
\(207\) | −3.12222 | − | 5.40784i | −0.217009 | − | 0.375871i | ||||
\(208\) | −2.84579 | + | 4.07177i | −0.197320 | + | 0.282326i | ||||
\(209\) | −22.9797 | −1.58954 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.90321 | −0.131023 | −0.0655113 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655113 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(212\) | −1.92618 | + | 3.33624i | −0.132290 | + | 0.229134i | ||||
\(213\) | −17.2286 | + | 9.94692i | −1.18048 | + | 0.681552i | ||||
\(214\) | −10.8516 | + | 6.26517i | −0.741800 | + | 0.428279i | ||||
\(215\) | 24.5143 | + | 14.1533i | 1.67186 | + | 0.965249i | ||||
\(216\) | 5.89829i | 0.401328i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.76049 | −0.390150 | ||||||||
\(219\) | −11.1044 | − | 6.41112i | −0.750365 | − | 0.433224i | ||||
\(220\) | −6.59210 | − | 11.4179i | −0.444440 | − | 0.769792i | ||||
\(221\) | 5.48380 | + | 11.7333i | 0.368880 | + | 0.789265i | ||||
\(222\) | 3.00000 | − | 5.19615i | 0.201347 | − | 0.348743i | ||||
\(223\) | 10.6336i | 0.712078i | 0.934471 | + | 0.356039i | \(0.115873\pi\) | ||||
−0.934471 | + | 0.356039i | \(0.884127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.1476 | −0.676510 | ||||||||
\(226\) | 5.05033 | + | 2.91581i | 0.335943 | + | 0.193957i | ||||
\(227\) | 13.0344 | − | 7.52543i | 0.865125 | − | 0.499480i | −0.000600144 | − | 1.00000i | \(-0.500191\pi\) |
0.865725 | + | 0.500520i | \(0.166858\pi\) | |||||||
\(228\) | 24.9997 | − | 14.4336i | 1.65564 | − | 0.955886i | ||||
\(229\) | −5.65930 | − | 3.26740i | −0.373977 | − | 0.215916i | 0.301218 | − | 0.953555i | \(-0.402607\pi\) |
−0.675195 | + | 0.737640i | \(0.735940\pi\) | |||||||
\(230\) | −7.26517 | −0.479051 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.98079i | 0.327005i | ||||||||
\(233\) | −13.9795 | + | 24.2132i | −0.915827 | + | 1.58626i | −0.110141 | + | 0.993916i | \(0.535130\pi\) |
−0.805686 | + | 0.592343i | \(0.798203\pi\) | |||||||
\(234\) | 4.28261 | − | 2.00157i | 0.279963 | − | 0.130847i | ||||
\(235\) | −3.02543 | − | 5.24019i | −0.197357 | − | 0.341833i | ||||
\(236\) | 9.68581 | + | 5.59210i | 0.630492 | + | 0.364015i | ||||
\(237\) | 9.91903 | 0.644310 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.5812i | − | 1.26660i | −0.773905 | − | 0.633301i | \(-0.781699\pi\) | ||
0.773905 | − | 0.633301i | \(-0.218301\pi\) | |||||||
\(240\) | 8.49261 | + | 4.90321i | 0.548196 | + | 0.316501i | ||||
\(241\) | 11.5679 | − | 6.67876i | 0.745157 | − | 0.430217i | −0.0787843 | − | 0.996892i | \(-0.525104\pi\) |
0.823941 | + | 0.566675i | \(0.191770\pi\) | |||||||
\(242\) | 2.24909 | − | 1.29851i | 0.144577 | − | 0.0834716i | ||||
\(243\) | −8.63259 | + | 14.9521i | −0.553781 | + | 0.959176i | ||||
\(244\) | 13.8064 | 0.883866 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.15257 | 0.0734849 | ||||||||
\(247\) | 25.2565 | + | 17.6519i | 1.60703 | + | 1.12317i | ||||
\(248\) | 7.08742 | + | 12.2758i | 0.450052 | + | 0.779512i | ||||
\(249\) | 20.7628 | − | 11.9874i | 1.31579 | − | 0.759671i | ||||
\(250\) | −0.367413 | + | 0.636377i | −0.0232372 | + | 0.0402480i | ||||
\(251\) | −3.29682 | −0.208093 | −0.104047 | − | 0.994572i | \(-0.533179\pi\) | ||||
−0.104047 | + | 0.994572i | \(0.533179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.82225i | − | 0.554650i | ||||||
\(254\) | 2.43855 | + | 1.40790i | 0.153008 | + | 0.0883392i | ||||
\(255\) | 22.1416 | − | 12.7835i | 1.38656 | − | 0.800531i | ||||
\(256\) | 4.94914 | + | 8.57217i | 0.309322 | + | 0.535761i | ||||
\(257\) | −11.8469 | + | 20.5194i | −0.738990 | + | 1.27997i | 0.213961 | + | 0.976842i | \(0.431364\pi\) |
−0.952951 | + | 0.303126i | \(0.901970\pi\) | |||||||
\(258\) | 13.4336i | 0.836337i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.52543 | + | 17.6128i | −0.0946030 | + | 1.09230i | ||||
\(261\) | −1.95161 | + | 3.38028i | −0.120801 | + | 0.209234i | ||||
\(262\) | 3.54366 | − | 2.04593i | 0.218928 | − | 0.126398i | ||||
\(263\) | −4.99532 | − | 8.65214i | −0.308024 | − | 0.533514i | 0.669906 | − | 0.742446i | \(-0.266335\pi\) |
−0.977930 | + | 0.208932i | \(0.933001\pi\) | |||||||
\(264\) | 7.23014 | − | 12.5230i | 0.444984 | − | 0.770736i | ||||
\(265\) | 8.11753i | 0.498656i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.8731i | 0.726622i | ||||||||
\(268\) | −0.566258 | − | 0.326929i | −0.0345897 | − | 0.0199704i | ||||
\(269\) | 9.10171 | + | 15.7646i | 0.554941 | + | 0.961186i | 0.997908 | + | 0.0646482i | \(0.0205925\pi\) |
−0.442967 | + | 0.896538i | \(0.646074\pi\) | |||||||
\(270\) | 2.68889 | + | 4.65730i | 0.163641 | + | 0.283434i | ||||
\(271\) | −20.9360 | − | 12.0874i | −1.27177 | − | 0.734258i | −0.296451 | − | 0.955048i | \(-0.595803\pi\) |
−0.975322 | + | 0.220789i | \(0.929137\pi\) | |||||||
\(272\) | −4.94914 | −0.300086 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2716 | 0.680944 | ||||||||
\(275\) | −12.4160 | − | 7.16839i | −0.748714 | − | 0.432270i | ||||
\(276\) | 5.54125 | + | 9.59772i | 0.333544 | + | 0.577715i | ||||
\(277\) | 0.847673 | + | 1.46821i | 0.0509317 | + | 0.0882163i | 0.890367 | − | 0.455243i | \(-0.150448\pi\) |
−0.839436 | + | 0.543459i | \(0.817114\pi\) | |||||||
\(278\) | −1.80776 | − | 1.04371i | −0.108422 | − | 0.0625976i | ||||
\(279\) | 11.1082i | 0.665028i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.6479i | − | 0.694854i | −0.937707 | − | 0.347427i | \(-0.887055\pi\) | ||
0.937707 | − | 0.347427i | \(-0.112945\pi\) | |||||||
\(282\) | 1.43578 | − | 2.48685i | 0.0854997 | − | 0.148090i | ||||
\(283\) | 6.06668 | + | 10.5078i | 0.360626 | + | 0.624623i | 0.988064 | − | 0.154043i | \(-0.0492296\pi\) |
−0.627438 | + | 0.778667i | \(0.715896\pi\) | |||||||
\(284\) | 11.8686 | − | 6.85236i | 0.704274 | − | 0.406613i | ||||
\(285\) | 30.4138 | − | 52.6783i | 1.80156 | − | 3.12039i | ||||
\(286\) | 6.65386 | + | 0.576283i | 0.393451 | + | 0.0340763i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 11.0509i | 0.651178i | ||||||||
\(289\) | 2.04839 | − | 3.54792i | 0.120494 | − | 0.208701i | ||||
\(290\) | 2.27062 | + | 3.93284i | 0.133336 | + | 0.230944i | ||||
\(291\) | −18.4645 | + | 10.6605i | −1.08241 | + | 0.624928i | ||||
\(292\) | 7.64973 | + | 4.41657i | 0.447666 | + | 0.258460i | ||||
\(293\) | − | 11.4538i | − | 0.669140i | −0.942371 | − | 0.334570i | \(-0.891409\pi\) | ||
0.942371 | − | 0.334570i | \(-0.108591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.5669 | 1.37212 | ||||||||
\(296\) | −4.77631 | + | 8.27282i | −0.277618 | + | 0.480848i | ||||
\(297\) | −5.65545 | + | 3.26517i | −0.328162 | + | 0.189465i | ||||
\(298\) | −5.00715 | − | 8.67263i | −0.290056 | − | 0.502392i | ||||
\(299\) | −6.77683 | + | 9.69633i | −0.391914 | + | 0.560753i | ||||
\(300\) | 18.0098 | 1.03980 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.7605 | −0.791827 | ||||||||
\(303\) | −15.1612 | + | 26.2600i | −0.870991 | + | 1.50860i | ||||
\(304\) | −10.1973 | + | 5.88739i | −0.584853 | + | 0.337665i | ||||
\(305\) | 25.1947 | − | 14.5462i | 1.44264 | − | 0.832911i | ||||
\(306\) | 4.07866 | + | 2.35482i | 0.233162 | + | 0.134616i | ||||
\(307\) | − | 3.96989i | − | 0.226574i | −0.993562 | − | 0.113287i | \(-0.963862\pi\) | ||
0.993562 | − | 0.113287i | \(-0.0361379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.2257 | 1.54882 | ||||||||
\(310\) | 11.1925 | + | 6.46198i | 0.635690 | + | 0.367016i | ||||
\(311\) | 13.6741 | + | 23.6842i | 0.775386 | + | 1.34301i | 0.934577 | + | 0.355760i | \(0.115778\pi\) |
−0.159192 | + | 0.987248i | \(0.550889\pi\) | |||||||
\(312\) | −17.5660 | + | 8.20986i | −0.994481 | + | 0.464792i | ||||
\(313\) | 9.55162 | − | 16.5439i | 0.539890 | − | 0.935116i | −0.459020 | − | 0.888426i | \(-0.651799\pi\) |
0.998909 | − | 0.0466901i | \(-0.0148673\pi\) | |||||||
\(314\) | 5.09679i | 0.287628i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.83314 | −0.384394 | ||||||||
\(317\) | −8.58070 | − | 4.95407i | −0.481940 | − | 0.278248i | 0.239285 | − | 0.970949i | \(-0.423087\pi\) |
−0.721225 | + | 0.692701i | \(0.756420\pi\) | |||||||
\(318\) | −3.33624 | + | 1.92618i | −0.187087 | + | 0.108015i | ||||
\(319\) | −4.77572 | + | 2.75726i | −0.267389 | + | 0.154377i | ||||
\(320\) | 3.46410 | + | 2.00000i | 0.193649 | + | 0.111803i | ||||
\(321\) | 40.2766 | 2.24802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.6987i | 1.70812i | ||||||||
\(324\) | 8.45653 | − | 14.6471i | 0.469807 | − | 0.813730i | ||||
\(325\) | 8.13974 | + | 17.4160i | 0.451511 | + | 0.966066i | ||||
\(326\) | −0.801502 | − | 1.38824i | −0.0443911 | − | 0.0768876i | ||||
\(327\) | 16.0354 | + | 9.25803i | 0.886758 | + | 0.511970i | ||||
\(328\) | −1.83500 | −0.101321 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 13.1842i | − | 0.725767i | ||||||
\(331\) | −20.2817 | − | 11.7096i | −1.11478 | − | 0.643620i | −0.174718 | − | 0.984618i | \(-0.555902\pi\) |
−0.940064 | + | 0.340999i | \(0.889235\pi\) | |||||||
\(332\) | −14.3033 | + | 8.25803i | −0.784997 | + | 0.453218i | ||||
\(333\) | −6.48302 | + | 3.74297i | −0.355267 | + | 0.205114i | ||||
\(334\) | 1.17876 | − | 2.04167i | 0.0644988 | − | 0.111715i | ||||
\(335\) | −1.37778 | −0.0752764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.51606 | 0.409426 | 0.204713 | − | 0.978822i | \(-0.434374\pi\) | ||||
0.204713 | + | 0.978822i | \(0.434374\pi\) | |||||||
\(338\) | −6.87043 | − | 5.74456i | −0.373702 | − | 0.312463i | ||||
\(339\) | −9.37233 | − | 16.2334i | −0.509035 | − | 0.881675i | ||||
\(340\) | −15.2532 | + | 8.80642i | −0.827219 | + | 0.477595i | ||||
\(341\) | −7.84691 | + | 13.5912i | −0.424934 | + | 0.736007i | ||||
\(342\) | 11.2050 | 0.605894 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 21.3876i | − | 1.15314i | ||||||
\(345\) | 20.2239 | + | 11.6763i | 1.08882 | + | 0.628631i | ||||
\(346\) | −4.93658 | + | 2.85013i | −0.265392 | + | 0.153224i | ||||
\(347\) | −2.82225 | − | 4.88827i | −0.151506 | − | 0.262416i | 0.780275 | − | 0.625436i | \(-0.215079\pi\) |
−0.931781 | + | 0.363020i | \(0.881746\pi\) | |||||||
\(348\) | 3.46367 | − | 5.99926i | 0.185672 | − | 0.321594i | ||||
\(349\) | − | 24.1590i | − | 1.29320i | −0.762828 | − | 0.646601i | \(-0.776190\pi\) | ||
0.762828 | − | 0.646601i | \(-0.223810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.72393 | + | 0.755569i | 0.465649 | + | 0.0403293i | ||||
\(352\) | −7.80642 | + | 13.5211i | −0.416084 | + | 0.720678i | ||||
\(353\) | 31.2886 | − | 18.0645i | 1.66532 | − | 0.961474i | 0.695213 | − | 0.718804i | \(-0.255310\pi\) |
0.970109 | − | 0.242670i | \(-0.0780231\pi\) | |||||||
\(354\) | 5.59210 | + | 9.68581i | 0.297217 | + | 0.514795i | ||||
\(355\) | 14.4390 | − | 25.0091i | 0.766343 | − | 1.32735i | ||||
\(356\) | − | 8.17929i | − | 0.433501i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1778i | 0.590763i | ||||||||
\(359\) | 15.0799 | + | 8.70641i | 0.795889 | + | 0.459507i | 0.842032 | − | 0.539428i | \(-0.181360\pi\) |
−0.0461427 | + | 0.998935i | \(0.514693\pi\) | |||||||
\(360\) | 7.42864 | + | 12.8668i | 0.391524 | + | 0.678139i | ||||
\(361\) | 27.0185 | + | 46.7975i | 1.42203 | + | 2.46302i | ||||
\(362\) | −5.49166 | − | 3.17061i | −0.288635 | − | 0.166644i | ||||
\(363\) | −8.34767 | −0.438139 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.6128 | 0.974241 | ||||||||
\(366\) | 11.9567 | + | 6.90321i | 0.624987 | + | 0.360837i | ||||
\(367\) | −1.46912 | − | 2.54460i | −0.0766876 | − | 0.132827i | 0.825131 | − | 0.564941i | \(-0.191101\pi\) |
−0.901819 | + | 0.432114i | \(0.857768\pi\) | |||||||
\(368\) | −2.26025 | − | 3.91487i | −0.117824 | − | 0.204077i | ||||
\(369\) | −1.24535 | − | 0.719004i | −0.0648304 | − | 0.0374298i | ||||
\(370\) | 8.70964i | 0.452792i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 19.7146i | − | 1.02215i | ||||||
\(373\) | 9.38493 | − | 16.2552i | 0.485933 | − | 0.841661i | −0.513936 | − | 0.857828i | \(-0.671813\pi\) |
0.999869 | + | 0.0161675i | \(0.00514648\pi\) | |||||||
\(374\) | 3.32693 | + | 5.76241i | 0.172031 | + | 0.297967i | ||||
\(375\) | 2.04552 | − | 1.18098i | 0.105630 | − | 0.0609856i | ||||
\(376\) | −2.28592 | + | 3.95933i | −0.117887 | + | 0.204187i | ||||
\(377\) | 7.36689 | + | 0.638037i | 0.379414 | + | 0.0328606i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6894i | 1.21684i | 0.793615 | + | 0.608421i | \(0.208197\pi\) | ||||
−0.793615 | + | 0.608421i | \(0.791803\pi\) | |||||||
\(380\) | −20.9518 | + | 36.2897i | −1.07481 | + | 1.86162i | ||||
\(381\) | −4.52543 | − | 7.83827i | −0.231845 | − | 0.401567i | ||||
\(382\) | −3.97820 | + | 2.29682i | −0.203543 | + | 0.117515i | ||||
\(383\) | −27.3775 | − | 15.8064i | −1.39893 | − | 0.807671i | −0.404646 | − | 0.914473i | \(-0.632605\pi\) |
−0.994280 | + | 0.106803i | \(0.965939\pi\) | |||||||
\(384\) | − | 23.8163i | − | 1.21537i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.1936 | 0.722434 | ||||||||
\(387\) | 8.38025 | − | 14.5150i | 0.425992 | − | 0.737839i | ||||
\(388\) | 12.7200 | − | 7.34392i | 0.645762 | − | 0.372831i | ||||
\(389\) | −10.0279 | − | 17.3688i | −0.508434 | − | 0.880634i | −0.999952 | − | 0.00976644i | \(-0.996891\pi\) |
0.491518 | − | 0.870867i | \(-0.336442\pi\) | |||||||
\(390\) | −10.1275 | + | 14.4905i | −0.512825 | + | 0.733753i | ||||
\(391\) | −11.7857 | −0.596027 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1526 | −0.663459 | ||||||||
\(394\) | −2.88247 | + | 4.99258i | −0.145217 | + | 0.251523i | ||||
\(395\) | −12.4695 | + | 7.19926i | −0.627408 | + | 0.362234i | ||||
\(396\) | −6.76056 | + | 3.90321i | −0.339731 | + | 0.196144i | ||||
\(397\) | 19.8087 | + | 11.4366i | 0.994169 | + | 0.573984i | 0.906518 | − | 0.422167i | \(-0.138730\pi\) |
0.0876515 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(398\) | 0.414349i | 0.0207695i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.34614 | −0.367307 | ||||||||
\(401\) | −4.86087 | − | 2.80642i | −0.242740 | − | 0.140146i | 0.373695 | − | 0.927552i | \(-0.378091\pi\) |
−0.616436 | + | 0.787405i | \(0.711424\pi\) | |||||||
\(402\) | −0.326929 | − | 0.566258i | −0.0163057 | − | 0.0282424i | ||||
\(403\) | 19.0645 | − | 8.91020i | 0.949670 | − | 0.443849i | ||||
\(404\) | 10.4445 | − | 18.0903i | 0.519631 | − | 0.900028i | ||||
\(405\) | − | 35.6385i | − | 1.77089i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5763 | −0.524247 | ||||||||
\(408\) | −16.7295 | − | 9.65878i | −0.828234 | − | 0.478181i | ||||
\(409\) | −22.6184 | + | 13.0588i | −1.11841 | + | 0.645714i | −0.940995 | − | 0.338422i | \(-0.890107\pi\) |
−0.177416 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(410\) | −1.44892 | + | 0.836535i | −0.0715571 | + | 0.0413135i | ||||
\(411\) | −31.3766 | − | 18.1153i | −1.54770 | − | 0.893562i | ||||
\(412\) | −18.7556 | −0.924021 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.30174i | 0.211419i | ||||||||
\(415\) | −17.4010 | + | 30.1394i | −0.854181 | + | 1.47948i | ||||
\(416\) | 18.9661 | − | 8.86423i | 0.929892 | − | 0.434605i | ||||
\(417\) | 3.35482 | + | 5.81072i | 0.164286 | + | 0.284552i | ||||
\(418\) | 13.7097 | + | 7.91528i | 0.670562 | + | 0.387149i | ||||
\(419\) | −25.2464 | −1.23337 | −0.616685 | − | 0.787210i | \(-0.711525\pi\) | ||||
−0.616685 | + | 0.787210i | \(0.711525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.22861i | − | 0.401038i | −0.979690 | − | 0.200519i | \(-0.935737\pi\) | ||
0.979690 | − | 0.200519i | \(-0.0642628\pi\) | |||||||
\(422\) | 1.13545 | + | 0.655554i | 0.0552730 | + | 0.0319119i | ||||
\(423\) | −3.10274 | + | 1.79137i | −0.150860 | + | 0.0870993i | ||||
\(424\) | 5.31164 | − | 3.06668i | 0.257956 | − | 0.148931i | ||||
\(425\) | −9.57628 | + | 16.5866i | −0.464518 | + | 0.804569i | ||||
\(426\) | 13.7047 | 0.663996 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.7462 | −1.34116 | ||||||||
\(429\) | −17.5961 | − | 12.2980i | −0.849545 | − | 0.593753i | ||||
\(430\) | −9.75012 | − | 16.8877i | −0.470192 | − | 0.814397i | ||||
\(431\) | −1.24535 | + | 0.719004i | −0.0599864 | + | 0.0346332i | −0.529693 | − | 0.848189i | \(-0.677693\pi\) |
0.469707 | + | 0.882822i | \(0.344360\pi\) | |||||||
\(432\) | −1.67307 | + | 2.89784i | −0.0804957 | + | 0.139423i | ||||
\(433\) | 16.5018 | 0.793024 | 0.396512 | − | 0.918029i | \(-0.370220\pi\) | ||||
0.396512 | + | 0.918029i | \(0.370220\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 14.5970i | − | 0.699874i | ||||||
\(436\) | −11.0466 | − | 6.37778i | −0.529038 | − | 0.305440i | ||||
\(437\) | −24.2833 | + | 14.0200i | −1.16163 | + | 0.670666i | ||||
\(438\) | 4.41657 | + | 7.64973i | 0.211032 | + | 0.365518i | ||||
\(439\) | −5.08097 | + | 8.80049i | −0.242501 | + | 0.420025i | −0.961426 | − | 0.275063i | \(-0.911301\pi\) |
0.718925 | + | 0.695088i | \(0.244635\pi\) | |||||||
\(440\) | 20.9906i | 1.00069i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.769859 | − | 8.88892i | 0.0366185 | − | 0.422803i | ||||
\(443\) | −1.60393 | + | 2.77809i | −0.0762052 | + | 0.131991i | −0.901610 | − | 0.432550i | \(-0.857614\pi\) |
0.825405 | + | 0.564542i | \(0.190947\pi\) | |||||||
\(444\) | 11.5059 | − | 6.64296i | 0.546048 | − | 0.315261i | ||||
\(445\) | −8.61753 | − | 14.9260i | −0.408510 | − | 0.707560i | ||||
\(446\) | 3.66270 | − | 6.34398i | 0.173434 | − | 0.300396i | ||||
\(447\) | 32.1891i | 1.52249i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4099i | 0.868817i | 0.900716 | + | 0.434409i | \(0.143043\pi\) | ||||
−0.900716 | + | 0.434409i | \(0.856957\pi\) | |||||||
\(450\) | 6.05406 | + | 3.49532i | 0.285391 | + | 0.164771i | ||||
\(451\) | −1.01582 | − | 1.75945i | −0.0478332 | − | 0.0828495i | ||||
\(452\) | 6.45653 | + | 11.1830i | 0.303690 | + | 0.526006i | ||||
\(453\) | 38.3048 | + | 22.1153i | 1.79972 | + | 1.03907i | ||||
\(454\) | −10.3684 | −0.486614 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −45.9595 | −2.15225 | ||||||||
\(457\) | −2.94706 | − | 1.70149i | −0.137858 | − | 0.0795922i | 0.429485 | − | 0.903074i | \(-0.358695\pi\) |
−0.567343 | + | 0.823482i | \(0.692028\pi\) | |||||||
\(458\) | 2.25088 | + | 3.89865i | 0.105177 | + | 0.182172i | ||||
\(459\) | 4.36196 | + | 7.55514i | 0.203599 | + | 0.352644i | ||||
\(460\) | −13.9321 | − | 8.04371i | −0.649588 | − | 0.375040i | ||||
\(461\) | 17.5714i | 0.818380i | 0.912449 | + | 0.409190i | \(0.134189\pi\) | ||||
−0.912449 | + | 0.409190i | \(0.865811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.7714i | − | 0.732959i | −0.930426 | − | 0.366479i | \(-0.880563\pi\) | ||
0.930426 | − | 0.366479i | \(-0.119437\pi\) | |||||||
\(464\) | −1.41282 | + | 2.44707i | −0.0655884 | + | 0.113602i | ||||
\(465\) | −20.7709 | − | 35.9762i | −0.963226 | − | 1.66836i | ||||
\(466\) | 16.6803 | − | 9.63036i | 0.772699 | − | 0.446118i | ||||
\(467\) | −1.88347 | + | 3.26227i | −0.0871567 | + | 0.150960i | −0.906308 | − | 0.422617i | \(-0.861111\pi\) |
0.819151 | + | 0.573577i | \(0.194445\pi\) | |||||||
\(468\) | 10.4286 | + | 0.903212i | 0.482064 | + | 0.0417510i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.16839i | 0.192273i | ||||||||
\(471\) | 8.19135 | − | 14.1878i | 0.377438 | − | 0.653741i | ||||
\(472\) | −8.90321 | − | 15.4208i | −0.409804 | − | 0.709801i | ||||
\(473\) | 20.5071 | − | 11.8398i | 0.942916 | − | 0.544393i | ||||
\(474\) | −5.91768 | − | 3.41657i | −0.271808 | − | 0.156928i | ||||
\(475\) | 45.5669i | 2.09075i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.80642 | 0.220071 | ||||||||
\(478\) | −6.74467 | + | 11.6821i | −0.308494 | + | 0.534327i | ||||
\(479\) | 10.4817 | − | 6.05162i | 0.478922 | − | 0.276506i | −0.241045 | − | 0.970514i | \(-0.577490\pi\) |
0.719967 | + | 0.694008i | \(0.244157\pi\) | |||||||
\(480\) | −20.6637 | − | 35.7906i | −0.943165 | − | 1.63361i | ||||
\(481\) | 11.6241 | + | 8.12420i | 0.530016 | + | 0.370432i | ||||
\(482\) | −9.20189 | −0.419135 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.75065 | 0.261393 | ||||||||
\(485\) | 15.4748 | − | 26.8032i | 0.702675 | − | 1.21707i | ||||
\(486\) | 10.3004 | − | 5.94692i | 0.467234 | − | 0.269758i | ||||
\(487\) | −15.0496 | + | 8.68889i | −0.681963 | + | 0.393731i | −0.800594 | − | 0.599207i | \(-0.795483\pi\) |
0.118631 | + | 0.992938i | \(0.462149\pi\) | |||||||
\(488\) | −19.0363 | − | 10.9906i | −0.861734 | − | 0.497523i | ||||
\(489\) | 5.15257i | 0.233007i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3921 | 0.875152 | 0.437576 | − | 0.899181i | \(-0.355837\pi\) | ||||
0.437576 | + | 0.899181i | \(0.355837\pi\) | |||||||
\(492\) | 2.21023 | + | 1.27607i | 0.0996446 | + | 0.0575299i | ||||
\(493\) | 3.68344 | + | 6.37991i | 0.165894 | + | 0.287337i | ||||
\(494\) | −8.98784 | − | 19.2306i | −0.404382 | − | 0.865226i | ||||
\(495\) | −8.22469 | + | 14.2456i | −0.369672 | + | 0.640291i | ||||
\(496\) | 8.04149i | 0.361073i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.5161 | −0.740102 | ||||||||
\(499\) | 9.24063 | + | 5.33508i | 0.413667 | + | 0.238831i | 0.692364 | − | 0.721548i | \(-0.256569\pi\) |
−0.278697 | + | 0.960379i | \(0.589903\pi\) | |||||||
\(500\) | −1.40914 | + | 0.813569i | −0.0630188 | + | 0.0363839i | ||||
\(501\) | −6.56258 | + | 3.78891i | −0.293194 | + | 0.169276i | ||||
\(502\) | 1.96688 | + | 1.13558i | 0.0877859 | + | 0.0506832i | ||||
\(503\) | −4.27655 | −0.190682 | −0.0953410 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953410 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 44.0163i | − | 1.95870i | ||||||
\(506\) | −3.03879 | + | 5.26334i | −0.135091 | + | 0.233984i | ||||
\(507\) | 9.89267 | + | 27.0329i | 0.439349 | + | 1.20057i | ||||
\(508\) | 3.11753 | + | 5.39972i | 0.138318 | + | 0.239574i | ||||
\(509\) | −28.6451 | − | 16.5383i | −1.26967 | − | 0.733046i | −0.294746 | − | 0.955576i | \(-0.595235\pi\) |
−0.974926 | + | 0.222530i | \(0.928568\pi\) | |||||||
\(510\) | −17.6128 | −0.779910 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.6923i | 0.649313i | ||||||||
\(513\) | 17.9748 | + | 10.3778i | 0.793609 | + | 0.458190i | ||||
\(514\) | 14.1357 | − | 8.16124i | 0.623498 | − | 0.359977i | ||||
\(515\) | −34.2262 | + | 19.7605i | −1.50819 | + | 0.870751i | ||||
\(516\) | −14.8731 | + | 25.7610i | −0.654752 | + | 1.13406i | ||||
\(517\) | −5.06175 | −0.222616 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3225 | 0.804268 | ||||||||
\(520\) | 16.1240 | − | 23.0703i | 0.707084 | − | 1.01170i | ||||
\(521\) | −12.1891 | − | 21.1122i | −0.534015 | − | 0.924942i | −0.999210 | − | 0.0397336i | \(-0.987349\pi\) |
0.465195 | − | 0.885208i | \(-0.345984\pi\) | |||||||
\(522\) | 2.32865 | − | 1.34445i | 0.101922 | − | 0.0588448i | ||||
\(523\) | −17.4701 | + | 30.2591i | −0.763915 | + | 1.32314i | 0.176903 | + | 0.984228i | \(0.443392\pi\) |
−0.940818 | + | 0.338912i | \(0.889941\pi\) | |||||||
\(524\) | 9.06070 | 0.395818 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.88247i | 0.300090i | ||||||||
\(527\) | 18.1566 | + | 10.4827i | 0.790914 | + | 0.456635i | ||||
\(528\) | 7.10437 | − | 4.10171i | 0.309178 | − | 0.178504i | ||||
\(529\) | 6.11753 | + | 10.5959i | 0.265980 | + | 0.460690i | ||||
\(530\) | 2.79605 | − | 4.84290i | 0.121453 | − | 0.210362i | ||||
\(531\) | − | 13.9541i | − | 0.605555i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.235063 | + | 2.71408i | −0.0101817 | + | 0.117560i | ||||
\(534\) | 4.08964 | − | 7.08347i | 0.176976 | − | 0.306532i | ||||
\(535\) | −50.6328 | + | 29.2328i | −2.18905 | + | 1.26385i | ||||
\(536\) | 0.520505 | + | 0.901542i | 0.0224824 | + | 0.0389407i | ||||
\(537\) | 17.9644 | − | 31.1153i | 0.775223 | − | 1.34273i | ||||
\(538\) | − | 12.5402i | − | 0.540646i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.9081i | 0.512445i | ||||||||
\(541\) | −26.4097 | − | 15.2477i | −1.13544 | − | 0.655548i | −0.190144 | − | 0.981756i | \(-0.560896\pi\) |
−0.945298 | + | 0.326208i | \(0.894229\pi\) | |||||||
\(542\) | 8.32693 | + | 14.4227i | 0.357672 | + | 0.619506i | ||||
\(543\) | 10.1914 | + | 17.6519i | 0.437353 | + | 0.757517i | ||||
\(544\) | 18.0629 | + | 10.4286i | 0.774442 | + | 0.447124i | ||||
\(545\) | −26.8780 | −1.15133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0049 | −0.427780 | −0.213890 | − | 0.976858i | \(-0.568613\pi\) | ||||
−0.213890 | + | 0.976858i | \(0.568613\pi\) | |||||||
\(548\) | 21.6151 | + | 12.4795i | 0.923352 | + | 0.533098i | ||||
\(549\) | −8.61285 | − | 14.9179i | −0.367587 | − | 0.636680i | ||||
\(550\) | 4.93825 | + | 8.55329i | 0.210568 | + | 0.364714i | ||||
\(551\) | 15.1788 | + | 8.76348i | 0.646638 | + | 0.373337i | ||||
\(552\) | − | 17.6445i | − | 0.750999i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 1.16791i | − | 0.0496198i | ||||||
\(555\) | 13.9978 | − | 24.2449i | 0.594173 | − | 1.02914i | ||||
\(556\) | −2.31111 | − | 4.00296i | −0.0980128 | − | 0.169763i | ||||
\(557\) | −12.2920 | + | 7.09679i | −0.520829 | + | 0.300701i | −0.737274 | − | 0.675594i | \(-0.763887\pi\) |
0.216445 | + | 0.976295i | \(0.430554\pi\) | |||||||
\(558\) | 3.82616 | − | 6.62711i | 0.161974 | − | 0.280548i | ||||
\(559\) | −31.6336 | − | 2.73975i | −1.33796 | − | 0.115879i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 21.3876i | − | 0.902986i | ||||||
\(562\) | −4.01207 | + | 6.94910i | −0.169239 | + | 0.293130i | ||||
\(563\) | −10.6795 | − | 18.4975i | −0.450088 | − | 0.779576i | 0.548303 | − | 0.836280i | \(-0.315274\pi\) |
−0.998391 | + | 0.0567041i | \(0.981941\pi\) | |||||||
\(564\) | 5.50668 | − | 3.17929i | 0.231873 | − | 0.133872i | ||||
\(565\) | 23.5644 | + | 13.6049i | 0.991364 | + | 0.572364i | ||||
\(566\) | − | 8.35857i | − | 0.351337i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.8193 | −0.915519 | ||||||||
\(569\) | 17.1336 | − | 29.6763i | 0.718278 | − | 1.24409i | −0.243404 | − | 0.969925i | \(-0.578264\pi\) |
0.961682 | − | 0.274168i | \(-0.0884025\pi\) | |||||||
\(570\) | −36.2897 | + | 20.9518i | −1.52001 | + | 0.877576i | ||||
\(571\) | −18.8247 | − | 32.6053i | −0.787789 | − | 1.36449i | −0.927318 | − | 0.374273i | \(-0.877892\pi\) |
0.139529 | − | 0.990218i | \(-0.455441\pi\) | |||||||
\(572\) | 12.1218 | + | 8.47200i | 0.506837 | + | 0.354232i | ||||
\(573\) | 14.7654 | 0.616834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.4938 | −0.729541 | ||||||||
\(576\) | 1.18421 | − | 2.05111i | 0.0493420 | − | 0.0854629i | ||||
\(577\) | 24.5925 | − | 14.1985i | 1.02380 | − | 0.591091i | 0.108598 | − | 0.994086i | \(-0.465364\pi\) |
0.915202 | + | 0.402995i | \(0.132031\pi\) | |||||||
\(578\) | −2.44414 | + | 1.41112i | −0.101663 | + | 0.0586950i | ||||
\(579\) | −39.5104 | − | 22.8113i | −1.64200 | − | 0.948007i | ||||
\(580\) | 10.0558i | 0.417543i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.6878 | 0.608830 | ||||||||
\(583\) | 5.88083 | + | 3.39530i | 0.243559 | + | 0.140619i | ||||
\(584\) | −7.03164 | − | 12.1792i | −0.290971 | − | 0.503977i | ||||
\(585\) | 19.9824 | − | 9.33918i | 0.826169 | − | 0.386127i | ||||
\(586\) | −3.94523 | + | 6.83333i | −0.162976 | + | 0.282282i | ||||
\(587\) | − | 6.23659i | − | 0.257412i | −0.991683 | − | 0.128706i | \(-0.958918\pi\) | ||
0.991683 | − | 0.128706i | \(-0.0410823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.8800 | 2.05527 | ||||||||
\(590\) | −14.0600 | − | 8.11753i | −0.578840 | − | 0.334193i | ||||
\(591\) | 16.0478 | − | 9.26517i | 0.660116 | − | 0.381118i | ||||
\(592\) | −4.69323 | + | 2.70964i | −0.192890 | + | 0.111365i | ||||
\(593\) | 15.2159 | + | 8.78491i | 0.624843 | + | 0.360753i | 0.778752 | − | 0.627332i | \(-0.215853\pi\) |
−0.153909 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(594\) | 4.49871 | 0.184584 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 22.1748i | − | 0.908317i | ||||||
\(597\) | 0.665926 | − | 1.15342i | 0.0272545 | − | 0.0472062i | ||||
\(598\) | 7.38291 | − | 3.45056i | 0.301909 | − | 0.141104i | ||||
\(599\) | −8.49063 | − | 14.7062i | −0.346918 | − | 0.600879i | 0.638782 | − | 0.769387i | \(-0.279438\pi\) |
−0.985700 | + | 0.168508i | \(0.946105\pi\) | |||||||
\(600\) | −24.8320 | − | 14.3368i | −1.01376 | − | 0.585296i | ||||
\(601\) | −18.7052 | −0.763001 | −0.381500 | − | 0.924369i | \(-0.624592\pi\) | ||||
−0.381500 | + | 0.924369i | \(0.624592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.815792i | 0.0332216i | ||||||||
\(604\) | −26.3879 | − | 15.2351i | −1.07371 | − | 0.619906i | ||||
\(605\) | 10.4941 | − | 6.05877i | 0.426645 | − | 0.246324i | ||||
\(606\) | 18.0903 | − | 10.4445i | 0.734870 | − | 0.424277i | ||||
\(607\) | 5.17876 | − | 8.96987i | 0.210199 | − | 0.364076i | −0.741577 | − | 0.670867i | \(-0.765922\pi\) |
0.951777 | + | 0.306791i | \(0.0992554\pi\) | |||||||
\(608\) | 49.6227 | 2.01247 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0415 | −0.811456 | ||||||||
\(611\) | 5.56326 | + | 3.88820i | 0.225065 | + | 0.157300i | ||||
\(612\) | 5.21432 | + | 9.03147i | 0.210776 | + | 0.365075i | ||||
\(613\) | −6.08147 | + | 3.51114i | −0.245628 | + | 0.141814i | −0.617761 | − | 0.786366i | \(-0.711960\pi\) |
0.372133 | + | 0.928180i | \(0.378627\pi\) | |||||||
\(614\) | −1.36741 | + | 2.36843i | −0.0551843 | + | 0.0955820i | ||||
\(615\) | 5.37778 | 0.216853 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.9813i | 1.20700i | 0.797363 | + | 0.603500i | \(0.206228\pi\) | ||||
−0.797363 | + | 0.603500i | \(0.793772\pi\) | |||||||
\(618\) | −16.2428 | − | 9.37778i | −0.653381 | − | 0.377230i | ||||
\(619\) | −0.0247512 | + | 0.0142901i | −0.000994834 | + | 0.000574368i | −0.500497 | − | 0.865738i | \(-0.666849\pi\) |
0.499503 | + | 0.866312i | \(0.333516\pi\) | |||||||
\(620\) | 14.3089 | + | 24.7837i | 0.574659 | + | 0.995338i | ||||
\(621\) | −3.98418 | + | 6.90080i | −0.159880 | + | 0.276920i | ||||
\(622\) | − | 18.8399i | − | 0.755412i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.9590 | − | 0.949145i | −0.438711 | − | 0.0379962i | ||||
\(625\) | 11.6153 | − | 20.1183i | 0.464612 | − | 0.804732i | ||||
\(626\) | −11.3970 | + | 6.58004i | −0.455514 | + | 0.262991i | ||||
\(627\) | −25.4422 | − | 44.0672i | −1.01607 | − | 1.75988i | ||||
\(628\) | −5.64296 | + | 9.77389i | −0.225179 | + | 0.390021i | ||||
\(629\) | 14.1289i | 0.563356i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1936i | 0.485419i | 0.970099 | + | 0.242709i | \(0.0780361\pi\) | ||||
−0.970099 | + | 0.242709i | \(0.921964\pi\) | |||||||
\(632\) | 9.42156 | + | 5.43954i | 0.374769 | + | 0.216373i | ||||
\(633\) | −2.10716 | − | 3.64971i | −0.0837521 | − | 0.145063i | ||||
\(634\) | 3.41282 | + | 5.91117i | 0.135540 | + | 0.234763i | ||||
\(635\) | 11.3781 | + | 6.56914i | 0.451525 | + | 0.260688i | ||||
\(636\) | −8.53035 | −0.338250 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.79892 | 0.150401 | ||||||||
\(639\) | −14.8080 | − | 8.54940i | −0.585795 | − | 0.338209i | ||||
\(640\) | 17.2859 | + | 29.9401i | 0.683286 | + | 1.18349i | ||||
\(641\) | −1.41258 | − | 2.44666i | −0.0557935 | − | 0.0966373i | 0.836780 | − | 0.547540i | \(-0.184436\pi\) |
−0.892573 | + | 0.450903i | \(0.851102\pi\) | |||||||
\(642\) | −24.0289 | − | 13.8731i | −0.948346 | − | 0.547528i | ||||
\(643\) | − | 37.7275i | − | 1.48783i | −0.668276 | − | 0.743913i | \(-0.732968\pi\) | ||
0.668276 | − | 0.743913i | \(-0.267032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 62.6800i | 2.46802i | ||||||||
\(646\) | 10.5741 | − | 18.3148i | 0.416031 | − | 0.720587i | ||||
\(647\) | 6.18320 | + | 10.7096i | 0.243087 | + | 0.421039i | 0.961592 | − | 0.274483i | \(-0.0885067\pi\) |
−0.718505 | + | 0.695522i | \(0.755173\pi\) | |||||||
\(648\) | −23.3198 | + | 13.4637i | −0.916087 | + | 0.528903i | ||||
\(649\) | 9.85728 | − | 17.0733i | 0.386932 | − | 0.670186i | ||||
\(650\) | 1.14272 | − | 13.1941i | 0.0448212 | − | 0.517513i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3.54956i | − | 0.139012i | ||||||
\(653\) | 16.5002 | − | 28.5793i | 0.645704 | − | 1.11839i | −0.338434 | − | 0.940990i | \(-0.609897\pi\) |
0.984138 | − | 0.177402i | \(-0.0567694\pi\) | |||||||
\(654\) | −6.37778 | − | 11.0466i | −0.249391 | − | 0.431958i | ||||
\(655\) | 16.5345 | − | 9.54617i | 0.646055 | − | 0.373000i | ||||
\(656\) | −0.901542 | − | 0.520505i | −0.0351993 | − | 0.0203223i | ||||
\(657\) | − | 11.0207i | − | 0.429960i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.8118 | 1.27817 | 0.639084 | − | 0.769137i | \(-0.279314\pi\) | ||||
0.639084 | + | 0.769137i | \(0.279314\pi\) | |||||||
\(660\) | 14.5970 | − | 25.2828i | 0.568188 | − | 0.984131i | ||||
\(661\) | 12.7364 | − | 7.35336i | 0.495388 | − | 0.286013i | −0.231419 | − | 0.972854i | \(-0.574337\pi\) |
0.726807 | + | 0.686842i | \(0.241003\pi\) | |||||||
\(662\) | 8.06668 | + | 13.9719i | 0.313520 | + | 0.543033i | ||||
\(663\) | −16.4290 | + | 23.5067i | −0.638048 | + | 0.912923i | ||||
\(664\) | 26.2953 | 1.02046 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.15701 | 0.199830 | ||||||||
\(667\) | −3.36442 | + | 5.82735i | −0.130271 | + | 0.225636i | ||||
\(668\) | 4.52091 | − | 2.61015i | 0.174919 | − | 0.100990i | ||||
\(669\) | −20.3916 | + | 11.7731i | −0.788384 | + | 0.455174i | ||||
\(670\) | 0.821984 | + | 0.474572i | 0.0317560 | + | 0.0183343i | ||||
\(671\) | − | 24.3368i | − | 0.939511i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.2908 | −0.820702 | −0.410351 | − | 0.911928i | \(-0.634594\pi\) | ||||
−0.410351 | + | 0.911928i | \(0.634594\pi\) | |||||||
\(674\) | −4.48407 | − | 2.58888i | −0.172720 | − | 0.0997198i | ||||
\(675\) | 6.47457 | + | 11.2143i | 0.249206 | + | 0.431638i | ||||
\(676\) | −6.81499 | − | 18.6228i | −0.262115 | − | 0.716260i | ||||
\(677\) | 1.53580 | − | 2.66008i | 0.0590256 | − | 0.102235i | −0.835003 | − | 0.550246i | \(-0.814534\pi\) |
0.894028 | + | 0.448011i | \(0.147867\pi\) | |||||||
\(678\) | 12.9131i | 0.495923i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 28.0415 | 1.07534 | ||||||||
\(681\) | 28.8624 | + | 16.6637i | 1.10601 | + | 0.638554i | ||||
\(682\) | 9.36290 | − | 5.40567i | 0.358524 | − | 0.206994i | ||||
\(683\) | 21.4749 | − | 12.3985i | 0.821713 | − | 0.474416i | −0.0292935 | − | 0.999571i | \(-0.509326\pi\) |
0.851007 | + | 0.525154i | \(0.175992\pi\) | |||||||
\(684\) | 21.4873 | + | 12.4057i | 0.821586 | + | 0.474343i | ||||
\(685\) | 52.5926 | 2.00946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.4701i | − | 0.552070i | ||||||
\(688\) | 6.06668 | − | 10.5078i | 0.231290 | − | 0.400606i | ||||
\(689\) | −3.85538 | − | 8.24908i | −0.146878 | − | 0.314265i | ||||
\(690\) | −8.04371 | − | 13.9321i | −0.306219 | − | 0.530387i | ||||
\(691\) | 23.4652 | + | 13.5476i | 0.892658 | + | 0.515376i | 0.874811 | − | 0.484465i | \(-0.160986\pi\) |
0.0178467 | + | 0.999841i | \(0.494319\pi\) | |||||||
\(692\) | −12.6222 | −0.479825 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.88845i | 0.147603i | ||||||||
\(695\) | −8.43487 | − | 4.86987i | −0.319953 | − | 0.184725i | ||||
\(696\) | −9.55144 | + | 5.51453i | −0.362047 | + | 0.209028i | ||||
\(697\) | −2.35046 | + | 1.35704i | −0.0890302 | + | 0.0514016i | ||||
\(698\) | −8.32148 | + | 14.4132i | −0.314973 | + | 0.545549i | ||||
\(699\) | −61.9101 | −2.34166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5205 | −0.510662 | −0.255331 | − | 0.966854i | \(-0.582185\pi\) | ||||
−0.255331 | + | 0.966854i | \(0.582185\pi\) | |||||||
\(702\) | −4.94443 | − | 3.45569i | −0.186615 | − | 0.130427i | ||||
\(703\) | 16.8074 | + | 29.1113i | 0.633904 | + | 1.09795i | ||||
\(704\) | 2.89784 | − | 1.67307i | 0.109217 | − | 0.0630562i | ||||
\(705\) | 6.69926 | − | 11.6035i | 0.252309 | − | 0.437012i | ||||
\(706\) | −24.8889 | −0.936707 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 24.7654i | 0.930741i | ||||||||
\(709\) | −44.1459 | − | 25.4876i | −1.65793 | − | 0.957209i | −0.973666 | − | 0.227977i | \(-0.926789\pi\) |
−0.684267 | − | 0.729231i | \(-0.739878\pi\) | |||||||
\(710\) | −17.2286 | + | 9.94692i | −0.646577 | + | 0.373301i | ||||
\(711\) | 4.26271 | + | 7.38324i | 0.159864 | + | 0.276893i | ||||
\(712\) | −6.51114 | + | 11.2776i | −0.244015 | + | 0.422647i | ||||
\(713\) | 19.1497i | 0.717160i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.0464 | + | 2.68889i | 1.16107 | + | 0.100559i | ||||
\(716\) | −12.3756 | + | 21.4351i | −0.462496 | + | 0.801067i | ||||
\(717\) | 37.5500 | − | 21.6795i | 1.40233 | − | 0.809637i | ||||
\(718\) | −5.99778 | − | 10.3885i | −0.223835 | − | 0.387694i | ||||
\(719\) | 20.7709 | − | 35.9762i | 0.774622 | − | 1.34169i | −0.160384 | − | 0.987055i | \(-0.551273\pi\) |
0.935006 | − | 0.354631i | \(-0.115393\pi\) | |||||||
\(720\) | 8.42864i | 0.314117i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 37.2257i | − | 1.38540i | ||||||
\(723\) | 25.6151 | + | 14.7889i | 0.952637 | + | 0.550005i | ||||
\(724\) | −7.02074 | − | 12.1603i | −0.260924 | − | 0.451933i | ||||
\(725\) | 5.46743 | + | 9.46986i | 0.203055 | + | 0.351702i | ||||
\(726\) | 4.98021 | + | 2.87532i | 0.184833 | + | 0.106713i | ||||
\(727\) | 20.8988 | 0.775092 | 0.387546 | − | 0.921850i | \(-0.373323\pi\) | ||||
0.387546 | + | 0.921850i | \(0.373323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | −11.1044 | − | 6.41112i | −0.410992 | − | 0.237286i | ||||
\(731\) | −15.8168 | − | 27.3955i | −0.585005 | − | 1.01326i | ||||
\(732\) | 15.2859 | + | 26.4760i | 0.564984 | + | 0.978581i | ||||
\(733\) | −16.7641 | − | 9.67876i | −0.619196 | − | 0.357493i | 0.157360 | − | 0.987541i | \(-0.449702\pi\) |
−0.776556 | + | 0.630048i | \(0.783035\pi\) | |||||||
\(734\) | 2.02413i | 0.0747122i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.0509i | 0.702224i | ||||||||
\(737\) | −0.576283 | + | 0.998151i | −0.0212276 | + | 0.0367674i | ||||
\(738\) | 0.495316 | + | 0.857913i | 0.0182328 | + | 0.0315802i | ||||
\(739\) | 1.13545 | − | 0.655554i | 0.0417683 | − | 0.0241149i | −0.478970 | − | 0.877831i | \(-0.658990\pi\) |
0.520739 | + | 0.853716i | \(0.325657\pi\) | |||||||
\(740\) | −9.64296 | + | 16.7021i | −0.354482 | + | 0.613981i | ||||
\(741\) | −5.88739 | + | 67.9768i | −0.216279 | + | 2.49719i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.5210i | − | 0.789528i | −0.918783 | − | 0.394764i | \(-0.870826\pi\) | ||
0.918783 | − | 0.394764i | \(-0.129174\pi\) | |||||||
\(744\) | −15.6938 | + | 27.1825i | −0.575363 | + | 0.996558i | ||||
\(745\) | −23.3630 | − | 40.4658i | −0.855953 | − | 1.48255i | ||||
\(746\) | −11.1981 | + | 6.46520i | −0.409990 | + | 0.236708i | ||||
\(747\) | 17.8457 | + | 10.3032i | 0.652939 | + | 0.376974i | ||||
\(748\) | 14.7338i | 0.538720i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.62714 | −0.0594147 | ||||||||
\(751\) | −8.15878 | + | 14.1314i | −0.297718 | + | 0.515663i | −0.975614 | − | 0.219495i | \(-0.929559\pi\) |
0.677895 | + | 0.735158i | \(0.262892\pi\) | |||||||
\(752\) | −2.24615 | + | 1.29682i | −0.0819088 | + | 0.0472901i | ||||
\(753\) | −3.65010 | − | 6.32217i | −0.133017 | − | 0.230393i | ||||
\(754\) | −4.17530 | − | 2.91815i | −0.152055 | − | 0.106273i | ||||
\(755\) | −64.2054 | −2.33667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7462 | −0.681342 | −0.340671 | − | 0.940183i | \(-0.610654\pi\) | ||||
−0.340671 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(758\) | 8.15971 | − | 14.1330i | 0.296374 | − | 0.513335i | ||||
\(759\) | 16.9180 | − | 9.76764i | 0.614086 | − | 0.354543i | ||||
\(760\) | 57.7769 | − | 33.3575i | 2.09579 | − | 1.21000i | ||||
\(761\) | −8.91731 | − | 5.14841i | −0.323252 | − | 0.186630i | 0.329589 | − | 0.944124i | \(-0.393090\pi\) |
−0.652841 | + | 0.757495i | \(0.726423\pi\) | |||||||
\(762\) | 6.23506i | 0.225873i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.1718 | −0.368002 | ||||||||
\(765\) | 19.0307 | + | 10.9874i | 0.688058 | + | 0.397250i | ||||
\(766\) | 10.8889 | + | 18.8602i | 0.393433 | + | 0.681445i | ||||
\(767\) | −23.9488 | + | 11.1930i | −0.864742 | + | 0.404155i | ||||
\(768\) | −10.9590 | + | 18.9815i | −0.395448 | + | 0.684937i | ||||
\(769\) | 9.36641i | 0.337761i | 0.985637 | + | 0.168881i | \(0.0540153\pi\) | ||||
−0.985637 | + | 0.168881i | \(0.945985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.4657 | −1.88951 | ||||||||
\(772\) | 27.2184 | + | 15.7146i | 0.979612 | + | 0.565579i | ||||
\(773\) | −3.21690 | + | 1.85728i | −0.115704 | + | 0.0668017i | −0.556735 | − | 0.830690i | \(-0.687946\pi\) |
0.441031 | + | 0.897492i | \(0.354613\pi\) | |||||||
\(774\) | −9.99928 | + | 5.77309i | −0.359417 | + | 0.207509i | ||||
\(775\) | 26.9503 | + | 15.5598i | 0.968084 | + | 0.558923i | ||||
\(776\) | −23.3846 | −0.839457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8163i | 0.495337i | ||||||||
\(779\) | −3.22861 | + | 5.59212i | −0.115677 | + | 0.200358i | ||||
\(780\) | −35.4643 | + | 16.5750i | −1.26983 | + | 0.593480i | ||||
\(781\) | −12.0787 | − | 20.9210i | −0.432211 | − | 0.748612i | ||||
\(782\) | 7.03131 | + | 4.05953i | 0.251439 | + | 0.145169i | ||||
\(783\) | 4.98079 | 0.177999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.7812i | 0.848789i | ||||||||
\(786\) | 7.84680 | + | 4.53035i | 0.279886 | + | 0.161592i | ||||
\(787\) | −5.40105 | + | 3.11830i | −0.192527 | + | 0.111155i | −0.593165 | − | 0.805081i | \(-0.702122\pi\) |
0.400638 | + | 0.916236i | \(0.368788\pi\) | |||||||
\(788\) | −11.0552 | + | 6.38271i | −0.393824 | + | 0.227375i | ||||
\(789\) | 11.0612 | − | 19.1586i | 0.393790 | − | 0.682064i | ||||
\(790\) | 9.91903 | 0.352903 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.4286 | 0.441632 | ||||||||
\(793\) | −18.6944 | + | 26.7480i | −0.663856 | + | 0.949849i | ||||
\(794\) | −7.87855 | − | 13.6460i | −0.279599 | − | 0.484280i | ||||
\(795\) | −15.5666 | + | 8.98741i | −0.552092 | + | 0.318750i | ||||
\(796\) | −0.458751 | + | 0.794580i | −0.0162600 | + | 0.0281631i | ||||
\(797\) | 40.0701 | 1.41935 | 0.709677 | − | 0.704527i | \(-0.248841\pi\) | ||||
0.709677 | + | 0.704527i | \(0.248841\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.76202i | 0.239223i | ||||||||
\(800\) | 26.8113 | + | 15.4795i | 0.947922 | + | 0.547283i | ||||
\(801\) | −8.83775 | + | 5.10248i | −0.312266 | + | 0.180287i | ||||
\(802\) | 1.93332 | + | 3.34861i | 0.0682680 | + | 0.118244i | ||||
\(803\) | 7.78515 | − | 13.4843i | 0.274732 | − | 0.475850i | ||||
\(804\) | − | 1.44785i | − | 0.0510618i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.4429 | − | 1.25088i | −0.508730 | − | 0.0440605i | ||||
\(807\) | −20.1541 | + | 34.9079i | −0.709458 | + | 1.22882i | ||||
\(808\) | −28.8017 | + | 16.6287i | −1.01324 | + | 0.584995i | ||||
\(809\) | 1.28568 | + | 2.22686i | 0.0452021 | + | 0.0782924i | 0.887741 | − | 0.460343i | \(-0.152273\pi\) |
−0.842539 | + | 0.538635i | \(0.818940\pi\) | |||||||
\(810\) | −12.2755 | + | 21.2619i | −0.431319 | + | 0.747066i | ||||
\(811\) | − | 28.3654i | − | 0.996042i | −0.867165 | − | 0.498021i | \(-0.834060\pi\) | ||
0.867165 | − | 0.498021i | \(-0.165940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 53.5308i | − | 1.87741i | ||||||
\(814\) | 6.30979 | + | 3.64296i | 0.221158 | + | 0.127686i | ||||
\(815\) | −3.73975 | − | 6.47743i | −0.130998 | − | 0.226895i | ||||
\(816\) | −5.47949 | − | 9.49076i | −0.191821 | − | 0.332243i | ||||
\(817\) | −65.1781 | − | 37.6306i | −2.28029 | − | 1.31653i | ||||
\(818\) | 17.9922 | 0.629081 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.70471 | −0.129374 | ||||||||
\(821\) | 27.5263 | + | 15.8923i | 0.960674 | + | 0.554646i | 0.896380 | − | 0.443285i | \(-0.146187\pi\) |
0.0642938 | + | 0.997931i | \(0.479521\pi\) | |||||||
\(822\) | 12.4795 | + | 21.6151i | 0.435272 | + | 0.753914i | ||||
\(823\) | 15.4565 | + | 26.7715i | 0.538781 | + | 0.933196i | 0.998970 | + | 0.0453747i | \(0.0144482\pi\) |
−0.460189 | + | 0.887821i | \(0.652218\pi\) | |||||||
\(824\) | 25.8602 | + | 14.9304i | 0.900884 | + | 0.520125i | ||||
\(825\) | − | 31.7462i | − | 1.10526i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 49.7560i | − | 1.73019i | −0.501610 | − | 0.865094i | \(-0.667259\pi\) | ||
0.501610 | − | 0.865094i | \(-0.332741\pi\) | |||||||
\(828\) | −4.76271 | + | 8.24926i | −0.165516 | + | 0.286682i | ||||
\(829\) | −9.95952 | − | 17.2504i | −0.345908 | − | 0.599131i | 0.639610 | − | 0.768700i | \(-0.279096\pi\) |
−0.985518 | + | 0.169569i | \(0.945763\pi\) | |||||||
\(830\) | 20.7628 | − | 11.9874i | 0.720687 | − | 0.416089i | ||||
\(831\) | −1.87702 | + | 3.25109i | −0.0651131 | + | 0.112779i | ||||
\(832\) | −4.47013 | − | 0.387152i | −0.154974 | − | 0.0134221i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 4.62222i | − | 0.160054i | ||||||
\(835\) | 5.50000 | − | 9.52628i | 0.190335 | − | 0.329670i | ||||
\(836\) | 17.5270 | + | 30.3576i | 0.606183 | + | 1.04994i | ||||
\(837\) | 12.2758 | − | 7.08742i | 0.424313 | − | 0.244977i | ||||
\(838\) | 15.0620 | + | 8.69604i | 0.520307 | + | 0.300400i | ||||
\(839\) | − | 11.5625i | − | 0.399181i | −0.979879 | − | 0.199590i | \(-0.936039\pi\) | ||
0.979879 | − | 0.199590i | \(-0.0639611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7940 | −0.854965 | ||||||||
\(842\) | −2.83431 | + | 4.90917i | −0.0976769 | + | 0.169181i | ||||
\(843\) | 22.3366 | − | 12.8961i | 0.769315 | − | 0.444164i | ||||
\(844\) | 1.45161 | + | 2.51426i | 0.0499663 | + | 0.0865442i | ||||
\(845\) | −32.0569 | − | 26.8037i | −1.10279 | − | 0.922075i | ||||
\(846\) | 2.46812 | 0.0848557 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.47949 | 0.119486 | ||||||||
\(849\) | −13.4336 | + | 23.2676i | −0.461039 | + | 0.798542i | ||||
\(850\) | 11.4264 | − | 6.59703i | 0.391922 | − | 0.226276i | ||||
\(851\) | −11.1762 | + | 6.45261i | −0.383117 | + | 0.221193i | ||||
\(852\) | 26.2809 | + | 15.1733i | 0.900370 | + | 0.519829i | ||||
\(853\) | − | 1.74467i | − | 0.0597363i | −0.999554 | − | 0.0298682i | \(-0.990491\pi\) | ||
0.999554 | − | 0.0298682i | \(-0.00950875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.2815 | 1.78799 | ||||||||
\(856\) | 38.2565 | + | 22.0874i | 1.30758 | + | 0.754932i | ||||
\(857\) | −21.1684 | − | 36.6647i | −0.723098 | − | 1.25244i | −0.959752 | − | 0.280849i | \(-0.909384\pi\) |
0.236654 | − | 0.971594i | \(-0.423949\pi\) | |||||||
\(858\) | 6.26177 | + | 13.3979i | 0.213773 | + | 0.457395i | ||||
\(859\) | 2.68889 | − | 4.65730i | 0.0917438 | − | 0.158905i | −0.816501 | − | 0.577344i | \(-0.804089\pi\) |
0.908245 | + | 0.418439i | \(0.137423\pi\) | |||||||
\(860\) | − | 43.1798i | − | 1.47242i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.990632 | 0.0337411 | ||||||||
\(863\) | −13.3620 | − | 7.71456i | −0.454848 | − | 0.262607i | 0.255027 | − | 0.966934i | \(-0.417915\pi\) |
−0.709875 | + | 0.704327i | \(0.751249\pi\) | |||||||
\(864\) | 12.2124 | − | 7.05086i | 0.415476 | − | 0.239875i | ||||
\(865\) | −23.0337 | + | 13.2985i | −0.783169 | + | 0.452163i | ||||
\(866\) | −9.84492 | − | 5.68397i | −0.334544 | − | 0.193149i | ||||
\(867\) | 9.07160 | 0.308088 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0449i | 0.408595i | ||||||||
\(870\) | −5.02789 | + | 8.70856i | −0.170461 | + | 0.295248i | ||||
\(871\) | 1.40011 | − | 0.654372i | 0.0474410 | − | 0.0221725i | ||||
\(872\) | 10.1541 | + | 17.5874i | 0.343861 | + | 0.595585i | ||||
\(873\) | −15.8703 | − | 9.16270i | −0.537127 | − | 0.310110i | ||||
\(874\) | 19.3165 | 0.653391 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.5594i | 0.660851i | ||||||||
\(877\) | −33.3576 | − | 19.2590i | −1.12641 | − | 0.650331i | −0.183378 | − | 0.983042i | \(-0.558703\pi\) |
−0.943029 | + | 0.332711i | \(0.892037\pi\) | |||||||
\(878\) | 6.06259 | − | 3.50024i | 0.204603 | − | 0.118127i | ||||
\(879\) | 21.9645 | − | 12.6812i | 0.740845 | − | 0.427727i | ||||
\(880\) | −5.95407 | + | 10.3127i | −0.200712 | + | 0.347643i | ||||
\(881\) | 41.7373 | 1.40617 | 0.703083 | − | 0.711108i | \(-0.251806\pi\) | ||||
0.703083 | + | 0.711108i | \(0.251806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.8439 | −1.77834 | −0.889170 | − | 0.457577i | \(-0.848717\pi\) | ||||
−0.889170 | + | 0.457577i | \(0.848717\pi\) | |||||||
\(884\) | 11.3178 | − | 16.1935i | 0.380658 | − | 0.544648i | ||||
\(885\) | 26.0923 | + | 45.1933i | 0.877084 | + | 1.51915i | ||||
\(886\) | 1.91381 | − | 1.10494i | 0.0642956 | − | 0.0371211i | ||||
\(887\) | −4.49532 | + | 7.78612i | −0.150938 | + | 0.261432i | −0.931573 | − | 0.363556i | \(-0.881563\pi\) |
0.780635 | + | 0.624988i | \(0.214896\pi\) | |||||||
\(888\) | −21.1526 | −0.709834 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.8731i | 0.397987i | ||||||||
\(891\) | −25.8187 | − | 14.9064i | −0.864959 | − | 0.499384i | ||||
\(892\) | 14.0476 | − | 8.11039i | 0.470348 | − | 0.271556i | ||||
\(893\) | 8.04395 | + | 13.9325i | 0.269180 | + | 0.466234i | ||||
\(894\) | 11.0874 | − | 19.2040i | 0.370819 | − | 0.642277i | ||||
\(895\) | 52.1546i | 1.74334i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.0973 | − | 2.26025i | −0.871362 | − | 0.0754676i | ||||
\(898\) | 6.34122 | − | 10.9833i | 0.211609 | − | 0.366518i | ||||
\(899\) | 10.3662 | − | 5.98494i | 0.345733 | − | 0.199609i | ||||
\(900\) | 7.73975 | + | 13.4056i | 0.257992 | + | 0.446855i | ||||
\(901\) | 4.53580 | − | 7.85623i | 0.151109 | − | 0.261729i | ||||
\(902\) | 1.39958i | 0.0466010i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 20.5589i | − | 0.683780i | ||||||
\(905\) | −25.6237 | − | 14.7938i | −0.851759 | − | 0.491764i | ||||
\(906\) | −15.2351 | − | 26.3879i | −0.506151 | − | 0.876679i | ||||
\(907\) | −10.3501 | − | 17.9270i | −0.343671 | − | 0.595255i | 0.641441 | − | 0.767173i | \(-0.278337\pi\) |
−0.985111 | + | 0.171918i | \(0.945004\pi\) | |||||||
\(908\) | −19.8831 | − | 11.4795i | −0.659843 | − | 0.380960i | ||||
\(909\) | −26.0622 | −0.864430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8988 | 0.990590 | 0.495295 | − | 0.868725i | \(-0.335060\pi\) | ||||
0.495295 | + | 0.868725i | \(0.335060\pi\) | |||||||
\(912\) | −22.5800 | − | 13.0366i | −0.747698 | − | 0.431684i | ||||
\(913\) | 14.5565 | + | 25.2127i | 0.481751 | + | 0.834418i | ||||
\(914\) | 1.17214 | + | 2.03021i | 0.0387710 | + | 0.0671533i | ||||
\(915\) | 55.7891 | + | 32.2099i | 1.84433 | + | 1.06483i | ||||
\(916\) | 9.96836i | 0.329364i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 6.00984i | − | 0.198354i | ||||||
\(919\) | −19.2924 | + | 33.4154i | −0.636397 | + | 1.10227i | 0.349821 | + | 0.936817i | \(0.386242\pi\) |
−0.986217 | + | 0.165455i | \(0.947091\pi\) | |||||||
\(920\) | 12.8064 | + | 22.1814i | 0.422215 | + | 0.731298i | ||||
\(921\) | 7.61289 | − | 4.39530i | 0.250853 | − | 0.144830i | ||||
\(922\) | 6.05239 | − | 10.4830i | 0.199325 | − | 0.345241i | ||||
\(923\) | −2.79505 | + | 32.2721i | −0.0920001 | + | 1.06225i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.9719i | 0.689552i | ||||||||
\(926\) | −5.43239 | + | 9.40918i | −0.178520 | + | 0.309205i | ||||
\(927\) | 11.7003 | + | 20.2655i | 0.384287 | + | 0.665605i | ||||
\(928\) | 10.3127 | − | 5.95407i | 0.338532 | − | 0.195452i | ||||
\(929\) | −2.81961 | − | 1.62790i | −0.0925085 | − | 0.0534098i | 0.453032 | − | 0.891494i | \(-0.350342\pi\) |
−0.545541 | + | 0.838084i | \(0.683676\pi\) | |||||||
\(930\) | 28.6178i | 0.938414i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.6494 | 1.39703 | ||||||||
\(933\) | −30.2788 | + | 52.4444i | −0.991283 | + | 1.71695i | ||||
\(934\) | 2.24735 | − | 1.29751i | 0.0735356 | − | 0.0424558i | ||||
\(935\) | 15.5232 | + | 26.8870i | 0.507663 | + | 0.879298i | ||||
\(936\) | −13.6600 | − | 9.54709i | −0.446492 | − | 0.312056i | ||||
\(937\) | −11.6840 | −0.381699 | −0.190849 | − | 0.981619i | \(-0.561124\pi\) | ||||
−0.190849 | + | 0.981619i | \(0.561124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.3007 | 1.38043 | ||||||||
\(940\) | −4.61507 | + | 7.99354i | −0.150527 | + | 0.260720i | ||||
\(941\) | −36.3470 | + | 20.9849i | −1.18488 | + | 0.684090i | −0.957138 | − | 0.289632i | \(-0.906467\pi\) |
−0.227740 | + | 0.973722i | \(0.573134\pi\) | |||||||
\(942\) | −9.77389 | + | 5.64296i | −0.318451 | + | 0.183858i | ||||
\(943\) | −2.14689 | − | 1.23951i | −0.0699124 | − | 0.0403640i | ||||
\(944\) | − | 10.1017i | − | 0.328783i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.3126 | −0.530370 | ||||||||
\(947\) | −17.6284 | − | 10.1778i | −0.572846 | − | 0.330733i | 0.185439 | − | 0.982656i | \(-0.440629\pi\) |
−0.758285 | + | 0.651923i | \(0.773962\pi\) | |||||||
\(948\) | −7.56538 | − | 13.1036i | −0.245712 | − | 0.425586i | ||||
\(949\) | −18.9145 | + | 8.84008i | −0.613990 | + | 0.286961i | ||||
\(950\) | 15.6953 | − | 27.1851i | 0.509224 | − | 0.882002i | ||||
\(951\) | − | 21.9398i | − | 0.711446i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.5496 | 0.989597 | 0.494799 | − | 0.869008i | \(-0.335242\pi\) | ||||
0.494799 | + | 0.869008i | \(0.335242\pi\) | |||||||
\(954\) | −2.86750 | − | 1.65555i | −0.0928389 | − | 0.0536005i | ||||
\(955\) | −18.5620 | + | 10.7168i | −0.600653 | + | 0.346787i | ||||
\(956\) | −25.8679 | + | 14.9349i | −0.836629 | + | 0.483028i | ||||
\(957\) | −10.5750 | − | 6.10546i | −0.341840 | − | 0.197362i | ||||
\(958\) | −8.33783 | −0.269383 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.85728i | 0.285867i | ||||||||
\(961\) | 1.53257 | − | 2.65449i | 0.0494378 | − | 0.0856288i | ||||
\(962\) | −4.13660 | − | 8.85077i | −0.133369 | − | 0.285360i | ||||
\(963\) | 17.3089 | + | 29.9799i | 0.557771 | + | 0.966088i | ||||
\(964\) | −17.6461 | − | 10.1880i | −0.568342 | − | 0.328132i | ||||
\(965\) | 66.2262 | 2.13190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.4548i | 1.75115i | 0.483084 | + | 0.875574i | \(0.339516\pi\) | ||||
−0.483084 | + | 0.875574i | \(0.660484\pi\) | |||||||
\(968\) | −7.92901 | − | 4.57781i | −0.254848 | − | 0.147137i | ||||
\(969\) | −58.8697 | + | 33.9884i | −1.89117 | + | 1.09187i | ||||
\(970\) | −18.4645 | + | 10.6605i | −0.592859 | + | 0.342287i | ||||
\(971\) | 27.3017 | − | 47.2880i | 0.876155 | − | 1.51754i | 0.0206267 | − | 0.999787i | \(-0.493434\pi\) |
0.855528 | − | 0.517757i | \(-0.173233\pi\) | |||||||
\(972\) | 26.3368 | 0.844752 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.9714 | 0.383589 | ||||||||
\(975\) | −24.3859 | + | 34.8915i | −0.780975 | + | 1.11742i | ||||
\(976\) | −6.23506 | − | 10.7994i | −0.199580 | − | 0.345682i | ||||
\(977\) | 28.2735 | − | 16.3237i | 0.904549 | − | 0.522242i | 0.0258756 | − | 0.999665i | \(-0.491763\pi\) |
0.878673 | + | 0.477424i | \(0.158429\pi\) | |||||||
\(978\) | 1.77478 | − | 3.07401i | 0.0567512 | − | 0.0982960i | ||||
\(979\) | −14.4177 | −0.460793 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9146i | 0.508114i | ||||||||
\(982\) | −11.5693 | − | 6.67952i | −0.369190 | − | 0.213152i | ||||
\(983\) | 23.8202 | − | 13.7526i | 0.759745 | − | 0.438639i | −0.0694590 | − | 0.997585i | \(-0.522127\pi\) |
0.829204 | + | 0.558946i | \(0.188794\pi\) | |||||||
\(984\) | −2.03164 | − | 3.51891i | −0.0647664 | − | 0.112179i | ||||
\(985\) | −13.4494 | + | 23.2950i | −0.428533 | + | 0.742241i | ||||
\(986\) | − | 5.07499i | − | 0.161621i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.05578 | − | 46.8287i | 0.129031 | − | 1.48982i | ||||
\(989\) | 14.4469 | − | 25.0228i | 0.459385 | − | 0.795679i | ||||
\(990\) | 9.81367 | − | 5.66593i | 0.311899 | − | 0.180075i | ||||
\(991\) | 3.14695 | + | 5.45068i | 0.0999662 | + | 0.173147i | 0.911670 | − | 0.410922i | \(-0.134793\pi\) |
−0.811704 | + | 0.584069i | \(0.801460\pi\) | |||||||
\(992\) | 16.9447 | − | 29.3491i | 0.537995 | − | 0.931834i | ||||
\(993\) | − | 51.8578i | − | 1.64566i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.93332i | 0.0612905i | ||||||||
\(996\) | −31.6721 | − | 18.2859i | −1.00357 | − | 0.579411i | ||||
\(997\) | 10.4351 | + | 18.0741i | 0.330483 | + | 0.572413i | 0.982607 | − | 0.185700i | \(-0.0594551\pi\) |
−0.652124 | + | 0.758112i | \(0.726122\pi\) | |||||||
\(998\) | −3.67529 | − | 6.36580i | −0.116339 | − | 0.201506i | ||||
\(999\) | 8.27282 | + | 4.77631i | 0.261740 | + | 0.151116i |
(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 | 637.2.r.e.324.3 | 12 | ||
7.2 | even | 3 | 91.2.c.a.64.4 | yes | 6 | ||
7.3 | odd | 6 | 637.2.r.d.116.4 | 12 | |||
7.4 | even | 3 | inner | 637.2.r.e.116.4 | 12 | ||
7.5 | odd | 6 | 637.2.c.d.246.4 | 6 | |||
7.6 | odd | 2 | 637.2.r.d.324.3 | 12 | |||
13.12 | even | 2 | inner | 637.2.r.e.324.4 | 12 | ||
21.2 | odd | 6 | 819.2.c.b.64.3 | 6 | |||
28.23 | odd | 6 | 1456.2.k.c.337.6 | 6 | |||
91.5 | even | 12 | 8281.2.a.bi.1.2 | 3 | |||
91.12 | odd | 6 | 637.2.c.d.246.3 | 6 | |||
91.25 | even | 6 | inner | 637.2.r.e.116.3 | 12 | ||
91.38 | odd | 6 | 637.2.r.d.116.3 | 12 | |||
91.44 | odd | 12 | 1183.2.a.j.1.2 | 3 | |||
91.47 | even | 12 | 8281.2.a.be.1.2 | 3 | |||
91.51 | even | 6 | 91.2.c.a.64.3 | ✓ | 6 | ||
91.86 | odd | 12 | 1183.2.a.h.1.2 | 3 | |||
91.90 | odd | 2 | 637.2.r.d.324.4 | 12 | |||
273.233 | odd | 6 | 819.2.c.b.64.4 | 6 | |||
364.51 | odd | 6 | 1456.2.k.c.337.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.3 | ✓ | 6 | 91.51 | even | 6 | ||
91.2.c.a.64.4 | yes | 6 | 7.2 | even | 3 | ||
637.2.c.d.246.3 | 6 | 91.12 | odd | 6 | |||
637.2.c.d.246.4 | 6 | 7.5 | odd | 6 | |||
637.2.r.d.116.3 | 12 | 91.38 | odd | 6 | |||
637.2.r.d.116.4 | 12 | 7.3 | odd | 6 | |||
637.2.r.d.324.3 | 12 | 7.6 | odd | 2 | |||
637.2.r.d.324.4 | 12 | 91.90 | odd | 2 | |||
637.2.r.e.116.3 | 12 | 91.25 | even | 6 | inner | ||
637.2.r.e.116.4 | 12 | 7.4 | even | 3 | inner | ||
637.2.r.e.324.3 | 12 | 1.1 | even | 1 | trivial | ||
637.2.r.e.324.4 | 12 | 13.12 | even | 2 | inner | ||
819.2.c.b.64.3 | 6 | 21.2 | odd | 6 | |||
819.2.c.b.64.4 | 6 | 273.233 | odd | 6 | |||
1183.2.a.h.1.2 | 3 | 91.86 | odd | 12 | |||
1183.2.a.j.1.2 | 3 | 91.44 | odd | 12 | |||
1456.2.k.c.337.5 | 6 | 364.51 | odd | 6 | |||
1456.2.k.c.337.6 | 6 | 28.23 | odd | 6 | |||
8281.2.a.be.1.2 | 3 | 91.47 | even | 12 | |||
8281.2.a.bi.1.2 | 3 | 91.5 | even | 12 |