Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(111,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.k (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.161 |
Dual form | 170.2.k.a.151.2 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.865619 | − | 2.08979i | 0.499766 | − | 1.20654i | −0.449844 | − | 0.893107i | \(-0.648521\pi\) |
0.949610 | − | 0.313434i | \(-0.101479\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.923880 | + | 0.382683i | 0.413171 | + | 0.171141i | ||||
\(6\) | −0.865619 | − | 2.08979i | −0.353388 | − | 0.853153i | ||||
\(7\) | −2.01367 | + | 0.834089i | −0.761096 | + | 0.315256i | −0.729260 | − | 0.684237i | \(-0.760135\pi\) |
−0.0318359 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.49661 | − | 1.49661i | −0.498869 | − | 0.498869i | ||||
\(10\) | 0.923880 | − | 0.382683i | 0.292156 | − | 0.121015i | ||||
\(11\) | 1.18524 | + | 2.86143i | 0.357364 | + | 0.862753i | 0.995669 | + | 0.0929696i | \(0.0296359\pi\) |
−0.638305 | + | 0.769784i | \(0.720364\pi\) | |||||||
\(12\) | −2.08979 | − | 0.865619i | −0.603270 | − | 0.249883i | ||||
\(13\) | 1.91761i | 0.531849i | 0.963994 | + | 0.265924i | \(0.0856771\pi\) | ||||
−0.963994 | + | 0.265924i | \(0.914323\pi\) | |||||||
\(14\) | −0.834089 | + | 2.01367i | −0.222920 | + | 0.538176i | ||||
\(15\) | 1.59946 | − | 1.59946i | 0.412978 | − | 0.412978i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.85403 | + | 1.46508i | −0.934740 | + | 0.355333i | ||||
\(18\) | −2.11652 | −0.498869 | ||||||||
\(19\) | 3.27564 | − | 3.27564i | 0.751484 | − | 0.751484i | −0.223272 | − | 0.974756i | \(-0.571674\pi\) |
0.974756 | + | 0.223272i | \(0.0716739\pi\) | |||||||
\(20\) | 0.382683 | − | 0.923880i | 0.0855706 | − | 0.206586i | ||||
\(21\) | 4.93015i | 1.07585i | ||||||||
\(22\) | 2.86143 | + | 1.18524i | 0.610059 | + | 0.252695i | ||||
\(23\) | −2.44155 | − | 5.89443i | −0.509099 | − | 1.22907i | −0.944403 | − | 0.328790i | \(-0.893359\pi\) |
0.435304 | − | 0.900284i | \(-0.356641\pi\) | |||||||
\(24\) | −2.08979 | + | 0.865619i | −0.426577 | + | 0.176694i | ||||
\(25\) | 0.707107 | + | 0.707107i | 0.141421 | + | 0.141421i | ||||
\(26\) | 1.35595 | + | 1.35595i | 0.265924 | + | 0.265924i | ||||
\(27\) | 1.84629 | − | 0.764757i | 0.355318 | − | 0.147178i | ||||
\(28\) | 0.834089 | + | 2.01367i | 0.157628 | + | 0.380548i | ||||
\(29\) | 6.49242 | + | 2.68925i | 1.20561 | + | 0.499381i | 0.892808 | − | 0.450437i | \(-0.148732\pi\) |
0.312803 | + | 0.949818i | \(0.398732\pi\) | |||||||
\(30\) | − | 2.26197i | − | 0.412978i | ||||||
\(31\) | −1.66078 | + | 4.00948i | −0.298285 | + | 0.720124i | 0.701686 | + | 0.712486i | \(0.252431\pi\) |
−0.999971 | + | 0.00763722i | \(0.997569\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 7.00575 | 1.21955 | ||||||||
\(34\) | −1.68925 | + | 3.76118i | −0.289703 | + | 0.645036i | ||||
\(35\) | −2.17958 | −0.368416 | ||||||||
\(36\) | −1.49661 | + | 1.49661i | −0.249434 | + | 0.249434i | ||||
\(37\) | −3.12132 | + | 7.53553i | −0.513142 | + | 1.23883i | 0.428904 | + | 0.903350i | \(0.358900\pi\) |
−0.942046 | + | 0.335484i | \(0.891100\pi\) | |||||||
\(38\) | − | 4.63246i | − | 0.751484i | ||||||
\(39\) | 4.00740 | + | 1.65992i | 0.641697 | + | 0.265800i | ||||
\(40\) | −0.382683 | − | 0.923880i | −0.0605076 | − | 0.146078i | ||||
\(41\) | −0.375285 | + | 0.155448i | −0.0586097 | + | 0.0242769i | −0.411796 | − | 0.911276i | \(-0.635098\pi\) |
0.353186 | + | 0.935553i | \(0.385098\pi\) | |||||||
\(42\) | 3.48614 | + | 3.48614i | 0.537924 | + | 0.537924i | ||||
\(43\) | −5.56854 | − | 5.56854i | −0.849194 | − | 0.849194i | 0.140839 | − | 0.990033i | \(-0.455020\pi\) |
−0.990033 | + | 0.140839i | \(0.955020\pi\) | |||||||
\(44\) | 2.86143 | − | 1.18524i | 0.431377 | − | 0.178682i | ||||
\(45\) | −0.809957 | − | 1.95541i | −0.120741 | − | 0.291495i | ||||
\(46\) | −5.89443 | − | 2.44155i | −0.869086 | − | 0.359987i | ||||
\(47\) | − | 0.118113i | − | 0.0172285i | −0.999963 | − | 0.00861427i | \(-0.997258\pi\) | ||
0.999963 | − | 0.00861427i | \(-0.00274204\pi\) | |||||||
\(48\) | −0.865619 | + | 2.08979i | −0.124941 | + | 0.301635i | ||||
\(49\) | −1.59059 | + | 1.59059i | −0.227227 | + | 0.227227i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.274423 | + | 9.32231i | −0.0384269 | + | 1.30539i | ||||
\(52\) | 1.91761 | 0.265924 | ||||||||
\(53\) | 2.75378 | − | 2.75378i | 0.378261 | − | 0.378261i | −0.492214 | − | 0.870474i | \(-0.663812\pi\) |
0.870474 | + | 0.492214i | \(0.163812\pi\) | |||||||
\(54\) | 0.764757 | − | 1.84629i | 0.104070 | − | 0.251248i | ||||
\(55\) | 3.09719i | 0.417625i | ||||||||
\(56\) | 2.01367 | + | 0.834089i | 0.269088 | + | 0.111460i | ||||
\(57\) | −4.00995 | − | 9.68087i | −0.531130 | − | 1.28226i | ||||
\(58\) | 6.49242 | − | 2.68925i | 0.852496 | − | 0.353115i | ||||
\(59\) | −6.89715 | − | 6.89715i | −0.897932 | − | 0.897932i | 0.0973207 | − | 0.995253i | \(-0.468973\pi\) |
−0.995253 | + | 0.0973207i | \(0.968973\pi\) | |||||||
\(60\) | −1.59946 | − | 1.59946i | −0.206489 | − | 0.206489i | ||||
\(61\) | −14.0416 | + | 5.81623i | −1.79785 | + | 0.744692i | −0.810576 | + | 0.585634i | \(0.800846\pi\) |
−0.987269 | + | 0.159058i | \(0.949154\pi\) | |||||||
\(62\) | 1.66078 | + | 4.00948i | 0.210919 | + | 0.509204i | ||||
\(63\) | 4.26197 | + | 1.76537i | 0.536958 | + | 0.222415i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.733837 | + | 1.77164i | −0.0910212 | + | 0.219745i | ||||
\(66\) | 4.95382 | − | 4.95382i | 0.609773 | − | 0.609773i | ||||
\(67\) | 9.13707 | 1.11627 | 0.558135 | − | 0.829750i | \(-0.311517\pi\) | ||||
0.558135 | + | 0.829750i | \(0.311517\pi\) | |||||||
\(68\) | 1.46508 | + | 3.85403i | 0.177667 | + | 0.467370i | ||||
\(69\) | −14.4316 | −1.73736 | ||||||||
\(70\) | −1.54120 | + | 1.54120i | −0.184208 | + | 0.184208i | ||||
\(71\) | 2.33489 | − | 5.63691i | 0.277100 | − | 0.668978i | −0.722653 | − | 0.691211i | \(-0.757077\pi\) |
0.999753 | + | 0.0222327i | \(0.00707746\pi\) | |||||||
\(72\) | 2.11652i | 0.249434i | ||||||||
\(73\) | 1.53701 | + | 0.636649i | 0.179893 | + | 0.0745141i | 0.470812 | − | 0.882234i | \(-0.343961\pi\) |
−0.290919 | + | 0.956748i | \(0.593961\pi\) | |||||||
\(74\) | 3.12132 | + | 7.53553i | 0.362846 | + | 0.875988i | ||||
\(75\) | 2.08979 | − | 0.865619i | 0.241308 | − | 0.0999531i | ||||
\(76\) | −3.27564 | − | 3.27564i | −0.375742 | − | 0.375742i | ||||
\(77\) | −4.77337 | − | 4.77337i | −0.543977 | − | 0.543977i | ||||
\(78\) | 4.00740 | − | 1.65992i | 0.453748 | − | 0.187949i | ||||
\(79\) | 3.76904 | + | 9.09927i | 0.424050 | + | 1.02375i | 0.981141 | + | 0.193296i | \(0.0619177\pi\) |
−0.557090 | + | 0.830452i | \(0.688082\pi\) | |||||||
\(80\) | −0.923880 | − | 0.382683i | −0.103293 | − | 0.0427853i | ||||
\(81\) | − | 10.8699i | − | 1.20777i | ||||||
\(82\) | −0.155448 | + | 0.375285i | −0.0171664 | + | 0.0414433i | ||||
\(83\) | 5.90036 | − | 5.90036i | 0.647648 | − | 0.647648i | −0.304776 | − | 0.952424i | \(-0.598582\pi\) |
0.952424 | + | 0.304776i | \(0.0985815\pi\) | |||||||
\(84\) | 4.93015 | 0.537924 | ||||||||
\(85\) | −4.12132 | − | 0.121320i | −0.447020 | − | 0.0131590i | ||||
\(86\) | −7.87510 | −0.849194 | ||||||||
\(87\) | 11.2399 | − | 11.2399i | 1.20505 | − | 1.20505i | ||||
\(88\) | 1.18524 | − | 2.86143i | 0.126347 | − | 0.305029i | ||||
\(89\) | − | 9.71832i | − | 1.03014i | −0.857148 | − | 0.515070i | \(-0.827766\pi\) | ||
0.857148 | − | 0.515070i | \(-0.172234\pi\) | |||||||
\(90\) | −1.95541 | − | 0.809957i | −0.206118 | − | 0.0853770i | ||||
\(91\) | −1.59946 | − | 3.86143i | −0.167669 | − | 0.404788i | ||||
\(92\) | −5.89443 | + | 2.44155i | −0.614537 | + | 0.254550i | ||||
\(93\) | 6.94137 | + | 6.94137i | 0.719786 | + | 0.719786i | ||||
\(94\) | −0.0835185 | − | 0.0835185i | −0.00861427 | − | 0.00861427i | ||||
\(95\) | 4.27983 | − | 1.77276i | 0.439102 | − | 0.181882i | ||||
\(96\) | 0.865619 | + | 2.08979i | 0.0883469 | + | 0.213288i | ||||
\(97\) | 1.28598 | + | 0.532672i | 0.130572 | + | 0.0540846i | 0.447013 | − | 0.894528i | \(-0.352488\pi\) |
−0.316441 | + | 0.948612i | \(0.602488\pi\) | |||||||
\(98\) | 2.24943i | 0.227227i | ||||||||
\(99\) | 2.50859 | − | 6.05627i | 0.252123 | − | 0.608678i | ||||
\(100\) | 0.707107 | − | 0.707107i | 0.0707107 | − | 0.0707107i | ||||
\(101\) | 5.83938 | 0.581040 | 0.290520 | − | 0.956869i | \(-0.406172\pi\) | ||||
0.290520 | + | 0.956869i | \(0.406172\pi\) | |||||||
\(102\) | 6.39782 | + | 6.78592i | 0.633479 | + | 0.671906i | ||||
\(103\) | −14.9378 | −1.47186 | −0.735932 | − | 0.677056i | \(-0.763256\pi\) | ||||
−0.735932 | + | 0.677056i | \(0.763256\pi\) | |||||||
\(104\) | 1.35595 | − | 1.35595i | 0.132962 | − | 0.132962i | ||||
\(105\) | −1.88669 | + | 4.55487i | −0.184122 | + | 0.444509i | ||||
\(106\) | − | 3.89443i | − | 0.378261i | ||||||
\(107\) | −18.6803 | − | 7.73765i | −1.80590 | − | 0.748027i | −0.983945 | − | 0.178471i | \(-0.942885\pi\) |
−0.821952 | − | 0.569556i | \(-0.807115\pi\) | |||||||
\(108\) | −0.764757 | − | 1.84629i | −0.0735888 | − | 0.177659i | ||||
\(109\) | −10.2687 | + | 4.25345i | −0.983566 | + | 0.407406i | −0.815745 | − | 0.578411i | \(-0.803673\pi\) |
−0.167821 | + | 0.985818i | \(0.553673\pi\) | |||||||
\(110\) | 2.19004 | + | 2.19004i | 0.208812 | + | 0.208812i | ||||
\(111\) | 13.0458 | + | 13.0458i | 1.23825 | + | 1.23825i | ||||
\(112\) | 2.01367 | − | 0.834089i | 0.190274 | − | 0.0788140i | ||||
\(113\) | −4.70338 | − | 11.3550i | −0.442457 | − | 1.06819i | −0.975084 | − | 0.221836i | \(-0.928795\pi\) |
0.532627 | − | 0.846350i | \(-0.321205\pi\) | |||||||
\(114\) | −9.68087 | − | 4.00995i | −0.906696 | − | 0.375566i | ||||
\(115\) | − | 6.38009i | − | 0.594946i | ||||||
\(116\) | 2.68925 | − | 6.49242i | 0.249690 | − | 0.602806i | ||||
\(117\) | 2.86990 | − | 2.86990i | 0.265323 | − | 0.265323i | ||||
\(118\) | −9.75404 | −0.897932 | ||||||||
\(119\) | 6.53874 | − | 6.16478i | 0.599405 | − | 0.565125i | ||||
\(120\) | −2.26197 | −0.206489 | ||||||||
\(121\) | 0.995200 | − | 0.995200i | 0.0904727 | − | 0.0904727i | ||||
\(122\) | −5.81623 | + | 14.0416i | −0.526577 | + | 1.27127i | ||||
\(123\) | 0.918827i | 0.0828478i | ||||||||
\(124\) | 4.00948 | + | 1.66078i | 0.360062 | + | 0.149143i | ||||
\(125\) | 0.382683 | + | 0.923880i | 0.0342282 | + | 0.0826343i | ||||
\(126\) | 4.26197 | − | 1.76537i | 0.379687 | − | 0.157271i | ||||
\(127\) | 9.87622 | + | 9.87622i | 0.876373 | + | 0.876373i | 0.993157 | − | 0.116784i | \(-0.0372586\pi\) |
−0.116784 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −16.4573 | + | 6.81684i | −1.44898 | + | 0.600189i | ||||
\(130\) | 0.733837 | + | 1.77164i | 0.0643617 | + | 0.155383i | ||||
\(131\) | 11.6230 | + | 4.81438i | 1.01550 | + | 0.420635i | 0.827459 | − | 0.561526i | \(-0.189786\pi\) |
0.188043 | + | 0.982161i | \(0.439786\pi\) | |||||||
\(132\) | − | 7.00575i | − | 0.609773i | ||||||
\(133\) | −3.86388 | + | 9.32824i | −0.335041 | + | 0.808861i | ||||
\(134\) | 6.46088 | − | 6.46088i | 0.558135 | − | 0.558135i | ||||
\(135\) | 1.99841 | 0.171996 | ||||||||
\(136\) | 3.76118 | + | 1.68925i | 0.322518 | + | 0.144852i | ||||
\(137\) | 10.0453 | 0.858230 | 0.429115 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429115 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(138\) | −10.2047 | + | 10.2047i | −0.868679 | + | 0.868679i | ||||
\(139\) | −0.523852 | + | 1.26469i | −0.0444326 | + | 0.107270i | −0.944538 | − | 0.328403i | \(-0.893490\pi\) |
0.900105 | + | 0.435673i | \(0.143490\pi\) | |||||||
\(140\) | 2.17958i | 0.184208i | ||||||||
\(141\) | −0.246831 | − | 0.102241i | −0.0207869 | − | 0.00861024i | ||||
\(142\) | −2.33489 | − | 5.63691i | −0.195939 | − | 0.473039i | ||||
\(143\) | −5.48710 | + | 2.27283i | −0.458854 | + | 0.190064i | ||||
\(144\) | 1.49661 | + | 1.49661i | 0.124717 | + | 0.124717i | ||||
\(145\) | 4.96908 | + | 4.96908i | 0.412660 | + | 0.412660i | ||||
\(146\) | 1.53701 | − | 0.636649i | 0.127203 | − | 0.0526894i | ||||
\(147\) | 1.94715 | + | 4.70084i | 0.160598 | + | 0.387718i | ||||
\(148\) | 7.53553 | + | 3.12132i | 0.619417 | + | 0.256571i | ||||
\(149\) | 14.4592i | 1.18454i | 0.805739 | + | 0.592270i | \(0.201768\pi\) | ||||
−0.805739 | + | 0.592270i | \(0.798232\pi\) | |||||||
\(150\) | 0.865619 | − | 2.08979i | 0.0706775 | − | 0.170631i | ||||
\(151\) | 6.14161 | − | 6.14161i | 0.499797 | − | 0.499797i | −0.411578 | − | 0.911375i | \(-0.635022\pi\) |
0.911375 | + | 0.411578i | \(0.135022\pi\) | |||||||
\(152\) | −4.63246 | −0.375742 | ||||||||
\(153\) | 7.96061 | + | 3.57532i | 0.643577 | + | 0.289048i | ||||
\(154\) | −6.75057 | −0.543977 | ||||||||
\(155\) | −3.06872 | + | 3.06872i | −0.246486 | + | 0.246486i | ||||
\(156\) | 1.65992 | − | 4.00740i | 0.132900 | − | 0.320849i | ||||
\(157\) | − | 16.3611i | − | 1.30576i | −0.757463 | − | 0.652878i | \(-0.773562\pi\) | ||
0.757463 | − | 0.652878i | \(-0.226438\pi\) | |||||||
\(158\) | 9.09927 | + | 3.76904i | 0.723899 | + | 0.299849i | ||||
\(159\) | −3.37109 | − | 8.13854i | −0.267345 | − | 0.645428i | ||||
\(160\) | −0.923880 | + | 0.382683i | −0.0730391 | + | 0.0302538i | ||||
\(161\) | 9.83296 | + | 9.83296i | 0.774946 | + | 0.774946i | ||||
\(162\) | −7.68618 | − | 7.68618i | −0.603883 | − | 0.603883i | ||||
\(163\) | −10.7843 | + | 4.46701i | −0.844694 | + | 0.349884i | −0.762702 | − | 0.646750i | \(-0.776128\pi\) |
−0.0819911 | + | 0.996633i | \(0.526128\pi\) | |||||||
\(164\) | 0.155448 | + | 0.375285i | 0.0121385 | + | 0.0293049i | ||||
\(165\) | 6.47247 | + | 2.68099i | 0.503881 | + | 0.208715i | ||||
\(166\) | − | 8.34436i | − | 0.647648i | ||||||
\(167\) | −5.40808 | + | 13.0563i | −0.418490 | + | 1.01032i | 0.564295 | + | 0.825573i | \(0.309148\pi\) |
−0.982785 | + | 0.184751i | \(0.940852\pi\) | |||||||
\(168\) | 3.48614 | − | 3.48614i | 0.268962 | − | 0.268962i | ||||
\(169\) | 9.32278 | 0.717137 | ||||||||
\(170\) | −3.00000 | + | 2.82843i | −0.230089 | + | 0.216930i | ||||
\(171\) | −9.80469 | −0.749783 | ||||||||
\(172\) | −5.56854 | + | 5.56854i | −0.424597 | + | 0.424597i | ||||
\(173\) | −0.893211 | + | 2.15640i | −0.0679096 | + | 0.163948i | −0.954190 | − | 0.299200i | \(-0.903280\pi\) |
0.886281 | + | 0.463148i | \(0.153280\pi\) | |||||||
\(174\) | − | 15.8956i | − | 1.20505i | ||||||
\(175\) | −2.01367 | − | 0.834089i | −0.152219 | − | 0.0630512i | ||||
\(176\) | −1.18524 | − | 2.86143i | −0.0893410 | − | 0.215688i | ||||
\(177\) | −20.3839 | + | 8.44329i | −1.53215 | + | 0.634636i | ||||
\(178\) | −6.87189 | − | 6.87189i | −0.515070 | − | 0.515070i | ||||
\(179\) | 7.20533 | + | 7.20533i | 0.538551 | + | 0.538551i | 0.923103 | − | 0.384552i | \(-0.125644\pi\) |
−0.384552 | + | 0.923103i | \(0.625644\pi\) | |||||||
\(180\) | −1.95541 | + | 0.809957i | −0.145748 | + | 0.0603706i | ||||
\(181\) | 0.857002 | + | 2.06899i | 0.0637005 | + | 0.153787i | 0.952524 | − | 0.304462i | \(-0.0984768\pi\) |
−0.888824 | + | 0.458249i | \(0.848477\pi\) | |||||||
\(182\) | −3.86143 | − | 1.59946i | −0.286228 | − | 0.118560i | ||||
\(183\) | 34.3787i | 2.54135i | ||||||||
\(184\) | −2.44155 | + | 5.89443i | −0.179994 | + | 0.434543i | ||||
\(185\) | −5.76745 | + | 5.76745i | −0.424031 | + | 0.424031i | ||||
\(186\) | 9.81657 | 0.719786 | ||||||||
\(187\) | −8.76017 | − | 9.29156i | −0.640607 | − | 0.679467i | ||||
\(188\) | −0.118113 | −0.00861427 | ||||||||
\(189\) | −3.07994 | + | 3.07994i | −0.224032 | + | 0.224032i | ||||
\(190\) | 1.77276 | − | 4.27983i | 0.128610 | − | 0.310492i | ||||
\(191\) | − | 12.2384i | − | 0.885541i | −0.896635 | − | 0.442771i | \(-0.853996\pi\) | ||
0.896635 | − | 0.442771i | \(-0.146004\pi\) | |||||||
\(192\) | 2.08979 | + | 0.865619i | 0.150818 | + | 0.0624707i | ||||
\(193\) | 9.00555 | + | 21.7413i | 0.648234 | + | 1.56498i | 0.815306 | + | 0.579030i | \(0.196569\pi\) |
−0.167072 | + | 0.985945i | \(0.553431\pi\) | |||||||
\(194\) | 1.28598 | − | 0.532672i | 0.0923282 | − | 0.0382436i | ||||
\(195\) | 3.06713 | + | 3.06713i | 0.219642 | + | 0.219642i | ||||
\(196\) | 1.59059 | + | 1.59059i | 0.113613 | + | 0.113613i | ||||
\(197\) | 24.9703 | − | 10.3430i | 1.77906 | − | 0.736911i | 0.786151 | − | 0.618034i | \(-0.212071\pi\) |
0.992909 | − | 0.118876i | \(-0.0379292\pi\) | |||||||
\(198\) | −2.50859 | − | 6.05627i | −0.178278 | − | 0.430400i | ||||
\(199\) | 16.1659 | + | 6.69613i | 1.14597 | + | 0.474676i | 0.873180 | − | 0.487398i | \(-0.162054\pi\) |
0.272789 | + | 0.962074i | \(0.412054\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 7.90923 | − | 19.0946i | 0.557874 | − | 1.34683i | ||||
\(202\) | 4.12906 | − | 4.12906i | 0.290520 | − | 0.290520i | ||||
\(203\) | −15.3167 | −1.07502 | ||||||||
\(204\) | 9.32231 | + | 0.274423i | 0.652693 | + | 0.0192135i | ||||
\(205\) | −0.406206 | −0.0283707 | ||||||||
\(206\) | −10.5626 | + | 10.5626i | −0.735932 | + | 0.735932i | ||||
\(207\) | −5.16760 | + | 12.4757i | −0.359173 | + | 0.867120i | ||||
\(208\) | − | 1.91761i | − | 0.132962i | ||||||
\(209\) | 13.2554 | + | 5.49059i | 0.916899 | + | 0.379792i | ||||
\(210\) | 1.88669 | + | 4.55487i | 0.130194 | + | 0.314316i | ||||
\(211\) | −11.5668 | + | 4.79111i | −0.796289 | + | 0.329834i | −0.743469 | − | 0.668770i | \(-0.766821\pi\) |
−0.0528202 | + | 0.998604i | \(0.516821\pi\) | |||||||
\(212\) | −2.75378 | − | 2.75378i | −0.189130 | − | 0.189130i | ||||
\(213\) | −9.75884 | − | 9.75884i | −0.668665 | − | 0.668665i | ||||
\(214\) | −18.6803 | + | 7.73765i | −1.27696 | + | 0.528935i | ||||
\(215\) | −3.01367 | − | 7.27564i | −0.205531 | − | 0.496195i | ||||
\(216\) | −1.84629 | − | 0.764757i | −0.125624 | − | 0.0520351i | ||||
\(217\) | − | 9.45901i | − | 0.642119i | ||||||
\(218\) | −4.25345 | + | 10.2687i | −0.288080 | + | 0.695486i | ||||
\(219\) | 2.66092 | − | 2.66092i | 0.179809 | − | 0.179809i | ||||
\(220\) | 3.09719 | 0.208812 | ||||||||
\(221\) | −2.80944 | − | 7.39052i | −0.188983 | − | 0.497140i | ||||
\(222\) | 18.4496 | 1.23825 | ||||||||
\(223\) | 0.416933 | − | 0.416933i | 0.0279199 | − | 0.0279199i | −0.693009 | − | 0.720929i | \(-0.743715\pi\) |
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(224\) | 0.834089 | − | 2.01367i | 0.0557299 | − | 0.134544i | ||||
\(225\) | − | 2.11652i | − | 0.141101i | ||||||
\(226\) | −11.3550 | − | 4.70338i | −0.755321 | − | 0.312864i | ||||
\(227\) | −6.70725 | − | 16.1927i | −0.445176 | − | 1.07475i | −0.974108 | − | 0.226085i | \(-0.927407\pi\) |
0.528932 | − | 0.848664i | \(-0.322593\pi\) | |||||||
\(228\) | −9.68087 | + | 4.00995i | −0.641131 | + | 0.265565i | ||||
\(229\) | −11.6753 | − | 11.6753i | −0.771527 | − | 0.771527i | 0.206846 | − | 0.978373i | \(-0.433680\pi\) |
−0.978373 | + | 0.206846i | \(0.933680\pi\) | |||||||
\(230\) | −4.51140 | − | 4.51140i | −0.297473 | − | 0.297473i | ||||
\(231\) | −14.1073 | + | 5.84343i | −0.928191 | + | 0.384469i | ||||
\(232\) | −2.68925 | − | 6.49242i | −0.176558 | − | 0.426248i | ||||
\(233\) | 19.1475 | + | 7.93116i | 1.25439 | + | 0.519587i | 0.908185 | − | 0.418570i | \(-0.137468\pi\) |
0.346210 | + | 0.938157i | \(0.387468\pi\) | |||||||
\(234\) | − | 4.05866i | − | 0.265323i | ||||||
\(235\) | 0.0451999 | − | 0.109122i | 0.00294851 | − | 0.00711834i | ||||
\(236\) | −6.89715 | + | 6.89715i | −0.448966 | + | 0.448966i | ||||
\(237\) | 22.2781 | 1.44712 | ||||||||
\(238\) | 0.264427 | − | 8.98275i | 0.0171403 | − | 0.582265i | ||||
\(239\) | 17.3225 | 1.12050 | 0.560251 | − | 0.828323i | \(-0.310705\pi\) | ||||
0.560251 | + | 0.828323i | \(0.310705\pi\) | |||||||
\(240\) | −1.59946 | + | 1.59946i | −0.103244 | + | 0.103244i | ||||
\(241\) | 10.5789 | − | 25.5397i | 0.681446 | − | 1.64516i | −0.0798937 | − | 0.996803i | \(-0.525458\pi\) |
0.761340 | − | 0.648353i | \(-0.224542\pi\) | |||||||
\(242\) | − | 1.40743i | − | 0.0904727i | ||||||
\(243\) | −17.1770 | − | 7.11493i | −1.10190 | − | 0.456423i | ||||
\(244\) | 5.81623 | + | 14.0416i | 0.372346 | + | 0.898923i | ||||
\(245\) | −2.07820 | + | 0.860819i | −0.132771 | + | 0.0549957i | ||||
\(246\) | 0.649709 | + | 0.649709i | 0.0414239 | + | 0.0414239i | ||||
\(247\) | 6.28140 | + | 6.28140i | 0.399676 | + | 0.399676i | ||||
\(248\) | 4.00948 | − | 1.66078i | 0.254602 | − | 0.105460i | ||||
\(249\) | −7.22304 | − | 17.4380i | −0.457742 | − | 1.10509i | ||||
\(250\) | 0.923880 | + | 0.382683i | 0.0584313 | + | 0.0242030i | ||||
\(251\) | − | 15.5217i | − | 0.979719i | −0.871802 | − | 0.489859i | \(-0.837048\pi\) | ||
0.871802 | − | 0.489859i | \(-0.162952\pi\) | |||||||
\(252\) | 1.76537 | − | 4.26197i | 0.111208 | − | 0.268479i | ||||
\(253\) | 13.9727 | − | 13.9727i | 0.878454 | − | 0.878454i | ||||
\(254\) | 13.9671 | 0.876373 | ||||||||
\(255\) | −3.82103 | + | 8.50768i | −0.239282 | + | 0.532771i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.5530 | + | 18.5530i | −1.15730 | + | 1.15730i | −0.172251 | + | 0.985053i | \(0.555104\pi\) |
−0.985053 | + | 0.172251i | \(0.944896\pi\) | |||||||
\(258\) | −6.81684 | + | 16.4573i | −0.424398 | + | 1.02459i | ||||
\(259\) | − | 17.7775i | − | 1.10464i | ||||||
\(260\) | 1.77164 | + | 0.733837i | 0.109872 | + | 0.0455106i | ||||
\(261\) | −5.69184 | − | 13.7413i | −0.352316 | − | 0.850567i | ||||
\(262\) | 11.6230 | − | 4.81438i | 0.718068 | − | 0.297434i | ||||
\(263\) | −1.78704 | − | 1.78704i | −0.110194 | − | 0.110194i | 0.649860 | − | 0.760054i | \(-0.274827\pi\) |
−0.760054 | + | 0.649860i | \(0.774827\pi\) | |||||||
\(264\) | −4.95382 | − | 4.95382i | −0.304886 | − | 0.304886i | ||||
\(265\) | 3.59798 | − | 1.49033i | 0.221022 | − | 0.0915505i | ||||
\(266\) | 3.86388 | + | 9.32824i | 0.236910 | + | 0.571951i | ||||
\(267\) | −20.3093 | − | 8.41237i | −1.24291 | − | 0.514829i | ||||
\(268\) | − | 9.13707i | − | 0.558135i | ||||||
\(269\) | 5.84337 | − | 14.1071i | 0.356276 | − | 0.860127i | −0.639541 | − | 0.768757i | \(-0.720875\pi\) |
0.995817 | − | 0.0913699i | \(-0.0291246\pi\) | |||||||
\(270\) | 1.41309 | − | 1.41309i | 0.0859978 | − | 0.0859978i | ||||
\(271\) | −15.7334 | −0.955738 | −0.477869 | − | 0.878431i | \(-0.658591\pi\) | ||||
−0.477869 | + | 0.878431i | \(0.658591\pi\) | |||||||
\(272\) | 3.85403 | − | 1.46508i | 0.233685 | − | 0.0888333i | ||||
\(273\) | −9.45410 | −0.572188 | ||||||||
\(274\) | 7.10311 | − | 7.10311i | 0.429115 | − | 0.429115i | ||||
\(275\) | −1.18524 | + | 2.86143i | −0.0714728 | + | 0.172551i | ||||
\(276\) | 14.4316i | 0.868679i | ||||||||
\(277\) | 24.4537 | + | 10.1291i | 1.46928 | + | 0.608596i | 0.966695 | − | 0.255930i | \(-0.0823818\pi\) |
0.502587 | + | 0.864527i | \(0.332382\pi\) | |||||||
\(278\) | 0.523852 | + | 1.26469i | 0.0314186 | + | 0.0758512i | ||||
\(279\) | 8.48614 | − | 3.51508i | 0.508052 | − | 0.210442i | ||||
\(280\) | 1.54120 | + | 1.54120i | 0.0921041 | + | 0.0921041i | ||||
\(281\) | 7.32983 | + | 7.32983i | 0.437261 | + | 0.437261i | 0.891089 | − | 0.453828i | \(-0.149942\pi\) |
−0.453828 | + | 0.891089i | \(0.649942\pi\) | |||||||
\(282\) | −0.246831 | + | 0.102241i | −0.0146986 | + | 0.00608836i | ||||
\(283\) | 1.92831 | + | 4.65534i | 0.114626 | + | 0.276731i | 0.970772 | − | 0.240002i | \(-0.0771480\pi\) |
−0.856147 | + | 0.516733i | \(0.827148\pi\) | |||||||
\(284\) | −5.63691 | − | 2.33489i | −0.334489 | − | 0.138550i | ||||
\(285\) | − | 10.4785i | − | 0.620692i | ||||||
\(286\) | −2.27283 | + | 5.48710i | −0.134395 | + | 0.324459i | ||||
\(287\) | 0.626043 | − | 0.626043i | 0.0369542 | − | 0.0369542i | ||||
\(288\) | 2.11652 | 0.124717 | ||||||||
\(289\) | 12.7071 | − | 11.2929i | 0.747477 | − | 0.664288i | ||||
\(290\) | 7.02734 | 0.412660 | ||||||||
\(291\) | 2.22634 | − | 2.22634i | 0.130511 | − | 0.130511i | ||||
\(292\) | 0.636649 | − | 1.53701i | 0.0372570 | − | 0.0899464i | ||||
\(293\) | − | 14.3469i | − | 0.838157i | −0.907950 | − | 0.419078i | \(-0.862353\pi\) | ||
0.907950 | − | 0.419078i | \(-0.137647\pi\) | |||||||
\(294\) | 4.70084 | + | 1.94715i | 0.274158 | + | 0.113560i | ||||
\(295\) | −3.73271 | − | 9.01156i | −0.217327 | − | 0.524673i | ||||
\(296\) | 7.53553 | − | 3.12132i | 0.437994 | − | 0.181423i | ||||
\(297\) | 4.37660 | + | 4.37660i | 0.253956 | + | 0.253956i | ||||
\(298\) | 10.2242 | + | 10.2242i | 0.592270 | + | 0.592270i | ||||
\(299\) | 11.3032 | − | 4.68194i | 0.653681 | − | 0.270764i | ||||
\(300\) | −0.865619 | − | 2.08979i | −0.0499766 | − | 0.120654i | ||||
\(301\) | 15.8578 | + | 6.56854i | 0.914031 | + | 0.378604i | ||||
\(302\) | − | 8.68554i | − | 0.499797i | ||||||
\(303\) | 5.05468 | − | 12.2031i | 0.290384 | − | 0.701048i | ||||
\(304\) | −3.27564 | + | 3.27564i | −0.187871 | + | 0.187871i | ||||
\(305\) | −15.1985 | −0.870266 | ||||||||
\(306\) | 8.15713 | − | 3.10086i | 0.466312 | − | 0.177264i | ||||
\(307\) | 23.7650 | 1.35634 | 0.678170 | − | 0.734905i | \(-0.262773\pi\) | ||||
0.678170 | + | 0.734905i | \(0.262773\pi\) | |||||||
\(308\) | −4.77337 | + | 4.77337i | −0.271988 | + | 0.271988i | ||||
\(309\) | −12.9304 | + | 31.2168i | −0.735587 | + | 1.77586i | ||||
\(310\) | 4.33983i | 0.246486i | ||||||||
\(311\) | −26.2186 | − | 10.8601i | −1.48672 | − | 0.615820i | −0.516120 | − | 0.856516i | \(-0.672624\pi\) |
−0.970600 | + | 0.240696i | \(0.922624\pi\) | |||||||
\(312\) | −1.65992 | − | 4.00740i | −0.0939744 | − | 0.226874i | ||||
\(313\) | −7.95541 | + | 3.29524i | −0.449666 | + | 0.186258i | −0.596012 | − | 0.802976i | \(-0.703249\pi\) |
0.146346 | + | 0.989234i | \(0.453249\pi\) | |||||||
\(314\) | −11.5690 | − | 11.5690i | −0.652878 | − | 0.652878i | ||||
\(315\) | 3.26197 | + | 3.26197i | 0.183791 | + | 0.183791i | ||||
\(316\) | 9.09927 | − | 3.76904i | 0.511874 | − | 0.212025i | ||||
\(317\) | 3.46436 | + | 8.36370i | 0.194578 | + | 0.469752i | 0.990814 | − | 0.135234i | \(-0.0431787\pi\) |
−0.796236 | + | 0.604986i | \(0.793179\pi\) | |||||||
\(318\) | −8.13854 | − | 3.37109i | −0.456387 | − | 0.189042i | ||||
\(319\) | 21.7650i | 1.21861i | ||||||||
\(320\) | −0.382683 | + | 0.923880i | −0.0213927 | + | 0.0516464i | ||||
\(321\) | −32.3401 | + | 32.3401i | −1.80505 | + | 1.80505i | ||||
\(322\) | 13.9059 | 0.774946 | ||||||||
\(323\) | −7.82536 | + | 17.4235i | −0.435415 | + | 0.969469i | ||||
\(324\) | −10.8699 | −0.603883 | ||||||||
\(325\) | −1.35595 | + | 1.35595i | −0.0752148 | + | 0.0752148i | ||||
\(326\) | −4.46701 | + | 10.7843i | −0.247405 | + | 0.597289i | ||||
\(327\) | 25.1414i | 1.39032i | ||||||||
\(328\) | 0.375285 | + | 0.155448i | 0.0207217 | + | 0.00858320i | ||||
\(329\) | 0.0985168 | + | 0.237841i | 0.00543141 | + | 0.0131126i | ||||
\(330\) | 6.47247 | − | 2.68099i | 0.356298 | − | 0.147583i | ||||
\(331\) | 2.06713 | + | 2.06713i | 0.113620 | + | 0.113620i | 0.761631 | − | 0.648011i | \(-0.224399\pi\) |
−0.648011 | + | 0.761631i | \(0.724399\pi\) | |||||||
\(332\) | −5.90036 | − | 5.90036i | −0.323824 | − | 0.323824i | ||||
\(333\) | 15.9491 | − | 6.60634i | 0.874006 | − | 0.362025i | ||||
\(334\) | 5.40808 | + | 13.0563i | 0.295917 | + | 0.714407i | ||||
\(335\) | 8.44155 | + | 3.49661i | 0.461211 | + | 0.191040i | ||||
\(336\) | − | 4.93015i | − | 0.268962i | ||||||
\(337\) | −5.10693 | + | 12.3292i | −0.278192 | + | 0.671616i | −0.999786 | − | 0.0207015i | \(-0.993410\pi\) |
0.721593 | + | 0.692317i | \(0.243410\pi\) | |||||||
\(338\) | 6.59220 | − | 6.59220i | 0.358568 | − | 0.358568i | ||||
\(339\) | −27.8008 | −1.50993 | ||||||||
\(340\) | −0.121320 | + | 4.12132i | −0.00657952 | + | 0.223510i | ||||
\(341\) | −13.4413 | −0.727885 | ||||||||
\(342\) | −6.93296 | + | 6.93296i | −0.374892 | + | 0.374892i | ||||
\(343\) | 7.71485 | − | 18.6253i | 0.416563 | − | 1.00567i | ||||
\(344\) | 7.87510i | 0.424597i | ||||||||
\(345\) | −13.3330 | − | 5.52273i | −0.717827 | − | 0.297334i | ||||
\(346\) | 0.893211 | + | 2.15640i | 0.0480193 | + | 0.115929i | ||||
\(347\) | −33.0738 | + | 13.6996i | −1.77549 | + | 0.735433i | −0.781769 | + | 0.623568i | \(0.785682\pi\) |
−0.993723 | + | 0.111865i | \(0.964318\pi\) | |||||||
\(348\) | −11.2399 | − | 11.2399i | −0.602523 | − | 0.602523i | ||||
\(349\) | −10.0303 | − | 10.0303i | −0.536909 | − | 0.536909i | 0.385711 | − | 0.922620i | \(-0.373956\pi\) |
−0.922620 | + | 0.385711i | \(0.873956\pi\) | |||||||
\(350\) | −2.01367 | + | 0.834089i | −0.107635 | + | 0.0445839i | ||||
\(351\) | 1.46650 | + | 3.54046i | 0.0782762 | + | 0.188976i | ||||
\(352\) | −2.86143 | − | 1.18524i | −0.152515 | − | 0.0631736i | ||||
\(353\) | − | 17.5181i | − | 0.932396i | −0.884680 | − | 0.466198i | \(-0.845623\pi\) | ||
0.884680 | − | 0.466198i | \(-0.154377\pi\) | |||||||
\(354\) | −8.44329 | + | 20.3839i | −0.448756 | + | 1.08339i | ||||
\(355\) | 4.31431 | − | 4.31431i | 0.228980 | − | 0.228980i | ||||
\(356\) | −9.71832 | −0.515070 | ||||||||
\(357\) | −7.22304 | − | 19.0010i | −0.382284 | − | 1.00564i | ||||
\(358\) | 10.1899 | 0.538551 | ||||||||
\(359\) | −19.5067 | + | 19.5067i | −1.02952 | + | 1.02952i | −0.0299733 | + | 0.999551i | \(0.509542\pi\) |
−0.999551 | + | 0.0299733i | \(0.990458\pi\) | |||||||
\(360\) | −0.809957 | + | 1.95541i | −0.0426885 | + | 0.103059i | ||||
\(361\) | − | 2.45967i | − | 0.129456i | ||||||
\(362\) | 2.06899 | + | 0.857002i | 0.108744 | + | 0.0450430i | ||||
\(363\) | −1.21829 | − | 2.94122i | −0.0639439 | − | 0.154374i | ||||
\(364\) | −3.86143 | + | 1.59946i | −0.202394 | + | 0.0838343i | ||||
\(365\) | 1.17637 | + | 1.17637i | 0.0615742 | + | 0.0615742i | ||||
\(366\) | 24.3094 | + | 24.3094i | 1.27067 | + | 1.27067i | ||||
\(367\) | 4.87216 | − | 2.01811i | 0.254324 | − | 0.105345i | −0.251879 | − | 0.967759i | \(-0.581048\pi\) |
0.506203 | + | 0.862414i | \(0.331048\pi\) | |||||||
\(368\) | 2.44155 | + | 5.89443i | 0.127275 | + | 0.307268i | ||||
\(369\) | 0.794299 | + | 0.329009i | 0.0413496 | + | 0.0171275i | ||||
\(370\) | 8.15640i | 0.424031i | ||||||||
\(371\) | −3.24830 | + | 7.84210i | −0.168643 | + | 0.407141i | ||||
\(372\) | 6.94137 | − | 6.94137i | 0.359893 | − | 0.359893i | ||||
\(373\) | −2.25490 | −0.116754 | −0.0583771 | − | 0.998295i | \(-0.518593\pi\) | ||||
−0.0583771 | + | 0.998295i | \(0.518593\pi\) | |||||||
\(374\) | −12.7645 | − | 0.375752i | −0.660037 | − | 0.0194297i | ||||
\(375\) | 2.26197 | 0.116808 | ||||||||
\(376\) | −0.0835185 | + | 0.0835185i | −0.00430714 | + | 0.00430714i | ||||
\(377\) | −5.15692 | + | 12.4499i | −0.265595 | + | 0.641203i | ||||
\(378\) | 4.35569i | 0.224032i | ||||||||
\(379\) | 5.79430 | + | 2.40008i | 0.297633 | + | 0.123284i | 0.526503 | − | 0.850173i | \(-0.323503\pi\) |
−0.228870 | + | 0.973457i | \(0.573503\pi\) | |||||||
\(380\) | −1.77276 | − | 4.27983i | −0.0909409 | − | 0.219551i | ||||
\(381\) | 29.1883 | − | 12.0902i | 1.49536 | − | 0.619399i | ||||
\(382\) | −8.65387 | − | 8.65387i | −0.442771 | − | 0.442771i | ||||
\(383\) | 9.29235 | + | 9.29235i | 0.474817 | + | 0.474817i | 0.903469 | − | 0.428653i | \(-0.141012\pi\) |
−0.428653 | + | 0.903469i | \(0.641012\pi\) | |||||||
\(384\) | 2.08979 | − | 0.865619i | 0.106644 | − | 0.0441735i | ||||
\(385\) | −2.58333 | − | 6.23671i | −0.131659 | − | 0.317852i | ||||
\(386\) | 21.7413 | + | 9.00555i | 1.10660 | + | 0.458371i | ||||
\(387\) | 16.6678i | 0.847272i | ||||||||
\(388\) | 0.532672 | − | 1.28598i | 0.0270423 | − | 0.0652859i | ||||
\(389\) | −15.5600 | + | 15.5600i | −0.788922 | + | 0.788922i | −0.981318 | − | 0.192395i | \(-0.938374\pi\) |
0.192395 | + | 0.981318i | \(0.438374\pi\) | |||||||
\(390\) | 4.33758 | 0.219642 | ||||||||
\(391\) | 18.0456 | + | 19.1403i | 0.912606 | + | 0.967964i | ||||
\(392\) | 2.24943 | 0.113613 | ||||||||
\(393\) | 20.1221 | − | 20.1221i | 1.01503 | − | 1.01503i | ||||
\(394\) | 10.3430 | − | 24.9703i | 0.521075 | − | 1.25799i | ||||
\(395\) | 9.84898i | 0.495556i | ||||||||
\(396\) | −6.05627 | − | 2.50859i | −0.304339 | − | 0.126061i | ||||
\(397\) | 0.990400 | + | 2.39104i | 0.0497067 | + | 0.120003i | 0.946782 | − | 0.321874i | \(-0.104313\pi\) |
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(398\) | 16.1659 | − | 6.69613i | 0.810322 | − | 0.335647i | ||||
\(399\) | 16.1494 | + | 16.1494i | 0.808482 | + | 0.808482i | ||||
\(400\) | −0.707107 | − | 0.707107i | −0.0353553 | − | 0.0353553i | ||||
\(401\) | 11.2964 | − | 4.67913i | 0.564116 | − | 0.233665i | −0.0823549 | − | 0.996603i | \(-0.526244\pi\) |
0.646471 | + | 0.762938i | \(0.276244\pi\) | |||||||
\(402\) | −7.90923 | − | 19.0946i | −0.394476 | − | 0.952350i | ||||
\(403\) | −7.68861 | − | 3.18473i | −0.382997 | − | 0.158642i | ||||
\(404\) | − | 5.83938i | − | 0.290520i | ||||||
\(405\) | 4.15973 | − | 10.0425i | 0.206699 | − | 0.499015i | ||||
\(406\) | −10.8305 | + | 10.8305i | −0.537509 | + | 0.537509i | ||||
\(407\) | −25.2619 | −1.25219 | ||||||||
\(408\) | 6.78592 | − | 6.39782i | 0.335953 | − | 0.316740i | ||||
\(409\) | −15.1513 | −0.749181 | −0.374591 | − | 0.927190i | \(-0.622217\pi\) | ||||
−0.374591 | + | 0.927190i | \(0.622217\pi\) | |||||||
\(410\) | −0.287231 | + | 0.287231i | −0.0141853 | + | 0.0141853i | ||||
\(411\) | 8.69543 | − | 20.9926i | 0.428914 | − | 1.03549i | ||||
\(412\) | 14.9378i | 0.735932i | ||||||||
\(413\) | 19.6414 | + | 8.13574i | 0.966491 | + | 0.400334i | ||||
\(414\) | 5.16760 | + | 12.4757i | 0.253974 | + | 0.613146i | ||||
\(415\) | 7.70919 | − | 3.19325i | 0.378429 | − | 0.156750i | ||||
\(416\) | −1.35595 | − | 1.35595i | −0.0664811 | − | 0.0664811i | ||||
\(417\) | 2.18948 | + | 2.18948i | 0.107219 | + | 0.107219i | ||||
\(418\) | 13.2554 | − | 5.49059i | 0.648345 | − | 0.268553i | ||||
\(419\) | −0.882820 | − | 2.13132i | −0.0431286 | − | 0.104122i | 0.900847 | − | 0.434136i | \(-0.142946\pi\) |
−0.943976 | + | 0.330015i | \(0.892946\pi\) | |||||||
\(420\) | 4.55487 | + | 1.88669i | 0.222255 | + | 0.0920609i | ||||
\(421\) | 4.11496i | 0.200551i | 0.994960 | + | 0.100275i | \(0.0319724\pi\) | ||||
−0.994960 | + | 0.100275i | \(0.968028\pi\) | |||||||
\(422\) | −4.79111 | + | 11.5668i | −0.233228 | + | 0.563062i | ||||
\(423\) | −0.176769 | + | 0.176769i | −0.00859478 | + | 0.00859478i | ||||
\(424\) | −3.89443 | −0.189130 | ||||||||
\(425\) | −3.76118 | − | 1.68925i | −0.182444 | − | 0.0819405i | ||||
\(426\) | −13.8011 | −0.668665 | ||||||||
\(427\) | 23.4239 | − | 23.4239i | 1.13356 | − | 1.13356i | ||||
\(428\) | −7.73765 | + | 18.6803i | −0.374014 | + | 0.902949i | ||||
\(429\) | 13.4343i | 0.648614i | ||||||||
\(430\) | −7.27564 | − | 3.01367i | −0.350863 | − | 0.145332i | ||||
\(431\) | 2.37887 | + | 5.74309i | 0.114586 | + | 0.276635i | 0.970760 | − | 0.240053i | \(-0.0771648\pi\) |
−0.856174 | + | 0.516688i | \(0.827165\pi\) | |||||||
\(432\) | −1.84629 | + | 0.764757i | −0.0888295 | + | 0.0367944i | ||||
\(433\) | −1.52706 | − | 1.52706i | −0.0733858 | − | 0.0733858i | 0.669461 | − | 0.742847i | \(-0.266525\pi\) |
−0.742847 | + | 0.669461i | \(0.766525\pi\) | |||||||
\(434\) | −6.68853 | − | 6.68853i | −0.321060 | − | 0.321060i | ||||
\(435\) | 14.6857 | − | 6.08300i | 0.704124 | − | 0.291658i | ||||
\(436\) | 4.25345 | + | 10.2687i | 0.203703 | + | 0.491783i | ||||
\(437\) | −27.3057 | − | 11.3104i | −1.30621 | − | 0.541049i | ||||
\(438\) | − | 3.76311i | − | 0.179809i | ||||||
\(439\) | 12.8375 | − | 30.9925i | 0.612700 | − | 1.47919i | −0.247322 | − | 0.968933i | \(-0.579551\pi\) |
0.860022 | − | 0.510256i | \(-0.170449\pi\) | |||||||
\(440\) | 2.19004 | − | 2.19004i | 0.104406 | − | 0.104406i | ||||
\(441\) | 4.76096 | 0.226712 | ||||||||
\(442\) | −7.21246 | − | 3.23931i | −0.343062 | − | 0.154078i | ||||
\(443\) | 17.8435 | 0.847772 | 0.423886 | − | 0.905716i | \(-0.360666\pi\) | ||||
0.423886 | + | 0.905716i | \(0.360666\pi\) | |||||||
\(444\) | 13.0458 | − | 13.0458i | 0.619127 | − | 0.619127i | ||||
\(445\) | 3.71904 | − | 8.97856i | 0.176299 | − | 0.425624i | ||||
\(446\) | − | 0.589632i | − | 0.0279199i | ||||||
\(447\) | 30.2166 | + | 12.5161i | 1.42920 | + | 0.591993i | ||||
\(448\) | −0.834089 | − | 2.01367i | −0.0394070 | − | 0.0951370i | ||||
\(449\) | 31.4026 | − | 13.0074i | 1.48198 | − | 0.613856i | 0.512425 | − | 0.858732i | \(-0.328747\pi\) |
0.969554 | + | 0.244877i | \(0.0787474\pi\) | |||||||
\(450\) | −1.49661 | − | 1.49661i | −0.0705507 | − | 0.0705507i | ||||
\(451\) | −0.889609 | − | 0.889609i | −0.0418900 | − | 0.0418900i | ||||
\(452\) | −11.3550 | + | 4.70338i | −0.534093 | + | 0.221229i | ||||
\(453\) | −7.51838 | − | 18.1510i | −0.353244 | − | 0.852807i | ||||
\(454\) | −16.1927 | − | 6.70725i | −0.759963 | − | 0.314787i | ||||
\(455\) | − | 4.17958i | − | 0.195942i | ||||||
\(456\) | −4.00995 | + | 9.68087i | −0.187783 | + | 0.453348i | ||||
\(457\) | −13.4932 | + | 13.4932i | −0.631188 | + | 0.631188i | −0.948366 | − | 0.317178i | \(-0.897265\pi\) |
0.317178 | + | 0.948366i | \(0.397265\pi\) | |||||||
\(458\) | −16.5114 | −0.771527 | ||||||||
\(459\) | −5.99522 | + | 5.65235i | −0.279833 | + | 0.263829i | ||||
\(460\) | −6.38009 | −0.297473 | ||||||||
\(461\) | 18.6471 | − | 18.6471i | 0.868483 | − | 0.868483i | −0.123821 | − | 0.992305i | \(-0.539515\pi\) |
0.992305 | + | 0.123821i | \(0.0395150\pi\) | |||||||
\(462\) | −5.84343 | + | 14.1073i | −0.271861 | + | 0.656330i | ||||
\(463\) | 11.5661i | 0.537521i | 0.963207 | + | 0.268761i | \(0.0866141\pi\) | ||||
−0.963207 | + | 0.268761i | \(0.913386\pi\) | |||||||
\(464\) | −6.49242 | − | 2.68925i | −0.301403 | − | 0.124845i | ||||
\(465\) | 3.75664 | + | 9.06933i | 0.174210 | + | 0.420580i | ||||
\(466\) | 19.1475 | − | 7.93116i | 0.886991 | − | 0.367404i | ||||
\(467\) | 0.546261 | + | 0.546261i | 0.0252779 | + | 0.0252779i | 0.719633 | − | 0.694355i | \(-0.244310\pi\) |
−0.694355 | + | 0.719633i | \(0.744310\pi\) | |||||||
\(468\) | −2.86990 | − | 2.86990i | −0.132661 | − | 0.132661i | ||||
\(469\) | −18.3990 | + | 7.62113i | −0.849589 | + | 0.351911i | ||||
\(470\) | −0.0451999 | − | 0.109122i | −0.00208491 | − | 0.00503343i | ||||
\(471\) | −34.1912 | − | 14.1625i | −1.57545 | − | 0.652572i | ||||
\(472\) | 9.75404i | 0.448966i | ||||||||
\(473\) | 9.33390 | − | 22.5340i | 0.429173 | − | 1.03612i | ||||
\(474\) | 15.7530 | − | 15.7530i | 0.723560 | − | 0.723560i | ||||
\(475\) | 4.63246 | 0.212552 | ||||||||
\(476\) | −6.16478 | − | 6.53874i | −0.282562 | − | 0.299703i | ||||
\(477\) | −8.24264 | −0.377405 | ||||||||
\(478\) | 12.2489 | − | 12.2489i | 0.560251 | − | 0.560251i | ||||
\(479\) | −2.38229 | + | 5.75135i | −0.108850 | + | 0.262786i | −0.968913 | − | 0.247401i | \(-0.920424\pi\) |
0.860064 | + | 0.510187i | \(0.170424\pi\) | |||||||
\(480\) | 2.26197i | 0.103244i | ||||||||
\(481\) | −14.4502 | − | 5.98547i | −0.658872 | − | 0.272914i | ||||
\(482\) | −10.5789 | − | 25.5397i | −0.481855 | − | 1.16330i | ||||
\(483\) | 29.0604 | − | 12.0372i | 1.32230 | − | 0.547713i | ||||
\(484\) | −0.995200 | − | 0.995200i | −0.0452364 | − | 0.0452364i | ||||
\(485\) | 0.984249 | + | 0.984249i | 0.0446925 | + | 0.0446925i | ||||
\(486\) | −17.1770 | + | 7.11493i | −0.779162 | + | 0.322740i | ||||
\(487\) | −2.70956 | − | 6.54146i | −0.122782 | − | 0.296422i | 0.850523 | − | 0.525938i | \(-0.176286\pi\) |
−0.973305 | + | 0.229516i | \(0.926286\pi\) | |||||||
\(488\) | 14.0416 | + | 5.81623i | 0.635634 | + | 0.263288i | ||||
\(489\) | 26.4037i | 1.19402i | ||||||||
\(490\) | −0.860819 | + | 2.07820i | −0.0388879 | + | 0.0938836i | ||||
\(491\) | −29.8236 | + | 29.8236i | −1.34592 | + | 1.34592i | −0.455879 | + | 0.890042i | \(0.650675\pi\) |
−0.890042 | + | 0.455879i | \(0.849325\pi\) | |||||||
\(492\) | 0.918827 | 0.0414239 | ||||||||
\(493\) | −28.9619 | − | 0.852559i | −1.30438 | − | 0.0383973i | ||||
\(494\) | 8.88324 | 0.399676 | ||||||||
\(495\) | 4.63527 | − | 4.63527i | 0.208340 | − | 0.208340i | ||||
\(496\) | 1.66078 | − | 4.00948i | 0.0745713 | − | 0.180031i | ||||
\(497\) | 13.2984i | 0.596514i | ||||||||
\(498\) | −17.4380 | − | 7.22304i | −0.781414 | − | 0.323672i | ||||
\(499\) | −12.6995 | − | 30.6592i | −0.568506 | − | 1.37249i | −0.902814 | − | 0.430031i | \(-0.858503\pi\) |
0.334309 | − | 0.942464i | \(-0.391497\pi\) | |||||||
\(500\) | 0.923880 | − | 0.382683i | 0.0413171 | − | 0.0171141i | ||||
\(501\) | 22.6035 | + | 22.6035i | 1.00985 | + | 1.00985i | ||||
\(502\) | −10.9755 | − | 10.9755i | −0.489859 | − | 0.489859i | ||||
\(503\) | −7.36754 | + | 3.05174i | −0.328502 | + | 0.136070i | −0.540838 | − | 0.841127i | \(-0.681893\pi\) |
0.212336 | + | 0.977197i | \(0.431893\pi\) | |||||||
\(504\) | −1.76537 | − | 4.26197i | −0.0786357 | − | 0.189843i | ||||
\(505\) | 5.39488 | + | 2.23463i | 0.240069 | + | 0.0994399i | ||||
\(506\) | − | 19.7603i | − | 0.878454i | ||||||
\(507\) | 8.06998 | − | 19.4827i | 0.358400 | − | 0.865255i | ||||
\(508\) | 9.87622 | − | 9.87622i | 0.438187 | − | 0.438187i | ||||
\(509\) | −16.4093 | −0.727331 | −0.363665 | − | 0.931530i | \(-0.618475\pi\) | ||||
−0.363665 | + | 0.931530i | \(0.618475\pi\) | |||||||
\(510\) | 3.31396 | + | 8.71771i | 0.146745 | + | 0.386027i | ||||
\(511\) | −3.62604 | −0.160407 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 3.54271 | − | 8.55285i | 0.156414 | − | 0.377618i | ||||
\(514\) | 26.2379i | 1.15730i | ||||||||
\(515\) | −13.8007 | − | 5.71644i | −0.608132 | − | 0.251897i | ||||
\(516\) | 6.81684 | + | 16.4573i | 0.300095 | + | 0.724492i | ||||
\(517\) | 0.337972 | − | 0.139993i | 0.0148640 | − | 0.00615686i | ||||
\(518\) | −12.5706 | − | 12.5706i | −0.552321 | − | 0.552321i | ||||
\(519\) | 3.73325 | + | 3.73325i | 0.163871 | + | 0.163871i | ||||
\(520\) | 1.77164 | − | 0.733837i | 0.0776915 | − | 0.0321809i | ||||
\(521\) | 4.54033 | + | 10.9613i | 0.198916 | + | 0.480225i | 0.991590 | − | 0.129421i | \(-0.0413118\pi\) |
−0.792674 | + | 0.609646i | \(0.791312\pi\) | |||||||
\(522\) | −13.7413 | − | 5.69184i | −0.601442 | − | 0.249125i | ||||
\(523\) | 37.8846i | 1.65658i | 0.560300 | + | 0.828290i | \(0.310686\pi\) | ||||
−0.560300 | + | 0.828290i | \(0.689314\pi\) | |||||||
\(524\) | 4.81438 | − | 11.6230i | 0.210317 | − | 0.507751i | ||||
\(525\) | −3.48614 | + | 3.48614i | −0.152148 | + | 0.152148i | ||||
\(526\) | −2.52726 | −0.110194 | ||||||||
\(527\) | 0.526510 | − | 17.8858i | 0.0229351 | − | 0.779119i | ||||
\(528\) | −7.00575 | −0.304886 | ||||||||
\(529\) | −12.5197 | + | 12.5197i | −0.544334 | + | 0.544334i | ||||
\(530\) | 1.49033 | − | 3.59798i | 0.0647360 | − | 0.156286i | ||||
\(531\) | 20.6446i | 0.895901i | ||||||||
\(532\) | 9.32824 | + | 3.86388i | 0.404431 | + | 0.167521i | ||||
\(533\) | −0.298089 | − | 0.719650i | −0.0129117 | − | 0.0311715i | ||||
\(534\) | −20.3093 | + | 8.41237i | −0.878867 | + | 0.364039i | ||||
\(535\) | −14.2973 | − | 14.2973i | −0.618127 | − | 0.618127i | ||||
\(536\) | −6.46088 | − | 6.46088i | −0.279068 | − | 0.279068i | ||||
\(537\) | 21.2947 | − | 8.82055i | 0.918934 | − | 0.380635i | ||||
\(538\) | −5.84337 | − | 14.1071i | −0.251925 | − | 0.608202i | ||||
\(539\) | −6.43658 | − | 2.66612i | −0.277243 | − | 0.114838i | ||||
\(540\) | − | 1.99841i | − | 0.0859978i | ||||||
\(541\) | 0.993942 | − | 2.39959i | 0.0427329 | − | 0.103166i | −0.901072 | − | 0.433670i | \(-0.857218\pi\) |
0.943805 | + | 0.330503i | \(0.107218\pi\) | |||||||
\(542\) | −11.1252 | + | 11.1252i | −0.477869 | + | 0.477869i | ||||
\(543\) | 5.06559 | 0.217385 | ||||||||
\(544\) | 1.68925 | − | 3.76118i | 0.0724258 | − | 0.161259i | ||||
\(545\) | −11.1148 | −0.476106 | ||||||||
\(546\) | −6.68506 | + | 6.68506i | −0.286094 | + | 0.286094i | ||||
\(547\) | −3.27444 | + | 7.90519i | −0.140005 | + | 0.338001i | −0.978293 | − | 0.207226i | \(-0.933557\pi\) |
0.838288 | + | 0.545227i | \(0.183557\pi\) | |||||||
\(548\) | − | 10.0453i | − | 0.429115i | ||||||
\(549\) | 29.7194 | + | 12.3102i | 1.26839 | + | 0.525385i | ||||
\(550\) | 1.18524 | + | 2.86143i | 0.0505389 | + | 0.122012i | ||||
\(551\) | 30.0758 | − | 12.4578i | 1.28127 | − | 0.530721i | ||||
\(552\) | 10.2047 | + | 10.2047i | 0.434339 | + | 0.434339i | ||||
\(553\) | −15.1792 | − | 15.1792i | −0.645486 | − | 0.645486i | ||||
\(554\) | 24.4537 | − | 10.1291i | 1.03894 | − | 0.430343i | ||||
\(555\) | 7.06034 | + | 17.0452i | 0.299695 | + | 0.723527i | ||||
\(556\) | 1.26469 | + | 0.523852i | 0.0536349 | + | 0.0222163i | ||||
\(557\) | 17.8744i | 0.757364i | 0.925527 | + | 0.378682i | \(0.123623\pi\) | ||||
−0.925527 | + | 0.378682i | \(0.876377\pi\) | |||||||
\(558\) | 3.51508 | − | 8.48614i | 0.148805 | − | 0.359247i | ||||
\(559\) | 10.6783 | − | 10.6783i | 0.451643 | − | 0.451643i | ||||
\(560\) | 2.17958 | 0.0921041 | ||||||||
\(561\) | −27.0004 | + | 10.2640i | −1.13996 | + | 0.433345i | ||||
\(562\) | 10.3659 | 0.437261 | ||||||||
\(563\) | −6.76659 | + | 6.76659i | −0.285178 | + | 0.285178i | −0.835170 | − | 0.549992i | \(-0.814631\pi\) |
0.549992 | + | 0.835170i | \(0.314631\pi\) | |||||||
\(564\) | −0.102241 | + | 0.246831i | −0.00430512 | + | 0.0103935i | ||||
\(565\) | − | 12.2905i | − | 0.517067i | ||||||
\(566\) | 4.65534 | + | 1.92831i | 0.195679 | + | 0.0810527i | ||||
\(567\) | 9.06647 | + | 21.8884i | 0.380756 | + | 0.919226i | ||||
\(568\) | −5.63691 | + | 2.33489i | −0.236520 | + | 0.0979696i | ||||
\(569\) | −13.4709 | − | 13.4709i | −0.564729 | − | 0.564729i | 0.365918 | − | 0.930647i | \(-0.380755\pi\) |
−0.930647 | + | 0.365918i | \(0.880755\pi\) | |||||||
\(570\) | −7.40941 | − | 7.40941i | −0.310346 | − | 0.310346i | ||||
\(571\) | −9.84467 | + | 4.07779i | −0.411986 | + | 0.170650i | −0.579043 | − | 0.815297i | \(-0.696574\pi\) |
0.167057 | + | 0.985947i | \(0.446574\pi\) | |||||||
\(572\) | 2.27283 | + | 5.48710i | 0.0950318 | + | 0.229427i | ||||
\(573\) | −25.5757 | − | 10.5938i | −1.06844 | − | 0.442563i | ||||
\(574\) | − | 0.885359i | − | 0.0369542i | ||||||
\(575\) | 2.44155 | − | 5.89443i | 0.101820 | − | 0.245815i | ||||
\(576\) | 1.49661 | − | 1.49661i | 0.0623586 | − | 0.0623586i | ||||
\(577\) | 3.43248 | 0.142896 | 0.0714480 | − | 0.997444i | \(-0.477238\pi\) | ||||
0.0714480 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(578\) | 1.00000 | − | 16.9706i | 0.0415945 | − | 0.705882i | ||||
\(579\) | 53.2302 | 2.21217 | ||||||||
\(580\) | 4.96908 | − | 4.96908i | 0.206330 | − | 0.206330i | ||||
\(581\) | −6.95995 | + | 16.8028i | −0.288747 | + | 0.697097i | ||||
\(582\) | − | 3.14853i | − | 0.130511i | ||||||
\(583\) | 11.1436 | + | 4.61585i | 0.461522 | + | 0.191169i | ||||
\(584\) | −0.636649 | − | 1.53701i | −0.0263447 | − | 0.0636017i | ||||
\(585\) | 3.74971 | − | 1.55318i | 0.155031 | − | 0.0642161i | ||||
\(586\) | −10.1448 | − | 10.1448i | −0.419078 | − | 0.419078i | ||||
\(587\) | 4.19531 | + | 4.19531i | 0.173159 | + | 0.173159i | 0.788366 | − | 0.615207i | \(-0.210927\pi\) |
−0.615207 | + | 0.788366i | \(0.710927\pi\) | |||||||
\(588\) | 4.70084 | − | 1.94715i | 0.193859 | − | 0.0802991i | ||||
\(589\) | 7.69350 | + | 18.5737i | 0.317005 | + | 0.765318i | ||||
\(590\) | −9.01156 | − | 3.73271i | −0.371000 | − | 0.153673i | ||||
\(591\) | − | 61.1358i | − | 2.51479i | ||||||
\(592\) | 3.12132 | − | 7.53553i | 0.128285 | − | 0.309709i | ||||
\(593\) | −8.23946 | + | 8.23946i | −0.338354 | + | 0.338354i | −0.855748 | − | 0.517394i | \(-0.826902\pi\) |
0.517394 | + | 0.855748i | \(0.326902\pi\) | |||||||
\(594\) | 6.18944 | 0.253956 | ||||||||
\(595\) | 8.40017 | − | 3.19325i | 0.344373 | − | 0.130910i | ||||
\(596\) | 14.4592 | 0.592270 | ||||||||
\(597\) | 27.9870 | − | 27.9870i | 1.14543 | − | 1.14543i | ||||
\(598\) | 4.68194 | − | 11.3032i | 0.191459 | − | 0.462222i | ||||
\(599\) | 7.52264i | 0.307367i | 0.988120 | + | 0.153683i | \(0.0491136\pi\) | ||||
−0.988120 | + | 0.153683i | \(0.950886\pi\) | |||||||
\(600\) | −2.08979 | − | 0.865619i | −0.0853153 | − | 0.0353388i | ||||
\(601\) | 8.72192 | + | 21.0566i | 0.355775 | + | 0.858916i | 0.995884 | + | 0.0906326i | \(0.0288889\pi\) |
−0.640110 | + | 0.768284i | \(0.721111\pi\) | |||||||
\(602\) | 15.8578 | − | 6.56854i | 0.646318 | − | 0.267714i | ||||
\(603\) | −13.6746 | − | 13.6746i | −0.556872 | − | 0.556872i | ||||
\(604\) | −6.14161 | − | 6.14161i | −0.249898 | − | 0.249898i | ||||
\(605\) | 1.30029 | − | 0.538598i | 0.0528644 | − | 0.0218971i | ||||
\(606\) | −5.05468 | − | 12.2031i | −0.205332 | − | 0.495716i | ||||
\(607\) | 2.47909 | + | 1.02687i | 0.100623 | + | 0.0416795i | 0.432427 | − | 0.901669i | \(-0.357657\pi\) |
−0.331804 | + | 0.943348i | \(0.607657\pi\) | |||||||
\(608\) | 4.63246i | 0.187871i | ||||||||
\(609\) | −13.2584 | + | 32.0086i | −0.537257 | + | 1.29705i | ||||
\(610\) | −10.7470 | + | 10.7470i | −0.435133 | + | 0.435133i | ||||
\(611\) | 0.226494 | 0.00916298 | ||||||||
\(612\) | 3.57532 | − | 7.96061i | 0.144524 | − | 0.321788i | ||||
\(613\) | 24.0425 | 0.971066 | 0.485533 | − | 0.874218i | \(-0.338626\pi\) | ||||
0.485533 | + | 0.874218i | \(0.338626\pi\) | |||||||
\(614\) | 16.8044 | − | 16.8044i | 0.678170 | − | 0.678170i | ||||
\(615\) | −0.351620 | + | 0.848885i | −0.0141787 | + | 0.0342304i | ||||
\(616\) | 6.75057i | 0.271988i | ||||||||
\(617\) | 30.0134 | + | 12.4320i | 1.20829 | + | 0.500492i | 0.893670 | − | 0.448724i | \(-0.148121\pi\) |
0.314624 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(618\) | 12.9304 | + | 31.2168i | 0.520138 | + | 1.25573i | ||||
\(619\) | −20.9655 | + | 8.68419i | −0.842675 | + | 0.349047i | −0.761908 | − | 0.647686i | \(-0.775737\pi\) |
−0.0807670 | + | 0.996733i | \(0.525737\pi\) | |||||||
\(620\) | 3.06872 | + | 3.06872i | 0.123243 | + | 0.123243i | ||||
\(621\) | −9.01562 | − | 9.01562i | −0.361784 | − | 0.361784i | ||||
\(622\) | −26.2186 | + | 10.8601i | −1.05127 | + | 0.435450i | ||||
\(623\) | 8.10595 | + | 19.5695i | 0.324758 | + | 0.784035i | ||||
\(624\) | −4.00740 | − | 1.65992i | −0.160424 | − | 0.0664499i | ||||
\(625\) | 1.00000i | 0.0400000i | ||||||||
\(626\) | −3.29524 | + | 7.95541i | −0.131704 | + | 0.317962i | ||||
\(627\) | 22.9483 | − | 22.9483i | 0.916469 | − | 0.916469i | ||||
\(628\) | −16.3611 | −0.652878 | ||||||||
\(629\) | 0.989538 | − | 33.6152i | 0.0394554 | − | 1.34032i | ||||
\(630\) | 4.61313 | 0.183791 | ||||||||
\(631\) | −11.6556 | + | 11.6556i | −0.464004 | + | 0.464004i | −0.899965 | − | 0.435962i | \(-0.856408\pi\) |
0.435962 | + | 0.899965i | \(0.356408\pi\) | |||||||
\(632\) | 3.76904 | − | 9.09927i | 0.149924 | − | 0.361949i | ||||
\(633\) | 28.3194i | 1.12560i | ||||||||
\(634\) | 8.36370 | + | 3.46436i | 0.332165 | + | 0.137587i | ||||
\(635\) | 5.34497 | + | 12.9039i | 0.212109 | + | 0.512076i | ||||
\(636\) | −8.13854 | + | 3.37109i | −0.322714 | + | 0.133673i | ||||
\(637\) | −3.05012 | − | 3.05012i | −0.120850 | − | 0.120850i | ||||
\(638\) | 15.3902 | + | 15.3902i | 0.609303 | + | 0.609303i | ||||
\(639\) | −11.9306 | + | 4.94183i | −0.471969 | + | 0.195496i | ||||
\(640\) | 0.382683 | + | 0.923880i | 0.0151269 | + | 0.0365195i | ||||
\(641\) | 22.8119 | + | 9.44900i | 0.901016 | + | 0.373213i | 0.784611 | − | 0.619989i | \(-0.212863\pi\) |
0.116405 | + | 0.993202i | \(0.462863\pi\) | |||||||
\(642\) | 45.7359i | 1.80505i | ||||||||
\(643\) | −2.25830 | + | 5.45202i | −0.0890586 | + | 0.215006i | −0.962133 | − | 0.272581i | \(-0.912123\pi\) |
0.873074 | + | 0.487587i | \(0.162123\pi\) | |||||||
\(644\) | 9.83296 | − | 9.83296i | 0.387473 | − | 0.387473i | ||||
\(645\) | −17.8133 | −0.701396 | ||||||||
\(646\) | 6.78690 | + | 17.8536i | 0.267027 | + | 0.702442i | ||||
\(647\) | 6.56743 | 0.258192 | 0.129096 | − | 0.991632i | \(-0.458792\pi\) | ||||
0.129096 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(648\) | −7.68618 | + | 7.68618i | −0.301942 | + | 0.301942i | ||||
\(649\) | 11.5609 | − | 27.9105i | 0.453805 | − | 1.09558i | ||||
\(650\) | 1.91761i | 0.0752148i | ||||||||
\(651\) | −19.7673 | − | 8.18790i | −0.774743 | − | 0.320909i | ||||
\(652\) | 4.46701 | + | 10.7843i | 0.174942 | + | 0.422347i | ||||
\(653\) | 0.744178 | − | 0.308249i | 0.0291219 | − | 0.0120627i | −0.368075 | − | 0.929796i | \(-0.619983\pi\) |
0.397197 | + | 0.917733i | \(0.369983\pi\) | |||||||
\(654\) | 17.7776 | + | 17.7776i | 0.695160 | + | 0.695160i | ||||
\(655\) | 8.89582 | + | 8.89582i | 0.347588 | + | 0.347588i | ||||
\(656\) | 0.375285 | − | 0.155448i | 0.0146524 | − | 0.00606924i | ||||
\(657\) | −1.34748 | − | 3.25310i | −0.0525702 | − | 0.126916i | ||||
\(658\) | 0.237841 | + | 0.0985168i | 0.00927199 | + | 0.00384058i | ||||
\(659\) | 5.39957i | 0.210337i | 0.994454 | + | 0.105169i | \(0.0335383\pi\) | ||||
−0.994454 | + | 0.105169i | \(0.966462\pi\) | |||||||
\(660\) | 2.68099 | − | 6.47247i | 0.104357 | − | 0.251941i | ||||
\(661\) | −27.6342 | + | 27.6342i | −1.07485 | + | 1.07485i | −0.0778836 | + | 0.996962i | \(0.524816\pi\) |
−0.996962 | + | 0.0778836i | \(0.975184\pi\) | |||||||
\(662\) | 2.92336 | 0.113620 | ||||||||
\(663\) | −17.8765 | − | 0.526236i | −0.694267 | − | 0.0204373i | ||||
\(664\) | −8.34436 | −0.323824 | ||||||||
\(665\) | −7.13953 | + | 7.13953i | −0.276859 | + | 0.276859i | ||||
\(666\) | 6.60634 | − | 15.9491i | 0.255990 | − | 0.618015i | ||||
\(667\) | − | 44.8350i | − | 1.73602i | ||||||
\(668\) | 13.0563 | + | 5.40808i | 0.505162 | + | 0.209245i | ||||
\(669\) | −0.510397 | − | 1.23221i | −0.0197331 | − | 0.0476399i | ||||
\(670\) | 8.44155 | − | 3.49661i | 0.326126 | − | 0.135086i | ||||
\(671\) | −33.2855 | − | 33.2855i | −1.28497 | − | 1.28497i | ||||
\(672\) | −3.48614 | − | 3.48614i | −0.134481 | − | 0.134481i | ||||
\(673\) | −15.1202 | + | 6.26298i | −0.582840 | + | 0.241420i | −0.654567 | − | 0.756004i | \(-0.727149\pi\) |
0.0717272 | + | 0.997424i | \(0.477149\pi\) | |||||||
\(674\) | 5.10693 | + | 12.3292i | 0.196712 | + | 0.474904i | ||||
\(675\) | 1.84629 | + | 0.764757i | 0.0710636 | + | 0.0294355i | ||||
\(676\) | − | 9.32278i | − | 0.358568i | ||||||
\(677\) | −12.4451 | + | 30.0452i | −0.478305 | + | 1.15473i | 0.482098 | + | 0.876117i | \(0.339875\pi\) |
−0.960403 | + | 0.278614i | \(0.910125\pi\) | |||||||
\(678\) | −19.6582 | + | 19.6582i | −0.754967 | + | 0.754967i | ||||
\(679\) | −3.03384 | −0.116428 | ||||||||
\(680\) | 2.82843 | + | 3.00000i | 0.108465 | + | 0.115045i | ||||
\(681\) | −39.6453 | −1.51921 | ||||||||
\(682\) | −9.50441 | + | 9.50441i | −0.363943 | + | 0.363943i | ||||
\(683\) | 0.600330 | − | 1.44932i | 0.0229710 | − | 0.0554569i | −0.911978 | − | 0.410239i | \(-0.865445\pi\) |
0.934949 | + | 0.354783i | \(0.115445\pi\) | |||||||
\(684\) | 9.80469i | 0.374892i | ||||||||
\(685\) | 9.28067 | + | 3.84418i | 0.354596 | + | 0.146878i | ||||
\(686\) | −7.71485 | − | 18.6253i | −0.294554 | − | 0.711117i | ||||
\(687\) | −34.5054 | + | 14.2926i | −1.31646 | + | 0.545296i | ||||
\(688\) | 5.56854 | + | 5.56854i | 0.212298 | + | 0.212298i | ||||
\(689\) | 5.28067 | + | 5.28067i | 0.201177 | + | 0.201177i | ||||
\(690\) | −13.3330 | + | 5.52273i | −0.507580 | + | 0.210247i | ||||
\(691\) | 0.492008 | + | 1.18781i | 0.0187169 | + | 0.0451865i | 0.932962 | − | 0.359976i | \(-0.117215\pi\) |
−0.914245 | + | 0.405162i | \(0.867215\pi\) | |||||||
\(692\) | 2.15640 | + | 0.893211i | 0.0819741 | + | 0.0339548i | ||||
\(693\) | 14.2877i | 0.542746i | ||||||||
\(694\) | −13.6996 | + | 33.0738i | −0.520030 | + | 1.25546i | ||||
\(695\) | −0.967953 | + | 0.967953i | −0.0367166 | + | 0.0367166i | ||||
\(696\) | −15.8956 | −0.602523 | ||||||||
\(697\) | 1.21862 | − | 1.14892i | 0.0461584 | − | 0.0435186i | ||||
\(698\) | −14.1850 | −0.536909 | ||||||||
\(699\) | 33.1489 | − | 33.1489i | 1.25381 | − | 1.25381i | ||||
\(700\) | −0.834089 | + | 2.01367i | −0.0315256 | + | 0.0761096i | ||||
\(701\) | 2.21212i | 0.0835505i | 0.999127 | + | 0.0417752i | \(0.0133013\pi\) | ||||
−0.999127 | + | 0.0417752i | \(0.986699\pi\) | |||||||
\(702\) | 3.54046 | + | 1.46650i | 0.133626 | + | 0.0553496i | ||||
\(703\) | 14.4594 | + | 34.9080i | 0.545346 | + | 1.31658i | ||||
\(704\) | −2.86143 | + | 1.18524i | −0.107844 | + | 0.0446705i | ||||
\(705\) | −0.188917 | − | 0.188917i | −0.00711501 | − | 0.00711501i | ||||
\(706\) | −12.3872 | − | 12.3872i | −0.466198 | − | 0.466198i | ||||
\(707\) | −11.7586 | + | 4.87056i | −0.442227 | + | 0.183176i | ||||
\(708\) | 8.44329 | + | 20.3839i | 0.317318 | + | 0.766074i | ||||
\(709\) | −25.3245 | − | 10.4898i | −0.951082 | − | 0.393951i | −0.147445 | − | 0.989070i | \(-0.547105\pi\) |
−0.803637 | + | 0.595119i | \(0.797105\pi\) | |||||||
\(710\) | − | 6.10135i | − | 0.228980i | ||||||
\(711\) | 7.97725 | − | 19.2588i | 0.299170 | − | 0.722261i | ||||
\(712\) | −6.87189 | + | 6.87189i | −0.257535 | + | 0.257535i | ||||
\(713\) | 27.6885 | 1.03694 | ||||||||
\(714\) | −18.5432 | − | 8.32824i | −0.693961 | − | 0.311677i | ||||
\(715\) | −5.93919 | −0.222113 | ||||||||
\(716\) | 7.20533 | − | 7.20533i | 0.269276 | − | 0.269276i | ||||
\(717\) | 14.9947 | − | 36.2005i | 0.559988 | − | 1.35193i | ||||
\(718\) | 27.5866i | 1.02952i | ||||||||
\(719\) | −13.5359 | − | 5.60674i | −0.504803 | − | 0.209096i | 0.115724 | − | 0.993281i | \(-0.463081\pi\) |
−0.620527 | + | 0.784185i | \(0.713081\pi\) | |||||||
\(720\) | 0.809957 | + | 1.95541i | 0.0301853 | + | 0.0728738i | ||||
\(721\) | 30.0798 | − | 12.4594i | 1.12023 | − | 0.464014i | ||||
\(722\) | −1.73925 | − | 1.73925i | −0.0647281 | − | 0.0647281i | ||||
\(723\) | −44.2153 | − | 44.2153i | −1.64439 | − | 1.64439i | ||||
\(724\) | 2.06899 | − | 0.857002i | 0.0768933 | − | 0.0318502i | ||||
\(725\) | 2.68925 | + | 6.49242i | 0.0998761 | + | 0.241122i | ||||
\(726\) | −2.94122 | − | 1.21829i | −0.109159 | − | 0.0452152i | ||||
\(727\) | 35.9003i | 1.33147i | 0.746188 | + | 0.665735i | \(0.231882\pi\) | ||||
−0.746188 | + | 0.665735i | \(0.768118\pi\) | |||||||
\(728\) | −1.59946 | + | 3.86143i | −0.0592798 | + | 0.143114i | ||||
\(729\) | −6.67887 | + | 6.67887i | −0.247365 | + | 0.247365i | ||||
\(730\) | 1.66364 | 0.0615742 | ||||||||
\(731\) | 29.6196 | + | 13.3030i | 1.09552 | + | 0.492029i | ||||
\(732\) | 34.3787 | 1.27067 | ||||||||
\(733\) | −28.7070 | + | 28.7070i | −1.06032 | + | 1.06032i | −0.0622582 | + | 0.998060i | \(0.519830\pi\) |
−0.998060 | + | 0.0622582i | \(0.980170\pi\) | |||||||
\(734\) | 2.01811 | − | 4.87216i | 0.0744899 | − | 0.179835i | ||||
\(735\) | 5.08815i | 0.187679i | ||||||||
\(736\) | 5.89443 | + | 2.44155i | 0.217272 | + | 0.0899968i | ||||
\(737\) | 10.8296 | + | 26.1451i | 0.398915 | + | 0.963066i | ||||
\(738\) | 0.794299 | − | 0.329009i | 0.0292386 | − | 0.0121110i | ||||
\(739\) | 15.1436 | + | 15.1436i | 0.557068 | + | 0.557068i | 0.928471 | − | 0.371404i | \(-0.121123\pi\) |
−0.371404 | + | 0.928471i | \(0.621123\pi\) | |||||||
\(740\) | 5.76745 | + | 5.76745i | 0.212016 | + | 0.212016i | ||||
\(741\) | 18.5641 | − | 7.68950i | 0.681969 | − | 0.282481i | ||||
\(742\) | 3.24830 | + | 7.84210i | 0.119249 | + | 0.287892i | ||||
\(743\) | −16.2739 | − | 6.74088i | −0.597032 | − | 0.247299i | 0.0636406 | − | 0.997973i | \(-0.479729\pi\) |
−0.660673 | + | 0.750674i | \(0.729729\pi\) | |||||||
\(744\) | − | 9.81657i | − | 0.359893i | ||||||
\(745\) | −5.53328 | + | 13.3585i | −0.202724 | + | 0.489418i | ||||
\(746\) | −1.59445 | + | 1.59445i | −0.0583771 | + | 0.0583771i | ||||
\(747\) | −17.6610 | −0.646183 | ||||||||
\(748\) | −9.29156 | + | 8.76017i | −0.339733 | + | 0.320304i | ||||
\(749\) | 44.0699 | 1.61028 | ||||||||
\(750\) | 1.59946 | − | 1.59946i | 0.0584039 | − | 0.0584039i | ||||
\(751\) | 14.2763 | − | 34.4661i | 0.520951 | − | 1.25769i | −0.416362 | − | 0.909199i | \(-0.636695\pi\) |
0.937313 | − | 0.348488i | \(-0.113305\pi\) | |||||||
\(752\) | 0.118113i | 0.00430714i | ||||||||
\(753\) | −32.4370 | − | 13.4359i | −1.18207 | − | 0.489630i | ||||
\(754\) | 5.15692 | + | 12.4499i | 0.187804 | + | 0.453399i | ||||
\(755\) | 8.02440 | − | 3.32381i | 0.292038 | − | 0.120966i | ||||
\(756\) | 3.07994 | + | 3.07994i | 0.112016 | + | 0.112016i | ||||
\(757\) | −25.3671 | − | 25.3671i | −0.921983 | − | 0.921983i | 0.0751869 | − | 0.997169i | \(-0.476045\pi\) |
−0.997169 | + | 0.0751869i | \(0.976045\pi\) | |||||||
\(758\) | 5.79430 | − | 2.40008i | 0.210458 | − | 0.0871747i | ||||
\(759\) | −17.1049 | − | 41.2949i | −0.620869 | − | 1.49891i | ||||
\(760\) | −4.27983 | − | 1.77276i | −0.155246 | − | 0.0643049i | ||||
\(761\) | − | 11.3236i | − | 0.410479i | −0.978712 | − | 0.205240i | \(-0.934203\pi\) | ||
0.978712 | − | 0.205240i | \(-0.0657974\pi\) | |||||||
\(762\) | 12.0902 | − | 29.1883i | 0.437981 | − | 1.05738i | ||||
\(763\) | 17.1301 | − | 17.1301i | 0.620151 | − | 0.620151i | ||||
\(764\) | −12.2384 | −0.442771 | ||||||||
\(765\) | 5.98642 | + | 6.34956i | 0.216440 | + | 0.229569i | ||||
\(766\) | 13.1414 | 0.474817 | ||||||||
\(767\) | 13.2260 | − | 13.2260i | 0.477564 | − | 0.477564i | ||||
\(768\) | 0.865619 | − | 2.08979i | 0.0312354 | − | 0.0754088i | ||||
\(769\) | − | 2.65802i | − | 0.0958505i | −0.998851 | − | 0.0479253i | \(-0.984739\pi\) | ||
0.998851 | − | 0.0479253i | \(-0.0152609\pi\) | |||||||
\(770\) | −6.23671 | − | 2.58333i | −0.224756 | − | 0.0930968i | ||||
\(771\) | 22.7120 | + | 54.8317i | 0.817954 | + | 1.97472i | ||||
\(772\) | 21.7413 | − | 9.00555i | 0.782488 | − | 0.324117i | ||||
\(773\) | 30.9014 | + | 30.9014i | 1.11145 | + | 1.11145i | 0.992955 | + | 0.118491i | \(0.0378057\pi\) |
0.118491 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(774\) | 11.7859 | + | 11.7859i | 0.423636 | + | 0.423636i | ||||
\(775\) | −4.00948 | + | 1.66078i | −0.144025 | + | 0.0596570i | ||||
\(776\) | −0.532672 | − | 1.28598i | −0.0191218 | − | 0.0461641i | ||||
\(777\) | −37.1513 | − | 15.3886i | −1.33280 | − | 0.552062i | ||||
\(778\) | 22.0051i | 0.788922i | ||||||||
\(779\) | −0.720108 | + | 1.73849i | −0.0258005 | + | 0.0622880i | ||||
\(780\) | 3.06713 | − | 3.06713i | 0.109821 | − | 0.109821i | ||||
\(781\) | 18.8970 | 0.676189 | ||||||||
\(782\) | 26.2944 | + | 0.774034i | 0.940285 | + | 0.0276794i | ||||
\(783\) | 14.0435 | 0.501873 | ||||||||
\(784\) | 1.59059 | − | 1.59059i | 0.0568067 | − | 0.0568067i | ||||
\(785\) | 6.26111 | − | 15.1157i | 0.223469 | − | 0.539501i | ||||
\(786\) | − | 28.4570i | − | 1.01503i | ||||||
\(787\) | −33.5552 | − | 13.8990i | −1.19611 | − | 0.495446i | −0.306371 | − | 0.951912i | \(-0.599115\pi\) |
−0.889741 | + | 0.456466i | \(0.849115\pi\) | |||||||
\(788\) | −10.3430 | − | 24.9703i | −0.368455 | − | 0.889530i | ||||
\(789\) | −5.28145 | + | 2.18765i | −0.188025 | + | 0.0778823i | ||||
\(790\) | 6.96428 | + | 6.96428i | 0.247778 | + | 0.247778i | ||||
\(791\) | 18.9421 | + | 18.9421i | 0.673504 | + | 0.673504i | ||||
\(792\) | −6.05627 | + | 2.50859i | −0.215200 | + | 0.0891389i | ||||
\(793\) | −11.1532 | − | 26.9263i | −0.396063 | − | 0.956182i | ||||
\(794\) | 2.39104 | + | 0.990400i | 0.0848547 | + | 0.0351480i | ||||
\(795\) | − | 8.80910i | − | 0.312426i | ||||||
\(796\) | 6.69613 | − | 16.1659i | 0.237338 | − | 0.572985i | ||||
\(797\) | 11.9755 | − | 11.9755i | 0.424193 | − | 0.424193i | −0.462452 | − | 0.886645i | \(-0.653030\pi\) |
0.886645 | + | 0.462452i | \(0.153030\pi\) | |||||||
\(798\) | 22.8387 | 0.808482 | ||||||||
\(799\) | 0.173044 | + | 0.455211i | 0.00612187 | + | 0.0161042i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −14.5445 | + | 14.5445i | −0.513905 | + | 0.513905i | ||||
\(802\) | 4.67913 | − | 11.2964i | 0.165226 | − | 0.398890i | ||||
\(803\) | 5.15261i | 0.181832i | ||||||||
\(804\) | −19.0946 | − | 7.90923i | −0.673413 | − | 0.278937i | ||||
\(805\) | 5.32156 | + | 12.8474i | 0.187560 | + | 0.452811i | ||||
\(806\) | −7.68861 | + | 3.18473i | −0.270820 | + | 0.112177i | ||||
\(807\) | −24.4228 | − | 24.4228i | −0.859724 | − | 0.859724i | ||||
\(808\) | −4.12906 | − | 4.12906i | −0.145260 | − | 0.145260i | ||||
\(809\) | 21.2912 | − | 8.81909i | 0.748558 | − | 0.310063i | 0.0244047 | − | 0.999702i | \(-0.492231\pi\) |
0.724153 | + | 0.689639i | \(0.242231\pi\) | |||||||
\(810\) | −4.15973 | − | 10.0425i | −0.146158 | − | 0.352857i | ||||
\(811\) | 9.13563 | + | 3.78410i | 0.320795 | + | 0.132878i | 0.537270 | − | 0.843411i | \(-0.319456\pi\) |
−0.216474 | + | 0.976288i | \(0.569456\pi\) | |||||||
\(812\) | 15.3167i | 0.537509i | ||||||||
\(813\) | −13.6192 | + | 32.8796i | −0.477645 | + | 1.15314i | ||||
\(814\) | −17.8629 | + | 17.8629i | −0.626093 | + | 0.626093i | ||||
\(815\) | −11.6729 | −0.408883 | ||||||||
\(816\) | 0.274423 | − | 9.32231i | 0.00960674 | − | 0.326346i | ||||
\(817\) | −36.4811 | −1.27631 | ||||||||
\(818\) | −10.7136 | + | 10.7136i | −0.374591 | + | 0.374591i | ||||
\(819\) | −3.38528 | + | 8.17279i | −0.118291 | + | 0.285580i | ||||
\(820\) | 0.406206i | 0.0141853i | ||||||||
\(821\) | −25.0560 | − | 10.3786i | −0.874462 | − | 0.362214i | −0.100115 | − | 0.994976i | \(-0.531921\pi\) |
−0.774346 | + | 0.632762i | \(0.781921\pi\) | |||||||
\(822\) | −8.69543 | − | 20.9926i | −0.303288 | − | 0.732201i | ||||
\(823\) | −29.3578 | + | 12.1604i | −1.02335 | + | 0.423884i | −0.830307 | − | 0.557307i | \(-0.811835\pi\) |
−0.193040 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(824\) | 10.5626 | + | 10.5626i | 0.367966 | + | 0.367966i | ||||
\(825\) | 4.95382 | + | 4.95382i | 0.172470 | + | 0.172470i | ||||
\(826\) | 19.6414 | − | 8.13574i | 0.683412 | − | 0.283079i | ||||
\(827\) | −10.6086 | − | 25.6115i | −0.368898 | − | 0.890598i | −0.993932 | − | 0.110000i | \(-0.964915\pi\) |
0.625034 | − | 0.780598i | \(-0.285085\pi\) | |||||||
\(828\) | 12.4757 | + | 5.16760i | 0.433560 | + | 0.179586i | ||||
\(829\) | − | 34.9929i | − | 1.21535i | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||
0.794185 | − | 0.607676i | \(-0.207898\pi\) | |||||||
\(830\) | 3.19325 | − | 7.70919i | 0.110839 | − | 0.267590i | ||||
\(831\) | 42.3352 | − | 42.3352i | 1.46859 | − | 1.46859i | ||||
\(832\) | −1.91761 | −0.0664811 | ||||||||
\(833\) | 3.79984 | − | 8.46050i | 0.131657 | − | 0.293139i | ||||
\(834\) | 3.09640 | 0.107219 | ||||||||
\(835\) | −9.99284 | + | 9.99284i | −0.345816 | + | 0.345816i | ||||
\(836\) | 5.49059 | − | 13.2554i | 0.189896 | − | 0.458449i | ||||
\(837\) | 8.67275i | 0.299774i | ||||||||
\(838\) | −2.13132 | − | 0.882820i | −0.0736251 | − | 0.0304965i | ||||
\(839\) | −0.199693 | − | 0.482102i | −0.00689418 | − | 0.0166440i | 0.920395 | − | 0.390990i | \(-0.127867\pi\) |
−0.927289 | + | 0.374346i | \(0.877867\pi\) | |||||||
\(840\) | 4.55487 | − | 1.88669i | 0.157158 | − | 0.0650969i | ||||
\(841\) | 14.4133 | + | 14.4133i | 0.497011 | + | 0.497011i | ||||
\(842\) | 2.90971 | + | 2.90971i | 0.100275 | + | 0.100275i | ||||
\(843\) | 21.6627 | − | 8.97297i | 0.746102 | − | 0.309045i | ||||
\(844\) | 4.79111 | + | 11.5668i | 0.164917 | + | 0.398145i | ||||
\(845\) | 8.61313 | + | 3.56767i | 0.296301 | + | 0.122732i | ||||
\(846\) | 0.249988i | 0.00859478i | ||||||||
\(847\) | −1.17392 | + | 2.83409i | −0.0403363 | + | 0.0973805i | ||||
\(848\) | −2.75378 | + | 2.75378i | −0.0945651 | + | 0.0945651i | ||||
\(849\) | 11.3979 | 0.391174 | ||||||||
\(850\) | −3.85403 | + | 1.46508i | −0.132192 | + | 0.0502517i | ||||
\(851\) | 52.0386 | 1.78386 | ||||||||
\(852\) | −9.75884 | + | 9.75884i | −0.334332 | + | 0.334332i | ||||
\(853\) | −7.00774 | + | 16.9182i | −0.239941 | + | 0.579268i | −0.997276 | − | 0.0737581i | \(-0.976501\pi\) |
0.757336 | + | 0.653026i | \(0.226501\pi\) | |||||||
\(854\) | − | 33.1264i | − | 1.13356i | ||||||
\(855\) | −9.05835 | − | 3.75209i | −0.309789 | − | 0.128319i | ||||
\(856\) | 7.73765 | + | 18.6803i | 0.264468 | + | 0.638481i | ||||
\(857\) | 11.0386 | − | 4.57235i | 0.377073 | − | 0.156189i | −0.186094 | − | 0.982532i | \(-0.559583\pi\) |
0.563167 | + | 0.826343i | \(0.309583\pi\) | |||||||
\(858\) | 9.49948 | + | 9.49948i | 0.324307 | + | 0.324307i | ||||
\(859\) | −5.54403 | − | 5.54403i | −0.189160 | − | 0.189160i | 0.606173 | − | 0.795333i | \(-0.292704\pi\) |
−0.795333 | + | 0.606173i | \(0.792704\pi\) | |||||||
\(860\) | −7.27564 | + | 3.01367i | −0.248097 | + | 0.102765i | ||||
\(861\) | −0.766384 | − | 1.85021i | −0.0261183 | − | 0.0630551i | ||||
\(862\) | 5.74309 | + | 2.37887i | 0.195610 | + | 0.0810245i | ||||
\(863\) | − | 29.2172i | − | 0.994564i | −0.867589 | − | 0.497282i | \(-0.834331\pi\) | ||
0.867589 | − | 0.497282i | \(-0.165669\pi\) | |||||||
\(864\) | −0.764757 | + | 1.84629i | −0.0260176 | + | 0.0628120i | ||||
\(865\) | −1.65044 | + | 1.65044i | −0.0561166 | + | 0.0561166i | ||||
\(866\) | −2.15959 | −0.0733858 | ||||||||
\(867\) | −12.6003 | − | 36.3305i | −0.427927 | − | 1.23385i | ||||
\(868\) | −9.45901 | −0.321060 | ||||||||
\(869\) | −21.5697 | + | 21.5697i | −0.731701 | + | 0.731701i | ||||
\(870\) | 6.08300 | − | 14.6857i | 0.206233 | − | 0.497891i | ||||
\(871\) | 17.5213i | 0.593687i | ||||||||
\(872\) | 10.2687 | + | 4.25345i | 0.347743 | + | 0.144040i | ||||
\(873\) | −1.12741 | − | 2.72181i | −0.0381571 | − | 0.0921193i | ||||
\(874\) | −27.3057 | + | 11.3104i | −0.923629 | + | 0.382580i | ||||
\(875\) | −1.54120 | − | 1.54120i | −0.0521019 | − | 0.0521019i | ||||
\(876\) | −2.66092 | − | 2.66092i | −0.0899043 | − | 0.0899043i | ||||
\(877\) | −33.1725 | + | 13.7405i | −1.12015 | + | 0.463983i | −0.864423 | − | 0.502765i | \(-0.832316\pi\) |
−0.255731 | + | 0.966748i | \(0.582316\pi\) | |||||||
\(878\) | −12.8375 | − | 30.9925i | −0.433245 | − | 1.04595i | ||||
\(879\) | −29.9821 | − | 12.4190i | −1.01127 | − | 0.418882i | ||||
\(880\) | − | 3.09719i | − | 0.104406i | ||||||
\(881\) | 11.9967 | − | 28.9626i | 0.404179 | − | 0.975773i | −0.582462 | − | 0.812858i | \(-0.697910\pi\) |
0.986640 | − | 0.162915i | \(-0.0520896\pi\) | |||||||
\(882\) | 3.36651 | − | 3.36651i | 0.113356 | − | 0.113356i | ||||
\(883\) | 7.04521 | 0.237090 | 0.118545 | − | 0.992949i | \(-0.462177\pi\) | ||||
0.118545 | + | 0.992949i | \(0.462177\pi\) | |||||||
\(884\) | −7.39052 | + | 2.80944i | −0.248570 | + | 0.0944917i | ||||
\(885\) | −22.0634 | −0.741652 | ||||||||
\(886\) | 12.6173 | − | 12.6173i | 0.423886 | − | 0.423886i | ||||
\(887\) | 3.87848 | − | 9.36347i | 0.130227 | − | 0.314395i | −0.845295 | − | 0.534301i | \(-0.820575\pi\) |
0.975521 | + | 0.219906i | \(0.0705750\pi\) | |||||||
\(888\) | − | 18.4496i | − | 0.619127i | ||||||
\(889\) | −28.1251 | − | 11.6498i | −0.943286 | − | 0.390722i | ||||
\(890\) | −3.71904 | − | 8.97856i | −0.124663 | − | 0.300962i | ||||
\(891\) | 31.1035 | − | 12.8835i | 1.04200 | − | 0.431613i | ||||
\(892\) | −0.416933 | − | 0.416933i | −0.0139599 | − | 0.0139599i | ||||
\(893\) | −0.386896 | − | 0.386896i | −0.0129470 | − | 0.0129470i | ||||
\(894\) | 30.2166 | − | 12.5161i | 1.01059 | − | 0.418602i | ||||
\(895\) | 3.89949 | + | 9.41421i | 0.130346 | + | 0.314682i | ||||
\(896\) | −2.01367 | − | 0.834089i | −0.0672720 | − | 0.0278650i | ||||
\(897\) | − | 27.6741i | − | 0.924012i | ||||||
\(898\) | 13.0074 | − | 31.4026i | 0.434062 | − | 1.04792i | ||||
\(899\) | −21.5650 | + | 21.5650i | −0.719232 | + | 0.719232i | ||||
\(900\) | −2.11652 | −0.0705507 | ||||||||
\(901\) | −6.57865 | + | 14.6476i | −0.219167 | + | 0.487984i | ||||
\(902\) | −1.25810 | −0.0418900 | ||||||||
\(903\) | 27.4537 | − | 27.4537i | 0.913603 | − | 0.913603i | ||||
\(904\) | −4.70338 | + | 11.3550i | −0.156432 | + | 0.377661i | ||||
\(905\) | 2.23946i | 0.0744420i | ||||||||
\(906\) | −18.1510 | − | 7.51838i | −0.603025 | − | 0.249781i | ||||
\(907\) | 19.9266 | + | 48.1070i | 0.661651 | + | 1.59737i | 0.795215 | + | 0.606327i | \(0.207358\pi\) |
−0.133564 | + | 0.991040i | \(0.542642\pi\) | |||||||
\(908\) | −16.1927 | + | 6.70725i | −0.537375 | + | 0.222588i | ||||
\(909\) | −8.73925 | − | 8.73925i | −0.289863 | − | 0.289863i | ||||
\(910\) | −2.95541 | − | 2.95541i | −0.0979709 | − | 0.0979709i | ||||
\(911\) | −24.5429 | + | 10.1660i | −0.813143 | + | 0.336815i | −0.750207 | − | 0.661203i | \(-0.770046\pi\) |
−0.0629355 | + | 0.998018i | \(0.520046\pi\) | |||||||
\(912\) | 4.00995 | + | 9.68087i | 0.132783 | + | 0.320565i | ||||
\(913\) | 23.8768 | + | 9.89010i | 0.790207 | + | 0.327314i | ||||
\(914\) | 19.0823i | 0.631188i | ||||||||
\(915\) | −13.1562 | + | 31.7618i | −0.434929 | + | 1.05001i | ||||
\(916\) | −11.6753 | + | 11.6753i | −0.385764 | + | 0.385764i | ||||
\(917\) | −27.4204 | −0.905502 | ||||||||
\(918\) | −0.242447 | + | 8.23608i | −0.00800196 | + | 0.271831i | ||||
\(919\) | 21.1045 | 0.696174 | 0.348087 | − | 0.937462i | \(-0.386831\pi\) | ||||
0.348087 | + | 0.937462i | \(0.386831\pi\) | |||||||
\(920\) | −4.51140 | + | 4.51140i | −0.148737 | + | 0.148737i | ||||
\(921\) | 20.5714 | − | 49.6639i | 0.677852 | − | 1.63648i | ||||
\(922\) | − | 26.3710i | − | 0.868483i | ||||||
\(923\) | 10.8094 | + | 4.47740i | 0.355795 | + | 0.147375i | ||||
\(924\) | 5.84343 | + | 14.1073i | 0.192235 | + | 0.464095i | ||||
\(925\) | −7.53553 | + | 3.12132i | −0.247767 | + | 0.102628i | ||||
\(926\) | 8.17845 | + | 8.17845i | 0.268761 | + | 0.268761i | ||||
\(927\) | 22.3560 | + | 22.3560i | 0.734267 | + | 0.734267i | ||||
\(928\) | −6.49242 | + | 2.68925i | −0.213124 | + | 0.0882788i | ||||
\(929\) | −13.4185 | − | 32.3951i | −0.440246 | − | 1.06285i | −0.975862 | − | 0.218387i | \(-0.929921\pi\) |
0.535616 | − | 0.844462i | \(-0.320079\pi\) | |||||||
\(930\) | 9.06933 | + | 3.75664i | 0.297395 | + | 0.123185i | ||||
\(931\) | 10.4204i | 0.341514i | ||||||||
\(932\) | 7.93116 | − | 19.1475i | 0.259794 | − | 0.627197i | ||||
\(933\) | −45.3907 | + | 45.3907i | −1.48602 | + | 1.48602i | ||||
\(934\) | 0.772529 | 0.0252779 | ||||||||
\(935\) | −4.53762 | − | 11.9367i | −0.148396 | − | 0.390370i | ||||
\(936\) | −4.05866 | −0.132661 | ||||||||
\(937\) | 5.36321 | − | 5.36321i | 0.175208 | − | 0.175208i | −0.614055 | − | 0.789263i | \(-0.710463\pi\) |
0.789263 | + | 0.614055i | \(0.210463\pi\) | |||||||
\(938\) | −7.62113 | + | 18.3990i | −0.248839 | + | 0.600750i | ||||
\(939\) | 19.4776i | 0.635626i | ||||||||
\(940\) | −0.109122 | − | 0.0451999i | −0.00355917 | − | 0.00147426i | ||||
\(941\) | −14.0258 | − | 33.8613i | −0.457228 | − | 1.10385i | −0.969515 | − | 0.245032i | \(-0.921202\pi\) |
0.512287 | − | 0.858814i | \(-0.328798\pi\) | |||||||
\(942\) | −34.1912 | + | 14.1625i | −1.11401 | + | 0.461438i | ||||
\(943\) | 1.83256 | + | 1.83256i | 0.0596763 | + | 0.0596763i | ||||
\(944\) | 6.89715 | + | 6.89715i | 0.224483 | + | 0.224483i | ||||
\(945\) | −4.02413 | + | 1.66685i | −0.130905 | + | 0.0542226i | ||||
\(946\) | −9.33390 | − | 22.5340i | −0.303471 | − | 0.732645i | ||||
\(947\) | 55.6670 | + | 23.0580i | 1.80893 | + | 0.749285i | 0.982503 | + | 0.186249i | \(0.0596331\pi\) |
0.826432 | + | 0.563036i | \(0.190367\pi\) | |||||||
\(948\) | − | 22.2781i | − | 0.723560i | ||||||
\(949\) | −1.22084 | + | 2.94737i | −0.0396302 | + | 0.0956758i | ||||
\(950\) | 3.27564 | − | 3.27564i | 0.106276 | − | 0.106276i | ||||
\(951\) | 20.4772 | 0.664018 | ||||||||
\(952\) | −8.98275 | − | 0.264427i | −0.291133 | − | 0.00857014i | ||||
\(953\) | 39.9833 | 1.29518 | 0.647592 | − | 0.761987i | \(-0.275776\pi\) | ||||
0.647592 | + | 0.761987i | \(0.275776\pi\) | |||||||
\(954\) | −5.82843 | + | 5.82843i | −0.188702 | + | 0.188702i | ||||
\(955\) | 4.68344 | − | 11.3068i | 0.151553 | − | 0.365880i | ||||
\(956\) | − | 17.3225i | − | 0.560251i | ||||||
\(957\) | 45.4843 | + | 18.8402i | 1.47030 | + | 0.609017i | ||||
\(958\) | 2.38229 | + | 5.75135i | 0.0769682 | + | 0.185818i | ||||
\(959\) | −20.2280 | + | 8.37870i | −0.653195 | + | 0.270562i | ||||
\(960\) | 1.59946 | + | 1.59946i | 0.0516222 | + | 0.0516222i | ||||
\(961\) | 8.60258 | + | 8.60258i | 0.277503 | + | 0.277503i | ||||
\(962\) | −14.4502 | + | 5.98547i | −0.465893 | + | 0.192979i | ||||
\(963\) | 16.3769 | + | 39.5373i | 0.527738 | + | 1.27407i | ||||
\(964\) | −25.5397 | − | 10.5789i | −0.822578 | − | 0.340723i | ||||
\(965\) | 23.5326i | 0.757543i | ||||||||
\(966\) | 12.0372 | − | 29.0604i | 0.387291 | − | 0.935004i | ||||
\(967\) | 21.2217 | − | 21.2217i | 0.682443 | − | 0.682443i | −0.278107 | − | 0.960550i | \(-0.589707\pi\) |
0.960550 | + | 0.278107i | \(0.0897071\pi\) | |||||||
\(968\) | −1.40743 | −0.0452364 | ||||||||
\(969\) | 29.6377 | + | 31.4355i | 0.952099 | + | 1.00985i | ||||
\(970\) | 1.39194 | 0.0446925 | ||||||||
\(971\) | −40.6704 | + | 40.6704i | −1.30518 | + | 1.30518i | −0.380322 | + | 0.924854i | \(0.624187\pi\) |
−0.924854 | + | 0.380322i | \(0.875813\pi\) | |||||||
\(972\) | −7.11493 | + | 17.1770i | −0.228211 | + | 0.550951i | ||||
\(973\) | − | 2.98361i | − | 0.0956502i | ||||||
\(974\) | −6.54146 | − | 2.70956i | −0.209602 | − | 0.0868200i | ||||
\(975\) | 1.65992 | + | 4.00740i | 0.0531599 | + | 0.128339i | ||||
\(976\) | 14.0416 | − | 5.81623i | 0.449461 | − | 0.186173i | ||||
\(977\) | −27.3214 | − | 27.3214i | −0.874088 | − | 0.874088i | 0.118827 | − | 0.992915i | \(-0.462087\pi\) |
−0.992915 | + | 0.118827i | \(0.962087\pi\) | |||||||
\(978\) | 18.6702 | + | 18.6702i | 0.597009 | + | 0.597009i | ||||
\(979\) | 27.8083 | − | 11.5186i | 0.888757 | − | 0.368135i | ||||
\(980\) | 0.860819 | + | 2.07820i | 0.0274979 | + | 0.0663857i | ||||
\(981\) | 21.7340 | + | 9.00251i | 0.693913 | + | 0.287428i | ||||
\(982\) | 42.1770i | 1.34592i | ||||||||
\(983\) | 14.1239 | − | 34.0981i | 0.450483 | − | 1.08756i | −0.521656 | − | 0.853156i | \(-0.674686\pi\) |
0.972139 | − | 0.234406i | \(-0.0753144\pi\) | |||||||
\(984\) | 0.649709 | − | 0.649709i | 0.0207120 | − | 0.0207120i | ||||
\(985\) | 27.0277 | 0.861173 | ||||||||
\(986\) | −21.0820 | + | 19.8763i | −0.671388 | + | 0.632991i | ||||
\(987\) | 0.582315 | 0.0185353 | ||||||||
\(988\) | 6.28140 | − | 6.28140i | 0.199838 | − | 0.199838i | ||||
\(989\) | −19.2275 | + | 46.4192i | −0.611398 | + | 1.47605i | ||||
\(990\) | − | 6.55526i | − | 0.208340i | ||||||
\(991\) | −29.2718 | − | 12.1248i | −0.929850 | − | 0.385156i | −0.134228 | − | 0.990950i | \(-0.542856\pi\) |
−0.795621 | + | 0.605794i | \(0.792856\pi\) | |||||||
\(992\) | −1.66078 | − | 4.00948i | −0.0527298 | − | 0.127301i | ||||
\(993\) | 6.10921 | − | 2.53052i | 0.193870 | − | 0.0803036i | ||||
\(994\) | 9.40338 | + | 9.40338i | 0.298257 | + | 0.298257i | ||||
\(995\) | 12.3728 | + | 12.3728i | 0.392245 | + | 0.392245i | ||||
\(996\) | −17.4380 | + | 7.22304i | −0.552543 | + | 0.228871i | ||||
\(997\) | 3.09573 | + | 7.47375i | 0.0980427 | + | 0.236696i | 0.965289 | − | 0.261183i | \(-0.0841125\pi\) |
−0.867247 | + | 0.497879i | \(0.834112\pi\) | |||||||
\(998\) | −30.6592 | − | 12.6995i | −0.970500 | − | 0.401994i | ||||
\(999\) | 16.2998i | 0.515703i |
(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 | 170.2.k.a.161.2 | yes | 8 | |
5.2 | odd | 4 | 850.2.o.c.399.1 | 8 | |||
5.3 | odd | 4 | 850.2.o.f.399.2 | 8 | |||
5.4 | even | 2 | 850.2.l.d.501.1 | 8 | |||
17.6 | odd | 16 | 2890.2.b.p.2311.2 | 8 | |||
17.7 | odd | 16 | 2890.2.a.bf.1.1 | 4 | |||
17.10 | odd | 16 | 2890.2.a.bc.1.4 | 4 | |||
17.11 | odd | 16 | 2890.2.b.p.2311.7 | 8 | |||
17.15 | even | 8 | inner | 170.2.k.a.151.2 | ✓ | 8 | |
85.32 | odd | 8 | 850.2.o.f.49.2 | 8 | |||
85.49 | even | 8 | 850.2.l.d.151.1 | 8 | |||
85.83 | odd | 8 | 850.2.o.c.49.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.k.a.151.2 | ✓ | 8 | 17.15 | even | 8 | inner | |
170.2.k.a.161.2 | yes | 8 | 1.1 | even | 1 | trivial | |
850.2.l.d.151.1 | 8 | 85.49 | even | 8 | |||
850.2.l.d.501.1 | 8 | 5.4 | even | 2 | |||
850.2.o.c.49.1 | 8 | 85.83 | odd | 8 | |||
850.2.o.c.399.1 | 8 | 5.2 | odd | 4 | |||
850.2.o.f.49.2 | 8 | 85.32 | odd | 8 | |||
850.2.o.f.399.2 | 8 | 5.3 | odd | 4 | |||
2890.2.a.bc.1.4 | 4 | 17.10 | odd | 16 | |||
2890.2.a.bf.1.1 | 4 | 17.7 | odd | 16 | |||
2890.2.b.p.2311.2 | 8 | 17.6 | odd | 16 | |||
2890.2.b.p.2311.7 | 8 | 17.11 | odd | 16 |