Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(121,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("195.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.bb (of order \(6\), degree \(2\), 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: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.191102976.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.3 | ||
Root | \(2.10121 + 0.563016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.121 |
Dual form | 195.2.bb.b.166.3 |
$q$-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 \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.975173 | + | 0.563016i | 0.689551 | + | 0.398113i | 0.803444 | − | 0.595380i | \(-0.202999\pi\) |
−0.113893 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.366025 | − | 0.633975i | −0.183013 | − | 0.316987i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.975173 | − | 0.563016i | 0.398113 | − | 0.229850i | ||||
\(7\) | 0.524827 | − | 0.303009i | 0.198366 | − | 0.114527i | −0.397527 | − | 0.917590i | \(-0.630132\pi\) |
0.595893 | + | 0.803064i | \(0.296798\pi\) | |||||||
\(8\) | − | 3.07638i | − | 1.08766i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.563016 | − | 0.975173i | 0.178041 | − | 0.308377i | ||||
\(11\) | 2.66422 | + | 1.53819i | 0.803293 | + | 0.463781i | 0.844621 | − | 0.535364i | \(-0.179826\pi\) |
−0.0413283 | + | 0.999146i | \(0.513159\pi\) | |||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | −0.176977 | + | 3.60121i | −0.0490845 | + | 0.998795i | ||||
\(14\) | 0.682396 | 0.182378 | ||||||||
\(15\) | −0.866025 | − | 0.500000i | −0.223607 | − | 0.129099i | ||||
\(16\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(17\) | 0.975173 | + | 1.68905i | 0.236514 | + | 0.409654i | 0.959712 | − | 0.280987i | \(-0.0906617\pi\) |
−0.723198 | + | 0.690641i | \(0.757328\pi\) | |||||||
\(18\) | − | 1.12603i | − | 0.265408i | ||||||
\(19\) | −4.23037 | + | 2.44240i | −0.970513 | + | 0.560326i | −0.899393 | − | 0.437142i | \(-0.855991\pi\) |
−0.0711202 | + | 0.997468i | \(0.522657\pi\) | |||||||
\(20\) | −0.633975 | + | 0.366025i | −0.141761 | + | 0.0818458i | ||||
\(21\) | − | 0.606018i | − | 0.132244i | ||||||
\(22\) | 1.73205 | + | 3.00000i | 0.369274 | + | 0.639602i | ||||
\(23\) | 0.932171 | − | 1.61457i | 0.194371 | − | 0.336660i | −0.752323 | − | 0.658794i | \(-0.771067\pi\) |
0.946694 | + | 0.322134i | \(0.104400\pi\) | |||||||
\(24\) | −2.66422 | − | 1.53819i | −0.543832 | − | 0.313982i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.20012 | + | 3.41216i | −0.431479 | + | 0.669179i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.384200 | − | 0.221818i | −0.0726070 | − | 0.0419197i | ||||
\(29\) | 1.39085 | − | 2.40903i | 0.258275 | − | 0.447345i | −0.707505 | − | 0.706708i | \(-0.750179\pi\) |
0.965780 | + | 0.259363i | \(0.0835127\pi\) | |||||||
\(30\) | −0.563016 | − | 0.975173i | −0.102792 | − | 0.178041i | ||||
\(31\) | 9.15276i | 1.64388i | 0.569572 | + | 0.821942i | \(0.307109\pi\) | ||||
−0.569572 | + | 0.821942i | \(0.692891\pi\) | |||||||
\(32\) | −3.37810 | + | 1.95035i | −0.597169 | + | 0.344776i | ||||
\(33\) | 2.66422 | − | 1.53819i | 0.463781 | − | 0.267764i | ||||
\(34\) | 2.19615i | 0.376637i | ||||||||
\(35\) | −0.303009 | − | 0.524827i | −0.0512179 | − | 0.0887120i | ||||
\(36\) | −0.366025 | + | 0.633975i | −0.0610042 | + | 0.105662i | ||||
\(37\) | 3.24581 | + | 1.87397i | 0.533607 | + | 0.308078i | 0.742484 | − | 0.669864i | \(-0.233647\pi\) |
−0.208877 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(38\) | −5.50045 | −0.892291 | ||||||||
\(39\) | 3.03025 | + | 1.95387i | 0.485228 | + | 0.312869i | ||||
\(40\) | −3.07638 | −0.486418 | ||||||||
\(41\) | 0.926751 | + | 0.535060i | 0.144734 | + | 0.0835623i | 0.570618 | − | 0.821215i | \(-0.306704\pi\) |
−0.425884 | + | 0.904778i | \(0.640037\pi\) | |||||||
\(42\) | 0.341198 | − | 0.590973i | 0.0526480 | − | 0.0911890i | ||||
\(43\) | −2.50542 | − | 4.33951i | −0.382073 | − | 0.661770i | 0.609285 | − | 0.792951i | \(-0.291456\pi\) |
−0.991358 | + | 0.131181i | \(0.958123\pi\) | |||||||
\(44\) | − | 2.25207i | − | 0.339512i | ||||||
\(45\) | −0.866025 | + | 0.500000i | −0.129099 | + | 0.0745356i | ||||
\(46\) | 1.81805 | − | 1.04965i | 0.268058 | − | 0.154763i | ||||
\(47\) | − | 10.2024i | − | 1.48817i | −0.668082 | − | 0.744087i | \(-0.732885\pi\) | ||
0.668082 | − | 0.744087i | \(-0.267115\pi\) | |||||||
\(48\) | −1.00000 | − | 1.73205i | −0.144338 | − | 0.250000i | ||||
\(49\) | −3.31637 | + | 5.74412i | −0.473767 | + | 0.820589i | ||||
\(50\) | −0.975173 | − | 0.563016i | −0.137910 | − | 0.0796225i | ||||
\(51\) | 1.95035 | 0.273103 | ||||||||
\(52\) | 2.34785 | − | 1.20593i | 0.325588 | − | 0.167233i | ||||
\(53\) | −10.6569 | −1.46384 | −0.731918 | − | 0.681393i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681393i | \(0.761375\pi\) | |||||||
\(54\) | −0.975173 | − | 0.563016i | −0.132704 | − | 0.0766168i | ||||
\(55\) | 1.53819 | − | 2.66422i | 0.207409 | − | 0.359244i | ||||
\(56\) | −0.932171 | − | 1.61457i | −0.124567 | − | 0.215756i | ||||
\(57\) | 4.88481i | 0.647008i | ||||||||
\(58\) | 2.71264 | − | 1.56615i | 0.356188 | − | 0.205645i | ||||
\(59\) | 10.0236 | − | 5.78712i | 1.30496 | − | 0.753419i | 0.323710 | − | 0.946156i | \(-0.395070\pi\) |
0.981251 | + | 0.192737i | \(0.0617363\pi\) | |||||||
\(60\) | 0.732051i | 0.0945074i | ||||||||
\(61\) | 3.13397 | + | 5.42820i | 0.401264 | + | 0.695010i | 0.993879 | − | 0.110476i | \(-0.0352375\pi\) |
−0.592614 | + | 0.805486i | \(0.701904\pi\) | |||||||
\(62\) | −5.15315 | + | 8.92552i | −0.654451 | + | 1.13354i | ||||
\(63\) | −0.524827 | − | 0.303009i | −0.0661220 | − | 0.0381756i | ||||
\(64\) | −8.39230 | −1.04904 | ||||||||
\(65\) | 3.60121 | + | 0.176977i | 0.446675 | + | 0.0219513i | ||||
\(66\) | 3.46410 | 0.426401 | ||||||||
\(67\) | −1.71288 | − | 0.988929i | −0.209261 | − | 0.120817i | 0.391707 | − | 0.920090i | \(-0.371885\pi\) |
−0.600968 | + | 0.799273i | \(0.705218\pi\) | |||||||
\(68\) | 0.713876 | − | 1.23647i | 0.0865702 | − | 0.149944i | ||||
\(69\) | −0.932171 | − | 1.61457i | −0.112220 | − | 0.194371i | ||||
\(70\) | − | 0.682396i | − | 0.0815620i | ||||||
\(71\) | −5.11557 | + | 2.95347i | −0.607106 | + | 0.350513i | −0.771832 | − | 0.635826i | \(-0.780659\pi\) |
0.164726 | + | 0.986339i | \(0.447326\pi\) | |||||||
\(72\) | −2.66422 | + | 1.53819i | −0.313982 | + | 0.181277i | ||||
\(73\) | − | 4.35395i | − | 0.509592i | −0.966995 | − | 0.254796i | \(-0.917992\pi\) | ||
0.966995 | − | 0.254796i | \(-0.0820083\pi\) | |||||||
\(74\) | 2.11015 | + | 3.65488i | 0.245300 | + | 0.424872i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 3.09684 | + | 1.78796i | 0.355232 | + | 0.205093i | ||||
\(77\) | 1.86434 | 0.212461 | ||||||||
\(78\) | 1.85495 | + | 3.61144i | 0.210032 | + | 0.408915i | ||||
\(79\) | −3.29546 | −0.370768 | −0.185384 | − | 0.982666i | \(-0.559353\pi\) | ||||
−0.185384 | + | 0.982666i | \(0.559353\pi\) | |||||||
\(80\) | −1.73205 | − | 1.00000i | −0.193649 | − | 0.111803i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.602495 | + | 1.04355i | 0.0665344 | + | 0.115241i | ||||
\(83\) | − | 6.97707i | − | 0.765833i | −0.923783 | − | 0.382916i | \(-0.874920\pi\) | ||
0.923783 | − | 0.382916i | \(-0.125080\pi\) | |||||||
\(84\) | −0.384200 | + | 0.221818i | −0.0419197 | + | 0.0242023i | ||||
\(85\) | 1.68905 | − | 0.975173i | 0.183203 | − | 0.105772i | ||||
\(86\) | − | 5.64237i | − | 0.608432i | ||||||
\(87\) | −1.39085 | − | 2.40903i | −0.149115 | − | 0.258275i | ||||
\(88\) | 4.73205 | − | 8.19615i | 0.504438 | − | 0.873713i | ||||
\(89\) | 14.1156 | + | 8.14963i | 1.49625 | + | 0.863859i | 0.999991 | − | 0.00431721i | \(-0.00137421\pi\) |
0.496257 | + | 0.868176i | \(0.334708\pi\) | |||||||
\(90\) | −1.12603 | −0.118694 | ||||||||
\(91\) | 0.998316 | + | 1.94364i | 0.104652 | + | 0.203748i | ||||
\(92\) | −1.36479 | −0.142289 | ||||||||
\(93\) | 7.92652 | + | 4.57638i | 0.821942 | + | 0.474548i | ||||
\(94\) | 5.74412 | − | 9.94911i | 0.592461 | − | 1.02617i | ||||
\(95\) | 2.44240 | + | 4.23037i | 0.250585 | + | 0.434026i | ||||
\(96\) | 3.90069i | 0.398113i | ||||||||
\(97\) | 11.4336 | − | 6.60121i | 1.16091 | − | 0.670251i | 0.209387 | − | 0.977833i | \(-0.432853\pi\) |
0.951522 | + | 0.307582i | \(0.0995198\pi\) | |||||||
\(98\) | −6.46807 | + | 3.73434i | −0.653374 | + | 0.377225i | ||||
\(99\) | − | 3.07638i | − | 0.309188i | ||||||
\(100\) | 0.366025 | + | 0.633975i | 0.0366025 | + | 0.0633975i | ||||
\(101\) | −3.93217 | + | 6.81072i | −0.391266 | + | 0.677692i | −0.992617 | − | 0.121293i | \(-0.961296\pi\) |
0.601351 | + | 0.798985i | \(0.294629\pi\) | |||||||
\(102\) | 1.90192 | + | 1.09808i | 0.188319 | + | 0.108726i | ||||
\(103\) | −15.1101 | −1.48885 | −0.744424 | − | 0.667708i | \(-0.767276\pi\) | ||||
−0.744424 | + | 0.667708i | \(0.767276\pi\) | |||||||
\(104\) | 11.0787 | + | 0.544447i | 1.08635 | + | 0.0533874i | ||||
\(105\) | −0.606018 | −0.0591413 | ||||||||
\(106\) | −10.3923 | − | 6.00000i | −1.00939 | − | 0.582772i | ||||
\(107\) | 4.10350 | − | 7.10746i | 0.396700 | − | 0.687104i | −0.596617 | − | 0.802526i | \(-0.703489\pi\) |
0.993317 | + | 0.115422i | \(0.0368220\pi\) | |||||||
\(108\) | 0.366025 | + | 0.633975i | 0.0352208 | + | 0.0610042i | ||||
\(109\) | 10.5927i | 1.01460i | 0.861770 | + | 0.507299i | \(0.169356\pi\) | ||||
−0.861770 | + | 0.507299i | \(0.830644\pi\) | |||||||
\(110\) | 3.00000 | − | 1.73205i | 0.286039 | − | 0.165145i | ||||
\(111\) | 3.24581 | − | 1.87397i | 0.308078 | − | 0.177869i | ||||
\(112\) | − | 1.21204i | − | 0.114527i | ||||||
\(113\) | −1.73205 | − | 3.00000i | −0.162938 | − | 0.282216i | 0.772983 | − | 0.634426i | \(-0.218764\pi\) |
−0.935921 | + | 0.352210i | \(0.885430\pi\) | |||||||
\(114\) | −2.75023 | + | 4.76353i | −0.257582 | + | 0.446146i | ||||
\(115\) | −1.61457 | − | 0.932171i | −0.150559 | − | 0.0869254i | ||||
\(116\) | −2.03635 | −0.189070 | ||||||||
\(117\) | 3.20722 | − | 1.64734i | 0.296508 | − | 0.152296i | ||||
\(118\) | 13.0330 | 1.19978 | ||||||||
\(119\) | 1.02359 | + | 0.590973i | 0.0938328 | + | 0.0541744i | ||||
\(120\) | −1.53819 | + | 2.66422i | −0.140417 | + | 0.243209i | ||||
\(121\) | −0.767949 | − | 1.33013i | −0.0698136 | − | 0.120921i | ||||
\(122\) | 7.05791i | 0.638994i | ||||||||
\(123\) | 0.926751 | − | 0.535060i | 0.0835623 | − | 0.0482447i | ||||
\(124\) | 5.80261 | − | 3.35014i | 0.521090 | − | 0.300852i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.341198 | − | 0.590973i | −0.0303963 | − | 0.0526480i | ||||
\(127\) | 9.02191 | − | 15.6264i | 0.800565 | − | 1.38662i | −0.118680 | − | 0.992933i | \(-0.537866\pi\) |
0.919245 | − | 0.393687i | \(-0.128801\pi\) | |||||||
\(128\) | −1.42775 | − | 0.824313i | −0.126197 | − | 0.0728597i | ||||
\(129\) | −5.01084 | −0.441180 | ||||||||
\(130\) | 3.41216 | + | 2.20012i | 0.299266 | + | 0.192963i | ||||
\(131\) | 1.11899 | 0.0977662 | 0.0488831 | − | 0.998805i | \(-0.484434\pi\) | ||||
0.0488831 | + | 0.998805i | \(0.484434\pi\) | |||||||
\(132\) | −1.95035 | − | 1.12603i | −0.169756 | − | 0.0980085i | ||||
\(133\) | −1.48014 | + | 2.56368i | −0.128345 | + | 0.222299i | ||||
\(134\) | −1.11357 | − | 1.92875i | −0.0961975 | − | 0.166619i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 5.19615 | − | 3.00000i | 0.445566 | − | 0.257248i | ||||
\(137\) | −7.54009 | + | 4.35327i | −0.644193 | + | 0.371925i | −0.786228 | − | 0.617937i | \(-0.787969\pi\) |
0.142035 | + | 0.989862i | \(0.454635\pi\) | |||||||
\(138\) | − | 2.09931i | − | 0.178705i | ||||||
\(139\) | −4.82844 | − | 8.36311i | −0.409543 | − | 0.709350i | 0.585295 | − | 0.810820i | \(-0.300979\pi\) |
−0.994839 | + | 0.101471i | \(0.967645\pi\) | |||||||
\(140\) | −0.221818 | + | 0.384200i | −0.0187471 | + | 0.0324708i | ||||
\(141\) | −8.83555 | − | 5.10121i | −0.744087 | − | 0.429599i | ||||
\(142\) | −6.65142 | −0.558174 | ||||||||
\(143\) | −6.01084 | + | 9.32218i | −0.502652 | + | 0.779560i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −2.40903 | − | 1.39085i | −0.200059 | − | 0.115504i | ||||
\(146\) | 2.45135 | − | 4.24586i | 0.202875 | − | 0.351390i | ||||
\(147\) | 3.31637 | + | 5.74412i | 0.273530 | + | 0.473767i | ||||
\(148\) | − | 2.74368i | − | 0.225529i | ||||||
\(149\) | 4.48228 | − | 2.58784i | 0.367202 | − | 0.212004i | −0.305033 | − | 0.952342i | \(-0.598668\pi\) |
0.672236 | + | 0.740337i | \(0.265334\pi\) | |||||||
\(150\) | −0.975173 | + | 0.563016i | −0.0796225 | + | 0.0459701i | ||||
\(151\) | − | 22.1451i | − | 1.80215i | −0.433668 | − | 0.901073i | \(-0.642781\pi\) | ||
0.433668 | − | 0.901073i | \(-0.357219\pi\) | |||||||
\(152\) | 7.51376 | + | 13.0142i | 0.609446 | + | 1.05559i | ||||
\(153\) | 0.975173 | − | 1.68905i | 0.0788380 | − | 0.136551i | ||||
\(154\) | 1.81805 | + | 1.04965i | 0.146503 | + | 0.0845836i | ||||
\(155\) | 9.15276 | 0.735167 | ||||||||
\(156\) | 0.129556 | − | 2.63627i | 0.0103728 | − | 0.211070i | ||||
\(157\) | −14.3756 | −1.14730 | −0.573650 | − | 0.819100i | \(-0.694473\pi\) | ||||
−0.573650 | + | 0.819100i | \(0.694473\pi\) | |||||||
\(158\) | −3.21364 | − | 1.85540i | −0.255664 | − | 0.147608i | ||||
\(159\) | −5.32844 | + | 9.22913i | −0.422573 | + | 0.731918i | ||||
\(160\) | 1.95035 | + | 3.37810i | 0.154188 | + | 0.267062i | ||||
\(161\) | − | 1.12983i | − | 0.0890427i | ||||||
\(162\) | −0.975173 | + | 0.563016i | −0.0766168 | + | 0.0442347i | ||||
\(163\) | −8.72098 | + | 5.03506i | −0.683080 | + | 0.394376i | −0.801014 | − | 0.598645i | \(-0.795706\pi\) |
0.117935 | + | 0.993021i | \(0.462373\pi\) | |||||||
\(164\) | − | 0.783382i | − | 0.0611719i | ||||||
\(165\) | −1.53819 | − | 2.66422i | −0.119748 | − | 0.207409i | ||||
\(166\) | 3.92820 | − | 6.80385i | 0.304888 | − | 0.528081i | ||||
\(167\) | −9.39030 | − | 5.42149i | −0.726643 | − | 0.419528i | 0.0905495 | − | 0.995892i | \(-0.471138\pi\) |
−0.817193 | + | 0.576364i | \(0.804471\pi\) | |||||||
\(168\) | −1.86434 | −0.143837 | ||||||||
\(169\) | −12.9374 | − | 1.27466i | −0.995181 | − | 0.0980507i | ||||
\(170\) | 2.19615 | 0.168437 | ||||||||
\(171\) | 4.23037 | + | 2.44240i | 0.323504 | + | 0.186775i | ||||
\(172\) | −1.83409 | + | 3.17674i | −0.139848 | + | 0.242225i | ||||
\(173\) | 12.3311 | + | 21.3581i | 0.937518 | + | 1.62383i | 0.770081 | + | 0.637947i | \(0.220216\pi\) |
0.167438 | + | 0.985883i | \(0.446451\pi\) | |||||||
\(174\) | − | 3.13229i | − | 0.237458i | ||||||
\(175\) | −0.524827 | + | 0.303009i | −0.0396732 | + | 0.0229053i | ||||
\(176\) | 5.32844 | − | 3.07638i | 0.401647 | − | 0.231891i | ||||
\(177\) | − | 11.5742i | − | 0.869974i | ||||||
\(178\) | 9.17674 | + | 15.8946i | 0.687826 | + | 1.19135i | ||||
\(179\) | −11.4199 | + | 19.7798i | −0.853561 | + | 1.47841i | 0.0244128 | + | 0.999702i | \(0.492228\pi\) |
−0.877974 | + | 0.478709i | \(0.841105\pi\) | |||||||
\(180\) | 0.633975 | + | 0.366025i | 0.0472537 | + | 0.0272819i | ||||
\(181\) | −17.4616 | −1.29791 | −0.648957 | − | 0.760825i | \(-0.724794\pi\) | ||||
−0.648957 | + | 0.760825i | \(0.724794\pi\) | |||||||
\(182\) | −0.120768 | + | 2.45745i | −0.00895194 | + | 0.182158i | ||||
\(183\) | 6.26795 | 0.463340 | ||||||||
\(184\) | −4.96702 | − | 2.86771i | −0.366173 | − | 0.211410i | ||||
\(185\) | 1.87397 | − | 3.24581i | 0.137777 | − | 0.238636i | ||||
\(186\) | 5.15315 | + | 8.92552i | 0.377847 | + | 0.654451i | ||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | −6.46807 | + | 3.73434i | −0.471732 | + | 0.272355i | ||||
\(189\) | −0.524827 | + | 0.303009i | −0.0381756 | + | 0.0220407i | ||||
\(190\) | 5.50045i | 0.399045i | ||||||||
\(191\) | −3.83678 | − | 6.64550i | −0.277620 | − | 0.480851i | 0.693173 | − | 0.720771i | \(-0.256212\pi\) |
−0.970793 | + | 0.239920i | \(0.922879\pi\) | |||||||
\(192\) | −4.19615 | + | 7.26795i | −0.302831 | + | 0.524519i | ||||
\(193\) | 18.1959 | + | 10.5054i | 1.30977 | + | 0.756197i | 0.982058 | − | 0.188581i | \(-0.0603887\pi\) |
0.327713 | + | 0.944777i | \(0.393722\pi\) | |||||||
\(194\) | 14.8663 | 1.06734 | ||||||||
\(195\) | 1.95387 | − | 3.03025i | 0.139919 | − | 0.217000i | ||||
\(196\) | 4.85550 | 0.346822 | ||||||||
\(197\) | −17.6475 | − | 10.1888i | −1.25734 | − | 0.725923i | −0.284780 | − | 0.958593i | \(-0.591921\pi\) |
−0.972556 | + | 0.232670i | \(0.925254\pi\) | |||||||
\(198\) | 1.73205 | − | 3.00000i | 0.123091 | − | 0.213201i | ||||
\(199\) | −7.40069 | − | 12.8184i | −0.524621 | − | 0.908670i | −0.999589 | − | 0.0286673i | \(-0.990874\pi\) |
0.474968 | − | 0.880003i | \(-0.342460\pi\) | |||||||
\(200\) | 3.07638i | 0.217533i | ||||||||
\(201\) | −1.71288 | + | 0.988929i | −0.120817 | + | 0.0697537i | ||||
\(202\) | −7.66909 | + | 4.42775i | −0.539595 | + | 0.311536i | ||||
\(203\) | − | 1.68576i | − | 0.118317i | ||||||
\(204\) | −0.713876 | − | 1.23647i | −0.0499813 | − | 0.0865702i | ||||
\(205\) | 0.535060 | − | 0.926751i | 0.0373702 | − | 0.0647271i | ||||
\(206\) | −14.7350 | − | 8.50726i | −1.02664 | − | 0.592729i | ||||
\(207\) | −1.86434 | −0.129581 | ||||||||
\(208\) | 6.06049 | + | 3.90774i | 0.420220 | + | 0.270953i | ||||
\(209\) | −15.0275 | −1.03947 | ||||||||
\(210\) | −0.590973 | − | 0.341198i | −0.0407810 | − | 0.0235449i | ||||
\(211\) | −2.61015 | + | 4.52091i | −0.179690 | + | 0.311232i | −0.941774 | − | 0.336246i | \(-0.890843\pi\) |
0.762084 | + | 0.647478i | \(0.224176\pi\) | |||||||
\(212\) | 3.90069 | + | 6.75620i | 0.267901 | + | 0.464017i | ||||
\(213\) | 5.90695i | 0.404737i | ||||||||
\(214\) | 8.00323 | − | 4.62067i | 0.547090 | − | 0.315862i | ||||
\(215\) | −4.33951 | + | 2.50542i | −0.295952 | + | 0.170868i | ||||
\(216\) | 3.07638i | 0.209321i | ||||||||
\(217\) | 2.77337 | + | 4.80362i | 0.188269 | + | 0.326091i | ||||
\(218\) | −5.96387 | + | 10.3297i | −0.403924 | + | 0.699617i | ||||
\(219\) | −3.77063 | − | 2.17698i | −0.254796 | − | 0.147106i | ||||
\(220\) | −2.25207 | −0.151834 | ||||||||
\(221\) | −6.25519 | + | 3.21288i | −0.420770 | + | 0.216121i | ||||
\(222\) | 4.22030 | 0.283248 | ||||||||
\(223\) | 5.34065 | + | 3.08342i | 0.357636 | + | 0.206481i | 0.668043 | − | 0.744122i | \(-0.267132\pi\) |
−0.310407 | + | 0.950604i | \(0.600465\pi\) | |||||||
\(224\) | −1.18195 | + | 2.04719i | −0.0789720 | + | 0.136784i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | − | 3.90069i | − | 0.259470i | ||||||
\(227\) | 14.8189 | − | 8.55568i | 0.983563 | − | 0.567860i | 0.0802192 | − | 0.996777i | \(-0.474438\pi\) |
0.903344 | + | 0.428917i | \(0.141105\pi\) | |||||||
\(228\) | 3.09684 | − | 1.78796i | 0.205093 | − | 0.118411i | ||||
\(229\) | 28.9206i | 1.91113i | 0.294788 | + | 0.955563i | \(0.404751\pi\) | ||||
−0.294788 | + | 0.955563i | \(0.595249\pi\) | |||||||
\(230\) | −1.04965 | − | 1.81805i | −0.0692122 | − | 0.119879i | ||||
\(231\) | 0.932171 | − | 1.61457i | 0.0613323 | − | 0.106231i | ||||
\(232\) | −7.41108 | − | 4.27879i | −0.486561 | − | 0.280916i | ||||
\(233\) | −11.3284 | −0.742151 | −0.371075 | − | 0.928603i | \(-0.621011\pi\) | ||||
−0.371075 | + | 0.928603i | \(0.621011\pi\) | |||||||
\(234\) | 4.05507 | + | 0.199281i | 0.265088 | + | 0.0130274i | ||||
\(235\) | −10.2024 | −0.665532 | ||||||||
\(236\) | −7.33778 | − | 4.23647i | −0.477649 | − | 0.275771i | ||||
\(237\) | −1.64773 | + | 2.85395i | −0.107032 | + | 0.185384i | ||||
\(238\) | 0.665454 | + | 1.15260i | 0.0431350 | + | 0.0747120i | ||||
\(239\) | − | 19.1298i | − | 1.23741i | −0.785625 | − | 0.618703i | \(-0.787659\pi\) | ||
0.785625 | − | 0.618703i | \(-0.212341\pi\) | |||||||
\(240\) | −1.73205 | + | 1.00000i | −0.111803 | + | 0.0645497i | ||||
\(241\) | 4.74075 | − | 2.73708i | 0.305379 | − | 0.176311i | −0.339478 | − | 0.940614i | \(-0.610250\pi\) |
0.644857 | + | 0.764303i | \(0.276917\pi\) | |||||||
\(242\) | − | 1.72947i | − | 0.111175i | ||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.29423 | − | 3.97372i | 0.146873 | − | 0.254391i | ||||
\(245\) | 5.74412 | + | 3.31637i | 0.366979 | + | 0.211875i | ||||
\(246\) | 1.20499 | 0.0768273 | ||||||||
\(247\) | −8.04692 | − | 15.6667i | −0.512013 | − | 0.996846i | ||||
\(248\) | 28.1573 | 1.78799 | ||||||||
\(249\) | −6.04232 | − | 3.48853i | −0.382916 | − | 0.221077i | ||||
\(250\) | −0.563016 | + | 0.975173i | −0.0356083 | + | 0.0616753i | ||||
\(251\) | 2.35992 | + | 4.08751i | 0.148957 | + | 0.258001i | 0.930842 | − | 0.365421i | \(-0.119075\pi\) |
−0.781885 | + | 0.623422i | \(0.785742\pi\) | |||||||
\(252\) | 0.443636i | 0.0279465i | ||||||||
\(253\) | 4.96702 | − | 2.86771i | 0.312274 | − | 0.180291i | ||||
\(254\) | 17.5958 | − | 10.1590i | 1.10406 | − | 0.637430i | ||||
\(255\) | − | 1.95035i | − | 0.122135i | ||||||
\(256\) | 7.46410 | + | 12.9282i | 0.466506 | + | 0.808013i | ||||
\(257\) | 3.63939 | − | 6.30362i | 0.227019 | − | 0.393209i | −0.729904 | − | 0.683550i | \(-0.760435\pi\) |
0.956923 | + | 0.290341i | \(0.0937687\pi\) | |||||||
\(258\) | −4.88643 | − | 2.82118i | −0.304216 | − | 0.175639i | ||||
\(259\) | 2.27132 | 0.141133 | ||||||||
\(260\) | −1.20593 | − | 2.34785i | −0.0747888 | − | 0.145608i | ||||
\(261\) | −2.78171 | −0.172183 | ||||||||
\(262\) | 1.09120 | + | 0.630007i | 0.0674148 | + | 0.0389220i | ||||
\(263\) | 0.643362 | − | 1.11434i | 0.0396714 | − | 0.0687129i | −0.845508 | − | 0.533963i | \(-0.820702\pi\) |
0.885179 | + | 0.465250i | \(0.154036\pi\) | |||||||
\(264\) | −4.73205 | − | 8.19615i | −0.291238 | − | 0.504438i | ||||
\(265\) | 10.6569i | 0.654647i | ||||||||
\(266\) | −2.88679 | + | 1.66669i | −0.177000 | + | 0.102191i | ||||
\(267\) | 14.1156 | − | 8.14963i | 0.863859 | − | 0.498749i | ||||
\(268\) | 1.44789i | 0.0884441i | ||||||||
\(269\) | −9.46952 | − | 16.4017i | −0.577367 | − | 1.00003i | −0.995780 | − | 0.0917720i | \(-0.970747\pi\) |
0.418413 | − | 0.908257i | \(-0.362586\pi\) | |||||||
\(270\) | −0.563016 | + | 0.975173i | −0.0342641 | + | 0.0593471i | ||||
\(271\) | 9.54719 | + | 5.51207i | 0.579950 | + | 0.334835i | 0.761114 | − | 0.648619i | \(-0.224653\pi\) |
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(272\) | 3.90069 | 0.236514 | ||||||||
\(273\) | 2.18240 | + | 0.107251i | 0.132085 | + | 0.00649113i | ||||
\(274\) | −9.80385 | −0.592272 | ||||||||
\(275\) | −2.66422 | − | 1.53819i | −0.160659 | − | 0.0927563i | ||||
\(276\) | −0.682396 | + | 1.18195i | −0.0410754 | + | 0.0711447i | ||||
\(277\) | 10.4607 | + | 18.1185i | 0.628525 | + | 1.08864i | 0.987848 | + | 0.155423i | \(0.0496742\pi\) |
−0.359323 | + | 0.933213i | \(0.616992\pi\) | |||||||
\(278\) | − | 10.8740i | − | 0.652177i | ||||||
\(279\) | 7.92652 | − | 4.57638i | 0.474548 | − | 0.273981i | ||||
\(280\) | −1.61457 | + | 0.932171i | −0.0964888 | + | 0.0557079i | ||||
\(281\) | − | 10.6653i | − | 0.636238i | −0.948051 | − | 0.318119i | \(-0.896949\pi\) | ||
0.948051 | − | 0.318119i | \(-0.103051\pi\) | |||||||
\(282\) | −5.74412 | − | 9.94911i | −0.342058 | − | 0.592461i | ||||
\(283\) | 1.39254 | − | 2.41194i | 0.0827777 | − | 0.143375i | −0.821664 | − | 0.569972i | \(-0.806954\pi\) |
0.904442 | + | 0.426596i | \(0.140288\pi\) | |||||||
\(284\) | 3.74486 | + | 2.16209i | 0.222216 | + | 0.128297i | ||||
\(285\) | 4.88481 | 0.289351 | ||||||||
\(286\) | −11.1101 | + | 5.70654i | −0.656957 | + | 0.337435i | ||||
\(287\) | 0.648512 | 0.0382805 | ||||||||
\(288\) | 3.37810 | + | 1.95035i | 0.199056 | + | 0.114925i | ||||
\(289\) | 6.59808 | − | 11.4282i | 0.388122 | − | 0.672247i | ||||
\(290\) | −1.56615 | − | 2.71264i | −0.0919672 | − | 0.159292i | ||||
\(291\) | − | 13.2024i | − | 0.773939i | ||||||
\(292\) | −2.76030 | + | 1.59366i | −0.161534 | + | 0.0932618i | ||||
\(293\) | 4.29428 | − | 2.47930i | 0.250874 | − | 0.144842i | −0.369290 | − | 0.929314i | \(-0.620399\pi\) |
0.620165 | + | 0.784472i | \(0.287066\pi\) | |||||||
\(294\) | 7.46868i | 0.435582i | ||||||||
\(295\) | −5.78712 | − | 10.0236i | −0.336939 | − | 0.583596i | ||||
\(296\) | 5.76503 | − | 9.98533i | 0.335086 | − | 0.580385i | ||||
\(297\) | −2.66422 | − | 1.53819i | −0.154594 | − | 0.0892548i | ||||
\(298\) | 5.82799 | 0.337606 | ||||||||
\(299\) | 5.64941 | + | 3.64268i | 0.326714 | + | 0.210662i | ||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | −2.62983 | − | 1.51833i | −0.151581 | − | 0.0875151i | ||||
\(302\) | 12.4681 | − | 21.5953i | 0.717457 | − | 1.24267i | ||||
\(303\) | 3.93217 | + | 6.81072i | 0.225897 | + | 0.391266i | ||||
\(304\) | 9.76961i | 0.560326i | ||||||||
\(305\) | 5.42820 | − | 3.13397i | 0.310818 | − | 0.179451i | ||||
\(306\) | 1.90192 | − | 1.09808i | 0.108726 | − | 0.0627728i | ||||
\(307\) | 9.60723i | 0.548314i | 0.961685 | + | 0.274157i | \(0.0883987\pi\) | ||||
−0.961685 | + | 0.274157i | \(0.911601\pi\) | |||||||
\(308\) | −0.682396 | − | 1.18195i | −0.0388831 | − | 0.0673476i | ||||
\(309\) | −7.55507 | + | 13.0858i | −0.429793 | + | 0.744424i | ||||
\(310\) | 8.92552 | + | 5.15315i | 0.506935 | + | 0.292679i | ||||
\(311\) | 26.0393 | 1.47655 | 0.738275 | − | 0.674499i | \(-0.235641\pi\) | ||||
0.738275 | + | 0.674499i | \(0.235641\pi\) | |||||||
\(312\) | 6.01084 | − | 9.32218i | 0.340297 | − | 0.527765i | ||||
\(313\) | 29.2311 | 1.65224 | 0.826121 | − | 0.563493i | \(-0.190543\pi\) | ||||
0.826121 | + | 0.563493i | \(0.190543\pi\) | |||||||
\(314\) | −14.0187 | − | 8.09371i | −0.791122 | − | 0.456755i | ||||
\(315\) | −0.303009 | + | 0.524827i | −0.0170726 | + | 0.0295707i | ||||
\(316\) | 1.20622 | + | 2.08924i | 0.0678553 | + | 0.117529i | ||||
\(317\) | − | 8.62570i | − | 0.484467i | −0.970218 | − | 0.242234i | \(-0.922120\pi\) | ||
0.970218 | − | 0.242234i | \(-0.0778801\pi\) | |||||||
\(318\) | −10.3923 | + | 6.00000i | −0.582772 | + | 0.336463i | ||||
\(319\) | 7.41108 | − | 4.27879i | 0.414941 | − | 0.239566i | ||||
\(320\) | 8.39230i | 0.469144i | ||||||||
\(321\) | −4.10350 | − | 7.10746i | −0.229035 | − | 0.396700i | ||||
\(322\) | 0.636110 | − | 1.10177i | 0.0354490 | − | 0.0613995i | ||||
\(323\) | −8.25068 | − | 4.76353i | −0.459080 | − | 0.265050i | ||||
\(324\) | 0.732051 | 0.0406695 | ||||||||
\(325\) | 0.176977 | − | 3.60121i | 0.00981690 | − | 0.199759i | ||||
\(326\) | −11.3393 | −0.628025 | ||||||||
\(327\) | 9.17356 | + | 5.29636i | 0.507299 | + | 0.292889i | ||||
\(328\) | 1.64605 | − | 2.85104i | 0.0908877 | − | 0.157422i | ||||
\(329\) | −3.09142 | − | 5.35450i | −0.170436 | − | 0.295203i | ||||
\(330\) | − | 3.46410i | − | 0.190693i | ||||||
\(331\) | 17.5822 | − | 10.1511i | 0.966404 | − | 0.557953i | 0.0682657 | − | 0.997667i | \(-0.478253\pi\) |
0.898138 | + | 0.439714i | \(0.144920\pi\) | |||||||
\(332\) | −4.42328 | + | 2.55378i | −0.242759 | + | 0.140157i | ||||
\(333\) | − | 3.74793i | − | 0.205386i | ||||||
\(334\) | −6.10478 | − | 10.5738i | −0.334039 | − | 0.578572i | ||||
\(335\) | −0.988929 | + | 1.71288i | −0.0540310 | + | 0.0935844i | ||||
\(336\) | −1.04965 | − | 0.606018i | −0.0572633 | − | 0.0330610i | ||||
\(337\) | 17.7847 | 0.968795 | 0.484397 | − | 0.874848i | \(-0.339039\pi\) | ||||
0.484397 | + | 0.874848i | \(0.339039\pi\) | |||||||
\(338\) | −11.8985 | − | 8.52696i | −0.647193 | − | 0.463805i | ||||
\(339\) | −3.46410 | −0.188144 | ||||||||
\(340\) | −1.23647 | − | 0.713876i | −0.0670570 | − | 0.0387154i | ||||
\(341\) | −14.0787 | + | 24.3850i | −0.762403 | + | 1.32052i | ||||
\(342\) | 2.75023 | + | 4.76353i | 0.148715 | + | 0.257582i | ||||
\(343\) | 8.26169i | 0.446089i | ||||||||
\(344\) | −13.3500 | + | 7.70762i | −0.719783 | + | 0.415567i | ||||
\(345\) | −1.61457 | + | 0.932171i | −0.0869254 | + | 0.0501864i | ||||
\(346\) | 27.7705i | 1.49295i | ||||||||
\(347\) | −4.29546 | − | 7.43996i | −0.230592 | − | 0.399398i | 0.727390 | − | 0.686224i | \(-0.240733\pi\) |
−0.957983 | + | 0.286826i | \(0.907400\pi\) | |||||||
\(348\) | −1.01817 | + | 1.76353i | −0.0545799 | + | 0.0945352i | ||||
\(349\) | 26.1369 | + | 15.0901i | 1.39908 | + | 0.807756i | 0.994296 | − | 0.106658i | \(-0.0340150\pi\) |
0.404779 | + | 0.914414i | \(0.367348\pi\) | |||||||
\(350\) | −0.682396 | −0.0364756 | ||||||||
\(351\) | 0.176977 | − | 3.60121i | 0.00944631 | − | 0.192218i | ||||
\(352\) | −12.0000 | −0.639602 | ||||||||
\(353\) | 24.7940 | + | 14.3148i | 1.31965 | + | 0.761903i | 0.983673 | − | 0.179966i | \(-0.0575988\pi\) |
0.335981 | + | 0.941869i | \(0.390932\pi\) | |||||||
\(354\) | 6.51649 | − | 11.2869i | 0.346348 | − | 0.599892i | ||||
\(355\) | 2.95347 | + | 5.11557i | 0.156754 | + | 0.271506i | ||||
\(356\) | − | 11.9319i | − | 0.632388i | ||||||
\(357\) | 1.02359 | − | 0.590973i | 0.0541744 | − | 0.0312776i | ||||
\(358\) | −22.2727 | + | 12.8591i | −1.17715 | + | 0.679627i | ||||
\(359\) | 17.4624i | 0.921632i | 0.887496 | + | 0.460816i | \(0.152443\pi\) | ||||
−0.887496 | + | 0.460816i | \(0.847557\pi\) | |||||||
\(360\) | 1.53819 | + | 2.66422i | 0.0810697 | + | 0.140417i | ||||
\(361\) | 2.43067 | − | 4.21004i | 0.127930 | − | 0.221581i | ||||
\(362\) | −17.0281 | − | 9.83118i | −0.894978 | − | 0.516716i | ||||
\(363\) | −1.53590 | −0.0806138 | ||||||||
\(364\) | 0.866807 | − | 1.34433i | 0.0454330 | − | 0.0704619i | ||||
\(365\) | −4.35395 | −0.227896 | ||||||||
\(366\) | 6.11233 | + | 3.52896i | 0.319497 | + | 0.184462i | ||||
\(367\) | −16.2483 | + | 28.1429i | −0.848155 | + | 1.46905i | 0.0346981 | + | 0.999398i | \(0.488953\pi\) |
−0.882853 | + | 0.469649i | \(0.844380\pi\) | |||||||
\(368\) | −1.86434 | − | 3.22913i | −0.0971855 | − | 0.168330i | ||||
\(369\) | − | 1.07012i | − | 0.0557082i | ||||||
\(370\) | 3.65488 | − | 2.11015i | 0.190008 | − | 0.109701i | ||||
\(371\) | −5.59302 | + | 3.22913i | −0.290375 | + | 0.167648i | ||||
\(372\) | − | 6.70028i | − | 0.347393i | ||||||
\(373\) | −5.37586 | − | 9.31127i | −0.278352 | − | 0.482119i | 0.692624 | − | 0.721299i | \(-0.256455\pi\) |
−0.970975 | + | 0.239180i | \(0.923121\pi\) | |||||||
\(374\) | −3.37810 | + | 5.85104i | −0.174677 | + | 0.302550i | ||||
\(375\) | 0.866025 | + | 0.500000i | 0.0447214 | + | 0.0258199i | ||||
\(376\) | −31.3865 | −1.61863 | ||||||||
\(377\) | 8.42925 | + | 5.43509i | 0.434129 | + | 0.279921i | ||||
\(378\) | −0.682396 | −0.0350987 | ||||||||
\(379\) | 5.05881 | + | 2.92071i | 0.259854 | + | 0.150027i | 0.624268 | − | 0.781210i | \(-0.285397\pi\) |
−0.364414 | + | 0.931237i | \(0.618731\pi\) | |||||||
\(380\) | 1.78796 | − | 3.09684i | 0.0917206 | − | 0.158865i | ||||
\(381\) | −9.02191 | − | 15.6264i | −0.462206 | − | 0.800565i | ||||
\(382\) | − | 8.64068i | − | 0.442095i | ||||||
\(383\) | −20.4762 | + | 11.8220i | −1.04629 | + | 0.604074i | −0.921607 | − | 0.388124i | \(-0.873123\pi\) |
−0.124679 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(384\) | −1.42775 | + | 0.824313i | −0.0728597 | + | 0.0420655i | ||||
\(385\) | − | 1.86434i | − | 0.0950156i | ||||||
\(386\) | 11.8294 | + | 20.4892i | 0.602103 | + | 1.04287i | ||||
\(387\) | −2.50542 | + | 4.33951i | −0.127358 | + | 0.220590i | ||||
\(388\) | −8.36999 | − | 4.83242i | −0.424922 | − | 0.245329i | ||||
\(389\) | −16.5939 | −0.841345 | −0.420673 | − | 0.907212i | \(-0.638206\pi\) | ||||
−0.420673 | + | 0.907212i | \(0.638206\pi\) | |||||||
\(390\) | 3.61144 | − | 1.85495i | 0.182872 | − | 0.0939293i | ||||
\(391\) | 3.63611 | 0.183886 | ||||||||
\(392\) | 17.6711 | + | 10.2024i | 0.892525 | + | 0.515300i | ||||
\(393\) | 0.559493 | − | 0.969070i | 0.0282227 | − | 0.0488831i | ||||
\(394\) | −11.4729 | − | 19.8717i | −0.577998 | − | 1.00112i | ||||
\(395\) | 3.29546i | 0.165813i | ||||||||
\(396\) | −1.95035 | + | 1.12603i | −0.0980085 | + | 0.0565853i | ||||
\(397\) | −20.2680 | + | 11.7017i | −1.01722 | + | 0.587293i | −0.913298 | − | 0.407292i | \(-0.866473\pi\) |
−0.103923 | + | 0.994585i | \(0.533140\pi\) | |||||||
\(398\) | − | 16.6668i | − | 0.835433i | ||||||
\(399\) | 1.48014 | + | 2.56368i | 0.0740997 | + | 0.128345i | ||||
\(400\) | −1.00000 | + | 1.73205i | −0.0500000 | + | 0.0866025i | ||||
\(401\) | 0.0968434 | + | 0.0559126i | 0.00483613 | + | 0.00279214i | 0.502416 | − | 0.864626i | \(-0.332445\pi\) |
−0.497580 | + | 0.867418i | \(0.665778\pi\) | |||||||
\(402\) | −2.22713 | −0.111079 | ||||||||
\(403\) | −32.9610 | − | 1.61982i | −1.64190 | − | 0.0806892i | ||||
\(404\) | 5.75710 | 0.286426 | ||||||||
\(405\) | 0.866025 | + | 0.500000i | 0.0430331 | + | 0.0248452i | ||||
\(406\) | 0.949113 | − | 1.64391i | 0.0471037 | − | 0.0815860i | ||||
\(407\) | 5.76503 | + | 9.98533i | 0.285762 | + | 0.494954i | ||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | 16.6974 | − | 9.64024i | 0.825633 | − | 0.476679i | −0.0267224 | − | 0.999643i | \(-0.508507\pi\) |
0.852355 | + | 0.522964i | \(0.175174\pi\) | |||||||
\(410\) | 1.04355 | − | 0.602495i | 0.0515373 | − | 0.0297551i | ||||
\(411\) | 8.70654i | 0.429462i | ||||||||
\(412\) | 5.53070 | + | 9.57945i | 0.272478 | + | 0.471946i | ||||
\(413\) | 3.50710 | − | 6.07448i | 0.172573 | − | 0.298906i | ||||
\(414\) | −1.81805 | − | 1.04965i | −0.0893525 | − | 0.0515877i | ||||
\(415\) | −6.97707 | −0.342491 | ||||||||
\(416\) | −6.42575 | − | 12.5104i | −0.315048 | − | 0.613372i | ||||
\(417\) | −9.65689 | −0.472900 | ||||||||
\(418\) | −14.6544 | − | 8.46073i | −0.716771 | − | 0.413828i | ||||
\(419\) | −11.0693 | + | 19.1726i | −0.540770 | + | 0.936641i | 0.458090 | + | 0.888906i | \(0.348534\pi\) |
−0.998860 | + | 0.0477351i | \(0.984800\pi\) | |||||||
\(420\) | 0.221818 | + | 0.384200i | 0.0108236 | + | 0.0187471i | ||||
\(421\) | 0.914785i | 0.0445839i | 0.999752 | + | 0.0222919i | \(0.00709633\pi\) | ||||
−0.999752 | + | 0.0222919i | \(0.992904\pi\) | |||||||
\(422\) | −5.09069 | + | 2.93911i | −0.247811 | + | 0.143074i | ||||
\(423\) | −8.83555 | + | 5.10121i | −0.429599 | + | 0.248029i | ||||
\(424\) | 32.7846i | 1.59216i | ||||||||
\(425\) | −0.975173 | − | 1.68905i | −0.0473028 | − | 0.0819309i | ||||
\(426\) | −3.32571 | + | 5.76030i | −0.161131 | + | 0.279087i | ||||
\(427\) | 3.28959 | + | 1.89925i | 0.159194 | + | 0.0919110i | ||||
\(428\) | −6.00793 | −0.290404 | ||||||||
\(429\) | 5.06783 | + | 9.86663i | 0.244677 | + | 0.476365i | ||||
\(430\) | −5.64237 | −0.272099 | ||||||||
\(431\) | 32.0231 | + | 18.4885i | 1.54250 | + | 0.890561i | 0.998680 | + | 0.0513577i | \(0.0163549\pi\) |
0.543817 | + | 0.839204i | \(0.316978\pi\) | |||||||
\(432\) | −1.00000 | + | 1.73205i | −0.0481125 | + | 0.0833333i | ||||
\(433\) | −14.3449 | − | 24.8461i | −0.689371 | − | 1.19403i | −0.972042 | − | 0.234809i | \(-0.924554\pi\) |
0.282670 | − | 0.959217i | \(-0.408780\pi\) | |||||||
\(434\) | 6.24581i | 0.299808i | ||||||||
\(435\) | −2.40903 | + | 1.39085i | −0.115504 | + | 0.0666863i | ||||
\(436\) | 6.71551 | − | 3.87720i | 0.321615 | − | 0.185684i | ||||
\(437\) | 9.10695i | 0.435644i | ||||||||
\(438\) | −2.45135 | − | 4.24586i | −0.117130 | − | 0.202875i | ||||
\(439\) | 2.63106 | − | 4.55713i | 0.125574 | − | 0.217500i | −0.796383 | − | 0.604792i | \(-0.793256\pi\) |
0.921957 | + | 0.387292i | \(0.126590\pi\) | |||||||
\(440\) | −8.19615 | − | 4.73205i | −0.390736 | − | 0.225592i | ||||
\(441\) | 6.63274 | 0.315845 | ||||||||
\(442\) | −7.90880 | − | 0.388668i | −0.376183 | − | 0.0184870i | ||||
\(443\) | 28.8275 | 1.36964 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) | ||||
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(444\) | −2.37610 | − | 1.37184i | −0.112765 | − | 0.0651046i | ||||
\(445\) | 8.14963 | − | 14.1156i | 0.386329 | − | 0.669142i | ||||
\(446\) | 3.47204 | + | 6.01374i | 0.164406 | + | 0.284759i | ||||
\(447\) | − | 5.17569i | − | 0.244802i | ||||||
\(448\) | −4.40451 | + | 2.54295i | −0.208094 | + | 0.120143i | ||||
\(449\) | 2.60523 | − | 1.50413i | 0.122948 | − | 0.0709843i | −0.437265 | − | 0.899333i | \(-0.644053\pi\) |
0.560213 | + | 0.828349i | \(0.310719\pi\) | |||||||
\(450\) | 1.12603i | 0.0530817i | ||||||||
\(451\) | 1.64605 | + | 2.85104i | 0.0775093 | + | 0.134250i | ||||
\(452\) | −1.26795 | + | 2.19615i | −0.0596393 | + | 0.103298i | ||||
\(453\) | −19.1782 | − | 11.0726i | −0.901073 | − | 0.520235i | ||||
\(454\) | 19.2679 | 0.904290 | ||||||||
\(455\) | 1.94364 | − | 0.998316i | 0.0911191 | − | 0.0468018i | ||||
\(456\) | 15.0275 | 0.703728 | ||||||||
\(457\) | 7.69620 | + | 4.44340i | 0.360013 | + | 0.207854i | 0.669087 | − | 0.743185i | \(-0.266686\pi\) |
−0.309073 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(458\) | −16.2828 | + | 28.2026i | −0.760843 | + | 1.31782i | ||||
\(459\) | −0.975173 | − | 1.68905i | −0.0455172 | − | 0.0788380i | ||||
\(460\) | 1.36479i | 0.0636338i | ||||||||
\(461\) | −18.2808 | + | 10.5544i | −0.851424 | + | 0.491570i | −0.861131 | − | 0.508383i | \(-0.830243\pi\) |
0.00970733 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(462\) | 1.81805 | − | 1.04965i | 0.0845836 | − | 0.0488343i | ||||
\(463\) | − | 24.4679i | − | 1.13712i | −0.822642 | − | 0.568560i | \(-0.807501\pi\) | ||
0.822642 | − | 0.568560i | \(-0.192499\pi\) | |||||||
\(464\) | −2.78171 | − | 4.81805i | −0.129137 | − | 0.223673i | ||||
\(465\) | 4.57638 | − | 7.92652i | 0.212224 | − | 0.367584i | ||||
\(466\) | −11.0472 | − | 6.37810i | −0.511751 | − | 0.295460i | ||||
\(467\) | 19.5058 | 0.902622 | 0.451311 | − | 0.892367i | \(-0.350957\pi\) | ||||
0.451311 | + | 0.892367i | \(0.350957\pi\) | |||||||
\(468\) | −2.21829 | − | 1.43033i | −0.102541 | − | 0.0661171i | ||||
\(469\) | −1.19862 | −0.0553470 | ||||||||
\(470\) | −9.94911 | − | 5.74412i | −0.458918 | − | 0.264957i | ||||
\(471\) | −7.18782 | + | 12.4497i | −0.331197 | + | 0.573650i | ||||
\(472\) | −17.8034 | − | 30.8364i | −0.819467 | − | 1.41936i | ||||
\(473\) | − | 15.4152i | − | 0.708793i | ||||||
\(474\) | −3.21364 | + | 1.85540i | −0.147608 | + | 0.0852213i | ||||
\(475\) | 4.23037 | − | 2.44240i | 0.194103 | − | 0.112065i | ||||
\(476\) | − | 0.865244i | − | 0.0396584i | ||||||
\(477\) | 5.32844 | + | 9.22913i | 0.243973 | + | 0.422573i | ||||
\(478\) | 10.7704 | − | 18.6549i | 0.492627 | − | 0.853255i | ||||
\(479\) | 23.4090 | + | 13.5152i | 1.06959 | + | 0.617526i | 0.928068 | − | 0.372410i | \(-0.121469\pi\) |
0.141518 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(480\) | 3.90069 | 0.178041 | ||||||||
\(481\) | −7.32297 | + | 11.3572i | −0.333899 | + | 0.517842i | ||||
\(482\) | 6.16407 | 0.280766 | ||||||||
\(483\) | −0.978457 | − | 0.564913i | −0.0445213 | − | 0.0257044i | ||||
\(484\) | −0.562178 | + | 0.973721i | −0.0255535 | + | 0.0442600i | ||||
\(485\) | −6.60121 | − | 11.4336i | −0.299745 | − | 0.519174i | ||||
\(486\) | 1.12603i | 0.0510779i | ||||||||
\(487\) | −4.51849 | + | 2.60875i | −0.204752 | + | 0.118214i | −0.598870 | − | 0.800846i | \(-0.704384\pi\) |
0.394118 | + | 0.919060i | \(0.371050\pi\) | |||||||
\(488\) | 16.6992 | − | 9.64129i | 0.755937 | − | 0.436441i | ||||
\(489\) | 10.0701i | 0.455387i | ||||||||
\(490\) | 3.73434 | + | 6.46807i | 0.168700 | + | 0.292198i | ||||
\(491\) | 7.39085 | − | 12.8013i | 0.333545 | − | 0.577716i | −0.649660 | − | 0.760225i | \(-0.725089\pi\) |
0.983204 | + | 0.182509i | \(0.0584219\pi\) | |||||||
\(492\) | −0.678429 | − | 0.391691i | −0.0305859 | − | 0.0176588i | ||||
\(493\) | 5.42529 | 0.244343 | ||||||||
\(494\) | 0.973451 | − | 19.8083i | 0.0437977 | − | 0.891215i | ||||
\(495\) | −3.07638 | −0.138273 | ||||||||
\(496\) | 15.8530 | + | 9.15276i | 0.711822 | + | 0.410971i | ||||
\(497\) | −1.78986 | + | 3.10013i | −0.0802862 | + | 0.139060i | ||||
\(498\) | −3.92820 | − | 6.80385i | −0.176027 | − | 0.304888i | ||||
\(499\) | − | 10.3171i | − | 0.461859i | −0.972971 | − | 0.230929i | \(-0.925823\pi\) | ||
0.972971 | − | 0.230929i | \(-0.0741766\pi\) | |||||||
\(500\) | 0.633975 | − | 0.366025i | 0.0283522 | − | 0.0163692i | ||||
\(501\) | −9.39030 | + | 5.42149i | −0.419528 | + | 0.242214i | ||||
\(502\) | 5.31470i | 0.237207i | ||||||||
\(503\) | −13.3171 | − | 23.0660i | −0.593782 | − | 1.02846i | −0.993718 | − | 0.111917i | \(-0.964301\pi\) |
0.399936 | − | 0.916543i | \(-0.369032\pi\) | |||||||
\(504\) | −0.932171 | + | 1.61457i | −0.0415222 | + | 0.0719185i | ||||
\(505\) | 6.81072 | + | 3.93217i | 0.303073 | + | 0.174979i | ||||
\(506\) | 6.45827 | 0.287105 | ||||||||
\(507\) | −7.57257 | + | 10.5668i | −0.336309 | + | 0.469286i | ||||
\(508\) | −13.2090 | −0.586054 | ||||||||
\(509\) | −1.23647 | − | 0.713876i | −0.0548055 | − | 0.0316420i | 0.472347 | − | 0.881413i | \(-0.343407\pi\) |
−0.527152 | + | 0.849771i | \(0.676740\pi\) | |||||||
\(510\) | 1.09808 | − | 1.90192i | 0.0486236 | − | 0.0842186i | ||||
\(511\) | −1.31929 | − | 2.28507i | −0.0583619 | − | 0.101086i | ||||
\(512\) | 20.1069i | 0.888608i | ||||||||
\(513\) | 4.23037 | − | 2.44240i | 0.186775 | − | 0.107835i | ||||
\(514\) | 7.09808 | − | 4.09808i | 0.313083 | − | 0.180758i | ||||
\(515\) | 15.1101i | 0.665833i | ||||||||
\(516\) | 1.83409 | + | 3.17674i | 0.0807415 | + | 0.139848i | ||||
\(517\) | 15.6932 | − | 27.1815i | 0.690188 | − | 1.19544i | ||||
\(518\) | 2.21493 | + | 1.27879i | 0.0973183 | + | 0.0561867i | ||||
\(519\) | 24.6623 | 1.08255 | ||||||||
\(520\) | 0.544447 | − | 11.0787i | 0.0238756 | − | 0.485832i | ||||
\(521\) | 12.8623 | 0.563509 | 0.281755 | − | 0.959486i | \(-0.409084\pi\) | ||||
0.281755 | + | 0.959486i | \(0.409084\pi\) | |||||||
\(522\) | −2.71264 | − | 1.56615i | −0.118729 | − | 0.0685483i | ||||
\(523\) | −7.55011 | + | 13.0772i | −0.330143 | + | 0.571825i | −0.982540 | − | 0.186053i | \(-0.940430\pi\) |
0.652397 | + | 0.757878i | \(0.273764\pi\) | |||||||
\(524\) | −0.409577 | − | 0.709409i | −0.0178925 | − | 0.0309907i | ||||
\(525\) | 0.606018i | 0.0264488i | ||||||||
\(526\) | 1.25478 | − | 0.724446i | 0.0547109 | − | 0.0315874i | ||||
\(527\) | −15.4595 | + | 8.92552i | −0.673424 | + | 0.388802i | ||||
\(528\) | − | 6.15276i | − | 0.267764i | ||||||
\(529\) | 9.76212 | + | 16.9085i | 0.424440 | + | 0.735151i | ||||
\(530\) | −6.00000 | + | 10.3923i | −0.260623 | + | 0.451413i | ||||
\(531\) | −10.0236 | − | 5.78712i | −0.434987 | − | 0.251140i | ||||
\(532\) | 2.16708 | 0.0939547 | ||||||||
\(533\) | −2.09087 | + | 3.24273i | −0.0905658 | + | 0.140458i | ||||
\(534\) | 18.3535 | 0.794233 | ||||||||
\(535\) | −7.10746 | − | 4.10350i | −0.307282 | − | 0.177410i | ||||
\(536\) | −3.04232 | + | 5.26945i | −0.131408 | + | 0.227606i | ||||
\(537\) | 11.4199 | + | 19.7798i | 0.492804 | + | 0.853561i | ||||
\(538\) | − | 21.3260i | − | 0.919428i | ||||||
\(539\) | −17.6711 | + | 10.2024i | −0.761148 | + | 0.439449i | ||||
\(540\) | 0.633975 | − | 0.366025i | 0.0272819 | − | 0.0157512i | ||||
\(541\) | − | 41.1084i | − | 1.76739i | −0.468064 | − | 0.883695i | \(-0.655048\pi\) | ||
0.468064 | − | 0.883695i | \(-0.344952\pi\) | |||||||
\(542\) | 6.20677 | + | 10.7504i | 0.266604 | + | 0.461771i | ||||
\(543\) | −8.73082 | + | 15.1222i | −0.374675 | + | 0.648957i | ||||
\(544\) | −6.58846 | − | 3.80385i | −0.282478 | − | 0.163089i | ||||
\(545\) | 10.5927 | 0.453742 | ||||||||
\(546\) | 2.06783 | + | 1.33331i | 0.0884949 | + | 0.0570605i | ||||
\(547\) | 30.1327 | 1.28838 | 0.644191 | − | 0.764864i | \(-0.277194\pi\) | ||||
0.644191 | + | 0.764864i | \(0.277194\pi\) | |||||||
\(548\) | 5.51973 | + | 3.18682i | 0.235791 | + | 0.136134i | ||||
\(549\) | 3.13397 | − | 5.42820i | 0.133755 | − | 0.231670i | ||||
\(550\) | −1.73205 | − | 3.00000i | −0.0738549 | − | 0.127920i | ||||
\(551\) | 13.5881i | 0.578872i | ||||||||
\(552\) | −4.96702 | + | 2.86771i | −0.211410 | + | 0.122058i | ||||
\(553\) | −1.72955 | + | 0.998555i | −0.0735479 | + | 0.0424629i | ||||
\(554\) | 23.5583i | 1.00089i | ||||||||
\(555\) | −1.87397 | − | 3.24581i | −0.0795455 | − | 0.137777i | ||||
\(556\) | −3.53467 | + | 6.12222i | −0.149903 | + | 0.259640i | ||||
\(557\) | −21.8274 | − | 12.6021i | −0.924856 | − | 0.533966i | −0.0396752 | − | 0.999213i | \(-0.512632\pi\) |
−0.885181 | + | 0.465247i | \(0.845966\pi\) | |||||||
\(558\) | 10.3063 | 0.436301 | ||||||||
\(559\) | 16.0709 | − | 8.25454i | 0.679726 | − | 0.349130i | ||||
\(560\) | −1.21204 | −0.0512179 | ||||||||
\(561\) | 5.19615 | + | 3.00000i | 0.219382 | + | 0.126660i | ||||
\(562\) | 6.00474 | − | 10.4005i | 0.253295 | − | 0.438719i | ||||
\(563\) | −3.59639 | − | 6.22913i | −0.151570 | − | 0.262527i | 0.780235 | − | 0.625487i | \(-0.215100\pi\) |
−0.931805 | + | 0.362960i | \(0.881766\pi\) | |||||||
\(564\) | 7.46868i | 0.314488i | ||||||||
\(565\) | −3.00000 | + | 1.73205i | −0.126211 | + | 0.0728679i | ||||
\(566\) | 2.71593 | − | 1.56804i | 0.114159 | − | 0.0659097i | ||||
\(567\) | 0.606018i | 0.0254504i | ||||||||
\(568\) | 9.08600 | + | 15.7374i | 0.381240 | + | 0.660328i | ||||
\(569\) | 9.17606 | − | 15.8934i | 0.384681 | − | 0.666286i | −0.607044 | − | 0.794668i | \(-0.707645\pi\) |
0.991725 | + | 0.128382i | \(0.0409783\pi\) | |||||||
\(570\) | 4.76353 | + | 2.75023i | 0.199522 | + | 0.115194i | ||||
\(571\) | 27.5433 | 1.15265 | 0.576325 | − | 0.817221i | \(-0.304486\pi\) | ||||
0.576325 | + | 0.817221i | \(0.304486\pi\) | |||||||
\(572\) | 8.11015 | + | 0.398563i | 0.339102 | + | 0.0166648i | ||||
\(573\) | −7.67356 | −0.320568 | ||||||||
\(574\) | 0.632411 | + | 0.365123i | 0.0263963 | + | 0.0152399i | ||||
\(575\) | −0.932171 | + | 1.61457i | −0.0388742 | + | 0.0673321i | ||||
\(576\) | 4.19615 | + | 7.26795i | 0.174840 | + | 0.302831i | ||||
\(577\) | 19.1378i | 0.796715i | 0.917230 | + | 0.398358i | \(0.130420\pi\) | ||||
−0.917230 | + | 0.398358i | \(0.869580\pi\) | |||||||
\(578\) | 12.8685 | − | 7.42965i | 0.535260 | − | 0.309033i | ||||
\(579\) | 18.1959 | − | 10.5054i | 0.756197 | − | 0.436590i | ||||
\(580\) | 2.03635i | 0.0845548i | ||||||||
\(581\) | −2.11412 | − | 3.66176i | −0.0877083 | − | 0.151915i | ||||
\(582\) | 7.43317 | − | 12.8746i | 0.308115 | − | 0.533671i | ||||
\(583\) | −28.3923 | − | 16.3923i | −1.17589 | − | 0.678900i | ||||
\(584\) | −13.3944 | −0.554264 | ||||||||
\(585\) | −1.64734 | − | 3.20722i | −0.0681090 | − | 0.132602i | ||||
\(586\) | 5.58355 | 0.230654 | ||||||||
\(587\) | −15.2092 | − | 8.78102i | −0.627750 | − | 0.362432i | 0.152130 | − | 0.988360i | \(-0.451387\pi\) |
−0.779880 | + | 0.625929i | \(0.784720\pi\) | |||||||
\(588\) | 2.42775 | − | 4.20499i | 0.100119 | − | 0.173411i | ||||
\(589\) | −22.3547 | − | 38.7195i | −0.921110 | − | 1.59541i | ||||
\(590\) | − | 13.0330i | − | 0.536559i | ||||||
\(591\) | −17.6475 | + | 10.1888i | −0.725923 | + | 0.419112i | ||||
\(592\) | 6.49161 | − | 3.74793i | 0.266804 | − | 0.154039i | ||||
\(593\) | − | 28.9248i | − | 1.18780i | −0.804538 | − | 0.593901i | \(-0.797587\pi\) | ||
0.804538 | − | 0.593901i | \(-0.202413\pi\) | |||||||
\(594\) | −1.73205 | − | 3.00000i | −0.0710669 | − | 0.123091i | ||||
\(595\) | 0.590973 | − | 1.02359i | 0.0242275 | − | 0.0419633i | ||||
\(596\) | −3.28125 | − | 1.89443i | −0.134405 | − | 0.0775990i | ||||
\(597\) | −14.8014 | −0.605780 | ||||||||
\(598\) | 3.45827 | + | 6.73295i | 0.141419 | + | 0.275331i | ||||
\(599\) | −46.1052 | −1.88381 | −0.941904 | − | 0.335882i | \(-0.890966\pi\) | ||||
−0.941904 | + | 0.335882i | \(0.890966\pi\) | |||||||
\(600\) | 2.66422 | + | 1.53819i | 0.108766 | + | 0.0627963i | ||||
\(601\) | 9.75496 | − | 16.8961i | 0.397913 | − | 0.689206i | −0.595555 | − | 0.803314i | \(-0.703068\pi\) |
0.993468 | + | 0.114109i | \(0.0364012\pi\) | |||||||
\(602\) | −1.70969 | − | 2.96127i | −0.0696817 | − | 0.120692i | ||||
\(603\) | 1.97786i | 0.0805446i | ||||||||
\(604\) | −14.0395 | + | 8.10568i | −0.571257 | + | 0.329815i | ||||
\(605\) | −1.33013 | + | 0.767949i | −0.0540774 | + | 0.0312216i | ||||
\(606\) | 8.85550i | 0.359730i | ||||||||
\(607\) | −12.7126 | − | 22.0189i | −0.515990 | − | 0.893721i | −0.999828 | − | 0.0185635i | \(-0.994091\pi\) |
0.483837 | − | 0.875158i | \(-0.339243\pi\) | |||||||
\(608\) | 9.52706 | − | 16.5014i | 0.386373 | − | 0.669218i | ||||
\(609\) | −1.45991 | − | 0.842882i | −0.0591587 | − | 0.0341553i | ||||
\(610\) | 7.05791 | 0.285767 | ||||||||
\(611\) | 36.7410 | + | 1.80559i | 1.48638 | + | 0.0730463i | ||||
\(612\) | −1.42775 | −0.0577135 | ||||||||
\(613\) | 28.9745 | + | 16.7285i | 1.17027 | + | 0.675656i | 0.953744 | − | 0.300621i | \(-0.0971939\pi\) |
0.216526 | + | 0.976277i | \(0.430527\pi\) | |||||||
\(614\) | −5.40903 | + | 9.36871i | −0.218291 | + | 0.378090i | ||||
\(615\) | −0.535060 | − | 0.926751i | −0.0215757 | − | 0.0373702i | ||||
\(616\) | − | 5.73542i | − | 0.231087i | ||||||
\(617\) | 12.0900 | − | 6.98015i | 0.486724 | − | 0.281010i | −0.236490 | − | 0.971634i | \(-0.575997\pi\) |
0.723214 | + | 0.690624i | \(0.242664\pi\) | |||||||
\(618\) | −14.7350 | + | 8.50726i | −0.592729 | + | 0.342212i | ||||
\(619\) | 42.1677i | 1.69486i | 0.530904 | + | 0.847432i | \(0.321852\pi\) | ||||
−0.530904 | + | 0.847432i | \(0.678148\pi\) | |||||||
\(620\) | −3.35014 | − | 5.80261i | −0.134545 | − | 0.233039i | ||||
\(621\) | −0.932171 | + | 1.61457i | −0.0374067 | + | 0.0647903i | ||||
\(622\) | 25.3928 | + | 14.6605i | 1.01816 | + | 0.587833i | ||||
\(623\) | 9.87765 | 0.395740 | ||||||||
\(624\) | 6.41445 | − | 3.29467i | 0.256783 | − | 0.131892i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.5054 | + | 16.4576i | 1.13931 | + | 0.657778i | ||||
\(627\) | −7.51376 | + | 13.0142i | −0.300071 | + | 0.519737i | ||||
\(628\) | 5.26185 | + | 9.11379i | 0.209971 | + | 0.363680i | ||||
\(629\) | 7.30977i | 0.291460i | ||||||||
\(630\) | −0.590973 | + | 0.341198i | −0.0235449 | + | 0.0135937i | ||||
\(631\) | −34.6143 | + | 19.9846i | −1.37797 | + | 0.795573i | −0.991915 | − | 0.126902i | \(-0.959497\pi\) |
−0.386058 | + | 0.922475i | \(0.626163\pi\) | |||||||
\(632\) | 10.1381i | 0.403271i | ||||||||
\(633\) | 2.61015 | + | 4.52091i | 0.103744 | + | 0.179690i | ||||
\(634\) | 4.85641 | − | 8.41154i | 0.192873 | − | 0.334065i | ||||
\(635\) | −15.6264 | − | 9.02191i | −0.620115 | − | 0.358024i | ||||
\(636\) | 7.80138 | 0.309345 | ||||||||
\(637\) | −20.0988 | − | 12.9595i | −0.796345 | − | 0.513474i | ||||
\(638\) | 9.63611 | 0.381497 | ||||||||
\(639\) | 5.11557 | + | 2.95347i | 0.202369 | + | 0.116838i | ||||
\(640\) | −0.824313 | + | 1.42775i | −0.0325838 | + | 0.0564369i | ||||
\(641\) | −13.3211 | − | 23.0728i | −0.526152 | − | 0.911322i | −0.999536 | − | 0.0304659i | \(-0.990301\pi\) |
0.473384 | − | 0.880856i | \(-0.343032\pi\) | |||||||
\(642\) | − | 9.24134i | − | 0.364727i | ||||||
\(643\) | −14.3921 | + | 8.30927i | −0.567568 | + | 0.327686i | −0.756177 | − | 0.654367i | \(-0.772935\pi\) |
0.188609 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(644\) | −0.716280 | + | 0.413545i | −0.0282254 | + | 0.0162959i | ||||
\(645\) | 5.01084i | 0.197302i | ||||||||
\(646\) | −5.36389 | − | 9.29053i | −0.211039 | − | 0.365531i | ||||
\(647\) | −10.2365 | + | 17.7301i | −0.402437 | + | 0.697042i | −0.994019 | − | 0.109203i | \(-0.965170\pi\) |
0.591582 | + | 0.806245i | \(0.298503\pi\) | |||||||
\(648\) | 2.66422 | + | 1.53819i | 0.104661 | + | 0.0604258i | ||||
\(649\) | 35.6068 | 1.39769 | ||||||||
\(650\) | 2.20012 | − | 3.41216i | 0.0862958 | − | 0.133836i | ||||
\(651\) | 5.54674 | 0.217394 | ||||||||
\(652\) | 6.38420 | + | 3.68592i | 0.250025 | + | 0.144352i | ||||
\(653\) | −2.88370 | + | 4.99471i | −0.112848 | + | 0.195458i | −0.916917 | − | 0.399077i | \(-0.869331\pi\) |
0.804070 | + | 0.594535i | \(0.202664\pi\) | |||||||
\(654\) | 5.96387 | + | 10.3297i | 0.233206 | + | 0.403924i | ||||
\(655\) | − | 1.11899i | − | 0.0437224i | ||||||
\(656\) | 1.85350 | − | 1.07012i | 0.0723671 | − | 0.0417812i | ||||
\(657\) | −3.77063 | + | 2.17698i | −0.147106 | + | 0.0849319i | ||||
\(658\) | − | 6.96209i | − | 0.271410i | ||||||
\(659\) | −15.4749 | − | 26.8034i | −0.602818 | − | 1.04411i | −0.992392 | − | 0.123116i | \(-0.960711\pi\) |
0.389574 | − | 0.920995i | \(-0.372622\pi\) | |||||||
\(660\) | −1.12603 | + | 1.95035i | −0.0438308 | + | 0.0759171i | ||||
\(661\) | 26.7433 | + | 15.4403i | 1.04020 | + | 0.600557i | 0.919889 | − | 0.392180i | \(-0.128279\pi\) |
0.120307 | + | 0.992737i | \(0.461612\pi\) | |||||||
\(662\) | 22.8609 | 0.888513 | ||||||||
\(663\) | −0.345166 | + | 7.02359i | −0.0134051 | + | 0.272774i | ||||
\(664\) | −21.4641 | −0.832969 | ||||||||
\(665\) | 2.56368 | + | 1.48014i | 0.0994152 | + | 0.0573974i | ||||
\(666\) | 2.11015 | − | 3.65488i | 0.0817666 | − | 0.141624i | ||||
\(667\) | −2.59302 | − | 4.49125i | −0.100402 | − | 0.173902i | ||||
\(668\) | 7.93762i | 0.307116i | ||||||||
\(669\) | 5.34065 | − | 3.08342i | 0.206481 | − | 0.119212i | ||||
\(670\) | −1.92875 | + | 1.11357i | −0.0745142 | + | 0.0430208i | ||||
\(671\) | 19.2826i | 0.744396i | ||||||||
\(672\) | 1.18195 | + | 2.04719i | 0.0455945 | + | 0.0789720i | ||||
\(673\) | 11.7540 | − | 20.3585i | 0.453082 | − | 0.784761i | −0.545494 | − | 0.838115i | \(-0.683658\pi\) |
0.998576 | + | 0.0533540i | \(0.0169912\pi\) | |||||||
\(674\) | 17.3432 | + | 10.0131i | 0.668034 | + | 0.385689i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 3.92730 | + | 8.66851i | 0.151050 | + | 0.333404i | ||||
\(677\) | −5.52213 | −0.212233 | −0.106116 | − | 0.994354i | \(-0.533842\pi\) | ||||
−0.106116 | + | 0.994354i | \(0.533842\pi\) | |||||||
\(678\) | −3.37810 | − | 1.95035i | −0.129735 | − | 0.0749026i | ||||
\(679\) | 4.00045 | − | 6.92898i | 0.153523 | − | 0.265910i | ||||
\(680\) | −3.00000 | − | 5.19615i | −0.115045 | − | 0.199263i | ||||
\(681\) | − | 17.1114i | − | 0.655709i | ||||||
\(682\) | −27.4583 | + | 15.8530i | −1.05143 | + | 0.607044i | ||||
\(683\) | −11.6675 | + | 6.73624i | −0.446445 | + | 0.257755i | −0.706328 | − | 0.707885i | \(-0.749649\pi\) |
0.259883 | + | 0.965640i | \(0.416316\pi\) | |||||||
\(684\) | − | 3.57593i | − | 0.136729i | ||||||
\(685\) | 4.35327 | + | 7.54009i | 0.166330 | + | 0.288092i | ||||
\(686\) | −4.65147 | + | 8.05658i | −0.177594 | + | 0.307602i | ||||
\(687\) | 25.0460 | + | 14.4603i | 0.955563 | + | 0.551694i | ||||
\(688\) | −10.0217 | −0.382073 | ||||||||
\(689\) | 1.88602 | − | 38.3776i | 0.0718516 | − | 1.46207i | ||||
\(690\) | −2.09931 | −0.0799193 | ||||||||
\(691\) | −36.8081 | − | 21.2512i | −1.40025 | − | 0.808432i | −0.405828 | − | 0.913950i | \(-0.633017\pi\) |
−0.994417 | + | 0.105518i | \(0.966350\pi\) | |||||||
\(692\) | 9.02701 | − | 15.6352i | 0.343156 | − | 0.594363i | ||||
\(693\) | −0.932171 | − | 1.61457i | −0.0354102 | − | 0.0613323i | ||||
\(694\) | − | 9.67366i | − | 0.367207i | ||||||
\(695\) | −8.36311 | + | 4.82844i | −0.317231 | + | 0.183153i | ||||
\(696\) | −7.41108 | + | 4.27879i | −0.280916 | + | 0.162187i | ||||
\(697\) | 2.08710i | 0.0790547i | ||||||||
\(698\) | 16.9920 | + | 29.4310i | 0.643156 | + | 1.11398i | ||||
\(699\) | −5.66422 | + | 9.81072i | −0.214241 | + | 0.371075i | ||||
\(700\) | 0.384200 | + | 0.221818i | 0.0145214 | + | 0.00838394i | ||||
\(701\) | 0.553573 | 0.0209082 | 0.0104541 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104541 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(702\) | 2.20012 | − | 3.41216i | 0.0830382 | − | 0.128784i | ||||
\(703\) | −18.3079 | −0.690497 | ||||||||
\(704\) | −22.3590 | − | 12.9090i | −0.842685 | − | 0.486524i | ||||
\(705\) | −5.10121 | + | 8.83555i | −0.192123 | + | 0.332766i | ||||
\(706\) | 16.1190 | + | 27.9189i | 0.606646 | + | 1.05074i | ||||
\(707\) | 4.76593i | 0.179241i | ||||||||
\(708\) | −7.33778 | + | 4.23647i | −0.275771 | + | 0.159216i | ||||
\(709\) | −11.2395 | + | 6.48914i | −0.422109 | + | 0.243705i | −0.695979 | − | 0.718062i | \(-0.745029\pi\) |
0.273870 | + | 0.961767i | \(0.411696\pi\) | |||||||
\(710\) | 6.65142i | 0.249623i | ||||||||
\(711\) | 1.64773 | + | 2.85395i | 0.0617947 | + | 0.107032i | ||||
\(712\) | 25.0713 | − | 43.4248i | 0.939588 | − | 1.62741i | ||||
\(713\) | 14.7777 | + | 8.53193i | 0.553431 | + | 0.319523i | ||||
\(714\) | 1.33091 | 0.0498080 | ||||||||
\(715\) | 9.32218 | + | 6.01084i | 0.348630 | + | 0.224793i | ||||
\(716\) | 16.7198 | 0.624850 | ||||||||
\(717\) | −16.5669 | − | 9.56491i | −0.618703 | − | 0.357208i | ||||
\(718\) | −9.83163 | + | 17.0289i | −0.366913 | + | 0.635512i | ||||
\(719\) | −11.2164 | − | 19.4273i | −0.418300 | − | 0.724517i | 0.577468 | − | 0.816413i | \(-0.304041\pi\) |
−0.995769 | + | 0.0918957i | \(0.970707\pi\) | |||||||
\(720\) | 2.00000i | 0.0745356i | ||||||||
\(721\) | −7.93022 | + | 4.57851i | −0.295337 | + | 0.170513i | ||||
\(722\) | 4.74064 | − | 2.73701i | 0.176428 | − | 0.101861i | ||||
\(723\) | − | 5.47415i | − | 0.203586i | ||||||
\(724\) | 6.39140 | + | 11.0702i | 0.237535 | + | 0.411422i | ||||
\(725\) | −1.39085 | + | 2.40903i | −0.0516550 | + | 0.0894690i | ||||
\(726\) | −1.49777 | − | 0.864736i | −0.0555873 | − | 0.0320934i | ||||
\(727\) | 48.3530 | 1.79331 | 0.896657 | − | 0.442725i | \(-0.145988\pi\) | ||||
0.896657 | + | 0.442725i | \(0.145988\pi\) | |||||||
\(728\) | 5.97936 | − | 3.07120i | 0.221610 | − | 0.113826i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.24586 | − | 2.45135i | −0.157146 | − | 0.0907284i | ||||
\(731\) | 4.88643 | − | 8.46355i | 0.180731 | − | 0.313036i | ||||
\(732\) | −2.29423 | − | 3.97372i | −0.0847971 | − | 0.146873i | ||||
\(733\) | 5.72579i | 0.211487i | 0.994393 | + | 0.105743i | \(0.0337222\pi\) | ||||
−0.994393 | + | 0.105743i | \(0.966278\pi\) | |||||||
\(734\) | −31.6898 | + | 18.2961i | −1.16969 | + | 0.675322i | ||||
\(735\) | 5.74412 | − | 3.31637i | 0.211875 | − | 0.122326i | ||||
\(736\) | 7.27222i | 0.268058i | ||||||||
\(737\) | −3.04232 | − | 5.26945i | −0.112065 | − | 0.194103i | ||||
\(738\) | 0.602495 | − | 1.04355i | 0.0221781 | − | 0.0384137i | ||||
\(739\) | −18.0968 | − | 10.4482i | −0.665703 | − | 0.384344i | 0.128743 | − | 0.991678i | \(-0.458906\pi\) |
−0.794447 | + | 0.607334i | \(0.792239\pi\) | |||||||
\(740\) | −2.74368 | −0.100860 | ||||||||
\(741\) | −17.5912 | − | 0.864497i | −0.646229 | − | 0.0317581i | ||||
\(742\) | −7.27222 | −0.266972 | ||||||||
\(743\) | 25.5991 | + | 14.7796i | 0.939139 | + | 0.542212i | 0.889690 | − | 0.456564i | \(-0.150920\pi\) |
0.0494487 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(744\) | 14.0787 | − | 24.3850i | 0.516149 | − | 0.893996i | ||||
\(745\) | −2.58784 | − | 4.48228i | −0.0948112 | − | 0.164218i | ||||
\(746\) | − | 12.1068i | − | 0.443261i | ||||||
\(747\) | −6.04232 | + | 3.48853i | −0.221077 | + | 0.127639i | ||||
\(748\) | 3.80385 | − | 2.19615i | 0.139082 | − | 0.0802993i | ||||
\(749\) | − | 4.97359i | − | 0.181731i | ||||||
\(750\) | 0.563016 | + | 0.975173i | 0.0205584 | + | 0.0356083i | ||||
\(751\) | −10.5234 | + | 18.2270i | −0.384003 | + | 0.665113i | −0.991630 | − | 0.129110i | \(-0.958788\pi\) |
0.607627 | + | 0.794222i | \(0.292121\pi\) | |||||||
\(752\) | −17.6711 | − | 10.2024i | −0.644398 | − | 0.372044i | ||||
\(753\) | 4.71985 | 0.172001 | ||||||||
\(754\) | 5.15994 | + | 10.0460i | 0.187914 | + | 0.365852i | ||||
\(755\) | −22.1451 | −0.805944 | ||||||||
\(756\) | 0.384200 | + | 0.221818i | 0.0139732 | + | 0.00806745i | ||||
\(757\) | −7.04245 | + | 12.1979i | −0.255962 | + | 0.443340i | −0.965156 | − | 0.261674i | \(-0.915726\pi\) |
0.709194 | + | 0.705013i | \(0.249059\pi\) | |||||||
\(758\) | 3.28881 | + | 5.69638i | 0.119455 | + | 0.206902i | ||||
\(759\) | − | 5.73542i | − | 0.208183i | ||||||
\(760\) | 13.0142 | − | 7.51376i | 0.472075 | − | 0.272553i | ||||
\(761\) | −39.3019 | + | 22.6909i | −1.42469 | + | 0.822546i | −0.996695 | − | 0.0812342i | \(-0.974114\pi\) |
−0.427997 | + | 0.903780i | \(0.640780\pi\) | |||||||
\(762\) | − | 20.3179i | − | 0.736041i | ||||||
\(763\) | 3.20969 | + | 5.55934i | 0.116199 | + | 0.201262i | ||||
\(764\) | −2.80872 | + | 4.86484i | −0.101616 | + | 0.176004i | ||||
\(765\) | −1.68905 | − | 0.975173i | −0.0610677 | − | 0.0352574i | ||||
\(766\) | −26.6238 | −0.961957 | ||||||||
\(767\) | 19.0667 | + | 37.1212i | 0.688458 | + | 1.34037i | ||||
\(768\) | 14.9282 | 0.538675 | ||||||||
\(769\) | −38.2583 | − | 22.0885i | −1.37963 | − | 0.796530i | −0.387516 | − | 0.921863i | \(-0.626667\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(770\) | 1.04965 | − | 1.81805i | 0.0378269 | − | 0.0655182i | ||||
\(771\) | −3.63939 | − | 6.30362i | −0.131070 | − | 0.227019i | ||||
\(772\) | − | 15.3810i | − | 0.553574i | ||||||
\(773\) | 30.9568 | − | 17.8729i | 1.11344 | − | 0.642843i | 0.173720 | − | 0.984795i | \(-0.444421\pi\) |
0.939717 | + | 0.341952i | \(0.111088\pi\) | |||||||
\(774\) | −4.88643 | + | 2.82118i | −0.175639 | + | 0.101405i | ||||
\(775\) | − | 9.15276i | − | 0.328777i | ||||||
\(776\) | −20.3078 | − | 35.1741i | −0.729008 | − | 1.26268i | ||||
\(777\) | 1.13566 | − | 1.96702i | 0.0407415 | − | 0.0705664i | ||||
\(778\) | −16.1819 | − | 9.34265i | −0.580151 | − | 0.334950i | ||||
\(779\) | −5.22733 | −0.187289 | ||||||||
\(780\) | −2.63627 | − | 0.129556i | −0.0943934 | − | 0.00463885i | ||||
\(781\) | −18.1720 | −0.650246 | ||||||||
\(782\) | 3.54584 | + | 2.04719i | 0.126799 | + | 0.0732073i | ||||
\(783\) | −1.39085 | + | 2.40903i | −0.0497050 | + | 0.0860916i | ||||
\(784\) | 6.63274 | + | 11.4882i | 0.236884 | + | 0.410294i | ||||
\(785\) | 14.3756i | 0.513088i | ||||||||
\(786\) | 1.09120 | − | 0.630007i | 0.0389220 | − | 0.0224716i | ||||
\(787\) | −8.81782 | + | 5.09097i | −0.314321 | + | 0.181474i | −0.648859 | − | 0.760909i | \(-0.724753\pi\) |
0.334537 | + | 0.942383i | \(0.391420\pi\) | |||||||
\(788\) | 14.9175i | 0.531413i | ||||||||
\(789\) | −0.643362 | − | 1.11434i | −0.0229043 | − | 0.0396714i | ||||
\(790\) | −1.85540 | + | 3.21364i | −0.0660121 | + | 0.114336i | ||||
\(791\) | −1.81805 | − | 1.04965i | −0.0646426 | − | 0.0373214i | ||||
\(792\) | −9.46410 | −0.336292 | ||||||||
\(793\) | −20.1027 | + | 10.3254i | −0.713868 | + | 0.366666i | ||||
\(794\) | −26.3531 | −0.935235 | ||||||||
\(795\) | 9.22913 | + | 5.32844i | 0.327324 | + | 0.188980i | ||||
\(796\) | −5.41768 | + | 9.38370i | −0.192025 | + | 0.332596i | ||||
\(797\) | −18.4428 | − | 31.9438i | −0.653277 | − | 1.13151i | −0.982323 | − | 0.187195i | \(-0.940060\pi\) |
0.329046 | − | 0.944314i | \(-0.393273\pi\) | |||||||
\(798\) | 3.33337i | 0.118000i | ||||||||
\(799\) | 17.2324 | − | 9.94911i | 0.609637 | − | 0.351974i | ||||
\(800\) | 3.37810 | − | 1.95035i | 0.119434 | − | 0.0689551i | ||||
\(801\) | − | 16.2993i | − | 0.575906i | ||||||
\(802\) | 0.0629594 | + | 0.109049i | 0.00222317 | + | 0.00385065i | ||||
\(803\) | 6.69720 | − | 11.5999i | 0.236339 | − | 0.409351i | ||||
\(804\) | 1.25391 | + | 0.723946i | 0.0442221 | + | 0.0255316i | ||||
\(805\) | −1.12983 | −0.0398211 | ||||||||
\(806\) | −31.2306 | − | 20.1372i | −1.10005 | − | 0.709301i | ||||
\(807\) | −18.9390 | −0.666686 | ||||||||
\(808\) | 20.9523 | + | 12.0968i | 0.737101 | + | 0.425565i | ||||
\(809\) | 6.08464 | − | 10.5389i | 0.213924 | − | 0.370528i | −0.739015 | − | 0.673689i | \(-0.764709\pi\) |
0.952939 | + | 0.303161i | \(0.0980420\pi\) | |||||||
\(810\) | 0.563016 | + | 0.975173i | 0.0197824 | + | 0.0342641i | ||||
\(811\) | 26.2312i | 0.921104i | 0.887633 | + | 0.460552i | \(0.152348\pi\) | ||||
−0.887633 | + | 0.460552i | \(0.847652\pi\) | |||||||
\(812\) | −1.06873 | + | 0.617033i | −0.0375051 | + | 0.0216536i | ||||
\(813\) | 9.54719 | − | 5.51207i | 0.334835 | − | 0.193317i | ||||
\(814\) | 12.9832i | 0.455062i | ||||||||
\(815\) | 5.03506 | + | 8.72098i | 0.176370 | + | 0.305483i | ||||
\(816\) | 1.95035 | − | 3.37810i | 0.0682757 | − | 0.118257i | ||||
\(817\) | 21.1977 | + | 12.2385i | 0.741613 | + | 0.428171i | ||||
\(818\) | 21.7104 | 0.759088 | ||||||||
\(819\) | 1.18408 | − | 1.83639i | 0.0413751 | − | 0.0641685i | ||||
\(820\) | −0.783382 | −0.0273569 | ||||||||
\(821\) | 14.3284 | + | 8.27253i | 0.500066 | + | 0.288713i | 0.728741 | − | 0.684790i | \(-0.240106\pi\) |
−0.228675 | + | 0.973503i | \(0.573439\pi\) | |||||||
\(822\) | −4.90192 | + | 8.49038i | −0.170974 | + | 0.296136i | ||||
\(823\) | 13.9646 | + | 24.1873i | 0.486774 | + | 0.843117i | 0.999884 | − | 0.0152057i | \(-0.00484030\pi\) |
−0.513111 | + | 0.858322i | \(0.671507\pi\) | |||||||
\(824\) | 46.4845i | 1.61937i | ||||||||
\(825\) | −2.66422 | + | 1.53819i | −0.0927563 | + | 0.0535529i | ||||
\(826\) | 6.84006 | − | 3.94911i | 0.237996 | − | 0.137407i | ||||
\(827\) | − | 1.83852i | − | 0.0639316i | −0.999489 | − | 0.0319658i | \(-0.989823\pi\) | ||
0.999489 | − | 0.0319658i | \(-0.0101768\pi\) | |||||||
\(828\) | 0.682396 | + | 1.18195i | 0.0237149 | + | 0.0410754i | ||||
\(829\) | −17.4866 | + | 30.2876i | −0.607333 | + | 1.05193i | 0.384345 | + | 0.923190i | \(0.374427\pi\) |
−0.991678 | + | 0.128743i | \(0.958906\pi\) | |||||||
\(830\) | −6.80385 | − | 3.92820i | −0.236165 | − | 0.136350i | ||||
\(831\) | 20.9215 | 0.725758 | ||||||||
\(832\) | 1.48524 | − | 30.2224i | 0.0514915 | − | 1.04777i | ||||
\(833\) | −12.9361 | −0.448211 | ||||||||
\(834\) | −9.41713 | − | 5.43698i | −0.326089 | − | 0.188267i | ||||
\(835\) | −5.42149 | + | 9.39030i | −0.187619 | + | 0.324965i | ||||
\(836\) | 5.50045 | + | 9.52706i | 0.190237 | + | 0.329500i | ||||
\(837\) | − | 9.15276i | − | 0.316366i | ||||||
\(838\) | −21.5889 | + | 12.4644i | −0.745777 | + | 0.430575i | ||||
\(839\) | 11.0093 | − | 6.35624i | 0.380085 | − | 0.219442i | −0.297771 | − | 0.954637i | \(-0.596243\pi\) |
0.677855 | + | 0.735196i | \(0.262910\pi\) | |||||||
\(840\) | 1.86434i | 0.0643259i | ||||||||
\(841\) | 10.6311 | + | 18.4135i | 0.366588 | + | 0.634949i | ||||
\(842\) | −0.515039 | + | 0.892073i | −0.0177494 | + | 0.0307429i | ||||
\(843\) | −9.23642 | − | 5.33265i | −0.318119 | − | 0.183666i | ||||
\(844\) | 3.82152 | 0.131542 | ||||||||
\(845\) | −1.27466 | + | 12.9374i | −0.0438496 | + | 0.445059i | ||||
\(846\) | −11.4882 | −0.394974 | ||||||||
\(847\) | −0.806081 | − | 0.465391i | −0.0276973 | − | 0.0159910i | ||||
\(848\) | −10.6569 | + | 18.4583i | −0.365959 | + | 0.633860i | ||||
\(849\) | −1.39254 | − | 2.41194i | −0.0477917 | − | 0.0827777i | ||||
\(850\) | − | 2.19615i | − | 0.0753274i | ||||||
\(851\) | 6.05129 | − | 3.49372i | 0.207436 | − | 0.119763i | ||||
\(852\) | 3.74486 | − | 2.16209i | 0.128297 | − | 0.0740721i | ||||
\(853\) | 20.2430i | 0.693106i | 0.938030 | + | 0.346553i | \(0.112648\pi\) | ||||
−0.938030 | + | 0.346553i | \(0.887352\pi\) | |||||||
\(854\) | 2.13861 | + | 3.70419i | 0.0731818 | + | 0.126755i | ||||
\(855\) | 2.44240 | − | 4.23037i | 0.0835284 | − | 0.144675i | ||||
\(856\) | −21.8652 | − | 12.6239i | −0.747339 | − | 0.431476i | ||||
\(857\) | −53.5208 | −1.82823 | −0.914117 | − | 0.405450i | \(-0.867115\pi\) | ||||
−0.914117 | + | 0.405450i | \(0.867115\pi\) | |||||||
\(858\) | −0.613065 | + | 12.4749i | −0.0209297 | + | 0.425887i | ||||
\(859\) | −0.969120 | −0.0330659 | −0.0165330 | − | 0.999863i | \(-0.505263\pi\) | ||||
−0.0165330 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(860\) | 3.17674 | + | 1.83409i | 0.108326 | + | 0.0625421i | ||||
\(861\) | 0.324256 | − | 0.561628i | 0.0110506 | − | 0.0191402i | ||||
\(862\) | 20.8187 | + | 36.0590i | 0.709087 | + | 1.22818i | ||||
\(863\) | 5.67766i | 0.193270i | 0.995320 | + | 0.0966349i | \(0.0308079\pi\) | ||||
−0.995320 | + | 0.0966349i | \(0.969192\pi\) | |||||||
\(864\) | 3.37810 | − | 1.95035i | 0.114925 | − | 0.0663521i | ||||
\(865\) | 21.3581 | − | 12.3311i | 0.726199 | − | 0.419271i | ||||
\(866\) | − | 32.3056i | − | 1.09779i | ||||||
\(867\) | −6.59808 | − | 11.4282i | −0.224082 | − | 0.388122i | ||||
\(868\) | 2.03025 | − | 3.51649i | 0.0689111 | − | 0.119357i | ||||
\(869\) | −8.77984 | − | 5.06904i | −0.297836 | − | 0.171955i | ||||
\(870\) | −3.13229 | −0.106195 | ||||||||
\(871\) | 3.86447 | − | 5.99340i | 0.130943 | − | 0.203079i | ||||
\(872\) | 32.5872 | 1.10354 | ||||||||
\(873\) | −11.4336 | − | 6.60121i | −0.386970 | − | 0.223417i | ||||
\(874\) | −5.12736 | + | 8.88085i | −0.173436 | + | 0.300399i | ||||
\(875\) | 0.303009 | + | 0.524827i | 0.0102436 | + | 0.0177424i | ||||
\(876\) | 3.18732i | 0.107689i | ||||||||
\(877\) | −27.9007 | + | 16.1085i | −0.942139 | + | 0.543944i | −0.890630 | − | 0.454728i | \(-0.849736\pi\) |
−0.0515091 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(878\) | 5.13147 | − | 2.96266i | 0.173179 | − | 0.0999848i | ||||
\(879\) | − | 4.95861i | − | 0.167250i | ||||||
\(880\) | −3.07638 | − | 5.32844i | −0.103705 | − | 0.179622i | ||||
\(881\) | 20.5576 | − | 35.6068i | 0.692602 | − | 1.19962i | −0.278380 | − | 0.960471i | \(-0.589797\pi\) |
0.970982 | − | 0.239151i | \(-0.0768692\pi\) | |||||||
\(882\) | 6.46807 | + | 3.73434i | 0.217791 | + | 0.125742i | ||||
\(883\) | 14.6027 | 0.491419 | 0.245709 | − | 0.969344i | \(-0.420979\pi\) | ||||
0.245709 | + | 0.969344i | \(0.420979\pi\) | |||||||
\(884\) | 4.32644 | + | 2.78964i | 0.145514 | + | 0.0938258i | ||||
\(885\) | −11.5742 | −0.389064 | ||||||||
\(886\) | 28.1118 | + | 16.2304i | 0.944435 | + | 0.545270i | ||||
\(887\) | −4.55279 | + | 7.88566i | −0.152868 | + | 0.264775i | −0.932281 | − | 0.361736i | \(-0.882184\pi\) |
0.779413 | + | 0.626511i | \(0.215518\pi\) | |||||||
\(888\) | −5.76503 | − | 9.98533i | −0.193462 | − | 0.335086i | ||||
\(889\) | − | 10.9349i | − | 0.366744i | ||||||
\(890\) | 15.8946 | − | 9.17674i | 0.532788 | − | 0.307605i | ||||
\(891\) | −2.66422 | + | 1.53819i | −0.0892548 | + | 0.0515313i | ||||
\(892\) | − | 4.51445i | − | 0.151155i | ||||||
\(893\) | 24.9184 | + | 43.1599i | 0.833863 | + | 1.44429i | ||||
\(894\) | 2.91400 | − | 5.04719i | 0.0974586 | − | 0.168803i | ||||
\(895\) | 19.7798 | + | 11.4199i | 0.661165 | + | 0.381724i | ||||
\(896\) | −0.999098 | −0.0333775 | ||||||||
\(897\) | 5.97936 | − | 3.07120i | 0.199645 | − | 0.102544i | ||||
\(898\) | 3.38740 | 0.113039 | ||||||||
\(899\) | 22.0492 | + | 12.7301i | 0.735383 | + | 0.424574i | ||||
\(900\) | 0.366025 | − | 0.633975i | 0.0122008 | − | 0.0211325i | ||||
\(901\) | −10.3923 | − | 18.0000i | −0.346218 | − | 0.599667i | ||||
\(902\) | 3.70700i | 0.123430i | ||||||||
\(903\) | −2.62983 | + | 1.51833i | −0.0875151 | + | 0.0505269i | ||||
\(904\) | −9.22913 | + | 5.32844i | −0.306956 | + | 0.177221i | ||||
\(905\) | 17.4616i | 0.580444i | ||||||||
\(906\) | −12.4681 | − | 21.5953i | −0.414224 | − | 0.717457i | ||||
\(907\) | −25.2580 | + | 43.7482i | −0.838679 | + | 1.45263i | 0.0523212 | + | 0.998630i | \(0.483338\pi\) |
−0.891000 | + | 0.454004i | \(0.849995\pi\) | |||||||
\(908\) | −10.8482 | − | 6.26319i | −0.360009 | − | 0.207851i | ||||
\(909\) | 7.86434 | 0.260844 | ||||||||
\(910\) | 2.45745 | + | 0.120768i | 0.0814636 | + | 0.00400343i | ||||
\(911\) | 45.3571 | 1.50275 | 0.751374 | − | 0.659876i | \(-0.229391\pi\) | ||||
0.751374 | + | 0.659876i | \(0.229391\pi\) | |||||||
\(912\) | 8.46073 | + | 4.88481i | 0.280163 | + | 0.161752i | ||||
\(913\) | 10.7321 | − | 18.5885i | 0.355179 | − | 0.615188i | ||||
\(914\) | 5.00342 | + | 8.66617i | 0.165498 | + | 0.286652i | ||||
\(915\) | − | 6.26795i | − | 0.207212i | ||||||
\(916\) | 18.3349 | − | 10.5857i | 0.605803 | − | 0.349760i | ||||
\(917\) | 0.587274 | − | 0.339063i | 0.0193935 | − | 0.0111968i | ||||
\(918\) | − | 2.19615i | − | 0.0724838i | ||||||
\(919\) | −2.15110 | − | 3.72581i | −0.0709582 | − | 0.122903i | 0.828363 | − | 0.560191i | \(-0.189272\pi\) |
−0.899322 | + | 0.437288i | \(0.855939\pi\) | |||||||
\(920\) | −2.86771 | + | 4.96702i | −0.0945456 | + | 0.163758i | ||||
\(921\) | 8.32011 | + | 4.80362i | 0.274157 | + | 0.158285i | ||||
\(922\) | −23.7693 | −0.782800 | ||||||||
\(923\) | −9.73073 | − | 18.9449i | −0.320291 | − | 0.623579i | ||||
\(924\) | −1.36479 | −0.0448984 | ||||||||
\(925\) | −3.24581 | − | 1.87397i | −0.106721 | − | 0.0616157i | ||||
\(926\) | 13.7758 | − | 23.8604i | 0.452702 | − | 0.784102i | ||||
\(927\) | 7.55507 | + | 13.0858i | 0.248141 | + | 0.429793i | ||||
\(928\) | 10.8506i | 0.356188i | ||||||||
\(929\) | 41.9047 | − | 24.1937i | 1.37485 | − | 0.793769i | 0.383315 | − | 0.923618i | \(-0.374783\pi\) |
0.991534 | + | 0.129849i | \(0.0414492\pi\) | |||||||
\(930\) | 8.92552 | − | 5.15315i | 0.292679 | − | 0.168978i | ||||
\(931\) | − | 32.3997i | − | 1.06186i | ||||||
\(932\) | 4.14650 | + | 7.18195i | 0.135823 | + | 0.235252i | ||||
\(933\) | 13.0196 | − | 22.5507i | 0.426243 | − | 0.738275i | ||||
\(934\) | 19.0215 | + | 10.9821i | 0.622404 | + | 0.359345i | ||||
\(935\) | 6.00000 | 0.196221 | ||||||||
\(936\) | −5.06783 | − | 9.86663i | −0.165647 | − | 0.322501i | ||||
\(937\) | 33.9291 | 1.10842 | 0.554208 | − | 0.832378i | \(-0.313021\pi\) | ||||
0.554208 | + | 0.832378i | \(0.313021\pi\) | |||||||
\(938\) | −1.16886 | − | 0.674841i | −0.0381646 | − | 0.0220344i | ||||
\(939\) | 14.6156 | − | 25.3149i | 0.476961 | − | 0.826121i | ||||
\(940\) | 3.73434 | + | 6.46807i | 0.121801 | + | 0.210965i | ||||
\(941\) | − | 8.20272i | − | 0.267401i | −0.991022 | − | 0.133701i | \(-0.957314\pi\) | ||
0.991022 | − | 0.133701i | \(-0.0426860\pi\) | |||||||
\(942\) | −14.0187 | + | 8.09371i | −0.456755 | + | 0.263707i | ||||
\(943\) | 1.72778 | − | 0.997534i | 0.0562643 | − | 0.0324842i | ||||
\(944\) | − | 23.1485i | − | 0.753419i | ||||||
\(945\) | 0.303009 | + | 0.524827i | 0.00985689 | + | 0.0170726i | ||||
\(946\) | 8.67903 | − | 15.0325i | 0.282180 | − | 0.488749i | ||||
\(947\) | −38.9792 | − | 22.5046i | −1.26665 | − | 0.731302i | −0.292300 | − | 0.956327i | \(-0.594421\pi\) |
−0.974353 | + | 0.225024i | \(0.927754\pi\) | |||||||
\(948\) | 2.41245 | 0.0783526 | ||||||||
\(949\) | 15.6795 | + | 0.770548i | 0.508977 | + | 0.0250130i | ||||
\(950\) | 5.50045 | 0.178458 | ||||||||
\(951\) | −7.47007 | − | 4.31285i | −0.242234 | − | 0.139854i | ||||
\(952\) | 1.81805 | − | 3.14896i | 0.0589235 | − | 0.102058i | ||||
\(953\) | 26.5094 | + | 45.9157i | 0.858724 | + | 1.48735i | 0.873146 | + | 0.487458i | \(0.162076\pi\) |
−0.0144217 | + | 0.999896i | \(0.504591\pi\) | |||||||
\(954\) | 12.0000i | 0.388514i | ||||||||
\(955\) | −6.64550 | + | 3.83678i | −0.215043 | + | 0.124155i | ||||
\(956\) | −12.1278 | + | 7.00200i | −0.392242 | + | 0.226461i | ||||
\(957\) | − | 8.55758i | − | 0.276627i | ||||||
\(958\) | 15.2186 | + | 26.3593i | 0.491689 | + | 0.851631i | ||||
\(959\) | −2.63816 | + | 4.56943i | −0.0851907 | + | 0.147555i | ||||
\(960\) | 7.26795 | + | 4.19615i | 0.234572 | + | 0.135430i | ||||
\(961\) | −52.7729 | −1.70235 | ||||||||
\(962\) | −13.5354 | + | 6.95225i | −0.436400 | + | 0.224149i | ||||
\(963\) | −8.20699 | −0.264467 | ||||||||
\(964\) | −3.47047 | − | 2.00368i | −0.111776 | − | 0.0645341i | ||||
\(965\) | 10.5054 | − | 18.1959i | 0.338181 | − | 0.585747i | ||||
\(966\) | −0.636110 | − | 1.10177i | −0.0204665 | − | 0.0354490i | ||||
\(967\) | − | 31.7061i | − | 1.01960i | −0.860293 | − | 0.509799i | \(-0.829720\pi\) | ||
0.860293 | − | 0.509799i | \(-0.170280\pi\) | |||||||
\(968\) | −4.09197 | + | 2.36250i | −0.131521 | + | 0.0759337i | ||||
\(969\) | −8.25068 | + | 4.76353i | −0.265050 | + | 0.153027i | ||||
\(970\) | − | 14.8663i | − | 0.477330i | ||||||
\(971\) | 14.8074 | + | 25.6471i | 0.475191 | + | 0.823054i | 0.999596 | − | 0.0284144i | \(-0.00904580\pi\) |
−0.524406 | + | 0.851469i | \(0.675712\pi\) | |||||||
\(972\) | 0.366025 | − | 0.633975i | 0.0117403 | − | 0.0203347i | ||||
\(973\) | −5.06820 | − | 2.92612i | −0.162479 | − | 0.0938073i | ||||
\(974\) | −5.87508 | −0.188250 | ||||||||
\(975\) | −3.03025 | − | 1.95387i | −0.0970456 | − | 0.0625739i | ||||
\(976\) | 12.5359 | 0.401264 | ||||||||
\(977\) | −1.06633 | − | 0.615644i | −0.0341148 | − | 0.0196962i | 0.482846 | − | 0.875706i | \(-0.339603\pi\) |
−0.516960 | + | 0.856009i | \(0.672937\pi\) | |||||||
\(978\) | −5.66964 | + | 9.82011i | −0.181295 | + | 0.314012i | ||||
\(979\) | 25.0713 | + | 43.4248i | 0.801283 | + | 1.38786i | ||||
\(980\) | − | 4.85550i | − | 0.155103i | ||||||
\(981\) | 9.17356 | − | 5.29636i | 0.292889 | − | 0.169100i | ||||
\(982\) | 14.4147 | − | 8.32234i | 0.459992 | − | 0.265577i | ||||
\(983\) | − | 25.1632i | − | 0.802581i | −0.915951 | − | 0.401290i | \(-0.868562\pi\) | ||
0.915951 | − | 0.401290i | \(-0.131438\pi\) | |||||||
\(984\) | −1.64605 | − | 2.85104i | −0.0524741 | − | 0.0908877i | ||||
\(985\) | −10.1888 | + | 17.6475i | −0.324643 | + | 0.562298i | ||||
\(986\) | 5.29059 | + | 3.05452i | 0.168487 | + | 0.0972759i | ||||
\(987\) | −6.18285 | −0.196802 | ||||||||
\(988\) | −6.98689 | + | 10.8359i | −0.222283 | + | 0.344737i | ||||
\(989\) | −9.34192 | −0.297056 | ||||||||
\(990\) | −3.00000 | − | 1.73205i | −0.0953463 | − | 0.0550482i | ||||
\(991\) | 29.7295 | − | 51.4929i | 0.944387 | − | 1.63573i | 0.187414 | − | 0.982281i | \(-0.439990\pi\) |
0.756974 | − | 0.653445i | \(-0.226677\pi\) | |||||||
\(992\) | −17.8510 | − | 30.9189i | −0.566771 | − | 0.981676i | ||||
\(993\) | − | 20.3021i | − | 0.644269i | ||||||
\(994\) | −3.49084 | + | 2.01544i | −0.110723 | + | 0.0639259i | ||||
\(995\) | −12.8184 | + | 7.40069i | −0.406370 | + | 0.234618i | ||||
\(996\) | 5.10757i | 0.161840i | ||||||||
\(997\) | −18.9610 | − | 32.8413i | −0.600499 | − | 1.04010i | −0.992745 | − | 0.120235i | \(-0.961635\pi\) |
0.392246 | − | 0.919860i | \(-0.371698\pi\) | |||||||
\(998\) | 5.80872 | − | 10.0610i | 0.183872 | − | 0.318475i | ||||
\(999\) | −3.24581 | − | 1.87397i | −0.102693 | − | 0.0592897i |
(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 | 195.2.bb.b.121.3 | ✓ | 8 | |
3.2 | odd | 2 | 585.2.bu.d.316.2 | 8 | |||
5.2 | odd | 4 | 975.2.w.i.199.2 | 8 | |||
5.3 | odd | 4 | 975.2.w.h.199.3 | 8 | |||
5.4 | even | 2 | 975.2.bc.j.901.2 | 8 | |||
13.6 | odd | 12 | 2535.2.a.bj.1.2 | 4 | |||
13.7 | odd | 12 | 2535.2.a.bk.1.3 | 4 | |||
13.10 | even | 6 | inner | 195.2.bb.b.166.3 | yes | 8 | |
39.20 | even | 12 | 7605.2.a.ch.1.2 | 4 | |||
39.23 | odd | 6 | 585.2.bu.d.361.2 | 8 | |||
39.32 | even | 12 | 7605.2.a.ci.1.3 | 4 | |||
65.23 | odd | 12 | 975.2.w.i.49.2 | 8 | |||
65.49 | even | 6 | 975.2.bc.j.751.2 | 8 | |||
65.62 | odd | 12 | 975.2.w.h.49.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.bb.b.121.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
195.2.bb.b.166.3 | yes | 8 | 13.10 | even | 6 | inner | |
585.2.bu.d.316.2 | 8 | 3.2 | odd | 2 | |||
585.2.bu.d.361.2 | 8 | 39.23 | odd | 6 | |||
975.2.w.h.49.3 | 8 | 65.62 | odd | 12 | |||
975.2.w.h.199.3 | 8 | 5.3 | odd | 4 | |||
975.2.w.i.49.2 | 8 | 65.23 | odd | 12 | |||
975.2.w.i.199.2 | 8 | 5.2 | odd | 4 | |||
975.2.bc.j.751.2 | 8 | 65.49 | even | 6 | |||
975.2.bc.j.901.2 | 8 | 5.4 | even | 2 | |||
2535.2.a.bj.1.2 | 4 | 13.6 | odd | 12 | |||
2535.2.a.bk.1.3 | 4 | 13.7 | odd | 12 | |||
7605.2.a.ch.1.2 | 4 | 39.20 | even | 12 | |||
7605.2.a.ci.1.3 | 4 | 39.32 | even | 12 |