Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.257 |
Dual form | 450.2.p.a.443.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | − | 0.258819i | −0.683013 | − | 0.183013i | ||||
\(3\) | 1.33195 | + | 1.10721i | 0.769002 | + | 0.639246i | ||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 1.41421i | −0.408248 | − | 0.577350i | ||||
\(7\) | −0.283763 | + | 1.05902i | −0.107252 | + | 0.400271i | −0.998591 | − | 0.0530669i | \(-0.983100\pi\) |
0.891339 | + | 0.453338i | \(0.149767\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0.548188 | + | 2.94949i | 0.182729 | + | 0.983163i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.44949 | + | 3.14626i | −1.64308 | + | 0.948634i | −0.663354 | + | 0.748305i | \(0.730868\pi\) |
−0.979729 | + | 0.200329i | \(0.935799\pi\) | |||||||
\(12\) | 0.599900 | + | 1.62484i | 0.173176 | + | 0.469052i | ||||
\(13\) | 0.896575 | + | 3.34607i | 0.248665 | + | 0.928032i | 0.971506 | + | 0.237016i | \(0.0761695\pi\) |
−0.722840 | + | 0.691015i | \(0.757164\pi\) | |||||||
\(14\) | 0.548188 | − | 0.949490i | 0.146509 | − | 0.253762i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 3.14626 | − | 3.14626i | 0.763081 | − | 0.763081i | −0.213797 | − | 0.976878i | \(-0.568583\pi\) |
0.976878 | + | 0.213797i | \(0.0685831\pi\) | |||||||
\(18\) | 0.233875 | − | 2.99087i | 0.0551249 | − | 0.704955i | ||||
\(19\) | 1.55051i | 0.355711i | 0.984057 | + | 0.177856i | \(0.0569160\pi\) | ||||
−0.984057 | + | 0.177856i | \(0.943084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.55051 | + | 1.09638i | −0.338349 | + | 0.239249i | ||||
\(22\) | 6.07812 | − | 1.62863i | 1.29586 | − | 0.347224i | ||||
\(23\) | −0.965926 | + | 0.258819i | −0.201409 | + | 0.0539675i | −0.358113 | − | 0.933678i | \(-0.616580\pi\) |
0.156704 | + | 0.987646i | \(0.449913\pi\) | |||||||
\(24\) | −0.158919 | − | 1.72474i | −0.0324391 | − | 0.352062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | −2.53553 | + | 4.53553i | −0.487964 | + | 0.872864i | ||||
\(28\) | −0.775255 | + | 0.775255i | −0.146509 | + | 0.146509i | ||||
\(29\) | 1.57313 | + | 2.72474i | 0.292123 | + | 0.505972i | 0.974312 | − | 0.225204i | \(-0.0723049\pi\) |
−0.682188 | + | 0.731177i | \(0.738972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.22474 | − | 3.85337i | 0.399576 | − | 0.692086i | −0.594098 | − | 0.804393i | \(-0.702491\pi\) |
0.993674 | + | 0.112307i | \(0.0358240\pi\) | |||||||
\(32\) | −0.258819 | − | 0.965926i | −0.0457532 | − | 0.170753i | ||||
\(33\) | −10.7420 | − | 1.84304i | −1.86995 | − | 0.320832i | ||||
\(34\) | −3.85337 | + | 2.22474i | −0.660848 | + | 0.381541i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 0.401302 | − | 1.49768i | 0.0650997 | − | 0.242955i | ||||
\(39\) | −2.51059 | + | 5.44949i | −0.402016 | + | 0.872617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.39898 | − | 1.96240i | −0.530831 | − | 0.306476i | 0.210524 | − | 0.977589i | \(-0.432483\pi\) |
−0.741355 | + | 0.671113i | \(0.765816\pi\) | |||||||
\(42\) | 1.78144 | − | 0.657717i | 0.274882 | − | 0.101488i | ||||
\(43\) | 3.34607 | + | 0.896575i | 0.510270 | + | 0.136726i | 0.504762 | − | 0.863258i | \(-0.331580\pi\) |
0.00550783 | + | 0.999985i | \(0.498247\pi\) | |||||||
\(44\) | −6.29253 | −0.948634 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −8.69333 | − | 2.32937i | −1.26805 | − | 0.339774i | −0.438768 | − | 0.898600i | \(-0.644585\pi\) |
−0.829285 | + | 0.558827i | \(0.811252\pi\) | |||||||
\(48\) | −0.292893 | + | 1.70711i | −0.0422755 | + | 0.246400i | ||||
\(49\) | 5.02118 | + | 2.89898i | 0.717311 | + | 0.414140i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.67423 | − | 0.707107i | 1.07461 | − | 0.0990148i | ||||
\(52\) | −0.896575 | + | 3.34607i | −0.124333 | + | 0.464016i | ||||
\(53\) | 6.61037 | + | 6.61037i | 0.908004 | + | 0.908004i | 0.996111 | − | 0.0881074i | \(-0.0280819\pi\) |
−0.0881074 | + | 0.996111i | \(0.528082\pi\) | |||||||
\(54\) | 3.62302 | − | 3.72474i | 0.493031 | − | 0.506874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.949490 | − | 0.548188i | 0.126881 | − | 0.0732547i | ||||
\(57\) | −1.71673 | + | 2.06520i | −0.227387 | + | 0.273543i | ||||
\(58\) | −0.814313 | − | 3.03906i | −0.106925 | − | 0.399048i | ||||
\(59\) | 5.90326 | − | 10.2247i | 0.768539 | − | 1.33115i | −0.169816 | − | 0.985476i | \(-0.554317\pi\) |
0.938355 | − | 0.345673i | \(-0.112349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.72474 | + | 4.71940i | 0.348868 | + | 0.604257i | 0.986049 | − | 0.166458i | \(-0.0532329\pi\) |
−0.637181 | + | 0.770714i | \(0.719900\pi\) | |||||||
\(62\) | −3.14626 | + | 3.14626i | −0.399576 | + | 0.399576i | ||||
\(63\) | −3.27912 | − | 0.256415i | −0.413130 | − | 0.0323053i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.89898 | + | 4.56048i | 1.21848 | + | 0.561356i | ||||
\(67\) | 3.65307 | − | 0.978838i | 0.446294 | − | 0.119584i | −0.0286709 | − | 0.999589i | \(-0.509127\pi\) |
0.474965 | + | 0.880005i | \(0.342461\pi\) | |||||||
\(68\) | 4.29788 | − | 1.15161i | 0.521194 | − | 0.139654i | ||||
\(69\) | −1.57313 | − | 0.724745i | −0.189383 | − | 0.0872490i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.635674i | − | 0.0754407i | −0.999288 | − | 0.0377203i | \(-0.987990\pi\) | ||
0.999288 | − | 0.0377203i | \(-0.0120096\pi\) | |||||||
\(72\) | 1.69798 | − | 2.47323i | 0.200108 | − | 0.291473i | ||||
\(73\) | −2.89898 | + | 2.89898i | −0.339300 | + | 0.339300i | −0.856104 | − | 0.516804i | \(-0.827122\pi\) |
0.516804 | + | 0.856104i | \(0.327122\pi\) | |||||||
\(74\) | −2.12132 | − | 3.67423i | −0.246598 | − | 0.427121i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.775255 | + | 1.34278i | −0.0889279 | + | 0.154028i | ||||
\(77\) | −1.78559 | − | 6.66390i | −0.203487 | − | 0.759422i | ||||
\(78\) | 3.83548 | − | 4.61401i | 0.434282 | − | 0.522434i | ||||
\(79\) | −2.12132 | + | 1.22474i | −0.238667 | + | 0.137795i | −0.614564 | − | 0.788867i | \(-0.710668\pi\) |
0.375897 | + | 0.926662i | \(0.377335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.39898 | + | 3.23375i | −0.933220 | + | 0.359306i | ||||
\(82\) | 2.77526 | + | 2.77526i | 0.306476 | + | 0.306476i | ||||
\(83\) | 0.142483 | − | 0.531752i | 0.0156395 | − | 0.0583674i | −0.957665 | − | 0.287885i | \(-0.907048\pi\) |
0.973305 | + | 0.229517i | \(0.0737147\pi\) | |||||||
\(84\) | −1.89097 | + | 0.174235i | −0.206322 | + | 0.0190106i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.00000 | − | 1.73205i | −0.323498 | − | 0.186772i | ||||
\(87\) | −0.921519 | + | 5.37101i | −0.0987973 | + | 0.575833i | ||||
\(88\) | 6.07812 | + | 1.62863i | 0.647929 | + | 0.173612i | ||||
\(89\) | 2.36773 | 0.250978 | 0.125489 | − | 0.992095i | \(-0.459950\pi\) | ||||
0.125489 | + | 0.992095i | \(0.459950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.79796 | −0.398134 | ||||||||
\(92\) | −0.965926 | − | 0.258819i | −0.100705 | − | 0.0269838i | ||||
\(93\) | 7.22973 | − | 2.66925i | 0.749688 | − | 0.276788i | ||||
\(94\) | 7.79423 | + | 4.50000i | 0.803913 | + | 0.464140i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.724745 | − | 1.57313i | 0.0739690 | − | 0.160557i | ||||
\(97\) | 2.89123 | − | 10.7902i | 0.293560 | − | 1.09558i | −0.648795 | − | 0.760963i | \(-0.724727\pi\) |
0.942355 | − | 0.334616i | \(-0.108607\pi\) | |||||||
\(98\) | −4.09978 | − | 4.09978i | −0.414140 | − | 0.414140i | ||||
\(99\) | −12.2672 | − | 14.3485i | −1.23290 | − | 1.44208i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.10102 | − | 0.635674i | 0.109556 | − | 0.0632520i | −0.444221 | − | 0.895917i | \(-0.646519\pi\) |
0.553777 | + | 0.832665i | \(0.313186\pi\) | |||||||
\(102\) | −7.59575 | − | 1.30323i | −0.752092 | − | 0.129039i | ||||
\(103\) | −1.06110 | − | 3.96008i | −0.104553 | − | 0.390198i | 0.893741 | − | 0.448584i | \(-0.148071\pi\) |
−0.998294 | + | 0.0583855i | \(0.981405\pi\) | |||||||
\(104\) | 1.73205 | − | 3.00000i | 0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.67423 | − | 8.09601i | −0.454002 | − | 0.786354i | ||||
\(107\) | 3.71051 | − | 3.71051i | 0.358708 | − | 0.358708i | −0.504628 | − | 0.863337i | \(-0.668370\pi\) |
0.863337 | + | 0.504628i | \(0.168370\pi\) | |||||||
\(108\) | −4.46360 | + | 2.66012i | −0.429510 | + | 0.255970i | ||||
\(109\) | − | 20.3485i | − | 1.94903i | −0.224323 | − | 0.974515i | \(-0.572017\pi\) | ||
0.224323 | − | 0.974515i | \(-0.427983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.674235 | + | 7.31747i | 0.0639955 | + | 0.694544i | ||||
\(112\) | −1.05902 | + | 0.283763i | −0.100068 | + | 0.0268131i | ||||
\(113\) | 13.3278 | − | 3.57117i | 1.25377 | − | 0.335948i | 0.429981 | − | 0.902838i | \(-0.358520\pi\) |
0.823793 | + | 0.566890i | \(0.191854\pi\) | |||||||
\(114\) | 2.19275 | − | 1.55051i | 0.205370 | − | 0.145219i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.14626i | 0.292123i | ||||||||
\(117\) | −9.37769 | + | 4.47871i | −0.866968 | + | 0.414057i | ||||
\(118\) | −8.34847 | + | 8.34847i | −0.768539 | + | 0.768539i | ||||
\(119\) | 2.43916 | + | 4.22474i | 0.223597 | + | 0.387282i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.2980 | − | 24.7648i | 1.29981 | − | 2.25134i | ||||
\(122\) | −1.41043 | − | 5.26380i | −0.127694 | − | 0.476562i | ||||
\(123\) | −2.35449 | − | 6.37720i | −0.212297 | − | 0.575012i | ||||
\(124\) | 3.85337 | − | 2.22474i | 0.346043 | − | 0.199788i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.10102 | + | 1.09638i | 0.276261 | + | 0.0976730i | ||||
\(127\) | −14.1237 | − | 14.1237i | −1.25328 | − | 1.25328i | −0.954242 | − | 0.299036i | \(-0.903335\pi\) |
−0.299036 | − | 0.954242i | \(-0.596665\pi\) | |||||||
\(128\) | 0.258819 | − | 0.965926i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | 3.46410 | + | 4.89898i | 0.304997 | + | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12372 | + | 5.26758i | 0.797143 | + | 0.460231i | 0.842471 | − | 0.538741i | \(-0.181100\pi\) |
−0.0453278 | + | 0.998972i | \(0.514433\pi\) | |||||||
\(132\) | −8.38134 | − | 6.96713i | −0.729502 | − | 0.606411i | ||||
\(133\) | −1.64202 | − | 0.439978i | −0.142381 | − | 0.0381509i | ||||
\(134\) | −3.78194 | −0.326710 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.44949 | −0.381541 | ||||||||
\(137\) | 2.12701 | + | 0.569930i | 0.181723 | + | 0.0486924i | 0.348533 | − | 0.937297i | \(-0.386680\pi\) |
−0.166810 | + | 0.985989i | \(0.553347\pi\) | |||||||
\(138\) | 1.33195 | + | 1.10721i | 0.113383 | + | 0.0942517i | ||||
\(139\) | −11.1708 | − | 6.44949i | −0.947499 | − | 0.547039i | −0.0551956 | − | 0.998476i | \(-0.517578\pi\) |
−0.892303 | + | 0.451437i | \(0.850912\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | − | 12.7279i | −0.757937 | − | 1.07188i | ||||
\(142\) | −0.164525 | + | 0.614014i | −0.0138066 | + | 0.0515269i | ||||
\(143\) | −15.4135 | − | 15.4135i | −1.28894 | − | 1.28894i | ||||
\(144\) | −2.28024 | + | 1.94949i | −0.190020 | + | 0.162457i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.55051 | − | 2.04989i | 0.293842 | − | 0.169650i | ||||
\(147\) | 3.47820 | + | 9.42078i | 0.286877 | + | 0.777013i | ||||
\(148\) | 1.09808 | + | 4.09808i | 0.0902613 | + | 0.336860i | ||||
\(149\) | −6.45145 | + | 11.1742i | −0.528523 | + | 0.915429i | 0.470924 | + | 0.882174i | \(0.343921\pi\) |
−0.999447 | + | 0.0332550i | \(0.989413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7980 | + | 18.7026i | 0.878725 | + | 1.52200i | 0.852741 | + | 0.522335i | \(0.174939\pi\) |
0.0259849 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(152\) | 1.09638 | − | 1.09638i | 0.0889279 | − | 0.0889279i | ||||
\(153\) | 11.0046 | + | 7.55513i | 0.889671 | + | 0.610796i | ||||
\(154\) | 6.89898i | 0.555936i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.89898 | + | 3.46410i | −0.392232 | + | 0.277350i | ||||
\(157\) | 5.94012 | − | 1.59165i | 0.474073 | − | 0.127028i | −0.0138684 | − | 0.999904i | \(-0.504415\pi\) |
0.487942 | + | 0.872876i | \(0.337748\pi\) | |||||||
\(158\) | 2.36603 | − | 0.633975i | 0.188231 | − | 0.0504363i | ||||
\(159\) | 1.48565 | + | 16.1237i | 0.117819 | + | 1.27869i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.09638i | − | 0.0864066i | ||||||
\(162\) | 8.94975 | − | 0.949747i | 0.703159 | − | 0.0746192i | ||||
\(163\) | 0.449490 | − | 0.449490i | 0.0352068 | − | 0.0352068i | −0.689284 | − | 0.724491i | \(-0.742075\pi\) |
0.724491 | + | 0.689284i | \(0.242075\pi\) | |||||||
\(164\) | −1.96240 | − | 3.39898i | −0.153238 | − | 0.265416i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.275255 | + | 0.476756i | −0.0213639 | + | 0.0370034i | ||||
\(167\) | 2.79472 | + | 10.4300i | 0.216262 | + | 0.807100i | 0.985719 | + | 0.168401i | \(0.0538603\pi\) |
−0.769457 | + | 0.638699i | \(0.779473\pi\) | |||||||
\(168\) | 1.87163 | + | 0.321121i | 0.144400 | + | 0.0247750i | ||||
\(169\) | 0.866025 | − | 0.500000i | 0.0666173 | − | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.57321 | + | 0.849971i | −0.349722 | + | 0.0649989i | ||||
\(172\) | 2.44949 | + | 2.44949i | 0.186772 | + | 0.186772i | ||||
\(173\) | −0.802603 | + | 2.99536i | −0.0610208 | + | 0.227733i | −0.989701 | − | 0.143148i | \(-0.954277\pi\) |
0.928680 | + | 0.370881i | \(0.120944\pi\) | |||||||
\(174\) | 2.28024 | − | 4.94949i | 0.172864 | − | 0.375220i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.44949 | − | 3.14626i | −0.410771 | − | 0.237159i | ||||
\(177\) | 19.1838 | − | 7.08274i | 1.44194 | − | 0.532371i | ||||
\(178\) | −2.28705 | − | 0.612812i | −0.171421 | − | 0.0459322i | ||||
\(179\) | 17.6062 | 1.31595 | 0.657976 | − | 0.753039i | \(-0.271413\pi\) | ||||
0.657976 | + | 0.753039i | \(0.271413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5505 | −0.784213 | −0.392107 | − | 0.919920i | \(-0.628254\pi\) | ||||
−0.392107 | + | 0.919920i | \(0.628254\pi\) | |||||||
\(182\) | 3.66855 | + | 0.982984i | 0.271931 | + | 0.0728636i | ||||
\(183\) | −1.59612 | + | 9.30286i | −0.117988 | + | 0.687687i | ||||
\(184\) | 0.866025 | + | 0.500000i | 0.0638442 | + | 0.0368605i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.67423 | + | 0.707107i | −0.562702 | + | 0.0518476i | ||||
\(187\) | −7.24656 | + | 27.0445i | −0.529921 | + | 1.97769i | ||||
\(188\) | −6.36396 | − | 6.36396i | −0.464140 | − | 0.464140i | ||||
\(189\) | −4.08372 | − | 3.97219i | −0.297047 | − | 0.288935i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.87628 | + | 1.66062i | −0.208120 | + | 0.120158i | −0.600437 | − | 0.799672i | \(-0.705007\pi\) |
0.392317 | + | 0.919830i | \(0.371673\pi\) | |||||||
\(192\) | −1.10721 | + | 1.33195i | −0.0799057 | + | 0.0961253i | ||||
\(193\) | −4.48288 | − | 16.7303i | −0.322685 | − | 1.20428i | −0.916619 | − | 0.399762i | \(-0.869093\pi\) |
0.593934 | − | 0.804513i | \(-0.297574\pi\) | |||||||
\(194\) | −5.58542 | + | 9.67423i | −0.401010 | + | 0.694570i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.89898 | + | 5.02118i | 0.207070 | + | 0.358656i | ||||
\(197\) | 6.92820 | − | 6.92820i | 0.493614 | − | 0.493614i | −0.415829 | − | 0.909443i | \(-0.636508\pi\) |
0.909443 | + | 0.415829i | \(0.136508\pi\) | |||||||
\(198\) | 8.13557 | + | 17.0345i | 0.578170 | + | 1.21059i | ||||
\(199\) | 3.55051i | 0.251689i | 0.992050 | + | 0.125844i | \(0.0401640\pi\) | ||||
−0.992050 | + | 0.125844i | \(0.959836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.94949 | + | 2.74094i | 0.419645 | + | 0.193331i | ||||
\(202\) | −1.22803 | + | 0.329049i | −0.0864038 | + | 0.0231518i | ||||
\(203\) | −3.33195 | + | 0.892794i | −0.233857 | + | 0.0626618i | ||||
\(204\) | 6.99964 | + | 3.22474i | 0.490073 | + | 0.225777i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.09978i | 0.285645i | ||||||||
\(207\) | −1.29289 | − | 2.70711i | −0.0898623 | − | 0.188157i | ||||
\(208\) | −2.44949 | + | 2.44949i | −0.169842 | + | 0.169842i | ||||
\(209\) | −4.87832 | − | 8.44949i | −0.337440 | − | 0.584463i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.44949 | + | 16.3670i | −0.650530 | + | 1.12675i | 0.332465 | + | 0.943116i | \(0.392120\pi\) |
−0.982995 | + | 0.183635i | \(0.941214\pi\) | |||||||
\(212\) | 2.41956 | + | 9.02993i | 0.166176 | + | 0.620178i | ||||
\(213\) | 0.703823 | − | 0.846687i | 0.0482251 | − | 0.0580141i | ||||
\(214\) | −4.54442 | + | 2.62372i | −0.310650 | + | 0.179354i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | − | 1.41421i | 0.340207 | − | 0.0962250i | ||||
\(217\) | 3.44949 | + | 3.44949i | 0.234167 | + | 0.234167i | ||||
\(218\) | −5.26657 | + | 19.6551i | −0.356697 | + | 1.33121i | ||||
\(219\) | −7.07107 | + | 0.651531i | −0.477818 | + | 0.0440264i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.3485 | + | 7.70674i | 0.897915 | + | 0.518412i | ||||
\(222\) | 1.24264 | − | 7.24264i | 0.0834006 | − | 0.486094i | ||||
\(223\) | 8.02714 | + | 2.15087i | 0.537537 | + | 0.144033i | 0.517367 | − | 0.855764i | \(-0.326912\pi\) |
0.0201706 | + | 0.999797i | \(0.493579\pi\) | |||||||
\(224\) | 1.09638 | 0.0732547 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7980 | −0.917827 | ||||||||
\(227\) | 14.5865 | + | 3.90843i | 0.968138 | + | 0.259412i | 0.708041 | − | 0.706171i | \(-0.249579\pi\) |
0.260096 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(228\) | −2.51934 | + | 0.930152i | −0.166847 | + | 0.0616008i | ||||
\(229\) | 14.1582 | + | 8.17423i | 0.935600 | + | 0.540169i | 0.888578 | − | 0.458725i | \(-0.151694\pi\) |
0.0470214 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.00000 | − | 10.8530i | 0.328976 | − | 0.714075i | ||||
\(232\) | 0.814313 | − | 3.03906i | 0.0534623 | − | 0.199524i | ||||
\(233\) | 10.9959 | + | 10.9959i | 0.720363 | + | 0.720363i | 0.968679 | − | 0.248316i | \(-0.0798770\pi\) |
−0.248316 | + | 0.968679i | \(0.579877\pi\) | |||||||
\(234\) | 10.2173 | − | 1.89898i | 0.667928 | − | 0.124140i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.2247 | − | 5.90326i | 0.665574 | − | 0.384269i | ||||
\(237\) | −4.18154 | − | 0.717439i | −0.271620 | − | 0.0466027i | ||||
\(238\) | −1.26260 | − | 4.71209i | −0.0818423 | − | 0.305439i | ||||
\(239\) | −8.48528 | + | 14.6969i | −0.548867 | + | 0.950666i | 0.449485 | + | 0.893288i | \(0.351607\pi\) |
−0.998353 | + | 0.0573782i | \(0.981726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | − | 16.4545i | −0.611949 | − | 1.05993i | −0.990912 | − | 0.134515i | \(-0.957053\pi\) |
0.378963 | − | 0.925412i | \(-0.376281\pi\) | |||||||
\(242\) | −20.2204 | + | 20.2204i | −1.29981 | + | 1.29981i | ||||
\(243\) | −14.7675 | − | 4.99221i | −0.947333 | − | 0.320250i | ||||
\(244\) | 5.44949i | 0.348868i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.623724 | + | 6.76928i | 0.0397672 | + | 0.431594i | ||||
\(247\) | −5.18811 | + | 1.39015i | −0.330111 | + | 0.0884531i | ||||
\(248\) | −4.29788 | + | 1.15161i | −0.272915 | + | 0.0731275i | ||||
\(249\) | 0.778539 | − | 0.550510i | 0.0493379 | − | 0.0348872i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.1708i | − | 0.705097i | −0.935793 | − | 0.352549i | \(-0.885315\pi\) | ||
0.935793 | − | 0.352549i | \(-0.114685\pi\) | |||||||
\(252\) | −2.71159 | − | 1.86162i | −0.170814 | − | 0.117271i | ||||
\(253\) | 4.44949 | − | 4.44949i | 0.279737 | − | 0.279737i | ||||
\(254\) | 9.98698 | + | 17.2980i | 0.626639 | + | 1.08537i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.74105 | + | 25.1579i | 0.420495 | + | 1.56931i | 0.773568 | + | 0.633713i | \(0.218470\pi\) |
−0.353073 | + | 0.935596i | \(0.614863\pi\) | |||||||
\(258\) | −2.07812 | − | 5.62863i | −0.129378 | − | 0.350423i | ||||
\(259\) | −4.02834 | + | 2.32577i | −0.250309 | + | 0.144516i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.17423 | + | 6.13361i | −0.444074 | + | 0.379661i | ||||
\(262\) | −7.44949 | − | 7.44949i | −0.460231 | − | 0.460231i | ||||
\(263\) | −3.28621 | + | 12.2643i | −0.202636 | + | 0.756249i | 0.787521 | + | 0.616288i | \(0.211364\pi\) |
−0.990157 | + | 0.139961i | \(0.955302\pi\) | |||||||
\(264\) | 6.29253 | + | 8.89898i | 0.387278 | + | 0.547694i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.47219 | + | 0.849971i | 0.0902660 | + | 0.0521151i | ||||
\(267\) | 3.15369 | + | 2.62156i | 0.193003 | + | 0.160437i | ||||
\(268\) | 3.65307 | + | 0.978838i | 0.223147 | + | 0.0597920i | ||||
\(269\) | −4.70334 | −0.286768 | −0.143384 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143384 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0454 | −0.974689 | −0.487345 | − | 0.873210i | \(-0.662034\pi\) | ||||
−0.487345 | + | 0.873210i | \(0.662034\pi\) | |||||||
\(272\) | 4.29788 | + | 1.15161i | 0.260597 | + | 0.0698268i | ||||
\(273\) | −5.05870 | − | 4.20512i | −0.306166 | − | 0.254506i | ||||
\(274\) | −1.90702 | − | 1.10102i | −0.115208 | − | 0.0665151i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | − | 1.41421i | −0.0601929 | − | 0.0851257i | ||||
\(277\) | 3.69723 | − | 13.7983i | 0.222145 | − | 0.829057i | −0.761383 | − | 0.648302i | \(-0.775479\pi\) |
0.983528 | − | 0.180754i | \(-0.0578539\pi\) | |||||||
\(278\) | 9.12096 | + | 9.12096i | 0.547039 | + | 0.547039i | ||||
\(279\) | 12.5851 | + | 4.44949i | 0.753448 | + | 0.266384i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.151531 | + | 0.0874863i | −0.00903957 | + | 0.00521900i | −0.504513 | − | 0.863404i | \(-0.668328\pi\) |
0.495473 | + | 0.868623i | \(0.334995\pi\) | |||||||
\(282\) | 5.39910 | + | 14.6236i | 0.321512 | + | 0.870823i | ||||
\(283\) | −1.78484 | − | 6.66112i | −0.106098 | − | 0.395962i | 0.892370 | − | 0.451305i | \(-0.149041\pi\) |
−0.998467 | + | 0.0553430i | \(0.982375\pi\) | |||||||
\(284\) | 0.317837 | − | 0.550510i | 0.0188602 | − | 0.0326668i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8990 | + | 18.8776i | 0.644470 | + | 1.11626i | ||||
\(287\) | 3.04272 | − | 3.04272i | 0.179606 | − | 0.179606i | ||||
\(288\) | 2.70711 | − | 1.29289i | 0.159518 | − | 0.0761845i | ||||
\(289\) | − | 2.79796i | − | 0.164586i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.7980 | − | 11.1708i | 0.926093 | − | 0.654846i | ||||
\(292\) | −3.96008 | + | 1.06110i | −0.231746 | + | 0.0620962i | ||||
\(293\) | −21.2942 | + | 5.70577i | −1.24402 | + | 0.333335i | −0.820024 | − | 0.572329i | \(-0.806040\pi\) |
−0.423998 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(294\) | −0.921404 | − | 10.0000i | −0.0537374 | − | 0.583212i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | −0.452623 | − | 32.6938i | −0.0262638 | − | 1.89709i | ||||
\(298\) | 9.12372 | − | 9.12372i | 0.528523 | − | 0.528523i | ||||
\(299\) | −1.73205 | − | 3.00000i | −0.100167 | − | 0.173494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89898 | + | 3.28913i | −0.109455 | + | 0.189582i | ||||
\(302\) | −5.58943 | − | 20.8601i | −0.321636 | − | 1.20036i | ||||
\(303\) | 2.17033 | + | 0.372369i | 0.124682 | + | 0.0213921i | ||||
\(304\) | −1.34278 | + | 0.775255i | −0.0770138 | + | 0.0444639i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.67423 | − | 10.1459i | −0.495873 | − | 0.580002i | ||||
\(307\) | −0.674235 | − | 0.674235i | −0.0384806 | − | 0.0384806i | 0.687605 | − | 0.726085i | \(-0.258662\pi\) |
−0.726085 | + | 0.687605i | \(0.758662\pi\) | |||||||
\(308\) | 1.78559 | − | 6.66390i | 0.101743 | − | 0.379711i | ||||
\(309\) | 2.97129 | − | 6.44949i | 0.169031 | − | 0.366899i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8207 | − | 10.2888i | −1.01052 | − | 0.583422i | −0.0991741 | − | 0.995070i | \(-0.531620\pi\) |
−0.911343 | + | 0.411648i | \(0.864953\pi\) | |||||||
\(312\) | 5.62863 | − | 2.07812i | 0.318658 | − | 0.117650i | ||||
\(313\) | 4.85009 | + | 1.29958i | 0.274143 | + | 0.0734564i | 0.393271 | − | 0.919422i | \(-0.371343\pi\) |
−0.119128 | + | 0.992879i | \(0.538010\pi\) | |||||||
\(314\) | −6.14966 | −0.347046 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.44949 | −0.137795 | ||||||||
\(317\) | −1.06350 | − | 0.284965i | −0.0597323 | − | 0.0160052i | 0.228829 | − | 0.973467i | \(-0.426510\pi\) |
−0.288561 | + | 0.957461i | \(0.593177\pi\) | |||||||
\(318\) | 2.73810 | − | 15.9588i | 0.153545 | − | 0.894927i | ||||
\(319\) | −17.1455 | − | 9.89898i | −0.959966 | − | 0.554236i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.05051 | − | 0.833917i | 0.505150 | − | 0.0465447i | ||||
\(322\) | −0.283763 | + | 1.05902i | −0.0158135 | + | 0.0590168i | ||||
\(323\) | 4.87832 | + | 4.87832i | 0.271437 | + | 0.271437i | ||||
\(324\) | −8.89060 | − | 1.39898i | −0.493922 | − | 0.0777211i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.550510 | + | 0.317837i | −0.0304899 | + | 0.0176034i | ||||
\(327\) | 22.5300 | − | 27.1032i | 1.24591 | − | 1.49881i | ||||
\(328\) | 1.01581 | + | 3.79107i | 0.0560889 | + | 0.209327i | ||||
\(329\) | 4.93369 | − | 8.54541i | 0.272003 | − | 0.471124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.22474 | + | 3.85337i | 0.122283 | + | 0.211800i | 0.920668 | − | 0.390347i | \(-0.127645\pi\) |
−0.798385 | + | 0.602148i | \(0.794312\pi\) | |||||||
\(332\) | 0.389270 | − | 0.389270i | 0.0213639 | − | 0.0213639i | ||||
\(333\) | −7.20390 | + | 10.4930i | −0.394772 | + | 0.575015i | ||||
\(334\) | − | 10.7980i | − | 0.590838i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.72474 | − | 0.794593i | −0.0940925 | − | 0.0433486i | ||||
\(337\) | −29.7766 | + | 7.97861i | −1.62203 | + | 0.434622i | −0.951598 | − | 0.307346i | \(-0.900559\pi\) |
−0.670435 | + | 0.741968i | \(0.733892\pi\) | |||||||
\(338\) | −0.965926 | + | 0.258819i | −0.0525394 | + | 0.0140779i | ||||
\(339\) | 21.7060 | + | 10.0000i | 1.17891 | + | 0.543125i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.9985i | 1.51621i | ||||||||
\(342\) | 4.63737 | + | 0.362626i | 0.250760 | + | 0.0196085i | ||||
\(343\) | −9.92168 | + | 9.92168i | −0.535721 | + | 0.535721i | ||||
\(344\) | −1.73205 | − | 3.00000i | −0.0933859 | − | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.55051 | − | 2.68556i | 0.0833559 | − | 0.144377i | ||||
\(347\) | 1.08757 | + | 4.05886i | 0.0583837 | + | 0.217891i | 0.988954 | − | 0.148222i | \(-0.0473550\pi\) |
−0.930570 | + | 0.366113i | \(0.880688\pi\) | |||||||
\(348\) | −3.48356 | + | 4.19067i | −0.186739 | + | 0.224644i | ||||
\(349\) | −13.0297 | + | 7.52270i | −0.697464 | + | 0.402681i | −0.806402 | − | 0.591367i | \(-0.798588\pi\) |
0.108938 | + | 0.994049i | \(0.465255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.4495 | − | 4.41761i | −0.931385 | − | 0.235795i | ||||
\(352\) | 4.44949 | + | 4.44949i | 0.237159 | + | 0.237159i | ||||
\(353\) | 8.87564 | − | 33.1244i | 0.472403 | − | 1.76303i | −0.158694 | − | 0.987328i | \(-0.550728\pi\) |
0.631097 | − | 0.775704i | \(-0.282605\pi\) | |||||||
\(354\) | −20.3632 | + | 1.87628i | −1.08229 | + | 0.0997229i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.05051 | + | 1.18386i | 0.108677 | + | 0.0627446i | ||||
\(357\) | −1.42883 | + | 8.32780i | −0.0756215 | + | 0.440754i | ||||
\(358\) | −17.0063 | − | 4.55683i | −0.898812 | − | 0.240836i | ||||
\(359\) | −17.4634 | −0.921682 | −0.460841 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5959 | 0.873469 | ||||||||
\(362\) | 10.1910 | + | 2.73067i | 0.535628 | + | 0.143521i | ||||
\(363\) | 46.4639 | − | 17.1547i | 2.43872 | − | 0.900388i | ||||
\(364\) | −3.28913 | − | 1.89898i | −0.172397 | − | 0.0995336i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.94949 | − | 8.57277i | 0.206443 | − | 0.448106i | ||||
\(367\) | −2.52520 | + | 9.42418i | −0.131814 | + | 0.491938i | −0.999991 | − | 0.00431778i | \(-0.998626\pi\) |
0.868176 | + | 0.496256i | \(0.165292\pi\) | |||||||
\(368\) | −0.707107 | − | 0.707107i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 3.92480 | − | 11.1010i | 0.204317 | − | 0.577896i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.87628 | + | 5.12472i | −0.460833 | + | 0.266062i | ||||
\(372\) | 7.59575 | + | 1.30323i | 0.393822 | + | 0.0675691i | ||||
\(373\) | −5.25190 | − | 19.6004i | −0.271933 | − | 1.01487i | −0.957869 | − | 0.287206i | \(-0.907273\pi\) |
0.685935 | − | 0.727662i | \(-0.259393\pi\) | |||||||
\(374\) | 13.9993 | − | 24.2474i | 0.723885 | − | 1.25381i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50000 | + | 7.79423i | 0.232070 | + | 0.401957i | ||||
\(377\) | −7.70674 | + | 7.70674i | −0.396917 | + | 0.396917i | ||||
\(378\) | 2.91649 | + | 4.89379i | 0.150008 | + | 0.251709i | ||||
\(379\) | − | 6.65153i | − | 0.341666i | −0.985300 | − | 0.170833i | \(-0.945354\pi\) | ||
0.985300 | − | 0.170833i | \(-0.0546459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.17423 | − | 34.4500i | −0.162621 | − | 1.76493i | ||||
\(382\) | 3.20807 | − | 0.859599i | 0.164139 | − | 0.0439809i | ||||
\(383\) | −26.8508 | + | 7.19464i | −1.37201 | + | 0.367629i | −0.868212 | − | 0.496193i | \(-0.834731\pi\) |
−0.503798 | + | 0.863822i | \(0.668064\pi\) | |||||||
\(384\) | 1.41421 | − | 1.00000i | 0.0721688 | − | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3205i | 0.881591i | ||||||||
\(387\) | −0.810167 | + | 10.3607i | −0.0411831 | + | 0.526663i | ||||
\(388\) | 7.89898 | − | 7.89898i | 0.401010 | − | 0.401010i | ||||
\(389\) | 2.81237 | + | 4.87117i | 0.142593 | + | 0.246978i | 0.928472 | − | 0.371402i | \(-0.121123\pi\) |
−0.785879 | + | 0.618380i | \(0.787789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.22474 | + | 3.85337i | −0.112510 | + | 0.194873i | ||||
\(392\) | −1.50062 | − | 5.60040i | −0.0757929 | − | 0.282863i | ||||
\(393\) | 6.32005 | + | 17.1180i | 0.318804 | + | 0.863489i | ||||
\(394\) | −8.48528 | + | 4.89898i | −0.427482 | + | 0.246807i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.44949 | − | 18.5597i | −0.173343 | − | 0.932662i | ||||
\(397\) | −15.4495 | − | 15.4495i | −0.775388 | − | 0.775388i | 0.203655 | − | 0.979043i | \(-0.434718\pi\) |
−0.979043 | + | 0.203655i | \(0.934718\pi\) | |||||||
\(398\) | 0.918940 | − | 3.42953i | 0.0460623 | − | 0.171907i | ||||
\(399\) | −1.69994 | − | 2.40408i | −0.0851036 | − | 0.120355i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.3485 | + | 12.9029i | 1.11603 | + | 0.644340i | 0.940384 | − | 0.340114i | \(-0.110466\pi\) |
0.175645 | + | 0.984454i | \(0.443799\pi\) | |||||||
\(402\) | −5.03736 | − | 4.18739i | −0.251241 | − | 0.208848i | ||||
\(403\) | 14.8883 | + | 3.98930i | 0.741638 | + | 0.198721i | ||||
\(404\) | 1.27135 | 0.0632520 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.44949 | 0.171195 | ||||||||
\(407\) | −25.7873 | − | 6.90968i | −1.27823 | − | 0.342500i | ||||
\(408\) | −5.92650 | − | 4.92650i | −0.293406 | − | 0.243898i | ||||
\(409\) | 16.5420 | + | 9.55051i | 0.817948 | + | 0.472242i | 0.849708 | − | 0.527253i | \(-0.176778\pi\) |
−0.0317605 | + | 0.999496i | \(0.510111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.20204 | + | 3.11416i | 0.108619 | + | 0.153610i | ||||
\(412\) | 1.06110 | − | 3.96008i | 0.0522767 | − | 0.195099i | ||||
\(413\) | 9.15306 | + | 9.15306i | 0.450393 | + | 0.450393i | ||||
\(414\) | 0.548188 | + | 2.94949i | 0.0269420 | + | 0.144960i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | −7.73810 | − | 20.9588i | −0.378937 | − | 1.02636i | ||||
\(418\) | 2.52520 | + | 9.42418i | 0.123512 | + | 0.460952i | ||||
\(419\) | 5.97469 | − | 10.3485i | 0.291883 | − | 0.505556i | −0.682372 | − | 0.731005i | \(-0.739052\pi\) |
0.974255 | + | 0.225449i | \(0.0723850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.44949 | + | 12.9029i | 0.363066 | + | 0.628849i | 0.988464 | − | 0.151457i | \(-0.0483966\pi\) |
−0.625398 | + | 0.780306i | \(0.715063\pi\) | |||||||
\(422\) | 13.3636 | − | 13.3636i | 0.650530 | − | 0.650530i | ||||
\(423\) | 2.10488 | − | 26.9178i | 0.102343 | − | 1.30879i | ||||
\(424\) | − | 9.34847i | − | 0.454002i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.898979 | + | 0.635674i | −0.0435557 | + | 0.0307985i | ||||
\(427\) | −5.77111 | + | 1.54636i | −0.279284 | + | 0.0748338i | ||||
\(428\) | 5.06865 | − | 1.35814i | 0.245002 | − | 0.0656482i | ||||
\(429\) | −3.46410 | − | 37.5959i | −0.167248 | − | 1.81515i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.5563i | − | 0.749323i | −0.927162 | − | 0.374661i | \(-0.877759\pi\) | ||
0.927162 | − | 0.374661i | \(-0.122241\pi\) | |||||||
\(432\) | −5.19565 | + | 0.0719302i | −0.249976 | + | 0.00346074i | ||||
\(433\) | −8.55051 | + | 8.55051i | −0.410911 | + | 0.410911i | −0.882056 | − | 0.471145i | \(-0.843841\pi\) |
0.471145 | + | 0.882056i | \(0.343841\pi\) | |||||||
\(434\) | −2.43916 | − | 4.22474i | −0.117083 | − | 0.202794i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1742 | − | 17.6223i | 0.487257 | − | 0.843955i | ||||
\(437\) | −0.401302 | − | 1.49768i | −0.0191969 | − | 0.0716436i | ||||
\(438\) | 6.99876 | + | 1.20080i | 0.334413 | + | 0.0573763i | ||||
\(439\) | 8.83523 | − | 5.10102i | 0.421682 | − | 0.243458i | −0.274114 | − | 0.961697i | \(-0.588385\pi\) |
0.695797 | + | 0.718239i | \(0.255051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.79796 | + | 16.3991i | −0.276093 | + | 0.780910i | ||||
\(442\) | −10.8990 | − | 10.8990i | −0.518412 | − | 0.518412i | ||||
\(443\) | −0.142483 | + | 0.531752i | −0.00676955 | + | 0.0252643i | −0.969228 | − | 0.246165i | \(-0.920830\pi\) |
0.962458 | + | 0.271429i | \(0.0874962\pi\) | |||||||
\(444\) | −3.07483 | + | 6.67423i | −0.145925 | + | 0.316745i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.19694 | − | 4.15515i | −0.340785 | − | 0.196752i | ||||
\(447\) | −20.9652 | + | 7.74045i | −0.991620 | + | 0.366111i | ||||
\(448\) | −1.05902 | − | 0.283763i | −0.0500339 | − | 0.0134065i | ||||
\(449\) | 21.7060 | 1.02437 | 0.512185 | − | 0.858875i | \(-0.328836\pi\) | ||||
0.512185 | + | 0.858875i | \(0.328836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6969 | 1.16293 | ||||||||
\(452\) | 13.3278 | + | 3.57117i | 0.626887 | + | 0.167974i | ||||
\(453\) | −6.32530 | + | 36.8665i | −0.297188 | + | 1.73214i | ||||
\(454\) | −13.0779 | − | 7.55051i | −0.613775 | − | 0.354363i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.67423 | − | 0.246405i | 0.125233 | − | 0.0115390i | ||||
\(457\) | −1.59165 | + | 5.94012i | −0.0744543 | + | 0.277867i | −0.993109 | − | 0.117194i | \(-0.962610\pi\) |
0.918655 | + | 0.395061i | \(0.129277\pi\) | |||||||
\(458\) | −11.5601 | − | 11.5601i | −0.540169 | − | 0.540169i | ||||
\(459\) | 6.29253 | + | 22.2474i | 0.293710 | + | 1.03842i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3763 | − | 9.45485i | 0.762719 | − | 0.440356i | −0.0675520 | − | 0.997716i | \(-0.521519\pi\) |
0.830271 | + | 0.557360i | \(0.188186\pi\) | |||||||
\(462\) | −7.63859 | + | 9.18910i | −0.355380 | + | 0.427516i | ||||
\(463\) | 8.54613 | + | 31.8946i | 0.397172 | + | 1.48227i | 0.818048 | + | 0.575150i | \(0.195056\pi\) |
−0.420876 | + | 0.907118i | \(0.638277\pi\) | |||||||
\(464\) | −1.57313 | + | 2.72474i | −0.0730308 | + | 0.126493i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.77526 | − | 13.4671i | −0.360182 | − | 0.623853i | ||||
\(467\) | −2.82843 | + | 2.82843i | −0.130884 | + | 0.130884i | −0.769514 | − | 0.638630i | \(-0.779501\pi\) |
0.638630 | + | 0.769514i | \(0.279501\pi\) | |||||||
\(468\) | −10.3607 | − | 0.810167i | −0.478922 | − | 0.0374500i | ||||
\(469\) | 4.14643i | 0.191464i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.67423 | + | 4.45694i | 0.445765 | + | 0.205365i | ||||
\(472\) | −11.4042 | + | 3.05575i | −0.524922 | + | 0.140652i | ||||
\(473\) | −21.0552 | + | 5.64173i | −0.968120 | + | 0.259407i | ||||
\(474\) | 3.85337 | + | 1.77526i | 0.176991 | + | 0.0815402i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.87832i | 0.223597i | ||||||||
\(477\) | −15.8735 | + | 23.1209i | −0.726797 | + | 1.05863i | ||||
\(478\) | 12.0000 | − | 12.0000i | 0.548867 | − | 0.548867i | ||||
\(479\) | −3.53553 | − | 6.12372i | −0.161543 | − | 0.279800i | 0.773879 | − | 0.633333i | \(-0.218314\pi\) |
−0.935422 | + | 0.353533i | \(0.884980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.34847 | + | 12.7279i | −0.335061 | + | 0.580343i | ||||
\(482\) | 4.91756 | + | 18.3526i | 0.223989 | + | 0.835938i | ||||
\(483\) | 1.21391 | − | 1.46032i | 0.0552350 | − | 0.0664469i | ||||
\(484\) | 24.7648 | − | 14.2980i | 1.12567 | − | 0.649907i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.9722 | + | 8.64420i | 0.588431 | + | 0.392109i | ||||
\(487\) | 12.0000 | + | 12.0000i | 0.543772 | + | 0.543772i | 0.924632 | − | 0.380861i | \(-0.124372\pi\) |
−0.380861 | + | 0.924632i | \(0.624372\pi\) | |||||||
\(488\) | 1.41043 | − | 5.26380i | 0.0638472 | − | 0.238281i | ||||
\(489\) | 1.09638 | − | 0.101021i | 0.0495799 | − | 0.00456831i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.247449 | + | 0.142865i | 0.0111672 | + | 0.00644739i | 0.505573 | − | 0.862784i | \(-0.331281\pi\) |
−0.494406 | + | 0.869231i | \(0.664614\pi\) | |||||||
\(492\) | 1.14955 | − | 6.70006i | 0.0518256 | − | 0.302062i | ||||
\(493\) | 13.5223 | + | 3.62328i | 0.609012 | + | 0.163184i | ||||
\(494\) | 5.37113 | 0.241658 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.44949 | 0.199788 | ||||||||
\(497\) | 0.673191 | + | 0.180381i | 0.0301967 | + | 0.00809119i | ||||
\(498\) | −0.894494 | + | 0.330251i | −0.0400832 | + | 0.0147989i | ||||
\(499\) | 7.70674 | + | 4.44949i | 0.345001 | + | 0.199187i | 0.662481 | − | 0.749078i | \(-0.269503\pi\) |
−0.317480 | + | 0.948265i | \(0.602837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.82577 | + | 16.9866i | −0.349629 | + | 0.758906i | ||||
\(502\) | −2.89123 | + | 10.7902i | −0.129042 | + | 0.481590i | ||||
\(503\) | 16.7563 | + | 16.7563i | 0.747125 | + | 0.747125i | 0.973938 | − | 0.226813i | \(-0.0728307\pi\) |
−0.226813 | + | 0.973938i | \(0.572831\pi\) | |||||||
\(504\) | 2.13737 | + | 2.50000i | 0.0952062 | + | 0.111359i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.44949 | + | 3.14626i | −0.242259 | + | 0.139869i | ||||
\(507\) | 1.70711 | + | 0.292893i | 0.0758153 | + | 0.0130078i | ||||
\(508\) | −5.16964 | − | 19.2934i | −0.229366 | − | 0.856005i | ||||
\(509\) | −19.8150 | + | 34.3207i | −0.878286 | + | 1.52124i | −0.0250662 | + | 0.999686i | \(0.507980\pi\) |
−0.853220 | + | 0.521551i | \(0.825354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.24745 | − | 3.89270i | −0.0994213 | − | 0.172203i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −7.03239 | − | 3.93137i | −0.310488 | − | 0.173574i | ||||
\(514\) | − | 26.0454i | − | 1.14881i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.550510 | + | 5.97469i | 0.0242349 | + | 0.263021i | ||||
\(517\) | 54.7030 | − | 14.6576i | 2.40584 | − | 0.644642i | ||||
\(518\) | 4.49303 | − | 1.20390i | 0.197413 | − | 0.0528965i | ||||
\(519\) | −4.38551 | + | 3.10102i | −0.192502 | + | 0.136120i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.4449i | − | 1.29000i | −0.764181 | − | 0.645001i | \(-0.776857\pi\) | ||
0.764181 | − | 0.645001i | \(-0.223143\pi\) | |||||||
\(522\) | 8.51727 | − | 4.06778i | 0.372791 | − | 0.178042i | ||||
\(523\) | −1.77526 | + | 1.77526i | −0.0776265 | + | 0.0776265i | −0.744854 | − | 0.667228i | \(-0.767481\pi\) |
0.667228 | + | 0.744854i | \(0.267481\pi\) | |||||||
\(524\) | 5.26758 | + | 9.12372i | 0.230116 | + | 0.398572i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.34847 | − | 10.9959i | 0.276806 | − | 0.479443i | ||||
\(527\) | −5.12409 | − | 19.1234i | −0.223209 | − | 0.833027i | ||||
\(528\) | −3.77489 | − | 10.2244i | −0.164281 | − | 0.444959i | ||||
\(529\) | −19.0526 | + | 11.0000i | −0.828372 | + | 0.478261i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.3939 | + | 11.8065i | 1.44917 | + | 0.512359i | ||||
\(532\) | −1.20204 | − | 1.20204i | −0.0521151 | − | 0.0521151i | ||||
\(533\) | 3.51888 | − | 13.1326i | 0.152420 | − | 0.568838i | ||||
\(534\) | −2.36773 | − | 3.34847i | −0.102461 | − | 0.144902i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.27526 | − | 1.89097i | −0.141469 | − | 0.0816774i | ||||
\(537\) | 23.4506 | + | 19.4937i | 1.01197 | + | 0.841217i | ||||
\(538\) | 4.54308 | + | 1.21731i | 0.195866 | + | 0.0524822i | ||||
\(539\) | −36.4838 | −1.57147 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.9444 | −1.11544 | −0.557718 | − | 0.830030i | \(-0.688323\pi\) | ||||
−0.557718 | + | 0.830030i | \(0.688323\pi\) | |||||||
\(542\) | 15.4987 | + | 4.15286i | 0.665725 | + | 0.178380i | ||||
\(543\) | −14.0528 | − | 11.6816i | −0.603062 | − | 0.501305i | ||||
\(544\) | −3.85337 | − | 2.22474i | −0.165212 | − | 0.0953851i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.79796 | + | 5.37113i | 0.162538 | + | 0.229863i | ||||
\(547\) | 5.53567 | − | 20.6594i | 0.236688 | − | 0.883332i | −0.740693 | − | 0.671844i | \(-0.765502\pi\) |
0.977381 | − | 0.211488i | \(-0.0678308\pi\) | |||||||
\(548\) | 1.55708 | + | 1.55708i | 0.0665151 | + | 0.0665151i | ||||
\(549\) | −12.4261 | + | 10.6237i | −0.530335 | + | 0.453410i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.22474 | + | 2.43916i | −0.179980 | + | 0.103912i | ||||
\(552\) | 0.599900 | + | 1.62484i | 0.0255335 | + | 0.0691580i | ||||
\(553\) | −0.695075 | − | 2.59405i | −0.0295576 | − | 0.110310i | ||||
\(554\) | −7.14250 | + | 12.3712i | −0.303456 | + | 0.525601i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.44949 | − | 11.1708i | −0.273519 | − | 0.473749i | ||||
\(557\) | −16.3670 | + | 16.3670i | −0.693492 | + | 0.693492i | −0.962999 | − | 0.269507i | \(-0.913139\pi\) |
0.269507 | + | 0.962999i | \(0.413139\pi\) | |||||||
\(558\) | −11.0046 | − | 7.55513i | −0.465863 | − | 0.319834i | ||||
\(559\) | 12.0000i | 0.507546i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.5959 | + | 27.9985i | −1.67174 | + | 1.18210i | ||||
\(562\) | 0.169011 | − | 0.0452863i | 0.00712928 | − | 0.00191029i | ||||
\(563\) | 33.1781 | − | 8.89004i | 1.39829 | − | 0.374670i | 0.520559 | − | 0.853826i | \(-0.325724\pi\) |
0.877730 | + | 0.479155i | \(0.159057\pi\) | |||||||
\(564\) | −1.43027 | − | 15.5227i | −0.0602251 | − | 0.653624i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.89610i | 0.289864i | ||||||||
\(567\) | −1.04128 | − | 9.81229i | −0.0437297 | − | 0.412077i | ||||
\(568\) | −0.449490 | + | 0.449490i | −0.0188602 | + | 0.0188602i | ||||
\(569\) | −13.0458 | − | 22.5959i | −0.546907 | − | 0.947270i | −0.998484 | − | 0.0550383i | \(-0.982472\pi\) |
0.451578 | − | 0.892232i | \(-0.350861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5505 | + | 23.4702i | −0.567071 | + | 0.982196i | 0.429782 | + | 0.902932i | \(0.358590\pi\) |
−0.996854 | + | 0.0792637i | \(0.974743\pi\) | |||||||
\(572\) | −5.64173 | − | 21.0552i | −0.235892 | − | 0.880363i | ||||
\(573\) | −5.66971 | − | 0.972768i | −0.236855 | − | 0.0406380i | ||||
\(574\) | −3.72656 | + | 2.15153i | −0.155544 | + | 0.0898032i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.94949 | + | 0.548188i | −0.122895 | + | 0.0228412i | ||||
\(577\) | 17.0000 | + | 17.0000i | 0.707719 | + | 0.707719i | 0.966055 | − | 0.258336i | \(-0.0831741\pi\) |
−0.258336 | + | 0.966055i | \(0.583174\pi\) | |||||||
\(578\) | −0.724165 | + | 2.70262i | −0.0301213 | + | 0.112414i | ||||
\(579\) | 12.5529 | − | 27.2474i | 0.521683 | − | 1.13237i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.522704 | + | 0.301783i | 0.0216854 | + | 0.0125201i | ||||
\(582\) | −18.1509 | + | 6.70139i | −0.752378 | + | 0.277782i | ||||
\(583\) | −56.8211 | − | 15.2252i | −2.35329 | − | 0.630562i | ||||
\(584\) | 4.09978 | 0.169650 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0454 | 0.910687 | ||||||||
\(587\) | −29.9876 | − | 8.03514i | −1.23772 | − | 0.331646i | −0.420138 | − | 0.907460i | \(-0.638019\pi\) |
−0.817581 | + | 0.575814i | \(0.804685\pi\) | |||||||
\(588\) | −1.69818 | + | 9.89774i | −0.0700319 | + | 0.408176i | ||||
\(589\) | 5.97469 | + | 3.44949i | 0.246183 | + | 0.142134i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8990 | − | 1.55708i | 0.695131 | − | 0.0640496i | ||||
\(592\) | −1.09808 | + | 4.09808i | −0.0451307 | + | 0.168430i | ||||
\(593\) | −10.0745 | − | 10.0745i | −0.413709 | − | 0.413709i | 0.469320 | − | 0.883028i | \(-0.344499\pi\) |
−0.883028 | + | 0.469320i | \(0.844499\pi\) | |||||||
\(594\) | −8.02458 | + | 31.6969i | −0.329252 | + | 1.30054i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.1742 | + | 6.45145i | −0.457714 | + | 0.264262i | ||||
\(597\) | −3.93115 | + | 4.72911i | −0.160891 | + | 0.193549i | ||||
\(598\) | 0.896575 | + | 3.34607i | 0.0366637 | + | 0.136831i | ||||
\(599\) | 16.8991 | − | 29.2702i | 0.690480 | − | 1.19595i | −0.281201 | − | 0.959649i | \(-0.590733\pi\) |
0.971681 | − | 0.236297i | \(-0.0759339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3485 | − | 30.0484i | −0.707659 | − | 1.22570i | −0.965723 | − | 0.259573i | \(-0.916418\pi\) |
0.258065 | − | 0.966128i | \(-0.416915\pi\) | |||||||
\(602\) | 2.68556 | − | 2.68556i | 0.109455 | − | 0.109455i | ||||
\(603\) | 4.88964 | + | 10.2381i | 0.199122 | + | 0.416928i | ||||
\(604\) | 21.5959i | 0.878725i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | − | 0.921404i | −0.0812444 | − | 0.0374295i | ||||
\(607\) | 21.4114 | − | 5.73717i | 0.869062 | − | 0.232864i | 0.203380 | − | 0.979100i | \(-0.434807\pi\) |
0.665682 | + | 0.746235i | \(0.268141\pi\) | |||||||
\(608\) | 1.49768 | − | 0.401302i | 0.0607389 | − | 0.0162749i | ||||
\(609\) | −5.42650 | − | 2.50000i | −0.219893 | − | 0.101305i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 31.1769i | − | 1.26128i | ||||||
\(612\) | 5.75272 | + | 12.0452i | 0.232540 | + | 0.486900i | ||||
\(613\) | 12.7980 | − | 12.7980i | 0.516905 | − | 0.516905i | −0.399729 | − | 0.916633i | \(-0.630896\pi\) |
0.916633 | + | 0.399729i | \(0.130896\pi\) | |||||||
\(614\) | 0.476756 | + | 0.825765i | 0.0192403 | + | 0.0333252i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.44949 | + | 5.97469i | −0.138984 | + | 0.240727i | ||||
\(617\) | −1.83788 | − | 6.85906i | −0.0739902 | − | 0.276135i | 0.919012 | − | 0.394229i | \(-0.128988\pi\) |
−0.993002 | + | 0.118094i | \(0.962322\pi\) | |||||||
\(618\) | −4.53930 | + | 5.46070i | −0.182597 | + | 0.219662i | ||||
\(619\) | 21.4275 | − | 12.3712i | 0.861244 | − | 0.497239i | −0.00318471 | − | 0.999995i | \(-0.501014\pi\) |
0.864429 | + | 0.502756i | \(0.167680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.27526 | − | 5.03723i | 0.0511742 | − | 0.202137i | ||||
\(622\) | 14.5505 | + | 14.5505i | 0.583422 | + | 0.583422i | ||||
\(623\) | −0.671873 | + | 2.50746i | −0.0269180 | + | 0.100459i | ||||
\(624\) | −5.97469 | + | 0.550510i | −0.239179 | + | 0.0220380i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.34847 | − | 2.51059i | −0.173800 | − | 0.100343i | ||||
\(627\) | 2.85765 | − | 16.6556i | 0.114124 | − | 0.665161i | ||||
\(628\) | 5.94012 | + | 1.59165i | 0.237037 | + | 0.0635138i | ||||
\(629\) | 18.8776 | 0.752699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8990 | −0.513500 | −0.256750 | − | 0.966478i | \(-0.582652\pi\) | ||||
−0.256750 | + | 0.966478i | \(0.582652\pi\) | |||||||
\(632\) | 2.36603 | + | 0.633975i | 0.0941154 | + | 0.0252182i | ||||
\(633\) | −30.7079 | + | 11.3375i | −1.22053 | + | 0.450625i | ||||
\(634\) | 0.953512 | + | 0.550510i | 0.0378688 | + | 0.0218636i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.77526 | + | 14.7064i | −0.268656 | + | 0.583146i | ||||
\(637\) | −5.19831 | + | 19.4003i | −0.205964 | + | 0.768670i | ||||
\(638\) | 13.9993 | + | 13.9993i | 0.554236 | + | 0.554236i | ||||
\(639\) | 1.87492 | − | 0.348469i | 0.0741705 | − | 0.0137852i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.74745 | + | 4.47299i | −0.306006 | + | 0.176673i | −0.645138 | − | 0.764066i | \(-0.723200\pi\) |
0.339132 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(642\) | −8.95796 | − | 1.53694i | −0.353542 | − | 0.0606583i | ||||
\(643\) | 8.22539 | + | 30.6976i | 0.324378 | + | 1.21059i | 0.914936 | + | 0.403599i | \(0.132241\pi\) |
−0.590558 | + | 0.806995i | \(0.701092\pi\) | |||||||
\(644\) | 0.548188 | − | 0.949490i | 0.0216016 | − | 0.0374151i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.44949 | − | 5.97469i | −0.135718 | − | 0.235071i | ||||
\(647\) | 24.9558 | − | 24.9558i | 0.981114 | − | 0.981114i | −0.0187105 | − | 0.999825i | \(-0.505956\pi\) |
0.999825 | + | 0.0187105i | \(0.00595608\pi\) | |||||||
\(648\) | 8.22558 | + | 3.65237i | 0.323131 | + | 0.143479i | ||||
\(649\) | 74.2929i | 2.91625i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.775255 | + | 8.41385i | 0.0303846 | + | 0.329765i | ||||
\(652\) | 0.614014 | − | 0.164525i | 0.0240467 | − | 0.00644328i | ||||
\(653\) | 20.8162 | − | 5.57768i | 0.814601 | − | 0.218272i | 0.172616 | − | 0.984989i | \(-0.444778\pi\) |
0.641985 | + | 0.766718i | \(0.278111\pi\) | |||||||
\(654\) | −28.7771 | + | 20.3485i | −1.12527 | + | 0.795688i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3.92480i | − | 0.153238i | ||||||
\(657\) | −10.1397 | − | 6.96132i | −0.395587 | − | 0.271587i | ||||
\(658\) | −6.97730 | + | 6.97730i | −0.272003 | + | 0.272003i | ||||
\(659\) | 5.65685 | + | 9.79796i | 0.220360 | + | 0.381674i | 0.954917 | − | 0.296872i | \(-0.0959435\pi\) |
−0.734557 | + | 0.678546i | \(0.762610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3485 | − | 26.5843i | 0.596986 | − | 1.03401i | −0.396277 | − | 0.918131i | \(-0.629698\pi\) |
0.993263 | − | 0.115880i | \(-0.0369687\pi\) | |||||||
\(662\) | −1.15161 | − | 4.29788i | −0.0447587 | − | 0.167042i | ||||
\(663\) | 9.24656 | + | 25.0445i | 0.359106 | + | 0.972648i | ||||
\(664\) | −0.476756 | + | 0.275255i | −0.0185017 | + | 0.0106820i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.67423 | − | 8.27098i | 0.374869 | − | 0.320494i | ||||
\(667\) | −2.22474 | − | 2.22474i | −0.0861425 | − | 0.0861425i | ||||
\(668\) | −2.79472 | + | 10.4300i | −0.108131 | + | 0.403550i | ||||
\(669\) | 8.31031 | + | 11.7526i | 0.321295 | + | 0.454380i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.6969 | − | 17.1455i | −1.14644 | − | 0.661896i | ||||
\(672\) | 1.46032 | + | 1.21391i | 0.0563331 | + | 0.0468278i | ||||
\(673\) | −15.7783 | − | 4.22778i | −0.608208 | − | 0.162969i | −0.0584468 | − | 0.998291i | \(-0.518615\pi\) |
−0.549762 | + | 0.835322i | \(0.685281\pi\) | |||||||
\(674\) | 30.8270 | 1.18741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −6.18587 | − | 1.65750i | −0.237742 | − | 0.0637028i | 0.137981 | − | 0.990435i | \(-0.455939\pi\) |
−0.375723 | + | 0.926732i | \(0.622606\pi\) | |||||||
\(678\) | −18.3782 | − | 15.2772i | −0.705811 | − | 0.586717i | ||||
\(679\) | 10.6066 | + | 6.12372i | 0.407044 | + | 0.235007i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.1010 | + | 21.3561i | 0.578672 | + | 0.818366i | ||||
\(682\) | 7.24656 | − | 27.0445i | 0.277485 | − | 1.03559i | ||||
\(683\) | −13.8564 | − | 13.8564i | −0.530201 | − | 0.530201i | 0.390431 | − | 0.920632i | \(-0.372326\pi\) |
−0.920632 | + | 0.390431i | \(0.872326\pi\) | |||||||
\(684\) | −4.38551 | − | 1.55051i | −0.167684 | − | 0.0592852i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.1515 | − | 7.01569i | 0.463948 | − | 0.267860i | ||||
\(687\) | 9.80745 | + | 26.5637i | 0.374178 | + | 1.01347i | ||||
\(688\) | 0.896575 | + | 3.34607i | 0.0341816 | + | 0.127568i | ||||
\(689\) | −16.1920 | + | 28.0454i | −0.616867 | + | 1.06844i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4722 | − | 28.5307i | −0.626632 | − | 1.08536i | −0.988223 | − | 0.153021i | \(-0.951100\pi\) |
0.361591 | − | 0.932337i | \(-0.382234\pi\) | |||||||
\(692\) | −2.19275 | + | 2.19275i | −0.0833559 | + | 0.0833559i | ||||
\(693\) | 18.6763 | − | 8.91964i | 0.709453 | − | 0.338829i | ||||
\(694\) | − | 4.20204i | − | 0.159507i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.44949 | − | 3.14626i | 0.168657 | − | 0.119259i | ||||
\(697\) | −16.8683 | + | 4.51985i | −0.638933 | + | 0.171202i | ||||
\(698\) | 14.5327 | − | 3.89404i | 0.550073 | − | 0.147392i | ||||
\(699\) | 2.47127 | + | 26.8207i | 0.0934719 | + | 1.01445i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9309i | 0.903857i | 0.892054 | + | 0.451928i | \(0.149264\pi\) | ||||
−0.892054 | + | 0.451928i | \(0.850736\pi\) | |||||||
\(702\) | 15.7116 | + | 8.78335i | 0.592994 | + | 0.331506i | ||||
\(703\) | −4.65153 | + | 4.65153i | −0.175436 | + | 0.175436i | ||||
\(704\) | −3.14626 | − | 5.44949i | −0.118579 | − | 0.205385i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.1464 | + | 29.6985i | −0.645314 | + | 1.11772i | ||||
\(707\) | 0.360762 | + | 1.34638i | 0.0135678 | + | 0.0506359i | ||||
\(708\) | 20.1550 | + | 3.45805i | 0.757471 | + | 0.129961i | ||||
\(709\) | 38.4069 | − | 22.1742i | 1.44240 | − | 0.832771i | 0.444392 | − | 0.895833i | \(-0.353420\pi\) |
0.998010 | + | 0.0630617i | \(0.0200865\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.77526 | − | 5.58542i | −0.179086 | − | 0.209470i | ||||
\(712\) | −1.67423 | − | 1.67423i | −0.0627446 | − | 0.0627446i | ||||
\(713\) | −1.15161 | + | 4.29788i | −0.0431282 | + | 0.160957i | ||||
\(714\) | 3.53553 | − | 7.67423i | 0.132314 | − | 0.287201i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.2474 | + | 8.80312i | 0.569824 | + | 0.328988i | ||||
\(717\) | −27.5745 | + | 10.1806i | −1.02979 | + | 0.380203i | ||||
\(718\) | 16.8683 | + | 4.51985i | 0.629520 | + | 0.168679i | ||||
\(719\) | 32.5269 | 1.21305 | 0.606525 | − | 0.795065i | \(-0.292563\pi\) | ||||
0.606525 | + | 0.795065i | \(0.292563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.49490 | 0.167399 | ||||||||
\(722\) | −16.0304 | − | 4.29534i | −0.596591 | − | 0.159856i | ||||
\(723\) | 5.56497 | − | 32.4350i | 0.206964 | − | 1.20627i | ||||
\(724\) | −9.13701 | − | 5.27526i | −0.339574 | − | 0.196053i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −49.3207 | + | 4.54442i | −1.83046 | + | 0.168659i | ||||
\(727\) | 8.11447 | − | 30.2836i | 0.300949 | − | 1.12316i | −0.635428 | − | 0.772160i | \(-0.719176\pi\) |
0.936377 | − | 0.350996i | \(-0.114157\pi\) | |||||||
\(728\) | 2.68556 | + | 2.68556i | 0.0995336 | + | 0.0995336i | ||||
\(729\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3485 | − | 7.70674i | 0.493711 | − | 0.285044i | ||||
\(732\) | −6.03371 | + | 7.25845i | −0.223012 | + | 0.268280i | ||||
\(733\) | 3.71385 | + | 13.8603i | 0.137174 | + | 0.511941i | 0.999979 | + | 0.00640470i | \(0.00203869\pi\) |
−0.862805 | + | 0.505536i | \(0.831295\pi\) | |||||||
\(734\) | 4.87832 | − | 8.44949i | 0.180062 | − | 0.311876i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | + | 0.866025i | 0.0184302 | + | 0.0319221i | ||||
\(737\) | −16.8277 | + | 16.8277i | −0.619856 | + | 0.619856i | ||||
\(738\) | −6.66422 | + | 9.70695i | −0.245313 | + | 0.357318i | ||||
\(739\) | − | 24.9444i | − | 0.917594i | −0.888541 | − | 0.458797i | \(-0.848280\pi\) | ||
0.888541 | − | 0.458797i | \(-0.151720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.44949 | − | 3.89270i | −0.310400 | − | 0.143002i | ||||
\(742\) | 9.90020 | − | 2.65275i | 0.363448 | − | 0.0973855i | ||||
\(743\) | −0.0975783 | + | 0.0261460i | −0.00357980 | + | 0.000959205i | −0.260609 | − | 0.965445i | \(-0.583923\pi\) |
0.257029 | + | 0.966404i | \(0.417257\pi\) | |||||||
\(744\) | −6.99964 | − | 3.22474i | −0.256619 | − | 0.118225i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.2918i | 0.742936i | ||||||||
\(747\) | 1.64650 | + | 0.128751i | 0.0602425 | + | 0.00471074i | ||||
\(748\) | −19.7980 | + | 19.7980i | −0.723885 | + | 0.723885i | ||||
\(749\) | 2.87659 | + | 4.98240i | 0.105108 | + | 0.182053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.34847 | − | 7.53177i | 0.158678 | − | 0.274838i | −0.775714 | − | 0.631084i | \(-0.782610\pi\) |
0.934392 | + | 0.356246i | \(0.115944\pi\) | |||||||
\(752\) | −2.32937 | − | 8.69333i | −0.0849434 | − | 0.317013i | ||||
\(753\) | 12.3684 | − | 14.8790i | 0.450731 | − | 0.542222i | ||||
\(754\) | 9.43879 | − | 5.44949i | 0.343741 | − | 0.198459i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.55051 | − | 5.48188i | −0.0563915 | − | 0.199374i | ||||
\(757\) | 22.0454 | + | 22.0454i | 0.801254 | + | 0.801254i | 0.983292 | − | 0.182038i | \(-0.0582693\pi\) |
−0.182038 | + | 0.983292i | \(0.558269\pi\) | |||||||
\(758\) | −1.72154 | + | 6.42489i | −0.0625293 | + | 0.233362i | ||||
\(759\) | 10.8530 | − | 1.00000i | 0.393939 | − | 0.0362977i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.3990 | − | 8.89060i | −0.558213 | − | 0.322284i | 0.194215 | − | 0.980959i | \(-0.437784\pi\) |
−0.752428 | + | 0.658675i | \(0.771117\pi\) | |||||||
\(762\) | −5.85024 | + | 34.0977i | −0.211932 | + | 1.23523i | ||||
\(763\) | 21.5494 | + | 5.77414i | 0.780141 | + | 0.209038i | ||||
\(764\) | −3.32124 | −0.120158 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.7980 | 1.00438 | ||||||||
\(767\) | 39.5054 | + | 10.5854i | 1.42646 | + | 0.382218i | ||||
\(768\) | −1.62484 | + | 0.599900i | −0.0586315 | + | 0.0216470i | ||||
\(769\) | −17.0580 | − | 9.84847i | −0.615129 | − | 0.355145i | 0.159841 | − | 0.987143i | \(-0.448902\pi\) |
−0.774970 | + | 0.631998i | \(0.782235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8763 | + | 40.9729i | −0.679812 | + | 1.47560i | ||||
\(772\) | 4.48288 | − | 16.7303i | 0.161342 | − | 0.602138i | ||||
\(773\) | −3.11416 | − | 3.11416i | −0.112008 | − | 0.112008i | 0.648881 | − | 0.760890i | \(-0.275237\pi\) |
−0.760890 | + | 0.648881i | \(0.775237\pi\) | |||||||
\(774\) | 3.46410 | − | 9.79796i | 0.124515 | − | 0.352180i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.67423 | + | 5.58542i | −0.347285 | + | 0.200505i | ||||
\(777\) | −7.94066 | − | 1.36240i | −0.284870 | − | 0.0488759i | ||||
\(778\) | −1.45579 | − | 5.43309i | −0.0521927 | − | 0.194786i | ||||
\(779\) | 3.04272 | − | 5.27015i | 0.109017 | − | 0.188823i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 3.14626 | − | 3.14626i | 0.112510 | − | 0.112510i | ||||
\(783\) | −16.3469 | + | 0.226311i | −0.584191 | + | 0.00808771i | ||||
\(784\) | 5.79796i | 0.207070i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.67423 | − | 18.1705i | −0.0597180 | − | 0.648120i | ||||
\(787\) | 3.96008 | − | 1.06110i | 0.141162 | − | 0.0378241i | −0.187546 | − | 0.982256i | \(-0.560053\pi\) |
0.328708 | + | 0.944432i | \(0.393387\pi\) | |||||||
\(788\) | 9.46410 | − | 2.53590i | 0.337145 | − | 0.0903376i | ||||
\(789\) | −17.9562 | + | 12.6969i | −0.639257 | + | 0.452023i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1278i | 0.537881i | ||||||||
\(792\) | −1.47167 | + | 18.8201i | −0.0522933 | + | 0.668744i | ||||
\(793\) | −13.3485 | + | 13.3485i | −0.474018 | + | 0.474018i | ||||
\(794\) | 10.9244 | + | 18.9217i | 0.387694 | + | 0.671505i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.77526 | + | 3.07483i | −0.0629222 | + | 0.108985i | ||||
\(797\) | 5.22867 | + | 19.5137i | 0.185209 | + | 0.691210i | 0.994586 | + | 0.103920i | \(0.0331385\pi\) |
−0.809377 | + | 0.587290i | \(0.800195\pi\) | |||||||
\(798\) | 1.01980 | + | 2.76214i | 0.0361004 | + | 0.0977788i | ||||
\(799\) | −34.6803 | + | 20.0227i | −1.22690 | + | 0.708352i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.29796 | + | 6.98358i | 0.0458611 | + | 0.246753i | ||||
\(802\) | −18.2474 | − | 18.2474i | −0.644340 | − | 0.644340i | ||||
\(803\) | 6.67700 | − | 24.9189i | 0.235626 | − | 0.879369i | ||||
\(804\) | 3.78194 | + | 5.34847i | 0.133379 | + | 0.188626i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.3485 | − | 7.70674i | −0.470180 | − | 0.271458i | ||||
\(807\) | −6.26462 | − | 5.20757i | −0.220525 | − | 0.183315i | ||||
\(808\) | −1.22803 | − | 0.329049i | −0.0432019 | − | 0.0115759i | ||||
\(809\) | −54.0901 | −1.90171 | −0.950853 | − | 0.309644i | \(-0.899790\pi\) | ||||
−0.950853 | + | 0.309644i | \(0.899790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6413 | 1.53245 | 0.766227 | − | 0.642570i | \(-0.222132\pi\) | ||||
0.766227 | + | 0.642570i | \(0.222132\pi\) | |||||||
\(812\) | −3.33195 | − | 0.892794i | −0.116929 | − | 0.0313309i | ||||
\(813\) | −21.3717 | − | 17.7656i | −0.749538 | − | 0.623066i | ||||
\(814\) | 23.1202 | + | 13.3485i | 0.810364 | + | 0.467864i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.44949 | + | 6.29253i | 0.155763 | + | 0.220283i | ||||
\(817\) | −1.39015 | + | 5.18811i | −0.0486352 | + | 0.181509i | ||||
\(818\) | −13.5065 | − | 13.5065i | −0.472242 | − | 0.472242i | ||||
\(819\) | −2.08200 | − | 11.2020i | −0.0727508 | − | 0.391431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3207 | + | 12.8868i | −0.778997 | + | 0.449754i | −0.836075 | − | 0.548616i | \(-0.815155\pi\) |
0.0570780 | + | 0.998370i | \(0.481822\pi\) | |||||||
\(822\) | −1.32101 | − | 3.57797i | −0.0460754 | − | 0.124796i | ||||
\(823\) | 12.5807 | + | 46.9519i | 0.438536 | + | 1.63664i | 0.732459 | + | 0.680811i | \(0.238373\pi\) |
−0.293923 | + | 0.955829i | \(0.594961\pi\) | |||||||
\(824\) | −2.04989 | + | 3.55051i | −0.0714112 | + | 0.123688i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.47219 | − | 11.2102i | −0.225196 | − | 0.390052i | ||||
\(827\) | 27.3235 | − | 27.3235i | 0.950133 | − | 0.950133i | −0.0486816 | − | 0.998814i | \(-0.515502\pi\) |
0.998814 | + | 0.0486816i | \(0.0155020\pi\) | |||||||
\(828\) | 0.233875 | − | 2.99087i | 0.00812772 | − | 0.103940i | ||||
\(829\) | − | 15.4495i | − | 0.536583i | −0.963338 | − | 0.268291i | \(-0.913541\pi\) | ||
0.963338 | − | 0.268291i | \(-0.0864590\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.2020 | − | 14.2850i | 0.700801 | − | 0.495541i | ||||
\(832\) | −3.34607 | + | 0.896575i | −0.116004 | + | 0.0310832i | ||||
\(833\) | 24.9189 | − | 6.67700i | 0.863389 | − | 0.231344i | ||||
\(834\) | 2.04989 | + | 22.2474i | 0.0709818 | + | 0.770366i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 9.75663i | − | 0.337440i | ||||||
\(837\) | 11.8362 | + | 19.8608i | 0.409118 | + | 0.686488i | ||||
\(838\) | −8.44949 | + | 8.44949i | −0.291883 | + | 0.291883i | ||||
\(839\) | −10.1459 | − | 17.5732i | −0.350275 | − | 0.606695i | 0.636022 | − | 0.771671i | \(-0.280579\pi\) |
−0.986298 | + | 0.164976i | \(0.947245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.55051 | − | 16.5420i | 0.329328 | − | 0.570413i | ||||
\(842\) | −3.85614 | − | 14.3913i | −0.132891 | − | 0.495957i | ||||
\(843\) | −0.298697 | − | 0.0512483i | −0.0102877 | − | 0.00176509i | ||||
\(844\) | −16.3670 | + | 9.44949i | −0.563375 | + | 0.325265i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | + | 25.4558i | −0.309426 | + | 0.875190i | ||||
\(847\) | 22.1691 | + | 22.1691i | 0.761740 | + | 0.761740i | ||||
\(848\) | −2.41956 | + | 9.02993i | −0.0830881 | + | 0.310089i | ||||
\(849\) | 4.99791 | − | 10.8485i | 0.171528 | − | 0.372319i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.67423 | − | 2.12132i | −0.125951 | − | 0.0727179i | ||||
\(852\) | 1.03287 | − | 0.381341i | 0.0353856 | − | 0.0130645i | ||||
\(853\) | −35.8547 | − | 9.60723i | −1.22764 | − | 0.328945i | −0.413980 | − | 0.910286i | \(-0.635862\pi\) |
−0.813660 | + | 0.581340i | \(0.802528\pi\) | |||||||
\(854\) | 5.97469 | 0.204450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.24745 | −0.179354 | ||||||||
\(857\) | −3.66855 | − | 0.982984i | −0.125315 | − | 0.0335781i | 0.195616 | − | 0.980680i | \(-0.437329\pi\) |
−0.320932 | + | 0.947102i | \(0.603996\pi\) | |||||||
\(858\) | −6.38447 | + | 37.2114i | −0.217962 | + | 1.27038i | ||||
\(859\) | −2.16064 | − | 1.24745i | −0.0737202 | − | 0.0425624i | 0.462687 | − | 0.886522i | \(-0.346885\pi\) |
−0.536407 | + | 0.843959i | \(0.680219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.42168 | − | 0.683837i | 0.252930 | − | 0.0233051i | ||||
\(862\) | −4.02628 | + | 15.0263i | −0.137136 | + | 0.511797i | ||||
\(863\) | −27.7842 | − | 27.7842i | −0.945787 | − | 0.945787i | 0.0528175 | − | 0.998604i | \(-0.483180\pi\) |
−0.998604 | + | 0.0528175i | \(0.983180\pi\) | |||||||
\(864\) | 5.03723 | + | 1.27526i | 0.171370 | + | 0.0433851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.4722 | − | 6.04612i | 0.355860 | − | 0.205456i | ||||
\(867\) | 3.09792 | − | 3.72674i | 0.105211 | − | 0.126567i | ||||
\(868\) | 1.26260 | + | 4.71209i | 0.0428555 | + | 0.159939i | ||||
\(869\) | 7.70674 | − | 13.3485i | 0.261433 | − | 0.452816i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.55051 | + | 11.3458i | 0.221956 | + | 0.384438i | ||||
\(872\) | −14.3885 | + | 14.3885i | −0.487257 | + | 0.487257i | ||||
\(873\) | 33.4105 | + | 2.61258i | 1.13078 | + | 0.0884225i | ||||
\(874\) | 1.55051i | 0.0524468i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.44949 | − | 2.97129i | −0.217908 | − | 0.100391i | ||||
\(877\) | 7.85813 | − | 2.10558i | 0.265350 | − | 0.0711004i | −0.123691 | − | 0.992321i | \(-0.539473\pi\) |
0.389041 | + | 0.921220i | \(0.372806\pi\) | |||||||
\(878\) | −9.85441 | + | 2.64048i | −0.332570 | + | 0.0891120i | ||||
\(879\) | −34.6803 | − | 15.9773i | −1.16974 | − | 0.538901i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.3006i | 1.96420i | 0.188368 | + | 0.982098i | \(0.439680\pi\) | ||||
−0.188368 | + | 0.982098i | \(0.560320\pi\) | |||||||
\(882\) | 9.84480 | − | 14.3397i | 0.331492 | − | 0.482843i | ||||
\(883\) | 40.2702 | − | 40.2702i | 1.35520 | − | 1.35520i | 0.475463 | − | 0.879736i | \(-0.342281\pi\) |
0.879736 | − | 0.475463i | \(-0.157719\pi\) | |||||||
\(884\) | 7.70674 | + | 13.3485i | 0.259206 | + | 0.448958i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.275255 | − | 0.476756i | 0.00924738 | − | 0.0160169i | ||||
\(887\) | −7.19464 | − | 26.8508i | −0.241572 | − | 0.901561i | −0.975075 | − | 0.221874i | \(-0.928783\pi\) |
0.733503 | − | 0.679686i | \(-0.237884\pi\) | |||||||
\(888\) | 4.69748 | − | 5.65099i | 0.157637 | − | 0.189635i | ||||
\(889\) | 18.9651 | − | 10.9495i | 0.636068 | − | 0.367234i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.5959 | − | 44.0477i | 1.19251 | − | 1.47565i | ||||
\(892\) | 5.87628 | + | 5.87628i | 0.196752 | + | 0.196752i | ||||
\(893\) | 3.61171 | − | 13.4791i | 0.120861 | − | 0.451061i | ||||
\(894\) | 22.2542 | − | 2.05051i | 0.744292 | − | 0.0685793i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.949490 | + | 0.548188i | 0.0317202 | + | 0.0183137i | ||||
\(897\) | 1.01461 | − | 5.91359i | 0.0338769 | − | 0.197449i | ||||
\(898\) | −20.9664 | − | 5.61793i | −0.699658 | − | 0.187473i | ||||
\(899\) | 13.9993 | 0.466902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5959 | 1.38576 | ||||||||
\(902\) | −23.8554 | − | 6.39204i | −0.794298 | − | 0.212832i | ||||
\(903\) | −6.17109 | + | 2.27840i | −0.205361 | + | 0.0758203i | ||||
\(904\) | −11.9494 | − | 6.89898i | −0.397431 | − | 0.229457i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.6515 | − | 33.9732i | 0.519987 | − | 1.12869i | ||||
\(907\) | −1.71089 | + | 6.38512i | −0.0568091 | + | 0.212015i | −0.988496 | − | 0.151248i | \(-0.951671\pi\) |
0.931687 | + | 0.363263i | \(0.118337\pi\) | |||||||
\(908\) | 10.6780 | + | 10.6780i | 0.354363 | + | 0.354363i | ||||
\(909\) | 2.47848 | + | 2.89898i | 0.0822061 | + | 0.0961531i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.12372 | − | 3.53553i | 0.202888 | − | 0.117137i | −0.395114 | − | 0.918632i | \(-0.629295\pi\) |
0.598002 | + | 0.801495i | \(0.295962\pi\) | |||||||
\(912\) | −2.64689 | − | 0.454134i | −0.0876472 | − | 0.0150379i | ||||
\(913\) | 0.896575 | + | 3.34607i | 0.0296723 | + | 0.110739i | ||||
\(914\) | 3.07483 | − | 5.32577i | 0.101706 | − | 0.176161i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.17423 | + | 14.1582i | 0.270084 | + | 0.467800i | ||||
\(917\) | −8.16744 | + | 8.16744i | −0.269713 | + | 0.269713i | ||||
\(918\) | −0.320053 | − | 23.1180i | −0.0105633 | − | 0.763008i | ||||
\(919\) | 27.3485i | 0.902143i | 0.892488 | + | 0.451071i | \(0.148958\pi\) | ||||
−0.892488 | + | 0.451071i | \(0.851042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.151531 | − | 1.64456i | −0.00499311 | − | 0.0541902i | ||||
\(922\) | −18.2654 | + | 4.89419i | −0.601538 | + | 0.161182i | ||||
\(923\) | 2.12701 | − | 0.569930i | 0.0700113 | − | 0.0187595i | ||||
\(924\) | 9.75663 | − | 6.89898i | 0.320970 | − | 0.226960i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 33.0197i | − | 1.08510i | ||||||
\(927\) | 11.0985 | − | 5.30057i | 0.364524 | − | 0.174094i | ||||
\(928\) | 2.22474 | − | 2.22474i | 0.0730308 | − | 0.0730308i | ||||
\(929\) | −23.9309 | − | 41.4495i | −0.785147 | − | 1.35991i | −0.928912 | − | 0.370302i | \(-0.879254\pi\) |
0.143765 | − | 0.989612i | \(-0.454079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.49490 | + | 7.78539i | −0.147314 | + | 0.255156i | ||||
\(932\) | 4.02477 | + | 15.0206i | 0.131836 | + | 0.492017i | ||||
\(933\) | −12.3445 | − | 33.4353i | −0.404140 | − | 1.09462i | ||||
\(934\) | 3.46410 | − | 2.00000i | 0.113349 | − | 0.0654420i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.79796 | + | 3.46410i | 0.320256 | + | 0.113228i | ||||
\(937\) | 12.8990 | + | 12.8990i | 0.421391 | + | 0.421391i | 0.885683 | − | 0.464291i | \(-0.153691\pi\) |
−0.464291 | + | 0.885683i | \(0.653691\pi\) | |||||||
\(938\) | 1.07317 | − | 4.00514i | 0.0350404 | − | 0.130773i | ||||
\(939\) | 5.02118 | + | 7.10102i | 0.163860 | + | 0.231733i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.47730 | + | 3.16232i | 0.178555 | + | 0.103089i | 0.586613 | − | 0.809867i | \(-0.300461\pi\) |
−0.408059 | + | 0.912956i | \(0.633794\pi\) | |||||||
\(942\) | −8.19105 | − | 6.80895i | −0.266879 | − | 0.221847i | ||||
\(943\) | 3.79107 | + | 1.01581i | 0.123454 | + | 0.0330795i | ||||
\(944\) | 11.8065 | 0.384269 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7980 | 0.708713 | ||||||||
\(947\) | −39.6468 | − | 10.6233i | −1.28835 | − | 0.345212i | −0.451316 | − | 0.892364i | \(-0.649045\pi\) |
−0.837033 | + | 0.547152i | \(0.815712\pi\) | |||||||
\(948\) | −3.26260 | − | 2.71209i | −0.105964 | − | 0.0880846i | ||||
\(949\) | −12.2993 | − | 7.10102i | −0.399253 | − | 0.230509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.10102 | − | 1.55708i | −0.0357030 | − | 0.0504917i | ||||
\(952\) | 1.26260 | − | 4.71209i | 0.0409211 | − | 0.152720i | ||||
\(953\) | 19.6561 | + | 19.6561i | 0.636724 | + | 0.636724i | 0.949746 | − | 0.313022i | \(-0.101341\pi\) |
−0.313022 | + | 0.949746i | \(0.601341\pi\) | |||||||
\(954\) | 21.3167 | − | 18.2247i | 0.690155 | − | 0.590048i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.6969 | + | 8.48528i | −0.475333 | + | 0.274434i | ||||
\(957\) | −11.8768 | − | 32.1686i | −0.383923 | − | 1.03986i | ||||
\(958\) | 1.83013 | + | 6.83013i | 0.0591287 | + | 0.220671i | ||||
\(959\) | −1.20713 | + | 2.09082i | −0.0389804 | + | 0.0675159i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.60102 | + | 9.70125i | 0.180678 | + | 0.312944i | ||||
\(962\) | 10.3923 | − | 10.3923i | 0.335061 | − | 0.335061i | ||||
\(963\) | 12.9782 | + | 8.91005i | 0.418215 | + | 0.287122i | ||||
\(964\) | − | 19.0000i | − | 0.611949i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.55051 | + | 1.09638i | −0.0498868 | + | 0.0352753i | ||||
\(967\) | −48.7319 | + | 13.0577i | −1.56711 | + | 0.419907i | −0.934907 | − | 0.354894i | \(-0.884517\pi\) |
−0.632206 | + | 0.774800i | \(0.717850\pi\) | |||||||
\(968\) | −27.6215 | + | 7.40117i | −0.887790 | + | 0.237883i | ||||
\(969\) | 1.09638 | + | 11.8990i | 0.0352207 | + | 0.382250i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 49.2117i | − | 1.57928i | −0.613570 | − | 0.789640i | \(-0.710267\pi\) | ||
0.613570 | − | 0.789640i | \(-0.289733\pi\) | |||||||
\(972\) | −10.2929 | − | 11.7071i | −0.330145 | − | 0.375506i | ||||
\(973\) | 10.0000 | − | 10.0000i | 0.320585 | − | 0.320585i | ||||
\(974\) | −8.48528 | − | 14.6969i | −0.271886 | − | 0.470920i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.72474 | + | 4.71940i | −0.0872170 | + | 0.151064i | ||||
\(977\) | −10.9985 | − | 41.0469i | −0.351873 | − | 1.31321i | −0.884374 | − | 0.466778i | \(-0.845415\pi\) |
0.532502 | − | 0.846429i | \(-0.321252\pi\) | |||||||
\(978\) | −1.08516 | − | 0.186185i | −0.0346997 | − | 0.00595353i | ||||
\(979\) | −12.9029 | + | 7.44949i | −0.412378 | + | 0.238087i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60.0176 | − | 11.1548i | 1.91621 | − | 0.356145i | ||||
\(982\) | −0.202041 | − | 0.202041i | −0.00644739 | − | 0.00644739i | ||||
\(983\) | −12.1122 | + | 45.2034i | −0.386319 | + | 1.44176i | 0.449757 | + | 0.893151i | \(0.351510\pi\) |
−0.836077 | + | 0.548612i | \(0.815156\pi\) | |||||||
\(984\) | −2.84448 | + | 6.17423i | −0.0906787 | + | 0.196827i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.1237 | − | 6.99964i | −0.386098 | − | 0.222914i | ||||
\(987\) | 16.0330 | − | 5.91945i | 0.510335 | − | 0.188418i | ||||
\(988\) | −5.18811 | − | 1.39015i | −0.165056 | − | 0.0442265i | ||||
\(989\) | −3.46410 | −0.110152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.7423 | −1.80248 | −0.901240 | − | 0.433320i | \(-0.857342\pi\) | ||||
−0.901240 | + | 0.433320i | \(0.857342\pi\) | |||||||
\(992\) | −4.29788 | − | 1.15161i | −0.136458 | − | 0.0365637i | ||||
\(993\) | −1.30323 | + | 7.59575i | −0.0413566 | + | 0.241044i | ||||
\(994\) | −0.603566 | − | 0.348469i | −0.0191440 | − | 0.0110528i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.949490 | − | 0.0874863i | 0.0300857 | − | 0.00277211i | ||||
\(997\) | 10.7053 | − | 39.9528i | 0.339041 | − | 1.26532i | −0.560381 | − | 0.828235i | \(-0.689345\pi\) |
0.899422 | − | 0.437082i | \(-0.143988\pi\) | |||||||
\(998\) | −6.29253 | − | 6.29253i | −0.199187 | − | 0.199187i | ||||
\(999\) | −21.2132 | + | 6.00000i | −0.671156 | + | 0.189832i |
(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 | 450.2.p.a.257.1 | 8 | ||
3.2 | odd | 2 | 1350.2.q.g.557.2 | 8 | |||
5.2 | odd | 4 | 90.2.l.a.23.2 | ✓ | 8 | ||
5.3 | odd | 4 | inner | 450.2.p.a.293.1 | 8 | ||
5.4 | even | 2 | 90.2.l.a.77.2 | yes | 8 | ||
9.2 | odd | 6 | inner | 450.2.p.a.407.1 | 8 | ||
9.7 | even | 3 | 1350.2.q.g.1007.2 | 8 | |||
15.2 | even | 4 | 270.2.m.a.233.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.g.1043.2 | 8 | |||
15.14 | odd | 2 | 270.2.m.a.17.1 | 8 | |||
20.7 | even | 4 | 720.2.cu.a.113.2 | 8 | |||
20.19 | odd | 2 | 720.2.cu.a.257.2 | 8 | |||
45.2 | even | 12 | 90.2.l.a.83.2 | yes | 8 | ||
45.4 | even | 6 | 810.2.f.b.647.1 | 8 | |||
45.7 | odd | 12 | 270.2.m.a.143.1 | 8 | |||
45.14 | odd | 6 | 810.2.f.b.647.4 | 8 | |||
45.22 | odd | 12 | 810.2.f.b.323.3 | 8 | |||
45.29 | odd | 6 | 90.2.l.a.47.2 | yes | 8 | ||
45.32 | even | 12 | 810.2.f.b.323.2 | 8 | |||
45.34 | even | 6 | 270.2.m.a.197.1 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.a.443.1 | 8 | ||
45.43 | odd | 12 | 1350.2.q.g.143.2 | 8 | |||
180.47 | odd | 12 | 720.2.cu.a.353.2 | 8 | |||
180.119 | even | 6 | 720.2.cu.a.497.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.a.23.2 | ✓ | 8 | 5.2 | odd | 4 | ||
90.2.l.a.47.2 | yes | 8 | 45.29 | odd | 6 | ||
90.2.l.a.77.2 | yes | 8 | 5.4 | even | 2 | ||
90.2.l.a.83.2 | yes | 8 | 45.2 | even | 12 | ||
270.2.m.a.17.1 | 8 | 15.14 | odd | 2 | |||
270.2.m.a.143.1 | 8 | 45.7 | odd | 12 | |||
270.2.m.a.197.1 | 8 | 45.34 | even | 6 | |||
270.2.m.a.233.1 | 8 | 15.2 | even | 4 | |||
450.2.p.a.257.1 | 8 | 1.1 | even | 1 | trivial | ||
450.2.p.a.293.1 | 8 | 5.3 | odd | 4 | inner | ||
450.2.p.a.407.1 | 8 | 9.2 | odd | 6 | inner | ||
450.2.p.a.443.1 | 8 | 45.38 | even | 12 | inner | ||
720.2.cu.a.113.2 | 8 | 20.7 | even | 4 | |||
720.2.cu.a.257.2 | 8 | 20.19 | odd | 2 | |||
720.2.cu.a.353.2 | 8 | 180.47 | odd | 12 | |||
720.2.cu.a.497.2 | 8 | 180.119 | even | 6 | |||
810.2.f.b.323.2 | 8 | 45.32 | even | 12 | |||
810.2.f.b.323.3 | 8 | 45.22 | odd | 12 | |||
810.2.f.b.647.1 | 8 | 45.4 | even | 6 | |||
810.2.f.b.647.4 | 8 | 45.14 | odd | 6 | |||
1350.2.q.g.143.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.g.557.2 | 8 | 3.2 | odd | 2 | |||
1350.2.q.g.1007.2 | 8 | 9.7 | even | 3 | |||
1350.2.q.g.1043.2 | 8 | 15.8 | even | 4 |