Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(87,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.m (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(116\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 87.18 | ||
Character | \(\chi\) | \(=\) | 731.87 |
Dual form | 731.2.m.b.689.18 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.544996 | + | 0.544996i | 0.385370 | + | 0.385370i | 0.873033 | − | 0.487662i | \(-0.162150\pi\) |
−0.487662 | + | 0.873033i | \(0.662150\pi\) | |||||||
\(3\) | −1.90994 | + | 0.791125i | −1.10271 | + | 0.456756i | −0.858420 | − | 0.512947i | \(-0.828554\pi\) |
−0.244287 | + | 0.969703i | \(0.578554\pi\) | |||||||
\(4\) | − | 1.40596i | − | 0.702979i | ||||||
\(5\) | 0.670095 | + | 1.61775i | 0.299676 | + | 0.723481i | 0.999954 | + | 0.00961115i | \(0.00305937\pi\) |
−0.700278 | + | 0.713870i | \(0.746941\pi\) | |||||||
\(6\) | −1.47207 | − | 0.609752i | −0.600971 | − | 0.248930i | ||||
\(7\) | 1.29182 | − | 3.11873i | 0.488263 | − | 1.17877i | −0.467330 | − | 0.884083i | \(-0.654784\pi\) |
0.955593 | − | 0.294688i | \(-0.0952158\pi\) | |||||||
\(8\) | 1.85623 | − | 1.85623i | 0.656278 | − | 0.656278i | ||||
\(9\) | 0.900688 | − | 0.900688i | 0.300229 | − | 0.300229i | ||||
\(10\) | −0.516470 | + | 1.24687i | −0.163322 | + | 0.394295i | ||||
\(11\) | −4.86339 | − | 2.01448i | −1.46637 | − | 0.607390i | −0.500341 | − | 0.865828i | \(-0.666792\pi\) |
−0.966028 | + | 0.258439i | \(0.916792\pi\) | |||||||
\(12\) | 1.11229 | + | 2.68530i | 0.321090 | + | 0.775180i | ||||
\(13\) | 2.36005i | 0.654559i | 0.944928 | + | 0.327280i | \(0.106132\pi\) | ||||
−0.944928 | + | 0.327280i | \(0.893868\pi\) | |||||||
\(14\) | 2.40374 | − | 0.995660i | 0.642426 | − | 0.266101i | ||||
\(15\) | −2.55969 | − | 2.55969i | −0.660909 | − | 0.660909i | ||||
\(16\) | −0.788636 | −0.197159 | ||||||||
\(17\) | −0.687043 | + | 4.06546i | −0.166632 | + | 0.986019i | ||||
\(18\) | 0.981743 | 0.231399 | ||||||||
\(19\) | −3.34074 | − | 3.34074i | −0.766419 | − | 0.766419i | 0.211055 | − | 0.977474i | \(-0.432310\pi\) |
−0.977474 | + | 0.211055i | \(0.932310\pi\) | |||||||
\(20\) | 2.27449 | − | 0.942126i | 0.508592 | − | 0.210666i | ||||
\(21\) | 6.97860i | 1.52286i | ||||||||
\(22\) | −1.55265 | − | 3.74842i | −0.331025 | − | 0.799165i | ||||
\(23\) | −7.31247 | − | 3.02893i | −1.52476 | − | 0.631575i | −0.546219 | − | 0.837643i | \(-0.683933\pi\) |
−0.978538 | + | 0.206068i | \(0.933933\pi\) | |||||||
\(24\) | −2.07679 | + | 5.01382i | −0.423923 | + | 1.02344i | ||||
\(25\) | 1.36744 | − | 1.36744i | 0.273487 | − | 0.273487i | ||||
\(26\) | −1.28622 | + | 1.28622i | −0.252248 | + | 0.252248i | ||||
\(27\) | 1.36567 | − | 3.29701i | 0.262823 | − | 0.634510i | ||||
\(28\) | −4.38481 | − | 1.81625i | −0.828652 | − | 0.343239i | ||||
\(29\) | −2.32635 | − | 5.61631i | −0.431992 | − | 1.04292i | −0.978644 | − | 0.205562i | \(-0.934098\pi\) |
0.546652 | − | 0.837360i | \(-0.315902\pi\) | |||||||
\(30\) | − | 2.79004i | − | 0.509390i | ||||||
\(31\) | −2.55067 | + | 1.05652i | −0.458115 | + | 0.189757i | −0.599793 | − | 0.800156i | \(-0.704750\pi\) |
0.141678 | + | 0.989913i | \(0.454750\pi\) | |||||||
\(32\) | −4.14227 | − | 4.14227i | −0.732257 | − | 0.732257i | ||||
\(33\) | 10.8825 | 1.89440 | ||||||||
\(34\) | −2.59010 | + | 1.84122i | −0.444198 | + | 0.315767i | ||||
\(35\) | 5.91099 | 0.999139 | ||||||||
\(36\) | −1.26633 | − | 1.26633i | −0.211055 | − | 0.211055i | ||||
\(37\) | 8.24203 | − | 3.41396i | 1.35498 | − | 0.561252i | 0.417307 | − | 0.908766i | \(-0.362974\pi\) |
0.937675 | + | 0.347514i | \(0.112974\pi\) | |||||||
\(38\) | − | 3.64138i | − | 0.590710i | ||||||
\(39\) | −1.86709 | − | 4.50756i | −0.298974 | − | 0.721787i | ||||
\(40\) | 4.24678 | + | 1.75908i | 0.671475 | + | 0.278134i | ||||
\(41\) | 1.86196 | − | 4.49517i | 0.290790 | − | 0.702028i | −0.709206 | − | 0.705001i | \(-0.750946\pi\) |
0.999996 | + | 0.00297314i | \(0.000946381\pi\) | |||||||
\(42\) | −3.80331 | + | 3.80331i | −0.586864 | + | 0.586864i | ||||
\(43\) | 0.707107 | − | 0.707107i | 0.107833 | − | 0.107833i | ||||
\(44\) | −2.83228 | + | 6.83773i | −0.426982 | + | 1.03083i | ||||
\(45\) | 2.06064 | + | 0.853545i | 0.307182 | + | 0.127239i | ||||
\(46\) | −2.33452 | − | 5.63602i | −0.344206 | − | 0.830986i | ||||
\(47\) | 11.2746i | 1.64457i | 0.569077 | + | 0.822284i | \(0.307301\pi\) | ||||
−0.569077 | + | 0.822284i | \(0.692699\pi\) | |||||||
\(48\) | 1.50625 | − | 0.623909i | 0.217409 | − | 0.0900536i | ||||
\(49\) | −3.10796 | − | 3.10796i | −0.443994 | − | 0.443994i | ||||
\(50\) | 1.49049 | 0.210788 | ||||||||
\(51\) | −1.90407 | − | 8.30834i | −0.266623 | − | 1.16340i | ||||
\(52\) | 3.31813 | 0.460141 | ||||||||
\(53\) | −1.82572 | − | 1.82572i | −0.250782 | − | 0.250782i | 0.570509 | − | 0.821291i | \(-0.306746\pi\) |
−0.821291 | + | 0.570509i | \(0.806746\pi\) | |||||||
\(54\) | 2.54114 | − | 1.05258i | 0.345806 | − | 0.143237i | ||||
\(55\) | − | 9.21767i | − | 1.24291i | ||||||
\(56\) | −3.39118 | − | 8.18703i | −0.453165 | − | 1.09404i | ||||
\(57\) | 9.02357 | + | 3.73769i | 1.19520 | + | 0.495069i | ||||
\(58\) | 1.79301 | − | 4.32872i | 0.235434 | − | 0.568389i | ||||
\(59\) | −0.966745 | + | 0.966745i | −0.125860 | + | 0.125860i | −0.767231 | − | 0.641371i | \(-0.778366\pi\) |
0.641371 | + | 0.767231i | \(0.278366\pi\) | |||||||
\(60\) | −3.59882 | + | 3.59882i | −0.464605 | + | 0.464605i | ||||
\(61\) | 4.96634 | − | 11.9898i | 0.635875 | − | 1.53514i | −0.196252 | − | 0.980554i | \(-0.562877\pi\) |
0.832127 | − | 0.554585i | \(-0.187123\pi\) | |||||||
\(62\) | −1.96591 | − | 0.814306i | −0.249671 | − | 0.103417i | ||||
\(63\) | −1.64548 | − | 3.97254i | −0.207311 | − | 0.500493i | ||||
\(64\) | − | 2.93777i | − | 0.367222i | ||||||
\(65\) | −3.81797 | + | 1.58146i | −0.473561 | + | 0.196156i | ||||
\(66\) | 5.93093 | + | 5.93093i | 0.730047 | + | 0.730047i | ||||
\(67\) | −5.57905 | −0.681589 | −0.340795 | − | 0.940138i | \(-0.610696\pi\) | ||||
−0.340795 | + | 0.940138i | \(0.610696\pi\) | |||||||
\(68\) | 5.71587 | + | 0.965954i | 0.693151 | + | 0.117139i | ||||
\(69\) | 16.3627 | 1.96983 | ||||||||
\(70\) | 3.22147 | + | 3.22147i | 0.385039 | + | 0.385039i | ||||
\(71\) | −2.89331 | + | 1.19845i | −0.343373 | + | 0.142230i | −0.547704 | − | 0.836672i | \(-0.684498\pi\) |
0.204331 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(72\) | − | 3.34378i | − | 0.394068i | ||||||
\(73\) | −1.38379 | − | 3.34076i | −0.161960 | − | 0.391006i | 0.821977 | − | 0.569520i | \(-0.192871\pi\) |
−0.983937 | + | 0.178514i | \(0.942871\pi\) | |||||||
\(74\) | 6.35247 | + | 2.63128i | 0.738460 | + | 0.305880i | ||||
\(75\) | −1.52991 | + | 3.69354i | −0.176659 | + | 0.426493i | ||||
\(76\) | −4.69694 | + | 4.69694i | −0.538776 | + | 0.538776i | ||||
\(77\) | −12.5653 | + | 12.5653i | −1.43195 | + | 1.43195i | ||||
\(78\) | 1.43904 | − | 3.47416i | 0.162940 | − | 0.393371i | ||||
\(79\) | −12.3676 | − | 5.12281i | −1.39146 | − | 0.576362i | −0.443939 | − | 0.896057i | \(-0.646419\pi\) |
−0.947520 | + | 0.319695i | \(0.896419\pi\) | |||||||
\(80\) | −0.528461 | − | 1.27582i | −0.0590838 | − | 0.142641i | ||||
\(81\) | 11.1988i | 1.24431i | ||||||||
\(82\) | 3.46461 | − | 1.43509i | 0.382603 | − | 0.158479i | ||||
\(83\) | −6.26970 | − | 6.26970i | −0.688189 | − | 0.688189i | 0.273642 | − | 0.961832i | \(-0.411772\pi\) |
−0.961832 | + | 0.273642i | \(0.911772\pi\) | |||||||
\(84\) | 9.81163 | 1.07054 | ||||||||
\(85\) | −7.03730 | + | 1.61278i | −0.763302 | + | 0.174931i | ||||
\(86\) | 0.770741 | 0.0831111 | ||||||||
\(87\) | 8.88640 | + | 8.88640i | 0.952722 | + | 0.952722i | ||||
\(88\) | −12.7670 | + | 5.28825i | −1.36096 | + | 0.563729i | ||||
\(89\) | 3.29131i | 0.348878i | 0.984668 | + | 0.174439i | \(0.0558112\pi\) | ||||
−0.984668 | + | 0.174439i | \(0.944189\pi\) | |||||||
\(90\) | 0.657862 | + | 1.58822i | 0.0693447 | + | 0.167413i | ||||
\(91\) | 7.36036 | + | 3.04876i | 0.771575 | + | 0.319597i | ||||
\(92\) | −4.25854 | + | 10.2810i | −0.443984 | + | 1.07187i | ||||
\(93\) | 4.03580 | − | 4.03580i | 0.418493 | − | 0.418493i | ||||
\(94\) | −6.14461 | + | 6.14461i | −0.633768 | + | 0.633768i | ||||
\(95\) | 3.16588 | − | 7.64311i | 0.324813 | − | 0.784167i | ||||
\(96\) | 11.1886 | + | 4.63445i | 1.14193 | + | 0.473002i | ||||
\(97\) | 3.23825 | + | 7.81783i | 0.328795 | + | 0.793780i | 0.998682 | + | 0.0513180i | \(0.0163422\pi\) |
−0.669888 | + | 0.742462i | \(0.733658\pi\) | |||||||
\(98\) | − | 3.38765i | − | 0.342204i | ||||||
\(99\) | −6.19483 | + | 2.56598i | −0.622603 | + | 0.257891i | ||||
\(100\) | −1.92256 | − | 1.92256i | −0.192256 | − | 0.192256i | ||||
\(101\) | −10.2345 | −1.01837 | −0.509186 | − | 0.860657i | \(-0.670053\pi\) | ||||
−0.509186 | + | 0.860657i | \(0.670053\pi\) | |||||||
\(102\) | 3.49030 | − | 5.56573i | 0.345591 | − | 0.551089i | ||||
\(103\) | 10.9607 | 1.07999 | 0.539997 | − | 0.841667i | \(-0.318425\pi\) | ||||
0.539997 | + | 0.841667i | \(0.318425\pi\) | |||||||
\(104\) | 4.38080 | + | 4.38080i | 0.429573 | + | 0.429573i | ||||
\(105\) | −11.2897 | + | 4.67633i | −1.10176 | + | 0.456363i | ||||
\(106\) | − | 1.99002i | − | 0.193288i | ||||||
\(107\) | −0.00422798 | − | 0.0102073i | −0.000408734 | − | 0.000986772i | 0.923675 | − | 0.383177i | \(-0.125170\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(108\) | −4.63546 | − | 1.92007i | −0.446047 | − | 0.184759i | ||||
\(109\) | 0.0587593 | − | 0.141858i | 0.00562812 | − | 0.0135875i | −0.921040 | − | 0.389467i | \(-0.872659\pi\) |
0.926669 | + | 0.375879i | \(0.122659\pi\) | |||||||
\(110\) | 5.02360 | − | 5.02360i | 0.478981 | − | 0.478981i | ||||
\(111\) | −13.0409 | + | 13.0409i | −1.23779 | + | 1.23779i | ||||
\(112\) | −1.01878 | + | 2.45955i | −0.0962654 | + | 0.232405i | ||||
\(113\) | 0.334452 | + | 0.138535i | 0.0314626 | + | 0.0130322i | 0.398359 | − | 0.917229i | \(-0.369580\pi\) |
−0.366897 | + | 0.930262i | \(0.619580\pi\) | |||||||
\(114\) | 2.88079 | + | 6.95484i | 0.269811 | + | 0.651380i | ||||
\(115\) | − | 13.8595i | − | 1.29240i | ||||||
\(116\) | −7.89629 | + | 3.27075i | −0.733153 | + | 0.303682i | ||||
\(117\) | 2.12567 | + | 2.12567i | 0.196518 | + | 0.196518i | ||||
\(118\) | −1.05374 | −0.0970051 | ||||||||
\(119\) | 11.7916 | + | 7.39456i | 1.08093 | + | 0.677858i | ||||
\(120\) | −9.50277 | −0.867480 | ||||||||
\(121\) | 11.8163 | + | 11.8163i | 1.07421 | + | 1.07421i | ||||
\(122\) | 9.24104 | − | 3.82777i | 0.836645 | − | 0.346550i | ||||
\(123\) | 10.0586i | 0.906951i | ||||||||
\(124\) | 1.48543 | + | 3.58614i | 0.133395 | + | 0.322045i | ||||
\(125\) | 11.2173 | + | 4.64634i | 1.00330 | + | 0.415581i | ||||
\(126\) | 1.26824 | − | 3.06180i | 0.112984 | − | 0.272767i | ||||
\(127\) | 8.21518 | − | 8.21518i | 0.728979 | − | 0.728979i | −0.241437 | − | 0.970416i | \(-0.577619\pi\) |
0.970416 | + | 0.241437i | \(0.0776188\pi\) | |||||||
\(128\) | −6.68347 | + | 6.68347i | −0.590741 | + | 0.590741i | ||||
\(129\) | −0.791125 | + | 1.90994i | −0.0696547 | + | 0.168161i | ||||
\(130\) | −2.94267 | − | 1.21889i | −0.258089 | − | 0.106904i | ||||
\(131\) | 5.92235 | + | 14.2978i | 0.517438 | + | 1.24921i | 0.939472 | + | 0.342626i | \(0.111316\pi\) |
−0.422034 | + | 0.906580i | \(0.638684\pi\) | |||||||
\(132\) | − | 15.3004i | − | 1.33173i | ||||||
\(133\) | −14.7345 | + | 6.10324i | −1.27765 | + | 0.529218i | ||||
\(134\) | −3.04056 | − | 3.04056i | −0.262664 | − | 0.262664i | ||||
\(135\) | 6.24888 | 0.537818 | ||||||||
\(136\) | 6.27113 | + | 8.82176i | 0.537745 | + | 0.756460i | ||||
\(137\) | 5.02391 | 0.429221 | 0.214611 | − | 0.976700i | \(-0.431152\pi\) | ||||
0.214611 | + | 0.976700i | \(0.431152\pi\) | |||||||
\(138\) | 8.91760 | + | 8.91760i | 0.759116 | + | 0.759116i | ||||
\(139\) | 8.29640 | − | 3.43648i | 0.703692 | − | 0.291479i | −0.00199967 | − | 0.999998i | \(-0.500637\pi\) |
0.705691 | + | 0.708519i | \(0.250637\pi\) | |||||||
\(140\) | − | 8.31060i | − | 0.702374i | ||||||
\(141\) | −8.91961 | − | 21.5338i | −0.751167 | − | 1.81348i | ||||
\(142\) | −2.22999 | − | 0.923693i | −0.187137 | − | 0.0775146i | ||||
\(143\) | 4.75428 | − | 11.4778i | 0.397572 | − | 0.959825i | ||||
\(144\) | −0.710315 | + | 0.710315i | −0.0591929 | + | 0.0591929i | ||||
\(145\) | 7.52692 | − | 7.52692i | 0.625077 | − | 0.625077i | ||||
\(146\) | 1.06654 | − | 2.57486i | 0.0882676 | − | 0.213097i | ||||
\(147\) | 8.39480 | + | 3.47724i | 0.692392 | + | 0.286798i | ||||
\(148\) | −4.79989 | − | 11.5880i | −0.394548 | − | 0.952524i | ||||
\(149\) | 19.8308i | 1.62461i | 0.583236 | + | 0.812303i | \(0.301786\pi\) | ||||
−0.583236 | + | 0.812303i | \(0.698214\pi\) | |||||||
\(150\) | −2.84676 | + | 1.17917i | −0.232437 | + | 0.0962786i | ||||
\(151\) | 12.1386 | + | 12.1386i | 0.987827 | + | 0.987827i | 0.999927 | − | 0.0120998i | \(-0.00385157\pi\) |
−0.0120998 | + | 0.999927i | \(0.503852\pi\) | |||||||
\(152\) | −12.4024 | −1.00597 | ||||||||
\(153\) | 3.04290 | + | 4.28052i | 0.246004 | + | 0.346060i | ||||
\(154\) | −13.6961 | −1.10366 | ||||||||
\(155\) | −3.41839 | − | 3.41839i | −0.274572 | − | 0.274572i | ||||
\(156\) | −6.33744 | + | 2.62505i | −0.507401 | + | 0.210172i | ||||
\(157\) | 5.60725i | 0.447508i | 0.974646 | + | 0.223754i | \(0.0718311\pi\) | ||||
−0.974646 | + | 0.223754i | \(0.928169\pi\) | |||||||
\(158\) | −3.94836 | − | 9.53219i | −0.314115 | − | 0.758340i | ||||
\(159\) | 4.93140 | + | 2.04265i | 0.391085 | + | 0.161993i | ||||
\(160\) | 3.92546 | − | 9.47689i | 0.310335 | − | 0.749214i | ||||
\(161\) | −18.8928 | + | 18.8928i | −1.48896 | + | 1.48896i | ||||
\(162\) | −6.10331 | + | 6.10331i | −0.479522 | + | 0.479522i | ||||
\(163\) | 4.94668 | − | 11.9424i | 0.387454 | − | 0.935397i | −0.603023 | − | 0.797723i | \(-0.706037\pi\) |
0.990478 | − | 0.137674i | \(-0.0439625\pi\) | |||||||
\(164\) | −6.32003 | − | 2.61784i | −0.493511 | − | 0.204419i | ||||
\(165\) | 7.29233 | + | 17.6052i | 0.567707 | + | 1.37057i | ||||
\(166\) | − | 6.83393i | − | 0.530416i | ||||||
\(167\) | 12.5187 | − | 5.18542i | 0.968727 | − | 0.401260i | 0.158489 | − | 0.987361i | \(-0.449338\pi\) |
0.810238 | + | 0.586101i | \(0.199338\pi\) | |||||||
\(168\) | 12.9539 | + | 12.9539i | 0.999417 | + | 0.999417i | ||||
\(169\) | 7.43018 | 0.571552 | ||||||||
\(170\) | −4.71426 | − | 2.95634i | −0.361567 | − | 0.226741i | ||||
\(171\) | −6.01793 | −0.460203 | ||||||||
\(172\) | −0.994163 | − | 0.994163i | −0.0758042 | − | 0.0758042i | ||||
\(173\) | −18.6961 | + | 7.74419i | −1.42144 | + | 0.588780i | −0.955222 | − | 0.295890i | \(-0.904384\pi\) |
−0.466218 | + | 0.884670i | \(0.654384\pi\) | |||||||
\(174\) | 9.68611i | 0.734302i | ||||||||
\(175\) | −2.49818 | − | 6.03115i | −0.188845 | − | 0.455912i | ||||
\(176\) | 3.83545 | + | 1.58869i | 0.289108 | + | 0.119752i | ||||
\(177\) | 1.08161 | − | 2.61125i | 0.0812990 | − | 0.196273i | ||||
\(178\) | −1.79375 | + | 1.79375i | −0.134447 | + | 0.134447i | ||||
\(179\) | −4.15779 | + | 4.15779i | −0.310768 | + | 0.310768i | −0.845207 | − | 0.534439i | \(-0.820523\pi\) |
0.534439 | + | 0.845207i | \(0.320523\pi\) | |||||||
\(180\) | 1.20005 | − | 2.89717i | 0.0894463 | − | 0.215942i | ||||
\(181\) | −22.5914 | − | 9.35768i | −1.67921 | − | 0.695551i | −0.679921 | − | 0.733285i | \(-0.737986\pi\) |
−0.999288 | + | 0.0377342i | \(0.987986\pi\) | |||||||
\(182\) | 2.34980 | + | 5.67293i | 0.174179 | + | 0.420506i | ||||
\(183\) | 26.8289i | 1.98325i | ||||||||
\(184\) | −19.1961 | + | 7.95127i | −1.41515 | + | 0.586175i | ||||
\(185\) | 11.0459 | + | 11.0459i | 0.812110 | + | 0.812110i | ||||
\(186\) | 4.39899 | 0.322550 | ||||||||
\(187\) | 11.5312 | − | 18.3879i | 0.843243 | − | 1.34466i | ||||
\(188\) | 15.8516 | 1.15610 | ||||||||
\(189\) | −8.51831 | − | 8.51831i | −0.619616 | − | 0.619616i | ||||
\(190\) | 5.89086 | − | 2.44007i | 0.427368 | − | 0.177022i | ||||
\(191\) | − | 9.32216i | − | 0.674528i | −0.941410 | − | 0.337264i | \(-0.890499\pi\) | ||
0.941410 | − | 0.337264i | \(-0.109501\pi\) | |||||||
\(192\) | 2.32415 | + | 5.61098i | 0.167731 | + | 0.404938i | ||||
\(193\) | −2.05390 | − | 0.850754i | −0.147843 | − | 0.0612386i | 0.307535 | − | 0.951537i | \(-0.400496\pi\) |
−0.455378 | + | 0.890298i | \(0.650496\pi\) | |||||||
\(194\) | −2.49585 | + | 6.02552i | −0.179192 | + | 0.432607i | ||||
\(195\) | 6.04099 | − | 6.04099i | 0.432604 | − | 0.432604i | ||||
\(196\) | −4.36966 | + | 4.36966i | −0.312118 | + | 0.312118i | ||||
\(197\) | 6.77556 | − | 16.3576i | 0.482739 | − | 1.16543i | −0.475565 | − | 0.879681i | \(-0.657756\pi\) |
0.958303 | − | 0.285753i | \(-0.0922438\pi\) | |||||||
\(198\) | −4.77461 | − | 1.97771i | −0.339316 | − | 0.140549i | ||||
\(199\) | 4.51683 | + | 10.9046i | 0.320190 | + | 0.773007i | 0.999242 | + | 0.0389170i | \(0.0123908\pi\) |
−0.679053 | + | 0.734090i | \(0.737609\pi\) | |||||||
\(200\) | − | 5.07656i | − | 0.358967i | ||||||
\(201\) | 10.6557 | − | 4.41372i | 0.751593 | − | 0.311320i | ||||
\(202\) | −5.57777 | − | 5.57777i | −0.392450 | − | 0.392450i | ||||
\(203\) | −20.5210 | −1.44029 | ||||||||
\(204\) | −11.6812 | + | 2.67705i | −0.817846 | + | 0.187431i | ||||
\(205\) | 8.51978 | 0.595047 | ||||||||
\(206\) | 5.97356 | + | 5.97356i | 0.416198 | + | 0.416198i | ||||
\(207\) | −9.31438 | + | 3.85814i | −0.647394 | + | 0.268159i | ||||
\(208\) | − | 1.86122i | − | 0.129052i | ||||||
\(209\) | 9.51747 | + | 22.9772i | 0.658337 | + | 1.58937i | ||||
\(210\) | −8.70140 | − | 3.60424i | −0.600454 | − | 0.248716i | ||||
\(211\) | −7.66707 | + | 18.5100i | −0.527823 | + | 1.27428i | 0.405123 | + | 0.914262i | \(0.367229\pi\) |
−0.932946 | + | 0.360016i | \(0.882771\pi\) | |||||||
\(212\) | −2.56689 | + | 2.56689i | −0.176295 | + | 0.176295i | ||||
\(213\) | 4.57794 | − | 4.57794i | 0.313675 | − | 0.313675i | ||||
\(214\) | 0.00325868 | − | 0.00786715i | 0.000222759 | − | 0.000537787i | ||||
\(215\) | 1.61775 | + | 0.670095i | 0.110330 | + | 0.0457001i | ||||
\(216\) | −3.58503 | − | 8.65502i | −0.243930 | − | 0.588900i | ||||
\(217\) | 9.31972i | 0.632664i | ||||||||
\(218\) | 0.109335 | − | 0.0452882i | 0.00740513 | − | 0.00306731i | ||||
\(219\) | 5.28591 | + | 5.28591i | 0.357189 | + | 0.357189i | ||||
\(220\) | −12.9597 | −0.873740 | ||||||||
\(221\) | −9.59468 | − | 1.62145i | −0.645408 | − | 0.109071i | ||||
\(222\) | −14.2145 | −0.954017 | ||||||||
\(223\) | 1.47780 | + | 1.47780i | 0.0989609 | + | 0.0989609i | 0.754854 | − | 0.655893i | \(-0.227708\pi\) |
−0.655893 | + | 0.754854i | \(0.727708\pi\) | |||||||
\(224\) | −18.2697 | + | 7.56757i | −1.22070 | + | 0.505629i | ||||
\(225\) | − | 2.46327i | − | 0.164218i | ||||||
\(226\) | 0.106774 | + | 0.257776i | 0.00710252 | + | 0.0171470i | ||||
\(227\) | −6.80375 | − | 2.81821i | −0.451581 | − | 0.187051i | 0.145289 | − | 0.989389i | \(-0.453589\pi\) |
−0.596869 | + | 0.802338i | \(0.703589\pi\) | |||||||
\(228\) | 5.25503 | − | 12.6868i | 0.348023 | − | 0.840202i | ||||
\(229\) | 0.306280 | − | 0.306280i | 0.0202395 | − | 0.0202395i | −0.696915 | − | 0.717154i | \(-0.745444\pi\) |
0.717154 | + | 0.696915i | \(0.245444\pi\) | |||||||
\(230\) | 7.55335 | − | 7.55335i | 0.498053 | − | 0.498053i | ||||
\(231\) | 14.0583 | − | 33.9397i | 0.924967 | − | 2.23307i | ||||
\(232\) | −14.7434 | − | 6.10693i | −0.967954 | − | 0.400940i | ||||
\(233\) | −8.63619 | − | 20.8496i | −0.565776 | − | 1.36590i | −0.905086 | − | 0.425229i | \(-0.860194\pi\) |
0.339310 | − | 0.940674i | \(-0.389806\pi\) | |||||||
\(234\) | 2.31696i | 0.151464i | ||||||||
\(235\) | −18.2395 | + | 7.55505i | −1.18981 | + | 0.492837i | ||||
\(236\) | 1.35920 | + | 1.35920i | 0.0884766 | + | 0.0884766i | ||||
\(237\) | 27.6741 | 1.79763 | ||||||||
\(238\) | 2.39635 | + | 10.4564i | 0.155332 | + | 0.677785i | ||||
\(239\) | 24.3048 | 1.57215 | 0.786073 | − | 0.618134i | \(-0.212111\pi\) | ||||
0.786073 | + | 0.618134i | \(0.212111\pi\) | |||||||
\(240\) | 2.01866 | + | 2.01866i | 0.130304 | + | 0.130304i | ||||
\(241\) | −5.13003 | + | 2.12493i | −0.330454 | + | 0.136879i | −0.541741 | − | 0.840546i | \(-0.682235\pi\) |
0.211287 | + | 0.977424i | \(0.432235\pi\) | |||||||
\(242\) | 12.8797i | 0.827936i | ||||||||
\(243\) | −4.76266 | − | 11.4981i | −0.305525 | − | 0.737602i | ||||
\(244\) | −16.8572 | − | 6.98247i | −1.07917 | − | 0.447007i | ||||
\(245\) | 2.94528 | − | 7.11053i | 0.188167 | − | 0.454275i | ||||
\(246\) | −5.48189 | + | 5.48189i | −0.349512 | + | 0.349512i | ||||
\(247\) | 7.88430 | − | 7.88430i | 0.501666 | − | 0.501666i | ||||
\(248\) | −2.77349 | + | 6.69580i | −0.176117 | + | 0.425184i | ||||
\(249\) | 16.9349 | + | 7.01467i | 1.07321 | + | 0.444536i | ||||
\(250\) | 3.58112 | + | 8.64560i | 0.226490 | + | 0.546796i | ||||
\(251\) | − | 19.5181i | − | 1.23197i | −0.787758 | − | 0.615984i | \(-0.788758\pi\) | ||
0.787758 | − | 0.615984i | \(-0.211242\pi\) | |||||||
\(252\) | −5.58522 | + | 2.31347i | −0.351836 | + | 0.145735i | ||||
\(253\) | 29.4617 | + | 29.4617i | 1.85224 | + | 1.85224i | ||||
\(254\) | 8.95448 | 0.561854 | ||||||||
\(255\) | 12.1649 | − | 8.64770i | 0.761798 | − | 0.541540i | ||||
\(256\) | −13.1605 | −0.822530 | ||||||||
\(257\) | −9.89797 | − | 9.89797i | −0.617418 | − | 0.617418i | 0.327450 | − | 0.944868i | \(-0.393811\pi\) |
−0.944868 | + | 0.327450i | \(0.893811\pi\) | |||||||
\(258\) | −1.47207 | + | 0.609752i | −0.0916472 | + | 0.0379615i | ||||
\(259\) | − | 30.1149i | − | 1.87125i | ||||||
\(260\) | 2.22346 | + | 5.36791i | 0.137893 | + | 0.332904i | ||||
\(261\) | −7.15386 | − | 2.96323i | −0.442813 | − | 0.183419i | ||||
\(262\) | −4.56460 | + | 11.0199i | −0.282002 | + | 0.680812i | ||||
\(263\) | 16.9773 | − | 16.9773i | 1.04686 | − | 1.04686i | 0.0480182 | − | 0.998846i | \(-0.484709\pi\) |
0.998846 | − | 0.0480182i | \(-0.0152905\pi\) | |||||||
\(264\) | 20.2005 | − | 20.2005i | 1.24326 | − | 1.24326i | ||||
\(265\) | 1.73016 | − | 4.17697i | 0.106283 | − | 0.256589i | ||||
\(266\) | −11.3565 | − | 4.70402i | −0.696312 | − | 0.288422i | ||||
\(267\) | −2.60384 | − | 6.28622i | −0.159352 | − | 0.384710i | ||||
\(268\) | 7.84391i | 0.479143i | ||||||||
\(269\) | 17.8616 | − | 7.39850i | 1.08904 | − | 0.451094i | 0.235367 | − | 0.971907i | \(-0.424371\pi\) |
0.853671 | + | 0.520812i | \(0.174371\pi\) | |||||||
\(270\) | 3.40562 | + | 3.40562i | 0.207259 | + | 0.207259i | ||||
\(271\) | 5.39034 | 0.327440 | 0.163720 | − | 0.986507i | \(-0.447651\pi\) | ||||
0.163720 | + | 0.986507i | \(0.447651\pi\) | |||||||
\(272\) | 0.541827 | − | 3.20617i | 0.0328531 | − | 0.194402i | ||||
\(273\) | −16.4698 | −0.996799 | ||||||||
\(274\) | 2.73801 | + | 2.73801i | 0.165409 | + | 0.165409i | ||||
\(275\) | −9.40505 | + | 3.89570i | −0.567146 | + | 0.234920i | ||||
\(276\) | − | 23.0052i | − | 1.38475i | ||||||
\(277\) | −5.27134 | − | 12.7261i | −0.316724 | − | 0.764639i | −0.999424 | − | 0.0339403i | \(-0.989194\pi\) |
0.682700 | − | 0.730699i | \(-0.260806\pi\) | |||||||
\(278\) | 6.39438 | + | 2.64864i | 0.383509 | + | 0.158855i | ||||
\(279\) | −1.34576 | + | 3.24896i | −0.0805688 | + | 0.194510i | ||||
\(280\) | 10.9722 | − | 10.9722i | 0.655713 | − | 0.655713i | ||||
\(281\) | 6.47732 | − | 6.47732i | 0.386405 | − | 0.386405i | −0.486998 | − | 0.873403i | \(-0.661908\pi\) |
0.873403 | + | 0.486998i | \(0.161908\pi\) | |||||||
\(282\) | 6.87471 | − | 16.5970i | 0.409383 | − | 0.988338i | ||||
\(283\) | −4.59699 | − | 1.90414i | −0.273263 | − | 0.113189i | 0.241844 | − | 0.970315i | \(-0.422248\pi\) |
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(284\) | 1.68497 | + | 4.06787i | 0.0999844 | + | 0.241384i | ||||
\(285\) | 17.1025i | 1.01307i | ||||||||
\(286\) | 8.84644 | − | 3.66431i | 0.523101 | − | 0.216675i | ||||
\(287\) | −11.6139 | − | 11.6139i | −0.685549 | − | 0.685549i | ||||
\(288\) | −7.46179 | −0.439690 | ||||||||
\(289\) | −16.0559 | − | 5.58630i | −0.944467 | − | 0.328606i | ||||
\(290\) | 8.20429 | 0.481772 | ||||||||
\(291\) | −12.3698 | − | 12.3698i | −0.725128 | − | 0.725128i | ||||
\(292\) | −4.69697 | + | 1.94555i | −0.274869 | + | 0.113855i | ||||
\(293\) | − | 12.6198i | − | 0.737258i | −0.929577 | − | 0.368629i | \(-0.879827\pi\) | ||
0.929577 | − | 0.368629i | \(-0.120173\pi\) | |||||||
\(294\) | 2.68005 | + | 6.47022i | 0.156304 | + | 0.377351i | ||||
\(295\) | −2.21177 | − | 0.916144i | −0.128774 | − | 0.0533400i | ||||
\(296\) | 8.96203 | − | 21.6362i | 0.520907 | − | 1.25758i | ||||
\(297\) | −13.2836 | + | 13.2836i | −0.770790 | + | 0.770790i | ||||
\(298\) | −10.8077 | + | 10.8077i | −0.626075 | + | 0.626075i | ||||
\(299\) | 7.14841 | − | 17.2578i | 0.413403 | − | 0.998043i | ||||
\(300\) | 5.19296 | + | 2.15099i | 0.299816 | + | 0.124188i | ||||
\(301\) | −1.29182 | − | 3.11873i | −0.0744594 | − | 0.179761i | ||||
\(302\) | 13.2310i | 0.761359i | ||||||||
\(303\) | 19.5473 | − | 8.09677i | 1.12297 | − | 0.465147i | ||||
\(304\) | 2.63463 | + | 2.63463i | 0.151106 | + | 0.151106i | ||||
\(305\) | 22.7245 | 1.30120 | ||||||||
\(306\) | −0.674500 | + | 3.99124i | −0.0385586 | + | 0.228164i | ||||
\(307\) | −22.7361 | −1.29762 | −0.648810 | − | 0.760950i | \(-0.724733\pi\) | ||||
−0.648810 | + | 0.760950i | \(0.724733\pi\) | |||||||
\(308\) | 17.6663 | + | 17.6663i | 1.00663 | + | 1.00663i | ||||
\(309\) | −20.9344 | + | 8.67132i | −1.19092 | + | 0.493294i | ||||
\(310\) | − | 3.72602i | − | 0.211624i | ||||||
\(311\) | 7.94091 | + | 19.1711i | 0.450288 | + | 1.08709i | 0.972213 | + | 0.234099i | \(0.0752141\pi\) |
−0.521925 | + | 0.852991i | \(0.674786\pi\) | |||||||
\(312\) | −11.8328 | − | 4.90132i | −0.669903 | − | 0.277483i | ||||
\(313\) | −3.65477 | + | 8.82340i | −0.206580 | + | 0.498728i | −0.992880 | − | 0.119116i | \(-0.961994\pi\) |
0.786300 | + | 0.617844i | \(0.211994\pi\) | |||||||
\(314\) | −3.05593 | + | 3.05593i | −0.172456 | + | 0.172456i | ||||
\(315\) | 5.32396 | − | 5.32396i | 0.299971 | − | 0.299971i | ||||
\(316\) | −7.20246 | + | 17.3883i | −0.405170 | + | 0.978167i | ||||
\(317\) | 13.8576 | + | 5.73999i | 0.778318 | + | 0.322390i | 0.736236 | − | 0.676724i | \(-0.236601\pi\) |
0.0420814 | + | 0.999114i | \(0.486601\pi\) | |||||||
\(318\) | 1.57436 | + | 3.80083i | 0.0882854 | + | 0.213140i | ||||
\(319\) | 32.0007i | 1.79170i | ||||||||
\(320\) | 4.75259 | − | 1.96859i | 0.265678 | − | 0.110047i | ||||
\(321\) | 0.0161504 | + | 0.0161504i | 0.000901429 | + | 0.000901429i | ||||
\(322\) | −20.5930 | −1.14761 | ||||||||
\(323\) | 15.8769 | − | 11.2864i | 0.883414 | − | 0.627993i | ||||
\(324\) | 15.7451 | 0.874726 | ||||||||
\(325\) | 3.22721 | + | 3.22721i | 0.179013 | + | 0.179013i | ||||
\(326\) | 9.20446 | − | 3.81261i | 0.509788 | − | 0.211161i | ||||
\(327\) | 0.317426i | 0.0175537i | ||||||||
\(328\) | −4.88786 | − | 11.8003i | −0.269887 | − | 0.651564i | ||||
\(329\) | 35.1625 | + | 14.5648i | 1.93857 | + | 0.802982i | ||||
\(330\) | −5.62050 | + | 13.5691i | −0.309398 | + | 0.746953i | ||||
\(331\) | −13.0890 | + | 13.0890i | −0.719438 | + | 0.719438i | −0.968490 | − | 0.249052i | \(-0.919881\pi\) |
0.249052 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(332\) | −8.81494 | + | 8.81494i | −0.483783 | + | 0.483783i | ||||
\(333\) | 4.34859 | − | 10.4984i | 0.238301 | − | 0.575310i | ||||
\(334\) | 9.64868 | + | 3.99662i | 0.527953 | + | 0.218685i | ||||
\(335\) | −3.73850 | − | 9.02553i | −0.204256 | − | 0.493117i | ||||
\(336\) | − | 5.50358i | − | 0.300245i | ||||||
\(337\) | −2.99213 | + | 1.23938i | −0.162991 | + | 0.0675133i | −0.462687 | − | 0.886521i | \(-0.653115\pi\) |
0.299696 | + | 0.954035i | \(0.403115\pi\) | |||||||
\(338\) | 4.04942 | + | 4.04942i | 0.220259 | + | 0.220259i | ||||
\(339\) | −0.748383 | −0.0406466 | ||||||||
\(340\) | 2.26750 | + | 9.89415i | 0.122973 | + | 0.536586i | ||||
\(341\) | 14.5333 | 0.787022 | ||||||||
\(342\) | −3.27975 | − | 3.27975i | −0.177349 | − | 0.177349i | ||||
\(343\) | 8.12333 | − | 3.36479i | 0.438619 | − | 0.181682i | ||||
\(344\) | − | 2.62511i | − | 0.141537i | ||||||
\(345\) | 10.9646 | + | 26.4708i | 0.590312 | + | 1.42514i | ||||
\(346\) | −14.4099 | − | 5.96876i | −0.774679 | − | 0.320883i | ||||
\(347\) | −10.7000 | + | 25.8320i | −0.574405 | + | 1.38674i | 0.323366 | + | 0.946274i | \(0.395185\pi\) |
−0.897771 | + | 0.440462i | \(0.854815\pi\) | |||||||
\(348\) | 12.4939 | − | 12.4939i | 0.669744 | − | 0.669744i | ||||
\(349\) | 17.7731 | − | 17.7731i | 0.951372 | − | 0.951372i | −0.0474988 | − | 0.998871i | \(-0.515125\pi\) |
0.998871 | + | 0.0474988i | \(0.0151250\pi\) | |||||||
\(350\) | 1.92545 | − | 4.64846i | 0.102920 | − | 0.248470i | ||||
\(351\) | 7.78110 | + | 3.22304i | 0.415324 | + | 0.172033i | ||||
\(352\) | 11.8010 | + | 28.4900i | 0.628993 | + | 1.51852i | ||||
\(353\) | − | 1.20551i | − | 0.0641630i | −0.999485 | − | 0.0320815i | \(-0.989786\pi\) | ||
0.999485 | − | 0.0320815i | \(-0.0102136\pi\) | |||||||
\(354\) | 2.01259 | − | 0.833644i | 0.106968 | − | 0.0443077i | ||||
\(355\) | −3.87759 | − | 3.87759i | −0.205801 | − | 0.205801i | ||||
\(356\) | 4.62744 | 0.245254 | ||||||||
\(357\) | −28.3712 | − | 4.79460i | −1.50157 | − | 0.253757i | ||||
\(358\) | −4.53196 | −0.239522 | ||||||||
\(359\) | 9.26083 | + | 9.26083i | 0.488768 | + | 0.488768i | 0.907917 | − | 0.419149i | \(-0.137672\pi\) |
−0.419149 | + | 0.907917i | \(0.637672\pi\) | |||||||
\(360\) | 5.40941 | − | 2.24065i | 0.285101 | − | 0.118093i | ||||
\(361\) | 3.32111i | 0.174795i | ||||||||
\(362\) | −7.21235 | − | 17.4122i | −0.379073 | − | 0.915162i | ||||
\(363\) | −31.9166 | − | 13.2203i | −1.67519 | − | 0.693885i | ||||
\(364\) | 4.28643 | − | 10.3484i | 0.224670 | − | 0.542401i | ||||
\(365\) | 4.47725 | − | 4.47725i | 0.234350 | − | 0.234350i | ||||
\(366\) | −14.6216 | + | 14.6216i | −0.764285 | + | 0.764285i | ||||
\(367\) | −6.42276 | + | 15.5059i | −0.335265 | + | 0.809402i | 0.662891 | + | 0.748716i | \(0.269329\pi\) |
−0.998157 | + | 0.0606868i | \(0.980671\pi\) | |||||||
\(368\) | 5.76688 | + | 2.38872i | 0.300619 | + | 0.124521i | ||||
\(369\) | −2.37170 | − | 5.72580i | −0.123466 | − | 0.298073i | ||||
\(370\) | 12.0399i | 0.625927i | ||||||||
\(371\) | −8.05244 | + | 3.33543i | −0.418062 | + | 0.173167i | ||||
\(372\) | −5.67417 | − | 5.67417i | −0.294192 | − | 0.294192i | ||||
\(373\) | −11.9519 | −0.618846 | −0.309423 | − | 0.950924i | \(-0.600136\pi\) | ||||
−0.309423 | + | 0.950924i | \(0.600136\pi\) | |||||||
\(374\) | 16.3058 | − | 3.73689i | 0.843152 | − | 0.193230i | ||||
\(375\) | −25.1002 | −1.29617 | ||||||||
\(376\) | 20.9283 | + | 20.9283i | 1.07929 | + | 1.07929i | ||||
\(377\) | 13.2547 | − | 5.49030i | 0.682654 | − | 0.282765i | ||||
\(378\) | − | 9.28489i | − | 0.477563i | ||||||
\(379\) | 9.19416 | + | 22.1967i | 0.472272 | + | 1.14017i | 0.963157 | + | 0.268941i | \(0.0866737\pi\) |
−0.490884 | + | 0.871225i | \(0.663326\pi\) | |||||||
\(380\) | −10.7459 | − | 4.45110i | −0.551253 | − | 0.228336i | ||||
\(381\) | −9.19130 | + | 22.1898i | −0.470885 | + | 1.13682i | ||||
\(382\) | 5.08054 | − | 5.08054i | 0.259943 | − | 0.259943i | ||||
\(383\) | −12.4160 | + | 12.4160i | −0.634427 | + | 0.634427i | −0.949175 | − | 0.314748i | \(-0.898080\pi\) |
0.314748 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(384\) | 7.47759 | − | 18.0525i | 0.381589 | − | 0.921238i | ||||
\(385\) | −28.7475 | − | 11.9076i | −1.46511 | − | 0.606867i | ||||
\(386\) | −0.655711 | − | 1.58303i | −0.0333748 | − | 0.0805739i | ||||
\(387\) | − | 1.27377i | − | 0.0647491i | ||||||
\(388\) | 10.9915 | − | 4.55285i | 0.558011 | − | 0.231136i | ||||
\(389\) | 8.66462 | + | 8.66462i | 0.439313 | + | 0.439313i | 0.891781 | − | 0.452467i | \(-0.149456\pi\) |
−0.452467 | + | 0.891781i | \(0.649456\pi\) | |||||||
\(390\) | 6.58463 | 0.333426 | ||||||||
\(391\) | 17.3380 | − | 27.6476i | 0.876819 | − | 1.39820i | ||||
\(392\) | −11.5382 | −0.582766 | ||||||||
\(393\) | −22.6227 | − | 22.6227i | −1.14116 | − | 1.14116i | ||||
\(394\) | 12.6075 | − | 5.22220i | 0.635157 | − | 0.263091i | ||||
\(395\) | − | 23.4404i | − | 1.17942i | ||||||
\(396\) | 3.60766 | + | 8.70967i | 0.181292 | + | 0.437677i | ||||
\(397\) | −19.9517 | − | 8.26429i | −1.00135 | − | 0.414773i | −0.179058 | − | 0.983839i | \(-0.557305\pi\) |
−0.822292 | + | 0.569066i | \(0.807305\pi\) | |||||||
\(398\) | −3.48131 | + | 8.40462i | −0.174502 | + | 0.421286i | ||||
\(399\) | 23.3137 | − | 23.3137i | 1.16715 | − | 1.16715i | ||||
\(400\) | −1.07841 | + | 1.07841i | −0.0539204 | + | 0.0539204i | ||||
\(401\) | 4.95492 | − | 11.9622i | 0.247437 | − | 0.597365i | −0.750548 | − | 0.660816i | \(-0.770211\pi\) |
0.997985 | + | 0.0634505i | \(0.0202105\pi\) | |||||||
\(402\) | 8.21276 | + | 3.40184i | 0.409615 | + | 0.169668i | ||||
\(403\) | −2.49344 | − | 6.01971i | −0.124207 | − | 0.299863i | ||||
\(404\) | 14.3893i | 0.715894i | ||||||||
\(405\) | −18.1169 | + | 7.50428i | −0.900237 | + | 0.372891i | ||||
\(406\) | −11.1839 | − | 11.1839i | −0.555046 | − | 0.555046i | ||||
\(407\) | −46.9616 | −2.32780 | ||||||||
\(408\) | −18.9566 | − | 11.8878i | −0.938493 | − | 0.588535i | ||||
\(409\) | −6.50659 | −0.321730 | −0.160865 | − | 0.986976i | \(-0.551428\pi\) | ||||
−0.160865 | + | 0.986976i | \(0.551428\pi\) | |||||||
\(410\) | 4.64324 | + | 4.64324i | 0.229314 | + | 0.229314i | ||||
\(411\) | −9.59538 | + | 3.97454i | −0.473305 | + | 0.196049i | ||||
\(412\) | − | 15.4103i | − | 0.759213i | ||||||
\(413\) | 1.76616 | + | 4.26389i | 0.0869070 | + | 0.209812i | ||||
\(414\) | −7.17897 | − | 2.97363i | −0.352827 | − | 0.146146i | ||||
\(415\) | 5.94154 | − | 14.3441i | 0.291658 | − | 0.704126i | ||||
\(416\) | 9.77595 | − | 9.77595i | 0.479306 | − | 0.479306i | ||||
\(417\) | −13.1270 | + | 13.1270i | −0.642831 | + | 0.642831i | ||||
\(418\) | −7.33551 | + | 17.7095i | −0.358791 | + | 0.866199i | ||||
\(419\) | −8.93282 | − | 3.70009i | −0.436397 | − | 0.180761i | 0.153659 | − | 0.988124i | \(-0.450894\pi\) |
−0.590056 | + | 0.807362i | \(0.700894\pi\) | |||||||
\(420\) | 6.57473 | + | 15.8728i | 0.320814 | + | 0.774513i | ||||
\(421\) | − | 34.3093i | − | 1.67213i | −0.548629 | − | 0.836066i | \(-0.684850\pi\) | ||
0.548629 | − | 0.836066i | \(-0.315150\pi\) | |||||||
\(422\) | −14.2664 | + | 5.90933i | −0.694476 | + | 0.287662i | ||||
\(423\) | 10.1549 | + | 10.1549i | 0.493748 | + | 0.493748i | ||||
\(424\) | −6.77793 | −0.329165 | ||||||||
\(425\) | 4.61977 | + | 6.49874i | 0.224092 | + | 0.315235i | ||||
\(426\) | 4.98992 | 0.241762 | ||||||||
\(427\) | −30.9774 | − | 30.9774i | −1.49910 | − | 1.49910i | ||||
\(428\) | −0.0143510 | + | 0.00594437i | −0.000693680 | + | 0.000287332i | ||||
\(429\) | 25.6833i | 1.24000i | ||||||||
\(430\) | 0.516470 | + | 1.24687i | 0.0249064 | + | 0.0601294i | ||||
\(431\) | 4.14191 | + | 1.71563i | 0.199509 | + | 0.0826392i | 0.480201 | − | 0.877159i | \(-0.340564\pi\) |
−0.280692 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(432\) | −1.07701 | + | 2.60014i | −0.0518178 | + | 0.125099i | ||||
\(433\) | 14.4126 | − | 14.4126i | 0.692628 | − | 0.692628i | −0.270182 | − | 0.962809i | \(-0.587084\pi\) |
0.962809 | + | 0.270182i | \(0.0870838\pi\) | |||||||
\(434\) | −5.07921 | + | 5.07921i | −0.243810 | + | 0.243810i | ||||
\(435\) | −8.42127 | + | 20.3307i | −0.403769 | + | 0.974784i | ||||
\(436\) | −0.199446 | − | 0.0826132i | −0.00955172 | − | 0.00395645i | ||||
\(437\) | 14.3102 | + | 34.5479i | 0.684551 | + | 1.65265i | ||||
\(438\) | 5.76160i | 0.275300i | ||||||||
\(439\) | 36.4740 | − | 15.1080i | 1.74081 | − | 0.721068i | 0.742101 | − | 0.670288i | \(-0.233829\pi\) |
0.998710 | − | 0.0507797i | \(-0.0161706\pi\) | |||||||
\(440\) | −17.1102 | − | 17.1102i | −0.815695 | − | 0.815695i | ||||
\(441\) | −5.59860 | −0.266600 | ||||||||
\(442\) | −4.34537 | − | 6.11275i | −0.206688 | − | 0.290754i | ||||
\(443\) | 24.4730 | 1.16275 | 0.581373 | − | 0.813637i | \(-0.302516\pi\) | ||||
0.581373 | + | 0.813637i | \(0.302516\pi\) | |||||||
\(444\) | 18.3350 | + | 18.3350i | 0.870142 | + | 0.870142i | ||||
\(445\) | −5.32453 | + | 2.20549i | −0.252407 | + | 0.104550i | ||||
\(446\) | 1.61079i | 0.0762732i | ||||||||
\(447\) | −15.6887 | − | 37.8758i | −0.742049 | − | 1.79146i | ||||
\(448\) | −9.16214 | − | 3.79508i | −0.432870 | − | 0.179301i | ||||
\(449\) | −2.23321 | + | 5.39145i | −0.105392 | + | 0.254438i | −0.967774 | − | 0.251819i | \(-0.918971\pi\) |
0.862383 | + | 0.506257i | \(0.168971\pi\) | |||||||
\(450\) | 1.34247 | − | 1.34247i | 0.0632847 | − | 0.0632847i | ||||
\(451\) | −18.1109 | + | 18.1109i | −0.852810 | + | 0.852810i | ||||
\(452\) | 0.194774 | − | 0.470226i | 0.00916139 | − | 0.0221176i | ||||
\(453\) | −32.7873 | − | 13.5809i | −1.54048 | − | 0.638088i | ||||
\(454\) | −2.17211 | − | 5.24393i | −0.101942 | − | 0.246110i | ||||
\(455\) | 13.9502i | 0.653996i | ||||||||
\(456\) | 23.6879 | − | 9.81184i | 1.10929 | − | 0.459482i | ||||
\(457\) | −20.5808 | − | 20.5808i | −0.962729 | − | 0.962729i | 0.0366008 | − | 0.999330i | \(-0.488347\pi\) |
−0.999330 | + | 0.0366008i | \(0.988347\pi\) | |||||||
\(458\) | 0.333843 | 0.0155994 | ||||||||
\(459\) | 12.4656 | + | 7.81725i | 0.581844 | + | 0.364878i | ||||
\(460\) | −19.4858 | −0.908531 | ||||||||
\(461\) | −19.9493 | − | 19.9493i | −0.929130 | − | 0.929130i | 0.0685196 | − | 0.997650i | \(-0.478172\pi\) |
−0.997650 | + | 0.0685196i | \(0.978172\pi\) | |||||||
\(462\) | 26.1587 | − | 10.8353i | 1.21701 | − | 0.504104i | ||||
\(463\) | 1.35223i | 0.0628437i | 0.999506 | + | 0.0314218i | \(0.0100035\pi\) | ||||
−0.999506 | + | 0.0314218i | \(0.989996\pi\) | |||||||
\(464\) | 1.83464 | + | 4.42922i | 0.0851712 | + | 0.205621i | ||||
\(465\) | 9.23331 | + | 3.82456i | 0.428184 | + | 0.177360i | ||||
\(466\) | 6.65627 | − | 16.0696i | 0.308346 | − | 0.744412i | ||||
\(467\) | 25.5854 | − | 25.5854i | 1.18395 | − | 1.18395i | 0.205242 | − | 0.978711i | \(-0.434202\pi\) |
0.978711 | − | 0.205242i | \(-0.0657980\pi\) | |||||||
\(468\) | 2.98860 | − | 2.98860i | 0.138148 | − | 0.138148i | ||||
\(469\) | −7.20714 | + | 17.3996i | −0.332795 | + | 0.803438i | ||||
\(470\) | −14.0579 | − | 5.82299i | −0.648444 | − | 0.268594i | ||||
\(471\) | −4.43604 | − | 10.7095i | −0.204402 | − | 0.493470i | ||||
\(472\) | 3.58901i | 0.165198i | ||||||||
\(473\) | −4.86339 | + | 2.01448i | −0.223619 | + | 0.0926261i | ||||
\(474\) | 15.0823 | + | 15.0823i | 0.692753 | + | 0.692753i | ||||
\(475\) | −9.13650 | −0.419211 | ||||||||
\(476\) | 10.3964 | − | 16.5784i | 0.476520 | − | 0.759871i | ||||
\(477\) | −3.28881 | −0.150584 | ||||||||
\(478\) | 13.2460 | + | 13.2460i | 0.605859 | + | 0.605859i | ||||
\(479\) | −37.0476 | + | 15.3456i | −1.69275 | + | 0.701159i | −0.999803 | − | 0.0198334i | \(-0.993686\pi\) |
−0.692943 | + | 0.720992i | \(0.743686\pi\) | |||||||
\(480\) | 21.2059i | 0.967911i | ||||||||
\(481\) | 8.05710 | + | 19.4516i | 0.367372 | + | 0.886915i | ||||
\(482\) | −3.95392 | − | 1.63777i | −0.180096 | − | 0.0745983i | ||||
\(483\) | 21.1377 | − | 51.0309i | 0.961797 | − | 2.32198i | ||||
\(484\) | 16.6132 | − | 16.6132i | 0.755146 | − | 0.755146i | ||||
\(485\) | −10.4774 | + | 10.4774i | −0.475754 | + | 0.475754i | ||||
\(486\) | 3.67078 | − | 8.86204i | 0.166510 | − | 0.401990i | ||||
\(487\) | 19.6571 | + | 8.14223i | 0.890748 | + | 0.368960i | 0.780656 | − | 0.624962i | \(-0.214885\pi\) |
0.110092 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(488\) | −13.0372 | − | 31.4746i | −0.590167 | − | 1.42479i | ||||
\(489\) | 26.7227i | 1.20844i | ||||||||
\(490\) | 5.48038 | − | 2.27005i | 0.247578 | − | 0.102550i | ||||
\(491\) | −23.9375 | − | 23.9375i | −1.08028 | − | 1.08028i | −0.996483 | − | 0.0838001i | \(-0.973294\pi\) |
−0.0838001 | − | 0.996483i | \(-0.526706\pi\) | |||||||
\(492\) | 14.1419 | 0.637568 | ||||||||
\(493\) | 24.4312 | − | 5.59904i | 1.10033 | − | 0.252168i | ||||
\(494\) | 8.59383 | 0.386655 | ||||||||
\(495\) | −8.30225 | − | 8.30225i | −0.373158 | − | 0.373158i | ||||
\(496\) | 2.01155 | − | 0.833212i | 0.0903214 | − | 0.0374123i | ||||
\(497\) | 10.5716i | 0.474203i | ||||||||
\(498\) | 5.40649 | + | 13.0524i | 0.242271 | + | 0.584893i | ||||
\(499\) | −22.8399 | − | 9.46059i | −1.02245 | − | 0.423514i | −0.192471 | − | 0.981303i | \(-0.561650\pi\) |
−0.829983 | + | 0.557788i | \(0.811650\pi\) | |||||||
\(500\) | 6.53256 | − | 15.7710i | 0.292145 | − | 0.705300i | ||||
\(501\) | −19.8077 | + | 19.8077i | −0.884944 | + | 0.884944i | ||||
\(502\) | 10.6373 | − | 10.6373i | 0.474764 | − | 0.474764i | ||||
\(503\) | −0.581084 | + | 1.40286i | −0.0259093 | + | 0.0625505i | −0.936305 | − | 0.351189i | \(-0.885778\pi\) |
0.910395 | + | 0.413739i | \(0.135778\pi\) | |||||||
\(504\) | −10.4284 | − | 4.31957i | −0.464516 | − | 0.192409i | ||||
\(505\) | −6.85810 | − | 16.5569i | −0.305181 | − | 0.736773i | ||||
\(506\) | 32.1131i | 1.42760i | ||||||||
\(507\) | −14.1912 | + | 5.87820i | −0.630255 | + | 0.261060i | ||||
\(508\) | −11.5502 | − | 11.5502i | −0.512457 | − | 0.512457i | ||||
\(509\) | 19.5958 | 0.868570 | 0.434285 | − | 0.900776i | \(-0.357001\pi\) | ||||
0.434285 | + | 0.900776i | \(0.357001\pi\) | |||||||
\(510\) | 11.3428 | + | 1.91688i | 0.502268 | + | 0.0848809i | ||||
\(511\) | −12.2065 | −0.539986 | ||||||||
\(512\) | 6.19453 | + | 6.19453i | 0.273762 | + | 0.273762i | ||||
\(513\) | −15.5768 | + | 6.45212i | −0.687733 | + | 0.284868i | ||||
\(514\) | − | 10.7887i | − | 0.475869i | ||||||
\(515\) | 7.34474 | + | 17.7318i | 0.323648 | + | 0.781356i | ||||
\(516\) | 2.68530 | + | 1.11229i | 0.118214 | + | 0.0489658i | ||||
\(517\) | 22.7125 | − | 54.8328i | 0.998894 | − | 2.41154i | ||||
\(518\) | 16.4125 | − | 16.4125i | 0.721125 | − | 0.721125i | ||||
\(519\) | 29.5819 | − | 29.5819i | 1.29850 | − | 1.29850i | ||||
\(520\) | −4.15150 | + | 10.0226i | −0.182055 | + | 0.439520i | ||||
\(521\) | 8.06285 | + | 3.33974i | 0.353240 | + | 0.146317i | 0.552245 | − | 0.833682i | \(-0.313771\pi\) |
−0.199005 | + | 0.979998i | \(0.563771\pi\) | |||||||
\(522\) | −2.28388 | − | 5.51377i | −0.0999627 | − | 0.241331i | ||||
\(523\) | − | 1.12779i | − | 0.0493150i | −0.999696 | − | 0.0246575i | \(-0.992150\pi\) | ||
0.999696 | − | 0.0246575i | \(-0.00784952\pi\) | |||||||
\(524\) | 20.1021 | − | 8.32658i | 0.878166 | − | 0.363748i | ||||
\(525\) | 9.54279 | + | 9.54279i | 0.416481 | + | 0.416481i | ||||
\(526\) | 18.5051 | 0.806861 | ||||||||
\(527\) | −2.54283 | − | 11.0955i | −0.110768 | − | 0.483329i | ||||
\(528\) | −8.58235 | −0.373499 | ||||||||
\(529\) | 28.0344 | + | 28.0344i | 1.21889 | + | 1.21889i | ||||
\(530\) | 3.21936 | − | 1.33350i | 0.139840 | − | 0.0579237i | ||||
\(531\) | 1.74147i | 0.0755735i | ||||||||
\(532\) | 8.58091 | + | 20.7161i | 0.372029 | + | 0.898159i | ||||
\(533\) | 10.6088 | + | 4.39432i | 0.459519 | + | 0.190339i | ||||
\(534\) | 2.00688 | − | 4.84505i | 0.0868463 | − | 0.209666i | ||||
\(535\) | 0.0136797 | − | 0.0136797i | 0.000591424 | − | 0.000591424i | ||||
\(536\) | −10.3560 | + | 10.3560i | −0.447312 | + | 0.447312i | ||||
\(537\) | 4.65182 | − | 11.2305i | 0.200741 | − | 0.484631i | ||||
\(538\) | 13.7666 | + | 5.70232i | 0.593522 | + | 0.245845i | ||||
\(539\) | 8.85429 | + | 21.3761i | 0.381381 | + | 0.920736i | ||||
\(540\) | − | 8.78566i | − | 0.378075i | ||||||
\(541\) | −19.2522 | + | 7.97453i | −0.827717 | + | 0.342852i | −0.755999 | − | 0.654573i | \(-0.772848\pi\) |
−0.0717185 | + | 0.997425i | \(0.522848\pi\) | |||||||
\(542\) | 2.93772 | + | 2.93772i | 0.126186 | + | 0.126186i | ||||
\(543\) | 50.5515 | 2.16937 | ||||||||
\(544\) | 19.6862 | − | 13.9943i | 0.844037 | − | 0.600002i | ||||
\(545\) | 0.268865 | 0.0115169 | ||||||||
\(546\) | −8.97599 | − | 8.97599i | −0.384137 | − | 0.384137i | ||||
\(547\) | −2.85098 | + | 1.18091i | −0.121899 | + | 0.0504922i | −0.442799 | − | 0.896621i | \(-0.646015\pi\) |
0.320900 | + | 0.947113i | \(0.396015\pi\) | |||||||
\(548\) | − | 7.06340i | − | 0.301734i | ||||||
\(549\) | −6.32596 | − | 15.2722i | −0.269985 | − | 0.651802i | ||||
\(550\) | −7.24886 | − | 3.00258i | −0.309092 | − | 0.128030i | ||||
\(551\) | −10.9909 | + | 26.5344i | −0.468228 | + | 1.13040i | ||||
\(552\) | 30.3730 | − | 30.3730i | 1.29276 | − | 1.29276i | ||||
\(553\) | −31.9534 | + | 31.9534i | −1.35880 | + | 1.35880i | ||||
\(554\) | 4.06283 | − | 9.80855i | 0.172613 | − | 0.416725i | ||||
\(555\) | −29.8357 | − | 12.3584i | −1.26646 | − | 0.524583i | ||||
\(556\) | −4.83155 | − | 11.6644i | −0.204903 | − | 0.494681i | ||||
\(557\) | − | 35.6120i | − | 1.50893i | −0.656340 | − | 0.754465i | \(-0.727896\pi\) | ||
0.656340 | − | 0.754465i | \(-0.272104\pi\) | |||||||
\(558\) | −2.50411 | + | 1.03724i | −0.106007 | + | 0.0439097i | ||||
\(559\) | 1.66880 | + | 1.66880i | 0.0705829 | + | 0.0705829i | ||||
\(560\) | −4.66162 | −0.196989 | ||||||||
\(561\) | −7.47676 | + | 44.2425i | −0.315669 | + | 1.86792i | ||||
\(562\) | 7.06023 | 0.297818 | ||||||||
\(563\) | 18.0901 | + | 18.0901i | 0.762405 | + | 0.762405i | 0.976757 | − | 0.214351i | \(-0.0687637\pi\) |
−0.214351 | + | 0.976757i | \(0.568764\pi\) | |||||||
\(564\) | −30.2757 | + | 12.5406i | −1.27484 | + | 0.528055i | ||||
\(565\) | 0.633893i | 0.0266681i | ||||||||
\(566\) | −1.46760 | − | 3.54309i | −0.0616877 | − | 0.148927i | ||||
\(567\) | 34.9261 | + | 14.4669i | 1.46676 | + | 0.607552i | ||||
\(568\) | −3.14606 | + | 7.59526i | −0.132006 | + | 0.318690i | ||||
\(569\) | −27.0270 | + | 27.0270i | −1.13303 | + | 1.13303i | −0.143361 | + | 0.989670i | \(0.545791\pi\) |
−0.989670 | + | 0.143361i | \(0.954209\pi\) | |||||||
\(570\) | −9.32081 | + | 9.32081i | −0.390406 | + | 0.390406i | ||||
\(571\) | 4.67128 | − | 11.2775i | 0.195487 | − | 0.471947i | −0.795492 | − | 0.605964i | \(-0.792788\pi\) |
0.990979 | + | 0.134017i | \(0.0427875\pi\) | |||||||
\(572\) | −16.1374 | − | 6.68431i | −0.674737 | − | 0.279485i | ||||
\(573\) | 7.37499 | + | 17.8048i | 0.308095 | + | 0.743806i | ||||
\(574\) | − | 12.6591i | − | 0.528380i | ||||||
\(575\) | −14.1412 | + | 5.85747i | −0.589729 | + | 0.244274i | ||||
\(576\) | −2.64602 | − | 2.64602i | −0.110251 | − | 0.110251i | ||||
\(577\) | 16.7957 | 0.699213 | 0.349606 | − | 0.936897i | \(-0.386315\pi\) | ||||
0.349606 | + | 0.936897i | \(0.386315\pi\) | |||||||
\(578\) | −5.70592 | − | 11.7949i | −0.237335 | − | 0.490605i | ||||
\(579\) | 4.59589 | 0.190999 | ||||||||
\(580\) | −10.5825 | − | 10.5825i | −0.439416 | − | 0.439416i | ||||
\(581\) | −27.6529 | + | 11.4542i | −1.14724 | + | 0.475200i | ||||
\(582\) | − | 13.4829i | − | 0.558886i | ||||||
\(583\) | 5.20131 | + | 12.5571i | 0.215416 | + | 0.520061i | ||||
\(584\) | −8.76986 | − | 3.63260i | −0.362899 | − | 0.150318i | ||||
\(585\) | −2.01440 | + | 4.86320i | −0.0832854 | + | 0.201069i | ||||
\(586\) | 6.87775 | − | 6.87775i | 0.284117 | − | 0.284117i | ||||
\(587\) | 22.2540 | − | 22.2540i | 0.918520 | − | 0.918520i | −0.0784014 | − | 0.996922i | \(-0.524982\pi\) |
0.996922 | + | 0.0784014i | \(0.0249816\pi\) | |||||||
\(588\) | 4.88886 | − | 11.8027i | 0.201613 | − | 0.486737i | ||||
\(589\) | 12.0507 | + | 4.99157i | 0.496541 | + | 0.205674i | ||||
\(590\) | −0.706110 | − | 1.70470i | −0.0290701 | − | 0.0701814i | ||||
\(591\) | 36.6025i | 1.50563i | ||||||||
\(592\) | −6.49996 | + | 2.69237i | −0.267147 | + | 0.110656i | ||||
\(593\) | 4.77643 | + | 4.77643i | 0.196145 | + | 0.196145i | 0.798345 | − | 0.602200i | \(-0.205709\pi\) |
−0.602200 | + | 0.798345i | \(0.705709\pi\) | |||||||
\(594\) | −14.4790 | −0.594079 | ||||||||
\(595\) | −4.06111 | + | 24.0309i | −0.166489 | + | 0.985171i | ||||
\(596\) | 27.8813 | 1.14206 | ||||||||
\(597\) | −17.2538 | − | 17.2538i | −0.706151 | − | 0.706151i | ||||
\(598\) | 13.3013 | − | 5.50957i | 0.543930 | − | 0.225303i | ||||
\(599\) | − | 33.0854i | − | 1.35183i | −0.736979 | − | 0.675916i | \(-0.763748\pi\) | ||
0.736979 | − | 0.675916i | \(-0.236252\pi\) | |||||||
\(600\) | 4.01619 | + | 9.69595i | 0.163960 | + | 0.395835i | ||||
\(601\) | −27.2027 | − | 11.2677i | −1.10962 | − | 0.459620i | −0.248814 | − | 0.968551i | \(-0.580041\pi\) |
−0.860807 | + | 0.508931i | \(0.830041\pi\) | |||||||
\(602\) | 0.995660 | − | 2.40374i | 0.0405801 | − | 0.0979690i | ||||
\(603\) | −5.02498 | + | 5.02498i | −0.204633 | + | 0.204633i | ||||
\(604\) | 17.0664 | − | 17.0664i | 0.694422 | − | 0.694422i | ||||
\(605\) | −11.1978 | + | 27.0339i | −0.455255 | + | 1.09908i | ||||
\(606\) | 15.0659 | + | 6.24051i | 0.612012 | + | 0.253504i | ||||
\(607\) | −15.3859 | − | 37.1449i | −0.624495 | − | 1.50766i | −0.846374 | − | 0.532590i | \(-0.821219\pi\) |
0.221879 | − | 0.975074i | \(-0.428781\pi\) | |||||||
\(608\) | 27.6765i | 1.12243i | ||||||||
\(609\) | 39.1940 | − | 16.2347i | 1.58822 | − | 0.657862i | ||||
\(610\) | 12.3848 | + | 12.3848i | 0.501444 | + | 0.501444i | ||||
\(611\) | −26.6086 | −1.07647 | ||||||||
\(612\) | 6.01824 | − | 4.27819i | 0.243273 | − | 0.172936i | ||||
\(613\) | −30.5740 | −1.23487 | −0.617435 | − | 0.786622i | \(-0.711828\pi\) | ||||
−0.617435 | + | 0.786622i | \(0.711828\pi\) | |||||||
\(614\) | −12.3911 | − | 12.3911i | −0.500064 | − | 0.500064i | ||||
\(615\) | −16.2723 | + | 6.74021i | −0.656162 | + | 0.271791i | ||||
\(616\) | 46.6482i | 1.87951i | ||||||||
\(617\) | −10.3840 | − | 25.0693i | −0.418046 | − | 1.00925i | −0.982913 | − | 0.184070i | \(-0.941073\pi\) |
0.564867 | − | 0.825182i | \(-0.308927\pi\) | |||||||
\(618\) | −16.1350 | − | 6.68334i | −0.649045 | − | 0.268843i | ||||
\(619\) | 2.58904 | − | 6.25050i | 0.104062 | − | 0.251229i | −0.863269 | − | 0.504744i | \(-0.831587\pi\) |
0.967331 | + | 0.253515i | \(0.0815868\pi\) | |||||||
\(620\) | −4.80611 | + | 4.80611i | −0.193018 | + | 0.193018i | ||||
\(621\) | −19.9728 | + | 19.9728i | −0.801481 | + | 0.801481i | ||||
\(622\) | −6.12039 | + | 14.7759i | −0.245405 | + | 0.592460i | ||||
\(623\) | 10.2647 | + | 4.25179i | 0.411247 | + | 0.170344i | ||||
\(624\) | 1.47245 | + | 3.55482i | 0.0589454 | + | 0.142307i | ||||
\(625\) | 11.5910i | 0.463641i | ||||||||
\(626\) | −6.80055 | + | 2.81688i | −0.271805 | + | 0.112585i | ||||
\(627\) | −36.3557 | − | 36.3557i | −1.45191 | − | 1.45191i | ||||
\(628\) | 7.88356 | 0.314588 | ||||||||
\(629\) | 8.21669 | + | 35.8532i | 0.327621 | + | 1.42956i | ||||
\(630\) | 5.80307 | 0.231200 | ||||||||
\(631\) | 26.3629 | + | 26.3629i | 1.04949 | + | 1.04949i | 0.998710 | + | 0.0507787i | \(0.0161703\pi\) |
0.0507787 | + | 0.998710i | \(0.483830\pi\) | |||||||
\(632\) | −32.4662 | + | 13.4480i | −1.29144 | + | 0.534931i | ||||
\(633\) | − | 41.4186i | − | 1.64624i | ||||||
\(634\) | 4.42404 | + | 10.6806i | 0.175701 | + | 0.424180i | ||||
\(635\) | 18.7951 | + | 7.78518i | 0.745860 | + | 0.308946i | ||||
\(636\) | 2.87188 | − | 6.93334i | 0.113878 | − | 0.274925i | ||||
\(637\) | 7.33492 | − | 7.33492i | 0.290620 | − | 0.290620i | ||||
\(638\) | −17.4403 | + | 17.4403i | −0.690467 | + | 0.690467i | ||||
\(639\) | −1.52654 | + | 3.68540i | −0.0603890 | + | 0.145792i | ||||
\(640\) | −15.2908 | − | 6.33364i | −0.604421 | − | 0.250359i | ||||
\(641\) | −12.6971 | − | 30.6535i | −0.501506 | − | 1.21074i | −0.948664 | − | 0.316287i | \(-0.897564\pi\) |
0.447158 | − | 0.894455i | \(-0.352436\pi\) | |||||||
\(642\) | 0.0176038i | 0.000694768i | ||||||||
\(643\) | 2.99720 | − | 1.24148i | 0.118198 | − | 0.0489593i | −0.322801 | − | 0.946467i | \(-0.604624\pi\) |
0.440999 | + | 0.897508i | \(0.354624\pi\) | |||||||
\(644\) | 26.5625 | + | 26.5625i | 1.04671 | + | 1.04671i | ||||
\(645\) | −3.61995 | −0.142535 | ||||||||
\(646\) | 14.8039 | + | 2.50179i | 0.582452 | + | 0.0984315i | ||||
\(647\) | −8.42170 | −0.331091 | −0.165546 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165546 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(648\) | 20.7876 | + | 20.7876i | 0.816615 | + | 0.816615i | ||||
\(649\) | 6.64916 | − | 2.75417i | 0.261002 | − | 0.108111i | ||||
\(650\) | 3.51763i | 0.137973i | ||||||||
\(651\) | −7.37306 | − | 17.8001i | −0.288973 | − | 0.697643i | ||||
\(652\) | −16.7904 | − | 6.95483i | −0.657565 | − | 0.272372i | ||||
\(653\) | −8.95953 | + | 21.6302i | −0.350613 | + | 0.846455i | 0.645931 | + | 0.763396i | \(0.276469\pi\) |
−0.996545 | + | 0.0830598i | \(0.973531\pi\) | |||||||
\(654\) | −0.172996 | + | 0.172996i | −0.00676468 | + | 0.00676468i | ||||
\(655\) | −19.1618 | + | 19.1618i | −0.748714 | + | 0.748714i | ||||
\(656\) | −1.46841 | + | 3.54505i | −0.0573318 | + | 0.138411i | ||||
\(657\) | −4.25534 | − | 1.76262i | −0.166017 | − | 0.0687664i | ||||
\(658\) | 11.2257 | + | 27.1012i | 0.437622 | + | 1.05651i | ||||
\(659\) | 32.9683i | 1.28426i | 0.766595 | + | 0.642131i | \(0.221949\pi\) | ||||
−0.766595 | + | 0.642131i | \(0.778051\pi\) | |||||||
\(660\) | 24.7522 | − | 10.2527i | 0.963479 | − | 0.399086i | ||||
\(661\) | 15.0077 | + | 15.0077i | 0.583730 | + | 0.583730i | 0.935926 | − | 0.352196i | \(-0.114565\pi\) |
−0.352196 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(662\) | −14.2669 | −0.554500 | ||||||||
\(663\) | 19.6081 | − | 4.49370i | 0.761514 | − | 0.174521i | ||||
\(664\) | −23.2761 | −0.903287 | ||||||||
\(665\) | −19.7471 | − | 19.7471i | −0.765759 | − | 0.765759i | ||||
\(666\) | 8.09156 | − | 3.35163i | 0.313541 | − | 0.129873i | ||||
\(667\) | 48.1154i | 1.86304i | ||||||||
\(668\) | −7.29049 | − | 17.6008i | −0.282077 | − | 0.680995i | ||||
\(669\) | −3.99164 | − | 1.65339i | −0.154326 | − | 0.0639239i | ||||
\(670\) | 2.88141 | − | 6.95634i | 0.111319 | − | 0.268747i | ||||
\(671\) | −48.3066 | + | 48.3066i | −1.86486 | + | 1.86486i | ||||
\(672\) | 28.9073 | − | 28.9073i | 1.11512 | − | 1.11512i | ||||
\(673\) | 2.19614 | − | 5.30194i | 0.0846548 | − | 0.204375i | −0.875883 | − | 0.482523i | \(-0.839721\pi\) |
0.960538 | + | 0.278148i | \(0.0897206\pi\) | |||||||
\(674\) | −2.30615 | − | 0.955240i | −0.0888297 | − | 0.0367945i | ||||
\(675\) | −2.64099 | − | 6.37591i | −0.101652 | − | 0.245409i | ||||
\(676\) | − | 10.4465i | − | 0.401789i | ||||||
\(677\) | 25.3105 | − | 10.4840i | 0.972763 | − | 0.402931i | 0.161023 | − | 0.986951i | \(-0.448521\pi\) |
0.811740 | + | 0.584019i | \(0.198521\pi\) | |||||||
\(678\) | −0.407866 | − | 0.407866i | −0.0156640 | − | 0.0156640i | ||||
\(679\) | 28.5650 | 1.09622 | ||||||||
\(680\) | −10.0692 | + | 16.0566i | −0.386135 | + | 0.615741i | ||||
\(681\) | 15.2243 | 0.583398 | ||||||||
\(682\) | 7.92058 | + | 7.92058i | 0.303295 | + | 0.303295i | ||||
\(683\) | 31.1640 | − | 12.9086i | 1.19246 | − | 0.493933i | 0.303904 | − | 0.952703i | \(-0.401710\pi\) |
0.888555 | + | 0.458770i | \(0.151710\pi\) | |||||||
\(684\) | 8.46096i | 0.323513i | ||||||||
\(685\) | 3.36650 | + | 8.12744i | 0.128627 | + | 0.310534i | ||||
\(686\) | 6.26098 | + | 2.59338i | 0.239045 | + | 0.0990159i | ||||
\(687\) | −0.342672 | + | 0.827283i | −0.0130737 | + | 0.0315628i | ||||
\(688\) | −0.557650 | + | 0.557650i | −0.0212602 | + | 0.0212602i | ||||
\(689\) | 4.30878 | − | 4.30878i | 0.164152 | − | 0.164152i | ||||
\(690\) | −8.45083 | + | 20.4021i | −0.321718 | + | 0.776695i | ||||
\(691\) | −4.88582 | − | 2.02377i | −0.185865 | − | 0.0769880i | 0.287810 | − | 0.957688i | \(-0.407073\pi\) |
−0.473675 | + | 0.880700i | \(0.657073\pi\) | |||||||
\(692\) | 10.8880 | + | 26.2860i | 0.413900 | + | 0.999243i | ||||
\(693\) | 22.6348i | 0.859825i | ||||||||
\(694\) | −19.9098 | + | 8.24691i | −0.755766 | + | 0.313049i | ||||
\(695\) | 11.1188 | + | 11.1188i | 0.421759 | + | 0.421759i | ||||
\(696\) | 32.9905 | 1.25050 | ||||||||
\(697\) | 16.9957 | + | 10.6581i | 0.643758 | + | 0.403705i | ||||
\(698\) | 19.3725 | 0.733262 | ||||||||
\(699\) | 32.9893 | + | 32.9893i | 1.24777 | + | 1.24777i | ||||
\(700\) | −8.47955 | + | 3.51234i | −0.320497 | + | 0.132754i | ||||
\(701\) | 12.0343i | 0.454529i | 0.973833 | + | 0.227264i | \(0.0729781\pi\) | ||||
−0.973833 | + | 0.227264i | \(0.927022\pi\) | |||||||
\(702\) | 2.48413 | + | 5.99721i | 0.0937573 | + | 0.226350i | ||||
\(703\) | −38.9396 | − | 16.1293i | −1.46864 | − | 0.608329i | ||||
\(704\) | −5.91810 | + | 14.2875i | −0.223047 | + | 0.538482i | ||||
\(705\) | 28.8595 | − | 28.8595i | 1.08691 | − | 1.08691i | ||||
\(706\) | 0.657000 | − | 0.657000i | 0.0247265 | − | 0.0247265i | ||||
\(707\) | −13.2212 | + | 31.9187i | −0.497233 | + | 1.20043i | ||||
\(708\) | −3.67130 | − | 1.52070i | −0.137976 | − | 0.0571515i | ||||
\(709\) | 5.56300 | + | 13.4303i | 0.208923 | + | 0.504384i | 0.993254 | − | 0.115958i | \(-0.0369937\pi\) |
−0.784331 | + | 0.620342i | \(0.786994\pi\) | |||||||
\(710\) | − | 4.22654i | − | 0.158619i | ||||||
\(711\) | −15.7534 | + | 6.52526i | −0.590798 | + | 0.244717i | ||||
\(712\) | 6.10944 | + | 6.10944i | 0.228961 | + | 0.228961i | ||||
\(713\) | 21.8519 | 0.818359 | ||||||||
\(714\) | −12.8492 | − | 18.0753i | −0.480868 | − | 0.676449i | ||||
\(715\) | 21.7541 | 0.813558 | ||||||||
\(716\) | 5.84569 | + | 5.84569i | 0.218464 | + | 0.218464i | ||||
\(717\) | −46.4208 | + | 19.2281i | −1.73362 | + | 0.718087i | ||||
\(718\) | 10.0942i | 0.376714i | ||||||||
\(719\) | −2.59407 | − | 6.26263i | −0.0967423 | − | 0.233557i | 0.868098 | − | 0.496392i | \(-0.165342\pi\) |
−0.964841 | + | 0.262836i | \(0.915342\pi\) | |||||||
\(720\) | −1.62509 | − | 0.673136i | −0.0605637 | − | 0.0250863i | ||||
\(721\) | 14.1593 | − | 34.1837i | 0.527321 | − | 1.27307i | ||||
\(722\) | −1.80999 | + | 1.80999i | −0.0673609 | + | 0.0673609i | ||||
\(723\) | 8.11699 | − | 8.11699i | 0.301874 | − | 0.301874i | ||||
\(724\) | −13.1565 | + | 31.7626i | −0.488958 | + | 1.18045i | ||||
\(725\) | −10.8611 | − | 4.49880i | −0.403370 | − | 0.167081i | ||||
\(726\) | −10.1894 | − | 24.5994i | −0.378165 | − | 0.912971i | ||||
\(727\) | − | 1.40583i | − | 0.0521393i | −0.999660 | − | 0.0260697i | \(-0.991701\pi\) | ||
0.999660 | − | 0.0260697i | \(-0.00829917\pi\) | |||||||
\(728\) | 19.3218 | − | 8.00334i | 0.716112 | − | 0.296623i | ||||
\(729\) | −5.56344 | − | 5.56344i | −0.206053 | − | 0.206053i | ||||
\(730\) | 4.88017 | 0.180623 | ||||||||
\(731\) | 2.38890 | + | 3.36053i | 0.0883567 | + | 0.124294i | ||||
\(732\) | 37.7203 | 1.39418 | ||||||||
\(733\) | −31.8645 | − | 31.8645i | −1.17694 | − | 1.17694i | −0.980519 | − | 0.196424i | \(-0.937067\pi\) |
−0.196424 | − | 0.980519i | \(-0.562933\pi\) | |||||||
\(734\) | −11.9510 | + | 4.95029i | −0.441121 | + | 0.182718i | ||||
\(735\) | 15.9108i | 0.586879i | ||||||||
\(736\) | 17.7436 | + | 42.8369i | 0.654039 | + | 1.57899i | ||||
\(737\) | 27.1331 | + | 11.2389i | 0.999461 | + | 0.413990i | ||||
\(738\) | 1.82797 | − | 4.41311i | 0.0672885 | − | 0.162449i | ||||
\(739\) | −17.3877 | + | 17.3877i | −0.639617 | + | 0.639617i | −0.950461 | − | 0.310844i | \(-0.899388\pi\) |
0.310844 | + | 0.950461i | \(0.399388\pi\) | |||||||
\(740\) | 15.5301 | − | 15.5301i | 0.570897 | − | 0.570897i | ||||
\(741\) | −8.82111 | + | 21.2961i | −0.324052 | + | 0.782330i | ||||
\(742\) | −6.20635 | − | 2.57075i | −0.227842 | − | 0.0943753i | ||||
\(743\) | −9.12312 | − | 22.0252i | −0.334695 | − | 0.808025i | −0.998207 | − | 0.0598593i | \(-0.980935\pi\) |
0.663512 | − | 0.748166i | \(-0.269065\pi\) | |||||||
\(744\) | − | 14.9828i | − | 0.549296i | ||||||
\(745\) | −32.0814 | + | 13.2886i | −1.17537 | + | 0.486855i | ||||
\(746\) | −6.51374 | − | 6.51374i | −0.238485 | − | 0.238485i | ||||
\(747\) | −11.2941 | −0.413229 | ||||||||
\(748\) | −25.8526 | − | 16.2123i | −0.945266 | − | 0.592782i | ||||
\(749\) | −0.0372955 | −0.00136275 | ||||||||
\(750\) | −13.6795 | − | 13.6795i | −0.499504 | − | 0.499504i | ||||
\(751\) | 34.9604 | − | 14.4811i | 1.27572 | − | 0.528422i | 0.361024 | − | 0.932557i | \(-0.382427\pi\) |
0.914700 | + | 0.404135i | \(0.132427\pi\) | |||||||
\(752\) | − | 8.89155i | − | 0.324241i | ||||||
\(753\) | 15.4412 | + | 37.2784i | 0.562709 | + | 1.35850i | ||||
\(754\) | 10.2160 | + | 4.23160i | 0.372044 | + | 0.154106i | ||||
\(755\) | −11.5033 | + | 27.7713i | −0.418647 | + | 1.01070i | ||||
\(756\) | −11.9764 | + | 11.9764i | −0.435577 | + | 0.435577i | ||||
\(757\) | 14.9302 | − | 14.9302i | 0.542647 | − | 0.542647i | −0.381657 | − | 0.924304i | \(-0.624646\pi\) |
0.924304 | + | 0.381657i | \(0.124646\pi\) | |||||||
\(758\) | −7.08631 | + | 17.1079i | −0.257386 | + | 0.621386i | ||||
\(759\) | −79.5782 | − | 32.9624i | −2.88850 | − | 1.19646i | ||||
\(760\) | −8.31079 | − | 20.0640i | −0.301464 | − | 0.727799i | ||||
\(761\) | 27.9358i | 1.01267i | 0.862337 | + | 0.506335i | \(0.169000\pi\) | ||||
−0.862337 | + | 0.506335i | \(0.831000\pi\) | |||||||
\(762\) | −17.1026 | + | 7.08411i | −0.619561 | + | 0.256630i | ||||
\(763\) | −0.366510 | − | 0.366510i | −0.0132685 | − | 0.0132685i | ||||
\(764\) | −13.1066 | −0.474179 | ||||||||
\(765\) | −4.88580 | + | 7.79102i | −0.176646 | + | 0.281685i | ||||
\(766\) | −13.5333 | −0.488979 | ||||||||
\(767\) | −2.28156 | − | 2.28156i | −0.0823825 | − | 0.0823825i | ||||
\(768\) | 25.1358 | − | 10.4116i | 0.907009 | − | 0.375695i | ||||
\(769\) | 6.47377i | 0.233450i | 0.993164 | + | 0.116725i | \(0.0372397\pi\) | ||||
−0.993164 | + | 0.116725i | \(0.962760\pi\) | |||||||
\(770\) | −9.17767 | − | 22.1569i | −0.330740 | − | 0.798478i | ||||
\(771\) | 26.7351 | + | 11.0740i | 0.962841 | + | 0.398822i | ||||
\(772\) | −1.19612 | + | 2.88770i | −0.0430495 | + | 0.103931i | ||||
\(773\) | 28.4108 | − | 28.4108i | 1.02186 | − | 1.02186i | 0.0221087 | − | 0.999756i | \(-0.492962\pi\) |
0.999756 | − | 0.0221087i | \(-0.00703798\pi\) | |||||||
\(774\) | 0.694197 | − | 0.694197i | 0.0249524 | − | 0.0249524i | ||||
\(775\) | −2.04315 | + | 4.93261i | −0.0733923 | + | 0.177185i | ||||
\(776\) | 20.5227 | + | 8.50077i | 0.736721 | + | 0.305160i | ||||
\(777\) | 23.8247 | + | 57.5178i | 0.854705 | + | 2.06344i | ||||
\(778\) | 9.44436i | 0.338597i | ||||||||
\(779\) | −21.2375 | + | 8.79688i | −0.760914 | + | 0.315181i | ||||
\(780\) | −8.49338 | − | 8.49338i | −0.304112 | − | 0.304112i | ||||
\(781\) | 16.4856 | 0.589900 | ||||||||
\(782\) | 24.5169 | − | 5.61870i | 0.876724 | − | 0.200924i | ||||
\(783\) | −21.6941 | −0.775282 | ||||||||
\(784\) | 2.45104 | + | 2.45104i | 0.0875373 | + | 0.0875373i | ||||
\(785\) | −9.07115 | + | 3.75739i | −0.323763 | + | 0.134107i | ||||
\(786\) | − | 24.6586i | − | 0.879542i | ||||||
\(787\) | −20.1603 | − | 48.6714i | −0.718638 | − | 1.73495i | −0.677193 | − | 0.735806i | \(-0.736804\pi\) |
−0.0414458 | − | 0.999141i | \(-0.513196\pi\) | |||||||
\(788\) | −22.9982 | − | 9.52615i | −0.819276 | − | 0.339355i | ||||
\(789\) | −18.9945 | + | 45.8568i | −0.676223 | + | 1.63255i | ||||
\(790\) | 12.7750 | − | 12.7750i | 0.454512 | − | 0.454512i | ||||
\(791\) | 0.864105 | − | 0.864105i | 0.0307241 | − | 0.0307241i | ||||
\(792\) | −6.73599 | + | 16.2621i | −0.239353 | + | 0.577849i | ||||
\(793\) | 28.2965 | + | 11.7208i | 1.00484 | + | 0.416218i | ||||
\(794\) | −6.36962 | − | 15.3776i | −0.226049 | − | 0.545732i | ||||
\(795\) | 9.34656i | 0.331488i | ||||||||
\(796\) | 15.3314 | − | 6.35048i | 0.543407 | − | 0.225087i | ||||
\(797\) | −23.5951 | − | 23.5951i | −0.835781 | − | 0.835781i | 0.152520 | − | 0.988300i | \(-0.451261\pi\) |
−0.988300 | + | 0.152520i | \(0.951261\pi\) | |||||||
\(798\) | 25.4118 | 0.899567 | ||||||||
\(799\) | −45.8364 | − | 7.74613i | −1.62158 | − | 0.274038i | ||||
\(800\) | −11.3286 | −0.400526 | ||||||||
\(801\) | 2.96444 | + | 2.96444i | 0.104743 | + | 0.104743i | ||||
\(802\) | 9.21978 | − | 3.81896i | 0.325562 | − | 0.134852i | ||||
\(803\) | 19.0350i | 0.671732i | ||||||||
\(804\) | −6.20551 | − | 14.9814i | −0.218852 | − | 0.528354i | ||||
\(805\) | −43.2240 | − | 17.9039i | −1.52344 | − | 0.631031i | ||||
\(806\) | 1.92180 | − | 4.63964i | 0.0676925 | − | 0.163424i | ||||
\(807\) | −28.2614 | + | 28.2614i | −0.994850 | + | 0.994850i | ||||
\(808\) | −18.9976 | + | 18.9976i | −0.668335 | + | 0.668335i | ||||
\(809\) | 16.2814 | − | 39.3067i | 0.572422 | − | 1.38195i | −0.327065 | − | 0.945002i | \(-0.606060\pi\) |
0.899487 | − | 0.436948i | \(-0.143940\pi\) | |||||||
\(810\) | −13.9635 | − | 5.78385i | −0.490626 | − | 0.203224i | ||||
\(811\) | 3.78500 | + | 9.13779i | 0.132909 | + | 0.320871i | 0.976297 | − | 0.216434i | \(-0.0694425\pi\) |
−0.843388 | + | 0.537305i | \(0.819442\pi\) | |||||||
\(812\) | 28.8517i | 1.01250i | ||||||||
\(813\) | −10.2953 | + | 4.26444i | −0.361070 | + | 0.149560i | ||||
\(814\) | −25.5939 | − | 25.5939i | −0.897066 | − | 0.897066i | ||||
\(815\) | 22.6345 | 0.792853 | ||||||||
\(816\) | 1.50162 | + | 6.55225i | 0.0525672 | + | 0.229375i | ||||
\(817\) | −4.72452 | −0.165290 | ||||||||
\(818\) | −3.54607 | − | 3.54607i | −0.123985 | − | 0.123985i | ||||
\(819\) | 9.37537 | − | 3.88341i | 0.327602 | − | 0.135697i | ||||
\(820\) | − | 11.9784i | − | 0.418306i | ||||||
\(821\) | −1.35519 | − | 3.27173i | −0.0472966 | − | 0.114184i | 0.898466 | − | 0.439044i | \(-0.144683\pi\) |
−0.945762 | + | 0.324860i | \(0.894683\pi\) | |||||||
\(822\) | −7.39555 | − | 3.06334i | −0.257950 | − | 0.106846i | ||||
\(823\) | −15.2899 | + | 36.9131i | −0.532973 | + | 1.28671i | 0.396573 | + | 0.918003i | \(0.370199\pi\) |
−0.929546 | + | 0.368707i | \(0.879801\pi\) | |||||||
\(824\) | 20.3457 | − | 20.3457i | 0.708776 | − | 0.708776i | ||||
\(825\) | 14.8811 | − | 14.8811i | 0.518095 | − | 0.518095i | ||||
\(826\) | −1.36125 | + | 3.28635i | −0.0473640 | + | 0.114347i | ||||
\(827\) | 14.9697 | + | 6.20065i | 0.520548 | + | 0.215618i | 0.627457 | − | 0.778651i | \(-0.284096\pi\) |
−0.106910 | + | 0.994269i | \(0.534096\pi\) | |||||||
\(828\) | 5.42439 | + | 13.0956i | 0.188510 | + | 0.455105i | ||||
\(829\) | − | 32.6413i | − | 1.13368i | −0.823828 | − | 0.566839i | \(-0.808166\pi\) | ||
0.823828 | − | 0.566839i | \(-0.191834\pi\) | |||||||
\(830\) | 11.0556 | − | 4.57938i | 0.383746 | − | 0.158953i | ||||
\(831\) | 20.1359 | + | 20.1359i | 0.698507 | + | 0.698507i | ||||
\(832\) | 6.93328 | 0.240368 | ||||||||
\(833\) | 14.7706 | − | 10.5000i | 0.511770 | − | 0.363802i | ||||
\(834\) | −14.3083 | −0.495456 | ||||||||
\(835\) | 16.7775 | + | 16.7775i | 0.580608 | + | 0.580608i | ||||
\(836\) | 32.3050 | − | 13.3812i | 1.11729 | − | 0.462798i | ||||
\(837\) | 9.85246i | 0.340551i | ||||||||
\(838\) | −2.85181 | − | 6.88489i | −0.0985143 | − | 0.237835i | ||||
\(839\) | 46.9502 | + | 19.4474i | 1.62090 | + | 0.671400i | 0.994169 | − | 0.107834i | \(-0.0343915\pi\) |
0.626733 | + | 0.779234i | \(0.284392\pi\) | |||||||
\(840\) | −12.2759 | + | 29.6366i | −0.423558 | + | 1.02256i | ||||
\(841\) | −5.62490 | + | 5.62490i | −0.193962 | + | 0.193962i | ||||
\(842\) | 18.6984 | − | 18.6984i | 0.644390 | − | 0.644390i | ||||
\(843\) | −7.24695 | + | 17.4957i | −0.249598 | + | 0.602584i | ||||
\(844\) | 26.0242 | + | 10.7796i | 0.895791 | + | 0.371049i | ||||
\(845\) | 4.97893 | + | 12.0202i | 0.171280 | + | 0.413508i | ||||
\(846\) | 11.0688i | 0.380552i | ||||||||
\(847\) | 52.1164 | − | 21.5873i | 1.79074 | − | 0.741749i | ||||
\(848\) | 1.43983 | + | 1.43983i | 0.0494439 | + | 0.0494439i | ||||
\(849\) | 10.2864 | 0.353029 | ||||||||
\(850\) | −1.02403 | + | 6.05954i | −0.0351241 | + | 0.207841i | ||||
\(851\) | −70.6103 | −2.42049 | ||||||||
\(852\) | −6.43639 | − | 6.43639i | −0.220507 | − | 0.220507i | ||||
\(853\) | −23.7822 | + | 9.85091i | −0.814287 | + | 0.337289i | −0.750663 | − | 0.660685i | \(-0.770266\pi\) |
−0.0636239 | + | 0.997974i | \(0.520266\pi\) | |||||||
\(854\) | − | 33.7652i | − | 1.15542i | ||||||
\(855\) | −4.03259 | − | 9.73553i | −0.137912 | − | 0.332948i | ||||
\(856\) | −0.0267952 | − | 0.0110989i | −0.000915840 | − | 0.000379353i | ||||
\(857\) | −1.45074 | + | 3.50241i | −0.0495565 | + | 0.119640i | −0.946719 | − | 0.322060i | \(-0.895625\pi\) |
0.897163 | + | 0.441700i | \(0.145625\pi\) | |||||||
\(858\) | −13.9973 | + | 13.9973i | −0.477859 | + | 0.477859i | ||||
\(859\) | 28.2076 | − | 28.2076i | 0.962431 | − | 0.962431i | −0.0368882 | − | 0.999319i | \(-0.511745\pi\) |
0.999319 | + | 0.0368882i | \(0.0117446\pi\) | |||||||
\(860\) | 0.942126 | − | 2.27449i | 0.0321262 | − | 0.0775596i | ||||
\(861\) | 31.3700 | + | 12.9939i | 1.06909 | + | 0.442831i | ||||
\(862\) | 1.32231 | + | 3.19234i | 0.0450381 | + | 0.108731i | ||||
\(863\) | 4.33919i | 0.147708i | 0.997269 | + | 0.0738539i | \(0.0235299\pi\) | ||||
−0.997269 | + | 0.0738539i | \(0.976470\pi\) | |||||||
\(864\) | −19.3141 | + | 8.00015i | −0.657078 | + | 0.272171i | ||||
\(865\) | −25.0564 | − | 25.0564i | −0.851942 | − | 0.851942i | ||||
\(866\) | 15.7097 | 0.533837 | ||||||||
\(867\) | 35.0854 | − | 2.03274i | 1.19156 | − | 0.0690355i | ||||
\(868\) | 13.1031 | 0.444749 | ||||||||
\(869\) | 49.8285 | + | 49.8285i | 1.69032 | + | 1.69032i | ||||
\(870\) | −15.6697 | + | 6.49062i | −0.531254 | + | 0.220053i | ||||
\(871\) | − | 13.1668i | − | 0.446140i | ||||||
\(872\) | −0.154250 | − | 0.372392i | −0.00522356 | − | 0.0126108i | ||||
\(873\) | 9.95808 | + | 4.12477i | 0.337030 | + | 0.139602i | ||||
\(874\) | −11.0295 | + | 26.6275i | −0.373078 | + | 0.900689i | ||||
\(875\) | 28.9814 | − | 28.9814i | 0.979750 | − | 0.979750i | ||||
\(876\) | 7.43177 | − | 7.43177i | 0.251096 | − | 0.251096i | ||||
\(877\) | 9.29907 | − | 22.4499i | 0.314007 | − | 0.758080i | −0.685541 | − | 0.728034i | \(-0.740434\pi\) |
0.999548 | − | 0.0300466i | \(-0.00956556\pi\) | |||||||
\(878\) | 28.1120 | + | 11.6444i | 0.948735 | + | 0.392979i | ||||
\(879\) | 9.98385 | + | 24.1031i | 0.336747 | + | 0.812979i | ||||
\(880\) | 7.26939i | 0.245051i | ||||||||
\(881\) | 26.7489 | − | 11.0797i | 0.901193 | − | 0.373286i | 0.116514 | − | 0.993189i | \(-0.462828\pi\) |
0.784679 | + | 0.619903i | \(0.212828\pi\) | |||||||
\(882\) | −3.05121 | − | 3.05121i | −0.102740 | − | 0.102740i | ||||
\(883\) | 56.3473 | 1.89624 | 0.948119 | − | 0.317914i | \(-0.102982\pi\) | ||||
0.948119 | + | 0.317914i | \(0.102982\pi\) | |||||||
\(884\) | −2.27970 | + | 13.4897i | −0.0766745 | + | 0.453708i | ||||
\(885\) | 4.94914 | 0.166363 | ||||||||
\(886\) | 13.3377 | + | 13.3377i | 0.448088 | + | 0.448088i | ||||
\(887\) | 17.7779 | − | 7.36386i | 0.596925 | − | 0.247254i | −0.0637019 | − | 0.997969i | \(-0.520291\pi\) |
0.660627 | + | 0.750715i | \(0.270291\pi\) | |||||||
\(888\) | 48.4141i | 1.62467i | ||||||||
\(889\) | −15.0084 | − | 36.2335i | −0.503366 | − | 1.21523i | ||||
\(890\) | −4.10383 | − | 1.69986i | −0.137561 | − | 0.0569795i | ||||
\(891\) | 22.5598 | − | 54.4643i | 0.755783 | − | 1.82462i | ||||
\(892\) | 2.07773 | − | 2.07773i | 0.0695675 | − | 0.0695675i | ||||
\(893\) | 37.6655 | − | 37.6655i | 1.26043 | − | 1.26043i | ||||
\(894\) | 12.0919 | − | 29.1924i | 0.404414 | − | 0.976341i | ||||
\(895\) | −9.51241 | − | 3.94017i | −0.317965 | − | 0.131705i | ||||
\(896\) | 12.2101 | + | 29.4778i | 0.407911 | + | 0.984785i | ||||
\(897\) | 38.6167i | 1.28937i | ||||||||
\(898\) | −4.15541 | + | 1.72123i | −0.138668 | + | 0.0574381i | ||||
\(899\) | 11.8675 | + | 11.8675i | 0.395804 | + | 0.395804i | ||||
\(900\) | −3.46325 | −0.115442 | ||||||||
\(901\) | 8.67674 | − | 6.16805i | 0.289064 | − | 0.205487i | ||||
\(902\) | −19.7408 | −0.657295 | ||||||||
\(903\) | 4.93462 | + | 4.93462i | 0.164214 | + | 0.164214i | ||||
\(904\) | 0.877974 | − | 0.363669i | 0.0292010 | − | 0.0120954i | ||||
\(905\) | − | 42.8179i | − | 1.42332i | ||||||
\(906\) | −10.4674 | − | 25.2705i | −0.347755 | − | 0.839555i | ||||
\(907\) | −30.5989 | − | 12.6745i | −1.01602 | − | 0.420849i | −0.188372 | − | 0.982098i | \(-0.560321\pi\) |
−0.827647 | + | 0.561249i | \(0.810321\pi\) | |||||||
\(908\) | −3.96228 | + | 9.56579i | −0.131493 | + | 0.317452i | ||||
\(909\) | −9.21810 | + | 9.21810i | −0.305745 | + | 0.305745i | ||||
\(910\) | −7.60281 | + | 7.60281i | −0.252031 | + | 0.252031i | ||||
\(911\) | −5.31036 | + | 12.8203i | −0.175940 | + | 0.424757i | −0.987108 | − | 0.160057i | \(-0.948832\pi\) |
0.811168 | + | 0.584813i | \(0.198832\pi\) | |||||||
\(912\) | −7.11631 | − | 2.94767i | −0.235645 | − | 0.0976072i | ||||
\(913\) | 17.8618 | + | 43.1223i | 0.591140 | + | 1.42714i | ||||
\(914\) | − | 22.4329i | − | 0.742015i | ||||||
\(915\) | −43.4025 | + | 17.9779i | −1.43484 | + | 0.594331i | ||||
\(916\) | −0.430616 | − | 0.430616i | −0.0142280 | − | 0.0142280i | ||||
\(917\) | 52.2417 | 1.72517 | ||||||||
\(918\) | 2.53333 | + | 11.0541i | 0.0836123 | + | 0.364839i | ||||
\(919\) | −19.1000 | −0.630052 | −0.315026 | − | 0.949083i | \(-0.602013\pi\) | ||||
−0.315026 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(920\) | −25.7264 | − | 25.7264i | −0.848174 | − | 0.848174i | ||||
\(921\) | 43.4248 | − | 17.9871i | 1.43089 | − | 0.592696i | ||||
\(922\) | − | 21.7446i | − | 0.716119i | ||||||
\(923\) | −2.82839 | − | 6.82834i | −0.0930976 | − | 0.224758i | ||||
\(924\) | −47.7178 | − | 19.7654i | −1.56980 | − | 0.650233i | ||||
\(925\) | 6.60207 | − | 15.9388i | 0.217075 | − | 0.524065i | ||||
\(926\) | −0.736963 | + | 0.736963i | −0.0242181 | + | 0.0242181i | ||||
\(927\) | 9.87221 | − | 9.87221i | 0.324246 | − | 0.324246i | ||||
\(928\) | −13.6279 | + | 32.9006i | −0.447358 | + | 1.08002i | ||||
\(929\) | −3.08240 | − | 1.27677i | −0.101130 | − | 0.0418895i | 0.331545 | − | 0.943439i | \(-0.392430\pi\) |
−0.432675 | + | 0.901550i | \(0.642430\pi\) | |||||||
\(930\) | 2.94775 | + | 7.11649i | 0.0966604 | + | 0.233359i | ||||
\(931\) | 20.7658i | 0.680570i | ||||||||
\(932\) | −29.3137 | + | 12.1421i | −0.960201 | + | 0.397728i | ||||
\(933\) | −30.3334 | − | 30.3334i | −0.993071 | − | 0.993071i | ||||
\(934\) | 27.8879 | 0.912521 | ||||||||
\(935\) | 37.4741 | + | 6.33294i | 1.22553 | + | 0.207109i | ||||
\(936\) | 7.89147 | 0.257941 | ||||||||
\(937\) | 10.5894 | + | 10.5894i | 0.345940 | + | 0.345940i | 0.858595 | − | 0.512655i | \(-0.171338\pi\) |
−0.512655 | + | 0.858595i | \(0.671338\pi\) | |||||||
\(938\) | −13.4106 | + | 5.55484i | −0.437871 | + | 0.181372i | ||||
\(939\) | − | 19.7436i | − | 0.644307i | ||||||
\(940\) | 10.6221 | + | 25.6440i | 0.346454 | + | 0.836415i | ||||
\(941\) | −48.5576 | − | 20.1132i | −1.58293 | − | 0.655673i | −0.594059 | − | 0.804422i | \(-0.702475\pi\) |
−0.988875 | + | 0.148749i | \(0.952475\pi\) | |||||||
\(942\) | 3.41904 | − | 8.25428i | 0.111398 | − | 0.268939i | ||||
\(943\) | −27.2311 | + | 27.2311i | −0.886767 | + | 0.886767i | ||||
\(944\) | 0.762410 | − | 0.762410i | 0.0248143 | − | 0.0248143i | ||||
\(945\) | 8.07244 | − | 19.4886i | 0.262597 | − | 0.633964i | ||||
\(946\) | −3.74842 | − | 1.55265i | −0.121872 | − | 0.0504809i | ||||
\(947\) | −5.68318 | − | 13.7204i | −0.184679 | − | 0.445854i | 0.804241 | − | 0.594303i | \(-0.202572\pi\) |
−0.988920 | + | 0.148449i | \(0.952572\pi\) | |||||||
\(948\) | − | 38.9087i | − | 1.26370i | ||||||
\(949\) | 7.88434 | − | 3.26580i | 0.255937 | − | 0.106012i | ||||
\(950\) | −4.97935 | − | 4.97935i | −0.161552 | − | 0.161552i | ||||
\(951\) | −31.0082 | −1.00551 | ||||||||
\(952\) | 35.6139 | − | 8.16186i | 1.15425 | − | 0.264527i | ||||
\(953\) | −15.8397 | −0.513099 | −0.256549 | − | 0.966531i | \(-0.582586\pi\) | ||||
−0.256549 | + | 0.966531i | \(0.582586\pi\) | |||||||
\(954\) | −1.79239 | − | 1.79239i | −0.0580307 | − | 0.0580307i | ||||
\(955\) | 15.0810 | − | 6.24674i | 0.488008 | − | 0.202140i | ||||
\(956\) | − | 34.1715i | − | 1.10519i | ||||||
\(957\) | −25.3166 | − | 61.1196i | −0.818368 | − | 1.97572i | ||||
\(958\) | −28.5541 | − | 11.8275i | −0.922540 | − | 0.382129i | ||||
\(959\) | 6.49000 | − | 15.6682i | 0.209573 | − | 0.505954i | ||||
\(960\) | −7.51979 | + | 7.51979i | −0.242700 | + | 0.242700i | ||||
\(961\) | −16.5306 | + | 16.5306i | −0.533246 | + | 0.533246i | ||||
\(962\) | −6.20994 | + | 14.9921i | −0.200217 | + | 0.483365i | ||||
\(963\) | −0.0130016 | − | 0.00538546i | −0.000418972 | − | 0.000173544i | ||||
\(964\) | 2.98756 | + | 7.21261i | 0.0962228 | + | 0.232302i | ||||
\(965\) | − | 3.89279i | − | 0.125313i | ||||||
\(966\) | 39.3316 | − | 16.2917i | 1.26547 | − | 0.524176i | ||||
\(967\) | −8.47076 | − | 8.47076i | −0.272401 | − | 0.272401i | 0.557665 | − | 0.830066i | \(-0.311697\pi\) |
−0.830066 | + | 0.557665i | \(0.811697\pi\) | |||||||
\(968\) | 43.8676 | 1.40996 | ||||||||
\(969\) | −21.3950 | + | 34.1170i | −0.687307 | + | 1.09600i | ||||
\(970\) | −11.4203 | −0.366683 | ||||||||
\(971\) | −29.1418 | − | 29.1418i | −0.935206 | − | 0.935206i | 0.0628186 | − | 0.998025i | \(-0.479991\pi\) |
−0.998025 | + | 0.0628186i | \(0.979991\pi\) | |||||||
\(972\) | −16.1658 | + | 6.69610i | −0.518519 | + | 0.214778i | ||||
\(973\) | − | 30.3136i | − | 0.971810i | ||||||
\(974\) | 6.27555 | + | 15.1505i | 0.201082 | + | 0.485454i | ||||
\(975\) | −8.71692 | − | 3.61067i | −0.279165 | − | 0.115634i | ||||
\(976\) | −3.91664 | + | 9.45560i | −0.125368 | + | 0.302666i | ||||
\(977\) | −22.5933 | + | 22.5933i | −0.722824 | + | 0.722824i | −0.969179 | − | 0.246356i | \(-0.920767\pi\) |
0.246356 | + | 0.969179i | \(0.420767\pi\) | |||||||
\(978\) | −14.5638 | + | 14.5638i | −0.465697 | + | 0.465697i | ||||
\(979\) | 6.63029 | − | 16.0069i | 0.211905 | − | 0.511584i | ||||
\(980\) | −9.99711 | − | 4.14094i | −0.319346 | − | 0.132277i | ||||
\(981\) | −0.0748456 | − | 0.180693i | −0.00238964 | − | 0.00576909i | ||||
\(982\) | − | 26.0917i | − | 0.832618i | ||||||
\(983\) | −24.8228 | + | 10.2819i | −0.791723 | + | 0.327942i | −0.741636 | − | 0.670802i | \(-0.765950\pi\) |
−0.0500870 | + | 0.998745i | \(0.515950\pi\) | |||||||
\(984\) | 18.6711 | + | 18.6711i | 0.595212 | + | 0.595212i | ||||
\(985\) | 31.0029 | 0.987835 | ||||||||
\(986\) | 16.3664 | + | 10.2634i | 0.521211 | + | 0.326855i | ||||
\(987\) | −78.6809 | −2.50444 | ||||||||
\(988\) | −11.0850 | − | 11.0850i | −0.352661 | − | 0.352661i | ||||
\(989\) | −7.31247 | + | 3.02893i | −0.232523 | + | 0.0963142i | ||||
\(990\) | − | 9.04939i | − | 0.287608i | ||||||
\(991\) | 21.3204 | + | 51.4720i | 0.677265 | + | 1.63506i | 0.768977 | + | 0.639277i | \(0.220766\pi\) |
−0.0917117 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(992\) | 14.9420 | + | 6.18918i | 0.474409 | + | 0.196507i | ||||
\(993\) | 14.6443 | − | 35.3544i | 0.464721 | − | 1.12194i | ||||
\(994\) | −5.76150 | + | 5.76150i | −0.182744 | + | 0.182744i | ||||
\(995\) | −14.6142 | + | 14.6142i | −0.463303 | + | 0.463303i | ||||
\(996\) | 9.86233 | − | 23.8098i | 0.312500 | − | 0.754441i | ||||
\(997\) | 19.8945 | + | 8.24055i | 0.630064 | + | 0.260981i | 0.674780 | − | 0.738019i | \(-0.264238\pi\) |
−0.0447165 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(998\) | −7.29167 | − | 17.6036i | −0.230814 | − | 0.557233i | ||||
\(999\) | − | 31.8364i | − | 1.00726i |
(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 | 731.2.m.b.87.18 | ✓ | 116 | |
17.9 | even | 8 | inner | 731.2.m.b.689.18 | yes | 116 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.m.b.87.18 | ✓ | 116 | 1.1 | even | 1 | trivial | |
731.2.m.b.689.18 | yes | 116 | 17.9 | even | 8 | inner |