Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(139,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 139.3 | ||
Character | \(\chi\) | \(=\) | 336.139 |
Dual form | 336.2.u.a.307.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27023 | − | 0.621708i | −0.898187 | − | 0.439614i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.22696 | + | 1.57942i | 0.613479 | + | 0.789711i | ||||
\(5\) | 1.90169 | − | 1.90169i | 0.850462 | − | 0.850462i | −0.139728 | − | 0.990190i | \(-0.544623\pi\) |
0.990190 | + | 0.139728i | \(0.0446227\pi\) | |||||||
\(6\) | 1.33780 | − | 0.458573i | 0.546155 | − | 0.187212i | ||||
\(7\) | 2.22978 | − | 1.42411i | 0.842777 | − | 0.538263i | ||||
\(8\) | −0.576579 | − | 2.76904i | −0.203851 | − | 0.979002i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −3.59788 | + | 1.23329i | −1.13775 | + | 0.389999i | ||||
\(11\) | −3.56463 | + | 3.56463i | −1.07477 | + | 1.07477i | −0.0778065 | + | 0.996968i | \(0.524792\pi\) |
−0.996968 | + | 0.0778065i | \(0.975208\pi\) | |||||||
\(12\) | −1.98441 | − | 0.249229i | −0.572850 | − | 0.0719461i | ||||
\(13\) | 1.66932 | + | 1.66932i | 0.462986 | + | 0.462986i | 0.899633 | − | 0.436647i | \(-0.143834\pi\) |
−0.436647 | + | 0.899633i | \(0.643834\pi\) | |||||||
\(14\) | −3.71771 | + | 0.422676i | −0.993599 | + | 0.112965i | ||||
\(15\) | 2.68940i | 0.694400i | ||||||||
\(16\) | −0.989144 | + | 3.87577i | −0.247286 | + | 0.968943i | ||||
\(17\) | − | 7.15496i | − | 1.73533i | −0.497147 | − | 0.867667i | \(-0.665619\pi\) | ||
0.497147 | − | 0.867667i | \(-0.334381\pi\) | |||||||
\(18\) | −0.621708 | + | 1.27023i | −0.146538 | + | 0.299396i | ||||
\(19\) | 3.10260 | − | 3.10260i | 0.711785 | − | 0.711785i | −0.255123 | − | 0.966908i | \(-0.582116\pi\) |
0.966908 | + | 0.255123i | \(0.0821161\pi\) | |||||||
\(20\) | 5.33687 | + | 0.670275i | 1.19336 | + | 0.149878i | ||||
\(21\) | −0.569692 | + | 2.58369i | −0.124317 | + | 0.563807i | ||||
\(22\) | 6.74404 | − | 2.31173i | 1.43783 | − | 0.492863i | ||||
\(23\) | 3.63389 | 0.757719 | 0.378860 | − | 0.925454i | \(-0.376316\pi\) | ||||
0.378860 | + | 0.925454i | \(0.376316\pi\) | |||||||
\(24\) | 2.36571 | + | 1.55030i | 0.482898 | + | 0.316454i | ||||
\(25\) | − | 2.23286i | − | 0.446572i | ||||||
\(26\) | −1.08259 | − | 3.15825i | −0.212313 | − | 0.619383i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 4.98512 | + | 1.77443i | 0.942098 | + | 0.335336i | ||||
\(29\) | 5.29845 | − | 5.29845i | 0.983898 | − | 0.983898i | −0.0159747 | − | 0.999872i | \(-0.505085\pi\) |
0.999872 | + | 0.0159747i | \(0.00508512\pi\) | |||||||
\(30\) | 1.67202 | − | 3.41615i | 0.305268 | − | 0.623701i | ||||
\(31\) | −0.906641 | −0.162838 | −0.0814188 | − | 0.996680i | \(-0.525945\pi\) | ||||
−0.0814188 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(32\) | 3.66604 | − | 4.30815i | 0.648070 | − | 0.761581i | ||||
\(33\) | − | 5.04114i | − | 0.877550i | ||||||
\(34\) | −4.44830 | + | 9.08843i | −0.762876 | + | 1.55865i | ||||
\(35\) | 1.53213 | − | 6.94857i | 0.258977 | − | 1.17452i | ||||
\(36\) | 1.57942 | − | 1.22696i | 0.263237 | − | 0.204493i | ||||
\(37\) | 2.51619 | + | 2.51619i | 0.413660 | + | 0.413660i | 0.883011 | − | 0.469352i | \(-0.155512\pi\) |
−0.469352 | + | 0.883011i | \(0.655512\pi\) | |||||||
\(38\) | −5.86992 | + | 2.01210i | −0.952226 | + | 0.326405i | ||||
\(39\) | −2.36078 | −0.378027 | ||||||||
\(40\) | −6.36233 | − | 4.16938i | −1.00597 | − | 0.659236i | ||||
\(41\) | −2.37705 | −0.371232 | −0.185616 | − | 0.982622i | \(-0.559428\pi\) | ||||
−0.185616 | + | 0.982622i | \(0.559428\pi\) | |||||||
\(42\) | 2.32994 | − | 2.92769i | 0.359517 | − | 0.451753i | ||||
\(43\) | −1.93434 | + | 1.93434i | −0.294984 | + | 0.294984i | −0.839045 | − | 0.544062i | \(-0.816886\pi\) |
0.544062 | + | 0.839045i | \(0.316886\pi\) | |||||||
\(44\) | −10.0037 | − | 1.25640i | −1.50811 | − | 0.189409i | ||||
\(45\) | −1.90169 | − | 1.90169i | −0.283487 | − | 0.283487i | ||||
\(46\) | −4.61587 | − | 2.25922i | −0.680573 | − | 0.333104i | ||||
\(47\) | −0.550905 | −0.0803577 | −0.0401789 | − | 0.999193i | \(-0.512793\pi\) | ||||
−0.0401789 | + | 0.999193i | \(0.512793\pi\) | |||||||
\(48\) | −2.04115 | − | 3.44001i | −0.294615 | − | 0.496523i | ||||
\(49\) | 2.94382 | − | 6.35090i | 0.420545 | − | 0.907272i | ||||
\(50\) | −1.38819 | + | 2.83624i | −0.196319 | + | 0.401106i | ||||
\(51\) | 5.05932 | + | 5.05932i | 0.708447 | + | 0.708447i | ||||
\(52\) | −0.588373 | + | 4.68475i | −0.0815927 | + | 0.649658i | ||||
\(53\) | 3.05130 | + | 3.05130i | 0.419128 | + | 0.419128i | 0.884903 | − | 0.465775i | \(-0.154224\pi\) |
−0.465775 | + | 0.884903i | \(0.654224\pi\) | |||||||
\(54\) | −0.458573 | − | 1.33780i | −0.0624039 | − | 0.182052i | ||||
\(55\) | 13.5576i | 1.82811i | ||||||||
\(56\) | −5.22906 | − | 5.35322i | −0.698762 | − | 0.715354i | ||||
\(57\) | 4.38774i | 0.581170i | ||||||||
\(58\) | −10.0243 | + | 3.43615i | −1.31626 | + | 0.451189i | ||||
\(59\) | 9.17593 | + | 9.17593i | 1.19460 | + | 1.19460i | 0.975760 | + | 0.218845i | \(0.0702289\pi\) |
0.218845 | + | 0.975760i | \(0.429771\pi\) | |||||||
\(60\) | −4.24769 | + | 3.29978i | −0.548375 | + | 0.426000i | ||||
\(61\) | −5.62319 | − | 5.62319i | −0.719976 | − | 0.719976i | 0.248624 | − | 0.968600i | \(-0.420022\pi\) |
−0.968600 | + | 0.248624i | \(0.920022\pi\) | |||||||
\(62\) | 1.15164 | + | 0.563666i | 0.146259 | + | 0.0715856i | ||||
\(63\) | −1.42411 | − | 2.22978i | −0.179421 | − | 0.280926i | ||||
\(64\) | −7.33511 | + | 3.19313i | −0.916889 | + | 0.399142i | ||||
\(65\) | 6.34907 | 0.787505 | ||||||||
\(66\) | −3.13412 | + | 6.40340i | −0.385783 | + | 0.788204i | ||||
\(67\) | 1.68616 | + | 1.68616i | 0.205997 | + | 0.205997i | 0.802564 | − | 0.596567i | \(-0.203469\pi\) |
−0.596567 | + | 0.802564i | \(0.703469\pi\) | |||||||
\(68\) | 11.3007 | − | 8.77884i | 1.37041 | − | 1.06459i | ||||
\(69\) | −2.56955 | + | 2.56955i | −0.309338 | + | 0.309338i | ||||
\(70\) | −6.26613 | + | 7.87373i | −0.748946 | + | 0.941091i | ||||
\(71\) | −11.6715 | −1.38515 | −0.692577 | − | 0.721344i | \(-0.743525\pi\) | ||||
−0.692577 | + | 0.721344i | \(0.743525\pi\) | |||||||
\(72\) | −2.76904 | + | 0.576579i | −0.326334 | + | 0.0679505i | ||||
\(73\) | 8.41083 | 0.984414 | 0.492207 | − | 0.870478i | \(-0.336190\pi\) | ||||
0.492207 | + | 0.870478i | \(0.336190\pi\) | |||||||
\(74\) | −1.63180 | − | 4.76048i | −0.189693 | − | 0.553394i | ||||
\(75\) | 1.57887 | + | 1.57887i | 0.182312 | + | 0.182312i | ||||
\(76\) | 8.70707 | + | 1.09355i | 0.998770 | + | 0.125439i | ||||
\(77\) | −2.87190 | + | 13.0247i | −0.327283 | + | 1.48431i | ||||
\(78\) | 2.99872 | + | 1.46771i | 0.339539 | + | 0.166186i | ||||
\(79\) | − | 12.6448i | − | 1.42265i | −0.702862 | − | 0.711327i | \(-0.748095\pi\) | ||
0.702862 | − | 0.711327i | \(-0.251905\pi\) | |||||||
\(80\) | 5.48947 | + | 9.25157i | 0.613742 | + | 1.03436i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 3.01939 | + | 1.47783i | 0.333436 | + | 0.163199i | ||||
\(83\) | −3.82605 | + | 3.82605i | −0.419964 | + | 0.419964i | −0.885191 | − | 0.465227i | \(-0.845973\pi\) |
0.465227 | + | 0.885191i | \(0.345973\pi\) | |||||||
\(84\) | −4.77972 | + | 2.27030i | −0.521511 | + | 0.247710i | ||||
\(85\) | −13.6065 | − | 13.6065i | −1.47584 | − | 1.47584i | ||||
\(86\) | 3.65964 | − | 1.25446i | 0.394629 | − | 0.135272i | ||||
\(87\) | 7.49314i | 0.803349i | ||||||||
\(88\) | 11.9259 | + | 7.81529i | 1.27130 | + | 0.833112i | ||||
\(89\) | −14.6937 | −1.55753 | −0.778765 | − | 0.627315i | \(-0.784154\pi\) | ||||
−0.778765 | + | 0.627315i | \(0.784154\pi\) | |||||||
\(90\) | 1.23329 | + | 3.59788i | 0.130000 | + | 0.379250i | ||||
\(91\) | 6.09951 | + | 1.34492i | 0.639403 | + | 0.140986i | ||||
\(92\) | 4.45864 | + | 5.73945i | 0.464845 | + | 0.598379i | ||||
\(93\) | 0.641092 | − | 0.641092i | 0.0664782 | − | 0.0664782i | ||||
\(94\) | 0.699775 | + | 0.342502i | 0.0721762 | + | 0.0353264i | ||||
\(95\) | − | 11.8004i | − | 1.21069i | ||||||
\(96\) | 0.454046 | + | 5.63860i | 0.0463409 | + | 0.575487i | ||||
\(97\) | 6.22825i | 0.632383i | 0.948695 | + | 0.316191i | \(0.102404\pi\) | ||||
−0.948695 | + | 0.316191i | \(0.897596\pi\) | |||||||
\(98\) | −7.68772 | + | 6.23690i | −0.776577 | + | 0.630022i | ||||
\(99\) | 3.56463 | + | 3.56463i | 0.358258 | + | 0.358258i | ||||
\(100\) | 3.52663 | − | 2.73963i | 0.352663 | − | 0.273963i | ||||
\(101\) | −13.7348 | + | 13.7348i | −1.36666 | + | 1.36666i | −0.501512 | + | 0.865150i | \(0.667223\pi\) |
−0.865150 | + | 0.501512i | \(0.832777\pi\) | |||||||
\(102\) | −3.28107 | − | 9.57191i | −0.324875 | − | 0.947761i | ||||
\(103\) | 2.12589i | 0.209471i | 0.994500 | + | 0.104735i | \(0.0333995\pi\) | ||||
−0.994500 | + | 0.104735i | \(0.966600\pi\) | |||||||
\(104\) | 3.65991 | − | 5.58490i | 0.358884 | − | 0.547645i | ||||
\(105\) | 3.83000 | + | 5.99676i | 0.373770 | + | 0.585224i | ||||
\(106\) | −1.97883 | − | 5.77286i | −0.192201 | − | 0.560710i | ||||
\(107\) | −9.07831 | + | 9.07831i | −0.877634 | + | 0.877634i | −0.993289 | − | 0.115656i | \(-0.963103\pi\) |
0.115656 | + | 0.993289i | \(0.463103\pi\) | |||||||
\(108\) | −0.249229 | + | 1.98441i | −0.0239820 | + | 0.190950i | ||||
\(109\) | −7.77089 | + | 7.77089i | −0.744316 | + | 0.744316i | −0.973405 | − | 0.229090i | \(-0.926425\pi\) |
0.229090 | + | 0.973405i | \(0.426425\pi\) | |||||||
\(110\) | 8.42889 | − | 17.2213i | 0.803663 | − | 1.64199i | ||||
\(111\) | −3.55843 | −0.337752 | ||||||||
\(112\) | 3.31395 | + | 10.0508i | 0.313139 | + | 0.949707i | ||||
\(113\) | 7.32742 | 0.689306 | 0.344653 | − | 0.938730i | \(-0.387997\pi\) | ||||
0.344653 | + | 0.938730i | \(0.387997\pi\) | |||||||
\(114\) | 2.72789 | − | 5.57343i | 0.255490 | − | 0.521999i | ||||
\(115\) | 6.91054 | − | 6.91054i | 0.644412 | − | 0.644412i | ||||
\(116\) | 14.8695 | + | 1.86751i | 1.38060 | + | 0.173394i | ||||
\(117\) | 1.66932 | − | 1.66932i | 0.154329 | − | 0.154329i | ||||
\(118\) | −5.95078 | − | 17.3603i | −0.547814 | − | 1.59814i | ||||
\(119\) | −10.1895 | − | 15.9540i | −0.934066 | − | 1.46250i | ||||
\(120\) | 7.44704 | − | 1.55065i | 0.679818 | − | 0.141554i | ||||
\(121\) | − | 14.4131i | − | 1.31028i | ||||||
\(122\) | 3.64675 | + | 10.6387i | 0.330161 | + | 0.963184i | ||||
\(123\) | 1.68083 | − | 1.68083i | 0.151555 | − | 0.151555i | ||||
\(124\) | −1.11241 | − | 1.43197i | −0.0998975 | − | 0.128595i | ||||
\(125\) | 5.26224 | + | 5.26224i | 0.470669 | + | 0.470669i | ||||
\(126\) | 0.422676 | + | 3.71771i | 0.0376549 | + | 0.331200i | ||||
\(127\) | 14.6589i | 1.30076i | 0.759608 | + | 0.650382i | \(0.225391\pi\) | ||||
−0.759608 | + | 0.650382i | \(0.774609\pi\) | |||||||
\(128\) | 11.3025 | + | 0.504288i | 0.999006 | + | 0.0445732i | ||||
\(129\) | − | 2.73556i | − | 0.240853i | ||||||
\(130\) | −8.06476 | − | 3.94726i | −0.707326 | − | 0.346198i | ||||
\(131\) | −5.52527 | + | 5.52527i | −0.482745 | + | 0.482745i | −0.906007 | − | 0.423262i | \(-0.860885\pi\) |
0.423262 | + | 0.906007i | \(0.360885\pi\) | |||||||
\(132\) | 7.96209 | − | 6.18527i | 0.693011 | − | 0.538359i | ||||
\(133\) | 2.49966 | − | 11.3365i | 0.216748 | − | 0.983004i | ||||
\(134\) | −1.09351 | − | 3.19010i | −0.0944646 | − | 0.275583i | ||||
\(135\) | 2.68940 | 0.231467 | ||||||||
\(136\) | −19.8123 | + | 4.12540i | −1.69889 | + | 0.353750i | ||||
\(137\) | − | 3.43937i | − | 0.293845i | −0.989148 | − | 0.146923i | \(-0.953063\pi\) | ||
0.989148 | − | 0.146923i | \(-0.0469368\pi\) | |||||||
\(138\) | 4.86143 | − | 1.66641i | 0.413832 | − | 0.141854i | ||||
\(139\) | −5.21179 | − | 5.21179i | −0.442058 | − | 0.442058i | 0.450645 | − | 0.892703i | \(-0.351194\pi\) |
−0.892703 | + | 0.450645i | \(0.851194\pi\) | |||||||
\(140\) | 12.8546 | − | 6.10573i | 1.08641 | − | 0.516028i | ||||
\(141\) | 0.389548 | − | 0.389548i | 0.0328059 | − | 0.0328059i | ||||
\(142\) | 14.8255 | + | 7.25628i | 1.24413 | + | 0.608933i | ||||
\(143\) | −11.9010 | −0.995212 | ||||||||
\(144\) | 3.87577 | + | 0.989144i | 0.322981 | + | 0.0824287i | ||||
\(145\) | − | 20.1520i | − | 1.67354i | ||||||
\(146\) | −10.6837 | − | 5.22908i | −0.884187 | − | 0.432762i | ||||
\(147\) | 2.40917 | + | 6.57236i | 0.198705 | + | 0.542079i | ||||
\(148\) | −0.886864 | + | 7.06139i | −0.0728998 | + | 0.580443i | ||||
\(149\) | 8.38511 | + | 8.38511i | 0.686935 | + | 0.686935i | 0.961553 | − | 0.274618i | \(-0.0885514\pi\) |
−0.274618 | + | 0.961553i | \(0.588551\pi\) | |||||||
\(150\) | −1.02393 | − | 2.98712i | −0.0836036 | − | 0.243898i | ||||
\(151\) | 3.21093 | 0.261302 | 0.130651 | − | 0.991428i | \(-0.458293\pi\) | ||||
0.130651 | + | 0.991428i | \(0.458293\pi\) | |||||||
\(152\) | −10.3801 | − | 6.80231i | −0.841937 | − | 0.551740i | ||||
\(153\) | −7.15496 | −0.578444 | ||||||||
\(154\) | 11.7456 | − | 14.7589i | 0.946484 | − | 1.18931i | ||||
\(155\) | −1.72415 | + | 1.72415i | −0.138487 | + | 0.138487i | ||||
\(156\) | −2.89657 | − | 3.72866i | −0.231912 | − | 0.298532i | ||||
\(157\) | 0.574508 | + | 0.574508i | 0.0458508 | + | 0.0458508i | 0.729660 | − | 0.683810i | \(-0.239678\pi\) |
−0.683810 | + | 0.729660i | \(0.739678\pi\) | |||||||
\(158\) | −7.86138 | + | 16.0618i | −0.625418 | + | 1.27781i | ||||
\(159\) | −4.31519 | −0.342217 | ||||||||
\(160\) | −1.22111 | − | 15.1644i | −0.0965373 | − | 1.19885i | ||||
\(161\) | 8.10277 | − | 5.17507i | 0.638588 | − | 0.407852i | ||||
\(162\) | 1.27023 | + | 0.621708i | 0.0997985 | + | 0.0488460i | ||||
\(163\) | −13.8383 | − | 13.8383i | −1.08390 | − | 1.08390i | −0.996142 | − | 0.0877597i | \(-0.972029\pi\) |
−0.0877597 | − | 0.996142i | \(-0.527971\pi\) | |||||||
\(164\) | −2.91654 | − | 3.75436i | −0.227743 | − | 0.293166i | ||||
\(165\) | −9.58670 | − | 9.58670i | −0.746323 | − | 0.746323i | ||||
\(166\) | 7.23865 | − | 2.48127i | 0.561828 | − | 0.192584i | ||||
\(167\) | − | 9.71401i | − | 0.751692i | −0.926682 | − | 0.375846i | \(-0.877352\pi\) | ||
0.926682 | − | 0.375846i | \(-0.122648\pi\) | |||||||
\(168\) | 7.48280 | + | 0.0877976i | 0.577311 | + | 0.00677373i | ||||
\(169\) | − | 7.42674i | − | 0.571287i | ||||||
\(170\) | 8.82411 | + | 25.7427i | 0.676778 | + | 1.97437i | ||||
\(171\) | −3.10260 | − | 3.10260i | −0.237262 | − | 0.237262i | ||||
\(172\) | −5.42848 | − | 0.681781i | −0.413918 | − | 0.0519853i | ||||
\(173\) | 3.57505 | + | 3.57505i | 0.271806 | + | 0.271806i | 0.829827 | − | 0.558021i | \(-0.188439\pi\) |
−0.558021 | + | 0.829827i | \(0.688439\pi\) | |||||||
\(174\) | 4.65854 | − | 9.51800i | 0.353163 | − | 0.721558i | ||||
\(175\) | −3.17984 | − | 4.97879i | −0.240374 | − | 0.376361i | ||||
\(176\) | −10.2897 | − | 17.3416i | −0.775618 | − | 1.30717i | ||||
\(177\) | −12.9767 | −0.975391 | ||||||||
\(178\) | 18.6644 | + | 9.13520i | 1.39895 | + | 0.684712i | ||||
\(179\) | 12.0824 | + | 12.0824i | 0.903078 | + | 0.903078i | 0.995701 | − | 0.0926229i | \(-0.0295251\pi\) |
−0.0926229 | + | 0.995701i | \(0.529525\pi\) | |||||||
\(180\) | 0.670275 | − | 5.33687i | 0.0499594 | − | 0.397787i | ||||
\(181\) | −14.7072 | + | 14.7072i | −1.09318 | + | 1.09318i | −0.0979893 | + | 0.995187i | \(0.531241\pi\) |
−0.995187 | + | 0.0979893i | \(0.968759\pi\) | |||||||
\(182\) | −6.91163 | − | 5.50046i | −0.512324 | − | 0.407722i | ||||
\(183\) | 7.95239 | 0.587858 | ||||||||
\(184\) | −2.09523 | − | 10.0624i | −0.154462 | − | 0.741808i | ||||
\(185\) | 9.57005 | 0.703604 | ||||||||
\(186\) | −1.21291 | + | 0.415761i | −0.0889345 | + | 0.0304851i | ||||
\(187\) | 25.5048 | + | 25.5048i | 1.86509 | + | 1.86509i | ||||
\(188\) | −0.675937 | − | 0.870111i | −0.0492978 | − | 0.0634593i | ||||
\(189\) | 2.58369 | + | 0.569692i | 0.187936 | + | 0.0414390i | ||||
\(190\) | −7.33638 | + | 14.9892i | −0.532237 | + | 1.08743i | ||||
\(191\) | 4.83855i | 0.350105i | 0.984559 | + | 0.175052i | \(0.0560095\pi\) | ||||
−0.984559 | + | 0.175052i | \(0.943991\pi\) | |||||||
\(192\) | 2.92882 | − | 7.44460i | 0.211369 | − | 0.537267i | ||||
\(193\) | 23.3996 | 1.68434 | 0.842169 | − | 0.539213i | \(-0.181278\pi\) | ||||
0.842169 | + | 0.539213i | \(0.181278\pi\) | |||||||
\(194\) | 3.87215 | − | 7.91129i | 0.278004 | − | 0.567998i | ||||
\(195\) | −4.48947 | + | 4.48947i | −0.321497 | + | 0.321497i | ||||
\(196\) | 13.6427 | − | 3.14277i | 0.974478 | − | 0.224483i | ||||
\(197\) | 5.84458 | + | 5.84458i | 0.416409 | + | 0.416409i | 0.883964 | − | 0.467555i | \(-0.154865\pi\) |
−0.467555 | + | 0.883964i | \(0.654865\pi\) | |||||||
\(198\) | −2.31173 | − | 6.74404i | −0.164288 | − | 0.479278i | ||||
\(199\) | 4.28359i | 0.303655i | 0.988407 | + | 0.151828i | \(0.0485159\pi\) | ||||
−0.988407 | + | 0.151828i | \(0.951484\pi\) | |||||||
\(200\) | −6.18287 | + | 1.28742i | −0.437195 | + | 0.0910344i | ||||
\(201\) | −2.38459 | −0.168196 | ||||||||
\(202\) | 25.9853 | − | 8.90729i | 1.82832 | − | 0.626715i | ||||
\(203\) | 4.26879 | − | 19.3600i | 0.299610 | − | 1.35880i | ||||
\(204\) | −1.78322 | + | 14.1984i | −0.124851 | + | 0.994086i | ||||
\(205\) | −4.52041 | + | 4.52041i | −0.315719 | + | 0.315719i | ||||
\(206\) | 1.32168 | − | 2.70037i | 0.0920861 | − | 0.188144i | ||||
\(207\) | − | 3.63389i | − | 0.252573i | ||||||
\(208\) | −8.12110 | + | 4.81870i | −0.563097 | + | 0.334117i | ||||
\(209\) | 22.1192i | 1.53002i | ||||||||
\(210\) | −1.13674 | − | 9.99839i | −0.0784427 | − | 0.689955i | ||||
\(211\) | −5.34715 | − | 5.34715i | −0.368113 | − | 0.368113i | 0.498676 | − | 0.866789i | \(-0.333820\pi\) |
−0.866789 | + | 0.498676i | \(0.833820\pi\) | |||||||
\(212\) | −1.07547 | + | 8.56311i | −0.0738635 | + | 0.588117i | ||||
\(213\) | 8.25301 | − | 8.25301i | 0.565487 | − | 0.565487i | ||||
\(214\) | 17.1756 | − | 5.88747i | 1.17410 | − | 0.402459i | ||||
\(215\) | 7.35702i | 0.501745i | ||||||||
\(216\) | 1.55030 | − | 2.36571i | 0.105485 | − | 0.160966i | ||||
\(217\) | −2.02161 | + | 1.29116i | −0.137236 | + | 0.0876495i | ||||
\(218\) | 14.7020 | − | 5.03958i | 0.995746 | − | 0.341323i | ||||
\(219\) | −5.94736 | + | 5.94736i | −0.401885 | + | 0.401885i | ||||
\(220\) | −21.4132 | + | 16.6347i | −1.44368 | + | 1.12151i | ||||
\(221\) | 11.9439 | − | 11.9439i | 0.803435 | − | 0.803435i | ||||
\(222\) | 4.52002 | + | 2.21231i | 0.303364 | + | 0.148480i | ||||
\(223\) | −28.4331 | −1.90402 | −0.952009 | − | 0.306070i | \(-0.900986\pi\) | ||||
−0.952009 | + | 0.306070i | \(0.900986\pi\) | |||||||
\(224\) | 2.03916 | − | 14.8271i | 0.136247 | − | 0.990675i | ||||
\(225\) | −2.23286 | −0.148857 | ||||||||
\(226\) | −9.30750 | − | 4.55552i | −0.619126 | − | 0.303028i | ||||
\(227\) | 19.1228 | − | 19.1228i | 1.26923 | − | 1.26923i | 0.322739 | − | 0.946488i | \(-0.395396\pi\) |
0.946488 | − | 0.322739i | \(-0.104604\pi\) | |||||||
\(228\) | −6.93009 | + | 5.38357i | −0.458956 | + | 0.356536i | ||||
\(229\) | 2.11755 | − | 2.11755i | 0.139932 | − | 0.139932i | −0.633671 | − | 0.773603i | \(-0.718453\pi\) |
0.773603 | + | 0.633671i | \(0.218453\pi\) | |||||||
\(230\) | −13.0743 | + | 4.48163i | −0.862094 | + | 0.295510i | ||||
\(231\) | −7.17914 | − | 11.2406i | −0.472353 | − | 0.739579i | ||||
\(232\) | −17.7266 | − | 11.6166i | −1.16381 | − | 0.762669i | ||||
\(233\) | 23.1104i | 1.51401i | 0.653408 | + | 0.757006i | \(0.273339\pi\) | ||||
−0.653408 | + | 0.757006i | \(0.726661\pi\) | |||||||
\(234\) | −3.15825 | + | 1.08259i | −0.206461 | + | 0.0707710i | ||||
\(235\) | −1.04765 | + | 1.04765i | −0.0683412 | + | 0.0683412i | ||||
\(236\) | −3.23417 | + | 25.7512i | −0.210527 | + | 1.67626i | ||||
\(237\) | 8.94124 | + | 8.94124i | 0.580796 | + | 0.580796i | ||||
\(238\) | 3.02423 | + | 26.6001i | 0.196032 | + | 1.72423i | ||||
\(239\) | − | 9.94538i | − | 0.643313i | −0.946856 | − | 0.321657i | \(-0.895760\pi\) | ||
0.946856 | − | 0.321657i | \(-0.104240\pi\) | |||||||
\(240\) | −10.4235 | − | 2.66020i | −0.672833 | − | 0.171715i | ||||
\(241\) | 11.4287i | 0.736187i | 0.929789 | + | 0.368093i | \(0.119989\pi\) | ||||
−0.929789 | + | 0.368093i | \(0.880011\pi\) | |||||||
\(242\) | −8.96074 | + | 18.3079i | −0.576018 | + | 1.17688i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 1.98196 | − | 15.7808i | 0.126882 | − | 1.01026i | ||||
\(245\) | −6.47922 | − | 17.6757i | −0.413942 | − | 1.12926i | ||||
\(246\) | −3.18001 | + | 1.09005i | −0.202750 | + | 0.0694990i | ||||
\(247\) | 10.3585 | 0.659093 | ||||||||
\(248\) | 0.522750 | + | 2.51052i | 0.0331947 | + | 0.159418i | ||||
\(249\) | − | 5.41086i | − | 0.342899i | ||||||
\(250\) | −3.41267 | − | 9.95583i | −0.215836 | − | 0.629662i | ||||
\(251\) | −11.4020 | − | 11.4020i | −0.719687 | − | 0.719687i | 0.248854 | − | 0.968541i | \(-0.419946\pi\) |
−0.968541 | + | 0.248854i | \(0.919946\pi\) | |||||||
\(252\) | 1.77443 | − | 4.98512i | 0.111779 | − | 0.314033i | ||||
\(253\) | −12.9535 | + | 12.9535i | −0.814378 | + | 0.814378i | ||||
\(254\) | 9.11352 | − | 18.6201i | 0.571833 | − | 1.16833i | ||||
\(255\) | 19.2425 | 1.20501 | ||||||||
\(256\) | −14.0432 | − | 7.66739i | −0.877699 | − | 0.479212i | ||||
\(257\) | 8.41347i | 0.524818i | 0.964957 | + | 0.262409i | \(0.0845169\pi\) | ||||
−0.964957 | + | 0.262409i | \(0.915483\pi\) | |||||||
\(258\) | −1.70072 | + | 3.47479i | −0.105882 | + | 0.216331i | ||||
\(259\) | 9.19389 | + | 2.02721i | 0.571280 | + | 0.125965i | ||||
\(260\) | 7.79004 | + | 10.0279i | 0.483118 | + | 0.621901i | ||||
\(261\) | −5.29845 | − | 5.29845i | −0.327966 | − | 0.327966i | ||||
\(262\) | 10.4535 | − | 3.58325i | 0.645817 | − | 0.221374i | ||||
\(263\) | −6.67247 | −0.411442 | −0.205721 | − | 0.978611i | \(-0.565954\pi\) | ||||
−0.205721 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(264\) | −13.9591 | + | 2.90662i | −0.859123 | + | 0.178890i | ||||
\(265\) | 11.6053 | 0.712906 | ||||||||
\(266\) | −10.2232 | + | 12.8459i | −0.626822 | + | 0.787635i | ||||
\(267\) | 10.3900 | − | 10.3900i | 0.635859 | − | 0.635859i | ||||
\(268\) | −0.594307 | + | 4.73200i | −0.0363031 | + | 0.289053i | ||||
\(269\) | 1.02225 | + | 1.02225i | 0.0623274 | + | 0.0623274i | 0.737583 | − | 0.675256i | \(-0.235967\pi\) |
−0.675256 | + | 0.737583i | \(0.735967\pi\) | |||||||
\(270\) | −3.41615 | − | 1.67202i | −0.207900 | − | 0.101756i | ||||
\(271\) | −5.47375 | −0.332507 | −0.166253 | − | 0.986083i | \(-0.553167\pi\) | ||||
−0.166253 | + | 0.986083i | \(0.553167\pi\) | |||||||
\(272\) | 27.7310 | + | 7.07729i | 1.68144 | + | 0.429124i | ||||
\(273\) | −5.26401 | + | 3.36201i | −0.318592 | + | 0.203478i | ||||
\(274\) | −2.13828 | + | 4.36878i | −0.129178 | + | 0.263928i | ||||
\(275\) | 7.95932 | + | 7.95932i | 0.479965 | + | 0.479965i | ||||
\(276\) | −7.21114 | − | 0.905671i | −0.434059 | − | 0.0545150i | ||||
\(277\) | 9.91118 | + | 9.91118i | 0.595505 | + | 0.595505i | 0.939113 | − | 0.343608i | \(-0.111649\pi\) |
−0.343608 | + | 0.939113i | \(0.611649\pi\) | |||||||
\(278\) | 3.37995 | + | 9.86038i | 0.202716 | + | 0.591386i | ||||
\(279\) | 0.906641i | 0.0542792i | ||||||||
\(280\) | −20.1242 | − | 0.236123i | −1.20265 | − | 0.0141110i | ||||
\(281\) | 19.6432i | 1.17182i | 0.810378 | + | 0.585908i | \(0.199262\pi\) | ||||
−0.810378 | + | 0.585908i | \(0.800738\pi\) | |||||||
\(282\) | −0.737001 | + | 0.252630i | −0.0438877 | + | 0.0150439i | ||||
\(283\) | −20.3051 | − | 20.3051i | −1.20701 | − | 1.20701i | −0.971990 | − | 0.235022i | \(-0.924484\pi\) |
−0.235022 | − | 0.971990i | \(-0.575516\pi\) | |||||||
\(284\) | −14.3205 | − | 18.4343i | −0.849764 | − | 1.09387i | ||||
\(285\) | 8.34412 | + | 8.34412i | 0.494263 | + | 0.494263i | ||||
\(286\) | 15.1170 | + | 7.39895i | 0.893886 | + | 0.437509i | ||||
\(287\) | −5.30028 | + | 3.38518i | −0.312866 | + | 0.199821i | ||||
\(288\) | −4.30815 | − | 3.66604i | −0.253860 | − | 0.216023i | ||||
\(289\) | −34.1935 | −2.01138 | ||||||||
\(290\) | −12.5287 | + | 25.5977i | −0.735710 | + | 1.50315i | ||||
\(291\) | −4.40404 | − | 4.40404i | −0.258169 | − | 0.258169i | ||||
\(292\) | 10.3197 | + | 13.2842i | 0.603917 | + | 0.777402i | ||||
\(293\) | −11.7526 | + | 11.7526i | −0.686597 | + | 0.686597i | −0.961478 | − | 0.274881i | \(-0.911361\pi\) |
0.274881 | + | 0.961478i | \(0.411361\pi\) | |||||||
\(294\) | 1.02589 | − | 9.84619i | 0.0598310 | − | 0.574242i | ||||
\(295\) | 34.8996 | 2.03193 | ||||||||
\(296\) | 5.51664 | − | 8.41821i | 0.320648 | − | 0.489299i | ||||
\(297\) | −5.04114 | −0.292517 | ||||||||
\(298\) | −5.43792 | − | 15.8641i | −0.315010 | − | 0.918983i | ||||
\(299\) | 6.06613 | + | 6.06613i | 0.350814 | + | 0.350814i | ||||
\(300\) | −0.556493 | + | 4.43092i | −0.0321292 | + | 0.255819i | ||||
\(301\) | −1.55843 | + | 7.06785i | −0.0898264 | + | 0.407384i | ||||
\(302\) | −4.07861 | − | 1.99626i | −0.234698 | − | 0.114872i | ||||
\(303\) | − | 19.4239i | − | 1.11588i | ||||||
\(304\) | 8.95604 | + | 15.0939i | 0.513664 | + | 0.865693i | ||||
\(305\) | −21.3871 | −1.22462 | ||||||||
\(306\) | 9.08843 | + | 4.44830i | 0.519551 | + | 0.254292i | ||||
\(307\) | 19.0195 | − | 19.0195i | 1.08550 | − | 1.08550i | 0.0895163 | − | 0.995985i | \(-0.471468\pi\) |
0.995985 | − | 0.0895163i | \(-0.0285321\pi\) | |||||||
\(308\) | −24.0953 | + | 11.4449i | −1.37295 | + | 0.652133i | ||||
\(309\) | −1.50323 | − | 1.50323i | −0.0855160 | − | 0.0855160i | ||||
\(310\) | 3.26199 | − | 1.11815i | 0.185268 | − | 0.0635065i | ||||
\(311\) | 13.7113i | 0.777499i | 0.921344 | + | 0.388749i | \(0.127093\pi\) | ||||
−0.921344 | + | 0.388749i | \(0.872907\pi\) | |||||||
\(312\) | 1.36117 | + | 6.53707i | 0.0770613 | + | 0.370089i | ||||
\(313\) | −4.84337 | −0.273764 | −0.136882 | − | 0.990587i | \(-0.543708\pi\) | ||||
−0.136882 | + | 0.990587i | \(0.543708\pi\) | |||||||
\(314\) | −0.372580 | − | 1.08693i | −0.0210259 | − | 0.0613392i | ||||
\(315\) | −6.94857 | − | 1.53213i | −0.391508 | − | 0.0863257i | ||||
\(316\) | 19.9715 | − | 15.5147i | 1.12348 | − | 0.872768i | ||||
\(317\) | −2.72533 | + | 2.72533i | −0.153070 | + | 0.153070i | −0.779488 | − | 0.626418i | \(-0.784520\pi\) |
0.626418 | + | 0.779488i | \(0.284520\pi\) | |||||||
\(318\) | 5.48128 | + | 2.68279i | 0.307375 | + | 0.150443i | ||||
\(319\) | 37.7740i | 2.11494i | ||||||||
\(320\) | −7.87677 | + | 20.0215i | −0.440325 | + | 1.11923i | ||||
\(321\) | − | 12.8387i | − | 0.716585i | ||||||
\(322\) | −13.5098 | + | 1.53596i | −0.752869 | + | 0.0855956i | ||||
\(323\) | −22.1990 | − | 22.1990i | −1.23518 | − | 1.23518i | ||||
\(324\) | −1.22696 | − | 1.57942i | −0.0681644 | − | 0.0877456i | ||||
\(325\) | 3.72736 | − | 3.72736i | 0.206757 | − | 0.206757i | ||||
\(326\) | 8.97444 | + | 26.1812i | 0.497048 | + | 1.45004i | ||||
\(327\) | − | 10.9897i | − | 0.607731i | ||||||
\(328\) | 1.37055 | + | 6.58212i | 0.0756762 | + | 0.363437i | ||||
\(329\) | −1.22839 | + | 0.784549i | −0.0677236 | + | 0.0432536i | ||||
\(330\) | 6.21717 | + | 18.1374i | 0.342244 | + | 0.998432i | ||||
\(331\) | 6.93803 | − | 6.93803i | 0.381349 | − | 0.381349i | −0.490239 | − | 0.871588i | \(-0.663091\pi\) |
0.871588 | + | 0.490239i | \(0.163091\pi\) | |||||||
\(332\) | −10.7374 | − | 1.34854i | −0.589289 | − | 0.0740108i | ||||
\(333\) | 2.51619 | − | 2.51619i | 0.137887 | − | 0.137887i | ||||
\(334\) | −6.03927 | + | 12.3390i | −0.330454 | + | 0.675160i | ||||
\(335\) | 6.41310 | 0.350385 | ||||||||
\(336\) | −9.45028 | − | 4.76364i | −0.515555 | − | 0.259878i | ||||
\(337\) | 2.95698 | 0.161077 | 0.0805384 | − | 0.996752i | \(-0.474336\pi\) | ||||
0.0805384 | + | 0.996752i | \(0.474336\pi\) | |||||||
\(338\) | −4.61726 | + | 9.43365i | −0.251146 | + | 0.513123i | ||||
\(339\) | −5.18127 | + | 5.18127i | −0.281408 | + | 0.281408i | ||||
\(340\) | 4.79579 | − | 38.1851i | 0.260088 | − | 2.07088i | ||||
\(341\) | 3.23184 | − | 3.23184i | 0.175014 | − | 0.175014i | ||||
\(342\) | 2.01210 | + | 5.86992i | 0.108802 | + | 0.317409i | ||||
\(343\) | −2.48033 | − | 18.3534i | −0.133925 | − | 0.990991i | ||||
\(344\) | 6.47154 | + | 4.24095i | 0.348922 | + | 0.228657i | ||||
\(345\) | 9.77299i | 0.526160i | ||||||||
\(346\) | −2.31849 | − | 6.76376i | −0.124643 | − | 0.363622i | ||||
\(347\) | −3.16858 | + | 3.16858i | −0.170098 | + | 0.170098i | −0.787023 | − | 0.616924i | \(-0.788378\pi\) |
0.616924 | + | 0.787023i | \(0.288378\pi\) | |||||||
\(348\) | −11.8348 | + | 9.19378i | −0.634413 | + | 0.492838i | ||||
\(349\) | 11.0951 | + | 11.0951i | 0.593908 | + | 0.593908i | 0.938685 | − | 0.344777i | \(-0.112045\pi\) |
−0.344777 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(350\) | 0.943776 | + | 8.30113i | 0.0504470 | + | 0.443714i | ||||
\(351\) | 2.36078i | 0.126009i | ||||||||
\(352\) | 2.28891 | + | 28.4250i | 0.121999 | + | 1.51506i | ||||
\(353\) | − | 30.8984i | − | 1.64455i | −0.569087 | − | 0.822277i | \(-0.692703\pi\) | ||
0.569087 | − | 0.822277i | \(-0.307297\pi\) | |||||||
\(354\) | 16.4834 | + | 8.06773i | 0.876083 | + | 0.428795i | ||||
\(355\) | −22.1956 | + | 22.1956i | −1.17802 | + | 1.17802i | ||||
\(356\) | −18.0286 | − | 23.2076i | −0.955513 | − | 1.23000i | ||||
\(357\) | 18.4862 | + | 4.07613i | 0.978393 | + | 0.215732i | ||||
\(358\) | −7.83566 | − | 22.8591i | −0.414127 | − | 1.20814i | ||||
\(359\) | 0.943215 | 0.0497810 | 0.0248905 | − | 0.999690i | \(-0.492076\pi\) | ||||
0.0248905 | + | 0.999690i | \(0.492076\pi\) | |||||||
\(360\) | −4.16938 | + | 6.36233i | −0.219745 | + | 0.335324i | ||||
\(361\) | − | 0.252238i | − | 0.0132757i | ||||||
\(362\) | 27.8251 | − | 9.53791i | 1.46245 | − | 0.501301i | ||||
\(363\) | 10.1916 | + | 10.1916i | 0.534921 | + | 0.534921i | ||||
\(364\) | 5.35966 | + | 11.2839i | 0.280923 | + | 0.591435i | ||||
\(365\) | 15.9948 | − | 15.9948i | 0.837207 | − | 0.837207i | ||||
\(366\) | −10.1014 | − | 4.94406i | −0.528006 | − | 0.258430i | ||||
\(367\) | 3.56906 | 0.186304 | 0.0931518 | − | 0.995652i | \(-0.470306\pi\) | ||||
0.0931518 | + | 0.995652i | \(0.470306\pi\) | |||||||
\(368\) | −3.59444 | + | 14.0841i | −0.187373 | + | 0.734186i | ||||
\(369\) | 2.37705i | 0.123744i | ||||||||
\(370\) | −12.1561 | − | 5.94977i | −0.631968 | − | 0.309314i | ||||
\(371\) | 11.1491 | + | 2.45833i | 0.578833 | + | 0.127630i | ||||
\(372\) | 1.79915 | + | 0.225961i | 0.0932815 | + | 0.0117155i | ||||
\(373\) | −0.693026 | − | 0.693026i | −0.0358835 | − | 0.0358835i | 0.688937 | − | 0.724821i | \(-0.258077\pi\) |
−0.724821 | + | 0.688937i | \(0.758077\pi\) | |||||||
\(374\) | −16.5404 | − | 48.2534i | −0.855281 | − | 2.49512i | ||||
\(375\) | −7.44194 | −0.384300 | ||||||||
\(376\) | 0.317640 | + | 1.52547i | 0.0163810 | + | 0.0786703i | ||||
\(377\) | 17.6896 | 0.911062 | ||||||||
\(378\) | −2.92769 | − | 2.32994i | −0.150584 | − | 0.119839i | ||||
\(379\) | 6.55229 | − | 6.55229i | 0.336569 | − | 0.336569i | −0.518506 | − | 0.855074i | \(-0.673511\pi\) |
0.855074 | + | 0.518506i | \(0.173511\pi\) | |||||||
\(380\) | 18.6378 | − | 14.4786i | 0.956097 | − | 0.742735i | ||||
\(381\) | −10.3654 | − | 10.3654i | −0.531034 | − | 0.531034i | ||||
\(382\) | 3.00816 | − | 6.14606i | 0.153911 | − | 0.314460i | ||||
\(383\) | 25.4405 | 1.29995 | 0.649975 | − | 0.759956i | \(-0.274779\pi\) | ||||
0.649975 | + | 0.759956i | \(0.274779\pi\) | |||||||
\(384\) | −8.34863 | + | 7.63546i | −0.426039 | + | 0.389646i | ||||
\(385\) | 19.3076 | + | 30.2305i | 0.984005 | + | 1.54069i | ||||
\(386\) | −29.7228 | − | 14.5477i | −1.51285 | − | 0.740459i | ||||
\(387\) | 1.93434 | + | 1.93434i | 0.0983278 | + | 0.0983278i | ||||
\(388\) | −9.83703 | + | 7.64180i | −0.499399 | + | 0.387954i | ||||
\(389\) | −11.6405 | − | 11.6405i | −0.590199 | − | 0.590199i | 0.347486 | − | 0.937685i | \(-0.387035\pi\) |
−0.937685 | + | 0.347486i | \(0.887035\pi\) | |||||||
\(390\) | 8.49379 | − | 2.91151i | 0.430100 | − | 0.147430i | ||||
\(391\) | − | 26.0004i | − | 1.31490i | ||||||
\(392\) | −19.2832 | − | 4.48974i | −0.973949 | − | 0.226766i | ||||
\(393\) | − | 7.81392i | − | 0.394160i | ||||||
\(394\) | −3.79033 | − | 11.0576i | −0.190954 | − | 0.557072i | ||||
\(395\) | −24.0465 | − | 24.0465i | −1.20991 | − | 1.20991i | ||||
\(396\) | −1.25640 | + | 10.0037i | −0.0631363 | + | 0.502705i | ||||
\(397\) | −18.3501 | − | 18.3501i | −0.920963 | − | 0.920963i | 0.0761349 | − | 0.997098i | \(-0.475742\pi\) |
−0.997098 | + | 0.0761349i | \(0.975742\pi\) | |||||||
\(398\) | 2.66314 | − | 5.44113i | 0.133491 | − | 0.272739i | ||||
\(399\) | 6.24862 | + | 9.78368i | 0.312822 | + | 0.489797i | ||||
\(400\) | 8.65406 | + | 2.20862i | 0.432703 | + | 0.110431i | ||||
\(401\) | 22.2529 | 1.11126 | 0.555630 | − | 0.831430i | \(-0.312477\pi\) | ||||
0.555630 | + | 0.831430i | \(0.312477\pi\) | |||||||
\(402\) | 3.02897 | + | 1.48252i | 0.151071 | + | 0.0739412i | ||||
\(403\) | −1.51347 | − | 1.51347i | −0.0753916 | − | 0.0753916i | ||||
\(404\) | −38.5450 | − | 4.84100i | −1.91769 | − | 0.240849i | ||||
\(405\) | −1.90169 | + | 1.90169i | −0.0944958 | + | 0.0944958i | ||||
\(406\) | −17.4586 | + | 21.9376i | −0.866454 | + | 1.08875i | ||||
\(407\) | −17.9386 | −0.889182 | ||||||||
\(408\) | 11.0923 | − | 16.9265i | 0.549153 | − | 0.837989i | ||||
\(409\) | 27.1395 | 1.34196 | 0.670981 | − | 0.741475i | \(-0.265873\pi\) | ||||
0.670981 | + | 0.741475i | \(0.265873\pi\) | |||||||
\(410\) | 8.55232 | − | 2.93158i | 0.422369 | − | 0.144780i | ||||
\(411\) | 2.43200 | + | 2.43200i | 0.119962 | + | 0.119962i | ||||
\(412\) | −3.35768 | + | 2.60838i | −0.165421 | + | 0.128506i | ||||
\(413\) | 33.5278 | + | 7.39274i | 1.64980 | + | 0.363773i | ||||
\(414\) | −2.25922 | + | 4.61587i | −0.111035 | + | 0.226858i | ||||
\(415\) | 14.5519i | 0.714327i | ||||||||
\(416\) | 13.3115 | − | 1.07190i | 0.652649 | − | 0.0525543i | ||||
\(417\) | 7.37059 | 0.360939 | ||||||||
\(418\) | 13.7517 | − | 28.0964i | 0.672617 | − | 1.37424i | ||||
\(419\) | −14.0335 | + | 14.0335i | −0.685582 | + | 0.685582i | −0.961252 | − | 0.275670i | \(-0.911100\pi\) |
0.275670 | + | 0.961252i | \(0.411100\pi\) | |||||||
\(420\) | −4.77216 | + | 13.4070i | −0.232857 | + | 0.654193i | ||||
\(421\) | 18.7350 | + | 18.7350i | 0.913087 | + | 0.913087i | 0.996514 | − | 0.0834270i | \(-0.0265866\pi\) |
−0.0834270 | + | 0.996514i | \(0.526587\pi\) | |||||||
\(422\) | 3.46774 | + | 10.1165i | 0.168807 | + | 0.492462i | ||||
\(423\) | 0.550905i | 0.0267859i | ||||||||
\(424\) | 6.68984 | − | 10.2085i | 0.324887 | − | 0.495767i | ||||
\(425\) | −15.9760 | −0.774952 | ||||||||
\(426\) | −15.6142 | + | 5.35225i | −0.756509 | + | 0.259317i | ||||
\(427\) | −20.5465 | − | 4.53042i | −0.994315 | − | 0.219242i | ||||
\(428\) | −25.4772 | − | 3.19977i | −1.23149 | − | 0.154667i | ||||
\(429\) | 8.41528 | − | 8.41528i | 0.406294 | − | 0.406294i | ||||
\(430\) | 4.57392 | − | 9.34510i | 0.220574 | − | 0.450661i | ||||
\(431\) | − | 24.5106i | − | 1.18063i | −0.807172 | − | 0.590317i | \(-0.799003\pi\) | ||
0.807172 | − | 0.590317i | \(-0.200997\pi\) | |||||||
\(432\) | −3.44001 | + | 2.04115i | −0.165508 | + | 0.0982050i | ||||
\(433\) | 10.3532i | 0.497542i | 0.968562 | + | 0.248771i | \(0.0800267\pi\) | ||||
−0.968562 | + | 0.248771i | \(0.919973\pi\) | |||||||
\(434\) | 3.37063 | − | 0.383215i | 0.161795 | − | 0.0183949i | ||||
\(435\) | 14.2496 | + | 14.2496i | 0.683218 | + | 0.683218i | ||||
\(436\) | −21.8081 | − | 2.73895i | −1.04442 | − | 0.131172i | ||||
\(437\) | 11.2745 | − | 11.2745i | 0.539333 | − | 0.539333i | ||||
\(438\) | 11.2520 | − | 3.85698i | 0.537642 | − | 0.184294i | ||||
\(439\) | 21.8589i | 1.04327i | 0.853170 | + | 0.521634i | \(0.174677\pi\) | ||||
−0.853170 | + | 0.521634i | \(0.825323\pi\) | |||||||
\(440\) | 37.5416 | − | 7.81705i | 1.78972 | − | 0.372663i | ||||
\(441\) | −6.35090 | − | 2.94382i | −0.302424 | − | 0.140182i | ||||
\(442\) | −22.5971 | + | 7.74588i | −1.07484 | + | 0.368434i | ||||
\(443\) | 8.82244 | − | 8.82244i | 0.419167 | − | 0.419167i | −0.465750 | − | 0.884916i | \(-0.654215\pi\) |
0.884916 | + | 0.465750i | \(0.154215\pi\) | |||||||
\(444\) | −4.36605 | − | 5.62027i | −0.207204 | − | 0.266726i | ||||
\(445\) | −27.9429 | + | 27.9429i | −1.32462 | + | 1.32462i | ||||
\(446\) | 36.1165 | + | 17.6771i | 1.71016 | + | 0.837033i | ||||
\(447\) | −11.8583 | −0.560880 | ||||||||
\(448\) | −11.8083 | + | 17.5660i | −0.557889 | + | 0.829915i | ||||
\(449\) | −15.3552 | −0.724657 | −0.362329 | − | 0.932050i | \(-0.618018\pi\) | ||||
−0.362329 | + | 0.932050i | \(0.618018\pi\) | |||||||
\(450\) | 2.83624 | + | 1.38819i | 0.133702 | + | 0.0654398i | ||||
\(451\) | 8.47328 | − | 8.47328i | 0.398991 | − | 0.398991i | ||||
\(452\) | 8.99045 | + | 11.5731i | 0.422875 | + | 0.544352i | ||||
\(453\) | −2.27047 | + | 2.27047i | −0.106676 | + | 0.106676i | ||||
\(454\) | −36.1792 | + | 12.4015i | −1.69797 | + | 0.582033i | ||||
\(455\) | 14.1570 | − | 9.04177i | 0.663691 | − | 0.423885i | ||||
\(456\) | 12.1498 | − | 2.52988i | 0.568966 | − | 0.118472i | ||||
\(457\) | − | 34.0509i | − | 1.59283i | −0.604748 | − | 0.796417i | \(-0.706726\pi\) | ||
0.604748 | − | 0.796417i | \(-0.293274\pi\) | |||||||
\(458\) | −4.00627 | + | 1.37327i | −0.187201 | + | 0.0641689i | ||||
\(459\) | 5.05932 | − | 5.05932i | 0.236149 | − | 0.236149i | ||||
\(460\) | 19.3936 | + | 2.43571i | 0.904232 | + | 0.113566i | ||||
\(461\) | −17.5033 | − | 17.5033i | −0.815210 | − | 0.815210i | 0.170200 | − | 0.985410i | \(-0.445559\pi\) |
−0.985410 | + | 0.170200i | \(0.945559\pi\) | |||||||
\(462\) | 2.13077 | + | 18.7415i | 0.0991323 | + | 0.871933i | ||||
\(463\) | 0.0530223i | 0.00246416i | 0.999999 | + | 0.00123208i | \(0.000392183\pi\) | ||||
−0.999999 | + | 0.00123208i | \(0.999608\pi\) | |||||||
\(464\) | 15.2946 | + | 25.7765i | 0.710036 | + | 1.19664i | ||||
\(465\) | − | 2.43832i | − | 0.113074i | ||||||
\(466\) | 14.3679 | − | 29.3555i | 0.665581 | − | 1.35987i | ||||
\(467\) | −8.39635 | + | 8.39635i | −0.388537 | + | 0.388537i | −0.874165 | − | 0.485629i | \(-0.838591\pi\) |
0.485629 | + | 0.874165i | \(0.338591\pi\) | |||||||
\(468\) | 4.68475 | + | 0.588373i | 0.216553 | + | 0.0271976i | ||||
\(469\) | 6.16103 | + | 1.35848i | 0.284490 | + | 0.0627288i | ||||
\(470\) | 1.98209 | − | 0.679423i | 0.0914269 | − | 0.0313394i | ||||
\(471\) | −0.812478 | −0.0374370 | ||||||||
\(472\) | 20.1178 | − | 30.6991i | 0.925998 | − | 1.41304i | ||||
\(473\) | − | 13.7904i | − | 0.634082i | ||||||
\(474\) | −5.79857 | − | 16.9162i | −0.266337 | − | 0.776989i | ||||
\(475\) | −6.92768 | − | 6.92768i | −0.317864 | − | 0.317864i | ||||
\(476\) | 12.6960 | − | 35.6683i | 0.581920 | − | 1.63485i | ||||
\(477\) | 3.05130 | − | 3.05130i | 0.139709 | − | 0.139709i | ||||
\(478\) | −6.18312 | + | 12.6329i | −0.282809 | + | 0.577816i | ||||
\(479\) | 36.9533 | 1.68844 | 0.844220 | − | 0.535997i | \(-0.180064\pi\) | ||||
0.844220 | + | 0.535997i | \(0.180064\pi\) | |||||||
\(480\) | 11.5863 | + | 9.85943i | 0.528842 | + | 0.450019i | ||||
\(481\) | 8.40067i | 0.383037i | ||||||||
\(482\) | 7.10531 | − | 14.5170i | 0.323638 | − | 0.661233i | ||||
\(483\) | −2.07020 | + | 9.38885i | −0.0941974 | + | 0.427208i | ||||
\(484\) | 22.7644 | − | 17.6843i | 1.03474 | − | 0.803831i | ||||
\(485\) | 11.8442 | + | 11.8442i | 0.537818 | + | 0.537818i | ||||
\(486\) | −1.33780 | + | 0.458573i | −0.0606839 | + | 0.0208013i | ||||
\(487\) | 14.6233 | 0.662647 | 0.331324 | − | 0.943517i | \(-0.392505\pi\) | ||||
0.331324 | + | 0.943517i | \(0.392505\pi\) | |||||||
\(488\) | −12.3286 | + | 18.8130i | −0.558089 | + | 0.851626i | ||||
\(489\) | 19.5703 | 0.885002 | ||||||||
\(490\) | −2.75902 | + | 26.4803i | −0.124640 | + | 1.19626i | ||||
\(491\) | 6.45924 | − | 6.45924i | 0.291502 | − | 0.291502i | −0.546172 | − | 0.837673i | \(-0.683915\pi\) |
0.837673 | + | 0.546172i | \(0.183915\pi\) | |||||||
\(492\) | 4.71703 | + | 0.592428i | 0.212660 | + | 0.0267087i | ||||
\(493\) | −37.9102 | − | 37.9102i | −1.70739 | − | 1.70739i | ||||
\(494\) | −13.1576 | − | 6.43994i | −0.591989 | − | 0.289747i | ||||
\(495\) | 13.5576 | 0.609370 | ||||||||
\(496\) | 0.896799 | − | 3.51393i | 0.0402675 | − | 0.157780i | ||||
\(497\) | −26.0249 | + | 16.6215i | −1.16738 | + | 0.745578i | ||||
\(498\) | −3.36397 | + | 6.87302i | −0.150743 | + | 0.307987i | ||||
\(499\) | 0.0937570 | + | 0.0937570i | 0.00419714 | + | 0.00419714i | 0.709202 | − | 0.705005i | \(-0.249055\pi\) |
−0.705005 | + | 0.709202i | \(0.749055\pi\) | |||||||
\(500\) | −1.85474 | + | 14.7679i | −0.0829467 | + | 0.660439i | ||||
\(501\) | 6.86884 | + | 6.86884i | 0.306877 | + | 0.306877i | ||||
\(502\) | 7.39442 | + | 21.5718i | 0.330029 | + | 0.962798i | ||||
\(503\) | 8.91797i | 0.397633i | 0.980037 | + | 0.198816i | \(0.0637097\pi\) | ||||
−0.980037 | + | 0.198816i | \(0.936290\pi\) | |||||||
\(504\) | −5.35322 | + | 5.22906i | −0.238451 | + | 0.232921i | ||||
\(505\) | 52.2387i | 2.32459i | ||||||||
\(506\) | 24.5071 | − | 8.40059i | 1.08947 | − | 0.373452i | ||||
\(507\) | 5.25150 | + | 5.25150i | 0.233227 | + | 0.233227i | ||||
\(508\) | −23.1525 | + | 17.9858i | −1.02723 | + | 0.797991i | ||||
\(509\) | −8.24799 | − | 8.24799i | −0.365586 | − | 0.365586i | 0.500279 | − | 0.865864i | \(-0.333231\pi\) |
−0.865864 | + | 0.500279i | \(0.833231\pi\) | |||||||
\(510\) | −24.4424 | − | 11.9632i | −1.08233 | − | 0.529741i | ||||
\(511\) | 18.7543 | − | 11.9780i | 0.829641 | − | 0.529874i | ||||
\(512\) | 13.0712 | + | 18.4701i | 0.577670 | + | 0.816271i | ||||
\(513\) | 4.38774 | 0.193723 | ||||||||
\(514\) | 5.23072 | − | 10.6870i | 0.230717 | − | 0.471384i | ||||
\(515\) | 4.04279 | + | 4.04279i | 0.178147 | + | 0.178147i | ||||
\(516\) | 4.32061 | − | 3.35643i | 0.190204 | − | 0.147758i | ||||
\(517\) | 1.96377 | − | 1.96377i | 0.0863664 | − | 0.0863664i | ||||
\(518\) | −10.4180 | − | 8.29093i | −0.457741 | − | 0.364283i | ||||
\(519\) | −5.05588 | −0.221929 | ||||||||
\(520\) | −3.66074 | − | 17.5808i | −0.160534 | − | 0.770969i | ||||
\(521\) | 22.1437 | 0.970135 | 0.485068 | − | 0.874477i | \(-0.338795\pi\) | ||||
0.485068 | + | 0.874477i | \(0.338795\pi\) | |||||||
\(522\) | 3.43615 | + | 10.0243i | 0.150396 | + | 0.438753i | ||||
\(523\) | 1.49811 | + | 1.49811i | 0.0655079 | + | 0.0655079i | 0.739102 | − | 0.673594i | \(-0.235250\pi\) |
−0.673594 | + | 0.739102i | \(0.735250\pi\) | |||||||
\(524\) | −15.5060 | − | 1.94745i | −0.677383 | − | 0.0850748i | ||||
\(525\) | 5.76902 | + | 1.27204i | 0.251781 | + | 0.0555166i | ||||
\(526\) | 8.47555 | + | 4.14832i | 0.369552 | + | 0.180876i | ||||
\(527\) | 6.48698i | 0.282577i | ||||||||
\(528\) | 19.5383 | + | 4.98642i | 0.850296 | + | 0.217006i | ||||
\(529\) | −9.79482 | −0.425862 | ||||||||
\(530\) | −14.7413 | − | 7.21508i | −0.640322 | − | 0.313403i | ||||
\(531\) | 9.17593 | − | 9.17593i | 0.398202 | − | 0.398202i | ||||
\(532\) | 20.9722 | − | 9.96146i | 0.909259 | − | 0.431884i | ||||
\(533\) | −3.96805 | − | 3.96805i | −0.171875 | − | 0.171875i | ||||
\(534\) | −19.6573 | + | 6.73814i | −0.850653 | + | 0.291588i | ||||
\(535\) | 34.5283i | 1.49279i | ||||||||
\(536\) | 3.69683 | − | 5.64123i | 0.159679 | − | 0.243664i | ||||
\(537\) | −17.0870 | −0.737360 | ||||||||
\(538\) | −0.662947 | − | 1.93402i | −0.0285817 | − | 0.0833817i | ||||
\(539\) | 12.1450 | + | 33.1322i | 0.523121 | + | 1.42710i | ||||
\(540\) | 3.29978 | + | 4.24769i | 0.142000 | + | 0.182792i | ||||
\(541\) | 3.10477 | − | 3.10477i | 0.133485 | − | 0.133485i | −0.637208 | − | 0.770692i | \(-0.719911\pi\) |
0.770692 | + | 0.637208i | \(0.219911\pi\) | |||||||
\(542\) | 6.95292 | + | 3.40308i | 0.298653 | + | 0.146175i | ||||
\(543\) | − | 20.7991i | − | 0.892575i | ||||||
\(544\) | −30.8247 | − | 26.2303i | −1.32160 | − | 1.12462i | ||||
\(545\) | 29.5557i | 1.26603i | ||||||||
\(546\) | 8.77667 | − | 0.997842i | 0.375607 | − | 0.0427037i | ||||
\(547\) | −1.79963 | − | 1.79963i | −0.0769465 | − | 0.0769465i | 0.667586 | − | 0.744533i | \(-0.267328\pi\) |
−0.744533 | + | 0.667586i | \(0.767328\pi\) | |||||||
\(548\) | 5.43221 | − | 4.21996i | 0.232053 | − | 0.180268i | ||||
\(549\) | −5.62319 | + | 5.62319i | −0.239992 | + | 0.239992i | ||||
\(550\) | −5.16178 | − | 15.0585i | −0.220099 | − | 0.642097i | ||||
\(551\) | − | 32.8779i | − | 1.40065i | ||||||
\(552\) | 8.59673 | + | 5.63363i | 0.365901 | + | 0.239783i | ||||
\(553\) | −18.0076 | − | 28.1951i | −0.765762 | − | 1.19898i | ||||
\(554\) | −6.42760 | − | 18.7513i | −0.273083 | − | 0.796667i | ||||
\(555\) | −6.76704 | + | 6.76704i | −0.287245 | + | 0.287245i | ||||
\(556\) | 1.83696 | − | 14.6263i | 0.0779045 | − | 0.620292i | ||||
\(557\) | −11.8995 | + | 11.8995i | −0.504196 | + | 0.504196i | −0.912739 | − | 0.408543i | \(-0.866037\pi\) |
0.408543 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(558\) | 0.563666 | − | 1.15164i | 0.0238619 | − | 0.0487529i | ||||
\(559\) | −6.45806 | −0.273147 | ||||||||
\(560\) | 25.4156 | + | 12.8113i | 1.07400 | + | 0.541377i | ||||
\(561\) | −36.0692 | −1.52284 | ||||||||
\(562\) | 12.2123 | − | 24.9514i | 0.515146 | − | 1.05251i | ||||
\(563\) | −0.635961 | + | 0.635961i | −0.0268026 | + | 0.0268026i | −0.720381 | − | 0.693578i | \(-0.756033\pi\) |
0.693578 | + | 0.720381i | \(0.256033\pi\) | |||||||
\(564\) | 1.09322 | + | 0.137301i | 0.0460329 | + | 0.00578143i | ||||
\(565\) | 13.9345 | − | 13.9345i | 0.586229 | − | 0.586229i | ||||
\(566\) | 13.1683 | + | 38.4159i | 0.553503 | + | 1.61474i | ||||
\(567\) | −2.22978 | + | 1.42411i | −0.0936419 | + | 0.0598070i | ||||
\(568\) | 6.72955 | + | 32.3189i | 0.282366 | + | 1.35607i | ||||
\(569\) | − | 0.425156i | − | 0.0178235i | −0.999960 | − | 0.00891174i | \(-0.997163\pi\) | ||
0.999960 | − | 0.00891174i | \(-0.00283673\pi\) | |||||||
\(570\) | −5.41133 | − | 15.7865i | −0.226656 | − | 0.661226i | ||||
\(571\) | −20.0961 | + | 20.0961i | −0.840997 | + | 0.840997i | −0.988989 | − | 0.147992i | \(-0.952719\pi\) |
0.147992 | + | 0.988989i | \(0.452719\pi\) | |||||||
\(572\) | −14.6020 | − | 18.7967i | −0.610542 | − | 0.785930i | ||||
\(573\) | −3.42137 | − | 3.42137i | −0.142930 | − | 0.142930i | ||||
\(574\) | 8.83716 | − | 1.00472i | 0.368856 | − | 0.0419362i | ||||
\(575\) | − | 8.11398i | − | 0.338376i | ||||||
\(576\) | 3.19313 | + | 7.33511i | 0.133047 | + | 0.305630i | ||||
\(577\) | 10.2508i | 0.426748i | 0.976971 | + | 0.213374i | \(0.0684453\pi\) | ||||
−0.976971 | + | 0.213374i | \(0.931555\pi\) | |||||||
\(578\) | 43.4335 | + | 21.2584i | 1.80660 | + | 0.884231i | ||||
\(579\) | −16.5460 | + | 16.5460i | −0.687628 | + | 0.687628i | ||||
\(580\) | 31.8286 | − | 24.7257i | 1.32161 | − | 1.02668i | ||||
\(581\) | −3.08252 | + | 13.9800i | −0.127885 | + | 0.579987i | ||||
\(582\) | 2.85611 | + | 8.33215i | 0.118389 | + | 0.345379i | ||||
\(583\) | −21.7535 | −0.900937 | ||||||||
\(584\) | −4.84951 | − | 23.2899i | −0.200674 | − | 0.963743i | ||||
\(585\) | − | 6.34907i | − | 0.262502i | ||||||
\(586\) | 22.2353 | − | 7.62183i | 0.918530 | − | 0.314855i | ||||
\(587\) | −19.3706 | − | 19.3706i | −0.799510 | − | 0.799510i | 0.183508 | − | 0.983018i | \(-0.441255\pi\) |
−0.983018 | + | 0.183508i | \(0.941255\pi\) | |||||||
\(588\) | −7.42457 | + | 11.8691i | −0.306184 | + | 0.489474i | ||||
\(589\) | −2.81294 | + | 2.81294i | −0.115905 | + | 0.115905i | ||||
\(590\) | −44.3304 | − | 21.6973i | −1.82506 | − | 0.893266i | ||||
\(591\) | −8.26548 | −0.339997 | ||||||||
\(592\) | −12.2411 | + | 7.26331i | −0.503105 | + | 0.298520i | ||||
\(593\) | − | 33.1941i | − | 1.36312i | −0.731764 | − | 0.681559i | \(-0.761302\pi\) | ||
0.731764 | − | 0.681559i | \(-0.238698\pi\) | |||||||
\(594\) | 6.40340 | + | 3.13412i | 0.262735 | + | 0.128594i | ||||
\(595\) | −49.7167 | − | 10.9623i | −2.03819 | − | 0.449412i | ||||
\(596\) | −2.95544 | + | 23.5318i | −0.121060 | + | 0.963901i | ||||
\(597\) | −3.02895 | − | 3.02895i | −0.123967 | − | 0.123967i | ||||
\(598\) | −3.93401 | − | 11.4767i | −0.160874 | − | 0.469319i | ||||
\(599\) | −1.68554 | −0.0688694 | −0.0344347 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344347 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(600\) | 3.46161 | − | 5.28230i | 0.141320 | − | 0.215649i | ||||
\(601\) | 2.90830 | 0.118632 | 0.0593160 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593160 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(602\) | 6.37370 | − | 8.00889i | 0.259773 | − | 0.326418i | ||||
\(603\) | 1.68616 | − | 1.68616i | 0.0686656 | − | 0.0686656i | ||||
\(604\) | 3.93968 | + | 5.07141i | 0.160303 | + | 0.206353i | ||||
\(605\) | −27.4093 | − | 27.4093i | −1.11435 | − | 1.11435i | ||||
\(606\) | −12.0760 | + | 24.6728i | −0.490554 | + | 1.00226i | ||||
\(607\) | 21.5383 | 0.874213 | 0.437106 | − | 0.899410i | \(-0.356003\pi\) | ||||
0.437106 | + | 0.899410i | \(0.356003\pi\) | |||||||
\(608\) | −1.99224 | − | 24.7407i | −0.0807958 | − | 1.00337i | ||||
\(609\) | 10.6711 | + | 16.7080i | 0.432413 | + | 0.677044i | ||||
\(610\) | 27.1666 | + | 13.2966i | 1.09994 | + | 0.538362i | ||||
\(611\) | −0.919637 | − | 0.919637i | −0.0372045 | − | 0.0372045i | ||||
\(612\) | −8.77884 | − | 11.3007i | −0.354864 | − | 0.456804i | ||||
\(613\) | 19.8687 | + | 19.8687i | 0.802488 | + | 0.802488i | 0.983484 | − | 0.180996i | \(-0.0579321\pi\) |
−0.180996 | + | 0.983484i | \(0.557932\pi\) | |||||||
\(614\) | −35.9837 | + | 12.3345i | −1.45218 | + | 0.497782i | ||||
\(615\) | − | 6.39282i | − | 0.257783i | ||||||
\(616\) | 37.7219 | + | 0.442600i | 1.51986 | + | 0.0178329i | ||||
\(617\) | − | 31.7899i | − | 1.27981i | −0.768453 | − | 0.639906i | \(-0.778973\pi\) | ||
0.768453 | − | 0.639906i | \(-0.221027\pi\) | |||||||
\(618\) | 0.974878 | + | 2.84402i | 0.0392153 | + | 0.114403i | ||||
\(619\) | −14.2152 | − | 14.2152i | −0.571358 | − | 0.571358i | 0.361150 | − | 0.932508i | \(-0.382384\pi\) |
−0.932508 | + | 0.361150i | \(0.882384\pi\) | |||||||
\(620\) | −4.83863 | − | 0.607699i | −0.194324 | − | 0.0244058i | ||||
\(621\) | 2.56955 | + | 2.56955i | 0.103113 | + | 0.103113i | ||||
\(622\) | 8.52445 | − | 17.4165i | 0.341799 | − | 0.698339i | ||||
\(623\) | −32.7637 | + | 20.9255i | −1.31265 | + | 0.838362i | ||||
\(624\) | 2.33515 | − | 9.14983i | 0.0934807 | − | 0.366286i | ||||
\(625\) | 31.1786 | 1.24715 | ||||||||
\(626\) | 6.15219 | + | 3.01116i | 0.245891 | + | 0.120350i | ||||
\(627\) | −15.6406 | − | 15.6406i | −0.624627 | − | 0.624627i | ||||
\(628\) | −0.202493 | + | 1.61229i | −0.00808034 | + | 0.0643373i | ||||
\(629\) | 18.0033 | − | 18.0033i | 0.717837 | − | 0.717837i | ||||
\(630\) | 7.87373 | + | 6.26613i | 0.313697 | + | 0.249649i | ||||
\(631\) | 7.63145 | 0.303803 | 0.151902 | − | 0.988396i | \(-0.451460\pi\) | ||||
0.151902 | + | 0.988396i | \(0.451460\pi\) | |||||||
\(632\) | −35.0139 | + | 7.29074i | −1.39278 | + | 0.290010i | ||||
\(633\) | 7.56202 | 0.300563 | ||||||||
\(634\) | 5.15616 | − | 1.76743i | 0.204777 | − | 0.0701938i | ||||
\(635\) | 27.8766 | + | 27.8766i | 1.10625 | + | 1.10625i | ||||
\(636\) | −5.29456 | − | 6.81550i | −0.209943 | − | 0.270252i | ||||
\(637\) | 15.5159 | − | 5.68752i | 0.614761 | − | 0.225348i | ||||
\(638\) | 23.4844 | − | 47.9816i | 0.929756 | − | 1.89961i | ||||
\(639\) | 11.6715i | 0.461718i | ||||||||
\(640\) | 22.4528 | − | 20.5348i | 0.887525 | − | 0.811709i | ||||
\(641\) | −24.3462 | −0.961616 | −0.480808 | − | 0.876826i | \(-0.659657\pi\) | ||||
−0.480808 | + | 0.876826i | \(0.659657\pi\) | |||||||
\(642\) | −7.98190 | + | 16.3080i | −0.315021 | + | 0.643627i | ||||
\(643\) | −21.6002 | + | 21.6002i | −0.851829 | + | 0.851829i | −0.990358 | − | 0.138529i | \(-0.955763\pi\) |
0.138529 | + | 0.990358i | \(0.455763\pi\) | |||||||
\(644\) | 18.1154 | + | 6.44810i | 0.713846 | + | 0.254091i | ||||
\(645\) | −5.20220 | − | 5.20220i | −0.204836 | − | 0.204836i | ||||
\(646\) | 14.3965 | + | 41.9990i | 0.566422 | + | 1.65243i | ||||
\(647\) | 34.5047i | 1.35652i | 0.734823 | + | 0.678259i | \(0.237265\pi\) | ||||
−0.734823 | + | 0.678259i | \(0.762735\pi\) | |||||||
\(648\) | 0.576579 | + | 2.76904i | 0.0226502 | + | 0.108778i | ||||
\(649\) | −65.4175 | −2.56786 | ||||||||
\(650\) | −7.05193 | + | 2.41727i | −0.276600 | + | 0.0948132i | ||||
\(651\) | 0.516507 | − | 2.34248i | 0.0202435 | − | 0.0918090i | ||||
\(652\) | 4.87749 | − | 38.8356i | 0.191017 | − | 1.52092i | ||||
\(653\) | 10.7862 | − | 10.7862i | 0.422097 | − | 0.422097i | −0.463828 | − | 0.885925i | \(-0.653525\pi\) |
0.885925 | + | 0.463828i | \(0.153525\pi\) | |||||||
\(654\) | −6.83238 | + | 13.9594i | −0.267167 | + | 0.545856i | ||||
\(655\) | 21.0147i | 0.821113i | ||||||||
\(656\) | 2.35124 | − | 9.21288i | 0.0918005 | − | 0.359703i | ||||
\(657\) | − | 8.41083i | − | 0.328138i | ||||||
\(658\) | 2.04810 | − | 0.232854i | 0.0798433 | − | 0.00907759i | ||||
\(659\) | −14.5491 | − | 14.5491i | −0.566754 | − | 0.566754i | 0.364464 | − | 0.931217i | \(-0.381252\pi\) |
−0.931217 | + | 0.364464i | \(0.881252\pi\) | |||||||
\(660\) | 3.37895 | − | 26.9039i | 0.131526 | − | 1.04723i | ||||
\(661\) | −25.2625 | + | 25.2625i | −0.982596 | + | 0.982596i | −0.999851 | − | 0.0172555i | \(-0.994507\pi\) |
0.0172555 | + | 0.999851i | \(0.494507\pi\) | |||||||
\(662\) | −13.1263 | + | 4.49946i | −0.510169 | + | 0.174876i | ||||
\(663\) | 16.8913i | 0.656002i | ||||||||
\(664\) | 12.8005 | + | 8.38845i | 0.496756 | + | 0.325535i | ||||
\(665\) | −16.8050 | − | 26.3122i | −0.651671 | − | 1.02034i | ||||
\(666\) | −4.76048 | + | 1.63180i | −0.184465 | + | 0.0632310i | ||||
\(667\) | 19.2540 | − | 19.2540i | 0.745518 | − | 0.745518i | ||||
\(668\) | 15.3425 | − | 11.9187i | 0.593620 | − | 0.461148i | ||||
\(669\) | 20.1052 | − | 20.1052i | 0.777312 | − | 0.777312i | ||||
\(670\) | −8.14610 | − | 3.98708i | −0.314711 | − | 0.154034i | ||||
\(671\) | 40.0891 | 1.54762 | ||||||||
\(672\) | 9.04242 | + | 11.9262i | 0.348819 | + | 0.460064i | ||||
\(673\) | 10.5919 | 0.408287 | 0.204144 | − | 0.978941i | \(-0.434559\pi\) | ||||
0.204144 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(674\) | −3.75603 | − | 1.83838i | −0.144677 | − | 0.0708116i | ||||
\(675\) | 1.57887 | − | 1.57887i | 0.0607708 | − | 0.0607708i | ||||
\(676\) | 11.7299 | − | 9.11230i | 0.451152 | − | 0.350473i | ||||
\(677\) | 27.0595 | − | 27.0595i | 1.03998 | − | 1.03998i | 0.0408138 | − | 0.999167i | \(-0.487005\pi\) |
0.999167 | − | 0.0408138i | \(-0.0129951\pi\) | |||||||
\(678\) | 9.80263 | − | 3.36016i | 0.376468 | − | 0.129046i | ||||
\(679\) | 8.86971 | + | 13.8876i | 0.340388 | + | 0.532957i | ||||
\(680\) | −29.8317 | + | 45.5222i | −1.14399 | + | 1.74570i | ||||
\(681\) | 27.0438i | 1.03632i | ||||||||
\(682\) | −6.11443 | + | 2.09591i | −0.234133 | + | 0.0802566i | ||||
\(683\) | 28.1993 | − | 28.1993i | 1.07901 | − | 1.07901i | 0.0824168 | − | 0.996598i | \(-0.473736\pi\) |
0.996598 | − | 0.0824168i | \(-0.0262639\pi\) | |||||||
\(684\) | 1.09355 | − | 8.70707i | 0.0418129 | − | 0.332923i | ||||
\(685\) | −6.54062 | − | 6.54062i | −0.249904 | − | 0.249904i | ||||
\(686\) | −8.25988 | + | 24.8551i | −0.315364 | + | 0.948971i | ||||
\(687\) | 2.99467i | 0.114254i | ||||||||
\(688\) | −5.58371 | − | 9.41038i | −0.212877 | − | 0.358767i | ||||
\(689\) | 10.1872i | 0.388101i | ||||||||
\(690\) | 6.07594 | − | 12.4139i | 0.231307 | − | 0.472590i | ||||
\(691\) | 2.94281 | − | 2.94281i | 0.111950 | − | 0.111950i | −0.648913 | − | 0.760863i | \(-0.724776\pi\) |
0.760863 | + | 0.648913i | \(0.224776\pi\) | |||||||
\(692\) | −1.26007 | + | 10.0329i | −0.0479007 | + | 0.381395i | ||||
\(693\) | 13.0247 | + | 2.87190i | 0.494769 | + | 0.109094i | ||||
\(694\) | 5.99475 | − | 2.05489i | 0.227558 | − | 0.0780025i | ||||
\(695\) | −19.8224 | −0.751908 | ||||||||
\(696\) | 20.7488 | − | 4.32039i | 0.786480 | − | 0.163764i | ||||
\(697\) | 17.0077i | 0.644211i | ||||||||
\(698\) | −7.19541 | − | 20.9913i | −0.272350 | − | 0.794531i | ||||
\(699\) | −16.3415 | − | 16.3415i | −0.618093 | − | 0.618093i | ||||
\(700\) | 3.96206 | − | 11.1311i | 0.149752 | − | 0.420715i | ||||
\(701\) | 14.0610 | − | 14.0610i | 0.531077 | − | 0.531077i | −0.389816 | − | 0.920893i | \(-0.627461\pi\) |
0.920893 | + | 0.389816i | \(0.127461\pi\) | |||||||
\(702\) | 1.46771 | − | 2.99872i | 0.0553953 | − | 0.113180i | ||||
\(703\) | 15.6135 | 0.588873 | ||||||||
\(704\) | 14.7646 | − | 37.5293i | 0.556462 | − | 1.41444i | ||||
\(705\) | − | 1.48160i | − | 0.0558004i | ||||||
\(706\) | −19.2098 | + | 39.2480i | −0.722969 | + | 1.47712i | ||||
\(707\) | −11.0657 | + | 50.1854i | −0.416167 | + | 1.88742i | ||||
\(708\) | −15.9219 | − | 20.4957i | −0.598382 | − | 0.770276i | ||||
\(709\) | −17.0650 | − | 17.0650i | −0.640890 | − | 0.640890i | 0.309884 | − | 0.950774i | \(-0.399710\pi\) |
−0.950774 | + | 0.309884i | \(0.899710\pi\) | |||||||
\(710\) | 41.9927 | − | 14.3943i | 1.57596 | − | 0.540209i | ||||
\(711\) | −12.6448 | −0.474218 | ||||||||
\(712\) | 8.47209 | + | 40.6874i | 0.317505 | + | 1.52483i | ||||
\(713\) | −3.29464 | −0.123385 | ||||||||
\(714\) | −20.9475 | − | 16.6706i | −0.783942 | − | 0.623882i | ||||
\(715\) | −22.6320 | + | 22.6320i | −0.846390 | + | 0.846390i | ||||
\(716\) | −4.25858 | + | 33.9077i | −0.159151 | + | 1.26719i | ||||
\(717\) | 7.03245 | + | 7.03245i | 0.262632 | + | 0.262632i | ||||
\(718\) | −1.19810 | − | 0.586404i | −0.0447126 | − | 0.0218844i | ||||
\(719\) | 4.08011 | 0.152162 | 0.0760812 | − | 0.997102i | \(-0.475759\pi\) | ||||
0.0760812 | + | 0.997102i | \(0.475759\pi\) | |||||||
\(720\) | 9.25157 | − | 5.48947i | 0.344786 | − | 0.204581i | ||||
\(721\) | 3.02751 | + | 4.74027i | 0.112750 | + | 0.176537i | ||||
\(722\) | −0.156819 | + | 0.320400i | −0.00583618 | + | 0.0119241i | ||||
\(723\) | −8.08131 | − | 8.08131i | −0.300547 | − | 0.300547i | ||||
\(724\) | −41.2740 | − | 5.18373i | −1.53393 | − | 0.192652i | ||||
\(725\) | −11.8307 | − | 11.8307i | −0.439382 | − | 0.439382i | ||||
\(726\) | −6.60946 | − | 19.2819i | −0.245300 | − | 0.715617i | ||||
\(727\) | 29.7494i | 1.10334i | 0.834061 | + | 0.551672i | \(0.186010\pi\) | ||||
−0.834061 | + | 0.551672i | \(0.813990\pi\) | |||||||
\(728\) | 0.207271 | − | 17.6652i | 0.00768196 | − | 0.654716i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −30.2612 | + | 10.3730i | −1.12002 | + | 0.383920i | ||||
\(731\) | 13.8401 | + | 13.8401i | 0.511895 | + | 0.511895i | ||||
\(732\) | 9.75726 | + | 12.5602i | 0.360639 | + | 0.464238i | ||||
\(733\) | 12.3461 | + | 12.3461i | 0.456014 | + | 0.456014i | 0.897345 | − | 0.441330i | \(-0.145493\pi\) |
−0.441330 | + | 0.897345i | \(0.645493\pi\) | |||||||
\(734\) | −4.53352 | − | 2.21891i | −0.167335 | − | 0.0819016i | ||||
\(735\) | 17.0801 | + | 7.91709i | 0.630009 | + | 0.292026i | ||||
\(736\) | 13.3220 | − | 15.6554i | 0.491055 | − | 0.577065i | ||||
\(737\) | −12.0210 | −0.442801 | ||||||||
\(738\) | 1.47783 | − | 3.01939i | 0.0543996 | − | 0.111145i | ||||
\(739\) | −12.7621 | − | 12.7621i | −0.469462 | − | 0.469462i | 0.432278 | − | 0.901740i | \(-0.357710\pi\) |
−0.901740 | + | 0.432278i | \(0.857710\pi\) | |||||||
\(740\) | 11.7421 | + | 15.1151i | 0.431646 | + | 0.555643i | ||||
\(741\) | −7.32454 | + | 7.32454i | −0.269074 | + | 0.269074i | ||||
\(742\) | −12.6335 | − | 10.0541i | −0.463792 | − | 0.369099i | ||||
\(743\) | −14.3254 | −0.525547 | −0.262774 | − | 0.964858i | \(-0.584637\pi\) | ||||
−0.262774 | + | 0.964858i | \(0.584637\pi\) | |||||||
\(744\) | −2.14485 | − | 1.40557i | −0.0786339 | − | 0.0515306i | ||||
\(745\) | 31.8918 | 1.16843 | ||||||||
\(746\) | 0.449441 | + | 1.31116i | 0.0164552 | + | 0.0480050i | ||||
\(747\) | 3.82605 | + | 3.82605i | 0.139988 | + | 0.139988i | ||||
\(748\) | −8.98947 | + | 71.5760i | −0.328688 | + | 2.61708i | ||||
\(749\) | −7.31409 | + | 33.1711i | −0.267251 | + | 1.21205i | ||||
\(750\) | 9.45296 | + | 4.62671i | 0.345173 | + | 0.168944i | ||||
\(751\) | 51.1794i | 1.86756i | 0.357846 | + | 0.933781i | \(0.383511\pi\) | ||||
−0.357846 | + | 0.933781i | \(0.616489\pi\) | |||||||
\(752\) | 0.544924 | − | 2.13518i | 0.0198713 | − | 0.0778620i | ||||
\(753\) | 16.1248 | 0.587622 | ||||||||
\(754\) | −22.4699 | − | 10.9978i | −0.818304 | − | 0.400516i | ||||
\(755\) | 6.10620 | − | 6.10620i | 0.222227 | − | 0.222227i | ||||
\(756\) | 2.27030 | + | 4.77972i | 0.0825699 | + | 0.173837i | ||||
\(757\) | −14.4521 | − | 14.4521i | −0.525271 | − | 0.525271i | 0.393888 | − | 0.919159i | \(-0.371130\pi\) |
−0.919159 | + | 0.393888i | \(0.871130\pi\) | |||||||
\(758\) | −12.3965 | + | 4.24929i | −0.450262 | + | 0.154341i | ||||
\(759\) | − | 18.3190i | − | 0.664936i | ||||||
\(760\) | −32.6756 | + | 6.80385i | −1.18527 | + | 0.246801i | ||||
\(761\) | 6.59268 | 0.238985 | 0.119492 | − | 0.992835i | \(-0.461873\pi\) | ||||
0.119492 | + | 0.992835i | \(0.461873\pi\) | |||||||
\(762\) | 6.72216 | + | 19.6106i | 0.243518 | + | 0.710418i | ||||
\(763\) | −6.26074 | + | 28.3939i | −0.226654 | + | 1.02793i | ||||
\(764\) | −7.64210 | + | 5.93670i | −0.276482 | + | 0.214782i | ||||
\(765\) | −13.6065 | + | 13.6065i | −0.491945 | + | 0.491945i | ||||
\(766\) | −32.3153 | − | 15.8166i | −1.16760 | − | 0.571476i | ||||
\(767\) | 30.6351i | 1.10617i | ||||||||
\(768\) | 15.3517 | − | 4.50837i | 0.553957 | − | 0.162682i | ||||
\(769\) | − | 2.21522i | − | 0.0798829i | −0.999202 | − | 0.0399414i | \(-0.987283\pi\) | ||
0.999202 | − | 0.0399414i | \(-0.0127171\pi\) | |||||||
\(770\) | −5.73048 | − | 50.4033i | −0.206512 | − | 1.81641i | ||||
\(771\) | −5.94922 | − | 5.94922i | −0.214256 | − | 0.214256i | ||||
\(772\) | 28.7103 | + | 36.9578i | 1.03331 | + | 1.33014i | ||||
\(773\) | −17.1592 | + | 17.1592i | −0.617173 | + | 0.617173i | −0.944805 | − | 0.327633i | \(-0.893749\pi\) |
0.327633 | + | 0.944805i | \(0.393749\pi\) | |||||||
\(774\) | −1.25446 | − | 3.65964i | −0.0450905 | − | 0.131543i | ||||
\(775\) | 2.02440i | 0.0727188i | ||||||||
\(776\) | 17.2462 | − | 3.59108i | 0.619104 | − | 0.128912i | ||||
\(777\) | −7.93452 | + | 5.06760i | −0.284649 | + | 0.181799i | ||||
\(778\) | 7.54913 | + | 22.0232i | 0.270649 | + | 0.789568i | ||||
\(779\) | −7.37502 | + | 7.37502i | −0.264237 | + | 0.264237i | ||||
\(780\) | −12.5992 | − | 1.58237i | −0.451122 | − | 0.0566579i | ||||
\(781\) | 41.6046 | − | 41.6046i | 1.48873 | − | 1.48873i | ||||
\(782\) | −16.1646 | + | 33.0264i | −0.578046 | + | 1.18102i | ||||
\(783\) | 7.49314 | 0.267783 | ||||||||
\(784\) | 21.7028 | + | 17.6915i | 0.775099 | + | 0.631840i | ||||
\(785\) | 2.18508 | 0.0779887 | ||||||||
\(786\) | −4.85797 | + | 9.92546i | −0.173278 | + | 0.354029i | ||||
\(787\) | 18.9133 | − | 18.9133i | 0.674188 | − | 0.674188i | −0.284491 | − | 0.958679i | \(-0.591825\pi\) |
0.958679 | + | 0.284491i | \(0.0918246\pi\) | |||||||
\(788\) | −2.06000 | + | 16.4021i | −0.0733843 | + | 0.584301i | ||||
\(789\) | 4.71815 | − | 4.71815i | 0.167970 | − | 0.167970i | ||||
\(790\) | 15.5947 | + | 45.4945i | 0.554834 | + | 1.61862i | ||||
\(791\) | 16.3385 | − | 10.4351i | 0.580931 | − | 0.371028i | ||||
\(792\) | 7.81529 | − | 11.9259i | 0.277704 | − | 0.423767i | ||||
\(793\) | − | 18.7738i | − | 0.666678i | ||||||
\(794\) | 11.9004 | + | 34.7171i | 0.422329 | + | 1.23206i | ||||
\(795\) | −8.20616 | + | 8.20616i | −0.291043 | + | 0.291043i | ||||
\(796\) | −6.76559 | + | 5.25578i | −0.239800 | + | 0.186286i | ||||
\(797\) | −0.285537 | − | 0.285537i | −0.0101142 | − | 0.0101142i | 0.702032 | − | 0.712146i | \(-0.252277\pi\) |
−0.712146 | + | 0.702032i | \(0.752277\pi\) | |||||||
\(798\) | −1.85459 | − | 16.3123i | −0.0656517 | − | 0.577450i | ||||
\(799\) | 3.94170i | 0.139447i | ||||||||
\(800\) | −9.61951 | − | 8.18575i | −0.340101 | − | 0.289410i | ||||
\(801\) | 14.6937i | 0.519177i | ||||||||
\(802\) | −28.2663 | − | 13.8348i | −0.998118 | − | 0.488525i | ||||
\(803\) | −29.9815 | + | 29.9815i | −1.05802 | + | 1.05802i | ||||
\(804\) | −2.92579 | − | 3.76627i | −0.103185 | − | 0.132826i | ||||
\(805\) | 5.56760 | − | 25.2504i | 0.196232 | − | 0.889958i | ||||
\(806\) | 0.981519 | + | 2.86340i | 0.0345725 | + | 0.100859i | ||||
\(807\) | −1.44567 | −0.0508901 | ||||||||
\(808\) | 45.9513 | + | 30.1129i | 1.61656 | + | 1.05937i | ||||
\(809\) | 20.9610i | 0.736948i | 0.929638 | + | 0.368474i | \(0.120120\pi\) | ||||
−0.929638 | + | 0.368474i | \(0.879880\pi\) | |||||||
\(810\) | 3.59788 | − | 1.23329i | 0.126417 | − | 0.0433332i | ||||
\(811\) | 8.09740 | + | 8.09740i | 0.284338 | + | 0.284338i | 0.834836 | − | 0.550498i | \(-0.185562\pi\) |
−0.550498 | + | 0.834836i | \(0.685562\pi\) | |||||||
\(812\) | 35.8151 | − | 17.0116i | 1.25687 | − | 0.596992i | ||||
\(813\) | 3.87053 | − | 3.87053i | 0.135745 | − | 0.135745i | ||||
\(814\) | 22.7861 | + | 11.1525i | 0.798651 | + | 0.390897i | ||||
\(815\) | −52.6325 | −1.84363 | ||||||||
\(816\) | −24.6132 | + | 14.6044i | −0.861633 | + | 0.511255i | ||||
\(817\) | 12.0029i | 0.419930i | ||||||||
\(818\) | −34.4734 | − | 16.8728i | −1.20533 | − | 0.589945i | ||||
\(819\) | 1.34492 | − | 6.09951i | 0.0469952 | − | 0.213134i | ||||
\(820\) | −12.6860 | − | 1.59327i | −0.443014 | − | 0.0556396i | ||||
\(821\) | −33.6935 | − | 33.6935i | −1.17591 | − | 1.17591i | −0.980776 | − | 0.195136i | \(-0.937485\pi\) |
−0.195136 | − | 0.980776i | \(-0.562515\pi\) | |||||||
\(822\) | −1.57720 | − | 4.60119i | −0.0550112 | − | 0.160485i | ||||
\(823\) | −46.3245 | −1.61477 | −0.807386 | − | 0.590023i | \(-0.799118\pi\) | ||||
−0.807386 | + | 0.590023i | \(0.799118\pi\) | |||||||
\(824\) | 5.88668 | − | 1.22575i | 0.205072 | − | 0.0427009i | ||||
\(825\) | −11.2562 | −0.391890 | ||||||||
\(826\) | −37.9919 | − | 30.2350i | −1.32191 | − | 1.05201i | ||||
\(827\) | −13.5597 | + | 13.5597i | −0.471516 | + | 0.471516i | −0.902405 | − | 0.430889i | \(-0.858200\pi\) |
0.430889 | + | 0.902405i | \(0.358200\pi\) | |||||||
\(828\) | 5.73945 | − | 4.45864i | 0.199460 | − | 0.154948i | ||||
\(829\) | −19.5380 | − | 19.5380i | −0.678582 | − | 0.678582i | 0.281097 | − | 0.959679i | \(-0.409302\pi\) |
−0.959679 | + | 0.281097i | \(0.909302\pi\) | |||||||
\(830\) | 9.04706 | − | 18.4843i | 0.314028 | − | 0.641599i | ||||
\(831\) | −14.0165 | −0.486228 | ||||||||
\(832\) | −17.5750 | − | 6.91429i | −0.609304 | − | 0.239710i | ||||
\(833\) | −45.4405 | − | 21.0629i | −1.57442 | − | 0.729786i | ||||
\(834\) | −9.36233 | − | 4.58235i | −0.324191 | − | 0.158674i | ||||
\(835\) | −18.4730 | − | 18.4730i | −0.639286 | − | 0.639286i | ||||
\(836\) | −34.9355 | + | 27.1394i | −1.20827 | + | 0.938634i | ||||
\(837\) | −0.641092 | − | 0.641092i | −0.0221594 | − | 0.0221594i | ||||
\(838\) | 26.5505 | − | 9.10102i | 0.917173 | − | 0.314390i | ||||
\(839\) | 1.94803i | 0.0672534i | 0.999434 | + | 0.0336267i | \(0.0107057\pi\) | ||||
−0.999434 | + | 0.0336267i | \(0.989294\pi\) | |||||||
\(840\) | 14.3969 | − | 14.0630i | 0.496742 | − | 0.485220i | ||||
\(841\) | − | 27.1472i | − | 0.936109i | ||||||
\(842\) | −12.1500 | − | 35.4454i | −0.418717 | − | 1.22153i | ||||
\(843\) | −13.8898 | − | 13.8898i | −0.478392 | − | 0.478392i | ||||
\(844\) | 1.88467 | − | 15.0061i | 0.0648731 | − | 0.516533i | ||||
\(845\) | −14.1234 | − | 14.1234i | −0.485858 | − | 0.485858i | ||||
\(846\) | 0.342502 | − | 0.699775i | 0.0117755 | − | 0.0240587i | ||||
\(847\) | −20.5259 | − | 32.1380i | −0.705277 | − | 1.10428i | ||||
\(848\) | −14.8443 | + | 8.80796i | −0.509756 | + | 0.302467i | ||||
\(849\) | 28.7157 | 0.985521 | ||||||||
\(850\) | 20.2932 | + | 9.93243i | 0.696052 | + | 0.340680i | ||||
\(851\) | 9.14358 | + | 9.14358i | 0.313438 | + | 0.313438i | ||||
\(852\) | 23.1611 | + | 2.90888i | 0.793486 | + | 0.0996565i | ||||
\(853\) | 15.1509 | − | 15.1509i | 0.518756 | − | 0.518756i | −0.398439 | − | 0.917195i | \(-0.630448\pi\) |
0.917195 | + | 0.398439i | \(0.130448\pi\) | |||||||
\(854\) | 23.2822 | + | 18.5286i | 0.796699 | + | 0.634035i | ||||
\(855\) | −11.8004 | −0.403564 | ||||||||
\(856\) | 30.3725 | + | 19.9038i | 1.03811 | + | 0.680298i | ||||
\(857\) | −28.4917 | −0.973259 | −0.486629 | − | 0.873609i | \(-0.661774\pi\) | ||||
−0.486629 | + | 0.873609i | \(0.661774\pi\) | |||||||
\(858\) | −15.9212 | + | 5.45748i | −0.543540 | + | 0.186315i | ||||
\(859\) | 4.12583 | + | 4.12583i | 0.140772 | + | 0.140772i | 0.773981 | − | 0.633209i | \(-0.218263\pi\) |
−0.633209 | + | 0.773981i | \(0.718263\pi\) | |||||||
\(860\) | −11.6198 | + | 9.02676i | −0.396233 | + | 0.307810i | ||||
\(861\) | 1.35418 | − | 6.14155i | 0.0461505 | − | 0.209303i | ||||
\(862\) | −15.2384 | + | 31.1340i | −0.519023 | + | 1.06043i | ||||
\(863\) | 13.9231i | 0.473949i | 0.971516 | + | 0.236974i | \(0.0761557\pi\) | ||||
−0.971516 | + | 0.236974i | \(0.923844\pi\) | |||||||
\(864\) | 5.63860 | − | 0.454046i | 0.191829 | − | 0.0154470i | ||||
\(865\) | 13.5973 | 0.462321 | ||||||||
\(866\) | 6.43666 | − | 13.1509i | 0.218726 | − | 0.446886i | ||||
\(867\) | 24.1784 | − | 24.1784i | 0.821143 | − | 0.821143i | ||||
\(868\) | −4.51971 | − | 1.60877i | −0.153409 | − | 0.0546054i | ||||
\(869\) | 45.0740 | + | 45.0740i | 1.52903 | + | 1.52903i | ||||
\(870\) | −9.24118 | − | 26.9594i | −0.313305 | − | 0.914010i | ||||
\(871\) | 5.62947i | 0.190747i | ||||||||
\(872\) | 25.9984 | + | 17.0373i | 0.880416 | + | 0.576957i | ||||
\(873\) | 6.22825 | 0.210794 | ||||||||
\(874\) | −21.3307 | + | 7.31175i | −0.721520 | + | 0.247324i | ||||
\(875\) | 19.2276 | + | 4.23961i | 0.650013 | + | 0.143325i | ||||
\(876\) | −16.6905 | − | 2.09622i | −0.563921 | − | 0.0708247i | ||||
\(877\) | 28.6830 | − | 28.6830i | 0.968557 | − | 0.968557i | −0.0309635 | − | 0.999521i | \(-0.509858\pi\) |
0.999521 | + | 0.0309635i | \(0.00985756\pi\) | |||||||
\(878\) | 13.5898 | − | 27.7658i | 0.458635 | − | 0.937049i | ||||
\(879\) | − | 16.6208i | − | 0.560604i | ||||||
\(880\) | −52.5463 | − | 13.4105i | −1.77133 | − | 0.452066i | ||||
\(881\) | 4.92697i | 0.165994i | 0.996550 | + | 0.0829969i | \(0.0264492\pi\) | ||||
−0.996550 | + | 0.0829969i | \(0.973551\pi\) | |||||||
\(882\) | 6.23690 | + | 7.68772i | 0.210007 | + | 0.258859i | ||||
\(883\) | 33.0133 | + | 33.0133i | 1.11099 | + | 1.11099i | 0.993017 | + | 0.117971i | \(0.0376389\pi\) |
0.117971 | + | 0.993017i | \(0.462361\pi\) | |||||||
\(884\) | 33.5192 | + | 4.20979i | 1.12737 | + | 0.141590i | ||||
\(885\) | −24.6777 | + | 24.6777i | −0.829533 | + | 0.829533i | ||||
\(886\) | −16.6915 | + | 5.72153i | −0.560762 | + | 0.192219i | ||||
\(887\) | 6.48099i | 0.217610i | 0.994063 | + | 0.108805i | \(0.0347025\pi\) | ||||
−0.994063 | + | 0.108805i | \(0.965298\pi\) | |||||||
\(888\) | 2.05172 | + | 9.85343i | 0.0688511 | + | 0.330659i | ||||
\(889\) | 20.8758 | + | 32.6860i | 0.700153 | + | 1.09625i | ||||
\(890\) | 52.8662 | − | 18.1215i | 1.77208 | − | 0.607436i | ||||
\(891\) | 3.56463 | − | 3.56463i | 0.119419 | − | 0.119419i | ||||
\(892\) | −34.8862 | − | 44.9078i | −1.16808 | − | 1.50362i | ||||
\(893\) | −1.70924 | + | 1.70924i | −0.0571974 | + | 0.0571974i | ||||
\(894\) | 15.0628 | + | 7.37242i | 0.503775 | + | 0.246571i | ||||
\(895\) | 45.9539 | 1.53607 | ||||||||
\(896\) | 25.9201 | − | 14.9715i | 0.865931 | − | 0.500163i | ||||
\(897\) | −8.57881 | −0.286438 | ||||||||
\(898\) | 19.5046 | + | 9.54646i | 0.650878 | + | 0.318569i | ||||
\(899\) | −4.80379 | + | 4.80379i | −0.160216 | + | 0.160216i | ||||
\(900\) | −2.73963 | − | 3.52663i | −0.0913210 | − | 0.117554i | ||||
\(901\) | 21.8319 | − | 21.8319i | 0.727327 | − | 0.727327i | ||||
\(902\) | −16.0309 | + | 5.49509i | −0.533770 | + | 0.182967i | ||||
\(903\) | −3.89575 | − | 6.09970i | −0.129642 | − | 0.202985i | ||||
\(904\) | −4.22484 | − | 20.2899i | −0.140516 | − | 0.674832i | ||||
\(905\) | 55.9371i | 1.85941i | ||||||||
\(906\) | 4.29558 | − | 1.47245i | 0.142711 | − | 0.0489187i | ||||
\(907\) | 33.5078 | − | 33.5078i | 1.11261 | − | 1.11261i | 0.119810 | − | 0.992797i | \(-0.461771\pi\) |
0.992797 | − | 0.119810i | \(-0.0382286\pi\) | |||||||
\(908\) | 53.6659 | + | 6.74008i | 1.78097 | + | 0.223678i | ||||
\(909\) | 13.7348 | + | 13.7348i | 0.455554 | + | 0.455554i | ||||
\(910\) | −23.6040 | + | 2.68359i | −0.782464 | + | 0.0889603i | ||||
\(911\) | 12.4867i | 0.413702i | 0.978372 | + | 0.206851i | \(0.0663215\pi\) | ||||
−0.978372 | + | 0.206851i | \(0.933679\pi\) | |||||||
\(912\) | −17.0059 | − | 4.34010i | −0.563120 | − | 0.143715i | ||||
\(913\) | − | 27.2769i | − | 0.902733i | ||||||
\(914\) | −21.1697 | + | 43.2524i | −0.700232 | + | 1.43066i | ||||
\(915\) | 15.1230 | − | 15.1230i | 0.499951 | − | 0.499951i | ||||
\(916\) | 5.94265 | + | 0.746357i | 0.196351 | + | 0.0246603i | ||||
\(917\) | −4.45153 | + | 20.1887i | −0.147002 | + | 0.666691i | ||||
\(918\) | −9.57191 | + | 3.28107i | −0.315920 | + | 0.108292i | ||||
\(919\) | −23.3667 | −0.770796 | −0.385398 | − | 0.922751i | \(-0.625936\pi\) | ||||
−0.385398 | + | 0.922751i | \(0.625936\pi\) | |||||||
\(920\) | −23.1200 | − | 15.1511i | −0.762244 | − | 0.499516i | ||||
\(921\) | 26.8977i | 0.886308i | ||||||||
\(922\) | 11.3512 | + | 33.1151i | 0.373833 | + | 1.09059i | ||||
\(923\) | −19.4835 | − | 19.4835i | −0.641308 | − | 0.641308i | ||||
\(924\) | 8.94517 | − | 25.1307i | 0.294274 | − | 0.826739i | ||||
\(925\) | 5.61831 | − | 5.61831i | 0.184729 | − | 0.184729i | ||||
\(926\) | 0.0329644 | − | 0.0673505i | 0.00108328 | − | 0.00221327i | ||||
\(927\) | 2.12589 | 0.0698235 | ||||||||
\(928\) | −3.40223 | − | 42.2509i | −0.111684 | − | 1.38695i | ||||
\(929\) | − | 22.6572i | − | 0.743357i | −0.928361 | − | 0.371679i | \(-0.878782\pi\) | ||
0.928361 | − | 0.371679i | \(-0.121218\pi\) | |||||||
\(930\) | −1.51592 | + | 3.09722i | −0.0497090 | + | 0.101562i | ||||
\(931\) | −10.5708 | − | 28.8378i | −0.346445 | − | 0.945120i | ||||
\(932\) | −36.5011 | + | 28.3555i | −1.19563 | + | 0.928815i | ||||
\(933\) | −9.69538 | − | 9.69538i | −0.317413 | − | 0.317413i | ||||
\(934\) | 15.8854 | − | 5.44520i | 0.519785 | − | 0.178172i | ||||
\(935\) | 97.0044 | 3.17238 | ||||||||
\(936\) | −5.58490 | − | 3.65991i | −0.182548 | − | 0.119628i | ||||
\(937\) | 23.8889 | 0.780417 | 0.390208 | − | 0.920727i | \(-0.372403\pi\) | ||||
0.390208 | + | 0.920727i | \(0.372403\pi\) | |||||||
\(938\) | −6.98133 | − | 5.55594i | −0.227949 | − | 0.181408i | ||||
\(939\) | 3.42478 | − | 3.42478i | 0.111764 | − | 0.111764i | ||||
\(940\) | −2.94011 | − | 0.369258i | −0.0958957 | − | 0.0120439i | ||||
\(941\) | 13.2546 | + | 13.2546i | 0.432088 | + | 0.432088i | 0.889338 | − | 0.457250i | \(-0.151166\pi\) |
−0.457250 | + | 0.889338i | \(0.651166\pi\) | |||||||
\(942\) | 1.03203 | + | 0.505124i | 0.0336254 | + | 0.0164578i | ||||
\(943\) | −8.63793 | −0.281290 | ||||||||
\(944\) | −44.6401 | + | 26.4875i | −1.45291 | + | 0.862094i | ||||
\(945\) | 5.99676 | − | 3.83000i | 0.195075 | − | 0.124590i | ||||
\(946\) | −8.57358 | + | 17.5169i | −0.278751 | + | 0.569524i | ||||
\(947\) | 7.30455 | + | 7.30455i | 0.237366 | + | 0.237366i | 0.815759 | − | 0.578393i | \(-0.196320\pi\) |
−0.578393 | + | 0.815759i | \(0.696320\pi\) | |||||||
\(948\) | −3.15145 | + | 25.0925i | −0.102354 | + | 0.814967i | ||||
\(949\) | 14.0404 | + | 14.0404i | 0.455770 | + | 0.455770i | ||||
\(950\) | 4.49274 | + | 13.1067i | 0.145764 | + | 0.425238i | ||||
\(951\) | − | 3.85421i | − | 0.124981i | ||||||
\(952\) | −38.3021 | + | 37.4137i | −1.24138 | + | 1.21258i | ||||
\(953\) | − | 27.8206i | − | 0.901198i | −0.892726 | − | 0.450599i | \(-0.851210\pi\) | ||
0.892726 | − | 0.450599i | \(-0.148790\pi\) | |||||||
\(954\) | −5.77286 | + | 1.97883i | −0.186903 | + | 0.0640670i | ||||
\(955\) | 9.20142 | + | 9.20142i | 0.297751 | + | 0.297751i | ||||
\(956\) | 15.7080 | − | 12.2026i | 0.508031 | − | 0.394660i | ||||
\(957\) | −26.7102 | − | 26.7102i | −0.863419 | − | 0.863419i | ||||
\(958\) | −46.9391 | − | 22.9742i | −1.51653 | − | 0.742262i | ||||
\(959\) | −4.89804 | − | 7.66903i | −0.158166 | − | 0.247646i | ||||
\(960\) | −8.58761 | − | 19.7270i | −0.277164 | − | 0.636687i | ||||
\(961\) | −30.1780 | −0.973484 | ||||||||
\(962\) | 5.22276 | − | 10.6708i | 0.168389 | − | 0.344039i | ||||
\(963\) | 9.07831 | + | 9.07831i | 0.292545 | + | 0.292545i | ||||
\(964\) | −18.0507 | + | 14.0225i | −0.581375 | + | 0.451635i | ||||
\(965\) | 44.4988 | − | 44.4988i | 1.43247 | − | 1.43247i | ||||
\(966\) | 8.46675 | − | 10.6389i | 0.272413 | − | 0.342302i | ||||
\(967\) | 23.9412 | 0.769898 | 0.384949 | − | 0.922938i | \(-0.374219\pi\) | ||||
0.384949 | + | 0.922938i | \(0.374219\pi\) | |||||||
\(968\) | −39.9104 | + | 8.31029i | −1.28277 | + | 0.267103i | ||||
\(969\) | 31.3941 | 1.00852 | ||||||||
\(970\) | −7.68121 | − | 22.4085i | −0.246629 | − | 0.719493i | ||||
\(971\) | 18.4212 | + | 18.4212i | 0.591165 | + | 0.591165i | 0.937946 | − | 0.346781i | \(-0.112725\pi\) |
−0.346781 | + | 0.937946i | \(0.612725\pi\) | |||||||
\(972\) | 1.98441 | + | 0.249229i | 0.0636500 | + | 0.00799401i | ||||
\(973\) | −19.0433 | − | 4.19897i | −0.610500 | − | 0.134613i | ||||
\(974\) | −18.5750 | − | 9.09145i | −0.595181 | − | 0.291309i | ||||
\(975\) | 5.27129i | 0.168816i | ||||||||
\(976\) | 27.3563 | − | 16.2320i | 0.875655 | − | 0.519575i | ||||
\(977\) | 41.8758 | 1.33973 | 0.669863 | − | 0.742484i | \(-0.266353\pi\) | ||||
0.669863 | + | 0.742484i | \(0.266353\pi\) | |||||||
\(978\) | −24.8588 | − | 12.1670i | −0.794897 | − | 0.389059i | ||||
\(979\) | 52.3776 | − | 52.3776i | 1.67399 | − | 1.67399i | ||||
\(980\) | 19.9676 | − | 31.9208i | 0.637842 | − | 1.01967i | ||||
\(981\) | 7.77089 | + | 7.77089i | 0.248105 | + | 0.248105i | ||||
\(982\) | −12.2205 | + | 4.18895i | −0.389971 | + | 0.133675i | ||||
\(983\) | 28.1376i | 0.897450i | 0.893670 | + | 0.448725i | \(0.148122\pi\) | ||||
−0.893670 | + | 0.448725i | \(0.851878\pi\) | |||||||
\(984\) | −5.62339 | − | 3.68514i | −0.179267 | − | 0.117478i | ||||
\(985\) | 22.2292 | 0.708281 | ||||||||
\(986\) | 24.5855 | + | 71.7237i | 0.782963 | + | 2.28415i | ||||
\(987\) | 0.313846 | − | 1.42337i | 0.00998983 | − | 0.0453063i | ||||
\(988\) | 12.7094 | + | 16.3604i | 0.404340 | + | 0.520493i | ||||
\(989\) | −7.02917 | + | 7.02917i | −0.223515 | + | 0.223515i | ||||
\(990\) | −17.2213 | − | 8.42889i | −0.547329 | − | 0.267888i | ||||
\(991\) | − | 57.5245i | − | 1.82733i | −0.406473 | − | 0.913663i | \(-0.633242\pi\) | ||
0.406473 | − | 0.913663i | \(-0.366758\pi\) | |||||||
\(992\) | −3.32378 | + | 3.90595i | −0.105530 | + | 0.124014i | ||||
\(993\) | 9.81186i | 0.311370i | ||||||||
\(994\) | 43.3913 | − | 4.93327i | 1.37629 | − | 0.156474i | ||||
\(995\) | 8.14606 | + | 8.14606i | 0.258248 | + | 0.258248i | ||||
\(996\) | 8.54602 | − | 6.63890i | 0.270791 | − | 0.210361i | ||||
\(997\) | −31.2570 | + | 31.2570i | −0.989919 | + | 0.989919i | −0.999950 | − | 0.0100311i | \(-0.996807\pi\) |
0.0100311 | + | 0.999950i | \(0.496807\pi\) | |||||||
\(998\) | −0.0608033 | − | 0.177382i | −0.00192470 | − | 0.00561494i | ||||
\(999\) | 3.55843i | 0.112584i |
(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 | 336.2.u.a.139.3 | ✓ | 64 | |
4.3 | odd | 2 | 1344.2.u.a.1231.19 | 64 | |||
7.6 | odd | 2 | inner | 336.2.u.a.139.4 | yes | 64 | |
16.3 | odd | 4 | inner | 336.2.u.a.307.4 | yes | 64 | |
16.13 | even | 4 | 1344.2.u.a.559.14 | 64 | |||
28.27 | even | 2 | 1344.2.u.a.1231.14 | 64 | |||
112.13 | odd | 4 | 1344.2.u.a.559.19 | 64 | |||
112.83 | even | 4 | inner | 336.2.u.a.307.3 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.3 | ✓ | 64 | 1.1 | even | 1 | trivial | |
336.2.u.a.139.4 | yes | 64 | 7.6 | odd | 2 | inner | |
336.2.u.a.307.3 | yes | 64 | 112.83 | even | 4 | inner | |
336.2.u.a.307.4 | yes | 64 | 16.3 | odd | 4 | inner | |
1344.2.u.a.559.14 | 64 | 16.13 | even | 4 | |||
1344.2.u.a.559.19 | 64 | 112.13 | odd | 4 | |||
1344.2.u.a.1231.14 | 64 | 28.27 | even | 2 | |||
1344.2.u.a.1231.19 | 64 | 4.3 | odd | 2 |