Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(36,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 56.3 | ||
Root | \(1.40994 + 0.109843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.56 |
Dual form | 65.2.m.a.36.3 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05628 | + | 0.609843i | 0.746903 | + | 0.431224i | 0.824574 | − | 0.565755i | \(-0.191415\pi\) |
−0.0776710 | + | 0.996979i | \(0.524748\pi\) | |||||||
\(3\) | −1.16612 | + | 2.01978i | −0.673262 | + | 1.16612i | 0.303712 | + | 0.952764i | \(0.401774\pi\) |
−0.976974 | + | 0.213359i | \(0.931559\pi\) | |||||||
\(4\) | −0.256182 | − | 0.443720i | −0.128091 | − | 0.221860i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −2.46350 | + | 1.42231i | −1.00572 | + | 0.580654i | ||||
\(7\) | 3.11786 | − | 1.80010i | 1.17844 | − | 0.680373i | 0.222787 | − | 0.974867i | \(-0.428484\pi\) |
0.955653 | + | 0.294494i | \(0.0951511\pi\) | |||||||
\(8\) | − | 3.06430i | − | 1.08339i | ||||||
\(9\) | −1.21969 | − | 2.11256i | −0.406562 | − | 0.704187i | ||||
\(10\) | −0.609843 | + | 1.05628i | −0.192849 | + | 0.334025i | ||||
\(11\) | −4.65213 | − | 2.68591i | −1.40267 | − | 0.809832i | −0.408004 | − | 0.912980i | \(-0.633775\pi\) |
−0.994666 | + | 0.103149i | \(0.967108\pi\) | |||||||
\(12\) | 1.19496 | 0.344955 | ||||||||
\(13\) | 1.81988 | + | 3.11256i | 0.504745 | + | 0.863269i | ||||
\(14\) | 4.39111 | 1.17357 | ||||||||
\(15\) | −2.01978 | − | 1.16612i | −0.521506 | − | 0.301092i | ||||
\(16\) | 1.35638 | − | 2.34932i | 0.339094 | − | 0.587329i | ||||
\(17\) | −0.565928 | − | 0.980215i | −0.137258 | − | 0.237737i | 0.789200 | − | 0.614136i | \(-0.210495\pi\) |
−0.926458 | + | 0.376399i | \(0.877162\pi\) | |||||||
\(18\) | − | 2.97527i | − | 0.701278i | ||||||
\(19\) | −1.96410 | + | 1.13397i | −0.450596 | + | 0.260152i | −0.708082 | − | 0.706130i | \(-0.750439\pi\) |
0.257486 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(20\) | 0.443720 | − | 0.256182i | 0.0992188 | − | 0.0572840i | ||||
\(21\) | 8.39654i | 1.83228i | ||||||||
\(22\) | −3.27597 | − | 5.67414i | −0.698438 | − | 1.20973i | ||||
\(23\) | −1.94644 | + | 3.37133i | −0.405860 | + | 0.702970i | −0.994421 | − | 0.105483i | \(-0.966361\pi\) |
0.588561 | + | 0.808453i | \(0.299695\pi\) | |||||||
\(24\) | 6.18922 | + | 3.57335i | 1.26337 | + | 0.729407i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.0241312 | + | 4.39758i | 0.00473251 | + | 0.862436i | ||||
\(27\) | −1.30752 | −0.251632 | ||||||||
\(28\) | −1.59748 | − | 0.922305i | −0.301895 | − | 0.174299i | ||||
\(29\) | 0.0123639 | − | 0.0214150i | 0.00229593 | − | 0.00397666i | −0.864875 | − | 0.501987i | \(-0.832603\pi\) |
0.867171 | + | 0.498010i | \(0.165936\pi\) | |||||||
\(30\) | −1.42231 | − | 2.46350i | −0.259676 | − | 0.449772i | ||||
\(31\) | − | 5.46410i | − | 0.981382i | −0.871334 | − | 0.490691i | \(-0.836744\pi\) | ||
0.871334 | − | 0.490691i | \(-0.163256\pi\) | |||||||
\(32\) | −2.44209 | + | 1.40994i | −0.431705 | + | 0.249245i | ||||
\(33\) | 10.8499 | − | 6.26420i | 1.88873 | − | 1.09046i | ||||
\(34\) | − | 1.38051i | − | 0.236755i | ||||||
\(35\) | 1.80010 | + | 3.11786i | 0.304272 | + | 0.527015i | ||||
\(36\) | −0.624924 | + | 1.08240i | −0.104154 | + | 0.180400i | ||||
\(37\) | 7.53794 | + | 4.35203i | 1.23923 | + | 0.715470i | 0.968937 | − | 0.247309i | \(-0.0795462\pi\) |
0.270293 | + | 0.962778i | \(0.412879\pi\) | |||||||
\(38\) | −2.76619 | −0.448735 | ||||||||
\(39\) | −8.40891 | + | 0.0461428i | −1.34650 | + | 0.00738877i | ||||
\(40\) | 3.06430 | 0.484508 | ||||||||
\(41\) | 3.23205 | + | 1.86603i | 0.504762 | + | 0.291424i | 0.730678 | − | 0.682723i | \(-0.239204\pi\) |
−0.225916 | + | 0.974147i | \(0.572538\pi\) | |||||||
\(42\) | −5.12058 | + | 8.86910i | −0.790122 | + | 1.36853i | ||||
\(43\) | −0.565928 | − | 0.980215i | −0.0863031 | − | 0.149481i | 0.819643 | − | 0.572875i | \(-0.194172\pi\) |
−0.905946 | + | 0.423394i | \(0.860839\pi\) | |||||||
\(44\) | 2.75232i | 0.414929i | ||||||||
\(45\) | 2.11256 | − | 1.21969i | 0.314922 | − | 0.181820i | ||||
\(46\) | −4.11196 | + | 2.37404i | −0.606276 | + | 0.350034i | ||||
\(47\) | 2.58535i | 0.377113i | 0.982062 | + | 0.188556i | \(0.0603808\pi\) | ||||
−0.982062 | + | 0.188556i | \(0.939619\pi\) | |||||||
\(48\) | 3.16341 | + | 5.47918i | 0.456598 | + | 0.790852i | ||||
\(49\) | 2.98070 | − | 5.16273i | 0.425815 | − | 0.737533i | ||||
\(50\) | −1.05628 | − | 0.609843i | −0.149381 | − | 0.0862449i | ||||
\(51\) | 2.63977 | 0.369641 | ||||||||
\(52\) | 0.914884 | − | 1.60490i | 0.126872 | − | 0.222560i | ||||
\(53\) | −4.43937 | −0.609795 | −0.304897 | − | 0.952385i | \(-0.598622\pi\) | ||||
−0.304897 | + | 0.952385i | \(0.598622\pi\) | |||||||
\(54\) | −1.38111 | − | 0.797382i | −0.187945 | − | 0.108510i | ||||
\(55\) | 2.68591 | − | 4.65213i | 0.362168 | − | 0.627293i | ||||
\(56\) | −5.51603 | − | 9.55405i | −0.737111 | − | 1.27671i | ||||
\(57\) | − | 5.28942i | − | 0.700600i | ||||||
\(58\) | 0.0261196 | − | 0.0150801i | 0.00342967 | − | 0.00198012i | ||||
\(59\) | −0.148458 | + | 0.0857123i | −0.0193276 | + | 0.0111588i | −0.509633 | − | 0.860392i | \(-0.670219\pi\) |
0.490305 | + | 0.871551i | \(0.336885\pi\) | |||||||
\(60\) | 1.19496i | 0.154269i | ||||||||
\(61\) | −1.68012 | − | 2.91005i | −0.215117 | − | 0.372594i | 0.738192 | − | 0.674591i | \(-0.235680\pi\) |
−0.953309 | + | 0.301997i | \(0.902347\pi\) | |||||||
\(62\) | 3.33225 | − | 5.77162i | 0.423196 | − | 0.732997i | ||||
\(63\) | −7.60563 | − | 4.39111i | −0.958219 | − | 0.553228i | ||||
\(64\) | −8.86488 | −1.10811 | ||||||||
\(65\) | −3.11256 | + | 1.81988i | −0.386066 | + | 0.225729i | ||||
\(66\) | 15.2807 | 1.88093 | ||||||||
\(67\) | 5.54239 | + | 3.19990i | 0.677111 | + | 0.390930i | 0.798766 | − | 0.601642i | \(-0.205487\pi\) |
−0.121655 | + | 0.992572i | \(0.538820\pi\) | |||||||
\(68\) | −0.289961 | + | 0.502227i | −0.0351629 | + | 0.0609040i | ||||
\(69\) | −4.53957 | − | 7.86276i | −0.546500 | − | 0.946566i | ||||
\(70\) | 4.39111i | 0.524838i | ||||||||
\(71\) | 9.35076 | − | 5.39866i | 1.10973 | − | 0.640703i | 0.170971 | − | 0.985276i | \(-0.445309\pi\) |
0.938760 | + | 0.344573i | \(0.111976\pi\) | |||||||
\(72\) | −6.47351 | + | 3.73748i | −0.762911 | + | 0.440467i | ||||
\(73\) | − | 4.70308i | − | 0.550454i | −0.961379 | − | 0.275227i | \(-0.911247\pi\) | ||
0.961379 | − | 0.275227i | \(-0.0887531\pi\) | |||||||
\(74\) | 5.30812 | + | 9.19393i | 0.617056 | + | 1.06877i | ||||
\(75\) | 1.16612 | − | 2.01978i | 0.134652 | − | 0.233225i | ||||
\(76\) | 1.00633 | + | 0.581008i | 0.115435 | + | 0.0666462i | ||||
\(77\) | −19.3396 | −2.20395 | ||||||||
\(78\) | −8.91030 | − | 5.07938i | −1.00889 | − | 0.575126i | ||||
\(79\) | −11.9826 | −1.34815 | −0.674075 | − | 0.738663i | \(-0.735457\pi\) | ||||
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(80\) | 2.34932 | + | 1.35638i | 0.262661 | + | 0.151648i | ||||
\(81\) | 5.18379 | − | 8.97859i | 0.575976 | − | 0.997621i | ||||
\(82\) | 2.27597 | + | 3.94209i | 0.251338 | + | 0.435331i | ||||
\(83\) | 12.1286i | 1.33129i | 0.746270 | + | 0.665643i | \(0.231843\pi\) | ||||
−0.746270 | + | 0.665643i | \(0.768157\pi\) | |||||||
\(84\) | 3.72572 | − | 2.15104i | 0.406509 | − | 0.234698i | ||||
\(85\) | 0.980215 | − | 0.565928i | 0.106319 | − | 0.0613835i | ||||
\(86\) | − | 1.38051i | − | 0.148864i | ||||||
\(87\) | 0.0288357 | + | 0.0499450i | 0.00309152 | + | 0.00535466i | ||||
\(88\) | −8.23042 | + | 14.2555i | −0.877366 | + | 1.51964i | ||||
\(89\) | 13.9898 | + | 8.07702i | 1.48292 | + | 0.856162i | 0.999812 | − | 0.0194001i | \(-0.00617565\pi\) |
0.483105 | + | 0.875562i | \(0.339509\pi\) | |||||||
\(90\) | 2.97527 | 0.313621 | ||||||||
\(91\) | 11.2771 | + | 6.42856i | 1.18216 | + | 0.673896i | ||||
\(92\) | 1.99457 | 0.207948 | ||||||||
\(93\) | 11.0363 | + | 6.37182i | 1.14441 | + | 0.660727i | ||||
\(94\) | −1.57666 | + | 2.73086i | −0.162620 | + | 0.281666i | ||||
\(95\) | −1.13397 | − | 1.96410i | −0.116343 | − | 0.201513i | ||||
\(96\) | − | 6.57666i | − | 0.671228i | ||||||
\(97\) | −10.5379 | + | 6.08408i | −1.06997 | + | 0.617745i | −0.928172 | − | 0.372151i | \(-0.878620\pi\) |
−0.141794 | + | 0.989896i | \(0.545287\pi\) | |||||||
\(98\) | 6.29692 | − | 3.63553i | 0.636085 | − | 0.367244i | ||||
\(99\) | 13.1039i | 1.31699i | ||||||||
\(100\) | 0.256182 | + | 0.443720i | 0.0256182 | + | 0.0443720i | ||||
\(101\) | −2.02721 | + | 3.51122i | −0.201714 | + | 0.349380i | −0.949081 | − | 0.315032i | \(-0.897985\pi\) |
0.747366 | + | 0.664412i | \(0.231318\pi\) | |||||||
\(102\) | 2.78833 | + | 1.60984i | 0.276086 | + | 0.159398i | ||||
\(103\) | 17.9035 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(104\) | 9.53781 | − | 5.57666i | 0.935259 | − | 0.546837i | ||||
\(105\) | −8.39654 | −0.819419 | ||||||||
\(106\) | −4.68922 | − | 2.70732i | −0.455457 | − | 0.262958i | ||||
\(107\) | 4.56593 | − | 7.90842i | 0.441405 | − | 0.764536i | −0.556389 | − | 0.830922i | \(-0.687814\pi\) |
0.997794 | + | 0.0663862i | \(0.0211469\pi\) | |||||||
\(108\) | 0.334963 | + | 0.580172i | 0.0322318 | + | 0.0558271i | ||||
\(109\) | − | 7.37605i | − | 0.706498i | −0.935529 | − | 0.353249i | \(-0.885077\pi\) | ||
0.935529 | − | 0.353249i | \(-0.114923\pi\) | |||||||
\(110\) | 5.67414 | − | 3.27597i | 0.541008 | − | 0.312351i | ||||
\(111\) | −17.5803 | + | 10.1500i | −1.66865 | + | 0.963396i | ||||
\(112\) | − | 9.76645i | − | 0.922843i | ||||||
\(113\) | −3.53794 | − | 6.12789i | −0.332821 | − | 0.576463i | 0.650243 | − | 0.759727i | \(-0.274667\pi\) |
−0.983064 | + | 0.183263i | \(0.941334\pi\) | |||||||
\(114\) | 3.22572 | − | 5.58710i | 0.302116 | − | 0.523280i | ||||
\(115\) | −3.37133 | − | 1.94644i | −0.314378 | − | 0.181506i | ||||
\(116\) | −0.0126697 | −0.00117635 | ||||||||
\(117\) | 4.35578 | − | 7.64096i | 0.402692 | − | 0.706407i | ||||
\(118\) | −0.209084 | −0.0192478 | ||||||||
\(119\) | −3.52897 | − | 2.03745i | −0.323500 | − | 0.186773i | ||||
\(120\) | −3.57335 | + | 6.18922i | −0.326201 | + | 0.564996i | ||||
\(121\) | 8.92820 | + | 15.4641i | 0.811655 | + | 1.40583i | ||||
\(122\) | − | 4.09843i | − | 0.371055i | ||||||
\(123\) | −7.53794 | + | 4.35203i | −0.679673 | + | 0.392409i | ||||
\(124\) | −2.42453 | + | 1.39980i | −0.217729 | + | 0.125706i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −5.35578 | − | 9.27648i | −0.477131 | − | 0.826415i | ||||
\(127\) | −5.71806 | + | 9.90396i | −0.507395 | + | 0.878835i | 0.492568 | + | 0.870274i | \(0.336058\pi\) |
−0.999963 | + | 0.00856072i | \(0.997275\pi\) | |||||||
\(128\) | −4.47962 | − | 2.58631i | −0.395946 | − | 0.228600i | ||||
\(129\) | 2.63977 | 0.232418 | ||||||||
\(130\) | −4.39758 | + | 0.0241312i | −0.385693 | + | 0.00211644i | ||||
\(131\) | −10.5680 | −0.923328 | −0.461664 | − | 0.887055i | \(-0.652747\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(132\) | −5.55910 | − | 3.20955i | −0.483858 | − | 0.279355i | ||||
\(133\) | −4.08253 | + | 7.07115i | −0.354000 | + | 0.613146i | ||||
\(134\) | 3.90288 | + | 6.75998i | 0.337157 | + | 0.583974i | ||||
\(135\) | − | 1.30752i | − | 0.112533i | ||||||
\(136\) | −3.00367 | + | 1.73417i | −0.257563 | + | 0.148704i | ||||
\(137\) | 3.27940 | − | 1.89336i | 0.280178 | − | 0.161761i | −0.353326 | − | 0.935500i | \(-0.614949\pi\) |
0.633504 | + | 0.773739i | \(0.281616\pi\) | |||||||
\(138\) | − | 11.0737i | − | 0.942656i | ||||||
\(139\) | −1.00693 | − | 1.74406i | −0.0854068 | − | 0.147929i | 0.820158 | − | 0.572138i | \(-0.193886\pi\) |
−0.905564 | + | 0.424209i | \(0.860552\pi\) | |||||||
\(140\) | 0.922305 | − | 1.59748i | 0.0779490 | − | 0.135012i | ||||
\(141\) | −5.22186 | − | 3.01484i | −0.439760 | − | 0.253895i | ||||
\(142\) | 13.1694 | 1.10515 | ||||||||
\(143\) | −0.106280 | − | 19.3681i | −0.00888757 | − | 1.61964i | ||||
\(144\) | −6.61742 | −0.551452 | ||||||||
\(145\) | 0.0214150 | + | 0.0123639i | 0.00177842 | + | 0.00102677i | ||||
\(146\) | 2.86814 | − | 4.96777i | 0.237369 | − | 0.411136i | ||||
\(147\) | 6.95174 | + | 12.0408i | 0.573370 | + | 0.993105i | ||||
\(148\) | − | 4.45965i | − | 0.366581i | ||||||
\(149\) | 4.77855 | − | 2.75890i | 0.391474 | − | 0.226018i | −0.291324 | − | 0.956624i | \(-0.594096\pi\) |
0.682799 | + | 0.730607i | \(0.260763\pi\) | |||||||
\(150\) | 2.46350 | − | 1.42231i | 0.201144 | − | 0.116131i | ||||
\(151\) | − | 4.88961i | − | 0.397911i | −0.980009 | − | 0.198956i | \(-0.936245\pi\) | ||
0.980009 | − | 0.198956i | \(-0.0637549\pi\) | |||||||
\(152\) | 3.47484 | + | 6.01859i | 0.281846 | + | 0.488172i | ||||
\(153\) | −1.38051 | + | 2.39111i | −0.111608 | + | 0.193310i | ||||
\(154\) | −20.4280 | − | 11.7941i | −1.64614 | − | 0.950397i | ||||
\(155\) | 5.46410 | 0.438887 | ||||||||
\(156\) | 2.17469 | + | 3.71938i | 0.174114 | + | 0.297789i | ||||
\(157\) | 10.0405 | 0.801323 | 0.400661 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400661 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(158\) | −12.6570 | − | 7.30752i | −1.00694 | − | 0.581355i | ||||
\(159\) | 5.17686 | − | 8.96658i | 0.410551 | − | 0.711096i | ||||
\(160\) | −1.40994 | − | 2.44209i | −0.111466 | − | 0.193064i | ||||
\(161\) | 14.0151i | 1.10454i | ||||||||
\(162\) | 10.9511 | − | 6.32260i | 0.860397 | − | 0.496750i | ||||
\(163\) | 5.87273 | − | 3.39062i | 0.459988 | − | 0.265574i | −0.252051 | − | 0.967714i | \(-0.581105\pi\) |
0.712039 | + | 0.702140i | \(0.247772\pi\) | |||||||
\(164\) | − | 1.91217i | − | 0.149315i | ||||||
\(165\) | 6.26420 | + | 10.8499i | 0.487667 | + | 0.844664i | ||||
\(166\) | −7.39654 | + | 12.8112i | −0.574083 | + | 0.994341i | ||||
\(167\) | −9.08444 | − | 5.24490i | −0.702975 | − | 0.405863i | 0.105479 | − | 0.994421i | \(-0.466362\pi\) |
−0.808455 | + | 0.588559i | \(0.799696\pi\) | |||||||
\(168\) | 25.7295 | 1.98507 | ||||||||
\(169\) | −6.37605 | + | 11.3290i | −0.490466 | + | 0.871460i | ||||
\(170\) | 1.38051 | 0.105880 | ||||||||
\(171\) | 4.79118 | + | 2.76619i | 0.366391 | + | 0.211536i | ||||
\(172\) | −0.289961 | + | 0.502227i | −0.0221093 | + | 0.0382944i | ||||
\(173\) | −2.22923 | − | 3.86113i | −0.169485 | − | 0.293557i | 0.768754 | − | 0.639545i | \(-0.220877\pi\) |
−0.938239 | + | 0.345988i | \(0.887544\pi\) | |||||||
\(174\) | 0.0703412i | 0.00533255i | ||||||||
\(175\) | −3.11786 | + | 1.80010i | −0.235688 | + | 0.136075i | ||||
\(176\) | −12.6201 | + | 7.28621i | −0.951275 | + | 0.549219i | ||||
\(177\) | − | 0.399804i | − | 0.0300511i | ||||||
\(178\) | 9.85143 | + | 17.0632i | 0.738396 | + | 1.27894i | ||||
\(179\) | 9.31564 | − | 16.1352i | 0.696284 | − | 1.20600i | −0.273462 | − | 0.961883i | \(-0.588169\pi\) |
0.969746 | − | 0.244116i | \(-0.0784979\pi\) | |||||||
\(180\) | −1.08240 | − | 0.624924i | −0.0806773 | − | 0.0465791i | ||||
\(181\) | −18.0900 | −1.34462 | −0.672310 | − | 0.740270i | \(-0.734698\pi\) | ||||
−0.672310 | + | 0.740270i | \(0.734698\pi\) | |||||||
\(182\) | 7.99131 | + | 13.6676i | 0.592355 | + | 1.01311i | ||||
\(183\) | 7.83690 | 0.579320 | ||||||||
\(184\) | 10.3307 | + | 5.96446i | 0.761593 | + | 0.439706i | ||||
\(185\) | −4.35203 | + | 7.53794i | −0.319968 | + | 0.554200i | ||||
\(186\) | 7.77162 | + | 13.4608i | 0.569843 | + | 0.986997i | ||||
\(187\) | 6.08012i | 0.444622i | ||||||||
\(188\) | 1.14717 | − | 0.662321i | 0.0836662 | − | 0.0483047i | ||||
\(189\) | −4.07666 | + | 2.35366i | −0.296533 | + | 0.171204i | ||||
\(190\) | − | 2.76619i | − | 0.200680i | ||||||
\(191\) | −13.6682 | − | 23.6740i | −0.988994 | − | 1.71299i | −0.622632 | − | 0.782515i | \(-0.713937\pi\) |
−0.366361 | − | 0.930473i | \(-0.619397\pi\) | |||||||
\(192\) | 10.3375 | − | 17.9052i | 0.746048 | − | 1.29219i | ||||
\(193\) | −18.8511 | − | 10.8837i | −1.35693 | − | 0.783425i | −0.367723 | − | 0.929935i | \(-0.619863\pi\) |
−0.989209 | + | 0.146510i | \(0.953196\pi\) | |||||||
\(194\) | −14.8413 | −1.06555 | ||||||||
\(195\) | −0.0461428 | − | 8.40891i | −0.00330436 | − | 0.602174i | ||||
\(196\) | −3.05441 | −0.218172 | ||||||||
\(197\) | −1.46940 | − | 0.848360i | −0.104691 | − | 0.0604432i | 0.446741 | − | 0.894664i | \(-0.352585\pi\) |
−0.551431 | + | 0.834220i | \(0.685918\pi\) | |||||||
\(198\) | −7.99131 | + | 13.8413i | −0.567917 | + | 0.983662i | ||||
\(199\) | 12.6627 | + | 21.9325i | 0.897637 | + | 1.55475i | 0.830506 | + | 0.557009i | \(0.188051\pi\) |
0.0671309 | + | 0.997744i | \(0.478615\pi\) | |||||||
\(200\) | 3.06430i | 0.216679i | ||||||||
\(201\) | −12.9262 | + | 7.46296i | −0.911746 | + | 0.526397i | ||||
\(202\) | −4.28259 | + | 2.47256i | −0.301322 | + | 0.173968i | ||||
\(203\) | − | 0.0890252i | − | 0.00624834i | ||||||
\(204\) | −0.676260 | − | 1.17132i | −0.0473477 | − | 0.0820086i | ||||
\(205\) | −1.86603 | + | 3.23205i | −0.130329 | + | 0.225736i | ||||
\(206\) | 18.9111 | + | 10.9183i | 1.31760 | + | 0.760715i | ||||
\(207\) | 9.49617 | 0.660030 | ||||||||
\(208\) | 9.78083 | − | 0.0536711i | 0.678179 | − | 0.00372142i | ||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | −8.86910 | − | 5.12058i | −0.612026 | − | 0.353353i | ||||
\(211\) | 0.167753 | − | 0.290558i | 0.0115486 | − | 0.0200028i | −0.860193 | − | 0.509968i | \(-0.829657\pi\) |
0.871742 | + | 0.489965i | \(0.162991\pi\) | |||||||
\(212\) | 1.13729 | + | 1.96984i | 0.0781092 | + | 0.135289i | ||||
\(213\) | 25.1820i | 1.72544i | ||||||||
\(214\) | 9.64579 | − | 5.56900i | 0.659373 | − | 0.380689i | ||||
\(215\) | 0.980215 | − | 0.565928i | 0.0668501 | − | 0.0385959i | ||||
\(216\) | 4.00663i | 0.272616i | ||||||||
\(217\) | −9.83592 | − | 17.0363i | −0.667706 | − | 1.15650i | ||||
\(218\) | 4.49824 | − | 7.79118i | 0.304659 | − | 0.527685i | ||||
\(219\) | 9.49922 | + | 5.48438i | 0.641898 | + | 0.370600i | ||||
\(220\) | −2.75232 | −0.185562 | ||||||||
\(221\) | 2.02106 | − | 3.54536i | 0.135951 | − | 0.238487i | ||||
\(222\) | −24.7597 | −1.66176 | ||||||||
\(223\) | −10.6493 | − | 6.14838i | −0.713130 | − | 0.411726i | 0.0990887 | − | 0.995079i | \(-0.468407\pi\) |
−0.812219 | + | 0.583353i | \(0.801741\pi\) | |||||||
\(224\) | −5.07606 | + | 8.79200i | −0.339159 | + | 0.587440i | ||||
\(225\) | 1.21969 | + | 2.11256i | 0.0813125 | + | 0.140837i | ||||
\(226\) | − | 8.63036i | − | 0.574083i | ||||||
\(227\) | 6.60974 | − | 3.81613i | 0.438704 | − | 0.253286i | −0.264344 | − | 0.964428i | \(-0.585155\pi\) |
0.703048 | + | 0.711143i | \(0.251822\pi\) | |||||||
\(228\) | −2.34702 | + | 1.35505i | −0.155435 | + | 0.0897406i | ||||
\(229\) | − | 14.4008i | − | 0.951631i | −0.879545 | − | 0.475815i | \(-0.842153\pi\) | ||
0.879545 | − | 0.475815i | \(-0.157847\pi\) | |||||||
\(230\) | −2.37404 | − | 4.11196i | −0.156540 | − | 0.271135i | ||||
\(231\) | 22.5523 | − | 39.0618i | 1.48384 | − | 2.57008i | ||||
\(232\) | −0.0656218 | − | 0.0378868i | −0.00430828 | − | 0.00248739i | ||||
\(233\) | −9.49617 | −0.622115 | −0.311057 | − | 0.950391i | \(-0.600683\pi\) | ||||
−0.311057 | + | 0.950391i | \(0.600683\pi\) | |||||||
\(234\) | 9.26071 | − | 5.41465i | 0.605392 | − | 0.353966i | ||||
\(235\) | −2.58535 | −0.168650 | ||||||||
\(236\) | 0.0760645 | + | 0.0439159i | 0.00495138 | + | 0.00285868i | ||||
\(237\) | 13.9732 | − | 24.2023i | 0.907657 | − | 1.57211i | ||||
\(238\) | −2.48505 | − | 4.30423i | −0.161082 | − | 0.279002i | ||||
\(239\) | 19.9143i | 1.28815i | 0.764962 | + | 0.644076i | \(0.222758\pi\) | ||||
−0.764962 | + | 0.644076i | \(0.777242\pi\) | |||||||
\(240\) | −5.47918 | + | 3.16341i | −0.353680 | + | 0.204197i | ||||
\(241\) | 20.1493 | − | 11.6332i | 1.29793 | − | 0.749360i | 0.317883 | − | 0.948130i | \(-0.397028\pi\) |
0.980046 | + | 0.198770i | \(0.0636947\pi\) | |||||||
\(242\) | 21.7792i | 1.40002i | ||||||||
\(243\) | 10.1286 | + | 17.5432i | 0.649750 | + | 1.12540i | ||||
\(244\) | −0.860832 | + | 1.49100i | −0.0551091 | + | 0.0954518i | ||||
\(245\) | 5.16273 | + | 2.98070i | 0.329835 | + | 0.190430i | ||||
\(246\) | −10.6162 | −0.676866 | ||||||||
\(247\) | −7.10400 | − | 4.04968i | −0.452017 | − | 0.257675i | ||||
\(248\) | −16.7436 | −1.06322 | ||||||||
\(249\) | −24.4972 | − | 14.1434i | −1.55244 | − | 0.896304i | ||||
\(250\) | 0.609843 | − | 1.05628i | 0.0385699 | − | 0.0668050i | ||||
\(251\) | 5.92008 | + | 10.2539i | 0.373672 | + | 0.647219i | 0.990127 | − | 0.140171i | \(-0.0447652\pi\) |
−0.616455 | + | 0.787390i | \(0.711432\pi\) | |||||||
\(252\) | 4.49969i | 0.283454i | ||||||||
\(253\) | 18.1101 | − | 10.4559i | 1.13858 | − | 0.657357i | ||||
\(254\) | −12.0797 | + | 6.97424i | −0.757950 | + | 0.437603i | ||||
\(255\) | 2.63977i | 0.165309i | ||||||||
\(256\) | 5.71040 | + | 9.89070i | 0.356900 | + | 0.618169i | ||||
\(257\) | −2.77501 | + | 4.80646i | −0.173100 | + | 0.299819i | −0.939502 | − | 0.342543i | \(-0.888712\pi\) |
0.766402 | + | 0.642361i | \(0.222045\pi\) | |||||||
\(258\) | 2.78833 | + | 1.60984i | 0.173594 | + | 0.100224i | ||||
\(259\) | 31.3363 | 1.94714 | ||||||||
\(260\) | 1.60490 | + | 0.914884i | 0.0995317 | + | 0.0567387i | ||||
\(261\) | −0.0603205 | −0.00373375 | ||||||||
\(262\) | −11.1627 | − | 6.44481i | −0.689636 | − | 0.398161i | ||||
\(263\) | −3.42983 | + | 5.94065i | −0.211493 | + | 0.366316i | −0.952182 | − | 0.305532i | \(-0.901166\pi\) |
0.740689 | + | 0.671848i | \(0.234499\pi\) | |||||||
\(264\) | −19.1954 | − | 33.2474i | −1.18139 | − | 2.04623i | ||||
\(265\) | − | 4.43937i | − | 0.272709i | ||||||
\(266\) | −8.62459 | + | 4.97941i | −0.528807 | + | 0.305307i | ||||
\(267\) | −32.6277 | + | 18.8376i | −1.99678 | + | 1.15284i | ||||
\(268\) | − | 3.27903i | − | 0.200299i | ||||||
\(269\) | 0.710994 | + | 1.23148i | 0.0433501 | + | 0.0750845i | 0.886886 | − | 0.461988i | \(-0.152864\pi\) |
−0.843536 | + | 0.537072i | \(0.819530\pi\) | |||||||
\(270\) | 0.797382 | − | 1.38111i | 0.0485271 | − | 0.0840514i | ||||
\(271\) | 8.63381 | + | 4.98473i | 0.524467 | + | 0.302801i | 0.738760 | − | 0.673968i | \(-0.235412\pi\) |
−0.214294 | + | 0.976769i | \(0.568745\pi\) | |||||||
\(272\) | −3.07045 | −0.186173 | ||||||||
\(273\) | −26.1347 | + | 15.2807i | −1.58175 | + | 0.924831i | ||||
\(274\) | 4.61862 | 0.279021 | ||||||||
\(275\) | 4.65213 | + | 2.68591i | 0.280534 | + | 0.161966i | ||||
\(276\) | −2.32591 | + | 4.02860i | −0.140003 | + | 0.242493i | ||||
\(277\) | −8.76187 | − | 15.1760i | −0.526449 | − | 0.911837i | −0.999525 | − | 0.0308154i | \(-0.990190\pi\) |
0.473076 | − | 0.881022i | \(-0.343144\pi\) | |||||||
\(278\) | − | 2.45628i | − | 0.147318i | ||||||
\(279\) | −11.5432 | + | 6.66449i | −0.691076 | + | 0.398993i | ||||
\(280\) | 9.55405 | − | 5.51603i | 0.570964 | − | 0.329646i | ||||
\(281\) | 10.7352i | 0.640406i | 0.947349 | + | 0.320203i | \(0.103751\pi\) | ||||
−0.947349 | + | 0.320203i | \(0.896249\pi\) | |||||||
\(282\) | −3.67716 | − | 6.36903i | −0.218972 | − | 0.379270i | ||||
\(283\) | 0.659192 | − | 1.14175i | 0.0391849 | − | 0.0678702i | −0.845768 | − | 0.533551i | \(-0.820857\pi\) |
0.884953 | + | 0.465681i | \(0.154191\pi\) | |||||||
\(284\) | −4.79099 | − | 2.76608i | −0.284293 | − | 0.164137i | ||||
\(285\) | 5.28942 | 0.313318 | ||||||||
\(286\) | 11.6992 | − | 20.5229i | 0.691790 | − | 1.21355i | ||||
\(287\) | 13.4361 | 0.793109 | ||||||||
\(288\) | 5.95717 | + | 3.43937i | 0.351030 | + | 0.202667i | ||||
\(289\) | 7.85945 | − | 13.6130i | 0.462321 | − | 0.800763i | ||||
\(290\) | 0.0150801 | + | 0.0261196i | 0.000885536 | + | 0.00153379i | ||||
\(291\) | − | 28.3792i | − | 1.66362i | ||||||
\(292\) | −2.08685 | + | 1.20485i | −0.122124 | + | 0.0705082i | ||||
\(293\) | 16.2316 | − | 9.37133i | 0.948261 | − | 0.547479i | 0.0557207 | − | 0.998446i | \(-0.482254\pi\) |
0.892540 | + | 0.450968i | \(0.148921\pi\) | |||||||
\(294\) | 16.9579i | 0.989004i | ||||||||
\(295\) | −0.0857123 | − | 0.148458i | −0.00499036 | − | 0.00864356i | ||||
\(296\) | 13.3359 | − | 23.0985i | 0.775134 | − | 1.34257i | ||||
\(297\) | 6.08275 | + | 3.51187i | 0.352957 | + | 0.203780i | ||||
\(298\) | 6.72998 | 0.389857 | ||||||||
\(299\) | −14.0357 | + | 0.0770194i | −0.811708 | + | 0.00445415i | ||||
\(300\) | −1.19496 | −0.0689910 | ||||||||
\(301\) | −3.52897 | − | 2.03745i | −0.203406 | − | 0.117437i | ||||
\(302\) | 2.98190 | − | 5.16480i | 0.171589 | − | 0.297201i | ||||
\(303\) | −4.72794 | − | 8.18904i | −0.271613 | − | 0.470448i | ||||
\(304\) | 6.15239i | 0.352864i | ||||||||
\(305\) | 2.91005 | − | 1.68012i | 0.166629 | − | 0.0962032i | ||||
\(306\) | −2.91641 | + | 1.68379i | −0.166720 | + | 0.0962558i | ||||
\(307\) | 14.3043i | 0.816387i | 0.912895 | + | 0.408194i | \(0.133841\pi\) | ||||
−0.912895 | + | 0.408194i | \(0.866159\pi\) | |||||||
\(308\) | 4.95445 | + | 8.58137i | 0.282306 | + | 0.488969i | ||||
\(309\) | −20.8777 | + | 36.1612i | −1.18769 | + | 2.05714i | ||||
\(310\) | 5.77162 | + | 3.33225i | 0.327806 | + | 0.189259i | ||||
\(311\) | −2.76102 | −0.156563 | −0.0782815 | − | 0.996931i | \(-0.524943\pi\) | ||||
−0.0782815 | + | 0.996931i | \(0.524943\pi\) | |||||||
\(312\) | 0.141395 | + | 25.7674i | 0.00800494 | + | 1.45879i | ||||
\(313\) | −16.3858 | −0.926179 | −0.463090 | − | 0.886311i | \(-0.653259\pi\) | ||||
−0.463090 | + | 0.886311i | \(0.653259\pi\) | |||||||
\(314\) | 10.6056 | + | 6.12316i | 0.598510 | + | 0.345550i | ||||
\(315\) | 4.39111 | − | 7.60563i | 0.247411 | − | 0.428529i | ||||
\(316\) | 3.06973 | + | 5.31693i | 0.172686 | + | 0.299101i | ||||
\(317\) | − | 1.78575i | − | 0.100297i | −0.998742 | − | 0.0501487i | \(-0.984030\pi\) | ||
0.998742 | − | 0.0501487i | \(-0.0159695\pi\) | |||||||
\(318\) | 10.9364 | − | 6.31414i | 0.613284 | − | 0.354080i | ||||
\(319\) | −0.115037 | + | 0.0664168i | −0.00644085 | + | 0.00371863i | ||||
\(320\) | − | 8.86488i | − | 0.495562i | ||||||
\(321\) | 10.6489 | + | 18.4444i | 0.594362 | + | 1.02946i | ||||
\(322\) | −8.54702 | + | 14.8039i | −0.476307 | + | 0.824987i | ||||
\(323\) | 2.22308 | + | 1.28349i | 0.123695 | + | 0.0714156i | ||||
\(324\) | −5.31197 | −0.295110 | ||||||||
\(325\) | −1.81988 | − | 3.11256i | −0.100949 | − | 0.172654i | ||||
\(326\) | 8.27099 | 0.458088 | ||||||||
\(327\) | 14.8980 | + | 8.60139i | 0.823864 | + | 0.475658i | ||||
\(328\) | 5.71806 | − | 9.90396i | 0.315727 | − | 0.546855i | ||||
\(329\) | 4.65389 | + | 8.06077i | 0.256577 | + | 0.444405i | ||||
\(330\) | 15.2807i | 0.841176i | ||||||||
\(331\) | −6.25652 | + | 3.61220i | −0.343889 | + | 0.198545i | −0.661991 | − | 0.749512i | \(-0.730288\pi\) |
0.318101 | + | 0.948057i | \(0.396955\pi\) | |||||||
\(332\) | 5.38170 | − | 3.10713i | 0.295359 | − | 0.170526i | ||||
\(333\) | − | 21.2325i | − | 1.16353i | ||||||
\(334\) | −6.39714 | − | 11.0802i | −0.350036 | − | 0.606280i | ||||
\(335\) | −3.19990 | + | 5.54239i | −0.174829 | + | 0.302813i | ||||
\(336\) | 19.7261 | + | 11.3889i | 1.07615 | + | 0.621315i | ||||
\(337\) | 4.36219 | 0.237624 | 0.118812 | − | 0.992917i | \(-0.462091\pi\) | ||||
0.118812 | + | 0.992917i | \(0.462091\pi\) | |||||||
\(338\) | −13.6438 | + | 8.07818i | −0.742125 | + | 0.439395i | ||||
\(339\) | 16.5027 | 0.896303 | ||||||||
\(340\) | −0.502227 | − | 0.289961i | −0.0272371 | − | 0.0157253i | ||||
\(341\) | −14.6761 | + | 25.4197i | −0.794754 | + | 1.37655i | ||||
\(342\) | 3.37388 | + | 5.84374i | 0.182439 | + | 0.315993i | ||||
\(343\) | 3.73913i | 0.201894i | ||||||||
\(344\) | −3.00367 | + | 1.73417i | −0.161947 | + | 0.0935002i | ||||
\(345\) | 7.86276 | − | 4.53957i | 0.423317 | − | 0.244402i | ||||
\(346\) | − | 5.43792i | − | 0.292344i | ||||||
\(347\) | 13.3536 | + | 23.1291i | 0.716858 | + | 1.24163i | 0.962239 | + | 0.272207i | \(0.0877537\pi\) |
−0.245381 | + | 0.969427i | \(0.578913\pi\) | |||||||
\(348\) | 0.0147744 | − | 0.0255900i | 0.000791991 | − | 0.00137177i | ||||
\(349\) | −20.4131 | − | 11.7855i | −1.09269 | − | 0.630865i | −0.158399 | − | 0.987375i | \(-0.550633\pi\) |
−0.934292 | + | 0.356510i | \(0.883967\pi\) | |||||||
\(350\) | −4.39111 | −0.234715 | ||||||||
\(351\) | −2.37953 | − | 4.06973i | −0.127010 | − | 0.217226i | ||||
\(352\) | 15.1479 | 0.807385 | ||||||||
\(353\) | 4.96862 | + | 2.86863i | 0.264453 | + | 0.152682i | 0.626364 | − | 0.779531i | \(-0.284542\pi\) |
−0.361911 | + | 0.932213i | \(0.617876\pi\) | |||||||
\(354\) | 0.243818 | − | 0.422305i | 0.0129588 | − | 0.0224453i | ||||
\(355\) | 5.39866 | + | 9.35076i | 0.286531 | + | 0.496287i | ||||
\(356\) | − | 8.27675i | − | 0.438667i | ||||||
\(357\) | 8.23042 | − | 4.75184i | 0.435600 | − | 0.251494i | ||||
\(358\) | 19.6799 | − | 11.3622i | 1.04011 | − | 0.600509i | ||||
\(359\) | − | 24.7583i | − | 1.30669i | −0.757059 | − | 0.653347i | \(-0.773364\pi\) | ||
0.757059 | − | 0.653347i | \(-0.226636\pi\) | |||||||
\(360\) | −3.73748 | − | 6.47351i | −0.196983 | − | 0.341184i | ||||
\(361\) | −6.92820 | + | 12.0000i | −0.364642 | + | 0.631579i | ||||
\(362\) | −19.1081 | − | 11.0321i | −1.00430 | − | 0.579833i | ||||
\(363\) | −41.6455 | −2.18582 | ||||||||
\(364\) | −0.0364951 | − | 6.65074i | −0.00191286 | − | 0.348593i | ||||
\(365\) | 4.70308 | 0.246171 | ||||||||
\(366\) | 8.27796 | + | 4.77928i | 0.432696 | + | 0.249817i | ||||
\(367\) | −13.0268 | + | 22.5630i | −0.679992 | + | 1.17778i | 0.294991 | + | 0.955500i | \(0.404683\pi\) |
−0.974983 | + | 0.222280i | \(0.928650\pi\) | |||||||
\(368\) | 5.28021 | + | 9.14558i | 0.275250 | + | 0.476747i | ||||
\(369\) | − | 9.10387i | − | 0.473928i | ||||||
\(370\) | −9.19393 | + | 5.30812i | −0.477969 | + | 0.275956i | ||||
\(371\) | −13.8413 | + | 7.99131i | −0.718607 | + | 0.414888i | ||||
\(372\) | − | 6.52938i | − | 0.338532i | ||||||
\(373\) | −6.60224 | − | 11.4354i | −0.341851 | − | 0.592103i | 0.642926 | − | 0.765929i | \(-0.277720\pi\) |
−0.984776 | + | 0.173826i | \(0.944387\pi\) | |||||||
\(374\) | −3.70792 | + | 6.42231i | −0.191732 | + | 0.332089i | ||||
\(375\) | 2.01978 | + | 1.16612i | 0.104301 | + | 0.0602183i | ||||
\(376\) | 7.92229 | 0.408561 | ||||||||
\(377\) | 0.0891563 | 0.000489234i | 0.00459178 | 2.51968e-5i | ||||||
\(378\) | −5.74146 | −0.295309 | ||||||||
\(379\) | 22.5147 | + | 12.9989i | 1.15650 | + | 0.667707i | 0.950463 | − | 0.310837i | \(-0.100609\pi\) |
0.206039 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(380\) | −0.581008 | + | 1.00633i | −0.0298051 | + | 0.0516239i | ||||
\(381\) | −13.3359 | − | 23.0985i | −0.683220 | − | 1.18337i | ||||
\(382\) | − | 33.3418i | − | 1.70591i | ||||||
\(383\) | 8.31401 | − | 4.80010i | 0.424826 | − | 0.245274i | −0.272314 | − | 0.962208i | \(-0.587789\pi\) |
0.697140 | + | 0.716935i | \(0.254456\pi\) | |||||||
\(384\) | 10.4476 | − | 6.03191i | 0.533151 | − | 0.307815i | ||||
\(385\) | − | 19.3396i | − | 0.985637i | ||||||
\(386\) | −13.2747 | − | 22.9924i | −0.675664 | − | 1.17028i | ||||
\(387\) | −1.38051 | + | 2.39111i | −0.0701752 | + | 0.121547i | ||||
\(388\) | 5.39926 | + | 3.11726i | 0.274106 | + | 0.158255i | ||||
\(389\) | −5.63129 | −0.285518 | −0.142759 | − | 0.989758i | \(-0.545597\pi\) | ||||
−0.142759 | + | 0.989758i | \(0.545597\pi\) | |||||||
\(390\) | 5.07938 | − | 8.91030i | 0.257204 | − | 0.451191i | ||||
\(391\) | 4.40617 | 0.222829 | ||||||||
\(392\) | −15.8201 | − | 9.13376i | −0.799038 | − | 0.461325i | ||||
\(393\) | 12.3236 | − | 21.3450i | 0.621641 | − | 1.07671i | ||||
\(394\) | −1.03473 | − | 1.79221i | −0.0521291 | − | 0.0902903i | ||||
\(395\) | − | 11.9826i | − | 0.602911i | ||||||
\(396\) | 5.81445 | − | 3.35697i | 0.292187 | − | 0.168694i | ||||
\(397\) | −14.5196 | + | 8.38291i | −0.728719 | + | 0.420726i | −0.817953 | − | 0.575285i | \(-0.804891\pi\) |
0.0892344 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(398\) | 30.8891i | 1.54833i | ||||||||
\(399\) | −9.52147 | − | 16.4917i | −0.476670 | − | 0.825616i | ||||
\(400\) | −1.35638 | + | 2.34932i | −0.0678189 | + | 0.117466i | ||||
\(401\) | 12.0187 | + | 6.93902i | 0.600187 | + | 0.346518i | 0.769115 | − | 0.639110i | \(-0.220697\pi\) |
−0.168928 | + | 0.985628i | \(0.554031\pi\) | |||||||
\(402\) | −18.2050 | −0.907980 | ||||||||
\(403\) | 17.0073 | − | 9.94402i | 0.847196 | − | 0.495347i | ||||
\(404\) | 2.07733 | 0.103351 | ||||||||
\(405\) | 8.97859 | + | 5.18379i | 0.446149 | + | 0.257585i | ||||
\(406\) | 0.0542914 | − | 0.0940355i | 0.00269444 | − | 0.00466690i | ||||
\(407\) | −23.3783 | − | 40.4924i | −1.15882 | − | 2.00713i | ||||
\(408\) | − | 8.08903i | − | 0.400466i | ||||||
\(409\) | −25.4829 | + | 14.7125i | −1.26005 | + | 0.727489i | −0.973083 | − | 0.230453i | \(-0.925979\pi\) |
−0.286964 | + | 0.957941i | \(0.592646\pi\) | |||||||
\(410\) | −3.94209 | + | 2.27597i | −0.194686 | + | 0.112402i | ||||
\(411\) | 8.83157i | 0.435629i | ||||||||
\(412\) | −4.58655 | − | 7.94413i | −0.225963 | − | 0.391379i | ||||
\(413\) | −0.308581 | + | 0.534478i | −0.0151843 | + | 0.0262999i | ||||
\(414\) | 10.0306 | + | 5.79118i | 0.492978 | + | 0.284621i | ||||
\(415\) | −12.1286 | −0.595369 | ||||||||
\(416\) | −8.83284 | − | 5.03522i | −0.433066 | − | 0.246872i | ||||
\(417\) | 4.69683 | 0.230005 | ||||||||
\(418\) | 12.8687 | + | 7.42973i | 0.629427 | + | 0.363400i | ||||
\(419\) | −3.48397 | + | 6.03440i | −0.170203 | + | 0.294800i | −0.938491 | − | 0.345305i | \(-0.887776\pi\) |
0.768288 | + | 0.640104i | \(0.221109\pi\) | |||||||
\(420\) | 2.15104 | + | 3.72572i | 0.104960 | + | 0.181796i | ||||
\(421\) | − | 7.12125i | − | 0.347069i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) | ||
0.984828 | − | 0.173534i | \(-0.0555188\pi\) | |||||||
\(422\) | 0.354389 | − | 0.204607i | 0.0172514 | − | 0.00996010i | ||||
\(423\) | 5.46171 | − | 3.15332i | 0.265558 | − | 0.153320i | ||||
\(424\) | 13.6036i | 0.660647i | ||||||||
\(425\) | 0.565928 | + | 0.980215i | 0.0274515 | + | 0.0475474i | ||||
\(426\) | −15.3571 | + | 26.5993i | −0.744054 | + | 1.28874i | ||||
\(427\) | −10.4767 | − | 6.04875i | −0.507005 | − | 0.292720i | ||||
\(428\) | −4.67883 | −0.226160 | ||||||||
\(429\) | 39.2433 | + | 22.3709i | 1.89468 | + | 1.08008i | ||||
\(430\) | 1.38051 | 0.0665740 | ||||||||
\(431\) | 26.1664 | + | 15.1072i | 1.26039 | + | 0.727687i | 0.973150 | − | 0.230171i | \(-0.0739286\pi\) |
0.287241 | + | 0.957858i | \(0.407262\pi\) | |||||||
\(432\) | −1.77349 | + | 3.07177i | −0.0853270 | + | 0.147791i | ||||
\(433\) | 0.600065 | + | 1.03934i | 0.0288373 | + | 0.0499476i | 0.880084 | − | 0.474818i | \(-0.157486\pi\) |
−0.851247 | + | 0.524766i | \(0.824153\pi\) | |||||||
\(434\) | − | 23.9935i | − | 1.15172i | ||||||
\(435\) | −0.0499450 | + | 0.0288357i | −0.00239468 | + | 0.00138257i | ||||
\(436\) | −3.27290 | + | 1.88961i | −0.156744 | + | 0.0904960i | ||||
\(437\) | − | 8.82884i | − | 0.422341i | ||||||
\(438\) | 6.68922 | + | 11.5861i | 0.319623 | + | 0.553604i | ||||
\(439\) | −8.27705 | + | 14.3363i | −0.395042 | + | 0.684233i | −0.993107 | − | 0.117215i | \(-0.962603\pi\) |
0.598064 | + | 0.801448i | \(0.295937\pi\) | |||||||
\(440\) | −14.2555 | − | 8.23042i | −0.679605 | − | 0.392370i | ||||
\(441\) | −14.5421 | −0.692481 | ||||||||
\(442\) | 4.29692 | − | 2.51236i | 0.204383 | − | 0.119501i | ||||
\(443\) | 4.55949 | 0.216628 | 0.108314 | − | 0.994117i | \(-0.465455\pi\) | ||||
0.108314 | + | 0.994117i | \(0.465455\pi\) | |||||||
\(444\) | 9.00753 | + | 5.20050i | 0.427478 | + | 0.246805i | ||||
\(445\) | −8.07702 | + | 13.9898i | −0.382887 | + | 0.663180i | ||||
\(446\) | −7.49910 | − | 12.9888i | −0.355093 | − | 0.615038i | ||||
\(447\) | 12.8689i | 0.608676i | ||||||||
\(448\) | −27.6395 | + | 15.9577i | −1.30584 | + | 0.753929i | ||||
\(449\) | 11.9963 | − | 6.92608i | 0.566142 | − | 0.326862i | −0.189465 | − | 0.981887i | \(-0.560675\pi\) |
0.755607 | + | 0.655025i | \(0.227342\pi\) | |||||||
\(450\) | 2.97527i | 0.140256i | ||||||||
\(451\) | −10.0239 | − | 17.3620i | −0.472009 | − | 0.817544i | ||||
\(452\) | −1.81271 | + | 3.13971i | −0.0852628 | + | 0.147680i | ||||
\(453\) | 9.87596 | + | 5.70189i | 0.464013 | + | 0.267898i | ||||
\(454\) | 9.30897 | 0.436892 | ||||||||
\(455\) | −6.42856 | + | 11.2771i | −0.301376 | + | 0.528676i | ||||
\(456\) | −16.2083 | −0.759025 | ||||||||
\(457\) | 34.7402 | + | 20.0573i | 1.62508 | + | 0.938240i | 0.985532 | + | 0.169489i | \(0.0542117\pi\) |
0.639548 | + | 0.768751i | \(0.279122\pi\) | |||||||
\(458\) | 8.78222 | − | 15.2113i | 0.410366 | − | 0.710775i | ||||
\(459\) | 0.739961 | + | 1.28165i | 0.0345384 | + | 0.0598223i | ||||
\(460\) | 1.99457i | 0.0929972i | ||||||||
\(461\) | 6.52897 | − | 3.76950i | 0.304084 | − | 0.175563i | −0.340192 | − | 0.940356i | \(-0.610492\pi\) |
0.644276 | + | 0.764793i | \(0.277159\pi\) | |||||||
\(462\) | 47.6432 | − | 27.5068i | 2.21656 | − | 1.27973i | ||||
\(463\) | 23.3031i | 1.08299i | 0.840705 | + | 0.541494i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541494i | \(0.817859\pi\) | |||||||
\(464\) | −0.0335403 | − | 0.0580936i | −0.00155707 | − | 0.00269693i | ||||
\(465\) | −6.37182 | + | 11.0363i | −0.295486 | + | 0.511797i | ||||
\(466\) | −10.0306 | − | 5.79118i | −0.464659 | − | 0.268271i | ||||
\(467\) | 22.6297 | 1.04718 | 0.523589 | − | 0.851971i | \(-0.324593\pi\) | ||||
0.523589 | + | 0.851971i | \(0.324593\pi\) | |||||||
\(468\) | −4.50632 | + | 0.0247279i | −0.208305 | + | 0.00114305i | ||||
\(469\) | 23.0405 | 1.06391 | ||||||||
\(470\) | −2.73086 | − | 1.57666i | −0.125965 | − | 0.0727260i | ||||
\(471\) | −11.7085 | + | 20.2797i | −0.539500 | + | 0.934441i | ||||
\(472\) | 0.262648 | + | 0.454919i | 0.0120893 | + | 0.0209394i | ||||
\(473\) | 6.08012i | 0.279564i | ||||||||
\(474\) | 29.5192 | − | 17.0429i | 1.35586 | − | 0.782808i | ||||
\(475\) | 1.96410 | − | 1.13397i | 0.0901192 | − | 0.0520303i | ||||
\(476\) | 2.08783i | 0.0956956i | ||||||||
\(477\) | 5.41465 | + | 9.37844i | 0.247920 | + | 0.429409i | ||||
\(478\) | −12.1446 | + | 21.0351i | −0.555482 | + | 0.962124i | ||||
\(479\) | −17.8789 | − | 10.3224i | −0.816910 | − | 0.471643i | 0.0324399 | − | 0.999474i | \(-0.489672\pi\) |
−0.849350 | + | 0.527831i | \(0.823006\pi\) | |||||||
\(480\) | 6.57666 | 0.300182 | ||||||||
\(481\) | 0.172207 | + | 31.3825i | 0.00785198 | + | 1.43092i | ||||
\(482\) | 28.3777 | 1.29257 | ||||||||
\(483\) | −28.3075 | − | 16.3433i | −1.28804 | − | 0.743648i | ||||
\(484\) | 4.57449 | − | 7.92325i | 0.207931 | − | 0.360148i | ||||
\(485\) | −6.08408 | − | 10.5379i | −0.276264 | − | 0.478503i | ||||
\(486\) | 24.7074i | 1.12075i | ||||||||
\(487\) | −2.62929 | + | 1.51802i | −0.119145 | + | 0.0687882i | −0.558388 | − | 0.829580i | \(-0.688580\pi\) |
0.439243 | + | 0.898368i | \(0.355247\pi\) | |||||||
\(488\) | −8.91725 | + | 5.14838i | −0.403665 | + | 0.233056i | ||||
\(489\) | 15.8155i | 0.715203i | ||||||||
\(490\) | 3.63553 | + | 6.29692i | 0.164236 | + | 0.284466i | ||||
\(491\) | 5.33401 | − | 9.23877i | 0.240720 | − | 0.416940i | −0.720199 | − | 0.693767i | \(-0.755950\pi\) |
0.960920 | + | 0.276827i | \(0.0892830\pi\) | |||||||
\(492\) | 3.86217 | + | 2.22982i | 0.174120 | + | 0.100528i | ||||
\(493\) | −0.0279884 | −0.00126053 | ||||||||
\(494\) | −5.03414 | − | 8.60992i | −0.226497 | − | 0.387379i | ||||
\(495\) | −13.1039 | −0.588975 | ||||||||
\(496\) | −12.8369 | − | 7.41139i | −0.576394 | − | 0.332781i | ||||
\(497\) | 19.4362 | − | 33.6646i | 0.871835 | − | 1.51006i | ||||
\(498\) | −17.2506 | − | 29.8789i | −0.773016 | − | 1.33890i | ||||
\(499\) | − | 33.9143i | − | 1.51821i | −0.650966 | − | 0.759107i | \(-0.725636\pi\) | ||
0.650966 | − | 0.759107i | \(-0.274364\pi\) | |||||||
\(500\) | −0.443720 | + | 0.256182i | −0.0198438 | + | 0.0114568i | ||||
\(501\) | 21.1872 | − | 12.2324i | 0.946572 | − | 0.546504i | ||||
\(502\) | 14.4413i | 0.644546i | ||||||||
\(503\) | 6.31380 | + | 10.9358i | 0.281518 | + | 0.487604i | 0.971759 | − | 0.235976i | \(-0.0758286\pi\) |
−0.690241 | + | 0.723580i | \(0.742495\pi\) | |||||||
\(504\) | −13.4557 | + | 23.3059i | −0.599363 | + | 1.03813i | ||||
\(505\) | −3.51122 | − | 2.02721i | −0.156247 | − | 0.0902095i | ||||
\(506\) | 25.5058 | 1.13387 | ||||||||
\(507\) | −15.4468 | − | 26.0893i | −0.686019 | − | 1.15866i | ||||
\(508\) | 5.85945 | 0.259971 | ||||||||
\(509\) | −20.9168 | − | 12.0763i | −0.927120 | − | 0.535273i | −0.0412201 | − | 0.999150i | \(-0.513124\pi\) |
−0.885899 | + | 0.463877i | \(0.846458\pi\) | |||||||
\(510\) | −1.60984 | + | 2.78833i | −0.0712851 | + | 0.123469i | ||||
\(511\) | −8.46601 | − | 14.6636i | −0.374514 | − | 0.648678i | ||||
\(512\) | 24.2750i | 1.07281i | ||||||||
\(513\) | 2.56810 | − | 1.48269i | 0.113384 | − | 0.0654625i | ||||
\(514\) | −5.86238 | + | 3.38465i | −0.258578 | + | 0.149290i | ||||
\(515\) | 17.9035i | 0.788921i | ||||||||
\(516\) | −0.676260 | − | 1.17132i | −0.0297707 | − | 0.0515644i | ||||
\(517\) | 6.94402 | − | 12.0274i | 0.305398 | − | 0.528964i | ||||
\(518\) | 33.0999 | + | 19.1103i | 1.45433 | + | 0.839656i | ||||
\(519\) | 10.3982 | 0.456431 | ||||||||
\(520\) | 5.57666 | + | 9.53781i | 0.244553 | + | 0.418261i | ||||
\(521\) | −24.7521 | −1.08441 | −0.542205 | − | 0.840246i | \(-0.682410\pi\) | ||||
−0.542205 | + | 0.840246i | \(0.682410\pi\) | |||||||
\(522\) | −0.0637154 | − | 0.0367861i | −0.00278875 | − | 0.00161008i | ||||
\(523\) | −18.5163 | + | 32.0712i | −0.809662 | + | 1.40238i | 0.103436 | + | 0.994636i | \(0.467016\pi\) |
−0.913098 | + | 0.407739i | \(0.866317\pi\) | |||||||
\(524\) | 2.70732 | + | 4.68922i | 0.118270 | + | 0.204850i | ||||
\(525\) | − | 8.39654i | − | 0.366455i | ||||||
\(526\) | −7.24573 | + | 4.18332i | −0.315929 | + | 0.182402i | ||||
\(527\) | −5.35600 | + | 3.09229i | −0.233311 | + | 0.134702i | ||||
\(528\) | − | 33.9865i | − | 1.47907i | ||||||
\(529\) | 3.92277 | + | 6.79444i | 0.170555 | + | 0.295410i | ||||
\(530\) | 2.70732 | − | 4.68922i | 0.117599 | − | 0.203687i | ||||
\(531\) | 0.362145 | + | 0.209084i | 0.0157157 | + | 0.00907348i | ||||
\(532\) | 4.18348 | 0.181377 | ||||||||
\(533\) | 0.0738376 | + | 13.4559i | 0.00319826 | + | 0.582840i | ||||
\(534\) | −45.9519 | −1.98854 | ||||||||
\(535\) | 7.90842 | + | 4.56593i | 0.341911 | + | 0.197402i | ||||
\(536\) | 9.80545 | − | 16.9835i | 0.423531 | − | 0.733577i | ||||
\(537\) | 21.7264 | + | 37.6312i | 0.937562 | + | 1.62391i | ||||
\(538\) | 1.73438i | 0.0747744i | ||||||||
\(539\) | −27.7332 | + | 16.0118i | −1.19456 | + | 0.689677i | ||||
\(540\) | −0.580172 | + | 0.334963i | −0.0249666 | + | 0.0144145i | ||||
\(541\) | − | 8.38144i | − | 0.360346i | −0.983635 | − | 0.180173i | \(-0.942334\pi\) | ||
0.983635 | − | 0.180173i | \(-0.0576658\pi\) | |||||||
\(542\) | 6.07981 | + | 10.5305i | 0.261150 | + | 0.452326i | ||||
\(543\) | 21.0952 | − | 36.5379i | 0.905281 | − | 1.56799i | ||||
\(544\) | 2.76409 | + | 1.59585i | 0.118509 | + | 0.0684215i | ||||
\(545\) | 7.37605 | 0.315955 | ||||||||
\(546\) | −36.9245 | + | 0.202618i | −1.58022 | + | 0.00867126i | ||||
\(547\) | −22.7842 | −0.974181 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(548\) | −1.68025 | − | 0.970090i | −0.0717765 | − | 0.0414402i | ||||
\(549\) | −4.09843 | + | 7.09870i | −0.174917 | + | 0.302965i | ||||
\(550\) | 3.27597 | + | 5.67414i | 0.139688 | + | 0.241946i | ||||
\(551\) | 0.0560816i | 0.00238915i | ||||||||
\(552\) | −24.0938 | + | 13.9106i | −1.02550 | + | 0.592074i | ||||
\(553\) | −37.3601 | + | 21.5699i | −1.58871 | + | 0.917245i | ||||
\(554\) | − | 21.3735i | − | 0.908071i | ||||||
\(555\) | −10.1500 | − | 17.5803i | −0.430844 | − | 0.746244i | ||||
\(556\) | −0.515915 | + | 0.893592i | −0.0218797 | + | 0.0378967i | ||||
\(557\) | 24.3810 | + | 14.0764i | 1.03306 | + | 0.596435i | 0.917858 | − | 0.396908i | \(-0.129917\pi\) |
0.115197 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(558\) | −16.2572 | −0.688222 | ||||||||
\(559\) | 2.02106 | − | 3.54536i | 0.0854816 | − | 0.149953i | ||||
\(560\) | 9.76645 | 0.412708 | ||||||||
\(561\) | −12.2805 | − | 7.09017i | −0.518484 | − | 0.299347i | ||||
\(562\) | −6.54676 | + | 11.3393i | −0.276159 | + | 0.478321i | ||||
\(563\) | −9.06514 | − | 15.7013i | −0.382050 | − | 0.661731i | 0.609305 | − | 0.792936i | \(-0.291449\pi\) |
−0.991355 | + | 0.131206i | \(0.958115\pi\) | |||||||
\(564\) | 3.08939i | 0.130087i | ||||||||
\(565\) | 6.12789 | − | 3.53794i | 0.257802 | − | 0.148842i | ||||
\(566\) | 1.39258 | − | 0.804007i | 0.0585346 | − | 0.0337950i | ||||
\(567\) | − | 37.3253i | − | 1.56752i | ||||||
\(568\) | −16.5431 | − | 28.6535i | −0.694133 | − | 1.20227i | ||||
\(569\) | 20.2992 | − | 35.1593i | 0.850988 | − | 1.47395i | −0.0293292 | − | 0.999570i | \(-0.509337\pi\) |
0.880317 | − | 0.474385i | \(-0.157330\pi\) | |||||||
\(570\) | 5.58710 | + | 3.22572i | 0.234018 | + | 0.135110i | ||||
\(571\) | −24.7159 | −1.03433 | −0.517164 | − | 0.855886i | \(-0.673012\pi\) | ||||
−0.517164 | + | 0.855886i | \(0.673012\pi\) | |||||||
\(572\) | −8.56677 | + | 5.00891i | −0.358195 | + | 0.209433i | ||||
\(573\) | 63.7551 | 2.66341 | ||||||||
\(574\) | 14.1923 | + | 8.19393i | 0.592375 | + | 0.342008i | ||||
\(575\) | 1.94644 | − | 3.37133i | 0.0811720 | − | 0.140594i | ||||
\(576\) | 10.8124 | + | 18.7276i | 0.450516 | + | 0.780317i | ||||
\(577\) | − | 23.0691i | − | 0.960379i | −0.877165 | − | 0.480189i | \(-0.840568\pi\) | ||
0.877165 | − | 0.480189i | \(-0.159432\pi\) | |||||||
\(578\) | 16.6036 | − | 9.58607i | 0.690617 | − | 0.398728i | ||||
\(579\) | 43.9654 | − | 25.3834i | 1.82714 | − | 1.05490i | ||||
\(580\) | − | 0.0126697i | − | 0.000526079i | ||||||
\(581\) | 21.8327 | + | 37.8153i | 0.905771 | + | 1.56884i | ||||
\(582\) | 17.3068 | − | 29.9763i | 0.717392 | − | 1.24256i | ||||
\(583\) | 20.6525 | + | 11.9237i | 0.855341 | + | 0.493831i | ||||
\(584\) | −14.4116 | −0.596358 | ||||||||
\(585\) | 7.64096 | + | 4.35578i | 0.315915 | + | 0.180089i | ||||
\(586\) | 22.8602 | 0.944345 | ||||||||
\(587\) | −17.6256 | − | 10.1762i | −0.727487 | − | 0.420015i | 0.0900152 | − | 0.995940i | \(-0.471308\pi\) |
−0.817502 | + | 0.575926i | \(0.804642\pi\) | |||||||
\(588\) | 3.56182 | − | 6.16925i | 0.146887 | − | 0.254416i | ||||
\(589\) | 6.19615 | + | 10.7321i | 0.255308 | + | 0.442206i | ||||
\(590\) | − | 0.209084i | − | 0.00860786i | ||||||
\(591\) | 3.42701 | − | 1.97859i | 0.140968 | − | 0.0813881i | ||||
\(592\) | 20.4486 | − | 11.8060i | 0.840432 | − | 0.485223i | ||||
\(593\) | 10.3834i | 0.426395i | 0.977009 | + | 0.213198i | \(0.0683878\pi\) | ||||
−0.977009 | + | 0.213198i | \(0.931612\pi\) | |||||||
\(594\) | 4.28339 | + | 7.41904i | 0.175750 | + | 0.304407i | ||||
\(595\) | 2.03745 | − | 3.52897i | 0.0835273 | − | 0.144674i | ||||
\(596\) | −2.44836 | − | 1.41356i | −0.100289 | − | 0.0579017i | ||||
\(597\) | −59.0652 | −2.41738 | ||||||||
\(598\) | −14.8726 | − | 8.47825i | −0.608187 | − | 0.346701i | ||||
\(599\) | −31.5965 | −1.29100 | −0.645499 | − | 0.763761i | \(-0.723351\pi\) | ||||
−0.645499 | + | 0.763761i | \(0.723351\pi\) | |||||||
\(600\) | −6.18922 | − | 3.57335i | −0.252674 | − | 0.145881i | ||||
\(601\) | 21.9423 | − | 38.0051i | 0.895044 | − | 1.55026i | 0.0612928 | − | 0.998120i | \(-0.480478\pi\) |
0.833751 | − | 0.552141i | \(-0.186189\pi\) | |||||||
\(602\) | −2.48505 | − | 4.30423i | −0.101283 | − | 0.175428i | ||||
\(603\) | − | 15.6115i | − | 0.635750i | ||||||
\(604\) | −2.16962 | + | 1.25263i | −0.0882806 | + | 0.0509688i | ||||
\(605\) | −15.4641 | + | 8.92820i | −0.628705 | + | 0.362983i | ||||
\(606\) | − | 11.5332i | − | 0.468505i | ||||||
\(607\) | −1.08770 | − | 1.88395i | −0.0441484 | − | 0.0764673i | 0.843107 | − | 0.537746i | \(-0.180724\pi\) |
−0.887255 | + | 0.461279i | \(0.847391\pi\) | |||||||
\(608\) | 3.19768 | − | 5.53854i | 0.129683 | − | 0.224617i | ||||
\(609\) | 0.179812 | + | 0.103814i | 0.00728634 | + | 0.00420677i | ||||
\(610\) | 4.09843 | 0.165941 | ||||||||
\(611\) | −8.04707 | + | 4.70504i | −0.325550 | + | 0.190346i | ||||
\(612\) | 1.41465 | 0.0571837 | ||||||||
\(613\) | −12.7843 | − | 7.38100i | −0.516352 | − | 0.298116i | 0.219089 | − | 0.975705i | \(-0.429691\pi\) |
−0.735441 | + | 0.677589i | \(0.763025\pi\) | |||||||
\(614\) | −8.72336 | + | 15.1093i | −0.352046 | + | 0.609762i | ||||
\(615\) | −4.35203 | − | 7.53794i | −0.175491 | − | 0.303959i | ||||
\(616\) | 59.2622i | 2.38774i | ||||||||
\(617\) | 17.5779 | − | 10.1486i | 0.707659 | − | 0.408567i | −0.102535 | − | 0.994729i | \(-0.532695\pi\) |
0.810194 | + | 0.586162i | \(0.199362\pi\) | |||||||
\(618\) | −44.1053 | + | 25.4642i | −1.77418 | + | 1.02432i | ||||
\(619\) | 9.94207i | 0.399605i | 0.979836 | + | 0.199803i | \(0.0640301\pi\) | ||||
−0.979836 | + | 0.199803i | \(0.935970\pi\) | |||||||
\(620\) | −1.39980 | − | 2.42453i | −0.0562175 | − | 0.0973716i | ||||
\(621\) | 2.54500 | − | 4.40807i | 0.102127 | − | 0.176890i | ||||
\(622\) | −2.91641 | − | 1.68379i | −0.116937 | − | 0.0675138i | ||||
\(623\) | 58.1577 | 2.33004 | ||||||||
\(624\) | −11.2973 | + | 19.8178i | −0.452252 | + | 0.793345i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.3080 | − | 9.99276i | −0.691766 | − | 0.399391i | ||||
\(627\) | −14.2069 | + | 24.6070i | −0.567368 | + | 0.982711i | ||||
\(628\) | −2.57221 | − | 4.45519i | −0.102642 | − | 0.177782i | ||||
\(629\) | − | 9.85174i | − | 0.392815i | ||||||
\(630\) | 9.27648 | − | 5.35578i | 0.369584 | − | 0.213379i | ||||
\(631\) | 0.843006 | − | 0.486710i | 0.0335596 | − | 0.0193756i | −0.483126 | − | 0.875551i | \(-0.660499\pi\) |
0.516686 | + | 0.856175i | \(0.327165\pi\) | |||||||
\(632\) | 36.7183i | 1.46058i | ||||||||
\(633\) | 0.391243 | + | 0.677652i | 0.0155505 | + | 0.0269342i | ||||
\(634\) | 1.08903 | − | 1.88625i | 0.0432507 | − | 0.0749124i | ||||
\(635\) | −9.90396 | − | 5.71806i | −0.393027 | − | 0.226914i | ||||
\(636\) | −5.30487 | −0.210352 | ||||||||
\(637\) | 21.4938 | − | 0.117945i | 0.851617 | − | 0.00467314i | ||||
\(638\) | −0.162015 | −0.00641425 | ||||||||
\(639\) | −22.8100 | − | 13.1694i | −0.902350 | − | 0.520972i | ||||
\(640\) | 2.58631 | − | 4.47962i | 0.102233 | − | 0.177072i | ||||
\(641\) | −6.31047 | − | 10.9301i | −0.249249 | − | 0.431711i | 0.714069 | − | 0.700075i | \(-0.246850\pi\) |
−0.963318 | + | 0.268364i | \(0.913517\pi\) | |||||||
\(642\) | 25.9766i | 1.02521i | ||||||||
\(643\) | −8.62599 | + | 4.98022i | −0.340176 | + | 0.196401i | −0.660350 | − | 0.750958i | \(-0.729592\pi\) |
0.320174 | + | 0.947359i | \(0.396259\pi\) | |||||||
\(644\) | 6.21878 | − | 3.59042i | 0.245054 | − | 0.141482i | ||||
\(645\) | 2.63977i | 0.103941i | ||||||||
\(646\) | 1.56546 | + | 2.71146i | 0.0615923 | + | 0.106681i | ||||
\(647\) | −18.1381 | + | 31.4162i | −0.713084 | + | 1.23510i | 0.250610 | + | 0.968088i | \(0.419369\pi\) |
−0.963694 | + | 0.267009i | \(0.913965\pi\) | |||||||
\(648\) | −27.5131 | − | 15.8847i | −1.08081 | − | 0.624009i | ||||
\(649\) | 0.920861 | 0.0361470 | ||||||||
\(650\) | −0.0241312 | − | 4.39758i | −0.000946502 | − | 0.172487i | ||||
\(651\) | 45.8796 | 1.79816 | ||||||||
\(652\) | −3.00898 | − | 1.73723i | −0.117841 | − | 0.0680353i | ||||
\(653\) | −6.87769 | + | 11.9125i | −0.269145 | + | 0.466172i | −0.968641 | − | 0.248464i | \(-0.920074\pi\) |
0.699497 | + | 0.714636i | \(0.253408\pi\) | |||||||
\(654\) | 10.4910 | + | 18.1709i | 0.410231 | + | 0.710540i | ||||
\(655\) | − | 10.5680i | − | 0.412925i | ||||||
\(656\) | 8.76776 | − | 5.06207i | 0.342324 | − | 0.197641i | ||||
\(657\) | −9.93555 | + | 5.73629i | −0.387623 | + | 0.223794i | ||||
\(658\) | 11.3526i | 0.442570i | ||||||||
\(659\) | 1.29092 | + | 2.23593i | 0.0502869 | + | 0.0870995i | 0.890073 | − | 0.455818i | \(-0.150653\pi\) |
−0.839786 | + | 0.542917i | \(0.817320\pi\) | |||||||
\(660\) | 3.20955 | − | 5.55910i | 0.124932 | − | 0.216388i | ||||
\(661\) | −21.5437 | − | 12.4382i | −0.837951 | − | 0.483791i | 0.0186163 | − | 0.999827i | \(-0.494074\pi\) |
−0.856567 | + | 0.516036i | \(0.827407\pi\) | |||||||
\(662\) | −8.81151 | −0.342469 | ||||||||
\(663\) | 4.80406 | + | 8.21643i | 0.186574 | + | 0.319100i | ||||
\(664\) | 37.1656 | 1.44231 | ||||||||
\(665\) | −7.07115 | − | 4.08253i | −0.274207 | − | 0.158314i | ||||
\(666\) | 12.9485 | − | 22.4274i | 0.501743 | − | 0.869045i | ||||
\(667\) | 0.0481312 | + | 0.0833657i | 0.00186365 | + | 0.00322793i | ||||
\(668\) | 5.37460i | 0.207949i | ||||||||
\(669\) | 24.8368 | − | 14.3395i | 0.960246 | − | 0.554398i | ||||
\(670\) | −6.75998 | + | 3.90288i | −0.261161 | + | 0.150781i | ||||
\(671\) | 18.0506i | 0.696834i | ||||||||
\(672\) | −11.8386 | − | 20.5051i | −0.456685 | − | 0.791002i | ||||
\(673\) | 21.6611 | − | 37.5181i | 0.834974 | − | 1.44622i | −0.0590774 | − | 0.998253i | \(-0.518816\pi\) |
0.894052 | − | 0.447964i | \(-0.147851\pi\) | |||||||
\(674\) | 4.60770 | + | 2.66025i | 0.177482 | + | 0.102469i | ||||
\(675\) | 1.30752 | 0.0503264 | ||||||||
\(676\) | 6.66033 | − | 0.0730977i | 0.256167 | − | 0.00281145i | ||||
\(677\) | −41.3625 | −1.58969 | −0.794845 | − | 0.606813i | \(-0.792448\pi\) | ||||
−0.794845 | + | 0.606813i | \(0.792448\pi\) | |||||||
\(678\) | 17.4315 | + | 10.0641i | 0.669451 | + | 0.386508i | ||||
\(679\) | −21.9039 | + | 37.9386i | −0.840594 | + | 1.45595i | ||||
\(680\) | −1.73417 | − | 3.00367i | −0.0665024 | − | 0.115186i | ||||
\(681\) | 17.8003i | 0.682110i | ||||||||
\(682\) | −31.0041 | + | 17.9002i | −1.18721 | + | 0.685435i | ||||
\(683\) | 2.27495 | − | 1.31344i | 0.0870484 | − | 0.0502574i | −0.455844 | − | 0.890060i | \(-0.650662\pi\) |
0.542892 | + | 0.839802i | \(0.317329\pi\) | |||||||
\(684\) | − | 2.83459i | − | 0.108383i | ||||||
\(685\) | 1.89336 | + | 3.27940i | 0.0723416 | + | 0.125299i | ||||
\(686\) | −2.28028 | + | 3.94957i | −0.0870617 | + | 0.150795i | ||||
\(687\) | 29.0865 | + | 16.7931i | 1.10972 | + | 0.640696i | ||||
\(688\) | −3.07045 | −0.117060 | ||||||||
\(689\) | −8.07914 | − | 13.8178i | −0.307791 | − | 0.526417i | ||||
\(690\) | 11.0737 | 0.421569 | ||||||||
\(691\) | −13.2288 | − | 7.63765i | −0.503247 | − | 0.290550i | 0.226806 | − | 0.973940i | \(-0.427172\pi\) |
−0.730053 | + | 0.683390i | \(0.760505\pi\) | |||||||
\(692\) | −1.14218 | + | 1.97831i | −0.0434190 | + | 0.0752039i | ||||
\(693\) | 23.5882 | + | 40.8560i | 0.896043 | + | 1.55199i | ||||
\(694\) | 32.5744i | 1.23651i | ||||||||
\(695\) | 1.74406 | − | 1.00693i | 0.0661558 | − | 0.0381951i | ||||
\(696\) | 0.153046 | − | 0.0883613i | 0.00580120 | − | 0.00334933i | ||||
\(697\) | − | 4.22414i | − | 0.160001i | ||||||
\(698\) | −14.3747 | − | 24.8976i | −0.544089 | − | 0.942390i | ||||
\(699\) | 11.0737 | − | 19.1802i | 0.418846 | − | 0.725463i | ||||
\(700\) | 1.59748 | + | 0.922305i | 0.0603790 | + | 0.0348599i | ||||
\(701\) | 48.1947 | 1.82029 | 0.910144 | − | 0.414292i | \(-0.135971\pi\) | ||||
0.910144 | + | 0.414292i | \(0.135971\pi\) | |||||||
\(702\) | −0.0315519 | − | 5.74991i | −0.00119085 | − | 0.217017i | ||||
\(703\) | −19.7404 | −0.744522 | ||||||||
\(704\) | 41.2406 | + | 23.8103i | 1.55431 | + | 0.897383i | ||||
\(705\) | 3.01484 | − | 5.22186i | 0.113546 | − | 0.196667i | ||||
\(706\) | 3.49884 | + | 6.06016i | 0.131680 | + | 0.228077i | ||||
\(707\) | 14.5967i | 0.548964i | ||||||||
\(708\) | −0.177401 | + | 0.102423i | −0.00666715 | + | 0.00384928i | ||||
\(709\) | −33.6624 | + | 19.4350i | −1.26422 | + | 0.729896i | −0.973887 | − | 0.227031i | \(-0.927098\pi\) |
−0.290329 | + | 0.956927i | \(0.593765\pi\) | |||||||
\(710\) | 13.1694i | 0.494237i | ||||||||
\(711\) | 14.6150 | + | 25.3140i | 0.548107 | + | 0.949349i | ||||
\(712\) | 24.7504 | − | 42.8689i | 0.927560 | − | 1.60658i | ||||
\(713\) | 18.4213 | + | 10.6355i | 0.689882 | + | 0.398304i | ||||
\(714\) | 11.5915 | 0.433801 | ||||||||
\(715\) | 19.3681 | − | 0.106280i | 0.724325 | − | 0.00397464i | ||||
\(716\) | −9.54600 | −0.356751 | ||||||||
\(717\) | −40.2227 | − | 23.2226i | −1.50214 | − | 0.867263i | ||||
\(718\) | 15.0987 | − | 26.1517i | 0.563478 | − | 0.975973i | ||||
\(719\) | 3.30830 | + | 5.73015i | 0.123379 | + | 0.213698i | 0.921098 | − | 0.389331i | \(-0.127294\pi\) |
−0.797719 | + | 0.603029i | \(0.793960\pi\) | |||||||
\(720\) | − | 6.61742i | − | 0.246617i | ||||||
\(721\) | 55.8205 | − | 32.2280i | 2.07887 | − | 1.20023i | ||||
\(722\) | −14.6362 | + | 8.45024i | −0.544705 | + | 0.314485i | ||||
\(723\) | 54.2629i | 2.01806i | ||||||||
\(724\) | 4.63433 | + | 8.02690i | 0.172234 | + | 0.298317i | ||||
\(725\) | −0.0123639 | + | 0.0214150i | −0.000459185 | + | 0.000795332i | ||||
\(726\) | −43.9893 | − | 25.3973i | −1.63260 | − | 0.942581i | ||||
\(727\) | 18.3735 | 0.681435 | 0.340717 | − | 0.940166i | \(-0.389330\pi\) | ||||
0.340717 | + | 0.940166i | \(0.389330\pi\) | |||||||
\(728\) | 19.6990 | − | 34.5562i | 0.730094 | − | 1.28074i | ||||
\(729\) | −16.1420 | −0.597853 | ||||||||
\(730\) | 4.96777 | + | 2.86814i | 0.183866 | + | 0.106155i | ||||
\(731\) | −0.640548 | + | 1.10946i | −0.0236915 | + | 0.0410349i | ||||
\(732\) | −2.00767 | − | 3.47739i | −0.0742057 | − | 0.128528i | ||||
\(733\) | − | 0.791131i | − | 0.0292211i | −0.999893 | − | 0.0146105i | \(-0.995349\pi\) | ||
0.999893 | − | 0.0146105i | \(-0.00465084\pi\) | |||||||
\(734\) | −27.5198 | + | 15.8886i | −1.01578 | + | 0.586458i | ||||
\(735\) | −12.0408 | + | 6.95174i | −0.444130 | + | 0.256419i | ||||
\(736\) | − | 10.9774i | − | 0.404634i | ||||||
\(737\) | −17.1893 | − | 29.7727i | −0.633175 | − | 1.09669i | ||||
\(738\) | 5.55193 | − | 9.61623i | 0.204369 | − | 0.353978i | ||||
\(739\) | −27.0073 | − | 15.5926i | −0.993478 | − | 0.573585i | −0.0871658 | − | 0.996194i | \(-0.527781\pi\) |
−0.906312 | + | 0.422609i | \(0.861114\pi\) | |||||||
\(740\) | 4.45965 | 0.163940 | ||||||||
\(741\) | 16.4636 | − | 9.62612i | 0.604806 | − | 0.353624i | ||||
\(742\) | −19.4938 | −0.715639 | ||||||||
\(743\) | 4.81773 | + | 2.78152i | 0.176745 | + | 0.102044i | 0.585763 | − | 0.810483i | \(-0.300795\pi\) |
−0.409017 | + | 0.912527i | \(0.634128\pi\) | |||||||
\(744\) | 19.5251 | − | 33.8185i | 0.715826 | − | 1.23985i | ||||
\(745\) | 2.75890 | + | 4.77855i | 0.101078 | + | 0.175073i | ||||
\(746\) | − | 16.1053i | − | 0.589658i | ||||||
\(747\) | 25.6224 | − | 14.7931i | 0.937474 | − | 0.541251i | ||||
\(748\) | 2.69787 | − | 1.55762i | 0.0986439 | − | 0.0569521i | ||||
\(749\) | − | 32.8765i | − | 1.20128i | ||||||
\(750\) | 1.42231 | + | 2.46350i | 0.0519352 | + | 0.0899545i | ||||
\(751\) | −17.6048 | + | 30.4925i | −0.642410 | + | 1.11269i | 0.342483 | + | 0.939524i | \(0.388732\pi\) |
−0.984893 | + | 0.173163i | \(0.944601\pi\) | |||||||
\(752\) | 6.07381 | + | 3.50672i | 0.221489 | + | 0.127877i | ||||
\(753\) | −27.6142 | −1.00632 | ||||||||
\(754\) | 0.0944723 | + | 0.0538546i | 0.00344048 | + | 0.00196127i | ||||
\(755\) | 4.88961 | 0.177951 | ||||||||
\(756\) | 2.08873 | + | 1.20593i | 0.0759665 | + | 0.0438593i | ||||
\(757\) | −25.0223 | + | 43.3399i | −0.909451 | + | 1.57522i | −0.0946237 | + | 0.995513i | \(0.530165\pi\) |
−0.814828 | + | 0.579703i | \(0.803169\pi\) | |||||||
\(758\) | 15.8545 | + | 27.4609i | 0.575863 | + | 0.997424i | ||||
\(759\) | 48.7715i | 1.77029i | ||||||||
\(760\) | −6.01859 | + | 3.47484i | −0.218317 | + | 0.126046i | ||||
\(761\) | 38.8161 | − | 22.4105i | 1.40708 | − | 0.812379i | 0.411975 | − | 0.911195i | \(-0.364839\pi\) |
0.995106 | + | 0.0988165i | \(0.0315057\pi\) | |||||||
\(762\) | − | 32.5313i | − | 1.17848i | ||||||
\(763\) | −13.2776 | − | 22.9975i | −0.480682 | − | 0.832566i | ||||
\(764\) | −7.00307 | + | 12.1297i | −0.253362 | + | 0.438836i | ||||
\(765\) | −2.39111 | − | 1.38051i | −0.0864508 | − | 0.0499124i | ||||
\(766\) | 11.7092 | 0.423072 | ||||||||
\(767\) | −0.536961 | − | 0.306098i | −0.0193885 | − | 0.0110526i | ||||
\(768\) | −26.6361 | −0.961148 | ||||||||
\(769\) | −34.0897 | − | 19.6817i | −1.22930 | − | 0.709739i | −0.262420 | − | 0.964954i | \(-0.584521\pi\) |
−0.966884 | + | 0.255215i | \(0.917854\pi\) | |||||||
\(770\) | 11.7941 | − | 20.4280i | 0.425031 | − | 0.736175i | ||||
\(771\) | −6.47201 | − | 11.2099i | −0.233084 | − | 0.403713i | ||||
\(772\) | 11.1528i | 0.401399i | ||||||||
\(773\) | −42.2452 | + | 24.3902i | −1.51945 | + | 0.877256i | −0.519715 | + | 0.854340i | \(0.673962\pi\) |
−0.999737 | + | 0.0229167i | \(0.992705\pi\) | |||||||
\(774\) | −2.91641 | + | 1.68379i | −0.104828 | + | 0.0605225i | ||||
\(775\) | 5.46410i | 0.196276i | ||||||||
\(776\) | 18.6434 | + | 32.2914i | 0.669260 | + | 1.15919i | ||||
\(777\) | −36.5420 | + | 63.2926i | −1.31094 | + | 2.27061i | ||||
\(778\) | −5.94822 | − | 3.43420i | −0.213254 | − | 0.123122i | ||||
\(779\) | −8.46410 | −0.303258 | ||||||||
\(780\) | −3.71938 | + | 2.17469i | −0.133175 | + | 0.0778662i | ||||
\(781\) | −58.0013 | −2.07545 | ||||||||
\(782\) | 4.65415 | + | 2.68707i | 0.166432 | + | 0.0960895i | ||||
\(783\) | −0.0161661 | + | 0.0280005i | −0.000577728 | + | 0.00100066i | ||||
\(784\) | −8.08592 | − | 14.0052i | −0.288783 | − | 0.500187i | ||||
\(785\) | 10.0405i | 0.358363i | ||||||||
\(786\) | 26.0342 | − | 15.0309i | 0.928611 | − | 0.536134i | ||||
\(787\) | 34.5204 | − | 19.9304i | 1.23052 | − | 0.710442i | 0.263382 | − | 0.964692i | \(-0.415162\pi\) |
0.967139 | + | 0.254250i | \(0.0818286\pi\) | |||||||
\(788\) | 0.869338i | 0.0309689i | ||||||||
\(789\) | −7.99922 | − | 13.8551i | −0.284780 | − | 0.493253i | ||||
\(790\) | 7.30752 | − | 12.6570i | 0.259990 | − | 0.450316i | ||||
\(791\) | −22.0616 | − | 12.7373i | −0.784420 | − | 0.452885i | ||||
\(792\) | 40.1541 | 1.42682 | ||||||||
\(793\) | 6.00008 | − | 10.5254i | 0.213069 | − | 0.373768i | ||||
\(794\) | −20.4490 | −0.725709 | ||||||||
\(795\) | 8.96658 | + | 5.17686i | 0.318012 | + | 0.183604i | ||||
\(796\) | 6.48793 | − | 11.2374i | 0.229958 | − | 0.398300i | ||||
\(797\) | 13.1059 | + | 22.7001i | 0.464235 | + | 0.804079i | 0.999167 | − | 0.0408167i | \(-0.0129960\pi\) |
−0.534932 | + | 0.844895i | \(0.679663\pi\) | |||||||
\(798\) | − | 23.2264i | − | 0.822206i | ||||||
\(799\) | 2.53420 | − | 1.46312i | 0.0896537 | − | 0.0517616i | ||||
\(800\) | 2.44209 | − | 1.40994i | 0.0863409 | − | 0.0498490i | ||||
\(801\) | − | 39.4057i | − | 1.39233i | ||||||
\(802\) | 8.46343 | + | 14.6591i | 0.298854 | + | 0.517630i | ||||
\(803\) | −12.6321 | + | 21.8794i | −0.445775 | + | 0.772106i | ||||
\(804\) | 6.62293 | + | 3.82375i | 0.233573 | + | 0.134853i | ||||
\(805\) | −14.0151 | −0.493968 | ||||||||
\(806\) | 24.0288 | − | 0.131855i | 0.846379 | − | 0.00464440i | ||||
\(807\) | −3.31643 | −0.116744 | ||||||||
\(808\) | 10.7594 | + | 6.21196i | 0.378515 | + | 0.218536i | ||||
\(809\) | −11.1068 | + | 19.2376i | −0.390495 | + | 0.676357i | −0.992515 | − | 0.122124i | \(-0.961029\pi\) |
0.602020 | + | 0.798481i | \(0.294363\pi\) | |||||||
\(810\) | 6.32260 | + | 10.9511i | 0.222153 | + | 0.384781i | ||||
\(811\) | − | 19.0950i | − | 0.670515i | −0.942127 | − | 0.335257i | \(-0.891177\pi\) | ||
0.942127 | − | 0.335257i | \(-0.108823\pi\) | |||||||
\(812\) | −0.0395023 | + | 0.0228066i | −0.00138626 | + | 0.000800356i | ||||
\(813\) | −20.1362 | + | 11.6256i | −0.706207 | + | 0.407729i | ||||
\(814\) | − | 57.0284i | − | 1.99885i | ||||||
\(815\) | 3.39062 | + | 5.87273i | 0.118768 | + | 0.205713i | ||||
\(816\) | 3.58052 | − | 6.20164i | 0.125343 | − | 0.217101i | ||||
\(817\) | 2.22308 | + | 1.28349i | 0.0777757 | + | 0.0449038i | ||||
\(818\) | −35.8894 | −1.25484 | ||||||||
\(819\) | −0.173754 | − | 31.6643i | −0.00607145 | − | 1.10644i | ||||
\(820\) | 1.91217 | 0.0667758 | ||||||||
\(821\) | −29.5820 | − | 17.0792i | −1.03242 | − | 0.596068i | −0.114743 | − | 0.993395i | \(-0.536604\pi\) |
−0.917677 | + | 0.397327i | \(0.869938\pi\) | |||||||
\(822\) | −5.38588 | + | 9.32861i | −0.187854 | + | 0.325373i | ||||
\(823\) | 2.03970 | + | 3.53286i | 0.0710995 | + | 0.123148i | 0.899383 | − | 0.437161i | \(-0.144016\pi\) |
−0.828284 | + | 0.560309i | \(0.810683\pi\) | |||||||
\(824\) | − | 54.8616i | − | 1.91119i | ||||||
\(825\) | −10.8499 | + | 6.26420i | −0.377745 | + | 0.218091i | ||||
\(826\) | −0.651896 | + | 0.376372i | −0.0226824 | + | 0.0130957i | ||||
\(827\) | − | 54.8780i | − | 1.90830i | −0.299337 | − | 0.954148i | \(-0.596765\pi\) | ||
0.299337 | − | 0.954148i | \(-0.403235\pi\) | |||||||
\(828\) | −2.43275 | − | 4.21364i | −0.0845438 | − | 0.146434i | ||||
\(829\) | 4.07475 | − | 7.05768i | 0.141522 | − | 0.245123i | −0.786548 | − | 0.617529i | \(-0.788134\pi\) |
0.928070 | + | 0.372406i | \(0.121467\pi\) | |||||||
\(830\) | −12.8112 | − | 7.39654i | −0.444683 | − | 0.256738i | ||||
\(831\) | 40.8697 | 1.41775 | ||||||||
\(832\) | −16.1330 | − | 27.5925i | −0.559313 | − | 0.956597i | ||||
\(833\) | −6.74745 | −0.233785 | ||||||||
\(834\) | 4.96116 | + | 2.86433i | 0.171791 | + | 0.0991836i | ||||
\(835\) | 5.24490 | − | 9.08444i | 0.181507 | − | 0.314380i | ||||
\(836\) | −3.12107 | − | 5.40585i | −0.107944 | − | 0.186965i | ||||
\(837\) | 7.14441i | 0.246947i | ||||||||
\(838\) | −7.36008 | + | 4.24935i | −0.254250 | + | 0.146791i | ||||
\(839\) | −18.9543 | + | 10.9433i | −0.654374 | + | 0.377803i | −0.790130 | − | 0.612939i | \(-0.789987\pi\) |
0.135756 | + | 0.990742i | \(0.456654\pi\) | |||||||
\(840\) | 25.7295i | 0.887752i | ||||||||
\(841\) | 14.4997 | + | 25.1142i | 0.499989 | + | 0.866007i | ||||
\(842\) | 4.34285 | − | 7.52204i | 0.149664 | − | 0.259226i | ||||
\(843\) | −21.6827 | − | 12.5185i | −0.746792 | − | 0.431160i | ||||
\(844\) | −0.171902 | −0.00591710 | ||||||||
\(845\) | −11.3290 | − | 6.37605i | −0.389729 | − | 0.219343i | ||||
\(846\) | 7.69213 | 0.264461 | ||||||||
\(847\) | 55.6738 | + | 32.1433i | 1.91297 | + | 1.10446i | ||||
\(848\) | −6.02147 | + | 10.4295i | −0.206778 | + | 0.358150i | ||||
\(849\) | 1.53740 | + | 2.66285i | 0.0527633 | + | 0.0913888i | ||||
\(850\) | 1.38051i | 0.0473511i | ||||||||
\(851\) | −29.3442 | + | 16.9419i | −1.00591 | + | 0.580761i | ||||
\(852\) | 11.1738 | − | 6.45118i | 0.382807 | − | 0.221014i | ||||
\(853\) | − | 19.2240i | − | 0.658217i | −0.944292 | − | 0.329108i | \(-0.893252\pi\) | ||
0.944292 | − | 0.329108i | \(-0.106748\pi\) | |||||||
\(854\) | −7.37758 | − | 12.7783i | −0.252456 | − | 0.437266i | ||||
\(855\) | −2.76619 | + | 4.79118i | −0.0946016 | + | 0.163855i | ||||
\(856\) | −24.2337 | − | 13.9914i | −0.828292 | − | 0.478215i | ||||
\(857\) | 27.8197 | 0.950302 | 0.475151 | − | 0.879904i | \(-0.342393\pi\) | ||||
0.475151 | + | 0.879904i | \(0.342393\pi\) | |||||||
\(858\) | 27.8091 | + | 47.5622i | 0.949388 | + | 1.62375i | ||||
\(859\) | 45.7355 | 1.56048 | 0.780238 | − | 0.625482i | \(-0.215098\pi\) | ||||
0.780238 | + | 0.625482i | \(0.215098\pi\) | |||||||
\(860\) | −0.502227 | − | 0.289961i | −0.0171258 | − | 0.00988758i | ||||
\(861\) | −15.6682 | + | 27.1381i | −0.533970 | + | 0.924862i | ||||
\(862\) | 18.4260 | + | 31.9148i | 0.627593 | + | 1.08702i | ||||
\(863\) | − | 54.8186i | − | 1.86605i | −0.359814 | − | 0.933024i | \(-0.617160\pi\) | ||
0.359814 | − | 0.933024i | \(-0.382840\pi\) | |||||||
\(864\) | 3.19308 | − | 1.84352i | 0.108631 | − | 0.0627180i | ||||
\(865\) | 3.86113 | − | 2.22923i | 0.131283 | − | 0.0757960i | ||||
\(866\) | 1.46378i | 0.0497413i | ||||||||
\(867\) | 18.3302 | + | 31.7488i | 0.622526 | + | 1.07825i | ||||
\(868\) | −5.03957 | + | 8.72879i | −0.171054 | + | 0.296274i | ||||
\(869\) | 55.7447 | + | 32.1842i | 1.89101 | + | 1.09177i | ||||
\(870\) | −0.0703412 | −0.00238479 | ||||||||
\(871\) | 0.126618 | + | 23.0745i | 0.00429030 | + | 0.781849i | ||||
\(872\) | −22.6024 | −0.765415 | ||||||||
\(873\) | 25.7060 | + | 14.8413i | 0.870015 | + | 0.502304i | ||||
\(874\) | 5.38421 | − | 9.32572i | 0.182124 | − | 0.315447i | ||||
\(875\) | −1.80010 | − | 3.11786i | −0.0608544 | − | 0.105403i | ||||
\(876\) | − | 5.61999i | − | 0.189882i | ||||||
\(877\) | 23.7113 | − | 13.6897i | 0.800673 | − | 0.462269i | −0.0430336 | − | 0.999074i | \(-0.513702\pi\) |
0.843706 | + | 0.536805i | \(0.180369\pi\) | |||||||
\(878\) | −17.4858 | + | 10.0954i | −0.590116 | + | 0.340704i | ||||
\(879\) | 43.7125i | 1.47439i | ||||||||
\(880\) | −7.28621 | − | 12.6201i | −0.245618 | − | 0.425423i | ||||
\(881\) | −17.2213 | + | 29.8282i | −0.580200 | + | 1.00494i | 0.415255 | + | 0.909705i | \(0.363692\pi\) |
−0.995455 | + | 0.0952310i | \(0.969641\pi\) | |||||||
\(882\) | −15.3605 | − | 8.86841i | −0.517216 | − | 0.298615i | ||||
\(883\) | 17.3592 | 0.584183 | 0.292092 | − | 0.956390i | \(-0.405649\pi\) | ||||
0.292092 | + | 0.956390i | \(0.405649\pi\) | |||||||
\(884\) | −2.09091 | + | 0.0114736i | −0.0703248 | + | 0.000385899i | ||||
\(885\) | 0.399804 | 0.0134393 | ||||||||
\(886\) | 4.81610 | + | 2.78058i | 0.161800 | + | 0.0934153i | ||||
\(887\) | 15.5714 | − | 26.9704i | 0.522835 | − | 0.905577i | −0.476812 | − | 0.879005i | \(-0.658208\pi\) |
0.999647 | − | 0.0265716i | \(-0.00845898\pi\) | |||||||
\(888\) | 31.1026 | + | 53.8714i | 1.04374 | + | 1.80780i | ||||
\(889\) | 41.1722i | 1.38087i | ||||||||
\(890\) | −17.0632 | + | 9.85143i | −0.571959 | + | 0.330221i | ||||
\(891\) | −48.2313 | + | 27.8464i | −1.61581 | + | 0.932888i | ||||
\(892\) | 6.30042i | 0.210954i | ||||||||
\(893\) | −2.93173 | − | 5.07790i | −0.0981065 | − | 0.169925i | ||||
\(894\) | −7.84799 | + | 13.5931i | −0.262476 | + | 0.454622i | ||||
\(895\) | 16.1352 | + | 9.31564i | 0.539339 | + | 0.311388i | ||||
\(896\) | −18.6224 | −0.622132 | ||||||||
\(897\) | 16.2118 | − | 28.4390i | 0.541298 | − | 0.949550i | ||||
\(898\) | 16.8953 | 0.563804 | ||||||||
\(899\) | −0.117014 | − | 0.0675578i | −0.00390262 | − | 0.00225318i | ||||
\(900\) | 0.624924 | − | 1.08240i | 0.0208308 | − | 0.0360800i | ||||
\(901\) | 2.51236 | + | 4.35154i | 0.0836990 | + | 0.144971i | ||||
\(902\) | − | 24.4521i | − | 0.814167i | ||||||
\(903\) | 8.23042 | − | 4.75184i | 0.273891 | − | 0.158131i | ||||
\(904\) | −18.7777 | + | 10.8413i | −0.624536 | + | 0.360576i | ||||
\(905\) | − | 18.0900i | − | 0.601332i | ||||||
\(906\) | 6.95452 | + | 12.0456i | 0.231048 | + | 0.400188i | ||||
\(907\) | 8.80284 | − | 15.2470i | 0.292294 | − | 0.506267i | −0.682058 | − | 0.731298i | \(-0.738915\pi\) |
0.974352 | + | 0.225031i | \(0.0722482\pi\) | |||||||
\(908\) | −3.38659 | − | 1.95525i | −0.112388 | − | 0.0648872i | ||||
\(909\) | 9.89022 | 0.328038 | ||||||||
\(910\) | −13.6676 | + | 7.99131i | −0.453076 | + | 0.264909i | ||||
\(911\) | 50.0232 | 1.65734 | 0.828671 | − | 0.559737i | \(-0.189098\pi\) | ||||
0.828671 | + | 0.559737i | \(0.189098\pi\) | |||||||
\(912\) | −12.4265 | − | 7.17445i | −0.411483 | − | 0.237570i | ||||
\(913\) | 32.5763 | − | 56.4238i | 1.07812 | − | 1.86735i | ||||
\(914\) | 24.4636 | + | 42.3722i | 0.809184 | + | 1.40155i | ||||
\(915\) | 7.83690i | 0.259080i | ||||||||
\(916\) | −6.38992 | + | 3.68922i | −0.211129 | + | 0.121895i | ||||
\(917\) | −32.9495 | + | 19.0234i | −1.08809 | + | 0.628207i | ||||
\(918\) | 1.80504i | 0.0595752i | ||||||||
\(919\) | 3.80778 | + | 6.59527i | 0.125607 | + | 0.217558i | 0.921970 | − | 0.387261i | \(-0.126579\pi\) |
−0.796363 | + | 0.604819i | \(0.793245\pi\) | |||||||
\(920\) | −5.96446 | + | 10.3307i | −0.196642 | + | 0.340595i | ||||
\(921\) | −28.8915 | − | 16.6805i | −0.952008 | − | 0.549642i | ||||
\(922\) | 9.19522 | 0.302828 | ||||||||
\(923\) | 33.8209 | + | 19.2799i | 1.11323 | + | 0.634604i | ||||
\(924\) | −23.1100 | −0.760264 | ||||||||
\(925\) | −7.53794 | − | 4.35203i | −0.247846 | − | 0.143094i | ||||
\(926\) | −14.2113 | + | 24.6146i | −0.467011 | + | 0.808887i | ||||
\(927\) | −21.8366 | − | 37.8222i | −0.717209 | − | 1.24224i | ||||
\(928\) | 0.0697297i | 0.00228899i | ||||||||
\(929\) | 12.2317 | − | 7.06196i | 0.401308 | − | 0.231695i | −0.285740 | − | 0.958307i | \(-0.592239\pi\) |
0.687048 | + | 0.726612i | \(0.258906\pi\) | |||||||
\(930\) | −13.4608 | + | 7.77162i | −0.441398 | + | 0.254841i | ||||
\(931\) | 13.5202i | 0.443106i | ||||||||
\(932\) | 2.43275 | + | 4.21364i | 0.0796873 | + | 0.138022i | ||||
\(933\) | 3.21969 | − | 5.57666i | 0.105408 | − | 0.182572i | ||||
\(934\) | 23.9033 | + | 13.8006i | 0.782140 | + | 0.451569i | ||||
\(935\) | −6.08012 | −0.198841 | ||||||||
\(936\) | −23.4142 | − | 13.3474i | −0.765316 | − | 0.436274i | ||||
\(937\) | −23.9317 | −0.781815 | −0.390908 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390908 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(938\) | 24.3373 | + | 14.0511i | 0.794640 | + | 0.458786i | ||||
\(939\) | 19.1078 | − | 33.0958i | 0.623561 | − | 1.08004i | ||||
\(940\) | 0.662321 | + | 1.14717i | 0.0216025 | + | 0.0374167i | ||||
\(941\) | 25.3591i | 0.826683i | 0.910576 | + | 0.413342i | \(0.135638\pi\) | ||||
−0.910576 | + | 0.413342i | \(0.864362\pi\) | |||||||
\(942\) | −24.7349 | + | 14.2807i | −0.805908 | + | 0.465291i | ||||
\(943\) | −12.5820 | + | 7.26420i | −0.409725 | + | 0.236555i | ||||
\(944\) | 0.465033i | 0.0151355i | ||||||||
\(945\) | −2.35366 | − | 4.07666i | −0.0765646 | − | 0.132614i | ||||
\(946\) | −3.70792 | + | 6.42231i | −0.120555 | + | 0.208807i | ||||
\(947\) | −35.8727 | − | 20.7111i | −1.16571 | − | 0.673021i | −0.213042 | − | 0.977043i | \(-0.568337\pi\) |
−0.952665 | + | 0.304022i | \(0.901670\pi\) | |||||||
\(948\) | −14.3187 | −0.465051 | ||||||||
\(949\) | 14.6386 | − | 8.55906i | 0.475190 | − | 0.277839i | ||||
\(950\) | 2.76619 | 0.0897470 | ||||||||
\(951\) | 3.60682 | + | 2.08240i | 0.116959 | + | 0.0675264i | ||||
\(952\) | −6.24335 | + | 10.8138i | −0.202348 | + | 0.350477i | ||||
\(953\) | 12.1513 | + | 21.0466i | 0.393619 | + | 0.681767i | 0.992924 | − | 0.118753i | \(-0.0378897\pi\) |
−0.599305 | + | 0.800521i | \(0.704556\pi\) | |||||||
\(954\) | 13.2083i | 0.427636i | ||||||||
\(955\) | 23.6740 | − | 13.6682i | 0.766071 | − | 0.442291i | ||||
\(956\) | 8.83639 | − | 5.10169i | 0.285789 | − | 0.165001i | ||||
\(957\) | − | 0.309801i | − | 0.0100144i | ||||||
\(958\) | −12.5901 | − | 21.8067i | −0.406768 | − | 0.704543i | ||||
\(959\) | 6.81647 | − | 11.8065i | 0.220115 | − | 0.381251i | ||||
\(960\) | 17.9052 | + | 10.3375i | 0.577886 | + | 0.333643i | ||||
\(961\) | 1.14359 | 0.0368901 | ||||||||
\(962\) | −18.9565 | + | 33.2537i | −0.611182 | + | 1.07214i | ||||
\(963\) | −22.2760 | −0.717834 | ||||||||
\(964\) | −10.3238 | − | 5.96043i | −0.332506 | − | 0.191972i | ||||
\(965\) | 10.8837 | − | 18.8511i | 0.350358 | − | 0.606839i | ||||
\(966\) | −19.9338 | − | 34.5263i | −0.641358 | − | 1.11086i | ||||
\(967\) | − | 23.6784i | − | 0.761445i | −0.924689 | − | 0.380722i | \(-0.875675\pi\) | ||
0.924689 | − | 0.380722i | \(-0.124325\pi\) | |||||||
\(968\) | 47.3866 | − | 27.3587i | 1.52306 | − | 0.879341i | ||||
\(969\) | −5.18477 | + | 2.99343i | −0.166559 | + | 0.0961627i | ||||
\(970\) | − | 14.8413i | − | 0.476527i | ||||||
\(971\) | 8.48609 | + | 14.6983i | 0.272332 | + | 0.471692i | 0.969458 | − | 0.245256i | \(-0.0788719\pi\) |
−0.697127 | + | 0.716948i | \(0.745539\pi\) | |||||||
\(972\) | 5.18953 | − | 8.98852i | 0.166454 | − | 0.288307i | ||||
\(973\) | −6.27895 | − | 3.62515i | −0.201294 | − | 0.116217i | ||||
\(974\) | −3.70303 | −0.118653 | ||||||||
\(975\) | 8.40891 | − | 0.0461428i | 0.269301 | − | 0.00147775i | ||||
\(976\) | −9.11550 | −0.291780 | ||||||||
\(977\) | 21.6501 | + | 12.4997i | 0.692649 | + | 0.399901i | 0.804604 | − | 0.593812i | \(-0.202378\pi\) |
−0.111955 | + | 0.993713i | \(0.535711\pi\) | |||||||
\(978\) | −9.64500 | + | 16.7056i | −0.308413 | + | 0.534187i | ||||
\(979\) | −43.3883 | − | 75.1507i | −1.38669 | − | 2.40183i | ||||
\(980\) | − | 3.05441i | − | 0.0975696i | ||||||
\(981\) | −15.5824 | + | 8.99648i | −0.497506 | + | 0.287235i | ||||
\(982\) | 11.2684 | − | 6.50582i | 0.359589 | − | 0.207609i | ||||
\(983\) | − | 27.3418i | − | 0.872068i | −0.899930 | − | 0.436034i | \(-0.856383\pi\) | ||
0.899930 | − | 0.436034i | \(-0.143617\pi\) | |||||||
\(984\) | 13.3359 | + | 23.0985i | 0.425134 | + | 0.736353i | ||||
\(985\) | 0.848360 | − | 1.46940i | 0.0270310 | − | 0.0468191i | ||||
\(986\) | −0.0295635 | − | 0.0170685i | −0.000941495 | − | 0.000543573i | ||||
\(987\) | −21.7080 | −0.690975 | ||||||||
\(988\) | 0.0229901 | + | 4.18964i | 0.000731414 | + | 0.133290i | ||||
\(989\) | 4.40617 | 0.140108 | ||||||||
\(990\) | −13.8413 | − | 7.99131i | −0.439907 | − | 0.253980i | ||||
\(991\) | −8.03802 | + | 13.9223i | −0.255336 | + | 0.442255i | −0.964987 | − | 0.262299i | \(-0.915519\pi\) |
0.709651 | + | 0.704554i | \(0.248853\pi\) | |||||||
\(992\) | 7.70406 | + | 13.3438i | 0.244604 | + | 0.423667i | ||||
\(993\) | − | 16.8491i | − | 0.534690i | ||||||
\(994\) | 41.0602 | − | 23.7061i | 1.30235 | − | 0.751913i | ||||
\(995\) | −21.9325 | + | 12.6627i | −0.695307 | + | 0.401436i | ||||
\(996\) | 14.4932i | 0.459234i | ||||||||
\(997\) | 17.2806 | + | 29.9309i | 0.547282 | + | 0.947920i | 0.998459 | + | 0.0554858i | \(0.0176708\pi\) |
−0.451178 | + | 0.892434i | \(0.648996\pi\) | |||||||
\(998\) | 20.6824 | − | 35.8230i | 0.654691 | − | 1.13396i | ||||
\(999\) | −9.85600 | − | 5.69036i | −0.311830 | − | 0.180035i |
(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 | 65.2.m.a.56.3 | yes | 8 | |
3.2 | odd | 2 | 585.2.bu.c.316.2 | 8 | |||
4.3 | odd | 2 | 1040.2.da.b.641.4 | 8 | |||
5.2 | odd | 4 | 325.2.m.b.199.2 | 8 | |||
5.3 | odd | 4 | 325.2.m.c.199.3 | 8 | |||
5.4 | even | 2 | 325.2.n.d.251.2 | 8 | |||
13.2 | odd | 12 | 845.2.e.n.146.3 | 8 | |||
13.3 | even | 3 | 845.2.m.g.361.2 | 8 | |||
13.4 | even | 6 | 845.2.c.g.506.6 | 8 | |||
13.5 | odd | 4 | 845.2.e.n.191.3 | 8 | |||
13.6 | odd | 12 | 845.2.a.l.1.2 | 4 | |||
13.7 | odd | 12 | 845.2.a.m.1.3 | 4 | |||
13.8 | odd | 4 | 845.2.e.m.191.2 | 8 | |||
13.9 | even | 3 | 845.2.c.g.506.3 | 8 | |||
13.10 | even | 6 | inner | 65.2.m.a.36.3 | ✓ | 8 | |
13.11 | odd | 12 | 845.2.e.m.146.2 | 8 | |||
13.12 | even | 2 | 845.2.m.g.316.2 | 8 | |||
39.20 | even | 12 | 7605.2.a.cf.1.2 | 4 | |||
39.23 | odd | 6 | 585.2.bu.c.361.2 | 8 | |||
39.32 | even | 12 | 7605.2.a.cj.1.3 | 4 | |||
52.23 | odd | 6 | 1040.2.da.b.881.4 | 8 | |||
65.19 | odd | 12 | 4225.2.a.bl.1.3 | 4 | |||
65.23 | odd | 12 | 325.2.m.b.49.2 | 8 | |||
65.49 | even | 6 | 325.2.n.d.101.2 | 8 | |||
65.59 | odd | 12 | 4225.2.a.bi.1.2 | 4 | |||
65.62 | odd | 12 | 325.2.m.c.49.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.3 | ✓ | 8 | 13.10 | even | 6 | inner | |
65.2.m.a.56.3 | yes | 8 | 1.1 | even | 1 | trivial | |
325.2.m.b.49.2 | 8 | 65.23 | odd | 12 | |||
325.2.m.b.199.2 | 8 | 5.2 | odd | 4 | |||
325.2.m.c.49.3 | 8 | 65.62 | odd | 12 | |||
325.2.m.c.199.3 | 8 | 5.3 | odd | 4 | |||
325.2.n.d.101.2 | 8 | 65.49 | even | 6 | |||
325.2.n.d.251.2 | 8 | 5.4 | even | 2 | |||
585.2.bu.c.316.2 | 8 | 3.2 | odd | 2 | |||
585.2.bu.c.361.2 | 8 | 39.23 | odd | 6 | |||
845.2.a.l.1.2 | 4 | 13.6 | odd | 12 | |||
845.2.a.m.1.3 | 4 | 13.7 | odd | 12 | |||
845.2.c.g.506.3 | 8 | 13.9 | even | 3 | |||
845.2.c.g.506.6 | 8 | 13.4 | even | 6 | |||
845.2.e.m.146.2 | 8 | 13.11 | odd | 12 | |||
845.2.e.m.191.2 | 8 | 13.8 | odd | 4 | |||
845.2.e.n.146.3 | 8 | 13.2 | odd | 12 | |||
845.2.e.n.191.3 | 8 | 13.5 | odd | 4 | |||
845.2.m.g.316.2 | 8 | 13.12 | even | 2 | |||
845.2.m.g.361.2 | 8 | 13.3 | even | 3 | |||
1040.2.da.b.641.4 | 8 | 4.3 | odd | 2 | |||
1040.2.da.b.881.4 | 8 | 52.23 | odd | 6 | |||
4225.2.a.bi.1.2 | 4 | 65.59 | odd | 12 | |||
4225.2.a.bl.1.3 | 4 | 65.19 | odd | 12 | |||
7605.2.a.cf.1.2 | 4 | 39.20 | even | 12 | |||
7605.2.a.cj.1.3 | 4 | 39.32 | even | 12 |