Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(146,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("845.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.e (of order \(3\), degree \(2\), not 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.3 | ||
Root | \(1.40994 - 0.109843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.146 |
Dual form | 845.2.e.n.191.3 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.609843 | + | 1.05628i | 0.431224 | + | 0.746903i | 0.996979 | − | 0.0776710i | \(-0.0247484\pi\) |
−0.565755 | + | 0.824574i | \(0.691415\pi\) | |||||||
\(3\) | −1.16612 | − | 2.01978i | −0.673262 | − | 1.16612i | −0.976974 | − | 0.213359i | \(-0.931559\pi\) |
0.303712 | − | 0.952764i | \(-0.401774\pi\) | |||||||
\(4\) | 0.256182 | − | 0.443720i | 0.128091 | − | 0.221860i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.42231 | − | 2.46350i | 0.580654 | − | 1.00572i | ||||
\(7\) | 1.80010 | − | 3.11786i | 0.680373 | − | 1.17844i | −0.294494 | − | 0.955653i | \(-0.595151\pi\) |
0.974867 | − | 0.222787i | \(-0.0715156\pi\) | |||||||
\(8\) | 3.06430 | 1.08339 | ||||||||
\(9\) | −1.21969 | + | 2.11256i | −0.406562 | + | 0.704187i | ||||
\(10\) | 0.609843 | + | 1.05628i | 0.192849 | + | 0.334025i | ||||
\(11\) | 2.68591 | + | 4.65213i | 0.809832 | + | 1.40267i | 0.912980 | + | 0.408004i | \(0.133775\pi\) |
−0.103149 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(12\) | −1.19496 | −0.344955 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.39111 | 1.17357 | ||||||||
\(15\) | −1.16612 | − | 2.01978i | −0.301092 | − | 0.521506i | ||||
\(16\) | 1.35638 | + | 2.34932i | 0.339094 | + | 0.587329i | ||||
\(17\) | 0.565928 | − | 0.980215i | 0.137258 | − | 0.237737i | −0.789200 | − | 0.614136i | \(-0.789505\pi\) |
0.926458 | + | 0.376399i | \(0.122838\pi\) | |||||||
\(18\) | −2.97527 | −0.701278 | ||||||||
\(19\) | 1.13397 | − | 1.96410i | 0.260152 | − | 0.450596i | −0.706130 | − | 0.708082i | \(-0.749561\pi\) |
0.966282 | + | 0.257486i | \(0.0828941\pi\) | |||||||
\(20\) | 0.256182 | − | 0.443720i | 0.0572840 | − | 0.0992188i | ||||
\(21\) | −8.39654 | −1.83228 | ||||||||
\(22\) | −3.27597 | + | 5.67414i | −0.698438 | + | 1.20973i | ||||
\(23\) | 1.94644 | + | 3.37133i | 0.405860 | + | 0.702970i | 0.994421 | − | 0.105483i | \(-0.0336387\pi\) |
−0.588561 | + | 0.808453i | \(0.700305\pi\) | |||||||
\(24\) | −3.57335 | − | 6.18922i | −0.729407 | − | 1.26337i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.30752 | −0.251632 | ||||||||
\(28\) | −0.922305 | − | 1.59748i | −0.174299 | − | 0.301895i | ||||
\(29\) | 0.0123639 | + | 0.0214150i | 0.00229593 | + | 0.00397666i | 0.867171 | − | 0.498010i | \(-0.165936\pi\) |
−0.864875 | + | 0.501987i | \(0.832603\pi\) | |||||||
\(30\) | 1.42231 | − | 2.46350i | 0.259676 | − | 0.449772i | ||||
\(31\) | −5.46410 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(32\) | 1.40994 | − | 2.44209i | 0.249245 | − | 0.431705i | ||||
\(33\) | 6.26420 | − | 10.8499i | 1.09046 | − | 1.88873i | ||||
\(34\) | 1.38051 | 0.236755 | ||||||||
\(35\) | 1.80010 | − | 3.11786i | 0.304272 | − | 0.527015i | ||||
\(36\) | 0.624924 | + | 1.08240i | 0.104154 | + | 0.180400i | ||||
\(37\) | −4.35203 | − | 7.53794i | −0.715470 | − | 1.23923i | −0.962778 | − | 0.270293i | \(-0.912879\pi\) |
0.247309 | − | 0.968937i | \(-0.420454\pi\) | |||||||
\(38\) | 2.76619 | 0.448735 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06430 | 0.484508 | ||||||||
\(41\) | 1.86603 | + | 3.23205i | 0.291424 | + | 0.504762i | 0.974147 | − | 0.225916i | \(-0.0725376\pi\) |
−0.682723 | + | 0.730678i | \(0.739204\pi\) | |||||||
\(42\) | −5.12058 | − | 8.86910i | −0.790122 | − | 1.36853i | ||||
\(43\) | 0.565928 | − | 0.980215i | 0.0863031 | − | 0.149481i | −0.819643 | − | 0.572875i | \(-0.805828\pi\) |
0.905946 | + | 0.423394i | \(0.139161\pi\) | |||||||
\(44\) | 2.75232 | 0.414929 | ||||||||
\(45\) | −1.21969 | + | 2.11256i | −0.181820 | + | 0.314922i | ||||
\(46\) | −2.37404 | + | 4.11196i | −0.350034 | + | 0.606276i | ||||
\(47\) | −2.58535 | −0.377113 | −0.188556 | − | 0.982062i | \(-0.560381\pi\) | ||||
−0.188556 | + | 0.982062i | \(0.560381\pi\) | |||||||
\(48\) | 3.16341 | − | 5.47918i | 0.456598 | − | 0.790852i | ||||
\(49\) | −2.98070 | − | 5.16273i | −0.425815 | − | 0.737533i | ||||
\(50\) | 0.609843 | + | 1.05628i | 0.0862449 | + | 0.149381i | ||||
\(51\) | −2.63977 | −0.369641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43937 | −0.609795 | −0.304897 | − | 0.952385i | \(-0.598622\pi\) | ||||
−0.304897 | + | 0.952385i | \(0.598622\pi\) | |||||||
\(54\) | −0.797382 | − | 1.38111i | −0.108510 | − | 0.187945i | ||||
\(55\) | 2.68591 | + | 4.65213i | 0.362168 | + | 0.627293i | ||||
\(56\) | 5.51603 | − | 9.55405i | 0.737111 | − | 1.27671i | ||||
\(57\) | −5.28942 | −0.700600 | ||||||||
\(58\) | −0.0150801 | + | 0.0261196i | −0.00198012 | + | 0.00342967i | ||||
\(59\) | −0.0857123 | + | 0.148458i | −0.0111588 | + | 0.0193276i | −0.871551 | − | 0.490305i | \(-0.836885\pi\) |
0.860392 | + | 0.509633i | \(0.170219\pi\) | |||||||
\(60\) | −1.19496 | −0.154269 | ||||||||
\(61\) | −1.68012 | + | 2.91005i | −0.215117 | + | 0.372594i | −0.953309 | − | 0.301997i | \(-0.902347\pi\) |
0.738192 | + | 0.674591i | \(0.235680\pi\) | |||||||
\(62\) | −3.33225 | − | 5.77162i | −0.423196 | − | 0.732997i | ||||
\(63\) | 4.39111 | + | 7.60563i | 0.553228 | + | 0.958219i | ||||
\(64\) | 8.86488 | 1.10811 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.2807 | 1.88093 | ||||||||
\(67\) | 3.19990 | + | 5.54239i | 0.390930 | + | 0.677111i | 0.992572 | − | 0.121655i | \(-0.0388200\pi\) |
−0.601642 | + | 0.798766i | \(0.705487\pi\) | |||||||
\(68\) | −0.289961 | − | 0.502227i | −0.0351629 | − | 0.0609040i | ||||
\(69\) | 4.53957 | − | 7.86276i | 0.546500 | − | 0.946566i | ||||
\(70\) | 4.39111 | 0.524838 | ||||||||
\(71\) | −5.39866 | + | 9.35076i | −0.640703 | + | 1.10973i | 0.344573 | + | 0.938760i | \(0.388024\pi\) |
−0.985276 | + | 0.170971i | \(0.945309\pi\) | |||||||
\(72\) | −3.73748 | + | 6.47351i | −0.440467 | + | 0.762911i | ||||
\(73\) | 4.70308 | 0.550454 | 0.275227 | − | 0.961379i | \(-0.411247\pi\) | ||||
0.275227 | + | 0.961379i | \(0.411247\pi\) | |||||||
\(74\) | 5.30812 | − | 9.19393i | 0.617056 | − | 1.06877i | ||||
\(75\) | −1.16612 | − | 2.01978i | −0.134652 | − | 0.233225i | ||||
\(76\) | −0.581008 | − | 1.00633i | −0.0666462 | − | 0.115435i | ||||
\(77\) | 19.3396 | 2.20395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9826 | −1.34815 | −0.674075 | − | 0.738663i | \(-0.735457\pi\) | ||||
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(80\) | 1.35638 | + | 2.34932i | 0.151648 | + | 0.262661i | ||||
\(81\) | 5.18379 | + | 8.97859i | 0.575976 | + | 0.997621i | ||||
\(82\) | −2.27597 | + | 3.94209i | −0.251338 | + | 0.435331i | ||||
\(83\) | 12.1286 | 1.33129 | 0.665643 | − | 0.746270i | \(-0.268157\pi\) | ||||
0.665643 | + | 0.746270i | \(0.268157\pi\) | |||||||
\(84\) | −2.15104 | + | 3.72572i | −0.234698 | + | 0.406509i | ||||
\(85\) | 0.565928 | − | 0.980215i | 0.0613835 | − | 0.106319i | ||||
\(86\) | 1.38051 | 0.148864 | ||||||||
\(87\) | 0.0288357 | − | 0.0499450i | 0.00309152 | − | 0.00535466i | ||||
\(88\) | 8.23042 | + | 14.2555i | 0.877366 | + | 1.51964i | ||||
\(89\) | −8.07702 | − | 13.9898i | −0.856162 | − | 1.48292i | −0.875562 | − | 0.483105i | \(-0.839509\pi\) |
0.0194001 | − | 0.999812i | \(-0.493824\pi\) | |||||||
\(90\) | −2.97527 | −0.313621 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.99457 | 0.207948 | ||||||||
\(93\) | 6.37182 | + | 11.0363i | 0.660727 | + | 1.14441i | ||||
\(94\) | −1.57666 | − | 2.73086i | −0.162620 | − | 0.281666i | ||||
\(95\) | 1.13397 | − | 1.96410i | 0.116343 | − | 0.201513i | ||||
\(96\) | −6.57666 | −0.671228 | ||||||||
\(97\) | 6.08408 | − | 10.5379i | 0.617745 | − | 1.06997i | −0.372151 | − | 0.928172i | \(-0.621380\pi\) |
0.989896 | − | 0.141794i | \(-0.0452869\pi\) | |||||||
\(98\) | 3.63553 | − | 6.29692i | 0.367244 | − | 0.636085i | ||||
\(99\) | −13.1039 | −1.31699 | ||||||||
\(100\) | 0.256182 | − | 0.443720i | 0.0256182 | − | 0.0443720i | ||||
\(101\) | 2.02721 | + | 3.51122i | 0.201714 | + | 0.349380i | 0.949081 | − | 0.315032i | \(-0.102015\pi\) |
−0.747366 | + | 0.664412i | \(0.768682\pi\) | |||||||
\(102\) | −1.60984 | − | 2.78833i | −0.159398 | − | 0.276086i | ||||
\(103\) | −17.9035 | −1.76408 | −0.882041 | − | 0.471173i | \(-0.843831\pi\) | ||||
−0.882041 | + | 0.471173i | \(0.843831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.39654 | −0.819419 | ||||||||
\(106\) | −2.70732 | − | 4.68922i | −0.262958 | − | 0.455457i | ||||
\(107\) | 4.56593 | + | 7.90842i | 0.441405 | + | 0.764536i | 0.997794 | − | 0.0663862i | \(-0.0211469\pi\) |
−0.556389 | + | 0.830922i | \(0.687814\pi\) | |||||||
\(108\) | −0.334963 | + | 0.580172i | −0.0322318 | + | 0.0558271i | ||||
\(109\) | −7.37605 | −0.706498 | −0.353249 | − | 0.935529i | \(-0.614923\pi\) | ||||
−0.353249 | + | 0.935529i | \(0.614923\pi\) | |||||||
\(110\) | −3.27597 | + | 5.67414i | −0.312351 | + | 0.541008i | ||||
\(111\) | −10.1500 | + | 17.5803i | −0.963396 | + | 1.66865i | ||||
\(112\) | 9.76645 | 0.922843 | ||||||||
\(113\) | −3.53794 | + | 6.12789i | −0.332821 | + | 0.576463i | −0.983064 | − | 0.183263i | \(-0.941334\pi\) |
0.650243 | + | 0.759727i | \(0.274667\pi\) | |||||||
\(114\) | −3.22572 | − | 5.58710i | −0.302116 | − | 0.523280i | ||||
\(115\) | 1.94644 | + | 3.37133i | 0.181506 | + | 0.314378i | ||||
\(116\) | 0.0126697 | 0.00117635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.209084 | −0.0192478 | ||||||||
\(119\) | −2.03745 | − | 3.52897i | −0.186773 | − | 0.323500i | ||||
\(120\) | −3.57335 | − | 6.18922i | −0.326201 | − | 0.564996i | ||||
\(121\) | −8.92820 | + | 15.4641i | −0.811655 | + | 1.40583i | ||||
\(122\) | −4.09843 | −0.371055 | ||||||||
\(123\) | 4.35203 | − | 7.53794i | 0.392409 | − | 0.679673i | ||||
\(124\) | −1.39980 | + | 2.42453i | −0.125706 | + | 0.217729i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.35578 | + | 9.27648i | −0.477131 | + | 0.826415i | ||||
\(127\) | 5.71806 | + | 9.90396i | 0.507395 | + | 0.878835i | 0.999963 | + | 0.00856072i | \(0.00272499\pi\) |
−0.492568 | + | 0.870274i | \(0.663942\pi\) | |||||||
\(128\) | 2.58631 | + | 4.47962i | 0.228600 | + | 0.395946i | ||||
\(129\) | −2.63977 | −0.232418 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5680 | −0.923328 | −0.461664 | − | 0.887055i | \(-0.652747\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(132\) | −3.20955 | − | 5.55910i | −0.279355 | − | 0.483858i | ||||
\(133\) | −4.08253 | − | 7.07115i | −0.354000 | − | 0.613146i | ||||
\(134\) | −3.90288 | + | 6.75998i | −0.337157 | + | 0.583974i | ||||
\(135\) | −1.30752 | −0.112533 | ||||||||
\(136\) | 1.73417 | − | 3.00367i | 0.148704 | − | 0.257563i | ||||
\(137\) | 1.89336 | − | 3.27940i | 0.161761 | − | 0.280178i | −0.773739 | − | 0.633504i | \(-0.781616\pi\) |
0.935500 | + | 0.353326i | \(0.114949\pi\) | |||||||
\(138\) | 11.0737 | 0.942656 | ||||||||
\(139\) | −1.00693 | + | 1.74406i | −0.0854068 | + | 0.147929i | −0.905564 | − | 0.424209i | \(-0.860552\pi\) |
0.820158 | + | 0.572138i | \(0.193886\pi\) | |||||||
\(140\) | −0.922305 | − | 1.59748i | −0.0779490 | − | 0.135012i | ||||
\(141\) | 3.01484 | + | 5.22186i | 0.253895 | + | 0.439760i | ||||
\(142\) | −13.1694 | −1.10515 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.61742 | −0.551452 | ||||||||
\(145\) | 0.0123639 | + | 0.0214150i | 0.00102677 | + | 0.00177842i | ||||
\(146\) | 2.86814 | + | 4.96777i | 0.237369 | + | 0.411136i | ||||
\(147\) | −6.95174 | + | 12.0408i | −0.573370 | + | 0.993105i | ||||
\(148\) | −4.45965 | −0.366581 | ||||||||
\(149\) | −2.75890 | + | 4.77855i | −0.226018 | + | 0.391474i | −0.956624 | − | 0.291324i | \(-0.905904\pi\) |
0.730607 | + | 0.682799i | \(0.239237\pi\) | |||||||
\(150\) | 1.42231 | − | 2.46350i | 0.116131 | − | 0.201144i | ||||
\(151\) | 4.88961 | 0.397911 | 0.198956 | − | 0.980009i | \(-0.436245\pi\) | ||||
0.198956 | + | 0.980009i | \(0.436245\pi\) | |||||||
\(152\) | 3.47484 | − | 6.01859i | 0.281846 | − | 0.488172i | ||||
\(153\) | 1.38051 | + | 2.39111i | 0.111608 | + | 0.193310i | ||||
\(154\) | 11.7941 | + | 20.4280i | 0.950397 | + | 1.64614i | ||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0405 | 0.801323 | 0.400661 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400661 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(158\) | −7.30752 | − | 12.6570i | −0.581355 | − | 1.00694i | ||||
\(159\) | 5.17686 | + | 8.96658i | 0.410551 | + | 0.711096i | ||||
\(160\) | 1.40994 | − | 2.44209i | 0.111466 | − | 0.193064i | ||||
\(161\) | 14.0151 | 1.10454 | ||||||||
\(162\) | −6.32260 | + | 10.9511i | −0.496750 | + | 0.860397i | ||||
\(163\) | 3.39062 | − | 5.87273i | 0.265574 | − | 0.459988i | −0.702140 | − | 0.712039i | \(-0.747772\pi\) |
0.967714 | + | 0.252051i | \(0.0811052\pi\) | |||||||
\(164\) | 1.91217 | 0.149315 | ||||||||
\(165\) | 6.26420 | − | 10.8499i | 0.487667 | − | 0.844664i | ||||
\(166\) | 7.39654 | + | 12.8112i | 0.574083 | + | 0.994341i | ||||
\(167\) | 5.24490 | + | 9.08444i | 0.405863 | + | 0.702975i | 0.994421 | − | 0.105479i | \(-0.0336377\pi\) |
−0.588559 | + | 0.808455i | \(0.700304\pi\) | |||||||
\(168\) | −25.7295 | −1.98507 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.38051 | 0.105880 | ||||||||
\(171\) | 2.76619 | + | 4.79118i | 0.211536 | + | 0.366391i | ||||
\(172\) | −0.289961 | − | 0.502227i | −0.0221093 | − | 0.0382944i | ||||
\(173\) | 2.22923 | − | 3.86113i | 0.169485 | − | 0.293557i | −0.768754 | − | 0.639545i | \(-0.779123\pi\) |
0.938239 | + | 0.345988i | \(0.112456\pi\) | |||||||
\(174\) | 0.0703412 | 0.00533255 | ||||||||
\(175\) | 1.80010 | − | 3.11786i | 0.136075 | − | 0.235688i | ||||
\(176\) | −7.28621 | + | 12.6201i | −0.549219 | + | 0.951275i | ||||
\(177\) | 0.399804 | 0.0300511 | ||||||||
\(178\) | 9.85143 | − | 17.0632i | 0.738396 | − | 1.27894i | ||||
\(179\) | −9.31564 | − | 16.1352i | −0.696284 | − | 1.20600i | −0.969746 | − | 0.244116i | \(-0.921502\pi\) |
0.273462 | − | 0.961883i | \(-0.411831\pi\) | |||||||
\(180\) | 0.624924 | + | 1.08240i | 0.0465791 | + | 0.0806773i | ||||
\(181\) | 18.0900 | 1.34462 | 0.672310 | − | 0.740270i | \(-0.265302\pi\) | ||||
0.672310 | + | 0.740270i | \(0.265302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.83690 | 0.579320 | ||||||||
\(184\) | 5.96446 | + | 10.3307i | 0.439706 | + | 0.761593i | ||||
\(185\) | −4.35203 | − | 7.53794i | −0.319968 | − | 0.554200i | ||||
\(186\) | −7.77162 | + | 13.4608i | −0.569843 | + | 0.986997i | ||||
\(187\) | 6.08012 | 0.444622 | ||||||||
\(188\) | −0.662321 | + | 1.14717i | −0.0483047 | + | 0.0836662i | ||||
\(189\) | −2.35366 | + | 4.07666i | −0.171204 | + | 0.296533i | ||||
\(190\) | 2.76619 | 0.200680 | ||||||||
\(191\) | −13.6682 | + | 23.6740i | −0.988994 | + | 1.71299i | −0.366361 | + | 0.930473i | \(0.619397\pi\) |
−0.622632 | + | 0.782515i | \(0.713937\pi\) | |||||||
\(192\) | −10.3375 | − | 17.9052i | −0.746048 | − | 1.29219i | ||||
\(193\) | 10.8837 | + | 18.8511i | 0.783425 | + | 1.35693i | 0.929935 | + | 0.367723i | \(0.119863\pi\) |
−0.146510 | + | 0.989209i | \(0.546804\pi\) | |||||||
\(194\) | 14.8413 | 1.06555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.05441 | −0.218172 | ||||||||
\(197\) | −0.848360 | − | 1.46940i | −0.0604432 | − | 0.104691i | 0.834220 | − | 0.551431i | \(-0.185918\pi\) |
−0.894664 | + | 0.446741i | \(0.852585\pi\) | |||||||
\(198\) | −7.99131 | − | 13.8413i | −0.567917 | − | 0.983662i | ||||
\(199\) | −12.6627 | + | 21.9325i | −0.897637 | + | 1.55475i | −0.0671309 | + | 0.997744i | \(0.521385\pi\) |
−0.830506 | + | 0.557009i | \(0.811949\pi\) | |||||||
\(200\) | 3.06430 | 0.216679 | ||||||||
\(201\) | 7.46296 | − | 12.9262i | 0.526397 | − | 0.911746i | ||||
\(202\) | −2.47256 | + | 4.28259i | −0.173968 | + | 0.301322i | ||||
\(203\) | 0.0890252 | 0.00624834 | ||||||||
\(204\) | −0.676260 | + | 1.17132i | −0.0473477 | + | 0.0820086i | ||||
\(205\) | 1.86603 | + | 3.23205i | 0.130329 | + | 0.225736i | ||||
\(206\) | −10.9183 | − | 18.9111i | −0.760715 | − | 1.31760i | ||||
\(207\) | −9.49617 | −0.660030 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | −5.12058 | − | 8.86910i | −0.353353 | − | 0.612026i | ||||
\(211\) | 0.167753 | + | 0.290558i | 0.0115486 | + | 0.0200028i | 0.871742 | − | 0.489965i | \(-0.162991\pi\) |
−0.860193 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(212\) | −1.13729 | + | 1.96984i | −0.0781092 | + | 0.135289i | ||||
\(213\) | 25.1820 | 1.72544 | ||||||||
\(214\) | −5.56900 | + | 9.64579i | −0.380689 | + | 0.659373i | ||||
\(215\) | 0.565928 | − | 0.980215i | 0.0385959 | − | 0.0668501i | ||||
\(216\) | −4.00663 | −0.272616 | ||||||||
\(217\) | −9.83592 | + | 17.0363i | −0.667706 | + | 1.15650i | ||||
\(218\) | −4.49824 | − | 7.79118i | −0.304659 | − | 0.527685i | ||||
\(219\) | −5.48438 | − | 9.49922i | −0.370600 | − | 0.641898i | ||||
\(220\) | 2.75232 | 0.185562 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −24.7597 | −1.66176 | ||||||||
\(223\) | −6.14838 | − | 10.6493i | −0.411726 | − | 0.713130i | 0.583353 | − | 0.812219i | \(-0.301741\pi\) |
−0.995079 | + | 0.0990887i | \(0.968407\pi\) | |||||||
\(224\) | −5.07606 | − | 8.79200i | −0.339159 | − | 0.587440i | ||||
\(225\) | −1.21969 | + | 2.11256i | −0.0813125 | + | 0.140837i | ||||
\(226\) | −8.63036 | −0.574083 | ||||||||
\(227\) | −3.81613 | + | 6.60974i | −0.253286 | + | 0.438704i | −0.964428 | − | 0.264344i | \(-0.914845\pi\) |
0.711143 | + | 0.703048i | \(0.248178\pi\) | |||||||
\(228\) | −1.35505 | + | 2.34702i | −0.0897406 | + | 0.155435i | ||||
\(229\) | 14.4008 | 0.951631 | 0.475815 | − | 0.879545i | \(-0.342153\pi\) | ||||
0.475815 | + | 0.879545i | \(0.342153\pi\) | |||||||
\(230\) | −2.37404 | + | 4.11196i | −0.156540 | + | 0.271135i | ||||
\(231\) | −22.5523 | − | 39.0618i | −1.48384 | − | 2.57008i | ||||
\(232\) | 0.0378868 | + | 0.0656218i | 0.00248739 | + | 0.00430828i | ||||
\(233\) | 9.49617 | 0.622115 | 0.311057 | − | 0.950391i | \(-0.399317\pi\) | ||||
0.311057 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58535 | −0.168650 | ||||||||
\(236\) | 0.0439159 | + | 0.0760645i | 0.00285868 | + | 0.00495138i | ||||
\(237\) | 13.9732 | + | 24.2023i | 0.907657 | + | 1.57211i | ||||
\(238\) | 2.48505 | − | 4.30423i | 0.161082 | − | 0.279002i | ||||
\(239\) | 19.9143 | 1.28815 | 0.644076 | − | 0.764962i | \(-0.277242\pi\) | ||||
0.644076 | + | 0.764962i | \(0.277242\pi\) | |||||||
\(240\) | 3.16341 | − | 5.47918i | 0.204197 | − | 0.353680i | ||||
\(241\) | 11.6332 | − | 20.1493i | 0.749360 | − | 1.29793i | −0.198770 | − | 0.980046i | \(-0.563695\pi\) |
0.948130 | − | 0.317883i | \(-0.102972\pi\) | |||||||
\(242\) | −21.7792 | −1.40002 | ||||||||
\(243\) | 10.1286 | − | 17.5432i | 0.649750 | − | 1.12540i | ||||
\(244\) | 0.860832 | + | 1.49100i | 0.0551091 | + | 0.0954518i | ||||
\(245\) | −2.98070 | − | 5.16273i | −0.190430 | − | 0.329835i | ||||
\(246\) | 10.6162 | 0.676866 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.7436 | −1.06322 | ||||||||
\(249\) | −14.1434 | − | 24.4972i | −0.896304 | − | 1.55244i | ||||
\(250\) | 0.609843 | + | 1.05628i | 0.0385699 | + | 0.0668050i | ||||
\(251\) | −5.92008 | + | 10.2539i | −0.373672 | + | 0.647219i | −0.990127 | − | 0.140171i | \(-0.955235\pi\) |
0.616455 | + | 0.787390i | \(0.288568\pi\) | |||||||
\(252\) | 4.49969 | 0.283454 | ||||||||
\(253\) | −10.4559 | + | 18.1101i | −0.657357 | + | 1.13858i | ||||
\(254\) | −6.97424 | + | 12.0797i | −0.437603 | + | 0.757950i | ||||
\(255\) | −2.63977 | −0.165309 | ||||||||
\(256\) | 5.71040 | − | 9.89070i | 0.356900 | − | 0.618169i | ||||
\(257\) | 2.77501 | + | 4.80646i | 0.173100 | + | 0.299819i | 0.939502 | − | 0.342543i | \(-0.111288\pi\) |
−0.766402 | + | 0.642361i | \(0.777955\pi\) | |||||||
\(258\) | −1.60984 | − | 2.78833i | −0.100224 | − | 0.173594i | ||||
\(259\) | −31.3363 | −1.94714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0603205 | −0.00373375 | ||||||||
\(262\) | −6.44481 | − | 11.1627i | −0.398161 | − | 0.689636i | ||||
\(263\) | −3.42983 | − | 5.94065i | −0.211493 | − | 0.366316i | 0.740689 | − | 0.671848i | \(-0.234499\pi\) |
−0.952182 | + | 0.305532i | \(0.901166\pi\) | |||||||
\(264\) | 19.1954 | − | 33.2474i | 1.18139 | − | 2.04623i | ||||
\(265\) | −4.43937 | −0.272709 | ||||||||
\(266\) | 4.97941 | − | 8.62459i | 0.305307 | − | 0.528807i | ||||
\(267\) | −18.8376 | + | 32.6277i | −1.15284 | + | 1.99678i | ||||
\(268\) | 3.27903 | 0.200299 | ||||||||
\(269\) | 0.710994 | − | 1.23148i | 0.0433501 | − | 0.0750845i | −0.843536 | − | 0.537072i | \(-0.819530\pi\) |
0.886886 | + | 0.461988i | \(0.152864\pi\) | |||||||
\(270\) | −0.797382 | − | 1.38111i | −0.0485271 | − | 0.0840514i | ||||
\(271\) | −4.98473 | − | 8.63381i | −0.302801 | − | 0.524467i | 0.673968 | − | 0.738760i | \(-0.264588\pi\) |
−0.976769 | + | 0.214294i | \(0.931255\pi\) | |||||||
\(272\) | 3.07045 | 0.186173 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.61862 | 0.279021 | ||||||||
\(275\) | 2.68591 | + | 4.65213i | 0.161966 | + | 0.280534i | ||||
\(276\) | −2.32591 | − | 4.02860i | −0.140003 | − | 0.242493i | ||||
\(277\) | 8.76187 | − | 15.1760i | 0.526449 | − | 0.911837i | −0.473076 | − | 0.881022i | \(-0.656856\pi\) |
0.999525 | − | 0.0308154i | \(-0.00981039\pi\) | |||||||
\(278\) | −2.45628 | −0.147318 | ||||||||
\(279\) | 6.66449 | − | 11.5432i | 0.398993 | − | 0.691076i | ||||
\(280\) | 5.51603 | − | 9.55405i | 0.329646 | − | 0.570964i | ||||
\(281\) | −10.7352 | −0.640406 | −0.320203 | − | 0.947349i | \(-0.603751\pi\) | ||||
−0.320203 | + | 0.947349i | \(0.603751\pi\) | |||||||
\(282\) | −3.67716 | + | 6.36903i | −0.218972 | + | 0.379270i | ||||
\(283\) | −0.659192 | − | 1.14175i | −0.0391849 | − | 0.0678702i | 0.845768 | − | 0.533551i | \(-0.179143\pi\) |
−0.884953 | + | 0.465681i | \(0.845809\pi\) | |||||||
\(284\) | 2.76608 | + | 4.79099i | 0.164137 | + | 0.284293i | ||||
\(285\) | −5.28942 | −0.313318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.4361 | 0.793109 | ||||||||
\(288\) | 3.43937 | + | 5.95717i | 0.202667 | + | 0.351030i | ||||
\(289\) | 7.85945 | + | 13.6130i | 0.462321 | + | 0.800763i | ||||
\(290\) | −0.0150801 | + | 0.0261196i | −0.000885536 | + | 0.00153379i | ||||
\(291\) | −28.3792 | −1.66362 | ||||||||
\(292\) | 1.20485 | − | 2.08685i | 0.0705082 | − | 0.122124i | ||||
\(293\) | 9.37133 | − | 16.2316i | 0.547479 | − | 0.948261i | −0.450968 | − | 0.892540i | \(-0.648921\pi\) |
0.998446 | − | 0.0557207i | \(-0.0177456\pi\) | |||||||
\(294\) | −16.9579 | −0.989004 | ||||||||
\(295\) | −0.0857123 | + | 0.148458i | −0.00499036 | + | 0.00864356i | ||||
\(296\) | −13.3359 | − | 23.0985i | −0.775134 | − | 1.34257i | ||||
\(297\) | −3.51187 | − | 6.08275i | −0.203780 | − | 0.352957i | ||||
\(298\) | −6.72998 | −0.389857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.19496 | −0.0689910 | ||||||||
\(301\) | −2.03745 | − | 3.52897i | −0.117437 | − | 0.203406i | ||||
\(302\) | 2.98190 | + | 5.16480i | 0.171589 | + | 0.297201i | ||||
\(303\) | 4.72794 | − | 8.18904i | 0.271613 | − | 0.470448i | ||||
\(304\) | 6.15239 | 0.352864 | ||||||||
\(305\) | −1.68012 | + | 2.91005i | −0.0962032 | + | 0.166629i | ||||
\(306\) | −1.68379 | + | 2.91641i | −0.0962558 | + | 0.166720i | ||||
\(307\) | −14.3043 | −0.816387 | −0.408194 | − | 0.912895i | \(-0.633841\pi\) | ||||
−0.408194 | + | 0.912895i | \(0.633841\pi\) | |||||||
\(308\) | 4.95445 | − | 8.58137i | 0.282306 | − | 0.488969i | ||||
\(309\) | 20.8777 | + | 36.1612i | 1.18769 | + | 2.05714i | ||||
\(310\) | −3.33225 | − | 5.77162i | −0.189259 | − | 0.327806i | ||||
\(311\) | 2.76102 | 0.156563 | 0.0782815 | − | 0.996931i | \(-0.475057\pi\) | ||||
0.0782815 | + | 0.996931i | \(0.475057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3858 | −0.926179 | −0.463090 | − | 0.886311i | \(-0.653259\pi\) | ||||
−0.463090 | + | 0.886311i | \(0.653259\pi\) | |||||||
\(314\) | 6.12316 | + | 10.6056i | 0.345550 | + | 0.598510i | ||||
\(315\) | 4.39111 | + | 7.60563i | 0.247411 | + | 0.428529i | ||||
\(316\) | −3.06973 | + | 5.31693i | −0.172686 | + | 0.299101i | ||||
\(317\) | −1.78575 | −0.100297 | −0.0501487 | − | 0.998742i | \(-0.515970\pi\) | ||||
−0.0501487 | + | 0.998742i | \(0.515970\pi\) | |||||||
\(318\) | −6.31414 | + | 10.9364i | −0.354080 | + | 0.613284i | ||||
\(319\) | −0.0664168 | + | 0.115037i | −0.00371863 | + | 0.00644085i | ||||
\(320\) | 8.86488 | 0.495562 | ||||||||
\(321\) | 10.6489 | − | 18.4444i | 0.594362 | − | 1.02946i | ||||
\(322\) | 8.54702 | + | 14.8039i | 0.476307 | + | 0.824987i | ||||
\(323\) | −1.28349 | − | 2.22308i | −0.0714156 | − | 0.123695i | ||||
\(324\) | 5.31197 | 0.295110 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.27099 | 0.458088 | ||||||||
\(327\) | 8.60139 | + | 14.8980i | 0.475658 | + | 0.823864i | ||||
\(328\) | 5.71806 | + | 9.90396i | 0.315727 | + | 0.546855i | ||||
\(329\) | −4.65389 | + | 8.06077i | −0.256577 | + | 0.444405i | ||||
\(330\) | 15.2807 | 0.841176 | ||||||||
\(331\) | 3.61220 | − | 6.25652i | 0.198545 | − | 0.343889i | −0.749512 | − | 0.661991i | \(-0.769712\pi\) |
0.948057 | + | 0.318101i | \(0.103045\pi\) | |||||||
\(332\) | 3.10713 | − | 5.38170i | 0.170526 | − | 0.295359i | ||||
\(333\) | 21.2325 | 1.16353 | ||||||||
\(334\) | −6.39714 | + | 11.0802i | −0.350036 | + | 0.606280i | ||||
\(335\) | 3.19990 | + | 5.54239i | 0.174829 | + | 0.302813i | ||||
\(336\) | −11.3889 | − | 19.7261i | −0.621315 | − | 1.07615i | ||||
\(337\) | −4.36219 | −0.237624 | −0.118812 | − | 0.992917i | \(-0.537909\pi\) | ||||
−0.118812 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5027 | 0.896303 | ||||||||
\(340\) | −0.289961 | − | 0.502227i | −0.0157253 | − | 0.0272371i | ||||
\(341\) | −14.6761 | − | 25.4197i | −0.794754 | − | 1.37655i | ||||
\(342\) | −3.37388 | + | 5.84374i | −0.182439 | + | 0.315993i | ||||
\(343\) | 3.73913 | 0.201894 | ||||||||
\(344\) | 1.73417 | − | 3.00367i | 0.0935002 | − | 0.161947i | ||||
\(345\) | 4.53957 | − | 7.86276i | 0.244402 | − | 0.423317i | ||||
\(346\) | 5.43792 | 0.292344 | ||||||||
\(347\) | 13.3536 | − | 23.1291i | 0.716858 | − | 1.24163i | −0.245381 | − | 0.969427i | \(-0.578913\pi\) |
0.962239 | − | 0.272207i | \(-0.0877537\pi\) | |||||||
\(348\) | −0.0147744 | − | 0.0255900i | −0.000791991 | − | 0.00137177i | ||||
\(349\) | 11.7855 | + | 20.4131i | 0.630865 | + | 1.09269i | 0.987375 | + | 0.158399i | \(0.0506333\pi\) |
−0.356510 | + | 0.934292i | \(0.616033\pi\) | |||||||
\(350\) | 4.39111 | 0.234715 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.1479 | 0.807385 | ||||||||
\(353\) | 2.86863 | + | 4.96862i | 0.152682 | + | 0.264453i | 0.932213 | − | 0.361911i | \(-0.117876\pi\) |
−0.779531 | + | 0.626364i | \(0.784542\pi\) | |||||||
\(354\) | 0.243818 | + | 0.422305i | 0.0129588 | + | 0.0224453i | ||||
\(355\) | −5.39866 | + | 9.35076i | −0.286531 | + | 0.496287i | ||||
\(356\) | −8.27675 | −0.438667 | ||||||||
\(357\) | −4.75184 | + | 8.23042i | −0.251494 | + | 0.435600i | ||||
\(358\) | 11.3622 | − | 19.6799i | 0.600509 | − | 1.04011i | ||||
\(359\) | 24.7583 | 1.30669 | 0.653347 | − | 0.757059i | \(-0.273364\pi\) | ||||
0.653347 | + | 0.757059i | \(0.273364\pi\) | |||||||
\(360\) | −3.73748 | + | 6.47351i | −0.196983 | + | 0.341184i | ||||
\(361\) | 6.92820 | + | 12.0000i | 0.364642 | + | 0.631579i | ||||
\(362\) | 11.0321 | + | 19.1081i | 0.579833 | + | 1.00430i | ||||
\(363\) | 41.6455 | 2.18582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.70308 | 0.246171 | ||||||||
\(366\) | 4.77928 | + | 8.27796i | 0.249817 | + | 0.432696i | ||||
\(367\) | −13.0268 | − | 22.5630i | −0.679992 | − | 1.17778i | −0.974983 | − | 0.222280i | \(-0.928650\pi\) |
0.294991 | − | 0.955500i | \(-0.404683\pi\) | |||||||
\(368\) | −5.28021 | + | 9.14558i | −0.275250 | + | 0.476747i | ||||
\(369\) | −9.10387 | −0.473928 | ||||||||
\(370\) | 5.30812 | − | 9.19393i | 0.275956 | − | 0.477969i | ||||
\(371\) | −7.99131 | + | 13.8413i | −0.414888 | + | 0.718607i | ||||
\(372\) | 6.52938 | 0.338532 | ||||||||
\(373\) | −6.60224 | + | 11.4354i | −0.341851 | + | 0.592103i | −0.984776 | − | 0.173826i | \(-0.944387\pi\) |
0.642926 | + | 0.765929i | \(0.277720\pi\) | |||||||
\(374\) | 3.70792 | + | 6.42231i | 0.191732 | + | 0.332089i | ||||
\(375\) | −1.16612 | − | 2.01978i | −0.0602183 | − | 0.104301i | ||||
\(376\) | −7.92229 | −0.408561 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.74146 | −0.295309 | ||||||||
\(379\) | 12.9989 | + | 22.5147i | 0.667707 | + | 1.15650i | 0.978544 | + | 0.206039i | \(0.0660572\pi\) |
−0.310837 | + | 0.950463i | \(0.600609\pi\) | |||||||
\(380\) | −0.581008 | − | 1.00633i | −0.0298051 | − | 0.0516239i | ||||
\(381\) | 13.3359 | − | 23.0985i | 0.683220 | − | 1.18337i | ||||
\(382\) | −33.3418 | −1.70591 | ||||||||
\(383\) | −4.80010 | + | 8.31401i | −0.245274 | + | 0.424826i | −0.962208 | − | 0.272314i | \(-0.912211\pi\) |
0.716935 | + | 0.697140i | \(0.245544\pi\) | |||||||
\(384\) | 6.03191 | − | 10.4476i | 0.307815 | − | 0.533151i | ||||
\(385\) | 19.3396 | 0.985637 | ||||||||
\(386\) | −13.2747 | + | 22.9924i | −0.675664 | + | 1.17028i | ||||
\(387\) | 1.38051 | + | 2.39111i | 0.0701752 | + | 0.121547i | ||||
\(388\) | −3.11726 | − | 5.39926i | −0.158255 | − | 0.274106i | ||||
\(389\) | 5.63129 | 0.285518 | 0.142759 | − | 0.989758i | \(-0.454403\pi\) | ||||
0.142759 | + | 0.989758i | \(0.454403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40617 | 0.222829 | ||||||||
\(392\) | −9.13376 | − | 15.8201i | −0.461325 | − | 0.799038i | ||||
\(393\) | 12.3236 | + | 21.3450i | 0.621641 | + | 1.07671i | ||||
\(394\) | 1.03473 | − | 1.79221i | 0.0521291 | − | 0.0902903i | ||||
\(395\) | −11.9826 | −0.602911 | ||||||||
\(396\) | −3.35697 | + | 5.81445i | −0.168694 | + | 0.292187i | ||||
\(397\) | −8.38291 | + | 14.5196i | −0.420726 | + | 0.728719i | −0.996011 | − | 0.0892344i | \(-0.971558\pi\) |
0.575285 | + | 0.817953i | \(0.304891\pi\) | |||||||
\(398\) | −30.8891 | −1.54833 | ||||||||
\(399\) | −9.52147 | + | 16.4917i | −0.476670 | + | 0.825616i | ||||
\(400\) | 1.35638 | + | 2.34932i | 0.0678189 | + | 0.117466i | ||||
\(401\) | −6.93902 | − | 12.0187i | −0.346518 | − | 0.600187i | 0.639110 | − | 0.769115i | \(-0.279303\pi\) |
−0.985628 | + | 0.168928i | \(0.945969\pi\) | |||||||
\(402\) | 18.2050 | 0.907980 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.07733 | 0.103351 | ||||||||
\(405\) | 5.18379 | + | 8.97859i | 0.257585 | + | 0.446149i | ||||
\(406\) | 0.0542914 | + | 0.0940355i | 0.00269444 | + | 0.00466690i | ||||
\(407\) | 23.3783 | − | 40.4924i | 1.15882 | − | 2.00713i | ||||
\(408\) | −8.08903 | −0.400466 | ||||||||
\(409\) | 14.7125 | − | 25.4829i | 0.727489 | − | 1.26005i | −0.230453 | − | 0.973083i | \(-0.574021\pi\) |
0.957941 | − | 0.286964i | \(-0.0926459\pi\) | |||||||
\(410\) | −2.27597 | + | 3.94209i | −0.112402 | + | 0.194686i | ||||
\(411\) | −8.83157 | −0.435629 | ||||||||
\(412\) | −4.58655 | + | 7.94413i | −0.225963 | + | 0.391379i | ||||
\(413\) | 0.308581 | + | 0.534478i | 0.0151843 | + | 0.0262999i | ||||
\(414\) | −5.79118 | − | 10.0306i | −0.284621 | − | 0.492978i | ||||
\(415\) | 12.1286 | 0.595369 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.69683 | 0.230005 | ||||||||
\(418\) | 7.42973 | + | 12.8687i | 0.363400 | + | 0.629427i | ||||
\(419\) | −3.48397 | − | 6.03440i | −0.170203 | − | 0.294800i | 0.768288 | − | 0.640104i | \(-0.221109\pi\) |
−0.938491 | + | 0.345305i | \(0.887776\pi\) | |||||||
\(420\) | −2.15104 | + | 3.72572i | −0.104960 | + | 0.181796i | ||||
\(421\) | −7.12125 | −0.347069 | −0.173534 | − | 0.984828i | \(-0.555519\pi\) | ||||
−0.173534 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(422\) | −0.204607 | + | 0.354389i | −0.00996010 | + | 0.0172514i | ||||
\(423\) | 3.15332 | − | 5.46171i | 0.153320 | − | 0.265558i | ||||
\(424\) | −13.6036 | −0.660647 | ||||||||
\(425\) | 0.565928 | − | 0.980215i | 0.0274515 | − | 0.0475474i | ||||
\(426\) | 15.3571 | + | 26.5993i | 0.744054 | + | 1.28874i | ||||
\(427\) | 6.04875 | + | 10.4767i | 0.292720 | + | 0.507005i | ||||
\(428\) | 4.67883 | 0.226160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.38051 | 0.0665740 | ||||||||
\(431\) | 15.1072 | + | 26.1664i | 0.727687 | + | 1.26039i | 0.957858 | + | 0.287241i | \(0.0927381\pi\) |
−0.230171 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(432\) | −1.77349 | − | 3.07177i | −0.0853270 | − | 0.147791i | ||||
\(433\) | −0.600065 | + | 1.03934i | −0.0288373 | + | 0.0499476i | −0.880084 | − | 0.474818i | \(-0.842514\pi\) |
0.851247 | + | 0.524766i | \(0.175847\pi\) | |||||||
\(434\) | −23.9935 | −1.15172 | ||||||||
\(435\) | 0.0288357 | − | 0.0499450i | 0.00138257 | − | 0.00239468i | ||||
\(436\) | −1.88961 | + | 3.27290i | −0.0904960 | + | 0.156744i | ||||
\(437\) | 8.82884 | 0.422341 | ||||||||
\(438\) | 6.68922 | − | 11.5861i | 0.319623 | − | 0.553604i | ||||
\(439\) | 8.27705 | + | 14.3363i | 0.395042 | + | 0.684233i | 0.993107 | − | 0.117215i | \(-0.0373966\pi\) |
−0.598064 | + | 0.801448i | \(0.704063\pi\) | |||||||
\(440\) | 8.23042 | + | 14.2555i | 0.392370 | + | 0.679605i | ||||
\(441\) | 14.5421 | 0.692481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.55949 | 0.216628 | 0.108314 | − | 0.994117i | \(-0.465455\pi\) | ||||
0.108314 | + | 0.994117i | \(0.465455\pi\) | |||||||
\(444\) | 5.20050 | + | 9.00753i | 0.246805 | + | 0.427478i | ||||
\(445\) | −8.07702 | − | 13.9898i | −0.382887 | − | 0.663180i | ||||
\(446\) | 7.49910 | − | 12.9888i | 0.355093 | − | 0.615038i | ||||
\(447\) | 12.8689 | 0.608676 | ||||||||
\(448\) | 15.9577 | − | 27.6395i | 0.753929 | − | 1.30584i | ||||
\(449\) | 6.92608 | − | 11.9963i | 0.326862 | − | 0.566142i | −0.655025 | − | 0.755607i | \(-0.727342\pi\) |
0.981887 | + | 0.189465i | \(0.0606754\pi\) | |||||||
\(450\) | −2.97527 | −0.140256 | ||||||||
\(451\) | −10.0239 | + | 17.3620i | −0.472009 | + | 0.817544i | ||||
\(452\) | 1.81271 | + | 3.13971i | 0.0852628 | + | 0.147680i | ||||
\(453\) | −5.70189 | − | 9.87596i | −0.267898 | − | 0.464013i | ||||
\(454\) | −9.30897 | −0.436892 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.2083 | −0.759025 | ||||||||
\(457\) | 20.0573 | + | 34.7402i | 0.938240 | + | 1.62508i | 0.768751 | + | 0.639548i | \(0.220878\pi\) |
0.169489 | + | 0.985532i | \(0.445788\pi\) | |||||||
\(458\) | 8.78222 | + | 15.2113i | 0.410366 | + | 0.710775i | ||||
\(459\) | −0.739961 | + | 1.28165i | −0.0345384 | + | 0.0598223i | ||||
\(460\) | 1.99457 | 0.0929972 | ||||||||
\(461\) | −3.76950 | + | 6.52897i | −0.175563 | + | 0.304084i | −0.940356 | − | 0.340192i | \(-0.889508\pi\) |
0.764793 | + | 0.644276i | \(0.222841\pi\) | |||||||
\(462\) | 27.5068 | − | 47.6432i | 1.27973 | − | 2.21656i | ||||
\(463\) | −23.3031 | −1.08299 | −0.541494 | − | 0.840705i | \(-0.682141\pi\) | ||||
−0.541494 | + | 0.840705i | \(0.682141\pi\) | |||||||
\(464\) | −0.0335403 | + | 0.0580936i | −0.00155707 | + | 0.00269693i | ||||
\(465\) | 6.37182 | + | 11.0363i | 0.295486 | + | 0.511797i | ||||
\(466\) | 5.79118 | + | 10.0306i | 0.268271 | + | 0.464659i | ||||
\(467\) | −22.6297 | −1.04718 | −0.523589 | − | 0.851971i | \(-0.675407\pi\) | ||||
−0.523589 | + | 0.851971i | \(0.675407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0405 | 1.06391 | ||||||||
\(470\) | −1.57666 | − | 2.73086i | −0.0727260 | − | 0.125965i | ||||
\(471\) | −11.7085 | − | 20.2797i | −0.539500 | − | 0.934441i | ||||
\(472\) | −0.262648 | + | 0.454919i | −0.0120893 | + | 0.0209394i | ||||
\(473\) | 6.08012 | 0.279564 | ||||||||
\(474\) | −17.0429 | + | 29.5192i | −0.782808 | + | 1.35586i | ||||
\(475\) | 1.13397 | − | 1.96410i | 0.0520303 | − | 0.0901192i | ||||
\(476\) | −2.08783 | −0.0956956 | ||||||||
\(477\) | 5.41465 | − | 9.37844i | 0.247920 | − | 0.429409i | ||||
\(478\) | 12.1446 | + | 21.0351i | 0.555482 | + | 0.962124i | ||||
\(479\) | 10.3224 | + | 17.8789i | 0.471643 | + | 0.816910i | 0.999474 | − | 0.0324399i | \(-0.0103278\pi\) |
−0.527831 | + | 0.849350i | \(0.676994\pi\) | |||||||
\(480\) | −6.57666 | −0.300182 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.3777 | 1.29257 | ||||||||
\(483\) | −16.3433 | − | 28.3075i | −0.743648 | − | 1.28804i | ||||
\(484\) | 4.57449 | + | 7.92325i | 0.207931 | + | 0.360148i | ||||
\(485\) | 6.08408 | − | 10.5379i | 0.276264 | − | 0.478503i | ||||
\(486\) | 24.7074 | 1.12075 | ||||||||
\(487\) | 1.51802 | − | 2.62929i | 0.0687882 | − | 0.119145i | −0.829580 | − | 0.558388i | \(-0.811420\pi\) |
0.898368 | + | 0.439243i | \(0.144753\pi\) | |||||||
\(488\) | −5.14838 | + | 8.91725i | −0.233056 | + | 0.403665i | ||||
\(489\) | −15.8155 | −0.715203 | ||||||||
\(490\) | 3.63553 | − | 6.29692i | 0.164236 | − | 0.284466i | ||||
\(491\) | −5.33401 | − | 9.23877i | −0.240720 | − | 0.416940i | 0.720199 | − | 0.693767i | \(-0.244050\pi\) |
−0.960920 | + | 0.276827i | \(0.910717\pi\) | |||||||
\(492\) | −2.22982 | − | 3.86217i | −0.100528 | − | 0.174120i | ||||
\(493\) | 0.0279884 | 0.00126053 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.1039 | −0.588975 | ||||||||
\(496\) | −7.41139 | − | 12.8369i | −0.332781 | − | 0.576394i | ||||
\(497\) | 19.4362 | + | 33.6646i | 0.871835 | + | 1.51006i | ||||
\(498\) | 17.2506 | − | 29.8789i | 0.773016 | − | 1.33890i | ||||
\(499\) | −33.9143 | −1.51821 | −0.759107 | − | 0.650966i | \(-0.774364\pi\) | ||||
−0.759107 | + | 0.650966i | \(0.774364\pi\) | |||||||
\(500\) | 0.256182 | − | 0.443720i | 0.0114568 | − | 0.0198438i | ||||
\(501\) | 12.2324 | − | 21.1872i | 0.546504 | − | 0.946572i | ||||
\(502\) | −14.4413 | −0.644546 | ||||||||
\(503\) | 6.31380 | − | 10.9358i | 0.281518 | − | 0.487604i | −0.690241 | − | 0.723580i | \(-0.742495\pi\) |
0.971759 | + | 0.235976i | \(0.0758286\pi\) | |||||||
\(504\) | 13.4557 | + | 23.3059i | 0.599363 | + | 1.03813i | ||||
\(505\) | 2.02721 | + | 3.51122i | 0.0902095 | + | 0.156247i | ||||
\(506\) | −25.5058 | −1.13387 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.85945 | 0.259971 | ||||||||
\(509\) | −12.0763 | − | 20.9168i | −0.535273 | − | 0.927120i | −0.999150 | − | 0.0412201i | \(-0.986876\pi\) |
0.463877 | − | 0.885899i | \(-0.346458\pi\) | |||||||
\(510\) | −1.60984 | − | 2.78833i | −0.0712851 | − | 0.123469i | ||||
\(511\) | 8.46601 | − | 14.6636i | 0.374514 | − | 0.648678i | ||||
\(512\) | 24.2750 | 1.07281 | ||||||||
\(513\) | −1.48269 | + | 2.56810i | −0.0654625 | + | 0.113384i | ||||
\(514\) | −3.38465 | + | 5.86238i | −0.149290 | + | 0.258578i | ||||
\(515\) | −17.9035 | −0.788921 | ||||||||
\(516\) | −0.676260 | + | 1.17132i | −0.0297707 | + | 0.0515644i | ||||
\(517\) | −6.94402 | − | 12.0274i | −0.305398 | − | 0.528964i | ||||
\(518\) | −19.1103 | − | 33.0999i | −0.839656 | − | 1.45433i | ||||
\(519\) | −10.3982 | −0.456431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7521 | −1.08441 | −0.542205 | − | 0.840246i | \(-0.682410\pi\) | ||||
−0.542205 | + | 0.840246i | \(0.682410\pi\) | |||||||
\(522\) | −0.0367861 | − | 0.0637154i | −0.00161008 | − | 0.00278875i | ||||
\(523\) | −18.5163 | − | 32.0712i | −0.809662 | − | 1.40238i | −0.913098 | − | 0.407739i | \(-0.866317\pi\) |
0.103436 | − | 0.994636i | \(-0.467016\pi\) | |||||||
\(524\) | −2.70732 | + | 4.68922i | −0.118270 | + | 0.204850i | ||||
\(525\) | −8.39654 | −0.366455 | ||||||||
\(526\) | 4.18332 | − | 7.24573i | 0.182402 | − | 0.315929i | ||||
\(527\) | −3.09229 | + | 5.35600i | −0.134702 | + | 0.233311i | ||||
\(528\) | 33.9865 | 1.47907 | ||||||||
\(529\) | 3.92277 | − | 6.79444i | 0.170555 | − | 0.295410i | ||||
\(530\) | −2.70732 | − | 4.68922i | −0.117599 | − | 0.203687i | ||||
\(531\) | −0.209084 | − | 0.362145i | −0.00907348 | − | 0.0157157i | ||||
\(532\) | −4.18348 | −0.181377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −45.9519 | −1.98854 | ||||||||
\(535\) | 4.56593 | + | 7.90842i | 0.197402 | + | 0.341911i | ||||
\(536\) | 9.80545 | + | 16.9835i | 0.423531 | + | 0.733577i | ||||
\(537\) | −21.7264 | + | 37.6312i | −0.937562 | + | 1.62391i | ||||
\(538\) | 1.73438 | 0.0747744 | ||||||||
\(539\) | 16.0118 | − | 27.7332i | 0.689677 | − | 1.19456i | ||||
\(540\) | −0.334963 | + | 0.580172i | −0.0144145 | + | 0.0249666i | ||||
\(541\) | 8.38144 | 0.360346 | 0.180173 | − | 0.983635i | \(-0.442334\pi\) | ||||
0.180173 | + | 0.983635i | \(0.442334\pi\) | |||||||
\(542\) | 6.07981 | − | 10.5305i | 0.261150 | − | 0.452326i | ||||
\(543\) | −21.0952 | − | 36.5379i | −0.905281 | − | 1.56799i | ||||
\(544\) | −1.59585 | − | 2.76409i | −0.0684215 | − | 0.118509i | ||||
\(545\) | −7.37605 | −0.315955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7842 | −0.974181 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(548\) | −0.970090 | − | 1.68025i | −0.0414402 | − | 0.0717765i | ||||
\(549\) | −4.09843 | − | 7.09870i | −0.174917 | − | 0.302965i | ||||
\(550\) | −3.27597 | + | 5.67414i | −0.139688 | + | 0.241946i | ||||
\(551\) | 0.0560816 | 0.00238915 | ||||||||
\(552\) | 13.9106 | − | 24.0938i | 0.592074 | − | 1.02550i | ||||
\(553\) | −21.5699 | + | 37.3601i | −0.917245 | + | 1.58871i | ||||
\(554\) | 21.3735 | 0.908071 | ||||||||
\(555\) | −10.1500 | + | 17.5803i | −0.430844 | + | 0.746244i | ||||
\(556\) | 0.515915 | + | 0.893592i | 0.0218797 | + | 0.0378967i | ||||
\(557\) | −14.0764 | − | 24.3810i | −0.596435 | − | 1.03306i | −0.993343 | − | 0.115197i | \(-0.963250\pi\) |
0.396908 | − | 0.917858i | \(-0.370083\pi\) | |||||||
\(558\) | 16.2572 | 0.688222 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.76645 | 0.412708 | ||||||||
\(561\) | −7.09017 | − | 12.2805i | −0.299347 | − | 0.518484i | ||||
\(562\) | −6.54676 | − | 11.3393i | −0.276159 | − | 0.478321i | ||||
\(563\) | 9.06514 | − | 15.7013i | 0.382050 | − | 0.661731i | −0.609305 | − | 0.792936i | \(-0.708551\pi\) |
0.991355 | + | 0.131206i | \(0.0418848\pi\) | |||||||
\(564\) | 3.08939 | 0.130087 | ||||||||
\(565\) | −3.53794 | + | 6.12789i | −0.148842 | + | 0.257802i | ||||
\(566\) | 0.804007 | − | 1.39258i | 0.0337950 | − | 0.0585346i | ||||
\(567\) | 37.3253 | 1.56752 | ||||||||
\(568\) | −16.5431 | + | 28.6535i | −0.694133 | + | 1.20227i | ||||
\(569\) | −20.2992 | − | 35.1593i | −0.850988 | − | 1.47395i | −0.880317 | − | 0.474385i | \(-0.842670\pi\) |
0.0293292 | − | 0.999570i | \(-0.490663\pi\) | |||||||
\(570\) | −3.22572 | − | 5.58710i | −0.135110 | − | 0.234018i | ||||
\(571\) | 24.7159 | 1.03433 | 0.517164 | − | 0.855886i | \(-0.326988\pi\) | ||||
0.517164 | + | 0.855886i | \(0.326988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 63.7551 | 2.66341 | ||||||||
\(574\) | 8.19393 | + | 14.1923i | 0.342008 | + | 0.592375i | ||||
\(575\) | 1.94644 | + | 3.37133i | 0.0811720 | + | 0.140594i | ||||
\(576\) | −10.8124 | + | 18.7276i | −0.450516 | + | 0.780317i | ||||
\(577\) | −23.0691 | −0.960379 | −0.480189 | − | 0.877165i | \(-0.659432\pi\) | ||||
−0.480189 | + | 0.877165i | \(0.659432\pi\) | |||||||
\(578\) | −9.58607 | + | 16.6036i | −0.398728 | + | 0.690617i | ||||
\(579\) | 25.3834 | − | 43.9654i | 1.05490 | − | 1.82714i | ||||
\(580\) | 0.0126697 | 0.000526079 | ||||||||
\(581\) | 21.8327 | − | 37.8153i | 0.905771 | − | 1.56884i | ||||
\(582\) | −17.3068 | − | 29.9763i | −0.717392 | − | 1.24256i | ||||
\(583\) | −11.9237 | − | 20.6525i | −0.493831 | − | 0.855341i | ||||
\(584\) | 14.4116 | 0.596358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.8602 | 0.944345 | ||||||||
\(587\) | −10.1762 | − | 17.6256i | −0.420015 | − | 0.727487i | 0.575926 | − | 0.817502i | \(-0.304642\pi\) |
−0.995940 | + | 0.0900152i | \(0.971308\pi\) | |||||||
\(588\) | 3.56182 | + | 6.16925i | 0.146887 | + | 0.254416i | ||||
\(589\) | −6.19615 | + | 10.7321i | −0.255308 | + | 0.442206i | ||||
\(590\) | −0.209084 | −0.00860786 | ||||||||
\(591\) | −1.97859 | + | 3.42701i | −0.0813881 | + | 0.140968i | ||||
\(592\) | 11.8060 | − | 20.4486i | 0.485223 | − | 0.840432i | ||||
\(593\) | −10.3834 | −0.426395 | −0.213198 | − | 0.977009i | \(-0.568388\pi\) | ||||
−0.213198 | + | 0.977009i | \(0.568388\pi\) | |||||||
\(594\) | 4.28339 | − | 7.41904i | 0.175750 | − | 0.304407i | ||||
\(595\) | −2.03745 | − | 3.52897i | −0.0835273 | − | 0.144674i | ||||
\(596\) | 1.41356 | + | 2.44836i | 0.0579017 | + | 0.100289i | ||||
\(597\) | 59.0652 | 2.41738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5965 | −1.29100 | −0.645499 | − | 0.763761i | \(-0.723351\pi\) | ||||
−0.645499 | + | 0.763761i | \(0.723351\pi\) | |||||||
\(600\) | −3.57335 | − | 6.18922i | −0.145881 | − | 0.252674i | ||||
\(601\) | 21.9423 | + | 38.0051i | 0.895044 | + | 1.55026i | 0.833751 | + | 0.552141i | \(0.186189\pi\) |
0.0612928 | + | 0.998120i | \(0.480478\pi\) | |||||||
\(602\) | 2.48505 | − | 4.30423i | 0.101283 | − | 0.175428i | ||||
\(603\) | −15.6115 | −0.635750 | ||||||||
\(604\) | 1.25263 | − | 2.16962i | 0.0509688 | − | 0.0882806i | ||||
\(605\) | −8.92820 | + | 15.4641i | −0.362983 | + | 0.628705i | ||||
\(606\) | 11.5332 | 0.468505 | ||||||||
\(607\) | −1.08770 | + | 1.88395i | −0.0441484 | + | 0.0764673i | −0.887255 | − | 0.461279i | \(-0.847391\pi\) |
0.843107 | + | 0.537746i | \(0.180724\pi\) | |||||||
\(608\) | −3.19768 | − | 5.53854i | −0.129683 | − | 0.224617i | ||||
\(609\) | −0.103814 | − | 0.179812i | −0.00420677 | − | 0.00728634i | ||||
\(610\) | −4.09843 | −0.165941 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.41465 | 0.0571837 | ||||||||
\(613\) | −7.38100 | − | 12.7843i | −0.298116 | − | 0.516352i | 0.677589 | − | 0.735441i | \(-0.263025\pi\) |
−0.975705 | + | 0.219089i | \(0.929691\pi\) | |||||||
\(614\) | −8.72336 | − | 15.1093i | −0.352046 | − | 0.609762i | ||||
\(615\) | 4.35203 | − | 7.53794i | 0.175491 | − | 0.303959i | ||||
\(616\) | 59.2622 | 2.38774 | ||||||||
\(617\) | −10.1486 | + | 17.5779i | −0.408567 | + | 0.707659i | −0.994729 | − | 0.102535i | \(-0.967305\pi\) |
0.586162 | + | 0.810194i | \(0.300638\pi\) | |||||||
\(618\) | −25.4642 | + | 44.1053i | −1.02432 | + | 1.77418i | ||||
\(619\) | −9.94207 | −0.399605 | −0.199803 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199803 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(620\) | −1.39980 | + | 2.42453i | −0.0562175 | + | 0.0973716i | ||||
\(621\) | −2.54500 | − | 4.40807i | −0.102127 | − | 0.176890i | ||||
\(622\) | 1.68379 | + | 2.91641i | 0.0675138 | + | 0.116937i | ||||
\(623\) | −58.1577 | −2.33004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.99276 | − | 17.3080i | −0.399391 | − | 0.691766i | ||||
\(627\) | −14.2069 | − | 24.6070i | −0.567368 | − | 0.982711i | ||||
\(628\) | 2.57221 | − | 4.45519i | 0.102642 | − | 0.177782i | ||||
\(629\) | −9.85174 | −0.392815 | ||||||||
\(630\) | −5.35578 | + | 9.27648i | −0.213379 | + | 0.369584i | ||||
\(631\) | 0.486710 | − | 0.843006i | 0.0193756 | − | 0.0335596i | −0.856175 | − | 0.516686i | \(-0.827165\pi\) |
0.875551 | + | 0.483126i | \(0.160499\pi\) | |||||||
\(632\) | −36.7183 | −1.46058 | ||||||||
\(633\) | 0.391243 | − | 0.677652i | 0.0155505 | − | 0.0269342i | ||||
\(634\) | −1.08903 | − | 1.88625i | −0.0432507 | − | 0.0749124i | ||||
\(635\) | 5.71806 | + | 9.90396i | 0.226914 | + | 0.393027i | ||||
\(636\) | 5.30487 | 0.210352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.162015 | −0.00641425 | ||||||||
\(639\) | −13.1694 | − | 22.8100i | −0.520972 | − | 0.902350i | ||||
\(640\) | 2.58631 | + | 4.47962i | 0.102233 | + | 0.177072i | ||||
\(641\) | 6.31047 | − | 10.9301i | 0.249249 | − | 0.431711i | −0.714069 | − | 0.700075i | \(-0.753150\pi\) |
0.963318 | + | 0.268364i | \(0.0864830\pi\) | |||||||
\(642\) | 25.9766 | 1.02521 | ||||||||
\(643\) | 4.98022 | − | 8.62599i | 0.196401 | − | 0.340176i | −0.750958 | − | 0.660350i | \(-0.770408\pi\) |
0.947359 | + | 0.320174i | \(0.103741\pi\) | |||||||
\(644\) | 3.59042 | − | 6.21878i | 0.141482 | − | 0.245054i | ||||
\(645\) | −2.63977 | −0.103941 | ||||||||
\(646\) | 1.56546 | − | 2.71146i | 0.0615923 | − | 0.106681i | ||||
\(647\) | 18.1381 | + | 31.4162i | 0.713084 | + | 1.23510i | 0.963694 | + | 0.267009i | \(0.0860354\pi\) |
−0.250610 | + | 0.968088i | \(0.580631\pi\) | |||||||
\(648\) | 15.8847 | + | 27.5131i | 0.624009 | + | 1.08081i | ||||
\(649\) | −0.920861 | −0.0361470 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.8796 | 1.79816 | ||||||||
\(652\) | −1.73723 | − | 3.00898i | −0.0680353 | − | 0.117841i | ||||
\(653\) | −6.87769 | − | 11.9125i | −0.269145 | − | 0.466172i | 0.699497 | − | 0.714636i | \(-0.253408\pi\) |
−0.968641 | + | 0.248464i | \(0.920074\pi\) | |||||||
\(654\) | −10.4910 | + | 18.1709i | −0.410231 | + | 0.710540i | ||||
\(655\) | −10.5680 | −0.412925 | ||||||||
\(656\) | −5.06207 | + | 8.76776i | −0.197641 | + | 0.342324i | ||||
\(657\) | −5.73629 | + | 9.93555i | −0.223794 | + | 0.387623i | ||||
\(658\) | −11.3526 | −0.442570 | ||||||||
\(659\) | 1.29092 | − | 2.23593i | 0.0502869 | − | 0.0870995i | −0.839786 | − | 0.542917i | \(-0.817320\pi\) |
0.890073 | + | 0.455818i | \(0.150653\pi\) | |||||||
\(660\) | −3.20955 | − | 5.55910i | −0.124932 | − | 0.216388i | ||||
\(661\) | 12.4382 | + | 21.5437i | 0.483791 | + | 0.837951i | 0.999827 | − | 0.0186163i | \(-0.00592609\pi\) |
−0.516036 | + | 0.856567i | \(0.672593\pi\) | |||||||
\(662\) | 8.81151 | 0.342469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.1656 | 1.44231 | ||||||||
\(665\) | −4.08253 | − | 7.07115i | −0.158314 | − | 0.274207i | ||||
\(666\) | 12.9485 | + | 22.4274i | 0.501743 | + | 0.869045i | ||||
\(667\) | −0.0481312 | + | 0.0833657i | −0.00186365 | + | 0.00322793i | ||||
\(668\) | 5.37460 | 0.207949 | ||||||||
\(669\) | −14.3395 | + | 24.8368i | −0.554398 | + | 0.960246i | ||||
\(670\) | −3.90288 | + | 6.75998i | −0.150781 | + | 0.261161i | ||||
\(671\) | −18.0506 | −0.696834 | ||||||||
\(672\) | −11.8386 | + | 20.5051i | −0.456685 | + | 0.791002i | ||||
\(673\) | −21.6611 | − | 37.5181i | −0.834974 | − | 1.44622i | −0.894052 | − | 0.447964i | \(-0.852149\pi\) |
0.0590774 | − | 0.998253i | \(-0.481184\pi\) | |||||||
\(674\) | −2.66025 | − | 4.60770i | −0.102469 | − | 0.177482i | ||||
\(675\) | −1.30752 | −0.0503264 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.3625 | −1.58969 | −0.794845 | − | 0.606813i | \(-0.792448\pi\) | ||||
−0.794845 | + | 0.606813i | \(0.792448\pi\) | |||||||
\(678\) | 10.0641 | + | 17.4315i | 0.386508 | + | 0.669451i | ||||
\(679\) | −21.9039 | − | 37.9386i | −0.840594 | − | 1.45595i | ||||
\(680\) | 1.73417 | − | 3.00367i | 0.0665024 | − | 0.115186i | ||||
\(681\) | 17.8003 | 0.682110 | ||||||||
\(682\) | 17.9002 | − | 31.0041i | 0.685435 | − | 1.18721i | ||||
\(683\) | 1.31344 | − | 2.27495i | 0.0502574 | − | 0.0870484i | −0.839802 | − | 0.542892i | \(-0.817329\pi\) |
0.890060 | + | 0.455844i | \(0.150662\pi\) | |||||||
\(684\) | 2.83459 | 0.108383 | ||||||||
\(685\) | 1.89336 | − | 3.27940i | 0.0723416 | − | 0.125299i | ||||
\(686\) | 2.28028 | + | 3.94957i | 0.0870617 | + | 0.150795i | ||||
\(687\) | −16.7931 | − | 29.0865i | −0.640696 | − | 1.10972i | ||||
\(688\) | 3.07045 | 0.117060 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.0737 | 0.421569 | ||||||||
\(691\) | −7.63765 | − | 13.2288i | −0.290550 | − | 0.503247i | 0.683390 | − | 0.730053i | \(-0.260505\pi\) |
−0.973940 | + | 0.226806i | \(0.927172\pi\) | |||||||
\(692\) | −1.14218 | − | 1.97831i | −0.0434190 | − | 0.0752039i | ||||
\(693\) | −23.5882 | + | 40.8560i | −0.896043 | + | 1.55199i | ||||
\(694\) | 32.5744 | 1.23651 | ||||||||
\(695\) | −1.00693 | + | 1.74406i | −0.0381951 | + | 0.0661558i | ||||
\(696\) | 0.0883613 | − | 0.153046i | 0.00334933 | − | 0.00580120i | ||||
\(697\) | 4.22414 | 0.160001 | ||||||||
\(698\) | −14.3747 | + | 24.8976i | −0.544089 | + | 0.942390i | ||||
\(699\) | −11.0737 | − | 19.1802i | −0.418846 | − | 0.725463i | ||||
\(700\) | −0.922305 | − | 1.59748i | −0.0348599 | − | 0.0603790i | ||||
\(701\) | −48.1947 | −1.82029 | −0.910144 | − | 0.414292i | \(-0.864029\pi\) | ||||
−0.910144 | + | 0.414292i | \(0.864029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7404 | −0.744522 | ||||||||
\(704\) | 23.8103 | + | 41.2406i | 0.897383 | + | 1.55431i | ||||
\(705\) | 3.01484 | + | 5.22186i | 0.113546 | + | 0.196667i | ||||
\(706\) | −3.49884 | + | 6.06016i | −0.131680 | + | 0.228077i | ||||
\(707\) | 14.5967 | 0.548964 | ||||||||
\(708\) | 0.102423 | − | 0.177401i | 0.00384928 | − | 0.00666715i | ||||
\(709\) | −19.4350 | + | 33.6624i | −0.729896 | + | 1.26422i | 0.227031 | + | 0.973887i | \(0.427098\pi\) |
−0.956927 | + | 0.290329i | \(0.906235\pi\) | |||||||
\(710\) | −13.1694 | −0.494237 | ||||||||
\(711\) | 14.6150 | − | 25.3140i | 0.548107 | − | 0.949349i | ||||
\(712\) | −24.7504 | − | 42.8689i | −0.927560 | − | 1.60658i | ||||
\(713\) | −10.6355 | − | 18.4213i | −0.398304 | − | 0.689882i | ||||
\(714\) | −11.5915 | −0.433801 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.54600 | −0.356751 | ||||||||
\(717\) | −23.2226 | − | 40.2227i | −0.867263 | − | 1.50214i | ||||
\(718\) | 15.0987 | + | 26.1517i | 0.563478 | + | 0.975973i | ||||
\(719\) | −3.30830 | + | 5.73015i | −0.123379 | + | 0.213698i | −0.921098 | − | 0.389331i | \(-0.872706\pi\) |
0.797719 | + | 0.603029i | \(0.206040\pi\) | |||||||
\(720\) | −6.61742 | −0.246617 | ||||||||
\(721\) | −32.2280 | + | 55.8205i | −1.20023 | + | 2.07887i | ||||
\(722\) | −8.45024 | + | 14.6362i | −0.314485 | + | 0.544705i | ||||
\(723\) | −54.2629 | −2.01806 | ||||||||
\(724\) | 4.63433 | − | 8.02690i | 0.172234 | − | 0.298317i | ||||
\(725\) | 0.0123639 | + | 0.0214150i | 0.000459185 | + | 0.000795332i | ||||
\(726\) | 25.3973 | + | 43.9893i | 0.942581 | + | 1.63260i | ||||
\(727\) | −18.3735 | −0.681435 | −0.340717 | − | 0.940166i | \(-0.610670\pi\) | ||||
−0.340717 | + | 0.940166i | \(0.610670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1420 | −0.597853 | ||||||||
\(730\) | 2.86814 | + | 4.96777i | 0.106155 | + | 0.183866i | ||||
\(731\) | −0.640548 | − | 1.10946i | −0.0236915 | − | 0.0410349i | ||||
\(732\) | 2.00767 | − | 3.47739i | 0.0742057 | − | 0.128528i | ||||
\(733\) | −0.791131 | −0.0292211 | −0.0146105 | − | 0.999893i | \(-0.504651\pi\) | ||||
−0.0146105 | + | 0.999893i | \(0.504651\pi\) | |||||||
\(734\) | 15.8886 | − | 27.5198i | 0.586458 | − | 1.01578i | ||||
\(735\) | −6.95174 | + | 12.0408i | −0.256419 | + | 0.444130i | ||||
\(736\) | 10.9774 | 0.404634 | ||||||||
\(737\) | −17.1893 | + | 29.7727i | −0.633175 | + | 1.09669i | ||||
\(738\) | −5.55193 | − | 9.61623i | −0.204369 | − | 0.353978i | ||||
\(739\) | 15.5926 | + | 27.0073i | 0.573585 | + | 0.993478i | 0.996194 | + | 0.0871658i | \(0.0277810\pi\) |
−0.422609 | + | 0.906312i | \(0.638886\pi\) | |||||||
\(740\) | −4.45965 | −0.163940 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4938 | −0.715639 | ||||||||
\(743\) | 2.78152 | + | 4.81773i | 0.102044 | + | 0.176745i | 0.912527 | − | 0.409017i | \(-0.134128\pi\) |
−0.810483 | + | 0.585763i | \(0.800795\pi\) | |||||||
\(744\) | 19.5251 | + | 33.8185i | 0.715826 | + | 1.23985i | ||||
\(745\) | −2.75890 | + | 4.77855i | −0.101078 | + | 0.175073i | ||||
\(746\) | −16.1053 | −0.589658 | ||||||||
\(747\) | −14.7931 | + | 25.6224i | −0.541251 | + | 0.937474i | ||||
\(748\) | 1.55762 | − | 2.69787i | 0.0569521 | − | 0.0986439i | ||||
\(749\) | 32.8765 | 1.20128 | ||||||||
\(750\) | 1.42231 | − | 2.46350i | 0.0519352 | − | 0.0899545i | ||||
\(751\) | 17.6048 | + | 30.4925i | 0.642410 | + | 1.11269i | 0.984893 | + | 0.173163i | \(0.0553987\pi\) |
−0.342483 | + | 0.939524i | \(0.611268\pi\) | |||||||
\(752\) | −3.50672 | − | 6.07381i | −0.127877 | − | 0.221489i | ||||
\(753\) | 27.6142 | 1.00632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.88961 | 0.177951 | ||||||||
\(756\) | 1.20593 | + | 2.08873i | 0.0438593 | + | 0.0759665i | ||||
\(757\) | −25.0223 | − | 43.3399i | −0.909451 | − | 1.57522i | −0.814828 | − | 0.579703i | \(-0.803169\pi\) |
−0.0946237 | − | 0.995513i | \(-0.530165\pi\) | |||||||
\(758\) | −15.8545 | + | 27.4609i | −0.575863 | + | 0.997424i | ||||
\(759\) | 48.7715 | 1.77029 | ||||||||
\(760\) | 3.47484 | − | 6.01859i | 0.126046 | − | 0.218317i | ||||
\(761\) | 22.4105 | − | 38.8161i | 0.812379 | − | 1.40708i | −0.0988165 | − | 0.995106i | \(-0.531506\pi\) |
0.911195 | − | 0.411975i | \(-0.135161\pi\) | |||||||
\(762\) | 32.5313 | 1.17848 | ||||||||
\(763\) | −13.2776 | + | 22.9975i | −0.480682 | + | 0.832566i | ||||
\(764\) | 7.00307 | + | 12.1297i | 0.253362 | + | 0.438836i | ||||
\(765\) | 1.38051 | + | 2.39111i | 0.0499124 | + | 0.0864508i | ||||
\(766\) | −11.7092 | −0.423072 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.6361 | −0.961148 | ||||||||
\(769\) | −19.6817 | − | 34.0897i | −0.709739 | − | 1.22930i | −0.964954 | − | 0.262420i | \(-0.915479\pi\) |
0.255215 | − | 0.966884i | \(-0.417854\pi\) | |||||||
\(770\) | 11.7941 | + | 20.4280i | 0.425031 | + | 0.736175i | ||||
\(771\) | 6.47201 | − | 11.2099i | 0.233084 | − | 0.403713i | ||||
\(772\) | 11.1528 | 0.401399 | ||||||||
\(773\) | 24.3902 | − | 42.2452i | 0.877256 | − | 1.51945i | 0.0229167 | − | 0.999737i | \(-0.492705\pi\) |
0.854340 | − | 0.519715i | \(-0.173962\pi\) | |||||||
\(774\) | −1.68379 | + | 2.91641i | −0.0605225 | + | 0.104828i | ||||
\(775\) | −5.46410 | −0.196276 | ||||||||
\(776\) | 18.6434 | − | 32.2914i | 0.669260 | − | 1.15919i | ||||
\(777\) | 36.5420 | + | 63.2926i | 1.31094 | + | 2.27061i | ||||
\(778\) | 3.43420 | + | 5.94822i | 0.123122 | + | 0.213254i | ||||
\(779\) | 8.46410 | 0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.0013 | −2.07545 | ||||||||
\(782\) | 2.68707 | + | 4.65415i | 0.0960895 | + | 0.166432i | ||||
\(783\) | −0.0161661 | − | 0.0280005i | −0.000577728 | − | 0.00100066i | ||||
\(784\) | 8.08592 | − | 14.0052i | 0.288783 | − | 0.500187i | ||||
\(785\) | 10.0405 | 0.358363 | ||||||||
\(786\) | −15.0309 | + | 26.0342i | −0.536134 | + | 0.928611i | ||||
\(787\) | 19.9304 | − | 34.5204i | 0.710442 | − | 1.23052i | −0.254250 | − | 0.967139i | \(-0.581829\pi\) |
0.964692 | − | 0.263382i | \(-0.0848381\pi\) | |||||||
\(788\) | −0.869338 | −0.0309689 | ||||||||
\(789\) | −7.99922 | + | 13.8551i | −0.284780 | + | 0.493253i | ||||
\(790\) | −7.30752 | − | 12.6570i | −0.259990 | − | 0.450316i | ||||
\(791\) | 12.7373 | + | 22.0616i | 0.452885 | + | 0.784420i | ||||
\(792\) | −40.1541 | −1.42682 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.4490 | −0.725709 | ||||||||
\(795\) | 5.17686 | + | 8.96658i | 0.183604 | + | 0.318012i | ||||
\(796\) | 6.48793 | + | 11.2374i | 0.229958 | + | 0.398300i | ||||
\(797\) | −13.1059 | + | 22.7001i | −0.464235 | + | 0.804079i | −0.999167 | − | 0.0408167i | \(-0.987004\pi\) |
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(798\) | −23.2264 | −0.822206 | ||||||||
\(799\) | −1.46312 | + | 2.53420i | −0.0517616 | + | 0.0896537i | ||||
\(800\) | 1.40994 | − | 2.44209i | 0.0498490 | − | 0.0863409i | ||||
\(801\) | 39.4057 | 1.39233 | ||||||||
\(802\) | 8.46343 | − | 14.6591i | 0.298854 | − | 0.517630i | ||||
\(803\) | 12.6321 | + | 21.8794i | 0.445775 | + | 0.772106i | ||||
\(804\) | −3.82375 | − | 6.62293i | −0.134853 | − | 0.233573i | ||||
\(805\) | 14.0151 | 0.493968 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.31643 | −0.116744 | ||||||||
\(808\) | 6.21196 | + | 10.7594i | 0.218536 | + | 0.378515i | ||||
\(809\) | −11.1068 | − | 19.2376i | −0.390495 | − | 0.676357i | 0.602020 | − | 0.798481i | \(-0.294363\pi\) |
−0.992515 | + | 0.122124i | \(0.961029\pi\) | |||||||
\(810\) | −6.32260 | + | 10.9511i | −0.222153 | + | 0.384781i | ||||
\(811\) | −19.0950 | −0.670515 | −0.335257 | − | 0.942127i | \(-0.608823\pi\) | ||||
−0.335257 | + | 0.942127i | \(0.608823\pi\) | |||||||
\(812\) | 0.0228066 | − | 0.0395023i | 0.000800356 | − | 0.00138626i | ||||
\(813\) | −11.6256 | + | 20.1362i | −0.407729 | + | 0.706207i | ||||
\(814\) | 57.0284 | 1.99885 | ||||||||
\(815\) | 3.39062 | − | 5.87273i | 0.118768 | − | 0.205713i | ||||
\(816\) | −3.58052 | − | 6.20164i | −0.125343 | − | 0.217101i | ||||
\(817\) | −1.28349 | − | 2.22308i | −0.0449038 | − | 0.0777757i | ||||
\(818\) | 35.8894 | 1.25484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91217 | 0.0667758 | ||||||||
\(821\) | −17.0792 | − | 29.5820i | −0.596068 | − | 1.03242i | −0.993395 | − | 0.114743i | \(-0.963396\pi\) |
0.397327 | − | 0.917677i | \(-0.369938\pi\) | |||||||
\(822\) | −5.38588 | − | 9.32861i | −0.187854 | − | 0.325373i | ||||
\(823\) | −2.03970 | + | 3.53286i | −0.0710995 | + | 0.123148i | −0.899383 | − | 0.437161i | \(-0.855984\pi\) |
0.828284 | + | 0.560309i | \(0.189317\pi\) | |||||||
\(824\) | −54.8616 | −1.91119 | ||||||||
\(825\) | 6.26420 | − | 10.8499i | 0.218091 | − | 0.377745i | ||||
\(826\) | −0.376372 | + | 0.651896i | −0.0130957 | + | 0.0226824i | ||||
\(827\) | 54.8780 | 1.90830 | 0.954148 | − | 0.299337i | \(-0.0967654\pi\) | ||||
0.954148 | + | 0.299337i | \(0.0967654\pi\) | |||||||
\(828\) | −2.43275 | + | 4.21364i | −0.0845438 | + | 0.146434i | ||||
\(829\) | −4.07475 | − | 7.05768i | −0.141522 | − | 0.245123i | 0.786548 | − | 0.617529i | \(-0.211866\pi\) |
−0.928070 | + | 0.372406i | \(0.878533\pi\) | |||||||
\(830\) | 7.39654 | + | 12.8112i | 0.256738 | + | 0.444683i | ||||
\(831\) | −40.8697 | −1.41775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.74745 | −0.233785 | ||||||||
\(834\) | 2.86433 | + | 4.96116i | 0.0991836 | + | 0.171791i | ||||
\(835\) | 5.24490 | + | 9.08444i | 0.181507 | + | 0.314380i | ||||
\(836\) | 3.12107 | − | 5.40585i | 0.107944 | − | 0.186965i | ||||
\(837\) | 7.14441 | 0.246947 | ||||||||
\(838\) | 4.24935 | − | 7.36008i | 0.146791 | − | 0.254250i | ||||
\(839\) | −10.9433 | + | 18.9543i | −0.377803 | + | 0.654374i | −0.990742 | − | 0.135756i | \(-0.956654\pi\) |
0.612939 | + | 0.790130i | \(0.289987\pi\) | |||||||
\(840\) | −25.7295 | −0.887752 | ||||||||
\(841\) | 14.4997 | − | 25.1142i | 0.499989 | − | 0.866007i | ||||
\(842\) | −4.34285 | − | 7.52204i | −0.149664 | − | 0.259226i | ||||
\(843\) | 12.5185 | + | 21.6827i | 0.431160 | + | 0.746792i | ||||
\(844\) | 0.171902 | 0.00591710 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.69213 | 0.264461 | ||||||||
\(847\) | 32.1433 | + | 55.6738i | 1.10446 | + | 1.91297i | ||||
\(848\) | −6.02147 | − | 10.4295i | −0.206778 | − | 0.358150i | ||||
\(849\) | −1.53740 | + | 2.66285i | −0.0527633 | + | 0.0913888i | ||||
\(850\) | 1.38051 | 0.0473511 | ||||||||
\(851\) | 16.9419 | − | 29.3442i | 0.580761 | − | 1.00591i | ||||
\(852\) | 6.45118 | − | 11.1738i | 0.221014 | − | 0.382807i | ||||
\(853\) | 19.2240 | 0.658217 | 0.329108 | − | 0.944292i | \(-0.393252\pi\) | ||||
0.329108 | + | 0.944292i | \(0.393252\pi\) | |||||||
\(854\) | −7.37758 | + | 12.7783i | −0.252456 | + | 0.437266i | ||||
\(855\) | 2.76619 | + | 4.79118i | 0.0946016 | + | 0.163855i | ||||
\(856\) | 13.9914 | + | 24.2337i | 0.478215 | + | 0.828292i | ||||
\(857\) | −27.8197 | −0.950302 | −0.475151 | − | 0.879904i | \(-0.657607\pi\) | ||||
−0.475151 | + | 0.879904i | \(0.657607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.7355 | 1.56048 | 0.780238 | − | 0.625482i | \(-0.215098\pi\) | ||||
0.780238 | + | 0.625482i | \(0.215098\pi\) | |||||||
\(860\) | −0.289961 | − | 0.502227i | −0.00988758 | − | 0.0171258i | ||||
\(861\) | −15.6682 | − | 27.1381i | −0.533970 | − | 0.924862i | ||||
\(862\) | −18.4260 | + | 31.9148i | −0.627593 | + | 1.08702i | ||||
\(863\) | −54.8186 | −1.86605 | −0.933024 | − | 0.359814i | \(-0.882840\pi\) | ||||
−0.933024 | + | 0.359814i | \(0.882840\pi\) | |||||||
\(864\) | −1.84352 | + | 3.19308i | −0.0627180 | + | 0.108631i | ||||
\(865\) | 2.22923 | − | 3.86113i | 0.0757960 | − | 0.131283i | ||||
\(866\) | −1.46378 | −0.0497413 | ||||||||
\(867\) | 18.3302 | − | 31.7488i | 0.622526 | − | 1.07825i | ||||
\(868\) | 5.03957 | + | 8.72879i | 0.171054 | + | 0.296274i | ||||
\(869\) | −32.1842 | − | 55.7447i | −1.09177 | − | 1.89101i | ||||
\(870\) | 0.0703412 | 0.00238479 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22.6024 | −0.765415 | ||||||||
\(873\) | 14.8413 | + | 25.7060i | 0.502304 | + | 0.870015i | ||||
\(874\) | 5.38421 | + | 9.32572i | 0.182124 | + | 0.315447i | ||||
\(875\) | 1.80010 | − | 3.11786i | 0.0608544 | − | 0.105403i | ||||
\(876\) | −5.61999 | −0.189882 | ||||||||
\(877\) | −13.6897 | + | 23.7113i | −0.462269 | + | 0.800673i | −0.999074 | − | 0.0430336i | \(-0.986298\pi\) |
0.536805 | + | 0.843706i | \(0.319631\pi\) | |||||||
\(878\) | −10.0954 | + | 17.4858i | −0.340704 | + | 0.590116i | ||||
\(879\) | −43.7125 | −1.47439 | ||||||||
\(880\) | −7.28621 | + | 12.6201i | −0.245618 | + | 0.425423i | ||||
\(881\) | 17.2213 | + | 29.8282i | 0.580200 | + | 1.00494i | 0.995455 | + | 0.0952310i | \(0.0303590\pi\) |
−0.415255 | + | 0.909705i | \(0.636308\pi\) | |||||||
\(882\) | 8.86841 | + | 15.3605i | 0.298615 | + | 0.517216i | ||||
\(883\) | −17.3592 | −0.584183 | −0.292092 | − | 0.956390i | \(-0.594351\pi\) | ||||
−0.292092 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.399804 | 0.0134393 | ||||||||
\(886\) | 2.78058 | + | 4.81610i | 0.0934153 | + | 0.161800i | ||||
\(887\) | 15.5714 | + | 26.9704i | 0.522835 | + | 0.905577i | 0.999647 | + | 0.0265716i | \(0.00845898\pi\) |
−0.476812 | + | 0.879005i | \(0.658208\pi\) | |||||||
\(888\) | −31.1026 | + | 53.8714i | −1.04374 | + | 1.80780i | ||||
\(889\) | 41.1722 | 1.38087 | ||||||||
\(890\) | 9.85143 | − | 17.0632i | 0.330221 | − | 0.571959i | ||||
\(891\) | −27.8464 | + | 48.2313i | −0.932888 | + | 1.61581i | ||||
\(892\) | −6.30042 | −0.210954 | ||||||||
\(893\) | −2.93173 | + | 5.07790i | −0.0981065 | + | 0.169925i | ||||
\(894\) | 7.84799 | + | 13.5931i | 0.262476 | + | 0.454622i | ||||
\(895\) | −9.31564 | − | 16.1352i | −0.311388 | − | 0.539339i | ||||
\(896\) | 18.6224 | 0.622132 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8953 | 0.563804 | ||||||||
\(899\) | −0.0675578 | − | 0.117014i | −0.00225318 | − | 0.00390262i | ||||
\(900\) | 0.624924 | + | 1.08240i | 0.0208308 | + | 0.0360800i | ||||
\(901\) | −2.51236 | + | 4.35154i | −0.0836990 | + | 0.144971i | ||||
\(902\) | −24.4521 | −0.814167 | ||||||||
\(903\) | −4.75184 | + | 8.23042i | −0.158131 | + | 0.273891i | ||||
\(904\) | −10.8413 | + | 18.7777i | −0.360576 | + | 0.624536i | ||||
\(905\) | 18.0900 | 0.601332 | ||||||||
\(906\) | 6.95452 | − | 12.0456i | 0.231048 | − | 0.400188i | ||||
\(907\) | −8.80284 | − | 15.2470i | −0.292294 | − | 0.506267i | 0.682058 | − | 0.731298i | \(-0.261085\pi\) |
−0.974352 | + | 0.225031i | \(0.927752\pi\) | |||||||
\(908\) | 1.95525 | + | 3.38659i | 0.0648872 | + | 0.112388i | ||||
\(909\) | −9.89022 | −0.328038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0232 | 1.65734 | 0.828671 | − | 0.559737i | \(-0.189098\pi\) | ||||
0.828671 | + | 0.559737i | \(0.189098\pi\) | |||||||
\(912\) | −7.17445 | − | 12.4265i | −0.237570 | − | 0.411483i | ||||
\(913\) | 32.5763 | + | 56.4238i | 1.07812 | + | 1.86735i | ||||
\(914\) | −24.4636 | + | 42.3722i | −0.809184 | + | 1.40155i | ||||
\(915\) | 7.83690 | 0.259080 | ||||||||
\(916\) | 3.68922 | − | 6.38992i | 0.121895 | − | 0.211129i | ||||
\(917\) | −19.0234 | + | 32.9495i | −0.628207 | + | 1.08809i | ||||
\(918\) | −1.80504 | −0.0595752 | ||||||||
\(919\) | 3.80778 | − | 6.59527i | 0.125607 | − | 0.217558i | −0.796363 | − | 0.604819i | \(-0.793245\pi\) |
0.921970 | + | 0.387261i | \(0.126579\pi\) | |||||||
\(920\) | 5.96446 | + | 10.3307i | 0.196642 | + | 0.340595i | ||||
\(921\) | 16.6805 | + | 28.8915i | 0.549642 | + | 0.952008i | ||||
\(922\) | −9.19522 | −0.302828 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.1100 | −0.760264 | ||||||||
\(925\) | −4.35203 | − | 7.53794i | −0.143094 | − | 0.247846i | ||||
\(926\) | −14.2113 | − | 24.6146i | −0.467011 | − | 0.808887i | ||||
\(927\) | 21.8366 | − | 37.8222i | 0.717209 | − | 1.24224i | ||||
\(928\) | 0.0697297 | 0.00228899 | ||||||||
\(929\) | −7.06196 | + | 12.2317i | −0.231695 | + | 0.401308i | −0.958307 | − | 0.285740i | \(-0.907761\pi\) |
0.726612 | + | 0.687048i | \(0.241094\pi\) | |||||||
\(930\) | −7.77162 | + | 13.4608i | −0.254841 | + | 0.441398i | ||||
\(931\) | −13.5202 | −0.443106 | ||||||||
\(932\) | 2.43275 | − | 4.21364i | 0.0796873 | − | 0.138022i | ||||
\(933\) | −3.21969 | − | 5.57666i | −0.105408 | − | 0.182572i | ||||
\(934\) | −13.8006 | − | 23.9033i | −0.451569 | − | 0.782140i | ||||
\(935\) | 6.08012 | 0.198841 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9317 | −0.781815 | −0.390908 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390908 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(938\) | 14.0511 | + | 24.3373i | 0.458786 | + | 0.794640i | ||||
\(939\) | 19.1078 | + | 33.0958i | 0.623561 | + | 1.08004i | ||||
\(940\) | −0.662321 | + | 1.14717i | −0.0216025 | + | 0.0374167i | ||||
\(941\) | 25.3591 | 0.826683 | 0.413342 | − | 0.910576i | \(-0.364362\pi\) | ||||
0.413342 | + | 0.910576i | \(0.364362\pi\) | |||||||
\(942\) | 14.2807 | − | 24.7349i | 0.465291 | − | 0.805908i | ||||
\(943\) | −7.26420 | + | 12.5820i | −0.236555 | + | 0.409725i | ||||
\(944\) | −0.465033 | −0.0151355 | ||||||||
\(945\) | −2.35366 | + | 4.07666i | −0.0765646 | + | 0.132614i | ||||
\(946\) | 3.70792 | + | 6.42231i | 0.120555 | + | 0.208807i | ||||
\(947\) | 20.7111 | + | 35.8727i | 0.673021 | + | 1.16571i | 0.977043 | + | 0.213042i | \(0.0683371\pi\) |
−0.304022 | + | 0.952665i | \(0.598330\pi\) | |||||||
\(948\) | 14.3187 | 0.465051 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.76619 | 0.0897470 | ||||||||
\(951\) | 2.08240 | + | 3.60682i | 0.0675264 | + | 0.116959i | ||||
\(952\) | −6.24335 | − | 10.8138i | −0.202348 | − | 0.350477i | ||||
\(953\) | −12.1513 | + | 21.0466i | −0.393619 | + | 0.681767i | −0.992924 | − | 0.118753i | \(-0.962110\pi\) |
0.599305 | + | 0.800521i | \(0.295444\pi\) | |||||||
\(954\) | 13.2083 | 0.427636 | ||||||||
\(955\) | −13.6682 | + | 23.6740i | −0.442291 | + | 0.766071i | ||||
\(956\) | 5.10169 | − | 8.83639i | 0.165001 | − | 0.285789i | ||||
\(957\) | 0.309801 | 0.0100144 | ||||||||
\(958\) | −12.5901 | + | 21.8067i | −0.406768 | + | 0.704543i | ||||
\(959\) | −6.81647 | − | 11.8065i | −0.220115 | − | 0.381251i | ||||
\(960\) | −10.3375 | − | 17.9052i | −0.333643 | − | 0.577886i | ||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.2760 | −0.717834 | ||||||||
\(964\) | −5.96043 | − | 10.3238i | −0.191972 | − | 0.332506i | ||||
\(965\) | 10.8837 | + | 18.8511i | 0.350358 | + | 0.606839i | ||||
\(966\) | 19.9338 | − | 34.5263i | 0.641358 | − | 1.11086i | ||||
\(967\) | −23.6784 | −0.761445 | −0.380722 | − | 0.924689i | \(-0.624325\pi\) | ||||
−0.380722 | + | 0.924689i | \(0.624325\pi\) | |||||||
\(968\) | −27.3587 | + | 47.3866i | −0.879341 | + | 1.52306i | ||||
\(969\) | −2.99343 | + | 5.18477i | −0.0961627 | + | 0.166559i | ||||
\(970\) | 14.8413 | 0.476527 | ||||||||
\(971\) | 8.48609 | − | 14.6983i | 0.272332 | − | 0.471692i | −0.697127 | − | 0.716948i | \(-0.745539\pi\) |
0.969458 | + | 0.245256i | \(0.0788719\pi\) | |||||||
\(972\) | −5.18953 | − | 8.98852i | −0.166454 | − | 0.288307i | ||||
\(973\) | 3.62515 | + | 6.27895i | 0.116217 | + | 0.201294i | ||||
\(974\) | 3.70303 | 0.118653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.11550 | −0.291780 | ||||||||
\(977\) | 12.4997 | + | 21.6501i | 0.399901 | + | 0.692649i | 0.993713 | − | 0.111955i | \(-0.0357112\pi\) |
−0.593812 | + | 0.804604i | \(0.702378\pi\) | |||||||
\(978\) | −9.64500 | − | 16.7056i | −0.308413 | − | 0.534187i | ||||
\(979\) | 43.3883 | − | 75.1507i | 1.38669 | − | 2.40183i | ||||
\(980\) | −3.05441 | −0.0975696 | ||||||||
\(981\) | 8.99648 | − | 15.5824i | 0.287235 | − | 0.497506i | ||||
\(982\) | 6.50582 | − | 11.2684i | 0.207609 | − | 0.359589i | ||||
\(983\) | 27.3418 | 0.872068 | 0.436034 | − | 0.899930i | \(-0.356383\pi\) | ||||
0.436034 | + | 0.899930i | \(0.356383\pi\) | |||||||
\(984\) | 13.3359 | − | 23.0985i | 0.425134 | − | 0.736353i | ||||
\(985\) | −0.848360 | − | 1.46940i | −0.0270310 | − | 0.0468191i | ||||
\(986\) | 0.0170685 | + | 0.0295635i | 0.000543573 | + | 0.000941495i | ||||
\(987\) | 21.7080 | 0.690975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.40617 | 0.140108 | ||||||||
\(990\) | −7.99131 | − | 13.8413i | −0.253980 | − | 0.439907i | ||||
\(991\) | −8.03802 | − | 13.9223i | −0.255336 | − | 0.442255i | 0.709651 | − | 0.704554i | \(-0.248853\pi\) |
−0.964987 | + | 0.262299i | \(0.915519\pi\) | |||||||
\(992\) | −7.70406 | + | 13.3438i | −0.244604 | + | 0.423667i | ||||
\(993\) | −16.8491 | −0.534690 | ||||||||
\(994\) | −23.7061 | + | 41.0602i | −0.751913 | + | 1.30235i | ||||
\(995\) | −12.6627 | + | 21.9325i | −0.401436 | + | 0.695307i | ||||
\(996\) | −14.4932 | −0.459234 | ||||||||
\(997\) | 17.2806 | − | 29.9309i | 0.547282 | − | 0.947920i | −0.451178 | − | 0.892434i | \(-0.648996\pi\) |
0.998459 | − | 0.0554858i | \(-0.0176708\pi\) | |||||||
\(998\) | −20.6824 | − | 35.8230i | −0.654691 | − | 1.13396i | ||||
\(999\) | 5.69036 | + | 9.85600i | 0.180035 | + | 0.311830i |
(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 | 845.2.e.n.146.3 | 8 | ||
13.2 | odd | 12 | 845.2.c.g.506.6 | 8 | |||
13.3 | even | 3 | 845.2.a.l.1.2 | 4 | |||
13.4 | even | 6 | 845.2.e.m.191.2 | 8 | |||
13.5 | odd | 4 | 65.2.m.a.36.3 | ✓ | 8 | ||
13.6 | odd | 12 | 845.2.m.g.316.2 | 8 | |||
13.7 | odd | 12 | 65.2.m.a.56.3 | yes | 8 | ||
13.8 | odd | 4 | 845.2.m.g.361.2 | 8 | |||
13.9 | even | 3 | inner | 845.2.e.n.191.3 | 8 | ||
13.10 | even | 6 | 845.2.a.m.1.3 | 4 | |||
13.11 | odd | 12 | 845.2.c.g.506.3 | 8 | |||
13.12 | even | 2 | 845.2.e.m.146.2 | 8 | |||
39.5 | even | 4 | 585.2.bu.c.361.2 | 8 | |||
39.20 | even | 12 | 585.2.bu.c.316.2 | 8 | |||
39.23 | odd | 6 | 7605.2.a.cf.1.2 | 4 | |||
39.29 | odd | 6 | 7605.2.a.cj.1.3 | 4 | |||
52.7 | even | 12 | 1040.2.da.b.641.4 | 8 | |||
52.31 | even | 4 | 1040.2.da.b.881.4 | 8 | |||
65.7 | even | 12 | 325.2.m.b.199.2 | 8 | |||
65.18 | even | 4 | 325.2.m.b.49.2 | 8 | |||
65.29 | even | 6 | 4225.2.a.bl.1.3 | 4 | |||
65.33 | even | 12 | 325.2.m.c.199.3 | 8 | |||
65.44 | odd | 4 | 325.2.n.d.101.2 | 8 | |||
65.49 | even | 6 | 4225.2.a.bi.1.2 | 4 | |||
65.57 | even | 4 | 325.2.m.c.49.3 | 8 | |||
65.59 | odd | 12 | 325.2.n.d.251.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.3 | ✓ | 8 | 13.5 | odd | 4 | ||
65.2.m.a.56.3 | yes | 8 | 13.7 | odd | 12 | ||
325.2.m.b.49.2 | 8 | 65.18 | even | 4 | |||
325.2.m.b.199.2 | 8 | 65.7 | even | 12 | |||
325.2.m.c.49.3 | 8 | 65.57 | even | 4 | |||
325.2.m.c.199.3 | 8 | 65.33 | even | 12 | |||
325.2.n.d.101.2 | 8 | 65.44 | odd | 4 | |||
325.2.n.d.251.2 | 8 | 65.59 | odd | 12 | |||
585.2.bu.c.316.2 | 8 | 39.20 | even | 12 | |||
585.2.bu.c.361.2 | 8 | 39.5 | even | 4 | |||
845.2.a.l.1.2 | 4 | 13.3 | even | 3 | |||
845.2.a.m.1.3 | 4 | 13.10 | even | 6 | |||
845.2.c.g.506.3 | 8 | 13.11 | odd | 12 | |||
845.2.c.g.506.6 | 8 | 13.2 | odd | 12 | |||
845.2.e.m.146.2 | 8 | 13.12 | even | 2 | |||
845.2.e.m.191.2 | 8 | 13.4 | even | 6 | |||
845.2.e.n.146.3 | 8 | 1.1 | even | 1 | trivial | ||
845.2.e.n.191.3 | 8 | 13.9 | even | 3 | inner | ||
845.2.m.g.316.2 | 8 | 13.6 | odd | 12 | |||
845.2.m.g.361.2 | 8 | 13.8 | odd | 4 | |||
1040.2.da.b.641.4 | 8 | 52.7 | even | 12 | |||
1040.2.da.b.881.4 | 8 | 52.31 | even | 4 | |||
4225.2.a.bi.1.2 | 4 | 65.49 | even | 6 | |||
4225.2.a.bl.1.3 | 4 | 65.29 | even | 6 | |||
7605.2.a.cf.1.2 | 4 | 39.23 | odd | 6 | |||
7605.2.a.cj.1.3 | 4 | 39.29 | odd | 6 |