Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(671,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.c (of order \(2\), degree \(1\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.2 | ||
Character | \(\chi\) | \(=\) | 804.671 |
Dual form | 804.2.c.b.671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41002 | + | 0.108878i | −0.997032 | + | 0.0769887i | ||||
\(3\) | 1.62789 | − | 0.591579i | 0.939864 | − | 0.341548i | ||||
\(4\) | 1.97629 | − | 0.307041i | 0.988145 | − | 0.153520i | ||||
\(5\) | 3.04949i | 1.36377i | 0.731458 | + | 0.681887i | \(0.238840\pi\) | ||||
−0.731458 | + | 0.681887i | \(0.761160\pi\) | |||||||
\(6\) | −2.23094 | + | 1.01138i | −0.910779 | + | 0.412893i | ||||
\(7\) | − | 0.278695i | − | 0.105337i | −0.998612 | − | 0.0526684i | \(-0.983227\pi\) | ||
0.998612 | − | 0.0526684i | \(-0.0167726\pi\) | |||||||
\(8\) | −2.75317 | + | 0.648108i | −0.973393 | + | 0.229141i | ||||
\(9\) | 2.30007 | − | 1.92605i | 0.766690 | − | 0.642018i | ||||
\(10\) | −0.332024 | − | 4.29983i | −0.104995 | − | 1.35973i | ||||
\(11\) | −5.07932 | −1.53147 | −0.765736 | − | 0.643155i | \(-0.777625\pi\) | ||||
−0.765736 | + | 0.643155i | \(0.777625\pi\) | |||||||
\(12\) | 3.03555 | − | 1.66896i | 0.876288 | − | 0.481787i | ||||
\(13\) | −5.86045 | −1.62540 | −0.812698 | − | 0.582685i | \(-0.802002\pi\) | ||||
−0.812698 | + | 0.582685i | \(0.802002\pi\) | |||||||
\(14\) | 0.0303439 | + | 0.392964i | 0.00810974 | + | 0.105024i | ||||
\(15\) | 1.80401 | + | 4.96424i | 0.465794 | + | 1.28176i | ||||
\(16\) | 3.81145 | − | 1.21360i | 0.952863 | − | 0.303401i | ||||
\(17\) | 7.60921i | 1.84550i | 0.385395 | + | 0.922752i | \(0.374065\pi\) | ||||
−0.385395 | + | 0.922752i | \(0.625935\pi\) | |||||||
\(18\) | −3.03343 | + | 2.96619i | −0.714986 | + | 0.699139i | ||||
\(19\) | 5.91318i | 1.35658i | 0.734796 | + | 0.678288i | \(0.237278\pi\) | ||||
−0.734796 | + | 0.678288i | \(0.762722\pi\) | |||||||
\(20\) | 0.936317 | + | 6.02668i | 0.209367 | + | 1.34761i | ||||
\(21\) | −0.164870 | − | 0.453686i | −0.0359776 | − | 0.0990023i | ||||
\(22\) | 7.16192 | − | 0.553028i | 1.52693 | − | 0.117906i | ||||
\(23\) | 2.24947 | 0.469047 | 0.234523 | − | 0.972110i | \(-0.424647\pi\) | ||||
0.234523 | + | 0.972110i | \(0.424647\pi\) | |||||||
\(24\) | −4.09846 | + | 2.68377i | −0.836595 | + | 0.547822i | ||||
\(25\) | −4.29939 | −0.859878 | ||||||||
\(26\) | 8.26333 | − | 0.638076i | 1.62057 | − | 0.125137i | ||||
\(27\) | 2.60486 | − | 4.49608i | 0.501305 | − | 0.865271i | ||||
\(28\) | −0.0855707 | − | 0.550782i | −0.0161713 | − | 0.104088i | ||||
\(29\) | 5.83061i | 1.08272i | 0.840792 | + | 0.541359i | \(0.182090\pi\) | ||||
−0.840792 | + | 0.541359i | \(0.817910\pi\) | |||||||
\(30\) | −3.08419 | − | 6.80324i | −0.563093 | − | 1.24210i | ||||
\(31\) | − | 4.34794i | − | 0.780912i | −0.920622 | − | 0.390456i | \(-0.872317\pi\) | ||
0.920622 | − | 0.390456i | \(-0.127683\pi\) | |||||||
\(32\) | −5.24207 | + | 2.12618i | −0.926676 | + | 0.375860i | ||||
\(33\) | −8.26859 | + | 3.00482i | −1.43938 | + | 0.523071i | ||||
\(34\) | −0.828478 | − | 10.7291i | −0.142083 | − | 1.84003i | ||||
\(35\) | 0.849878 | 0.143656 | ||||||||
\(36\) | 3.95423 | − | 4.51266i | 0.659038 | − | 0.752109i | ||||
\(37\) | −6.86393 | −1.12842 | −0.564211 | − | 0.825630i | \(-0.690820\pi\) | ||||
−0.564211 | + | 0.825630i | \(0.690820\pi\) | |||||||
\(38\) | −0.643818 | − | 8.33768i | −0.104441 | − | 1.35255i | ||||
\(39\) | −9.54018 | + | 3.46692i | −1.52765 | + | 0.555151i | ||||
\(40\) | −1.97640 | − | 8.39577i | −0.312496 | − | 1.32749i | ||||
\(41\) | − | 8.48285i | − | 1.32480i | −0.749151 | − | 0.662399i | \(-0.769538\pi\) | ||
0.749151 | − | 0.662399i | \(-0.230462\pi\) | |||||||
\(42\) | 0.281866 | + | 0.621753i | 0.0434929 | + | 0.0959386i | ||||
\(43\) | 2.79230i | 0.425821i | 0.977072 | + | 0.212911i | \(0.0682943\pi\) | ||||
−0.977072 | + | 0.212911i | \(0.931706\pi\) | |||||||
\(44\) | −10.0382 | + | 1.55956i | −1.51332 | + | 0.235112i | ||||
\(45\) | 5.87348 | + | 7.01404i | 0.875567 | + | 1.04559i | ||||
\(46\) | −3.17179 | + | 0.244919i | −0.467655 | + | 0.0361113i | ||||
\(47\) | 0.455070 | 0.0663787 | 0.0331894 | − | 0.999449i | \(-0.489434\pi\) | ||||
0.0331894 | + | 0.999449i | \(0.489434\pi\) | |||||||
\(48\) | 5.48669 | − | 4.23039i | 0.791936 | − | 0.610604i | ||||
\(49\) | 6.92233 | 0.988904 | ||||||||
\(50\) | 6.06221 | − | 0.468111i | 0.857326 | − | 0.0662008i | ||||
\(51\) | 4.50144 | + | 12.3870i | 0.630328 | + | 1.73452i | ||||
\(52\) | −11.5820 | + | 1.79940i | −1.60613 | + | 0.249531i | ||||
\(53\) | 5.43602i | 0.746694i | 0.927692 | + | 0.373347i | \(0.121790\pi\) | ||||
−0.927692 | + | 0.373347i | \(0.878210\pi\) | |||||||
\(54\) | −3.18336 | + | 6.62316i | −0.433201 | + | 0.901297i | ||||
\(55\) | − | 15.4893i | − | 2.08858i | ||||||
\(56\) | 0.180624 | + | 0.767295i | 0.0241369 | + | 0.102534i | ||||
\(57\) | 3.49811 | + | 9.62603i | 0.463336 | + | 1.27500i | ||||
\(58\) | −0.634828 | − | 8.22125i | −0.0833569 | − | 1.07950i | ||||
\(59\) | −0.908582 | −0.118287 | −0.0591436 | − | 0.998249i | \(-0.518837\pi\) | ||||
−0.0591436 | + | 0.998249i | \(0.518837\pi\) | |||||||
\(60\) | 5.08948 | + | 9.25688i | 0.657049 | + | 1.19506i | ||||
\(61\) | 1.16382 | 0.149012 | 0.0745059 | − | 0.997221i | \(-0.476262\pi\) | ||||
0.0745059 | + | 0.997221i | \(0.476262\pi\) | |||||||
\(62\) | 0.473396 | + | 6.13066i | 0.0601214 | + | 0.778594i | ||||
\(63\) | −0.536781 | − | 0.641018i | −0.0676281 | − | 0.0807607i | ||||
\(64\) | 7.15991 | − | 3.56870i | 0.894989 | − | 0.446088i | ||||
\(65\) | − | 17.8714i | − | 2.21667i | ||||||
\(66\) | 11.3317 | − | 5.13711i | 1.39483 | − | 0.632334i | ||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 2.33634 | + | 15.0380i | 0.283322 | + | 1.82363i | ||||
\(69\) | 3.66190 | − | 1.33074i | 0.440841 | − | 0.160202i | ||||
\(70\) | −1.19834 | + | 0.0925333i | −0.143229 | + | 0.0110598i | ||||
\(71\) | −4.54985 | −0.539967 | −0.269984 | − | 0.962865i | \(-0.587018\pi\) | ||||
−0.269984 | + | 0.962865i | \(0.587018\pi\) | |||||||
\(72\) | −5.08420 | + | 6.79345i | −0.599178 | + | 0.800615i | ||||
\(73\) | 13.5119 | 1.58145 | 0.790726 | − | 0.612171i | \(-0.209704\pi\) | ||||
0.790726 | + | 0.612171i | \(0.209704\pi\) | |||||||
\(74\) | 9.67825 | − | 0.747333i | 1.12507 | − | 0.0868757i | ||||
\(75\) | −6.99894 | + | 2.54343i | −0.808168 | + | 0.293690i | ||||
\(76\) | 1.81559 | + | 11.6862i | 0.208262 | + | 1.34050i | ||||
\(77\) | 1.41558i | 0.161320i | ||||||||
\(78\) | 13.0743 | − | 5.92713i | 1.48038 | − | 0.671115i | ||||
\(79\) | 12.3343i | 1.38772i | 0.720110 | + | 0.693860i | \(0.244091\pi\) | ||||
−0.720110 | + | 0.693860i | \(0.755909\pi\) | |||||||
\(80\) | 3.70087 | + | 11.6230i | 0.413770 | + | 1.29949i | ||||
\(81\) | 1.58064 | − | 8.86011i | 0.175627 | − | 0.984457i | ||||
\(82\) | 0.923599 | + | 11.9610i | 0.101994 | + | 1.32087i | ||||
\(83\) | 2.79368 | 0.306646 | 0.153323 | − | 0.988176i | \(-0.451003\pi\) | ||||
0.153323 | + | 0.988176i | \(0.451003\pi\) | |||||||
\(84\) | −0.465131 | − | 0.845993i | −0.0507499 | − | 0.0923054i | ||||
\(85\) | −23.2042 | −2.51685 | ||||||||
\(86\) | −0.304021 | − | 3.93718i | −0.0327834 | − | 0.424557i | ||||
\(87\) | 3.44926 | + | 9.49161i | 0.369800 | + | 1.01761i | ||||
\(88\) | 13.9842 | − | 3.29194i | 1.49072 | − | 0.350923i | ||||
\(89\) | − | 1.69189i | − | 0.179340i | −0.995972 | − | 0.0896698i | \(-0.971419\pi\) | ||
0.995972 | − | 0.0896698i | \(-0.0285812\pi\) | |||||||
\(90\) | −9.04538 | − | 9.25041i | −0.953466 | − | 0.975079i | ||||
\(91\) | 1.63328i | 0.171214i | ||||||||
\(92\) | 4.44561 | − | 0.690679i | 0.463487 | − | 0.0720082i | ||||
\(93\) | −2.57215 | − | 7.07797i | −0.266719 | − | 0.733952i | ||||
\(94\) | −0.641656 | + | 0.0495473i | −0.0661817 | + | 0.00511041i | ||||
\(95\) | −18.0322 | −1.85006 | ||||||||
\(96\) | −7.27573 | + | 6.56230i | −0.742576 | + | 0.669762i | ||||
\(97\) | 4.26115 | 0.432654 | 0.216327 | − | 0.976321i | \(-0.430592\pi\) | ||||
0.216327 | + | 0.976321i | \(0.430592\pi\) | |||||||
\(98\) | −9.76060 | + | 0.753692i | −0.985969 | + | 0.0761344i | ||||
\(99\) | −11.6828 | + | 9.78304i | −1.17416 | + | 0.983232i | ||||
\(100\) | −8.49684 | + | 1.32009i | −0.849684 | + | 0.132009i | ||||
\(101\) | 0.355994i | 0.0354227i | 0.999843 | + | 0.0177114i | \(0.00563800\pi\) | ||||
−0.999843 | + | 0.0177114i | \(0.994362\pi\) | |||||||
\(102\) | −7.69578 | − | 16.9757i | −0.761996 | − | 1.68085i | ||||
\(103\) | 10.6829i | 1.05262i | 0.850292 | + | 0.526311i | \(0.176425\pi\) | ||||
−0.850292 | + | 0.526311i | \(0.823575\pi\) | |||||||
\(104\) | 16.1348 | − | 3.79820i | 1.58215 | − | 0.372444i | ||||
\(105\) | 1.38351 | − | 0.502769i | 0.135017 | − | 0.0490653i | ||||
\(106\) | −0.591865 | − | 7.66487i | −0.0574870 | − | 0.744478i | ||||
\(107\) | −3.37528 | −0.326300 | −0.163150 | − | 0.986601i | \(-0.552166\pi\) | ||||
−0.163150 | + | 0.986601i | \(0.552166\pi\) | |||||||
\(108\) | 3.76747 | − | 9.68536i | 0.362525 | − | 0.931974i | ||||
\(109\) | 8.52614 | 0.816656 | 0.408328 | − | 0.912835i | \(-0.366112\pi\) | ||||
0.408328 | + | 0.912835i | \(0.366112\pi\) | |||||||
\(110\) | 1.68645 | + | 21.8402i | 0.160797 | + | 2.08238i | ||||
\(111\) | −11.1737 | + | 4.06055i | −1.06056 | + | 0.385411i | ||||
\(112\) | −0.338225 | − | 1.06223i | −0.0319593 | − | 0.100372i | ||||
\(113\) | − | 15.8507i | − | 1.49111i | −0.666443 | − | 0.745556i | \(-0.732184\pi\) | ||
0.666443 | − | 0.745556i | \(-0.267816\pi\) | |||||||
\(114\) | −5.98046 | − | 13.1920i | −0.560121 | − | 1.23554i | ||||
\(115\) | 6.85974i | 0.639674i | ||||||||
\(116\) | 1.79023 | + | 11.5230i | 0.166219 | + | 1.06988i | ||||
\(117\) | −13.4794 | + | 11.2875i | −1.24617 | + | 1.04353i | ||||
\(118\) | 1.28111 | − | 0.0989249i | 0.117936 | − | 0.00910678i | ||||
\(119\) | 2.12065 | 0.194399 | ||||||||
\(120\) | −8.18412 | − | 12.4982i | −0.747105 | − | 1.14093i | ||||
\(121\) | 14.7995 | 1.34541 | ||||||||
\(122\) | −1.64100 | + | 0.126715i | −0.148569 | + | 0.0114722i | ||||
\(123\) | −5.01827 | − | 13.8092i | −0.452482 | − | 1.24513i | ||||
\(124\) | −1.33499 | − | 8.59278i | −0.119886 | − | 0.771655i | ||||
\(125\) | 2.13651i | 0.191095i | ||||||||
\(126\) | 0.826663 | + | 0.845402i | 0.0736450 | + | 0.0753144i | ||||
\(127\) | 2.01361i | 0.178679i | 0.996001 | + | 0.0893393i | \(0.0284755\pi\) | ||||
−0.996001 | + | 0.0893393i | \(0.971524\pi\) | |||||||
\(128\) | −9.70704 | + | 5.81149i | −0.857989 | + | 0.513668i | ||||
\(129\) | 1.65186 | + | 4.54556i | 0.145438 | + | 0.400214i | ||||
\(130\) | 1.94581 | + | 25.1989i | 0.170659 | + | 2.21009i | ||||
\(131\) | −3.98147 | −0.347862 | −0.173931 | − | 0.984758i | \(-0.555647\pi\) | ||||
−0.173931 | + | 0.984758i | \(0.555647\pi\) | |||||||
\(132\) | −15.4185 | + | 8.47718i | −1.34201 | + | 0.737844i | ||||
\(133\) | 1.64797 | 0.142897 | ||||||||
\(134\) | −0.108878 | − | 1.41002i | −0.00940566 | − | 0.121807i | ||||
\(135\) | 13.7107 | + | 7.94348i | 1.18003 | + | 0.683666i | ||||
\(136\) | −4.93158 | − | 20.9495i | −0.422880 | − | 1.79640i | ||||
\(137\) | 8.83469i | 0.754798i | 0.926051 | + | 0.377399i | \(0.123182\pi\) | ||||
−0.926051 | + | 0.377399i | \(0.876818\pi\) | |||||||
\(138\) | −5.01844 | + | 2.27506i | −0.427198 | + | 0.193666i | ||||
\(139\) | − | 12.3675i | − | 1.04899i | −0.851412 | − | 0.524497i | \(-0.824253\pi\) | ||
0.851412 | − | 0.524497i | \(-0.175747\pi\) | |||||||
\(140\) | 1.67961 | − | 0.260947i | 0.141953 | − | 0.0220540i | ||||
\(141\) | 0.740805 | − | 0.269209i | 0.0623870 | − | 0.0226715i | ||||
\(142\) | 6.41535 | − | 0.495380i | 0.538365 | − | 0.0415714i | ||||
\(143\) | 29.7671 | 2.48925 | ||||||||
\(144\) | 6.42914 | − | 10.1324i | 0.535762 | − | 0.844369i | ||||
\(145\) | −17.7804 | −1.47658 | ||||||||
\(146\) | −19.0520 | + | 1.47116i | −1.57676 | + | 0.121754i | ||||
\(147\) | 11.2688 | − | 4.09510i | 0.929436 | − | 0.337758i | ||||
\(148\) | −13.5651 | + | 2.10750i | −1.11505 | + | 0.173236i | ||||
\(149\) | − | 10.4788i | − | 0.858457i | −0.903196 | − | 0.429229i | \(-0.858785\pi\) | ||
0.903196 | − | 0.429229i | \(-0.141215\pi\) | |||||||
\(150\) | 9.59170 | − | 4.34831i | 0.783159 | − | 0.355038i | ||||
\(151\) | 7.69810i | 0.626463i | 0.949677 | + | 0.313231i | \(0.101412\pi\) | ||||
−0.949677 | + | 0.313231i | \(0.898588\pi\) | |||||||
\(152\) | −3.83238 | − | 16.2800i | −0.310847 | − | 1.32048i | ||||
\(153\) | 14.6557 | + | 17.5017i | 1.18485 | + | 1.41493i | ||||
\(154\) | −0.154126 | − | 1.99599i | −0.0124198 | − | 0.160842i | ||||
\(155\) | 13.2590 | 1.06499 | ||||||||
\(156\) | −17.7897 | + | 9.78086i | −1.42432 | + | 0.783095i | ||||
\(157\) | −12.0712 | −0.963384 | −0.481692 | − | 0.876340i | \(-0.659978\pi\) | ||||
−0.481692 | + | 0.876340i | \(0.659978\pi\) | |||||||
\(158\) | −1.34294 | − | 17.3916i | −0.106839 | − | 1.38360i | ||||
\(159\) | 3.21583 | + | 8.84925i | 0.255032 | + | 0.701791i | ||||
\(160\) | −6.48378 | − | 15.9857i | −0.512588 | − | 1.26378i | ||||
\(161\) | − | 0.626916i | − | 0.0494079i | ||||||
\(162\) | −1.26405 | + | 12.6650i | −0.0993135 | + | 0.995056i | ||||
\(163\) | 9.41541i | 0.737472i | 0.929534 | + | 0.368736i | \(0.120209\pi\) | ||||
−0.929534 | + | 0.368736i | \(0.879791\pi\) | |||||||
\(164\) | −2.60458 | − | 16.7646i | −0.203384 | − | 1.30909i | ||||
\(165\) | −9.16316 | − | 25.2150i | −0.713351 | − | 1.96298i | ||||
\(166\) | −3.93913 | + | 0.304171i | −0.305736 | + | 0.0236082i | ||||
\(167\) | −21.0838 | −1.63151 | −0.815756 | − | 0.578396i | \(-0.803679\pi\) | ||||
−0.815756 | + | 0.578396i | \(0.803679\pi\) | |||||||
\(168\) | 0.747953 | + | 1.14222i | 0.0577058 | + | 0.0881243i | ||||
\(169\) | 21.3449 | 1.64191 | ||||||||
\(170\) | 32.7183 | − | 2.52644i | 2.50938 | − | 0.193769i | ||||
\(171\) | 11.3891 | + | 13.6007i | 0.870946 | + | 1.04007i | ||||
\(172\) | 0.857348 | + | 5.51839i | 0.0653722 | + | 0.420773i | ||||
\(173\) | − | 18.9189i | − | 1.43838i | −0.694815 | − | 0.719188i | \(-0.744514\pi\) | ||
0.694815 | − | 0.719188i | \(-0.255486\pi\) | |||||||
\(174\) | −5.89695 | − | 13.0078i | −0.447047 | − | 0.986117i | ||||
\(175\) | 1.19822i | 0.0905768i | ||||||||
\(176\) | −19.3596 | + | 6.16428i | −1.45928 | + | 0.464650i | ||||
\(177\) | −1.47907 | + | 0.537497i | −0.111174 | + | 0.0404008i | ||||
\(178\) | 0.184210 | + | 2.38559i | 0.0138071 | + | 0.178807i | ||||
\(179\) | 25.3930 | 1.89796 | 0.948982 | − | 0.315331i | \(-0.102115\pi\) | ||||
0.948982 | + | 0.315331i | \(0.102115\pi\) | |||||||
\(180\) | 13.7613 | + | 12.0584i | 1.02571 | + | 0.898779i | ||||
\(181\) | −9.38501 | −0.697582 | −0.348791 | − | 0.937200i | \(-0.613408\pi\) | ||||
−0.348791 | + | 0.937200i | \(0.613408\pi\) | |||||||
\(182\) | −0.177829 | − | 2.30295i | −0.0131815 | − | 0.170706i | ||||
\(183\) | 1.89457 | − | 0.688490i | 0.140051 | − | 0.0508947i | ||||
\(184\) | −6.19318 | + | 1.45790i | −0.456567 | + | 0.107478i | ||||
\(185\) | − | 20.9315i | − | 1.53891i | ||||||
\(186\) | 4.39740 | + | 9.70000i | 0.322433 | + | 0.711239i | ||||
\(187\) | − | 38.6496i | − | 2.82634i | ||||||
\(188\) | 0.899350 | − | 0.139725i | 0.0655918 | − | 0.0101905i | ||||
\(189\) | −1.25303 | − | 0.725960i | −0.0911449 | − | 0.0528058i | ||||
\(190\) | 25.4257 | − | 1.96332i | 1.84457 | − | 0.142434i | ||||
\(191\) | −4.93877 | −0.357357 | −0.178678 | − | 0.983908i | \(-0.557182\pi\) | ||||
−0.178678 | + | 0.983908i | \(0.557182\pi\) | |||||||
\(192\) | 9.54440 | − | 10.0451i | 0.688808 | − | 0.724944i | ||||
\(193\) | 20.3135 | 1.46220 | 0.731099 | − | 0.682271i | \(-0.239008\pi\) | ||||
0.731099 | + | 0.682271i | \(0.239008\pi\) | |||||||
\(194\) | −6.00829 | + | 0.463947i | −0.431370 | + | 0.0333094i | ||||
\(195\) | −10.5723 | − | 29.0927i | −0.757100 | − | 2.08337i | ||||
\(196\) | 13.6805 | − | 2.12544i | 0.977181 | − | 0.151817i | ||||
\(197\) | 13.3758i | 0.952990i | 0.879177 | + | 0.476495i | \(0.158093\pi\) | ||||
−0.879177 | + | 0.476495i | \(0.841907\pi\) | |||||||
\(198\) | 15.4078 | − | 15.0662i | 1.09498 | − | 1.07071i | ||||
\(199\) | − | 13.1693i | − | 0.933548i | −0.884377 | − | 0.466774i | \(-0.845416\pi\) | ||
0.884377 | − | 0.466774i | \(-0.154584\pi\) | |||||||
\(200\) | 11.8370 | − | 2.78647i | 0.836999 | − | 0.197033i | ||||
\(201\) | 0.591579 | + | 1.62789i | 0.0417267 | + | 0.114823i | ||||
\(202\) | −0.0387601 | − | 0.501957i | −0.00272715 | − | 0.0353176i | ||||
\(203\) | 1.62496 | 0.114050 | ||||||||
\(204\) | 12.6995 | + | 23.0981i | 0.889140 | + | 1.61719i | ||||
\(205\) | 25.8684 | 1.80673 | ||||||||
\(206\) | −1.16314 | − | 15.0631i | −0.0810400 | − | 1.04950i | ||||
\(207\) | 5.17394 | − | 4.33260i | 0.359614 | − | 0.301136i | ||||
\(208\) | −22.3368 | + | 7.11226i | −1.54878 | + | 0.493147i | ||||
\(209\) | − | 30.0349i | − | 2.07756i | ||||||
\(210\) | −1.89603 | + | 0.859547i | −0.130839 | + | 0.0593144i | ||||
\(211\) | − | 4.89617i | − | 0.337066i | −0.985696 | − | 0.168533i | \(-0.946097\pi\) | ||
0.985696 | − | 0.168533i | \(-0.0539030\pi\) | |||||||
\(212\) | 1.66908 | + | 10.7431i | 0.114633 | + | 0.737843i | ||||
\(213\) | −7.40666 | + | 2.69159i | −0.507496 | + | 0.184425i | ||||
\(214\) | 4.75920 | − | 0.367495i | 0.325332 | − | 0.0251214i | ||||
\(215\) | −8.51508 | −0.580723 | ||||||||
\(216\) | −4.25767 | + | 14.0667i | −0.289698 | + | 0.957118i | ||||
\(217\) | −1.21175 | −0.0822588 | ||||||||
\(218\) | −12.0220 | + | 0.928313i | −0.814233 | + | 0.0628733i | ||||
\(219\) | 21.9960 | − | 7.99336i | 1.48635 | − | 0.540141i | ||||
\(220\) | −4.75585 | − | 30.6114i | −0.320640 | − | 2.06382i | ||||
\(221\) | − | 44.5934i | − | 2.99967i | ||||||
\(222\) | 15.3130 | − | 6.94202i | 1.02774 | − | 0.465918i | ||||
\(223\) | 27.0230i | 1.80959i | 0.425845 | + | 0.904796i | \(0.359977\pi\) | ||||
−0.425845 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(224\) | 0.592557 | + | 1.46094i | 0.0395919 | + | 0.0976131i | ||||
\(225\) | −9.88889 | + | 8.28085i | −0.659260 | + | 0.552057i | ||||
\(226\) | 1.72580 | + | 22.3498i | 0.114799 | + | 1.48669i | ||||
\(227\) | −0.0417672 | −0.00277218 | −0.00138609 | − | 0.999999i | \(-0.500441\pi\) | ||||
−0.00138609 | + | 0.999999i | \(0.500441\pi\) | |||||||
\(228\) | 9.86887 | + | 17.9498i | 0.653582 | + | 1.18875i | ||||
\(229\) | 14.7269 | 0.973180 | 0.486590 | − | 0.873631i | \(-0.338241\pi\) | ||||
0.486590 | + | 0.873631i | \(0.338241\pi\) | |||||||
\(230\) | −0.746877 | − | 9.67234i | −0.0492476 | − | 0.637775i | ||||
\(231\) | 0.837427 | + | 2.30441i | 0.0550987 | + | 0.151619i | ||||
\(232\) | −3.77886 | − | 16.0527i | −0.248094 | − | 1.05391i | ||||
\(233\) | 22.8772i | 1.49874i | 0.662154 | + | 0.749368i | \(0.269642\pi\) | ||||
−0.662154 | + | 0.749368i | \(0.730358\pi\) | |||||||
\(234\) | 17.7773 | − | 17.3832i | 1.16214 | − | 1.13638i | ||||
\(235\) | 1.38773i | 0.0905255i | ||||||||
\(236\) | −1.79562 | + | 0.278971i | −0.116885 | + | 0.0181595i | ||||
\(237\) | 7.29672 | + | 20.0789i | 0.473973 | + | 1.30427i | ||||
\(238\) | −2.99015 | + | 0.230893i | −0.193822 | + | 0.0149666i | ||||
\(239\) | −6.80444 | −0.440142 | −0.220071 | − | 0.975484i | \(-0.570629\pi\) | ||||
−0.220071 | + | 0.975484i | \(0.570629\pi\) | |||||||
\(240\) | 12.9005 | + | 16.7316i | 0.832726 | + | 1.08002i | ||||
\(241\) | −0.959498 | −0.0618067 | −0.0309034 | − | 0.999522i | \(-0.509838\pi\) | ||||
−0.0309034 | + | 0.999522i | \(0.509838\pi\) | |||||||
\(242\) | −20.8675 | + | 1.61134i | −1.34141 | + | 0.103581i | ||||
\(243\) | −2.66834 | − | 15.3584i | −0.171174 | − | 0.985241i | ||||
\(244\) | 2.30004 | − | 0.357340i | 0.147245 | − | 0.0228763i | ||||
\(245\) | 21.1096i | 1.34864i | ||||||||
\(246\) | 8.57937 | + | 18.9248i | 0.547000 | + | 1.20660i | ||||
\(247\) | − | 34.6539i | − | 2.20498i | ||||||
\(248\) | 2.81793 | + | 11.9706i | 0.178939 | + | 0.760135i | ||||
\(249\) | 4.54780 | − | 1.65268i | 0.288205 | − | 0.104734i | ||||
\(250\) | −0.232619 | − | 3.01251i | −0.0147121 | − | 0.190528i | ||||
\(251\) | −11.7116 | −0.739227 | −0.369613 | − | 0.929186i | \(-0.620510\pi\) | ||||
−0.369613 | + | 0.929186i | \(0.620510\pi\) | |||||||
\(252\) | −1.25765 | − | 1.10202i | −0.0792248 | − | 0.0694210i | ||||
\(253\) | −11.4258 | −0.718332 | ||||||||
\(254\) | −0.219238 | − | 2.83922i | −0.0137562 | − | 0.178148i | ||||
\(255\) | −37.7739 | + | 13.7271i | −2.36550 | + | 0.859625i | ||||
\(256\) | 13.0543 | − | 9.25118i | 0.815896 | − | 0.578199i | ||||
\(257\) | 1.54522i | 0.0963883i | 0.998838 | + | 0.0481941i | \(0.0153466\pi\) | ||||
−0.998838 | + | 0.0481941i | \(0.984653\pi\) | |||||||
\(258\) | −2.82407 | − | 6.22946i | −0.175819 | − | 0.387829i | ||||
\(259\) | 1.91294i | 0.118864i | ||||||||
\(260\) | −5.48724 | − | 35.3191i | −0.340304 | − | 2.19039i | ||||
\(261\) | 11.2301 | + | 13.4108i | 0.695123 | + | 0.830108i | ||||
\(262\) | 5.61393 | − | 0.433496i | 0.346830 | − | 0.0267815i | ||||
\(263\) | 25.4945 | 1.57206 | 0.786029 | − | 0.618190i | \(-0.212134\pi\) | ||||
0.786029 | + | 0.618190i | \(0.212134\pi\) | |||||||
\(264\) | 20.8174 | − | 13.6317i | 1.28122 | − | 0.838974i | ||||
\(265\) | −16.5771 | −1.01832 | ||||||||
\(266\) | −2.32367 | + | 0.179429i | −0.142473 | + | 0.0110015i | ||||
\(267\) | −1.00088 | − | 2.75421i | −0.0612531 | − | 0.168555i | ||||
\(268\) | 0.307041 | + | 1.97629i | 0.0187555 | + | 0.120721i | ||||
\(269\) | 11.3415i | 0.691505i | 0.938326 | + | 0.345752i | \(0.112376\pi\) | ||||
−0.938326 | + | 0.345752i | \(0.887624\pi\) | |||||||
\(270\) | −20.1973 | − | 9.70763i | −1.22917 | − | 0.590788i | ||||
\(271\) | 3.42034i | 0.207771i | 0.994589 | + | 0.103885i | \(0.0331275\pi\) | ||||
−0.994589 | + | 0.103885i | \(0.966872\pi\) | |||||||
\(272\) | 9.23456 | + | 29.0021i | 0.559927 | + | 1.75851i | ||||
\(273\) | 0.966212 | + | 2.65880i | 0.0584778 | + | 0.160918i | ||||
\(274\) | −0.961907 | − | 12.4571i | −0.0581109 | − | 0.752558i | ||||
\(275\) | 21.8380 | 1.31688 | ||||||||
\(276\) | 6.82838 | − | 3.75428i | 0.411020 | − | 0.225981i | ||||
\(277\) | 11.3806 | 0.683793 | 0.341897 | − | 0.939738i | \(-0.388931\pi\) | ||||
0.341897 | + | 0.939738i | \(0.388931\pi\) | |||||||
\(278\) | 1.34655 | + | 17.4383i | 0.0807607 | + | 1.04588i | ||||
\(279\) | −8.37435 | − | 10.0006i | −0.501359 | − | 0.598717i | ||||
\(280\) | −2.33986 | + | 0.550812i | −0.139833 | + | 0.0329173i | ||||
\(281\) | 9.82446i | 0.586078i | 0.956101 | + | 0.293039i | \(0.0946666\pi\) | ||||
−0.956101 | + | 0.293039i | \(0.905333\pi\) | |||||||
\(282\) | −1.01524 | + | 0.460247i | −0.0604564 | + | 0.0274073i | ||||
\(283\) | 17.7063i | 1.05253i | 0.850320 | + | 0.526265i | \(0.176408\pi\) | ||||
−0.850320 | + | 0.526265i | \(0.823592\pi\) | |||||||
\(284\) | −8.99182 | + | 1.39699i | −0.533566 | + | 0.0828959i | ||||
\(285\) | −29.3545 | + | 10.6675i | −1.73881 | + | 0.631886i | ||||
\(286\) | −41.9721 | + | 3.24099i | −2.48186 | + | 0.191644i | ||||
\(287\) | −2.36413 | −0.139550 | ||||||||
\(288\) | −7.96199 | + | 14.9869i | −0.469165 | + | 0.883111i | ||||
\(289\) | −40.9000 | −2.40588 | ||||||||
\(290\) | 25.0706 | − | 1.93590i | 1.47220 | − | 0.113680i | ||||
\(291\) | 6.93669 | − | 2.52080i | 0.406636 | − | 0.147772i | ||||
\(292\) | 26.7035 | − | 4.14871i | 1.56270 | − | 0.242785i | ||||
\(293\) | − | 15.7258i | − | 0.918712i | −0.888252 | − | 0.459356i | \(-0.848080\pi\) | ||
0.888252 | − | 0.459356i | \(-0.151920\pi\) | |||||||
\(294\) | −15.4433 | + | 7.00109i | −0.900674 | + | 0.408312i | ||||
\(295\) | − | 2.77071i | − | 0.161317i | ||||||
\(296\) | 18.8976 | − | 4.44856i | 1.09840 | − | 0.258567i | ||||
\(297\) | −13.2309 | + | 22.8370i | −0.767734 | + | 1.32514i | ||||
\(298\) | 1.14092 | + | 14.7753i | 0.0660915 | + | 0.855909i | ||||
\(299\) | −13.1829 | −0.762387 | ||||||||
\(300\) | −13.0510 | + | 7.17551i | −0.753501 | + | 0.414278i | ||||
\(301\) | 0.778199 | 0.0448546 | ||||||||
\(302\) | −0.838157 | − | 10.8544i | −0.0482305 | − | 0.624603i | ||||
\(303\) | 0.210598 | + | 0.579520i | 0.0120986 | + | 0.0332926i | ||||
\(304\) | 7.17626 | + | 22.5378i | 0.411587 | + | 1.29263i | ||||
\(305\) | 3.54905i | 0.203218i | ||||||||
\(306\) | −22.5704 | − | 23.0820i | −1.29026 | − | 1.31951i | ||||
\(307\) | 17.3222i | 0.988632i | 0.869282 | + | 0.494316i | \(0.164581\pi\) | ||||
−0.869282 | + | 0.494316i | \(0.835419\pi\) | |||||||
\(308\) | 0.434641 | + | 2.79760i | 0.0247660 | + | 0.159408i | ||||
\(309\) | 6.31980 | + | 17.3907i | 0.359521 | + | 0.989322i | ||||
\(310\) | −18.6954 | + | 1.44362i | −1.06183 | + | 0.0819919i | ||||
\(311\) | 16.1322 | 0.914776 | 0.457388 | − | 0.889267i | \(-0.348785\pi\) | ||||
0.457388 | + | 0.889267i | \(0.348785\pi\) | |||||||
\(312\) | 24.0188 | − | 15.7281i | 1.35980 | − | 0.890427i | ||||
\(313\) | 16.6044 | 0.938535 | 0.469267 | − | 0.883056i | \(-0.344518\pi\) | ||||
0.469267 | + | 0.883056i | \(0.344518\pi\) | |||||||
\(314\) | 17.0205 | − | 1.31429i | 0.960525 | − | 0.0741697i | ||||
\(315\) | 1.95478 | − | 1.63691i | 0.110139 | − | 0.0922294i | ||||
\(316\) | 3.78714 | + | 24.3762i | 0.213043 | + | 1.37127i | ||||
\(317\) | − | 17.6587i | − | 0.991813i | −0.868376 | − | 0.495907i | \(-0.834836\pi\) | ||
0.868376 | − | 0.495907i | \(-0.165164\pi\) | |||||||
\(318\) | −5.49786 | − | 12.1275i | −0.308305 | − | 0.680074i | ||||
\(319\) | − | 29.6155i | − | 1.65815i | ||||||
\(320\) | 10.8827 | + | 21.8341i | 0.608363 | + | 1.22056i | ||||
\(321\) | −5.49459 | + | 1.99674i | −0.306678 | + | 0.111447i | ||||
\(322\) | 0.0682576 | + | 0.883962i | 0.00380385 | + | 0.0492613i | ||||
\(323\) | −44.9946 | −2.50357 | ||||||||
\(324\) | 0.403393 | − | 17.9955i | 0.0224107 | − | 0.999749i | ||||
\(325\) | 25.1964 | 1.39764 | ||||||||
\(326\) | −1.02513 | − | 13.2759i | −0.0567770 | − | 0.735283i | ||||
\(327\) | 13.8796 | − | 5.04388i | 0.767546 | − | 0.278927i | ||||
\(328\) | 5.49780 | + | 23.3547i | 0.303565 | + | 1.28955i | ||||
\(329\) | − | 0.126826i | − | 0.00699212i | ||||||
\(330\) | 15.6656 | + | 34.5558i | 0.862361 | + | 1.90224i | ||||
\(331\) | − | 34.2868i | − | 1.88457i | −0.334810 | − | 0.942286i | \(-0.608672\pi\) | ||
0.334810 | − | 0.942286i | \(-0.391328\pi\) | |||||||
\(332\) | 5.52112 | − | 0.857772i | 0.303011 | − | 0.0470763i | ||||
\(333\) | −15.7875 | + | 13.2203i | −0.865150 | + | 0.724467i | ||||
\(334\) | 29.7285 | − | 2.29557i | 1.62667 | − | 0.125608i | ||||
\(335\) | −3.04949 | −0.166611 | ||||||||
\(336\) | −1.17899 | − | 1.52911i | −0.0643191 | − | 0.0834200i | ||||
\(337\) | 6.16304 | 0.335722 | 0.167861 | − | 0.985811i | \(-0.446314\pi\) | ||||
0.167861 | + | 0.985811i | \(0.446314\pi\) | |||||||
\(338\) | −30.0966 | + | 2.32400i | −1.63704 | + | 0.126409i | ||||
\(339\) | −9.37695 | − | 25.8033i | −0.509286 | − | 1.40144i | ||||
\(340\) | −45.8582 | + | 7.12463i | −2.48701 | + | 0.386387i | ||||
\(341\) | 22.0845i | 1.19595i | ||||||||
\(342\) | −17.5396 | − | 17.9372i | −0.948435 | − | 0.969934i | ||||
\(343\) | − | 3.88008i | − | 0.209505i | ||||||
\(344\) | −1.80971 | − | 7.68767i | −0.0975729 | − | 0.414491i | ||||
\(345\) | 4.05807 | + | 11.1669i | 0.218479 | + | 0.601207i | ||||
\(346\) | 2.05986 | + | 26.6759i | 0.110739 | + | 1.43411i | ||||
\(347\) | −7.81789 | −0.419686 | −0.209843 | − | 0.977735i | \(-0.567295\pi\) | ||||
−0.209843 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(348\) | 9.73106 | + | 17.6991i | 0.521639 | + | 0.948772i | ||||
\(349\) | −21.3355 | −1.14206 | −0.571031 | − | 0.820929i | \(-0.693456\pi\) | ||||
−0.571031 | + | 0.820929i | \(0.693456\pi\) | |||||||
\(350\) | −0.130460 | − | 1.68951i | −0.00697338 | − | 0.0903079i | ||||
\(351\) | −15.2656 | + | 26.3490i | −0.814819 | + | 1.40641i | ||||
\(352\) | 26.6262 | − | 10.7996i | 1.41918 | − | 0.575619i | ||||
\(353\) | − | 13.3348i | − | 0.709739i | −0.934916 | − | 0.354869i | \(-0.884525\pi\) | ||
0.934916 | − | 0.354869i | \(-0.115475\pi\) | |||||||
\(354\) | 2.02700 | − | 0.918919i | 0.107734 | − | 0.0488400i | ||||
\(355\) | − | 13.8747i | − | 0.736393i | ||||||
\(356\) | −0.519478 | − | 3.34366i | −0.0275323 | − | 0.177214i | ||||
\(357\) | 3.45219 | − | 1.25453i | 0.182709 | − | 0.0663968i | ||||
\(358\) | −35.8046 | + | 2.76475i | −1.89233 | + | 0.146122i | ||||
\(359\) | 19.0196 | 1.00381 | 0.501907 | − | 0.864922i | \(-0.332632\pi\) | ||||
0.501907 | + | 0.864922i | \(0.332632\pi\) | |||||||
\(360\) | −20.7165 | − | 15.5042i | −1.09186 | − | 0.817144i | ||||
\(361\) | −15.9657 | −0.840301 | ||||||||
\(362\) | 13.2330 | − | 1.02182i | 0.695512 | − | 0.0537059i | ||||
\(363\) | 24.0920 | − | 8.75505i | 1.26450 | − | 0.459521i | ||||
\(364\) | 0.501483 | + | 3.22783i | 0.0262848 | + | 0.169184i | ||||
\(365\) | 41.2045i | 2.15674i | ||||||||
\(366\) | −2.59642 | + | 1.17706i | −0.135717 | + | 0.0615259i | ||||
\(367\) | − | 1.97931i | − | 0.103319i | −0.998665 | − | 0.0516596i | \(-0.983549\pi\) | ||
0.998665 | − | 0.0516596i | \(-0.0164511\pi\) | |||||||
\(368\) | 8.57375 | − | 2.72996i | 0.446938 | − | 0.142309i | ||||
\(369\) | −16.3384 | − | 19.5111i | −0.850544 | − | 1.01571i | ||||
\(370\) | 2.27899 | + | 29.5137i | 0.118479 | + | 1.53435i | ||||
\(371\) | 1.51499 | 0.0786544 | ||||||||
\(372\) | −7.25653 | − | 13.1984i | −0.376234 | − | 0.684304i | ||||
\(373\) | 16.1265 | 0.834998 | 0.417499 | − | 0.908677i | \(-0.362907\pi\) | ||||
0.417499 | + | 0.908677i | \(0.362907\pi\) | |||||||
\(374\) | 4.20810 | + | 54.4965i | 0.217596 | + | 2.81795i | ||||
\(375\) | 1.26391 | + | 3.47800i | 0.0652681 | + | 0.179603i | ||||
\(376\) | −1.25289 | + | 0.294934i | −0.0646126 | + | 0.0152101i | ||||
\(377\) | − | 34.1700i | − | 1.75984i | ||||||
\(378\) | 1.84584 | + | 0.887187i | 0.0949398 | + | 0.0456320i | ||||
\(379\) | − | 27.2364i | − | 1.39904i | −0.714612 | − | 0.699521i | \(-0.753397\pi\) | ||
0.714612 | − | 0.699521i | \(-0.246603\pi\) | |||||||
\(380\) | −35.6369 | + | 5.53661i | −1.82813 | + | 0.284022i | ||||
\(381\) | 1.19121 | + | 3.27793i | 0.0610273 | + | 0.167934i | ||||
\(382\) | 6.96374 | − | 0.537725i | 0.356296 | − | 0.0275124i | ||||
\(383\) | −31.3840 | −1.60365 | −0.801825 | − | 0.597560i | \(-0.796137\pi\) | ||||
−0.801825 | + | 0.597560i | \(0.796137\pi\) | |||||||
\(384\) | −12.3641 | + | 15.2030i | −0.630951 | + | 0.775823i | ||||
\(385\) | −4.31680 | −0.220004 | ||||||||
\(386\) | −28.6424 | + | 2.21170i | −1.45786 | + | 0.112573i | ||||
\(387\) | 5.37811 | + | 6.42247i | 0.273385 | + | 0.326473i | ||||
\(388\) | 8.42127 | − | 1.30835i | 0.427525 | − | 0.0664212i | ||||
\(389\) | 7.82281i | 0.396632i | 0.980138 | + | 0.198316i | \(0.0635473\pi\) | ||||
−0.980138 | + | 0.198316i | \(0.936453\pi\) | |||||||
\(390\) | 18.0747 | + | 39.8701i | 0.915249 | + | 2.01890i | ||||
\(391\) | 17.1167i | 0.865628i | ||||||||
\(392\) | −19.0584 | + | 4.48641i | −0.962593 | + | 0.226598i | ||||
\(393\) | −6.48140 | + | 2.35535i | −0.326944 | + | 0.118812i | ||||
\(394\) | −1.45634 | − | 18.8602i | −0.0733694 | − | 0.950161i | ||||
\(395\) | −37.6134 | −1.89253 | ||||||||
\(396\) | −20.0848 | + | 22.9212i | −1.00930 | + | 1.15183i | ||||
\(397\) | −25.8514 | −1.29744 | −0.648721 | − | 0.761026i | \(-0.724696\pi\) | ||||
−0.648721 | + | 0.761026i | \(0.724696\pi\) | |||||||
\(398\) | 1.43385 | + | 18.5689i | 0.0718726 | + | 0.930777i | ||||
\(399\) | 2.68273 | − | 0.974906i | 0.134304 | − | 0.0488064i | ||||
\(400\) | −16.3869 | + | 5.21775i | −0.819346 | + | 0.260888i | ||||
\(401\) | − | 1.90320i | − | 0.0950413i | −0.998870 | − | 0.0475207i | \(-0.984868\pi\) | ||
0.998870 | − | 0.0475207i | \(-0.0151320\pi\) | |||||||
\(402\) | −1.01138 | − | 2.23094i | −0.0504429 | − | 0.111269i | ||||
\(403\) | 25.4809i | 1.26929i | ||||||||
\(404\) | 0.109305 | + | 0.703548i | 0.00543811 | + | 0.0350028i | ||||
\(405\) | 27.0188 | + | 4.82015i | 1.34258 | + | 0.239515i | ||||
\(406\) | −2.29122 | + | 0.176923i | −0.113711 | + | 0.00878055i | ||||
\(407\) | 34.8641 | 1.72815 | ||||||||
\(408\) | −20.4213 | − | 31.1860i | −1.01101 | − | 1.54394i | ||||
\(409\) | −18.6244 | −0.920917 | −0.460459 | − | 0.887681i | \(-0.652315\pi\) | ||||
−0.460459 | + | 0.887681i | \(0.652315\pi\) | |||||||
\(410\) | −36.4748 | + | 2.81651i | −1.80136 | + | 0.139097i | ||||
\(411\) | 5.22641 | + | 14.3819i | 0.257800 | + | 0.709408i | ||||
\(412\) | 3.28010 | + | 21.1126i | 0.161599 | + | 1.04014i | ||||
\(413\) | 0.253217i | 0.0124600i | ||||||||
\(414\) | −6.82361 | + | 6.67236i | −0.335362 | + | 0.327929i | ||||
\(415\) | 8.51929i | 0.418195i | ||||||||
\(416\) | 30.7209 | − | 12.4604i | 1.50622 | − | 0.610921i | ||||
\(417\) | −7.31633 | − | 20.1329i | −0.358282 | − | 0.985913i | ||||
\(418\) | 3.27016 | + | 42.3497i | 0.159949 | + | 2.07139i | ||||
\(419\) | 20.4330 | 0.998217 | 0.499109 | − | 0.866539i | \(-0.333661\pi\) | ||||
0.499109 | + | 0.866539i | \(0.333661\pi\) | |||||||
\(420\) | 2.57985 | − | 1.41841i | 0.125884 | − | 0.0692114i | ||||
\(421\) | 15.8138 | 0.770716 | 0.385358 | − | 0.922767i | \(-0.374078\pi\) | ||||
0.385358 | + | 0.922767i | \(0.374078\pi\) | |||||||
\(422\) | 0.533087 | + | 6.90368i | 0.0259503 | + | 0.336066i | ||||
\(423\) | 1.04669 | − | 0.876488i | 0.0508919 | − | 0.0426163i | ||||
\(424\) | −3.52312 | − | 14.9663i | −0.171098 | − | 0.726827i | ||||
\(425\) | − | 32.7149i | − | 1.58691i | ||||||
\(426\) | 10.1505 | − | 4.60161i | 0.491791 | − | 0.222949i | ||||
\(427\) | − | 0.324350i | − | 0.0156964i | ||||||
\(428\) | −6.67053 | + | 1.03635i | −0.322432 | + | 0.0500937i | ||||
\(429\) | 48.4576 | − | 17.6096i | 2.33956 | − | 0.850198i | ||||
\(430\) | 12.0064 | − | 0.927108i | 0.579000 | − | 0.0447091i | ||||
\(431\) | 20.0667 | 0.966578 | 0.483289 | − | 0.875461i | \(-0.339442\pi\) | ||||
0.483289 | + | 0.875461i | \(0.339442\pi\) | |||||||
\(432\) | 4.47183 | − | 20.2979i | 0.215151 | − | 0.976581i | ||||
\(433\) | −13.1719 | −0.633003 | −0.316501 | − | 0.948592i | \(-0.602508\pi\) | ||||
−0.316501 | + | 0.948592i | \(0.602508\pi\) | |||||||
\(434\) | 1.70858 | − | 0.131933i | 0.0820147 | − | 0.00633299i | ||||
\(435\) | −28.9446 | + | 10.5185i | −1.38779 | + | 0.504323i | ||||
\(436\) | 16.8501 | − | 2.61787i | 0.806975 | − | 0.125373i | ||||
\(437\) | 13.3015i | 0.636298i | ||||||||
\(438\) | −30.1444 | + | 13.6657i | −1.44035 | + | 0.652970i | ||||
\(439\) | − | 22.2901i | − | 1.06385i | −0.846793 | − | 0.531923i | \(-0.821469\pi\) | ||
0.846793 | − | 0.531923i | \(-0.178531\pi\) | |||||||
\(440\) | 10.0388 | + | 42.6448i | 0.478579 | + | 2.03301i | ||||
\(441\) | 15.9218 | − | 13.3328i | 0.758183 | − | 0.634894i | ||||
\(442\) | 4.85525 | + | 62.8774i | 0.230941 | + | 2.99077i | ||||
\(443\) | 15.4580 | 0.734430 | 0.367215 | − | 0.930136i | \(-0.380311\pi\) | ||||
0.367215 | + | 0.930136i | \(0.380311\pi\) | |||||||
\(444\) | −20.8358 | + | 11.4556i | −0.988823 | + | 0.543660i | ||||
\(445\) | 5.15939 | 0.244579 | ||||||||
\(446\) | −2.94222 | − | 38.1028i | −0.139318 | − | 1.80422i | ||||
\(447\) | −6.19904 | − | 17.0584i | −0.293204 | − | 0.806833i | ||||
\(448\) | −0.994580 | − | 1.99543i | −0.0469895 | − | 0.0942753i | ||||
\(449\) | − | 24.9972i | − | 1.17969i | −0.807516 | − | 0.589845i | \(-0.799189\pi\) | ||
0.807516 | − | 0.589845i | \(-0.200811\pi\) | |||||||
\(450\) | 13.0419 | − | 12.7528i | 0.614801 | − | 0.601174i | ||||
\(451\) | 43.0871i | 2.02889i | ||||||||
\(452\) | −4.86682 | − | 31.3257i | −0.228916 | − | 1.47344i | ||||
\(453\) | 4.55403 | + | 12.5317i | 0.213967 | + | 0.588790i | ||||
\(454\) | 0.0588924 | − | 0.00454754i | 0.00276396 | − | 0.000213427i | ||||
\(455\) | −4.98066 | −0.233497 | ||||||||
\(456\) | −15.8696 | − | 24.2350i | −0.743162 | − | 1.13491i | ||||
\(457\) | −13.8327 | −0.647064 | −0.323532 | − | 0.946217i | \(-0.604870\pi\) | ||||
−0.323532 | + | 0.946217i | \(0.604870\pi\) | |||||||
\(458\) | −20.7651 | + | 1.60344i | −0.970291 | + | 0.0749238i | ||||
\(459\) | 34.2116 | + | 19.8209i | 1.59686 | + | 0.925160i | ||||
\(460\) | 2.10622 | + | 13.5568i | 0.0982029 | + | 0.632091i | ||||
\(461\) | 0.355681i | 0.0165657i | 0.999966 | + | 0.00828286i | \(0.00263655\pi\) | ||||
−0.999966 | + | 0.00828286i | \(0.997363\pi\) | |||||||
\(462\) | −1.43169 | − | 3.15808i | −0.0666081 | − | 0.146927i | ||||
\(463\) | − | 3.72249i | − | 0.172999i | −0.996252 | − | 0.0864994i | \(-0.972432\pi\) | ||
0.996252 | − | 0.0864994i | \(-0.0275681\pi\) | |||||||
\(464\) | 7.07605 | + | 22.2231i | 0.328497 | + | 1.03168i | ||||
\(465\) | 21.5842 | − | 7.84373i | 1.00094 | − | 0.363744i | ||||
\(466\) | −2.49083 | − | 32.2572i | −0.115386 | − | 1.49429i | ||||
\(467\) | 33.9317 | 1.57017 | 0.785086 | − | 0.619387i | \(-0.212619\pi\) | ||||
0.785086 | + | 0.619387i | \(0.212619\pi\) | |||||||
\(468\) | −23.1736 | + | 26.4462i | −1.07120 | + | 1.22248i | ||||
\(469\) | 0.278695 | 0.0128689 | ||||||||
\(470\) | −0.151094 | − | 1.95672i | −0.00696944 | − | 0.0902569i | ||||
\(471\) | −19.6506 | + | 7.14105i | −0.905451 | + | 0.329042i | ||||
\(472\) | 2.50148 | − | 0.588859i | 0.115140 | − | 0.0271044i | ||||
\(473\) | − | 14.1830i | − | 0.652133i | ||||||
\(474\) | −12.4747 | − | 27.5172i | −0.572980 | − | 1.26391i | ||||
\(475\) | − | 25.4231i | − | 1.16649i | ||||||
\(476\) | 4.19102 | − | 0.651125i | 0.192095 | − | 0.0298443i | ||||
\(477\) | 10.4701 | + | 12.5032i | 0.479391 | + | 0.572483i | ||||
\(478\) | 9.59436 | − | 0.740856i | 0.438836 | − | 0.0338860i | ||||
\(479\) | 7.68288 | 0.351040 | 0.175520 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175520 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(480\) | −20.0117 | − | 22.1873i | −0.913403 | − | 1.01271i | ||||
\(481\) | 40.2257 | 1.83413 | ||||||||
\(482\) | 1.35291 | − | 0.104469i | 0.0616233 | − | 0.00475842i | ||||
\(483\) | −0.370870 | − | 1.02055i | −0.0168752 | − | 0.0464367i | ||||
\(484\) | 29.2481 | − | 4.54404i | 1.32946 | − | 0.206547i | ||||
\(485\) | 12.9943i | 0.590042i | ||||||||
\(486\) | 5.43460 | + | 21.3650i | 0.246518 | + | 0.969138i | ||||
\(487\) | 33.8111i | 1.53213i | 0.642766 | + | 0.766063i | \(0.277787\pi\) | ||||
−0.642766 | + | 0.766063i | \(0.722213\pi\) | |||||||
\(488\) | −3.20419 | + | 0.754280i | −0.145047 | + | 0.0341446i | ||||
\(489\) | 5.56995 | + | 15.3273i | 0.251882 | + | 0.693123i | ||||
\(490\) | −2.29838 | − | 29.7648i | −0.103830 | − | 1.34464i | ||||
\(491\) | 43.0765 | 1.94401 | 0.972007 | − | 0.234952i | \(-0.0754932\pi\) | ||||
0.972007 | + | 0.234952i | \(0.0754932\pi\) | |||||||
\(492\) | −14.1575 | − | 25.7501i | −0.638271 | − | 1.16091i | ||||
\(493\) | −44.3663 | −1.99816 | ||||||||
\(494\) | 3.77306 | + | 48.8626i | 0.169758 | + | 2.19843i | ||||
\(495\) | −29.8333 | − | 35.6265i | −1.34091 | − | 1.60129i | ||||
\(496\) | −5.27667 | − | 16.5719i | −0.236929 | − | 0.744102i | ||||
\(497\) | 1.26802i | 0.0568784i | ||||||||
\(498\) | −6.23254 | + | 2.82546i | −0.279287 | + | 0.126612i | ||||
\(499\) | 31.2747i | 1.40005i | 0.714118 | + | 0.700025i | \(0.246828\pi\) | ||||
−0.714118 | + | 0.700025i | \(0.753172\pi\) | |||||||
\(500\) | 0.655994 | + | 4.22236i | 0.0293370 | + | 0.188830i | ||||
\(501\) | −34.3222 | + | 12.4727i | −1.53340 | + | 0.557240i | ||||
\(502\) | 16.5135 | − | 1.27514i | 0.737033 | − | 0.0569121i | ||||
\(503\) | 11.9246 | 0.531690 | 0.265845 | − | 0.964016i | \(-0.414349\pi\) | ||||
0.265845 | + | 0.964016i | \(0.414349\pi\) | |||||||
\(504\) | 1.89330 | + | 1.41694i | 0.0843343 | + | 0.0631156i | ||||
\(505\) | −1.08560 | −0.0483086 | ||||||||
\(506\) | 16.1105 | − | 1.24402i | 0.716200 | − | 0.0553034i | ||||
\(507\) | 34.7472 | − | 12.6272i | 1.54318 | − | 0.560792i | ||||
\(508\) | 0.618259 | + | 3.97947i | 0.0274308 | + | 0.176560i | ||||
\(509\) | 18.5710i | 0.823145i | 0.911377 | + | 0.411572i | \(0.135020\pi\) | ||||
−0.911377 | + | 0.411572i | \(0.864980\pi\) | |||||||
\(510\) | 51.7673 | − | 23.4682i | 2.29229 | − | 1.03919i | ||||
\(511\) | − | 3.76571i | − | 0.166585i | ||||||
\(512\) | −17.3996 | + | 14.4656i | −0.768960 | + | 0.639297i | ||||
\(513\) | 26.5861 | + | 15.4030i | 1.17381 | + | 0.680058i | ||||
\(514\) | −0.168241 | − | 2.17879i | −0.00742080 | − | 0.0961022i | ||||
\(515\) | −32.5775 | −1.43554 | ||||||||
\(516\) | 4.66023 | + | 8.47616i | 0.205155 | + | 0.373142i | ||||
\(517\) | −2.31144 | −0.101657 | ||||||||
\(518\) | −0.208278 | − | 2.69728i | −0.00915121 | − | 0.118512i | ||||
\(519\) | −11.1920 | − | 30.7979i | −0.491275 | − | 1.35188i | ||||
\(520\) | 11.5826 | + | 49.2030i | 0.507930 | + | 2.15769i | ||||
\(521\) | 7.64072i | 0.334746i | 0.985894 | + | 0.167373i | \(0.0535284\pi\) | ||||
−0.985894 | + | 0.167373i | \(0.946472\pi\) | |||||||
\(522\) | −17.2947 | − | 17.6867i | −0.756969 | − | 0.774128i | ||||
\(523\) | 21.5819i | 0.943711i | 0.881676 | + | 0.471855i | \(0.156416\pi\) | ||||
−0.881676 | + | 0.471855i | \(0.843584\pi\) | |||||||
\(524\) | −7.86854 | + | 1.22247i | −0.343739 | + | 0.0534040i | ||||
\(525\) | 0.708840 | + | 1.95057i | 0.0309363 | + | 0.0851299i | ||||
\(526\) | −35.9476 | + | 2.77580i | −1.56739 | + | 0.121031i | ||||
\(527\) | 33.0843 | 1.44118 | ||||||||
\(528\) | −27.8687 | + | 21.4875i | −1.21283 | + | 0.935123i | ||||
\(529\) | −17.9399 | −0.779995 | ||||||||
\(530\) | 23.3739 | − | 1.80489i | 1.01530 | − | 0.0783992i | ||||
\(531\) | −2.08980 | + | 1.74998i | −0.0906896 | + | 0.0759425i | ||||
\(532\) | 3.25688 | − | 0.505995i | 0.141204 | − | 0.0219377i | ||||
\(533\) | 49.7133i | 2.15332i | ||||||||
\(534\) | 1.71114 | + | 3.77451i | 0.0740481 | + | 0.163339i | ||||
\(535\) | − | 10.2929i | − | 0.445000i | ||||||
\(536\) | −0.648108 | − | 2.75317i | −0.0279940 | − | 0.118919i | ||||
\(537\) | 41.3371 | − | 15.0220i | 1.78383 | − | 0.648246i | ||||
\(538\) | −1.23485 | − | 15.9917i | −0.0532380 | − | 0.689452i | ||||
\(539\) | −35.1607 | −1.51448 | ||||||||
\(540\) | 29.5354 | + | 11.4889i | 1.27100 | + | 0.494402i | ||||
\(541\) | −18.2680 | −0.785402 | −0.392701 | − | 0.919666i | \(-0.628459\pi\) | ||||
−0.392701 | + | 0.919666i | \(0.628459\pi\) | |||||||
\(542\) | −0.372401 | − | 4.82274i | −0.0159960 | − | 0.207154i | ||||
\(543\) | −15.2778 | + | 5.55197i | −0.655633 | + | 0.238258i | ||||
\(544\) | −16.1786 | − | 39.8880i | −0.693651 | − | 1.71018i | ||||
\(545\) | 26.0004i | 1.11373i | ||||||||
\(546\) | −1.65186 | − | 3.64375i | −0.0706931 | − | 0.155938i | ||||
\(547\) | − | 0.148820i | − | 0.00636309i | −0.999995 | − | 0.00318155i | \(-0.998987\pi\) | ||
0.999995 | − | 0.00318155i | \(-0.00101272\pi\) | |||||||
\(548\) | 2.71261 | + | 17.4599i | 0.115877 | + | 0.745851i | ||||
\(549\) | 2.67686 | − | 2.24158i | 0.114246 | − | 0.0956681i | ||||
\(550\) | −30.7919 | + | 2.37768i | −1.31297 | + | 0.101385i | ||||
\(551\) | −34.4775 | −1.46879 | ||||||||
\(552\) | −9.21937 | + | 6.03705i | −0.392402 | + | 0.256954i | ||||
\(553\) | 3.43751 | 0.146178 | ||||||||
\(554\) | −16.0468 | + | 1.23910i | −0.681764 | + | 0.0526443i | ||||
\(555\) | −12.3826 | − | 34.0742i | −0.525613 | − | 1.44637i | ||||
\(556\) | −3.79731 | − | 24.4417i | −0.161042 | − | 1.03656i | ||||
\(557\) | 9.99434i | 0.423474i | 0.977327 | + | 0.211737i | \(0.0679120\pi\) | ||||
−0.977327 | + | 0.211737i | \(0.932088\pi\) | |||||||
\(558\) | 12.8968 | + | 13.1892i | 0.545966 | + | 0.558341i | ||||
\(559\) | − | 16.3641i | − | 0.692128i | ||||||
\(560\) | 3.23927 | − | 1.03141i | 0.136884 | − | 0.0435852i | ||||
\(561\) | −22.8643 | − | 62.9174i | −0.965330 | − | 2.65637i | ||||
\(562\) | −1.06967 | − | 13.8526i | −0.0451213 | − | 0.584338i | ||||
\(563\) | −21.6148 | −0.910954 | −0.455477 | − | 0.890247i | \(-0.650531\pi\) | ||||
−0.455477 | + | 0.890247i | \(0.650531\pi\) | |||||||
\(564\) | 1.38139 | − | 0.759493i | 0.0581669 | − | 0.0319804i | ||||
\(565\) | 48.3367 | 2.03354 | ||||||||
\(566\) | −1.92783 | − | 24.9662i | −0.0810329 | − | 1.04941i | ||||
\(567\) | −2.46927 | − | 0.440517i | −0.103700 | − | 0.0185000i | ||||
\(568\) | 12.5265 | − | 2.94879i | 0.525601 | − | 0.123728i | ||||
\(569\) | − | 4.62418i | − | 0.193856i | −0.995291 | − | 0.0969279i | \(-0.969098\pi\) | ||
0.995291 | − | 0.0969279i | \(-0.0309016\pi\) | |||||||
\(570\) | 40.2288 | − | 18.2374i | 1.68500 | − | 0.763879i | ||||
\(571\) | 0.855969i | 0.0358212i | 0.999840 | + | 0.0179106i | \(0.00570142\pi\) | ||||
−0.999840 | + | 0.0179106i | \(0.994299\pi\) | |||||||
\(572\) | 58.8284 | − | 9.13971i | 2.45974 | − | 0.382150i | ||||
\(573\) | −8.03979 | + | 2.92167i | −0.335867 | + | 0.122054i | ||||
\(574\) | 3.33346 | − | 0.257403i | 0.139136 | − | 0.0107438i | ||||
\(575\) | −9.67135 | −0.403323 | ||||||||
\(576\) | 9.59479 | − | 21.9986i | 0.399783 | − | 0.916610i | ||||
\(577\) | 16.9778 | 0.706796 | 0.353398 | − | 0.935473i | \(-0.385026\pi\) | ||||
0.353398 | + | 0.935473i | \(0.385026\pi\) | |||||||
\(578\) | 57.6697 | − | 4.45313i | 2.39874 | − | 0.185226i | ||||
\(579\) | 33.0682 | − | 12.0170i | 1.37427 | − | 0.499411i | ||||
\(580\) | −35.1392 | + | 5.45930i | −1.45908 | + | 0.226685i | ||||
\(581\) | − | 0.778583i | − | 0.0323011i | ||||||
\(582\) | −9.50638 | + | 4.30963i | −0.394052 | + | 0.178640i | ||||
\(583\) | − | 27.6113i | − | 1.14354i | ||||||
\(584\) | −37.2007 | + | 8.75718i | −1.53937 | + | 0.362375i | ||||
\(585\) | −34.4212 | − | 41.1054i | −1.42314 | − | 1.69950i | ||||
\(586\) | 1.71220 | + | 22.1737i | 0.0707304 | + | 0.915985i | ||||
\(587\) | 11.4625 | 0.473108 | 0.236554 | − | 0.971618i | \(-0.423982\pi\) | ||||
0.236554 | + | 0.971618i | \(0.423982\pi\) | |||||||
\(588\) | 21.0131 | − | 11.5531i | 0.866565 | − | 0.476442i | ||||
\(589\) | 25.7101 | 1.05937 | ||||||||
\(590\) | 0.301671 | + | 3.90675i | 0.0124196 | + | 0.160838i | ||||
\(591\) | 7.91286 | + | 21.7744i | 0.325492 | + | 0.895681i | ||||
\(592\) | −26.1615 | + | 8.33008i | −1.07523 | + | 0.342364i | ||||
\(593\) | 29.2647i | 1.20176i | 0.799340 | + | 0.600880i | \(0.205183\pi\) | ||||
−0.799340 | + | 0.600880i | \(0.794817\pi\) | |||||||
\(594\) | 16.1693 | − | 33.6411i | 0.663435 | − | 1.38031i | ||||
\(595\) | 6.46689i | 0.265117i | ||||||||
\(596\) | −3.21742 | − | 20.7092i | −0.131791 | − | 0.848281i | ||||
\(597\) | −7.79068 | − | 21.4382i | −0.318851 | − | 0.877408i | ||||
\(598\) | 18.5881 | − | 1.43533i | 0.760124 | − | 0.0586952i | ||||
\(599\) | 43.1247 | 1.76203 | 0.881014 | − | 0.473090i | \(-0.156861\pi\) | ||||
0.881014 | + | 0.473090i | \(0.156861\pi\) | |||||||
\(600\) | 17.6209 | − | 11.5386i | 0.719370 | − | 0.471060i | ||||
\(601\) | −9.96034 | −0.406291 | −0.203145 | − | 0.979149i | \(-0.565116\pi\) | ||||
−0.203145 | + | 0.979149i | \(0.565116\pi\) | |||||||
\(602\) | −1.09727 | + | 0.0847290i | −0.0447215 | + | 0.00345330i | ||||
\(603\) | 1.92605 | + | 2.30007i | 0.0784349 | + | 0.0936661i | ||||
\(604\) | 2.36363 | + | 15.2137i | 0.0961747 | + | 0.619036i | ||||
\(605\) | 45.1309i | 1.83483i | ||||||||
\(606\) | −0.360044 | − | 0.794203i | −0.0146258 | − | 0.0322623i | ||||
\(607\) | 7.00955i | 0.284509i | 0.989830 | + | 0.142255i | \(0.0454351\pi\) | ||||
−0.989830 | + | 0.142255i | \(0.954565\pi\) | |||||||
\(608\) | −12.5725 | − | 30.9973i | −0.509883 | − | 1.25711i | ||||
\(609\) | 2.64526 | − | 0.961293i | 0.107191 | − | 0.0389535i | ||||
\(610\) | −0.386415 | − | 5.00422i | −0.0156455 | − | 0.202615i | ||||
\(611\) | −2.66691 | −0.107892 | ||||||||
\(612\) | 34.3377 | + | 30.0886i | 1.38802 | + | 1.21626i | ||||
\(613\) | 4.42637 | 0.178779 | 0.0893897 | − | 0.995997i | \(-0.471508\pi\) | ||||
0.0893897 | + | 0.995997i | \(0.471508\pi\) | |||||||
\(614\) | −1.88602 | − | 24.4246i | −0.0761134 | − | 0.985698i | ||||
\(615\) | 42.1109 | − | 15.3032i | 1.69808 | − | 0.617083i | ||||
\(616\) | −0.917449 | − | 3.89734i | −0.0369651 | − | 0.157028i | ||||
\(617\) | 26.4466i | 1.06470i | 0.846524 | + | 0.532350i | \(0.178691\pi\) | ||||
−0.846524 | + | 0.532350i | \(0.821309\pi\) | |||||||
\(618\) | −10.8045 | − | 23.8331i | −0.434621 | − | 0.958707i | ||||
\(619\) | − | 5.44867i | − | 0.219000i | −0.993987 | − | 0.109500i | \(-0.965075\pi\) | ||
0.993987 | − | 0.109500i | \(-0.0349250\pi\) | |||||||
\(620\) | 26.2036 | − | 4.07105i | 1.05236 | − | 0.163497i | ||||
\(621\) | 5.85954 | − | 10.1138i | 0.235135 | − | 0.405853i | ||||
\(622\) | −22.7467 | + | 1.75645i | −0.912061 | + | 0.0704274i | ||||
\(623\) | −0.471520 | −0.0188911 | ||||||||
\(624\) | −32.1545 | + | 24.7920i | −1.28721 | + | 0.992474i | ||||
\(625\) | −28.0122 | −1.12049 | ||||||||
\(626\) | −23.4124 | + | 1.80786i | −0.935749 | + | 0.0722565i | ||||
\(627\) | −17.7680 | − | 48.8937i | −0.709586 | − | 1.95262i | ||||
\(628\) | −23.8561 | + | 3.70634i | −0.951964 | + | 0.147899i | ||||
\(629\) | − | 52.2290i | − | 2.08251i | ||||||
\(630\) | −2.57804 | + | 2.52090i | −0.102712 | + | 0.100435i | ||||
\(631\) | 25.6253i | 1.02013i | 0.860137 | + | 0.510063i | \(0.170378\pi\) | ||||
−0.860137 | + | 0.510063i | \(0.829622\pi\) | |||||||
\(632\) | −7.99397 | − | 33.9585i | −0.317983 | − | 1.35080i | ||||
\(633\) | −2.89647 | − | 7.97044i | −0.115124 | − | 0.316797i | ||||
\(634\) | 1.92265 | + | 24.8991i | 0.0763584 | + | 0.988870i | ||||
\(635\) | −6.14047 | −0.243677 | ||||||||
\(636\) | 9.07250 | + | 16.5013i | 0.359748 | + | 0.654319i | ||||
\(637\) | −40.5680 | −1.60736 | ||||||||
\(638\) | 3.22449 | + | 41.7584i | 0.127659 | + | 1.65323i | ||||
\(639\) | −10.4650 | + | 8.76324i | −0.413987 | + | 0.346668i | ||||
\(640\) | −17.7221 | − | 29.6015i | −0.700527 | − | 1.17010i | ||||
\(641\) | 2.81491i | 0.111182i | 0.998454 | + | 0.0555911i | \(0.0177043\pi\) | ||||
−0.998454 | + | 0.0555911i | \(0.982296\pi\) | |||||||
\(642\) | 7.53006 | − | 3.41368i | 0.297188 | − | 0.134727i | ||||
\(643\) | 29.8717i | 1.17802i | 0.808125 | + | 0.589011i | \(0.200483\pi\) | ||||
−0.808125 | + | 0.589011i | \(0.799517\pi\) | |||||||
\(644\) | −0.192489 | − | 1.23897i | −0.00758512 | − | 0.0488222i | ||||
\(645\) | −13.8616 | + | 5.03734i | −0.545801 | + | 0.198345i | ||||
\(646\) | 63.4431 | − | 4.89894i | 2.49614 | − | 0.192746i | ||||
\(647\) | −42.3369 | −1.66443 | −0.832217 | − | 0.554450i | \(-0.812929\pi\) | ||||
−0.832217 | + | 0.554450i | \(0.812929\pi\) | |||||||
\(648\) | 1.39053 | + | 25.4178i | 0.0546251 | + | 0.998507i | ||||
\(649\) | 4.61498 | 0.181154 | ||||||||
\(650\) | −35.5273 | + | 2.74334i | −1.39349 | + | 0.107603i | ||||
\(651\) | −1.97260 | + | 0.716844i | −0.0773121 | + | 0.0280953i | ||||
\(652\) | 2.89091 | + | 18.6076i | 0.113217 | + | 0.728729i | ||||
\(653\) | − | 43.8697i | − | 1.71676i | −0.513018 | − | 0.858378i | \(-0.671473\pi\) | ||
0.513018 | − | 0.858378i | \(-0.328527\pi\) | |||||||
\(654\) | −19.0214 | + | 8.62315i | −0.743794 | + | 0.337192i | ||||
\(655\) | − | 12.1414i | − | 0.474406i | ||||||
\(656\) | −10.2948 | − | 32.3320i | −0.401945 | − | 1.26235i | ||||
\(657\) | 31.0784 | − | 26.0247i | 1.21248 | − | 1.01532i | ||||
\(658\) | 0.0138086 | + | 0.178826i | 0.000538314 | + | 0.00697137i | ||||
\(659\) | −30.2207 | −1.17723 | −0.588616 | − | 0.808413i | \(-0.700327\pi\) | ||||
−0.588616 | + | 0.808413i | \(0.700327\pi\) | |||||||
\(660\) | −25.8511 | − | 47.0187i | −1.00625 | − | 1.83020i | ||||
\(661\) | 9.40563 | 0.365837 | 0.182918 | − | 0.983128i | \(-0.441446\pi\) | ||||
0.182918 | + | 0.983128i | \(0.441446\pi\) | |||||||
\(662\) | 3.73309 | + | 48.3449i | 0.145091 | + | 1.87898i | ||||
\(663\) | −26.3805 | − | 72.5932i | −1.02453 | − | 2.81929i | ||||
\(664\) | −7.69147 | + | 1.81060i | −0.298487 | + | 0.0702650i | ||||
\(665\) | 5.02548i | 0.194880i | ||||||||
\(666\) | 20.8212 | − | 20.3597i | 0.806807 | − | 0.788924i | ||||
\(667\) | 13.1158i | 0.507845i | ||||||||
\(668\) | −41.6677 | + | 6.47358i | −1.61217 | + | 0.250470i | ||||
\(669\) | 15.9862 | + | 43.9905i | 0.618063 | + | 1.70077i | ||||
\(670\) | 4.29983 | − | 0.332024i | 0.166117 | − | 0.0128272i | ||||
\(671\) | −5.91141 | −0.228207 | ||||||||
\(672\) | 1.82888 | + | 2.02771i | 0.0705506 | + | 0.0782206i | ||||
\(673\) | −50.0563 | −1.92953 | −0.964764 | − | 0.263117i | \(-0.915249\pi\) | ||||
−0.964764 | + | 0.263117i | \(0.915249\pi\) | |||||||
\(674\) | −8.68998 | + | 0.671021i | −0.334725 | + | 0.0258468i | ||||
\(675\) | −11.1993 | + | 19.3304i | −0.431061 | + | 0.744027i | ||||
\(676\) | 42.1837 | − | 6.55374i | 1.62245 | − | 0.252067i | ||||
\(677\) | − | 20.9155i | − | 0.803848i | −0.915673 | − | 0.401924i | \(-0.868342\pi\) | ||
0.915673 | − | 0.401924i | \(-0.131658\pi\) | |||||||
\(678\) | 16.0311 | + | 35.3621i | 0.615670 | + | 1.35807i | ||||
\(679\) | − | 1.18756i | − | 0.0455744i | ||||||
\(680\) | 63.8852 | − | 15.0388i | 2.44988 | − | 0.576712i | ||||
\(681\) | −0.0679925 | + | 0.0247086i | −0.00260548 | + | 0.000946834i | ||||
\(682\) | −2.40453 | − | 31.1396i | −0.0920742 | − | 1.19240i | ||||
\(683\) | −15.8548 | −0.606666 | −0.303333 | − | 0.952885i | \(-0.598099\pi\) | ||||
−0.303333 | + | 0.952885i | \(0.598099\pi\) | |||||||
\(684\) | 26.6842 | + | 23.3821i | 1.02029 | + | 0.894036i | ||||
\(685\) | −26.9413 | −1.02937 | ||||||||
\(686\) | 0.422457 | + | 5.47098i | 0.0161295 | + | 0.208883i | ||||
\(687\) | 23.9738 | − | 8.71211i | 0.914657 | − | 0.332388i | ||||
\(688\) | 3.38874 | + | 10.6427i | 0.129194 | + | 0.405749i | ||||
\(689\) | − | 31.8575i | − | 1.21367i | ||||||
\(690\) | −6.93778 | − | 15.3037i | −0.264117 | − | 0.582602i | ||||
\(691\) | 9.43178i | 0.358802i | 0.983776 | + | 0.179401i | \(0.0574159\pi\) | ||||
−0.983776 | + | 0.179401i | \(0.942584\pi\) | |||||||
\(692\) | −5.80887 | − | 37.3892i | −0.220820 | − | 1.42132i | ||||
\(693\) | 2.72648 | + | 3.25593i | 0.103571 | + | 0.123683i | ||||
\(694\) | 11.0234 | − | 0.851200i | 0.418441 | − | 0.0323111i | ||||
\(695\) | 37.7145 | 1.43059 | ||||||||
\(696\) | −15.6480 | − | 23.8965i | −0.593136 | − | 0.905796i | ||||
\(697\) | 64.5478 | 2.44492 | ||||||||
\(698\) | 30.0834 | − | 2.32297i | 1.13867 | − | 0.0879258i | ||||
\(699\) | 13.5337 | + | 37.2416i | 0.511890 | + | 1.40861i | ||||
\(700\) | 0.367902 | + | 2.36803i | 0.0139054 | + | 0.0895030i | ||||
\(701\) | 29.7093i | 1.12210i | 0.827780 | + | 0.561052i | \(0.189603\pi\) | ||||
−0.827780 | + | 0.561052i | \(0.810397\pi\) | |||||||
\(702\) | 18.6559 | − | 38.8147i | 0.704123 | − | 1.46497i | ||||
\(703\) | − | 40.5876i | − | 1.53079i | ||||||
\(704\) | −36.3675 | + | 18.1266i | −1.37065 | + | 0.683171i | ||||
\(705\) | 0.820951 | + | 2.25908i | 0.0309188 | + | 0.0850817i | ||||
\(706\) | 1.45187 | + | 18.8023i | 0.0546418 | + | 0.707632i | ||||
\(707\) | 0.0992138 | 0.00373132 | ||||||||
\(708\) | −2.75805 | + | 1.51639i | −0.103654 | + | 0.0569893i | ||||
\(709\) | 35.4570 | 1.33162 | 0.665808 | − | 0.746123i | \(-0.268087\pi\) | ||||
0.665808 | + | 0.746123i | \(0.268087\pi\) | |||||||
\(710\) | 1.51066 | + | 19.5636i | 0.0566939 | + | 0.734207i | ||||
\(711\) | 23.7565 | + | 28.3698i | 0.890940 | + | 1.06395i | ||||
\(712\) | 1.09652 | + | 4.65806i | 0.0410940 | + | 0.174568i | ||||
\(713\) | − | 9.78055i | − | 0.366285i | ||||||
\(714\) | −4.73105 | + | 2.14478i | −0.177055 | + | 0.0802662i | ||||
\(715\) | 90.7744i | 3.39477i | ||||||||
\(716\) | 50.1840 | − | 7.79669i | 1.87546 | − | 0.291376i | ||||
\(717\) | −11.0769 | + | 4.02536i | −0.413674 | + | 0.150330i | ||||
\(718\) | −26.8179 | + | 2.07082i | −1.00083 | + | 0.0772823i | ||||
\(719\) | 30.8444 | 1.15030 | 0.575152 | − | 0.818047i | \(-0.304943\pi\) | ||||
0.575152 | + | 0.818047i | \(0.304943\pi\) | |||||||
\(720\) | 30.8987 | + | 19.6056i | 1.15153 | + | 0.730658i | ||||
\(721\) | 2.97728 | 0.110880 | ||||||||
\(722\) | 22.5119 | − | 1.73832i | 0.837807 | − | 0.0646936i | ||||
\(723\) | −1.56196 | + | 0.567619i | −0.0580899 | + | 0.0211100i | ||||
\(724\) | −18.5475 | + | 2.88158i | −0.689313 | + | 0.107093i | ||||
\(725\) | − | 25.0681i | − | 0.931004i | ||||||
\(726\) | −33.0168 | + | 14.9679i | −1.22537 | + | 0.555509i | ||||
\(727\) | 19.2654i | 0.714513i | 0.934006 | + | 0.357257i | \(0.116288\pi\) | ||||
−0.934006 | + | 0.357257i | \(0.883712\pi\) | |||||||
\(728\) | −1.05854 | − | 4.49670i | −0.0392321 | − | 0.166659i | ||||
\(729\) | −13.4295 | − | 23.4233i | −0.497387 | − | 0.867529i | ||||
\(730\) | −4.48628 | − | 58.0990i | −0.166045 | − | 2.15034i | ||||
\(731\) | −21.2472 | −0.785854 | ||||||||
\(732\) | 3.53283 | − | 1.94237i | 0.130577 | − | 0.0717920i | ||||
\(733\) | −12.3277 | −0.455334 | −0.227667 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227667 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(734\) | 0.215504 | + | 2.79086i | 0.00795440 | + | 0.103013i | ||||
\(735\) | 12.4880 | + | 34.3641i | 0.460626 | + | 1.26754i | ||||
\(736\) | −11.7919 | + | 4.78279i | −0.434655 | + | 0.176296i | ||||
\(737\) | − | 5.07932i | − | 0.187099i | ||||||
\(738\) | 25.1618 | + | 25.7321i | 0.926218 | + | 0.947213i | ||||
\(739\) | − | 45.7058i | − | 1.68131i | −0.541568 | − | 0.840657i | \(-0.682169\pi\) | ||
0.541568 | − | 0.840657i | \(-0.317831\pi\) | |||||||
\(740\) | −6.42681 | − | 41.3667i | −0.236254 | − | 1.52067i | ||||
\(741\) | −20.5005 | − | 56.4128i | −0.753105 | − | 2.07238i | ||||
\(742\) | −2.13616 | + | 0.164950i | −0.0784209 | + | 0.00605550i | ||||
\(743\) | −42.4107 | −1.55590 | −0.777948 | − | 0.628328i | \(-0.783739\pi\) | ||||
−0.777948 | + | 0.628328i | \(0.783739\pi\) | |||||||
\(744\) | 11.6688 | + | 17.8198i | 0.427801 | + | 0.653307i | ||||
\(745\) | 31.9550 | 1.17074 | ||||||||
\(746\) | −22.7386 | + | 1.75583i | −0.832520 | + | 0.0642854i | ||||
\(747\) | 6.42565 | − | 5.38077i | 0.235102 | − | 0.196872i | ||||
\(748\) | −11.8670 | − | 76.3828i | −0.433900 | − | 2.79283i | ||||
\(749\) | 0.940673i | 0.0343714i | ||||||||
\(750\) | −2.16082 | − | 4.76643i | −0.0789018 | − | 0.174045i | ||||
\(751\) | 27.0706i | 0.987819i | 0.869513 | + | 0.493910i | \(0.164433\pi\) | ||||
−0.869513 | + | 0.493910i | \(0.835567\pi\) | |||||||
\(752\) | 1.73448 | − | 0.552274i | 0.0632498 | − | 0.0201394i | ||||
\(753\) | −19.0652 | + | 6.92831i | −0.694773 | + | 0.252482i | ||||
\(754\) | 3.72037 | + | 48.1802i | 0.135488 | + | 1.75462i | ||||
\(755\) | −23.4753 | −0.854353 | ||||||||
\(756\) | −2.69926 | − | 1.04998i | −0.0981712 | − | 0.0381873i | ||||
\(757\) | −6.61541 | −0.240441 | −0.120221 | − | 0.992747i | \(-0.538360\pi\) | ||||
−0.120221 | + | 0.992747i | \(0.538360\pi\) | |||||||
\(758\) | 2.96546 | + | 38.4038i | 0.107710 | + | 1.39489i | ||||
\(759\) | −18.5999 | + | 6.75924i | −0.675135 | + | 0.245345i | ||||
\(760\) | 49.6457 | − | 11.6868i | 1.80084 | − | 0.423925i | ||||
\(761\) | − | 22.7202i | − | 0.823606i | −0.911273 | − | 0.411803i | \(-0.864899\pi\) | ||
0.911273 | − | 0.411803i | \(-0.135101\pi\) | |||||||
\(762\) | −2.03652 | − | 4.49224i | −0.0737752 | − | 0.162737i | ||||
\(763\) | − | 2.37619i | − | 0.0860240i | ||||||
\(764\) | −9.76044 | + | 1.51640i | −0.353120 | + | 0.0548615i | ||||
\(765\) | −53.3713 | + | 44.6925i | −1.92964 | + | 1.61586i | ||||
\(766\) | 44.2520 | − | 3.41704i | 1.59889 | − | 0.123463i | ||||
\(767\) | 5.32470 | 0.192264 | ||||||||
\(768\) | 15.7783 | − | 22.7826i | 0.569349 | − | 0.822096i | ||||
\(769\) | 32.2780 | 1.16397 | 0.581987 | − | 0.813198i | \(-0.302275\pi\) | ||||
0.581987 | + | 0.813198i | \(0.302275\pi\) | |||||||
\(770\) | 6.08676 | − | 0.470006i | 0.219351 | − | 0.0169378i | ||||
\(771\) | 0.914120 | + | 2.51545i | 0.0329212 | + | 0.0905919i | ||||
\(772\) | 40.1454 | − | 6.23707i | 1.44486 | − | 0.224477i | ||||
\(773\) | 46.0146i | 1.65503i | 0.561443 | + | 0.827515i | \(0.310246\pi\) | ||||
−0.561443 | + | 0.827515i | \(0.689754\pi\) | |||||||
\(774\) | −8.28249 | − | 8.47023i | −0.297708 | − | 0.304456i | ||||
\(775\) | 18.6935i | 0.671489i | ||||||||
\(776\) | −11.7317 | + | 2.76168i | −0.421142 | + | 0.0991386i | ||||
\(777\) | 1.13166 | + | 3.11406i | 0.0405979 | + | 0.111716i | ||||
\(778\) | −0.851735 | − | 11.0303i | −0.0305362 | − | 0.395455i | ||||
\(779\) | 50.1606 | 1.79719 | ||||||||
\(780\) | −29.8266 | − | 54.2495i | −1.06796 | − | 1.94244i | ||||
\(781\) | 23.1101 | 0.826945 | ||||||||
\(782\) | −1.86364 | − | 24.1348i | −0.0666435 | − | 0.863059i | ||||
\(783\) | 26.2149 | + | 15.1879i | 0.936844 | + | 0.542771i | ||||
\(784\) | 26.3841 | − | 8.40096i | 0.942290 | − | 0.300034i | ||||
\(785\) | − | 36.8109i | − | 1.31384i | ||||||
\(786\) | 8.88244 | − | 4.02677i | 0.316826 | − | 0.143630i | ||||
\(787\) | 29.8961i | 1.06568i | 0.846216 | + | 0.532841i | \(0.178875\pi\) | ||||
−0.846216 | + | 0.532841i | \(0.821125\pi\) | |||||||
\(788\) | 4.10693 | + | 26.4346i | 0.146303 | + | 0.941692i | ||||
\(789\) | 41.5023 | − | 15.0820i | 1.47752 | − | 0.536933i | ||||
\(790\) | 53.0355 | − | 4.09528i | 1.88692 | − | 0.145704i | ||||
\(791\) | −4.41752 | −0.157069 | ||||||||
\(792\) | 25.8243 | − | 34.5061i | 0.917625 | − | 1.22612i | ||||
\(793\) | −6.82050 | −0.242203 | ||||||||
\(794\) | 36.4508 | − | 2.81465i | 1.29359 | − | 0.0998884i | ||||
\(795\) | −26.9857 | + | 9.80664i | −0.957084 | + | 0.347806i | ||||
\(796\) | −4.04351 | − | 26.0264i | −0.143319 | − | 0.922481i | ||||
\(797\) | 4.97969i | 0.176390i | 0.996103 | + | 0.0881949i | \(0.0281098\pi\) | ||||
−0.996103 | + | 0.0881949i | \(0.971890\pi\) | |||||||
\(798\) | −3.67654 | + | 1.66672i | −0.130148 | + | 0.0590014i | ||||
\(799\) | 3.46272i | 0.122502i | ||||||||
\(800\) | 22.5377 | − | 9.14130i | 0.796829 | − | 0.323194i | ||||
\(801\) | −3.25866 | − | 3.89146i | −0.115139 | − | 0.137498i | ||||
\(802\) | 0.207218 | + | 2.68354i | 0.00731710 | + | 0.0947593i | ||||
\(803\) | −68.6314 | −2.42195 | ||||||||
\(804\) | 1.66896 | + | 3.03555i | 0.0588597 | + | 0.107056i | ||||
\(805\) | 1.91177 | 0.0673812 | ||||||||
\(806\) | −2.77431 | − | 35.9284i | −0.0977211 | − | 1.26552i | ||||
\(807\) | 6.70940 | + | 18.4628i | 0.236182 | + | 0.649921i | ||||
\(808\) | −0.230722 | − | 0.980113i | −0.00811679 | − | 0.0344802i | ||||
\(809\) | 6.05334i | 0.212824i | 0.994322 | + | 0.106412i | \(0.0339363\pi\) | ||||
−0.994322 | + | 0.106412i | \(0.966064\pi\) | |||||||
\(810\) | −38.6218 | − | 3.85472i | −1.35703 | − | 0.135441i | ||||
\(811\) | 26.9465i | 0.946219i | 0.881004 | + | 0.473110i | \(0.156869\pi\) | ||||
−0.881004 | + | 0.473110i | \(0.843131\pi\) | |||||||
\(812\) | 3.21140 | − | 0.498929i | 0.112698 | − | 0.0175090i | ||||
\(813\) | 2.02340 | + | 5.56795i | 0.0709637 | + | 0.195276i | ||||
\(814\) | −49.1589 | + | 3.79594i | −1.72302 | + | 0.133048i | ||||
\(815\) | −28.7122 | −1.00574 | ||||||||
\(816\) | 32.1899 | + | 41.7494i | 1.12687 | + | 1.46152i | ||||
\(817\) | −16.5114 | −0.577659 | ||||||||
\(818\) | 26.2607 | − | 2.02779i | 0.918184 | − | 0.0709002i | ||||
\(819\) | 3.14578 | + | 3.75665i | 0.109922 | + | 0.131268i | ||||
\(820\) | 51.1234 | − | 7.94264i | 1.78531 | − | 0.277369i | ||||
\(821\) | − | 14.1175i | − | 0.492704i | −0.969180 | − | 0.246352i | \(-0.920768\pi\) | ||
0.969180 | − | 0.246352i | \(-0.0792319\pi\) | |||||||
\(822\) | −8.93521 | − | 19.7097i | −0.311651 | − | 0.687455i | ||||
\(823\) | 5.56238i | 0.193892i | 0.995290 | + | 0.0969462i | \(0.0309075\pi\) | ||||
−0.995290 | + | 0.0969462i | \(0.969093\pi\) | |||||||
\(824\) | −6.92370 | − | 29.4120i | −0.241199 | − | 1.02462i | ||||
\(825\) | 35.5499 | − | 12.9189i | 1.23769 | − | 0.449777i | ||||
\(826\) | −0.0275699 | − | 0.357040i | −0.000959279 | − | 0.0124230i | ||||
\(827\) | −22.3916 | −0.778631 | −0.389316 | − | 0.921104i | \(-0.627288\pi\) | ||||
−0.389316 | + | 0.921104i | \(0.627288\pi\) | |||||||
\(828\) | 8.89492 | − | 10.1511i | 0.309120 | − | 0.352775i | ||||
\(829\) | −6.35913 | −0.220862 | −0.110431 | − | 0.993884i | \(-0.535223\pi\) | ||||
−0.110431 | + | 0.993884i | \(0.535223\pi\) | |||||||
\(830\) | −0.927566 | − | 12.0123i | −0.0321963 | − | 0.416954i | ||||
\(831\) | 18.5264 | − | 6.73251i | 0.642673 | − | 0.233548i | ||||
\(832\) | −41.9603 | + | 20.9142i | −1.45471 | + | 0.725070i | ||||
\(833\) | 52.6734i | 1.82503i | ||||||||
\(834\) | 12.5082 | + | 27.5911i | 0.433123 | + | 0.955403i | ||||
\(835\) | − | 64.2948i | − | 2.22501i | ||||||
\(836\) | −9.22194 | − | 59.3578i | −0.318948 | − | 2.05293i | ||||
\(837\) | −19.5487 | − | 11.3257i | −0.675701 | − | 0.391475i | ||||
\(838\) | −28.8109 | + | 2.22471i | −0.995255 | + | 0.0768514i | ||||
\(839\) | −35.8596 | −1.23801 | −0.619006 | − | 0.785387i | \(-0.712464\pi\) | ||||
−0.619006 | + | 0.785387i | \(0.712464\pi\) | |||||||
\(840\) | −3.48319 | + | 2.28087i | −0.120182 | + | 0.0786976i | ||||
\(841\) | −4.99601 | −0.172276 | ||||||||
\(842\) | −22.2977 | + | 1.72178i | −0.768429 | + | 0.0593364i | ||||
\(843\) | 5.81194 | + | 15.9932i | 0.200174 | + | 0.550834i | ||||
\(844\) | −1.50332 | − | 9.67626i | −0.0517465 | − | 0.333070i | ||||
\(845\) | 65.0910i | 2.23920i | ||||||||
\(846\) | −1.38042 | + | 1.34982i | −0.0474599 | + | 0.0464079i | ||||
\(847\) | − | 4.12454i | − | 0.141721i | ||||||
\(848\) | 6.59717 | + | 20.7191i | 0.226548 | + | 0.711497i | ||||
\(849\) | 10.4747 | + | 28.8240i | 0.359490 | + | 0.989236i | ||||
\(850\) | 3.56195 | + | 46.1286i | 0.122174 | + | 1.58220i | ||||
\(851\) | −15.4402 | −0.529283 | ||||||||
\(852\) | −13.8113 | + | 7.59351i | −0.473167 | + | 0.260149i | ||||
\(853\) | −27.3634 | −0.936905 | −0.468452 | − | 0.883489i | \(-0.655188\pi\) | ||||
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(854\) | 0.0353148 | + | 0.457339i | 0.00120845 | + | 0.0156498i | ||||
\(855\) | −41.4753 | + | 34.7309i | −1.41842 | + | 1.18777i | ||||
\(856\) | 9.29272 | − | 2.18754i | 0.317619 | − | 0.0747687i | ||||
\(857\) | 32.6483i | 1.11525i | 0.830094 | + | 0.557623i | \(0.188287\pi\) | ||||
−0.830094 | + | 0.557623i | \(0.811713\pi\) | |||||||
\(858\) | −66.4087 | + | 30.1058i | −2.26716 | + | 1.02779i | ||||
\(859\) | 7.82213i | 0.266888i | 0.991056 | + | 0.133444i | \(0.0426036\pi\) | ||||
−0.991056 | + | 0.133444i | \(0.957396\pi\) | |||||||
\(860\) | −16.8283 | + | 2.61447i | −0.573839 | + | 0.0891528i | ||||
\(861\) | −3.84855 | + | 1.39857i | −0.131158 | + | 0.0476631i | ||||
\(862\) | −28.2943 | + | 2.18483i | −0.963709 | + | 0.0744155i | ||||
\(863\) | 12.3680 | 0.421010 | 0.210505 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210505 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(864\) | −4.09535 | + | 29.1072i | −0.139327 | + | 0.990246i | ||||
\(865\) | 57.6929 | 1.96162 | ||||||||
\(866\) | 18.5726 | − | 1.43414i | 0.631124 | − | 0.0487340i | ||||
\(867\) | −66.5808 | + | 24.1956i | −2.26120 | + | 0.821725i | ||||
\(868\) | −2.39477 | + | 0.372056i | −0.0812837 | + | 0.0126284i | ||||
\(869\) | − | 62.6499i | − | 2.12525i | ||||||
\(870\) | 39.6671 | − | 17.9827i | 1.34484 | − | 0.609670i | ||||
\(871\) | − | 5.86045i | − | 0.198574i | ||||||
\(872\) | −23.4739 | + | 5.52586i | −0.794928 | + | 0.187129i | ||||
\(873\) | 9.80094 | − | 8.20719i | 0.331711 | − | 0.277771i | ||||
\(874\) | −1.44825 | − | 18.7554i | −0.0489878 | − | 0.634410i | ||||
\(875\) | 0.595434 | 0.0201293 | ||||||||
\(876\) | 41.0161 | − | 22.5509i | 1.38581 | − | 0.761923i | ||||
\(877\) | −18.5878 | −0.627666 | −0.313833 | − | 0.949478i | \(-0.601613\pi\) | ||||
−0.313833 | + | 0.949478i | \(0.601613\pi\) | |||||||
\(878\) | 2.42691 | + | 31.4293i | 0.0819041 | + | 1.06069i | ||||
\(879\) | −9.30305 | − | 25.5999i | −0.313784 | − | 0.863465i | ||||
\(880\) | −18.7979 | − | 59.0368i | −0.633677 | − | 1.99013i | ||||
\(881\) | − | 47.9022i | − | 1.61387i | −0.590642 | − | 0.806933i | \(-0.701126\pi\) | ||
0.590642 | − | 0.806933i | \(-0.298874\pi\) | |||||||
\(882\) | −20.9984 | + | 20.5330i | −0.707053 | + | 0.691381i | ||||
\(883\) | 35.6876i | 1.20098i | 0.799630 | + | 0.600492i | \(0.205029\pi\) | ||||
−0.799630 | + | 0.600492i | \(0.794971\pi\) | |||||||
\(884\) | −13.6920 | − | 88.1295i | −0.460511 | − | 2.96412i | ||||
\(885\) | −1.63909 | − | 4.51042i | −0.0550975 | − | 0.151616i | ||||
\(886\) | −21.7960 | + | 1.68304i | −0.732250 | + | 0.0565428i | ||||
\(887\) | −15.3867 | −0.516635 | −0.258318 | − | 0.966060i | \(-0.583168\pi\) | ||||
−0.258318 | + | 0.966060i | \(0.583168\pi\) | |||||||
\(888\) | 28.1315 | − | 18.4212i | 0.944033 | − | 0.618174i | ||||
\(889\) | 0.561182 | 0.0188214 | ||||||||
\(890\) | −7.27483 | + | 0.561746i | −0.243853 | + | 0.0188298i | ||||
\(891\) | −8.02858 | + | 45.0033i | −0.268968 | + | 1.50767i | ||||
\(892\) | 8.29715 | + | 53.4053i | 0.277809 | + | 1.78814i | ||||
\(893\) | 2.69091i | 0.0900479i | ||||||||
\(894\) | 10.5980 | + | 23.3776i | 0.354451 | + | 0.781865i | ||||
\(895\) | 77.4358i | 2.58839i | ||||||||
\(896\) | 1.61963 | + | 2.70530i | 0.0541081 | + | 0.0903778i | ||||
\(897\) | −21.4604 | + | 7.79873i | −0.716541 | + | 0.260392i | ||||
\(898\) | 2.72166 | + | 35.2465i | 0.0908228 | + | 1.17619i | ||||
\(899\) | 25.3511 | 0.845507 | ||||||||
\(900\) | −17.0008 | + | 19.4017i | −0.566692 | + | 0.646722i | ||||
\(901\) | −41.3638 | −1.37803 | ||||||||
\(902\) | −4.69125 | − | 60.7535i | −0.156202 | − | 2.02287i | ||||
\(903\) | 1.26682 | − | 0.460366i | 0.0421573 | − | 0.0153200i | ||||
\(904\) | 10.2730 | + | 43.6398i | 0.341674 | + | 1.45144i | ||||
\(905\) | − | 28.6195i | − | 0.951344i | ||||||
\(906\) | −7.78569 | − | 17.1740i | −0.258662 | − | 0.570569i | ||||
\(907\) | − | 18.6850i | − | 0.620425i | −0.950667 | − | 0.310213i | \(-0.899600\pi\) | ||
0.950667 | − | 0.310213i | \(-0.100400\pi\) | |||||||
\(908\) | −0.0825441 | + | 0.0128242i | −0.00273932 | + | 0.000425587i | ||||
\(909\) | 0.685663 | + | 0.818811i | 0.0227420 | + | 0.0271582i | ||||
\(910\) | 7.02282 | − | 0.542287i | 0.232804 | − | 0.0179766i | ||||
\(911\) | −39.4070 | −1.30561 | −0.652805 | − | 0.757526i | \(-0.726408\pi\) | ||||
−0.652805 | + | 0.757526i | \(0.726408\pi\) | |||||||
\(912\) | 25.0151 | + | 32.4438i | 0.828331 | + | 1.07432i | ||||
\(913\) | −14.1900 | −0.469619 | ||||||||
\(914\) | 19.5043 | − | 1.50608i | 0.645144 | − | 0.0498166i | ||||
\(915\) | 2.09954 | + | 5.77748i | 0.0694088 | + | 0.190998i | ||||
\(916\) | 29.1046 | − | 4.52175i | 0.961643 | − | 0.149403i | ||||
\(917\) | 1.10962i | 0.0366427i | ||||||||
\(918\) | −50.3970 | − | 24.2229i | −1.66335 | − | 0.799473i | ||||
\(919\) | − | 40.3364i | − | 1.33058i | −0.746587 | − | 0.665288i | \(-0.768309\pi\) | ||
0.746587 | − | 0.665288i | \(-0.231691\pi\) | |||||||
\(920\) | −4.44585 | − | 18.8860i | −0.146575 | − | 0.622654i | ||||
\(921\) | 10.2475 | + | 28.1987i | 0.337665 | + | 0.929180i | ||||
\(922\) | −0.0387260 | − | 0.501516i | −0.00127537 | − | 0.0165166i | ||||
\(923\) | 26.6641 | 0.877661 | ||||||||
\(924\) | 2.36255 | + | 4.29707i | 0.0777221 | + | 0.141363i | ||||
\(925\) | 29.5107 | 0.970306 | ||||||||
\(926\) | 0.405299 | + | 5.24877i | 0.0133189 | + | 0.172485i | ||||
\(927\) | 20.5759 | + | 24.5715i | 0.675802 | + | 0.807035i | ||||
\(928\) | −12.3970 | − | 30.5645i | −0.406950 | − | 1.00333i | ||||
\(929\) | 53.7081i | 1.76211i | 0.473017 | + | 0.881053i | \(0.343165\pi\) | ||||
−0.473017 | + | 0.881053i | \(0.656835\pi\) | |||||||
\(930\) | −29.5801 | + | 13.4098i | −0.969969 | + | 0.439726i | ||||
\(931\) | 40.9330i | 1.34152i | ||||||||
\(932\) | 7.02423 | + | 45.2120i | 0.230086 | + | 1.48097i | ||||
\(933\) | 26.2616 | − | 9.54349i | 0.859765 | − | 0.312440i | ||||
\(934\) | −47.8442 | + | 3.69443i | −1.56551 | + | 0.120885i | ||||
\(935\) | 117.862 | 3.85448 | ||||||||
\(936\) | 29.7957 | − | 39.8127i | 0.973902 | − | 1.30132i | ||||
\(937\) | −26.0917 | −0.852379 | −0.426189 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426189 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(938\) | −0.392964 | + | 0.0303439i | −0.0128307 | + | 0.000990762i | ||||
\(939\) | 27.0301 | − | 9.82279i | 0.882095 | − | 0.320555i | ||||
\(940\) | 0.426090 | + | 2.74256i | 0.0138975 | + | 0.0894524i | ||||
\(941\) | − | 33.4974i | − | 1.09198i | −0.837791 | − | 0.545992i | \(-0.816153\pi\) | ||
0.837791 | − | 0.545992i | \(-0.183847\pi\) | |||||||
\(942\) | 26.9301 | − | 12.2085i | 0.877431 | − | 0.397775i | ||||
\(943\) | − | 19.0819i | − | 0.621393i | ||||||
\(944\) | −3.46302 | + | 1.10266i | −0.112712 | + | 0.0358884i | ||||
\(945\) | 2.21381 | − | 3.82112i | 0.0720152 | − | 0.124301i | ||||
\(946\) | 1.54422 | + | 19.9982i | 0.0502068 | + | 0.650198i | ||||
\(947\) | 8.25639 | 0.268297 | 0.134148 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134148 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(948\) | 20.5855 | + | 37.4415i | 0.668586 | + | 1.21604i | ||||
\(949\) | −79.1859 | −2.57048 | ||||||||
\(950\) | 2.76802 | + | 35.8469i | 0.0898065 | + | 1.16303i | ||||
\(951\) | −10.4465 | − | 28.7465i | −0.338752 | − | 0.932170i | ||||
\(952\) | −5.83851 | + | 1.37441i | −0.189227 | + | 0.0445448i | ||||
\(953\) | 41.6462i | 1.34905i | 0.738251 | + | 0.674526i | \(0.235652\pi\) | ||||
−0.738251 | + | 0.674526i | \(0.764348\pi\) | |||||||
\(954\) | −16.1243 | − | 16.4898i | −0.522043 | − | 0.533876i | ||||
\(955\) | − | 15.0607i | − | 0.487354i | ||||||
\(956\) | −13.4475 | + | 2.08924i | −0.434925 | + | 0.0675708i | ||||
\(957\) | −17.5199 | − | 48.2109i | −0.566338 | − | 1.55844i | ||||
\(958\) | −10.8330 | + | 0.836500i | −0.349998 | + | 0.0270261i | ||||
\(959\) | 2.46218 | 0.0795081 | ||||||||
\(960\) | 30.6325 | + | 29.1056i | 0.988659 | + | 0.939378i | ||||
\(961\) | 12.0955 | 0.390176 | ||||||||
\(962\) | −56.7189 | + | 4.37971i | −1.82869 | + | 0.141208i | ||||
\(963\) | −7.76337 | + | 6.50096i | −0.250171 | + | 0.209491i | ||||
\(964\) | −1.89625 | + | 0.294605i | −0.0610740 | + | 0.00948858i | ||||
\(965\) | 61.9458i | 1.99411i | ||||||||
\(966\) | 0.634049 | + | 1.39862i | 0.0204002 | + | 0.0449997i | ||||
\(967\) | 25.9318i | 0.833909i | 0.908927 | + | 0.416955i | \(0.136903\pi\) | ||||
−0.908927 | + | 0.416955i | \(0.863097\pi\) | |||||||
\(968\) | −40.7455 | + | 9.59165i | −1.30961 | + | 0.308287i | ||||
\(969\) | −73.2464 | + | 26.6179i | −2.35301 | + | 0.855089i | ||||
\(970\) | −1.41480 | − | 18.3222i | −0.0454265 | − | 0.588291i | ||||
\(971\) | 15.8140 | 0.507495 | 0.253747 | − | 0.967271i | \(-0.418337\pi\) | ||||
0.253747 | + | 0.967271i | \(0.418337\pi\) | |||||||
\(972\) | −9.98906 | − | 29.5333i | −0.320399 | − | 0.947283i | ||||
\(973\) | −3.44675 | −0.110498 | ||||||||
\(974\) | −3.68129 | − | 47.6741i | −0.117956 | − | 1.52758i | ||||
\(975\) | 41.0170 | − | 14.9056i | 1.31359 | − | 0.477362i | ||||
\(976\) | 4.43584 | − | 1.41241i | 0.141988 | − | 0.0452103i | ||||
\(977\) | 18.5153i | 0.592358i | 0.955133 | + | 0.296179i | \(0.0957124\pi\) | ||||
−0.955133 | + | 0.296179i | \(0.904288\pi\) | |||||||
\(978\) | −9.52253 | − | 21.0053i | −0.304497 | − | 0.671674i | ||||
\(979\) | 8.59363i | 0.274654i | ||||||||
\(980\) | 6.48150 | + | 41.7187i | 0.207044 | + | 1.33265i | ||||
\(981\) | 19.6107 | − | 16.4218i | 0.626122 | − | 0.524308i | ||||
\(982\) | −60.7385 | + | 4.69010i | −1.93824 | + | 0.149667i | ||||
\(983\) | 57.7929 | 1.84331 | 0.921654 | − | 0.388013i | \(-0.126839\pi\) | ||||
0.921654 | + | 0.388013i | \(0.126839\pi\) | |||||||
\(984\) | 22.7660 | + | 34.7666i | 0.725754 | + | 1.10832i | ||||
\(985\) | −40.7895 | −1.29966 | ||||||||
\(986\) | 62.5572 | − | 4.83053i | 1.99223 | − | 0.153836i | ||||
\(987\) | −0.0750273 | − | 0.206459i | −0.00238815 | − | 0.00657165i | ||||
\(988\) | −10.6402 | − | 68.4862i | −0.338508 | − | 2.17884i | ||||
\(989\) | 6.28119i | 0.199730i | ||||||||
\(990\) | 45.9444 | + | 46.9858i | 1.46021 | + | 1.49331i | ||||
\(991\) | 23.4620i | 0.745293i | 0.927973 | + | 0.372647i | \(0.121550\pi\) | ||||
−0.927973 | + | 0.372647i | \(0.878450\pi\) | |||||||
\(992\) | 9.24451 | + | 22.7922i | 0.293514 | + | 0.723653i | ||||
\(993\) | −20.2833 | − | 55.8152i | −0.643672 | − | 1.77124i | ||||
\(994\) | −0.138060 | − | 1.78793i | −0.00437899 | − | 0.0567096i | ||||
\(995\) | 40.1597 | 1.27315 | ||||||||
\(996\) | 8.48035 | − | 4.66253i | 0.268710 | − | 0.147738i | ||||
\(997\) | −5.00191 | −0.158412 | −0.0792061 | − | 0.996858i | \(-0.525239\pi\) | ||||
−0.0792061 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(998\) | −3.40514 | − | 44.0979i | −0.107788 | − | 1.39589i | ||||
\(999\) | −17.8795 | + | 30.8608i | −0.565684 | + | 0.976391i |
(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 | 804.2.c.b.671.2 | yes | 128 | |
3.2 | odd | 2 | inner | 804.2.c.b.671.127 | yes | 128 | |
4.3 | odd | 2 | inner | 804.2.c.b.671.128 | yes | 128 | |
12.11 | even | 2 | inner | 804.2.c.b.671.1 | ✓ | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.c.b.671.1 | ✓ | 128 | 12.11 | even | 2 | inner | |
804.2.c.b.671.2 | yes | 128 | 1.1 | even | 1 | trivial | |
804.2.c.b.671.127 | yes | 128 | 3.2 | odd | 2 | inner | |
804.2.c.b.671.128 | yes | 128 | 4.3 | odd | 2 | inner |