Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(91,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.n (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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.12 | ||
Character | \(\chi\) | \(=\) | 552.91 |
Dual form | 552.2.n.b.91.10 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.409868 | + | 1.35352i | −0.289821 | + | 0.957081i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.66402 | − | 1.10953i | −0.832008 | − | 0.554764i | ||||
\(5\) | 3.34475 | 1.49582 | 0.747908 | − | 0.663803i | \(-0.231059\pi\) | ||||
0.747908 | + | 0.663803i | \(0.231059\pi\) | |||||||
\(6\) | 0.409868 | − | 1.35352i | 0.167328 | − | 0.552571i | ||||
\(7\) | −4.25021 | −1.60643 | −0.803214 | − | 0.595690i | \(-0.796879\pi\) | ||||
−0.803214 | + | 0.595690i | \(0.796879\pi\) | |||||||
\(8\) | 2.18379 | − | 1.79751i | 0.772087 | − | 0.635517i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.37091 | + | 4.52717i | −0.433518 | + | 1.43162i | ||||
\(11\) | 1.35797i | 0.409444i | 0.978820 | + | 0.204722i | \(0.0656290\pi\) | ||||
−0.978820 | + | 0.204722i | \(0.934371\pi\) | |||||||
\(12\) | 1.66402 | + | 1.10953i | 0.480360 | + | 0.320293i | ||||
\(13\) | 2.36562i | 0.656106i | 0.944659 | + | 0.328053i | \(0.106392\pi\) | ||||
−0.944659 | + | 0.328053i | \(0.893608\pi\) | |||||||
\(14\) | 1.74203 | − | 5.75273i | 0.465576 | − | 1.53748i | ||||
\(15\) | −3.34475 | −0.863610 | ||||||||
\(16\) | 1.53790 | + | 3.69254i | 0.384474 | + | 0.923136i | ||||
\(17\) | 1.28704i | 0.312152i | 0.987745 | + | 0.156076i | \(0.0498846\pi\) | ||||
−0.987745 | + | 0.156076i | \(0.950115\pi\) | |||||||
\(18\) | −0.409868 | + | 1.35352i | −0.0966069 | + | 0.319027i | ||||
\(19\) | 1.70310i | 0.390717i | 0.980732 | + | 0.195359i | \(0.0625871\pi\) | ||||
−0.980732 | + | 0.195359i | \(0.937413\pi\) | |||||||
\(20\) | −5.56571 | − | 3.71109i | −1.24453 | − | 0.829824i | ||||
\(21\) | 4.25021 | 0.927472 | ||||||||
\(22\) | −1.83804 | − | 0.556590i | −0.391871 | − | 0.118665i | ||||
\(23\) | 1.27490 | + | 4.62327i | 0.265834 | + | 0.964019i | ||||
\(24\) | −2.18379 | + | 1.79751i | −0.445765 | + | 0.366916i | ||||
\(25\) | 6.18732 | 1.23746 | ||||||||
\(26\) | −3.20191 | − | 0.969595i | −0.627947 | − | 0.190153i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.07242 | + | 4.71573i | 1.33656 | + | 0.891188i | ||||
\(29\) | 7.24930i | 1.34616i | 0.739569 | + | 0.673080i | \(0.235029\pi\) | ||||
−0.739569 | + | 0.673080i | \(0.764971\pi\) | |||||||
\(30\) | 1.37091 | − | 4.52717i | 0.250292 | − | 0.826544i | ||||
\(31\) | 9.70810i | 1.74363i | 0.489838 | + | 0.871813i | \(0.337056\pi\) | ||||
−0.489838 | + | 0.871813i | \(0.662944\pi\) | |||||||
\(32\) | −5.62825 | + | 0.568111i | −0.994944 | + | 0.100429i | ||||
\(33\) | − | 1.35797i | − | 0.236393i | ||||||
\(34\) | −1.74203 | − | 0.527516i | −0.298755 | − | 0.0904683i | ||||
\(35\) | −14.2159 | −2.40292 | ||||||||
\(36\) | −1.66402 | − | 1.10953i | −0.277336 | − | 0.184921i | ||||
\(37\) | −3.06582 | −0.504018 | −0.252009 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252009 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(38\) | −2.30517 | − | 0.698046i | −0.373948 | − | 0.113238i | ||||
\(39\) | − | 2.36562i | − | 0.378803i | ||||||
\(40\) | 7.30423 | − | 6.01222i | 1.15490 | − | 0.950616i | ||||
\(41\) | −2.62473 | −0.409913 | −0.204957 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204957 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(42\) | −1.74203 | + | 5.75273i | −0.268801 | + | 0.887666i | ||||
\(43\) | − | 10.3795i | − | 1.58286i | −0.611261 | − | 0.791429i | \(-0.709337\pi\) | ||
0.611261 | − | 0.791429i | \(-0.290663\pi\) | |||||||
\(44\) | 1.50671 | − | 2.25969i | 0.227145 | − | 0.340661i | ||||
\(45\) | 3.34475 | 0.498605 | ||||||||
\(46\) | −6.78022 | − | 0.169341i | −0.999688 | − | 0.0249680i | ||||
\(47\) | − | 6.05402i | − | 0.883070i | −0.897244 | − | 0.441535i | \(-0.854434\pi\) | ||
0.897244 | − | 0.441535i | \(-0.145566\pi\) | |||||||
\(48\) | −1.53790 | − | 3.69254i | −0.221976 | − | 0.532973i | ||||
\(49\) | 11.0643 | 1.58061 | ||||||||
\(50\) | −2.53599 | + | 8.37464i | −0.358643 | + | 1.18435i | ||||
\(51\) | − | 1.28704i | − | 0.180221i | ||||||
\(52\) | 2.62473 | − | 3.93644i | 0.363984 | − | 0.545885i | ||||
\(53\) | −11.7344 | −1.61184 | −0.805919 | − | 0.592026i | \(-0.798328\pi\) | ||||
−0.805919 | + | 0.592026i | \(0.798328\pi\) | |||||||
\(54\) | 0.409868 | − | 1.35352i | 0.0557760 | − | 0.184190i | ||||
\(55\) | 4.54207i | 0.612453i | ||||||||
\(56\) | −9.28158 | + | 7.63981i | −1.24030 | + | 1.02091i | ||||
\(57\) | − | 1.70310i | − | 0.225581i | ||||||
\(58\) | −9.81205 | − | 2.97126i | −1.28838 | − | 0.390145i | ||||
\(59\) | 7.81205 | 1.01704 | 0.508521 | − | 0.861050i | \(-0.330192\pi\) | ||||
0.508521 | + | 0.861050i | \(0.330192\pi\) | |||||||
\(60\) | 5.56571 | + | 3.71109i | 0.718530 | + | 0.479099i | ||||
\(61\) | −6.82148 | −0.873401 | −0.436701 | − | 0.899607i | \(-0.643853\pi\) | ||||
−0.436701 | + | 0.899607i | \(0.643853\pi\) | |||||||
\(62\) | −13.1401 | − | 3.97904i | −1.66879 | − | 0.505339i | ||||
\(63\) | −4.25021 | −0.535476 | ||||||||
\(64\) | 1.53790 | − | 7.85079i | 0.192237 | − | 0.981349i | ||||
\(65\) | 7.91241i | 0.981414i | ||||||||
\(66\) | 1.83804 | + | 0.556590i | 0.226247 | + | 0.0685115i | ||||
\(67\) | 7.98334i | 0.975321i | 0.873033 | + | 0.487660i | \(0.162150\pi\) | ||||
−0.873033 | + | 0.487660i | \(0.837850\pi\) | |||||||
\(68\) | 1.42800 | − | 2.14165i | 0.173171 | − | 0.259713i | ||||
\(69\) | −1.27490 | − | 4.62327i | −0.153479 | − | 0.556577i | ||||
\(70\) | 5.82664 | − | 19.2414i | 0.696416 | − | 2.29979i | ||||
\(71\) | 13.4634i | 1.59781i | 0.601457 | + | 0.798905i | \(0.294587\pi\) | ||||
−0.601457 | + | 0.798905i | \(0.705413\pi\) | |||||||
\(72\) | 2.18379 | − | 1.79751i | 0.257362 | − | 0.211839i | ||||
\(73\) | 6.03134 | 0.705915 | 0.352957 | − | 0.935639i | \(-0.385176\pi\) | ||||
0.352957 | + | 0.935639i | \(0.385176\pi\) | |||||||
\(74\) | 1.25658 | − | 4.14964i | 0.146075 | − | 0.482386i | ||||
\(75\) | −6.18732 | −0.714450 | ||||||||
\(76\) | 1.88963 | − | 2.83398i | 0.216756 | − | 0.325080i | ||||
\(77\) | − | 5.77167i | − | 0.657742i | ||||||
\(78\) | 3.20191 | + | 0.969595i | 0.362545 | + | 0.109785i | ||||
\(79\) | 14.0413 | 1.57977 | 0.789887 | − | 0.613253i | \(-0.210139\pi\) | ||||
0.789887 | + | 0.613253i | \(0.210139\pi\) | |||||||
\(80\) | 5.14387 | + | 12.3506i | 0.575102 | + | 1.38084i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.07579 | − | 3.55261i | 0.118801 | − | 0.392320i | ||||
\(83\) | 0.0200280i | 0.00219836i | 0.999999 | + | 0.00109918i | \(0.000349880\pi\) | ||||
−0.999999 | + | 0.00109918i | \(0.999650\pi\) | |||||||
\(84\) | −7.07242 | − | 4.71573i | −0.771664 | − | 0.514528i | ||||
\(85\) | 4.30481i | 0.466923i | ||||||||
\(86\) | 14.0488 | + | 4.25423i | 1.51492 | + | 0.458745i | ||||
\(87\) | − | 7.24930i | − | 0.777206i | ||||||
\(88\) | 2.44097 | + | 2.96553i | 0.260208 | + | 0.316126i | ||||
\(89\) | − | 2.91920i | − | 0.309435i | −0.987959 | − | 0.154717i | \(-0.950553\pi\) | ||
0.987959 | − | 0.154717i | \(-0.0494467\pi\) | |||||||
\(90\) | −1.37091 | + | 4.52717i | −0.144506 | + | 0.477206i | ||||
\(91\) | − | 10.0544i | − | 1.05399i | ||||||
\(92\) | 3.00820 | − | 9.10773i | 0.313627 | − | 0.949546i | ||||
\(93\) | − | 9.70810i | − | 1.00668i | ||||||
\(94\) | 8.19422 | + | 2.48135i | 0.845169 | + | 0.255932i | ||||
\(95\) | 5.69642i | 0.584441i | ||||||||
\(96\) | 5.62825 | − | 0.568111i | 0.574431 | − | 0.0579826i | ||||
\(97\) | 13.4664i | 1.36730i | 0.729810 | + | 0.683650i | \(0.239609\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760391\pi\) | |||||||
\(98\) | −4.53490 | + | 14.9757i | −0.458094 | + | 1.51277i | ||||
\(99\) | 1.35797i | 0.136481i | ||||||||
\(100\) | −10.2958 | − | 6.86500i | −1.02958 | − | 0.686500i | ||||
\(101\) | − | 1.47763i | − | 0.147030i | −0.997294 | − | 0.0735149i | \(-0.976578\pi\) | ||
0.997294 | − | 0.0735149i | \(-0.0234217\pi\) | |||||||
\(102\) | 1.74203 | + | 0.527516i | 0.172486 | + | 0.0522319i | ||||
\(103\) | 9.62302 | 0.948184 | 0.474092 | − | 0.880475i | \(-0.342776\pi\) | ||||
0.474092 | + | 0.880475i | \(0.342776\pi\) | |||||||
\(104\) | 4.25224 | + | 5.16603i | 0.416966 | + | 0.506571i | ||||
\(105\) | 14.2159 | 1.38733 | ||||||||
\(106\) | 4.80954 | − | 15.8826i | 0.467144 | − | 1.54266i | ||||
\(107\) | − | 19.4666i | − | 1.88191i | −0.338529 | − | 0.940956i | \(-0.609929\pi\) | ||
0.338529 | − | 0.940956i | \(-0.390071\pi\) | |||||||
\(108\) | 1.66402 | + | 1.10953i | 0.160120 | + | 0.106764i | ||||
\(109\) | −5.61561 | −0.537878 | −0.268939 | − | 0.963157i | \(-0.586673\pi\) | ||||
−0.268939 | + | 0.963157i | \(0.586673\pi\) | |||||||
\(110\) | −6.14777 | − | 1.86165i | −0.586167 | − | 0.177501i | ||||
\(111\) | 3.06582 | 0.290995 | ||||||||
\(112\) | −6.53638 | − | 15.6941i | −0.617630 | − | 1.48295i | ||||
\(113\) | − | 8.30335i | − | 0.781113i | −0.920579 | − | 0.390557i | \(-0.872283\pi\) | ||
0.920579 | − | 0.390557i | \(-0.127717\pi\) | |||||||
\(114\) | 2.30517 | + | 0.698046i | 0.215899 | + | 0.0653780i | ||||
\(115\) | 4.26420 | + | 15.4637i | 0.397639 | + | 1.44199i | ||||
\(116\) | 8.04330 | − | 12.0629i | 0.746801 | − | 1.12002i | ||||
\(117\) | 2.36562i | 0.218702i | ||||||||
\(118\) | −3.20191 | + | 10.5737i | −0.294760 | + | 0.973391i | ||||
\(119\) | − | 5.47018i | − | 0.501451i | ||||||
\(120\) | −7.30423 | + | 6.01222i | −0.666782 | + | 0.548838i | ||||
\(121\) | 9.15591 | 0.832356 | ||||||||
\(122\) | 2.79591 | − | 9.23299i | 0.253130 | − | 0.835916i | ||||
\(123\) | 2.62473 | 0.236664 | ||||||||
\(124\) | 10.7714 | − | 16.1544i | 0.967301 | − | 1.45071i | ||||
\(125\) | 3.97129 | 0.355203 | ||||||||
\(126\) | 1.74203 | − | 5.75273i | 0.155192 | − | 0.512494i | ||||
\(127\) | 9.31101i | 0.826218i | 0.910682 | + | 0.413109i | \(0.135557\pi\) | ||||
−0.910682 | + | 0.413109i | \(0.864443\pi\) | |||||||
\(128\) | 9.99584 | + | 5.29936i | 0.883516 | + | 0.468402i | ||||
\(129\) | 10.3795i | 0.913864i | ||||||||
\(130\) | −10.7096 | − | 3.24305i | −0.939292 | − | 0.284434i | ||||
\(131\) | 6.40382 | 0.559505 | 0.279752 | − | 0.960072i | \(-0.409748\pi\) | ||||
0.279752 | + | 0.960072i | \(0.409748\pi\) | |||||||
\(132\) | −1.50671 | + | 2.25969i | −0.131142 | + | 0.196680i | ||||
\(133\) | − | 7.23852i | − | 0.627659i | ||||||
\(134\) | −10.8056 | − | 3.27212i | −0.933461 | − | 0.282668i | ||||
\(135\) | −3.34475 | −0.287870 | ||||||||
\(136\) | 2.31347 | + | 2.81062i | 0.198378 | + | 0.241009i | ||||
\(137\) | − | 2.62498i | − | 0.224267i | −0.993693 | − | 0.112134i | \(-0.964232\pi\) | ||
0.993693 | − | 0.112134i | \(-0.0357685\pi\) | |||||||
\(138\) | 6.78022 | + | 0.169341i | 0.577170 | + | 0.0144153i | ||||
\(139\) | −9.34793 | −0.792881 | −0.396441 | − | 0.918060i | \(-0.629755\pi\) | ||||
−0.396441 | + | 0.918060i | \(0.629755\pi\) | |||||||
\(140\) | 23.6554 | + | 15.7729i | 1.99925 | + | 1.33305i | ||||
\(141\) | 6.05402i | 0.509841i | ||||||||
\(142\) | −18.2229 | − | 5.51822i | −1.52923 | − | 0.463079i | ||||
\(143\) | −3.21245 | −0.268639 | ||||||||
\(144\) | 1.53790 | + | 3.69254i | 0.128158 | + | 0.307712i | ||||
\(145\) | 24.2471i | 2.01361i | ||||||||
\(146\) | −2.47206 | + | 8.16352i | −0.204589 | + | 0.675617i | ||||
\(147\) | −11.0643 | −0.912567 | ||||||||
\(148\) | 5.10158 | + | 3.40162i | 0.419347 | + | 0.279611i | ||||
\(149\) | 8.80052 | 0.720967 | 0.360483 | − | 0.932766i | \(-0.382612\pi\) | ||||
0.360483 | + | 0.932766i | \(0.382612\pi\) | |||||||
\(150\) | 2.53599 | − | 8.37464i | 0.207063 | − | 0.683787i | ||||
\(151\) | − | 9.50018i | − | 0.773114i | −0.922266 | − | 0.386557i | \(-0.873664\pi\) | ||
0.922266 | − | 0.386557i | \(-0.126336\pi\) | |||||||
\(152\) | 3.06134 | + | 3.71921i | 0.248307 | + | 0.301668i | ||||
\(153\) | 1.28704i | 0.104051i | ||||||||
\(154\) | 7.81205 | + | 2.36562i | 0.629513 | + | 0.190627i | ||||
\(155\) | 32.4711i | 2.60814i | ||||||||
\(156\) | −2.62473 | + | 3.93644i | −0.210146 | + | 0.315167i | ||||
\(157\) | 22.6741 | 1.80959 | 0.904793 | − | 0.425851i | \(-0.140025\pi\) | ||||
0.904793 | + | 0.425851i | \(0.140025\pi\) | |||||||
\(158\) | −5.75510 | + | 19.0052i | −0.457851 | + | 1.51197i | ||||
\(159\) | 11.7344 | 0.930595 | ||||||||
\(160\) | −18.8251 | + | 1.90019i | −1.48825 | + | 0.150223i | ||||
\(161\) | −5.41857 | − | 19.6499i | −0.427043 | − | 1.54863i | ||||
\(162\) | −0.409868 | + | 1.35352i | −0.0322023 | + | 0.106342i | ||||
\(163\) | −7.96419 | −0.623804 | −0.311902 | − | 0.950114i | \(-0.600966\pi\) | ||||
−0.311902 | + | 0.950114i | \(0.600966\pi\) | |||||||
\(164\) | 4.36758 | + | 2.91221i | 0.341051 | + | 0.227405i | ||||
\(165\) | − | 4.54207i | − | 0.353600i | ||||||
\(166\) | −0.0271083 | − | 0.00820885i | −0.00210401 | − | 0.000637130i | ||||
\(167\) | − | 22.5603i | − | 1.74576i | −0.487930 | − | 0.872882i | \(-0.662248\pi\) | ||
0.487930 | − | 0.872882i | \(-0.337752\pi\) | |||||||
\(168\) | 9.28158 | − | 7.63981i | 0.716089 | − | 0.589424i | ||||
\(169\) | 7.40382 | 0.569525 | ||||||||
\(170\) | −5.82664 | − | 1.76441i | −0.446883 | − | 0.135324i | ||||
\(171\) | 1.70310i | 0.130239i | ||||||||
\(172\) | −11.5163 | + | 17.2716i | −0.878113 | + | 1.31695i | ||||
\(173\) | 10.1830i | 0.774199i | 0.922038 | + | 0.387100i | \(0.126523\pi\) | ||||
−0.922038 | + | 0.387100i | \(0.873477\pi\) | |||||||
\(174\) | 9.81205 | + | 2.97126i | 0.743849 | + | 0.225251i | ||||
\(175\) | −26.2974 | −1.98790 | ||||||||
\(176\) | −5.01437 | + | 2.08842i | −0.377972 | + | 0.157421i | ||||
\(177\) | −7.81205 | −0.587189 | ||||||||
\(178\) | 3.95119 | + | 1.19649i | 0.296154 | + | 0.0896806i | ||||
\(179\) | 12.0913 | 0.903746 | 0.451873 | − | 0.892082i | \(-0.350756\pi\) | ||||
0.451873 | + | 0.892082i | \(0.350756\pi\) | |||||||
\(180\) | −5.56571 | − | 3.71109i | −0.414843 | − | 0.276608i | ||||
\(181\) | −4.93435 | −0.366767 | −0.183384 | − | 0.983041i | \(-0.558705\pi\) | ||||
−0.183384 | + | 0.983041i | \(0.558705\pi\) | |||||||
\(182\) | 13.6088 | + | 4.12098i | 1.00875 | + | 0.305467i | ||||
\(183\) | 6.82148 | 0.504258 | ||||||||
\(184\) | 11.0945 | + | 7.80462i | 0.817897 | + | 0.575365i | ||||
\(185\) | −10.2544 | −0.753918 | ||||||||
\(186\) | 13.1401 | + | 3.97904i | 0.963477 | + | 0.291758i | ||||
\(187\) | −1.74776 | −0.127809 | ||||||||
\(188\) | −6.71711 | + | 10.0740i | −0.489895 | + | 0.734721i | ||||
\(189\) | 4.25021 | 0.309157 | ||||||||
\(190\) | −7.71021 | − | 2.33478i | −0.559357 | − | 0.169383i | ||||
\(191\) | −18.5834 | −1.34465 | −0.672323 | − | 0.740258i | \(-0.734703\pi\) | ||||
−0.672323 | + | 0.740258i | \(0.734703\pi\) | |||||||
\(192\) | −1.53790 | + | 7.85079i | −0.110988 | + | 0.566582i | ||||
\(193\) | −0.968591 | −0.0697207 | −0.0348604 | − | 0.999392i | \(-0.511099\pi\) | ||||
−0.0348604 | + | 0.999392i | \(0.511099\pi\) | |||||||
\(194\) | −18.2269 | − | 5.51943i | −1.30862 | − | 0.396272i | ||||
\(195\) | − | 7.91241i | − | 0.566619i | ||||||
\(196\) | −18.4111 | − | 12.2761i | −1.31508 | − | 0.876867i | ||||
\(197\) | − | 13.0210i | − | 0.927705i | −0.885912 | − | 0.463853i | \(-0.846467\pi\) | ||
0.885912 | − | 0.463853i | \(-0.153533\pi\) | |||||||
\(198\) | −1.83804 | − | 0.556590i | −0.130624 | − | 0.0395551i | ||||
\(199\) | −13.8735 | −0.983469 | −0.491734 | − | 0.870745i | \(-0.663637\pi\) | ||||
−0.491734 | + | 0.870745i | \(0.663637\pi\) | |||||||
\(200\) | 13.5118 | − | 11.1218i | 0.955430 | − | 0.786429i | ||||
\(201\) | − | 7.98334i | − | 0.563102i | ||||||
\(202\) | 2.00000 | + | 0.605635i | 0.140720 | + | 0.0426123i | ||||
\(203\) | − | 30.8110i | − | 2.16251i | ||||||
\(204\) | −1.42800 | + | 2.14165i | −0.0999803 | + | 0.149946i | ||||
\(205\) | −8.77904 | −0.613155 | ||||||||
\(206\) | −3.94417 | + | 13.0249i | −0.274803 | + | 0.907489i | ||||
\(207\) | 1.27490 | + | 4.62327i | 0.0886113 | + | 0.321340i | ||||
\(208\) | −8.73517 | + | 3.63808i | −0.605675 | + | 0.252256i | ||||
\(209\) | −2.31276 | −0.159977 | ||||||||
\(210\) | −5.82664 | + | 19.2414i | −0.402076 | + | 1.32778i | ||||
\(211\) | −15.1196 | −1.04088 | −0.520439 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520439 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(212\) | 19.5261 | + | 13.0196i | 1.34106 | + | 0.894189i | ||||
\(213\) | − | 13.4634i | − | 0.922496i | ||||||
\(214\) | 26.3484 | + | 7.97877i | 1.80114 | + | 0.545417i | ||||
\(215\) | − | 34.7168i | − | 2.36766i | ||||||
\(216\) | −2.18379 | + | 1.79751i | −0.148588 | + | 0.122305i | ||||
\(217\) | − | 41.2615i | − | 2.80101i | ||||||
\(218\) | 2.30166 | − | 7.60083i | 0.155888 | − | 0.514793i | ||||
\(219\) | −6.03134 | −0.407560 | ||||||||
\(220\) | 5.03955 | − | 7.55808i | 0.339767 | − | 0.509565i | ||||
\(221\) | −3.04465 | −0.204805 | ||||||||
\(222\) | −1.25658 | + | 4.14964i | −0.0843364 | + | 0.278506i | ||||
\(223\) | 10.5610i | 0.707215i | 0.935394 | + | 0.353607i | \(0.115045\pi\) | ||||
−0.935394 | + | 0.353607i | \(0.884955\pi\) | |||||||
\(224\) | 23.9213 | − | 2.41459i | 1.59831 | − | 0.161332i | ||||
\(225\) | 6.18732 | 0.412488 | ||||||||
\(226\) | 11.2387 | + | 3.40328i | 0.747589 | + | 0.226383i | ||||
\(227\) | 3.11219i | 0.206563i | 0.994652 | + | 0.103282i | \(0.0329343\pi\) | ||||
−0.994652 | + | 0.103282i | \(0.967066\pi\) | |||||||
\(228\) | −1.88963 | + | 2.83398i | −0.125144 | + | 0.187685i | ||||
\(229\) | 17.0499 | 1.12669 | 0.563343 | − | 0.826223i | \(-0.309515\pi\) | ||||
0.563343 | + | 0.826223i | \(0.309515\pi\) | |||||||
\(230\) | −22.6781 | − | 0.566404i | −1.49535 | − | 0.0373476i | ||||
\(231\) | 5.77167i | 0.379748i | ||||||||
\(232\) | 13.0307 | + | 15.8310i | 0.855508 | + | 1.03935i | ||||
\(233\) | −14.5284 | −0.951787 | −0.475894 | − | 0.879503i | \(-0.657875\pi\) | ||||
−0.475894 | + | 0.879503i | \(0.657875\pi\) | |||||||
\(234\) | −3.20191 | − | 0.969595i | −0.209316 | − | 0.0633844i | ||||
\(235\) | − | 20.2492i | − | 1.32091i | ||||||
\(236\) | −12.9994 | − | 8.66768i | −0.846187 | − | 0.564218i | ||||
\(237\) | −14.0413 | −0.912083 | ||||||||
\(238\) | 7.40398 | + | 2.24205i | 0.479929 | + | 0.145331i | ||||
\(239\) | − | 1.56887i | − | 0.101482i | −0.998712 | − | 0.0507408i | \(-0.983842\pi\) | ||
0.998712 | − | 0.0507408i | \(-0.0161582\pi\) | |||||||
\(240\) | −5.14387 | − | 12.3506i | −0.332035 | − | 0.797229i | ||||
\(241\) | − | 13.8541i | − | 0.892423i | −0.894928 | − | 0.446211i | \(-0.852773\pi\) | ||
0.894928 | − | 0.446211i | \(-0.147227\pi\) | |||||||
\(242\) | −3.75272 | + | 12.3927i | −0.241234 | + | 0.796632i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.3511 | + | 7.56862i | 0.726677 | + | 0.484531i | ||||
\(245\) | 37.0072 | 2.36430 | ||||||||
\(246\) | −1.07579 | + | 3.55261i | −0.0685900 | + | 0.226506i | ||||
\(247\) | −4.02889 | −0.256352 | ||||||||
\(248\) | 17.4504 | + | 21.2005i | 1.10810 | + | 1.34623i | ||||
\(249\) | − | 0.0200280i | − | 0.00126922i | ||||||
\(250\) | −1.62771 | + | 5.37520i | −0.102945 | + | 0.339958i | ||||
\(251\) | 22.7472i | 1.43579i | 0.696151 | + | 0.717896i | \(0.254895\pi\) | ||||
−0.696151 | + | 0.717896i | \(0.745105\pi\) | |||||||
\(252\) | 7.07242 | + | 4.71573i | 0.445520 | + | 0.297063i | ||||
\(253\) | −6.27827 | + | 1.73127i | −0.394712 | + | 0.108844i | ||||
\(254\) | −12.6026 | − | 3.81629i | −0.790758 | − | 0.239455i | ||||
\(255\) | − | 4.30481i | − | 0.269578i | ||||||
\(256\) | −11.2698 | + | 11.3575i | −0.704359 | + | 0.709843i | ||||
\(257\) | 1.56221 | 0.0974479 | 0.0487239 | − | 0.998812i | \(-0.484485\pi\) | ||||
0.0487239 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(258\) | −14.0488 | − | 4.25423i | −0.874641 | − | 0.264857i | ||||
\(259\) | 13.0304 | 0.809669 | ||||||||
\(260\) | 8.77904 | − | 13.1664i | 0.544453 | − | 0.816544i | ||||
\(261\) | 7.24930i | 0.448720i | ||||||||
\(262\) | −2.62473 | + | 8.66768i | −0.162156 | + | 0.535491i | ||||
\(263\) | 11.0502 | 0.681385 | 0.340693 | − | 0.940175i | \(-0.389338\pi\) | ||||
0.340693 | + | 0.940175i | \(0.389338\pi\) | |||||||
\(264\) | −2.44097 | − | 2.96553i | −0.150231 | − | 0.182516i | ||||
\(265\) | −39.2484 | −2.41101 | ||||||||
\(266\) | 9.79746 | + | 2.96684i | 0.600721 | + | 0.181909i | ||||
\(267\) | 2.91920i | 0.178652i | ||||||||
\(268\) | 8.85774 | − | 13.2844i | 0.541073 | − | 0.811474i | ||||
\(269\) | − | 17.7522i | − | 1.08237i | −0.840903 | − | 0.541186i | \(-0.817976\pi\) | ||
0.840903 | − | 0.541186i | \(-0.182024\pi\) | |||||||
\(270\) | 1.37091 | − | 4.52717i | 0.0834307 | − | 0.275515i | ||||
\(271\) | − | 5.16603i | − | 0.313814i | −0.987613 | − | 0.156907i | \(-0.949848\pi\) | ||
0.987613 | − | 0.156907i | \(-0.0501523\pi\) | |||||||
\(272\) | −4.75244 | + | 1.97933i | −0.288159 | + | 0.120015i | ||||
\(273\) | 10.0544i | 0.608520i | ||||||||
\(274\) | 3.55296 | + | 1.07590i | 0.214642 | + | 0.0649973i | ||||
\(275\) | 8.40221i | 0.506672i | ||||||||
\(276\) | −3.00820 | + | 9.10773i | −0.181073 | + | 0.548221i | ||||
\(277\) | − | 23.9970i | − | 1.44184i | −0.693019 | − | 0.720919i | \(-0.743720\pi\) | ||
0.693019 | − | 0.720919i | \(-0.256280\pi\) | |||||||
\(278\) | 3.83142 | − | 12.6526i | 0.229794 | − | 0.758852i | ||||
\(279\) | 9.70810i | 0.581209i | ||||||||
\(280\) | −31.0445 | + | 25.5532i | −1.85526 | + | 1.52710i | ||||
\(281\) | 13.6894i | 0.816642i | 0.912838 | + | 0.408321i | \(0.133886\pi\) | ||||
−0.912838 | + | 0.408321i | \(0.866114\pi\) | |||||||
\(282\) | −8.19422 | − | 2.48135i | −0.487959 | − | 0.147762i | ||||
\(283\) | − | 13.2256i | − | 0.786182i | −0.919500 | − | 0.393091i | \(-0.871406\pi\) | ||
0.919500 | − | 0.393091i | \(-0.128594\pi\) | |||||||
\(284\) | 14.9380 | − | 22.4033i | 0.886408 | − | 1.32939i | ||||
\(285\) | − | 5.69642i | − | 0.337427i | ||||||
\(286\) | 1.31668 | − | 4.34811i | 0.0778571 | − | 0.257109i | ||||
\(287\) | 11.1556 | 0.658496 | ||||||||
\(288\) | −5.62825 | + | 0.568111i | −0.331648 | + | 0.0334763i | ||||
\(289\) | 15.3435 | 0.902561 | ||||||||
\(290\) | −32.8188 | − | 9.93810i | −1.92719 | − | 0.583586i | ||||
\(291\) | − | 13.4664i | − | 0.789412i | ||||||
\(292\) | −10.0362 | − | 6.69194i | −0.587326 | − | 0.391616i | ||||
\(293\) | −29.3779 | −1.71627 | −0.858137 | − | 0.513421i | \(-0.828378\pi\) | ||||
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(294\) | 4.53490 | − | 14.9757i | 0.264481 | − | 0.873400i | ||||
\(295\) | 26.1293 | 1.52131 | ||||||||
\(296\) | −6.69512 | + | 5.51085i | −0.389146 | + | 0.320312i | ||||
\(297\) | − | 1.35797i | − | 0.0787975i | ||||||
\(298\) | −3.60706 | + | 11.9116i | −0.208951 | + | 0.690023i | ||||
\(299\) | −10.9369 | + | 3.01592i | −0.632499 | + | 0.174415i | ||||
\(300\) | 10.2958 | + | 6.86500i | 0.594428 | + | 0.396351i | ||||
\(301\) | 44.1150i | 2.54275i | ||||||||
\(302\) | 12.8587 | + | 3.89383i | 0.739933 | + | 0.224064i | ||||
\(303\) | 1.47763i | 0.0848877i | ||||||||
\(304\) | −6.28876 | + | 2.61919i | −0.360685 | + | 0.150221i | ||||
\(305\) | −22.8161 | −1.30645 | ||||||||
\(306\) | −1.74203 | − | 0.527516i | −0.0995851 | − | 0.0301561i | ||||
\(307\) | −30.6840 | −1.75123 | −0.875614 | − | 0.483012i | \(-0.839543\pi\) | ||||
−0.875614 | + | 0.483012i | \(0.839543\pi\) | |||||||
\(308\) | −6.40382 | + | 9.60414i | −0.364892 | + | 0.547247i | ||||
\(309\) | −9.62302 | −0.547434 | ||||||||
\(310\) | −43.9502 | − | 13.3089i | −2.49620 | − | 0.755894i | ||||
\(311\) | 0.622018i | 0.0352714i | 0.999844 | + | 0.0176357i | \(0.00561391\pi\) | ||||
−0.999844 | + | 0.0176357i | \(0.994386\pi\) | |||||||
\(312\) | −4.25224 | − | 5.16603i | −0.240736 | − | 0.292469i | ||||
\(313\) | 10.1923i | 0.576101i | 0.957615 | + | 0.288050i | \(0.0930071\pi\) | ||||
−0.957615 | + | 0.288050i | \(0.906993\pi\) | |||||||
\(314\) | −9.29338 | + | 30.6897i | −0.524456 | + | 1.73192i | ||||
\(315\) | −14.2159 | −0.800974 | ||||||||
\(316\) | −23.3650 | − | 15.5793i | −1.31438 | − | 0.876401i | ||||
\(317\) | 15.3301i | 0.861023i | 0.902585 | + | 0.430512i | \(0.141667\pi\) | ||||
−0.902585 | + | 0.430512i | \(0.858333\pi\) | |||||||
\(318\) | −4.80954 | + | 15.8826i | −0.269706 | + | 0.890654i | ||||
\(319\) | −9.84434 | −0.551177 | ||||||||
\(320\) | 5.14387 | − | 26.2589i | 0.287551 | − | 1.46792i | ||||
\(321\) | 19.4666i | 1.08652i | ||||||||
\(322\) | 28.8173 | + | 0.719737i | 1.60593 | + | 0.0401094i | ||||
\(323\) | −2.19195 | −0.121963 | ||||||||
\(324\) | −1.66402 | − | 1.10953i | −0.0924453 | − | 0.0616404i | ||||
\(325\) | 14.6369i | 0.811908i | ||||||||
\(326\) | 3.26427 | − | 10.7797i | 0.180791 | − | 0.597031i | ||||
\(327\) | 5.61561 | 0.310544 | ||||||||
\(328\) | −5.73185 | + | 4.71798i | −0.316489 | + | 0.260507i | ||||
\(329\) | 25.7309i | 1.41859i | ||||||||
\(330\) | 6.14777 | + | 1.86165i | 0.338424 | + | 0.102481i | ||||
\(331\) | 17.6536 | 0.970329 | 0.485165 | − | 0.874423i | \(-0.338760\pi\) | ||||
0.485165 | + | 0.874423i | \(0.338760\pi\) | |||||||
\(332\) | 0.0222216 | − | 0.0333269i | 0.00121957 | − | 0.00182905i | ||||
\(333\) | −3.06582 | −0.168006 | ||||||||
\(334\) | 30.5357 | + | 9.24674i | 1.67084 | + | 0.505959i | ||||
\(335\) | 26.7023i | 1.45890i | ||||||||
\(336\) | 6.53638 | + | 15.6941i | 0.356589 | + | 0.856182i | ||||
\(337\) | 17.1184i | 0.932501i | 0.884653 | + | 0.466251i | \(0.154396\pi\) | ||||
−0.884653 | + | 0.466251i | \(0.845604\pi\) | |||||||
\(338\) | −3.03459 | + | 10.0212i | −0.165060 | + | 0.545081i | ||||
\(339\) | 8.30335i | 0.450976i | ||||||||
\(340\) | 4.77631 | − | 7.16328i | 0.259032 | − | 0.388483i | ||||
\(341\) | −13.1833 | −0.713917 | ||||||||
\(342\) | −2.30517 | − | 0.698046i | −0.124649 | − | 0.0377460i | ||||
\(343\) | −17.2741 | −0.932712 | ||||||||
\(344\) | −18.6573 | − | 22.6667i | −1.00593 | − | 1.22210i | ||||
\(345\) | −4.26420 | − | 15.4637i | −0.229577 | − | 0.832536i | ||||
\(346\) | −13.7829 | − | 4.17369i | −0.740971 | − | 0.224379i | ||||
\(347\) | 5.59562 | 0.300388 | 0.150194 | − | 0.988657i | \(-0.452010\pi\) | ||||
0.150194 | + | 0.988657i | \(0.452010\pi\) | |||||||
\(348\) | −8.04330 | + | 12.0629i | −0.431166 | + | 0.646642i | ||||
\(349\) | − | 17.1844i | − | 0.919858i | −0.887956 | − | 0.459929i | \(-0.847875\pi\) | ||
0.887956 | − | 0.459929i | \(-0.152125\pi\) | |||||||
\(350\) | 10.7785 | − | 35.5940i | 0.576134 | − | 1.90258i | ||||
\(351\) | − | 2.36562i | − | 0.126268i | ||||||
\(352\) | −0.771479 | − | 7.64301i | −0.0411200 | − | 0.407374i | ||||
\(353\) | −9.60017 | −0.510966 | −0.255483 | − | 0.966814i | \(-0.582234\pi\) | ||||
−0.255483 | + | 0.966814i | \(0.582234\pi\) | |||||||
\(354\) | 3.20191 | − | 10.5737i | 0.170180 | − | 0.561988i | ||||
\(355\) | 45.0316i | 2.39003i | ||||||||
\(356\) | −3.23893 | + | 4.85759i | −0.171663 | + | 0.257452i | ||||
\(357\) | 5.47018i | 0.289513i | ||||||||
\(358\) | −4.95584 | + | 16.3658i | −0.261924 | + | 0.864958i | ||||
\(359\) | 19.4677 | 1.02746 | 0.513732 | − | 0.857951i | \(-0.328263\pi\) | ||||
0.513732 | + | 0.857951i | \(0.328263\pi\) | |||||||
\(360\) | 7.30423 | − | 6.01222i | 0.384967 | − | 0.316872i | ||||
\(361\) | 16.0995 | 0.847340 | ||||||||
\(362\) | 2.02243 | − | 6.67873i | 0.106297 | − | 0.351026i | ||||
\(363\) | −9.15591 | −0.480561 | ||||||||
\(364\) | −11.1556 | + | 16.7307i | −0.584714 | + | 0.876926i | ||||
\(365\) | 20.1733 | 1.05592 | ||||||||
\(366\) | −2.79591 | + | 9.23299i | −0.146145 | + | 0.482616i | ||||
\(367\) | 7.81885 | 0.408141 | 0.204070 | − | 0.978956i | \(-0.434583\pi\) | ||||
0.204070 | + | 0.978956i | \(0.434583\pi\) | |||||||
\(368\) | −15.1110 | + | 11.8177i | −0.787714 | + | 0.616041i | ||||
\(369\) | −2.62473 | −0.136638 | ||||||||
\(370\) | 4.20295 | − | 13.8795i | 0.218501 | − | 0.721561i | ||||
\(371\) | 49.8735 | 2.58930 | ||||||||
\(372\) | −10.7714 | + | 16.1544i | −0.558471 | + | 0.837568i | ||||
\(373\) | −5.26079 | −0.272394 | −0.136197 | − | 0.990682i | \(-0.543488\pi\) | ||||
−0.136197 | + | 0.990682i | \(0.543488\pi\) | |||||||
\(374\) | 0.716352 | − | 2.36562i | 0.0370417 | − | 0.122323i | ||||
\(375\) | −3.97129 | −0.205076 | ||||||||
\(376\) | −10.8822 | − | 13.2207i | −0.561206 | − | 0.681807i | ||||
\(377\) | −17.1491 | −0.883224 | ||||||||
\(378\) | −1.74203 | + | 5.75273i | −0.0896002 | + | 0.295889i | ||||
\(379\) | − | 12.7052i | − | 0.652621i | −0.945263 | − | 0.326310i | \(-0.894195\pi\) | ||
0.945263 | − | 0.326310i | \(-0.105805\pi\) | |||||||
\(380\) | 6.32034 | − | 9.47894i | 0.324227 | − | 0.486259i | ||||
\(381\) | − | 9.31101i | − | 0.477017i | ||||||
\(382\) | 7.61674 | − | 25.1529i | 0.389706 | − | 1.28693i | ||||
\(383\) | 32.8964 | 1.68093 | 0.840463 | − | 0.541869i | \(-0.182283\pi\) | ||||
0.840463 | + | 0.541869i | \(0.182283\pi\) | |||||||
\(384\) | −9.99584 | − | 5.29936i | −0.510098 | − | 0.270432i | ||||
\(385\) | − | 19.3048i | − | 0.983861i | ||||||
\(386\) | 0.396995 | − | 1.31100i | 0.0202065 | − | 0.0667284i | ||||
\(387\) | − | 10.3795i | − | 0.527619i | ||||||
\(388\) | 14.9413 | − | 22.4082i | 0.758529 | − | 1.13761i | ||||
\(389\) | −4.95326 | −0.251140 | −0.125570 | − | 0.992085i | \(-0.540076\pi\) | ||||
−0.125570 | + | 0.992085i | \(0.540076\pi\) | |||||||
\(390\) | 10.7096 | + | 3.24305i | 0.542301 | + | 0.164218i | ||||
\(391\) | −5.95033 | + | 1.64084i | −0.300921 | + | 0.0829807i | ||||
\(392\) | 24.1621 | − | 19.8882i | 1.22037 | − | 1.00451i | ||||
\(393\) | −6.40382 | −0.323030 | ||||||||
\(394\) | 17.6241 | + | 5.33688i | 0.887889 | + | 0.268868i | ||||
\(395\) | 46.9647 | 2.36305 | ||||||||
\(396\) | 1.50671 | − | 2.25969i | 0.0757149 | − | 0.113554i | ||||
\(397\) | 15.7353i | 0.789733i | 0.918739 | + | 0.394866i | \(0.129209\pi\) | ||||
−0.918739 | + | 0.394866i | \(0.870791\pi\) | |||||||
\(398\) | 5.68632 | − | 18.7781i | 0.285030 | − | 0.941259i | ||||
\(399\) | 7.23852i | 0.362379i | ||||||||
\(400\) | 9.51546 | + | 22.8470i | 0.475773 | + | 1.14235i | ||||
\(401\) | − | 23.5821i | − | 1.17764i | −0.808266 | − | 0.588818i | \(-0.799594\pi\) | ||
0.808266 | − | 0.588818i | \(-0.200406\pi\) | |||||||
\(402\) | 10.8056 | + | 3.27212i | 0.538934 | + | 0.163199i | ||||
\(403\) | −22.9657 | −1.14400 | ||||||||
\(404\) | −1.63947 | + | 2.45880i | −0.0815669 | + | 0.122330i | ||||
\(405\) | 3.34475 | 0.166202 | ||||||||
\(406\) | 41.7033 | + | 12.6285i | 2.06970 | + | 0.626741i | ||||
\(407\) | − | 4.16330i | − | 0.206367i | ||||||
\(408\) | −2.31347 | − | 2.81062i | −0.114534 | − | 0.139147i | ||||
\(409\) | 28.8959 | 1.42881 | 0.714404 | − | 0.699733i | \(-0.246698\pi\) | ||||
0.714404 | + | 0.699733i | \(0.246698\pi\) | |||||||
\(410\) | 3.59825 | − | 11.8826i | 0.177705 | − | 0.586839i | ||||
\(411\) | 2.62498i | 0.129481i | ||||||||
\(412\) | −16.0129 | − | 10.6770i | −0.788897 | − | 0.526018i | ||||
\(413\) | −33.2028 | −1.63380 | ||||||||
\(414\) | −6.78022 | − | 0.169341i | −0.333229 | − | 0.00832268i | ||||
\(415\) | 0.0669886i | 0.00328834i | ||||||||
\(416\) | −1.34394 | − | 13.3143i | −0.0658920 | − | 0.652789i | ||||
\(417\) | 9.34793 | 0.457770 | ||||||||
\(418\) | 0.947926 | − | 3.13036i | 0.0463646 | − | 0.153111i | ||||
\(419\) | 12.2149i | 0.596738i | 0.954451 | + | 0.298369i | \(0.0964425\pi\) | ||||
−0.954451 | + | 0.298369i | \(0.903557\pi\) | |||||||
\(420\) | −23.6554 | − | 15.7729i | −1.15427 | − | 0.769639i | ||||
\(421\) | 24.3542 | 1.18695 | 0.593475 | − | 0.804852i | \(-0.297755\pi\) | ||||
0.593475 | + | 0.804852i | \(0.297755\pi\) | |||||||
\(422\) | 6.19705 | − | 20.4647i | 0.301668 | − | 0.996204i | ||||
\(423\) | − | 6.05402i | − | 0.294357i | ||||||
\(424\) | −25.6254 | + | 21.0926i | −1.24448 | + | 1.02435i | ||||
\(425\) | 7.96332i | 0.386278i | ||||||||
\(426\) | 18.2229 | + | 5.51822i | 0.882904 | + | 0.267359i | ||||
\(427\) | 28.9927 | 1.40306 | ||||||||
\(428\) | −21.5988 | + | 32.3928i | −1.04402 | + | 1.56577i | ||||
\(429\) | 3.21245 | 0.155099 | ||||||||
\(430\) | 46.9897 | + | 14.2293i | 2.26605 | + | 0.686198i | ||||
\(431\) | 6.09907 | 0.293782 | 0.146891 | − | 0.989153i | \(-0.453073\pi\) | ||||
0.146891 | + | 0.989153i | \(0.453073\pi\) | |||||||
\(432\) | −1.53790 | − | 3.69254i | −0.0739921 | − | 0.177658i | ||||
\(433\) | − | 12.5605i | − | 0.603619i | −0.953368 | − | 0.301809i | \(-0.902409\pi\) | ||
0.953368 | − | 0.301809i | \(-0.0975906\pi\) | |||||||
\(434\) | 55.8481 | + | 16.9118i | 2.68079 | + | 0.811791i | ||||
\(435\) | − | 24.2471i | − | 1.16256i | ||||||
\(436\) | 9.34447 | + | 6.23068i | 0.447519 | + | 0.298395i | ||||
\(437\) | −7.87388 | + | 2.17127i | −0.376659 | + | 0.103866i | ||||
\(438\) | 2.47206 | − | 8.16352i | 0.118119 | − | 0.390068i | ||||
\(439\) | 6.97400i | 0.332851i | 0.986054 | + | 0.166426i | \(0.0532225\pi\) | ||||
−0.986054 | + | 0.166426i | \(0.946777\pi\) | |||||||
\(440\) | 8.16443 | + | 9.91894i | 0.389224 | + | 0.472867i | ||||
\(441\) | 11.0643 | 0.526871 | ||||||||
\(442\) | 1.24790 | − | 4.12098i | 0.0593568 | − | 0.196015i | ||||
\(443\) | −20.7732 | −0.986965 | −0.493482 | − | 0.869756i | \(-0.664276\pi\) | ||||
−0.493482 | + | 0.869756i | \(0.664276\pi\) | |||||||
\(444\) | −5.10158 | − | 3.40162i | −0.242110 | − | 0.161434i | ||||
\(445\) | − | 9.76398i | − | 0.462857i | ||||||
\(446\) | −14.2945 | − | 4.32861i | −0.676862 | − | 0.204966i | ||||
\(447\) | −8.80052 | −0.416250 | ||||||||
\(448\) | −6.53638 | + | 33.3675i | −0.308815 | + | 1.57647i | ||||
\(449\) | −6.90397 | −0.325819 | −0.162909 | − | 0.986641i | \(-0.552088\pi\) | ||||
−0.162909 | + | 0.986641i | \(0.552088\pi\) | |||||||
\(450\) | −2.53599 | + | 8.37464i | −0.119548 | + | 0.394784i | ||||
\(451\) | − | 3.56430i | − | 0.167836i | ||||||
\(452\) | −9.21280 | + | 13.8169i | −0.433334 | + | 0.649893i | ||||
\(453\) | 9.50018i | 0.446358i | ||||||||
\(454\) | −4.21240 | − | 1.27559i | −0.197698 | − | 0.0598663i | ||||
\(455\) | − | 33.6294i | − | 1.57657i | ||||||
\(456\) | −3.06134 | − | 3.71921i | −0.143360 | − | 0.174168i | ||||
\(457\) | 36.9076i | 1.72646i | 0.504807 | + | 0.863232i | \(0.331564\pi\) | ||||
−0.504807 | + | 0.863232i | \(0.668436\pi\) | |||||||
\(458\) | −6.98820 | + | 23.0773i | −0.326537 | + | 1.07833i | ||||
\(459\) | − | 1.28704i | − | 0.0600738i | ||||||
\(460\) | 10.0617 | − | 30.4630i | 0.469128 | − | 1.42035i | ||||
\(461\) | − | 7.66472i | − | 0.356982i | −0.983942 | − | 0.178491i | \(-0.942879\pi\) | ||
0.983942 | − | 0.178491i | \(-0.0571215\pi\) | |||||||
\(462\) | −7.81205 | − | 2.36562i | −0.363449 | − | 0.110059i | ||||
\(463\) | 20.2293i | 0.940137i | 0.882630 | + | 0.470069i | \(0.155771\pi\) | ||||
−0.882630 | + | 0.470069i | \(0.844229\pi\) | |||||||
\(464\) | −26.7683 | + | 11.1487i | −1.24269 | + | 0.517564i | ||||
\(465\) | − | 32.4711i | − | 1.50581i | ||||||
\(466\) | 5.95473 | − | 19.6644i | 0.275848 | − | 0.910937i | ||||
\(467\) | − | 33.0233i | − | 1.52814i | −0.645136 | − | 0.764068i | \(-0.723199\pi\) | ||
0.645136 | − | 0.764068i | \(-0.276801\pi\) | |||||||
\(468\) | 2.62473 | − | 3.93644i | 0.121328 | − | 0.181962i | ||||
\(469\) | − | 33.9309i | − | 1.56678i | ||||||
\(470\) | 27.4076 | + | 8.29949i | 1.26422 | + | 0.382827i | ||||
\(471\) | −22.6741 | −1.04477 | ||||||||
\(472\) | 17.0599 | − | 14.0423i | 0.785245 | − | 0.646347i | ||||
\(473\) | 14.0951 | 0.648092 | ||||||||
\(474\) | 5.75510 | − | 19.0052i | 0.264341 | − | 0.872937i | ||||
\(475\) | 10.5376i | 0.483498i | ||||||||
\(476\) | −6.06932 | + | 9.10247i | −0.278187 | + | 0.417211i | ||||
\(477\) | −11.7344 | −0.537279 | ||||||||
\(478\) | 2.12349 | + | 0.643030i | 0.0971261 | + | 0.0294115i | ||||
\(479\) | −42.3499 | −1.93502 | −0.967508 | − | 0.252839i | \(-0.918636\pi\) | ||||
−0.967508 | + | 0.252839i | \(0.918636\pi\) | |||||||
\(480\) | 18.8251 | − | 1.90019i | 0.859243 | − | 0.0867313i | ||||
\(481\) | − | 7.25258i | − | 0.330689i | ||||||
\(482\) | 18.7518 | + | 5.67837i | 0.854121 | + | 0.258643i | ||||
\(483\) | 5.41857 | + | 19.6499i | 0.246554 | + | 0.894100i | ||||
\(484\) | −15.2356 | − | 10.1587i | −0.692526 | − | 0.461761i | ||||
\(485\) | 45.0415i | 2.04523i | ||||||||
\(486\) | 0.409868 | − | 1.35352i | 0.0185920 | − | 0.0613968i | ||||
\(487\) | 3.10189i | 0.140560i | 0.997527 | + | 0.0702801i | \(0.0223893\pi\) | ||||
−0.997527 | + | 0.0702801i | \(0.977611\pi\) | |||||||
\(488\) | −14.8967 | + | 12.2617i | −0.674342 | + | 0.555061i | ||||
\(489\) | 7.96419 | 0.360153 | ||||||||
\(490\) | −15.1681 | + | 50.0899i | −0.685225 | + | 2.26283i | ||||
\(491\) | 8.49112 | 0.383199 | 0.191599 | − | 0.981473i | \(-0.438633\pi\) | ||||
0.191599 | + | 0.981473i | \(0.438633\pi\) | |||||||
\(492\) | −4.36758 | − | 2.91221i | −0.196906 | − | 0.131292i | ||||
\(493\) | −9.33012 | −0.420207 | ||||||||
\(494\) | 1.65131 | − | 5.45316i | 0.0742961 | − | 0.245349i | ||||
\(495\) | 4.54207i | 0.204151i | ||||||||
\(496\) | −35.8476 | + | 14.9301i | −1.60960 | + | 0.670379i | ||||
\(497\) | − | 57.2222i | − | 2.56677i | ||||||
\(498\) | 0.0271083 | + | 0.00820885i | 0.00121475 | + | 0.000367847i | ||||
\(499\) | 34.1211 | 1.52747 | 0.763736 | − | 0.645529i | \(-0.223363\pi\) | ||||
0.763736 | + | 0.645529i | \(0.223363\pi\) | |||||||
\(500\) | −6.60828 | − | 4.40625i | −0.295531 | − | 0.197054i | ||||
\(501\) | 22.5603i | 1.00792i | ||||||||
\(502\) | −30.7887 | − | 9.32337i | −1.37417 | − | 0.416122i | ||||
\(503\) | 27.0619 | 1.20663 | 0.603316 | − | 0.797502i | \(-0.293846\pi\) | ||||
0.603316 | + | 0.797502i | \(0.293846\pi\) | |||||||
\(504\) | −9.28158 | + | 7.63981i | −0.413434 | + | 0.340304i | ||||
\(505\) | − | 4.94230i | − | 0.219930i | ||||||
\(506\) | 0.229961 | − | 9.20734i | 0.0102230 | − | 0.409316i | ||||
\(507\) | −7.40382 | −0.328815 | ||||||||
\(508\) | 10.3308 | − | 15.4937i | 0.458356 | − | 0.687420i | ||||
\(509\) | − | 22.9056i | − | 1.01527i | −0.861571 | − | 0.507637i | \(-0.830519\pi\) | ||
0.861571 | − | 0.507637i | \(-0.169481\pi\) | |||||||
\(510\) | 5.82664 | + | 1.76441i | 0.258008 | + | 0.0781293i | ||||
\(511\) | −25.6344 | −1.13400 | ||||||||
\(512\) | −10.7534 | − | 19.9089i | −0.475240 | − | 0.879856i | ||||
\(513\) | − | 1.70310i | − | 0.0751935i | ||||||
\(514\) | −0.640300 | + | 2.11448i | −0.0282424 | + | 0.0932655i | ||||
\(515\) | 32.1865 | 1.41831 | ||||||||
\(516\) | 11.5163 | − | 17.2716i | 0.506979 | − | 0.760342i | ||||
\(517\) | 8.22119 | 0.361568 | ||||||||
\(518\) | −5.34075 | + | 17.6369i | −0.234659 | + | 0.774919i | ||||
\(519\) | − | 10.1830i | − | 0.446984i | ||||||
\(520\) | 14.2227 | + | 17.2791i | 0.623705 | + | 0.757737i | ||||
\(521\) | 39.7228i | 1.74029i | 0.492799 | + | 0.870143i | \(0.335974\pi\) | ||||
−0.492799 | + | 0.870143i | \(0.664026\pi\) | |||||||
\(522\) | −9.81205 | − | 2.97126i | −0.429462 | − | 0.130048i | ||||
\(523\) | 4.07132i | 0.178027i | 0.996030 | + | 0.0890133i | \(0.0283714\pi\) | ||||
−0.996030 | + | 0.0890133i | \(0.971629\pi\) | |||||||
\(524\) | −10.6561 | − | 7.10522i | −0.465512 | − | 0.310393i | ||||
\(525\) | 26.2974 | 1.14771 | ||||||||
\(526\) | −4.52913 | + | 14.9566i | −0.197480 | + | 0.652141i | ||||
\(527\) | −12.4947 | −0.544277 | ||||||||
\(528\) | 5.01437 | − | 2.08842i | 0.218222 | − | 0.0908868i | ||||
\(529\) | −19.7493 | + | 11.7884i | −0.858665 | + | 0.512538i | ||||
\(530\) | 16.0867 | − | 53.1234i | 0.698761 | − | 2.30753i | ||||
\(531\) | 7.81205 | 0.339014 | ||||||||
\(532\) | −8.03134 | + | 12.0450i | −0.348203 | + | 0.522217i | ||||
\(533\) | − | 6.20911i | − | 0.268947i | ||||||
\(534\) | −3.95119 | − | 1.19649i | −0.170985 | − | 0.0517771i | ||||
\(535\) | − | 65.1110i | − | 2.81499i | ||||||
\(536\) | 14.3502 | + | 17.4340i | 0.619833 | + | 0.753033i | ||||
\(537\) | −12.0913 | −0.521778 | ||||||||
\(538\) | 24.0279 | + | 7.27607i | 1.03592 | + | 0.313694i | ||||
\(539\) | 15.0250i | 0.647172i | ||||||||
\(540\) | 5.56571 | + | 3.71109i | 0.239510 | + | 0.159700i | ||||
\(541\) | 39.1455i | 1.68300i | 0.540260 | + | 0.841498i | \(0.318326\pi\) | ||||
−0.540260 | + | 0.841498i | \(0.681674\pi\) | |||||||
\(542\) | 6.99231 | + | 2.11739i | 0.300345 | + | 0.0909498i | ||||
\(543\) | 4.93435 | 0.211753 | ||||||||
\(544\) | −0.731181 | − | 7.24378i | −0.0313491 | − | 0.310574i | ||||
\(545\) | −18.7828 | −0.804566 | ||||||||
\(546\) | −13.6088 | − | 4.12098i | −0.582403 | − | 0.176362i | ||||
\(547\) | 14.4989 | 0.619928 | 0.309964 | − | 0.950748i | \(-0.399683\pi\) | ||||
0.309964 | + | 0.950748i | \(0.399683\pi\) | |||||||
\(548\) | −2.91249 | + | 4.36801i | −0.124415 | + | 0.186592i | ||||
\(549\) | −6.82148 | −0.291134 | ||||||||
\(550\) | −11.3725 | − | 3.44380i | −0.484926 | − | 0.146844i | ||||
\(551\) | −12.3463 | −0.525968 | ||||||||
\(552\) | −11.0945 | − | 7.80462i | −0.472213 | − | 0.332187i | ||||
\(553\) | −59.6786 | −2.53779 | ||||||||
\(554\) | 32.4803 | + | 9.83560i | 1.37996 | + | 0.417875i | ||||
\(555\) | 10.2544 | 0.435275 | ||||||||
\(556\) | 15.5551 | + | 10.3718i | 0.659684 | + | 0.439862i | ||||
\(557\) | −17.8720 | −0.757261 | −0.378630 | − | 0.925548i | \(-0.623605\pi\) | ||||
−0.378630 | + | 0.925548i | \(0.623605\pi\) | |||||||
\(558\) | −13.1401 | − | 3.97904i | −0.556264 | − | 0.168446i | ||||
\(559\) | 24.5540 | 1.03852 | ||||||||
\(560\) | −21.8625 | − | 52.4927i | −0.923861 | − | 2.21822i | ||||
\(561\) | 1.74776 | 0.0737905 | ||||||||
\(562\) | −18.5289 | − | 5.61086i | −0.781593 | − | 0.236680i | ||||
\(563\) | 12.3543i | 0.520671i | 0.965518 | + | 0.260335i | \(0.0838332\pi\) | ||||
−0.965518 | + | 0.260335i | \(0.916167\pi\) | |||||||
\(564\) | 6.71711 | − | 10.0740i | 0.282841 | − | 0.424191i | ||||
\(565\) | − | 27.7726i | − | 1.16840i | ||||||
\(566\) | 17.9011 | + | 5.42077i | 0.752440 | + | 0.227852i | ||||
\(567\) | −4.25021 | −0.178492 | ||||||||
\(568\) | 24.2006 | + | 29.4013i | 1.01544 | + | 1.23365i | ||||
\(569\) | − | 26.1457i | − | 1.09609i | −0.836450 | − | 0.548043i | \(-0.815373\pi\) | ||
0.836450 | − | 0.548043i | \(-0.184627\pi\) | |||||||
\(570\) | 7.71021 | + | 2.33478i | 0.322945 | + | 0.0977934i | ||||
\(571\) | 28.1823i | 1.17939i | 0.807626 | + | 0.589696i | \(0.200752\pi\) | ||||
−0.807626 | + | 0.589696i | \(0.799248\pi\) | |||||||
\(572\) | 5.34557 | + | 3.56430i | 0.223509 | + | 0.149031i | ||||
\(573\) | 18.5834 | 0.776332 | ||||||||
\(574\) | −4.57234 | + | 15.0993i | −0.190846 | + | 0.630234i | ||||
\(575\) | 7.88819 | + | 28.6057i | 0.328960 | + | 1.19294i | ||||
\(576\) | 1.53790 | − | 7.85079i | 0.0640790 | − | 0.327116i | ||||
\(577\) | −2.99961 | −0.124875 | −0.0624377 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624377 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(578\) | −6.28883 | + | 20.7677i | −0.261581 | + | 0.863824i | ||||
\(579\) | 0.968591 | 0.0402533 | ||||||||
\(580\) | 26.9028 | − | 40.3475i | 1.11708 | − | 1.67534i | ||||
\(581\) | − | 0.0851233i | − | 0.00353151i | ||||||
\(582\) | 18.2269 | + | 5.51943i | 0.755531 | + | 0.228788i | ||||
\(583\) | − | 15.9349i | − | 0.659957i | ||||||
\(584\) | 13.1712 | − | 10.8414i | 0.545028 | − | 0.448621i | ||||
\(585\) | 7.91241i | 0.327138i | ||||||||
\(586\) | 12.0411 | − | 39.7634i | 0.497412 | − | 1.64261i | ||||
\(587\) | 16.3160 | 0.673432 | 0.336716 | − | 0.941606i | \(-0.390684\pi\) | ||||
0.336716 | + | 0.941606i | \(0.390684\pi\) | |||||||
\(588\) | 18.4111 | + | 12.2761i | 0.759263 | + | 0.506259i | ||||
\(589\) | −16.5338 | −0.681265 | ||||||||
\(590\) | −10.7096 | + | 35.3665i | −0.440906 | + | 1.45601i | ||||
\(591\) | 13.0210i | 0.535611i | ||||||||
\(592\) | −4.71492 | − | 11.3207i | −0.193782 | − | 0.465277i | ||||
\(593\) | 28.8694 | 1.18552 | 0.592762 | − | 0.805378i | \(-0.298038\pi\) | ||||
0.592762 | + | 0.805378i | \(0.298038\pi\) | |||||||
\(594\) | 1.83804 | + | 0.556590i | 0.0754156 | + | 0.0228372i | ||||
\(595\) | − | 18.2964i | − | 0.750078i | ||||||
\(596\) | −14.6442 | − | 9.76442i | −0.599850 | − | 0.399966i | ||||
\(597\) | 13.8735 | 0.567806 | ||||||||
\(598\) | 0.400598 | − | 16.0394i | 0.0163817 | − | 0.655901i | ||||
\(599\) | 12.3970i | 0.506528i | 0.967397 | + | 0.253264i | \(0.0815041\pi\) | ||||
−0.967397 | + | 0.253264i | \(0.918496\pi\) | |||||||
\(600\) | −13.5118 | + | 11.1218i | −0.551618 | + | 0.454045i | ||||
\(601\) | 3.40375 | 0.138842 | 0.0694210 | − | 0.997587i | \(-0.477885\pi\) | ||||
0.0694210 | + | 0.997587i | \(0.477885\pi\) | |||||||
\(602\) | −59.7104 | − | 18.0814i | −2.43362 | − | 0.736941i | ||||
\(603\) | 7.98334i | 0.325107i | ||||||||
\(604\) | −10.5407 | + | 15.8085i | −0.428896 | + | 0.643237i | ||||
\(605\) | 30.6242 | 1.24505 | ||||||||
\(606\) | −2.00000 | − | 0.605635i | −0.0812444 | − | 0.0246022i | ||||
\(607\) | 43.7821i | 1.77706i | 0.458817 | + | 0.888531i | \(0.348273\pi\) | ||||
−0.458817 | + | 0.888531i | \(0.651727\pi\) | |||||||
\(608\) | −0.967548 | − | 9.58546i | −0.0392393 | − | 0.388742i | ||||
\(609\) | 30.8110i | 1.24853i | ||||||||
\(610\) | 9.35161 | − | 30.8820i | 0.378635 | − | 1.25038i | ||||
\(611\) | 14.3215 | 0.579388 | ||||||||
\(612\) | 1.42800 | − | 2.14165i | 0.0577236 | − | 0.0865711i | ||||
\(613\) | −10.2363 | −0.413442 | −0.206721 | − | 0.978400i | \(-0.566279\pi\) | ||||
−0.206721 | + | 0.978400i | \(0.566279\pi\) | |||||||
\(614\) | 12.5764 | − | 41.5313i | 0.507542 | − | 1.67607i | ||||
\(615\) | 8.77904 | 0.354005 | ||||||||
\(616\) | −10.3746 | − | 12.6041i | −0.418006 | − | 0.507834i | ||||
\(617\) | 40.8145i | 1.64313i | 0.570114 | + | 0.821566i | \(0.306899\pi\) | ||||
−0.570114 | + | 0.821566i | \(0.693101\pi\) | |||||||
\(618\) | 3.94417 | − | 13.0249i | 0.158658 | − | 0.523939i | ||||
\(619\) | − | 15.9260i | − | 0.640122i | −0.947397 | − | 0.320061i | \(-0.896297\pi\) | ||
0.947397 | − | 0.320061i | \(-0.103703\pi\) | |||||||
\(620\) | 36.0276 | − | 54.0325i | 1.44690 | − | 2.17000i | ||||
\(621\) | −1.27490 | − | 4.62327i | −0.0511598 | − | 0.185526i | ||||
\(622\) | −0.841911 | − | 0.254945i | −0.0337576 | − | 0.0102224i | ||||
\(623\) | 12.4072i | 0.497085i | ||||||||
\(624\) | 8.73517 | − | 3.63808i | 0.349687 | − | 0.145640i | ||||
\(625\) | −17.6537 | −0.706146 | ||||||||
\(626\) | −13.7954 | − | 4.17749i | −0.551375 | − | 0.166966i | ||||
\(627\) | 2.31276 | 0.0923626 | ||||||||
\(628\) | −37.7300 | − | 25.1575i | −1.50559 | − | 1.00389i | ||||
\(629\) | − | 3.94583i | − | 0.157331i | ||||||
\(630\) | 5.82664 | − | 19.2414i | 0.232139 | − | 0.766597i | ||||
\(631\) | 24.7354 | 0.984699 | 0.492349 | − | 0.870398i | \(-0.336138\pi\) | ||||
0.492349 | + | 0.870398i | \(0.336138\pi\) | |||||||
\(632\) | 30.6634 | − | 25.2395i | 1.21972 | − | 1.00397i | ||||
\(633\) | 15.1196 | 0.600951 | ||||||||
\(634\) | −20.7495 | − | 6.28332i | −0.824069 | − | 0.249542i | ||||
\(635\) | 31.1429i | 1.23587i | ||||||||
\(636\) | −19.5261 | − | 13.0196i | −0.774262 | − | 0.516260i | ||||
\(637\) | 26.1739i | 1.03705i | ||||||||
\(638\) | 4.03489 | − | 13.3245i | 0.159743 | − | 0.527521i | ||||
\(639\) | 13.4634i | 0.532604i | ||||||||
\(640\) | 33.4335 | + | 17.7250i | 1.32158 | + | 0.700642i | ||||
\(641\) | − | 1.77955i | − | 0.0702880i | −0.999382 | − | 0.0351440i | \(-0.988811\pi\) | ||
0.999382 | − | 0.0351440i | \(-0.0111890\pi\) | |||||||
\(642\) | −26.3484 | − | 7.97877i | −1.03989 | − | 0.314897i | ||||
\(643\) | − | 25.4338i | − | 1.00301i | −0.865154 | − | 0.501506i | \(-0.832779\pi\) | ||
0.865154 | − | 0.501506i | \(-0.167221\pi\) | |||||||
\(644\) | −12.7855 | + | 38.7098i | −0.503819 | + | 1.52538i | ||||
\(645\) | 34.7168i | 1.36697i | ||||||||
\(646\) | 0.898411 | − | 2.96684i | 0.0353475 | − | 0.116729i | ||||
\(647\) | − | 17.3176i | − | 0.680824i | −0.940276 | − | 0.340412i | \(-0.889434\pi\) | ||
0.940276 | − | 0.340412i | \(-0.110566\pi\) | |||||||
\(648\) | 2.18379 | − | 1.79751i | 0.0857875 | − | 0.0706130i | ||||
\(649\) | 10.6085i | 0.416422i | ||||||||
\(650\) | −19.8113 | − | 5.99919i | −0.777061 | − | 0.235308i | ||||
\(651\) | 41.2615i | 1.61716i | ||||||||
\(652\) | 13.2525 | + | 8.83649i | 0.519009 | + | 0.346064i | ||||
\(653\) | − | 13.6867i | − | 0.535602i | −0.963474 | − | 0.267801i | \(-0.913703\pi\) | ||
0.963474 | − | 0.267801i | \(-0.0862970\pi\) | |||||||
\(654\) | −2.30166 | + | 7.60083i | −0.0900021 | + | 0.297216i | ||||
\(655\) | 21.4192 | 0.836916 | ||||||||
\(656\) | −4.03656 | − | 9.69191i | −0.157601 | − | 0.378406i | ||||
\(657\) | 6.03134 | 0.235305 | ||||||||
\(658\) | −34.8272 | − | 10.5463i | −1.35770 | − | 0.411136i | ||||
\(659\) | − | 19.5992i | − | 0.763476i | −0.924271 | − | 0.381738i | \(-0.875326\pi\) | ||
0.924271 | − | 0.381738i | \(-0.124674\pi\) | |||||||
\(660\) | −5.03955 | + | 7.55808i | −0.196164 | + | 0.294198i | ||||
\(661\) | 34.8466 | 1.35537 | 0.677687 | − | 0.735351i | \(-0.262982\pi\) | ||||
0.677687 | + | 0.735351i | \(0.262982\pi\) | |||||||
\(662\) | −7.23565 | + | 23.8944i | −0.281222 | + | 0.928683i | ||||
\(663\) | 3.04465 | 0.118244 | ||||||||
\(664\) | 0.0360006 | + | 0.0437370i | 0.00139709 | + | 0.00169733i | ||||
\(665\) | − | 24.2110i | − | 0.938862i | ||||||
\(666\) | 1.25658 | − | 4.14964i | 0.0486916 | − | 0.160795i | ||||
\(667\) | −33.5155 | + | 9.24209i | −1.29772 | + | 0.357855i | ||||
\(668\) | −25.0312 | + | 37.5406i | −0.968487 | + | 1.45249i | ||||
\(669\) | − | 10.5610i | − | 0.408311i | ||||||
\(670\) | −36.1419 | − | 10.9444i | −1.39629 | − | 0.422819i | ||||
\(671\) | − | 9.26338i | − | 0.357609i | ||||||
\(672\) | −23.9213 | + | 2.41459i | −0.922783 | + | 0.0931449i | ||||
\(673\) | 29.8650 | 1.15121 | 0.575605 | − | 0.817728i | \(-0.304766\pi\) | ||||
0.575605 | + | 0.817728i | \(0.304766\pi\) | |||||||
\(674\) | −23.1701 | − | 7.01631i | −0.892479 | − | 0.270258i | ||||
\(675\) | −6.18732 | −0.238150 | ||||||||
\(676\) | −12.3201 | − | 8.21475i | −0.473849 | − | 0.315952i | ||||
\(677\) | 7.52207 | 0.289097 | 0.144548 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144548 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(678\) | −11.2387 | − | 3.40328i | −0.431621 | − | 0.130702i | ||||
\(679\) | − | 57.2348i | − | 2.19647i | ||||||
\(680\) | 7.73796 | + | 9.40082i | 0.296737 | + | 0.360505i | ||||
\(681\) | − | 3.11219i | − | 0.119259i | ||||||
\(682\) | 5.40343 | − | 17.8439i | 0.206908 | − | 0.683277i | ||||
\(683\) | −17.6865 | −0.676753 | −0.338377 | − | 0.941011i | \(-0.609878\pi\) | ||||
−0.338377 | + | 0.941011i | \(0.609878\pi\) | |||||||
\(684\) | 1.88963 | − | 2.83398i | 0.0722519 | − | 0.108360i | ||||
\(685\) | − | 8.77989i | − | 0.335463i | ||||||
\(686\) | 7.08010 | − | 23.3807i | 0.270319 | − | 0.892681i | ||||
\(687\) | −17.0499 | −0.650493 | ||||||||
\(688\) | 38.3267 | − | 15.9626i | 1.46119 | − | 0.608568i | ||||
\(689\) | − | 27.7591i | − | 1.05754i | ||||||
\(690\) | 22.6781 | + | 0.566404i | 0.863340 | + | 0.0215626i | ||||
\(691\) | −12.1619 | −0.462660 | −0.231330 | − | 0.972875i | \(-0.574308\pi\) | ||||
−0.231330 | + | 0.972875i | \(0.574308\pi\) | |||||||
\(692\) | 11.2983 | − | 16.9447i | 0.429498 | − | 0.644140i | ||||
\(693\) | − | 5.77167i | − | 0.219247i | ||||||
\(694\) | −2.29347 | + | 7.57376i | −0.0870588 | + | 0.287496i | ||||
\(695\) | −31.2665 | −1.18600 | ||||||||
\(696\) | −13.0307 | − | 15.8310i | −0.493928 | − | 0.600071i | ||||
\(697\) | − | 3.37812i | − | 0.127955i | ||||||
\(698\) | 23.2593 | + | 7.04333i | 0.880378 | + | 0.266594i | ||||
\(699\) | 14.5284 | 0.549515 | ||||||||
\(700\) | 43.7593 | + | 29.1777i | 1.65395 | + | 1.10281i | ||||
\(701\) | −22.2613 | −0.840799 | −0.420399 | − | 0.907339i | \(-0.638110\pi\) | ||||
−0.420399 | + | 0.907339i | \(0.638110\pi\) | |||||||
\(702\) | 3.20191 | + | 0.969595i | 0.120848 | + | 0.0365950i | ||||
\(703\) | − | 5.22139i | − | 0.196929i | ||||||
\(704\) | 10.6611 | + | 2.08842i | 0.401807 | + | 0.0787103i | ||||
\(705\) | 20.2492i | 0.762628i | ||||||||
\(706\) | 3.93481 | − | 12.9940i | 0.148088 | − | 0.489035i | ||||
\(707\) | 6.28025i | 0.236193i | ||||||||
\(708\) | 12.9994 | + | 8.66768i | 0.488546 | + | 0.325751i | ||||
\(709\) | −45.4947 | −1.70859 | −0.854295 | − | 0.519788i | \(-0.826011\pi\) | ||||
−0.854295 | + | 0.519788i | \(0.826011\pi\) | |||||||
\(710\) | −60.9511 | − | 18.4570i | −2.28745 | − | 0.692680i | ||||
\(711\) | 14.0413 | 0.526591 | ||||||||
\(712\) | −5.24730 | − | 6.37493i | −0.196651 | − | 0.238910i | ||||
\(713\) | −44.8832 | + | 12.3768i | −1.68089 | + | 0.463515i | ||||
\(714\) | −7.40398 | − | 2.24205i | −0.277087 | − | 0.0839068i | ||||
\(715\) | −10.7448 | −0.401834 | ||||||||
\(716\) | −20.1201 | − | 13.4156i | −0.751924 | − | 0.501366i | ||||
\(717\) | 1.56887i | 0.0585905i | ||||||||
\(718\) | −7.97918 | + | 26.3498i | −0.297780 | + | 0.983366i | ||||
\(719\) | − | 2.02839i | − | 0.0756463i | −0.999284 | − | 0.0378232i | \(-0.987958\pi\) | ||
0.999284 | − | 0.0378232i | \(-0.0120424\pi\) | |||||||
\(720\) | 5.14387 | + | 12.3506i | 0.191701 | + | 0.460280i | ||||
\(721\) | −40.8998 | −1.52319 | ||||||||
\(722\) | −6.59866 | + | 21.7909i | −0.245577 | + | 0.810973i | ||||
\(723\) | 13.8541i | 0.515240i | ||||||||
\(724\) | 8.21084 | + | 5.47480i | 0.305153 | + | 0.203469i | ||||
\(725\) | 44.8537i | 1.66583i | ||||||||
\(726\) | 3.75272 | − | 12.3927i | 0.139277 | − | 0.459936i | ||||
\(727\) | 43.0958 | 1.59834 | 0.799168 | − | 0.601108i | \(-0.205274\pi\) | ||||
0.799168 | + | 0.601108i | \(0.205274\pi\) | |||||||
\(728\) | −18.0729 | − | 21.9567i | −0.669827 | − | 0.813770i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.26839 | + | 27.3049i | −0.306027 | + | 1.01060i | ||||
\(731\) | 13.3588 | 0.494093 | ||||||||
\(732\) | −11.3511 | − | 7.56862i | −0.419547 | − | 0.279744i | ||||
\(733\) | 13.4280 | 0.495975 | 0.247987 | − | 0.968763i | \(-0.420231\pi\) | ||||
0.247987 | + | 0.968763i | \(0.420231\pi\) | |||||||
\(734\) | −3.20470 | + | 10.5829i | −0.118288 | + | 0.390624i | ||||
\(735\) | −37.0072 | −1.36503 | ||||||||
\(736\) | −9.80197 | − | 25.2967i | −0.361305 | − | 0.932448i | ||||
\(737\) | −10.8412 | −0.399339 | ||||||||
\(738\) | 1.07579 | − | 3.55261i | 0.0396005 | − | 0.130773i | ||||
\(739\) | −0.341465 | −0.0125610 | −0.00628050 | − | 0.999980i | \(-0.501999\pi\) | ||||
−0.00628050 | + | 0.999980i | \(0.501999\pi\) | |||||||
\(740\) | 17.0635 | + | 11.3775i | 0.627266 | + | 0.418247i | ||||
\(741\) | 4.02889 | 0.148005 | ||||||||
\(742\) | −20.4416 | + | 67.5046i | −0.750433 | + | 2.47817i | ||||
\(743\) | −10.7100 | −0.392913 | −0.196456 | − | 0.980513i | \(-0.562943\pi\) | ||||
−0.196456 | + | 0.980513i | \(0.562943\pi\) | |||||||
\(744\) | −17.4504 | − | 21.2005i | −0.639764 | − | 0.777247i | ||||
\(745\) | 29.4355 | 1.07843 | ||||||||
\(746\) | 2.15623 | − | 7.12057i | 0.0789453 | − | 0.260703i | ||||
\(747\) | 0.0200280i | 0.000732787i | ||||||||
\(748\) | 2.90830 | + | 1.93919i | 0.106338 | + | 0.0709038i | ||||
\(749\) | 82.7373i | 3.02316i | ||||||||
\(750\) | 1.62771 | − | 5.37520i | 0.0594354 | − | 0.196275i | ||||
\(751\) | −13.3151 | −0.485874 | −0.242937 | − | 0.970042i | \(-0.578111\pi\) | ||||
−0.242937 | + | 0.970042i | \(0.578111\pi\) | |||||||
\(752\) | 22.3547 | − | 9.31046i | 0.815193 | − | 0.339517i | ||||
\(753\) | − | 22.7472i | − | 0.828955i | ||||||
\(754\) | 7.02888 | − | 23.2116i | 0.255977 | − | 0.845317i | ||||
\(755\) | − | 31.7757i | − | 1.15644i | ||||||
\(756\) | −7.07242 | − | 4.71573i | −0.257221 | − | 0.171509i | ||||
\(757\) | −8.38541 | −0.304773 | −0.152387 | − | 0.988321i | \(-0.548696\pi\) | ||||
−0.152387 | + | 0.988321i | \(0.548696\pi\) | |||||||
\(758\) | 17.1967 | + | 5.20745i | 0.624611 | + | 0.189143i | ||||
\(759\) | 6.27827 | − | 1.73127i | 0.227887 | − | 0.0628412i | ||||
\(760\) | 10.2394 | + | 12.4398i | 0.371422 | + | 0.451239i | ||||
\(761\) | −53.0560 | −1.92328 | −0.961639 | − | 0.274318i | \(-0.911548\pi\) | ||||
−0.961639 | + | 0.274318i | \(0.911548\pi\) | |||||||
\(762\) | 12.6026 | + | 3.81629i | 0.456544 | + | 0.138250i | ||||
\(763\) | 23.8675 | 0.864063 | ||||||||
\(764\) | 30.9230 | + | 20.6188i | 1.11876 | + | 0.745961i | ||||
\(765\) | 4.30481i | 0.155641i | ||||||||
\(766\) | −13.4832 | + | 44.5258i | −0.487167 | + | 1.60878i | ||||
\(767\) | 18.4804i | 0.667287i | ||||||||
\(768\) | 11.2698 | − | 11.3575i | 0.406662 | − | 0.409828i | ||||
\(769\) | − | 39.6654i | − | 1.43037i | −0.698935 | − | 0.715185i | \(-0.746343\pi\) | ||
0.698935 | − | 0.715185i | \(-0.253657\pi\) | |||||||
\(770\) | 26.1293 | + | 7.91241i | 0.941635 | + | 0.285143i | ||||
\(771\) | −1.56221 | −0.0562616 | ||||||||
\(772\) | 1.61175 | + | 1.07468i | 0.0580082 | + | 0.0386785i | ||||
\(773\) | 28.5395 | 1.02650 | 0.513248 | − | 0.858240i | \(-0.328442\pi\) | ||||
0.513248 | + | 0.858240i | \(0.328442\pi\) | |||||||
\(774\) | 14.0488 | + | 4.25423i | 0.504974 | + | 0.152915i | ||||
\(775\) | 60.0671i | 2.15768i | ||||||||
\(776\) | 24.2059 | + | 29.4077i | 0.868943 | + | 1.05568i | ||||
\(777\) | −13.0304 | −0.467463 | ||||||||
\(778\) | 2.03018 | − | 6.70432i | 0.0727856 | − | 0.240361i | ||||
\(779\) | − | 4.47016i | − | 0.160160i | ||||||
\(780\) | −8.77904 | + | 13.1664i | −0.314340 | + | 0.471432i | ||||
\(781\) | −18.2829 | −0.654214 | ||||||||
\(782\) | 0.217949 | − | 8.72639i | 0.00779383 | − | 0.312055i | ||||
\(783\) | − | 7.24930i | − | 0.259069i | ||||||
\(784\) | 17.0157 | + | 40.8554i | 0.607704 | + | 1.45912i | ||||
\(785\) | 75.8389 | 2.70681 | ||||||||
\(786\) | 2.62473 | − | 8.66768i | 0.0936209 | − | 0.309166i | ||||
\(787\) | 6.16750i | 0.219848i | 0.993940 | + | 0.109924i | \(0.0350607\pi\) | ||||
−0.993940 | + | 0.109924i | \(0.964939\pi\) | |||||||
\(788\) | −14.4471 | + | 21.6671i | −0.514657 | + | 0.771858i | ||||
\(789\) | −11.0502 | −0.393398 | ||||||||
\(790\) | −19.2493 | + | 63.5675i | −0.684861 | + | 2.26163i | ||||
\(791\) | 35.2910i | 1.25480i | ||||||||
\(792\) | 2.44097 | + | 2.96553i | 0.0867362 | + | 0.105375i | ||||
\(793\) | − | 16.1371i | − | 0.573044i | ||||||
\(794\) | −21.2980 | − | 6.44941i | −0.755838 | − | 0.228881i | ||||
\(795\) | 39.2484 | 1.39200 | ||||||||
\(796\) | 23.0858 | + | 15.3931i | 0.818254 | + | 0.545593i | ||||
\(797\) | −3.67557 | −0.130195 | −0.0650977 | − | 0.997879i | \(-0.520736\pi\) | ||||
−0.0650977 | + | 0.997879i | \(0.520736\pi\) | |||||||
\(798\) | −9.79746 | − | 2.96684i | −0.346826 | − | 0.105025i | ||||
\(799\) | 7.79176 | 0.275652 | ||||||||
\(800\) | −34.8238 | + | 3.51509i | −1.23121 | + | 0.124277i | ||||
\(801\) | − | 2.91920i | − | 0.103145i | ||||||
\(802\) | 31.9188 | + | 9.66558i | 1.12709 | + | 0.341303i | ||||
\(803\) | 8.19039i | 0.289032i | ||||||||
\(804\) | −8.85774 | + | 13.2844i | −0.312388 | + | 0.468505i | ||||
\(805\) | −18.1237 | − | 65.7238i | −0.638778 | − | 2.31646i | ||||
\(806\) | 9.41292 | − | 31.0845i | 0.331556 | − | 1.09490i | ||||
\(807\) | 17.7522i | 0.624907i | ||||||||
\(808\) | −2.65606 | − | 3.22684i | −0.0934400 | − | 0.113520i | ||||
\(809\) | 43.7199 | 1.53711 | 0.768556 | − | 0.639783i | \(-0.220976\pi\) | ||||
0.768556 | + | 0.639783i | \(0.220976\pi\) | |||||||
\(810\) | −1.37091 | + | 4.52717i | −0.0481687 | + | 0.159069i | ||||
\(811\) | −1.77417 | −0.0622995 | −0.0311498 | − | 0.999515i | \(-0.509917\pi\) | ||||
−0.0311498 | + | 0.999515i | \(0.509917\pi\) | |||||||
\(812\) | −34.1857 | + | 51.2701i | −1.19968 | + | 1.79923i | ||||
\(813\) | 5.16603i | 0.181181i | ||||||||
\(814\) | 5.63510 | + | 1.70641i | 0.197510 | + | 0.0598095i | ||||
\(815\) | −26.6382 | −0.933095 | ||||||||
\(816\) | 4.75244 | − | 1.97933i | 0.166369 | − | 0.0692904i | ||||
\(817\) | 17.6773 | 0.618450 | ||||||||
\(818\) | −11.8435 | + | 39.1110i | −0.414098 | + | 1.36748i | ||||
\(819\) | − | 10.0544i | − | 0.351329i | ||||||
\(820\) | 14.6085 | + | 9.74059i | 0.510149 | + | 0.340156i | ||||
\(821\) | 18.0724i | 0.630730i | 0.948971 | + | 0.315365i | \(0.102127\pi\) | ||||
−0.948971 | + | 0.315365i | \(0.897873\pi\) | |||||||
\(822\) | −3.55296 | − | 1.07590i | −0.123924 | − | 0.0375262i | ||||
\(823\) | − | 27.3675i | − | 0.953971i | −0.878911 | − | 0.476985i | \(-0.841729\pi\) | ||
0.878911 | − | 0.476985i | \(-0.158271\pi\) | |||||||
\(824\) | 21.0147 | − | 17.2975i | 0.732081 | − | 0.602587i | ||||
\(825\) | − | 8.40221i | − | 0.292527i | ||||||
\(826\) | 13.6088 | − | 44.9406i | 0.473511 | − | 1.56368i | ||||
\(827\) | 30.2311i | 1.05124i | 0.850720 | + | 0.525619i | \(0.176166\pi\) | ||||
−0.850720 | + | 0.525619i | \(0.823834\pi\) | |||||||
\(828\) | 3.00820 | − | 9.10773i | 0.104542 | − | 0.316515i | ||||
\(829\) | − | 28.8709i | − | 1.00273i | −0.865237 | − | 0.501363i | \(-0.832832\pi\) | ||
0.865237 | − | 0.501363i | \(-0.167168\pi\) | |||||||
\(830\) | −0.0906702 | − | 0.0274565i | −0.00314721 | − | 0.000953030i | ||||
\(831\) | 23.9970i | 0.832446i | ||||||||
\(832\) | 18.5720 | + | 3.63808i | 0.643869 | + | 0.126128i | ||||
\(833\) | 14.2402i | 0.493392i | ||||||||
\(834\) | −3.83142 | + | 12.6526i | −0.132671 | + | 0.438123i | ||||
\(835\) | − | 75.4583i | − | 2.61134i | ||||||
\(836\) | 3.84846 | + | 2.56607i | 0.133102 | + | 0.0887493i | ||||
\(837\) | − | 9.70810i | − | 0.335561i | ||||||
\(838\) | −16.5331 | − | 5.00651i | −0.571126 | − | 0.172947i | ||||
\(839\) | −53.7723 | −1.85643 | −0.928213 | − | 0.372048i | \(-0.878656\pi\) | ||||
−0.928213 | + | 0.372048i | \(0.878656\pi\) | |||||||
\(840\) | 31.0445 | − | 25.5532i | 1.07114 | − | 0.881669i | ||||
\(841\) | −23.5523 | −0.812149 | ||||||||
\(842\) | −9.98202 | + | 32.9638i | −0.344003 | + | 1.13601i | ||||
\(843\) | − | 13.6894i | − | 0.471489i | ||||||
\(844\) | 25.1593 | + | 16.7756i | 0.866018 | + | 0.577441i | ||||
\(845\) | 24.7639 | 0.851904 | ||||||||
\(846\) | 8.19422 | + | 2.48135i | 0.281723 | + | 0.0853107i | ||||
\(847\) | −38.9146 | −1.33712 | ||||||||
\(848\) | −18.0462 | − | 43.3296i | −0.619709 | − | 1.48794i | ||||
\(849\) | 13.2256i | 0.453902i | ||||||||
\(850\) | −10.7785 | − | 3.26391i | −0.369699 | − | 0.111951i | ||||
\(851\) | −3.90860 | − | 14.1741i | −0.133985 | − | 0.485883i | ||||
\(852\) | −14.9380 | + | 22.4033i | −0.511768 | + | 0.767524i | ||||
\(853\) | − | 30.6100i | − | 1.04807i | −0.851698 | − | 0.524033i | \(-0.824427\pi\) | ||
0.851698 | − | 0.524033i | \(-0.175573\pi\) | |||||||
\(854\) | −11.8832 | + | 39.2421i | −0.406635 | + | 1.34284i | ||||
\(855\) | 5.69642i | 0.194814i | ||||||||
\(856\) | −34.9915 | − | 42.5111i | −1.19599 | − | 1.45300i | ||||
\(857\) | −1.65741 | −0.0566162 | −0.0283081 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283081 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(858\) | −1.31668 | + | 4.34811i | −0.0449508 | + | 0.148442i | ||||
\(859\) | 1.69125 | 0.0577049 | 0.0288524 | − | 0.999584i | \(-0.490815\pi\) | ||||
0.0288524 | + | 0.999584i | \(0.490815\pi\) | |||||||
\(860\) | −38.5192 | + | 57.7692i | −1.31349 | + | 1.96991i | ||||
\(861\) | −11.1556 | −0.380183 | ||||||||
\(862\) | −2.49982 | + | 8.25519i | −0.0851441 | + | 0.281173i | ||||
\(863\) | 31.6977i | 1.07900i | 0.841985 | + | 0.539501i | \(0.181387\pi\) | ||||
−0.841985 | + | 0.539501i | \(0.818613\pi\) | |||||||
\(864\) | 5.62825 | − | 0.568111i | 0.191477 | − | 0.0193275i | ||||
\(865\) | 34.0596i | 1.15806i | ||||||||
\(866\) | 17.0008 | + | 5.14815i | 0.577712 | + | 0.174941i | ||||
\(867\) | −15.3435 | −0.521094 | ||||||||
\(868\) | −45.7807 | + | 68.6597i | −1.55390 | + | 2.33046i | ||||
\(869\) | 19.0677i | 0.646829i | ||||||||
\(870\) | 32.8188 | + | 9.93810i | 1.11266 | + | 0.336933i | ||||
\(871\) | −18.8856 | −0.639914 | ||||||||
\(872\) | −12.2633 | + | 10.0941i | −0.415289 | + | 0.341831i | ||||
\(873\) | 13.4664i | 0.455767i | ||||||||
\(874\) | 0.288405 | − | 11.5474i | 0.00975544 | − | 0.390595i | ||||
\(875\) | −16.8788 | −0.570608 | ||||||||
\(876\) | 10.0362 | + | 6.69194i | 0.339093 | + | 0.226100i | ||||
\(877\) | − | 8.42097i | − | 0.284356i | −0.989841 | − | 0.142178i | \(-0.954589\pi\) | ||
0.989841 | − | 0.142178i | \(-0.0454106\pi\) | |||||||
\(878\) | −9.43943 | − | 2.85842i | −0.318565 | − | 0.0964671i | ||||
\(879\) | 29.3779 | 0.990891 | ||||||||
\(880\) | −16.7718 | + | 6.98523i | −0.565377 | + | 0.235472i | ||||
\(881\) | − | 0.409682i | − | 0.0138025i | −0.999976 | − | 0.00690126i | \(-0.997803\pi\) | ||
0.999976 | − | 0.00690126i | \(-0.00219676\pi\) | |||||||
\(882\) | −4.53490 | + | 14.9757i | −0.152698 | + | 0.504258i | ||||
\(883\) | 5.67751 | 0.191063 | 0.0955317 | − | 0.995426i | \(-0.469545\pi\) | ||||
0.0955317 | + | 0.995426i | \(0.469545\pi\) | |||||||
\(884\) | 5.06634 | + | 3.37812i | 0.170399 | + | 0.113618i | ||||
\(885\) | −26.1293 | −0.878327 | ||||||||
\(886\) | 8.51428 | − | 28.1169i | 0.286043 | − | 0.944605i | ||||
\(887\) | − | 11.9861i | − | 0.402454i | −0.979545 | − | 0.201227i | \(-0.935507\pi\) | ||
0.979545 | − | 0.201227i | \(-0.0644929\pi\) | |||||||
\(888\) | 6.69512 | − | 5.51085i | 0.224673 | − | 0.184932i | ||||
\(889\) | − | 39.5737i | − | 1.32726i | ||||||
\(890\) | 13.2157 | + | 4.00195i | 0.442992 | + | 0.134146i | ||||
\(891\) | 1.35797i | 0.0454938i | ||||||||
\(892\) | 11.7177 | − | 17.5736i | 0.392337 | − | 0.588408i | ||||
\(893\) | 10.3106 | 0.345031 | ||||||||
\(894\) | 3.60706 | − | 11.9116i | 0.120638 | − | 0.398385i | ||||
\(895\) | 40.4423 | 1.35184 | ||||||||
\(896\) | −42.4844 | − | 22.5234i | −1.41930 | − | 0.752454i | ||||
\(897\) | 10.9369 | − | 3.01592i | 0.365173 | − | 0.100699i | ||||
\(898\) | 2.82972 | − | 9.34464i | 0.0944290 | − | 0.311835i | ||||
\(899\) | −70.3769 | −2.34720 | ||||||||
\(900\) | −10.2958 | − | 6.86500i | −0.343193 | − | 0.228833i | ||||
\(901\) | − | 15.1026i | − | 0.503139i | ||||||
\(902\) | 4.82434 | + | 1.46090i | 0.160633 | + | 0.0486425i | ||||
\(903\) | − | 44.1150i | − | 1.46806i | ||||||
\(904\) | −14.9254 | − | 18.1328i | −0.496411 | − | 0.603088i | ||||
\(905\) | −16.5041 | −0.548616 | ||||||||
\(906\) | −12.8587 | − | 3.89383i | −0.427200 | − | 0.129364i | ||||
\(907\) | 37.0908i | 1.23158i | 0.787910 | + | 0.615790i | \(0.211163\pi\) | ||||
−0.787910 | + | 0.615790i | \(0.788837\pi\) | |||||||
\(908\) | 3.45306 | − | 5.17873i | 0.114594 | − | 0.171862i | ||||
\(909\) | − | 1.47763i | − | 0.0490100i | ||||||
\(910\) | 45.5180 | + | 13.7836i | 1.50891 | + | 0.456923i | ||||
\(911\) | 27.3370 | 0.905717 | 0.452858 | − | 0.891582i | \(-0.350404\pi\) | ||||
0.452858 | + | 0.891582i | \(0.350404\pi\) | |||||||
\(912\) | 6.28876 | − | 2.61919i | 0.208242 | − | 0.0867299i | ||||
\(913\) | −0.0271975 | −0.000900105 | ||||||||
\(914\) | −49.9551 | − | 15.1273i | −1.65237 | − | 0.500365i | ||||
\(915\) | 22.8161 | 0.754277 | ||||||||
\(916\) | −28.3712 | − | 18.9173i | −0.937412 | − | 0.625045i | ||||
\(917\) | −27.2176 | −0.898804 | ||||||||
\(918\) | 1.74203 | + | 0.527516i | 0.0574955 | + | 0.0174106i | ||||
\(919\) | 25.0423 | 0.826069 | 0.413035 | − | 0.910715i | \(-0.364469\pi\) | ||||
0.413035 | + | 0.910715i | \(0.364469\pi\) | |||||||
\(920\) | 37.1083 | + | 26.1045i | 1.22342 | + | 0.860639i | ||||
\(921\) | 30.6840 | 1.01107 | ||||||||
\(922\) | 10.3743 | + | 3.14153i | 0.341660 | + | 0.103461i | ||||
\(923\) | −31.8493 | −1.04833 | ||||||||
\(924\) | 6.40382 | − | 9.60414i | 0.210670 | − | 0.315953i | ||||
\(925\) | −18.9692 | −0.623704 | ||||||||
\(926\) | −27.3808 | − | 8.29137i | −0.899787 | − | 0.272471i | ||||
\(927\) | 9.62302 | 0.316061 | ||||||||
\(928\) | −4.11841 | − | 40.8009i | −0.135193 | − | 1.33935i | ||||
\(929\) | 45.5702 | 1.49511 | 0.747555 | − | 0.664200i | \(-0.231228\pi\) | ||||
0.747555 | + | 0.664200i | \(0.231228\pi\) | |||||||
\(930\) | 43.9502 | + | 13.3089i | 1.44118 | + | 0.436416i | ||||
\(931\) | 18.8435i | 0.617572i | ||||||||
\(932\) | 24.1755 | + | 16.1197i | 0.791894 | + | 0.528017i | ||||
\(933\) | − | 0.622018i | − | 0.0203639i | ||||||
\(934\) | 44.6976 | + | 13.5352i | 1.46255 | + | 0.442885i | ||||
\(935\) | −5.84582 | −0.191179 | ||||||||
\(936\) | 4.25224 | + | 5.16603i | 0.138989 | + | 0.168857i | ||||
\(937\) | 18.4326i | 0.602166i | 0.953598 | + | 0.301083i | \(0.0973481\pi\) | ||||
−0.953598 | + | 0.301083i | \(0.902652\pi\) | |||||||
\(938\) | 45.9260 | + | 13.9072i | 1.49954 | + | 0.454086i | ||||
\(939\) | − | 10.1923i | − | 0.332612i | ||||||
\(940\) | −22.4670 | + | 33.6949i | −0.732793 | + | 1.09901i | ||||
\(941\) | −7.16226 | −0.233483 | −0.116741 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116741 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(942\) | 9.29338 | − | 30.6897i | 0.302795 | − | 0.999925i | ||||
\(943\) | −3.34625 | − | 12.1348i | −0.108969 | − | 0.395164i | ||||
\(944\) | 12.0141 | + | 28.8463i | 0.391026 | + | 0.938868i | ||||
\(945\) | 14.2159 | 0.462442 | ||||||||
\(946\) | −5.77712 | + | 19.0779i | −0.187830 | + | 0.620276i | ||||
\(947\) | 5.24153 | 0.170327 | 0.0851634 | − | 0.996367i | \(-0.472859\pi\) | ||||
0.0851634 | + | 0.996367i | \(0.472859\pi\) | |||||||
\(948\) | 23.3650 | + | 15.5793i | 0.758860 | + | 0.505991i | ||||
\(949\) | 14.2679i | 0.463155i | ||||||||
\(950\) | −14.2628 | − | 4.31903i | −0.462747 | − | 0.140128i | ||||
\(951\) | − | 15.3301i | − | 0.497112i | ||||||
\(952\) | −9.83272 | − | 11.9457i | −0.318680 | − | 0.387164i | ||||
\(953\) | 47.7506i | 1.54679i | 0.633923 | + | 0.773397i | \(0.281444\pi\) | ||||
−0.633923 | + | 0.773397i | \(0.718556\pi\) | |||||||
\(954\) | 4.80954 | − | 15.8826i | 0.155715 | − | 0.514220i | ||||
\(955\) | −62.1567 | −2.01134 | ||||||||
\(956\) | −1.74070 | + | 2.61062i | −0.0562984 | + | 0.0844335i | ||||
\(957\) | 9.84434 | 0.318222 | ||||||||
\(958\) | 17.3579 | − | 57.3213i | 0.560808 | − | 1.85197i | ||||
\(959\) | 11.1567i | 0.360269i | ||||||||
\(960\) | −5.14387 | + | 26.2589i | −0.166018 | + | 0.847502i | ||||
\(961\) | −63.2472 | −2.04023 | ||||||||
\(962\) | 9.81649 | + | 2.97261i | 0.316496 | + | 0.0958406i | ||||
\(963\) | − | 19.4666i | − | 0.627304i | ||||||
\(964\) | −15.3715 | + | 23.0535i | −0.495084 | + | 0.742503i | ||||
\(965\) | −3.23969 | −0.104289 | ||||||||
\(966\) | −28.8173 | − | 0.719737i | −0.927183 | − | 0.0231572i | ||||
\(967\) | 20.1259i | 0.647205i | 0.946193 | + | 0.323603i | \(0.104894\pi\) | ||||
−0.946193 | + | 0.323603i | \(0.895106\pi\) | |||||||
\(968\) | 19.9946 | − | 16.4579i | 0.642651 | − | 0.528976i | ||||
\(969\) | 2.19195 | 0.0704156 | ||||||||
\(970\) | −60.9645 | − | 18.4611i | −1.95745 | − | 0.592750i | ||||
\(971\) | − | 1.26842i | − | 0.0407055i | −0.999793 | − | 0.0203528i | \(-0.993521\pi\) | ||
0.999793 | − | 0.0203528i | \(-0.00647893\pi\) | |||||||
\(972\) | 1.66402 | + | 1.10953i | 0.0533733 | + | 0.0355881i | ||||
\(973\) | 39.7307 | 1.27371 | ||||||||
\(974\) | −4.19846 | − | 1.27137i | −0.134527 | − | 0.0407373i | ||||
\(975\) | − | 14.6369i | − | 0.468755i | ||||||
\(976\) | −10.4907 | − | 25.1886i | −0.335800 | − | 0.806268i | ||||
\(977\) | − | 1.39122i | − | 0.0445091i | −0.999752 | − | 0.0222546i | \(-0.992916\pi\) | ||
0.999752 | − | 0.0222546i | \(-0.00708443\pi\) | |||||||
\(978\) | −3.26427 | + | 10.7797i | −0.104380 | + | 0.344696i | ||||
\(979\) | 3.96419 | 0.126696 | ||||||||
\(980\) | −61.5806 | − | 41.0605i | −1.96712 | − | 1.31163i | ||||
\(981\) | −5.61561 | −0.179293 | ||||||||
\(982\) | −3.48024 | + | 11.4929i | −0.111059 | + | 0.366752i | ||||
\(983\) | 50.0347 | 1.59586 | 0.797929 | − | 0.602752i | \(-0.205929\pi\) | ||||
0.797929 | + | 0.602752i | \(0.205929\pi\) | |||||||
\(984\) | 5.73185 | − | 4.71798i | 0.182725 | − | 0.150404i | ||||
\(985\) | − | 43.5518i | − | 1.38768i | ||||||
\(986\) | 3.82412 | − | 12.6285i | 0.121785 | − | 0.402173i | ||||
\(987\) | − | 25.7309i | − | 0.819023i | ||||||
\(988\) | 6.70413 | + | 4.47016i | 0.213287 | + | 0.142215i | ||||
\(989\) | 47.9872 | − | 13.2328i | 1.52591 | − | 0.420778i | ||||
\(990\) | −6.14777 | − | 1.86165i | −0.195389 | − | 0.0591672i | ||||
\(991\) | 43.7351i | 1.38929i | 0.719352 | + | 0.694646i | \(0.244439\pi\) | ||||
−0.719352 | + | 0.694646i | \(0.755561\pi\) | |||||||
\(992\) | −5.51528 | − | 54.6397i | −0.175110 | − | 1.73481i | ||||
\(993\) | −17.6536 | −0.560220 | ||||||||
\(994\) | 77.4513 | + | 23.4536i | 2.45661 | + | 0.743903i | ||||
\(995\) | −46.4034 | −1.47109 | ||||||||
\(996\) | −0.0222216 | + | 0.0333269i | −0.000704120 | + | 0.00105600i | ||||
\(997\) | 46.9693i | 1.48753i | 0.668440 | + | 0.743766i | \(0.266962\pi\) | ||||
−0.668440 | + | 0.743766i | \(0.733038\pi\) | |||||||
\(998\) | −13.9852 | + | 46.1835i | −0.442693 | + | 1.46191i | ||||
\(999\) | 3.06582 | 0.0969983 |
(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 | 552.2.n.b.91.12 | yes | 24 | |
4.3 | odd | 2 | 2208.2.n.b.367.23 | 24 | |||
8.3 | odd | 2 | inner | 552.2.n.b.91.9 | ✓ | 24 | |
8.5 | even | 2 | 2208.2.n.b.367.1 | 24 | |||
23.22 | odd | 2 | inner | 552.2.n.b.91.11 | yes | 24 | |
92.91 | even | 2 | 2208.2.n.b.367.2 | 24 | |||
184.45 | odd | 2 | 2208.2.n.b.367.24 | 24 | |||
184.91 | even | 2 | inner | 552.2.n.b.91.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.n.b.91.9 | ✓ | 24 | 8.3 | odd | 2 | inner | |
552.2.n.b.91.10 | yes | 24 | 184.91 | even | 2 | inner | |
552.2.n.b.91.11 | yes | 24 | 23.22 | odd | 2 | inner | |
552.2.n.b.91.12 | yes | 24 | 1.1 | even | 1 | trivial | |
2208.2.n.b.367.1 | 24 | 8.5 | even | 2 | |||
2208.2.n.b.367.2 | 24 | 92.91 | even | 2 | |||
2208.2.n.b.367.23 | 24 | 4.3 | odd | 2 | |||
2208.2.n.b.367.24 | 24 | 184.45 | odd | 2 |