Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(146,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 146.23 | ||
Character | \(\chi\) | \(=\) | 441.146 |
Dual form | 441.2.o.e.293.23 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23278 | + | 1.28910i | 1.57882 | + | 0.911529i | 0.995025 | + | 0.0996245i | \(0.0317642\pi\) |
0.583790 | + | 0.811905i | \(0.301569\pi\) | |||||||
\(3\) | −1.71146 | − | 0.266270i | −0.988113 | − | 0.153731i | ||||
\(4\) | 2.32354 | + | 4.02449i | 1.16177 | + | 2.01225i | ||||
\(5\) | 1.16595 | + | 2.01948i | 0.521427 | + | 0.903138i | 0.999689 | + | 0.0249208i | \(0.00793335\pi\) |
−0.478263 | + | 0.878217i | \(0.658733\pi\) | |||||||
\(6\) | −3.47807 | − | 2.80076i | −1.41992 | − | 1.14341i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.82470i | 2.41290i | ||||||||
\(9\) | 2.85820 | + | 0.911422i | 0.952734 | + | 0.303807i | ||||
\(10\) | 6.01207i | 1.90118i | ||||||||
\(11\) | −3.78114 | − | 2.18304i | −1.14006 | − | 0.658212i | −0.193612 | − | 0.981078i | \(-0.562020\pi\) |
−0.946444 | + | 0.322867i | \(0.895353\pi\) | |||||||
\(12\) | −2.90505 | − | 7.50646i | −0.838616 | − | 2.16693i | ||||
\(13\) | −1.14392 | + | 0.660445i | −0.317267 | + | 0.183174i | −0.650174 | − | 0.759785i | \(-0.725304\pi\) |
0.332906 | + | 0.942960i | \(0.391971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.45774 | − | 3.76671i | −0.376388 | − | 0.972561i | ||||
\(16\) | −4.15061 | + | 7.18908i | −1.03765 | + | 1.79727i | ||||
\(17\) | 5.78655 | 1.40344 | 0.701722 | − | 0.712451i | \(-0.252415\pi\) | ||||
0.701722 | + | 0.712451i | \(0.252415\pi\) | |||||||
\(18\) | 5.20683 | + | 5.71950i | 1.22726 | + | 1.34810i | ||||
\(19\) | 0.675357i | 0.154937i | 0.996995 | + | 0.0774687i | \(0.0246838\pi\) | ||||
−0.996995 | + | 0.0774687i | \(0.975316\pi\) | |||||||
\(20\) | −5.41825 | + | 9.38468i | −1.21156 | + | 2.09848i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.62830 | − | 9.74851i | −1.19996 | − | 2.07839i | ||||
\(23\) | −4.81799 | + | 2.78167i | −1.00462 | + | 0.580018i | −0.909612 | − | 0.415459i | \(-0.863621\pi\) |
−0.0950080 | + | 0.995477i | \(0.530288\pi\) | |||||||
\(24\) | 1.81721 | − | 11.6802i | 0.370937 | − | 2.38421i | ||||
\(25\) | −0.218858 | + | 0.379074i | −0.0437717 | + | 0.0758147i | ||||
\(26\) | −3.40551 | −0.667875 | ||||||||
\(27\) | −4.64902 | − | 2.32092i | −0.894704 | − | 0.446661i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.86926 | + | 2.23392i | 0.718503 | + | 0.414828i | 0.814202 | − | 0.580582i | \(-0.197175\pi\) |
−0.0956983 | + | 0.995410i | \(0.530508\pi\) | |||||||
\(30\) | 1.60083 | − | 10.2894i | 0.292271 | − | 1.87858i | ||||
\(31\) | 3.47965 | − | 2.00898i | 0.624964 | − | 0.360823i | −0.153835 | − | 0.988097i | \(-0.549162\pi\) |
0.778799 | + | 0.627273i | \(0.215829\pi\) | |||||||
\(32\) | −6.71411 | + | 3.87639i | −1.18690 | + | 0.685256i | ||||
\(33\) | 5.88999 | + | 4.74299i | 1.02532 | + | 0.825649i | ||||
\(34\) | 12.9201 | + | 7.45942i | 2.21578 | + | 1.27928i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.97314 | + | 13.6205i | 0.495523 | + | 2.27009i | ||||
\(37\) | 3.01658 | 0.495923 | 0.247961 | − | 0.968770i | \(-0.420239\pi\) | ||||
0.247961 | + | 0.968770i | \(0.420239\pi\) | |||||||
\(38\) | −0.870601 | + | 1.50792i | −0.141230 | + | 0.244618i | ||||
\(39\) | 2.13364 | − | 0.825733i | 0.341656 | − | 0.132223i | ||||
\(40\) | −13.7823 | + | 7.95723i | −2.17918 | + | 1.25815i | ||||
\(41\) | −3.29501 | − | 5.70713i | −0.514594 | − | 0.891303i | −0.999857 | − | 0.0169348i | \(-0.994609\pi\) |
0.485262 | − | 0.874369i | \(-0.338724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.89217 | − | 6.74143i | 0.593550 | − | 1.02806i | −0.400200 | − | 0.916428i | \(-0.631059\pi\) |
0.993750 | − | 0.111631i | \(-0.0356074\pi\) | |||||||
\(44\) | − | 20.2896i | − | 3.05877i | ||||||
\(45\) | 1.49191 | + | 6.83474i | 0.222401 | + | 1.01886i | ||||
\(46\) | −14.3434 | −2.11481 | ||||||||
\(47\) | 0.246705 | − | 0.427306i | 0.0359856 | − | 0.0623289i | −0.847472 | − | 0.530841i | \(-0.821876\pi\) |
0.883457 | + | 0.468512i | \(0.155210\pi\) | |||||||
\(48\) | 9.01785 | − | 11.1986i | 1.30161 | − | 1.61638i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.977326 | + | 0.564259i | −0.138215 | + | 0.0797983i | ||||
\(51\) | −9.90345 | − | 1.54078i | −1.38676 | − | 0.215753i | ||||
\(52\) | −5.31591 | − | 3.06914i | −0.737184 | − | 0.425614i | ||||
\(53\) | − | 4.14566i | − | 0.569451i | −0.958609 | − | 0.284725i | \(-0.908098\pi\) | ||
0.958609 | − | 0.284725i | \(-0.0919024\pi\) | |||||||
\(54\) | −7.38835 | − | 11.1751i | −1.00543 | − | 1.52074i | ||||
\(55\) | − | 10.1812i | − | 1.37284i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.179827 | − | 1.15585i | 0.0238187 | − | 0.153096i | ||||
\(58\) | 5.75947 | + | 9.97570i | 0.756256 | + | 1.30987i | ||||
\(59\) | 2.15699 | + | 3.73602i | 0.280816 | + | 0.486388i | 0.971586 | − | 0.236687i | \(-0.0760615\pi\) |
−0.690770 | + | 0.723075i | \(0.742728\pi\) | |||||||
\(60\) | 11.7720 | − | 14.6188i | 1.51976 | − | 1.88728i | ||||
\(61\) | 1.77661 | + | 1.02572i | 0.227471 | + | 0.131330i | 0.609405 | − | 0.792859i | \(-0.291408\pi\) |
−0.381934 | + | 0.924190i | \(0.624742\pi\) | |||||||
\(62\) | 10.3591 | 1.31560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.38572 | −0.423215 | ||||||||
\(65\) | −2.66751 | − | 1.54009i | −0.330863 | − | 0.191024i | ||||
\(66\) | 7.03689 | + | 18.1828i | 0.866181 | + | 2.23815i | ||||
\(67\) | 2.41218 | + | 4.17802i | 0.294695 | + | 0.510427i | 0.974914 | − | 0.222582i | \(-0.0714486\pi\) |
−0.680219 | + | 0.733009i | \(0.738115\pi\) | |||||||
\(68\) | 13.4453 | + | 23.2879i | 1.63048 | + | 2.82408i | ||||
\(69\) | 8.98648 | − | 3.47783i | 1.08184 | − | 0.418681i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.17135i | − | 0.139014i | −0.997581 | − | 0.0695068i | \(-0.977857\pi\) | ||
0.997581 | − | 0.0695068i | \(-0.0221426\pi\) | |||||||
\(72\) | −6.22018 | + | 19.5064i | −0.733055 | + | 2.29885i | ||||
\(73\) | − | 15.1153i | − | 1.76911i | −0.466432 | − | 0.884557i | \(-0.654461\pi\) | ||
0.466432 | − | 0.884557i | \(-0.345539\pi\) | |||||||
\(74\) | 6.73536 | + | 3.88866i | 0.782970 | + | 0.452048i | ||||
\(75\) | 0.475504 | − | 0.590495i | 0.0549064 | − | 0.0681844i | ||||
\(76\) | −2.71797 | + | 1.56922i | −0.311772 | + | 0.180002i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.82840 | + | 0.906785i | 0.659936 | + | 0.102673i | ||||
\(79\) | 5.30428 | − | 9.18728i | 0.596778 | − | 1.03365i | −0.396515 | − | 0.918028i | \(-0.629781\pi\) |
0.993293 | − | 0.115622i | \(-0.0368861\pi\) | |||||||
\(80\) | −19.3576 | −2.16424 | ||||||||
\(81\) | 7.33862 | + | 5.21005i | 0.815402 | + | 0.578895i | ||||
\(82\) | − | 16.9904i | − | 1.87627i | ||||||
\(83\) | −5.32432 | + | 9.22199i | −0.584420 | + | 1.01225i | 0.410527 | + | 0.911848i | \(0.365345\pi\) |
−0.994947 | + | 0.100397i | \(0.967989\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.74680 | + | 11.6858i | 0.731793 | + | 1.26750i | ||||
\(86\) | 17.3807 | − | 10.0348i | 1.87421 | − | 1.08208i | ||||
\(87\) | −6.02726 | − | 4.85353i | −0.646190 | − | 0.520353i | ||||
\(88\) | 14.8986 | − | 25.8051i | 1.58820 | − | 2.75084i | ||||
\(89\) | 3.32535 | 0.352486 | 0.176243 | − | 0.984347i | \(-0.443605\pi\) | ||||
0.176243 | + | 0.984347i | \(0.443605\pi\) | |||||||
\(90\) | −5.47953 | + | 17.1837i | −0.577593 | + | 1.81132i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −22.3896 | − | 12.9266i | −2.33428 | − | 1.34770i | ||||
\(93\) | −6.49022 | + | 2.51176i | −0.673005 | + | 0.260458i | ||||
\(94\) | 1.10168 | − | 0.636053i | 0.113629 | − | 0.0656039i | ||||
\(95\) | −1.36387 | + | 0.787429i | −0.139930 | + | 0.0807886i | ||||
\(96\) | 12.5231 | − | 4.84653i | 1.27813 | − | 0.494647i | ||||
\(97\) | −12.7531 | − | 7.36299i | −1.29488 | − | 0.747598i | −0.315363 | − | 0.948971i | \(-0.602126\pi\) |
−0.979515 | + | 0.201373i | \(0.935460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.81758 | − | 9.68578i | −0.886200 | − | 0.973458i | ||||
\(100\) | −2.03411 | −0.203411 | ||||||||
\(101\) | −0.832092 | + | 1.44123i | −0.0827963 | + | 0.143407i | −0.904450 | − | 0.426580i | \(-0.859718\pi\) |
0.821654 | + | 0.569987i | \(0.193052\pi\) | |||||||
\(102\) | −20.1260 | − | 16.2067i | −1.99277 | − | 1.60471i | ||||
\(103\) | 1.40783 | − | 0.812812i | 0.138718 | − | 0.0800887i | −0.429035 | − | 0.903288i | \(-0.641146\pi\) |
0.567753 | + | 0.823199i | \(0.307813\pi\) | |||||||
\(104\) | −4.50734 | − | 7.80694i | −0.441981 | − | 0.765533i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.34416 | − | 9.25636i | 0.519071 | − | 0.899057i | ||||
\(107\) | 18.3130i | 1.77039i | 0.465221 | + | 0.885194i | \(0.345975\pi\) | ||||
−0.465221 | + | 0.885194i | \(0.654025\pi\) | |||||||
\(108\) | −1.46167 | − | 24.1027i | −0.140650 | − | 2.31928i | ||||
\(109\) | −15.9736 | −1.52999 | −0.764995 | − | 0.644036i | \(-0.777259\pi\) | ||||
−0.764995 | + | 0.644036i | \(0.777259\pi\) | |||||||
\(110\) | 13.1246 | − | 22.7325i | 1.25138 | − | 2.16746i | ||||
\(111\) | −5.16276 | − | 0.803225i | −0.490027 | − | 0.0762387i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.07612 | + | 2.93070i | −0.477521 | + | 0.275697i | −0.719383 | − | 0.694614i | \(-0.755575\pi\) |
0.241862 | + | 0.970311i | \(0.422242\pi\) | |||||||
\(114\) | 1.89151 | − | 2.34894i | 0.177157 | − | 0.219998i | ||||
\(115\) | −11.2350 | − | 6.48654i | −1.04767 | − | 0.604873i | ||||
\(116\) | 20.7624i | 1.92774i | ||||||||
\(117\) | −3.87151 | + | 0.845087i | −0.357921 | + | 0.0781283i | ||||
\(118\) | 11.1223i | 1.02389i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 25.7067 | − | 9.94867i | 2.34669 | − | 0.908185i | ||||
\(121\) | 4.03134 | + | 6.98248i | 0.366485 | + | 0.634771i | ||||
\(122\) | 2.64451 | + | 4.58043i | 0.239423 | + | 0.414693i | ||||
\(123\) | 4.11965 | + | 10.6449i | 0.371456 | + | 0.959817i | ||||
\(124\) | 16.1702 | + | 9.33589i | 1.45213 | + | 0.838388i | ||||
\(125\) | 10.6387 | 0.951559 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.5710 | −1.47044 | −0.735218 | − | 0.677831i | \(-0.762920\pi\) | ||||
−0.735218 | + | 0.677831i | \(0.762920\pi\) | |||||||
\(128\) | 5.86864 | + | 3.38826i | 0.518719 | + | 0.299483i | ||||
\(129\) | −8.45633 | + | 10.5013i | −0.744539 | + | 0.924591i | ||||
\(130\) | −3.97064 | − | 6.87735i | −0.348248 | − | 0.603183i | ||||
\(131\) | −3.55989 | − | 6.16591i | −0.311029 | − | 0.538718i | 0.667556 | − | 0.744559i | \(-0.267340\pi\) |
−0.978585 | + | 0.205841i | \(0.934007\pi\) | |||||||
\(132\) | −5.40250 | + | 34.7248i | −0.470227 | + | 3.02241i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.4382i | 1.07449i | ||||||||
\(135\) | −0.733463 | − | 12.0946i | −0.0631264 | − | 1.04094i | ||||
\(136\) | 39.4914i | 3.38636i | ||||||||
\(137\) | −0.716584 | − | 0.413720i | −0.0612219 | − | 0.0353465i | 0.469077 | − | 0.883157i | \(-0.344587\pi\) |
−0.530298 | + | 0.847811i | \(0.677920\pi\) | |||||||
\(138\) | 24.5481 | + | 3.81920i | 2.08967 | + | 0.325112i | ||||
\(139\) | −12.0735 | + | 6.97062i | −1.02406 | + | 0.591241i | −0.915277 | − | 0.402825i | \(-0.868028\pi\) |
−0.108782 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.536005 | + | 0.665627i | −0.0451397 | + | 0.0560559i | ||||
\(142\) | 1.50998 | − | 2.61537i | 0.126715 | − | 0.219477i | ||||
\(143\) | 5.76711 | 0.482270 | ||||||||
\(144\) | −18.4156 | + | 16.7649i | −1.53463 | + | 1.39707i | ||||
\(145\) | 10.4185i | 0.865210i | ||||||||
\(146\) | 19.4851 | − | 33.7492i | 1.61260 | − | 2.79310i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.00915 | + | 12.1402i | 0.576149 | + | 0.997919i | ||||
\(149\) | −9.46916 | + | 5.46702i | −0.775744 | + | 0.447876i | −0.834920 | − | 0.550372i | \(-0.814486\pi\) |
0.0591761 | + | 0.998248i | \(0.481153\pi\) | |||||||
\(150\) | 1.82290 | − | 0.705475i | 0.148839 | − | 0.0576018i | ||||
\(151\) | 6.97277 | − | 12.0772i | 0.567436 | − | 0.982828i | −0.429383 | − | 0.903123i | \(-0.641269\pi\) |
0.996818 | − | 0.0797050i | \(-0.0253978\pi\) | |||||||
\(152\) | −4.60911 | −0.373848 | ||||||||
\(153\) | 16.5391 | + | 5.27399i | 1.33711 | + | 0.426376i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.11417 | + | 4.68472i | 0.651746 | + | 0.376286i | ||||
\(156\) | 8.28076 | + | 6.66819i | 0.662991 | + | 0.533882i | ||||
\(157\) | −13.6641 | + | 7.88894i | −1.09051 | + | 0.629606i | −0.933712 | − | 0.358024i | \(-0.883450\pi\) |
−0.156798 | + | 0.987631i | \(0.550117\pi\) | |||||||
\(158\) | 23.6866 | − | 13.6755i | 1.88440 | − | 1.08796i | ||||
\(159\) | −1.10387 | + | 7.09514i | −0.0875423 | + | 0.562681i | ||||
\(160\) | −15.6566 | − | 9.03932i | −1.23776 | − | 0.714621i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.66928 | + | 21.0931i | 0.759690 | + | 1.65723i | ||||
\(163\) | −6.76552 | −0.529916 | −0.264958 | − | 0.964260i | \(-0.585358\pi\) | ||||
−0.264958 | + | 0.964260i | \(0.585358\pi\) | |||||||
\(164\) | 15.3122 | − | 26.5215i | 1.19568 | − | 2.07098i | ||||
\(165\) | −2.71096 | + | 17.4248i | −0.211048 | + | 1.35652i | ||||
\(166\) | −23.7761 | + | 13.7271i | −1.84538 | + | 1.06543i | ||||
\(167\) | 9.54631 | + | 16.5347i | 0.738716 | + | 1.27949i | 0.953074 | + | 0.302738i | \(0.0979008\pi\) |
−0.214358 | + | 0.976755i | \(0.568766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.62763 | + | 9.74733i | −0.432894 | + | 0.749795i | ||||
\(170\) | 34.7891i | 2.66820i | ||||||||
\(171\) | −0.615535 | + | 1.93031i | −0.0470711 | + | 0.147614i | ||||
\(172\) | 36.1745 | 2.75828 | ||||||||
\(173\) | −10.9246 | + | 18.9219i | −0.830579 | + | 1.43860i | 0.0670016 | + | 0.997753i | \(0.478657\pi\) |
−0.897580 | + | 0.440851i | \(0.854677\pi\) | |||||||
\(174\) | −7.20089 | − | 18.6066i | −0.545898 | − | 1.41056i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 31.3881 | − | 18.1219i | 2.36597 | − | 1.36599i | ||||
\(177\) | −2.69682 | − | 6.96840i | −0.202705 | − | 0.523777i | ||||
\(178\) | 7.42478 | + | 4.28670i | 0.556511 | + | 0.321302i | ||||
\(179\) | − | 17.1896i | − | 1.28481i | −0.766364 | − | 0.642406i | \(-0.777936\pi\) | ||
0.766364 | − | 0.642406i | \(-0.222064\pi\) | |||||||
\(180\) | −24.0398 | + | 21.8850i | −1.79182 | + | 1.63121i | ||||
\(181\) | − | 16.6462i | − | 1.23730i | −0.785666 | − | 0.618650i | \(-0.787680\pi\) | ||
0.785666 | − | 0.618650i | \(-0.212320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.76747 | − | 2.22854i | −0.204577 | − | 0.164739i | ||||
\(184\) | −18.9840 | − | 32.8813i | −1.39952 | − | 2.42404i | ||||
\(185\) | 3.51717 | + | 6.09191i | 0.258587 | + | 0.447886i | ||||
\(186\) | −17.7292 | − | 2.75831i | −1.29996 | − | 0.202249i | ||||
\(187\) | −21.8797 | − | 12.6323i | −1.60000 | − | 0.923763i | ||||
\(188\) | 2.29292 | 0.167228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.06029 | −0.294565 | ||||||||
\(191\) | 0.826254 | + | 0.477038i | 0.0597857 | + | 0.0345173i | 0.529595 | − | 0.848251i | \(-0.322344\pi\) |
−0.469809 | + | 0.882768i | \(0.655677\pi\) | |||||||
\(192\) | 5.79453 | + | 0.901516i | 0.418184 | + | 0.0650613i | ||||
\(193\) | 0.847203 | + | 1.46740i | 0.0609830 | + | 0.105626i | 0.894905 | − | 0.446257i | \(-0.147243\pi\) |
−0.833922 | + | 0.551882i | \(0.813910\pi\) | |||||||
\(194\) | −18.9832 | − | 32.8799i | −1.36292 | − | 2.36064i | ||||
\(195\) | 4.15526 | + | 3.34607i | 0.297564 | + | 0.239617i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7486i | 0.908301i | 0.890925 | + | 0.454150i | \(0.150057\pi\) | ||||
−0.890925 | + | 0.454150i | \(0.849943\pi\) | |||||||
\(198\) | −7.20182 | − | 32.9929i | −0.511811 | − | 2.34471i | ||||
\(199\) | − | 4.35807i | − | 0.308935i | −0.987998 | − | 0.154468i | \(-0.950634\pi\) | ||
0.987998 | − | 0.154468i | \(-0.0493662\pi\) | |||||||
\(200\) | −2.58706 | − | 1.49364i | −0.182933 | − | 0.105616i | ||||
\(201\) | −3.01588 | − | 7.79282i | −0.212724 | − | 0.549663i | ||||
\(202\) | −3.71576 | + | 2.14530i | −0.261440 | + | 0.150942i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.8102 | − | 43.4365i | −1.17695 | − | 3.04116i | ||||
\(205\) | 7.68361 | − | 13.3084i | 0.536646 | − | 0.929499i | ||||
\(206\) | 4.19117 | 0.292013 | ||||||||
\(207\) | −16.3060 | + | 3.55934i | −1.13335 | + | 0.247391i | ||||
\(208\) | − | 10.9650i | − | 0.760287i | ||||||
\(209\) | 1.47433 | − | 2.55362i | 0.101982 | − | 0.176637i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.24368 | − | 3.88617i | −0.154461 | − | 0.267535i | 0.778401 | − | 0.627767i | \(-0.216031\pi\) |
−0.932863 | + | 0.360232i | \(0.882698\pi\) | |||||||
\(212\) | 16.6842 | − | 9.63263i | 1.14588 | − | 0.661571i | ||||
\(213\) | −0.311895 | + | 2.00472i | −0.0213707 | + | 0.137361i | ||||
\(214\) | −23.6073 | + | 40.8890i | −1.61376 | + | 2.79512i | ||||
\(215\) | 18.1522 | 1.23797 | ||||||||
\(216\) | 15.8396 | − | 31.7281i | 1.07775 | − | 2.15883i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −35.6655 | − | 20.5915i | −2.41557 | − | 1.39463i | ||||
\(219\) | −4.02476 | + | 25.8693i | −0.271968 | + | 1.74808i | ||||
\(220\) | 40.9743 | − | 23.6565i | 2.76249 | − | 1.59492i | ||||
\(221\) | −6.61937 | + | 3.82170i | −0.445267 | + | 0.257075i | ||||
\(222\) | −10.4919 | − | 8.44872i | −0.704169 | − | 0.567041i | ||||
\(223\) | 18.0005 | + | 10.3926i | 1.20540 | + | 0.695939i | 0.961751 | − | 0.273924i | \(-0.0883218\pi\) |
0.243650 | + | 0.969863i | \(0.421655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.971037 | + | 0.883997i | −0.0647358 | + | 0.0589331i | ||||
\(226\) | −15.1118 | −1.00522 | ||||||||
\(227\) | 14.1579 | − | 24.5223i | 0.939696 | − | 1.62760i | 0.173657 | − | 0.984806i | \(-0.444442\pi\) |
0.766039 | − | 0.642795i | \(-0.222225\pi\) | |||||||
\(228\) | 5.06954 | − | 1.96195i | 0.335738 | − | 0.129933i | ||||
\(229\) | 18.8670 | − | 10.8929i | 1.24677 | − | 0.719821i | 0.276303 | − | 0.961071i | \(-0.410891\pi\) |
0.970463 | + | 0.241250i | \(0.0775573\pi\) | |||||||
\(230\) | −16.7236 | − | 28.9661i | −1.10272 | − | 1.90997i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.2458 | + | 26.4065i | −1.00094 | + | 1.73367i | ||||
\(233\) | − | 15.2335i | − | 0.997978i | −0.866608 | − | 0.498989i | \(-0.833705\pi\) | ||
0.866608 | − | 0.498989i | \(-0.166295\pi\) | |||||||
\(234\) | −9.73363 | − | 3.10386i | −0.636307 | − | 0.202905i | ||||
\(235\) | 1.15058 | 0.0750554 | ||||||||
\(236\) | −10.0237 | + | 17.3616i | −0.652489 | + | 1.13014i | ||||
\(237\) | −11.5244 | + | 14.3113i | −0.748588 | + | 0.929619i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.95125 | + | 2.85861i | −0.320270 | + | 0.184908i | −0.651513 | − | 0.758638i | \(-0.725865\pi\) |
0.331243 | + | 0.943545i | \(0.392532\pi\) | |||||||
\(240\) | 33.1297 | + | 5.15434i | 2.13851 | + | 0.332711i | ||||
\(241\) | −3.87212 | − | 2.23557i | −0.249425 | − | 0.144006i | 0.370076 | − | 0.929002i | \(-0.379332\pi\) |
−0.619501 | + | 0.784996i | \(0.712665\pi\) | |||||||
\(242\) | 20.7871i | 1.33625i | ||||||||
\(243\) | −11.1725 | − | 10.8709i | −0.716715 | − | 0.697366i | ||||
\(244\) | 9.53325i | 0.610304i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.52402 | + | 29.0783i | −0.288441 | + | 1.85397i | ||||
\(247\) | −0.446036 | − | 0.772557i | −0.0283806 | − | 0.0491566i | ||||
\(248\) | 13.7107 | + | 23.7476i | 0.870629 | + | 1.50797i | ||||
\(249\) | 11.5679 | − | 14.3654i | 0.733086 | − | 0.910369i | ||||
\(250\) | 23.7540 | + | 13.7144i | 1.50234 | + | 0.867374i | ||||
\(251\) | −11.6265 | −0.733861 | −0.366931 | − | 0.930248i | \(-0.619591\pi\) | ||||
−0.366931 | + | 0.930248i | \(0.619591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.2900 | 1.52710 | ||||||||
\(254\) | −36.9993 | − | 21.3616i | −2.32155 | − | 1.34034i | ||||
\(255\) | −8.43531 | − | 21.7963i | −0.528240 | − | 1.36494i | ||||
\(256\) | 12.1213 | + | 20.9947i | 0.757582 | + | 1.31217i | ||||
\(257\) | 1.05140 | + | 1.82108i | 0.0655846 | + | 0.113596i | 0.896953 | − | 0.442126i | \(-0.145775\pi\) |
−0.831369 | + | 0.555721i | \(0.812442\pi\) | |||||||
\(258\) | −32.4184 | + | 12.5461i | −2.01828 | + | 0.781089i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 14.3138i | − | 0.887705i | ||||||
\(261\) | 9.02308 | + | 9.91151i | 0.558514 | + | 0.613507i | ||||
\(262\) | − | 18.3562i | − | 1.13405i | ||||||
\(263\) | −1.90773 | − | 1.10143i | −0.117636 | − | 0.0679170i | 0.440028 | − | 0.897984i | \(-0.354969\pi\) |
−0.557663 | + | 0.830067i | \(0.688302\pi\) | |||||||
\(264\) | −32.3695 | + | 40.1974i | −1.99221 | + | 2.47398i | ||||
\(265\) | 8.37207 | − | 4.83362i | 0.514292 | − | 0.296927i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.69121 | − | 0.885441i | −0.348296 | − | 0.0541881i | ||||
\(268\) | −11.2096 | + | 19.4156i | −0.684737 | + | 1.18600i | ||||
\(269\) | −27.8623 | −1.69880 | −0.849398 | − | 0.527753i | \(-0.823035\pi\) | ||||
−0.849398 | + | 0.527753i | \(0.823035\pi\) | |||||||
\(270\) | 13.9535 | − | 27.9502i | 0.849183 | − | 1.70100i | ||||
\(271\) | − | 11.4804i | − | 0.697382i | −0.937238 | − | 0.348691i | \(-0.886626\pi\) | ||
0.937238 | − | 0.348691i | \(-0.113374\pi\) | |||||||
\(272\) | −24.0177 | + | 41.5999i | −1.45629 | + | 2.52237i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.06665 | − | 1.84749i | −0.0644387 | − | 0.111611i | ||||
\(275\) | 1.65507 | − | 0.955553i | 0.0998043 | − | 0.0576220i | ||||
\(276\) | 34.8770 | + | 28.0851i | 2.09935 | + | 1.69053i | ||||
\(277\) | 5.10000 | − | 8.83346i | 0.306429 | − | 0.530751i | −0.671149 | − | 0.741322i | \(-0.734199\pi\) |
0.977579 | + | 0.210571i | \(0.0675323\pi\) | |||||||
\(278\) | −35.9432 | −2.15573 | ||||||||
\(279\) | 11.7766 | − | 2.57063i | 0.705045 | − | 0.153900i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.45116 | + | 5.45663i | 0.563809 | + | 0.325515i | 0.754673 | − | 0.656101i | \(-0.227796\pi\) |
−0.190864 | + | 0.981617i | \(0.561129\pi\) | |||||||
\(282\) | −2.05484 | + | 0.795237i | −0.122364 | + | 0.0473557i | ||||
\(283\) | 10.2766 | − | 5.93322i | 0.610882 | − | 0.352693i | −0.162428 | − | 0.986720i | \(-0.551933\pi\) |
0.773311 | + | 0.634027i | \(0.218599\pi\) | |||||||
\(284\) | 4.71409 | − | 2.72168i | 0.279730 | − | 0.161502i | ||||
\(285\) | 2.54388 | − | 0.984498i | 0.150686 | − | 0.0583166i | ||||
\(286\) | 12.8767 | + | 7.43437i | 0.761415 | + | 0.439603i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −22.7233 | + | 4.96012i | −1.33898 | + | 0.292278i | ||||
\(289\) | 16.4841 | 0.969655 | ||||||||
\(290\) | −13.4305 | + | 23.2622i | −0.788664 | + | 1.36601i | ||||
\(291\) | 19.8658 | + | 15.9972i | 1.16456 | + | 0.937774i | ||||
\(292\) | 60.8315 | − | 35.1211i | 3.55989 | − | 2.05531i | ||||
\(293\) | 9.55012 | + | 16.5413i | 0.557924 | + | 0.966353i | 0.997670 | + | 0.0682302i | \(0.0217352\pi\) |
−0.439746 | + | 0.898122i | \(0.644931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.02987 | + | 8.71199i | −0.292850 | + | 0.507232i | ||||
\(296\) | 20.5872i | 1.19661i | ||||||||
\(297\) | 12.5119 | + | 18.9247i | 0.726015 | + | 1.09812i | ||||
\(298\) | −28.1901 | −1.63301 | ||||||||
\(299\) | 3.67427 | − | 6.36403i | 0.212489 | − | 0.368041i | ||||
\(300\) | 3.48129 | + | 0.541622i | 0.200993 | + | 0.0312705i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 31.1373 | − | 17.9772i | 1.79175 | − | 1.03447i | ||||
\(303\) | 1.80785 | − | 2.24504i | 0.103858 | − | 0.128974i | ||||
\(304\) | −4.85519 | − | 2.80315i | −0.278464 | − | 0.160771i | ||||
\(305\) | 4.78375i | 0.273917i | ||||||||
\(306\) | 30.1296 | + | 33.0962i | 1.72239 | + | 1.89198i | ||||
\(307\) | − | 2.35488i | − | 0.134400i | −0.997740 | − | 0.0672001i | \(-0.978593\pi\) | ||
0.997740 | − | 0.0672001i | \(-0.0214066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.62588 | + | 1.01623i | −0.149381 | + | 0.0578114i | ||||
\(310\) | 12.0781 | + | 20.9199i | 0.685991 | + | 1.18817i | ||||
\(311\) | 3.92483 | + | 6.79801i | 0.222557 | + | 0.385480i | 0.955584 | − | 0.294720i | \(-0.0952263\pi\) |
−0.733027 | + | 0.680200i | \(0.761893\pi\) | |||||||
\(312\) | 5.63538 | + | 14.5614i | 0.319041 | + | 0.824379i | ||||
\(313\) | −26.0268 | − | 15.0266i | −1.47112 | − | 0.849352i | −0.471647 | − | 0.881787i | \(-0.656340\pi\) |
−0.999474 | + | 0.0324349i | \(0.989674\pi\) | |||||||
\(314\) | −40.6785 | −2.29562 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 49.2989 | 2.77328 | ||||||||
\(317\) | −9.61906 | − | 5.55356i | −0.540260 | − | 0.311919i | 0.204924 | − | 0.978778i | \(-0.434305\pi\) |
−0.745184 | + | 0.666859i | \(0.767639\pi\) | |||||||
\(318\) | −11.6110 | + | 14.4189i | −0.651114 | + | 0.808573i | ||||
\(319\) | −9.75347 | − | 16.8935i | −0.546089 | − | 0.945854i | ||||
\(320\) | −3.94757 | − | 6.83739i | −0.220676 | − | 0.382222i | ||||
\(321\) | 4.87621 | − | 31.3421i | 0.272164 | − | 1.74934i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.90798i | 0.217446i | ||||||||
\(324\) | −3.91622 | + | 41.6400i | −0.217568 | + | 2.31333i | ||||
\(325\) | − | 0.578175i | − | 0.0320714i | ||||||
\(326\) | −15.1059 | − | 8.72141i | −0.836640 | − | 0.483034i | ||||
\(327\) | 27.3381 | + | 4.25328i | 1.51180 | + | 0.235207i | ||||
\(328\) | 38.9494 | − | 22.4875i | 2.15062 | − | 1.24166i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −28.5152 | + | 35.4110i | −1.56971 | + | 1.94931i | ||||
\(331\) | 8.63362 | − | 14.9539i | 0.474547 | − | 0.821939i | −0.525028 | − | 0.851085i | \(-0.675945\pi\) |
0.999575 | + | 0.0291457i | \(0.00927866\pi\) | |||||||
\(332\) | −49.4851 | −2.71585 | ||||||||
\(333\) | 8.62199 | + | 2.74938i | 0.472482 | + | 0.150665i | ||||
\(334\) | 49.2245i | 2.69345i | ||||||||
\(335\) | −5.62495 | + | 9.74270i | −0.307324 | + | 0.532300i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.82962 | − | 6.63309i | −0.208612 | − | 0.361327i | 0.742665 | − | 0.669663i | \(-0.233561\pi\) |
−0.951278 | + | 0.308336i | \(0.900228\pi\) | |||||||
\(338\) | −25.1305 | + | 14.5091i | −1.36692 | + | 0.789192i | ||||
\(339\) | 9.46794 | − | 3.66416i | 0.514228 | − | 0.199010i | ||||
\(340\) | −31.3530 | + | 54.3049i | −1.70035 | + | 2.94510i | ||||
\(341\) | −17.5427 | −0.949992 | ||||||||
\(342\) | −3.86271 | + | 3.51647i | −0.208871 | + | 0.190149i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 46.0082 | + | 26.5629i | 2.48060 | + | 1.43217i | ||||
\(345\) | 17.5011 | + | 14.0930i | 0.942230 | + | 0.758743i | ||||
\(346\) | −48.7843 | + | 28.1656i | −2.62266 | + | 1.51419i | ||||
\(347\) | −11.4014 | + | 6.58262i | −0.612061 | + | 0.353374i | −0.773772 | − | 0.633465i | \(-0.781632\pi\) |
0.161711 | + | 0.986838i | \(0.448299\pi\) | |||||||
\(348\) | 5.52841 | − | 35.5341i | 0.296354 | − | 1.90483i | ||||
\(349\) | −1.05185 | − | 0.607283i | −0.0563040 | − | 0.0325071i | 0.471584 | − | 0.881821i | \(-0.343682\pi\) |
−0.527888 | + | 0.849314i | \(0.677016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.85096 | − | 0.415467i | 0.365677 | − | 0.0221760i | ||||
\(352\) | 33.8493 | 1.80417 | ||||||||
\(353\) | −13.4114 | + | 23.2292i | −0.713816 | + | 1.23637i | 0.249598 | + | 0.968349i | \(0.419701\pi\) |
−0.963414 | + | 0.268016i | \(0.913632\pi\) | |||||||
\(354\) | 2.96153 | − | 19.0354i | 0.157404 | − | 1.01172i | ||||
\(355\) | 2.36551 | − | 1.36573i | 0.125548 | − | 0.0724854i | ||||
\(356\) | 7.72659 | + | 13.3829i | 0.409509 | + | 0.709290i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.1591 | − | 38.3807i | 1.17114 | − | 2.02848i | ||||
\(359\) | − | 7.45024i | − | 0.393208i | −0.980483 | − | 0.196604i | \(-0.937009\pi\) | ||
0.980483 | − | 0.196604i | \(-0.0629914\pi\) | |||||||
\(360\) | −46.6450 | + | 10.1818i | −2.45841 | + | 0.536630i | ||||
\(361\) | 18.5439 | 0.975994 | ||||||||
\(362\) | 21.4585 | − | 37.1673i | 1.12784 | − | 1.95347i | ||||
\(363\) | −5.04025 | − | 13.0237i | −0.264545 | − | 0.683565i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.5250 | − | 17.6236i | 1.59775 | − | 0.922463i | ||||
\(366\) | −3.30635 | − | 8.54339i | −0.172826 | − | 0.446570i | ||||
\(367\) | 30.3000 | + | 17.4937i | 1.58165 | + | 0.913166i | 0.994619 | + | 0.103601i | \(0.0330365\pi\) |
0.587031 | + | 0.809565i | \(0.300297\pi\) | |||||||
\(368\) | − | 46.1825i | − | 2.40743i | ||||||
\(369\) | −4.21620 | − | 19.3153i | −0.219487 | − | 1.00551i | ||||
\(370\) | 18.1359i | 0.942840i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −25.1889 | − | 20.2837i | −1.30598 | − | 1.05166i | ||||
\(373\) | 15.0495 | + | 26.0665i | 0.779233 | + | 1.34967i | 0.932384 | + | 0.361469i | \(0.117725\pi\) |
−0.153151 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(374\) | −32.5684 | − | 56.4102i | −1.68407 | − | 2.91690i | ||||
\(375\) | −18.2078 | − | 2.83278i | −0.940247 | − | 0.146284i | ||||
\(376\) | 2.91623 | + | 1.68369i | 0.150393 | + | 0.0868295i | ||||
\(377\) | −5.90152 | −0.303944 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0996 | −1.39201 | −0.696006 | − | 0.718036i | \(-0.745041\pi\) | ||||
−0.696006 | + | 0.718036i | \(0.745041\pi\) | |||||||
\(380\) | −6.33801 | − | 3.65925i | −0.325133 | − | 0.187716i | ||||
\(381\) | 28.3606 | + | 4.41235i | 1.45296 | + | 0.226052i | ||||
\(382\) | 1.22990 | + | 2.13024i | 0.0629270 | + | 0.108993i | ||||
\(383\) | 1.83015 | + | 3.16992i | 0.0935164 | + | 0.161975i | 0.908988 | − | 0.416821i | \(-0.136856\pi\) |
−0.815472 | + | 0.578796i | \(0.803523\pi\) | |||||||
\(384\) | −9.14176 | − | 7.36152i | −0.466513 | − | 0.375666i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.36851i | 0.222351i | ||||||||
\(387\) | 17.2689 | − | 15.7210i | 0.877827 | − | 0.799141i | ||||
\(388\) | − | 68.4329i | − | 3.47415i | ||||||
\(389\) | 10.5387 | + | 6.08449i | 0.534331 | + | 0.308496i | 0.742778 | − | 0.669537i | \(-0.233508\pi\) |
−0.208447 | + | 0.978034i | \(0.566841\pi\) | |||||||
\(390\) | 4.96436 | + | 12.8276i | 0.251380 | + | 0.649550i | ||||
\(391\) | −27.8795 | + | 16.0962i | −1.40993 | + | 0.814022i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.45082 | + | 11.5006i | 0.224514 | + | 0.580129i | ||||
\(394\) | −16.4342 | + | 28.4649i | −0.827943 | + | 1.43404i | ||||
\(395\) | 24.7380 | 1.24470 | ||||||||
\(396\) | 18.4923 | − | 57.9916i | 0.929275 | − | 2.91419i | ||||
\(397\) | 26.7741i | 1.34375i | 0.740663 | + | 0.671876i | \(0.234511\pi\) | ||||
−0.740663 | + | 0.671876i | \(0.765489\pi\) | |||||||
\(398\) | 5.61797 | − | 9.73061i | 0.281603 | − | 0.487752i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.81679 | − | 3.14678i | −0.0908397 | − | 0.157339i | ||||
\(401\) | 6.69428 | − | 3.86494i | 0.334296 | − | 0.193006i | −0.323451 | − | 0.946245i | \(-0.604843\pi\) |
0.657747 | + | 0.753239i | \(0.271510\pi\) | |||||||
\(402\) | 3.31191 | − | 21.2874i | 0.165183 | − | 1.06172i | ||||
\(403\) | −2.65364 | + | 4.59624i | −0.132187 | + | 0.228955i | ||||
\(404\) | −7.73361 | −0.384761 | ||||||||
\(405\) | −1.96515 | + | 20.8948i | −0.0976490 | + | 1.03827i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4061 | − | 6.58532i | −0.565380 | − | 0.326422i | ||||
\(408\) | 10.5154 | − | 67.5881i | 0.520589 | − | 3.34611i | ||||
\(409\) | −7.84660 | + | 4.53024i | −0.387989 | + | 0.224006i | −0.681289 | − | 0.732015i | \(-0.738580\pi\) |
0.293299 | + | 0.956021i | \(0.405247\pi\) | |||||||
\(410\) | 34.3116 | − | 19.8098i | 1.69453 | − | 0.978338i | ||||
\(411\) | 1.11624 | + | 0.898870i | 0.0550603 | + | 0.0443380i | ||||
\(412\) | 6.54231 | + | 3.77720i | 0.322316 | + | 0.186090i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −40.9962 | − | 13.0728i | −2.01485 | − | 0.642495i | ||||
\(415\) | −24.8315 | −1.21893 | ||||||||
\(416\) | 5.12029 | − | 8.86860i | 0.251043 | − | 0.434819i | ||||
\(417\) | 22.5194 | − | 8.71515i | 1.10278 | − | 0.426783i | ||||
\(418\) | 6.58372 | − | 3.80111i | 0.322020 | − | 0.185919i | ||||
\(419\) | −3.30466 | − | 5.72384i | −0.161443 | − | 0.279628i | 0.773943 | − | 0.633255i | \(-0.218282\pi\) |
−0.935386 | + | 0.353627i | \(0.884948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.39209 | − | 11.0714i | 0.311531 | − | 0.539588i | −0.667163 | − | 0.744912i | \(-0.732491\pi\) |
0.978694 | + | 0.205324i | \(0.0658248\pi\) | |||||||
\(422\) | − | 11.5693i | − | 0.563184i | ||||||
\(423\) | 1.09459 | − | 0.996473i | 0.0532207 | − | 0.0484502i | ||||
\(424\) | 28.2929 | 1.37403 | ||||||||
\(425\) | −1.26643 | + | 2.19353i | −0.0614311 | + | 0.106402i | ||||
\(426\) | −3.28067 | + | 4.07404i | −0.158949 | + | 0.197388i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −73.7007 | + | 42.5511i | −3.56246 | + | 2.05679i | ||||
\(429\) | −9.87019 | − | 1.53561i | −0.476537 | − | 0.0741399i | ||||
\(430\) | 40.5299 | + | 23.4000i | 1.95453 | + | 1.12845i | ||||
\(431\) | − | 21.9112i | − | 1.05542i | −0.849424 | − | 0.527712i | \(-0.823050\pi\) | ||
0.849424 | − | 0.527712i | \(-0.176950\pi\) | |||||||
\(432\) | 35.9815 | − | 23.7889i | 1.73116 | − | 1.14454i | ||||
\(433\) | − | 8.21181i | − | 0.394635i | −0.980340 | − | 0.197317i | \(-0.936777\pi\) | ||
0.980340 | − | 0.197317i | \(-0.0632229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.77414 | − | 17.8309i | 0.133010 | − | 0.854925i | ||||
\(436\) | −37.1153 | − | 64.2855i | −1.77750 | − | 3.07872i | ||||
\(437\) | −1.87862 | − | 3.25386i | −0.0898665 | − | 0.155653i | ||||
\(438\) | −42.3344 | + | 52.5722i | −2.02282 | + | 2.51199i | ||||
\(439\) | 32.7996 | + | 18.9368i | 1.56544 | + | 0.903806i | 0.996690 | + | 0.0812949i | \(0.0259056\pi\) |
0.568749 | + | 0.822511i | \(0.307428\pi\) | |||||||
\(440\) | 69.4838 | 3.31251 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.7061 | −0.937326 | ||||||||
\(443\) | 17.7210 | + | 10.2312i | 0.841950 | + | 0.486100i | 0.857926 | − | 0.513773i | \(-0.171752\pi\) |
−0.0159769 | + | 0.999872i | \(0.505086\pi\) | |||||||
\(444\) | −8.76332 | − | 22.6438i | −0.415889 | − | 1.07463i | ||||
\(445\) | 3.87718 | + | 6.71547i | 0.183796 | + | 0.318344i | ||||
\(446\) | 26.7941 | + | 46.4087i | 1.26874 | + | 2.19752i | ||||
\(447\) | 17.6618 | − | 6.83524i | 0.835375 | − | 0.323296i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 35.7054i | − | 1.68504i | −0.538665 | − | 0.842520i | \(-0.681071\pi\) | ||
0.538665 | − | 0.842520i | \(-0.318929\pi\) | |||||||
\(450\) | −3.30767 | + | 0.722010i | −0.155925 | + | 0.0340359i | ||||
\(451\) | 28.7726i | 1.35485i | ||||||||
\(452\) | −23.5892 | − | 13.6192i | −1.10954 | − | 0.640594i | ||||
\(453\) | −15.1494 | + | 18.8130i | −0.711782 | + | 0.883912i | ||||
\(454\) | 63.2232 | − | 36.5019i | 2.96721 | − | 1.71312i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.88831 | + | 1.22727i | 0.369404 | + | 0.0574720i | ||||
\(457\) | 0.127090 | − | 0.220126i | 0.00594501 | − | 0.0102971i | −0.863038 | − | 0.505140i | \(-0.831441\pi\) |
0.868983 | + | 0.494843i | \(0.164774\pi\) | |||||||
\(458\) | 56.1678 | 2.62455 | ||||||||
\(459\) | −26.9018 | − | 13.4301i | −1.25567 | − | 0.626863i | ||||
\(460\) | − | 60.2870i | − | 2.81090i | ||||||
\(461\) | −12.2175 | + | 21.1613i | −0.569025 | + | 0.985581i | 0.427637 | + | 0.903950i | \(0.359346\pi\) |
−0.996663 | + | 0.0816304i | \(0.973987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.409986 | + | 0.710116i | 0.0190536 | + | 0.0330019i | 0.875395 | − | 0.483408i | \(-0.160601\pi\) |
−0.856341 | + | 0.516410i | \(0.827268\pi\) | |||||||
\(464\) | −32.1196 | + | 18.5443i | −1.49112 | + | 0.860896i | ||||
\(465\) | −12.6397 | − | 10.1783i | −0.586152 | − | 0.472006i | ||||
\(466\) | 19.6374 | − | 34.0130i | 0.909686 | − | 1.57562i | ||||
\(467\) | −1.81925 | −0.0841848 | −0.0420924 | − | 0.999114i | \(-0.513402\pi\) | ||||
−0.0420924 | + | 0.999114i | \(0.513402\pi\) | |||||||
\(468\) | −12.3967 | − | 13.6173i | −0.573036 | − | 0.629458i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.56899 | + | 1.48321i | 0.118499 | + | 0.0684152i | ||||
\(471\) | 25.4861 | − | 9.86330i | 1.17434 | − | 0.454477i | ||||
\(472\) | −25.4972 | + | 14.7208i | −1.17360 | + | 0.677581i | ||||
\(473\) | −29.4336 | + | 16.9935i | −1.35336 | + | 0.781363i | ||||
\(474\) | −44.1801 | + | 17.0980i | −2.02926 | + | 0.785337i | ||||
\(475\) | −0.256010 | − | 0.147807i | −0.0117465 | − | 0.00678187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.77845 | − | 11.8491i | 0.173003 | − | 0.542535i | ||||
\(478\) | −14.7401 | −0.674196 | ||||||||
\(479\) | −0.681074 | + | 1.17965i | −0.0311191 | + | 0.0538998i | −0.881166 | − | 0.472808i | \(-0.843240\pi\) |
0.850046 | + | 0.526708i | \(0.176574\pi\) | |||||||
\(480\) | 24.3887 | + | 19.6393i | 1.11319 | + | 0.896409i | ||||
\(481\) | −3.45074 | + | 1.99228i | −0.157340 | + | 0.0908403i | ||||
\(482\) | −5.76373 | − | 9.98308i | −0.262531 | − | 0.454717i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.7340 | + | 32.4482i | −0.851544 | + | 1.47492i | ||||
\(485\) | − | 34.3394i | − | 1.55927i | ||||||
\(486\) | −10.9321 | − | 38.6747i | −0.495892 | − | 1.75432i | ||||
\(487\) | 31.6121 | 1.43248 | 0.716241 | − | 0.697853i | \(-0.245861\pi\) | ||||
0.716241 | + | 0.697853i | \(0.245861\pi\) | |||||||
\(488\) | −7.00026 | + | 12.1248i | −0.316887 | + | 0.548864i | ||||
\(489\) | 11.5789 | + | 1.80145i | 0.523617 | + | 0.0814646i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97415 | + | 1.13977i | −0.0890919 | + | 0.0514373i | −0.543884 | − | 0.839160i | \(-0.683047\pi\) |
0.454792 | + | 0.890598i | \(0.349714\pi\) | |||||||
\(492\) | −33.2681 | + | 41.3133i | −1.49984 | + | 1.86255i | ||||
\(493\) | 22.3897 | + | 12.9267i | 1.00838 | + | 0.582188i | ||||
\(494\) | − | 2.29993i | − | 0.103479i | ||||||
\(495\) | 9.27939 | − | 29.1000i | 0.417078 | − | 1.30795i | ||||
\(496\) | 33.3540i | 1.49764i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 44.3470 | − | 17.1626i | 1.98724 | − | 0.769074i | ||||
\(499\) | −13.5195 | − | 23.4164i | −0.605215 | − | 1.04826i | −0.992017 | − | 0.126101i | \(-0.959754\pi\) |
0.386802 | − | 0.922163i | \(-0.373580\pi\) | |||||||
\(500\) | 24.7196 | + | 42.8156i | 1.10549 | + | 1.91477i | ||||
\(501\) | −11.9355 | − | 30.8404i | −0.533237 | − | 1.37785i | ||||
\(502\) | −25.9595 | − | 14.9877i | −1.15863 | − | 0.668936i | ||||
\(503\) | −0.276948 | −0.0123485 | −0.00617426 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617426 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.88070 | −0.172689 | ||||||||
\(506\) | 54.2342 | + | 31.3121i | 2.41100 | + | 1.39199i | ||||
\(507\) | 12.2269 | − | 15.1837i | 0.543015 | − | 0.674333i | ||||
\(508\) | −38.5033 | − | 66.6897i | −1.70831 | − | 2.95888i | ||||
\(509\) | −9.21476 | − | 15.9604i | −0.408437 | − | 0.707434i | 0.586278 | − | 0.810110i | \(-0.300593\pi\) |
−0.994715 | + | 0.102676i | \(0.967259\pi\) | |||||||
\(510\) | 9.26330 | − | 59.5402i | 0.410186 | − | 2.63649i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 48.9492i | 2.16327i | ||||||||
\(513\) | 1.56745 | − | 3.13974i | 0.0692045 | − | 0.138623i | ||||
\(514\) | 5.42143i | 0.239129i | ||||||||
\(515\) | 3.28291 | + | 1.89539i | 0.144662 | + | 0.0835208i | ||||
\(516\) | −61.9112 | − | 9.63217i | −2.72549 | − | 0.424033i | ||||
\(517\) | −1.86565 | + | 1.07713i | −0.0820512 | + | 0.0473723i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.7353 | − | 29.4752i | 1.04186 | − | 1.29382i | ||||
\(520\) | 10.5106 | − | 18.2049i | 0.460921 | − | 0.798339i | ||||
\(521\) | −23.2527 | −1.01872 | −0.509360 | − | 0.860554i | \(-0.670118\pi\) | ||||
−0.509360 | + | 0.860554i | \(0.670118\pi\) | |||||||
\(522\) | 7.36966 | + | 33.7619i | 0.322561 | + | 1.47772i | ||||
\(523\) | 13.3052i | 0.581798i | 0.956754 | + | 0.290899i | \(0.0939543\pi\) | ||||
−0.956754 | + | 0.290899i | \(0.906046\pi\) | |||||||
\(524\) | 16.5431 | − | 28.6535i | 0.722689 | − | 1.25173i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.83970 | − | 4.91850i | −0.123817 | − | 0.214457i | ||||
\(527\) | 20.1352 | − | 11.6251i | 0.877102 | − | 0.506395i | ||||
\(528\) | −58.5448 | + | 22.6573i | −2.54784 | + | 0.986031i | ||||
\(529\) | 3.97534 | − | 6.88549i | 0.172841 | − | 0.299369i | ||||
\(530\) | 24.9240 | 1.08263 | ||||||||
\(531\) | 2.76003 | + | 12.6442i | 0.119775 | + | 0.548712i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.53848 | + | 4.35235i | 0.326528 | + | 0.188521i | ||||
\(534\) | −11.5658 | − | 9.31352i | −0.500501 | − | 0.403035i | ||||
\(535\) | −36.9828 | + | 21.3520i | −1.59890 | + | 0.923128i | ||||
\(536\) | −28.5138 | + | 16.4624i | −1.23161 | + | 0.711069i | ||||
\(537\) | −4.57708 | + | 29.4194i | −0.197516 | + | 1.26954i | ||||
\(538\) | −62.2105 | − | 35.9172i | −2.68208 | − | 1.54850i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 46.9706 | − | 31.0542i | 2.02129 | − | 1.33636i | ||||
\(541\) | −30.1692 | −1.29707 | −0.648537 | − | 0.761183i | \(-0.724619\pi\) | ||||
−0.648537 | + | 0.761183i | \(0.724619\pi\) | |||||||
\(542\) | 14.7993 | − | 25.6331i | 0.635684 | − | 1.10104i | ||||
\(543\) | −4.43238 | + | 28.4893i | −0.190212 | + | 1.22259i | ||||
\(544\) | −38.8515 | + | 22.4309i | −1.66574 | + | 0.961718i | ||||
\(545\) | −18.6243 | − | 32.2582i | −0.797778 | − | 1.38179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.572061 | + | 0.990840i | −0.0244596 | + | 0.0423652i | −0.877996 | − | 0.478668i | \(-0.841120\pi\) |
0.853537 | + | 0.521033i | \(0.174453\pi\) | |||||||
\(548\) | − | 3.84518i | − | 0.164258i | ||||||
\(549\) | 4.14303 | + | 4.55096i | 0.176820 | + | 0.194230i | ||||
\(550\) | 4.92720 | 0.210097 | ||||||||
\(551\) | −1.50869 | + | 2.61313i | −0.0642724 | + | 0.111323i | ||||
\(552\) | 23.7351 | + | 61.3300i | 1.01023 | + | 2.61038i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.7744 | − | 13.1488i | 0.967591 | − | 0.558639i | ||||
\(555\) | −4.39740 | − | 11.3626i | −0.186659 | − | 0.482315i | ||||
\(556\) | −56.1065 | − | 32.3931i | −2.37944 | − | 1.37377i | ||||
\(557\) | 9.64623i | 0.408724i | 0.978895 | + | 0.204362i | \(0.0655120\pi\) | ||||
−0.978895 | + | 0.204362i | \(0.934488\pi\) | |||||||
\(558\) | 29.6083 | + | 9.44148i | 1.25342 | + | 0.399690i | ||||
\(559\) | 10.2822i | 0.434893i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.0827 | + | 27.4456i | 1.43897 | + | 1.15875i | ||||
\(562\) | 14.0683 | + | 24.3669i | 0.593434 | + | 1.02786i | ||||
\(563\) | 1.54395 | + | 2.67420i | 0.0650698 | + | 0.112704i | 0.896725 | − | 0.442588i | \(-0.145940\pi\) |
−0.831655 | + | 0.555292i | \(0.812606\pi\) | |||||||
\(564\) | −3.92424 | − | 0.610535i | −0.165240 | − | 0.0257082i | ||||
\(565\) | −11.8370 | − | 6.83407i | −0.497985 | − | 0.287512i | ||||
\(566\) | 30.5940 | 1.28596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.99411 | 0.335425 | ||||||||
\(569\) | 7.30588 | + | 4.21805i | 0.306278 | + | 0.176830i | 0.645260 | − | 0.763963i | \(-0.276749\pi\) |
−0.338982 | + | 0.940793i | \(0.610082\pi\) | |||||||
\(570\) | 6.94903 | + | 1.08113i | 0.291063 | + | 0.0452837i | ||||
\(571\) | 17.0208 | + | 29.4808i | 0.712297 | + | 1.23373i | 0.963993 | + | 0.265928i | \(0.0856782\pi\) |
−0.251696 | + | 0.967806i | \(0.580988\pi\) | |||||||
\(572\) | 13.4001 | + | 23.2097i | 0.560288 | + | 0.970447i | ||||
\(573\) | −1.28708 | − | 1.03644i | −0.0537686 | − | 0.0432979i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.43516i | − | 0.101553i | ||||||
\(576\) | −9.67707 | − | 3.08582i | −0.403211 | − | 0.128576i | ||||
\(577\) | − | 18.1052i | − | 0.753730i | −0.926268 | − | 0.376865i | \(-0.877002\pi\) | ||
0.926268 | − | 0.376865i | \(-0.122998\pi\) | |||||||
\(578\) | 36.8055 | + | 21.2497i | 1.53091 | + | 0.883869i | ||||
\(579\) | −1.05923 | − | 2.73698i | −0.0440201 | − | 0.113745i | ||||
\(580\) | −41.9292 | + | 24.2078i | −1.74102 | + | 1.00518i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 23.7341 | + | 61.3273i | 0.983810 | + | 2.54210i | ||||
\(583\) | −9.05015 | + | 15.6753i | −0.374819 | + | 0.649206i | ||||
\(584\) | 103.157 | 4.26869 | ||||||||
\(585\) | −6.22060 | − | 6.83310i | −0.257190 | − | 0.282514i | ||||
\(586\) | 49.2441i | 2.03426i | ||||||||
\(587\) | 4.04900 | − | 7.01308i | 0.167120 | − | 0.289461i | −0.770286 | − | 0.637699i | \(-0.779887\pi\) |
0.937406 | + | 0.348238i | \(0.113220\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.35678 | + | 2.35001i | 0.0559050 | + | 0.0968304i | ||||
\(590\) | −22.4612 | + | 12.9680i | −0.924713 | + | 0.533883i | ||||
\(591\) | 3.39457 | − | 21.8188i | 0.139634 | − | 0.897504i | ||||
\(592\) | −12.5207 | + | 21.6864i | −0.514596 | + | 0.891306i | ||||
\(593\) | 6.66433 | 0.273671 | 0.136836 | − | 0.990594i | \(-0.456307\pi\) | ||||
0.136836 | + | 0.990594i | \(0.456307\pi\) | |||||||
\(594\) | 3.54060 | + | 58.3838i | 0.145273 | + | 2.39552i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −44.0040 | − | 25.4057i | −1.80247 | − | 1.04066i | ||||
\(597\) | −1.16042 | + | 7.45866i | −0.0474929 | + | 0.305263i | ||||
\(598\) | 16.4077 | − | 9.47299i | 0.670961 | − | 0.387380i | ||||
\(599\) | −3.10562 | + | 1.79303i | −0.126892 | + | 0.0732614i | −0.562103 | − | 0.827068i | \(-0.690007\pi\) |
0.435210 | + | 0.900329i | \(0.356674\pi\) | |||||||
\(600\) | 4.02995 | + | 3.24517i | 0.164522 | + | 0.132483i | ||||
\(601\) | 4.86949 | + | 2.81140i | 0.198631 | + | 0.114679i | 0.596017 | − | 0.802972i | \(-0.296749\pi\) |
−0.397386 | + | 0.917652i | \(0.630083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.08656 | + | 14.1401i | 0.125695 | + | 0.575831i | ||||
\(604\) | 64.8061 | 2.63692 | ||||||||
\(605\) | −9.40064 | + | 16.2824i | −0.382190 | + | 0.661973i | ||||
\(606\) | 6.93061 | − | 2.68220i | 0.281537 | − | 0.108957i | ||||
\(607\) | −1.93239 | + | 1.11566i | −0.0784332 | + | 0.0452834i | −0.538704 | − | 0.842495i | \(-0.681086\pi\) |
0.460270 | + | 0.887779i | \(0.347752\pi\) | |||||||
\(608\) | −2.61795 | − | 4.53442i | −0.106172 | − | 0.183895i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.16672 | + | 10.6811i | −0.249683 | + | 0.432464i | ||||
\(611\) | 0.651740i | 0.0263666i | ||||||||
\(612\) | 17.2042 | + | 78.8159i | 0.695439 | + | 3.18594i | ||||
\(613\) | −6.82038 | −0.275473 | −0.137736 | − | 0.990469i | \(-0.543983\pi\) | ||||
−0.137736 | + | 0.990469i | \(0.543983\pi\) | |||||||
\(614\) | 3.03567 | − | 5.25793i | 0.122510 | − | 0.212193i | ||||
\(615\) | −16.6938 | + | 20.7309i | −0.673160 | + | 0.835950i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.35139 | + | 1.35757i | −0.0946632 | + | 0.0546538i | −0.546584 | − | 0.837404i | \(-0.684072\pi\) |
0.451921 | + | 0.892058i | \(0.350739\pi\) | |||||||
\(618\) | −7.17303 | − | 1.11598i | −0.288542 | − | 0.0448914i | ||||
\(619\) | 23.1886 | + | 13.3880i | 0.932029 | + | 0.538107i | 0.887453 | − | 0.460899i | \(-0.152473\pi\) |
0.0445762 | + | 0.999006i | \(0.485806\pi\) | |||||||
\(620\) | 43.5406i | 1.74863i | ||||||||
\(621\) | 28.8549 | − | 1.74987i | 1.15791 | − | 0.0702197i | ||||
\(622\) | 20.2380i | 0.811469i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.91965 | + | 18.7662i | −0.116880 | + | 0.751249i | ||||
\(625\) | 13.4985 | + | 23.3801i | 0.539940 | + | 0.935203i | ||||
\(626\) | −38.7414 | − | 67.1021i | −1.54842 | − | 2.68194i | ||||
\(627\) | −3.20321 | + | 3.97785i | −0.127924 | + | 0.158860i | ||||
\(628\) | −63.4980 | − | 36.6606i | −2.53385 | − | 1.46292i | ||||
\(629\) | 17.4556 | 0.696000 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1620 | −0.444354 | −0.222177 | − | 0.975006i | \(-0.571316\pi\) | ||||
−0.222177 | + | 0.975006i | \(0.571316\pi\) | |||||||
\(632\) | 62.7004 | + | 36.2001i | 2.49409 | + | 1.43996i | ||||
\(633\) | 2.80520 | + | 7.24845i | 0.111497 | + | 0.288100i | ||||
\(634\) | −14.3182 | − | 24.7998i | −0.568647 | − | 0.984926i | ||||
\(635\) | −19.3208 | − | 33.4647i | −0.766724 | − | 1.32801i | ||||
\(636\) | −31.1192 | + | 12.0434i | −1.23396 | + | 0.477551i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 50.2927i | − | 1.99111i | ||||||
\(639\) | 1.06759 | − | 3.34795i | 0.0422334 | − | 0.132443i | ||||
\(640\) | 15.8021i | 0.624633i | ||||||||
\(641\) | 38.6251 | + | 22.3002i | 1.52560 | + | 0.880805i | 0.999539 | + | 0.0303565i | \(0.00966427\pi\) |
0.526059 | + | 0.850448i | \(0.323669\pi\) | |||||||
\(642\) | 51.2905 | − | 63.6941i | 2.02427 | − | 2.51380i | ||||
\(643\) | −23.6268 | + | 13.6410i | −0.931751 | + | 0.537947i | −0.887365 | − | 0.461068i | \(-0.847466\pi\) |
−0.0443860 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.0668 | − | 4.83339i | −1.22326 | − | 0.190315i | ||||
\(646\) | −5.03777 | + | 8.72568i | −0.198208 | + | 0.343307i | ||||
\(647\) | −44.9350 | −1.76658 | −0.883288 | − | 0.468831i | \(-0.844675\pi\) | ||||
−0.883288 | + | 0.468831i | \(0.844675\pi\) | |||||||
\(648\) | −35.5570 | + | 50.0839i | −1.39681 | + | 1.96748i | ||||
\(649\) | − | 18.8352i | − | 0.739347i | ||||||
\(650\) | 0.745324 | − | 1.29094i | 0.0292340 | − | 0.0506348i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7200 | − | 27.2278i | −0.615642 | − | 1.06632i | ||||
\(653\) | −24.0549 | + | 13.8881i | −0.941343 | + | 0.543484i | −0.890381 | − | 0.455216i | \(-0.849562\pi\) |
−0.0509617 | + | 0.998701i | \(0.516229\pi\) | |||||||
\(654\) | 55.5572 | + | 44.7382i | 2.17246 | + | 1.74940i | ||||
\(655\) | 8.30128 | − | 14.3782i | 0.324358 | − | 0.561804i | ||||
\(656\) | 54.7053 | 2.13588 | ||||||||
\(657\) | 13.7764 | − | 43.2026i | 0.537470 | − | 1.68549i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.801975 | + | 0.463021i | 0.0312405 | + | 0.0180367i | 0.515539 | − | 0.856866i | \(-0.327592\pi\) |
−0.484298 | + | 0.874903i | \(0.660925\pi\) | |||||||
\(660\) | −76.4249 | + | 29.5770i | −2.97484 | + | 1.15128i | ||||
\(661\) | 28.3028 | − | 16.3406i | 1.10085 | − | 0.635577i | 0.164408 | − | 0.986392i | \(-0.447429\pi\) |
0.936445 | + | 0.350815i | \(0.114095\pi\) | |||||||
\(662\) | 38.5540 | − | 22.2592i | 1.49844 | − | 0.865126i | ||||
\(663\) | 12.3464 | − | 4.77814i | 0.479495 | − | 0.185568i | ||||
\(664\) | −62.9373 | − | 36.3369i | −2.44244 | − | 1.41014i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.7068 | + | 17.2533i | 0.608626 | + | 0.668553i | ||||
\(667\) | −24.8561 | −0.962430 | ||||||||
\(668\) | −44.3625 | + | 76.8382i | −1.71644 | + | 2.97296i | ||||
\(669\) | −28.0399 | − | 22.5795i | −1.08409 | − | 0.872974i | ||||
\(670\) | −25.1186 | + | 14.5022i | −0.970415 | + | 0.560269i | ||||
\(671\) | −4.47839 | − | 7.75681i | −0.172886 | − | 0.299448i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.6947 | + | 27.1840i | −0.604987 | + | 1.04787i | 0.387067 | + | 0.922052i | \(0.373488\pi\) |
−0.992054 | + | 0.125816i | \(0.959845\pi\) | |||||||
\(674\) | − | 19.7470i | − | 0.760625i | ||||||
\(675\) | 1.89727 | − | 1.25437i | 0.0730261 | − | 0.0482806i | ||||
\(676\) | −52.3041 | −2.01170 | ||||||||
\(677\) | 10.7882 | − | 18.6858i | 0.414626 | − | 0.718153i | −0.580763 | − | 0.814072i | \(-0.697246\pi\) |
0.995389 | + | 0.0959196i | \(0.0305792\pi\) | |||||||
\(678\) | 25.8633 | + | 4.02383i | 0.993274 | + | 0.154534i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −79.7521 | + | 46.0449i | −3.05835 | + | 1.76574i | ||||
\(681\) | −30.7603 | + | 38.1991i | −1.17874 | + | 1.46379i | ||||
\(682\) | −39.1691 | − | 22.6143i | −1.49986 | − | 0.865946i | ||||
\(683\) | 36.2593i | 1.38742i | 0.720253 | + | 0.693711i | \(0.244026\pi\) | ||||
−0.720253 | + | 0.693711i | \(0.755974\pi\) | |||||||
\(684\) | −9.19872 | + | 2.00793i | −0.351722 | + | 0.0767751i | ||||
\(685\) | − | 1.92950i | − | 0.0737224i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.1906 | + | 13.6190i | −1.34260 | + | 0.519597i | ||||
\(688\) | 32.3098 | + | 55.9622i | 1.23180 | + | 2.13354i | ||||
\(689\) | 2.73798 | + | 4.74232i | 0.104309 | + | 0.180668i | ||||
\(690\) | 20.9089 | + | 54.0273i | 0.795990 | + | 2.05678i | ||||
\(691\) | −6.16389 | − | 3.55872i | −0.234485 | − | 0.135380i | 0.378154 | − | 0.925743i | \(-0.376559\pi\) |
−0.612640 | + | 0.790362i | \(0.709892\pi\) | |||||||
\(692\) | −101.535 | −3.85977 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.9426 | −1.28844 | ||||||||
\(695\) | −28.1540 | − | 16.2547i | −1.06794 | − | 0.616577i | ||||
\(696\) | 33.1239 | − | 41.1342i | 1.25556 | − | 1.55919i | ||||
\(697\) | −19.0667 | − | 33.0246i | −0.722204 | − | 1.25089i | ||||
\(698\) | −1.56569 | − | 2.71186i | −0.0592624 | − | 0.102645i | ||||
\(699\) | −4.05622 | + | 26.0715i | −0.153420 | + | 0.986115i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.4609i | − | 1.11272i | −0.830940 | − | 0.556362i | \(-0.812197\pi\) | ||
0.830940 | − | 0.556362i | \(-0.187803\pi\) | |||||||
\(702\) | 15.8323 | + | 7.90390i | 0.597551 | + | 0.298314i | ||||
\(703\) | 2.03727i | 0.0768370i | ||||||||
\(704\) | 12.8019 | + | 7.39117i | 0.482489 | + | 0.278565i | ||||
\(705\) | −1.96917 | − | 0.306364i | −0.0741632 | − | 0.0115384i | ||||
\(706\) | −59.8894 | + | 34.5772i | −2.25397 | + | 1.30133i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.7781 | − | 27.0447i | 0.818471 | − | 1.01640i | ||||
\(709\) | 19.0361 | − | 32.9715i | 0.714916 | − | 1.23827i | −0.248076 | − | 0.968740i | \(-0.579798\pi\) |
0.962992 | − | 0.269530i | \(-0.0868683\pi\) | |||||||
\(710\) | 7.04224 | 0.264290 | ||||||||
\(711\) | 23.5342 | − | 21.4247i | 0.882601 | − | 0.803488i | ||||
\(712\) | 22.6945i | 0.850513i | ||||||||
\(713\) | −11.1766 | + | 19.3585i | −0.418568 | + | 0.724980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.72414 | + | 11.6466i | 0.251469 | + | 0.435556i | ||||
\(716\) | 69.1795 | − | 39.9408i | 2.58536 | − | 1.49266i | ||||
\(717\) | 9.23504 | − | 3.57403i | 0.344889 | − | 0.133474i | ||||
\(718\) | 9.60408 | − | 16.6348i | 0.358421 | − | 0.620803i | ||||
\(719\) | 38.2114 | 1.42505 | 0.712523 | − | 0.701649i | \(-0.247553\pi\) | ||||
0.712523 | + | 0.701649i | \(0.247553\pi\) | |||||||
\(720\) | −55.3278 | − | 17.6429i | −2.06195 | − | 0.657512i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 41.4045 | + | 23.9049i | 1.54091 | + | 0.889647i | ||||
\(723\) | 6.03172 | + | 4.85712i | 0.224322 | + | 0.180638i | ||||
\(724\) | 66.9924 | − | 38.6781i | 2.48975 | − | 1.43746i | ||||
\(725\) | −1.69364 | + | 0.977823i | −0.0629002 | + | 0.0363154i | ||||
\(726\) | 5.53499 | − | 35.5764i | 0.205423 | − | 1.32036i | ||||
\(727\) | 17.7563 | + | 10.2516i | 0.658546 | + | 0.380212i | 0.791723 | − | 0.610881i | \(-0.209184\pi\) |
−0.133177 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.2267 | + | 21.5800i | 0.600989 | + | 0.799257i | ||||
\(730\) | 90.8743 | 3.36341 | ||||||||
\(731\) | 22.5222 | − | 39.0096i | 0.833014 | − | 1.44282i | ||||
\(732\) | 2.53842 | − | 16.3158i | 0.0938227 | − | 0.603049i | ||||
\(733\) | 0.900627 | − | 0.519977i | 0.0332654 | − | 0.0192058i | −0.483275 | − | 0.875469i | \(-0.660553\pi\) |
0.516540 | + | 0.856263i | \(0.327220\pi\) | |||||||
\(734\) | 45.1023 | + | 78.1194i | 1.66475 | + | 2.88344i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.5657 | − | 37.3528i | 0.794921 | − | 1.37684i | ||||
\(737\) | − | 21.0636i | − | 0.775887i | ||||||
\(738\) | 15.4854 | − | 48.5618i | 0.570025 | − | 1.78759i | ||||
\(739\) | 24.1609 | 0.888774 | 0.444387 | − | 0.895835i | \(-0.353422\pi\) | ||||
0.444387 | + | 0.895835i | \(0.353422\pi\) | |||||||
\(740\) | −16.3446 | + | 28.3096i | −0.600839 | + | 1.04068i | ||||
\(741\) | 0.557665 | + | 1.44097i | 0.0204863 | + | 0.0529353i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.1637 | + | 7.60008i | −0.482930 | + | 0.278820i | −0.721637 | − | 0.692272i | \(-0.756610\pi\) |
0.238707 | + | 0.971092i | \(0.423277\pi\) | |||||||
\(744\) | −17.1420 | − | 44.2938i | −0.628457 | − | 1.62389i | ||||
\(745\) | −22.0810 | − | 12.7485i | −0.808987 | − | 0.467069i | ||||
\(746\) | 77.6010i | 2.84118i | ||||||||
\(747\) | −23.6231 | + | 21.5056i | −0.864324 | + | 0.786849i | ||||
\(748\) | − | 117.406i | − | 4.29281i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −37.0023 | − | 29.7966i | −1.35113 | − | 1.08802i | ||||
\(751\) | −1.52037 | − | 2.63336i | −0.0554791 | − | 0.0960926i | 0.836952 | − | 0.547276i | \(-0.184335\pi\) |
−0.892431 | + | 0.451184i | \(0.851002\pi\) | |||||||
\(752\) | 2.04795 | + | 3.54716i | 0.0746812 | + | 0.129352i | ||||
\(753\) | 19.8984 | + | 3.09580i | 0.725138 | + | 0.112817i | ||||
\(754\) | −13.1768 | − | 7.60763i | −0.479871 | − | 0.277053i | ||||
\(755\) | 32.5195 | 1.18350 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.3700 | 1.57631 | 0.788155 | − | 0.615477i | \(-0.211036\pi\) | ||||
0.788155 | + | 0.615477i | \(0.211036\pi\) | |||||||
\(758\) | −60.5075 | − | 34.9340i | −2.19773 | − | 1.26886i | ||||
\(759\) | −41.5713 | − | 6.46769i | −1.50894 | − | 0.234762i | ||||
\(760\) | −5.37397 | − | 9.30799i | −0.194934 | − | 0.337636i | ||||
\(761\) | 14.6319 | + | 25.3432i | 0.530406 | + | 0.918690i | 0.999371 | + | 0.0354731i | \(0.0112938\pi\) |
−0.468965 | + | 0.883217i | \(0.655373\pi\) | |||||||
\(762\) | 57.6350 | + | 46.4113i | 2.08790 | + | 1.68131i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.43367i | 0.160405i | ||||||||
\(765\) | 8.63302 | + | 39.5495i | 0.312127 | + | 1.42992i | ||||
\(766\) | 9.43698i | 0.340972i | ||||||||
\(767\) | −4.93487 | − | 2.84915i | −0.178188 | − | 0.102877i | ||||
\(768\) | −15.1549 | − | 39.1592i | −0.546855 | − | 1.41304i | ||||
\(769\) | 29.6496 | − | 17.1182i | 1.06919 | − | 0.617299i | 0.141232 | − | 0.989977i | \(-0.454894\pi\) |
0.927961 | + | 0.372678i | \(0.121560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.31453 | − | 3.39666i | −0.0473418 | − | 0.122328i | ||||
\(772\) | −3.93702 | + | 6.81912i | −0.141697 | + | 0.245426i | ||||
\(773\) | −33.9854 | −1.22237 | −0.611185 | − | 0.791488i | \(-0.709307\pi\) | ||||
−0.611185 | + | 0.791488i | \(0.709307\pi\) | |||||||
\(774\) | 58.8235 | − | 12.8402i | 2.11437 | − | 0.461531i | ||||
\(775\) | 1.75873i | 0.0631753i | ||||||||
\(776\) | 50.2502 | − | 87.0359i | 1.80388 | − | 3.12441i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.6870 | + | 27.1707i | 0.562406 | + | 0.974117i | ||||
\(779\) | 3.85435 | − | 2.22531i | 0.138096 | − | 0.0797299i | ||||
\(780\) | −3.81134 | + | 24.4975i | −0.136468 | + | 0.877153i | ||||
\(781\) | −2.55710 | + | 4.42904i | −0.0915004 | + | 0.158483i | ||||
\(782\) | −82.9985 | −2.96802 | ||||||||
\(783\) | −12.8035 | − | 19.3657i | −0.457560 | − | 0.692075i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.8631 | − | 18.3962i | −1.13724 | − | 0.656587i | ||||
\(786\) | −4.88770 | + | 31.4159i | −0.174338 | + | 1.12057i | ||||
\(787\) | −23.8225 | + | 13.7539i | −0.849180 | + | 0.490274i | −0.860374 | − | 0.509663i | \(-0.829770\pi\) |
0.0111939 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(788\) | −51.3067 | + | 29.6219i | −1.82773 | + | 1.05524i | ||||
\(789\) | 2.97173 | + | 2.39303i | 0.105796 | + | 0.0851940i | ||||
\(790\) | 55.2346 | + | 31.8897i | 1.96516 | + | 1.13458i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 66.1025 | − | 60.1773i | 2.34885 | − | 2.13831i | ||||
\(793\) | −2.70974 | −0.0962255 | ||||||||
\(794\) | −34.5144 | + | 59.7807i | −1.22487 | + | 2.12154i | ||||
\(795\) | −15.6155 | + | 6.04332i | −0.553826 | + | 0.214334i | ||||
\(796\) | 17.5390 | − | 10.1262i | 0.621654 | − | 0.358912i | ||||
\(797\) | −21.0873 | − | 36.5243i | −0.746952 | − | 1.29376i | −0.949277 | − | 0.314440i | \(-0.898183\pi\) |
0.202326 | − | 0.979318i | \(-0.435150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.42757 | − | 2.47262i | 0.0505038 | − | 0.0874751i | ||||
\(800\) | − | 3.39352i | − | 0.119979i | ||||||
\(801\) | 9.50452 | + | 3.03080i | 0.335826 | + | 0.107088i | ||||
\(802\) | 19.9292 | 0.703723 | ||||||||
\(803\) | −32.9974 | + | 57.1531i | −1.16445 | + | 2.01689i | ||||
\(804\) | 24.3546 | − | 30.2443i | 0.858922 | − | 1.06664i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.8500 | + | 6.84160i | −0.417398 | + | 0.240985i | ||||
\(807\) | 47.6853 | + | 7.41890i | 1.67860 | + | 0.261158i | ||||
\(808\) | −9.83594 | − | 5.67878i | −0.346027 | − | 0.199779i | ||||
\(809\) | − | 4.83100i | − | 0.169849i | −0.996387 | − | 0.0849245i | \(-0.972935\pi\) | ||
0.996387 | − | 0.0849245i | \(-0.0270649\pi\) | |||||||
\(810\) | −31.3232 | + | 44.1203i | −1.10058 | + | 1.55023i | ||||
\(811\) | − | 6.46035i | − | 0.226853i | −0.993546 | − | 0.113427i | \(-0.963817\pi\) | ||
0.993546 | − | 0.113427i | \(-0.0361827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.05687 | + | 19.6482i | −0.107209 | + | 0.689092i | ||||
\(814\) | −16.9782 | − | 29.4071i | −0.595086 | − | 1.03072i | ||||
\(815\) | −7.88823 | − | 13.6628i | −0.276313 | − | 0.478587i | ||||
\(816\) | 52.1822 | − | 64.8015i | 1.82674 | − | 2.26851i | ||||
\(817\) | 4.55287 | + | 2.62860i | 0.159285 | + | 0.0919631i | ||||
\(818\) | −23.3597 | −0.816751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 71.4128 | 2.49384 | ||||||||
\(821\) | 14.5455 | + | 8.39783i | 0.507640 | + | 0.293086i | 0.731863 | − | 0.681452i | \(-0.238651\pi\) |
−0.224223 | + | 0.974538i | \(0.571984\pi\) | |||||||
\(822\) | 1.33360 | + | 3.44593i | 0.0465146 | + | 0.120191i | ||||
\(823\) | 7.51749 | + | 13.0207i | 0.262043 | + | 0.453872i | 0.966785 | − | 0.255592i | \(-0.0822703\pi\) |
−0.704741 | + | 0.709464i | \(0.748937\pi\) | |||||||
\(824\) | 5.54719 | + | 9.60802i | 0.193246 | + | 0.334711i | ||||
\(825\) | −3.08702 | + | 1.19470i | −0.107476 | + | 0.0415940i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2462i | 1.01699i | 0.861065 | + | 0.508495i | \(0.169798\pi\) | ||||
−0.861065 | + | 0.508495i | \(0.830202\pi\) | |||||||
\(828\) | −52.2123 | − | 57.3533i | −1.81450 | − | 1.99317i | ||||
\(829\) | 1.50423i | 0.0522440i | 0.999659 | + | 0.0261220i | \(0.00831584\pi\) | ||||
−0.999659 | + | 0.0261220i | \(0.991684\pi\) | |||||||
\(830\) | −55.4433 | − | 32.0102i | −1.92446 | − | 1.11109i | ||||
\(831\) | −11.0805 | + | 13.7602i | −0.384380 | + | 0.477334i | ||||
\(832\) | 3.87301 | − | 2.23608i | 0.134272 | − | 0.0775222i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 61.5155 | + | 9.57061i | 2.13011 | + | 0.331403i | ||||
\(835\) | −22.2610 | + | 38.5571i | −0.770373 | + | 1.33432i | ||||
\(836\) | 13.7027 | 0.473917 | ||||||||
\(837\) | −20.8396 | + | 1.26379i | −0.720323 | + | 0.0436830i | ||||
\(838\) | − | 17.0401i | − | 0.588641i | ||||||
\(839\) | 22.9477 | − | 39.7466i | 0.792243 | − | 1.37221i | −0.132331 | − | 0.991206i | \(-0.542246\pi\) |
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.51923 | − | 7.82753i | −0.155835 | − | 0.269915i | ||||
\(842\) | 28.5443 | − | 16.4800i | 0.983701 | − | 0.567940i | ||||
\(843\) | −14.7224 | − | 11.8554i | −0.507065 | − | 0.408321i | ||||
\(844\) | 10.4266 | − | 18.0593i | 0.358897 | − | 0.621628i | ||||
\(845\) | −26.2460 | −0.902891 | ||||||||
\(846\) | 3.72853 | − | 0.813876i | 0.128189 | − | 0.0279816i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 29.8035 | + | 17.2071i | 1.02346 | + | 0.590893i | ||||
\(849\) | −19.1679 | + | 7.41811i | −0.657840 | + | 0.254589i | ||||
\(850\) | −5.65534 | + | 3.26511i | −0.193977 | + | 0.111992i | ||||
\(851\) | −14.5338 | + | 8.39112i | −0.498214 | + | 0.287644i | ||||
\(852\) | −8.79269 | + | 3.40283i | −0.301232 | + | 0.116579i | ||||
\(853\) | 24.3086 | + | 14.0346i | 0.832310 | + | 0.480534i | 0.854643 | − | 0.519216i | \(-0.173776\pi\) |
−0.0223330 | + | 0.999751i | \(0.507109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.61589 | + | 1.00757i | −0.157860 | + | 0.0344583i | ||||
\(856\) | −124.981 | −4.27176 | ||||||||
\(857\) | 8.55426 | − | 14.8164i | 0.292208 | − | 0.506119i | −0.682123 | − | 0.731237i | \(-0.738943\pi\) |
0.974332 | + | 0.225118i | \(0.0722767\pi\) | |||||||
\(858\) | −20.0584 | − | 16.1523i | −0.684784 | − | 0.551431i | ||||
\(859\) | −4.50996 | + | 2.60383i | −0.153878 | + | 0.0888414i | −0.574962 | − | 0.818180i | \(-0.694983\pi\) |
0.421084 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(860\) | 42.1775 | + | 73.0535i | 1.43824 | + | 2.49110i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2456 | − | 48.9228i | 0.962049 | − | 1.66632i | ||||
\(863\) | 44.7024i | 1.52169i | 0.648935 | + | 0.760844i | \(0.275215\pi\) | ||||
−0.648935 | + | 0.760844i | \(0.724785\pi\) | |||||||
\(864\) | 40.2108 | − | 2.43853i | 1.36800 | − | 0.0829603i | ||||
\(865\) | −50.9497 | −1.73234 | ||||||||
\(866\) | 10.5858 | − | 18.3352i | 0.359721 | − | 0.623055i | ||||
\(867\) | −28.2120 | − | 4.38923i | −0.958129 | − | 0.149066i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.1124 | + | 23.1589i | −1.36072 | + | 0.785613i | ||||
\(870\) | 29.1798 | − | 36.2363i | 0.989287 | − | 1.22853i | ||||
\(871\) | −5.51871 | − | 3.18623i | −0.186994 | − | 0.107961i | ||||
\(872\) | − | 109.015i | − | 3.69171i | ||||||
\(873\) | −29.7400 | − | 32.6683i | −1.00655 | − | 1.10566i | ||||
\(874\) | − | 9.68688i | − | 0.327664i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −113.462 | + | 43.9108i | −3.83354 | + | 1.48361i | ||||
\(877\) | 2.87432 | + | 4.97846i | 0.0970587 | + | 0.168111i | 0.910466 | − | 0.413584i | \(-0.135723\pi\) |
−0.813407 | + | 0.581695i | \(0.802390\pi\) | |||||||
\(878\) | 48.8229 | + | 84.5637i | 1.64769 | + | 2.85389i | ||||
\(879\) | −11.9402 | − | 30.8527i | −0.402733 | − | 1.04064i | ||||
\(880\) | 73.1936 | + | 42.2584i | 2.46736 | + | 1.42453i | ||||
\(881\) | −9.98120 | −0.336275 | −0.168138 | − | 0.985764i | \(-0.553775\pi\) | ||||
−0.168138 | + | 0.985764i | \(0.553775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.0942 | −1.08006 | −0.540028 | − | 0.841647i | \(-0.681586\pi\) | ||||
−0.540028 | + | 0.841647i | \(0.681586\pi\) | |||||||
\(884\) | −30.7608 | − | 17.7597i | −1.03460 | − | 0.597325i | ||||
\(885\) | 10.9282 | − | 13.5709i | 0.367346 | − | 0.456182i | ||||
\(886\) | 26.3781 | + | 45.6881i | 0.886188 | + | 1.53492i | ||||
\(887\) | −4.26812 | − | 7.39260i | −0.143309 | − | 0.248219i | 0.785432 | − | 0.618949i | \(-0.212441\pi\) |
−0.928741 | + | 0.370729i | \(0.879108\pi\) | |||||||
\(888\) | 5.48177 | − | 35.2343i | 0.183956 | − | 1.18239i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 19.9922i | 0.670141i | ||||||||
\(891\) | −16.3746 | − | 35.7204i | −0.548569 | − | 1.19668i | ||||
\(892\) | 96.5904i | 3.23409i | ||||||||
\(893\) | 0.288584 | + | 0.166614i | 0.00965709 | + | 0.00557552i | ||||
\(894\) | 48.2462 | + | 7.50617i | 1.61360 | + | 0.251044i | ||||
\(895\) | 34.7140 | − | 20.0422i | 1.16036 | − | 0.669935i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.98293 | + | 9.91344i | −0.266542 | + | 0.331000i | ||||
\(898\) | 46.0277 | − | 79.7223i | 1.53596 | − | 2.66037i | ||||
\(899\) | 17.9516 | 0.598718 | ||||||||
\(900\) | −5.81388 | − | 1.85393i | −0.193796 | − | 0.0617976i | ||||
\(901\) | − | 23.9891i | − | 0.799192i | ||||||
\(902\) | −37.0906 | + | 64.2429i | −1.23498 | + | 2.13905i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.0011 | − | 34.6430i | −0.665228 | − | 1.15221i | ||||
\(905\) | 33.6166 | − | 19.4085i | 1.11745 | − | 0.645162i | ||||
\(906\) | −58.0771 | + | 22.4763i | −1.92948 | + | 0.746724i | ||||
\(907\) | −16.0272 | + | 27.7599i | −0.532175 | + | 0.921754i | 0.467120 | + | 0.884194i | \(0.345292\pi\) |
−0.999294 | + | 0.0375597i | \(0.988042\pi\) | |||||||
\(908\) | 131.586 | 4.36685 | ||||||||
\(909\) | −3.69185 | + | 3.36093i | −0.122451 | + | 0.111475i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3261 | + | 15.1994i | 0.872221 | + | 0.503577i | 0.868086 | − | 0.496414i | \(-0.165350\pi\) |
0.00413539 | + | 0.999991i | \(0.498684\pi\) | |||||||
\(912\) | 7.56308 | + | 6.09027i | 0.250439 | + | 0.201669i | ||||
\(913\) | 40.2640 | − | 23.2464i | 1.33254 | − | 0.769344i | ||||
\(914\) | 0.567527 | − | 0.327662i | 0.0187721 | − | 0.0108381i | ||||
\(915\) | 1.27377 | − | 8.18721i | 0.0421095 | − | 0.270661i | ||||
\(916\) | 87.6765 | + | 50.6201i | 2.89691 | + | 1.67253i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −42.7530 | − | 64.6654i | −1.41106 | − | 2.13428i | ||||
\(919\) | −17.4431 | −0.575393 | −0.287697 | − | 0.957722i | \(-0.592889\pi\) | ||||
−0.287697 | + | 0.957722i | \(0.592889\pi\) | |||||||
\(920\) | 44.2687 | − | 76.6757i | 1.45950 | − | 2.52792i | ||||
\(921\) | −0.627034 | + | 4.03029i | −0.0206615 | + | 0.132802i | ||||
\(922\) | −54.5580 | + | 31.4991i | −1.79677 | + | 1.03737i | ||||
\(923\) | 0.773612 | + | 1.33994i | 0.0254637 | + | 0.0441045i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.660203 | + | 1.14351i | −0.0217074 | + | 0.0375982i | ||||
\(926\) | 2.11405i | 0.0694718i | ||||||||
\(927\) | 4.76468 | − | 1.04005i | 0.156493 | − | 0.0341598i | ||||
\(928\) | −34.6382 | −1.13705 | ||||||||
\(929\) | −5.21392 | + | 9.03077i | −0.171063 | + | 0.296290i | −0.938792 | − | 0.344485i | \(-0.888054\pi\) |
0.767729 | + | 0.640775i | \(0.221387\pi\) | |||||||
\(930\) | −15.1009 | − | 39.0197i | −0.495178 | − | 1.27951i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 61.3070 | − | 35.3956i | 2.00818 | − | 1.15942i | ||||
\(933\) | −4.90710 | − | 12.6796i | −0.160651 | − | 0.415111i | ||||
\(934\) | −4.06199 | − | 2.34519i | −0.132912 | − | 0.0767369i | ||||
\(935\) | − | 58.9142i | − | 1.92670i | ||||||
\(936\) | −5.76746 | − | 26.4219i | −0.188515 | − | 0.863626i | ||||
\(937\) | 51.3201i | 1.67655i | 0.545245 | + | 0.838277i | \(0.316437\pi\) | ||||
−0.545245 | + | 0.838277i | \(0.683563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.5427 | + | 32.6476i | 1.32306 | + | 1.06541i | ||||
\(940\) | 2.67342 | + | 4.63049i | 0.0871973 | + | 0.151030i | ||||
\(941\) | −24.6673 | − | 42.7251i | −0.804133 | − | 1.39280i | −0.916875 | − | 0.399174i | \(-0.869297\pi\) |
0.112742 | − | 0.993624i | \(-0.464037\pi\) | |||||||
\(942\) | 69.6196 | + | 10.8315i | 2.26833 | + | 0.352908i | ||||
\(943\) | 31.7506 | + | 18.3312i | 1.03394 | + | 0.596947i | ||||
\(944\) | −35.8114 | −1.16556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −87.6252 | −2.84894 | ||||||||
\(947\) | −38.0468 | − | 21.9663i | −1.23636 | − | 0.713810i | −0.268008 | − | 0.963417i | \(-0.586365\pi\) |
−0.968347 | + | 0.249607i | \(0.919699\pi\) | |||||||
\(948\) | −84.3731 | − | 13.1268i | −2.74031 | − | 0.426339i | ||||
\(949\) | 9.98283 | + | 17.2908i | 0.324056 | + | 0.561282i | ||||
\(950\) | −0.381076 | − | 0.660044i | −0.0123637 | − | 0.0214146i | ||||
\(951\) | 14.9839 | + | 12.0660i | 0.485886 | + | 0.391266i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0833i | 0.682956i | 0.939890 | + | 0.341478i | \(0.110928\pi\) | ||||
−0.939890 | + | 0.341478i | \(0.889072\pi\) | |||||||
\(954\) | 23.7111 | − | 21.5858i | 0.767676 | − | 0.698865i | ||||
\(955\) | 2.22480i | 0.0719929i | ||||||||
\(956\) | −23.0089 | − | 13.2842i | −0.744161 | − | 0.429641i | ||||
\(957\) | 12.1945 | + | 31.5096i | 0.394191 | + | 1.01856i | ||||
\(958\) | −3.04138 | + | 1.75594i | −0.0982625 | + | 0.0567319i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.93552 | + | 12.7530i | 0.159293 | + | 0.411603i | ||||
\(961\) | −7.42801 | + | 12.8657i | −0.239613 | + | 0.415022i | ||||
\(962\) | −10.2730 | −0.331215 | ||||||||
\(963\) | −16.6909 | + | 52.3423i | −0.537857 | + | 1.68671i | ||||
\(964\) | − | 20.7778i | − | 0.669207i | ||||||
\(965\) | −1.97558 | + | 3.42181i | −0.0635963 | + | 0.110152i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.6671 | − | 47.9209i | −0.889716 | − | 1.54103i | −0.840212 | − | 0.542259i | \(-0.817569\pi\) |
−0.0495039 | − | 0.998774i | \(-0.515764\pi\) | |||||||
\(968\) | −47.6533 | + | 27.5127i | −1.53164 | + | 0.884290i | ||||
\(969\) | 1.04058 | − | 6.68837i | 0.0334282 | − | 0.214861i | ||||
\(970\) | 44.2668 | − | 76.6723i | 1.42132 | − | 2.46180i | ||||
\(971\) | 6.83465 | 0.219334 | 0.109667 | − | 0.993968i | \(-0.465021\pi\) | ||||
0.109667 | + | 0.993968i | \(0.465021\pi\) | |||||||
\(972\) | 17.7900 | − | 70.2225i | 0.570613 | − | 2.25239i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 70.5830 | + | 40.7511i | 2.26162 | + | 1.30575i | ||||
\(975\) | −0.153951 | + | 0.989525i | −0.00493037 | + | 0.0316902i | ||||
\(976\) | −14.7480 | + | 8.51477i | −0.472072 | + | 0.272551i | ||||
\(977\) | 31.1982 | − | 18.0123i | 0.998118 | − | 0.576264i | 0.0904272 | − | 0.995903i | \(-0.471177\pi\) |
0.907691 | + | 0.419639i | \(0.137843\pi\) | |||||||
\(978\) | 23.5310 | + | 18.9486i | 0.752437 | + | 0.605910i | ||||
\(979\) | −12.5736 | − | 7.25938i | −0.401854 | − | 0.232011i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.6557 | − | 14.5587i | −1.45767 | − | 0.464822i | ||||
\(982\) | −5.87711 | −0.187546 | ||||||||
\(983\) | 20.6863 | − | 35.8298i | 0.659791 | − | 1.14279i | −0.320878 | − | 0.947120i | \(-0.603978\pi\) |
0.980670 | − | 0.195671i | \(-0.0626886\pi\) | |||||||
\(984\) | −72.6482 | + | 28.1154i | −2.31594 | + | 0.896285i | ||||
\(985\) | −25.7455 | + | 14.8642i | −0.820321 | + | 0.473612i | ||||
\(986\) | 33.3275 | + | 57.7249i | 1.06136 | + | 1.83833i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.07277 | − | 3.59014i | 0.0659435 | − | 0.114218i | ||||
\(989\) | 43.3068i | 1.37708i | ||||||||
\(990\) | 58.2316 | − | 53.0119i | 1.85072 | − | 1.68483i | ||||
\(991\) | −21.6734 | −0.688478 | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(992\) | −15.5752 | + | 26.9770i | −0.494512 | + | 0.856520i | ||||
\(993\) | −18.7579 | + | 23.2941i | −0.595263 | + | 0.739216i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.80102 | − | 5.08127i | 0.279011 | − | 0.161087i | ||||
\(996\) | 84.6919 | + | 13.1764i | 2.68357 | + | 0.417510i | ||||
\(997\) | −11.8699 | − | 6.85308i | −0.375923 | − | 0.217039i | 0.300120 | − | 0.953901i | \(-0.402973\pi\) |
−0.676043 | + | 0.736862i | \(0.736307\pi\) | |||||||
\(998\) | − | 69.7117i | − | 2.20669i | ||||||
\(999\) | −14.0241 | − | 7.00123i | −0.443704 | − | 0.221509i |
(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 | 441.2.o.e.146.23 | ✓ | 48 | |
3.2 | odd | 2 | 1323.2.o.e.440.2 | 48 | |||
7.2 | even | 3 | 441.2.i.d.227.2 | 48 | |||
7.3 | odd | 6 | 441.2.s.d.362.1 | 48 | |||
7.4 | even | 3 | 441.2.s.d.362.2 | 48 | |||
7.5 | odd | 6 | 441.2.i.d.227.1 | 48 | |||
7.6 | odd | 2 | inner | 441.2.o.e.146.24 | yes | 48 | |
9.4 | even | 3 | 1323.2.o.e.881.1 | 48 | |||
9.5 | odd | 6 | inner | 441.2.o.e.293.24 | yes | 48 | |
21.2 | odd | 6 | 1323.2.i.d.521.2 | 48 | |||
21.5 | even | 6 | 1323.2.i.d.521.14 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.656.23 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.656.24 | 48 | |||
21.20 | even | 2 | 1323.2.o.e.440.1 | 48 | |||
63.4 | even | 3 | 1323.2.i.d.1097.14 | 48 | |||
63.5 | even | 6 | 441.2.s.d.374.2 | 48 | |||
63.13 | odd | 6 | 1323.2.o.e.881.2 | 48 | |||
63.23 | odd | 6 | 441.2.s.d.374.1 | 48 | |||
63.31 | odd | 6 | 1323.2.i.d.1097.2 | 48 | |||
63.32 | odd | 6 | 441.2.i.d.68.23 | 48 | |||
63.40 | odd | 6 | 1323.2.s.d.962.23 | 48 | |||
63.41 | even | 6 | inner | 441.2.o.e.293.23 | yes | 48 | |
63.58 | even | 3 | 1323.2.s.d.962.24 | 48 | |||
63.59 | even | 6 | 441.2.i.d.68.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.23 | 48 | 63.32 | odd | 6 | |||
441.2.i.d.68.24 | 48 | 63.59 | even | 6 | |||
441.2.i.d.227.1 | 48 | 7.5 | odd | 6 | |||
441.2.i.d.227.2 | 48 | 7.2 | even | 3 | |||
441.2.o.e.146.23 | ✓ | 48 | 1.1 | even | 1 | trivial | |
441.2.o.e.146.24 | yes | 48 | 7.6 | odd | 2 | inner | |
441.2.o.e.293.23 | yes | 48 | 63.41 | even | 6 | inner | |
441.2.o.e.293.24 | yes | 48 | 9.5 | odd | 6 | inner | |
441.2.s.d.362.1 | 48 | 7.3 | odd | 6 | |||
441.2.s.d.362.2 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.1 | 48 | 63.23 | odd | 6 | |||
441.2.s.d.374.2 | 48 | 63.5 | even | 6 | |||
1323.2.i.d.521.2 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.14 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.1097.2 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.1097.14 | 48 | 63.4 | even | 3 | |||
1323.2.o.e.440.1 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.440.2 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.881.1 | 48 | 9.4 | even | 3 | |||
1323.2.o.e.881.2 | 48 | 63.13 | odd | 6 | |||
1323.2.s.d.656.23 | 48 | 21.11 | odd | 6 | |||
1323.2.s.d.656.24 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.23 | 48 | 63.40 | odd | 6 | |||
1323.2.s.d.962.24 | 48 | 63.58 | even | 3 |