Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\), 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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.10 | ||
Character | \(\chi\) | \(=\) | 171.106 |
Dual form | 171.2.g.c.121.10 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0973467 | + | 0.168609i | 0.0688345 | + | 0.119225i | 0.898389 | − | 0.439202i | \(-0.144739\pi\) |
−0.829554 | + | 0.558426i | \(0.811405\pi\) | |||||||
\(3\) | 1.55267 | + | 0.767609i | 0.896433 | + | 0.443179i | ||||
\(4\) | 0.981047 | − | 1.69922i | 0.490524 | − | 0.849612i | ||||
\(5\) | −1.90563 | −0.852225 | −0.426113 | − | 0.904670i | \(-0.640117\pi\) | ||||
−0.426113 | + | 0.904670i | \(0.640117\pi\) | |||||||
\(6\) | 0.0217210 | + | 0.336519i | 0.00886757 | + | 0.137383i | ||||
\(7\) | 1.69446 | − | 2.93489i | 0.640445 | − | 1.10928i | −0.344889 | − | 0.938644i | \(-0.612083\pi\) |
0.985334 | − | 0.170639i | \(-0.0545833\pi\) | |||||||
\(8\) | 0.771394 | 0.272729 | ||||||||
\(9\) | 1.82155 | + | 2.38368i | 0.607185 | + | 0.794561i | ||||
\(10\) | −0.185507 | − | 0.321308i | −0.0586625 | − | 0.101606i | ||||
\(11\) | −0.311589 | + | 0.539688i | −0.0939477 | + | 0.162722i | −0.909169 | − | 0.416428i | \(-0.863282\pi\) |
0.815221 | + | 0.579150i | \(0.196615\pi\) | |||||||
\(12\) | 2.82758 | − | 1.88527i | 0.816252 | − | 0.544230i | ||||
\(13\) | −1.84489 | + | 3.19545i | −0.511681 | + | 0.886258i | 0.488227 | + | 0.872717i | \(0.337644\pi\) |
−0.999908 | + | 0.0135411i | \(0.995690\pi\) | |||||||
\(14\) | 0.659800 | 0.176339 | ||||||||
\(15\) | −2.95882 | − | 1.46278i | −0.763963 | − | 0.377688i | ||||
\(16\) | −1.88700 | − | 3.26838i | −0.471750 | − | 0.817096i | ||||
\(17\) | −3.04830 | + | 5.27981i | −0.739321 | + | 1.28054i | 0.213481 | + | 0.976947i | \(0.431520\pi\) |
−0.952802 | + | 0.303594i | \(0.901813\pi\) | |||||||
\(18\) | −0.224589 | + | 0.539175i | −0.0529362 | + | 0.127085i | ||||
\(19\) | −1.14464 | + | 4.20592i | −0.262599 | + | 0.964905i | ||||
\(20\) | −1.86952 | + | 3.23810i | −0.418037 | + | 0.724061i | ||||
\(21\) | 4.88377 | − | 3.25622i | 1.06573 | − | 0.710566i | ||||
\(22\) | −0.121329 | −0.0258674 | ||||||||
\(23\) | 3.92442 | − | 6.79729i | 0.818297 | − | 1.41733i | −0.0886387 | − | 0.996064i | \(-0.528252\pi\) |
0.906936 | − | 0.421269i | \(-0.138415\pi\) | |||||||
\(24\) | 1.19772 | + | 0.592129i | 0.244483 | + | 0.120868i | ||||
\(25\) | −1.36856 | −0.273712 | ||||||||
\(26\) | −0.718377 | −0.140885 | ||||||||
\(27\) | 0.998533 | + | 5.09931i | 0.192168 | + | 0.981362i | ||||
\(28\) | −3.32469 | − | 5.75853i | −0.628307 | − | 1.08826i | ||||
\(29\) | −1.18459 | −0.219972 | −0.109986 | − | 0.993933i | \(-0.535081\pi\) | ||||
−0.109986 | + | 0.993933i | \(0.535081\pi\) | |||||||
\(30\) | −0.0413923 | − | 0.641281i | −0.00755717 | − | 0.117081i | ||||
\(31\) | −0.910124 | − | 1.57638i | −0.163463 | − | 0.283126i | 0.772645 | − | 0.634838i | \(-0.218933\pi\) |
−0.936108 | + | 0.351711i | \(0.885600\pi\) | |||||||
\(32\) | 1.13878 | − | 1.97243i | 0.201310 | − | 0.348679i | ||||
\(33\) | −0.898064 | + | 0.598778i | −0.156333 | + | 0.104234i | ||||
\(34\) | −1.18697 | −0.203563 | ||||||||
\(35\) | −3.22902 | + | 5.59282i | −0.545803 | + | 0.945359i | ||||
\(36\) | 5.83744 | − | 0.756723i | 0.972907 | − | 0.126120i | ||||
\(37\) | 5.63896 | 0.927039 | 0.463520 | − | 0.886087i | \(-0.346586\pi\) | ||||
0.463520 | + | 0.886087i | \(0.346586\pi\) | |||||||
\(38\) | −0.820586 | + | 0.216435i | −0.133117 | + | 0.0351104i | ||||
\(39\) | −5.31736 | + | 3.54531i | −0.851459 | + | 0.567704i | ||||
\(40\) | −1.46999 | −0.232426 | ||||||||
\(41\) | −4.03639 | −0.630378 | −0.315189 | − | 0.949029i | \(-0.602068\pi\) | ||||
−0.315189 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(42\) | 1.02445 | + | 0.506468i | 0.158076 | + | 0.0781497i | ||||
\(43\) | −2.54719 | − | 4.41186i | −0.388442 | − | 0.672802i | 0.603798 | − | 0.797138i | \(-0.293653\pi\) |
−0.992240 | + | 0.124335i | \(0.960320\pi\) | |||||||
\(44\) | 0.611367 | + | 1.05892i | 0.0921671 | + | 0.159638i | ||||
\(45\) | −3.47121 | − | 4.54242i | −0.517458 | − | 0.677145i | ||||
\(46\) | 1.52812 | 0.225308 | ||||||||
\(47\) | −12.8718 | −1.87754 | −0.938772 | − | 0.344539i | \(-0.888035\pi\) | ||||
−0.938772 | + | 0.344539i | \(0.888035\pi\) | |||||||
\(48\) | −0.421048 | − | 6.52319i | −0.0607730 | − | 0.941542i | ||||
\(49\) | −2.24237 | − | 3.88391i | −0.320339 | − | 0.554844i | ||||
\(50\) | −0.133225 | − | 0.230752i | −0.0188408 | − | 0.0326333i | ||||
\(51\) | −8.78582 | + | 5.85788i | −1.23026 | + | 0.820268i | ||||
\(52\) | 3.61985 | + | 6.26977i | 0.501983 | + | 0.869461i | ||||
\(53\) | 1.93076 | + | 3.34418i | 0.265211 | + | 0.459359i | 0.967619 | − | 0.252416i | \(-0.0812251\pi\) |
−0.702408 | + | 0.711775i | \(0.747892\pi\) | |||||||
\(54\) | −0.762588 | + | 0.664763i | −0.103775 | + | 0.0904628i | ||||
\(55\) | 0.593775 | − | 1.02845i | 0.0800646 | − | 0.138676i | ||||
\(56\) | 1.30709 | − | 2.26395i | 0.174668 | − | 0.302534i | ||||
\(57\) | −5.00575 | + | 5.65176i | −0.663028 | + | 0.748594i | ||||
\(58\) | −0.115316 | − | 0.199733i | −0.0151417 | − | 0.0262262i | ||||
\(59\) | 8.50437 | 1.10717 | 0.553587 | − | 0.832791i | \(-0.313259\pi\) | ||||
0.553587 | + | 0.832791i | \(0.313259\pi\) | |||||||
\(60\) | −5.38833 | + | 3.59263i | −0.695630 | + | 0.463807i | ||||
\(61\) | 3.64691 | 0.466939 | 0.233469 | − | 0.972364i | \(-0.424992\pi\) | ||||
0.233469 | + | 0.972364i | \(0.424992\pi\) | |||||||
\(62\) | 0.177195 | − | 0.306911i | 0.0225038 | − | 0.0389778i | ||||
\(63\) | 10.0824 | − | 1.30701i | 1.27026 | − | 0.164667i | ||||
\(64\) | −7.10458 | −0.888073 | ||||||||
\(65\) | 3.51569 | − | 6.08935i | 0.436068 | − | 0.755291i | ||||
\(66\) | −0.188383 | − | 0.0931330i | −0.0231884 | − | 0.0114639i | ||||
\(67\) | −0.523023 | + | 0.905902i | −0.0638974 | + | 0.110674i | −0.896204 | − | 0.443641i | \(-0.853686\pi\) |
0.832307 | + | 0.554315i | \(0.187020\pi\) | |||||||
\(68\) | 5.98105 | + | 10.3595i | 0.725309 | + | 1.25627i | ||||
\(69\) | 11.3110 | − | 7.54151i | 1.36168 | − | 0.907892i | ||||
\(70\) | −1.25734 | −0.150280 | ||||||||
\(71\) | 1.56289 | − | 2.70700i | 0.185481 | − | 0.321262i | −0.758258 | − | 0.651955i | \(-0.773949\pi\) |
0.943738 | + | 0.330693i | \(0.107282\pi\) | |||||||
\(72\) | 1.40514 | + | 1.83876i | 0.165597 | + | 0.216700i | ||||
\(73\) | 2.06890 | − | 3.58345i | 0.242147 | − | 0.419411i | −0.719179 | − | 0.694825i | \(-0.755482\pi\) |
0.961326 | + | 0.275414i | \(0.0888151\pi\) | |||||||
\(74\) | 0.548934 | + | 0.950782i | 0.0638123 | + | 0.110526i | ||||
\(75\) | −2.12492 | − | 1.05052i | −0.245365 | − | 0.121303i | ||||
\(76\) | 6.02386 | + | 6.07121i | 0.690984 | + | 0.696416i | ||||
\(77\) | 1.05595 | + | 1.82896i | 0.120337 | + | 0.208429i | ||||
\(78\) | −1.11540 | − | 0.551432i | −0.126294 | − | 0.0624374i | ||||
\(79\) | 8.16729 | + | 14.1462i | 0.918892 | + | 1.59157i | 0.801100 | + | 0.598530i | \(0.204248\pi\) |
0.117792 | + | 0.993038i | \(0.462418\pi\) | |||||||
\(80\) | 3.59593 | + | 6.22834i | 0.402038 | + | 0.696350i | ||||
\(81\) | −2.36388 | + | 8.68401i | −0.262654 | + | 0.964890i | ||||
\(82\) | −0.392929 | − | 0.680574i | −0.0433918 | − | 0.0751568i | ||||
\(83\) | 5.35528 | − | 9.27561i | 0.587818 | − | 1.01813i | −0.406700 | − | 0.913562i | \(-0.633321\pi\) |
0.994518 | − | 0.104569i | \(-0.0333462\pi\) | |||||||
\(84\) | −0.741839 | − | 11.4931i | −0.0809413 | − | 1.25400i | ||||
\(85\) | 5.80894 | − | 10.0614i | 0.630068 | − | 1.09131i | ||||
\(86\) | 0.495921 | − | 0.858960i | 0.0534765 | − | 0.0926240i | ||||
\(87\) | −1.83927 | − | 0.909299i | −0.197190 | − | 0.0974871i | ||||
\(88\) | −0.240358 | + | 0.416312i | −0.0256222 | + | 0.0443790i | ||||
\(89\) | −5.25259 | − | 9.09775i | −0.556773 | − | 0.964359i | −0.997763 | − | 0.0668472i | \(-0.978706\pi\) |
0.440990 | − | 0.897512i | \(-0.354627\pi\) | |||||||
\(90\) | 0.427984 | − | 1.02747i | 0.0451135 | − | 0.108305i | ||||
\(91\) | 6.25218 | + | 10.8291i | 0.655407 | + | 1.13520i | ||||
\(92\) | −7.70007 | − | 13.3369i | −0.802788 | − | 1.39047i | ||||
\(93\) | −0.203077 | − | 3.14622i | −0.0210581 | − | 0.326247i | ||||
\(94\) | −1.25303 | − | 2.17031i | −0.129240 | − | 0.223850i | ||||
\(95\) | 2.18127 | − | 8.01495i | 0.223794 | − | 0.822316i | ||||
\(96\) | 3.28220 | − | 2.18838i | 0.334988 | − | 0.223351i | ||||
\(97\) | −7.34332 | − | 12.7190i | −0.745602 | − | 1.29142i | −0.949913 | − | 0.312514i | \(-0.898829\pi\) |
0.204312 | − | 0.978906i | \(-0.434504\pi\) | |||||||
\(98\) | 0.436576 | − | 0.756171i | 0.0441008 | − | 0.0763848i | ||||
\(99\) | −1.85402 | + | 0.240342i | −0.186336 | + | 0.0241553i | ||||
\(100\) | −1.34262 | + | 2.32549i | −0.134262 | + | 0.232549i | ||||
\(101\) | 8.53801 | 0.849563 | 0.424782 | − | 0.905296i | \(-0.360351\pi\) | ||||
0.424782 | + | 0.905296i | \(0.360351\pi\) | |||||||
\(102\) | −1.84297 | − | 0.911126i | −0.182481 | − | 0.0902149i | ||||
\(103\) | 6.69656 | + | 11.5988i | 0.659832 | + | 1.14286i | 0.980659 | + | 0.195725i | \(0.0627059\pi\) |
−0.320827 | + | 0.947138i | \(0.603961\pi\) | |||||||
\(104\) | −1.42314 | + | 2.46495i | −0.139550 | + | 0.241708i | ||||
\(105\) | −9.30668 | + | 6.20517i | −0.908239 | + | 0.605563i | ||||
\(106\) | −0.375907 | + | 0.651090i | −0.0365113 | + | 0.0632395i | ||||
\(107\) | 10.1943 | 0.985524 | 0.492762 | − | 0.870164i | \(-0.335987\pi\) | ||||
0.492762 | + | 0.870164i | \(0.335987\pi\) | |||||||
\(108\) | 9.64447 | + | 3.30593i | 0.928040 | + | 0.318113i | ||||
\(109\) | −0.945297 | + | 1.63730i | −0.0905431 | + | 0.156825i | −0.907740 | − | 0.419534i | \(-0.862194\pi\) |
0.817197 | + | 0.576359i | \(0.195527\pi\) | |||||||
\(110\) | 0.231208 | 0.0220448 | ||||||||
\(111\) | 8.75543 | + | 4.32851i | 0.831029 | + | 0.410844i | ||||
\(112\) | −12.7898 | −1.20852 | ||||||||
\(113\) | −4.93706 | − | 8.55125i | −0.464440 | − | 0.804434i | 0.534736 | − | 0.845019i | \(-0.320411\pi\) |
−0.999176 | + | 0.0405856i | \(0.987078\pi\) | |||||||
\(114\) | −1.44023 | − | 0.293837i | −0.134890 | − | 0.0275203i | ||||
\(115\) | −7.47850 | + | 12.9531i | −0.697374 | + | 1.20789i | ||||
\(116\) | −1.16214 | + | 2.01288i | −0.107902 | + | 0.186891i | ||||
\(117\) | −10.9775 | + | 1.42304i | −1.01487 | + | 0.131560i | ||||
\(118\) | 0.827873 | + | 1.43392i | 0.0762118 | + | 0.132003i | ||||
\(119\) | 10.3304 | + | 17.8928i | 0.946988 | + | 1.64023i | ||||
\(120\) | −2.28241 | − | 1.12838i | −0.208355 | − | 0.103007i | ||||
\(121\) | 5.30582 | + | 9.18996i | 0.482348 | + | 0.835451i | ||||
\(122\) | 0.355014 | + | 0.614903i | 0.0321415 | + | 0.0556707i | ||||
\(123\) | −6.26717 | − | 3.09837i | −0.565092 | − | 0.279371i | ||||
\(124\) | −3.57150 | −0.320730 | ||||||||
\(125\) | 12.1361 | 1.08549 | ||||||||
\(126\) | 1.20186 | + | 1.57275i | 0.107070 | + | 0.140112i | ||||
\(127\) | −4.32772 | − | 7.49583i | −0.384023 | − | 0.665148i | 0.607610 | − | 0.794236i | \(-0.292128\pi\) |
−0.991633 | + | 0.129088i | \(0.958795\pi\) | |||||||
\(128\) | −2.96917 | − | 5.14275i | −0.262440 | − | 0.454559i | ||||
\(129\) | −0.568356 | − | 8.80539i | −0.0500409 | − | 0.775272i | ||||
\(130\) | 1.36896 | 0.120066 | ||||||||
\(131\) | 2.08447 | 0.182121 | 0.0910604 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910604 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(132\) | 0.136415 | + | 2.11344i | 0.0118734 | + | 0.183951i | ||||
\(133\) | 10.4044 | + | 10.4862i | 0.902172 | + | 0.909265i | ||||
\(134\) | −0.203658 | −0.0175934 | ||||||||
\(135\) | −1.90284 | − | 9.71741i | −0.163770 | − | 0.836342i | ||||
\(136\) | −2.35144 | + | 4.07281i | −0.201634 | + | 0.349241i | ||||
\(137\) | −17.0350 | −1.45540 | −0.727700 | − | 0.685896i | \(-0.759411\pi\) | ||||
−0.727700 | + | 0.685896i | \(0.759411\pi\) | |||||||
\(138\) | 2.37266 | + | 1.17300i | 0.201974 | + | 0.0998520i | ||||
\(139\) | −1.13106 | + | 1.95905i | −0.0959351 | + | 0.166164i | −0.909998 | − | 0.414612i | \(-0.863917\pi\) |
0.814063 | + | 0.580776i | \(0.197251\pi\) | |||||||
\(140\) | 6.33563 | + | 10.9736i | 0.535459 | + | 0.927442i | ||||
\(141\) | −19.9856 | − | 9.88050i | −1.68309 | − | 0.832088i | ||||
\(142\) | 0.608568 | 0.0510699 | ||||||||
\(143\) | −1.14970 | − | 1.99133i | −0.0961425 | − | 0.166524i | ||||
\(144\) | 4.35351 | − | 10.4515i | 0.362793 | − | 0.870962i | ||||
\(145\) | 2.25739 | 0.187466 | ||||||||
\(146\) | 0.805604 | 0.0666723 | ||||||||
\(147\) | −0.500342 | − | 7.75168i | −0.0412675 | − | 0.639348i | ||||
\(148\) | 5.53209 | − | 9.58186i | 0.454735 | − | 0.787624i | ||||
\(149\) | 2.40529 | 0.197049 | 0.0985246 | − | 0.995135i | \(-0.468588\pi\) | ||||
0.0985246 | + | 0.995135i | \(0.468588\pi\) | |||||||
\(150\) | −0.0297266 | − | 0.460546i | −0.00242716 | − | 0.0376034i | ||||
\(151\) | 3.86313 | − | 6.69114i | 0.314377 | − | 0.544517i | −0.664928 | − | 0.746908i | \(-0.731538\pi\) |
0.979305 | + | 0.202391i | \(0.0648710\pi\) | |||||||
\(152\) | −0.882971 | + | 3.24442i | −0.0716184 | + | 0.263157i | ||||
\(153\) | −18.1380 | + | 2.35128i | −1.46637 | + | 0.190090i | ||||
\(154\) | −0.205586 | + | 0.356086i | −0.0165666 | + | 0.0286942i | ||||
\(155\) | 1.73436 | + | 3.00401i | 0.139307 | + | 0.241288i | ||||
\(156\) | 0.807700 | + | 12.5135i | 0.0646678 | + | 1.00188i | ||||
\(157\) | −5.43874 | −0.434058 | −0.217029 | − | 0.976165i | \(-0.569637\pi\) | ||||
−0.217029 | + | 0.976165i | \(0.569637\pi\) | |||||||
\(158\) | −1.59012 | + | 2.75417i | −0.126503 | + | 0.219110i | ||||
\(159\) | 0.430813 | + | 6.67448i | 0.0341657 | + | 0.529320i | ||||
\(160\) | −2.17010 | + | 3.75872i | −0.171561 | + | 0.297153i | ||||
\(161\) | −13.2995 | − | 23.0354i | −1.04815 | − | 1.81545i | ||||
\(162\) | −1.69432 | + | 0.446787i | −0.133119 | + | 0.0351029i | ||||
\(163\) | −7.27424 | −0.569763 | −0.284881 | − | 0.958563i | \(-0.591954\pi\) | ||||
−0.284881 | + | 0.958563i | \(0.591954\pi\) | |||||||
\(164\) | −3.95989 | + | 6.85873i | −0.309216 | + | 0.535577i | ||||
\(165\) | 1.71138 | − | 1.14105i | 0.133231 | − | 0.0888307i | ||||
\(166\) | 2.08527 | 0.161849 | ||||||||
\(167\) | 2.23165 | − | 3.86534i | 0.172691 | − | 0.299109i | −0.766669 | − | 0.642042i | \(-0.778087\pi\) |
0.939360 | + | 0.342934i | \(0.111421\pi\) | |||||||
\(168\) | 3.76731 | − | 2.51183i | 0.290655 | − | 0.193792i | ||||
\(169\) | −0.307257 | − | 0.532185i | −0.0236352 | − | 0.0409373i | ||||
\(170\) | 2.26192 | 0.173482 | ||||||||
\(171\) | −12.1106 | + | 4.93285i | −0.926122 | + | 0.377225i | ||||
\(172\) | −9.99565 | −0.762161 | ||||||||
\(173\) | −6.00303 | − | 10.3976i | −0.456402 | − | 0.790512i | 0.542365 | − | 0.840143i | \(-0.317529\pi\) |
−0.998768 | + | 0.0496308i | \(0.984196\pi\) | |||||||
\(174\) | −0.0257305 | − | 0.398636i | −0.00195062 | − | 0.0302205i | ||||
\(175\) | −2.31897 | + | 4.01657i | −0.175298 | + | 0.303624i | ||||
\(176\) | 2.35188 | 0.177279 | ||||||||
\(177\) | 13.2045 | + | 6.52803i | 0.992508 | + | 0.490677i | ||||
\(178\) | 1.02264 | − | 1.77127i | 0.0766504 | − | 0.132762i | ||||
\(179\) | 20.0123 | 1.49579 | 0.747897 | − | 0.663815i | \(-0.231064\pi\) | ||||
0.747897 | + | 0.663815i | \(0.231064\pi\) | |||||||
\(180\) | −11.1240 | + | 1.44204i | −0.829136 | + | 0.107483i | ||||
\(181\) | −6.04514 | − | 10.4705i | −0.449332 | − | 0.778265i | 0.549011 | − | 0.835815i | \(-0.315005\pi\) |
−0.998343 | + | 0.0575498i | \(0.981671\pi\) | |||||||
\(182\) | −1.21726 | + | 2.10836i | −0.0902293 | + | 0.156282i | ||||
\(183\) | 5.66243 | + | 2.79940i | 0.418579 | + | 0.206937i | ||||
\(184\) | 3.02727 | − | 5.24339i | 0.223173 | − | 0.386548i | ||||
\(185\) | −10.7458 | −0.790046 | ||||||||
\(186\) | 0.510713 | − | 0.340514i | 0.0374473 | − | 0.0249677i | ||||
\(187\) | −1.89963 | − | 3.29026i | −0.138915 | − | 0.240608i | ||||
\(188\) | −12.6278 | + | 21.8721i | −0.920980 | + | 1.59518i | ||||
\(189\) | 16.6579 | + | 5.70998i | 1.21168 | + | 0.415340i | ||||
\(190\) | 1.56374 | − | 0.412446i | 0.113445 | − | 0.0299220i | ||||
\(191\) | 1.34685 | − | 2.33282i | 0.0974548 | − | 0.168797i | −0.813176 | − | 0.582018i | \(-0.802263\pi\) |
0.910631 | + | 0.413222i | \(0.135597\pi\) | |||||||
\(192\) | −11.0311 | − | 5.45354i | −0.796098 | − | 0.393575i | ||||
\(193\) | 12.5244 | 0.901523 | 0.450762 | − | 0.892644i | \(-0.351152\pi\) | ||||
0.450762 | + | 0.892644i | \(0.351152\pi\) | |||||||
\(194\) | 1.42970 | − | 2.47631i | 0.102646 | − | 0.177789i | ||||
\(195\) | 10.1329 | − | 6.75607i | 0.725635 | − | 0.483812i | ||||
\(196\) | −8.79950 | −0.628536 | ||||||||
\(197\) | −11.8545 | −0.844595 | −0.422297 | − | 0.906457i | \(-0.638776\pi\) | ||||
−0.422297 | + | 0.906457i | \(0.638776\pi\) | |||||||
\(198\) | −0.221007 | − | 0.289209i | −0.0157063 | − | 0.0205532i | ||||
\(199\) | 3.01833 | + | 5.22790i | 0.213964 | + | 0.370596i | 0.952952 | − | 0.303123i | \(-0.0980292\pi\) |
−0.738988 | + | 0.673719i | \(0.764696\pi\) | |||||||
\(200\) | −1.05570 | −0.0746492 | ||||||||
\(201\) | −1.50746 | + | 1.00509i | −0.106328 | + | 0.0708934i | ||||
\(202\) | 0.831147 | + | 1.43959i | 0.0584793 | + | 0.101289i | ||||
\(203\) | −2.00723 | + | 3.47663i | −0.140880 | + | 0.244012i | ||||
\(204\) | 1.33455 | + | 20.6759i | 0.0934375 | + | 1.44760i | ||||
\(205\) | 7.69188 | 0.537224 | ||||||||
\(206\) | −1.30378 | + | 2.25821i | −0.0908385 | + | 0.157337i | ||||
\(207\) | 23.3511 | − | 3.02707i | 1.62301 | − | 0.210396i | ||||
\(208\) | 13.9253 | 0.965543 | ||||||||
\(209\) | −1.91323 | − | 1.92827i | −0.132341 | − | 0.133381i | ||||
\(210\) | −1.95223 | − | 0.965142i | −0.134716 | − | 0.0666011i | ||||
\(211\) | −5.65425 | −0.389255 | −0.194627 | − | 0.980877i | \(-0.562350\pi\) | ||||
−0.194627 | + | 0.980877i | \(0.562350\pi\) | |||||||
\(212\) | 7.57669 | 0.520369 | ||||||||
\(213\) | 4.50457 | − | 3.00339i | 0.308648 | − | 0.205789i | ||||
\(214\) | 0.992386 | + | 1.71886i | 0.0678381 | + | 0.117499i | ||||
\(215\) | 4.85401 | + | 8.40739i | 0.331040 | + | 0.573379i | ||||
\(216\) | 0.770262 | + | 3.93357i | 0.0524097 | + | 0.267646i | ||||
\(217\) | −6.16867 | −0.418757 | ||||||||
\(218\) | −0.368086 | −0.0249300 | ||||||||
\(219\) | 5.96301 | − | 3.97579i | 0.402943 | − | 0.268659i | ||||
\(220\) | −1.16504 | − | 2.01791i | −0.0785471 | − | 0.136048i | ||||
\(221\) | −11.2476 | − | 19.4813i | −0.756593 | − | 1.31046i | ||||
\(222\) | 0.122484 | + | 1.89762i | 0.00822059 | + | 0.127360i | ||||
\(223\) | −14.5197 | − | 25.1489i | −0.972312 | − | 1.68409i | −0.688535 | − | 0.725203i | \(-0.741746\pi\) |
−0.283777 | − | 0.958890i | \(-0.591587\pi\) | |||||||
\(224\) | −3.85923 | − | 6.68439i | −0.257856 | − | 0.446619i | ||||
\(225\) | −2.49291 | − | 3.26221i | −0.166194 | − | 0.217481i | ||||
\(226\) | 0.961214 | − | 1.66487i | 0.0639390 | − | 0.110746i | ||||
\(227\) | −11.5488 | + | 20.0031i | −0.766522 | + | 1.32765i | 0.172916 | + | 0.984937i | \(0.444681\pi\) |
−0.939438 | + | 0.342718i | \(0.888652\pi\) | |||||||
\(228\) | 4.69273 | + | 14.0505i | 0.310784 | + | 0.930520i | ||||
\(229\) | −1.94136 | − | 3.36253i | −0.128289 | − | 0.222202i | 0.794725 | − | 0.606970i | \(-0.207615\pi\) |
−0.923014 | + | 0.384767i | \(0.874282\pi\) | |||||||
\(230\) | −2.91203 | −0.192014 | ||||||||
\(231\) | 0.235615 | + | 3.65032i | 0.0155023 | + | 0.240173i | ||||
\(232\) | −0.913783 | −0.0599928 | ||||||||
\(233\) | −3.05545 | + | 5.29220i | −0.200169 | + | 0.346703i | −0.948583 | − | 0.316529i | \(-0.897483\pi\) |
0.748414 | + | 0.663232i | \(0.230816\pi\) | |||||||
\(234\) | −1.30856 | − | 1.71238i | −0.0855434 | − | 0.111942i | ||||
\(235\) | 24.5289 | 1.60009 | ||||||||
\(236\) | 8.34319 | − | 14.4508i | 0.543095 | − | 0.940669i | ||||
\(237\) | 1.82237 | + | 28.2336i | 0.118376 | + | 1.83397i | ||||
\(238\) | −2.01127 | + | 3.48361i | −0.130371 | + | 0.225809i | ||||
\(239\) | −9.61029 | − | 16.6455i | −0.621638 | − | 1.07671i | −0.989181 | − | 0.146702i | \(-0.953134\pi\) |
0.367543 | − | 0.930007i | \(-0.380199\pi\) | |||||||
\(240\) | 0.802363 | + | 12.4308i | 0.0517923 | + | 0.802406i | ||||
\(241\) | 10.6740 | 0.687573 | 0.343786 | − | 0.939048i | \(-0.388290\pi\) | ||||
0.343786 | + | 0.939048i | \(0.388290\pi\) | |||||||
\(242\) | −1.03301 | + | 1.78922i | −0.0664044 | + | 0.115016i | ||||
\(243\) | −10.3362 | + | 11.6688i | −0.663070 | + | 0.748557i | ||||
\(244\) | 3.57779 | − | 6.19691i | 0.229044 | − | 0.396717i | ||||
\(245\) | 4.27314 | + | 7.40130i | 0.273001 | + | 0.472852i | ||||
\(246\) | −0.0876746 | − | 1.35832i | −0.00558993 | − | 0.0866034i | ||||
\(247\) | −11.3281 | − | 11.4171i | −0.720787 | − | 0.726454i | ||||
\(248\) | −0.702064 | − | 1.21601i | −0.0445811 | − | 0.0772168i | ||||
\(249\) | 15.4350 | − | 10.2912i | 0.978153 | − | 0.652177i | ||||
\(250\) | 1.18141 | + | 2.04627i | 0.0747192 | + | 0.129417i | ||||
\(251\) | 9.04512 | + | 15.6666i | 0.570923 | + | 0.988867i | 0.996471 | + | 0.0839318i | \(0.0267478\pi\) |
−0.425549 | + | 0.904936i | \(0.639919\pi\) | |||||||
\(252\) | 7.67040 | − | 18.4145i | 0.483190 | − | 1.16000i | ||||
\(253\) | 2.44561 | + | 4.23592i | 0.153754 | + | 0.266310i | ||||
\(254\) | 0.842579 | − | 1.45939i | 0.0528681 | − | 0.0915702i | ||||
\(255\) | 16.7425 | − | 11.1630i | 1.04846 | − | 0.699053i | ||||
\(256\) | −6.52650 | + | 11.3042i | −0.407906 | + | 0.706515i | ||||
\(257\) | −11.6856 | + | 20.2401i | −0.728930 | + | 1.26254i | 0.228406 | + | 0.973566i | \(0.426649\pi\) |
−0.957336 | + | 0.288978i | \(0.906685\pi\) | |||||||
\(258\) | 1.42935 | − | 0.953006i | 0.0889871 | − | 0.0593316i | ||||
\(259\) | 9.55498 | − | 16.5497i | 0.593718 | − | 1.02835i | ||||
\(260\) | −6.89811 | − | 11.9479i | −0.427803 | − | 0.740976i | ||||
\(261\) | −2.15779 | − | 2.82368i | −0.133564 | − | 0.174781i | ||||
\(262\) | 0.202916 | + | 0.351461i | 0.0125362 | + | 0.0217133i | ||||
\(263\) | 12.1983 | + | 21.1280i | 0.752177 | + | 1.30281i | 0.946766 | + | 0.321924i | \(0.104330\pi\) |
−0.194589 | + | 0.980885i | \(0.562337\pi\) | |||||||
\(264\) | −0.692761 | + | 0.461894i | −0.0426365 | + | 0.0284276i | ||||
\(265\) | −3.67933 | − | 6.37279i | −0.226019 | − | 0.391477i | ||||
\(266\) | −0.755235 | + | 2.77507i | −0.0463064 | + | 0.170150i | ||||
\(267\) | −1.17201 | − | 18.1577i | −0.0717260 | − | 1.11123i | ||||
\(268\) | 1.02622 | + | 1.77746i | 0.0626864 | + | 0.108576i | ||||
\(269\) | 12.5243 | − | 21.6927i | 0.763620 | − | 1.32263i | −0.177354 | − | 0.984147i | \(-0.556754\pi\) |
0.940973 | − | 0.338481i | \(-0.109913\pi\) | |||||||
\(270\) | 1.45321 | − | 1.26679i | 0.0884397 | − | 0.0770947i | ||||
\(271\) | −1.42509 | + | 2.46833i | −0.0865679 | + | 0.149940i | −0.906058 | − | 0.423153i | \(-0.860923\pi\) |
0.819490 | + | 0.573093i | \(0.194257\pi\) | |||||||
\(272\) | 23.0086 | 1.39510 | ||||||||
\(273\) | 1.39505 | + | 21.6132i | 0.0844325 | + | 1.30809i | ||||
\(274\) | −1.65830 | − | 2.87226i | −0.100182 | − | 0.173520i | ||||
\(275\) | 0.426429 | − | 0.738596i | 0.0257146 | − | 0.0445390i | ||||
\(276\) | −1.71812 | − | 26.6184i | −0.103419 | − | 1.60224i | ||||
\(277\) | −1.14916 | + | 1.99041i | −0.0690465 | + | 0.119592i | −0.898482 | − | 0.439011i | \(-0.855329\pi\) |
0.829435 | + | 0.558603i | \(0.188662\pi\) | |||||||
\(278\) | −0.440419 | −0.0264146 | ||||||||
\(279\) | 2.09975 | − | 5.04091i | 0.125709 | − | 0.301791i | ||||
\(280\) | −2.49084 | + | 4.31427i | −0.148856 | + | 0.257827i | ||||
\(281\) | 14.1908 | 0.846554 | 0.423277 | − | 0.906000i | \(-0.360880\pi\) | ||||
0.423277 | + | 0.906000i | \(0.360880\pi\) | |||||||
\(282\) | −0.279589 | − | 4.33160i | −0.0166493 | − | 0.257943i | ||||
\(283\) | −8.27764 | −0.492055 | −0.246027 | − | 0.969263i | \(-0.579125\pi\) | ||||
−0.246027 | + | 0.969263i | \(0.579125\pi\) | |||||||
\(284\) | −3.06654 | − | 5.31140i | −0.181965 | − | 0.315173i | ||||
\(285\) | 9.53913 | − | 10.7702i | 0.565049 | − | 0.637971i | ||||
\(286\) | 0.223838 | − | 0.387700i | 0.0132358 | − | 0.0229252i | ||||
\(287\) | −6.83949 | + | 11.8464i | −0.403723 | + | 0.699268i | ||||
\(288\) | 6.77599 | − | 0.878389i | 0.399279 | − | 0.0517596i | ||||
\(289\) | −10.0842 | − | 17.4664i | −0.593190 | − | 1.02744i | ||||
\(290\) | 0.219749 | + | 0.380617i | 0.0129041 | + | 0.0223506i | ||||
\(291\) | −1.63852 | − | 25.3852i | −0.0960518 | − | 1.48811i | ||||
\(292\) | −4.05939 | − | 7.03106i | −0.237558 | − | 0.411462i | ||||
\(293\) | 9.90459 | + | 17.1553i | 0.578632 | + | 1.00222i | 0.995637 | + | 0.0933160i | \(0.0297467\pi\) |
−0.417004 | + | 0.908905i | \(0.636920\pi\) | |||||||
\(294\) | 1.25830 | − | 0.838963i | 0.0733856 | − | 0.0489293i | ||||
\(295\) | −16.2062 | −0.943562 | ||||||||
\(296\) | 4.34986 | 0.252830 | ||||||||
\(297\) | −3.06317 | − | 1.04999i | −0.177743 | − | 0.0609267i | ||||
\(298\) | 0.234147 | + | 0.405555i | 0.0135638 | + | 0.0234932i | ||||
\(299\) | 14.4803 | + | 25.0805i | 0.837415 | + | 1.45044i | ||||
\(300\) | −3.86971 | + | 2.58011i | −0.223418 | + | 0.148962i | ||||
\(301\) | −17.2644 | −0.995104 | ||||||||
\(302\) | 1.50425 | 0.0865600 | ||||||||
\(303\) | 13.2567 | + | 6.55385i | 0.761577 | + | 0.376509i | ||||
\(304\) | 15.9065 | − | 4.19545i | 0.912301 | − | 0.240626i | ||||
\(305\) | −6.94967 | −0.397937 | ||||||||
\(306\) | −2.16212 | − | 2.82935i | −0.123600 | − | 0.161743i | ||||
\(307\) | −9.08098 | + | 15.7287i | −0.518279 | + | 0.897685i | 0.481496 | + | 0.876448i | \(0.340094\pi\) |
−0.999774 | + | 0.0212367i | \(0.993240\pi\) | |||||||
\(308\) | 4.14374 | 0.236112 | ||||||||
\(309\) | 1.49421 | + | 23.1494i | 0.0850025 | + | 1.31692i | ||||
\(310\) | −0.337669 | + | 0.584860i | −0.0191783 | + | 0.0332178i | ||||
\(311\) | −1.15887 | − | 2.00723i | −0.0657137 | − | 0.113820i | 0.831297 | − | 0.555829i | \(-0.187599\pi\) |
−0.897010 | + | 0.442010i | \(0.854266\pi\) | |||||||
\(312\) | −4.10178 | + | 2.73483i | −0.232217 | + | 0.154829i | ||||
\(313\) | 18.7101 | 1.05756 | 0.528779 | − | 0.848759i | \(-0.322650\pi\) | ||||
0.528779 | + | 0.848759i | \(0.322650\pi\) | |||||||
\(314\) | −0.529443 | − | 0.917023i | −0.0298782 | − | 0.0517506i | ||||
\(315\) | −19.2133 | + | 2.49068i | −1.08255 | + | 0.140334i | ||||
\(316\) | 32.0500 | 1.80295 | ||||||||
\(317\) | −14.3891 | −0.808171 | −0.404086 | − | 0.914721i | \(-0.632410\pi\) | ||||
−0.404086 | + | 0.914721i | \(0.632410\pi\) | |||||||
\(318\) | −1.08344 | + | 0.722377i | −0.0607564 | + | 0.0405089i | ||||
\(319\) | 0.369105 | − | 0.639308i | 0.0206659 | − | 0.0357944i | ||||
\(320\) | 13.5387 | 0.756838 | ||||||||
\(321\) | 15.8284 | + | 7.82527i | 0.883457 | + | 0.436764i | ||||
\(322\) | 2.58933 | − | 4.48485i | 0.144298 | − | 0.249931i | ||||
\(323\) | −18.7172 | − | 18.8644i | −1.04146 | − | 1.04964i | ||||
\(324\) | 12.4370 | + | 12.5362i | 0.690944 | + | 0.696455i | ||||
\(325\) | 2.52485 | − | 4.37316i | 0.140053 | − | 0.242580i | ||||
\(326\) | −0.708124 | − | 1.22651i | −0.0392194 | − | 0.0679299i | ||||
\(327\) | −2.72454 | + | 1.81657i | −0.150667 | + | 0.100457i | ||||
\(328\) | −3.11365 | −0.171922 | ||||||||
\(329\) | −21.8107 | + | 37.7773i | −1.20246 | + | 2.08273i | ||||
\(330\) | 0.358989 | + | 0.177477i | 0.0197617 | + | 0.00976980i | ||||
\(331\) | −14.2961 | + | 24.7615i | −0.785784 | + | 1.36102i | 0.142746 | + | 0.989759i | \(0.454407\pi\) |
−0.928530 | + | 0.371258i | \(0.878927\pi\) | |||||||
\(332\) | −10.5076 | − | 18.1996i | −0.576677 | − | 0.998834i | ||||
\(333\) | 10.2717 | + | 13.4415i | 0.562884 | + | 0.736589i | ||||
\(334\) | 0.868977 | 0.0475483 | ||||||||
\(335\) | 0.996689 | − | 1.72632i | 0.0544550 | − | 0.0943188i | ||||
\(336\) | −19.8583 | − | 9.81754i | −1.08336 | − | 0.535591i | ||||
\(337\) | 20.3107 | 1.10640 | 0.553199 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553199 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(338\) | 0.0598209 | − | 0.103613i | 0.00325383 | − | 0.00563580i | ||||
\(339\) | −1.10161 | − | 17.0670i | −0.0598312 | − | 0.926951i | ||||
\(340\) | −11.3977 | − | 19.7414i | −0.618126 | − | 1.07063i | ||||
\(341\) | 1.13434 | 0.0614279 | ||||||||
\(342\) | −2.01065 | − | 1.56177i | −0.108724 | − | 0.0844507i | ||||
\(343\) | 8.52398 | 0.460251 | ||||||||
\(344\) | −1.96488 | − | 3.40328i | −0.105939 | − | 0.183493i | ||||
\(345\) | −21.5546 | + | 14.3714i | −1.16046 | + | 0.773728i | ||||
\(346\) | 1.16875 | − | 2.02434i | 0.0628325 | − | 0.108829i | ||||
\(347\) | −35.7597 | −1.91968 | −0.959841 | − | 0.280544i | \(-0.909485\pi\) | ||||
−0.959841 | + | 0.280544i | \(0.909485\pi\) | |||||||
\(348\) | −3.34951 | + | 2.23327i | −0.179553 | + | 0.119716i | ||||
\(349\) | −1.94971 | + | 3.37700i | −0.104366 | + | 0.180767i | −0.913479 | − | 0.406886i | \(-0.866615\pi\) |
0.809113 | + | 0.587653i | \(0.199948\pi\) | |||||||
\(350\) | −0.902976 | −0.0482661 | ||||||||
\(351\) | −18.1368 | − | 6.21691i | −0.968068 | − | 0.331834i | ||||
\(352\) | 0.709663 | + | 1.22917i | 0.0378252 | + | 0.0655151i | ||||
\(353\) | 5.00251 | − | 8.66460i | 0.266257 | − | 0.461170i | −0.701635 | − | 0.712536i | \(-0.747546\pi\) |
0.967892 | + | 0.251366i | \(0.0808798\pi\) | |||||||
\(354\) | 0.184724 | + | 2.86188i | 0.00981795 | + | 0.152107i | ||||
\(355\) | −2.97829 | + | 5.15856i | −0.158071 | + | 0.273788i | ||||
\(356\) | −20.6121 | −1.09244 | ||||||||
\(357\) | 2.30503 | + | 35.7113i | 0.121995 | + | 1.89004i | ||||
\(358\) | 1.94814 | + | 3.37427i | 0.102962 | + | 0.178336i | ||||
\(359\) | 2.25793 | − | 3.91084i | 0.119169 | − | 0.206406i | −0.800270 | − | 0.599640i | \(-0.795310\pi\) |
0.919439 | + | 0.393234i | \(0.128644\pi\) | |||||||
\(360\) | −2.67767 | − | 3.50400i | −0.141126 | − | 0.184677i | ||||
\(361\) | −16.3796 | − | 9.62856i | −0.862083 | − | 0.506766i | ||||
\(362\) | 1.17695 | − | 2.03854i | 0.0618591 | − | 0.107143i | ||||
\(363\) | 1.18389 | + | 18.3417i | 0.0621382 | + | 0.962692i | ||||
\(364\) | 24.5348 | 1.28597 | ||||||||
\(365\) | −3.94257 | + | 6.82874i | −0.206364 | + | 0.357432i | ||||
\(366\) | 0.0792146 | + | 1.22725i | 0.00414061 | + | 0.0641495i | ||||
\(367\) | −23.4866 | −1.22599 | −0.612996 | − | 0.790086i | \(-0.710036\pi\) | ||||
−0.612996 | + | 0.790086i | \(0.710036\pi\) | |||||||
\(368\) | −29.6215 | −1.54413 | ||||||||
\(369\) | −7.35251 | − | 9.62147i | −0.382756 | − | 0.500874i | ||||
\(370\) | −1.04607 | − | 1.81184i | −0.0543825 | − | 0.0941932i | ||||
\(371\) | 13.0864 | 0.679412 | ||||||||
\(372\) | −5.54535 | − | 2.74151i | −0.287513 | − | 0.142141i | ||||
\(373\) | −12.2017 | − | 21.1340i | −0.631782 | − | 1.09428i | −0.987187 | − | 0.159566i | \(-0.948991\pi\) |
0.355406 | − | 0.934712i | \(-0.384343\pi\) | |||||||
\(374\) | 0.369846 | − | 0.640592i | 0.0191243 | − | 0.0331242i | ||||
\(375\) | 18.8434 | + | 9.31581i | 0.973069 | + | 0.481066i | ||||
\(376\) | −9.92922 | −0.512061 | ||||||||
\(377\) | 2.18544 | − | 3.78529i | 0.112556 | − | 0.194952i | ||||
\(378\) | 0.658832 | + | 3.36452i | 0.0338867 | + | 0.173052i | ||||
\(379\) | −17.7118 | −0.909793 | −0.454896 | − | 0.890544i | \(-0.650324\pi\) | ||||
−0.454896 | + | 0.890544i | \(0.650324\pi\) | |||||||
\(380\) | −11.4793 | − | 11.5695i | −0.588874 | − | 0.593503i | ||||
\(381\) | −0.965647 | − | 14.9605i | −0.0494716 | − | 0.766451i | ||||
\(382\) | 0.524447 | 0.0268330 | ||||||||
\(383\) | 4.07577 | 0.208262 | 0.104131 | − | 0.994564i | \(-0.466794\pi\) | ||||
0.104131 | + | 0.994564i | \(0.466794\pi\) | |||||||
\(384\) | −0.662512 | − | 10.2641i | −0.0338087 | − | 0.523790i | ||||
\(385\) | −2.01225 | − | 3.48532i | −0.102554 | − | 0.177629i | ||||
\(386\) | 1.21921 | + | 2.11173i | 0.0620559 | + | 0.107484i | ||||
\(387\) | 5.87663 | − | 14.1081i | 0.298726 | − | 0.717156i | ||||
\(388\) | −28.8166 | −1.46294 | ||||||||
\(389\) | 5.31159 | 0.269308 | 0.134654 | − | 0.990893i | \(-0.457008\pi\) | ||||
0.134654 | + | 0.990893i | \(0.457008\pi\) | |||||||
\(390\) | 2.12555 | + | 1.05083i | 0.107631 | + | 0.0532107i | ||||
\(391\) | 23.9256 | + | 41.4403i | 1.20997 | + | 2.09573i | ||||
\(392\) | −1.72975 | − | 2.99602i | −0.0873657 | − | 0.151322i | ||||
\(393\) | 3.23648 | + | 1.60005i | 0.163259 | + | 0.0807121i | ||||
\(394\) | −1.15399 | − | 1.99877i | −0.0581373 | − | 0.100697i | ||||
\(395\) | −15.5639 | − | 26.9574i | −0.783103 | − | 1.35637i | ||||
\(396\) | −1.41049 | + | 3.38618i | −0.0708797 | + | 0.170162i | ||||
\(397\) | 9.38913 | − | 16.2624i | 0.471227 | − | 0.816189i | −0.528232 | − | 0.849100i | \(-0.677145\pi\) |
0.999458 | + | 0.0329117i | \(0.0104780\pi\) | |||||||
\(398\) | −0.587649 | + | 1.01784i | −0.0294562 | + | 0.0510196i | ||||
\(399\) | 8.10525 | + | 24.2680i | 0.405770 | + | 1.21492i | ||||
\(400\) | 2.58248 | + | 4.47298i | 0.129124 | + | 0.223649i | ||||
\(401\) | 20.9083 | 1.04411 | 0.522055 | − | 0.852912i | \(-0.325166\pi\) | ||||
0.522055 | + | 0.852912i | \(0.325166\pi\) | |||||||
\(402\) | −0.316213 | − | 0.156330i | −0.0157713 | − | 0.00779702i | ||||
\(403\) | 6.71633 | 0.334564 | ||||||||
\(404\) | 8.37619 | − | 14.5080i | 0.416731 | − | 0.721799i | ||||
\(405\) | 4.50469 | − | 16.5485i | 0.223840 | − | 0.822304i | ||||
\(406\) | −0.781590 | −0.0387897 | ||||||||
\(407\) | −1.75704 | + | 3.04328i | −0.0870932 | + | 0.150850i | ||||
\(408\) | −6.77733 | + | 4.51874i | −0.335528 | + | 0.223711i | ||||
\(409\) | 0.569856 | − | 0.987019i | 0.0281776 | − | 0.0488050i | −0.851593 | − | 0.524204i | \(-0.824363\pi\) |
0.879770 | + | 0.475399i | \(0.157696\pi\) | |||||||
\(410\) | 0.748780 | + | 1.29692i | 0.0369796 | + | 0.0640505i | ||||
\(411\) | −26.4497 | − | 13.0762i | −1.30467 | − | 0.645002i | ||||
\(412\) | 26.2786 | 1.29465 | ||||||||
\(413\) | 14.4103 | − | 24.9594i | 0.709084 | − | 1.22817i | ||||
\(414\) | 2.78355 | + | 3.64254i | 0.136804 | + | 0.179021i | ||||
\(415\) | −10.2052 | + | 17.6759i | −0.500953 | + | 0.867676i | ||||
\(416\) | 4.20186 | + | 7.27783i | 0.206013 | + | 0.356825i | ||||
\(417\) | −3.25994 | + | 2.17354i | −0.159640 | + | 0.106439i | ||||
\(418\) | 0.138878 | − | 0.510299i | 0.00679275 | − | 0.0249596i | ||||
\(419\) | 3.86547 | + | 6.69519i | 0.188840 | + | 0.327081i | 0.944864 | − | 0.327463i | \(-0.106194\pi\) |
−0.756023 | + | 0.654545i | \(0.772860\pi\) | |||||||
\(420\) | 1.41367 | + | 21.9017i | 0.0689802 | + | 1.06869i | ||||
\(421\) | 6.69993 | + | 11.6046i | 0.326535 | + | 0.565575i | 0.981822 | − | 0.189805i | \(-0.0607856\pi\) |
−0.655287 | + | 0.755380i | \(0.727452\pi\) | |||||||
\(422\) | −0.550423 | − | 0.953361i | −0.0267942 | − | 0.0464089i | ||||
\(423\) | −23.4467 | − | 30.6823i | −1.14002 | − | 1.49182i | ||||
\(424\) | 1.48938 | + | 2.57968i | 0.0723307 | + | 0.125280i | ||||
\(425\) | 4.17178 | − | 7.22574i | 0.202361 | − | 0.350500i | ||||
\(426\) | 0.944905 | + | 0.467142i | 0.0457808 | + | 0.0226331i | ||||
\(427\) | 6.17953 | − | 10.7033i | 0.299048 | − | 0.517967i | ||||
\(428\) | 10.0011 | − | 17.3225i | 0.483423 | − | 0.837313i | ||||
\(429\) | −0.256533 | − | 3.97440i | −0.0123855 | − | 0.191886i | ||||
\(430\) | −0.945043 | + | 1.63686i | −0.0455740 | + | 0.0789365i | ||||
\(431\) | 17.1747 | + | 29.7474i | 0.827275 | + | 1.43288i | 0.900168 | + | 0.435542i | \(0.143443\pi\) |
−0.0728934 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(432\) | 14.7823 | − | 12.8860i | 0.711212 | − | 0.619977i | ||||
\(433\) | −0.930181 | − | 1.61112i | −0.0447016 | − | 0.0774255i | 0.842809 | − | 0.538213i | \(-0.180900\pi\) |
−0.887511 | + | 0.460787i | \(0.847567\pi\) | |||||||
\(434\) | −0.600500 | − | 1.04010i | −0.0288249 | − | 0.0499262i | ||||
\(435\) | 3.50498 | + | 1.73279i | 0.168051 | + | 0.0830810i | ||||
\(436\) | 1.85476 | + | 3.21254i | 0.0888270 | + | 0.153853i | ||||
\(437\) | 24.0968 | + | 24.2863i | 1.15271 | + | 1.16177i | ||||
\(438\) | 1.25084 | + | 0.618389i | 0.0597672 | + | 0.0295478i | ||||
\(439\) | 7.53926 | + | 13.0584i | 0.359829 | + | 0.623243i | 0.987932 | − | 0.154888i | \(-0.0495016\pi\) |
−0.628103 | + | 0.778130i | \(0.716168\pi\) | |||||||
\(440\) | 0.458034 | − | 0.793338i | 0.0218359 | − | 0.0378209i | ||||
\(441\) | 5.17339 | − | 12.4199i | 0.246352 | − | 0.591422i | ||||
\(442\) | 2.18983 | − | 3.79289i | 0.104159 | − | 0.180409i | ||||
\(443\) | 5.10805 | 0.242691 | 0.121345 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121345 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(444\) | 15.9446 | − | 10.6310i | 0.756698 | − | 0.504523i | ||||
\(445\) | 10.0095 | + | 17.3370i | 0.474496 | + | 0.821851i | ||||
\(446\) | 2.82689 | − | 4.89632i | 0.133857 | − | 0.231848i | ||||
\(447\) | 3.73462 | + | 1.84632i | 0.176641 | + | 0.0873281i | ||||
\(448\) | −12.0384 | + | 20.8511i | −0.568762 | + | 0.985124i | ||||
\(449\) | −13.4001 | −0.632392 | −0.316196 | − | 0.948694i | \(-0.602406\pi\) | ||||
−0.316196 | + | 0.948694i | \(0.602406\pi\) | |||||||
\(450\) | 0.307364 | − | 0.737894i | 0.0144893 | − | 0.0347846i | ||||
\(451\) | 1.25770 | − | 2.17839i | 0.0592226 | − | 0.102577i | ||||
\(452\) | −19.3740 | −0.911275 | ||||||||
\(453\) | 11.1343 | − | 7.42374i | 0.523137 | − | 0.348798i | ||||
\(454\) | −4.49696 | −0.211053 | ||||||||
\(455\) | −11.9144 | − | 20.6363i | −0.558554 | − | 0.967445i | ||||
\(456\) | −3.86141 | + | 4.35974i | −0.180827 | + | 0.204163i | ||||
\(457\) | −12.1509 | + | 21.0459i | −0.568394 | + | 0.984487i | 0.428331 | + | 0.903622i | \(0.359102\pi\) |
−0.996725 | + | 0.0808654i | \(0.974232\pi\) | |||||||
\(458\) | 0.377970 | − | 0.654663i | 0.0176614 | − | 0.0305904i | ||||
\(459\) | −29.9672 | − | 10.2721i | −1.39875 | − | 0.479463i | ||||
\(460\) | 14.6735 | + | 25.4153i | 0.684156 | + | 1.18499i | ||||
\(461\) | −2.28981 | − | 3.96607i | −0.106647 | − | 0.184719i | 0.807763 | − | 0.589508i | \(-0.200678\pi\) |
−0.914410 | + | 0.404789i | \(0.867345\pi\) | |||||||
\(462\) | −0.592542 | + | 0.395073i | −0.0275676 | + | 0.0183805i | ||||
\(463\) | −14.8382 | − | 25.7005i | −0.689589 | − | 1.19440i | −0.971971 | − | 0.235101i | \(-0.924458\pi\) |
0.282382 | − | 0.959302i | \(-0.408875\pi\) | |||||||
\(464\) | 2.23532 | + | 3.87168i | 0.103772 | + | 0.179738i | ||||
\(465\) | 0.386990 | + | 5.99553i | 0.0179462 | + | 0.278036i | ||||
\(466\) | −1.18975 | −0.0551142 | ||||||||
\(467\) | 38.8322 | 1.79694 | 0.898469 | − | 0.439037i | \(-0.144680\pi\) | ||||
0.898469 | + | 0.439037i | \(0.144680\pi\) | |||||||
\(468\) | −8.35138 | + | 20.0493i | −0.386043 | + | 0.926779i | ||||
\(469\) | 1.77248 | + | 3.07002i | 0.0818455 | + | 0.141761i | ||||
\(470\) | 2.38781 | + | 4.13581i | 0.110141 | + | 0.190771i | ||||
\(471\) | −8.44455 | − | 4.17482i | −0.389104 | − | 0.192366i | ||||
\(472\) | 6.56022 | 0.301959 | ||||||||
\(473\) | 3.17470 | 0.145973 | ||||||||
\(474\) | −4.58305 | + | 3.05572i | −0.210506 | + | 0.140354i | ||||
\(475\) | 1.56651 | − | 5.75606i | 0.0718766 | − | 0.264106i | ||||
\(476\) | 40.5385 | 1.85808 | ||||||||
\(477\) | −4.45448 | + | 10.6939i | −0.203956 | + | 0.489642i | ||||
\(478\) | 1.87106 | − | 3.24077i | 0.0855803 | − | 0.148229i | ||||
\(479\) | 9.99299 | 0.456591 | 0.228296 | − | 0.973592i | \(-0.426685\pi\) | ||||
0.228296 | + | 0.973592i | \(0.426685\pi\) | |||||||
\(480\) | −6.25467 | + | 4.17026i | −0.285485 | + | 0.190345i | ||||
\(481\) | −10.4033 | + | 18.0190i | −0.474349 | + | 0.821596i | ||||
\(482\) | 1.03908 | + | 1.79974i | 0.0473287 | + | 0.0819758i | ||||
\(483\) | −2.96753 | − | 45.9752i | −0.135027 | − | 2.09194i | ||||
\(484\) | 20.8211 | 0.946412 | ||||||||
\(485\) | 13.9937 | + | 24.2378i | 0.635421 | + | 1.10058i | ||||
\(486\) | −2.97368 | − | 0.606865i | −0.134889 | − | 0.0275279i | ||||
\(487\) | −17.8510 | −0.808906 | −0.404453 | − | 0.914559i | \(-0.632538\pi\) | ||||
−0.404453 | + | 0.914559i | \(0.632538\pi\) | |||||||
\(488\) | 2.81320 | 0.127348 | ||||||||
\(489\) | −11.2945 | − | 5.58377i | −0.510754 | − | 0.252507i | ||||
\(490\) | −0.831953 | + | 1.44098i | −0.0375838 | + | 0.0650971i | ||||
\(491\) | −13.4844 | −0.608544 | −0.304272 | − | 0.952585i | \(-0.598413\pi\) | ||||
−0.304272 | + | 0.952585i | \(0.598413\pi\) | |||||||
\(492\) | −11.4132 | + | 7.60969i | −0.514548 | + | 0.343071i | ||||
\(493\) | 3.61097 | − | 6.25439i | 0.162630 | − | 0.281684i | ||||
\(494\) | 0.822285 | − | 3.02144i | 0.0369964 | − | 0.135941i | ||||
\(495\) | 3.53309 | − | 0.458003i | 0.158800 | − | 0.0205857i | ||||
\(496\) | −3.43481 | + | 5.94927i | −0.154228 | + | 0.267130i | ||||
\(497\) | −5.29650 | − | 9.17380i | −0.237580 | − | 0.411501i | ||||
\(498\) | 3.23774 | + | 1.60067i | 0.145086 | + | 0.0717279i | ||||
\(499\) | 15.2752 | 0.683811 | 0.341905 | − | 0.939734i | \(-0.388928\pi\) | ||||
0.341905 | + | 0.939734i | \(0.388928\pi\) | |||||||
\(500\) | 11.9061 | − | 20.6220i | 0.532458 | − | 0.922245i | ||||
\(501\) | 6.43208 | − | 4.28855i | 0.287364 | − | 0.191598i | ||||
\(502\) | −1.76103 | + | 3.05019i | −0.0785984 | + | 0.136136i | ||||
\(503\) | 0.700770 | + | 1.21377i | 0.0312458 | + | 0.0541193i | 0.881225 | − | 0.472696i | \(-0.156719\pi\) |
−0.849980 | + | 0.526816i | \(0.823386\pi\) | |||||||
\(504\) | 7.77749 | − | 1.00822i | 0.346437 | − | 0.0449095i | ||||
\(505\) | −16.2703 | −0.724019 | ||||||||
\(506\) | −0.476144 | + | 0.824706i | −0.0211672 | + | 0.0366627i | ||||
\(507\) | −0.0685584 | − | 1.06216i | −0.00304479 | − | 0.0471721i | ||||
\(508\) | −16.9828 | −0.753490 | ||||||||
\(509\) | −7.65770 | + | 13.2635i | −0.339421 | + | 0.587895i | −0.984324 | − | 0.176370i | \(-0.943565\pi\) |
0.644903 | + | 0.764265i | \(0.276898\pi\) | |||||||
\(510\) | 3.51202 | + | 1.73627i | 0.155515 | + | 0.0768834i | ||||
\(511\) | −7.01134 | − | 12.1440i | −0.310163 | − | 0.537219i | ||||
\(512\) | −14.4180 | −0.637192 | ||||||||
\(513\) | −22.5903 | − | 1.63713i | −0.997384 | − | 0.0722812i | ||||
\(514\) | −4.55023 | −0.200702 | ||||||||
\(515\) | −12.7612 | − | 22.1030i | −0.562325 | − | 0.973976i | ||||
\(516\) | −15.5199 | − | 7.67274i | −0.683226 | − | 0.337774i | ||||
\(517\) | 4.01071 | − | 6.94675i | 0.176391 | − | 0.305518i | ||||
\(518\) | 3.72058 | 0.163473 | ||||||||
\(519\) | −1.33946 | − | 20.7519i | −0.0587958 | − | 0.910909i | ||||
\(520\) | 2.71198 | − | 4.69729i | 0.118928 | − | 0.205990i | ||||
\(521\) | 23.8486 | 1.04483 | 0.522414 | − | 0.852692i | \(-0.325032\pi\) | ||||
0.522414 | + | 0.852692i | \(0.325032\pi\) | |||||||
\(522\) | 0.266045 | − | 0.638700i | 0.0116445 | − | 0.0279551i | ||||
\(523\) | 7.28432 | + | 12.6168i | 0.318521 | + | 0.551694i | 0.980180 | − | 0.198111i | \(-0.0634805\pi\) |
−0.661659 | + | 0.749805i | \(0.730147\pi\) | |||||||
\(524\) | 2.04496 | − | 3.54198i | 0.0893345 | − | 0.154732i | ||||
\(525\) | −6.68374 | + | 4.45634i | −0.291702 | + | 0.194491i | ||||
\(526\) | −2.37492 | + | 4.11348i | −0.103552 | + | 0.179356i | ||||
\(527\) | 11.0973 | 0.483407 | ||||||||
\(528\) | 3.65168 | + | 1.80532i | 0.158919 | + | 0.0785665i | ||||
\(529\) | −19.3021 | − | 33.4322i | −0.839221 | − | 1.45357i | ||||
\(530\) | 0.716341 | − | 1.24074i | 0.0311159 | − | 0.0538943i | ||||
\(531\) | 15.4912 | + | 20.2717i | 0.672259 | + | 0.879718i | ||||
\(532\) | 28.0255 | − | 7.39192i | 1.21506 | − | 0.320480i | ||||
\(533\) | 7.44671 | − | 12.8981i | 0.322553 | − | 0.558678i | ||||
\(534\) | 2.94747 | − | 1.96521i | 0.127549 | − | 0.0850428i | ||||
\(535\) | −19.4267 | −0.839889 | ||||||||
\(536\) | −0.403456 | + | 0.698807i | −0.0174267 | + | 0.0301839i | ||||
\(537\) | 31.0725 | + | 15.3617i | 1.34088 | + | 0.662904i | ||||
\(538\) | 4.87680 | 0.210254 | ||||||||
\(539\) | 2.79480 | 0.120380 | ||||||||
\(540\) | −18.3788 | − | 6.29989i | −0.790899 | − | 0.271104i | ||||
\(541\) | 20.7123 | + | 35.8747i | 0.890490 | + | 1.54237i | 0.839289 | + | 0.543686i | \(0.182972\pi\) |
0.0512015 | + | 0.998688i | \(0.483695\pi\) | |||||||
\(542\) | −0.554911 | −0.0238355 | ||||||||
\(543\) | −1.34886 | − | 20.8975i | −0.0578849 | − | 0.896797i | ||||
\(544\) | 6.94268 | + | 12.0251i | 0.297665 | + | 0.515571i | ||||
\(545\) | 1.80139 | − | 3.12010i | 0.0771631 | − | 0.133650i | ||||
\(546\) | −3.50839 | + | 2.33920i | −0.150145 | + | 0.100108i | ||||
\(547\) | 34.3461 | 1.46853 | 0.734266 | − | 0.678862i | \(-0.237526\pi\) | ||||
0.734266 | + | 0.678862i | \(0.237526\pi\) | |||||||
\(548\) | −16.7122 | + | 28.9463i | −0.713908 | + | 1.23652i | ||||
\(549\) | 6.64304 | + | 8.69307i | 0.283518 | + | 0.371011i | ||||
\(550\) | 0.166046 | 0.00708021 | ||||||||
\(551\) | 1.35593 | − | 4.98228i | 0.0577645 | − | 0.212252i | ||||
\(552\) | 8.72521 | − | 5.81748i | 0.371370 | − | 0.247608i | ||||
\(553\) | 55.3565 | 2.35400 | ||||||||
\(554\) | −0.447469 | −0.0190111 | ||||||||
\(555\) | −16.6846 | − | 8.24856i | −0.708224 | − | 0.350132i | ||||
\(556\) | 2.21924 | + | 3.84384i | 0.0941168 | + | 0.163015i | ||||
\(557\) | 2.91894 | + | 5.05575i | 0.123679 | + | 0.214219i | 0.921216 | − | 0.389052i | \(-0.127197\pi\) |
−0.797537 | + | 0.603271i | \(0.793864\pi\) | |||||||
\(558\) | 1.05435 | − | 0.136678i | 0.0446342 | − | 0.00578605i | ||||
\(559\) | 18.7971 | 0.795035 | ||||||||
\(560\) | 24.3726 | 1.02993 | ||||||||
\(561\) | −0.423866 | − | 6.56685i | −0.0178956 | − | 0.277253i | ||||
\(562\) | 1.38143 | + | 2.39271i | 0.0582721 | + | 0.100930i | ||||
\(563\) | 17.0958 | + | 29.6108i | 0.720503 | + | 1.24795i | 0.960799 | + | 0.277247i | \(0.0894222\pi\) |
−0.240296 | + | 0.970700i | \(0.577244\pi\) | |||||||
\(564\) | −36.3960 | + | 24.2668i | −1.53255 | + | 1.02182i | ||||
\(565\) | 9.40823 | + | 16.2955i | 0.395807 | + | 0.685559i | ||||
\(566\) | −0.805801 | − | 1.39569i | −0.0338704 | − | 0.0586652i | ||||
\(567\) | 21.4811 | + | 21.6524i | 0.902121 | + | 0.909316i | ||||
\(568\) | 1.20560 | − | 2.08817i | 0.0505860 | − | 0.0876175i | ||||
\(569\) | −20.3407 | + | 35.2311i | −0.852727 | + | 1.47697i | 0.0260109 | + | 0.999662i | \(0.491720\pi\) |
−0.878738 | + | 0.477305i | \(0.841614\pi\) | |||||||
\(570\) | 2.74456 | + | 0.559945i | 0.114957 | + | 0.0234535i | ||||
\(571\) | 2.75438 | + | 4.77073i | 0.115267 | + | 0.199649i | 0.917887 | − | 0.396843i | \(-0.129894\pi\) |
−0.802619 | + | 0.596492i | \(0.796561\pi\) | |||||||
\(572\) | −4.51163 | −0.188641 | ||||||||
\(573\) | 3.88191 | − | 2.58823i | 0.162169 | − | 0.108125i | ||||
\(574\) | −2.66321 | −0.111160 | ||||||||
\(575\) | −5.37080 | + | 9.30250i | −0.223978 | + | 0.387941i | ||||
\(576\) | −12.9414 | − | 16.9351i | −0.539224 | − | 0.705628i | ||||
\(577\) | −39.7898 | −1.65647 | −0.828235 | − | 0.560381i | \(-0.810655\pi\) | ||||
−0.828235 | + | 0.560381i | \(0.810655\pi\) | |||||||
\(578\) | 1.96333 | − | 3.40059i | 0.0816639 | − | 0.141446i | ||||
\(579\) | 19.4462 | + | 9.61381i | 0.808155 | + | 0.399536i | ||||
\(580\) | 2.21461 | − | 3.83581i | 0.0919565 | − | 0.159273i | ||||
\(581\) | −18.1486 | − | 31.4343i | −0.752930 | − | 1.30411i | ||||
\(582\) | 4.12068 | − | 2.74744i | 0.170808 | − | 0.113885i | ||||
\(583\) | −2.40642 | −0.0996638 | ||||||||
\(584\) | 1.59594 | − | 2.76425i | 0.0660405 | − | 0.114385i | ||||
\(585\) | 20.9191 | − | 2.71180i | 0.864898 | − | 0.112119i | ||||
\(586\) | −1.92836 | + | 3.34002i | −0.0796598 | + | 0.137975i | ||||
\(587\) | −2.86972 | − | 4.97050i | −0.118446 | − | 0.205154i | 0.800706 | − | 0.599057i | \(-0.204458\pi\) |
−0.919152 | + | 0.393903i | \(0.871125\pi\) | |||||||
\(588\) | −13.6627 | − | 6.75457i | −0.563440 | − | 0.278554i | ||||
\(589\) | 7.67191 | − | 2.02352i | 0.316115 | − | 0.0833776i | ||||
\(590\) | −1.57762 | − | 2.73252i | −0.0649497 | − | 0.112496i | ||||
\(591\) | −18.4060 | − | 9.09958i | −0.757123 | − | 0.374307i | ||||
\(592\) | −10.6407 | − | 18.4303i | −0.437331 | − | 0.757480i | ||||
\(593\) | −13.0607 | − | 22.6219i | −0.536340 | − | 0.928968i | −0.999097 | − | 0.0424831i | \(-0.986473\pi\) |
0.462757 | − | 0.886485i | \(-0.346860\pi\) | |||||||
\(594\) | −0.121151 | − | 0.618692i | −0.00497088 | − | 0.0253853i | ||||
\(595\) | −19.6860 | − | 34.0971i | −0.807047 | − | 1.39785i | ||||
\(596\) | 2.35970 | − | 4.08713i | 0.0966573 | − | 0.167415i | ||||
\(597\) | 0.673482 | + | 10.4341i | 0.0275638 | + | 0.427039i | ||||
\(598\) | −2.81921 | + | 4.88301i | −0.115286 | + | 0.199681i | ||||
\(599\) | 18.0733 | − | 31.3039i | 0.738456 | − | 1.27904i | −0.214734 | − | 0.976673i | \(-0.568888\pi\) |
0.953190 | − | 0.302371i | \(-0.0977783\pi\) | |||||||
\(600\) | −1.63915 | − | 0.810364i | −0.0669180 | − | 0.0330830i | ||||
\(601\) | −20.5640 | + | 35.6178i | −0.838821 | + | 1.45288i | 0.0520595 | + | 0.998644i | \(0.483421\pi\) |
−0.890881 | + | 0.454237i | \(0.849912\pi\) | |||||||
\(602\) | −1.68063 | − | 2.91094i | −0.0684975 | − | 0.118641i | ||||
\(603\) | −3.11210 | + | 0.403429i | −0.126734 | + | 0.0164289i | ||||
\(604\) | −7.57983 | − | 13.1286i | −0.308419 | − | 0.534197i | ||||
\(605\) | −10.1110 | − | 17.5127i | −0.411069 | − | 0.711992i | ||||
\(606\) | 0.185454 | + | 2.87320i | 0.00753357 | + | 0.116716i | ||||
\(607\) | −18.4789 | − | 32.0064i | −0.750035 | − | 1.29910i | −0.947805 | − | 0.318850i | \(-0.896703\pi\) |
0.197770 | − | 0.980248i | \(-0.436630\pi\) | |||||||
\(608\) | 6.99238 | + | 7.04735i | 0.283578 | + | 0.285808i | ||||
\(609\) | −5.78526 | + | 3.85728i | −0.234430 | + | 0.156305i | ||||
\(610\) | −0.676527 | − | 1.17178i | −0.0273918 | − | 0.0474440i | ||||
\(611\) | 23.7471 | − | 41.1311i | 0.960704 | − | 1.66399i | ||||
\(612\) | −13.7989 | + | 33.1273i | −0.557788 | + | 1.33909i | ||||
\(613\) | 16.4713 | − | 28.5292i | 0.665270 | − | 1.15228i | −0.313942 | − | 0.949442i | \(-0.601650\pi\) |
0.979212 | − | 0.202839i | \(-0.0650169\pi\) | |||||||
\(614\) | −3.53601 | −0.142702 | ||||||||
\(615\) | 11.9429 | + | 5.90436i | 0.481586 | + | 0.238087i | ||||
\(616\) | 0.814553 | + | 1.41085i | 0.0328193 | + | 0.0568446i | ||||
\(617\) | 6.58944 | − | 11.4132i | 0.265281 | − | 0.459480i | −0.702356 | − | 0.711826i | \(-0.747869\pi\) |
0.967637 | + | 0.252346i | \(0.0812020\pi\) | |||||||
\(618\) | −3.75775 | + | 2.50546i | −0.151159 | + | 0.100784i | ||||
\(619\) | −15.4316 | + | 26.7283i | −0.620249 | + | 1.07430i | 0.369190 | + | 0.929354i | \(0.379635\pi\) |
−0.989439 | + | 0.144949i | \(0.953698\pi\) | |||||||
\(620\) | 6.80597 | 0.273334 | ||||||||
\(621\) | 38.5801 | + | 13.2245i | 1.54817 | + | 0.530680i | ||||
\(622\) | 0.225625 | − | 0.390794i | 0.00904675 | − | 0.0156694i | ||||
\(623\) | −35.6011 | −1.42633 | ||||||||
\(624\) | 21.6213 | + | 10.6892i | 0.865545 | + | 0.427909i | ||||
\(625\) | −16.2842 | −0.651369 | ||||||||
\(626\) | 1.82137 | + | 3.15470i | 0.0727966 | + | 0.126087i | ||||
\(627\) | −1.49045 | − | 4.46257i | −0.0595229 | − | 0.178218i | ||||
\(628\) | −5.33566 | + | 9.24163i | −0.212916 | + | 0.368781i | ||||
\(629\) | −17.1892 | + | 29.7726i | −0.685379 | + | 1.18711i | ||||
\(630\) | −2.29031 | − | 2.99709i | −0.0912480 | − | 0.119407i | ||||
\(631\) | −9.33975 | − | 16.1769i | −0.371810 | − | 0.643993i | 0.618034 | − | 0.786151i | \(-0.287929\pi\) |
−0.989844 | + | 0.142158i | \(0.954596\pi\) | |||||||
\(632\) | 6.30020 | + | 10.9123i | 0.250609 | + | 0.434067i | ||||
\(633\) | −8.77918 | − | 4.34025i | −0.348941 | − | 0.172510i | ||||
\(634\) | −1.40073 | − | 2.42613i | −0.0556301 | − | 0.0963541i | ||||
\(635\) | 8.24705 | + | 14.2843i | 0.327274 | + | 0.566856i | ||||
\(636\) | 11.7641 | + | 5.81593i | 0.466476 | + | 0.230617i | ||||
\(637\) | 16.5478 | 0.655646 | ||||||||
\(638\) | 0.143724 | 0.00569011 | ||||||||
\(639\) | 9.29952 | − | 1.20552i | 0.367883 | − | 0.0476897i | ||||
\(640\) | 5.65815 | + | 9.80020i | 0.223658 | + | 0.387387i | ||||
\(641\) | 12.3252 | + | 21.3478i | 0.486815 | + | 0.843188i | 0.999885 | − | 0.0151588i | \(-0.00482537\pi\) |
−0.513070 | + | 0.858347i | \(0.671492\pi\) | |||||||
\(642\) | 0.221432 | + | 3.43059i | 0.00873921 | + | 0.135394i | ||||
\(643\) | 5.23393 | 0.206406 | 0.103203 | − | 0.994660i | \(-0.467091\pi\) | ||||
0.103203 | + | 0.994660i | \(0.467091\pi\) | |||||||
\(644\) | −52.1898 | −2.05657 | ||||||||
\(645\) | 1.08308 | + | 16.7799i | 0.0426461 | + | 0.660706i | ||||
\(646\) | 1.35865 | − | 4.99229i | 0.0534555 | − | 0.196419i | ||||
\(647\) | −7.54367 | −0.296572 | −0.148286 | − | 0.988944i | \(-0.547376\pi\) | ||||
−0.148286 | + | 0.988944i | \(0.547376\pi\) | |||||||
\(648\) | −1.82348 | + | 6.69879i | −0.0716332 | + | 0.263153i | ||||
\(649\) | −2.64987 | + | 4.58971i | −0.104016 | + | 0.180162i | ||||
\(650\) | 0.983143 | 0.0385620 | ||||||||
\(651\) | −9.57789 | − | 4.73512i | −0.375387 | − | 0.185584i | ||||
\(652\) | −7.13638 | + | 12.3606i | −0.279482 | + | 0.484077i | ||||
\(653\) | 9.82702 | + | 17.0209i | 0.384561 | + | 0.666079i | 0.991708 | − | 0.128510i | \(-0.0410195\pi\) |
−0.607147 | + | 0.794589i | \(0.707686\pi\) | |||||||
\(654\) | −0.571516 | − | 0.282546i | −0.0223480 | − | 0.0110484i | ||||
\(655\) | −3.97223 | −0.155208 | ||||||||
\(656\) | 7.61668 | + | 13.1925i | 0.297381 | + | 0.515080i | ||||
\(657\) | 12.3104 | − | 1.59583i | 0.480275 | − | 0.0622594i | ||||
\(658\) | −8.49280 | −0.331084 | ||||||||
\(659\) | −34.9152 | −1.36010 | −0.680051 | − | 0.733165i | \(-0.738042\pi\) | ||||
−0.680051 | + | 0.733165i | \(0.738042\pi\) | |||||||
\(660\) | −0.259957 | − | 4.02744i | −0.0101188 | − | 0.156768i | ||||
\(661\) | 12.1794 | − | 21.0954i | 0.473725 | − | 0.820515i | −0.525823 | − | 0.850594i | \(-0.676243\pi\) |
0.999548 | + | 0.0300790i | \(0.00957589\pi\) | |||||||
\(662\) | −5.56671 | −0.216356 | ||||||||
\(663\) | −2.50968 | − | 38.8818i | −0.0974677 | − | 1.51004i | ||||
\(664\) | 4.13103 | − | 7.15515i | 0.160315 | − | 0.277674i | ||||
\(665\) | −19.8269 | − | 19.9828i | −0.768854 | − | 0.774899i | ||||
\(666\) | −1.26645 | + | 3.04039i | −0.0490739 | + | 0.117813i | ||||
\(667\) | −4.64881 | + | 8.05198i | −0.180003 | + | 0.311774i | ||||
\(668\) | −4.37872 | − | 7.58416i | −0.169418 | − | 0.293440i | ||||
\(669\) | −3.23979 | − | 50.1933i | −0.125258 | − | 1.94059i | ||||
\(670\) | 0.388098 | 0.0149935 | ||||||||
\(671\) | −1.13634 | + | 1.96819i | −0.0438678 | + | 0.0759812i | ||||
\(672\) | −0.861113 | − | 13.3410i | −0.0332181 | − | 0.514641i | ||||
\(673\) | −7.88496 | + | 13.6572i | −0.303943 | + | 0.526445i | −0.977025 | − | 0.213123i | \(-0.931637\pi\) |
0.673083 | + | 0.739567i | \(0.264970\pi\) | |||||||
\(674\) | 1.97718 | + | 3.42458i | 0.0761583 | + | 0.131910i | ||||
\(675\) | −1.36655 | − | 6.97871i | −0.0525987 | − | 0.268611i | ||||
\(676\) | −1.20573 | −0.0463744 | ||||||||
\(677\) | −19.7783 | + | 34.2569i | −0.760140 | + | 1.31660i | 0.182638 | + | 0.983180i | \(0.441536\pi\) |
−0.942778 | + | 0.333421i | \(0.891797\pi\) | |||||||
\(678\) | 2.77042 | − | 1.84716i | 0.106397 | − | 0.0709396i | ||||
\(679\) | −49.7718 | −1.91007 | ||||||||
\(680\) | 4.48098 | − | 7.76128i | 0.171838 | − | 0.297632i | ||||
\(681\) | −33.2861 | + | 22.1933i | −1.27552 | + | 0.850447i | ||||
\(682\) | 0.110424 | + | 0.191260i | 0.00422836 | + | 0.00732374i | ||||
\(683\) | 4.78389 | 0.183051 | 0.0915253 | − | 0.995803i | \(-0.470826\pi\) | ||||
0.0915253 | + | 0.995803i | \(0.470826\pi\) | |||||||
\(684\) | −3.49907 | + | 25.4180i | −0.133790 | + | 0.971882i | ||||
\(685\) | 32.4625 | 1.24033 | ||||||||
\(686\) | 0.829781 | + | 1.43722i | 0.0316812 | + | 0.0548734i | ||||
\(687\) | −0.433177 | − | 6.71110i | −0.0165267 | − | 0.256044i | ||||
\(688\) | −9.61310 | + | 16.6504i | −0.366496 | + | 0.634789i | ||||
\(689\) | −14.2482 | −0.542814 | ||||||||
\(690\) | −4.52141 | − | 2.23530i | −0.172127 | − | 0.0850964i | ||||
\(691\) | 8.12539 | − | 14.0736i | 0.309104 | − | 0.535384i | −0.669062 | − | 0.743206i | \(-0.733304\pi\) |
0.978167 | + | 0.207822i | \(0.0666375\pi\) | |||||||
\(692\) | −23.5570 | −0.895504 | ||||||||
\(693\) | −2.43619 | + | 5.84859i | −0.0925430 | + | 0.222170i | ||||
\(694\) | −3.48109 | − | 6.02943i | −0.132140 | − | 0.228874i | ||||
\(695\) | 2.15538 | − | 3.73323i | 0.0817583 | − | 0.141610i | ||||
\(696\) | −1.41880 | − | 0.701428i | −0.0537795 | − | 0.0265876i | ||||
\(697\) | 12.3041 | − | 21.3114i | 0.466052 | − | 0.807225i | ||||
\(698\) | −0.759192 | −0.0287358 | ||||||||
\(699\) | −8.80644 | + | 5.87163i | −0.333090 | + | 0.222086i | ||||
\(700\) | 4.55004 | + | 7.88089i | 0.171975 | + | 0.297870i | ||||
\(701\) | −11.1768 | + | 19.3588i | −0.422142 | + | 0.731171i | −0.996149 | − | 0.0876795i | \(-0.972055\pi\) |
0.574007 | + | 0.818850i | \(0.305388\pi\) | |||||||
\(702\) | −0.717323 | − | 3.66322i | −0.0270736 | − | 0.138260i | ||||
\(703\) | −6.45460 | + | 23.7170i | −0.243440 | + | 0.894505i | ||||
\(704\) | 2.21371 | − | 3.83426i | 0.0834323 | − | 0.144509i | ||||
\(705\) | 38.0853 | + | 18.8286i | 1.43437 | + | 0.709127i | ||||
\(706\) | 1.94791 | 0.0733106 | ||||||||
\(707\) | 14.4673 | − | 25.0581i | 0.544098 | − | 0.942406i | ||||
\(708\) | 24.0468 | − | 16.0330i | 0.903733 | − | 0.602558i | ||||
\(709\) | −16.7749 | −0.629993 | −0.314996 | − | 0.949093i | \(-0.602003\pi\) | ||||
−0.314996 | + | 0.949093i | \(0.602003\pi\) | |||||||
\(710\) | −1.15971 | −0.0435231 | ||||||||
\(711\) | −18.8428 | + | 45.2362i | −0.706660 | + | 1.69649i | ||||
\(712\) | −4.05181 | − | 7.01795i | −0.151848 | − | 0.263009i | ||||
\(713\) | −14.2868 | −0.535046 | ||||||||
\(714\) | −5.79688 | + | 3.86503i | −0.216943 | + | 0.144645i | ||||
\(715\) | 2.19090 | + | 3.79475i | 0.0819350 | + | 0.141916i | ||||
\(716\) | 19.6331 | − | 34.0055i | 0.733722 | − | 1.27084i | ||||
\(717\) | −2.14435 | − | 33.2219i | −0.0800822 | − | 1.24069i | ||||
\(718\) | 0.879207 | 0.0328117 | ||||||||
\(719\) | −24.2869 | + | 42.0661i | −0.905747 | + | 1.56880i | −0.0858361 | + | 0.996309i | \(0.527356\pi\) |
−0.819911 | + | 0.572491i | \(0.805977\pi\) | |||||||
\(720\) | −8.29620 | + | 19.9168i | −0.309181 | + | 0.742256i | ||||
\(721\) | 45.3882 | 1.69034 | ||||||||
\(722\) | 0.0289680 | − | 3.69906i | 0.00107808 | − | 0.137665i | ||||
\(723\) | 16.5732 | + | 8.19345i | 0.616363 | + | 0.304718i | ||||
\(724\) | −23.7223 | −0.881631 | ||||||||
\(725\) | 1.62118 | 0.0602091 | ||||||||
\(726\) | −2.97734 | + | 1.98512i | −0.110500 | + | 0.0736749i | ||||
\(727\) | −15.7902 | − | 27.3495i | −0.585627 | − | 1.01434i | −0.994797 | − | 0.101877i | \(-0.967515\pi\) |
0.409170 | − | 0.912458i | \(-0.365818\pi\) | |||||||
\(728\) | 4.82290 | + | 8.35350i | 0.178748 | + | 0.309601i | ||||
\(729\) | −25.0059 | + | 10.1837i | −0.926143 | + | 0.377172i | ||||
\(730\) | −1.53519 | −0.0568198 | ||||||||
\(731\) | 31.0583 | 1.14873 | ||||||||
\(732\) | 10.3119 | − | 6.87540i | 0.381139 | − | 0.254122i | ||||
\(733\) | −17.0488 | − | 29.5294i | −0.629712 | − | 1.09069i | −0.987609 | − | 0.156932i | \(-0.949840\pi\) |
0.357898 | − | 0.933761i | \(-0.383494\pi\) | |||||||
\(734\) | −2.28634 | − | 3.96007i | −0.0843905 | − | 0.146169i | ||||
\(735\) | 0.953469 | + | 14.7719i | 0.0351692 | + | 0.544868i | ||||
\(736\) | −8.93810 | − | 15.4812i | −0.329463 | − | 0.570646i | ||||
\(737\) | −0.325936 | − | 0.564538i | −0.0120060 | − | 0.0207950i | ||||
\(738\) | 0.906529 | − | 2.17632i | 0.0333698 | − | 0.0801115i | ||||
\(739\) | 16.0360 | − | 27.7752i | 0.589894 | − | 1.02173i | −0.404352 | − | 0.914603i | \(-0.632503\pi\) |
0.994246 | − | 0.107123i | \(-0.0341637\pi\) | |||||||
\(740\) | −10.5421 | + | 18.2595i | −0.387536 | + | 0.671233i | ||||
\(741\) | −8.82484 | − | 26.4225i | −0.324189 | − | 0.970656i | ||||
\(742\) | 1.27392 | + | 2.20649i | 0.0467670 | + | 0.0810028i | ||||
\(743\) | −19.2215 | −0.705170 | −0.352585 | − | 0.935780i | \(-0.614697\pi\) | ||||
−0.352585 | + | 0.935780i | \(0.614697\pi\) | |||||||
\(744\) | −0.156652 | − | 2.42697i | −0.00574314 | − | 0.0889771i | ||||
\(745\) | −4.58360 | −0.167930 | ||||||||
\(746\) | 2.37560 | − | 4.11465i | 0.0869768 | − | 0.150648i | ||||
\(747\) | 31.8650 | − | 4.13075i | 1.16588 | − | 0.151136i | ||||
\(748\) | −7.45452 | −0.272564 | ||||||||
\(749\) | 17.2739 | − | 29.9192i | 0.631174 | − | 1.09323i | ||||
\(750\) | 0.263610 | + | 4.08404i | 0.00962566 | + | 0.149128i | ||||
\(751\) | −11.1484 | + | 19.3096i | −0.406811 | + | 0.704618i | −0.994530 | − | 0.104447i | \(-0.966693\pi\) |
0.587719 | + | 0.809065i | \(0.300026\pi\) | |||||||
\(752\) | 24.2891 | + | 42.0700i | 0.885732 | + | 1.53413i | ||||
\(753\) | 2.01824 | + | 31.2681i | 0.0735489 | + | 1.13947i | ||||
\(754\) | 0.850980 | 0.0309909 | ||||||||
\(755\) | −7.36171 | + | 12.7509i | −0.267920 | + | 0.464051i | ||||
\(756\) | 26.0447 | − | 22.7037i | 0.947236 | − | 0.825725i | ||||
\(757\) | 12.7479 | − | 22.0801i | 0.463331 | − | 0.802513i | −0.535793 | − | 0.844349i | \(-0.679987\pi\) |
0.999124 | + | 0.0418359i | \(0.0133207\pi\) | |||||||
\(758\) | −1.72418 | − | 2.98637i | −0.0626252 | − | 0.108470i | ||||
\(759\) | 0.545691 | + | 8.45425i | 0.0198073 | + | 0.306870i | ||||
\(760\) | 1.68262 | − | 6.18268i | 0.0610350 | − | 0.224269i | ||||
\(761\) | 6.39108 | + | 11.0697i | 0.231676 | + | 0.401275i | 0.958302 | − | 0.285759i | \(-0.0922456\pi\) |
−0.726625 | + | 0.687034i | \(0.758912\pi\) | |||||||
\(762\) | 2.42849 | − | 1.61918i | 0.0879747 | − | 0.0586566i | ||||
\(763\) | 3.20353 | + | 5.54868i | 0.115976 | + | 0.200876i | ||||
\(764\) | −2.64265 | − | 4.57721i | −0.0956078 | − | 0.165598i | ||||
\(765\) | 34.5644 | − | 4.48068i | 1.24968 | − | 0.161999i | ||||
\(766\) | 0.396763 | + | 0.687214i | 0.0143356 | + | 0.0248301i | ||||
\(767\) | −15.6896 | + | 27.1753i | −0.566520 | + | 0.981242i | ||||
\(768\) | −18.8107 | + | 12.5419i | −0.678773 | + | 0.452568i | ||||
\(769\) | −0.952422 | + | 1.64964i | −0.0343452 | + | 0.0594877i | −0.882687 | − | 0.469961i | \(-0.844268\pi\) |
0.848342 | + | 0.529449i | \(0.177601\pi\) | |||||||
\(770\) | 0.391772 | − | 0.678570i | 0.0141185 | − | 0.0244539i | ||||
\(771\) | −33.6804 | + | 22.4562i | −1.21297 | + | 0.808740i | ||||
\(772\) | 12.2870 | − | 21.2817i | 0.442218 | − | 0.765945i | ||||
\(773\) | 16.8937 | + | 29.2607i | 0.607623 | + | 1.05243i | 0.991631 | + | 0.129104i | \(0.0412102\pi\) |
−0.384008 | + | 0.923330i | \(0.625456\pi\) | |||||||
\(774\) | 2.95083 | − | 0.382524i | 0.106066 | − | 0.0137496i | ||||
\(775\) | 1.24556 | + | 2.15737i | 0.0447419 | + | 0.0774952i | ||||
\(776\) | −5.66460 | − | 9.81137i | −0.203347 | − | 0.352208i | ||||
\(777\) | 27.5394 | − | 18.3617i | 0.987971 | − | 0.658723i | ||||
\(778\) | 0.517066 | + | 0.895584i | 0.0185377 | + | 0.0321082i | ||||
\(779\) | 4.62023 | − | 16.9768i | 0.165537 | − | 0.608255i | ||||
\(780\) | −1.53918 | − | 23.8461i | −0.0551115 | − | 0.853829i | ||||
\(781\) | 0.973958 | + | 1.68695i | 0.0348510 | + | 0.0603636i | ||||
\(782\) | −4.65815 | + | 8.06816i | −0.166575 | + | 0.288517i | ||||
\(783\) | −1.18285 | − | 6.04057i | −0.0422716 | − | 0.215873i | ||||
\(784\) | −8.46273 | + | 14.6579i | −0.302240 | + | 0.523496i | ||||
\(785\) | 10.3642 | 0.369916 | ||||||||
\(786\) | 0.0452768 | + | 0.701462i | 0.00161497 | + | 0.0250203i | ||||
\(787\) | −0.571053 | − | 0.989094i | −0.0203559 | − | 0.0352574i | 0.855668 | − | 0.517525i | \(-0.173147\pi\) |
−0.876024 | + | 0.482268i | \(0.839813\pi\) | |||||||
\(788\) | −11.6298 | + | 20.1434i | −0.414294 | + | 0.717578i | ||||
\(789\) | 2.72181 | + | 42.1683i | 0.0968988 | + | 1.50123i | ||||
\(790\) | 3.03018 | − | 5.24843i | 0.107809 | − | 0.186731i | ||||
\(791\) | −33.4626 | −1.18979 | ||||||||
\(792\) | −1.43018 | + | 0.185398i | −0.0508193 | + | 0.00658784i | ||||
\(793\) | −6.72815 | + | 11.6535i | −0.238924 | + | 0.413828i | ||||
\(794\) | 3.65600 | 0.129747 | ||||||||
\(795\) | −0.820971 | − | 12.7191i | −0.0291168 | − | 0.451100i | ||||
\(796\) | 11.8445 | 0.419817 | ||||||||
\(797\) | −14.0447 | − | 24.3261i | −0.497488 | − | 0.861674i | 0.502508 | − | 0.864573i | \(-0.332411\pi\) |
−0.999996 | + | 0.00289827i | \(0.999077\pi\) | |||||||
\(798\) | −3.30279 | + | 3.72903i | −0.116918 | + | 0.132006i | ||||
\(799\) | 39.2371 | − | 67.9606i | 1.38811 | − | 2.40427i | ||||
\(800\) | −1.55849 | + | 2.69939i | −0.0551010 | + | 0.0954377i | ||||
\(801\) | 12.1183 | − | 29.0925i | 0.428178 | − | 1.02793i | ||||
\(802\) | 2.03535 | + | 3.52533i | 0.0718708 | + | 0.124484i | ||||
\(803\) | 1.28930 | + | 2.23313i | 0.0454983 | + | 0.0788053i | ||||
\(804\) | 0.228981 | + | 3.54755i | 0.00807554 | + | 0.125112i | ||||
\(805\) | 25.3440 | + | 43.8971i | 0.893259 | + | 1.54717i | ||||
\(806\) | 0.653812 | + | 1.13244i | 0.0230296 | + | 0.0398884i | ||||
\(807\) | 36.0976 | − | 24.0678i | 1.27069 | − | 0.847227i | ||||
\(808\) | 6.58616 | 0.231700 | ||||||||
\(809\) | −19.5465 | −0.687217 | −0.343609 | − | 0.939113i | \(-0.611649\pi\) | ||||
−0.343609 | + | 0.939113i | \(0.611649\pi\) | |||||||
\(810\) | 3.22876 | − | 0.851413i | 0.113447 | − | 0.0299156i | ||||
\(811\) | 11.5944 | + | 20.0821i | 0.407134 | + | 0.705176i | 0.994567 | − | 0.104096i | \(-0.0331950\pi\) |
−0.587433 | + | 0.809272i | \(0.699862\pi\) | |||||||
\(812\) | 3.93838 | + | 6.82148i | 0.138210 | + | 0.239387i | ||||
\(813\) | −4.10740 | + | 2.73858i | −0.144053 | + | 0.0960462i | ||||
\(814\) | −0.684168 | −0.0239801 | ||||||||
\(815\) | 13.8620 | 0.485566 | ||||||||
\(816\) | 35.7247 | + | 17.6616i | 1.25061 | + | 0.618279i | ||||
\(817\) | 21.4716 | − | 5.66327i | 0.751195 | − | 0.198133i | ||||
\(818\) | 0.221894 | 0.00775835 | ||||||||
\(819\) | −14.4244 | + | 34.6290i | −0.504031 | + | 1.21004i | ||||
\(820\) | 7.54610 | − | 13.0702i | 0.263521 | − | 0.456432i | ||||
\(821\) | −1.73188 | −0.0604429 | −0.0302214 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302214 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(822\) | −0.370018 | − | 5.73260i | −0.0129059 | − | 0.199947i | ||||
\(823\) | 5.42401 | − | 9.39465i | 0.189069 | − | 0.327477i | −0.755871 | − | 0.654720i | \(-0.772786\pi\) |
0.944940 | + | 0.327243i | \(0.106120\pi\) | |||||||
\(824\) | 5.16569 | + | 8.94723i | 0.179955 | + | 0.311692i | ||||
\(825\) | 1.22905 | − | 0.819464i | 0.0427902 | − | 0.0285301i | ||||
\(826\) | 5.61118 | 0.195238 | ||||||||
\(827\) | 23.9980 | + | 41.5658i | 0.834493 | + | 1.44538i | 0.894442 | + | 0.447183i | \(0.147573\pi\) |
−0.0599489 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(828\) | 17.7649 | − | 42.6485i | 0.617372 | − | 1.48214i | ||||
\(829\) | −36.8202 | −1.27882 | −0.639409 | − | 0.768867i | \(-0.720821\pi\) | ||||
−0.639409 | + | 0.768867i | \(0.720821\pi\) | |||||||
\(830\) | −3.97377 | −0.137932 | ||||||||
\(831\) | −3.31212 | + | 2.20833i | −0.114896 | + | 0.0766063i | ||||
\(832\) | 13.1072 | − | 22.7023i | 0.454410 | − | 0.787061i | ||||
\(833\) | 27.3417 | 0.947333 | ||||||||
\(834\) | −0.683825 | − | 0.338070i | −0.0236789 | − | 0.0117064i | ||||
\(835\) | −4.25271 | + | 7.36592i | −0.147171 | + | 0.254908i | ||||
\(836\) | −5.15353 | + | 1.35928i | −0.178239 | + | 0.0470117i | ||||
\(837\) | 7.12966 | − | 6.21507i | 0.246437 | − | 0.214824i | ||||
\(838\) | −0.752581 | + | 1.30351i | −0.0259975 | + | 0.0450290i | ||||
\(839\) | −12.9609 | − | 22.4490i | −0.447461 | − | 0.775025i | 0.550759 | − | 0.834664i | \(-0.314338\pi\) |
−0.998220 | + | 0.0596394i | \(0.981005\pi\) | |||||||
\(840\) | −7.17912 | + | 4.78663i | −0.247703 | + | 0.165154i | ||||
\(841\) | −27.5968 | −0.951612 | ||||||||
\(842\) | −1.30443 | + | 2.25934i | −0.0449537 | + | 0.0778621i | ||||
\(843\) | 22.0336 | + | 10.8930i | 0.758879 | + | 0.375175i | ||||
\(844\) | −5.54709 | + | 9.60784i | −0.190939 | + | 0.330716i | ||||
\(845\) | 0.585519 | + | 1.01415i | 0.0201425 | + | 0.0348878i | ||||
\(846\) | 2.89086 | − | 6.94015i | 0.0993900 | − | 0.238607i | ||||
\(847\) | 35.9620 | 1.23567 | ||||||||
\(848\) | 7.28671 | − | 12.6210i | 0.250227 | − | 0.433405i | ||||
\(849\) | −12.8524 | − | 6.35399i | −0.441094 | − | 0.218068i | ||||
\(850\) | 1.62444 | 0.0557177 | ||||||||
\(851\) | 22.1296 | − | 38.3296i | 0.758594 | − | 1.31392i | ||||
\(852\) | −0.684238 | − | 10.6007i | −0.0234416 | − | 0.363175i | ||||
\(853\) | −21.3868 | − | 37.0430i | −0.732270 | − | 1.26833i | −0.955911 | − | 0.293658i | \(-0.905127\pi\) |
0.223640 | − | 0.974672i | \(-0.428206\pi\) | |||||||
\(854\) | 2.40623 | 0.0823394 | ||||||||
\(855\) | 23.0784 | − | 9.40021i | 0.789264 | − | 0.321480i | ||||
\(856\) | 7.86385 | 0.268781 | ||||||||
\(857\) | 16.8665 | + | 29.2136i | 0.576149 | + | 0.997919i | 0.995916 | + | 0.0902869i | \(0.0287784\pi\) |
−0.419767 | + | 0.907632i | \(0.637888\pi\) | |||||||
\(858\) | 0.645148 | − | 0.430148i | 0.0220250 | − | 0.0146850i | ||||
\(859\) | −4.24540 | + | 7.35325i | −0.144851 | + | 0.250890i | −0.929317 | − | 0.369282i | \(-0.879604\pi\) |
0.784466 | + | 0.620172i | \(0.212937\pi\) | |||||||
\(860\) | 19.0480 | 0.649533 | ||||||||
\(861\) | −19.7128 | + | 13.1434i | −0.671811 | + | 0.447926i | ||||
\(862\) | −3.34380 | + | 5.79162i | −0.113890 | + | 0.197264i | ||||
\(863\) | −1.25544 | −0.0427358 | −0.0213679 | − | 0.999772i | \(-0.506802\pi\) | ||||
−0.0213679 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(864\) | 11.1951 | + | 3.83746i | 0.380866 | + | 0.130553i | ||||
\(865\) | 11.4396 | + | 19.8139i | 0.388958 | + | 0.673694i | ||||
\(866\) | 0.181100 | − | 0.313675i | 0.00615403 | − | 0.0106591i | ||||
\(867\) | −2.25010 | − | 34.8603i | −0.0764174 | − | 1.18392i | ||||
\(868\) | −6.05176 | + | 10.4819i | −0.205410 | + | 0.355780i | ||||
\(869\) | −10.1794 | −0.345311 | ||||||||
\(870\) | 0.0490328 | + | 0.759654i | 0.00166237 | + | 0.0257547i | ||||
\(871\) | −1.92984 | − | 3.34258i | −0.0653902 | − | 0.113259i | ||||
\(872\) | −0.729197 | + | 1.26301i | −0.0246937 | + | 0.0427708i | ||||
\(873\) | 16.9418 | − | 40.6725i | 0.573394 | − | 1.37656i | ||||
\(874\) | −1.74915 | + | 6.42714i | −0.0591658 | + | 0.217401i | ||||
\(875\) | 20.5642 | − | 35.6182i | 0.695196 | − | 1.20412i | ||||
\(876\) | −0.905773 | − | 14.0329i | −0.0306032 | − | 0.474128i | ||||
\(877\) | −3.81281 | −0.128750 | −0.0643748 | − | 0.997926i | \(-0.520505\pi\) | ||||
−0.0643748 | + | 0.997926i | \(0.520505\pi\) | |||||||
\(878\) | −1.46785 | + | 2.54238i | −0.0495374 | + | 0.0858012i | ||||
\(879\) | 2.21002 | + | 34.2393i | 0.0745420 | + | 1.15486i | ||||
\(880\) | −4.48182 | −0.151082 | ||||||||
\(881\) | −17.1658 | −0.578331 | −0.289165 | − | 0.957279i | \(-0.593378\pi\) | ||||
−0.289165 | + | 0.957279i | \(0.593378\pi\) | |||||||
\(882\) | 2.59772 | − | 0.336749i | 0.0874697 | − | 0.0113389i | ||||
\(883\) | −1.40205 | − | 2.42843i | −0.0471829 | − | 0.0817231i | 0.841469 | − | 0.540305i | \(-0.181691\pi\) |
−0.888652 | + | 0.458582i | \(0.848358\pi\) | |||||||
\(884\) | −44.1376 | −1.48451 | ||||||||
\(885\) | −25.1629 | − | 12.4400i | −0.845840 | − | 0.418167i | ||||
\(886\) | 0.497252 | + | 0.861265i | 0.0167055 | + | 0.0289348i | ||||
\(887\) | 19.9965 | − | 34.6349i | 0.671416 | − | 1.16293i | −0.306087 | − | 0.952004i | \(-0.599020\pi\) |
0.977503 | − | 0.210923i | \(-0.0676469\pi\) | |||||||
\(888\) | 6.75389 | + | 3.33899i | 0.226646 | + | 0.112049i | ||||
\(889\) | −29.3326 | −0.983783 | ||||||||
\(890\) | −1.94878 | + | 3.37539i | −0.0653234 | + | 0.113143i | ||||
\(891\) | −3.95010 | − | 3.98160i | −0.132333 | − | 0.133389i | ||||
\(892\) | −56.9781 | −1.90777 | ||||||||
\(893\) | 14.7336 | − | 54.1378i | 0.493041 | − | 1.81165i | ||||
\(894\) | 0.0522454 | + | 0.809426i | 0.00174735 | + | 0.0270712i | ||||
\(895\) | −38.1362 | −1.27475 | ||||||||
\(896\) | −20.1245 | −0.672313 | ||||||||
\(897\) | 3.23099 | + | 50.0569i | 0.107880 | + | 1.67135i | ||||
\(898\) | −1.30446 | − | 2.25939i | −0.0435304 | − | 0.0753968i | ||||
\(899\) | 1.07812 | + | 1.86736i | 0.0359574 | + | 0.0622800i | ||||
\(900\) | −7.98889 | + | 1.03562i | −0.266296 | + | 0.0345207i | ||||
\(901\) | −23.5422 | −0.784304 | ||||||||
\(902\) | 0.489730 | 0.0163062 | ||||||||
\(903\) | −26.8059 | − | 13.2523i | −0.892044 | − | 0.441009i | ||||
\(904\) | −3.80842 | − | 6.59638i | −0.126666 | − | 0.219392i | ||||
\(905\) | 11.5198 | + | 19.9529i | 0.382932 | + | 0.663257i | ||||
\(906\) | 2.33560 | + | 1.15468i | 0.0775952 | + | 0.0383616i | ||||
\(907\) | 27.7430 | + | 48.0523i | 0.921192 | + | 1.59555i | 0.797574 | + | 0.603221i | \(0.206116\pi\) |
0.123618 | + | 0.992330i | \(0.460550\pi\) | |||||||
\(908\) | 22.6599 | + | 39.2480i | 0.751994 | + | 1.30249i | ||||
\(909\) | 15.5524 | + | 20.3519i | 0.515842 | + | 0.675030i | ||||
\(910\) | 2.31965 | − | 4.01775i | 0.0768957 | − | 0.133187i | ||||
\(911\) | 1.10191 | − | 1.90856i | 0.0365078 | − | 0.0632334i | −0.847194 | − | 0.531283i | \(-0.821710\pi\) |
0.883702 | + | 0.468050i | \(0.155043\pi\) | |||||||
\(912\) | 27.9180 | + | 5.69583i | 0.924457 | + | 0.188608i | ||||
\(913\) | 3.33729 | + | 5.78036i | 0.110448 | + | 0.191302i | ||||
\(914\) | −4.73139 | −0.156501 | ||||||||
\(915\) | −10.7905 | − | 5.33462i | −0.356724 | − | 0.176357i | ||||
\(916\) | −7.61826 | −0.251714 | ||||||||
\(917\) | 3.53204 | − | 6.11767i | 0.116638 | − | 0.202023i | ||||
\(918\) | −1.18523 | − | 6.05271i | −0.0391183 | − | 0.199769i | ||||
\(919\) | 23.5600 | 0.777173 | 0.388587 | − | 0.921412i | \(-0.372963\pi\) | ||||
0.388587 | + | 0.921412i | \(0.372963\pi\) | |||||||
\(920\) | −5.76887 | + | 9.99197i | −0.190194 | + | 0.329426i | ||||
\(921\) | −26.1732 | + | 17.4508i | −0.862437 | + | 0.575024i | ||||
\(922\) | 0.445812 | − | 0.772169i | 0.0146820 | − | 0.0254300i | ||||
\(923\) | 5.76672 | + | 9.98826i | 0.189814 | + | 0.328768i | ||||
\(924\) | 6.43386 | + | 3.18077i | 0.211658 | + | 0.104640i | ||||
\(925\) | −7.71726 | −0.253742 | ||||||||
\(926\) | 2.88890 | − | 5.00372i | 0.0949351 | − | 0.164432i | ||||
\(927\) | −15.4497 | + | 37.0903i | −0.507434 | + | 1.21821i | ||||
\(928\) | −1.34899 | + | 2.33651i | −0.0442826 | + | 0.0766997i | ||||
\(929\) | 4.86468 | + | 8.42587i | 0.159605 | + | 0.276444i | 0.934726 | − | 0.355369i | \(-0.115645\pi\) |
−0.775121 | + | 0.631812i | \(0.782311\pi\) | |||||||
\(930\) | −0.973232 | + | 0.648896i | −0.0319135 | + | 0.0212781i | ||||
\(931\) | 18.9021 | − | 4.98557i | 0.619492 | − | 0.163395i | ||||
\(932\) | 5.99508 | + | 10.3838i | 0.196376 | + | 0.340132i | ||||
\(933\) | −0.258580 | − | 4.00612i | −0.00846554 | − | 0.131155i | ||||
\(934\) | 3.78018 | + | 6.54747i | 0.123691 | + | 0.214240i | ||||
\(935\) | 3.62000 | + | 6.27003i | 0.118387 | + | 0.205052i | ||||
\(936\) | −8.46798 | + | 1.09773i | −0.276785 | + | 0.0358803i | ||||
\(937\) | 0.131215 | + | 0.227271i | 0.00428661 | + | 0.00742463i | 0.868161 | − | 0.496283i | \(-0.165302\pi\) |
−0.863874 | + | 0.503708i | \(0.831969\pi\) | |||||||
\(938\) | −0.345090 | + | 0.597714i | −0.0112676 | + | 0.0195160i | ||||
\(939\) | 29.0506 | + | 14.3621i | 0.948031 | + | 0.468688i | ||||
\(940\) | 24.0640 | − | 41.6801i | 0.784882 | − | 1.35946i | ||||
\(941\) | −1.75150 | + | 3.03369i | −0.0570974 | + | 0.0988956i | −0.893161 | − | 0.449737i | \(-0.851518\pi\) |
0.836064 | + | 0.548632i | \(0.184851\pi\) | |||||||
\(942\) | −0.118135 | − | 1.83024i | −0.00384905 | − | 0.0596323i | ||||
\(943\) | −15.8405 | + | 27.4365i | −0.515837 | + | 0.893456i | ||||
\(944\) | −16.0478 | − | 27.7955i | −0.522310 | − | 0.904668i | ||||
\(945\) | −31.7438 | − | 10.8811i | −1.03263 | − | 0.353963i | ||||
\(946\) | 0.309047 | + | 0.535285i | 0.0100480 | + | 0.0174036i | ||||
\(947\) | −4.20377 | − | 7.28114i | −0.136604 | − | 0.236605i | 0.789605 | − | 0.613616i | \(-0.210286\pi\) |
−0.926209 | + | 0.377010i | \(0.876952\pi\) | |||||||
\(948\) | 49.7630 | + | 24.6019i | 1.61623 | + | 0.799031i | ||||
\(949\) | 7.63381 | + | 13.2221i | 0.247804 | + | 0.429209i | ||||
\(950\) | 1.12302 | − | 0.296205i | 0.0364356 | − | 0.00961015i | ||||
\(951\) | −22.3415 | − | 11.0452i | −0.724471 | − | 0.358164i | ||||
\(952\) | 7.96882 | + | 13.8024i | 0.258271 | + | 0.447339i | ||||
\(953\) | 1.92560 | − | 3.33524i | 0.0623764 | − | 0.108039i | −0.833151 | − | 0.553046i | \(-0.813465\pi\) |
0.895527 | + | 0.445007i | \(0.146799\pi\) | |||||||
\(954\) | −2.23673 | + | 0.289953i | −0.0724167 | + | 0.00938758i | ||||
\(955\) | −2.56661 | + | 4.44550i | −0.0830535 | + | 0.143853i | ||||
\(956\) | −37.7126 | −1.21971 | ||||||||
\(957\) | 1.06383 | − | 0.709305i | 0.0343889 | − | 0.0229286i | ||||
\(958\) | 0.972785 | + | 1.68491i | 0.0314293 | + | 0.0544371i | ||||
\(959\) | −28.8651 | + | 49.9958i | −0.932103 | + | 1.61445i | ||||
\(960\) | 21.0211 | + | 10.3924i | 0.678455 | + | 0.335415i | ||||
\(961\) | 13.8433 | − | 23.9774i | 0.446560 | − | 0.773464i | ||||
\(962\) | −4.05090 | −0.130606 | ||||||||
\(963\) | 18.5695 | + | 24.3001i | 0.598395 | + | 0.783059i | ||||
\(964\) | 10.4717 | − | 18.1375i | 0.337271 | − | 0.584170i | ||||
\(965\) | −23.8668 | −0.768301 | ||||||||
\(966\) | 7.46297 | − | 4.97589i | 0.240117 | − | 0.160097i | ||||
\(967\) | 42.6171 | 1.37047 | 0.685236 | − | 0.728321i | \(-0.259699\pi\) | ||||
0.685236 | + | 0.728321i | \(0.259699\pi\) | |||||||
\(968\) | 4.09288 | + | 7.08908i | 0.131550 | + | 0.227852i | ||||
\(969\) | −14.5812 | − | 43.6577i | −0.468415 | − | 1.40249i | ||||
\(970\) | −2.72448 | + | 4.71894i | −0.0874777 | + | 0.151516i | ||||
\(971\) | 28.5146 | − | 49.3887i | 0.915076 | − | 1.58496i | 0.108286 | − | 0.994120i | \(-0.465464\pi\) |
0.806790 | − | 0.590838i | \(-0.201203\pi\) | |||||||
\(972\) | 9.68764 | + | 29.0113i | 0.310731 | + | 0.930537i | ||||
\(973\) | 3.83306 | + | 6.63905i | 0.122882 | + | 0.212838i | ||||
\(974\) | −1.73774 | − | 3.00985i | −0.0556807 | − | 0.0964417i | ||||
\(975\) | 7.27713 | − | 4.85198i | 0.233055 | − | 0.155388i | ||||
\(976\) | −6.88172 | − | 11.9195i | −0.220278 | − | 0.381534i | ||||
\(977\) | −12.6223 | − | 21.8624i | −0.403822 | − | 0.699441i | 0.590361 | − | 0.807139i | \(-0.298985\pi\) |
−0.994184 | + | 0.107698i | \(0.965652\pi\) | |||||||
\(978\) | −0.158004 | − | 2.44792i | −0.00505241 | − | 0.0782758i | ||||
\(979\) | 6.54659 | 0.209230 | ||||||||
\(980\) | 16.7686 | 0.535654 | ||||||||
\(981\) | −5.62472 | + | 0.729148i | −0.179584 | + | 0.0232799i | ||||
\(982\) | −1.31266 | − | 2.27360i | −0.0418888 | − | 0.0725536i | ||||
\(983\) | −1.33119 | − | 2.30569i | −0.0424584 | − | 0.0735400i | 0.844015 | − | 0.536319i | \(-0.180186\pi\) |
−0.886474 | + | 0.462779i | \(0.846852\pi\) | |||||||
\(984\) | −4.83446 | − | 2.39006i | −0.154117 | − | 0.0761924i | ||||
\(985\) | 22.5902 | 0.719785 | ||||||||
\(986\) | 1.40607 | 0.0447783 | ||||||||
\(987\) | −62.8629 | + | 41.9134i | −2.00095 | + | 1.33412i | ||||
\(988\) | −30.5136 | + | 8.04818i | −0.970767 | + | 0.256047i | ||||
\(989\) | −39.9849 | −1.27145 | ||||||||
\(990\) | 0.421158 | + | 0.551127i | 0.0133853 | + | 0.0175160i | ||||
\(991\) | 10.1431 | − | 17.5684i | 0.322207 | − | 0.558079i | −0.658736 | − | 0.752374i | \(-0.728909\pi\) |
0.980943 | + | 0.194295i | \(0.0622418\pi\) | |||||||
\(992\) | −4.14573 | −0.131627 | ||||||||
\(993\) | −41.2042 | + | 27.4726i | −1.30758 | + | 0.871818i | ||||
\(994\) | 1.03119 | − | 1.78608i | 0.0327075 | − | 0.0566510i | ||||
\(995\) | −5.75183 | − | 9.96246i | −0.182345 | − | 0.315831i | ||||
\(996\) | −2.34456 | − | 36.3237i | −0.0742901 | − | 1.15096i | ||||
\(997\) | 28.4073 | 0.899668 | 0.449834 | − | 0.893112i | \(-0.351483\pi\) | ||||
0.449834 | + | 0.893112i | \(0.351483\pi\) | |||||||
\(998\) | 1.48699 | + | 2.57554i | 0.0470698 | + | 0.0815273i | ||||
\(999\) | 5.63069 | + | 28.7548i | 0.178147 | + | 0.909761i |
(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 | 171.2.g.c.106.10 | ✓ | 32 | |
3.2 | odd | 2 | 513.2.g.c.505.7 | 32 | |||
9.4 | even | 3 | 171.2.h.c.49.7 | yes | 32 | ||
9.5 | odd | 6 | 513.2.h.c.334.10 | 32 | |||
19.7 | even | 3 | 171.2.h.c.7.7 | yes | 32 | ||
57.26 | odd | 6 | 513.2.h.c.235.10 | 32 | |||
171.121 | even | 3 | inner | 171.2.g.c.121.10 | yes | 32 | |
171.140 | odd | 6 | 513.2.g.c.64.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.10 | ✓ | 32 | 1.1 | even | 1 | trivial | |
171.2.g.c.121.10 | yes | 32 | 171.121 | even | 3 | inner | |
171.2.h.c.7.7 | yes | 32 | 19.7 | even | 3 | ||
171.2.h.c.49.7 | yes | 32 | 9.4 | even | 3 | ||
513.2.g.c.64.7 | 32 | 171.140 | odd | 6 | |||
513.2.g.c.505.7 | 32 | 3.2 | odd | 2 | |||
513.2.h.c.235.10 | 32 | 57.26 | odd | 6 | |||
513.2.h.c.334.10 | 32 | 9.5 | odd | 6 |