Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(419,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.20 | ||
Character | \(\chi\) | \(=\) | 456.419 |
Dual form | 456.2.j.e.419.19 |
$q$-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 \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(343\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.960810 | + | 1.03771i | 0.679395 | + | 0.733773i | ||||
\(3\) | 0.153689 | + | 1.72522i | 0.0887324 | + | 0.996056i | ||||
\(4\) | −0.153689 | + | 1.99409i | −0.0768445 | + | 0.997043i | ||||
\(5\) | 1.97287 | 0.882296 | 0.441148 | − | 0.897434i | \(-0.354571\pi\) | ||||
0.441148 | + | 0.897434i | \(0.354571\pi\) | |||||||
\(6\) | −1.64261 | + | 1.81709i | −0.670594 | + | 0.741825i | ||||
\(7\) | − | 2.35621i | − | 0.890564i | −0.895390 | − | 0.445282i | \(-0.853104\pi\) | ||
0.895390 | − | 0.445282i | \(-0.146896\pi\) | |||||||
\(8\) | −2.21695 | + | 1.75645i | −0.783811 | + | 0.621000i | ||||
\(9\) | −2.95276 | + | 0.530294i | −0.984253 | + | 0.176765i | ||||
\(10\) | 1.89556 | + | 2.04727i | 0.599427 | + | 0.647404i | ||||
\(11\) | 4.83256i | 1.45707i | 0.685007 | + | 0.728537i | \(0.259799\pi\) | ||||
−0.685007 | + | 0.728537i | \(0.740201\pi\) | |||||||
\(12\) | −3.46386 | + | 0.0413220i | −0.999929 | + | 0.0119286i | ||||
\(13\) | 2.14536i | 0.595014i | 0.954720 | + | 0.297507i | \(0.0961552\pi\) | ||||
−0.954720 | + | 0.297507i | \(0.903845\pi\) | |||||||
\(14\) | 2.44507 | − | 2.26387i | 0.653471 | − | 0.605045i | ||||
\(15\) | 0.303209 | + | 3.40364i | 0.0782882 | + | 0.878816i | ||||
\(16\) | −3.95276 | − | 0.612938i | −0.988190 | − | 0.153235i | ||||
\(17\) | − | 5.22103i | − | 1.26629i | −0.774035 | − | 0.633143i | \(-0.781764\pi\) | ||
0.774035 | − | 0.633143i | \(-0.218236\pi\) | |||||||
\(18\) | −3.38733 | − | 2.55460i | −0.798402 | − | 0.602125i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.303209 | + | 3.93408i | −0.0677996 | + | 0.879687i | ||||
\(21\) | 4.06498 | − | 0.362124i | 0.887051 | − | 0.0790219i | ||||
\(22\) | −5.01481 | + | 4.64318i | −1.06916 | + | 0.989928i | ||||
\(23\) | 8.06939 | 1.68258 | 0.841292 | − | 0.540580i | \(-0.181795\pi\) | ||||
0.841292 | + | 0.540580i | \(0.181795\pi\) | |||||||
\(24\) | −3.37099 | − | 3.55478i | −0.688100 | − | 0.725616i | ||||
\(25\) | −1.10777 | −0.221554 | ||||||||
\(26\) | −2.22626 | + | 2.06128i | −0.436605 | + | 0.404250i | ||||
\(27\) | −1.36868 | − | 5.01266i | −0.263403 | − | 0.964686i | ||||
\(28\) | 4.69849 | + | 0.362124i | 0.887930 | + | 0.0684349i | ||||
\(29\) | 0.590664 | 0.109684 | 0.0548418 | − | 0.998495i | \(-0.482535\pi\) | ||||
0.0548418 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(30\) | −3.24067 | + | 3.58489i | −0.591662 | + | 0.654509i | ||||
\(31\) | 4.48507i | 0.805543i | 0.915301 | + | 0.402771i | \(0.131953\pi\) | ||||
−0.915301 | + | 0.402771i | \(0.868047\pi\) | |||||||
\(32\) | −3.16180 | − | 4.69074i | −0.558932 | − | 0.829213i | ||||
\(33\) | −8.33723 | + | 0.742712i | −1.45133 | + | 0.129290i | ||||
\(34\) | 5.41793 | − | 5.01642i | 0.929167 | − | 0.860309i | ||||
\(35\) | − | 4.64850i | − | 0.785740i | ||||||
\(36\) | −0.603646 | − | 5.96956i | −0.100608 | − | 0.994926i | ||||
\(37\) | − | 8.77578i | − | 1.44273i | −0.692555 | − | 0.721365i | \(-0.743515\pi\) | ||
0.692555 | − | 0.721365i | \(-0.256485\pi\) | |||||||
\(38\) | 0.960810 | + | 1.03771i | 0.155864 | + | 0.168339i | ||||
\(39\) | −3.70121 | + | 0.329718i | −0.592667 | + | 0.0527971i | ||||
\(40\) | −4.37376 | + | 3.46526i | −0.691553 | + | 0.547906i | ||||
\(41\) | − | 6.54069i | − | 1.02148i | −0.859734 | − | 0.510742i | \(-0.829371\pi\) | ||
0.859734 | − | 0.510742i | \(-0.170629\pi\) | |||||||
\(42\) | 4.28145 | + | 3.87034i | 0.660642 | + | 0.597207i | ||||
\(43\) | −1.36072 | −0.207508 | −0.103754 | − | 0.994603i | \(-0.533086\pi\) | ||||
−0.103754 | + | 0.994603i | \(0.533086\pi\) | |||||||
\(44\) | −9.63655 | − | 0.742712i | −1.45276 | − | 0.111968i | ||||
\(45\) | −5.82542 | + | 1.04620i | −0.868402 | + | 0.155959i | ||||
\(46\) | 7.75315 | + | 8.37370i | 1.14314 | + | 1.23463i | ||||
\(47\) | −5.54780 | −0.809230 | −0.404615 | − | 0.914487i | \(-0.632594\pi\) | ||||
−0.404615 | + | 0.914487i | \(0.632594\pi\) | |||||||
\(48\) | 0.449957 | − | 6.91358i | 0.0649457 | − | 0.997889i | ||||
\(49\) | 1.44828 | 0.206896 | ||||||||
\(50\) | −1.06436 | − | 1.14955i | −0.150523 | − | 0.162570i | ||||
\(51\) | 9.00743 | − | 0.802416i | 1.26129 | − | 0.112361i | ||||
\(52\) | −4.27802 | − | 0.329718i | −0.593255 | − | 0.0457236i | ||||
\(53\) | 13.0520 | 1.79283 | 0.896416 | − | 0.443214i | \(-0.146162\pi\) | ||||
0.896416 | + | 0.443214i | \(0.146162\pi\) | |||||||
\(54\) | 3.88665 | − | 6.23650i | 0.528906 | − | 0.848681i | ||||
\(55\) | 9.53404i | 1.28557i | ||||||||
\(56\) | 4.13857 | + | 5.22360i | 0.553040 | + | 0.698033i | ||||
\(57\) | 0.153689 | + | 1.72522i | 0.0203566 | + | 0.228511i | ||||
\(58\) | 0.567516 | + | 0.612938i | 0.0745184 | + | 0.0804828i | ||||
\(59\) | 14.0204i | 1.82530i | 0.408744 | + | 0.912649i | \(0.365967\pi\) | ||||
−0.408744 | + | 0.912649i | \(0.634033\pi\) | |||||||
\(60\) | −6.83375 | + | 0.0815230i | −0.882233 | + | 0.0105246i | ||||
\(61\) | − | 10.1557i | − | 1.30031i | −0.759804 | − | 0.650153i | \(-0.774705\pi\) | ||
0.759804 | − | 0.650153i | \(-0.225295\pi\) | |||||||
\(62\) | −4.65421 | + | 4.30930i | −0.591085 | + | 0.547282i | ||||
\(63\) | 1.24948 | + | 6.95732i | 0.157420 | + | 0.876540i | ||||
\(64\) | 1.82975 | − | 7.78794i | 0.228718 | − | 0.973493i | ||||
\(65\) | 4.23251i | 0.524979i | ||||||||
\(66\) | −8.78121 | − | 7.93803i | −1.08089 | − | 0.977104i | ||||
\(67\) | 5.68558 | 0.694604 | 0.347302 | − | 0.937753i | \(-0.387098\pi\) | ||||
0.347302 | + | 0.937753i | \(0.387098\pi\) | |||||||
\(68\) | 10.4112 | + | 0.802416i | 1.26254 | + | 0.0973072i | ||||
\(69\) | 1.24018 | + | 13.9215i | 0.149300 | + | 1.67595i | ||||
\(70\) | 4.82380 | − | 4.46633i | 0.576555 | − | 0.533828i | ||||
\(71\) | 3.57493 | 0.424266 | 0.212133 | − | 0.977241i | \(-0.431959\pi\) | ||||
0.212133 | + | 0.977241i | \(0.431959\pi\) | |||||||
\(72\) | 5.61469 | − | 6.36202i | 0.661697 | − | 0.749771i | ||||
\(73\) | −3.06303 | −0.358501 | −0.179250 | − | 0.983803i | \(-0.557367\pi\) | ||||
−0.179250 | + | 0.983803i | \(0.557367\pi\) | |||||||
\(74\) | 9.10673 | − | 8.43186i | 1.05864 | − | 0.980184i | ||||
\(75\) | −0.170252 | − | 1.91115i | −0.0196590 | − | 0.220680i | ||||
\(76\) | −0.153689 | + | 1.99409i | −0.0176293 | + | 0.228737i | ||||
\(77\) | 11.3865 | 1.29762 | ||||||||
\(78\) | −3.89831 | − | 3.52399i | −0.441396 | − | 0.399013i | ||||
\(79\) | 3.01433i | 0.339139i | 0.985518 | + | 0.169570i | \(0.0542377\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(80\) | −7.79829 | − | 1.20925i | −0.871876 | − | 0.135198i | ||||
\(81\) | 8.43758 | − | 3.13166i | 0.937508 | − | 0.347963i | ||||
\(82\) | 6.78735 | − | 6.28436i | 0.749538 | − | 0.693992i | ||||
\(83\) | − | 6.41871i | − | 0.704545i | −0.935898 | − | 0.352272i | \(-0.885409\pi\) | ||
0.935898 | − | 0.352272i | \(-0.114591\pi\) | |||||||
\(84\) | 0.0973633 | + | 8.16157i | 0.0106232 | + | 0.890500i | ||||
\(85\) | − | 10.3004i | − | 1.11724i | ||||||
\(86\) | −1.30740 | − | 1.41204i | −0.140980 | − | 0.152264i | ||||
\(87\) | 0.0907785 | + | 1.01902i | 0.00973248 | + | 0.109251i | ||||
\(88\) | −8.48817 | − | 10.7136i | −0.904842 | − | 1.14207i | ||||
\(89\) | 6.77889i | 0.718561i | 0.933230 | + | 0.359280i | \(0.116978\pi\) | ||||
−0.933230 | + | 0.359280i | \(0.883022\pi\) | |||||||
\(90\) | −6.68278 | − | 5.03990i | −0.704427 | − | 0.531252i | ||||
\(91\) | 5.05491 | 0.529898 | ||||||||
\(92\) | −1.24018 | + | 16.0911i | −0.129297 | + | 1.67761i | ||||
\(93\) | −7.73773 | + | 0.689307i | −0.802365 | + | 0.0714778i | ||||
\(94\) | −5.33038 | − | 5.75702i | −0.549787 | − | 0.593791i | ||||
\(95\) | 1.97287 | 0.202413 | ||||||||
\(96\) | 7.60662 | − | 6.17571i | 0.776347 | − | 0.630305i | ||||
\(97\) | −12.2390 | −1.24268 | −0.621340 | − | 0.783541i | \(-0.713411\pi\) | ||||
−0.621340 | + | 0.783541i | \(0.713411\pi\) | |||||||
\(98\) | 1.39152 | + | 1.50289i | 0.140564 | + | 0.151815i | ||||
\(99\) | −2.56268 | − | 14.2694i | −0.257559 | − | 1.43413i | ||||
\(100\) | 0.170252 | − | 2.20899i | 0.0170252 | − | 0.220899i | ||||
\(101\) | 1.74580 | 0.173714 | 0.0868568 | − | 0.996221i | \(-0.472318\pi\) | ||||
0.0868568 | + | 0.996221i | \(0.472318\pi\) | |||||||
\(102\) | 9.48710 | + | 8.57614i | 0.939363 | + | 0.849164i | ||||
\(103\) | − | 13.1313i | − | 1.29387i | −0.762547 | − | 0.646933i | \(-0.776051\pi\) | ||
0.762547 | − | 0.646933i | \(-0.223949\pi\) | |||||||
\(104\) | −3.76821 | − | 4.75615i | −0.369504 | − | 0.466379i | ||||
\(105\) | 8.01969 | − | 0.714424i | 0.782641 | − | 0.0697206i | ||||
\(106\) | 12.5405 | + | 13.5442i | 1.21804 | + | 1.31553i | ||||
\(107\) | 9.99113i | 0.965879i | 0.875654 | + | 0.482940i | \(0.160431\pi\) | ||||
−0.875654 | + | 0.482940i | \(0.839569\pi\) | |||||||
\(108\) | 10.2060 | − | 1.95888i | 0.982075 | − | 0.188493i | ||||
\(109\) | − | 4.66192i | − | 0.446531i | −0.974758 | − | 0.223266i | \(-0.928328\pi\) | ||
0.974758 | − | 0.223266i | \(-0.0716717\pi\) | |||||||
\(110\) | −9.89358 | + | 9.16040i | −0.943316 | + | 0.873410i | ||||
\(111\) | 15.1401 | − | 1.34874i | 1.43704 | − | 0.128017i | ||||
\(112\) | −1.44421 | + | 9.31353i | −0.136465 | + | 0.880046i | ||||
\(113\) | 15.4604i | 1.45439i | 0.686432 | + | 0.727194i | \(0.259176\pi\) | ||||
−0.686432 | + | 0.727194i | \(0.740824\pi\) | |||||||
\(114\) | −1.64261 | + | 1.81709i | −0.153845 | + | 0.170186i | ||||
\(115\) | 15.9199 | 1.48454 | ||||||||
\(116\) | −0.0907785 | + | 1.17783i | −0.00842858 | + | 0.109359i | ||||
\(117\) | −1.13767 | − | 6.33472i | −0.105178 | − | 0.585645i | ||||
\(118\) | −14.5491 | + | 13.4709i | −1.33935 | + | 1.24010i | ||||
\(119\) | −12.3019 | −1.12771 | ||||||||
\(120\) | −6.65053 | − | 7.01313i | −0.607107 | − | 0.640208i | ||||
\(121\) | −12.3537 | −1.12306 | ||||||||
\(122\) | 10.5387 | − | 9.75770i | 0.954128 | − | 0.883421i | ||||
\(123\) | 11.2841 | − | 1.00523i | 1.01746 | − | 0.0906388i | ||||
\(124\) | −8.94362 | − | 0.689307i | −0.803161 | − | 0.0619016i | ||||
\(125\) | −12.0499 | −1.07777 | ||||||||
\(126\) | −6.01917 | + | 7.98127i | −0.536230 | + | 0.711028i | ||||
\(127\) | − | 11.0587i | − | 0.981300i | −0.871357 | − | 0.490650i | \(-0.836759\pi\) | ||
0.871357 | − | 0.490650i | \(-0.163241\pi\) | |||||||
\(128\) | 9.83967 | − | 5.58398i | 0.869712 | − | 0.493559i | ||||
\(129\) | −0.209128 | − | 2.34754i | −0.0184127 | − | 0.206690i | ||||
\(130\) | −4.39213 | + | 4.06664i | −0.385215 | + | 0.356668i | ||||
\(131\) | − | 5.46142i | − | 0.477166i | −0.971122 | − | 0.238583i | \(-0.923317\pi\) | ||
0.971122 | − | 0.238583i | \(-0.0766829\pi\) | |||||||
\(132\) | −0.199691 | − | 16.7393i | −0.0173809 | − | 1.45697i | ||||
\(133\) | − | 2.35621i | − | 0.204309i | ||||||
\(134\) | 5.46276 | + | 5.89999i | 0.471911 | + | 0.509681i | ||||
\(135\) | −2.70023 | − | 9.88933i | −0.232399 | − | 0.851138i | ||||
\(136\) | 9.17050 | + | 11.5748i | 0.786364 | + | 0.992529i | ||||
\(137\) | 1.19513i | 0.102106i | 0.998696 | + | 0.0510532i | \(0.0162578\pi\) | ||||
−0.998696 | + | 0.0510532i | \(0.983742\pi\) | |||||||
\(138\) | −13.2549 | + | 14.6628i | −1.12833 | + | 1.24818i | ||||
\(139\) | −4.81905 | −0.408746 | −0.204373 | − | 0.978893i | \(-0.565516\pi\) | ||||
−0.204373 | + | 0.978893i | \(0.565516\pi\) | |||||||
\(140\) | 9.26952 | + | 0.714424i | 0.783417 | + | 0.0603799i | ||||
\(141\) | −0.852636 | − | 9.57117i | −0.0718049 | − | 0.806038i | ||||
\(142\) | 3.43483 | + | 3.70974i | 0.288244 | + | 0.311315i | ||||
\(143\) | −10.3676 | −0.866980 | ||||||||
\(144\) | 11.9966 | − | 0.286267i | 0.999715 | − | 0.0238556i | ||||
\(145\) | 1.16530 | 0.0967733 | ||||||||
\(146\) | −2.94299 | − | 3.17854i | −0.243564 | − | 0.263058i | ||||
\(147\) | 0.222584 | + | 2.49859i | 0.0183584 | + | 0.206080i | ||||
\(148\) | 17.4997 | + | 1.34874i | 1.43846 | + | 0.110866i | ||||
\(149\) | −23.1362 | −1.89539 | −0.947697 | − | 0.319172i | \(-0.896595\pi\) | ||||
−0.947697 | + | 0.319172i | \(0.896595\pi\) | |||||||
\(150\) | 1.81964 | − | 2.01292i | 0.148573 | − | 0.164354i | ||||
\(151\) | 5.63190i | 0.458317i | 0.973389 | + | 0.229159i | \(0.0735975\pi\) | ||||
−0.973389 | + | 0.229159i | \(0.926403\pi\) | |||||||
\(152\) | −2.21695 | + | 1.75645i | −0.179819 | + | 0.142467i | ||||
\(153\) | 2.76869 | + | 15.4165i | 0.223835 | + | 1.24635i | ||||
\(154\) | 10.9403 | + | 11.8159i | 0.881594 | + | 0.952155i | ||||
\(155\) | 8.84848i | 0.710727i | ||||||||
\(156\) | −0.0886503 | − | 7.43120i | −0.00709771 | − | 0.594972i | ||||
\(157\) | − | 4.71242i | − | 0.376092i | −0.982160 | − | 0.188046i | \(-0.939785\pi\) | ||
0.982160 | − | 0.188046i | \(-0.0602154\pi\) | |||||||
\(158\) | −3.12801 | + | 2.89620i | −0.248851 | + | 0.230409i | ||||
\(159\) | 2.00595 | + | 22.5176i | 0.159082 | + | 1.78576i | ||||
\(160\) | −6.23782 | − | 9.25424i | −0.493143 | − | 0.731612i | ||||
\(161\) | − | 19.0132i | − | 1.49845i | ||||||
\(162\) | 11.3567 | + | 5.74683i | 0.892264 | + | 0.451514i | ||||
\(163\) | −21.8296 | −1.70983 | −0.854913 | − | 0.518771i | \(-0.826390\pi\) | ||||
−0.854913 | + | 0.518771i | \(0.826390\pi\) | |||||||
\(164\) | 13.0427 | + | 1.00523i | 1.01846 | + | 0.0784955i | ||||
\(165\) | −16.4483 | + | 1.46528i | −1.28050 | + | 0.114072i | ||||
\(166\) | 6.66077 | − | 6.16716i | 0.516976 | − | 0.478664i | ||||
\(167\) | 0.772221 | 0.0597562 | 0.0298781 | − | 0.999554i | \(-0.490488\pi\) | ||||
0.0298781 | + | 0.999554i | \(0.490488\pi\) | |||||||
\(168\) | −8.37580 | + | 7.94275i | −0.646207 | + | 0.612797i | ||||
\(169\) | 8.39745 | 0.645958 | ||||||||
\(170\) | 10.6889 | − | 9.89676i | 0.819800 | − | 0.759047i | ||||
\(171\) | −2.95276 | + | 0.530294i | −0.225803 | + | 0.0405526i | ||||
\(172\) | 0.209128 | − | 2.71340i | 0.0159459 | − | 0.206895i | ||||
\(173\) | 2.64330 | 0.200966 | 0.100483 | − | 0.994939i | \(-0.467961\pi\) | ||||
0.100483 | + | 0.994939i | \(0.467961\pi\) | |||||||
\(174\) | −0.970232 | + | 1.07329i | −0.0735531 | + | 0.0813659i | ||||
\(175\) | 2.61014i | 0.197308i | ||||||||
\(176\) | 2.96206 | − | 19.1020i | 0.223274 | − | 1.43986i | ||||
\(177\) | −24.1882 | + | 2.15478i | −1.81810 | + | 0.161963i | ||||
\(178\) | −7.03453 | + | 6.51322i | −0.527260 | + | 0.488187i | ||||
\(179\) | − | 13.7988i | − | 1.03137i | −0.856778 | − | 0.515686i | \(-0.827537\pi\) | ||
0.856778 | − | 0.515686i | \(-0.172463\pi\) | |||||||
\(180\) | −1.19092 | − | 11.7772i | −0.0887657 | − | 0.877819i | ||||
\(181\) | 12.3871i | 0.920729i | 0.887730 | + | 0.460365i | \(0.152281\pi\) | ||||
−0.887730 | + | 0.460365i | \(0.847719\pi\) | |||||||
\(182\) | 4.85680 | + | 5.24553i | 0.360010 | + | 0.388825i | ||||
\(183\) | 17.5208 | − | 1.56082i | 1.29518 | − | 0.115379i | ||||
\(184\) | −17.8895 | + | 14.1735i | −1.31883 | + | 1.04488i | ||||
\(185\) | − | 17.3135i | − | 1.27291i | ||||||
\(186\) | −8.14979 | − | 7.36724i | −0.597572 | − | 0.540192i | ||||
\(187\) | 25.2310 | 1.84507 | ||||||||
\(188\) | 0.852636 | − | 11.0628i | 0.0621849 | − | 0.806837i | ||||
\(189\) | −11.8109 | + | 3.22490i | −0.859114 | + | 0.234577i | ||||
\(190\) | 1.89556 | + | 2.04727i | 0.137518 | + | 0.148525i | ||||
\(191\) | 0.794407 | 0.0574813 | 0.0287406 | − | 0.999587i | \(-0.490850\pi\) | ||||
0.0287406 | + | 0.999587i | \(0.490850\pi\) | |||||||
\(192\) | 13.7171 | + | 1.95979i | 0.989947 | + | 0.141436i | ||||
\(193\) | −10.5422 | −0.758842 | −0.379421 | − | 0.925224i | \(-0.623877\pi\) | ||||
−0.379421 | + | 0.925224i | \(0.623877\pi\) | |||||||
\(194\) | −11.7593 | − | 12.7005i | −0.844271 | − | 0.911845i | ||||
\(195\) | −7.30201 | + | 0.650491i | −0.522908 | + | 0.0465826i | ||||
\(196\) | −0.222584 | + | 2.88799i | −0.0158989 | + | 0.206285i | ||||
\(197\) | 10.3447 | 0.737032 | 0.368516 | − | 0.929621i | \(-0.379866\pi\) | ||||
0.368516 | + | 0.929621i | \(0.379866\pi\) | |||||||
\(198\) | 12.3453 | − | 16.3695i | 0.877340 | − | 1.16333i | ||||
\(199\) | − | 11.1911i | − | 0.793315i | −0.917967 | − | 0.396657i | \(-0.870170\pi\) | ||
0.917967 | − | 0.396657i | \(-0.129830\pi\) | |||||||
\(200\) | 2.45587 | − | 1.94575i | 0.173657 | − | 0.137585i | ||||
\(201\) | 0.873811 | + | 9.80887i | 0.0616339 | + | 0.691864i | ||||
\(202\) | 1.67738 | + | 1.81164i | 0.118020 | + | 0.127466i | ||||
\(203\) | − | 1.39173i | − | 0.0976801i | ||||||
\(204\) | 0.215743 | + | 18.0849i | 0.0151051 | + | 1.26620i | ||||
\(205\) | − | 12.9040i | − | 0.901252i | ||||||
\(206\) | 13.6265 | − | 12.6167i | 0.949403 | − | 0.879046i | ||||
\(207\) | −23.8270 | + | 4.27915i | −1.65609 | + | 0.297422i | ||||
\(208\) | 1.31497 | − | 8.48007i | 0.0911768 | − | 0.587987i | ||||
\(209\) | 4.83256i | 0.334275i | ||||||||
\(210\) | 8.44676 | + | 7.63569i | 0.582882 | + | 0.526913i | ||||
\(211\) | −5.93112 | −0.408315 | −0.204158 | − | 0.978938i | \(-0.565446\pi\) | ||||
−0.204158 | + | 0.978938i | \(0.565446\pi\) | |||||||
\(212\) | −2.00595 | + | 26.0268i | −0.137769 | + | 1.78753i | ||||
\(213\) | 0.549427 | + | 6.16753i | 0.0376461 | + | 0.422592i | ||||
\(214\) | −10.3679 | + | 9.59958i | −0.708736 | + | 0.656214i | ||||
\(215\) | −2.68453 | −0.183084 | ||||||||
\(216\) | 11.8388 | + | 8.70879i | 0.805528 | + | 0.592558i | ||||
\(217\) | 10.5678 | 0.717387 | ||||||||
\(218\) | 4.83773 | − | 4.47922i | 0.327652 | − | 0.303371i | ||||
\(219\) | −0.470754 | − | 5.28440i | −0.0318106 | − | 0.357087i | ||||
\(220\) | −19.0117 | − | 1.46528i | −1.28177 | − | 0.0987890i | ||||
\(221\) | 11.2010 | 0.753459 | ||||||||
\(222\) | 15.9464 | + | 14.4152i | 1.07025 | + | 0.967486i | ||||
\(223\) | 3.45829i | 0.231584i | 0.993273 | + | 0.115792i | \(0.0369406\pi\) | ||||
−0.993273 | + | 0.115792i | \(0.963059\pi\) | |||||||
\(224\) | −11.0524 | + | 7.44986i | −0.738467 | + | 0.497765i | ||||
\(225\) | 3.27098 | − | 0.587445i | 0.218065 | − | 0.0391630i | ||||
\(226\) | −16.0434 | + | 14.8545i | −1.06719 | + | 0.988104i | ||||
\(227\) | 14.3152i | 0.950130i | 0.879951 | + | 0.475065i | \(0.157576\pi\) | ||||
−0.879951 | + | 0.475065i | \(0.842424\pi\) | |||||||
\(228\) | −3.46386 | + | 0.0413220i | −0.229399 | + | 0.00273661i | ||||
\(229\) | − | 13.4895i | − | 0.891412i | −0.895179 | − | 0.445706i | \(-0.852953\pi\) | ||
0.895179 | − | 0.445706i | \(-0.147047\pi\) | |||||||
\(230\) | 15.2960 | + | 16.5202i | 1.00859 | + | 1.08931i | ||||
\(231\) | 1.74999 | + | 19.6443i | 0.115141 | + | 1.29250i | ||||
\(232\) | −1.30947 | + | 1.03747i | −0.0859711 | + | 0.0681134i | ||||
\(233\) | − | 14.0612i | − | 0.921181i | −0.887613 | − | 0.460591i | \(-0.847638\pi\) | ||
0.887613 | − | 0.460591i | \(-0.152362\pi\) | |||||||
\(234\) | 5.48052 | − | 7.26703i | 0.358273 | − | 0.475061i | ||||
\(235\) | −10.9451 | −0.713980 | ||||||||
\(236\) | −27.9579 | − | 2.15478i | −1.81990 | − | 0.140264i | ||||
\(237\) | −5.20039 | + | 0.463270i | −0.337801 | + | 0.0300926i | ||||
\(238\) | −11.8197 | − | 12.7658i | −0.766160 | − | 0.827482i | ||||
\(239\) | −10.9776 | −0.710079 | −0.355040 | − | 0.934851i | \(-0.615533\pi\) | ||||
−0.355040 | + | 0.934851i | \(0.615533\pi\) | |||||||
\(240\) | 0.887708 | − | 13.6396i | 0.0573013 | − | 0.880433i | ||||
\(241\) | −12.3554 | −0.795878 | −0.397939 | − | 0.917412i | \(-0.630275\pi\) | ||||
−0.397939 | + | 0.917412i | \(0.630275\pi\) | |||||||
\(242\) | −11.8695 | − | 12.8196i | −0.763003 | − | 0.824072i | ||||
\(243\) | 6.69957 | + | 14.0754i | 0.429777 | + | 0.902935i | ||||
\(244\) | 20.2514 | + | 1.56082i | 1.29646 | + | 0.0999213i | ||||
\(245\) | 2.85726 | 0.182544 | ||||||||
\(246\) | 11.8850 | + | 10.7438i | 0.757763 | + | 0.685001i | ||||
\(247\) | 2.14536i | 0.136506i | ||||||||
\(248\) | −7.87782 | − | 9.94319i | −0.500242 | − | 0.631393i | ||||
\(249\) | 11.0737 | − | 0.986485i | 0.701766 | − | 0.0625160i | ||||
\(250\) | −11.5776 | − | 12.5043i | −0.732233 | − | 0.790840i | ||||
\(251\) | 3.35841i | 0.211981i | 0.994367 | + | 0.105991i | \(0.0338013\pi\) | ||||
−0.994367 | + | 0.105991i | \(0.966199\pi\) | |||||||
\(252\) | −14.0655 | + | 1.42232i | −0.886045 | + | 0.0895975i | ||||
\(253\) | 38.9959i | 2.45165i | ||||||||
\(254\) | 11.4757 | − | 10.6253i | 0.720051 | − | 0.666691i | ||||
\(255\) | 17.7705 | − | 1.58306i | 1.11283 | − | 0.0991354i | ||||
\(256\) | 15.2486 | + | 4.84560i | 0.953038 | + | 0.302850i | ||||
\(257\) | − | 5.93733i | − | 0.370360i | −0.982705 | − | 0.185180i | \(-0.940713\pi\) | ||
0.982705 | − | 0.185180i | \(-0.0592868\pi\) | |||||||
\(258\) | 2.23514 | − | 2.47256i | 0.139154 | − | 0.153935i | ||||
\(259\) | −20.6776 | −1.28484 | ||||||||
\(260\) | −8.44000 | − | 0.650491i | −0.523426 | − | 0.0403417i | ||||
\(261\) | −1.74409 | + | 0.313226i | −0.107956 | + | 0.0193882i | ||||
\(262\) | 5.66737 | − | 5.24738i | 0.350132 | − | 0.324184i | ||||
\(263\) | −21.0419 | −1.29750 | −0.648749 | − | 0.761002i | \(-0.724707\pi\) | ||||
−0.648749 | + | 0.761002i | \(0.724707\pi\) | |||||||
\(264\) | 17.1787 | − | 16.2905i | 1.05728 | − | 1.00261i | ||||
\(265\) | 25.7500 | 1.58181 | ||||||||
\(266\) | 2.44507 | − | 2.26387i | 0.149917 | − | 0.138807i | ||||
\(267\) | −11.6951 | + | 1.04184i | −0.715727 | + | 0.0637596i | ||||
\(268\) | −0.873811 | + | 11.3375i | −0.0533765 | + | 0.692550i | ||||
\(269\) | −10.4505 | −0.637180 | −0.318590 | − | 0.947893i | \(-0.603209\pi\) | ||||
−0.318590 | + | 0.947893i | \(0.603209\pi\) | |||||||
\(270\) | 7.66786 | − | 12.3038i | 0.466651 | − | 0.748787i | ||||
\(271\) | − | 31.8860i | − | 1.93694i | −0.249131 | − | 0.968470i | \(-0.580145\pi\) | ||
0.249131 | − | 0.968470i | \(-0.419855\pi\) | |||||||
\(272\) | −3.20017 | + | 20.6375i | −0.194039 | + | 1.25133i | ||||
\(273\) | 0.776884 | + | 8.72082i | 0.0470191 | + | 0.527808i | ||||
\(274\) | −1.24020 | + | 1.14829i | −0.0749229 | + | 0.0693706i | ||||
\(275\) | − | 5.35337i | − | 0.322821i | ||||||
\(276\) | −27.9512 | + | 0.333443i | −1.68247 | + | 0.0200709i | ||||
\(277\) | 19.3036i | 1.15984i | 0.814674 | + | 0.579920i | \(0.196916\pi\) | ||||
−0.814674 | + | 0.579920i | \(0.803084\pi\) | |||||||
\(278\) | −4.63019 | − | 5.00078i | −0.277700 | − | 0.299927i | ||||
\(279\) | −2.37841 | − | 13.2433i | −0.142392 | − | 0.792858i | ||||
\(280\) | 8.16488 | + | 10.3055i | 0.487945 | + | 0.615872i | ||||
\(281\) | − | 3.94758i | − | 0.235493i | −0.993044 | − | 0.117747i | \(-0.962433\pi\) | ||
0.993044 | − | 0.117747i | \(-0.0375670\pi\) | |||||||
\(282\) | 9.11289 | − | 10.0809i | 0.542665 | − | 0.600307i | ||||
\(283\) | −16.8230 | −1.00002 | −0.500011 | − | 0.866019i | \(-0.666671\pi\) | ||||
−0.500011 | + | 0.866019i | \(0.666671\pi\) | |||||||
\(284\) | −0.549427 | + | 7.12872i | −0.0326025 | + | 0.423011i | ||||
\(285\) | 0.303209 | + | 3.40364i | 0.0179606 | + | 0.201614i | ||||
\(286\) | −9.96126 | − | 10.7585i | −0.589022 | − | 0.636166i | ||||
\(287\) | −15.4112 | −0.909697 | ||||||||
\(288\) | 11.8235 | + | 12.1739i | 0.696706 | + | 0.717356i | ||||
\(289\) | −10.2592 | −0.603482 | ||||||||
\(290\) | 1.11964 | + | 1.20925i | 0.0657473 | + | 0.0710096i | ||||
\(291\) | −1.88100 | − | 21.1149i | −0.110266 | − | 1.23778i | ||||
\(292\) | 0.470754 | − | 6.10795i | 0.0275488 | − | 0.357441i | ||||
\(293\) | −10.1353 | −0.592112 | −0.296056 | − | 0.955171i | \(-0.595671\pi\) | ||||
−0.296056 | + | 0.955171i | \(0.595671\pi\) | |||||||
\(294\) | −2.37896 | + | 2.63165i | −0.138744 | + | 0.153481i | ||||
\(295\) | 27.6604i | 1.61045i | ||||||||
\(296\) | 15.4142 | + | 19.4555i | 0.895935 | + | 1.13083i | ||||
\(297\) | 24.2240 | − | 6.61424i | 1.40562 | − | 0.383797i | ||||
\(298\) | −22.2295 | − | 24.0087i | −1.28772 | − | 1.39079i | ||||
\(299\) | 17.3117i | 1.00116i | ||||||||
\(300\) | 3.83716 | − | 0.0457753i | 0.221538 | − | 0.00264284i | ||||
\(301\) | 3.20615i | 0.184799i | ||||||||
\(302\) | −5.84428 | + | 5.41118i | −0.336301 | + | 0.311379i | ||||
\(303\) | 0.268310 | + | 3.01189i | 0.0154140 | + | 0.173028i | ||||
\(304\) | −3.95276 | − | 0.612938i | −0.226706 | − | 0.0351544i | ||||
\(305\) | − | 20.0359i | − | 1.14725i | ||||||
\(306\) | −13.3377 | + | 17.6854i | −0.762463 | + | 1.01101i | ||||
\(307\) | 26.0177 | 1.48491 | 0.742454 | − | 0.669897i | \(-0.233662\pi\) | ||||
0.742454 | + | 0.669897i | \(0.233662\pi\) | |||||||
\(308\) | −1.74999 | + | 22.7057i | −0.0997147 | + | 1.29378i | ||||
\(309\) | 22.6544 | − | 2.01814i | 1.28876 | − | 0.114808i | ||||
\(310\) | −9.18217 | + | 8.50171i | −0.521512 | + | 0.482865i | ||||
\(311\) | −24.6649 | −1.39862 | −0.699309 | − | 0.714819i | \(-0.746509\pi\) | ||||
−0.699309 | + | 0.714819i | \(0.746509\pi\) | |||||||
\(312\) | 7.62626 | − | 7.23196i | 0.431752 | − | 0.409429i | ||||
\(313\) | 23.7033 | 1.33979 | 0.669894 | − | 0.742456i | \(-0.266339\pi\) | ||||
0.669894 | + | 0.742456i | \(0.266339\pi\) | |||||||
\(314\) | 4.89013 | − | 4.52774i | 0.275966 | − | 0.255515i | ||||
\(315\) | 2.46508 | + | 13.7259i | 0.138891 | + | 0.773368i | ||||
\(316\) | −6.01084 | − | 0.463270i | −0.338136 | − | 0.0260610i | ||||
\(317\) | 24.2250 | 1.36061 | 0.680306 | − | 0.732928i | \(-0.261847\pi\) | ||||
0.680306 | + | 0.732928i | \(0.261847\pi\) | |||||||
\(318\) | −21.4394 | + | 23.7167i | −1.20226 | + | 1.32997i | ||||
\(319\) | 2.85442i | 0.159817i | ||||||||
\(320\) | 3.60986 | − | 15.3646i | 0.201797 | − | 0.858908i | ||||
\(321\) | −17.2369 | + | 1.53553i | −0.962069 | + | 0.0857048i | ||||
\(322\) | 19.7302 | − | 18.2681i | 1.09952 | − | 1.01804i | ||||
\(323\) | − | 5.22103i | − | 0.290506i | ||||||
\(324\) | 4.94804 | + | 17.3066i | 0.274891 | + | 0.961475i | ||||
\(325\) | − | 2.37656i | − | 0.131828i | ||||||
\(326\) | −20.9741 | − | 22.6528i | −1.16165 | − | 1.25462i | ||||
\(327\) | 8.04283 | − | 0.716486i | 0.444770 | − | 0.0396218i | ||||
\(328\) | 11.4884 | + | 14.5004i | 0.634342 | + | 0.800651i | ||||
\(329\) | 13.0718i | 0.720671i | ||||||||
\(330\) | −17.3242 | − | 15.6607i | −0.953667 | − | 0.862095i | ||||
\(331\) | −19.4306 | −1.06800 | −0.534001 | − | 0.845484i | \(-0.679312\pi\) | ||||
−0.534001 | + | 0.845484i | \(0.679312\pi\) | |||||||
\(332\) | 12.7995 | + | 0.986485i | 0.702462 | + | 0.0541404i | ||||
\(333\) | 4.65375 | + | 25.9128i | 0.255024 | + | 1.42001i | ||||
\(334\) | 0.741957 | + | 0.801342i | 0.0405981 | + | 0.0438475i | ||||
\(335\) | 11.2169 | 0.612846 | ||||||||
\(336\) | −16.2898 | − | 1.06019i | −0.888683 | − | 0.0578383i | ||||
\(337\) | 3.54860 | 0.193305 | 0.0966524 | − | 0.995318i | \(-0.469186\pi\) | ||||
0.0966524 | + | 0.995318i | \(0.469186\pi\) | |||||||
\(338\) | 8.06835 | + | 8.71413i | 0.438861 | + | 0.473986i | ||||
\(339\) | −26.6725 | + | 2.37609i | −1.44865 | + | 0.129051i | ||||
\(340\) | 20.5400 | + | 1.58306i | 1.11394 | + | 0.0858537i | ||||
\(341\) | −21.6744 | −1.17373 | ||||||||
\(342\) | −3.38733 | − | 2.55460i | −0.183166 | − | 0.138137i | ||||
\(343\) | − | 19.9059i | − | 1.07482i | ||||||
\(344\) | 3.01666 | − | 2.39004i | 0.162647 | − | 0.128863i | ||||
\(345\) | 2.44671 | + | 27.4653i | 0.131727 | + | 1.47868i | ||||
\(346\) | 2.53971 | + | 2.74298i | 0.136535 | + | 0.147463i | ||||
\(347\) | 19.3122i | 1.03673i | 0.855158 | + | 0.518367i | \(0.173460\pi\) | ||||
−0.855158 | + | 0.518367i | \(0.826540\pi\) | |||||||
\(348\) | −2.04597 | + | 0.0244074i | −0.109676 | + | 0.00130837i | ||||
\(349\) | 13.9086i | 0.744510i | 0.928130 | + | 0.372255i | \(0.121415\pi\) | ||||
−0.928130 | + | 0.372255i | \(0.878585\pi\) | |||||||
\(350\) | −2.70857 | + | 2.50785i | −0.144779 | + | 0.134050i | ||||
\(351\) | 10.7539 | − | 2.93631i | 0.574002 | − | 0.156728i | ||||
\(352\) | 22.6683 | − | 15.2796i | 1.20822 | − | 0.814405i | ||||
\(353\) | − | 17.9380i | − | 0.954744i | −0.878701 | − | 0.477372i | \(-0.841589\pi\) | ||
0.878701 | − | 0.477372i | \(-0.158411\pi\) | |||||||
\(354\) | −25.4763 | − | 23.0301i | −1.35405 | − | 1.22403i | ||||
\(355\) | 7.05288 | 0.374328 | ||||||||
\(356\) | −13.5177 | − | 1.04184i | −0.716436 | − | 0.0552175i | ||||
\(357\) | −1.89066 | − | 21.2234i | −0.100064 | − | 1.12326i | ||||
\(358\) | 14.3192 | − | 13.2580i | 0.756792 | − | 0.700709i | ||||
\(359\) | −32.0012 | −1.68896 | −0.844479 | − | 0.535589i | \(-0.820090\pi\) | ||||
−0.844479 | + | 0.535589i | \(0.820090\pi\) | |||||||
\(360\) | 11.0771 | − | 12.5515i | 0.583813 | − | 0.661520i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.8543 | + | 11.9017i | −0.675606 | + | 0.625539i | ||||
\(363\) | −1.89863 | − | 21.3128i | −0.0996520 | − | 1.11863i | ||||
\(364\) | −0.776884 | + | 10.0799i | −0.0407198 | + | 0.528331i | ||||
\(365\) | −6.04297 | −0.316304 | ||||||||
\(366\) | 18.4539 | + | 16.6819i | 0.964598 | + | 0.871977i | ||||
\(367\) | 14.3595i | 0.749558i | 0.927114 | + | 0.374779i | \(0.122281\pi\) | ||||
−0.927114 | + | 0.374779i | \(0.877719\pi\) | |||||||
\(368\) | −31.8964 | − | 4.94604i | −1.66271 | − | 0.257830i | ||||
\(369\) | 3.46849 | + | 19.3131i | 0.180563 | + | 1.00540i | ||||
\(370\) | 17.9664 | − | 16.6350i | 0.934030 | − | 0.864812i | ||||
\(371\) | − | 30.7533i | − | 1.59663i | ||||||
\(372\) | −0.185332 | − | 15.5356i | −0.00960902 | − | 0.805486i | ||||
\(373\) | 22.3799i | 1.15879i | 0.815048 | + | 0.579393i | \(0.196710\pi\) | ||||
−0.815048 | + | 0.579393i | \(0.803290\pi\) | |||||||
\(374\) | 24.2422 | + | 26.1825i | 1.25353 | + | 1.35386i | ||||
\(375\) | −1.85193 | − | 20.7886i | −0.0956333 | − | 1.07352i | ||||
\(376\) | 12.2992 | − | 9.74445i | 0.634283 | − | 0.502532i | ||||
\(377\) | 1.26718i | 0.0652633i | ||||||||
\(378\) | −14.6945 | − | 9.15776i | −0.755804 | − | 0.471024i | ||||
\(379\) | 27.5634 | 1.41583 | 0.707917 | − | 0.706295i | \(-0.249635\pi\) | ||||
0.707917 | + | 0.706295i | \(0.249635\pi\) | |||||||
\(380\) | −0.303209 | + | 3.93408i | −0.0155543 | + | 0.201814i | ||||
\(381\) | 19.0787 | − | 1.69960i | 0.977430 | − | 0.0870731i | ||||
\(382\) | 0.763274 | + | 0.824365i | 0.0390525 | + | 0.0421782i | ||||
\(383\) | 34.4356 | 1.75958 | 0.879788 | − | 0.475367i | \(-0.157685\pi\) | ||||
0.879788 | + | 0.475367i | \(0.157685\pi\) | |||||||
\(384\) | 11.1458 | + | 16.1174i | 0.568784 | + | 0.822487i | ||||
\(385\) | 22.4642 | 1.14488 | ||||||||
\(386\) | −10.1290 | − | 10.9397i | −0.515554 | − | 0.556817i | ||||
\(387\) | 4.01789 | − | 0.721583i | 0.204241 | − | 0.0366801i | ||||
\(388\) | 1.88100 | − | 24.4056i | 0.0954932 | − | 1.23901i | ||||
\(389\) | 9.55684 | 0.484551 | 0.242276 | − | 0.970207i | \(-0.422106\pi\) | ||||
0.242276 | + | 0.970207i | \(0.422106\pi\) | |||||||
\(390\) | −7.69087 | − | 6.95238i | −0.389442 | − | 0.352048i | ||||
\(391\) | − | 42.1306i | − | 2.13063i | ||||||
\(392\) | −3.21076 | + | 2.54383i | −0.162168 | + | 0.128483i | ||||
\(393\) | 9.42214 | − | 0.839360i | 0.475284 | − | 0.0423401i | ||||
\(394\) | 9.93932 | + | 10.7348i | 0.500736 | + | 0.540814i | ||||
\(395\) | 5.94690i | 0.299221i | ||||||||
\(396\) | 28.8483 | − | 2.91716i | 1.44968 | − | 0.146593i | ||||
\(397\) | − | 17.6792i | − | 0.887295i | −0.896201 | − | 0.443647i | \(-0.853684\pi\) | ||
0.896201 | − | 0.443647i | \(-0.146316\pi\) | |||||||
\(398\) | 11.6131 | − | 10.7525i | 0.582113 | − | 0.538974i | ||||
\(399\) | 4.06498 | − | 0.362124i | 0.203503 | − | 0.0181289i | ||||
\(400\) | 4.37875 | + | 0.678995i | 0.218938 | + | 0.0339498i | ||||
\(401\) | 34.3290i | 1.71431i | 0.515058 | + | 0.857155i | \(0.327770\pi\) | ||||
−0.515058 | + | 0.857155i | \(0.672230\pi\) | |||||||
\(402\) | −9.33921 | + | 10.3312i | −0.465797 | + | 0.515274i | ||||
\(403\) | −9.62207 | −0.479310 | ||||||||
\(404\) | −0.268310 | + | 3.48127i | −0.0133489 | + | 0.173200i | ||||
\(405\) | 16.6463 | − | 6.17838i | 0.827160 | − | 0.307006i | ||||
\(406\) | 1.44421 | − | 1.33719i | 0.0716750 | − | 0.0663634i | ||||
\(407\) | 42.4095 | 2.10216 | ||||||||
\(408\) | −18.5596 | + | 17.6000i | −0.918838 | + | 0.871332i | ||||
\(409\) | −21.2316 | −1.04983 | −0.524917 | − | 0.851154i | \(-0.675904\pi\) | ||||
−0.524917 | + | 0.851154i | \(0.675904\pi\) | |||||||
\(410\) | 13.3906 | − | 12.3983i | 0.661314 | − | 0.612306i | ||||
\(411\) | −2.06185 | + | 0.183678i | −0.101704 | + | 0.00906015i | ||||
\(412\) | 26.1850 | + | 2.01814i | 1.29004 | + | 0.0994265i | ||||
\(413\) | 33.0350 | 1.62554 | ||||||||
\(414\) | −27.3337 | − | 20.6141i | −1.34338 | − | 1.01313i | ||||
\(415\) | − | 12.6633i | − | 0.621617i | ||||||
\(416\) | 10.0633 | − | 6.78318i | 0.493394 | − | 0.332573i | ||||
\(417\) | −0.740635 | − | 8.31391i | −0.0362690 | − | 0.407134i | ||||
\(418\) | −5.01481 | + | 4.64318i | −0.245282 | + | 0.227105i | ||||
\(419\) | 16.7076i | 0.816219i | 0.912933 | + | 0.408110i | \(0.133812\pi\) | ||||
−0.912933 | + | 0.408110i | \(0.866188\pi\) | |||||||
\(420\) | 0.192085 | + | 16.1017i | 0.00937281 | + | 0.785685i | ||||
\(421\) | 3.19194i | 0.155565i | 0.996970 | + | 0.0777827i | \(0.0247840\pi\) | ||||
−0.996970 | + | 0.0777827i | \(0.975216\pi\) | |||||||
\(422\) | −5.69868 | − | 6.15479i | −0.277407 | − | 0.299611i | ||||
\(423\) | 16.3813 | − | 2.94197i | 0.796487 | − | 0.143043i | ||||
\(424\) | −28.9357 | + | 22.9252i | −1.40524 | + | 1.11335i | ||||
\(425\) | 5.78371i | 0.280551i | ||||||||
\(426\) | −5.87222 | + | 6.49597i | −0.284510 | + | 0.314731i | ||||
\(427\) | −23.9290 | −1.15800 | ||||||||
\(428\) | −19.9232 | − | 1.53553i | −0.963023 | − | 0.0742225i | ||||
\(429\) | −1.59338 | − | 17.8863i | −0.0769292 | − | 0.863560i | ||||
\(430\) | −2.57933 | − | 2.78577i | −0.124386 | − | 0.134342i | ||||
\(431\) | −17.4859 | −0.842267 | −0.421133 | − | 0.906999i | \(-0.638368\pi\) | ||||
−0.421133 | + | 0.906999i | \(0.638368\pi\) | |||||||
\(432\) | 2.33762 | + | 20.6527i | 0.112469 | + | 0.993655i | ||||
\(433\) | −5.03086 | −0.241768 | −0.120884 | − | 0.992667i | \(-0.538573\pi\) | ||||
−0.120884 | + | 0.992667i | \(0.538573\pi\) | |||||||
\(434\) | 10.1536 | + | 10.9663i | 0.487389 | + | 0.526399i | ||||
\(435\) | 0.179095 | + | 2.01041i | 0.00858693 | + | 0.0963916i | ||||
\(436\) | 9.29627 | + | 0.716486i | 0.445211 | + | 0.0343135i | ||||
\(437\) | 8.06939 | 0.386011 | ||||||||
\(438\) | 5.03137 | − | 5.56581i | 0.240408 | − | 0.265945i | ||||
\(439\) | − | 1.24339i | − | 0.0593439i | −0.999560 | − | 0.0296719i | \(-0.990554\pi\) | ||
0.999560 | − | 0.0296719i | \(-0.00944625\pi\) | |||||||
\(440\) | −16.7461 | − | 21.1365i | −0.798338 | − | 1.00764i | ||||
\(441\) | −4.27641 | + | 0.768012i | −0.203639 | + | 0.0365720i | ||||
\(442\) | 10.7620 | + | 11.6234i | 0.511896 | + | 0.552868i | ||||
\(443\) | 7.28527i | 0.346134i | 0.984910 | + | 0.173067i | \(0.0553677\pi\) | ||||
−0.984910 | + | 0.173067i | \(0.944632\pi\) | |||||||
\(444\) | 0.362633 | + | 30.3980i | 0.0172098 | + | 1.44263i | ||||
\(445\) | 13.3739i | 0.633983i | ||||||||
\(446\) | −3.58870 | + | 3.32276i | −0.169930 | + | 0.157337i | ||||
\(447\) | −3.55578 | − | 39.9151i | −0.168183 | − | 1.88792i | ||||
\(448\) | −18.3500 | − | 4.31127i | −0.866957 | − | 0.203688i | ||||
\(449\) | − | 35.0658i | − | 1.65486i | −0.561571 | − | 0.827429i | \(-0.689803\pi\) | ||
0.561571 | − | 0.827429i | \(-0.310197\pi\) | |||||||
\(450\) | 3.75239 | + | 2.82991i | 0.176889 | + | 0.133403i | ||||
\(451\) | 31.6083 | 1.48838 | ||||||||
\(452\) | −30.8293 | − | 2.37609i | −1.45009 | − | 0.111762i | ||||
\(453\) | −9.71626 | + | 0.865561i | −0.456510 | + | 0.0406676i | ||||
\(454\) | −14.8550 | + | 13.7541i | −0.697180 | + | 0.645514i | ||||
\(455\) | 9.97269 | 0.467527 | ||||||||
\(456\) | −3.37099 | − | 3.55478i | −0.157861 | − | 0.166468i | ||||
\(457\) | −2.98914 | −0.139826 | −0.0699130 | − | 0.997553i | \(-0.522272\pi\) | ||||
−0.0699130 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(458\) | 13.9982 | − | 12.9609i | 0.654094 | − | 0.605621i | ||||
\(459\) | −26.1712 | + | 7.14593i | −1.22157 | + | 0.333543i | ||||
\(460\) | −2.44671 | + | 31.7456i | −0.114079 | + | 1.48015i | ||||
\(461\) | 21.9864 | 1.02401 | 0.512005 | − | 0.858983i | \(-0.328903\pi\) | ||||
0.512005 | + | 0.858983i | \(0.328903\pi\) | |||||||
\(462\) | −18.7037 | + | 20.6904i | −0.870173 | + | 0.962604i | ||||
\(463\) | 14.2465i | 0.662089i | 0.943615 | + | 0.331045i | \(0.107401\pi\) | ||||
−0.943615 | + | 0.331045i | \(0.892599\pi\) | |||||||
\(464\) | −2.33475 | − | 0.362040i | −0.108388 | − | 0.0168073i | ||||
\(465\) | −15.2656 | + | 1.35991i | −0.707924 | + | 0.0630645i | ||||
\(466\) | 14.5915 | − | 13.5102i | 0.675938 | − | 0.625846i | ||||
\(467\) | − | 7.12691i | − | 0.329794i | −0.986311 | − | 0.164897i | \(-0.947271\pi\) | ||
0.986311 | − | 0.164897i | \(-0.0527292\pi\) | |||||||
\(468\) | 12.8068 | − | 1.29504i | 0.591995 | − | 0.0598630i | ||||
\(469\) | − | 13.3964i | − | 0.618589i | ||||||
\(470\) | −10.5162 | − | 11.3579i | −0.485075 | − | 0.523899i | ||||
\(471\) | 8.12995 | − | 0.724247i | 0.374609 | − | 0.0333716i | ||||
\(472\) | −24.6261 | − | 31.0825i | −1.13351 | − | 1.43069i | ||||
\(473\) | − | 6.57578i | − | 0.302355i | ||||||
\(474\) | −5.47732 | − | 4.95139i | −0.251582 | − | 0.227425i | ||||
\(475\) | −1.10777 | −0.0508280 | ||||||||
\(476\) | 1.89066 | − | 24.5310i | 0.0866583 | − | 1.12437i | ||||
\(477\) | −38.5395 | + | 6.92141i | −1.76460 | + | 0.316910i | ||||
\(478\) | −10.5473 | − | 11.3915i | −0.482424 | − | 0.521037i | ||||
\(479\) | −1.78303 | −0.0814687 | −0.0407344 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407344 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(480\) | 15.0069 | − | 12.1839i | 0.684968 | − | 0.556116i | ||||
\(481\) | 18.8272 | 0.858445 | ||||||||
\(482\) | −11.8711 | − | 12.8213i | −0.540716 | − | 0.583994i | ||||
\(483\) | 32.8019 | − | 2.92212i | 1.49254 | − | 0.132961i | ||||
\(484\) | 1.89863 | − | 24.6343i | 0.0863011 | − | 1.11974i | ||||
\(485\) | −24.1460 | −1.09641 | ||||||||
\(486\) | −8.16915 | + | 20.4760i | −0.370560 | + | 0.928808i | ||||
\(487\) | 14.2210i | 0.644417i | 0.946669 | + | 0.322208i | \(0.104425\pi\) | ||||
−0.946669 | + | 0.322208i | \(0.895575\pi\) | |||||||
\(488\) | 17.8380 | + | 22.5147i | 0.807489 | + | 1.01919i | ||||
\(489\) | −3.35497 | − | 37.6608i | −0.151717 | − | 1.70308i | ||||
\(490\) | 2.74529 | + | 2.96501i | 0.124019 | + | 0.133946i | ||||
\(491\) | 6.44379i | 0.290804i | 0.989373 | + | 0.145402i | \(0.0464476\pi\) | ||||
−0.989373 | + | 0.145402i | \(0.953552\pi\) | |||||||
\(492\) | 0.270274 | + | 22.6560i | 0.0121849 | + | 1.02141i | ||||
\(493\) | − | 3.08388i | − | 0.138891i | ||||||
\(494\) | −2.22626 | + | 2.06128i | −0.100164 | + | 0.0927413i | ||||
\(495\) | −5.05585 | − | 28.1517i | −0.227243 | − | 1.26533i | ||||
\(496\) | 2.74907 | − | 17.7284i | 0.123437 | − | 0.796029i | ||||
\(497\) | − | 8.42328i | − | 0.377836i | ||||||
\(498\) | 11.6634 | + | 10.5435i | 0.522649 | + | 0.472463i | ||||
\(499\) | −36.1251 | −1.61718 | −0.808592 | − | 0.588370i | \(-0.799770\pi\) | ||||
−0.808592 | + | 0.588370i | \(0.799770\pi\) | |||||||
\(500\) | 1.85193 | − | 24.0285i | 0.0828209 | − | 1.07459i | ||||
\(501\) | 0.118682 | + | 1.33225i | 0.00530232 | + | 0.0595205i | ||||
\(502\) | −3.48506 | + | 3.22680i | −0.155546 | + | 0.144019i | ||||
\(503\) | 30.4980 | 1.35984 | 0.679919 | − | 0.733288i | \(-0.262015\pi\) | ||||
0.679919 | + | 0.733288i | \(0.262015\pi\) | |||||||
\(504\) | −14.9903 | − | 13.2294i | −0.667719 | − | 0.589283i | ||||
\(505\) | 3.44424 | 0.153267 | ||||||||
\(506\) | −40.4664 | + | 37.4676i | −1.79895 | + | 1.66564i | ||||
\(507\) | 1.29060 | + | 14.4874i | 0.0573174 | + | 0.643410i | ||||
\(508\) | 22.0520 | + | 1.69960i | 0.978399 | + | 0.0754076i | ||||
\(509\) | 10.9622 | 0.485889 | 0.242944 | − | 0.970040i | \(-0.421887\pi\) | ||||
0.242944 | + | 0.970040i | \(0.421887\pi\) | |||||||
\(510\) | 18.7168 | + | 16.9196i | 0.828796 | + | 0.749214i | ||||
\(511\) | 7.21714i | 0.319268i | ||||||||
\(512\) | 9.62269 | + | 20.4794i | 0.425267 | + | 0.905068i | ||||
\(513\) | −1.36868 | − | 5.01266i | −0.0604287 | − | 0.221314i | ||||
\(514\) | 6.16123 | − | 5.70464i | 0.271760 | − | 0.251621i | ||||
\(515\) | − | 25.9064i | − | 1.14157i | ||||||
\(516\) | 4.71335 | − | 0.0562277i | 0.207493 | − | 0.00247529i | ||||
\(517\) | − | 26.8101i | − | 1.17911i | ||||||
\(518\) | −19.8672 | − | 21.4574i | −0.872916 | − | 0.942782i | ||||
\(519\) | 0.406246 | + | 4.56026i | 0.0178322 | + | 0.200173i | ||||
\(520\) | −7.43421 | − | 9.38328i | −0.326012 | − | 0.411484i | ||||
\(521\) | 8.00895i | 0.350879i | 0.984490 | + | 0.175439i | \(0.0561346\pi\) | ||||
−0.984490 | + | 0.175439i | \(0.943865\pi\) | |||||||
\(522\) | −2.00077 | − | 1.50891i | −0.0875715 | − | 0.0660432i | ||||
\(523\) | −14.1920 | −0.620572 | −0.310286 | − | 0.950643i | \(-0.600425\pi\) | ||||
−0.310286 | + | 0.950643i | \(0.600425\pi\) | |||||||
\(524\) | 10.8905 | + | 0.839360i | 0.475755 | + | 0.0366676i | ||||
\(525\) | −4.50306 | + | 0.401150i | −0.196530 | + | 0.0175076i | ||||
\(526\) | −20.2172 | − | 21.8354i | −0.881514 | − | 0.952069i | ||||
\(527\) | 23.4167 | 1.02005 | ||||||||
\(528\) | 33.4103 | + | 2.17445i | 1.45400 | + | 0.0946306i | ||||
\(529\) | 42.1151 | 1.83109 | ||||||||
\(530\) | 24.7408 | + | 26.7210i | 1.07467 | + | 1.16069i | ||||
\(531\) | −7.43493 | − | 41.3988i | −0.322649 | − | 1.79656i | ||||
\(532\) | 4.69849 | + | 0.362124i | 0.203705 | + | 0.0157001i | ||||
\(533\) | 14.0321 | 0.607798 | ||||||||
\(534\) | −12.3179 | − | 11.1351i | −0.533046 | − | 0.481863i | ||||
\(535\) | 19.7112i | 0.852191i | ||||||||
\(536\) | −12.6047 | + | 9.98645i | −0.544438 | + | 0.431349i | ||||
\(537\) | 23.8060 | − | 2.12073i | 1.02730 | − | 0.0915161i | ||||
\(538\) | −10.0410 | − | 10.8446i | −0.432897 | − | 0.467546i | ||||
\(539\) | 6.99888i | 0.301463i | ||||||||
\(540\) | 20.1352 | − | 3.86462i | 0.866480 | − | 0.166307i | ||||
\(541\) | − | 17.1733i | − | 0.738337i | −0.929362 | − | 0.369168i | \(-0.879643\pi\) | ||
0.929362 | − | 0.369168i | \(-0.120357\pi\) | |||||||
\(542\) | 33.0885 | − | 30.6364i | 1.42127 | − | 1.31595i | ||||
\(543\) | −21.3705 | + | 1.90377i | −0.917098 | + | 0.0816985i | ||||
\(544\) | −24.4905 | + | 16.5079i | −1.05002 | + | 0.707768i | ||||
\(545\) | − | 9.19738i | − | 0.393972i | ||||||
\(546\) | −8.30326 | + | 9.18523i | −0.355347 | + | 0.393092i | ||||
\(547\) | 20.0528 | 0.857394 | 0.428697 | − | 0.903448i | \(-0.358973\pi\) | ||||
0.428697 | + | 0.903448i | \(0.358973\pi\) | |||||||
\(548\) | −2.38318 | − | 0.183678i | −0.101805 | − | 0.00784632i | ||||
\(549\) | 5.38551 | + | 29.9874i | 0.229848 | + | 1.27983i | ||||
\(550\) | 5.55526 | − | 5.14357i | 0.236877 | − | 0.219323i | ||||
\(551\) | 0.590664 | 0.0251631 | ||||||||
\(552\) | −27.2018 | − | 28.6849i | −1.15779 | − | 1.22091i | ||||
\(553\) | 7.10241 | 0.302025 | ||||||||
\(554\) | −20.0315 | + | 18.5471i | −0.851058 | + | 0.787989i | ||||
\(555\) | 29.8696 | − | 2.66090i | 1.26789 | − | 0.112949i | ||||
\(556\) | 0.740635 | − | 9.60960i | 0.0314099 | − | 0.407538i | ||||
\(557\) | 20.5897 | 0.872414 | 0.436207 | − | 0.899846i | \(-0.356322\pi\) | ||||
0.436207 | + | 0.899846i | \(0.356322\pi\) | |||||||
\(558\) | 11.4576 | − | 15.1924i | 0.485037 | − | 0.643147i | ||||
\(559\) | − | 2.91923i | − | 0.123470i | ||||||
\(560\) | −2.84925 | + | 18.3744i | −0.120403 | + | 0.776461i | ||||
\(561\) | 3.87773 | + | 43.5290i | 0.163718 | + | 1.83779i | ||||
\(562\) | 4.09645 | − | 3.79288i | 0.172798 | − | 0.159993i | ||||
\(563\) | 3.87489i | 0.163307i | 0.996661 | + | 0.0816536i | \(0.0260201\pi\) | ||||
−0.996661 | + | 0.0816536i | \(0.973980\pi\) | |||||||
\(564\) | 19.2168 | − | 0.229246i | 0.809173 | − | 0.00965301i | ||||
\(565\) | 30.5013i | 1.28320i | ||||||||
\(566\) | −16.1637 | − | 17.4574i | −0.679411 | − | 0.733789i | ||||
\(567\) | −7.37886 | − | 19.8807i | −0.309883 | − | 0.834911i | ||||
\(568\) | −7.92544 | + | 6.27919i | −0.332544 | + | 0.263469i | ||||
\(569\) | 0.630264i | 0.0264220i | 0.999913 | + | 0.0132110i | \(0.00420532\pi\) | ||||
−0.999913 | + | 0.0132110i | \(0.995795\pi\) | |||||||
\(570\) | −3.24067 | + | 3.58489i | −0.135737 | + | 0.150155i | ||||
\(571\) | 10.7705 | 0.450731 | 0.225365 | − | 0.974274i | \(-0.427642\pi\) | ||||
0.225365 | + | 0.974274i | \(0.427642\pi\) | |||||||
\(572\) | 1.59338 | − | 20.6738i | 0.0666226 | − | 0.864416i | ||||
\(573\) | 0.122092 | + | 1.37053i | 0.00510045 | + | 0.0572545i | ||||
\(574\) | −14.8073 | − | 15.9924i | −0.618044 | − | 0.667511i | ||||
\(575\) | −8.93904 | −0.372784 | ||||||||
\(576\) | −1.27290 | + | 23.9662i | −0.0530376 | + | 0.998593i | ||||
\(577\) | 34.5776 | 1.43948 | 0.719742 | − | 0.694241i | \(-0.244260\pi\) | ||||
0.719742 | + | 0.694241i | \(0.244260\pi\) | |||||||
\(578\) | −9.85714 | − | 10.6461i | −0.410003 | − | 0.442819i | ||||
\(579\) | −1.62022 | − | 18.1875i | −0.0673339 | − | 0.755849i | ||||
\(580\) | −0.179095 | + | 2.32372i | −0.00743650 | + | 0.0964871i | ||||
\(581\) | −15.1238 | −0.627442 | ||||||||
\(582\) | 20.1039 | − | 22.2394i | 0.833334 | − | 0.921851i | ||||
\(583\) | 63.0747i | 2.61229i | ||||||||
\(584\) | 6.79059 | − | 5.38007i | 0.280997 | − | 0.222629i | ||||
\(585\) | −2.24448 | − | 12.4976i | −0.0927978 | − | 0.516712i | ||||
\(586\) | −9.73812 | − | 10.5175i | −0.402278 | − | 0.434476i | ||||
\(587\) | 15.2181i | 0.628116i | 0.949404 | + | 0.314058i | \(0.101689\pi\) | ||||
−0.949404 | + | 0.314058i | \(0.898311\pi\) | |||||||
\(588\) | −5.01662 | + | 0.0598456i | −0.206882 | + | 0.00246799i | ||||
\(589\) | 4.48507i | 0.184804i | ||||||||
\(590\) | −28.7035 | + | 26.5764i | −1.18171 | + | 1.09413i | ||||
\(591\) | 1.58987 | + | 17.8469i | 0.0653986 | + | 0.734124i | ||||
\(592\) | −5.37901 | + | 34.6886i | −0.221076 | + | 1.42569i | ||||
\(593\) | 4.83383i | 0.198502i | 0.995062 | + | 0.0992509i | \(0.0316446\pi\) | ||||
−0.995062 | + | 0.0992509i | \(0.968355\pi\) | |||||||
\(594\) | 30.1383 | + | 18.7825i | 1.23659 | + | 0.770654i | ||||
\(595\) | −24.2700 | −0.994973 | ||||||||
\(596\) | 3.55578 | − | 46.1356i | 0.145651 | − | 1.88979i | ||||
\(597\) | 19.3071 | − | 1.71995i | 0.790185 | − | 0.0703927i | ||||
\(598\) | −17.9646 | + | 16.6333i | −0.734625 | + | 0.680185i | ||||
\(599\) | 42.3775 | 1.73150 | 0.865748 | − | 0.500480i | \(-0.166843\pi\) | ||||
0.865748 | + | 0.500480i | \(0.166843\pi\) | |||||||
\(600\) | 3.73428 | + | 3.93788i | 0.152451 | + | 0.160763i | ||||
\(601\) | −6.13637 | −0.250308 | −0.125154 | − | 0.992137i | \(-0.539942\pi\) | ||||
−0.125154 | + | 0.992137i | \(0.539942\pi\) | |||||||
\(602\) | −3.32706 | + | 3.08050i | −0.135601 | + | 0.125552i | ||||
\(603\) | −16.7881 | + | 3.01503i | −0.683666 | + | 0.122782i | ||||
\(604\) | −11.2305 | − | 0.865561i | −0.456962 | − | 0.0352192i | ||||
\(605\) | −24.3722 | −0.990873 | ||||||||
\(606\) | −2.86767 | + | 3.17228i | −0.116491 | + | 0.128865i | ||||
\(607\) | − | 40.2074i | − | 1.63197i | −0.578074 | − | 0.815985i | \(-0.696195\pi\) | ||
0.578074 | − | 0.815985i | \(-0.303805\pi\) | |||||||
\(608\) | −3.16180 | − | 4.69074i | −0.128228 | − | 0.190235i | ||||
\(609\) | 2.40103 | − | 0.213893i | 0.0972948 | − | 0.00866739i | ||||
\(610\) | 20.7915 | − | 19.2507i | 0.841823 | − | 0.779439i | ||||
\(611\) | − | 11.9020i | − | 0.481504i | ||||||
\(612\) | −31.1673 | + | 3.15166i | −1.25986 | + | 0.127398i | ||||
\(613\) | 41.5016i | 1.67623i | 0.545491 | + | 0.838117i | \(0.316343\pi\) | ||||
−0.545491 | + | 0.838117i | \(0.683657\pi\) | |||||||
\(614\) | 24.9981 | + | 26.9989i | 1.00884 | + | 1.08959i | ||||
\(615\) | 22.2622 | − | 1.98320i | 0.897697 | − | 0.0799702i | ||||
\(616\) | −25.2434 | + | 19.9999i | −1.01709 | + | 0.805819i | ||||
\(617\) | 43.6944i | 1.75907i | 0.475834 | + | 0.879535i | \(0.342146\pi\) | ||||
−0.475834 | + | 0.879535i | \(0.657854\pi\) | |||||||
\(618\) | 23.8608 | + | 21.5697i | 0.959822 | + | 0.867659i | ||||
\(619\) | −7.56093 | −0.303900 | −0.151950 | − | 0.988388i | \(-0.548555\pi\) | ||||
−0.151950 | + | 0.988388i | \(0.548555\pi\) | |||||||
\(620\) | −17.6446 | − | 1.35991i | −0.708626 | − | 0.0546155i | ||||
\(621\) | −11.0444 | − | 40.4491i | −0.443197 | − | 1.62317i | ||||
\(622\) | −23.6983 | − | 25.5951i | −0.950215 | − | 1.02627i | ||||
\(623\) | 15.9725 | 0.639924 | ||||||||
\(624\) | 14.8321 | + | 0.965318i | 0.593758 | + | 0.0386436i | ||||
\(625\) | −18.2340 | −0.729360 | ||||||||
\(626\) | 22.7743 | + | 24.5972i | 0.910246 | + | 0.983100i | ||||
\(627\) | −8.33723 | + | 0.742712i | −0.332957 | + | 0.0296611i | ||||
\(628\) | 9.39697 | + | 0.724247i | 0.374980 | + | 0.0289006i | ||||
\(629\) | −45.8187 | −1.82691 | ||||||||
\(630\) | −11.8751 | + | 15.7460i | −0.473114 | + | 0.627337i | ||||
\(631\) | 36.6940i | 1.46077i | 0.683038 | + | 0.730383i | \(0.260658\pi\) | ||||
−0.683038 | + | 0.730383i | \(0.739342\pi\) | |||||||
\(632\) | −5.29454 | − | 6.68263i | −0.210605 | − | 0.265821i | ||||
\(633\) | −0.911549 | − | 10.2325i | −0.0362308 | − | 0.406705i | ||||
\(634\) | 23.2756 | + | 25.1386i | 0.924393 | + | 0.998380i | ||||
\(635\) | − | 21.8174i | − | 0.865797i | ||||||
\(636\) | −45.2103 | + | 0.539335i | −1.79270 | + | 0.0213860i | ||||
\(637\) | 3.10707i | 0.123106i | ||||||||
\(638\) | −2.96206 | + | 2.74256i | −0.117269 | + | 0.108579i | ||||
\(639\) | −10.5559 | + | 1.89576i | −0.417585 | + | 0.0749953i | ||||
\(640\) | 19.4124 | − | 11.0165i | 0.767344 | − | 0.435465i | ||||
\(641\) | 17.5329i | 0.692508i | 0.938141 | + | 0.346254i | \(0.112546\pi\) | ||||
−0.938141 | + | 0.346254i | \(0.887454\pi\) | |||||||
\(642\) | −18.1548 | − | 16.4116i | −0.716513 | − | 0.647713i | ||||
\(643\) | −42.2395 | −1.66576 | −0.832882 | − | 0.553451i | \(-0.813311\pi\) | ||||
−0.832882 | + | 0.553451i | \(0.813311\pi\) | |||||||
\(644\) | 37.9139 | + | 2.92212i | 1.49402 | + | 0.115148i | ||||
\(645\) | −0.412583 | − | 4.63141i | −0.0162455 | − | 0.182361i | ||||
\(646\) | 5.41793 | − | 5.01642i | 0.213165 | − | 0.197368i | ||||
\(647\) | −46.4035 | −1.82431 | −0.912156 | − | 0.409844i | \(-0.865583\pi\) | ||||
−0.912156 | + | 0.409844i | \(0.865583\pi\) | |||||||
\(648\) | −13.2051 | + | 21.7629i | −0.518744 | + | 0.854929i | ||||
\(649\) | −67.7544 | −2.65959 | ||||||||
\(650\) | 2.46619 | − | 2.28342i | 0.0967317 | − | 0.0895633i | ||||
\(651\) | 1.62415 | + | 18.2317i | 0.0636555 | + | 0.714557i | ||||
\(652\) | 3.35497 | − | 43.5301i | 0.131391 | − | 1.70477i | ||||
\(653\) | −21.8338 | −0.854422 | −0.427211 | − | 0.904152i | \(-0.640504\pi\) | ||||
−0.427211 | + | 0.904152i | \(0.640504\pi\) | |||||||
\(654\) | 8.47114 | + | 7.65773i | 0.331248 | + | 0.299441i | ||||
\(655\) | − | 10.7747i | − | 0.421002i | ||||||
\(656\) | −4.00904 | + | 25.8538i | −0.156527 | + | 1.00942i | ||||
\(657\) | 9.04440 | − | 1.62431i | 0.352855 | − | 0.0633703i | ||||
\(658\) | −13.5647 | + | 12.5595i | −0.528809 | + | 0.489620i | ||||
\(659\) | 6.39325i | 0.249046i | 0.992217 | + | 0.124523i | \(0.0397400\pi\) | ||||
−0.992217 | + | 0.124523i | \(0.960260\pi\) | |||||||
\(660\) | −0.393965 | − | 33.0245i | −0.0153351 | − | 1.28548i | ||||
\(661\) | − | 12.6013i | − | 0.490136i | −0.969506 | − | 0.245068i | \(-0.921190\pi\) | ||
0.969506 | − | 0.245068i | \(-0.0788102\pi\) | |||||||
\(662\) | −18.6691 | − | 20.1633i | −0.725595 | − | 0.783671i | ||||
\(663\) | 1.72147 | + | 19.3241i | 0.0668562 | + | 0.750487i | ||||
\(664\) | 11.2742 | + | 14.2300i | 0.437522 | + | 0.552230i | ||||
\(665\) | − | 4.64850i | − | 0.180261i | ||||||
\(666\) | −22.4186 | + | 29.7265i | −0.868704 | + | 1.15188i | ||||
\(667\) | 4.76630 | 0.184552 | ||||||||
\(668\) | −0.118682 | + | 1.53987i | −0.00459194 | + | 0.0595795i | ||||
\(669\) | −5.96630 | + | 0.531501i | −0.230671 | + | 0.0205490i | ||||
\(670\) | 10.7773 | + | 11.6399i | 0.416365 | + | 0.449690i | ||||
\(671\) | 49.0781 | 1.89464 | ||||||||
\(672\) | −14.5513 | − | 17.9228i | −0.561327 | − | 0.691387i | ||||
\(673\) | 18.0854 | 0.697141 | 0.348571 | − | 0.937282i | \(-0.386667\pi\) | ||||
0.348571 | + | 0.937282i | \(0.386667\pi\) | |||||||
\(674\) | 3.40953 | + | 3.68242i | 0.131330 | + | 0.141842i | ||||
\(675\) | 1.51618 | + | 5.55287i | 0.0583580 | + | 0.213730i | ||||
\(676\) | −1.29060 | + | 16.7452i | −0.0496383 | + | 0.644048i | ||||
\(677\) | 49.8380 | 1.91543 | 0.957715 | − | 0.287717i | \(-0.0928964\pi\) | ||||
0.957715 | + | 0.287717i | \(0.0928964\pi\) | |||||||
\(678\) | −28.0929 | − | 25.3954i | −1.07890 | − | 0.975304i | ||||
\(679\) | 28.8376i | 1.10669i | ||||||||
\(680\) | 18.0922 | + | 22.8356i | 0.693806 | + | 0.875704i | ||||
\(681\) | −24.6968 | + | 2.20008i | −0.946382 | + | 0.0843073i | ||||
\(682\) | −20.8250 | − | 22.4918i | −0.797430 | − | 0.861254i | ||||
\(683\) | 13.6776i | 0.523359i | 0.965155 | + | 0.261680i | \(0.0842764\pi\) | ||||
−0.965155 | + | 0.261680i | \(0.915724\pi\) | |||||||
\(684\) | −0.603646 | − | 5.96956i | −0.0230810 | − | 0.228252i | ||||
\(685\) | 2.35783i | 0.0900881i | ||||||||
\(686\) | 20.6566 | − | 19.1258i | 0.788672 | − | 0.730226i | ||||
\(687\) | 23.2724 | − | 2.07319i | 0.887896 | − | 0.0790971i | ||||
\(688\) | 5.37861 | + | 0.834039i | 0.205058 | + | 0.0317974i | ||||
\(689\) | 28.0012i | 1.06676i | ||||||||
\(690\) | −26.1502 | + | 28.9279i | −0.995522 | + | 1.10127i | ||||
\(691\) | 14.8089 | 0.563357 | 0.281679 | − | 0.959509i | \(-0.409109\pi\) | ||||
0.281679 | + | 0.959509i | \(0.409109\pi\) | |||||||
\(692\) | −0.406246 | + | 5.27096i | −0.0154431 | + | 0.200372i | ||||
\(693\) | −33.6217 | + | 6.03822i | −1.27718 | + | 0.229373i | ||||
\(694\) | −20.0405 | + | 18.5554i | −0.760727 | + | 0.704352i | ||||
\(695\) | −9.50737 | −0.360635 | ||||||||
\(696\) | −1.99112 | − | 2.09968i | −0.0754732 | − | 0.0795881i | ||||
\(697\) | −34.1492 | −1.29349 | ||||||||
\(698\) | −14.4331 | + | 13.3635i | −0.546301 | + | 0.505817i | ||||
\(699\) | 24.2587 | − | 2.16106i | 0.917548 | − | 0.0817386i | ||||
\(700\) | −5.20485 | − | 0.401150i | −0.196725 | − | 0.0151620i | ||||
\(701\) | −35.9252 | −1.35688 | −0.678438 | − | 0.734658i | \(-0.737343\pi\) | ||||
−0.678438 | + | 0.734658i | \(0.737343\pi\) | |||||||
\(702\) | 13.3795 | + | 8.33824i | 0.504977 | + | 0.314707i | ||||
\(703\) | − | 8.77578i | − | 0.330985i | ||||||
\(704\) | 37.6357 | + | 8.84237i | 1.41845 | + | 0.333260i | ||||
\(705\) | −1.68214 | − | 18.8827i | −0.0633532 | − | 0.711164i | ||||
\(706\) | 18.6145 | − | 17.2350i | 0.700565 | − | 0.648649i | ||||
\(707\) | − | 4.11347i | − | 0.154703i | ||||||
\(708\) | −0.579350 | − | 48.5646i | −0.0217733 | − | 1.82517i | ||||
\(709\) | 31.3446i | 1.17717i | 0.808435 | + | 0.588585i | \(0.200315\pi\) | ||||
−0.808435 | + | 0.588585i | \(0.799685\pi\) | |||||||
\(710\) | 6.77648 | + | 7.31885i | 0.254317 | + | 0.274672i | ||||
\(711\) | −1.59848 | − | 8.90061i | −0.0599479 | − | 0.333799i | ||||
\(712\) | −11.9068 | − | 15.0285i | −0.446226 | − | 0.563216i | ||||
\(713\) | 36.1918i | 1.35539i | ||||||||
\(714\) | 20.2072 | − | 22.3536i | 0.756235 | − | 0.836562i | ||||
\(715\) | −20.4539 | −0.764932 | ||||||||
\(716\) | 27.5160 | + | 2.12073i | 1.02832 | + | 0.0792552i | ||||
\(717\) | −1.68713 | − | 18.9387i | −0.0630070 | − | 0.707278i | ||||
\(718\) | −30.7470 | − | 33.2080i | −1.14747 | − | 1.23931i | ||||
\(719\) | −33.9669 | −1.26675 | −0.633377 | − | 0.773844i | \(-0.718332\pi\) | ||||
−0.633377 | + | 0.773844i | \(0.718332\pi\) | |||||||
\(720\) | 23.6677 | − | 0.564768i | 0.882045 | − | 0.0210477i | ||||
\(721\) | −30.9401 | −1.15227 | ||||||||
\(722\) | 0.960810 | + | 1.03771i | 0.0357576 | + | 0.0386196i | ||||
\(723\) | −1.89888 | − | 21.3157i | −0.0706202 | − | 0.792739i | ||||
\(724\) | −24.7010 | − | 1.90377i | −0.918007 | − | 0.0707530i | ||||
\(725\) | −0.654320 | −0.0243008 | ||||||||
\(726\) | 20.2923 | − | 22.4478i | 0.753118 | − | 0.833115i | ||||
\(727\) | 4.72559i | 0.175263i | 0.996153 | + | 0.0876313i | \(0.0279297\pi\) | ||||
−0.996153 | + | 0.0876313i | \(0.972070\pi\) | |||||||
\(728\) | −11.2065 | + | 8.87870i | −0.415340 | + | 0.329067i | ||||
\(729\) | −23.2534 | + | 13.7214i | −0.861238 | + | 0.508202i | ||||
\(730\) | −5.80615 | − | 6.27086i | −0.214895 | − | 0.232095i | ||||
\(731\) | 7.10438i | 0.262765i | ||||||||
\(732\) | 0.419654 | + | 35.1779i | 0.0155109 | + | 1.30021i | ||||
\(733\) | 32.6808i | 1.20709i | 0.797328 | + | 0.603546i | \(0.206246\pi\) | ||||
−0.797328 | + | 0.603546i | \(0.793754\pi\) | |||||||
\(734\) | −14.9010 | + | 13.7967i | −0.550005 | + | 0.509246i | ||||
\(735\) | 0.439130 | + | 4.92941i | 0.0161976 | + | 0.181824i | ||||
\(736\) | −25.5138 | − | 37.8514i | −0.940451 | − | 1.39522i | ||||
\(737\) | 27.4759i | 1.01209i | ||||||||
\(738\) | −16.7089 | + | 22.1555i | −0.615061 | + | 0.815555i | ||||
\(739\) | 36.5392 | 1.34412 | 0.672059 | − | 0.740498i | \(-0.265410\pi\) | ||||
0.672059 | + | 0.740498i | \(0.265410\pi\) | |||||||
\(740\) | 34.5246 | + | 2.66090i | 1.26915 | + | 0.0978165i | ||||
\(741\) | −3.70121 | + | 0.329718i | −0.135967 | + | 0.0121125i | ||||
\(742\) | 31.9130 | − | 29.5481i | 1.17156 | − | 1.08474i | ||||
\(743\) | −20.4413 | −0.749917 | −0.374958 | − | 0.927042i | \(-0.622343\pi\) | ||||
−0.374958 | + | 0.927042i | \(0.622343\pi\) | |||||||
\(744\) | 15.9434 | − | 15.1191i | 0.584515 | − | 0.554294i | ||||
\(745\) | −45.6448 | −1.67230 | ||||||||
\(746\) | −23.2239 | + | 21.5028i | −0.850286 | + | 0.787274i | ||||
\(747\) | 3.40381 | + | 18.9529i | 0.124539 | + | 0.693450i | ||||
\(748\) | −3.87773 | + | 50.3128i | −0.141784 | + | 1.83962i | ||||
\(749\) | 23.5412 | 0.860177 | ||||||||
\(750\) | 19.7933 | − | 21.8957i | 0.722747 | − | 0.799518i | ||||
\(751\) | 16.0510i | 0.585709i | 0.956157 | + | 0.292855i | \(0.0946052\pi\) | ||||
−0.956157 | + | 0.292855i | \(0.905395\pi\) | |||||||
\(752\) | 21.9291 | + | 3.40046i | 0.799673 | + | 0.124002i | ||||
\(753\) | −5.79400 | + | 0.516151i | −0.211145 | + | 0.0188096i | ||||
\(754\) | −1.31497 | + | 1.21752i | −0.0478884 | + | 0.0443395i | ||||
\(755\) | 11.1110i | 0.404371i | ||||||||
\(756\) | −4.61553 | − | 24.0475i | −0.167865 | − | 0.874600i | ||||
\(757\) | 11.7433i | 0.426817i | 0.976963 | + | 0.213408i | \(0.0684565\pi\) | ||||
−0.976963 | + | 0.213408i | \(0.931543\pi\) | |||||||
\(758\) | 26.4832 | + | 28.6028i | 0.961911 | + | 1.03890i | ||||
\(759\) | −67.2764 | + | 5.99324i | −2.44198 | + | 0.217541i | ||||
\(760\) | −4.37376 | + | 3.46526i | −0.158653 | + | 0.125698i | ||||
\(761\) | − | 35.7369i | − | 1.29546i | −0.761870 | − | 0.647730i | \(-0.775718\pi\) | ||
0.761870 | − | 0.647730i | \(-0.224282\pi\) | |||||||
\(762\) | 20.0947 | + | 18.1652i | 0.727953 | + | 0.658054i | ||||
\(763\) | −10.9845 | −0.397664 | ||||||||
\(764\) | −0.122092 | + | 1.58412i | −0.00441712 | + | 0.0573113i | ||||
\(765\) | 5.46227 | + | 30.4147i | 0.197489 | + | 1.09965i | ||||
\(766\) | 33.0860 | + | 35.7342i | 1.19545 | + | 1.29113i | ||||
\(767\) | −30.0787 | −1.08608 | ||||||||
\(768\) | −6.01617 | + | 27.0519i | −0.217090 | + | 0.976152i | ||||
\(769\) | 40.1108 | 1.44643 | 0.723216 | − | 0.690622i | \(-0.242663\pi\) | ||||
0.723216 | + | 0.690622i | \(0.242663\pi\) | |||||||
\(770\) | 21.5838 | + | 23.3113i | 0.777827 | + | 0.840083i | ||||
\(771\) | 10.2432 | − | 0.912502i | 0.368899 | − | 0.0328630i | ||||
\(772\) | 1.62022 | − | 21.0220i | 0.0583128 | − | 0.756598i | ||||
\(773\) | 23.0364 | 0.828561 | 0.414280 | − | 0.910149i | \(-0.364033\pi\) | ||||
0.414280 | + | 0.910149i | \(0.364033\pi\) | |||||||
\(774\) | 4.60922 | + | 3.47610i | 0.165675 | + | 0.124946i | ||||
\(775\) | − | 4.96843i | − | 0.178471i | ||||||
\(776\) | 27.1332 | − | 21.4972i | 0.974026 | − | 0.771704i | ||||
\(777\) | −3.17792 | − | 35.6734i | −0.114007 | − | 1.27977i | ||||
\(778\) | 9.18231 | + | 9.91724i | 0.329202 | + | 0.355550i | ||||
\(779\) | − | 6.54069i | − | 0.234345i | ||||||
\(780\) | −0.174896 | − | 14.6608i | −0.00626228 | − | 0.524941i | ||||
\(781\) | 17.2761i | 0.618187i | ||||||||
\(782\) | 43.7194 | − | 40.4795i | 1.56340 | − | 1.44754i | ||||
\(783\) | −0.808430 | − | 2.96079i | −0.0288909 | − | 0.105810i | ||||
\(784\) | −5.72468 | − | 0.887704i | −0.204453 | − | 0.0317037i | ||||
\(785\) | − | 9.29701i | − | 0.331824i | ||||||
\(786\) | 9.92390 | + | 8.97099i | 0.353974 | + | 0.319985i | ||||
\(787\) | 28.5826 | 1.01886 | 0.509430 | − | 0.860512i | \(-0.329856\pi\) | ||||
0.509430 | + | 0.860512i | \(0.329856\pi\) | |||||||
\(788\) | −1.58987 | + | 20.6283i | −0.0566368 | + | 0.734852i | ||||
\(789\) | −3.23391 | − | 36.3018i | −0.115130 | − | 1.29238i | ||||
\(790\) | −6.17117 | + | 5.71384i | −0.219560 | + | 0.203289i | ||||
\(791\) | 36.4278 | 1.29522 | ||||||||
\(792\) | 30.7449 | + | 27.1333i | 1.09247 | + | 0.964141i | ||||
\(793\) | 21.7876 | 0.773700 | ||||||||
\(794\) | 18.3459 | − | 16.9864i | 0.651073 | − | 0.602824i | ||||
\(795\) | 3.95749 | + | 44.4243i | 0.140358 | + | 1.57557i | ||||
\(796\) | 22.3160 | + | 1.71995i | 0.790969 | + | 0.0609619i | ||||
\(797\) | 4.29989 | 0.152310 | 0.0761549 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761549 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(798\) | 4.28145 | + | 3.87034i | 0.151562 | + | 0.137009i | ||||
\(799\) | 28.9653i | 1.02472i | ||||||||
\(800\) | 3.50255 | + | 5.19627i | 0.123834 | + | 0.183716i | ||||
\(801\) | −3.59481 | − | 20.0164i | −0.127016 | − | 0.707246i | ||||
\(802\) | −35.6236 | + | 32.9837i | −1.25791 | + | 1.16469i | ||||
\(803\) | − | 14.8023i | − | 0.522362i | ||||||
\(804\) | −19.6940 | + | 0.234939i | −0.694555 | + | 0.00828567i | ||||
\(805\) | − | 37.5106i | − | 1.32208i | ||||||
\(806\) | −9.24498 | − | 9.98493i | −0.325641 | − | 0.351704i | ||||
\(807\) | −1.60613 | − | 18.0295i | −0.0565386 | − | 0.634667i | ||||
\(808\) | −3.87035 | + | 3.06641i | −0.136159 | + | 0.107876i | ||||
\(809\) | − | 15.9007i | − | 0.559038i | −0.960140 | − | 0.279519i | \(-0.909825\pi\) | ||
0.960140 | − | 0.279519i | \(-0.0901750\pi\) | |||||||
\(810\) | 22.4053 | + | 11.3378i | 0.787241 | + | 0.398369i | ||||
\(811\) | 31.8029 | 1.11675 | 0.558376 | − | 0.829588i | \(-0.311425\pi\) | ||||
0.558376 | + | 0.829588i | \(0.311425\pi\) | |||||||
\(812\) | 2.77523 | + | 0.213893i | 0.0973913 | + | 0.00750618i | ||||
\(813\) | 55.0104 | − | 4.90054i | 1.92930 | − | 0.171869i | ||||
\(814\) | 40.7475 | + | 44.0089i | 1.42820 | + | 1.54251i | ||||
\(815\) | −43.0670 | −1.50857 | ||||||||
\(816\) | −36.0960 | − | 2.34924i | −1.26361 | − | 0.0822399i | ||||
\(817\) | −1.36072 | −0.0476056 | ||||||||
\(818\) | −20.3995 | − | 22.0322i | −0.713252 | − | 0.770339i | ||||
\(819\) | −14.9259 | + | 2.68059i | −0.521554 | + | 0.0936674i | ||||
\(820\) | 25.7316 | + | 1.98320i | 0.898587 | + | 0.0692562i | ||||
\(821\) | 12.9857 | 0.453204 | 0.226602 | − | 0.973987i | \(-0.427238\pi\) | ||||
0.226602 | + | 0.973987i | \(0.427238\pi\) | |||||||
\(822\) | −2.17165 | − | 1.96313i | −0.0757451 | − | 0.0684720i | ||||
\(823\) | − | 27.8018i | − | 0.969108i | −0.874761 | − | 0.484554i | \(-0.838982\pi\) | ||
0.874761 | − | 0.484554i | \(-0.161018\pi\) | |||||||
\(824\) | 23.0645 | + | 29.1115i | 0.803491 | + | 1.01415i | ||||
\(825\) | 9.23574 | − | 0.822755i | 0.321547 | − | 0.0286447i | ||||
\(826\) | 31.7403 | + | 34.2808i | 1.10439 | + | 1.19278i | ||||
\(827\) | 10.5836i | 0.368028i | 0.982924 | + | 0.184014i | \(0.0589092\pi\) | ||||
−0.982924 | + | 0.184014i | \(0.941091\pi\) | |||||||
\(828\) | −4.87106 | − | 48.1707i | −0.169281 | − | 1.67405i | ||||
\(829\) | − | 4.56921i | − | 0.158695i | −0.996847 | − | 0.0793477i | \(-0.974716\pi\) | ||
0.996847 | − | 0.0793477i | \(-0.0252837\pi\) | |||||||
\(830\) | 13.1408 | − | 12.1670i | 0.456125 | − | 0.422323i | ||||
\(831\) | −33.3029 | + | 2.96675i | −1.15526 | + | 0.102915i | ||||
\(832\) | 16.7079 | + | 3.92546i | 0.579242 | + | 0.136091i | ||||
\(833\) | − | 7.56150i | − | 0.261990i | ||||||
\(834\) | 7.91583 | − | 8.75665i | 0.274103 | − | 0.303218i | ||||
\(835\) | 1.52349 | 0.0527227 | ||||||||
\(836\) | −9.63655 | − | 0.742712i | −0.333287 | − | 0.0256872i | ||||
\(837\) | 22.4821 | − | 6.13863i | 0.777096 | − | 0.212182i | ||||
\(838\) | −17.3377 | + | 16.0528i | −0.598919 | + | 0.554535i | ||||
\(839\) | −32.2093 | −1.11199 | −0.555994 | − | 0.831187i | \(-0.687662\pi\) | ||||
−0.555994 | + | 0.831187i | \(0.687662\pi\) | |||||||
\(840\) | −16.5244 | + | 15.6700i | −0.570146 | + | 0.540668i | ||||
\(841\) | −28.6511 | −0.987970 | ||||||||
\(842\) | −3.31231 | + | 3.06684i | −0.114150 | + | 0.105690i | ||||
\(843\) | 6.81044 | − | 0.606700i | 0.234564 | − | 0.0208959i | ||||
\(844\) | 0.911549 | − | 11.8272i | 0.0313768 | − | 0.407108i | ||||
\(845\) | 16.5671 | 0.569926 | ||||||||
\(846\) | 18.7923 | + | 14.1724i | 0.646091 | + | 0.487258i | ||||
\(847\) | 29.1079i | 1.00016i | ||||||||
\(848\) | −51.5915 | − | 8.00008i | −1.77166 | − | 0.274724i | ||||
\(849\) | −2.58551 | − | 29.0233i | −0.0887344 | − | 0.996078i | ||||
\(850\) | −6.00182 | + | 5.55705i | −0.205861 | + | 0.190605i | ||||
\(851\) | − | 70.8152i | − | 2.42752i | ||||||
\(852\) | −12.3830 | + | 0.147723i | −0.424236 | + | 0.00506091i | ||||
\(853\) | − | 32.0084i | − | 1.09595i | −0.836496 | − | 0.547974i | \(-0.815399\pi\) | ||
0.836496 | − | 0.547974i | \(-0.184601\pi\) | |||||||
\(854\) | −22.9912 | − | 24.8314i | −0.786742 | − | 0.849712i | ||||
\(855\) | −5.82542 | + | 1.04620i | −0.199225 | + | 0.0357794i | ||||
\(856\) | −17.5489 | − | 22.1499i | −0.599811 | − | 0.757066i | ||||
\(857\) | − | 23.9200i | − | 0.817092i | −0.912738 | − | 0.408546i | \(-0.866036\pi\) | ||
0.912738 | − | 0.408546i | \(-0.133964\pi\) | |||||||
\(858\) | 17.0299 | − | 18.8388i | 0.581391 | − | 0.643147i | ||||
\(859\) | 42.0614 | 1.43512 | 0.717559 | − | 0.696498i | \(-0.245259\pi\) | ||||
0.717559 | + | 0.696498i | \(0.245259\pi\) | |||||||
\(860\) | 0.412583 | − | 5.35319i | 0.0140690 | − | 0.182542i | ||||
\(861\) | −2.36854 | − | 26.5878i | −0.0807196 | − | 0.906109i | ||||
\(862\) | −16.8006 | − | 18.1453i | −0.572232 | − | 0.618032i | ||||
\(863\) | −29.7612 | −1.01308 | −0.506542 | − | 0.862215i | \(-0.669076\pi\) | ||||
−0.506542 | + | 0.862215i | \(0.669076\pi\) | |||||||
\(864\) | −19.1856 | + | 22.2691i | −0.652706 | + | 0.757611i | ||||
\(865\) | 5.21489 | 0.177312 | ||||||||
\(866\) | −4.83370 | − | 5.22058i | −0.164256 | − | 0.177403i | ||||
\(867\) | −1.57673 | − | 17.6994i | −0.0535484 | − | 0.601102i | ||||
\(868\) | −1.62415 | + | 21.0731i | −0.0551273 | + | 0.715266i | ||||
\(869\) | −14.5670 | −0.494151 | ||||||||
\(870\) | −1.91414 | + | 2.11747i | −0.0648956 | + | 0.0717888i | ||||
\(871\) | 12.1976i | 0.413299i | ||||||||
\(872\) | 8.18844 | + | 10.3353i | 0.277296 | + | 0.349996i | ||||
\(873\) | 36.1388 | − | 6.49026i | 1.22311 | − | 0.219662i | ||||
\(874\) | 7.75315 | + | 8.37370i | 0.262254 | + | 0.283245i | ||||
\(875\) | 28.3920i | 0.959825i | ||||||||
\(876\) | 10.6099 | − | 0.126571i | 0.358475 | − | 0.00427642i | ||||
\(877\) | − | 48.6451i | − | 1.64263i | −0.570476 | − | 0.821314i | \(-0.693241\pi\) | ||
0.570476 | − | 0.821314i | \(-0.306759\pi\) | |||||||
\(878\) | 1.29028 | − | 1.19466i | 0.0435449 | − | 0.0403179i | ||||
\(879\) | −1.55769 | − | 17.4857i | −0.0525395 | − | 0.589776i | ||||
\(880\) | 5.84378 | − | 37.6858i | 0.196994 | − | 1.27039i | ||||
\(881\) | − | 26.7539i | − | 0.901362i | −0.892685 | − | 0.450681i | \(-0.851181\pi\) | ||
0.892685 | − | 0.450681i | \(-0.148819\pi\) | |||||||
\(882\) | −4.90579 | − | 3.69976i | −0.165187 | − | 0.124578i | ||||
\(883\) | 17.6253 | 0.593139 | 0.296569 | − | 0.955011i | \(-0.404157\pi\) | ||||
0.296569 | + | 0.955011i | \(0.404157\pi\) | |||||||
\(884\) | −1.72147 | + | 22.3357i | −0.0578992 | + | 0.751231i | ||||
\(885\) | −47.7203 | + | 4.25111i | −1.60410 | + | 0.142899i | ||||
\(886\) | −7.56001 | + | 6.99976i | −0.253983 | + | 0.235162i | ||||
\(887\) | −25.2876 | −0.849075 | −0.424538 | − | 0.905410i | \(-0.639563\pi\) | ||||
−0.424538 | + | 0.905410i | \(0.639563\pi\) | |||||||
\(888\) | −31.1960 | + | 29.5830i | −1.04687 | + | 0.992742i | ||||
\(889\) | −26.0566 | −0.873910 | ||||||||
\(890\) | −13.8782 | + | 12.8498i | −0.465200 | + | 0.430725i | ||||
\(891\) | 15.1340 | + | 40.7751i | 0.507007 | + | 1.36602i | ||||
\(892\) | −6.89612 | − | 0.531501i | −0.230899 | − | 0.0177960i | ||||
\(893\) | −5.54780 | −0.185650 | ||||||||
\(894\) | 38.0039 | − | 42.0407i | 1.27104 | − | 1.40605i | ||||
\(895\) | − | 27.2233i | − | 0.909975i | ||||||
\(896\) | −13.1570 | − | 23.1843i | −0.439545 | − | 0.774534i | ||||
\(897\) | −29.8665 | + | 2.66062i | −0.997213 | + | 0.0888355i | ||||
\(898\) | 36.3882 | − | 33.6916i | 1.21429 | − | 1.12430i | ||||
\(899\) | 2.64917i | 0.0883548i | ||||||||
\(900\) | 0.668701 | + | 6.61290i | 0.0222900 | + | 0.220430i | ||||
\(901\) | − | 68.1450i | − | 2.27024i | ||||||
\(902\) | 30.3696 | + | 32.8003i | 1.01120 | + | 1.09213i | ||||
\(903\) | −5.53131 | + | 0.492750i | −0.184070 | + | 0.0163977i | ||||
\(904\) | −27.1554 | − | 34.2749i | −0.903175 | − | 1.13996i | ||||
\(905\) | 24.4383i | 0.812356i | ||||||||
\(906\) | −10.2337 | − | 9.25103i | −0.339991 | − | 0.307345i | ||||
\(907\) | −51.6403 | −1.71469 | −0.857344 | − | 0.514744i | \(-0.827887\pi\) | ||||
−0.857344 | + | 0.514744i | \(0.827887\pi\) | |||||||
\(908\) | −28.5457 | − | 2.20008i | −0.947321 | − | 0.0730123i | ||||
\(909\) | −5.15493 | + | 0.925788i | −0.170978 | + | 0.0307064i | ||||
\(910\) | 9.58186 | + | 10.3488i | 0.317636 | + | 0.343058i | ||||
\(911\) | 37.8190 | 1.25300 | 0.626500 | − | 0.779421i | \(-0.284487\pi\) | ||||
0.626500 | + | 0.779421i | \(0.284487\pi\) | |||||||
\(912\) | 0.449957 | − | 6.91358i | 0.0148996 | − | 0.228931i | ||||
\(913\) | 31.0188 | 1.02657 | ||||||||
\(914\) | −2.87199 | − | 3.10186i | −0.0949970 | − | 0.102600i | ||||
\(915\) | 34.5663 | − | 3.07930i | 1.14273 | − | 0.101799i | ||||
\(916\) | 26.8993 | + | 2.07319i | 0.888776 | + | 0.0685001i | ||||
\(917\) | −12.8682 | −0.424947 | ||||||||
\(918\) | −32.5610 | − | 20.2923i | −1.07467 | − | 0.669746i | ||||
\(919\) | − | 20.0850i | − | 0.662543i | −0.943535 | − | 0.331272i | \(-0.892522\pi\) | ||
0.943535 | − | 0.331272i | \(-0.107478\pi\) | |||||||
\(920\) | −35.2936 | + | 27.9625i | −1.16360 | + | 0.921897i | ||||
\(921\) | 3.99864 | + | 44.8862i | 0.131760 | + | 1.47905i | ||||
\(922\) | 21.1248 | + | 22.8155i | 0.695707 | + | 0.751390i | ||||
\(923\) | 7.66949i | 0.252444i | ||||||||
\(924\) | −39.4413 | + | 0.470514i | −1.29752 | + | 0.0154788i | ||||
\(925\) | 9.72156i | 0.319643i | ||||||||
\(926\) | −14.7837 | + | 13.6881i | −0.485823 | + | 0.449820i | ||||
\(927\) | 6.96346 | + | 38.7736i | 0.228710 | + | 1.27349i | ||||
\(928\) | −1.86756 | − | 2.77065i | −0.0613056 | − | 0.0909510i | ||||
\(929\) | 18.8526i | 0.618533i | 0.950975 | + | 0.309267i | \(0.100084\pi\) | ||||
−0.950975 | + | 0.309267i | \(0.899916\pi\) | |||||||
\(930\) | −16.0785 | − | 14.5346i | −0.527235 | − | 0.476609i | ||||
\(931\) | 1.44828 | 0.0474653 | ||||||||
\(932\) | 28.0393 | + | 2.16106i | 0.918457 | + | 0.0707877i | ||||
\(933\) | −3.79073 | − | 42.5524i | −0.124103 | − | 1.39310i | ||||
\(934\) | 7.39568 | − | 6.84761i | 0.241994 | − | 0.224061i | ||||
\(935\) | 49.7775 | 1.62790 | ||||||||
\(936\) | 13.6488 | + | 12.0455i | 0.446125 | + | 0.393719i | ||||
\(937\) | 23.1082 | 0.754911 | 0.377456 | − | 0.926028i | \(-0.376799\pi\) | ||||
0.377456 | + | 0.926028i | \(0.376799\pi\) | |||||||
\(938\) | 13.9016 | − | 12.8714i | 0.453904 | − | 0.420266i | ||||
\(939\) | 3.64294 | + | 40.8934i | 0.118883 | + | 1.33450i | ||||
\(940\) | 1.68214 | − | 21.8255i | 0.0548655 | − | 0.711869i | ||||
\(941\) | −49.7606 | −1.62215 | −0.811075 | − | 0.584942i | \(-0.801117\pi\) | ||||
−0.811075 | + | 0.584942i | \(0.801117\pi\) | |||||||
\(942\) | 8.56290 | + | 7.74068i | 0.278994 | + | 0.252205i | ||||
\(943\) | − | 52.7794i | − | 1.71873i | ||||||
\(944\) | 8.59363 | − | 55.4192i | 0.279699 | − | 1.80374i | ||||
\(945\) | −23.3013 | + | 6.36232i | −0.757993 | + | 0.206966i | ||||
\(946\) | 6.82376 | − | 6.31807i | 0.221860 | − | 0.205418i | ||||
\(947\) | − | 35.0676i | − | 1.13954i | −0.821803 | − | 0.569772i | \(-0.807031\pi\) | ||
0.821803 | − | 0.569772i | \(-0.192969\pi\) | |||||||
\(948\) | −0.124558 | − | 10.4412i | −0.00404546 | − | 0.339115i | ||||
\(949\) | − | 6.57129i | − | 0.213313i | ||||||
\(950\) | −1.06436 | − | 1.14955i | −0.0345323 | − | 0.0372962i | ||||
\(951\) | 3.72312 | + | 41.7934i | 0.120730 | + | 1.35525i | ||||
\(952\) | 27.2726 | − | 21.6076i | 0.883910 | − | 0.700307i | ||||
\(953\) | − | 23.3921i | − | 0.757745i | −0.925449 | − | 0.378872i | \(-0.876312\pi\) | ||
0.925449 | − | 0.378872i | \(-0.123688\pi\) | |||||||
\(954\) | −44.2115 | − | 33.3427i | −1.43140 | − | 1.07951i | ||||
\(955\) | 1.56726 | 0.0507155 | ||||||||
\(956\) | 1.68713 | − | 21.8902i | 0.0545657 | − | 0.707979i | ||||
\(957\) | −4.92450 | + | 0.438693i | −0.159186 | + | 0.0141809i | ||||
\(958\) | −1.71315 | − | 1.85027i | −0.0553494 | − | 0.0597795i | ||||
\(959\) | 2.81597 | 0.0909323 | ||||||||
\(960\) | 27.0621 | + | 3.86643i | 0.873426 | + | 0.124788i | ||||
\(961\) | 10.8841 | 0.351101 | ||||||||
\(962\) | 18.0893 | + | 19.5372i | 0.583223 | + | 0.629904i | ||||
\(963\) | −5.29824 | − | 29.5014i | −0.170733 | − | 0.950669i | ||||
\(964\) | 1.89888 | − | 24.6376i | 0.0611589 | − | 0.793525i | ||||
\(965\) | −20.7984 | −0.669523 | ||||||||
\(966\) | 34.5487 | + | 31.2313i | 1.11159 | + | 1.00485i | ||||
\(967\) | − | 17.4787i | − | 0.562076i | −0.959697 | − | 0.281038i | \(-0.909321\pi\) | ||
0.959697 | − | 0.281038i | \(-0.0906786\pi\) | |||||||
\(968\) | 27.3875 | − | 21.6987i | 0.880268 | − | 0.697421i | ||||
\(969\) | 9.00743 | − | 0.802416i | 0.289360 | − | 0.0257773i | ||||
\(970\) | −23.1997 | − | 25.0565i | −0.744897 | − | 0.804517i | ||||
\(971\) | 13.4578i | 0.431882i | 0.976406 | + | 0.215941i | \(0.0692819\pi\) | ||||
−0.976406 | + | 0.215941i | \(0.930718\pi\) | |||||||
\(972\) | −29.0971 | + | 11.1963i | −0.933291 | + | 0.359121i | ||||
\(973\) | 11.3547i | 0.364015i | ||||||||
\(974\) | −14.7573 | + | 13.6637i | −0.472855 | + | 0.437814i | ||||
\(975\) | 4.10009 | − | 0.365252i | 0.131308 | − | 0.0116974i | ||||
\(976\) | −6.22482 | + | 40.1431i | −0.199252 | + | 1.28495i | ||||
\(977\) | 16.8194i | 0.538101i | 0.963126 | + | 0.269051i | \(0.0867099\pi\) | ||||
−0.963126 | + | 0.269051i | \(0.913290\pi\) | |||||||
\(978\) | 35.8576 | − | 39.6664i | 1.14660 | − | 1.26839i | ||||
\(979\) | −32.7594 | −1.04700 | ||||||||
\(980\) | −0.439130 | + | 5.69763i | −0.0140275 | + | 0.182004i | ||||
\(981\) | 2.47219 | + | 13.7655i | 0.0789310 | + | 0.439500i | ||||
\(982\) | −6.68679 | + | 6.19126i | −0.213384 | + | 0.197571i | ||||
\(983\) | −21.2785 | −0.678678 | −0.339339 | − | 0.940664i | \(-0.610203\pi\) | ||||
−0.339339 | + | 0.940664i | \(0.610203\pi\) | |||||||
\(984\) | −23.2507 | + | 22.0486i | −0.741206 | + | 0.702883i | ||||
\(985\) | 20.4088 | 0.650280 | ||||||||
\(986\) | 3.20017 | − | 2.96302i | 0.101914 | − | 0.0943617i | ||||
\(987\) | −22.5517 | + | 2.00899i | −0.717828 | + | 0.0639469i | ||||
\(988\) | −4.27802 | − | 0.329718i | −0.136102 | − | 0.0104897i | ||||
\(989\) | −10.9802 | −0.349150 | ||||||||
\(990\) | 24.3556 | − | 32.2950i | 0.774073 | − | 1.02640i | ||||
\(991\) | 25.4403i | 0.808139i | 0.914728 | + | 0.404069i | \(0.132405\pi\) | ||||
−0.914728 | + | 0.404069i | \(0.867595\pi\) | |||||||
\(992\) | 21.0383 | − | 14.1809i | 0.667967 | − | 0.450244i | ||||
\(993\) | −2.98627 | − | 33.5220i | −0.0947664 | − | 1.06379i | ||||
\(994\) | 8.74093 | − | 8.09317i | 0.277246 | − | 0.256700i | ||||
\(995\) | − | 22.0786i | − | 0.699938i | ||||||
\(996\) | 0.265234 | + | 22.2335i | 0.00840425 | + | 0.704495i | ||||
\(997\) | 44.9174i | 1.42255i | 0.702915 | + | 0.711274i | \(0.251881\pi\) | ||||
−0.702915 | + | 0.711274i | \(0.748119\pi\) | |||||||
\(998\) | −34.7094 | − | 37.4875i | −1.09871 | − | 1.18664i | ||||
\(999\) | −43.9900 | + | 12.0112i | −1.39178 | + | 0.380019i |
(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 | 456.2.j.e.419.20 | yes | 24 | |
3.2 | odd | 2 | inner | 456.2.j.e.419.5 | ✓ | 24 | |
4.3 | odd | 2 | 1824.2.j.d.1103.14 | 24 | |||
8.3 | odd | 2 | inner | 456.2.j.e.419.6 | yes | 24 | |
8.5 | even | 2 | 1824.2.j.d.1103.13 | 24 | |||
12.11 | even | 2 | 1824.2.j.d.1103.15 | 24 | |||
24.5 | odd | 2 | 1824.2.j.d.1103.16 | 24 | |||
24.11 | even | 2 | inner | 456.2.j.e.419.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.j.e.419.5 | ✓ | 24 | 3.2 | odd | 2 | inner | |
456.2.j.e.419.6 | yes | 24 | 8.3 | odd | 2 | inner | |
456.2.j.e.419.19 | yes | 24 | 24.11 | even | 2 | inner | |
456.2.j.e.419.20 | yes | 24 | 1.1 | even | 1 | trivial | |
1824.2.j.d.1103.13 | 24 | 8.5 | even | 2 | |||
1824.2.j.d.1103.14 | 24 | 4.3 | odd | 2 | |||
1824.2.j.d.1103.15 | 24 | 12.11 | even | 2 | |||
1824.2.j.d.1103.16 | 24 | 24.5 | odd | 2 |