Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(323,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("552.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.24 | ||
Character | \(\chi\) | \(=\) | 552.323 |
Dual form | 552.2.j.d.323.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.484105 | + | 1.32877i | 0.342314 | + | 0.939586i | ||||
\(3\) | −1.59465 | + | 0.676097i | −0.920669 | + | 0.390345i | ||||
\(4\) | −1.53128 | + | 1.28653i | −0.765642 | + | 0.643267i | ||||
\(5\) | −1.67234 | −0.747893 | −0.373947 | − | 0.927450i | \(-0.621996\pi\) | ||||
−0.373947 | + | 0.927450i | \(0.621996\pi\) | |||||||
\(6\) | −1.67036 | − | 1.79162i | −0.681920 | − | 0.731427i | ||||
\(7\) | − | 2.28745i | − | 0.864574i | −0.901736 | − | 0.432287i | \(-0.857707\pi\) | ||
0.901736 | − | 0.432287i | \(-0.142293\pi\) | |||||||
\(8\) | −2.45082 | − | 1.41191i | −0.866494 | − | 0.499187i | ||||
\(9\) | 2.08579 | − | 2.15627i | 0.695262 | − | 0.718756i | ||||
\(10\) | −0.809588 | − | 2.22216i | −0.256014 | − | 0.702710i | ||||
\(11\) | − | 2.91064i | − | 0.877590i | −0.898587 | − | 0.438795i | \(-0.855405\pi\) | ||
0.898587 | − | 0.438795i | \(-0.144595\pi\) | |||||||
\(12\) | 1.57203 | − | 3.08686i | 0.453807 | − | 0.891100i | ||||
\(13\) | 4.63743i | 1.28619i | 0.765786 | + | 0.643096i | \(0.222350\pi\) | ||||
−0.765786 | + | 0.643096i | \(0.777650\pi\) | |||||||
\(14\) | 3.03950 | − | 1.10737i | 0.812341 | − | 0.295956i | ||||
\(15\) | 2.66679 | − | 1.13066i | 0.688562 | − | 0.291936i | ||||
\(16\) | 0.689663 | − | 3.94010i | 0.172416 | − | 0.985024i | ||||
\(17\) | − | 3.10443i | − | 0.752934i | −0.926430 | − | 0.376467i | \(-0.877139\pi\) | ||
0.926430 | − | 0.376467i | \(-0.122861\pi\) | |||||||
\(18\) | 3.87494 | + | 1.72768i | 0.913331 | + | 0.407218i | ||||
\(19\) | 7.70658 | 1.76801 | 0.884005 | − | 0.467477i | \(-0.154837\pi\) | ||||
0.884005 | + | 0.467477i | \(0.154837\pi\) | |||||||
\(20\) | 2.56083 | − | 2.15152i | 0.572618 | − | 0.481095i | ||||
\(21\) | 1.54654 | + | 3.64767i | 0.337482 | + | 0.795986i | ||||
\(22\) | 3.86758 | − | 1.40905i | 0.824571 | − | 0.300411i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 4.86277 | + | 0.594514i | 0.992609 | + | 0.121355i | ||||
\(25\) | −2.20328 | −0.440656 | ||||||||
\(26\) | −6.16210 | + | 2.24500i | −1.20849 | + | 0.440281i | ||||
\(27\) | −1.86824 | + | 4.84868i | −0.359544 | + | 0.933128i | ||||
\(28\) | 2.94288 | + | 3.50273i | 0.556152 | + | 0.661954i | ||||
\(29\) | −8.53054 | −1.58408 | −0.792041 | − | 0.610468i | \(-0.790982\pi\) | ||||
−0.792041 | + | 0.610468i | \(0.790982\pi\) | |||||||
\(30\) | 2.79340 | + | 2.99620i | 0.510003 | + | 0.547029i | ||||
\(31\) | − | 7.88372i | − | 1.41596i | −0.706234 | − | 0.707979i | \(-0.749607\pi\) | ||
0.706234 | − | 0.707979i | \(-0.250393\pi\) | |||||||
\(32\) | 5.56937 | − | 0.991014i | 0.984535 | − | 0.175188i | ||||
\(33\) | 1.96787 | + | 4.64143i | 0.342563 | + | 0.807970i | ||||
\(34\) | 4.12508 | − | 1.50287i | 0.707446 | − | 0.257740i | ||||
\(35\) | 3.82539i | 0.646609i | ||||||||
\(36\) | −0.419820 | + | 5.98529i | −0.0699700 | + | 0.997549i | ||||
\(37\) | − | 3.97637i | − | 0.653711i | −0.945074 | − | 0.326856i | \(-0.894011\pi\) | ||
0.945074 | − | 0.326856i | \(-0.105989\pi\) | |||||||
\(38\) | 3.73079 | + | 10.2403i | 0.605215 | + | 1.66120i | ||||
\(39\) | −3.13535 | − | 7.39505i | −0.502058 | − | 1.18416i | ||||
\(40\) | 4.09860 | + | 2.36120i | 0.648045 | + | 0.373339i | ||||
\(41\) | − | 5.01274i | − | 0.782859i | −0.920208 | − | 0.391429i | \(-0.871981\pi\) | ||
0.920208 | − | 0.391429i | \(-0.128019\pi\) | |||||||
\(42\) | −4.09824 | + | 3.82085i | −0.632373 | + | 0.589570i | ||||
\(43\) | 7.62705 | 1.16311 | 0.581557 | − | 0.813505i | \(-0.302444\pi\) | ||||
0.581557 | + | 0.813505i | \(0.302444\pi\) | |||||||
\(44\) | 3.74463 | + | 4.45701i | 0.564525 | + | 0.671920i | ||||
\(45\) | −3.48814 | + | 3.60601i | −0.519982 | + | 0.537553i | ||||
\(46\) | 0.484105 | + | 1.32877i | 0.0713774 | + | 0.195917i | ||||
\(47\) | 4.61765 | 0.673554 | 0.336777 | − | 0.941584i | \(-0.390663\pi\) | ||||
0.336777 | + | 0.941584i | \(0.390663\pi\) | |||||||
\(48\) | 1.56412 | + | 6.74934i | 0.225761 | + | 0.974183i | ||||
\(49\) | 1.76758 | 0.252512 | ||||||||
\(50\) | −1.06662 | − | 2.92766i | −0.150843 | − | 0.414034i | ||||
\(51\) | 2.09889 | + | 4.95046i | 0.293904 | + | 0.693203i | ||||
\(52\) | −5.96621 | − | 7.10122i | −0.827364 | − | 0.984762i | ||||
\(53\) | −0.427900 | −0.0587766 | −0.0293883 | − | 0.999568i | \(-0.509356\pi\) | ||||
−0.0293883 | + | 0.999568i | \(0.509356\pi\) | |||||||
\(54\) | −7.34723 | − | 0.135204i | −0.999831 | − | 0.0183989i | ||||
\(55\) | 4.86757i | 0.656344i | ||||||||
\(56\) | −3.22968 | + | 5.60611i | −0.431584 | + | 0.749148i | ||||
\(57\) | −12.2893 | + | 5.21039i | −1.62775 | + | 0.690133i | ||||
\(58\) | −4.12968 | − | 11.3352i | −0.542254 | − | 1.48838i | ||||
\(59\) | − | 9.10118i | − | 1.18487i | −0.805617 | − | 0.592436i | \(-0.798166\pi\) | ||
0.805617 | − | 0.592436i | \(-0.201834\pi\) | |||||||
\(60\) | −2.62897 | + | 5.16228i | −0.339399 | + | 0.666447i | ||||
\(61\) | − | 9.06577i | − | 1.16075i | −0.814348 | − | 0.580376i | \(-0.802905\pi\) | ||
0.814348 | − | 0.580376i | \(-0.197095\pi\) | |||||||
\(62\) | 10.4757 | − | 3.81655i | 1.33041 | − | 0.484702i | ||||
\(63\) | −4.93235 | − | 4.77113i | −0.621418 | − | 0.601106i | ||||
\(64\) | 4.01300 | + | 6.92068i | 0.501624 | + | 0.865085i | ||||
\(65\) | − | 7.75536i | − | 0.961933i | ||||||
\(66\) | −5.21476 | + | 4.86180i | −0.641893 | + | 0.598446i | ||||
\(67\) | −8.29515 | −1.01341 | −0.506707 | − | 0.862118i | \(-0.669137\pi\) | ||||
−0.506707 | + | 0.862118i | \(0.669137\pi\) | |||||||
\(68\) | 3.99395 | + | 4.75376i | 0.484337 | + | 0.576478i | ||||
\(69\) | −1.59465 | + | 0.676097i | −0.191973 | + | 0.0813925i | ||||
\(70\) | −5.08308 | + | 1.85189i | −0.607544 | + | 0.221343i | ||||
\(71\) | −4.33432 | −0.514390 | −0.257195 | − | 0.966360i | \(-0.582798\pi\) | ||||
−0.257195 | + | 0.966360i | \(0.582798\pi\) | |||||||
\(72\) | −8.15635 | + | 2.33967i | −0.961234 | + | 0.275732i | ||||
\(73\) | 6.91010 | 0.808766 | 0.404383 | − | 0.914590i | \(-0.367486\pi\) | ||||
0.404383 | + | 0.914590i | \(0.367486\pi\) | |||||||
\(74\) | 5.28370 | − | 1.92498i | 0.614218 | − | 0.223775i | ||||
\(75\) | 3.51345 | − | 1.48963i | 0.405698 | − | 0.172008i | ||||
\(76\) | −11.8010 | + | 9.91477i | −1.35366 | + | 1.13730i | ||||
\(77\) | −6.65793 | −0.758742 | ||||||||
\(78\) | 8.30852 | − | 7.74616i | 0.940755 | − | 0.877080i | ||||
\(79\) | − | 6.46025i | − | 0.726835i | −0.931626 | − | 0.363418i | \(-0.881610\pi\) | ||
0.931626 | − | 0.363418i | \(-0.118390\pi\) | |||||||
\(80\) | −1.15335 | + | 6.58918i | −0.128949 | + | 0.736693i | ||||
\(81\) | −0.298990 | − | 8.99503i | −0.0332212 | − | 0.999448i | ||||
\(82\) | 6.66080 | − | 2.42669i | 0.735563 | − | 0.267983i | ||||
\(83\) | − | 12.7870i | − | 1.40355i | −0.712396 | − | 0.701777i | \(-0.752390\pi\) | ||
0.712396 | − | 0.701777i | \(-0.247610\pi\) | |||||||
\(84\) | −7.06103 | − | 3.59595i | −0.770422 | − | 0.392350i | ||||
\(85\) | 5.19165i | 0.563114i | ||||||||
\(86\) | 3.69230 | + | 10.1346i | 0.398150 | + | 1.09285i | ||||
\(87\) | 13.6032 | − | 5.76747i | 1.45842 | − | 0.618338i | ||||
\(88\) | −4.10957 | + | 7.13344i | −0.438082 | + | 0.760427i | ||||
\(89\) | 4.52095i | 0.479220i | 0.970869 | + | 0.239610i | \(0.0770195\pi\) | ||||
−0.970869 | + | 0.239610i | \(0.922980\pi\) | |||||||
\(90\) | −6.48021 | − | 2.88927i | −0.683074 | − | 0.304555i | ||||
\(91\) | 10.6079 | 1.11201 | ||||||||
\(92\) | −1.53128 | + | 1.28653i | −0.159647 | + | 0.134130i | ||||
\(93\) | 5.33016 | + | 12.5717i | 0.552712 | + | 1.30363i | ||||
\(94\) | 2.23543 | + | 6.13582i | 0.230567 | + | 0.632861i | ||||
\(95\) | −12.8880 | −1.32228 | ||||||||
\(96\) | −8.21115 | + | 5.34575i | −0.838047 | + | 0.545598i | ||||
\(97\) | −8.58440 | −0.871613 | −0.435807 | − | 0.900040i | \(-0.643537\pi\) | ||||
−0.435807 | + | 0.900040i | \(0.643537\pi\) | |||||||
\(98\) | 0.855696 | + | 2.34872i | 0.0864383 | + | 0.237256i | ||||
\(99\) | −6.27612 | − | 6.07097i | −0.630774 | − | 0.610155i | ||||
\(100\) | 3.37385 | − | 2.83459i | 0.337385 | − | 0.283459i | ||||
\(101\) | −19.6859 | −1.95882 | −0.979412 | − | 0.201874i | \(-0.935297\pi\) | ||||
−0.979412 | + | 0.201874i | \(0.935297\pi\) | |||||||
\(102\) | −5.56196 | + | 5.18550i | −0.550716 | + | 0.513441i | ||||
\(103\) | − | 2.89731i | − | 0.285481i | −0.989760 | − | 0.142740i | \(-0.954409\pi\) | ||
0.989760 | − | 0.142740i | \(-0.0455914\pi\) | |||||||
\(104\) | 6.54765 | − | 11.3655i | 0.642050 | − | 1.11448i | ||||
\(105\) | −2.58633 | − | 6.10014i | −0.252400 | − | 0.595313i | ||||
\(106\) | −0.207149 | − | 0.568583i | −0.0201201 | − | 0.0552257i | ||||
\(107\) | − | 2.73473i | − | 0.264376i | −0.991225 | − | 0.132188i | \(-0.957800\pi\) | ||
0.991225 | − | 0.132188i | \(-0.0422003\pi\) | |||||||
\(108\) | −3.37717 | − | 9.82826i | −0.324969 | − | 0.945725i | ||||
\(109\) | 18.5012i | 1.77210i | 0.463592 | + | 0.886049i | \(0.346560\pi\) | ||||
−0.463592 | + | 0.886049i | \(0.653440\pi\) | |||||||
\(110\) | −6.46791 | + | 2.35642i | −0.616691 | + | 0.224676i | ||||
\(111\) | 2.68841 | + | 6.34090i | 0.255173 | + | 0.601852i | ||||
\(112\) | −9.01277 | − | 1.57757i | −0.851626 | − | 0.149066i | ||||
\(113\) | − | 3.69006i | − | 0.347131i | −0.984822 | − | 0.173566i | \(-0.944471\pi\) | ||
0.984822 | − | 0.173566i | \(-0.0555289\pi\) | |||||||
\(114\) | −12.8727 | − | 13.8073i | −1.20564 | − | 1.29317i | ||||
\(115\) | −1.67234 | −0.155946 | ||||||||
\(116\) | 13.0627 | − | 10.9748i | 1.21284 | − | 1.01899i | ||||
\(117\) | 9.99954 | + | 9.67269i | 0.924458 | + | 0.894240i | ||||
\(118\) | 12.0934 | − | 4.40593i | 1.11329 | − | 0.405599i | ||||
\(119\) | −7.10121 | −0.650967 | ||||||||
\(120\) | −8.13221 | − | 0.994229i | −0.742366 | − | 0.0907603i | ||||
\(121\) | 2.52819 | 0.229835 | ||||||||
\(122\) | 12.0464 | − | 4.38879i | 1.09063 | − | 0.397342i | ||||
\(123\) | 3.38910 | + | 7.99354i | 0.305585 | + | 0.720753i | ||||
\(124\) | 10.1427 | + | 12.0722i | 0.910839 | + | 1.08412i | ||||
\(125\) | 12.0463 | 1.07746 | ||||||||
\(126\) | 3.95198 | − | 8.86371i | 0.352070 | − | 0.789642i | ||||
\(127\) | 3.49738i | 0.310342i | 0.987888 | + | 0.155171i | \(0.0495929\pi\) | ||||
−0.987888 | + | 0.155171i | \(0.950407\pi\) | |||||||
\(128\) | −7.25332 | + | 8.68271i | −0.641109 | + | 0.767450i | ||||
\(129\) | −12.1624 | + | 5.15663i | −1.07084 | + | 0.454016i | ||||
\(130\) | 10.3051 | − | 3.75441i | 0.903819 | − | 0.329283i | ||||
\(131\) | 2.59666i | 0.226871i | 0.993545 | + | 0.113436i | \(0.0361856\pi\) | ||||
−0.993545 | + | 0.113436i | \(0.963814\pi\) | |||||||
\(132\) | −8.98473 | − | 4.57562i | −0.782021 | − | 0.398257i | ||||
\(133\) | − | 17.6284i | − | 1.52858i | ||||||
\(134\) | −4.01573 | − | 11.0224i | −0.346906 | − | 0.952189i | ||||
\(135\) | 3.12434 | − | 8.10863i | 0.268900 | − | 0.697880i | ||||
\(136\) | −4.38318 | + | 7.60838i | −0.375855 | + | 0.652413i | ||||
\(137\) | 18.1669i | 1.55210i | 0.630668 | + | 0.776052i | \(0.282781\pi\) | ||||
−0.630668 | + | 0.776052i | \(0.717219\pi\) | |||||||
\(138\) | −1.67036 | − | 1.79162i | −0.142190 | − | 0.152513i | ||||
\(139\) | −4.65828 | −0.395110 | −0.197555 | − | 0.980292i | \(-0.563300\pi\) | ||||
−0.197555 | + | 0.980292i | \(0.563300\pi\) | |||||||
\(140\) | −4.92149 | − | 5.85776i | −0.415942 | − | 0.495071i | ||||
\(141\) | −7.36352 | + | 3.12198i | −0.620120 | + | 0.262918i | ||||
\(142\) | −2.09827 | − | 5.75934i | −0.176083 | − | 0.483313i | ||||
\(143\) | 13.4979 | 1.12875 | ||||||||
\(144\) | −7.05742 | − | 9.70530i | −0.588118 | − | 0.808775i | ||||
\(145\) | 14.2660 | 1.18472 | ||||||||
\(146\) | 3.34521 | + | 9.18196i | 0.276852 | + | 0.759905i | ||||
\(147\) | −2.81867 | + | 1.19506i | −0.232480 | + | 0.0985666i | ||||
\(148\) | 5.11573 | + | 6.08896i | 0.420511 | + | 0.500509i | ||||
\(149\) | −14.7435 | −1.20784 | −0.603919 | − | 0.797045i | \(-0.706395\pi\) | ||||
−0.603919 | + | 0.797045i | \(0.706395\pi\) | |||||||
\(150\) | 3.68026 | + | 3.94745i | 0.300492 | + | 0.322308i | ||||
\(151\) | 8.88943i | 0.723412i | 0.932292 | + | 0.361706i | \(0.117806\pi\) | ||||
−0.932292 | + | 0.361706i | \(0.882194\pi\) | |||||||
\(152\) | −18.8874 | − | 10.8810i | −1.53197 | − | 0.882568i | ||||
\(153\) | −6.69398 | − | 6.47517i | −0.541176 | − | 0.523486i | ||||
\(154\) | −3.22314 | − | 8.84689i | −0.259728 | − | 0.712903i | ||||
\(155\) | 13.1843i | 1.05899i | ||||||||
\(156\) | 14.3151 | + | 7.29020i | 1.14612 | + | 0.583683i | ||||
\(157\) | 8.04774i | 0.642279i | 0.947032 | + | 0.321140i | \(0.104066\pi\) | ||||
−0.947032 | + | 0.321140i | \(0.895934\pi\) | |||||||
\(158\) | 8.58422 | − | 3.12744i | 0.682924 | − | 0.248806i | ||||
\(159\) | 0.682349 | − | 0.289302i | 0.0541138 | − | 0.0229431i | ||||
\(160\) | −9.31388 | + | 1.65731i | −0.736327 | + | 0.131022i | ||||
\(161\) | − | 2.28745i | − | 0.180276i | ||||||
\(162\) | 11.8076 | − | 4.75183i | 0.927695 | − | 0.373339i | ||||
\(163\) | −8.22815 | −0.644479 | −0.322239 | − | 0.946658i | \(-0.604436\pi\) | ||||
−0.322239 | + | 0.946658i | \(0.604436\pi\) | |||||||
\(164\) | 6.44906 | + | 7.67593i | 0.503587 | + | 0.599389i | ||||
\(165\) | −3.29095 | − | 7.76205i | −0.256200 | − | 0.604275i | ||||
\(166\) | 16.9910 | − | 6.19025i | 1.31876 | − | 0.480457i | ||||
\(167\) | −17.1392 | −1.32627 | −0.663134 | − | 0.748501i | \(-0.730774\pi\) | ||||
−0.663134 | + | 0.748501i | \(0.730774\pi\) | |||||||
\(168\) | 1.35992 | − | 11.1233i | 0.104920 | − | 0.858184i | ||||
\(169\) | −8.50574 | −0.654288 | ||||||||
\(170\) | −6.89854 | + | 2.51331i | −0.529094 | + | 0.192762i | ||||
\(171\) | 16.0743 | − | 16.6175i | 1.22923 | − | 1.27077i | ||||
\(172\) | −11.6792 | + | 9.81246i | −0.890530 | + | 0.748193i | ||||
\(173\) | 20.0458 | 1.52405 | 0.762027 | − | 0.647546i | \(-0.224204\pi\) | ||||
0.762027 | + | 0.647546i | \(0.224204\pi\) | |||||||
\(174\) | 14.2490 | + | 15.2835i | 1.08022 | + | 1.15864i | ||||
\(175\) | 5.03989i | 0.380980i | ||||||||
\(176\) | −11.4682 | − | 2.00736i | −0.864448 | − | 0.151310i | ||||
\(177\) | 6.15328 | + | 14.5131i | 0.462509 | + | 1.09088i | ||||
\(178\) | −6.00732 | + | 2.18861i | −0.450268 | + | 0.164044i | ||||
\(179\) | − | 13.0220i | − | 0.973309i | −0.873594 | − | 0.486655i | \(-0.838217\pi\) | ||
0.873594 | − | 0.486655i | \(-0.161783\pi\) | |||||||
\(180\) | 0.702082 | − | 10.0094i | 0.0523301 | − | 0.746060i | ||||
\(181\) | − | 21.4856i | − | 1.59701i | −0.601987 | − | 0.798506i | \(-0.705624\pi\) | ||
0.601987 | − | 0.798506i | \(-0.294376\pi\) | |||||||
\(182\) | 5.13533 | + | 14.0955i | 0.380656 | + | 1.04483i | ||||
\(183\) | 6.12934 | + | 14.4567i | 0.453094 | + | 1.06867i | ||||
\(184\) | −2.45082 | − | 1.41191i | −0.180677 | − | 0.104088i | ||||
\(185\) | 6.64984i | 0.488906i | ||||||||
\(186\) | −14.1246 | + | 13.1686i | −1.03567 | + | 0.965570i | ||||
\(187\) | −9.03586 | −0.660767 | ||||||||
\(188\) | −7.07094 | + | 5.94076i | −0.515701 | + | 0.433275i | ||||
\(189\) | 11.0911 | + | 4.27351i | 0.806759 | + | 0.310852i | ||||
\(190\) | −6.23916 | − | 17.1253i | −0.452636 | − | 1.24240i | ||||
\(191\) | 22.2870 | 1.61263 | 0.806314 | − | 0.591488i | \(-0.201459\pi\) | ||||
0.806314 | + | 0.591488i | \(0.201459\pi\) | |||||||
\(192\) | −11.0784 | − | 8.32286i | −0.799511 | − | 0.600651i | ||||
\(193\) | 5.72840 | 0.412339 | 0.206170 | − | 0.978516i | \(-0.433900\pi\) | ||||
0.206170 | + | 0.978516i | \(0.433900\pi\) | |||||||
\(194\) | −4.15575 | − | 11.4067i | −0.298366 | − | 0.818955i | ||||
\(195\) | 5.24337 | + | 12.3670i | 0.375486 | + | 0.885622i | ||||
\(196\) | −2.70667 | + | 2.27405i | −0.193334 | + | 0.162432i | ||||
\(197\) | 12.4216 | 0.884999 | 0.442499 | − | 0.896769i | \(-0.354092\pi\) | ||||
0.442499 | + | 0.896769i | \(0.354092\pi\) | |||||||
\(198\) | 5.02865 | − | 11.2785i | 0.357370 | − | 0.801530i | ||||
\(199\) | − | 14.2662i | − | 1.01130i | −0.862738 | − | 0.505650i | \(-0.831253\pi\) | ||
0.862738 | − | 0.505650i | \(-0.168747\pi\) | |||||||
\(200\) | 5.39983 | + | 3.11084i | 0.381826 | + | 0.219970i | ||||
\(201\) | 13.2278 | − | 5.60832i | 0.933019 | − | 0.395581i | ||||
\(202\) | −9.53006 | − | 26.1582i | −0.670533 | − | 1.84048i | ||||
\(203\) | 19.5132i | 1.36956i | ||||||||
\(204\) | −9.58293 | − | 4.88026i | −0.670939 | − | 0.341687i | ||||
\(205\) | 8.38300i | 0.585494i | ||||||||
\(206\) | 3.84988 | − | 1.40260i | 0.268234 | − | 0.0977241i | ||||
\(207\) | 2.08579 | − | 2.15627i | 0.144972 | − | 0.149871i | ||||
\(208\) | 18.2719 | + | 3.19826i | 1.26693 | + | 0.221760i | ||||
\(209\) | − | 22.4311i | − | 1.55159i | ||||||
\(210\) | 6.85365 | − | 6.38976i | 0.472947 | − | 0.440936i | ||||
\(211\) | −25.3506 | −1.74521 | −0.872604 | − | 0.488428i | \(-0.837571\pi\) | ||||
−0.872604 | + | 0.488428i | \(0.837571\pi\) | |||||||
\(212\) | 0.655237 | − | 0.550508i | 0.0450019 | − | 0.0378090i | ||||
\(213\) | 6.91171 | − | 2.93042i | 0.473582 | − | 0.200789i | ||||
\(214\) | 3.63384 | − | 1.32390i | 0.248404 | − | 0.0904996i | ||||
\(215\) | −12.7550 | −0.869885 | ||||||||
\(216\) | 11.4246 | − | 9.24542i | 0.777348 | − | 0.629071i | ||||
\(217\) | −18.0336 | −1.22420 | ||||||||
\(218\) | −24.5840 | + | 8.95655i | −1.66504 | + | 0.606614i | ||||
\(219\) | −11.0192 | + | 4.67189i | −0.744605 | + | 0.315697i | ||||
\(220\) | −6.26230 | − | 7.45364i | −0.422204 | − | 0.502524i | ||||
\(221\) | 14.3966 | 0.968417 | ||||||||
\(222\) | −7.12416 | + | 6.64196i | −0.478142 | + | 0.445779i | ||||
\(223\) | − | 4.13720i | − | 0.277048i | −0.990359 | − | 0.138524i | \(-0.955764\pi\) | ||
0.990359 | − | 0.138524i | \(-0.0442358\pi\) | |||||||
\(224\) | −2.26689 | − | 12.7396i | −0.151463 | − | 0.851203i | ||||
\(225\) | −4.59557 | + | 4.75086i | −0.306371 | + | 0.316724i | ||||
\(226\) | 4.90325 | − | 1.78638i | 0.326160 | − | 0.118828i | ||||
\(227\) | 11.1121i | 0.737536i | 0.929522 | + | 0.368768i | \(0.120220\pi\) | ||||
−0.929522 | + | 0.368768i | \(0.879780\pi\) | |||||||
\(228\) | 12.1150 | − | 23.7891i | 0.802336 | − | 1.57547i | ||||
\(229\) | 8.33587i | 0.550850i | 0.961323 | + | 0.275425i | \(0.0888185\pi\) | ||||
−0.961323 | + | 0.275425i | \(0.911182\pi\) | |||||||
\(230\) | −0.809588 | − | 2.22216i | −0.0533827 | − | 0.146525i | ||||
\(231\) | 10.6170 | − | 4.50141i | 0.698550 | − | 0.296171i | ||||
\(232\) | 20.9068 | + | 12.0444i | 1.37260 | + | 0.790753i | ||||
\(233\) | 1.94318i | 0.127302i | 0.997972 | + | 0.0636510i | \(0.0202744\pi\) | ||||
−0.997972 | + | 0.0636510i | \(0.979726\pi\) | |||||||
\(234\) | −8.01199 | + | 17.9697i | −0.523760 | + | 1.17472i | ||||
\(235\) | −7.72228 | −0.503746 | ||||||||
\(236\) | 11.7090 | + | 13.9365i | 0.762189 | + | 0.907188i | ||||
\(237\) | 4.36776 | + | 10.3018i | 0.283716 | + | 0.669175i | ||||
\(238\) | −3.43773 | − | 9.43591i | −0.222835 | − | 0.611639i | ||||
\(239\) | 16.9988 | 1.09956 | 0.549781 | − | 0.835309i | \(-0.314711\pi\) | ||||
0.549781 | + | 0.835309i | \(0.314711\pi\) | |||||||
\(240\) | −2.61574 | − | 11.2872i | −0.168845 | − | 0.728584i | ||||
\(241\) | 4.17570 | 0.268981 | 0.134490 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134490 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(242\) | 1.22391 | + | 3.35939i | 0.0786758 | + | 0.215950i | ||||
\(243\) | 6.55830 | + | 14.1417i | 0.420715 | + | 0.907193i | ||||
\(244\) | 11.6634 | + | 13.8823i | 0.746674 | + | 0.888721i | ||||
\(245\) | −2.95600 | −0.188852 | ||||||||
\(246\) | −8.98094 | + | 8.37306i | −0.572604 | + | 0.533847i | ||||
\(247\) | 35.7387i | 2.27400i | ||||||||
\(248\) | −11.1311 | + | 19.3215i | −0.706828 | + | 1.22692i | ||||
\(249\) | 8.64524 | + | 20.3907i | 0.547870 | + | 1.29221i | ||||
\(250\) | 5.83169 | + | 16.0069i | 0.368829 | + | 1.01236i | ||||
\(251\) | 2.42594i | 0.153124i | 0.997065 | + | 0.0765619i | \(0.0243943\pi\) | ||||
−0.997065 | + | 0.0765619i | \(0.975606\pi\) | |||||||
\(252\) | 13.6910 | + | 0.960317i | 0.862455 | + | 0.0604943i | ||||
\(253\) | − | 2.91064i | − | 0.182990i | ||||||
\(254\) | −4.64723 | + | 1.69310i | −0.291593 | + | 0.106235i | ||||
\(255\) | −3.51006 | − | 8.27885i | −0.219809 | − | 0.518442i | ||||
\(256\) | −15.0487 | − | 5.43468i | −0.940546 | − | 0.339668i | ||||
\(257\) | − | 6.11395i | − | 0.381378i | −0.981651 | − | 0.190689i | \(-0.938928\pi\) | ||
0.981651 | − | 0.190689i | \(-0.0610722\pi\) | |||||||
\(258\) | −12.7399 | − | 13.6648i | −0.793151 | − | 0.850733i | ||||
\(259\) | −9.09574 | −0.565182 | ||||||||
\(260\) | 9.97752 | + | 11.8757i | 0.618780 | + | 0.736497i | ||||
\(261\) | −17.7929 | + | 18.3941i | −1.10135 | + | 1.13857i | ||||
\(262\) | −3.45038 | + | 1.25706i | −0.213165 | + | 0.0776613i | ||||
\(263\) | −6.15397 | −0.379470 | −0.189735 | − | 0.981835i | \(-0.560763\pi\) | ||||
−0.189735 | + | 0.981835i | \(0.560763\pi\) | |||||||
\(264\) | 1.73041 | − | 14.1538i | 0.106500 | − | 0.871104i | ||||
\(265\) | 0.715594 | 0.0439586 | ||||||||
\(266\) | 23.4242 | − | 8.53400i | 1.43623 | − | 0.523253i | ||||
\(267\) | −3.05660 | − | 7.20931i | −0.187061 | − | 0.441203i | ||||
\(268\) | 12.7022 | − | 10.6720i | 0.775913 | − | 0.651896i | ||||
\(269\) | 20.4694 | 1.24804 | 0.624021 | − | 0.781407i | \(-0.285498\pi\) | ||||
0.624021 | + | 0.781407i | \(0.285498\pi\) | |||||||
\(270\) | 12.2871 | + | 0.226107i | 0.747766 | + | 0.0137604i | ||||
\(271\) | 5.78075i | 0.351156i | 0.984466 | + | 0.175578i | \(0.0561794\pi\) | ||||
−0.984466 | + | 0.175578i | \(0.943821\pi\) | |||||||
\(272\) | −12.2317 | − | 2.14101i | −0.741658 | − | 0.129818i | ||||
\(273\) | −16.9158 | + | 7.17195i | −1.02379 | + | 0.434066i | ||||
\(274\) | −24.1397 | + | 8.79470i | −1.45834 | + | 0.531307i | ||||
\(275\) | 6.41295i | 0.386715i | ||||||||
\(276\) | 1.57203 | − | 3.08686i | 0.0946253 | − | 0.185807i | ||||
\(277\) | − | 6.92990i | − | 0.416377i | −0.978089 | − | 0.208189i | \(-0.933243\pi\) | ||
0.978089 | − | 0.208189i | \(-0.0667568\pi\) | |||||||
\(278\) | −2.25510 | − | 6.18981i | −0.135252 | − | 0.371240i | ||||
\(279\) | −16.9994 | − | 16.4438i | −1.01773 | − | 0.984462i | ||||
\(280\) | 5.40112 | − | 9.37533i | 0.322779 | − | 0.560283i | ||||
\(281\) | 6.80878i | 0.406178i | 0.979160 | + | 0.203089i | \(0.0650980\pi\) | ||||
−0.979160 | + | 0.203089i | \(0.934902\pi\) | |||||||
\(282\) | −7.71312 | − | 8.27309i | −0.459310 | − | 0.492655i | ||||
\(283\) | 23.2198 | 1.38027 | 0.690136 | − | 0.723679i | \(-0.257551\pi\) | ||||
0.690136 | + | 0.723679i | \(0.257551\pi\) | |||||||
\(284\) | 6.63708 | − | 5.57625i | 0.393838 | − | 0.330890i | ||||
\(285\) | 20.5518 | − | 8.71355i | 1.21738 | − | 0.516146i | ||||
\(286\) | 6.53439 | + | 17.9356i | 0.386387 | + | 1.06056i | ||||
\(287\) | −11.4664 | −0.676839 | ||||||||
\(288\) | 9.47963 | − | 14.0761i | 0.558592 | − | 0.829442i | ||||
\(289\) | 7.36254 | 0.433091 | ||||||||
\(290\) | 6.90623 | + | 18.9563i | 0.405548 | + | 1.11315i | ||||
\(291\) | 13.6891 | − | 5.80388i | 0.802467 | − | 0.340230i | ||||
\(292\) | −10.5813 | + | 8.89007i | −0.619225 | + | 0.520252i | ||||
\(293\) | −4.43092 | −0.258857 | −0.129429 | − | 0.991589i | \(-0.541314\pi\) | ||||
−0.129429 | + | 0.991589i | \(0.541314\pi\) | |||||||
\(294\) | −2.95249 | − | 3.16684i | −0.172193 | − | 0.184694i | ||||
\(295\) | 15.2203i | 0.886158i | ||||||||
\(296\) | −5.61430 | + | 9.74535i | −0.326324 | + | 0.566437i | ||||
\(297\) | 14.1127 | + | 5.43778i | 0.818904 | + | 0.315532i | ||||
\(298\) | −7.13743 | − | 19.5909i | −0.413460 | − | 1.13487i | ||||
\(299\) | 4.63743i | 0.268189i | ||||||||
\(300\) | −3.46363 | + | 6.80122i | −0.199973 | + | 0.392669i | ||||
\(301\) | − | 17.4465i | − | 1.00560i | ||||||
\(302\) | −11.8121 | + | 4.30342i | −0.679707 | + | 0.247634i | ||||
\(303\) | 31.3921 | − | 13.3096i | 1.80343 | − | 0.764616i | ||||
\(304\) | 5.31495 | − | 30.3647i | 0.304833 | − | 1.74153i | ||||
\(305\) | 15.1610i | 0.868119i | ||||||||
\(306\) | 5.36345 | − | 12.0295i | 0.306608 | − | 0.687678i | ||||
\(307\) | 24.5271 | 1.39983 | 0.699917 | − | 0.714224i | \(-0.253220\pi\) | ||||
0.699917 | + | 0.714224i | \(0.253220\pi\) | |||||||
\(308\) | 10.1952 | − | 8.56565i | 0.580925 | − | 0.488073i | ||||
\(309\) | 1.95886 | + | 4.62019i | 0.111436 | + | 0.262833i | ||||
\(310\) | −17.5189 | + | 6.38257i | −0.995007 | + | 0.362505i | ||||
\(311\) | −6.45799 | −0.366199 | −0.183100 | − | 0.983094i | \(-0.558613\pi\) | ||||
−0.183100 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(312\) | −2.75702 | + | 22.5508i | −0.156085 | + | 1.27669i | ||||
\(313\) | −1.06905 | −0.0604265 | −0.0302132 | − | 0.999543i | \(-0.509619\pi\) | ||||
−0.0302132 | + | 0.999543i | \(0.509619\pi\) | |||||||
\(314\) | −10.6936 | + | 3.89595i | −0.603476 | + | 0.219861i | ||||
\(315\) | 8.24857 | + | 7.97895i | 0.464754 | + | 0.449563i | ||||
\(316\) | 8.31133 | + | 9.89248i | 0.467549 | + | 0.556496i | ||||
\(317\) | −5.60014 | −0.314535 | −0.157268 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157268 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(318\) | 0.714746 | + | 0.766635i | 0.0400810 | + | 0.0429908i | ||||
\(319\) | 24.8293i | 1.39018i | ||||||||
\(320\) | −6.71109 | − | 11.5737i | −0.375161 | − | 0.646991i | ||||
\(321\) | 1.84894 | + | 4.36092i | 0.103198 | + | 0.243403i | ||||
\(322\) | 3.03950 | − | 1.10737i | 0.169385 | − | 0.0617111i | ||||
\(323\) | − | 23.9245i | − | 1.33120i | ||||||
\(324\) | 12.0302 | + | 13.3893i | 0.668347 | + | 0.743849i | ||||
\(325\) | − | 10.2176i | − | 0.566768i | ||||||
\(326\) | −3.98329 | − | 10.9334i | −0.220614 | − | 0.605543i | ||||
\(327\) | −12.5086 | − | 29.5029i | −0.691729 | − | 1.63151i | ||||
\(328\) | −7.07756 | + | 12.2853i | −0.390793 | + | 0.678342i | ||||
\(329\) | − | 10.5626i | − | 0.582337i | ||||||
\(330\) | 8.72086 | − | 8.13058i | 0.480067 | − | 0.447574i | ||||
\(331\) | −3.95776 | −0.217538 | −0.108769 | − | 0.994067i | \(-0.534691\pi\) | ||||
−0.108769 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(332\) | 16.4509 | + | 19.5805i | 0.902860 | + | 1.07462i | ||||
\(333\) | −8.57413 | − | 8.29386i | −0.469859 | − | 0.454501i | ||||
\(334\) | −8.29715 | − | 22.7741i | −0.454000 | − | 1.24614i | ||||
\(335\) | 13.8723 | 0.757925 | ||||||||
\(336\) | 15.4388 | − | 3.57784i | 0.842253 | − | 0.195187i | ||||
\(337\) | −15.1916 | −0.827540 | −0.413770 | − | 0.910381i | \(-0.635788\pi\) | ||||
−0.413770 | + | 0.910381i | \(0.635788\pi\) | |||||||
\(338\) | −4.11767 | − | 11.3022i | −0.223972 | − | 0.614759i | ||||
\(339\) | 2.49483 | + | 5.88433i | 0.135501 | + | 0.319593i | ||||
\(340\) | −6.67924 | − | 7.94990i | −0.362232 | − | 0.431144i | ||||
\(341\) | −22.9467 | −1.24263 | ||||||||
\(342\) | 29.8625 | + | 13.3145i | 1.61478 | + | 0.719966i | ||||
\(343\) | − | 20.0554i | − | 1.08289i | ||||||
\(344\) | −18.6925 | − | 10.7687i | −1.00783 | − | 0.580612i | ||||
\(345\) | 2.66679 | − | 1.13066i | 0.143575 | − | 0.0608729i | ||||
\(346\) | 9.70427 | + | 26.6363i | 0.521705 | + | 1.43198i | ||||
\(347\) | 17.8879i | 0.960272i | 0.877194 | + | 0.480136i | \(0.159413\pi\) | ||||
−0.877194 | + | 0.480136i | \(0.840587\pi\) | |||||||
\(348\) | −13.4103 | + | 26.3326i | −0.718868 | + | 1.41158i | ||||
\(349\) | − | 6.58198i | − | 0.352325i | −0.984361 | − | 0.176163i | \(-0.943632\pi\) | ||
0.984361 | − | 0.176163i | \(-0.0563685\pi\) | |||||||
\(350\) | −6.69688 | + | 2.43984i | −0.357963 | + | 0.130415i | ||||
\(351\) | −22.4854 | − | 8.66384i | −1.20018 | − | 0.462442i | ||||
\(352\) | −2.88448 | − | 16.2104i | −0.153743 | − | 0.864018i | ||||
\(353\) | 19.9404i | 1.06132i | 0.847584 | + | 0.530661i | \(0.178056\pi\) | ||||
−0.847584 | + | 0.530661i | \(0.821944\pi\) | |||||||
\(354\) | −16.3059 | + | 15.2022i | −0.866647 | + | 0.807988i | ||||
\(355\) | 7.24846 | 0.384708 | ||||||||
\(356\) | −5.81635 | − | 6.92286i | −0.308266 | − | 0.366911i | ||||
\(357\) | 11.3239 | − | 4.80111i | 0.599325 | − | 0.254102i | ||||
\(358\) | 17.3033 | − | 6.30401i | 0.914507 | − | 0.333177i | ||||
\(359\) | 20.8705 | 1.10150 | 0.550752 | − | 0.834669i | \(-0.314341\pi\) | ||||
0.550752 | + | 0.834669i | \(0.314341\pi\) | |||||||
\(360\) | 13.6402 | − | 3.91272i | 0.718901 | − | 0.206218i | ||||
\(361\) | 40.3914 | 2.12586 | ||||||||
\(362\) | 28.5495 | − | 10.4013i | 1.50053 | − | 0.546680i | ||||
\(363\) | −4.03156 | + | 1.70930i | −0.211602 | + | 0.0897150i | ||||
\(364\) | −16.2437 | + | 13.6474i | −0.851400 | + | 0.715317i | ||||
\(365\) | −11.5560 | −0.604870 | ||||||||
\(366\) | −16.2424 | + | 15.1431i | −0.849006 | + | 0.791541i | ||||
\(367\) | 28.7454i | 1.50050i | 0.661155 | + | 0.750249i | \(0.270066\pi\) | ||||
−0.661155 | + | 0.750249i | \(0.729934\pi\) | |||||||
\(368\) | 0.689663 | − | 3.94010i | 0.0359512 | − | 0.205392i | ||||
\(369\) | −10.8088 | − | 10.4555i | −0.562684 | − | 0.544292i | ||||
\(370\) | −8.83614 | + | 3.21922i | −0.459369 | + | 0.167359i | ||||
\(371\) | 0.978799i | 0.0508167i | ||||||||
\(372\) | −24.3359 | − | 12.3935i | −1.26176 | − | 0.642572i | ||||
\(373\) | 2.12022i | 0.109781i | 0.998492 | + | 0.0548903i | \(0.0174809\pi\) | ||||
−0.998492 | + | 0.0548903i | \(0.982519\pi\) | |||||||
\(374\) | −4.37431 | − | 12.0066i | −0.226190 | − | 0.620848i | ||||
\(375\) | −19.2096 | + | 8.14449i | −0.991981 | + | 0.420579i | ||||
\(376\) | −11.3170 | − | 6.51973i | −0.583630 | − | 0.336229i | ||||
\(377\) | − | 39.5598i | − | 2.03743i | ||||||
\(378\) | −0.309272 | + | 16.8064i | −0.0159073 | + | 0.864428i | ||||
\(379\) | −17.5425 | −0.901099 | −0.450550 | − | 0.892751i | \(-0.648772\pi\) | ||||
−0.450550 | + | 0.892751i | \(0.648772\pi\) | |||||||
\(380\) | 19.7352 | − | 16.5809i | 1.01240 | − | 0.850580i | ||||
\(381\) | −2.36457 | − | 5.57708i | −0.121141 | − | 0.285723i | ||||
\(382\) | 10.7892 | + | 29.6143i | 0.552025 | + | 1.51520i | ||||
\(383\) | 13.6105 | 0.695464 | 0.347732 | − | 0.937594i | \(-0.386952\pi\) | ||||
0.347732 | + | 0.937594i | \(0.386952\pi\) | |||||||
\(384\) | 5.69612 | − | 18.7498i | 0.290679 | − | 0.956821i | ||||
\(385\) | 11.1343 | 0.567458 | ||||||||
\(386\) | 2.77315 | + | 7.61175i | 0.141150 | + | 0.387428i | ||||
\(387\) | 15.9084 | − | 16.4460i | 0.808670 | − | 0.835996i | ||||
\(388\) | 13.1452 | − | 11.0441i | 0.667344 | − | 0.560680i | ||||
\(389\) | −9.47011 | −0.480154 | −0.240077 | − | 0.970754i | \(-0.577173\pi\) | ||||
−0.240077 | + | 0.970754i | \(0.577173\pi\) | |||||||
\(390\) | −13.8947 | + | 12.9542i | −0.703584 | + | 0.655962i | ||||
\(391\) | − | 3.10443i | − | 0.156998i | ||||||
\(392\) | −4.33202 | − | 2.49567i | −0.218800 | − | 0.126051i | ||||
\(393\) | −1.75559 | − | 4.14075i | −0.0885580 | − | 0.208873i | ||||
\(394\) | 6.01334 | + | 16.5054i | 0.302948 | + | 0.831532i | ||||
\(395\) | 10.8037i | 0.543595i | ||||||||
\(396\) | 17.4210 | + | 1.22194i | 0.875439 | + | 0.0614050i | ||||
\(397\) | − | 22.0808i | − | 1.10821i | −0.832448 | − | 0.554103i | \(-0.813061\pi\) | ||
0.832448 | − | 0.554103i | \(-0.186939\pi\) | |||||||
\(398\) | 18.9565 | − | 6.90632i | 0.950204 | − | 0.346183i | ||||
\(399\) | 11.9185 | + | 28.1110i | 0.596671 | + | 1.40731i | ||||
\(400\) | −1.51952 | + | 8.68114i | −0.0759761 | + | 0.434057i | ||||
\(401\) | − | 15.5379i | − | 0.775927i | −0.921675 | − | 0.387963i | \(-0.873179\pi\) | ||
0.921675 | − | 0.387963i | \(-0.126821\pi\) | |||||||
\(402\) | 13.8559 | + | 14.8618i | 0.691067 | + | 0.741238i | ||||
\(403\) | 36.5602 | 1.82119 | ||||||||
\(404\) | 30.1448 | − | 25.3266i | 1.49976 | − | 1.26005i | ||||
\(405\) | 0.500013 | + | 15.0427i | 0.0248459 | + | 0.747480i | ||||
\(406\) | −25.9286 | + | 9.44643i | −1.28682 | + | 0.468818i | ||||
\(407\) | −11.5738 | −0.573691 | ||||||||
\(408\) | 1.84562 | − | 15.0961i | 0.0913720 | − | 0.747369i | ||||
\(409\) | −27.3129 | −1.35054 | −0.675268 | − | 0.737572i | \(-0.735972\pi\) | ||||
−0.675268 | + | 0.737572i | \(0.735972\pi\) | |||||||
\(410\) | −11.1391 | + | 4.05826i | −0.550122 | + | 0.200423i | ||||
\(411\) | −12.2826 | − | 28.9698i | −0.605856 | − | 1.42897i | ||||
\(412\) | 3.72749 | + | 4.43661i | 0.183640 | + | 0.218576i | ||||
\(413\) | −20.8185 | −1.02441 | ||||||||
\(414\) | 3.87494 | + | 1.72768i | 0.190443 | + | 0.0849108i | ||||
\(415\) | 21.3842i | 1.04971i | ||||||||
\(416\) | 4.59576 | + | 25.8276i | 0.225326 | + | 1.26630i | ||||
\(417\) | 7.42831 | − | 3.14945i | 0.363766 | − | 0.154229i | ||||
\(418\) | 29.8058 | − | 10.8590i | 1.45785 | − | 0.531131i | ||||
\(419\) | − | 26.1832i | − | 1.27913i | −0.768736 | − | 0.639566i | \(-0.779114\pi\) | ||
0.768736 | − | 0.639566i | \(-0.220886\pi\) | |||||||
\(420\) | 11.8084 | + | 6.01364i | 0.576193 | + | 0.293436i | ||||
\(421\) | − | 13.1612i | − | 0.641436i | −0.947175 | − | 0.320718i | \(-0.896076\pi\) | ||
0.947175 | − | 0.320718i | \(-0.103924\pi\) | |||||||
\(422\) | −12.2724 | − | 33.6853i | −0.597409 | − | 1.63977i | ||||
\(423\) | 9.63144 | − | 9.95690i | 0.468296 | − | 0.484121i | ||||
\(424\) | 1.04870 | + | 0.604158i | 0.0509296 | + | 0.0293405i | ||||
\(425\) | 6.83992i | 0.331785i | ||||||||
\(426\) | 7.23986 | + | 7.76547i | 0.350773 | + | 0.376238i | ||||
\(427\) | −20.7375 | −1.00356 | ||||||||
\(428\) | 3.51832 | + | 4.18765i | 0.170064 | + | 0.202417i | ||||
\(429\) | −21.5243 | + | 9.12587i | −1.03920 | + | 0.440601i | ||||
\(430\) | −6.17477 | − | 16.9486i | −0.297774 | − | 0.817332i | ||||
\(431\) | 9.94800 | 0.479178 | 0.239589 | − | 0.970874i | \(-0.422987\pi\) | ||||
0.239589 | + | 0.970874i | \(0.422987\pi\) | |||||||
\(432\) | 17.8158 | + | 10.7050i | 0.857163 | + | 0.515045i | ||||
\(433\) | −2.05253 | −0.0986383 | −0.0493192 | − | 0.998783i | \(-0.515705\pi\) | ||||
−0.0493192 | + | 0.998783i | \(0.515705\pi\) | |||||||
\(434\) | −8.73016 | − | 23.9626i | −0.419061 | − | 1.15024i | ||||
\(435\) | −22.7492 | + | 9.64517i | −1.09074 | + | 0.462451i | ||||
\(436\) | −23.8025 | − | 28.3307i | −1.13993 | − | 1.35679i | ||||
\(437\) | 7.70658 | 0.368656 | ||||||||
\(438\) | −11.5423 | − | 12.3803i | −0.551514 | − | 0.591553i | ||||
\(439\) | − | 32.5669i | − | 1.55433i | −0.629296 | − | 0.777166i | \(-0.716657\pi\) | ||
0.629296 | − | 0.777166i | \(-0.283343\pi\) | |||||||
\(440\) | 6.87260 | − | 11.9295i | 0.327638 | − | 0.568718i | ||||
\(441\) | 3.68680 | − | 3.81138i | 0.175562 | − | 0.181494i | ||||
\(442\) | 6.96945 | + | 19.1298i | 0.331503 | + | 0.909911i | ||||
\(443\) | 16.4142i | 0.779861i | 0.920844 | + | 0.389931i | \(0.127501\pi\) | ||||
−0.920844 | + | 0.389931i | \(0.872499\pi\) | |||||||
\(444\) | −12.2745 | − | 6.25099i | −0.582522 | − | 0.296659i | ||||
\(445\) | − | 7.56056i | − | 0.358405i | ||||||
\(446\) | 5.49741 | − | 2.00284i | 0.260310 | − | 0.0948373i | ||||
\(447\) | 23.5107 | − | 9.96807i | 1.11202 | − | 0.471473i | ||||
\(448\) | 15.8307 | − | 9.17952i | 0.747930 | − | 0.433691i | ||||
\(449\) | 30.6773i | 1.44775i | 0.689929 | + | 0.723877i | \(0.257642\pi\) | ||||
−0.689929 | + | 0.723877i | \(0.742358\pi\) | |||||||
\(450\) | −8.53757 | − | 3.80656i | −0.402465 | − | 0.179443i | ||||
\(451\) | −14.5903 | −0.687029 | ||||||||
\(452\) | 4.74738 | + | 5.65052i | 0.223298 | + | 0.265778i | ||||
\(453\) | −6.01012 | − | 14.1755i | −0.282380 | − | 0.666023i | ||||
\(454\) | −14.7655 | + | 5.37942i | −0.692978 | + | 0.252469i | ||||
\(455\) | −17.7400 | −0.831663 | ||||||||
\(456\) | 37.4753 | + | 4.58167i | 1.75494 | + | 0.214556i | ||||
\(457\) | −21.4345 | −1.00266 | −0.501331 | − | 0.865255i | \(-0.667156\pi\) | ||||
−0.501331 | + | 0.865255i | \(0.667156\pi\) | |||||||
\(458\) | −11.0765 | + | 4.03544i | −0.517570 | + | 0.188564i | ||||
\(459\) | 15.0524 | + | 5.79982i | 0.702584 | + | 0.270712i | ||||
\(460\) | 2.56083 | − | 2.15152i | 0.119399 | − | 0.100315i | ||||
\(461\) | −9.57418 | −0.445914 | −0.222957 | − | 0.974828i | \(-0.571571\pi\) | ||||
−0.222957 | + | 0.974828i | \(0.571571\pi\) | |||||||
\(462\) | 11.1211 | + | 11.9285i | 0.517401 | + | 0.554964i | ||||
\(463\) | 23.0254i | 1.07008i | 0.844826 | + | 0.535042i | \(0.179704\pi\) | ||||
−0.844826 | + | 0.535042i | \(0.820296\pi\) | |||||||
\(464\) | −5.88320 | + | 33.6112i | −0.273121 | + | 1.56036i | ||||
\(465\) | −8.91383 | − | 21.0242i | −0.413369 | − | 0.974975i | ||||
\(466\) | −2.58205 | + | 0.940704i | −0.119611 | + | 0.0435773i | ||||
\(467\) | − | 31.8460i | − | 1.47366i | −0.676080 | − | 0.736828i | \(-0.736323\pi\) | ||
0.676080 | − | 0.736828i | \(-0.263677\pi\) | |||||||
\(468\) | −27.7564 | − | 1.94689i | −1.28304 | − | 0.0899948i | ||||
\(469\) | 18.9747i | 0.876171i | ||||||||
\(470\) | −3.73840 | − | 10.2612i | −0.172439 | − | 0.473313i | ||||
\(471\) | −5.44105 | − | 12.8333i | −0.250710 | − | 0.591326i | ||||
\(472\) | −12.8501 | + | 22.3053i | −0.591473 | + | 1.02669i | ||||
\(473\) | − | 22.1996i | − | 1.02074i | ||||||
\(474\) | −11.5743 | + | 10.7909i | −0.531627 | + | 0.495644i | ||||
\(475\) | −16.9798 | −0.779084 | ||||||||
\(476\) | 10.8740 | − | 9.13595i | 0.498408 | − | 0.418745i | ||||
\(477\) | −0.892508 | + | 0.922668i | −0.0408652 | + | 0.0422461i | ||||
\(478\) | 8.22921 | + | 22.5876i | 0.376395 | + | 1.03313i | ||||
\(479\) | −8.50882 | −0.388778 | −0.194389 | − | 0.980925i | \(-0.562272\pi\) | ||||
−0.194389 | + | 0.980925i | \(0.562272\pi\) | |||||||
\(480\) | 13.7318 | − | 8.93991i | 0.626769 | − | 0.408049i | ||||
\(481\) | 18.4401 | 0.840798 | ||||||||
\(482\) | 2.02148 | + | 5.54857i | 0.0920759 | + | 0.252730i | ||||
\(483\) | 1.54654 | + | 3.64767i | 0.0703698 | + | 0.165975i | ||||
\(484\) | −3.87137 | + | 3.25260i | −0.175972 | + | 0.147845i | ||||
\(485\) | 14.3560 | 0.651874 | ||||||||
\(486\) | −15.6163 | + | 15.5606i | −0.708369 | + | 0.705843i | ||||
\(487\) | 10.2419i | 0.464104i | 0.972703 | + | 0.232052i | \(0.0745440\pi\) | ||||
−0.972703 | + | 0.232052i | \(0.925456\pi\) | |||||||
\(488\) | −12.8001 | + | 22.2185i | −0.579433 | + | 1.00579i | ||||
\(489\) | 13.1210 | − | 5.56303i | 0.593351 | − | 0.251569i | ||||
\(490\) | −1.43101 | − | 3.92786i | −0.0646466 | − | 0.177442i | ||||
\(491\) | − | 32.3151i | − | 1.45836i | −0.684321 | − | 0.729181i | \(-0.739901\pi\) | ||
0.684321 | − | 0.729181i | \(-0.260099\pi\) | |||||||
\(492\) | −15.4736 | − | 7.88020i | −0.697605 | − | 0.355267i | ||||
\(493\) | 26.4824i | 1.19271i | ||||||||
\(494\) | −47.4887 | + | 17.3013i | −2.13662 | + | 0.778422i | ||||
\(495\) | 10.4958 | + | 10.1527i | 0.471751 | + | 0.456331i | ||||
\(496\) | −31.0626 | − | 5.43711i | −1.39475 | − | 0.244134i | ||||
\(497\) | 9.91454i | 0.444728i | ||||||||
\(498\) | −22.9095 | + | 21.3588i | −1.02660 | + | 0.957112i | ||||
\(499\) | −42.5250 | −1.90368 | −0.951841 | − | 0.306593i | \(-0.900811\pi\) | ||||
−0.951841 | + | 0.306593i | \(0.900811\pi\) | |||||||
\(500\) | −18.4464 | + | 15.4980i | −0.824946 | + | 0.693092i | ||||
\(501\) | 27.3309 | − | 11.5877i | 1.22105 | − | 0.517702i | ||||
\(502\) | −3.22352 | + | 1.17441i | −0.143873 | + | 0.0524164i | ||||
\(503\) | 6.73586 | 0.300337 | 0.150168 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150168 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(504\) | 5.35186 | + | 18.6572i | 0.238391 | + | 0.831058i | ||||
\(505\) | 32.9216 | 1.46499 | ||||||||
\(506\) | 3.86758 | − | 1.40905i | 0.171935 | − | 0.0626401i | ||||
\(507\) | 13.5636 | − | 5.75070i | 0.602382 | − | 0.255398i | ||||
\(508\) | −4.49950 | − | 5.35549i | −0.199633 | − | 0.237611i | ||||
\(509\) | 41.3469 | 1.83267 | 0.916334 | − | 0.400416i | \(-0.131134\pi\) | ||||
0.916334 | + | 0.400416i | \(0.131134\pi\) | |||||||
\(510\) | 9.30148 | − | 8.67191i | 0.411877 | − | 0.383999i | ||||
\(511\) | − | 15.8065i | − | 0.699238i | ||||||
\(512\) | −0.0637002 | − | 22.6273i | −0.00281518 | − | 0.999996i | ||||
\(513\) | −14.3978 | + | 37.3667i | −0.635677 | + | 1.64978i | ||||
\(514\) | 8.12407 | − | 2.95980i | 0.358337 | − | 0.130551i | ||||
\(515\) | 4.84529i | 0.213509i | ||||||||
\(516\) | 11.9900 | − | 23.5436i | 0.527830 | − | 1.03645i | ||||
\(517\) | − | 13.4403i | − | 0.591104i | ||||||
\(518\) | −4.40330 | − | 12.0862i | −0.193470 | − | 0.531037i | ||||
\(519\) | −31.9659 | + | 13.5529i | −1.40315 | + | 0.594906i | ||||
\(520\) | −10.9499 | + | 19.0069i | −0.480185 | + | 0.833510i | ||||
\(521\) | 24.8813i | 1.09007i | 0.838413 | + | 0.545035i | \(0.183484\pi\) | ||||
−0.838413 | + | 0.545035i | \(0.816516\pi\) | |||||||
\(522\) | −33.0553 | − | 14.7380i | −1.44679 | − | 0.645067i | ||||
\(523\) | −6.99915 | −0.306052 | −0.153026 | − | 0.988222i | \(-0.548902\pi\) | ||||
−0.153026 | + | 0.988222i | \(0.548902\pi\) | |||||||
\(524\) | −3.34069 | − | 3.97623i | −0.145939 | − | 0.173702i | ||||
\(525\) | −3.40745 | − | 8.03683i | −0.148713 | − | 0.350756i | ||||
\(526\) | −2.97917 | − | 8.17724i | −0.129898 | − | 0.356545i | ||||
\(527\) | −24.4744 | −1.06612 | ||||||||
\(528\) | 19.6449 | − | 4.55258i | 0.854933 | − | 0.198126i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.346423 | + | 0.950864i | 0.0150477 | + | 0.0413029i | ||||
\(531\) | −19.6246 | − | 18.9831i | −0.851635 | − | 0.823797i | ||||
\(532\) | 22.6795 | + | 26.9941i | 0.983282 | + | 1.17034i | ||||
\(533\) | 23.2462 | 1.00691 | ||||||||
\(534\) | 8.09983 | − | 7.55159i | 0.350514 | − | 0.326789i | ||||
\(535\) | 4.57339i | 0.197725i | ||||||||
\(536\) | 20.3299 | + | 11.7120i | 0.878117 | + | 0.505883i | ||||
\(537\) | 8.80412 | + | 20.7655i | 0.379926 | + | 0.896095i | ||||
\(538\) | 9.90936 | + | 27.1993i | 0.427223 | + | 1.17264i | ||||
\(539\) | − | 5.14479i | − | 0.221602i | ||||||
\(540\) | 5.64778 | + | 16.4362i | 0.243042 | + | 0.707301i | ||||
\(541\) | 0.299027i | 0.0128562i | 0.999979 | + | 0.00642808i | \(0.00204614\pi\) | ||||
−0.999979 | + | 0.00642808i | \(0.997954\pi\) | |||||||
\(542\) | −7.68132 | + | 2.79849i | −0.329941 | + | 0.120205i | ||||
\(543\) | 14.5263 | + | 34.2619i | 0.623385 | + | 1.47032i | ||||
\(544\) | −3.07653 | − | 17.2897i | −0.131905 | − | 0.741290i | ||||
\(545\) | − | 30.9404i | − | 1.32534i | ||||||
\(546\) | −17.7189 | − | 19.0053i | −0.758300 | − | 0.813352i | ||||
\(547\) | −22.3488 | −0.955564 | −0.477782 | − | 0.878478i | \(-0.658559\pi\) | ||||
−0.477782 | + | 0.878478i | \(0.658559\pi\) | |||||||
\(548\) | −23.3724 | − | 27.8187i | −0.998417 | − | 1.18836i | ||||
\(549\) | −19.5482 | − | 18.9093i | −0.834298 | − | 0.807028i | ||||
\(550\) | −8.52137 | + | 3.10454i | −0.363352 | + | 0.132378i | ||||
\(551\) | −65.7413 | −2.80067 | ||||||||
\(552\) | 4.86277 | + | 0.594514i | 0.206973 | + | 0.0253042i | ||||
\(553\) | −14.7775 | −0.628403 | ||||||||
\(554\) | 9.20827 | − | 3.35480i | 0.391222 | − | 0.142532i | ||||
\(555\) | −4.49594 | − | 10.6041i | −0.190842 | − | 0.450121i | ||||
\(556\) | 7.13316 | − | 5.99304i | 0.302513 | − | 0.254161i | ||||
\(557\) | 16.6755 | 0.706562 | 0.353281 | − | 0.935517i | \(-0.385066\pi\) | ||||
0.353281 | + | 0.935517i | \(0.385066\pi\) | |||||||
\(558\) | 13.6205 | − | 30.5489i | 0.576603 | − | 1.29324i | ||||
\(559\) | 35.3699i | 1.49599i | ||||||||
\(560\) | 15.0724 | + | 2.63823i | 0.636925 | + | 0.111486i | ||||
\(561\) | 14.4090 | − | 6.10912i | 0.608348 | − | 0.257927i | ||||
\(562\) | −9.04733 | + | 3.29617i | −0.381639 | + | 0.139040i | ||||
\(563\) | 12.6843i | 0.534578i | 0.963616 | + | 0.267289i | \(0.0861279\pi\) | ||||
−0.963616 | + | 0.267289i | \(0.913872\pi\) | |||||||
\(564\) | 7.25911 | − | 14.2540i | 0.305664 | − | 0.600204i | ||||
\(565\) | 6.17103i | 0.259617i | ||||||||
\(566\) | 11.2408 | + | 30.8539i | 0.472487 | + | 1.29688i | ||||
\(567\) | −20.5757 | + | 0.683925i | −0.864097 | + | 0.0287221i | ||||
\(568\) | 10.6226 | + | 6.11969i | 0.445716 | + | 0.256777i | ||||
\(569\) | − | 23.7045i | − | 0.993743i | −0.867824 | − | 0.496872i | \(-0.834482\pi\) | ||
0.867824 | − | 0.496872i | \(-0.165518\pi\) | |||||||
\(570\) | 21.5276 | + | 23.0905i | 0.901691 | + | 0.967153i | ||||
\(571\) | −14.6959 | −0.615004 | −0.307502 | − | 0.951548i | \(-0.599493\pi\) | ||||
−0.307502 | + | 0.951548i | \(0.599493\pi\) | |||||||
\(572\) | −20.6691 | + | 17.3655i | −0.864218 | + | 0.726087i | ||||
\(573\) | −35.5398 | + | 15.0681i | −1.48470 | + | 0.629481i | ||||
\(574\) | −5.55094 | − | 15.2362i | −0.231692 | − | 0.635948i | ||||
\(575\) | −2.20328 | −0.0918831 | ||||||||
\(576\) | 23.2931 | + | 5.78197i | 0.970546 | + | 0.240915i | ||||
\(577\) | 10.0148 | 0.416920 | 0.208460 | − | 0.978031i | \(-0.433155\pi\) | ||||
0.208460 | + | 0.978031i | \(0.433155\pi\) | |||||||
\(578\) | 3.56424 | + | 9.78316i | 0.148253 | + | 0.406926i | ||||
\(579\) | −9.13476 | + | 3.87295i | −0.379628 | + | 0.160954i | ||||
\(580\) | −21.8453 | + | 18.3536i | −0.907075 | + | 0.762094i | ||||
\(581\) | −29.2496 | −1.21348 | ||||||||
\(582\) | 14.3390 | + | 15.3800i | 0.594371 | + | 0.637521i | ||||
\(583\) | 1.24546i | 0.0515818i | ||||||||
\(584\) | −16.9354 | − | 9.75647i | −0.700791 | − | 0.403725i | ||||
\(585\) | −16.7226 | − | 16.1760i | −0.691396 | − | 0.668796i | ||||
\(586\) | −2.14503 | − | 5.88770i | −0.0886105 | − | 0.243219i | ||||
\(587\) | − | 31.6906i | − | 1.30801i | −0.756489 | − | 0.654006i | \(-0.773087\pi\) | ||
0.756489 | − | 0.654006i | \(-0.226913\pi\) | |||||||
\(588\) | 2.77870 | − | 5.45628i | 0.114592 | − | 0.225013i | ||||
\(589\) | − | 60.7565i | − | 2.50343i | ||||||
\(590\) | −20.2243 | + | 7.36821i | −0.832621 | + | 0.303344i | ||||
\(591\) | −19.8080 | + | 8.39817i | −0.814791 | + | 0.345455i | ||||
\(592\) | −15.6673 | − | 2.74236i | −0.643922 | − | 0.112710i | ||||
\(593\) | 23.0186i | 0.945262i | 0.881261 | + | 0.472631i | \(0.156696\pi\) | ||||
−0.881261 | + | 0.472631i | \(0.843304\pi\) | |||||||
\(594\) | −0.393530 | + | 21.3851i | −0.0161467 | + | 0.877442i | ||||
\(595\) | 11.8756 | 0.486854 | ||||||||
\(596\) | 22.5766 | − | 18.9681i | 0.924772 | − | 0.776962i | ||||
\(597\) | 9.64530 | + | 22.7495i | 0.394756 | + | 0.931073i | ||||
\(598\) | −6.16210 | + | 2.24500i | −0.251987 | + | 0.0918050i | ||||
\(599\) | 11.4463 | 0.467681 | 0.233841 | − | 0.972275i | \(-0.424871\pi\) | ||||
0.233841 | + | 0.972275i | \(0.424871\pi\) | |||||||
\(600\) | −10.7140 | − | 1.30988i | −0.437399 | − | 0.0534756i | ||||
\(601\) | −31.9168 | −1.30191 | −0.650957 | − | 0.759114i | \(-0.725632\pi\) | ||||
−0.650957 | + | 0.759114i | \(0.725632\pi\) | |||||||
\(602\) | 23.1824 | − | 8.44593i | 0.944846 | − | 0.344231i | ||||
\(603\) | −17.3019 | + | 17.8866i | −0.704588 | + | 0.728398i | ||||
\(604\) | −11.4366 | − | 13.6123i | −0.465347 | − | 0.553875i | ||||
\(605\) | −4.22799 | −0.171892 | ||||||||
\(606\) | 32.8825 | + | 35.2697i | 1.33576 | + | 1.43274i | ||||
\(607\) | 8.79097i | 0.356815i | 0.983957 | + | 0.178407i | \(0.0570945\pi\) | ||||
−0.983957 | + | 0.178407i | \(0.942906\pi\) | |||||||
\(608\) | 42.9208 | − | 7.63733i | 1.74067 | − | 0.309735i | ||||
\(609\) | −13.1928 | − | 31.1166i | −0.534599 | − | 1.26091i | ||||
\(610\) | −20.1456 | + | 7.33954i | −0.815672 | + | 0.297169i | ||||
\(611\) | 21.4140i | 0.866319i | ||||||||
\(612\) | 18.5809 | + | 1.30330i | 0.751089 | + | 0.0526828i | ||||
\(613\) | − | 23.9647i | − | 0.967925i | −0.875089 | − | 0.483963i | \(-0.839197\pi\) | ||
0.875089 | − | 0.483963i | \(-0.160803\pi\) | |||||||
\(614\) | 11.8737 | + | 32.5910i | 0.479183 | + | 1.31526i | ||||
\(615\) | −5.66772 | − | 13.3679i | −0.228545 | − | 0.539046i | ||||
\(616\) | 16.3174 | + | 9.40043i | 0.657445 | + | 0.378754i | ||||
\(617\) | 20.0313i | 0.806431i | 0.915105 | + | 0.403215i | \(0.132107\pi\) | ||||
−0.915105 | + | 0.403215i | \(0.867893\pi\) | |||||||
\(618\) | −5.19089 | + | 4.83955i | −0.208808 | + | 0.194675i | ||||
\(619\) | 36.0899 | 1.45057 | 0.725287 | − | 0.688446i | \(-0.241707\pi\) | ||||
0.725287 | + | 0.688446i | \(0.241707\pi\) | |||||||
\(620\) | −16.9620 | − | 20.1888i | −0.681210 | − | 0.810804i | ||||
\(621\) | −1.86824 | + | 4.84868i | −0.0749700 | + | 0.194571i | ||||
\(622\) | −3.12635 | − | 8.58122i | −0.125355 | − | 0.344075i | ||||
\(623\) | 10.3414 | 0.414321 | ||||||||
\(624\) | −31.2996 | + | 7.25349i | −1.25299 | + | 0.290372i | ||||
\(625\) | −9.12916 | −0.365166 | ||||||||
\(626\) | −0.517534 | − | 1.42053i | −0.0206848 | − | 0.0567758i | ||||
\(627\) | 15.1656 | + | 35.7696i | 0.605654 | + | 1.42850i | ||||
\(628\) | −10.3537 | − | 12.3234i | −0.413157 | − | 0.491756i | ||||
\(629\) | −12.3444 | −0.492202 | ||||||||
\(630\) | −6.60905 | + | 14.8231i | −0.263311 | + | 0.590568i | ||||
\(631\) | 23.6810i | 0.942725i | 0.881940 | + | 0.471362i | \(0.156238\pi\) | ||||
−0.881940 | + | 0.471362i | \(0.843762\pi\) | |||||||
\(632\) | −9.12132 | + | 15.8329i | −0.362827 | + | 0.629799i | ||||
\(633\) | 40.4252 | − | 17.1395i | 1.60676 | − | 0.681233i | ||||
\(634\) | −2.71106 | − | 7.44132i | −0.107670 | − | 0.295533i | ||||
\(635\) | − | 5.84881i | − | 0.232103i | ||||||
\(636\) | −0.672674 | + | 1.32087i | −0.0266732 | + | 0.0523758i | ||||
\(637\) | 8.19704i | 0.324778i | ||||||||
\(638\) | −32.9926 | + | 12.0200i | −1.30619 | + | 0.475877i | ||||
\(639\) | −9.04047 | + | 9.34597i | −0.357636 | + | 0.369721i | ||||
\(640\) | 12.1300 | − | 14.5204i | 0.479481 | − | 0.573971i | ||||
\(641\) | 20.8766i | 0.824577i | 0.911053 | + | 0.412288i | \(0.135270\pi\) | ||||
−0.911053 | + | 0.412288i | \(0.864730\pi\) | |||||||
\(642\) | −4.89960 | + | 4.56797i | −0.193372 | + | 0.180283i | ||||
\(643\) | 33.5342 | 1.32246 | 0.661230 | − | 0.750183i | \(-0.270035\pi\) | ||||
0.661230 | + | 0.750183i | \(0.270035\pi\) | |||||||
\(644\) | 2.94288 | + | 3.50273i | 0.115966 | + | 0.138027i | ||||
\(645\) | 20.3397 | − | 8.62363i | 0.800876 | − | 0.339555i | ||||
\(646\) | 31.7903 | − | 11.5820i | 1.25077 | − | 0.455687i | ||||
\(647\) | 18.4765 | 0.726385 | 0.363193 | − | 0.931714i | \(-0.381687\pi\) | ||||
0.363193 | + | 0.931714i | \(0.381687\pi\) | |||||||
\(648\) | −11.9674 | + | 22.4673i | −0.470126 | + | 0.882600i | ||||
\(649\) | −26.4902 | −1.03983 | ||||||||
\(650\) | 13.5768 | − | 4.94637i | 0.532527 | − | 0.194013i | ||||
\(651\) | 28.7572 | − | 12.1925i | 1.12708 | − | 0.477860i | ||||
\(652\) | 12.5996 | − | 10.5858i | 0.493440 | − | 0.414572i | ||||
\(653\) | 23.6502 | 0.925504 | 0.462752 | − | 0.886488i | \(-0.346862\pi\) | ||||
0.462752 | + | 0.886488i | \(0.346862\pi\) | |||||||
\(654\) | 33.1472 | − | 30.9037i | 1.29616 | − | 1.20843i | ||||
\(655\) | − | 4.34250i | − | 0.169676i | ||||||
\(656\) | −19.7507 | − | 3.45710i | −0.771135 | − | 0.134977i | ||||
\(657\) | 14.4130 | − | 14.9000i | 0.562304 | − | 0.581305i | ||||
\(658\) | 14.0354 | − | 5.11343i | 0.547156 | − | 0.199342i | ||||
\(659\) | 22.5920i | 0.880059i | 0.897983 | + | 0.440029i | \(0.145032\pi\) | ||||
−0.897983 | + | 0.440029i | \(0.854968\pi\) | |||||||
\(660\) | 15.0255 | + | 7.65199i | 0.584868 | + | 0.297853i | ||||
\(661\) | − | 40.2172i | − | 1.56427i | −0.623110 | − | 0.782135i | \(-0.714131\pi\) | ||
0.623110 | − | 0.782135i | \(-0.285869\pi\) | |||||||
\(662\) | −1.91597 | − | 5.25897i | −0.0744663 | − | 0.204396i | ||||
\(663\) | −22.9574 | + | 9.73346i | −0.891591 | + | 0.378016i | ||||
\(664\) | −18.0541 | + | 31.3386i | −0.700636 | + | 1.21617i | ||||
\(665\) | 29.4807i | 1.14321i | ||||||||
\(666\) | 6.86989 | − | 15.4082i | 0.266203 | − | 0.597055i | ||||
\(667\) | −8.53054 | −0.330304 | ||||||||
\(668\) | 26.2449 | − | 22.0501i | 1.01545 | − | 0.853144i | ||||
\(669\) | 2.79715 | + | 6.59737i | 0.108144 | + | 0.255069i | ||||
\(670\) | 6.71566 | + | 18.4332i | 0.259448 | + | 0.712136i | ||||
\(671\) | −26.3872 | −1.01867 | ||||||||
\(672\) | 12.2281 | + | 18.7826i | 0.471710 | + | 0.724554i | ||||
\(673\) | 9.31167 | 0.358939 | 0.179469 | − | 0.983764i | \(-0.442562\pi\) | ||||
0.179469 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(674\) | −7.35434 | − | 20.1862i | −0.283279 | − | 0.777545i | ||||
\(675\) | 4.11626 | − | 10.6830i | 0.158435 | − | 0.411189i | ||||
\(676\) | 13.0247 | − | 10.9429i | 0.500950 | − | 0.420882i | ||||
\(677\) | 15.7282 | 0.604482 | 0.302241 | − | 0.953231i | \(-0.402265\pi\) | ||||
0.302241 | + | 0.953231i | \(0.402265\pi\) | |||||||
\(678\) | −6.61119 | + | 6.16371i | −0.253901 | + | 0.236716i | ||||
\(679\) | 19.6364i | 0.753574i | ||||||||
\(680\) | 7.33017 | − | 12.7238i | 0.281099 | − | 0.487935i | ||||
\(681\) | −7.51285 | − | 17.7199i | −0.287893 | − | 0.679026i | ||||
\(682\) | −11.1086 | − | 30.4909i | −0.425370 | − | 1.16756i | ||||
\(683\) | 29.9693i | 1.14674i | 0.819295 | + | 0.573372i | \(0.194365\pi\) | ||||
−0.819295 | + | 0.573372i | \(0.805635\pi\) | |||||||
\(684\) | −3.23538 | + | 46.1261i | −0.123708 | + | 1.76368i | ||||
\(685\) | − | 30.3813i | − | 1.16081i | ||||||
\(686\) | 26.6491 | − | 9.70892i | 1.01747 | − | 0.370688i | ||||
\(687\) | −5.63585 | − | 13.2927i | −0.215021 | − | 0.507150i | ||||
\(688\) | 5.26010 | − | 30.0513i | 0.200539 | − | 1.14570i | ||||
\(689\) | − | 1.98436i | − | 0.0755980i | ||||||
\(690\) | 2.79340 | + | 2.99620i | 0.106343 | + | 0.114063i | ||||
\(691\) | 10.7673 | 0.409606 | 0.204803 | − | 0.978803i | \(-0.434345\pi\) | ||||
0.204803 | + | 0.978803i | \(0.434345\pi\) | |||||||
\(692\) | −30.6958 | + | 25.7896i | −1.16688 | + | 0.980373i | ||||
\(693\) | −13.8870 | + | 14.3563i | −0.527524 | + | 0.545350i | ||||
\(694\) | −23.7690 | + | 8.65962i | −0.902257 | + | 0.328714i | ||||
\(695\) | 7.79023 | 0.295500 | ||||||||
\(696\) | −41.4821 | − | 5.07153i | −1.57237 | − | 0.192236i | ||||
\(697\) | −15.5617 | −0.589441 | ||||||||
\(698\) | 8.74597 | − | 3.18637i | 0.331040 | − | 0.120606i | ||||
\(699\) | −1.31378 | − | 3.09868i | −0.0496916 | − | 0.117203i | ||||
\(700\) | −6.48398 | − | 7.71750i | −0.245072 | − | 0.291694i | ||||
\(701\) | 39.5604 | 1.49417 | 0.747087 | − | 0.664726i | \(-0.231452\pi\) | ||||
0.747087 | + | 0.664726i | \(0.231452\pi\) | |||||||
\(702\) | 0.626999 | − | 34.0722i | 0.0236646 | − | 1.28597i | ||||
\(703\) | − | 30.6442i | − | 1.15577i | ||||||
\(704\) | 20.1436 | − | 11.6804i | 0.759191 | − | 0.440221i | ||||
\(705\) | 12.3143 | − | 5.22101i | 0.463783 | − | 0.196635i | ||||
\(706\) | −26.4963 | + | 9.65326i | −0.997203 | + | 0.363305i | ||||
\(707\) | 45.0305i | 1.69355i | ||||||||
\(708\) | −28.0941 | − | 14.3074i | −1.05584 | − | 0.537704i | ||||
\(709\) | 31.7211i | 1.19131i | 0.803240 | + | 0.595655i | \(0.203108\pi\) | ||||
−0.803240 | + | 0.595655i | \(0.796892\pi\) | |||||||
\(710\) | 3.50902 | + | 9.63157i | 0.131691 | + | 0.361466i | ||||
\(711\) | −13.9300 | − | 13.4747i | −0.522417 | − | 0.505341i | ||||
\(712\) | 6.38319 | − | 11.0800i | 0.239220 | − | 0.415241i | ||||
\(713\) | − | 7.88372i | − | 0.295248i | ||||||
\(714\) | 11.8616 | + | 12.7227i | 0.443908 | + | 0.476135i | ||||
\(715\) | −22.5730 | −0.844183 | ||||||||
\(716\) | 16.7532 | + | 19.9404i | 0.626097 | + | 0.745207i | ||||
\(717\) | −27.1071 | + | 11.4928i | −1.01233 | + | 0.429208i | ||||
\(718\) | 10.1035 | + | 27.7322i | 0.377061 | + | 1.03496i | ||||
\(719\) | 16.6643 | 0.621475 | 0.310737 | − | 0.950496i | \(-0.399424\pi\) | ||||
0.310737 | + | 0.950496i | \(0.399424\pi\) | |||||||
\(720\) | 11.8024 | + | 16.2306i | 0.439849 | + | 0.604877i | ||||
\(721\) | −6.62746 | −0.246819 | ||||||||
\(722\) | 19.5537 | + | 53.6710i | 0.727712 | + | 1.99743i | ||||
\(723\) | −6.65876 | + | 2.82318i | −0.247642 | + | 0.104995i | ||||
\(724\) | 27.6419 | + | 32.9006i | 1.02730 | + | 1.22274i | ||||
\(725\) | 18.7952 | 0.698035 | ||||||||
\(726\) | −4.22297 | − | 4.52956i | −0.156729 | − | 0.168108i | ||||
\(727\) | − | 28.4645i | − | 1.05569i | −0.849341 | − | 0.527845i | \(-0.823000\pi\) | ||
0.849341 | − | 0.527845i | \(-0.177000\pi\) | |||||||
\(728\) | −25.9979 | − | 14.9774i | −0.963548 | − | 0.555100i | ||||
\(729\) | −20.0193 | − | 18.1170i | −0.741457 | − | 0.671000i | ||||
\(730\) | −5.59433 | − | 15.3554i | −0.207056 | − | 0.568327i | ||||
\(731\) | − | 23.6776i | − | 0.875748i | ||||||
\(732\) | −27.9848 | − | 14.2517i | −1.03435 | − | 0.526758i | ||||
\(733\) | 19.2342i | 0.710431i | 0.934785 | + | 0.355215i | \(0.115592\pi\) | ||||
−0.934785 | + | 0.355215i | \(0.884408\pi\) | |||||||
\(734\) | −38.1962 | + | 13.9158i | −1.40985 | + | 0.513642i | ||||
\(735\) | 4.71377 | − | 1.99854i | 0.173870 | − | 0.0737173i | ||||
\(736\) | 5.56937 | − | 0.991014i | 0.205290 | − | 0.0365293i | ||||
\(737\) | 24.1442i | 0.889362i | ||||||||
\(738\) | 8.66041 | − | 19.4240i | 0.318794 | − | 0.715009i | ||||
\(739\) | −21.7895 | −0.801538 | −0.400769 | − | 0.916179i | \(-0.631257\pi\) | ||||
−0.400769 | + | 0.916179i | \(0.631257\pi\) | |||||||
\(740\) | −8.55525 | − | 10.1828i | −0.314497 | − | 0.374327i | ||||
\(741\) | −24.1628 | − | 56.9906i | −0.887644 | − | 2.09360i | ||||
\(742\) | −1.30060 | + | 0.473842i | −0.0477467 | + | 0.0173953i | ||||
\(743\) | 24.4226 | 0.895980 | 0.447990 | − | 0.894039i | \(-0.352140\pi\) | ||||
0.447990 | + | 0.894039i | \(0.352140\pi\) | |||||||
\(744\) | 4.68698 | − | 38.3367i | 0.171833 | − | 1.40549i | ||||
\(745\) | 24.6562 | 0.903334 | ||||||||
\(746\) | −2.81729 | + | 1.02641i | −0.103148 | + | 0.0375794i | ||||
\(747\) | −27.5722 | − | 26.6709i | −1.00881 | − | 0.975838i | ||||
\(748\) | 13.8365 | − | 11.6249i | 0.505911 | − | 0.425050i | ||||
\(749\) | −6.25555 | −0.228573 | ||||||||
\(750\) | −20.1217 | − | 21.5825i | −0.734739 | − | 0.788081i | ||||
\(751\) | 13.8921i | 0.506931i | 0.967344 | + | 0.253465i | \(0.0815704\pi\) | ||||
−0.967344 | + | 0.253465i | \(0.918430\pi\) | |||||||
\(752\) | 3.18463 | − | 18.1940i | 0.116131 | − | 0.663467i | ||||
\(753\) | −1.64017 | − | 3.86851i | −0.0597710 | − | 0.140976i | ||||
\(754\) | 52.5660 | − | 19.1511i | 1.91434 | − | 0.697442i | ||||
\(755\) | − | 14.8662i | − | 0.541035i | ||||||
\(756\) | −22.4816 | + | 7.72511i | −0.817649 | + | 0.280960i | ||||
\(757\) | − | 8.05974i | − | 0.292936i | −0.989215 | − | 0.146468i | \(-0.953209\pi\) | ||
0.989215 | − | 0.146468i | \(-0.0467906\pi\) | |||||||
\(758\) | −8.49243 | − | 23.3101i | −0.308459 | − | 0.846660i | ||||
\(759\) | 1.96787 | + | 4.64143i | 0.0714293 | + | 0.168473i | ||||
\(760\) | 31.5862 | + | 18.1968i | 1.14575 | + | 0.660066i | ||||
\(761\) | − | 18.9559i | − | 0.687151i | −0.939125 | − | 0.343576i | \(-0.888362\pi\) | ||
0.939125 | − | 0.343576i | \(-0.111638\pi\) | |||||||
\(762\) | 6.26599 | − | 5.84187i | 0.226993 | − | 0.211629i | ||||
\(763\) | 42.3206 | 1.53211 | ||||||||
\(764\) | −34.1277 | + | 28.6729i | −1.23470 | + | 1.03735i | ||||
\(765\) | 11.1946 | + | 10.8287i | 0.404742 | + | 0.391512i | ||||
\(766\) | 6.58892 | + | 18.0853i | 0.238067 | + | 0.653448i | ||||
\(767\) | 42.2061 | 1.52397 | ||||||||
\(768\) | 27.6718 | − | 1.50801i | 0.998518 | − | 0.0544155i | ||||
\(769\) | 33.9584 | 1.22457 | 0.612286 | − | 0.790636i | \(-0.290250\pi\) | ||||
0.612286 | + | 0.790636i | \(0.290250\pi\) | |||||||
\(770\) | 5.39018 | + | 14.7950i | 0.194249 | + | 0.533175i | ||||
\(771\) | 4.13362 | + | 9.74959i | 0.148869 | + | 0.351123i | ||||
\(772\) | −8.77181 | + | 7.36978i | −0.315704 | + | 0.265244i | ||||
\(773\) | −2.59044 | −0.0931716 | −0.0465858 | − | 0.998914i | \(-0.514834\pi\) | ||||
−0.0465858 | + | 0.998914i | \(0.514834\pi\) | |||||||
\(774\) | 29.5543 | + | 13.1771i | 1.06231 | + | 0.473641i | ||||
\(775\) | 17.3700i | 0.623950i | ||||||||
\(776\) | 21.0388 | + | 12.1204i | 0.755248 | + | 0.435098i | ||||
\(777\) | 14.5045 | − | 6.14960i | 0.520345 | − | 0.220616i | ||||
\(778\) | −4.58453 | − | 12.5836i | −0.164363 | − | 0.451145i | ||||
\(779\) | − | 38.6311i | − | 1.38410i | ||||||
\(780\) | −23.9397 | − | 12.1917i | −0.857179 | − | 0.436532i | ||||
\(781\) | 12.6156i | 0.451423i | ||||||||
\(782\) | 4.12508 | − | 1.50287i | 0.147513 | − | 0.0537425i | ||||
\(783\) | 15.9371 | − | 41.3619i | 0.569546 | − | 1.47815i | ||||
\(784\) | 1.21904 | − | 6.96445i | 0.0435370 | − | 0.248730i | ||||
\(785\) | − | 13.4585i | − | 0.480356i | ||||||
\(786\) | 4.65224 | − | 4.33735i | 0.165940 | − | 0.154708i | ||||
\(787\) | 22.7336 | 0.810365 | 0.405182 | − | 0.914236i | \(-0.367208\pi\) | ||||
0.405182 | + | 0.914236i | \(0.367208\pi\) | |||||||
\(788\) | −19.0209 | + | 15.9807i | −0.677592 | + | 0.569290i | ||||
\(789\) | 9.81340 | − | 4.16068i | 0.349366 | − | 0.148124i | ||||
\(790\) | −14.3557 | + | 5.23015i | −0.510754 | + | 0.186080i | ||||
\(791\) | −8.44081 | −0.300121 | ||||||||
\(792\) | 6.80992 | + | 23.7402i | 0.241980 | + | 0.843570i | ||||
\(793\) | 42.0419 | 1.49295 | ||||||||
\(794\) | 29.3405 | − | 10.6895i | 1.04125 | − | 0.379355i | ||||
\(795\) | −1.14112 | + | 0.483811i | −0.0404713 | + | 0.0171590i | ||||
\(796\) | 18.3539 | + | 21.8455i | 0.650536 | + | 0.774295i | ||||
\(797\) | −44.9272 | −1.59140 | −0.795702 | − | 0.605689i | \(-0.792898\pi\) | ||||
−0.795702 | + | 0.605689i | \(0.792898\pi\) | |||||||
\(798\) | −31.5834 | + | 29.4457i | −1.11804 | + | 1.04237i | ||||
\(799\) | − | 14.3352i | − | 0.507141i | ||||||
\(800\) | −12.2709 | + | 2.18348i | −0.433841 | + | 0.0771977i | ||||
\(801\) | 9.74838 | + | 9.42973i | 0.344442 | + | 0.333183i | ||||
\(802\) | 20.6464 | − | 7.52199i | 0.729050 | − | 0.265611i | ||||
\(803\) | − | 20.1128i | − | 0.709765i | ||||||
\(804\) | −13.0403 | + | 25.6060i | −0.459895 | + | 0.903053i | ||||
\(805\) | 3.82539i | 0.134827i | ||||||||
\(806\) | 17.6990 | + | 48.5803i | 0.623420 | + | 1.71117i | ||||
\(807\) | −32.6415 | + | 13.8393i | −1.14903 | + | 0.487167i | ||||
\(808\) | 48.2466 | + | 27.7948i | 1.69731 | + | 0.977819i | ||||
\(809\) | − | 37.6032i | − | 1.32206i | −0.750361 | − | 0.661028i | \(-0.770120\pi\) | ||
0.750361 | − | 0.661028i | \(-0.229880\pi\) | |||||||
\(810\) | −19.7464 | + | 7.94668i | −0.693817 | + | 0.279218i | ||||
\(811\) | 9.33068 | 0.327644 | 0.163822 | − | 0.986490i | \(-0.447618\pi\) | ||||
0.163822 | + | 0.986490i | \(0.447618\pi\) | |||||||
\(812\) | −25.1044 | − | 29.8802i | −0.880990 | − | 1.04859i | ||||
\(813\) | −3.90835 | − | 9.21825i | −0.137072 | − | 0.323298i | ||||
\(814\) | −5.60293 | − | 15.3789i | −0.196382 | − | 0.539032i | ||||
\(815\) | 13.7603 | 0.482001 | ||||||||
\(816\) | 20.9528 | − | 4.85569i | 0.733495 | − | 0.169983i | ||||
\(817\) | 58.7785 | 2.05640 | ||||||||
\(818\) | −13.2223 | − | 36.2927i | −0.462308 | − | 1.26894i | ||||
\(819\) | 22.1258 | − | 22.8734i | 0.773137 | − | 0.799262i | ||||
\(820\) | −10.7850 | − | 12.8368i | −0.376629 | − | 0.448279i | ||||
\(821\) | −32.4718 | −1.13327 | −0.566636 | − | 0.823968i | \(-0.691756\pi\) | ||||
−0.566636 | + | 0.823968i | \(0.691756\pi\) | |||||||
\(822\) | 32.5483 | − | 30.3452i | 1.13525 | − | 1.05841i | ||||
\(823\) | − | 32.3017i | − | 1.12597i | −0.826468 | − | 0.562983i | \(-0.809653\pi\) | ||
0.826468 | − | 0.562983i | \(-0.190347\pi\) | |||||||
\(824\) | −4.09076 | + | 7.10078i | −0.142508 | + | 0.247368i | ||||
\(825\) | −4.33577 | − | 10.2264i | −0.150952 | − | 0.356037i | ||||
\(826\) | −10.0783 | − | 27.6631i | −0.350670 | − | 0.962521i | ||||
\(827\) | 47.3767i | 1.64745i | 0.566989 | + | 0.823725i | \(0.308108\pi\) | ||||
−0.566989 | + | 0.823725i | \(0.691892\pi\) | |||||||
\(828\) | −0.419820 | + | 5.98529i | −0.0145898 | + | 0.208003i | ||||
\(829\) | 10.6496i | 0.369875i | 0.982750 | + | 0.184937i | \(0.0592082\pi\) | ||||
−0.982750 | + | 0.184937i | \(0.940792\pi\) | |||||||
\(830\) | −28.4148 | + | 10.3522i | −0.986291 | + | 0.359330i | ||||
\(831\) | 4.68528 | + | 11.0507i | 0.162531 | + | 0.383346i | ||||
\(832\) | −32.0942 | + | 18.6100i | −1.11267 | + | 0.645185i | ||||
\(833\) | − | 5.48733i | − | 0.190125i | ||||||
\(834\) | 7.78099 | + | 8.34588i | 0.269434 | + | 0.288994i | ||||
\(835\) | 28.6625 | 0.991906 | ||||||||
\(836\) | 28.8583 | + | 34.3483i | 0.998085 | + | 1.18796i | ||||
\(837\) | 38.2256 | + | 14.7287i | 1.32127 | + | 0.509098i | ||||
\(838\) | 34.7915 | − | 12.6754i | 1.20185 | − | 0.437865i | ||||
\(839\) | −48.9856 | −1.69117 | −0.845585 | − | 0.533841i | \(-0.820748\pi\) | ||||
−0.845585 | + | 0.533841i | \(0.820748\pi\) | |||||||
\(840\) | −2.27425 | + | 18.6020i | −0.0784690 | + | 0.641830i | ||||
\(841\) | 43.7702 | 1.50932 | ||||||||
\(842\) | 17.4882 | − | 6.37139i | 0.602684 | − | 0.219573i | ||||
\(843\) | −4.60339 | − | 10.8576i | −0.158549 | − | 0.373955i | ||||
\(844\) | 38.8190 | − | 32.6144i | 1.33621 | − | 1.12263i | ||||
\(845\) | 14.2245 | 0.489337 | ||||||||
\(846\) | 17.8931 | + | 7.97782i | 0.615178 | + | 0.274283i | ||||
\(847\) | − | 5.78310i | − | 0.198710i | ||||||
\(848\) | −0.295107 | + | 1.68597i | −0.0101340 | + | 0.0578964i | ||||
\(849\) | −37.0273 | + | 15.6988i | −1.27077 | + | 0.538782i | ||||
\(850\) | −9.08871 | + | 3.31124i | −0.311740 | + | 0.113575i | ||||
\(851\) | − | 3.97637i | − | 0.136308i | ||||||
\(852\) | −6.81370 | + | 13.3795i | −0.233434 | + | 0.458372i | ||||
\(853\) | − | 7.48762i | − | 0.256371i | −0.991750 | − | 0.128186i | \(-0.959085\pi\) | ||
0.991750 | − | 0.128186i | \(-0.0409153\pi\) | |||||||
\(854\) | −10.0391 | − | 27.5554i | −0.343532 | − | 0.942928i | ||||
\(855\) | −26.8817 | + | 27.7900i | −0.919333 | + | 0.950399i | ||||
\(856\) | −3.86120 | + | 6.70231i | −0.131973 | + | 0.229080i | ||||
\(857\) | 21.3312i | 0.728659i | 0.931270 | + | 0.364330i | \(0.118702\pi\) | ||||
−0.931270 | + | 0.364330i | \(0.881298\pi\) | |||||||
\(858\) | −22.5463 | − | 24.1831i | −0.769717 | − | 0.825597i | ||||
\(859\) | 35.6085 | 1.21495 | 0.607474 | − | 0.794340i | \(-0.292183\pi\) | ||||
0.607474 | + | 0.794340i | \(0.292183\pi\) | |||||||
\(860\) | 19.5316 | − | 16.4098i | 0.666021 | − | 0.559568i | ||||
\(861\) | 18.2848 | − | 7.75238i | 0.623145 | − | 0.264201i | ||||
\(862\) | 4.81588 | + | 13.2187i | 0.164030 | + | 0.450229i | ||||
\(863\) | 16.0883 | 0.547653 | 0.273827 | − | 0.961779i | \(-0.411711\pi\) | ||||
0.273827 | + | 0.961779i | \(0.411711\pi\) | |||||||
\(864\) | −5.59983 | + | 28.8555i | −0.190510 | + | 0.981685i | ||||
\(865\) | −33.5234 | −1.13983 | ||||||||
\(866\) | −0.993641 | − | 2.72735i | −0.0337653 | − | 0.0926792i | ||||
\(867\) | −11.7406 | + | 4.97779i | −0.398733 | + | 0.169055i | ||||
\(868\) | 27.6146 | − | 23.2008i | 0.937299 | − | 0.787487i | ||||
\(869\) | −18.8035 | −0.637864 | ||||||||
\(870\) | −23.8292 | − | 25.5592i | −0.807887 | − | 0.866539i | ||||
\(871\) | − | 38.4682i | − | 1.30344i | ||||||
\(872\) | 26.1222 | − | 45.3431i | 0.884608 | − | 1.53551i | ||||
\(873\) | −17.9052 | + | 18.5103i | −0.606000 | + | 0.626478i | ||||
\(874\) | 3.73079 | + | 10.2403i | 0.126196 | + | 0.346384i | ||||
\(875\) | − | 27.5554i | − | 0.931541i | ||||||
\(876\) | 10.8629 | − | 21.3305i | 0.367024 | − | 0.720691i | ||||
\(877\) | − | 30.9575i | − | 1.04536i | −0.852529 | − | 0.522680i | \(-0.824932\pi\) | ||
0.852529 | − | 0.522680i | \(-0.175068\pi\) | |||||||
\(878\) | 43.2740 | − | 15.7658i | 1.46043 | − | 0.532070i | ||||
\(879\) | 7.06575 | − | 2.99573i | 0.238322 | − | 0.101044i | ||||
\(880\) | 19.1787 | + | 3.35699i | 0.646514 | + | 0.113164i | ||||
\(881\) | 35.0906i | 1.18223i | 0.806586 | + | 0.591116i | \(0.201313\pi\) | ||||
−0.806586 | + | 0.591116i | \(0.798687\pi\) | |||||||
\(882\) | 6.84927 | + | 3.05382i | 0.230627 | + | 0.102827i | ||||
\(883\) | −30.4343 | −1.02420 | −0.512098 | − | 0.858927i | \(-0.671131\pi\) | ||||
−0.512098 | + | 0.858927i | \(0.671131\pi\) | |||||||
\(884\) | −22.0452 | + | 18.5216i | −0.741461 | + | 0.622950i | ||||
\(885\) | −10.2904 | − | 24.2709i | −0.345907 | − | 0.815858i | ||||
\(886\) | −21.8107 | + | 7.94619i | −0.732746 | + | 0.266957i | ||||
\(887\) | 35.1003 | 1.17855 | 0.589277 | − | 0.807931i | \(-0.299413\pi\) | ||||
0.589277 | + | 0.807931i | \(0.299413\pi\) | |||||||
\(888\) | 2.36401 | − | 19.3362i | 0.0793309 | − | 0.648880i | ||||
\(889\) | 8.00008 | 0.268314 | ||||||||
\(890\) | 10.0463 | − | 3.66011i | 0.336752 | − | 0.122687i | ||||
\(891\) | −26.1813 | + | 0.870253i | −0.877106 | + | 0.0291546i | ||||
\(892\) | 5.32265 | + | 6.33524i | 0.178216 | + | 0.212119i | ||||
\(893\) | 35.5863 | 1.19085 | ||||||||
\(894\) | 24.6270 | + | 26.4149i | 0.823649 | + | 0.883445i | ||||
\(895\) | 21.7772i | 0.727931i | ||||||||
\(896\) | 19.8612 | + | 16.5916i | 0.663517 | + | 0.554286i | ||||
\(897\) | −3.13535 | − | 7.39505i | −0.104686 | − | 0.246914i | ||||
\(898\) | −40.7633 | + | 14.8511i | −1.36029 | + | 0.495586i | ||||
\(899\) | 67.2524i | 2.24299i | ||||||||
\(900\) | 0.924981 | − | 13.1873i | 0.0308327 | − | 0.439576i | ||||
\(901\) | 1.32838i | 0.0442549i | ||||||||
\(902\) | −7.06323 | − | 19.3872i | −0.235180 | − | 0.645523i | ||||
\(903\) | 11.7955 | + | 27.8210i | 0.392530 | + | 0.925823i | ||||
\(904\) | −5.21004 | + | 9.04365i | −0.173283 | + | 0.300787i | ||||
\(905\) | 35.9312i | 1.19439i | ||||||||
\(906\) | 15.9265 | − | 14.8485i | 0.529123 | − | 0.493309i | ||||
\(907\) | −6.22500 | −0.206698 | −0.103349 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103349 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(908\) | −14.2961 | − | 17.0158i | −0.474432 | − | 0.564689i | ||||
\(909\) | −41.0606 | + | 42.4482i | −1.36190 | + | 1.40792i | ||||
\(910\) | −8.58801 | − | 23.5724i | −0.284690 | − | 0.781418i | ||||
\(911\) | 12.2456 | 0.405714 | 0.202857 | − | 0.979208i | \(-0.434977\pi\) | ||||
0.202857 | + | 0.979208i | \(0.434977\pi\) | |||||||
\(912\) | 12.0540 | + | 52.0143i | 0.399148 | + | 1.72237i | ||||
\(913\) | −37.2183 | −1.23175 | ||||||||
\(914\) | −10.3765 | − | 28.4816i | −0.343226 | − | 0.942088i | ||||
\(915\) | −10.2503 | − | 24.1765i | −0.338866 | − | 0.799250i | ||||
\(916\) | −10.7244 | − | 12.7646i | −0.354343 | − | 0.421754i | ||||
\(917\) | 5.93973 | 0.196147 | ||||||||
\(918\) | −0.419731 | + | 22.8089i | −0.0138532 | + | 0.752806i | ||||
\(919\) | − | 23.4762i | − | 0.774407i | −0.921994 | − | 0.387203i | \(-0.873441\pi\) | ||
0.921994 | − | 0.387203i | \(-0.126559\pi\) | |||||||
\(920\) | 4.09860 | + | 2.36120i | 0.135127 | + | 0.0778465i | ||||
\(921\) | −39.1120 | + | 16.5827i | −1.28878 | + | 0.546418i | ||||
\(922\) | −4.63491 | − | 12.7219i | −0.152643 | − | 0.418974i | ||||
\(923\) | − | 20.1001i | − | 0.661603i | ||||||
\(924\) | −10.4665 | + | 20.5521i | −0.344322 | + | 0.676115i | ||||
\(925\) | 8.76106i | 0.288062i | ||||||||
\(926\) | −30.5956 | + | 11.1467i | −1.00543 | + | 0.366305i | ||||
\(927\) | −6.24739 | − | 6.04318i | −0.205191 | − | 0.198484i | ||||
\(928\) | −47.5098 | + | 8.45389i | −1.55958 | + | 0.277513i | ||||
\(929\) | 8.59904i | 0.282126i | 0.990001 | + | 0.141063i | \(0.0450519\pi\) | ||||
−0.990001 | + | 0.141063i | \(0.954948\pi\) | |||||||
\(930\) | 23.6212 | − | 22.0224i | 0.774570 | − | 0.722143i | ||||
\(931\) | 13.6220 | 0.446443 | ||||||||
\(932\) | −2.49997 | − | 2.97556i | −0.0818891 | − | 0.0974678i | ||||
\(933\) | 10.2982 | − | 4.36623i | 0.337148 | − | 0.142944i | ||||
\(934\) | 42.3161 | − | 15.4168i | 1.38463 | − | 0.504453i | ||||
\(935\) | 15.1110 | 0.494183 | ||||||||
\(936\) | −10.8500 | − | 37.8245i | −0.354644 | − | 1.23633i | ||||
\(937\) | 40.6559 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(938\) | −25.2131 | + | 9.18576i | −0.823238 | + | 0.299926i | ||||
\(939\) | 1.70476 | − | 0.722784i | 0.0556328 | − | 0.0235872i | ||||
\(940\) | 11.8250 | − | 9.93498i | 0.385689 | − | 0.324043i | ||||
\(941\) | −11.6231 | −0.378901 | −0.189450 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189450 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(942\) | 14.4185 | − | 13.4426i | 0.469780 | − | 0.437983i | ||||
\(943\) | − | 5.01274i | − | 0.163237i | ||||||
\(944\) | −35.8595 | − | 6.27675i | −1.16713 | − | 0.204291i | ||||
\(945\) | −18.5481 | − | 7.14676i | −0.603369 | − | 0.232484i | ||||
\(946\) | 29.4982 | − | 10.7469i | 0.959071 | − | 0.349413i | ||||
\(947\) | − | 30.2719i | − | 0.983705i | −0.870678 | − | 0.491853i | \(-0.836320\pi\) | ||
0.870678 | − | 0.491853i | \(-0.163680\pi\) | |||||||
\(948\) | −19.9419 | − | 10.1557i | −0.647683 | − | 0.329843i | ||||
\(949\) | 32.0451i | 1.04023i | ||||||||
\(950\) | −8.21999 | − | 22.5623i | −0.266692 | − | 0.732017i | ||||
\(951\) | 8.93023 | − | 3.78623i | 0.289583 | − | 0.122777i | ||||
\(952\) | 17.4038 | + | 10.0263i | 0.564059 | + | 0.324954i | ||||
\(953\) | − | 2.66840i | − | 0.0864379i | −0.999066 | − | 0.0432189i | \(-0.986239\pi\) | ||
0.999066 | − | 0.0432189i | \(-0.0137613\pi\) | |||||||
\(954\) | −1.65809 | − | 0.739274i | −0.0536825 | − | 0.0239349i | ||||
\(955\) | −37.2714 | −1.20607 | ||||||||
\(956\) | −26.0300 | + | 21.8695i | −0.841871 | + | 0.707311i | ||||
\(957\) | −16.7870 | − | 39.5940i | −0.542647 | − | 1.27989i | ||||
\(958\) | −4.11916 | − | 11.3063i | −0.133084 | − | 0.365290i | ||||
\(959\) | 41.5559 | 1.34191 | ||||||||
\(960\) | 18.5268 | + | 13.9187i | 0.597949 | + | 0.449223i | ||||
\(961\) | −31.1530 | −1.00494 | ||||||||
\(962\) | 8.92697 | + | 24.5028i | 0.287817 | + | 0.790002i | ||||
\(963\) | −5.89681 | − | 5.70406i | −0.190022 | − | 0.183811i | ||||
\(964\) | −6.39419 | + | 5.37218i | −0.205943 | + | 0.173026i | ||||
\(965\) | −9.57983 | −0.308386 | ||||||||
\(966\) | −4.09824 | + | 3.82085i | −0.131859 | + | 0.122934i | ||||
\(967\) | − | 41.6296i | − | 1.33872i | −0.742939 | − | 0.669359i | \(-0.766569\pi\) | ||
0.742939 | − | 0.669359i | \(-0.233431\pi\) | |||||||
\(968\) | −6.19612 | − | 3.56959i | −0.199151 | − | 0.114731i | ||||
\(969\) | 16.1753 | + | 38.1511i | 0.519625 | + | 1.22559i | ||||
\(970\) | 6.94983 | + | 19.0759i | 0.223145 | + | 0.612491i | ||||
\(971\) | 31.1228i | 0.998778i | 0.866378 | + | 0.499389i | \(0.166442\pi\) | ||||
−0.866378 | + | 0.499389i | \(0.833558\pi\) | |||||||
\(972\) | −28.2364 | − | 13.2176i | −0.905684 | − | 0.423953i | ||||
\(973\) | 10.6556i | 0.341602i | ||||||||
\(974\) | −13.6092 | + | 4.95815i | −0.436066 | + | 0.158869i | ||||
\(975\) | 6.90805 | + | 16.2934i | 0.221235 | + | 0.521806i | ||||
\(976\) | −35.7200 | − | 6.25233i | −1.14337 | − | 0.200132i | ||||
\(977\) | 20.3893i | 0.652312i | 0.945316 | + | 0.326156i | \(0.105753\pi\) | ||||
−0.945316 | + | 0.326156i | \(0.894247\pi\) | |||||||
\(978\) | 13.7439 | + | 14.7417i | 0.439483 | + | 0.471389i | ||||
\(979\) | 13.1588 | 0.420558 | ||||||||
\(980\) | 4.52647 | − | 3.80299i | 0.144593 | − | 0.121482i | ||||
\(981\) | 39.8937 | + | 38.5896i | 1.27371 | + | 1.23207i | ||||
\(982\) | 42.9395 | − | 15.6439i | 1.37026 | − | 0.499218i | ||||
\(983\) | −54.2769 | −1.73116 | −0.865582 | − | 0.500766i | \(-0.833052\pi\) | ||||
−0.865582 | + | 0.500766i | \(0.833052\pi\) | |||||||
\(984\) | 2.98014 | − | 24.3758i | 0.0950035 | − | 0.777073i | ||||
\(985\) | −20.7731 | −0.661884 | ||||||||
\(986\) | −35.1892 | + | 12.8203i | −1.12065 | + | 0.408281i | ||||
\(987\) | 7.14137 | + | 16.8437i | 0.227312 | + | 0.536140i | ||||
\(988\) | −45.9790 | − | 54.7261i | −1.46279 | − | 1.74107i | ||||
\(989\) | 7.62705 | 0.242526 | ||||||||
\(990\) | −8.40961 | + | 18.8615i | −0.267275 | + | 0.599459i | ||||
\(991\) | − | 50.6391i | − | 1.60861i | −0.594220 | − | 0.804303i | \(-0.702539\pi\) | ||
0.594220 | − | 0.804303i | \(-0.297461\pi\) | |||||||
\(992\) | −7.81288 | − | 43.9074i | −0.248059 | − | 1.39406i | ||||
\(993\) | 6.31122 | − | 2.67583i | 0.200281 | − | 0.0849148i | ||||
\(994\) | −13.1742 | + | 4.79968i | −0.417860 | + | 0.152237i | ||||
\(995\) | 23.8579i | 0.756345i | ||||||||
\(996\) | −39.4717 | − | 20.1016i | −1.25071 | − | 0.636943i | ||||
\(997\) | 42.5149i | 1.34646i | 0.739433 | + | 0.673230i | \(0.235094\pi\) | ||||
−0.739433 | + | 0.673230i | \(0.764906\pi\) | |||||||
\(998\) | −20.5866 | − | 56.5062i | −0.651657 | − | 1.78867i | ||||
\(999\) | 19.2801 | + | 7.42883i | 0.609997 | + | 0.235038i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 552.2.j.d.323.24 | yes | 42 | |
3.2 | odd | 2 | 552.2.j.c.323.19 | ✓ | 42 | ||
4.3 | odd | 2 | 2208.2.j.d.47.37 | 42 | |||
8.3 | odd | 2 | 552.2.j.c.323.20 | yes | 42 | ||
8.5 | even | 2 | 2208.2.j.c.47.37 | 42 | |||
12.11 | even | 2 | 2208.2.j.c.47.38 | 42 | |||
24.5 | odd | 2 | 2208.2.j.d.47.38 | 42 | |||
24.11 | even | 2 | inner | 552.2.j.d.323.23 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.j.c.323.19 | ✓ | 42 | 3.2 | odd | 2 | ||
552.2.j.c.323.20 | yes | 42 | 8.3 | odd | 2 | ||
552.2.j.d.323.23 | yes | 42 | 24.11 | even | 2 | inner | |
552.2.j.d.323.24 | yes | 42 | 1.1 | even | 1 | trivial | |
2208.2.j.c.47.37 | 42 | 8.5 | even | 2 | |||
2208.2.j.c.47.38 | 42 | 12.11 | even | 2 | |||
2208.2.j.d.47.37 | 42 | 4.3 | odd | 2 | |||
2208.2.j.d.47.38 | 42 | 24.5 | odd | 2 |