Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [555,2,Mod(454,555)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(555, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("555.454");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 555 = 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 555.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.43169731218\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 454.18 | ||
Character | \(\chi\) | \(=\) | 555.454 |
Dual form | 555.2.bb.a.544.18 |
$q$-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 \(\left(\mathbb{Z}/555\mathbb{Z}\right)^\times\).
\(n\) | \(76\) | \(112\) | \(371\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.113794 | − | 0.0656990i | −0.0804645 | − | 0.0464562i | 0.459228 | − | 0.888318i | \(-0.348126\pi\) |
−0.539692 | + | 0.841862i | \(0.681459\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.991367 | − | 1.71710i | −0.495684 | − | 0.858549i | ||||
\(5\) | 0.217380 | − | 2.22548i | 0.0972155 | − | 0.995263i | ||||
\(6\) | 0.131398 | 0.0536430 | ||||||||
\(7\) | −1.67003 | + | 0.964193i | −0.631213 | + | 0.364431i | −0.781222 | − | 0.624254i | \(-0.785403\pi\) |
0.150009 | + | 0.988685i | \(0.452070\pi\) | |||||||
\(8\) | 0.523323i | 0.185023i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.170948 | + | 0.238964i | −0.0540585 | + | 0.0755671i | ||||
\(11\) | −4.70575 | −1.41884 | −0.709418 | − | 0.704788i | \(-0.751042\pi\) | ||||
−0.709418 | + | 0.704788i | \(0.751042\pi\) | |||||||
\(12\) | 1.71710 | + | 0.991367i | 0.495684 | + | 0.286183i | ||||
\(13\) | 0.630070 | − | 0.363771i | 0.174750 | − | 0.100892i | −0.410074 | − | 0.912052i | \(-0.634497\pi\) |
0.584824 | + | 0.811160i | \(0.301164\pi\) | |||||||
\(14\) | 0.253386 | 0.0677203 | ||||||||
\(15\) | 0.924481 | + | 2.03601i | 0.238700 | + | 0.525695i | ||||
\(16\) | −1.94835 | + | 3.37465i | −0.487088 | + | 0.843661i | ||||
\(17\) | 2.98832 | + | 1.72531i | 0.724775 | + | 0.418449i | 0.816508 | − | 0.577335i | \(-0.195907\pi\) |
−0.0917325 | + | 0.995784i | \(0.529240\pi\) | |||||||
\(18\) | −0.113794 | + | 0.0656990i | −0.0268215 | + | 0.0154854i | ||||
\(19\) | 1.88651 | + | 3.26753i | 0.432796 | + | 0.749624i | 0.997113 | − | 0.0759341i | \(-0.0241939\pi\) |
−0.564317 | + | 0.825558i | \(0.690861\pi\) | |||||||
\(20\) | −4.03687 | + | 1.83300i | −0.902671 | + | 0.409872i | ||||
\(21\) | 0.964193 | − | 1.67003i | 0.210404 | − | 0.364431i | ||||
\(22\) | 0.535486 | + | 0.309163i | 0.114166 | + | 0.0659138i | ||||
\(23\) | 4.47345i | 0.932778i | 0.884580 | + | 0.466389i | \(0.154445\pi\) | ||||
−0.884580 | + | 0.466389i | \(0.845555\pi\) | |||||||
\(24\) | −0.261662 | − | 0.453211i | −0.0534115 | − | 0.0925113i | ||||
\(25\) | −4.90549 | − | 0.967550i | −0.981098 | − | 0.193510i | ||||
\(26\) | −0.0955976 | −0.0187482 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.31123 | + | 1.91174i | 0.625764 | + | 0.361285i | ||||
\(29\) | 0.0315057 | 0.00585045 | 0.00292523 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292523 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(30\) | 0.0285633 | − | 0.292423i | 0.00521493 | − | 0.0533889i | ||||
\(31\) | −5.76147 | −1.03479 | −0.517395 | − | 0.855747i | \(-0.673098\pi\) | ||||
−0.517395 | + | 0.855747i | \(0.673098\pi\) | |||||||
\(32\) | 1.34984 | − | 0.779333i | 0.238621 | − | 0.137768i | ||||
\(33\) | 4.07530 | − | 2.35287i | 0.709418 | − | 0.409583i | ||||
\(34\) | −0.226702 | − | 0.392660i | −0.0388791 | − | 0.0673406i | ||||
\(35\) | 1.78276 | + | 3.92621i | 0.301341 | + | 0.663651i | ||||
\(36\) | −1.98273 | −0.330456 | ||||||||
\(37\) | −2.34626 | + | 5.61205i | −0.385723 | + | 0.922615i | ||||
\(38\) | − | 0.495768i | − | 0.0804241i | ||||||
\(39\) | −0.363771 | + | 0.630070i | −0.0582500 | + | 0.100892i | ||||
\(40\) | 1.16464 | + | 0.113760i | 0.184146 | + | 0.0179871i | ||||
\(41\) | −4.60419 | − | 7.97469i | −0.719054 | − | 1.24544i | −0.961375 | − | 0.275242i | \(-0.911242\pi\) |
0.242321 | − | 0.970196i | \(-0.422091\pi\) | |||||||
\(42\) | −0.219439 | + | 0.126693i | −0.0338601 | + | 0.0195492i | ||||
\(43\) | 7.05252i | 1.07550i | 0.843104 | + | 0.537750i | \(0.180726\pi\) | ||||
−0.843104 | + | 0.537750i | \(0.819274\pi\) | |||||||
\(44\) | 4.66513 | + | 8.08024i | 0.703294 | + | 1.21814i | ||||
\(45\) | −1.81863 | − | 1.30100i | −0.271105 | − | 0.193941i | ||||
\(46\) | 0.293901 | − | 0.509051i | 0.0433333 | − | 0.0750555i | ||||
\(47\) | − | 0.393644i | − | 0.0574189i | −0.999588 | − | 0.0287095i | \(-0.990860\pi\) | ||
0.999588 | − | 0.0287095i | \(-0.00913976\pi\) | |||||||
\(48\) | − | 3.89671i | − | 0.562441i | ||||||
\(49\) | −1.64066 | + | 2.84171i | −0.234380 | + | 0.405959i | ||||
\(50\) | 0.494648 | + | 0.432387i | 0.0699538 | + | 0.0611488i | ||||
\(51\) | −3.45062 | −0.483183 | ||||||||
\(52\) | −1.24926 | − | 0.721262i | −0.173241 | − | 0.100021i | ||||
\(53\) | −6.17510 | − | 3.56520i | −0.848216 | − | 0.489718i | 0.0118327 | − | 0.999930i | \(-0.496233\pi\) |
−0.860048 | + | 0.510212i | \(0.829567\pi\) | |||||||
\(54\) | 0.0656990 | − | 0.113794i | 0.00894050 | − | 0.0154854i | ||||
\(55\) | −1.02294 | + | 10.4725i | −0.137933 | + | 1.41212i | ||||
\(56\) | −0.504585 | − | 0.873967i | −0.0674280 | − | 0.116789i | ||||
\(57\) | −3.26753 | − | 1.88651i | −0.432796 | − | 0.249875i | ||||
\(58\) | −0.00358515 | − | 0.00206989i | −0.000470754 | − | 0.000271790i | ||||
\(59\) | 3.77054 | − | 6.53076i | 0.490882 | − | 0.850233i | −0.509063 | − | 0.860729i | \(-0.670008\pi\) |
0.999945 | + | 0.0104965i | \(0.00334119\pi\) | |||||||
\(60\) | 2.57953 | − | 3.60586i | 0.333016 | − | 0.465514i | ||||
\(61\) | −2.80510 | − | 4.85857i | −0.359156 | − | 0.622076i | 0.628664 | − | 0.777677i | \(-0.283602\pi\) |
−0.987820 | + | 0.155601i | \(0.950269\pi\) | |||||||
\(62\) | 0.655620 | + | 0.378523i | 0.0832639 | + | 0.0480724i | ||||
\(63\) | 1.92839i | 0.242954i | ||||||||
\(64\) | 7.58861 | 0.948576 | ||||||||
\(65\) | −0.672599 | − | 1.48128i | −0.0834257 | − | 0.183731i | ||||
\(66\) | −0.618326 | −0.0761107 | ||||||||
\(67\) | −10.5416 | + | 6.08619i | −1.28786 | + | 0.743547i | −0.978272 | − | 0.207324i | \(-0.933525\pi\) |
−0.309588 | + | 0.950871i | \(0.600191\pi\) | |||||||
\(68\) | − | 6.84166i | − | 0.829674i | ||||||
\(69\) | −2.23672 | − | 3.87412i | −0.269270 | − | 0.466389i | ||||
\(70\) | 0.0550812 | − | 0.563905i | 0.00658346 | − | 0.0673995i | ||||
\(71\) | −4.60707 | − | 7.97969i | −0.546759 | − | 0.947014i | −0.998494 | − | 0.0548623i | \(-0.982528\pi\) |
0.451735 | − | 0.892152i | \(-0.350805\pi\) | |||||||
\(72\) | 0.453211 | + | 0.261662i | 0.0534115 | + | 0.0308371i | ||||
\(73\) | − | 2.63048i | − | 0.307875i | −0.988081 | − | 0.153937i | \(-0.950805\pi\) | ||
0.988081 | − | 0.153937i | \(-0.0491954\pi\) | |||||||
\(74\) | 0.635696 | − | 0.484470i | 0.0738982 | − | 0.0563185i | ||||
\(75\) | 4.73206 | − | 1.61482i | 0.546411 | − | 0.186464i | ||||
\(76\) | 3.74045 | − | 6.47865i | 0.429059 | − | 0.743153i | ||||
\(77\) | 7.85875 | − | 4.53725i | 0.895588 | − | 0.517068i | ||||
\(78\) | 0.0827899 | − | 0.0477988i | 0.00937412 | − | 0.00541215i | ||||
\(79\) | 3.61265 | + | 6.25729i | 0.406454 | + | 0.704000i | 0.994490 | − | 0.104836i | \(-0.0334316\pi\) |
−0.588035 | + | 0.808835i | \(0.700098\pi\) | |||||||
\(80\) | 7.08666 | + | 5.06960i | 0.792313 | + | 0.566798i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.20996i | 0.133618i | ||||||||
\(83\) | −10.7476 | − | 6.20513i | −1.17970 | − | 0.681101i | −0.223757 | − | 0.974645i | \(-0.571832\pi\) |
−0.955946 | + | 0.293544i | \(0.905165\pi\) | |||||||
\(84\) | −3.82348 | −0.417176 | ||||||||
\(85\) | 4.48924 | − | 6.27540i | 0.486926 | − | 0.680662i | ||||
\(86\) | 0.463344 | − | 0.802535i | 0.0499636 | − | 0.0865395i | ||||
\(87\) | −0.0272847 | + | 0.0157528i | −0.00292523 | + | 0.00168888i | ||||
\(88\) | − | 2.46263i | − | 0.262517i | ||||||
\(89\) | −1.10616 | + | 1.91592i | −0.117252 | + | 0.203087i | −0.918678 | − | 0.395007i | \(-0.870742\pi\) |
0.801425 | + | 0.598095i | \(0.204075\pi\) | |||||||
\(90\) | 0.121475 | + | 0.267527i | 0.0128046 | + | 0.0281999i | ||||
\(91\) | −0.701492 | + | 1.21502i | −0.0735363 | + | 0.127369i | ||||
\(92\) | 7.68135 | − | 4.43483i | 0.800836 | − | 0.462363i | ||||
\(93\) | 4.98958 | − | 2.88073i | 0.517395 | − | 0.298718i | ||||
\(94\) | −0.0258620 | + | 0.0447943i | −0.00266746 | + | 0.00462018i | ||||
\(95\) | 7.68191 | − | 3.48809i | 0.788148 | − | 0.357871i | ||||
\(96\) | −0.779333 | + | 1.34984i | −0.0795403 | + | 0.137768i | ||||
\(97\) | 10.7793i | 1.09447i | 0.836978 | + | 0.547237i | \(0.184320\pi\) | ||||
−0.836978 | + | 0.547237i | \(0.815680\pi\) | |||||||
\(98\) | 0.373395 | − | 0.215580i | 0.0377186 | − | 0.0217768i | ||||
\(99\) | −2.35287 | + | 4.07530i | −0.236473 | + | 0.409583i | ||||
\(100\) | 3.20177 | + | 9.38241i | 0.320177 | + | 0.938241i | ||||
\(101\) | 7.32587 | 0.728951 | 0.364476 | − | 0.931213i | \(-0.381248\pi\) | ||||
0.364476 | + | 0.931213i | \(0.381248\pi\) | |||||||
\(102\) | 0.392660 | + | 0.226702i | 0.0388791 | + | 0.0224469i | ||||
\(103\) | 4.94014i | 0.486766i | 0.969930 | + | 0.243383i | \(0.0782572\pi\) | ||||
−0.969930 | + | 0.243383i | \(0.921743\pi\) | |||||||
\(104\) | 0.190370 | + | 0.329730i | 0.0186673 | + | 0.0323327i | ||||
\(105\) | −3.50702 | − | 2.50882i | −0.342250 | − | 0.244836i | ||||
\(106\) | 0.468460 | + | 0.811396i | 0.0455008 | + | 0.0788098i | ||||
\(107\) | 11.7114 | − | 6.76157i | 1.13218 | − | 0.653665i | 0.187699 | − | 0.982227i | \(-0.439897\pi\) |
0.944483 | + | 0.328561i | \(0.106564\pi\) | |||||||
\(108\) | 1.71710 | − | 0.991367i | 0.165228 | − | 0.0953944i | ||||
\(109\) | 3.63311 | − | 6.29273i | 0.347989 | − | 0.602734i | −0.637903 | − | 0.770117i | \(-0.720198\pi\) |
0.985892 | + | 0.167382i | \(0.0535314\pi\) | |||||||
\(110\) | 0.804439 | − | 1.12451i | 0.0767003 | − | 0.107217i | ||||
\(111\) | −0.774103 | − | 6.03330i | −0.0734746 | − | 0.572656i | ||||
\(112\) | − | 7.51436i | − | 0.710040i | ||||||
\(113\) | 4.19749 | + | 2.42342i | 0.394866 | + | 0.227976i | 0.684266 | − | 0.729232i | \(-0.260123\pi\) |
−0.289400 | + | 0.957208i | \(0.593456\pi\) | |||||||
\(114\) | 0.247884 | + | 0.429347i | 0.0232164 | + | 0.0402121i | ||||
\(115\) | 9.95555 | + | 0.972439i | 0.928360 | + | 0.0906804i | ||||
\(116\) | −0.0312337 | − | 0.0540983i | −0.00289997 | − | 0.00502290i | ||||
\(117\) | − | 0.727542i | − | 0.0672613i | ||||||
\(118\) | −0.858129 | + | 0.495441i | −0.0789972 | + | 0.0456090i | ||||
\(119\) | −6.65413 | −0.609983 | ||||||||
\(120\) | −1.06549 | + | 0.483803i | −0.0972656 | + | 0.0441649i | ||||
\(121\) | 11.1441 | 1.01310 | ||||||||
\(122\) | 0.737168i | 0.0667401i | ||||||||
\(123\) | 7.97469 | + | 4.60419i | 0.719054 | + | 0.415146i | ||||
\(124\) | 5.71173 | + | 9.89301i | 0.512929 | + | 0.888418i | ||||
\(125\) | −3.21962 | + | 10.7067i | −0.287971 | + | 0.957639i | ||||
\(126\) | 0.126693 | − | 0.219439i | 0.0112867 | − | 0.0195492i | ||||
\(127\) | −0.938941 | − | 0.542098i | −0.0833176 | − | 0.0481034i | 0.457762 | − | 0.889075i | \(-0.348651\pi\) |
−0.541080 | + | 0.840971i | \(0.681984\pi\) | |||||||
\(128\) | −3.56323 | − | 2.05723i | −0.314948 | − | 0.181835i | ||||
\(129\) | −3.52626 | − | 6.10766i | −0.310470 | − | 0.537750i | ||||
\(130\) | −0.0207810 | + | 0.212750i | −0.00182262 | + | 0.0186594i | ||||
\(131\) | −5.54027 | + | 9.59603i | −0.484056 | + | 0.838409i | −0.999832 | − | 0.0183140i | \(-0.994170\pi\) |
0.515777 | + | 0.856723i | \(0.327503\pi\) | |||||||
\(132\) | −8.08024 | − | 4.66513i | −0.703294 | − | 0.406047i | ||||
\(133\) | −6.30107 | − | 3.63793i | −0.546372 | − | 0.315448i | ||||
\(134\) | 1.59943 | 0.138169 | ||||||||
\(135\) | 2.22548 | + | 0.217380i | 0.191539 | + | 0.0187091i | ||||
\(136\) | −0.902895 | + | 1.56386i | −0.0774226 | + | 0.134100i | ||||
\(137\) | − | 14.1232i | − | 1.20662i | −0.797506 | − | 0.603311i | \(-0.793848\pi\) | ||
0.797506 | − | 0.603311i | \(-0.206152\pi\) | |||||||
\(138\) | 0.587802i | 0.0500370i | ||||||||
\(139\) | 8.68951 | − | 15.0507i | 0.737035 | − | 1.27658i | −0.216790 | − | 0.976218i | \(-0.569559\pi\) |
0.953825 | − | 0.300363i | \(-0.0971079\pi\) | |||||||
\(140\) | 4.97433 | − | 6.95349i | 0.420407 | − | 0.587677i | ||||
\(141\) | 0.196822 | + | 0.340906i | 0.0165754 | + | 0.0287095i | ||||
\(142\) | 1.21072i | 0.101601i | ||||||||
\(143\) | −2.96495 | + | 1.71182i | −0.247942 | + | 0.143149i | ||||
\(144\) | 1.94835 | + | 3.37465i | 0.162363 | + | 0.281220i | ||||
\(145\) | 0.00684871 | − | 0.0701151i | 0.000568755 | − | 0.00582274i | ||||
\(146\) | −0.172820 | + | 0.299333i | −0.0143027 | + | 0.0247730i | ||||
\(147\) | − | 3.28132i | − | 0.270639i | ||||||
\(148\) | 11.9624 | − | 1.53484i | 0.983307 | − | 0.126163i | ||||
\(149\) | 4.50166 | 0.368790 | 0.184395 | − | 0.982852i | \(-0.440967\pi\) | ||||
0.184395 | + | 0.982852i | \(0.440967\pi\) | |||||||
\(150\) | −0.644572 | − | 0.127134i | −0.0526290 | − | 0.0103805i | ||||
\(151\) | −0.499345 | − | 0.864891i | −0.0406361 | − | 0.0703838i | 0.844992 | − | 0.534779i | \(-0.179605\pi\) |
−0.885628 | + | 0.464395i | \(0.846272\pi\) | |||||||
\(152\) | −1.70998 | + | 0.987255i | −0.138697 | + | 0.0800770i | ||||
\(153\) | 2.98832 | − | 1.72531i | 0.241592 | − | 0.139483i | ||||
\(154\) | −1.19237 | −0.0960840 | ||||||||
\(155\) | −1.25243 | + | 12.8220i | −0.100598 | + | 1.02989i | ||||
\(156\) | 1.44252 | 0.115494 | ||||||||
\(157\) | −6.86341 | − | 3.96259i | −0.547760 | − | 0.316249i | 0.200458 | − | 0.979702i | \(-0.435757\pi\) |
−0.748218 | + | 0.663453i | \(0.769090\pi\) | |||||||
\(158\) | − | 0.949389i | − | 0.0755293i | ||||||
\(159\) | 7.13040 | 0.565477 | ||||||||
\(160\) | −1.44096 | − | 3.17346i | −0.113918 | − | 0.250884i | ||||
\(161\) | −4.31327 | − | 7.47080i | −0.339933 | − | 0.588781i | ||||
\(162\) | 0.131398i | 0.0103236i | ||||||||
\(163\) | −13.4995 | − | 7.79392i | −1.05736 | − | 0.610467i | −0.132659 | − | 0.991162i | \(-0.542351\pi\) |
−0.924701 | + | 0.380695i | \(0.875685\pi\) | |||||||
\(164\) | −9.12889 | + | 15.8117i | −0.712847 | + | 1.23469i | ||||
\(165\) | −4.35038 | − | 9.58095i | −0.338676 | − | 0.745876i | ||||
\(166\) | 0.815341 | + | 1.41221i | 0.0632828 | + | 0.109609i | ||||
\(167\) | −17.8657 | + | 10.3148i | −1.38249 | + | 0.798180i | −0.992454 | − | 0.122620i | \(-0.960870\pi\) |
−0.390035 | + | 0.920800i | \(0.627537\pi\) | |||||||
\(168\) | 0.873967 | + | 0.504585i | 0.0674280 | + | 0.0389296i | ||||
\(169\) | −6.23534 | + | 10.7999i | −0.479642 | + | 0.830764i | ||||
\(170\) | −0.923136 | + | 0.419164i | −0.0708013 | + | 0.0321484i | ||||
\(171\) | 3.77302 | 0.288530 | ||||||||
\(172\) | 12.1099 | − | 6.99164i | 0.923369 | − | 0.533108i | ||||
\(173\) | −8.06540 | − | 4.65656i | −0.613201 | − | 0.354032i | 0.161016 | − | 0.986952i | \(-0.448523\pi\) |
−0.774217 | + | 0.632920i | \(0.781856\pi\) | |||||||
\(174\) | 0.00413978 | 0.000313836 | ||||||||
\(175\) | 9.12523 | − | 3.11400i | 0.689803 | − | 0.235397i | ||||
\(176\) | 9.16846 | − | 15.8802i | 0.691099 | − | 1.19702i | ||||
\(177\) | 7.54108i | 0.566822i | ||||||||
\(178\) | 0.251748 | − | 0.145347i | 0.0188693 | − | 0.0108942i | ||||
\(179\) | −2.75912 | −0.206226 | −0.103113 | − | 0.994670i | \(-0.532880\pi\) | ||||
−0.103113 | + | 0.994670i | \(0.532880\pi\) | |||||||
\(180\) | −0.431008 | + | 4.41253i | −0.0321254 | + | 0.328891i | ||||
\(181\) | −10.1108 | − | 17.5124i | −0.751528 | − | 1.30168i | −0.947082 | − | 0.320992i | \(-0.895984\pi\) |
0.195554 | − | 0.980693i | \(-0.437350\pi\) | |||||||
\(182\) | 0.159651 | − | 0.0921746i | 0.0118341 | − | 0.00683243i | ||||
\(183\) | 4.85857 | + | 2.80510i | 0.359156 | + | 0.207359i | ||||
\(184\) | −2.34106 | −0.172585 | ||||||||
\(185\) | 11.9794 | + | 6.44150i | 0.880746 | + | 0.473588i | ||||
\(186\) | −0.757045 | −0.0555092 | ||||||||
\(187\) | −14.0623 | − | 8.11888i | −1.02834 | − | 0.593711i | ||||
\(188\) | −0.675926 | + | 0.390246i | −0.0492970 | + | 0.0284616i | ||||
\(189\) | −0.964193 | − | 1.67003i | −0.0701348 | − | 0.121477i | ||||
\(190\) | −1.10332 | − | 0.107770i | −0.0800432 | − | 0.00781847i | ||||
\(191\) | −12.1924 | −0.882212 | −0.441106 | − | 0.897455i | \(-0.645414\pi\) | ||||
−0.441106 | + | 0.897455i | \(0.645414\pi\) | |||||||
\(192\) | −6.57193 | + | 3.79430i | −0.474288 | + | 0.273830i | ||||
\(193\) | 17.2710i | 1.24319i | 0.783338 | + | 0.621596i | \(0.213516\pi\) | ||||
−0.783338 | + | 0.621596i | \(0.786484\pi\) | |||||||
\(194\) | 0.708190 | − | 1.22662i | 0.0508451 | − | 0.0880663i | ||||
\(195\) | 1.32313 | + | 0.946529i | 0.0947513 | + | 0.0677824i | ||||
\(196\) | 6.50599 | 0.464714 | ||||||||
\(197\) | −8.51791 | − | 4.91781i | −0.606876 | − | 0.350380i | 0.164866 | − | 0.986316i | \(-0.447281\pi\) |
−0.771742 | + | 0.635936i | \(0.780614\pi\) | |||||||
\(198\) | 0.535486 | − | 0.309163i | 0.0380553 | − | 0.0219713i | ||||
\(199\) | −13.4990 | −0.956918 | −0.478459 | − | 0.878110i | \(-0.658805\pi\) | ||||
−0.478459 | + | 0.878110i | \(0.658805\pi\) | |||||||
\(200\) | 0.506341 | − | 2.56716i | 0.0358037 | − | 0.181525i | ||||
\(201\) | 6.08619 | − | 10.5416i | 0.429287 | − | 0.743547i | ||||
\(202\) | −0.833640 | − | 0.481302i | −0.0586547 | − | 0.0338643i | ||||
\(203\) | −0.0526155 | + | 0.0303775i | −0.00369288 | + | 0.00213209i | ||||
\(204\) | 3.42083 | + | 5.92505i | 0.239506 | + | 0.414837i | ||||
\(205\) | −18.7484 | + | 8.51298i | −1.30944 | + | 0.594572i | ||||
\(206\) | 0.324562 | − | 0.562158i | 0.0226133 | − | 0.0391674i | ||||
\(207\) | 3.87412 | + | 2.23672i | 0.269270 | + | 0.155463i | ||||
\(208\) | 2.83502i | 0.196573i | ||||||||
\(209\) | −8.87745 | − | 15.3762i | −0.614066 | − | 1.06359i | ||||
\(210\) | 0.234251 | + | 0.515896i | 0.0161648 | + | 0.0356002i | ||||
\(211\) | −21.8381 | −1.50339 | −0.751697 | − | 0.659509i | \(-0.770764\pi\) | ||||
−0.751697 | + | 0.659509i | \(0.770764\pi\) | |||||||
\(212\) | 14.1377i | 0.970980i | ||||||||
\(213\) | 7.97969 | + | 4.60707i | 0.546759 | + | 0.315671i | ||||
\(214\) | −1.77691 | −0.121467 | ||||||||
\(215\) | 15.6952 | + | 1.53308i | 1.07041 | + | 0.104555i | ||||
\(216\) | −0.523323 | −0.0356076 | ||||||||
\(217\) | 9.62184 | − | 5.55517i | 0.653173 | − | 0.377110i | ||||
\(218\) | −0.826852 | + | 0.477383i | −0.0560015 | + | 0.0323325i | ||||
\(219\) | 1.31524 | + | 2.27807i | 0.0888758 | + | 0.153937i | ||||
\(220\) | 18.9965 | − | 8.62564i | 1.28074 | − | 0.581541i | ||||
\(221\) | 2.51047 | 0.168873 | ||||||||
\(222\) | −0.308294 | + | 0.737411i | −0.0206913 | + | 0.0494918i | ||||
\(223\) | 4.02134i | 0.269289i | 0.990894 | + | 0.134644i | \(0.0429892\pi\) | ||||
−0.990894 | + | 0.134644i | \(0.957011\pi\) | |||||||
\(224\) | −1.50286 | + | 2.60302i | −0.100414 | + | 0.173922i | ||||
\(225\) | −3.29067 | + | 3.76451i | −0.219378 | + | 0.250967i | ||||
\(226\) | −0.318432 | − | 0.551541i | −0.0211818 | − | 0.0366880i | ||||
\(227\) | 21.8135 | − | 12.5941i | 1.44782 | − | 0.835897i | 0.449465 | − | 0.893298i | \(-0.351615\pi\) |
0.998351 | + | 0.0574013i | \(0.0182815\pi\) | |||||||
\(228\) | 7.48091i | 0.495435i | ||||||||
\(229\) | 7.22513 | + | 12.5143i | 0.477450 | + | 0.826968i | 0.999666 | − | 0.0258457i | \(-0.00822787\pi\) |
−0.522216 | + | 0.852813i | \(0.674895\pi\) | |||||||
\(230\) | −1.06899 | − | 0.764727i | −0.0704873 | − | 0.0504246i | ||||
\(231\) | −4.53725 | + | 7.85875i | −0.298529 | + | 0.517068i | ||||
\(232\) | 0.0164876i | 0.00108247i | ||||||||
\(233\) | 16.4445i | 1.07731i | 0.842525 | + | 0.538657i | \(0.181068\pi\) | ||||
−0.842525 | + | 0.538657i | \(0.818932\pi\) | |||||||
\(234\) | −0.0477988 | + | 0.0827899i | −0.00312471 | + | 0.00541215i | ||||
\(235\) | −0.876046 | − | 0.0855705i | −0.0571469 | − | 0.00558201i | ||||
\(236\) | −14.9520 | −0.973289 | ||||||||
\(237\) | −6.25729 | − | 3.61265i | −0.406454 | − | 0.234667i | ||||
\(238\) | 0.757200 | + | 0.437170i | 0.0490820 | + | 0.0283375i | ||||
\(239\) | 8.61112 | − | 14.9149i | 0.557007 | − | 0.964765i | −0.440737 | − | 0.897636i | \(-0.645283\pi\) |
0.997744 | − | 0.0671284i | \(-0.0213837\pi\) | |||||||
\(240\) | −8.67203 | − | 0.847067i | −0.559777 | − | 0.0546780i | ||||
\(241\) | −0.986408 | − | 1.70851i | −0.0635401 | − | 0.110055i | 0.832505 | − | 0.554017i | \(-0.186906\pi\) |
−0.896045 | + | 0.443962i | \(0.853572\pi\) | |||||||
\(242\) | −1.26813 | − | 0.732155i | −0.0815184 | − | 0.0470647i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −5.56176 | + | 9.63326i | −0.356055 | + | 0.616706i | ||||
\(245\) | 5.96751 | + | 4.26899i | 0.381250 | + | 0.272736i | ||||
\(246\) | −0.604981 | − | 1.04786i | −0.0385722 | − | 0.0668090i | ||||
\(247\) | 2.37727 | + | 1.37252i | 0.151262 | + | 0.0873312i | ||||
\(248\) | − | 3.01511i | − | 0.191460i | ||||||
\(249\) | 12.4103 | 0.786468 | ||||||||
\(250\) | 1.06979 | − | 1.00684i | 0.0676597 | − | 0.0636779i | ||||
\(251\) | 14.2516 | 0.899551 | 0.449775 | − | 0.893142i | \(-0.351504\pi\) | ||||
0.449775 | + | 0.893142i | \(0.351504\pi\) | |||||||
\(252\) | 3.31123 | − | 1.91174i | 0.208588 | − | 0.120428i | ||||
\(253\) | − | 21.0509i | − | 1.32346i | ||||||
\(254\) | 0.0712306 | + | 0.123375i | 0.00446940 | + | 0.00774123i | ||||
\(255\) | −0.750097 | + | 7.67927i | −0.0469729 | + | 0.480895i | ||||
\(256\) | −7.31829 | − | 12.6756i | −0.457393 | − | 0.792228i | ||||
\(257\) | 16.0273 | + | 9.25337i | 0.999756 | + | 0.577209i | 0.908176 | − | 0.418588i | \(-0.137475\pi\) |
0.0915798 | + | 0.995798i | \(0.470808\pi\) | |||||||
\(258\) | 0.926687i | 0.0576930i | ||||||||
\(259\) | −1.49277 | − | 11.6345i | −0.0927562 | − | 0.722936i | ||||
\(260\) | −1.87672 | + | 2.62342i | −0.116389 | + | 0.162697i | ||||
\(261\) | 0.0157528 | − | 0.0272847i | 0.000975076 | − | 0.00168888i | ||||
\(262\) | 1.26090 | − | 0.727980i | 0.0778986 | − | 0.0449748i | ||||
\(263\) | −8.83757 | + | 5.10237i | −0.544948 | + | 0.314626i | −0.747082 | − | 0.664732i | \(-0.768546\pi\) |
0.202134 | + | 0.979358i | \(0.435212\pi\) | |||||||
\(264\) | 1.23131 | + | 2.13270i | 0.0757821 | + | 0.131259i | ||||
\(265\) | −9.27661 | + | 12.9675i | −0.569858 | + | 0.796590i | ||||
\(266\) | 0.478016 | + | 0.827948i | 0.0293090 | + | 0.0507647i | ||||
\(267\) | − | 2.21231i | − | 0.135391i | ||||||
\(268\) | 20.9012 | + | 12.0673i | 1.27674 | + | 0.737128i | ||||
\(269\) | 6.13164 | 0.373852 | 0.186926 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186926 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(270\) | −0.238964 | − | 0.170948i | −0.0145429 | − | 0.0104036i | ||||
\(271\) | −15.0976 | + | 26.1498i | −0.917113 | + | 1.58849i | −0.113334 | + | 0.993557i | \(0.536153\pi\) |
−0.803778 | + | 0.594929i | \(0.797180\pi\) | |||||||
\(272\) | −11.6446 | + | 6.72303i | −0.706059 | + | 0.407643i | ||||
\(273\) | − | 1.40298i | − | 0.0849124i | ||||||
\(274\) | −0.927877 | + | 1.60713i | −0.0560551 | + | 0.0970903i | ||||
\(275\) | 23.0840 | + | 4.55305i | 1.39202 | + | 0.274559i | ||||
\(276\) | −4.43483 | + | 7.68135i | −0.266945 | + | 0.462363i | ||||
\(277\) | 12.1146 | − | 6.99434i | 0.727893 | − | 0.420249i | −0.0897577 | − | 0.995964i | \(-0.528609\pi\) |
0.817651 | + | 0.575714i | \(0.195276\pi\) | |||||||
\(278\) | −1.97763 | + | 1.14178i | −0.118610 | + | 0.0684796i | ||||
\(279\) | −2.88073 | + | 4.98958i | −0.172465 | + | 0.298718i | ||||
\(280\) | −2.05468 | + | 0.932958i | −0.122791 | + | 0.0557549i | ||||
\(281\) | −6.68503 | + | 11.5788i | −0.398796 | + | 0.690734i | −0.993578 | − | 0.113153i | \(-0.963905\pi\) |
0.594782 | + | 0.803887i | \(0.297238\pi\) | |||||||
\(282\) | − | 0.0517240i | − | 0.00308012i | ||||||
\(283\) | 16.5340 | − | 9.54594i | 0.982847 | − | 0.567447i | 0.0797186 | − | 0.996817i | \(-0.474598\pi\) |
0.903128 | + | 0.429370i | \(0.141265\pi\) | |||||||
\(284\) | −9.13460 | + | 15.8216i | −0.542039 | + | 0.938839i | ||||
\(285\) | −4.90869 | + | 6.86173i | −0.290765 | + | 0.406454i | ||||
\(286\) | 0.449858 | 0.0266007 | ||||||||
\(287\) | 15.3783 | + | 8.87866i | 0.907752 | + | 0.524091i | ||||
\(288\) | − | 1.55867i | − | 0.0918452i | ||||||
\(289\) | −2.54661 | − | 4.41086i | −0.149801 | − | 0.259462i | ||||
\(290\) | −0.00538583 | + | 0.00752872i | −0.000316267 | + | 0.000442102i | ||||
\(291\) | −5.38966 | − | 9.33516i | −0.315947 | − | 0.547237i | ||||
\(292\) | −4.51680 | + | 2.60778i | −0.264326 | + | 0.152609i | ||||
\(293\) | −20.6245 | + | 11.9076i | −1.20490 | + | 0.695648i | −0.961640 | − | 0.274314i | \(-0.911549\pi\) |
−0.243257 | + | 0.969962i | \(0.578216\pi\) | |||||||
\(294\) | −0.215580 | + | 0.373395i | −0.0125729 | + | 0.0217768i | ||||
\(295\) | −13.7144 | − | 9.81090i | −0.798484 | − | 0.571213i | ||||
\(296\) | −2.93691 | − | 1.22785i | −0.170705 | − | 0.0713675i | ||||
\(297\) | − | 4.70575i | − | 0.273055i | ||||||
\(298\) | −0.512261 | − | 0.295754i | −0.0296745 | − | 0.0171326i | ||||
\(299\) | 1.62731 | + | 2.81859i | 0.0941098 | + | 0.163003i | ||||
\(300\) | −7.46401 | − | 6.52452i | −0.430935 | − | 0.376693i | ||||
\(301\) | −6.80000 | − | 11.7779i | −0.391945 | − | 0.678869i | ||||
\(302\) | 0.131226i | 0.00755120i | ||||||||
\(303\) | −6.34439 | + | 3.66294i | −0.364476 | + | 0.210430i | ||||
\(304\) | −14.7024 | −0.843238 | ||||||||
\(305\) | −11.4224 | + | 5.18652i | −0.654045 | + | 0.296979i | ||||
\(306\) | −0.453404 | −0.0259194 | ||||||||
\(307\) | 0.184371i | 0.0105226i | 0.999986 | + | 0.00526130i | \(0.00167473\pi\) | ||||
−0.999986 | + | 0.00526130i | \(0.998325\pi\) | |||||||
\(308\) | −15.5818 | − | 8.99617i | −0.887857 | − | 0.512604i | ||||
\(309\) | −2.47007 | − | 4.27828i | −0.140517 | − | 0.243383i | ||||
\(310\) | 0.984912 | − | 1.37678i | 0.0559392 | − | 0.0781961i | ||||
\(311\) | −13.5188 | + | 23.4152i | −0.766580 | + | 1.32775i | 0.172828 | + | 0.984952i | \(0.444710\pi\) |
−0.939407 | + | 0.342803i | \(0.888624\pi\) | |||||||
\(312\) | −0.329730 | − | 0.190370i | −0.0186673 | − | 0.0107776i | ||||
\(313\) | 22.2068 | + | 12.8211i | 1.25520 | + | 0.724692i | 0.972138 | − | 0.234409i | \(-0.0753154\pi\) |
0.283065 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(314\) | 0.520676 | + | 0.901838i | 0.0293835 | + | 0.0508936i | ||||
\(315\) | 4.29158 | + | 0.419193i | 0.241803 | + | 0.0236189i | ||||
\(316\) | 7.16292 | − | 12.4065i | 0.402946 | − | 0.697922i | ||||
\(317\) | −27.2695 | − | 15.7441i | −1.53161 | − | 0.884275i | −0.999288 | − | 0.0377320i | \(-0.987987\pi\) |
−0.532321 | − | 0.846543i | \(-0.678680\pi\) | |||||||
\(318\) | −0.811396 | − | 0.468460i | −0.0455008 | − | 0.0262699i | ||||
\(319\) | −0.148258 | −0.00830084 | ||||||||
\(320\) | 1.64961 | − | 16.8883i | 0.0922162 | − | 0.944083i | ||||
\(321\) | −6.76157 | + | 11.7114i | −0.377394 | + | 0.653665i | ||||
\(322\) | 1.13351i | 0.0631680i | ||||||||
\(323\) | 13.0193i | 0.724412i | ||||||||
\(324\) | −0.991367 | + | 1.71710i | −0.0550760 | + | 0.0953944i | ||||
\(325\) | −3.44277 | + | 1.17485i | −0.190971 | + | 0.0651691i | ||||
\(326\) | 1.02410 | + | 1.77380i | 0.0567199 | + | 0.0982418i | ||||
\(327\) | 7.26622i | 0.401823i | ||||||||
\(328\) | 4.17334 | − | 2.40948i | 0.230434 | − | 0.133041i | ||||
\(329\) | 0.379549 | + | 0.657399i | 0.0209252 | + | 0.0362436i | ||||
\(330\) | −0.134412 | + | 1.37607i | −0.00739913 | + | 0.0757501i | ||||
\(331\) | 1.73146 | − | 2.99897i | 0.0951694 | − | 0.164838i | −0.814510 | − | 0.580150i | \(-0.802994\pi\) |
0.909679 | + | 0.415311i | \(0.136327\pi\) | |||||||
\(332\) | 24.6063i | 1.35044i | ||||||||
\(333\) | 3.68704 | + | 4.83794i | 0.202049 | + | 0.265118i | ||||
\(334\) | 2.71068 | 0.148322 | ||||||||
\(335\) | 11.2531 | + | 24.7831i | 0.614825 | + | 1.35404i | ||||
\(336\) | 3.75718 | + | 6.50762i | 0.204971 | + | 0.355020i | ||||
\(337\) | −15.2132 | + | 8.78334i | −0.828715 | + | 0.478459i | −0.853413 | − | 0.521236i | \(-0.825471\pi\) |
0.0246972 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(338\) | 1.41909 | − | 0.819311i | 0.0771882 | − | 0.0445646i | ||||
\(339\) | −4.84684 | −0.263244 | ||||||||
\(340\) | −15.2260 | − | 1.48724i | −0.825744 | − | 0.0806571i | ||||
\(341\) | 27.1120 | 1.46820 | ||||||||
\(342\) | −0.429347 | − | 0.247884i | −0.0232164 | − | 0.0134040i | ||||
\(343\) | − | 19.8264i | − | 1.07052i | ||||||
\(344\) | −3.69075 | −0.198992 | ||||||||
\(345\) | −9.10798 | + | 4.13562i | −0.490357 | + | 0.222654i | ||||
\(346\) | 0.611863 | + | 1.05978i | 0.0328940 | + | 0.0569740i | ||||
\(347\) | 25.2741i | 1.35678i | 0.734701 | + | 0.678391i | \(0.237323\pi\) | ||||
−0.734701 | + | 0.678391i | \(0.762677\pi\) | |||||||
\(348\) | 0.0540983 | + | 0.0312337i | 0.00289997 | + | 0.00167430i | ||||
\(349\) | 14.5392 | − | 25.1827i | 0.778267 | − | 1.34800i | −0.154673 | − | 0.987966i | \(-0.549432\pi\) |
0.932940 | − | 0.360033i | \(-0.117234\pi\) | |||||||
\(350\) | −1.24298 | − | 0.245164i | −0.0664403 | − | 0.0131046i | ||||
\(351\) | 0.363771 | + | 0.630070i | 0.0194167 | + | 0.0336307i | ||||
\(352\) | −6.35203 | + | 3.66734i | −0.338564 | + | 0.195470i | ||||
\(353\) | −27.2188 | − | 15.7148i | −1.44871 | − | 0.836412i | −0.450304 | − | 0.892875i | \(-0.648684\pi\) |
−0.998405 | + | 0.0564629i | \(0.982018\pi\) | |||||||
\(354\) | 0.495441 | − | 0.858129i | 0.0263324 | − | 0.0456090i | ||||
\(355\) | −18.7601 | + | 8.51831i | −0.995682 | + | 0.452105i | ||||
\(356\) | 4.38643 | 0.232480 | ||||||||
\(357\) | 5.76265 | − | 3.32707i | 0.304992 | − | 0.176087i | ||||
\(358\) | 0.313971 | + | 0.181271i | 0.0165939 | + | 0.00958047i | ||||
\(359\) | 34.5378 | 1.82283 | 0.911417 | − | 0.411483i | \(-0.134989\pi\) | ||||
0.911417 | + | 0.411483i | \(0.134989\pi\) | |||||||
\(360\) | 0.680841 | − | 0.951731i | 0.0358835 | − | 0.0501606i | ||||
\(361\) | 2.38215 | − | 4.12600i | 0.125376 | − | 0.217158i | ||||
\(362\) | 2.65707i | 0.139653i | ||||||||
\(363\) | −9.65106 | + | 5.57204i | −0.506549 | + | 0.292456i | ||||
\(364\) | 2.78174 | 0.145803 | ||||||||
\(365\) | −5.85408 | − | 0.571816i | −0.306417 | − | 0.0299302i | ||||
\(366\) | −0.368584 | − | 0.638406i | −0.0192662 | − | 0.0333700i | ||||
\(367\) | 28.5194 | − | 16.4657i | 1.48870 | − | 0.859500i | 0.488782 | − | 0.872406i | \(-0.337441\pi\) |
0.999917 | + | 0.0129056i | \(0.00410811\pi\) | |||||||
\(368\) | −15.0963 | − | 8.71585i | −0.786949 | − | 0.454345i | ||||
\(369\) | −9.20838 | −0.479369 | ||||||||
\(370\) | −0.939989 | − | 1.52004i | −0.0488677 | − | 0.0790232i | ||||
\(371\) | 13.7502 | 0.713873 | ||||||||
\(372\) | −9.89301 | − | 5.71173i | −0.512929 | − | 0.296139i | ||||
\(373\) | −2.49061 | + | 1.43795i | −0.128959 | + | 0.0744544i | −0.563092 | − | 0.826394i | \(-0.690388\pi\) |
0.434133 | + | 0.900849i | \(0.357055\pi\) | |||||||
\(374\) | 1.06680 | + | 1.84776i | 0.0551631 | + | 0.0955453i | ||||
\(375\) | −2.56509 | − | 10.8821i | −0.132461 | − | 0.561950i | ||||
\(376\) | 0.206003 | 0.0106238 | ||||||||
\(377\) | 0.0198508 | − | 0.0114609i | 0.00102237 | − | 0.000590264i | ||||
\(378\) | 0.253386i | 0.0130328i | ||||||||
\(379\) | −5.77117 | + | 9.99596i | −0.296445 | + | 0.513458i | −0.975320 | − | 0.220796i | \(-0.929135\pi\) |
0.678875 | + | 0.734254i | \(0.262468\pi\) | |||||||
\(380\) | −13.6050 | − | 9.73262i | −0.697921 | − | 0.499273i | ||||
\(381\) | 1.08420 | 0.0555450 | ||||||||
\(382\) | 1.38742 | + | 0.801029i | 0.0709868 | + | 0.0409842i | ||||
\(383\) | 20.0001 | − | 11.5471i | 1.02196 | − | 0.590028i | 0.107288 | − | 0.994228i | \(-0.465783\pi\) |
0.914671 | + | 0.404200i | \(0.132450\pi\) | |||||||
\(384\) | 4.11446 | 0.209965 | ||||||||
\(385\) | −8.38921 | − | 18.4758i | −0.427554 | − | 0.941613i | ||||
\(386\) | 1.13469 | − | 1.96533i | 0.0577540 | − | 0.100033i | ||||
\(387\) | 6.10766 | + | 3.52626i | 0.310470 | + | 0.179250i | ||||
\(388\) | 18.5091 | − | 10.6863i | 0.939659 | − | 0.542513i | ||||
\(389\) | −2.74022 | − | 4.74619i | −0.138934 | − | 0.240642i | 0.788159 | − | 0.615472i | \(-0.211034\pi\) |
−0.927094 | + | 0.374830i | \(0.877701\pi\) | |||||||
\(390\) | −0.0883782 | − | 0.194638i | −0.00447520 | − | 0.00985586i | ||||
\(391\) | −7.71808 | + | 13.3681i | −0.390320 | + | 0.676054i | ||||
\(392\) | −1.48713 | − | 0.858596i | −0.0751115 | − | 0.0433657i | ||||
\(393\) | − | 11.0805i | − | 0.558939i | ||||||
\(394\) | 0.646191 | + | 1.11924i | 0.0325546 | + | 0.0563863i | ||||
\(395\) | 14.7108 | − | 6.67965i | 0.740179 | − | 0.336090i | ||||
\(396\) | 9.33025 | 0.468863 | ||||||||
\(397\) | − | 10.3805i | − | 0.520981i | −0.965476 | − | 0.260490i | \(-0.916116\pi\) | ||
0.965476 | − | 0.260490i | \(-0.0838843\pi\) | |||||||
\(398\) | 1.53610 | + | 0.886870i | 0.0769979 | + | 0.0444548i | ||||
\(399\) | 7.27585 | 0.364248 | ||||||||
\(400\) | 12.8228 | − | 14.6692i | 0.641138 | − | 0.733458i | ||||
\(401\) | −8.40952 | −0.419951 | −0.209976 | − | 0.977707i | \(-0.567338\pi\) | ||||
−0.209976 | + | 0.977707i | \(0.567338\pi\) | |||||||
\(402\) | −1.38514 | + | 0.799713i | −0.0690847 | + | 0.0398861i | ||||
\(403\) | −3.63013 | + | 2.09586i | −0.180830 | + | 0.104402i | ||||
\(404\) | −7.26263 | − | 12.5792i | −0.361329 | − | 0.625841i | ||||
\(405\) | −2.03601 | + | 0.924481i | −0.101170 | + | 0.0459378i | ||||
\(406\) | 0.00798310 | 0.000396194 | ||||||||
\(407\) | 11.0409 | − | 26.4089i | 0.547278 | − | 1.30904i | ||||
\(408\) | − | 1.80579i | − | 0.0893999i | ||||||
\(409\) | 7.53047 | − | 13.0432i | 0.372358 | − | 0.644943i | −0.617570 | − | 0.786516i | \(-0.711883\pi\) |
0.989928 | + | 0.141573i | \(0.0452161\pi\) | |||||||
\(410\) | 2.69274 | + | 0.263022i | 0.132985 | + | 0.0129897i | ||||
\(411\) | 7.06158 | + | 12.2310i | 0.348322 | + | 0.603311i | ||||
\(412\) | 8.48270 | − | 4.89749i | 0.417913 | − | 0.241282i | ||||
\(413\) | 14.5421i | 0.715571i | ||||||||
\(414\) | −0.293901 | − | 0.509051i | −0.0144444 | − | 0.0250185i | ||||
\(415\) | −16.1457 | + | 22.5697i | −0.792561 | + | 1.10790i | ||||
\(416\) | 0.566998 | − | 0.982069i | 0.0277993 | − | 0.0481499i | ||||
\(417\) | 17.3790i | 0.851054i | ||||||||
\(418\) | 2.33296i | 0.114109i | ||||||||
\(419\) | −3.93907 | + | 6.82267i | −0.192436 | + | 0.333309i | −0.946057 | − | 0.324000i | \(-0.894972\pi\) |
0.753621 | + | 0.657309i | \(0.228305\pi\) | |||||||
\(420\) | −0.831149 | + | 8.50906i | −0.0405559 | + | 0.415200i | ||||
\(421\) | 39.1270 | 1.90693 | 0.953466 | − | 0.301500i | \(-0.0974873\pi\) | ||||
0.953466 | + | 0.301500i | \(0.0974873\pi\) | |||||||
\(422\) | 2.48504 | + | 1.43474i | 0.120970 | + | 0.0698420i | ||||
\(423\) | −0.340906 | − | 0.196822i | −0.0165754 | − | 0.00956982i | ||||
\(424\) | 1.86575 | − | 3.23158i | 0.0906089 | − | 0.156939i | ||||
\(425\) | −12.9899 | − | 11.3548i | −0.630102 | − | 0.550791i | ||||
\(426\) | −0.605360 | − | 1.04851i | −0.0293298 | − | 0.0508007i | ||||
\(427\) | 9.36920 | + | 5.40931i | 0.453408 | + | 0.261775i | ||||
\(428\) | −23.2205 | − | 13.4064i | −1.12241 | − | 0.648022i | ||||
\(429\) | 1.71182 | − | 2.96495i | 0.0826473 | − | 0.143149i | ||||
\(430\) | −1.68530 | − | 1.20562i | −0.0812724 | − | 0.0581399i | ||||
\(431\) | −7.96516 | − | 13.7961i | −0.383668 | − | 0.664533i | 0.607915 | − | 0.794002i | \(-0.292006\pi\) |
−0.991583 | + | 0.129469i | \(0.958673\pi\) | |||||||
\(432\) | −3.37465 | − | 1.94835i | −0.162363 | − | 0.0937402i | ||||
\(433\) | 33.5864i | 1.61406i | 0.590511 | + | 0.807029i | \(0.298926\pi\) | ||||
−0.590511 | + | 0.807029i | \(0.701074\pi\) | |||||||
\(434\) | −1.45988 | −0.0700763 | ||||||||
\(435\) | 0.0291264 | + | 0.0641458i | 0.00139650 | + | 0.00307556i | ||||
\(436\) | −14.4070 | −0.689970 | ||||||||
\(437\) | −14.6171 | + | 8.43921i | −0.699233 | + | 0.403702i | ||||
\(438\) | − | 0.345640i | − | 0.0165153i | ||||||
\(439\) | 2.10728 | + | 3.64991i | 0.100575 | + | 0.174201i | 0.911922 | − | 0.410364i | \(-0.134598\pi\) |
−0.811347 | + | 0.584565i | \(0.801265\pi\) | |||||||
\(440\) | −5.48052 | − | 0.535327i | −0.261274 | − | 0.0255207i | ||||
\(441\) | 1.64066 | + | 2.84171i | 0.0781268 | + | 0.135320i | ||||
\(442\) | −0.285677 | − | 0.164935i | −0.0135883 | − | 0.00784518i | ||||
\(443\) | − | 24.7062i | − | 1.17383i | −0.809649 | − | 0.586914i | \(-0.800343\pi\) | ||
0.809649 | − | 0.586914i | \(-0.199657\pi\) | |||||||
\(444\) | −9.59236 | + | 7.31043i | −0.455233 | + | 0.346938i | ||||
\(445\) | 4.02338 | + | 2.87821i | 0.190726 | + | 0.136440i | ||||
\(446\) | 0.264198 | − | 0.457604i | 0.0125101 | − | 0.0216682i | ||||
\(447\) | −3.89855 | + | 2.25083i | −0.184395 | + | 0.106461i | ||||
\(448\) | −12.6732 | + | 7.31688i | −0.598753 | + | 0.345690i | ||||
\(449\) | −14.8316 | − | 25.6891i | −0.699947 | − | 1.21234i | −0.968484 | − | 0.249075i | \(-0.919874\pi\) |
0.268537 | − | 0.963269i | \(-0.413460\pi\) | |||||||
\(450\) | 0.621782 | − | 0.212184i | 0.0293111 | − | 0.0100025i | ||||
\(451\) | 21.6662 | + | 37.5269i | 1.02022 | + | 1.76707i | ||||
\(452\) | − | 9.60999i | − | 0.452016i | ||||||
\(453\) | 0.864891 | + | 0.499345i | 0.0406361 | + | 0.0234613i | ||||
\(454\) | −3.30967 | −0.155330 | ||||||||
\(455\) | 2.55151 | + | 1.82527i | 0.119616 | + | 0.0855702i | ||||
\(456\) | 0.987255 | − | 1.70998i | 0.0462325 | − | 0.0800770i | ||||
\(457\) | −17.7792 | + | 10.2648i | −0.831674 | + | 0.480167i | −0.854425 | − | 0.519574i | \(-0.826091\pi\) |
0.0227515 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(458\) | − | 1.89873i | − | 0.0887220i | ||||||
\(459\) | −1.72531 | + | 2.98832i | −0.0805306 | + | 0.139483i | ||||
\(460\) | −8.19983 | − | 18.0587i | −0.382319 | − | 0.841991i | ||||
\(461\) | −10.8248 | + | 18.7491i | −0.504162 | + | 0.873235i | 0.495826 | + | 0.868422i | \(0.334865\pi\) |
−0.999988 | + | 0.00481284i | \(0.998468\pi\) | |||||||
\(462\) | 1.03262 | − | 0.596186i | 0.0480420 | − | 0.0277371i | ||||
\(463\) | 22.6762 | − | 13.0921i | 1.05385 | − | 0.608443i | 0.130129 | − | 0.991497i | \(-0.458461\pi\) |
0.923726 | + | 0.383054i | \(0.125128\pi\) | |||||||
\(464\) | −0.0613841 | + | 0.106320i | −0.00284969 | + | 0.00493580i | ||||
\(465\) | −5.32637 | − | 11.7304i | −0.247004 | − | 0.543984i | ||||
\(466\) | 1.08039 | − | 1.87128i | 0.0500479 | − | 0.0866855i | ||||
\(467\) | 36.9707i | 1.71080i | 0.517969 | + | 0.855400i | \(0.326688\pi\) | ||||
−0.517969 | + | 0.855400i | \(0.673312\pi\) | |||||||
\(468\) | −1.24926 | + | 0.721262i | −0.0577472 | + | 0.0333403i | ||||
\(469\) | 11.7365 | − | 20.3283i | 0.541943 | − | 0.938672i | ||||
\(470\) | 0.0940669 | + | 0.0672927i | 0.00433898 | + | 0.00310398i | ||||
\(471\) | 7.92518 | 0.365173 | ||||||||
\(472\) | 3.41770 | + | 1.97321i | 0.157312 | + | 0.0908244i | ||||
\(473\) | − | 33.1874i | − | 1.52596i | ||||||
\(474\) | 0.474694 | + | 0.822195i | 0.0218034 | + | 0.0377647i | ||||
\(475\) | −6.09277 | − | 17.8542i | −0.279555 | − | 0.819205i | ||||
\(476\) | 6.59669 | + | 11.4258i | 0.302359 | + | 0.523701i | ||||
\(477\) | −6.17510 | + | 3.56520i | −0.282739 | + | 0.163239i | ||||
\(478\) | −1.95979 | + | 1.13148i | −0.0896386 | + | 0.0517529i | ||||
\(479\) | −14.9311 | + | 25.8614i | −0.682217 | + | 1.18164i | 0.292085 | + | 0.956392i | \(0.405651\pi\) |
−0.974303 | + | 0.225243i | \(0.927682\pi\) | |||||||
\(480\) | 2.83463 | + | 2.02782i | 0.129383 | + | 0.0925567i | ||||
\(481\) | 0.563192 | + | 4.38949i | 0.0256794 | + | 0.200143i | ||||
\(482\) | 0.259224i | 0.0118073i | ||||||||
\(483\) | 7.47080 | + | 4.31327i | 0.339933 | + | 0.196260i | ||||
\(484\) | −11.0479 | − | 19.1355i | −0.502176 | − | 0.869795i | ||||
\(485\) | 23.9891 | + | 2.34321i | 1.08929 | + | 0.106400i | ||||
\(486\) | −0.0656990 | − | 0.113794i | −0.00298017 | − | 0.00516180i | ||||
\(487\) | − | 27.2480i | − | 1.23472i | −0.786679 | − | 0.617362i | \(-0.788201\pi\) | ||
0.786679 | − | 0.617362i | \(-0.211799\pi\) | |||||||
\(488\) | 2.54260 | − | 1.46797i | 0.115098 | − | 0.0664520i | ||||
\(489\) | 15.5878 | 0.704906 | ||||||||
\(490\) | −0.398599 | − | 0.877844i | −0.0180069 | − | 0.0396570i | ||||
\(491\) | 23.3549 | 1.05399 | 0.526996 | − | 0.849868i | \(-0.323318\pi\) | ||||
0.526996 | + | 0.849868i | \(0.323318\pi\) | |||||||
\(492\) | − | 18.2578i | − | 0.823124i | ||||||
\(493\) | 0.0941491 | + | 0.0543570i | 0.00424026 | + | 0.00244812i | ||||
\(494\) | −0.180346 | − | 0.312368i | −0.00811415 | − | 0.0140541i | ||||
\(495\) | 8.55801 | + | 6.12216i | 0.384654 | + | 0.275171i | ||||
\(496\) | 11.2254 | − | 19.4429i | 0.504034 | − | 0.873013i | ||||
\(497\) | 15.3879 | + | 8.88422i | 0.690243 | + | 0.398512i | ||||
\(498\) | −1.41221 | − | 0.815341i | −0.0632828 | − | 0.0365363i | ||||
\(499\) | 10.2603 | + | 17.7714i | 0.459314 | + | 0.795556i | 0.998925 | − | 0.0463591i | \(-0.0147618\pi\) |
−0.539611 | + | 0.841915i | \(0.681429\pi\) | |||||||
\(500\) | 21.5763 | − | 5.08590i | 0.964923 | − | 0.227448i | ||||
\(501\) | 10.3148 | − | 17.8657i | 0.460830 | − | 0.798180i | ||||
\(502\) | −1.62174 | − | 0.936313i | −0.0723819 | − | 0.0417897i | ||||
\(503\) | −15.2193 | − | 8.78687i | −0.678596 | − | 0.391787i | 0.120730 | − | 0.992685i | \(-0.461476\pi\) |
−0.799326 | + | 0.600898i | \(0.794810\pi\) | |||||||
\(504\) | −1.00917 | −0.0449520 | ||||||||
\(505\) | 1.59250 | − | 16.3036i | 0.0708654 | − | 0.725499i | ||||
\(506\) | −1.38302 | + | 2.39547i | −0.0614829 | + | 0.106492i | ||||
\(507\) | − | 12.4707i | − | 0.553842i | ||||||
\(508\) | 2.14967i | 0.0953763i | ||||||||
\(509\) | 2.55351 | − | 4.42280i | 0.113182 | − | 0.196037i | −0.803869 | − | 0.594806i | \(-0.797229\pi\) |
0.917052 | + | 0.398769i | \(0.130562\pi\) | |||||||
\(510\) | 0.589877 | − | 0.824574i | 0.0261202 | − | 0.0365128i | ||||
\(511\) | 2.53630 | + | 4.39299i | 0.112199 | + | 0.194335i | ||||
\(512\) | 10.1521i | 0.448665i | ||||||||
\(513\) | −3.26753 | + | 1.88651i | −0.144265 | + | 0.0832915i | ||||
\(514\) | −1.21587 | − | 2.10596i | −0.0536299 | − | 0.0928897i | ||||
\(515\) | 10.9942 | + | 1.07389i | 0.484461 | + | 0.0473212i | ||||
\(516\) | −6.99164 | + | 12.1099i | −0.307790 | + | 0.533108i | ||||
\(517\) | 1.85239i | 0.0814681i | ||||||||
\(518\) | −0.594510 | + | 1.42201i | −0.0261213 | + | 0.0624797i | ||||
\(519\) | 9.31313 | 0.408801 | ||||||||
\(520\) | 0.775190 | − | 0.351987i | 0.0339943 | − | 0.0154356i | ||||
\(521\) | 12.7661 | + | 22.1115i | 0.559291 | + | 0.968721i | 0.997556 | + | 0.0698751i | \(0.0222601\pi\) |
−0.438264 | + | 0.898846i | \(0.644407\pi\) | |||||||
\(522\) | −0.00358515 | + | 0.00206989i | −0.000156918 | + | 9.05966e-5i | ||||
\(523\) | 28.1108 | − | 16.2298i | 1.22920 | − | 0.709679i | 0.262337 | − | 0.964976i | \(-0.415507\pi\) |
0.966862 | + | 0.255298i | \(0.0821735\pi\) | |||||||
\(524\) | 21.9698 | 0.959754 | ||||||||
\(525\) | −6.34568 | + | 7.25942i | −0.276948 | + | 0.316827i | ||||
\(526\) | 1.34088 | 0.0584653 | ||||||||
\(527\) | −17.2171 | − | 9.94032i | −0.749990 | − | 0.433007i | ||||
\(528\) | 18.3369i | 0.798012i | ||||||||
\(529\) | 2.98828 | 0.129925 | ||||||||
\(530\) | 1.90758 | − | 0.866165i | 0.0828598 | − | 0.0376238i | ||||
\(531\) | −3.77054 | − | 6.53076i | −0.163627 | − | 0.283411i | ||||
\(532\) | 14.4261i | 0.625450i | ||||||||
\(533\) | −5.80193 | − | 3.34974i | −0.251309 | − | 0.145094i | ||||
\(534\) | −0.145347 | + | 0.251748i | −0.00628977 | + | 0.0108942i | ||||
\(535\) | −12.5019 | − | 27.5332i | −0.540504 | − | 1.19037i | ||||
\(536\) | −3.18505 | − | 5.51666i | −0.137573 | − | 0.238283i | ||||
\(537\) | 2.38946 | − | 1.37956i | 0.103113 | − | 0.0595323i | ||||
\(538\) | −0.697743 | − | 0.402842i | −0.0300818 | − | 0.0173678i | ||||
\(539\) | 7.72054 | − | 13.3724i | 0.332547 | − | 0.575989i | ||||
\(540\) | −1.83300 | − | 4.03687i | −0.0788798 | − | 0.173719i | ||||
\(541\) | 21.8256 | 0.938355 | 0.469177 | − | 0.883104i | \(-0.344551\pi\) | ||||
0.469177 | + | 0.883104i | \(0.344551\pi\) | |||||||
\(542\) | 3.43603 | − | 1.98379i | 0.147590 | − | 0.0852111i | ||||
\(543\) | 17.5124 | + | 10.1108i | 0.751528 | + | 0.433895i | ||||
\(544\) | 5.37836 | 0.230595 | ||||||||
\(545\) | −13.2146 | − | 9.45332i | −0.566050 | − | 0.404936i | ||||
\(546\) | −0.0921746 | + | 0.159651i | −0.00394471 | + | 0.00683243i | ||||
\(547\) | − | 7.15186i | − | 0.305791i | −0.988242 | − | 0.152896i | \(-0.951140\pi\) | ||
0.988242 | − | 0.152896i | \(-0.0488598\pi\) | |||||||
\(548\) | −24.2509 | + | 14.0012i | −1.03595 | + | 0.598103i | ||||
\(549\) | −5.61019 | −0.239437 | ||||||||
\(550\) | −2.32769 | − | 2.03471i | −0.0992531 | − | 0.0867601i | ||||
\(551\) | 0.0594358 | + | 0.102946i | 0.00253205 | + | 0.00438564i | ||||
\(552\) | 2.02742 | − | 1.17053i | 0.0862926 | − | 0.0498210i | ||||
\(553\) | −12.0665 | − | 6.96658i | −0.513119 | − | 0.296249i | ||||
\(554\) | −1.83808 | −0.0780927 | ||||||||
\(555\) | −13.5953 | + | 0.411225i | −0.577086 | + | 0.0174555i | ||||
\(556\) | −34.4580 | −1.46134 | ||||||||
\(557\) | −7.70945 | − | 4.45105i | −0.326660 | − | 0.188597i | 0.327697 | − | 0.944783i | \(-0.393727\pi\) |
−0.654357 | + | 0.756186i | \(0.727061\pi\) | |||||||
\(558\) | 0.655620 | − | 0.378523i | 0.0277546 | − | 0.0160241i | ||||
\(559\) | 2.56550 | + | 4.44358i | 0.108509 | + | 0.187944i | ||||
\(560\) | −16.7230 | − | 1.63347i | −0.706677 | − | 0.0690269i | ||||
\(561\) | 16.2378 | 0.685559 | ||||||||
\(562\) | 1.52143 | − | 0.878400i | 0.0641778 | − | 0.0370531i | ||||
\(563\) | 15.2521i | 0.642799i | 0.946944 | + | 0.321399i | \(0.104153\pi\) | ||||
−0.946944 | + | 0.321399i | \(0.895847\pi\) | |||||||
\(564\) | 0.390246 | − | 0.675926i | 0.0164323 | − | 0.0284616i | ||||
\(565\) | 6.30571 | − | 8.81460i | 0.265283 | − | 0.370833i | ||||
\(566\) | −2.50863 | −0.105446 | ||||||||
\(567\) | 1.67003 | + | 0.964193i | 0.0701348 | + | 0.0404923i | ||||
\(568\) | 4.17595 | − | 2.41099i | 0.175219 | − | 0.101163i | ||||
\(569\) | 15.7504 | 0.660292 | 0.330146 | − | 0.943930i | \(-0.392902\pi\) | ||||
0.330146 | + | 0.943930i | \(0.392902\pi\) | |||||||
\(570\) | 1.00939 | − | 0.458328i | 0.0422786 | − | 0.0191972i | ||||
\(571\) | −12.4399 | + | 21.5465i | −0.520593 | + | 0.901694i | 0.479120 | + | 0.877750i | \(0.340956\pi\) |
−0.999713 | + | 0.0239449i | \(0.992377\pi\) | |||||||
\(572\) | 5.87871 | + | 3.39408i | 0.245801 | + | 0.141914i | ||||
\(573\) | 10.5589 | − | 6.09621i | 0.441106 | − | 0.254673i | ||||
\(574\) | −1.16664 | − | 2.02068i | −0.0486945 | − | 0.0843414i | ||||
\(575\) | 4.32828 | − | 21.9445i | 0.180502 | − | 0.915147i | ||||
\(576\) | 3.79430 | − | 6.57193i | 0.158096 | − | 0.273830i | ||||
\(577\) | 31.7849 | + | 18.3510i | 1.32322 | + | 0.763962i | 0.984241 | − | 0.176832i | \(-0.0565849\pi\) |
0.338980 | + | 0.940794i | \(0.389918\pi\) | |||||||
\(578\) | 0.669239i | 0.0278367i | ||||||||
\(579\) | −8.63549 | − | 14.9571i | −0.358879 | − | 0.621596i | ||||
\(580\) | −0.127184 | + | 0.0577499i | −0.00528103 | + | 0.00239793i | ||||
\(581\) | 23.9318 | 0.992858 | ||||||||
\(582\) | 1.41638i | 0.0587108i | ||||||||
\(583\) | 29.0585 | + | 16.7769i | 1.20348 | + | 0.694829i | ||||
\(584\) | 1.37659 | 0.0569638 | ||||||||
\(585\) | −1.61913 | − | 0.158153i | −0.0669427 | − | 0.00653884i | ||||
\(586\) | 3.12926 | 0.129269 | ||||||||
\(587\) | 10.1890 | − | 5.88263i | 0.420545 | − | 0.242802i | −0.274765 | − | 0.961511i | \(-0.588600\pi\) |
0.695311 | + | 0.718709i | \(0.255267\pi\) | |||||||
\(588\) | −5.63436 | + | 3.25300i | −0.232357 | + | 0.134151i | ||||
\(589\) | −10.8691 | − | 18.8258i | −0.447853 | − | 0.775703i | ||||
\(590\) | 0.916052 | + | 2.01745i | 0.0377133 | + | 0.0830569i | ||||
\(591\) | 9.83563 | 0.404584 | ||||||||
\(592\) | −14.3673 | − | 18.8520i | −0.590494 | − | 0.774814i | ||||
\(593\) | − | 3.11542i | − | 0.127935i | −0.997952 | − | 0.0639675i | \(-0.979625\pi\) | ||
0.997952 | − | 0.0639675i | \(-0.0203754\pi\) | |||||||
\(594\) | −0.309163 | + | 0.535486i | −0.0126851 | + | 0.0219713i | ||||
\(595\) | −1.44648 | + | 14.8086i | −0.0592998 | + | 0.607094i | ||||
\(596\) | −4.46280 | − | 7.72979i | −0.182803 | − | 0.316625i | ||||
\(597\) | 11.6905 | − | 6.74950i | 0.478459 | − | 0.276239i | ||||
\(598\) | − | 0.427651i | − | 0.0174879i | ||||||
\(599\) | 8.80233 | + | 15.2461i | 0.359653 | + | 0.622938i | 0.987903 | − | 0.155074i | \(-0.0495616\pi\) |
−0.628249 | + | 0.778012i | \(0.716228\pi\) | |||||||
\(600\) | 0.845074 | + | 2.47639i | 0.0345000 | + | 0.101098i | ||||
\(601\) | −3.56489 | + | 6.17458i | −0.145415 | + | 0.251866i | −0.929528 | − | 0.368752i | \(-0.879785\pi\) |
0.784113 | + | 0.620619i | \(0.213118\pi\) | |||||||
\(602\) | 1.78701i | 0.0728331i | ||||||||
\(603\) | 12.1724i | 0.495698i | ||||||||
\(604\) | −0.990069 | + | 1.71485i | −0.0402853 | + | 0.0697762i | ||||
\(605\) | 2.42250 | − | 24.8009i | 0.0984888 | − | 1.00830i | ||||
\(606\) | 0.962605 | 0.0391031 | ||||||||
\(607\) | −35.5966 | − | 20.5517i | −1.44482 | − | 0.834167i | −0.446654 | − | 0.894707i | \(-0.647385\pi\) |
−0.998166 | + | 0.0605396i | \(0.980718\pi\) | |||||||
\(608\) | 5.09299 | + | 2.94044i | 0.206548 | + | 0.119251i | ||||
\(609\) | 0.0303775 | − | 0.0526155i | 0.00123096 | − | 0.00213209i | ||||
\(610\) | 1.64055 | + | 0.160246i | 0.0664239 | + | 0.00648817i | ||||
\(611\) | −0.143196 | − | 0.248024i | −0.00579311 | − | 0.0100340i | ||||
\(612\) | −5.92505 | − | 3.42083i | −0.239506 | − | 0.138279i | ||||
\(613\) | −22.6416 | − | 13.0721i | −0.914487 | − | 0.527979i | −0.0326146 | − | 0.999468i | \(-0.510383\pi\) |
−0.881872 | + | 0.471489i | \(0.843717\pi\) | |||||||
\(614\) | 0.0121130 | − | 0.0209803i | 0.000488840 | − | 0.000846695i | ||||
\(615\) | 11.9801 | − | 16.7466i | 0.483083 | − | 0.675289i | ||||
\(616\) | 2.37445 | + | 4.11267i | 0.0956693 | + | 0.165704i | ||||
\(617\) | 2.29295 | + | 1.32384i | 0.0923108 | + | 0.0532957i | 0.545445 | − | 0.838147i | \(-0.316361\pi\) |
−0.453134 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(618\) | 0.649124i | 0.0261116i | ||||||||
\(619\) | −39.5201 | −1.58845 | −0.794223 | − | 0.607626i | \(-0.792122\pi\) | ||||
−0.794223 | + | 0.607626i | \(0.792122\pi\) | |||||||
\(620\) | 23.2583 | − | 10.5608i | 0.934075 | − | 0.424131i | ||||
\(621\) | −4.47345 | −0.179513 | ||||||||
\(622\) | 3.07671 | − | 1.77634i | 0.123365 | − | 0.0712247i | ||||
\(623\) | − | 4.26620i | − | 0.170922i | ||||||
\(624\) | −1.41751 | − | 2.45520i | −0.0567458 | − | 0.0982866i | ||||
\(625\) | 23.1277 | + | 9.49261i | 0.925108 | + | 0.379705i | ||||
\(626\) | −1.68467 | − | 2.91793i | −0.0673329 | − | 0.116624i | ||||
\(627\) | 15.3762 | + | 8.87745i | 0.614066 | + | 0.354531i | ||||
\(628\) | 15.7135i | 0.627038i | ||||||||
\(629\) | −16.6939 | + | 12.7226i | −0.665630 | + | 0.507283i | ||||
\(630\) | −0.460815 | − | 0.329654i | −0.0183593 | − | 0.0131337i | ||||
\(631\) | 3.35439 | − | 5.80997i | 0.133536 | − | 0.231291i | −0.791501 | − | 0.611168i | \(-0.790700\pi\) |
0.925037 | + | 0.379876i | \(0.124033\pi\) | |||||||
\(632\) | −3.27458 | + | 1.89058i | −0.130256 | + | 0.0752033i | ||||
\(633\) | 18.9123 | − | 10.9190i | 0.751697 | − | 0.433993i | ||||
\(634\) | 2.06874 | + | 3.58316i | 0.0821601 | + | 0.142305i | ||||
\(635\) | −1.41053 | + | 1.97175i | −0.0559753 | + | 0.0782465i | ||||
\(636\) | −7.06884 | − | 12.2436i | −0.280298 | − | 0.485490i | ||||
\(637\) | 2.38730i | 0.0945884i | ||||||||
\(638\) | 0.0168708 | + | 0.00974038i | 0.000667923 | + | 0.000385625i | ||||
\(639\) | −9.21415 | −0.364506 | ||||||||
\(640\) | −5.35289 | + | 7.48267i | −0.211592 | + | 0.295779i | ||||
\(641\) | 14.5975 | − | 25.2837i | 0.576568 | − | 0.998646i | −0.419301 | − | 0.907847i | \(-0.637725\pi\) |
0.995869 | − | 0.0907984i | \(-0.0289419\pi\) | |||||||
\(642\) | 1.53885 | − | 0.888456i | 0.0607336 | − | 0.0350646i | ||||
\(643\) | − | 32.3849i | − | 1.27713i | −0.769566 | − | 0.638567i | \(-0.779527\pi\) | ||
0.769566 | − | 0.638567i | \(-0.220473\pi\) | |||||||
\(644\) | −8.55206 | + | 14.8126i | −0.336999 | + | 0.583699i | ||||
\(645\) | −14.3590 | + | 6.51993i | −0.565385 | + | 0.256722i | ||||
\(646\) | 0.855353 | − | 1.48151i | 0.0336534 | − | 0.0582894i | ||||
\(647\) | −29.1274 | + | 16.8167i | −1.14511 | + | 0.661132i | −0.947692 | − | 0.319186i | \(-0.896591\pi\) |
−0.197423 | + | 0.980318i | \(0.563257\pi\) | |||||||
\(648\) | 0.453211 | − | 0.261662i | 0.0178038 | − | 0.0102790i | ||||
\(649\) | −17.7432 | + | 30.7321i | −0.696482 | + | 1.20634i | ||||
\(650\) | 0.468953 | + | 0.0924954i | 0.0183939 | + | 0.00362797i | ||||
\(651\) | −5.55517 | + | 9.62184i | −0.217724 | + | 0.377110i | ||||
\(652\) | 30.9065i | 1.21039i | ||||||||
\(653\) | −2.52052 | + | 1.45522i | −0.0986356 | + | 0.0569473i | −0.548506 | − | 0.836146i | \(-0.684803\pi\) |
0.449871 | + | 0.893094i | \(0.351470\pi\) | |||||||
\(654\) | 0.477383 | − | 0.826852i | 0.0186672 | − | 0.0323325i | ||||
\(655\) | 20.1514 | + | 14.4157i | 0.787380 | + | 0.563269i | ||||
\(656\) | 35.8824 | 1.40097 | ||||||||
\(657\) | −2.27807 | − | 1.31524i | −0.0888758 | − | 0.0513125i | ||||
\(658\) | − | 0.0997440i | − | 0.00388843i | ||||||
\(659\) | −6.40101 | − | 11.0869i | −0.249348 | − | 0.431884i | 0.713997 | − | 0.700149i | \(-0.246883\pi\) |
−0.963345 | + | 0.268265i | \(0.913550\pi\) | |||||||
\(660\) | −12.1386 | + | 16.9683i | −0.472495 | + | 0.660489i | ||||
\(661\) | 25.5237 | + | 44.2084i | 0.992758 | + | 1.71951i | 0.600414 | + | 0.799689i | \(0.295002\pi\) |
0.392344 | + | 0.919818i | \(0.371664\pi\) | |||||||
\(662\) | −0.394058 | + | 0.227510i | −0.0153155 | + | 0.00884242i | ||||
\(663\) | −2.17413 | + | 1.25524i | −0.0844363 | + | 0.0487493i | ||||
\(664\) | 3.24729 | − | 5.62447i | 0.126019 | − | 0.218272i | ||||
\(665\) | −9.46585 | + | 13.2321i | −0.367070 | + | 0.513118i | ||||
\(666\) | −0.101715 | − | 0.792764i | −0.00394140 | − | 0.0307190i | ||||
\(667\) | 0.140939i | 0.00545717i | ||||||||
\(668\) | 35.4229 | + | 20.4514i | 1.37055 | + | 0.791290i | ||||
\(669\) | −2.01067 | − | 3.48258i | −0.0777369 | − | 0.134644i | ||||
\(670\) | 0.347684 | − | 3.55949i | 0.0134322 | − | 0.137515i | ||||
\(671\) | 13.2001 | + | 22.8632i | 0.509584 | + | 0.882625i | ||||
\(672\) | − | 3.00571i | − | 0.115948i | ||||||
\(673\) | −23.2784 | + | 13.4398i | −0.897316 | + | 0.518066i | −0.876328 | − | 0.481714i | \(-0.840014\pi\) |
−0.0209874 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(674\) | 2.30823 | 0.0889095 | ||||||||
\(675\) | 0.967550 | − | 4.90549i | 0.0372410 | − | 0.188812i | ||||
\(676\) | 24.7261 | 0.951002 | ||||||||
\(677\) | − | 21.9115i | − | 0.842126i | −0.907031 | − | 0.421063i | \(-0.861657\pi\) | ||
0.907031 | − | 0.421063i | \(-0.138343\pi\) | |||||||
\(678\) | 0.551541 | + | 0.318432i | 0.0211818 | + | 0.0122293i | ||||
\(679\) | −10.3933 | − | 18.0018i | −0.398860 | − | 0.690846i | ||||
\(680\) | 3.28406 | + | 2.34932i | 0.125938 | + | 0.0900924i | ||||
\(681\) | −12.5941 | + | 21.8135i | −0.482605 | + | 0.835897i | ||||
\(682\) | −3.08519 | − | 1.78123i | −0.118138 | − | 0.0682069i | ||||
\(683\) | 21.5260 | + | 12.4280i | 0.823668 | + | 0.475545i | 0.851680 | − | 0.524063i | \(-0.175584\pi\) |
−0.0280118 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(684\) | −3.74045 | − | 6.47865i | −0.143020 | − | 0.247718i | ||||
\(685\) | −31.4308 | − | 3.07010i | −1.20091 | − | 0.117302i | ||||
\(686\) | −1.30257 | + | 2.25612i | −0.0497324 | + | 0.0861391i | ||||
\(687\) | −12.5143 | − | 7.22513i | −0.477450 | − | 0.275656i | ||||
\(688\) | −23.7998 | − | 13.7408i | −0.907358 | − | 0.523863i | ||||
\(689\) | −5.18767 | −0.197634 | ||||||||
\(690\) | 1.30814 | + | 0.127777i | 0.0498000 | + | 0.00486437i | ||||
\(691\) | 20.7722 | − | 35.9785i | 0.790213 | − | 1.36869i | −0.135623 | − | 0.990761i | \(-0.543303\pi\) |
0.925835 | − | 0.377928i | \(-0.123363\pi\) | |||||||
\(692\) | 18.4655i | 0.701951i | ||||||||
\(693\) | − | 9.07451i | − | 0.344712i | ||||||
\(694\) | 1.66048 | − | 2.87604i | 0.0630310 | − | 0.109173i | ||||
\(695\) | −31.6060 | − | 22.6100i | −1.19888 | − | 0.857647i | ||||
\(696\) | −0.00824382 | − | 0.0142787i | −0.000312481 | − | 0.000541233i | ||||
\(697\) | − | 31.7746i | − | 1.20355i | ||||||
\(698\) | −3.30895 | + | 1.91043i | −0.125246 | + | 0.0723107i | ||||
\(699\) | −8.22224 | − | 14.2413i | −0.310994 | − | 0.538657i | ||||
\(700\) | −14.3935 | − | 12.5818i | −0.544024 | − | 0.475547i | ||||
\(701\) | 12.6739 | − | 21.9518i | 0.478687 | − | 0.829109i | −0.521015 | − | 0.853548i | \(-0.674446\pi\) |
0.999701 | + | 0.0244382i | \(0.00777970\pi\) | |||||||
\(702\) | − | 0.0955976i | − | 0.00360810i | ||||||
\(703\) | −22.7638 | + | 2.92071i | −0.858553 | + | 0.110157i | ||||
\(704\) | −35.7101 | −1.34587 | ||||||||
\(705\) | 0.801463 | − | 0.363917i | 0.0301849 | − | 0.0137059i | ||||
\(706\) | 2.06489 | + | 3.57649i | 0.0777131 | + | 0.134603i | ||||
\(707\) | −12.2344 | + | 7.06356i | −0.460123 | + | 0.265652i | ||||
\(708\) | 12.9488 | − | 7.47598i | 0.486645 | − | 0.280964i | ||||
\(709\) | 28.4972 | 1.07024 | 0.535118 | − | 0.844778i | \(-0.320267\pi\) | ||||
0.535118 | + | 0.844778i | \(0.320267\pi\) | |||||||
\(710\) | 2.69443 | + | 0.263187i | 0.101120 | + | 0.00987722i | ||||
\(711\) | 7.22529 | 0.270970 | ||||||||
\(712\) | −1.00265 | − | 0.578878i | −0.0375757 | − | 0.0216944i | ||||
\(713\) | − | 25.7736i | − | 0.965230i | ||||||
\(714\) | −0.874339 | −0.0327213 | ||||||||
\(715\) | 3.16508 | + | 6.97055i | 0.118367 | + | 0.260684i | ||||
\(716\) | 2.73530 | + | 4.73767i | 0.102223 | + | 0.177055i | ||||
\(717\) | 17.2222i | 0.643176i | ||||||||
\(718\) | −3.93019 | − | 2.26910i | −0.146673 | − | 0.0846820i | ||||
\(719\) | 7.87395 | − | 13.6381i | 0.293649 | − | 0.508614i | −0.681021 | − | 0.732264i | \(-0.738464\pi\) |
0.974670 | + | 0.223649i | \(0.0717971\pi\) | |||||||
\(720\) | 7.93373 | − | 3.60243i | 0.295673 | − | 0.134255i | ||||
\(721\) | −4.76325 | − | 8.25019i | −0.177393 | − | 0.307253i | ||||
\(722\) | −0.542147 | + | 0.313009i | −0.0201766 | + | 0.0116490i | ||||
\(723\) | 1.70851 | + | 0.986408i | 0.0635401 | + | 0.0366849i | ||||
\(724\) | −20.0470 | + | 34.7224i | −0.745040 | + | 1.29045i | ||||
\(725\) | −0.154551 | − | 0.0304833i | −0.00573987 | − | 0.00113212i | ||||
\(726\) | 1.46431 | 0.0543456 | ||||||||
\(727\) | 5.32240 | − | 3.07289i | 0.197397 | − | 0.113967i | −0.398044 | − | 0.917366i | \(-0.630311\pi\) |
0.595441 | + | 0.803399i | \(0.296977\pi\) | |||||||
\(728\) | −0.635848 | − | 0.367107i | −0.0235661 | − | 0.0136059i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.628591 | + | 0.449676i | 0.0232652 | + | 0.0166433i | ||||
\(731\) | −12.1678 | + | 21.0752i | −0.450042 | + | 0.779495i | ||||
\(732\) | − | 11.1235i | − | 0.411137i | ||||||
\(733\) | −23.0501 | + | 13.3080i | −0.851375 | + | 0.491542i | −0.861115 | − | 0.508411i | \(-0.830233\pi\) |
0.00973930 | + | 0.999953i | \(0.496900\pi\) | |||||||
\(734\) | −4.32711 | −0.159716 | ||||||||
\(735\) | −7.30251 | − | 0.713295i | −0.269357 | − | 0.0263103i | ||||
\(736\) | 3.48630 | + | 6.03845i | 0.128507 | + | 0.222580i | ||||
\(737\) | 49.6061 | − | 28.6401i | 1.82726 | − | 1.05497i | ||||
\(738\) | 1.04786 | + | 0.604981i | 0.0385722 | + | 0.0222697i | ||||
\(739\) | −43.7638 | −1.60988 | −0.804938 | − | 0.593359i | \(-0.797802\pi\) | ||||
−0.804938 | + | 0.593359i | \(0.797802\pi\) | |||||||
\(740\) | −0.815350 | − | 26.9558i | −0.0299729 | − | 0.990914i | ||||
\(741\) | −2.74504 | −0.100841 | ||||||||
\(742\) | −1.56469 | − | 0.903372i | −0.0574414 | − | 0.0331638i | ||||
\(743\) | −17.8071 | + | 10.2809i | −0.653280 | + | 0.377171i | −0.789712 | − | 0.613478i | \(-0.789770\pi\) |
0.136432 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(744\) | 1.50755 | + | 2.61116i | 0.0552696 | + | 0.0957298i | ||||
\(745\) | 0.978572 | − | 10.0183i | 0.0358521 | − | 0.367043i | ||||
\(746\) | 0.377888 | 0.0138355 | ||||||||
\(747\) | −10.7476 | + | 6.20513i | −0.393234 | + | 0.227034i | ||||
\(748\) | 32.1952i | 1.17717i | ||||||||
\(749\) | −13.0389 | + | 22.5841i | −0.476432 | + | 0.825204i | ||||
\(750\) | −0.423051 | + | 1.40684i | −0.0154476 | + | 0.0513706i | ||||
\(751\) | 1.02130 | 0.0372678 | 0.0186339 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186339 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(752\) | 1.32841 | + | 0.766958i | 0.0484421 | + | 0.0279681i | ||||
\(753\) | −12.3422 | + | 7.12578i | −0.449775 | + | 0.259678i | ||||
\(754\) | −0.00301187 | −0.000109686 | ||||||||
\(755\) | −2.03334 | + | 0.923271i | −0.0740009 | + | 0.0336013i | ||||
\(756\) | −1.91174 | + | 3.31123i | −0.0695293 | + | 0.120428i | ||||
\(757\) | −5.10352 | − | 2.94652i | −0.185491 | − | 0.107093i | 0.404379 | − | 0.914591i | \(-0.367488\pi\) |
−0.589870 | + | 0.807498i | \(0.700821\pi\) | |||||||
\(758\) | 1.31345 | − | 0.758320i | 0.0477066 | − | 0.0275434i | ||||
\(759\) | 10.5255 | + | 18.2306i | 0.382050 | + | 0.661730i | ||||
\(760\) | 1.82540 | + | 4.02012i | 0.0662142 | + | 0.145825i | ||||
\(761\) | −19.3400 | + | 33.4978i | −0.701073 | + | 1.21429i | 0.267017 | + | 0.963692i | \(0.413962\pi\) |
−0.968090 | + | 0.250603i | \(0.919371\pi\) | |||||||
\(762\) | −0.123375 | − | 0.0712306i | −0.00446940 | − | 0.00258041i | ||||
\(763\) | 14.0121i | 0.507272i | ||||||||
\(764\) | 12.0872 | + | 20.9356i | 0.437298 | + | 0.757423i | ||||
\(765\) | −3.19003 | − | 7.02549i | −0.115336 | − | 0.254007i | ||||
\(766\) | −3.03452 | −0.109642 | ||||||||
\(767\) | − | 5.48645i | − | 0.198104i | ||||||
\(768\) | 12.6756 | + | 7.31829i | 0.457393 | + | 0.264076i | ||||
\(769\) | −18.0409 | −0.650573 | −0.325287 | − | 0.945615i | \(-0.605461\pi\) | ||||
−0.325287 | + | 0.945615i | \(0.605461\pi\) | |||||||
\(770\) | −0.259198 | + | 2.65359i | −0.00934085 | + | 0.0956289i | ||||
\(771\) | −18.5067 | −0.666504 | ||||||||
\(772\) | 29.6560 | − | 17.1219i | 1.06734 | − | 0.616230i | ||||
\(773\) | 20.0181 | − | 11.5574i | 0.720000 | − | 0.415692i | −0.0947528 | − | 0.995501i | \(-0.530206\pi\) |
0.814753 | + | 0.579809i | \(0.196873\pi\) | |||||||
\(774\) | −0.463344 | − | 0.802535i | −0.0166545 | − | 0.0288465i | ||||
\(775\) | 28.2628 | + | 5.57451i | 1.01523 | + | 0.200242i | ||||
\(776\) | −5.64107 | −0.202502 | ||||||||
\(777\) | 7.11005 | + | 9.32943i | 0.255072 | + | 0.334691i | ||||
\(778\) | 0.720117i | 0.0258175i | ||||||||
\(779\) | 17.3717 | − | 30.0887i | 0.622407 | − | 1.07804i | ||||
\(780\) | 0.313576 | − | 3.21030i | 0.0112278 | − | 0.114947i | ||||
\(781\) | 21.6797 | + | 37.5504i | 0.775762 | + | 1.34366i | ||||
\(782\) | 1.75654 | − | 1.01414i | 0.0628138 | − | 0.0362656i | ||||
\(783\) | 0.0315057i | 0.00112592i | ||||||||
\(784\) | −6.39318 | − | 11.0733i | −0.228328 | − | 0.395475i | ||||
\(785\) | −10.3106 | + | 14.4130i | −0.368002 | + | 0.514421i | ||||
\(786\) | −0.727980 | + | 1.26090i | −0.0259662 | + | 0.0449748i | ||||
\(787\) | 44.3883i | 1.58227i | 0.611641 | + | 0.791135i | \(0.290510\pi\) | ||||
−0.611641 | + | 0.791135i | \(0.709490\pi\) | |||||||
\(788\) | 19.5014i | 0.694710i | ||||||||
\(789\) | 5.10237 | − | 8.83757i | 0.181649 | − | 0.314626i | ||||
\(790\) | −2.11284 | − | 0.206378i | −0.0751716 | − | 0.00734262i | ||||
\(791\) | −9.34658 | −0.332326 | ||||||||
\(792\) | −2.13270 | − | 1.23131i | −0.0757821 | − | 0.0437528i | ||||
\(793\) | −3.53482 | − | 2.04083i | −0.125525 | − | 0.0724719i | ||||
\(794\) | −0.681986 | + | 1.18124i | −0.0242028 | + | 0.0419205i | ||||
\(795\) | 1.55001 | − | 15.8685i | 0.0549731 | − | 0.562799i | ||||
\(796\) | 13.3825 | + | 23.1791i | 0.474329 | + | 0.821561i | ||||
\(797\) | −9.09440 | − | 5.25066i | −0.322140 | − | 0.185988i | 0.330206 | − | 0.943909i | \(-0.392882\pi\) |
−0.652346 | + | 0.757921i | \(0.726215\pi\) | |||||||
\(798\) | −0.827948 | − | 0.478016i | −0.0293090 | − | 0.0169216i | ||||
\(799\) | 0.679158 | − | 1.17634i | 0.0240269 | − | 0.0416158i | ||||
\(800\) | −7.37569 | + | 2.51697i | −0.260770 | + | 0.0889883i | ||||
\(801\) | 1.10616 | + | 1.91592i | 0.0390841 | + | 0.0676957i | ||||
\(802\) | 0.956952 | + | 0.552497i | 0.0337912 | + | 0.0195093i | ||||
\(803\) | 12.3784i | 0.436824i | ||||||||
\(804\) | −24.1346 | −0.851162 | ||||||||
\(805\) | −17.5637 | + | 7.97507i | −0.619039 | + | 0.281084i | ||||
\(806\) | 0.550783 | 0.0194005 | ||||||||
\(807\) | −5.31015 | + | 3.06582i | −0.186926 | + | 0.107922i | ||||
\(808\) | 3.83380i | 0.134873i | ||||||||
\(809\) | −15.9119 | − | 27.5603i | −0.559433 | − | 0.968967i | −0.997544 | − | 0.0700457i | \(-0.977685\pi\) |
0.438110 | − | 0.898921i | \(-0.355648\pi\) | |||||||
\(810\) | 0.292423 | + | 0.0285633i | 0.0102747 | + | 0.00100361i | ||||
\(811\) | 2.66697 | + | 4.61934i | 0.0936501 | + | 0.162207i | 0.909044 | − | 0.416699i | \(-0.136813\pi\) |
−0.815394 | + | 0.578906i | \(0.803480\pi\) | |||||||
\(812\) | 0.104322 | + | 0.0602306i | 0.00366100 | + | 0.00211368i | ||||
\(813\) | − | 30.1952i | − | 1.05899i | ||||||
\(814\) | −2.99143 | + | 2.27980i | −0.104849 | + | 0.0799068i | ||||
\(815\) | −20.2797 | + | 28.3485i | −0.710367 | + | 0.993004i | ||||
\(816\) | 6.72303 | − | 11.6446i | 0.235353 | − | 0.407643i | ||||
\(817\) | −23.0444 | + | 13.3047i | −0.806220 | + | 0.465471i | ||||
\(818\) | −1.71384 | + | 0.989488i | −0.0599232 | + | 0.0345966i | ||||
\(819\) | 0.701492 | + | 1.21502i | 0.0245121 | + | 0.0424562i | ||||
\(820\) | 33.2041 | + | 23.7533i | 1.15954 | + | 0.829501i | ||||
\(821\) | −16.5642 | − | 28.6900i | −0.578094 | − | 1.00129i | −0.995698 | − | 0.0926596i | \(-0.970463\pi\) |
0.417603 | − | 0.908629i | \(-0.362870\pi\) | |||||||
\(822\) | − | 1.85575i | − | 0.0647269i | ||||||
\(823\) | −32.1686 | − | 18.5726i | −1.12133 | − | 0.647399i | −0.179588 | − | 0.983742i | \(-0.557477\pi\) |
−0.941740 | + | 0.336343i | \(0.890810\pi\) | |||||||
\(824\) | −2.58529 | −0.0900628 | ||||||||
\(825\) | −22.2679 | + | 7.59895i | −0.775268 | + | 0.264562i | ||||
\(826\) | 0.955402 | − | 1.65480i | 0.0332427 | − | 0.0575780i | ||||
\(827\) | 20.2648 | − | 11.6999i | 0.704677 | − | 0.406846i | −0.104410 | − | 0.994534i | \(-0.533295\pi\) |
0.809087 | + | 0.587689i | \(0.199962\pi\) | |||||||
\(828\) | − | 8.86966i | − | 0.308242i | ||||||
\(829\) | 7.90893 | − | 13.6987i | 0.274689 | − | 0.475775i | −0.695368 | − | 0.718654i | \(-0.744759\pi\) |
0.970057 | + | 0.242879i | \(0.0780919\pi\) | |||||||
\(830\) | 3.32009 | − | 1.50754i | 0.115242 | − | 0.0523273i | ||||
\(831\) | −6.99434 | + | 12.1146i | −0.242631 | + | 0.420249i | ||||
\(832\) | 4.78135 | − | 2.76052i | 0.165764 | − | 0.0957037i | ||||
\(833\) | −9.80566 | + | 5.66130i | −0.339746 | + | 0.196152i | ||||
\(834\) | 1.14178 | − | 1.97763i | 0.0395367 | − | 0.0684796i | ||||
\(835\) | 19.0716 | + | 42.0019i | 0.660000 | + | 1.45354i | ||||
\(836\) | −17.6016 | + | 30.4869i | −0.608765 | + | 1.05441i | ||||
\(837\) | − | 5.76147i | − | 0.199145i | ||||||
\(838\) | 0.896485 | − | 0.517586i | 0.0309685 | − | 0.0178797i | ||||
\(839\) | 4.74656 | − | 8.22129i | 0.163870 | − | 0.283830i | −0.772384 | − | 0.635156i | \(-0.780936\pi\) |
0.936253 | + | 0.351326i | \(0.114269\pi\) | |||||||
\(840\) | 1.31292 | − | 1.83531i | 0.0453002 | − | 0.0633240i | ||||
\(841\) | −28.9990 | −0.999966 | ||||||||
\(842\) | −4.45241 | − | 2.57060i | −0.153440 | − | 0.0885888i | ||||
\(843\) | − | 13.3701i | − | 0.460490i | ||||||
\(844\) | 21.6495 | + | 37.4981i | 0.745208 | + | 1.29074i | ||||
\(845\) | 22.6795 | + | 16.2243i | 0.780200 | + | 0.558133i | ||||
\(846\) | 0.0258620 | + | 0.0447943i | 0.000889155 | + | 0.00154006i | ||||
\(847\) | −18.6110 | + | 10.7450i | −0.639480 | + | 0.369204i | ||||
\(848\) | 24.0626 | − | 13.8925i | 0.826312 | − | 0.477071i | ||||
\(849\) | −9.54594 | + | 16.5340i | −0.327616 | + | 0.567447i | ||||
\(850\) | 0.732168 | + | 2.14553i | 0.0251132 | + | 0.0735912i | ||||
\(851\) | −25.1052 | − | 10.4959i | −0.860595 | − | 0.359794i | ||||
\(852\) | − | 18.2692i | − | 0.625893i | ||||||
\(853\) | 27.9396 | + | 16.1309i | 0.956634 | + | 0.552313i | 0.895135 | − | 0.445794i | \(-0.147079\pi\) |
0.0614986 | + | 0.998107i | \(0.480412\pi\) | |||||||
\(854\) | −0.710773 | − | 1.23109i | −0.0243221 | − | 0.0421272i | ||||
\(855\) | 0.820181 | − | 8.39678i | 0.0280496 | − | 0.287164i | ||||
\(856\) | 3.53848 | + | 6.12883i | 0.120943 | + | 0.209479i | ||||
\(857\) | 10.6197i | 0.362761i | 0.983413 | + | 0.181380i | \(0.0580565\pi\) | ||||
−0.983413 | + | 0.181380i | \(0.941944\pi\) | |||||||
\(858\) | −0.389589 | + | 0.224929i | −0.0133003 | + | 0.00767896i | ||||
\(859\) | −1.98651 | −0.0677790 | −0.0338895 | − | 0.999426i | \(-0.510789\pi\) | ||||
−0.0338895 | + | 0.999426i | \(0.510789\pi\) | |||||||
\(860\) | −12.9273 | − | 28.4701i | −0.440817 | − | 0.970822i | ||||
\(861\) | −17.7573 | −0.605168 | ||||||||
\(862\) | 2.09321i | 0.0712951i | ||||||||
\(863\) | 35.6325 | + | 20.5725i | 1.21295 | + | 0.700295i | 0.963400 | − | 0.268068i | \(-0.0863853\pi\) |
0.249546 | + | 0.968363i | \(0.419719\pi\) | |||||||
\(864\) | 0.779333 | + | 1.34984i | 0.0265134 | + | 0.0459226i | ||||
\(865\) | −12.1163 | + | 16.9371i | −0.411968 | + | 0.575879i | ||||
\(866\) | 2.20659 | − | 3.82193i | 0.0749830 | − | 0.129874i | ||||
\(867\) | 4.41086 | + | 2.54661i | 0.149801 | + | 0.0864874i | ||||
\(868\) | −19.0775 | − | 11.0144i | −0.647534 | − | 0.373854i | ||||
\(869\) | −17.0002 | − | 29.4452i | −0.576693 | − | 0.998861i | ||||
\(870\) | 0.000899907 | − | 0.00921298i | 3.05097e−5 | − | 0.000312349i | ||||
\(871\) | −4.42796 | + | 7.66946i | −0.150036 | + | 0.259870i | ||||
\(872\) | 3.29313 | + | 1.90129i | 0.111520 | + | 0.0643858i | ||||
\(873\) | 9.33516 | + | 5.38966i | 0.315947 | + | 0.182412i | ||||
\(874\) | 2.21779 | 0.0750179 | ||||||||
\(875\) | −4.94650 | − | 20.9849i | −0.167222 | − | 0.709420i | ||||
\(876\) | 2.60778 | − | 4.51680i | 0.0881086 | − | 0.152609i | ||||
\(877\) | 57.2662i | 1.93374i | 0.255267 | + | 0.966871i | \(0.417837\pi\) | ||||
−0.255267 | + | 0.966871i | \(0.582163\pi\) | |||||||
\(878\) | − | 0.553784i | − | 0.0186893i | ||||||
\(879\) | 11.9076 | − | 20.6245i | 0.401632 | − | 0.695648i | ||||
\(880\) | −33.3481 | − | 23.8562i | −1.12416 | − | 0.804194i | ||||
\(881\) | 9.57031 | + | 16.5763i | 0.322432 | + | 0.558469i | 0.980989 | − | 0.194062i | \(-0.0621663\pi\) |
−0.658557 | + | 0.752531i | \(0.728833\pi\) | |||||||
\(882\) | − | 0.431159i | − | 0.0145179i | ||||||
\(883\) | −11.1806 | + | 6.45510i | −0.376256 | + | 0.217231i | −0.676188 | − | 0.736729i | \(-0.736369\pi\) |
0.299932 | + | 0.953961i | \(0.403036\pi\) | |||||||
\(884\) | −2.48880 | − | 4.31073i | −0.0837074 | − | 0.144986i | ||||
\(885\) | 16.7825 | + | 1.63928i | 0.564137 | + | 0.0551039i | ||||
\(886\) | −1.62317 | + | 2.81142i | −0.0545316 | + | 0.0944515i | ||||
\(887\) | − | 24.7920i | − | 0.832433i | −0.909266 | − | 0.416216i | \(-0.863356\pi\) | ||
0.909266 | − | 0.416216i | \(-0.136644\pi\) | |||||||
\(888\) | 3.15737 | − | 0.405106i | 0.105954 | − | 0.0135945i | ||||
\(889\) | 2.09075 | 0.0701215 | ||||||||
\(890\) | −0.268741 | − | 0.591855i | −0.00900821 | − | 0.0198390i | ||||
\(891\) | 2.35287 | + | 4.07530i | 0.0788243 | + | 0.136528i | ||||
\(892\) | 6.90503 | − | 3.98662i | 0.231198 | − | 0.133482i | ||||
\(893\) | 1.28625 | − | 0.742615i | 0.0430426 | − | 0.0248506i | ||||
\(894\) | 0.591509 | 0.0197830 | ||||||||
\(895\) | −0.599778 | + | 6.14035i | −0.0200484 | + | 0.205249i | ||||
\(896\) | 7.93427 | 0.265065 | ||||||||
\(897\) | −2.81859 | − | 1.62731i | −0.0941098 | − | 0.0543343i | ||||
\(898\) | 3.89769i | 0.130068i | ||||||||
\(899\) | −0.181519 | −0.00605399 | ||||||||
\(900\) | 9.72629 | + | 1.91839i | 0.324210 | + | 0.0639465i | ||||
\(901\) | −12.3021 | − | 21.3079i | −0.409844 | − | 0.709870i | ||||
\(902\) | − | 5.69378i | − | 0.189582i | ||||||
\(903\) | 11.7779 | + | 6.80000i | 0.391945 | + | 0.226290i | ||||
\(904\) | −1.26823 | + | 2.19664i | −0.0421808 | + | 0.0730592i | ||||
\(905\) | −41.1713 | + | 18.6944i | −1.36858 | + | 0.621425i | ||||
\(906\) | −0.0656129 | − | 0.113645i | −0.00217984 | − | 0.00377560i | ||||
\(907\) | −47.0385 | + | 27.1577i | −1.56189 | + | 0.901756i | −0.564821 | + | 0.825214i | \(0.691055\pi\) |
−0.997066 | + | 0.0765424i | \(0.975612\pi\) | |||||||
\(908\) | −43.2505 | − | 24.9707i | −1.43532 | − | 0.828681i | ||||
\(909\) | 3.66294 | − | 6.34439i | 0.121492 | − | 0.210430i | ||||
\(910\) | −0.170427 | − | 0.375337i | −0.00564961 | − | 0.0124423i | ||||
\(911\) | −1.28498 | −0.0425732 | −0.0212866 | − | 0.999773i | \(-0.506776\pi\) | ||||
−0.0212866 | + | 0.999773i | \(0.506776\pi\) | |||||||
\(912\) | 12.7326 | − | 7.35118i | 0.421619 | − | 0.243422i | ||||
\(913\) | 50.5755 | + | 29.1998i | 1.67381 | + | 0.966372i | ||||
\(914\) | 2.69755 | 0.0892270 | ||||||||
\(915\) | 7.29884 | − | 10.2029i | 0.241292 | − | 0.337296i | ||||
\(916\) | 14.3255 | − | 24.8125i | 0.473328 | − | 0.819829i | ||||
\(917\) | − | 21.3676i | − | 0.705619i | ||||||
\(918\) | 0.392660 | − | 0.226702i | 0.0129597 | − | 0.00748229i | ||||
\(919\) | 54.4437 | 1.79593 | 0.897966 | − | 0.440064i | \(-0.145044\pi\) | ||||
0.897966 | + | 0.440064i | \(0.145044\pi\) | |||||||
\(920\) | −0.508900 | + | 5.20997i | −0.0167779 | + | 0.171768i | ||||
\(921\) | −0.0921854 | − | 0.159670i | −0.00303761 | − | 0.00526130i | ||||
\(922\) | 2.46360 | − | 1.42236i | 0.0811343 | − | 0.0468429i | ||||
\(923\) | −5.80556 | − | 3.35184i | −0.191092 | − | 0.110327i | ||||
\(924\) | 17.9923 | 0.591904 | ||||||||
\(925\) | 16.9395 | − | 25.2597i | 0.556967 | − | 0.830535i | ||||
\(926\) | −3.44056 | −0.113064 | ||||||||
\(927\) | 4.27828 | + | 2.47007i | 0.140517 | + | 0.0811277i | ||||
\(928\) | 0.0425277 | − | 0.0245534i | 0.00139604 | − | 0.000806005i | ||||
\(929\) | 4.43388 | + | 7.67971i | 0.145471 | + | 0.251963i | 0.929549 | − | 0.368700i | \(-0.120197\pi\) |
−0.784078 | + | 0.620663i | \(0.786864\pi\) | |||||||
\(930\) | −0.164567 | + | 1.68479i | −0.00539636 | + | 0.0552463i | ||||
\(931\) | −12.3805 | −0.405755 | ||||||||
\(932\) | 28.2368 | − | 16.3025i | 0.924926 | − | 0.534007i | ||||
\(933\) | − | 27.0376i | − | 0.885170i | ||||||
\(934\) | 2.42894 | − | 4.20704i | 0.0794772 | − | 0.137659i | ||||
\(935\) | −21.1252 | + | 29.5305i | −0.690869 | + | 0.965749i | ||||
\(936\) | 0.380740 | 0.0124449 | ||||||||
\(937\) | 23.2218 | + | 13.4071i | 0.758623 | + | 0.437991i | 0.828801 | − | 0.559543i | \(-0.189023\pi\) |
−0.0701779 | + | 0.997534i | \(0.522357\pi\) | |||||||
\(938\) | −2.67109 | + | 1.54216i | −0.0872143 | + | 0.0503532i | ||||
\(939\) | −25.6422 | −0.836802 | ||||||||
\(940\) | 0.721550 | + | 1.58909i | 0.0235344 | + | 0.0518304i | ||||
\(941\) | 1.53591 | − | 2.66028i | 0.0500693 | − | 0.0867226i | −0.839905 | − | 0.542734i | \(-0.817389\pi\) |
0.889974 | + | 0.456012i | \(0.150722\pi\) | |||||||
\(942\) | −0.901838 | − | 0.520676i | −0.0293835 | − | 0.0169645i | ||||
\(943\) | 35.6744 | − | 20.5966i | 1.16172 | − | 0.670718i | ||||
\(944\) | 14.6927 | + | 25.4485i | 0.478206 | + | 0.828277i | ||||
\(945\) | −3.92621 | + | 1.78276i | −0.127720 | + | 0.0579931i | ||||
\(946\) | −2.18038 | + | 3.77653i | −0.0708902 | + | 0.122785i | ||||
\(947\) | 13.3413 | + | 7.70260i | 0.433534 | + | 0.250301i | 0.700851 | − | 0.713308i | \(-0.252804\pi\) |
−0.267317 | + | 0.963609i | \(0.586137\pi\) | |||||||
\(948\) | 14.3258i | 0.465282i | ||||||||
\(949\) | −0.956895 | − | 1.65739i | −0.0310621 | − | 0.0538012i | ||||
\(950\) | −0.479680 | + | 2.43198i | −0.0155629 | + | 0.0789040i | ||||
\(951\) | 31.4881 | 1.02107 | ||||||||
\(952\) | − | 3.48226i | − | 0.112861i | ||||||
\(953\) | 24.0471 | + | 13.8836i | 0.778963 | + | 0.449735i | 0.836063 | − | 0.548634i | \(-0.184852\pi\) |
−0.0570996 | + | 0.998368i | \(0.518185\pi\) | |||||||
\(954\) | 0.936919 | 0.0303339 | ||||||||
\(955\) | −2.65039 | + | 27.1339i | −0.0857647 | + | 0.878034i | ||||
\(956\) | −34.1471 | −1.10440 | ||||||||
\(957\) | 0.128395 | − | 0.0741289i | 0.00415042 | − | 0.00239625i | ||||
\(958\) | 3.39813 | − | 1.96191i | 0.109789 | − | 0.0633865i | ||||
\(959\) | 13.6175 | + | 23.5861i | 0.439731 | + | 0.761636i | ||||
\(960\) | 7.01552 | + | 15.4505i | 0.226425 | + | 0.498662i | ||||
\(961\) | 2.19452 | 0.0707908 | ||||||||
\(962\) | 0.224297 | − | 0.536498i | 0.00723162 | − | 0.0172974i | ||||
\(963\) | − | 13.5231i | − | 0.435777i | ||||||
\(964\) | −1.95579 | + | 3.38752i | −0.0629916 | + | 0.109105i | ||||
\(965\) | 38.4362 | + | 3.75437i | 1.23730 | + | 0.120858i | ||||
\(966\) | −0.566755 | − | 0.981648i | −0.0182350 | − | 0.0315840i | ||||
\(967\) | −12.6278 | + | 7.29068i | −0.406083 | + | 0.234452i | −0.689106 | − | 0.724661i | \(-0.741996\pi\) |
0.283022 | + | 0.959113i | \(0.408663\pi\) | |||||||
\(968\) | 5.83196i | 0.187446i | ||||||||
\(969\) | −6.50964 | − | 11.2750i | −0.209120 | − | 0.362206i | ||||
\(970\) | −2.57587 | − | 1.84270i | −0.0827062 | − | 0.0591656i | ||||
\(971\) | −16.2950 | + | 28.2238i | −0.522932 | + | 0.905744i | 0.476712 | + | 0.879059i | \(0.341828\pi\) |
−0.999644 | + | 0.0266848i | \(0.991505\pi\) | |||||||
\(972\) | − | 1.98273i | − | 0.0635962i | ||||||
\(973\) | 33.5135i | 1.07439i | ||||||||
\(974\) | −1.79017 | + | 3.10066i | −0.0573606 | + | 0.0993515i | ||||
\(975\) | 2.39410 | − | 2.73884i | 0.0766726 | − | 0.0877130i | ||||
\(976\) | 21.8613 | 0.699762 | ||||||||
\(977\) | 3.25389 | + | 1.87863i | 0.104101 | + | 0.0601028i | 0.551147 | − | 0.834408i | \(-0.314190\pi\) |
−0.447046 | + | 0.894511i | \(0.647524\pi\) | |||||||
\(978\) | −1.77380 | − | 1.02410i | −0.0567199 | − | 0.0327473i | ||||
\(979\) | 5.20530 | − | 9.01584i | 0.166362 | − | 0.288148i | ||||
\(980\) | 1.41428 | − | 14.4789i | 0.0451774 | − | 0.462513i | ||||
\(981\) | −3.63311 | − | 6.29273i | −0.115996 | − | 0.200911i | ||||
\(982\) | −2.65765 | − | 1.53439i | −0.0848089 | − | 0.0489645i | ||||
\(983\) | −10.6986 | − | 6.17682i | −0.341231 | − | 0.197010i | 0.319585 | − | 0.947558i | \(-0.396457\pi\) |
−0.660816 | + | 0.750548i | \(0.729790\pi\) | |||||||
\(984\) | −2.40948 | + | 4.17334i | −0.0768114 | + | 0.133041i | ||||
\(985\) | −12.7961 | + | 17.8874i | −0.407718 | + | 0.569939i | ||||
\(986\) | −0.00714240 | − | 0.0123710i | −0.000227460 | − | 0.000393973i | ||||
\(987\) | −0.657399 | − | 0.379549i | −0.0209252 | − | 0.0120812i | ||||
\(988\) | − | 5.44268i | − | 0.173155i | ||||||
\(989\) | −31.5491 | −1.00320 | ||||||||
\(990\) | −0.571631 | − | 1.25892i | −0.0181676 | − | 0.0400110i | ||||
\(991\) | −51.5517 | −1.63759 | −0.818797 | − | 0.574083i | \(-0.805359\pi\) | ||||
−0.818797 | + | 0.574083i | \(0.805359\pi\) | |||||||
\(992\) | −7.77708 | + | 4.49010i | −0.246923 | + | 0.142561i | ||||
\(993\) | 3.46291i | 0.109892i | ||||||||
\(994\) | −1.16737 | − | 2.02194i | −0.0370267 | − | 0.0641321i | ||||
\(995\) | −2.93442 | + | 30.0417i | −0.0930272 | + | 0.952386i | ||||
\(996\) | −12.3031 | − | 21.3096i | −0.389839 | − | 0.675222i | ||||
\(997\) | −20.2958 | − | 11.7178i | −0.642773 | − | 0.371105i | 0.142909 | − | 0.989736i | \(-0.454354\pi\) |
−0.785682 | + | 0.618631i | \(0.787688\pi\) | |||||||
\(998\) | − | 2.69637i | − | 0.0853520i | ||||||
\(999\) | −5.61205 | − | 2.34626i | −0.177557 | − | 0.0742324i |
(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 | 555.2.bb.a.454.18 | ✓ | 72 | |
5.4 | even | 2 | inner | 555.2.bb.a.454.19 | yes | 72 | |
37.26 | even | 3 | inner | 555.2.bb.a.544.19 | yes | 72 | |
185.174 | even | 6 | inner | 555.2.bb.a.544.18 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
555.2.bb.a.454.18 | ✓ | 72 | 1.1 | even | 1 | trivial | |
555.2.bb.a.454.19 | yes | 72 | 5.4 | even | 2 | inner | |
555.2.bb.a.544.18 | yes | 72 | 185.174 | even | 6 | inner | |
555.2.bb.a.544.19 | yes | 72 | 37.26 | even | 3 | inner |