Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(36,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.q (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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.6 | ||
Root | \(-1.30089 - 0.554694i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.43 |
Dual form | 91.2.q.a.36.6 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.82678 | + | 1.05469i | 1.29173 | + | 0.745781i | 0.978961 | − | 0.204047i | \(-0.0654097\pi\) |
0.312770 | + | 0.949829i | \(0.398743\pi\) | |||||||
\(3\) | −1.13082 | + | 1.95864i | −0.652882 | + | 1.13082i | 0.329539 | + | 0.944142i | \(0.393107\pi\) |
−0.982420 | + | 0.186682i | \(0.940227\pi\) | |||||||
\(4\) | 1.22476 | + | 2.12135i | 0.612380 | + | 1.06067i | ||||
\(5\) | − | 3.60178i | − | 1.61076i | −0.592756 | − | 0.805382i | \(-0.701960\pi\) | ||
0.592756 | − | 0.805382i | \(-0.298040\pi\) | |||||||
\(6\) | −4.13154 | + | 2.38535i | −1.68670 | + | 0.973814i | ||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | 0.948212i | 0.335243i | ||||||||
\(9\) | −1.05753 | − | 1.83169i | −0.352509 | − | 0.610563i | ||||
\(10\) | 3.79878 | − | 6.57967i | 1.20128 | − | 2.08068i | ||||
\(11\) | 0.767631 | + | 0.443192i | 0.231450 | + | 0.133627i | 0.611241 | − | 0.791445i | \(-0.290671\pi\) |
−0.379791 | + | 0.925072i | \(0.624004\pi\) | |||||||
\(12\) | −5.53995 | −1.59925 | ||||||||
\(13\) | −1.17349 | + | 3.40924i | −0.325467 | + | 0.945553i | ||||
\(14\) | −2.10939 | −0.563758 | ||||||||
\(15\) | 7.05461 | + | 4.07298i | 1.82149 | + | 1.05164i | ||||
\(16\) | 1.44945 | − | 2.51051i | 0.362362 | − | 0.627629i | ||||
\(17\) | −2.48008 | − | 4.29563i | −0.601508 | − | 1.04184i | −0.992593 | − | 0.121488i | \(-0.961233\pi\) |
0.391085 | − | 0.920355i | \(-0.372100\pi\) | |||||||
\(18\) | − | 4.46147i | − | 1.05158i | ||||||
\(19\) | 2.06008 | − | 1.18939i | 0.472615 | − | 0.272864i | −0.244719 | − | 0.969594i | \(-0.578696\pi\) |
0.717334 | + | 0.696730i | \(0.245362\pi\) | |||||||
\(20\) | 7.64062 | − | 4.41132i | 1.70849 | − | 0.986400i | ||||
\(21\) | − | 2.26165i | − | 0.493532i | ||||||
\(22\) | 0.934864 | + | 1.61923i | 0.199314 | + | 0.345222i | ||||
\(23\) | −1.92926 | + | 3.34157i | −0.402278 | + | 0.696765i | −0.994000 | − | 0.109376i | \(-0.965115\pi\) |
0.591723 | + | 0.806142i | \(0.298448\pi\) | |||||||
\(24\) | −1.85721 | − | 1.07226i | −0.379101 | − | 0.218874i | ||||
\(25\) | −7.97282 | −1.59456 | ||||||||
\(26\) | −5.73942 | + | 4.99028i | −1.12559 | + | 0.978674i | ||||
\(27\) | −2.00144 | −0.385177 | ||||||||
\(28\) | −2.12135 | − | 1.22476i | −0.400897 | − | 0.231458i | ||||
\(29\) | −0.640986 | + | 1.11022i | −0.119028 | + | 0.206163i | −0.919383 | − | 0.393364i | \(-0.871311\pi\) |
0.800355 | + | 0.599527i | \(0.204645\pi\) | |||||||
\(30\) | 8.59150 | + | 14.8809i | 1.56859 | + | 2.71687i | ||||
\(31\) | 8.46921i | 1.52111i | 0.649271 | + | 0.760557i | \(0.275074\pi\) | ||||
−0.649271 | + | 0.760557i | \(0.724926\pi\) | |||||||
\(32\) | 6.93800 | − | 4.00566i | 1.22648 | − | 0.708107i | ||||
\(33\) | −1.73611 | + | 1.00234i | −0.302218 | + | 0.174486i | ||||
\(34\) | − | 10.4629i | − | 1.79437i | ||||||
\(35\) | 1.80089 | + | 3.11923i | 0.304406 | + | 0.527247i | ||||
\(36\) | 2.59043 | − | 4.48676i | 0.431739 | − | 0.747793i | ||||
\(37\) | −8.34686 | − | 4.81906i | −1.37222 | − | 0.792249i | −0.381009 | − | 0.924571i | \(-0.624423\pi\) |
−0.991207 | + | 0.132323i | \(0.957757\pi\) | |||||||
\(38\) | 5.01776 | 0.813988 | ||||||||
\(39\) | −5.35049 | − | 6.15370i | −0.856763 | − | 0.985380i | ||||
\(40\) | 3.41525 | 0.539998 | ||||||||
\(41\) | 10.4652 | + | 6.04207i | 1.63438 | + | 0.943612i | 0.982719 | + | 0.185106i | \(0.0592628\pi\) |
0.651666 | + | 0.758506i | \(0.274071\pi\) | |||||||
\(42\) | 2.38535 | − | 4.13154i | 0.368067 | − | 0.637511i | ||||
\(43\) | −1.82125 | − | 3.15450i | −0.277738 | − | 0.481056i | 0.693084 | − | 0.720856i | \(-0.256251\pi\) |
−0.970822 | + | 0.239800i | \(0.922918\pi\) | |||||||
\(44\) | 2.17122i | 0.327323i | ||||||||
\(45\) | −6.59734 | + | 3.80898i | −0.983474 | + | 0.567809i | ||||
\(46\) | −7.04867 | + | 4.06955i | −1.03927 | + | 0.600022i | ||||
\(47\) | − | 2.98229i | − | 0.435012i | −0.976059 | − | 0.217506i | \(-0.930208\pi\) | ||
0.976059 | − | 0.217506i | \(-0.0697922\pi\) | |||||||
\(48\) | 3.27814 | + | 5.67790i | 0.473158 | + | 0.819535i | ||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | −14.5646 | − | 8.40888i | −2.05975 | − | 1.18920i | ||||
\(51\) | 11.2181 | 1.57085 | ||||||||
\(52\) | −8.66942 | + | 1.68613i | −1.20223 | + | 0.233824i | ||||
\(53\) | 4.92032 | 0.675858 | 0.337929 | − | 0.941172i | \(-0.390274\pi\) | ||||
0.337929 | + | 0.941172i | \(0.390274\pi\) | |||||||
\(54\) | −3.65619 | − | 2.11090i | −0.497545 | − | 0.287258i | ||||
\(55\) | 1.59628 | − | 2.76484i | 0.215242 | − | 0.372811i | ||||
\(56\) | −0.474106 | − | 0.821175i | −0.0633551 | − | 0.109734i | ||||
\(57\) | 5.37995i | 0.712592i | ||||||||
\(58\) | −2.34189 | + | 1.35209i | −0.307505 | + | 0.177538i | ||||
\(59\) | 6.34577 | − | 3.66373i | 0.826148 | − | 0.476977i | −0.0263837 | − | 0.999652i | \(-0.508399\pi\) |
0.852532 | + | 0.522675i | \(0.175066\pi\) | |||||||
\(60\) | 19.9537i | 2.57601i | ||||||||
\(61\) | 0.769632 | + | 1.33304i | 0.0985412 | + | 0.170678i | 0.911081 | − | 0.412227i | \(-0.135249\pi\) |
−0.812540 | + | 0.582906i | \(0.801916\pi\) | |||||||
\(62\) | −8.93242 | + | 15.4714i | −1.13442 | + | 1.96487i | ||||
\(63\) | 1.83169 | + | 1.05753i | 0.230771 | + | 0.133236i | ||||
\(64\) | 11.1012 | 1.38765 | ||||||||
\(65\) | 12.2793 | + | 4.22664i | 1.52306 | + | 0.524250i | ||||
\(66\) | −4.22867 | −0.520513 | ||||||||
\(67\) | 7.29756 | + | 4.21325i | 0.891539 | + | 0.514730i | 0.874445 | − | 0.485124i | \(-0.161225\pi\) |
0.0170931 | + | 0.999854i | \(0.494559\pi\) | |||||||
\(68\) | 6.07501 | − | 10.5222i | 0.736703 | − | 1.27601i | ||||
\(69\) | −4.36330 | − | 7.55745i | −0.525279 | − | 0.909811i | ||||
\(70\) | 7.59755i | 0.908081i | ||||||||
\(71\) | −5.58490 | + | 3.22444i | −0.662805 | + | 0.382671i | −0.793345 | − | 0.608772i | \(-0.791662\pi\) |
0.130540 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(72\) | 1.73683 | − | 1.00276i | 0.204687 | − | 0.118176i | ||||
\(73\) | 7.14859i | 0.836679i | 0.908291 | + | 0.418340i | \(0.137388\pi\) | ||||
−0.908291 | + | 0.418340i | \(0.862612\pi\) | |||||||
\(74\) | −10.1653 | − | 17.6068i | −1.18169 | − | 2.04675i | ||||
\(75\) | 9.01585 | − | 15.6159i | 1.04106 | − | 1.80317i | ||||
\(76\) | 5.04621 | + | 2.91343i | 0.578840 | + | 0.334193i | ||||
\(77\) | −0.886384 | −0.101013 | ||||||||
\(78\) | −3.28391 | − | 16.8846i | −0.371830 | − | 1.91180i | ||||
\(79\) | 0.757551 | 0.0852311 | 0.0426156 | − | 0.999092i | \(-0.486431\pi\) | ||||
0.0426156 | + | 0.999092i | \(0.486431\pi\) | |||||||
\(80\) | −9.04232 | − | 5.22059i | −1.01096 | − | 0.583679i | ||||
\(81\) | 5.43585 | − | 9.41518i | 0.603984 | − | 1.04613i | ||||
\(82\) | 12.7451 | + | 22.0751i | 1.40746 | + | 2.43779i | ||||
\(83\) | − | 4.76766i | − | 0.523319i | −0.965160 | − | 0.261659i | \(-0.915730\pi\) | ||
0.965160 | − | 0.261659i | \(-0.0842697\pi\) | |||||||
\(84\) | 4.79774 | − | 2.76998i | 0.523476 | − | 0.302229i | ||||
\(85\) | −15.4719 | + | 8.93270i | −1.67816 | + | 0.968888i | ||||
\(86\) | − | 7.68344i | − | 0.828527i | ||||||
\(87\) | −1.44969 | − | 2.51093i | −0.155423 | − | 0.269200i | ||||
\(88\) | −0.420240 | + | 0.727877i | −0.0447977 | + | 0.0775919i | ||||
\(89\) | 3.13400 | + | 1.80942i | 0.332204 | + | 0.191798i | 0.656819 | − | 0.754048i | \(-0.271902\pi\) |
−0.324615 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(90\) | −16.0692 | −1.69385 | ||||||||
\(91\) | −0.688351 | − | 3.53923i | −0.0721588 | − | 0.371012i | ||||
\(92\) | −9.45150 | −0.985387 | ||||||||
\(93\) | −16.5882 | − | 9.57719i | −1.72011 | − | 0.993108i | ||||
\(94\) | 3.14541 | − | 5.44800i | 0.324424 | − | 0.561919i | ||||
\(95\) | −4.28391 | − | 7.41995i | −0.439520 | − | 0.761271i | ||||
\(96\) | 18.1188i | 1.84924i | ||||||||
\(97\) | −0.401229 | + | 0.231650i | −0.0407386 | + | 0.0235205i | −0.520231 | − | 0.854026i | \(-0.674154\pi\) |
0.479492 | + | 0.877546i | \(0.340821\pi\) | |||||||
\(98\) | 1.82678 | − | 1.05469i | 0.184533 | − | 0.106540i | ||||
\(99\) | − | 1.87475i | − | 0.188419i | ||||||
\(100\) | −9.76479 | − | 16.9131i | −0.976479 | − | 1.69131i | ||||
\(101\) | 2.91152 | − | 5.04289i | 0.289707 | − | 0.501787i | −0.684033 | − | 0.729451i | \(-0.739776\pi\) |
0.973740 | + | 0.227664i | \(0.0731089\pi\) | |||||||
\(102\) | 20.4931 | + | 11.8317i | 2.02912 | + | 1.17151i | ||||
\(103\) | −8.23888 | −0.811801 | −0.405901 | − | 0.913917i | \(-0.633042\pi\) | ||||
−0.405901 | + | 0.913917i | \(0.633042\pi\) | |||||||
\(104\) | −3.23268 | − | 1.11271i | −0.316991 | − | 0.109111i | ||||
\(105\) | −8.14596 | −0.794964 | ||||||||
\(106\) | 8.98837 | + | 5.18944i | 0.873027 | + | 0.504043i | ||||
\(107\) | 1.91630 | − | 3.31913i | 0.185256 | − | 0.320872i | −0.758407 | − | 0.651781i | \(-0.774022\pi\) |
0.943663 | + | 0.330909i | \(0.107355\pi\) | |||||||
\(108\) | −2.45128 | − | 4.24574i | −0.235875 | − | 0.408547i | ||||
\(109\) | − | 10.4180i | − | 0.997867i | −0.866640 | − | 0.498934i | \(-0.833725\pi\) | ||
0.866640 | − | 0.498934i | \(-0.166275\pi\) | |||||||
\(110\) | 5.83212 | − | 3.36718i | 0.556071 | − | 0.321048i | ||||
\(111\) | 18.8777 | − | 10.8990i | 1.79179 | − | 1.03449i | ||||
\(112\) | 2.89889i | 0.273920i | ||||||||
\(113\) | 2.45505 | + | 4.25228i | 0.230952 | + | 0.400021i | 0.958089 | − | 0.286472i | \(-0.0924826\pi\) |
−0.727136 | + | 0.686493i | \(0.759149\pi\) | |||||||
\(114\) | −5.67421 | + | 9.82801i | −0.531438 | + | 0.920478i | ||||
\(115\) | 12.0356 | + | 6.94875i | 1.12233 | + | 0.647975i | ||||
\(116\) | −3.14022 | −0.291562 | ||||||||
\(117\) | 7.48567 | − | 1.45590i | 0.692050 | − | 0.134598i | ||||
\(118\) | 15.4565 | 1.42288 | ||||||||
\(119\) | 4.29563 | + | 2.48008i | 0.393779 | + | 0.227349i | ||||
\(120\) | −3.86205 | + | 6.68926i | −0.352555 | + | 0.610643i | ||||
\(121\) | −5.10716 | − | 8.84586i | −0.464287 | − | 0.804169i | ||||
\(122\) | 3.24690i | 0.293961i | ||||||||
\(123\) | −23.6685 | + | 13.6650i | −2.13412 | + | 1.23213i | ||||
\(124\) | −17.9661 | + | 10.3727i | −1.61341 | + | 0.931500i | ||||
\(125\) | 10.7074i | 0.957702i | ||||||||
\(126\) | 2.23073 | + | 3.86375i | 0.198730 | + | 0.344210i | ||||
\(127\) | −6.15508 | + | 10.6609i | −0.546175 | + | 0.946003i | 0.452357 | + | 0.891837i | \(0.350583\pi\) |
−0.998532 | + | 0.0541658i | \(0.982750\pi\) | |||||||
\(128\) | 6.40347 | + | 3.69704i | 0.565992 | + | 0.326776i | ||||
\(129\) | 8.23805 | 0.725320 | ||||||||
\(130\) | 17.9739 | + | 20.6721i | 1.57641 | + | 1.81306i | ||||
\(131\) | −8.20265 | −0.716669 | −0.358335 | − | 0.933593i | \(-0.616655\pi\) | ||||
−0.358335 | + | 0.933593i | \(0.616655\pi\) | |||||||
\(132\) | −4.25264 | − | 2.45526i | −0.370145 | − | 0.213703i | ||||
\(133\) | −1.18939 | + | 2.06008i | −0.103133 | + | 0.178632i | ||||
\(134\) | 8.88737 | + | 15.3934i | 0.767752 | + | 1.32979i | ||||
\(135\) | 7.20874i | 0.620429i | ||||||||
\(136\) | 4.07316 | − | 2.35164i | 0.349271 | − | 0.201652i | ||||
\(137\) | 6.45670 | − | 3.72778i | 0.551633 | − | 0.318485i | −0.198147 | − | 0.980172i | \(-0.563492\pi\) |
0.749780 | + | 0.661687i | \(0.230159\pi\) | |||||||
\(138\) | − | 18.4078i | − | 1.56697i | ||||||
\(139\) | −8.34028 | − | 14.4458i | −0.707413 | − | 1.22528i | −0.965813 | − | 0.259238i | \(-0.916529\pi\) |
0.258400 | − | 0.966038i | \(-0.416805\pi\) | |||||||
\(140\) | −4.41132 | + | 7.64062i | −0.372824 | + | 0.645750i | ||||
\(141\) | 5.84125 | + | 3.37245i | 0.491922 | + | 0.284011i | ||||
\(142\) | −13.6032 | −1.14156 | ||||||||
\(143\) | −2.41175 | + | 2.09696i | −0.201681 | + | 0.175357i | ||||
\(144\) | −6.13131 | −0.510943 | ||||||||
\(145\) | 3.99877 | + | 2.30869i | 0.332080 | + | 0.191726i | ||||
\(146\) | −7.53958 | + | 13.0589i | −0.623980 | + | 1.08076i | ||||
\(147\) | 1.13082 | + | 1.95864i | 0.0932688 | + | 0.161546i | ||||
\(148\) | − | 23.6088i | − | 1.94063i | ||||||
\(149\) | −2.18380 | + | 1.26082i | −0.178904 | + | 0.103290i | −0.586777 | − | 0.809748i | \(-0.699604\pi\) |
0.407874 | + | 0.913038i | \(0.366270\pi\) | |||||||
\(150\) | 32.9400 | − | 19.0179i | 2.68954 | − | 1.55281i | ||||
\(151\) | 15.8972i | 1.29370i | 0.762618 | + | 0.646849i | \(0.223914\pi\) | ||||
−0.762618 | + | 0.646849i | \(0.776086\pi\) | |||||||
\(152\) | 1.12779 | + | 1.95339i | 0.0914760 | + | 0.158441i | ||||
\(153\) | −5.24550 | + | 9.08548i | −0.424074 | + | 0.734517i | ||||
\(154\) | −1.61923 | − | 0.934864i | −0.130481 | − | 0.0753335i | ||||
\(155\) | 30.5042 | 2.45016 | ||||||||
\(156\) | 6.50106 | − | 18.8870i | 0.520502 | − | 1.51217i | ||||
\(157\) | 12.9831 | 1.03616 | 0.518082 | − | 0.855331i | \(-0.326646\pi\) | ||||
0.518082 | + | 0.855331i | \(0.326646\pi\) | |||||||
\(158\) | 1.38388 | + | 0.798985i | 0.110096 | + | 0.0635638i | ||||
\(159\) | −5.56402 | + | 9.63717i | −0.441256 | + | 0.764277i | ||||
\(160\) | −14.4275 | − | 24.9892i | −1.14059 | − | 1.97557i | ||||
\(161\) | − | 3.85851i | − | 0.304093i | ||||||
\(162\) | 19.8603 | − | 11.4663i | 1.56037 | − | 0.900880i | ||||
\(163\) | −2.00873 | + | 1.15974i | −0.157336 | + | 0.0908378i | −0.576601 | − | 0.817026i | \(-0.695621\pi\) |
0.419265 | + | 0.907864i | \(0.362288\pi\) | |||||||
\(164\) | 29.6003i | 2.31140i | ||||||||
\(165\) | 3.61023 | + | 6.25309i | 0.281056 | + | 0.486803i | ||||
\(166\) | 5.02843 | − | 8.70949i | 0.390282 | − | 0.675987i | ||||
\(167\) | −11.9441 | − | 6.89591i | −0.924260 | − | 0.533622i | −0.0392682 | − | 0.999229i | \(-0.512503\pi\) |
−0.884992 | + | 0.465607i | \(0.845836\pi\) | |||||||
\(168\) | 2.14452 | 0.165453 | ||||||||
\(169\) | −10.2459 | − | 8.00140i | −0.788143 | − | 0.615493i | ||||
\(170\) | −37.6851 | −2.89031 | ||||||||
\(171\) | −4.35718 | − | 2.51562i | −0.333202 | − | 0.192374i | ||||
\(172\) | 4.46118 | − | 7.72700i | 0.340162 | − | 0.589178i | ||||
\(173\) | −1.84216 | − | 3.19071i | −0.140057 | − | 0.242585i | 0.787461 | − | 0.616364i | \(-0.211395\pi\) |
−0.927518 | + | 0.373779i | \(0.878062\pi\) | |||||||
\(174\) | − | 6.11590i | − | 0.463645i | ||||||
\(175\) | 6.90466 | − | 3.98641i | 0.521943 | − | 0.301344i | ||||
\(176\) | 2.22528 | − | 1.28477i | 0.167737 | − | 0.0968429i | ||||
\(177\) | 16.5721i | 1.24564i | ||||||||
\(178\) | 3.81677 | + | 6.61083i | 0.286079 | + | 0.495503i | ||||
\(179\) | −2.94638 | + | 5.10328i | −0.220223 | + | 0.381437i | −0.954876 | − | 0.297006i | \(-0.904012\pi\) |
0.734653 | + | 0.678443i | \(0.237345\pi\) | |||||||
\(180\) | −16.1603 | − | 9.33017i | −1.20452 | − | 0.695430i | ||||
\(181\) | −2.11543 | −0.157239 | −0.0786193 | − | 0.996905i | \(-0.525051\pi\) | ||||
−0.0786193 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(182\) | 2.47534 | − | 7.19141i | 0.183484 | − | 0.533063i | ||||
\(183\) | −3.48127 | −0.257343 | ||||||||
\(184\) | −3.16851 | − | 1.82934i | −0.233586 | − | 0.134861i | ||||
\(185\) | −17.3572 | + | 30.0635i | −1.27613 | + | 2.21032i | ||||
\(186\) | −20.2020 | − | 34.9909i | −1.48128 | − | 2.56566i | ||||
\(187\) | − | 4.39661i | − | 0.321512i | ||||||
\(188\) | 6.32647 | − | 3.65259i | 0.461406 | − | 0.266393i | ||||
\(189\) | 1.73330 | − | 1.00072i | 0.126079 | − | 0.0727916i | ||||
\(190\) | − | 18.0729i | − | 1.31114i | ||||||
\(191\) | 5.68333 | + | 9.84381i | 0.411231 | + | 0.712273i | 0.995025 | − | 0.0996290i | \(-0.0317656\pi\) |
−0.583794 | + | 0.811902i | \(0.698432\pi\) | |||||||
\(192\) | −12.5535 | + | 21.7433i | −0.905970 | + | 1.56919i | ||||
\(193\) | 12.2017 | + | 7.04468i | 0.878301 | + | 0.507087i | 0.870098 | − | 0.492879i | \(-0.164055\pi\) |
0.00820314 | + | 0.999966i | \(0.497389\pi\) | |||||||
\(194\) | −0.977279 | −0.0701645 | ||||||||
\(195\) | −22.1643 | + | 19.2713i | −1.58722 | + | 1.38004i | ||||
\(196\) | 2.44952 | 0.174966 | ||||||||
\(197\) | −19.8815 | − | 11.4786i | −1.41650 | − | 0.817814i | −0.420507 | − | 0.907289i | \(-0.638148\pi\) |
−0.995989 | + | 0.0894753i | \(0.971481\pi\) | |||||||
\(198\) | 1.97729 | − | 3.42476i | 0.140520 | − | 0.243387i | ||||
\(199\) | −1.57492 | − | 2.72785i | −0.111643 | − | 0.193372i | 0.804790 | − | 0.593560i | \(-0.202278\pi\) |
−0.916433 | + | 0.400188i | \(0.868945\pi\) | |||||||
\(200\) | − | 7.55992i | − | 0.534567i | ||||||
\(201\) | −16.5045 | + | 9.52888i | −1.16414 | + | 0.672116i | ||||
\(202\) | 10.6374 | − | 6.14152i | 0.748446 | − | 0.432116i | ||||
\(203\) | − | 1.28197i | − | 0.0899768i | ||||||
\(204\) | 13.7395 | + | 23.7976i | 0.961959 | + | 1.66616i | ||||
\(205\) | 21.7622 | − | 37.6932i | 1.51994 | − | 2.63261i | ||||
\(206\) | −15.0507 | − | 8.68950i | −1.04863 | − | 0.605426i | ||||
\(207\) | 8.16096 | 0.567226 | ||||||||
\(208\) | 6.85804 | + | 7.88757i | 0.475520 | + | 0.546905i | ||||
\(209\) | 2.10851 | 0.145849 | ||||||||
\(210\) | −14.8809 | − | 8.59150i | −1.02688 | − | 0.592870i | ||||
\(211\) | 7.43191 | − | 12.8725i | 0.511634 | − | 0.886176i | −0.488275 | − | 0.872690i | \(-0.662374\pi\) |
0.999909 | − | 0.0134864i | \(-0.00429298\pi\) | |||||||
\(212\) | 6.02621 | + | 10.4377i | 0.413882 | + | 0.716865i | ||||
\(213\) | − | 14.5851i | − | 0.999355i | ||||||
\(214\) | 7.00133 | − | 4.04222i | 0.478601 | − | 0.276321i | ||||
\(215\) | −11.3618 | + | 6.55974i | −0.774868 | + | 0.447370i | ||||
\(216\) | − | 1.89779i | − | 0.129128i | ||||||
\(217\) | −4.23460 | − | 7.33455i | −0.287464 | − | 0.497902i | ||||
\(218\) | 10.9878 | − | 19.0315i | 0.744191 | − | 1.28898i | ||||
\(219\) | −14.0016 | − | 8.08380i | −0.946137 | − | 0.546253i | ||||
\(220\) | 7.82024 | 0.527241 | ||||||||
\(221\) | 17.5552 | − | 3.41433i | 1.18089 | − | 0.229673i | ||||
\(222\) | 45.9805 | 3.08601 | ||||||||
\(223\) | 3.79396 | + | 2.19044i | 0.254062 | + | 0.146683i | 0.621623 | − | 0.783317i | \(-0.286474\pi\) |
−0.367561 | + | 0.930000i | \(0.619807\pi\) | |||||||
\(224\) | −4.00566 | + | 6.93800i | −0.267639 | + | 0.463565i | ||||
\(225\) | 8.43147 | + | 14.6037i | 0.562098 | + | 0.973582i | ||||
\(226\) | 10.3573i | 0.688959i | ||||||||
\(227\) | 11.7488 | − | 6.78316i | 0.779793 | − | 0.450214i | −0.0565636 | − | 0.998399i | \(-0.518014\pi\) |
0.836357 | + | 0.548185i | \(0.184681\pi\) | |||||||
\(228\) | −11.4127 | + | 6.58915i | −0.755827 | + | 0.436377i | ||||
\(229\) | − | 16.5180i | − | 1.09154i | −0.837935 | − | 0.545770i | \(-0.816237\pi\) | ||
0.837935 | − | 0.545770i | \(-0.183763\pi\) | |||||||
\(230\) | 14.6576 | + | 25.3877i | 0.966495 | + | 1.67402i | ||||
\(231\) | 1.00234 | − | 1.73611i | 0.0659494 | − | 0.114228i | ||||
\(232\) | −1.05272 | − | 0.607791i | −0.0691147 | − | 0.0399034i | ||||
\(233\) | 16.5026 | 1.08112 | 0.540561 | − | 0.841305i | \(-0.318212\pi\) | ||||
0.540561 | + | 0.841305i | \(0.318212\pi\) | |||||||
\(234\) | 15.2102 | + | 5.23548i | 0.994324 | + | 0.342254i | ||||
\(235\) | −10.7416 | −0.700702 | ||||||||
\(236\) | 15.5441 | + | 8.97438i | 1.01183 | + | 0.584182i | ||||
\(237\) | −0.856657 | + | 1.48377i | −0.0556458 | + | 0.0963814i | ||||
\(238\) | 5.23145 | + | 9.06114i | 0.339105 | + | 0.587347i | ||||
\(239\) | 30.4210i | 1.96777i | 0.178796 | + | 0.983886i | \(0.442780\pi\) | ||||
−0.178796 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(240\) | 20.4506 | − | 11.8071i | 1.32008 | − | 0.762147i | ||||
\(241\) | −25.5602 | + | 14.7572i | −1.64648 | + | 0.950593i | −0.668018 | + | 0.744145i | \(0.732857\pi\) |
−0.978458 | + | 0.206448i | \(0.933810\pi\) | |||||||
\(242\) | − | 21.5460i | − | 1.38503i | ||||||
\(243\) | 9.29184 | + | 16.0939i | 0.596072 | + | 1.03243i | ||||
\(244\) | −1.88523 | + | 3.26531i | −0.120689 | + | 0.209040i | ||||
\(245\) | −3.11923 | − | 1.80089i | −0.199280 | − | 0.115055i | ||||
\(246\) | −57.6497 | −3.67561 | ||||||||
\(247\) | 1.63743 | + | 8.41904i | 0.104187 | + | 0.535691i | ||||
\(248\) | −8.03060 | −0.509944 | ||||||||
\(249\) | 9.33816 | + | 5.39139i | 0.591782 | + | 0.341665i | ||||
\(250\) | −11.2931 | + | 19.5602i | −0.714236 | + | 1.23709i | ||||
\(251\) | −6.49134 | − | 11.2433i | −0.409730 | − | 0.709673i | 0.585130 | − | 0.810940i | \(-0.301044\pi\) |
−0.994859 | + | 0.101267i | \(0.967710\pi\) | |||||||
\(252\) | 5.18087i | 0.326364i | ||||||||
\(253\) | −2.96191 | + | 1.71006i | −0.186214 | + | 0.107511i | ||||
\(254\) | −22.4880 | + | 12.9835i | −1.41102 | + | 0.814654i | ||||
\(255\) | − | 40.4053i | − | 2.53028i | ||||||
\(256\) | −3.30268 | − | 5.72042i | −0.206418 | − | 0.357526i | ||||
\(257\) | −2.29261 | + | 3.97091i | −0.143009 | + | 0.247698i | −0.928628 | − | 0.371011i | \(-0.879011\pi\) |
0.785620 | + | 0.618710i | \(0.212344\pi\) | |||||||
\(258\) | 15.0491 | + | 8.68862i | 0.936918 | + | 0.540930i | ||||
\(259\) | 9.63812 | 0.598884 | ||||||||
\(260\) | 6.07307 | + | 31.2253i | 0.376636 | + | 1.93651i | ||||
\(261\) | 2.71144 | 0.167834 | ||||||||
\(262\) | −14.9845 | − | 8.65129i | −0.925744 | − | 0.534479i | ||||
\(263\) | 1.33250 | − | 2.30795i | 0.0821652 | − | 0.142314i | −0.822015 | − | 0.569466i | \(-0.807150\pi\) |
0.904180 | + | 0.427152i | \(0.140483\pi\) | |||||||
\(264\) | −0.950435 | − | 1.64620i | −0.0584952 | − | 0.101317i | ||||
\(265\) | − | 17.7219i | − | 1.08865i | ||||||
\(266\) | −4.34551 | + | 2.50888i | −0.266440 | + | 0.153829i | ||||
\(267\) | −7.08801 | + | 4.09227i | −0.433779 | + | 0.250443i | ||||
\(268\) | 20.6409i | 1.26084i | ||||||||
\(269\) | −5.96282 | − | 10.3279i | −0.363559 | − | 0.629703i | 0.624984 | − | 0.780637i | \(-0.285105\pi\) |
−0.988544 | + | 0.150934i | \(0.951772\pi\) | |||||||
\(270\) | −7.60301 | + | 13.1688i | −0.462705 | + | 0.801428i | ||||
\(271\) | −11.2828 | − | 6.51416i | −0.685384 | − | 0.395707i | 0.116496 | − | 0.993191i | \(-0.462834\pi\) |
−0.801881 | + | 0.597484i | \(0.796167\pi\) | |||||||
\(272\) | −14.3790 | −0.871853 | ||||||||
\(273\) | 7.71051 | + | 2.65402i | 0.466661 | + | 0.160628i | ||||
\(274\) | 15.7267 | 0.950082 | ||||||||
\(275\) | −6.12018 | − | 3.53349i | −0.369061 | − | 0.213077i | ||||
\(276\) | 10.6880 | − | 18.5121i | 0.643341 | − | 1.11430i | ||||
\(277\) | 10.6824 | + | 18.5025i | 0.641846 | + | 1.11171i | 0.985020 | + | 0.172438i | \(0.0551646\pi\) |
−0.343174 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(278\) | − | 35.1858i | − | 2.11030i | ||||||
\(279\) | 15.5130 | − | 8.95641i | 0.928737 | − | 0.536206i | ||||
\(280\) | −2.95769 | + | 1.70762i | −0.176756 | + | 0.102050i | ||||
\(281\) | − | 17.2678i | − | 1.03011i | −0.857158 | − | 0.515054i | \(-0.827772\pi\) | ||
0.857158 | − | 0.515054i | \(-0.172228\pi\) | |||||||
\(282\) | 7.11380 | + | 12.3215i | 0.423621 | + | 0.733733i | ||||
\(283\) | −10.6201 | + | 18.3946i | −0.631299 | + | 1.09344i | 0.355987 | + | 0.934491i | \(0.384145\pi\) |
−0.987286 | + | 0.158952i | \(0.949189\pi\) | |||||||
\(284\) | −13.6803 | − | 7.89833i | −0.811777 | − | 0.468680i | ||||
\(285\) | 19.3774 | 1.14782 | ||||||||
\(286\) | −6.61741 | + | 1.28703i | −0.391295 | + | 0.0761037i | ||||
\(287\) | −12.0841 | −0.713304 | ||||||||
\(288\) | −14.6742 | − | 8.47218i | −0.864688 | − | 0.499228i | ||||
\(289\) | −3.80160 | + | 6.58457i | −0.223624 | + | 0.387327i | ||||
\(290\) | 4.86993 | + | 8.43496i | 0.285972 | + | 0.495318i | ||||
\(291\) | − | 1.04782i | − | 0.0614243i | ||||||
\(292\) | −15.1646 | + | 8.75531i | −0.887443 | + | 0.512366i | ||||
\(293\) | −0.363782 | + | 0.210030i | −0.0212524 | + | 0.0122701i | −0.510589 | − | 0.859825i | \(-0.670572\pi\) |
0.489336 | + | 0.872095i | \(0.337239\pi\) | |||||||
\(294\) | 4.77070i | 0.278233i | ||||||||
\(295\) | −13.1959 | − | 22.8561i | −0.768298 | − | 1.33073i | ||||
\(296\) | 4.56949 | − | 7.91459i | 0.265596 | − | 0.460026i | ||||
\(297\) | −1.53637 | − | 0.887022i | −0.0891490 | − | 0.0514702i | ||||
\(298\) | −5.31910 | −0.308127 | ||||||||
\(299\) | −9.12826 | − | 10.4986i | −0.527901 | − | 0.607149i | ||||
\(300\) | 44.1690 | 2.55010 | ||||||||
\(301\) | 3.15450 | + | 1.82125i | 0.181822 | + | 0.104975i | ||||
\(302\) | −16.7667 | + | 29.0408i | −0.964817 | + | 1.67111i | ||||
\(303\) | 6.58482 | + | 11.4053i | 0.378288 | + | 0.655215i | ||||
\(304\) | − | 6.89581i | − | 0.395502i | ||||||
\(305\) | 4.80132 | − | 2.77204i | 0.274923 | − | 0.158727i | ||||
\(306\) | −19.1648 | + | 11.0648i | −1.09558 | + | 0.632533i | ||||
\(307\) | 14.0807i | 0.803628i | 0.915721 | + | 0.401814i | \(0.131620\pi\) | ||||
−0.915721 | + | 0.401814i | \(0.868380\pi\) | |||||||
\(308\) | −1.08561 | − | 1.88033i | −0.0618583 | − | 0.107142i | ||||
\(309\) | 9.31673 | − | 16.1370i | 0.530010 | − | 0.918004i | ||||
\(310\) | 55.7246 | + | 32.1726i | 3.16495 | + | 1.82728i | ||||
\(311\) | −10.3848 | −0.588867 | −0.294434 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294434 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(312\) | 5.83501 | − | 5.07339i | 0.330342 | − | 0.287224i | ||||
\(313\) | 6.84759 | 0.387048 | 0.193524 | − | 0.981096i | \(-0.438008\pi\) | ||||
0.193524 | + | 0.981096i | \(0.438008\pi\) | |||||||
\(314\) | 23.7173 | + | 13.6932i | 1.33845 | + | 0.772752i | ||||
\(315\) | 3.80898 | − | 6.59734i | 0.214612 | − | 0.371718i | ||||
\(316\) | 0.927818 | + | 1.60703i | 0.0521938 | + | 0.0904024i | ||||
\(317\) | − | 0.701249i | − | 0.0393861i | −0.999806 | − | 0.0196930i | \(-0.993731\pi\) | ||
0.999806 | − | 0.0196930i | \(-0.00626889\pi\) | |||||||
\(318\) | −20.3285 | + | 11.7367i | −1.13997 | + | 0.658160i | ||||
\(319\) | −0.984082 | + | 0.568160i | −0.0550980 | + | 0.0318109i | ||||
\(320\) | − | 39.9840i | − | 2.23518i | ||||||
\(321\) | 4.33400 | + | 7.50670i | 0.241900 | + | 0.418983i | ||||
\(322\) | 4.06955 | − | 7.04867i | 0.226787 | − | 0.392807i | ||||
\(323\) | −10.2183 | − | 5.89956i | −0.568563 | − | 0.328260i | ||||
\(324\) | 26.6305 | 1.47947 | ||||||||
\(325\) | 9.35600 | − | 27.1813i | 0.518977 | − | 1.50774i | ||||
\(326\) | −4.89268 | −0.270980 | ||||||||
\(327\) | 20.4052 | + | 11.7810i | 1.12841 | + | 0.651489i | ||||
\(328\) | −5.72916 | + | 9.92319i | −0.316340 | + | 0.547917i | ||||
\(329\) | 1.49115 | + | 2.58274i | 0.0822095 | + | 0.142391i | ||||
\(330\) | 15.2307i | 0.838424i | ||||||||
\(331\) | 3.63613 | − | 2.09932i | 0.199860 | − | 0.115389i | −0.396730 | − | 0.917935i | \(-0.629855\pi\) |
0.596590 | + | 0.802546i | \(0.296522\pi\) | |||||||
\(332\) | 10.1139 | − | 5.83924i | 0.555070 | − | 0.320470i | ||||
\(333\) | 20.3851i | 1.11710i | ||||||||
\(334\) | −14.5462 | − | 25.1947i | −0.795930 | − | 1.37859i | ||||
\(335\) | 15.1752 | − | 26.2842i | 0.829109 | − | 1.43606i | ||||
\(336\) | −5.67790 | − | 3.27814i | −0.309755 | − | 0.178837i | ||||
\(337\) | −20.4278 | −1.11278 | −0.556388 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(338\) | −10.2779 | − | 25.4231i | −0.559046 | − | 1.38283i | ||||
\(339\) | −11.1049 | −0.603138 | ||||||||
\(340\) | −37.8987 | − | 21.8808i | −2.05535 | − | 1.18665i | ||||
\(341\) | −3.75349 | + | 6.50123i | −0.203263 | + | 0.352061i | ||||
\(342\) | −5.30642 | − | 9.19098i | −0.286938 | − | 0.496991i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 2.99113 | − | 1.72693i | 0.161271 | − | 0.0931098i | ||||
\(345\) | −27.2203 | + | 15.7156i | −1.46549 | + | 0.846102i | ||||
\(346\) | − | 7.77165i | − | 0.417807i | ||||||
\(347\) | −3.98500 | − | 6.90222i | −0.213926 | − | 0.370531i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901959\pi\) | |||||||
\(348\) | 3.55103 | − | 6.15057i | 0.190355 | − | 0.329705i | ||||
\(349\) | 18.7038 | + | 10.7986i | 1.00119 | + | 0.578037i | 0.908600 | − | 0.417668i | \(-0.137152\pi\) |
0.0925892 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(350\) | 16.8178 | 0.898947 | ||||||||
\(351\) | 2.34866 | − | 6.82338i | 0.125362 | − | 0.364205i | ||||
\(352\) | 7.10110 | 0.378490 | ||||||||
\(353\) | 18.7214 | + | 10.8088i | 0.996439 | + | 0.575295i | 0.907193 | − | 0.420715i | \(-0.138221\pi\) |
0.0892465 | + | 0.996010i | \(0.471554\pi\) | |||||||
\(354\) | −17.4785 | + | 30.2737i | −0.928974 | + | 1.60903i | ||||
\(355\) | 11.6137 | + | 20.1156i | 0.616393 | + | 1.06762i | ||||
\(356\) | 8.86441i | 0.469813i | ||||||||
\(357\) | −9.71520 | + | 5.60907i | −0.514183 | + | 0.296863i | ||||
\(358\) | −10.7648 | + | 6.21507i | −0.568938 | + | 0.328476i | ||||
\(359\) | − | 13.6834i | − | 0.722180i | −0.932531 | − | 0.361090i | \(-0.882405\pi\) | ||
0.932531 | − | 0.361090i | \(-0.117595\pi\) | |||||||
\(360\) | −3.61172 | − | 6.25568i | −0.190354 | − | 0.329703i | ||||
\(361\) | −6.67071 | + | 11.5540i | −0.351090 | + | 0.608106i | ||||
\(362\) | −3.86443 | − | 2.23113i | −0.203110 | − | 0.117266i | ||||
\(363\) | 23.1012 | 1.21250 | ||||||||
\(364\) | 6.66487 | − | 5.79494i | 0.349334 | − | 0.303737i | ||||
\(365\) | 25.7477 | 1.34769 | ||||||||
\(366\) | −6.35953 | − | 3.67168i | −0.332418 | − | 0.191922i | ||||
\(367\) | 5.70638 | − | 9.88374i | 0.297871 | − | 0.515927i | −0.677778 | − | 0.735267i | \(-0.737057\pi\) |
0.975649 | + | 0.219339i | \(0.0703902\pi\) | |||||||
\(368\) | 5.59271 | + | 9.68685i | 0.291540 | + | 0.504962i | ||||
\(369\) | − | 25.5586i | − | 1.33053i | ||||||
\(370\) | −63.4157 | + | 36.6131i | −3.29683 | + | 1.90342i | ||||
\(371\) | −4.26112 | + | 2.46016i | −0.221227 | + | 0.127725i | ||||
\(372\) | − | 46.9190i | − | 2.43264i | ||||||
\(373\) | 15.6404 | + | 27.0900i | 0.809830 | + | 1.40267i | 0.912981 | + | 0.408002i | \(0.133774\pi\) |
−0.103151 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(374\) | 4.63708 | − | 8.03166i | 0.239778 | − | 0.415307i | ||||
\(375\) | −20.9721 | − | 12.1082i | −1.08299 | − | 0.625266i | ||||
\(376\) | 2.82784 | 0.145835 | ||||||||
\(377\) | −3.03282 | − | 3.48811i | −0.156198 | − | 0.179647i | ||||
\(378\) | 4.22181 | 0.217146 | ||||||||
\(379\) | 23.7421 | + | 13.7075i | 1.21955 | + | 0.704108i | 0.964822 | − | 0.262904i | \(-0.0846803\pi\) |
0.254729 | + | 0.967012i | \(0.418014\pi\) | |||||||
\(380\) | 10.4935 | − | 18.1753i | 0.538307 | − | 0.932374i | ||||
\(381\) | −13.9206 | − | 24.1112i | −0.713175 | − | 1.23526i | ||||
\(382\) | 23.9767i | 1.22675i | ||||||||
\(383\) | 13.9436 | − | 8.05032i | 0.712483 | − | 0.411352i | −0.0994967 | − | 0.995038i | \(-0.531723\pi\) |
0.811980 | + | 0.583686i | \(0.198390\pi\) | |||||||
\(384\) | −14.4824 | + | 8.36142i | −0.739052 | + | 0.426692i | ||||
\(385\) | 3.19256i | 0.162708i | ||||||||
\(386\) | 14.8600 | + | 25.7382i | 0.756353 | + | 1.31004i | ||||
\(387\) | −3.85204 | + | 6.67193i | −0.195810 | + | 0.339153i | ||||
\(388\) | −0.982819 | − | 0.567431i | −0.0498951 | − | 0.0288069i | ||||
\(389\) | −21.1380 | −1.07174 | −0.535870 | − | 0.844301i | \(-0.680016\pi\) | ||||
−0.535870 | + | 0.844301i | \(0.680016\pi\) | |||||||
\(390\) | −60.8146 | + | 11.8279i | −3.07947 | + | 0.598930i | ||||
\(391\) | 19.1388 | 0.967893 | ||||||||
\(392\) | 0.821175 | + | 0.474106i | 0.0414756 | + | 0.0239460i | ||||
\(393\) | 9.27576 | − | 16.0661i | 0.467900 | − | 0.810427i | ||||
\(394\) | −24.2128 | − | 41.9377i | −1.21982 | − | 2.11279i | ||||
\(395\) | − | 2.72853i | − | 0.137287i | ||||||
\(396\) | 3.97699 | − | 2.29612i | 0.199851 | − | 0.115384i | ||||
\(397\) | 11.3436 | − | 6.54921i | 0.569317 | − | 0.328695i | −0.187560 | − | 0.982253i | \(-0.560058\pi\) |
0.756876 | + | 0.653558i | \(0.226724\pi\) | |||||||
\(398\) | − | 6.64426i | − | 0.333046i | ||||||
\(399\) | −2.68998 | − | 4.65918i | −0.134667 | − | 0.233251i | ||||
\(400\) | −11.5562 | + | 20.0159i | −0.577808 | + | 1.00079i | ||||
\(401\) | 16.8396 | + | 9.72236i | 0.840930 | + | 0.485511i | 0.857580 | − | 0.514350i | \(-0.171967\pi\) |
−0.0166501 | + | 0.999861i | \(0.505300\pi\) | |||||||
\(402\) | −40.2002 | −2.00501 | ||||||||
\(403\) | −28.8736 | − | 9.93851i | −1.43830 | − | 0.495072i | ||||
\(404\) | 14.2636 | 0.709642 | ||||||||
\(405\) | −33.9114 | − | 19.5788i | −1.68507 | − | 0.972876i | ||||
\(406\) | 1.35209 | − | 2.34189i | 0.0671031 | − | 0.116226i | ||||
\(407\) | −4.27154 | − | 7.39853i | −0.211732 | − | 0.366731i | ||||
\(408\) | 10.6372i | 0.526618i | ||||||||
\(409\) | 20.8330 | − | 12.0279i | 1.03013 | − | 0.594743i | 0.113105 | − | 0.993583i | \(-0.463921\pi\) |
0.917020 | + | 0.398840i | \(0.130587\pi\) | |||||||
\(410\) | 79.5096 | − | 45.9049i | 3.92670 | − | 2.26708i | ||||
\(411\) | 16.8618i | 0.831733i | ||||||||
\(412\) | −10.0907 | − | 17.4775i | −0.497131 | − | 0.861056i | ||||
\(413\) | −3.66373 | + | 6.34577i | −0.180280 | + | 0.312255i | ||||
\(414\) | 14.9083 | + | 8.60732i | 0.732703 | + | 0.423026i | ||||
\(415\) | −17.1721 | −0.842944 | ||||||||
\(416\) | 5.51460 | + | 28.3539i | 0.270375 | + | 1.39016i | ||||
\(417\) | 37.7256 | 1.84743 | ||||||||
\(418\) | 3.85179 | + | 2.22383i | 0.188397 | + | 0.108771i | ||||
\(419\) | −19.5119 | + | 33.7956i | −0.953218 | + | 1.65102i | −0.214825 | + | 0.976653i | \(0.568918\pi\) |
−0.738394 | + | 0.674370i | \(0.764415\pi\) | |||||||
\(420\) | −9.97684 | − | 17.2804i | −0.486820 | − | 0.843197i | ||||
\(421\) | 22.0284i | 1.07360i | 0.843710 | + | 0.536799i | \(0.180367\pi\) | ||||
−0.843710 | + | 0.536799i | \(0.819633\pi\) | |||||||
\(422\) | 27.1530 | − | 15.6768i | 1.32179 | − | 0.763134i | ||||
\(423\) | −5.46263 | + | 3.15385i | −0.265602 | + | 0.153346i | ||||
\(424\) | 4.66551i | 0.226577i | ||||||||
\(425\) | 19.7732 | + | 34.2482i | 0.959142 | + | 1.66128i | ||||
\(426\) | 15.3828 | − | 26.6438i | 0.745301 | − | 1.29090i | ||||
\(427\) | −1.33304 | − | 0.769632i | −0.0645104 | − | 0.0372451i | ||||
\(428\) | 9.38803 | 0.453787 | ||||||||
\(429\) | −1.37993 | − | 7.09506i | −0.0666237 | − | 0.342553i | ||||
\(430\) | −27.6741 | −1.33456 | ||||||||
\(431\) | −31.0727 | − | 17.9398i | −1.49672 | − | 0.864131i | −0.496726 | − | 0.867907i | \(-0.665465\pi\) |
−0.999993 | + | 0.00377645i | \(0.998798\pi\) | |||||||
\(432\) | −2.90098 | + | 5.02464i | −0.139573 | + | 0.241748i | ||||
\(433\) | 6.10678 | + | 10.5773i | 0.293473 | + | 0.508310i | 0.974629 | − | 0.223828i | \(-0.0718555\pi\) |
−0.681155 | + | 0.732139i | \(0.738522\pi\) | |||||||
\(434\) | − | 17.8648i | − | 0.857540i | ||||||
\(435\) | −9.04381 | + | 5.22145i | −0.433618 | + | 0.250349i | ||||
\(436\) | 22.1003 | − | 12.7596i | 1.05841 | − | 0.611074i | ||||
\(437\) | 9.17853i | 0.439069i | ||||||||
\(438\) | −17.0519 | − | 29.5347i | −0.814770 | − | 1.41122i | ||||
\(439\) | −7.87765 | + | 13.6445i | −0.375980 | + | 0.651216i | −0.990473 | − | 0.137706i | \(-0.956027\pi\) |
0.614493 | + | 0.788922i | \(0.289361\pi\) | |||||||
\(440\) | 2.62165 | + | 1.51361i | 0.124982 | + | 0.0721586i | ||||
\(441\) | −2.11505 | −0.100717 | ||||||||
\(442\) | 35.6706 | + | 12.2781i | 1.69668 | + | 0.584009i | ||||
\(443\) | −15.0706 | −0.716028 | −0.358014 | − | 0.933716i | \(-0.616546\pi\) | ||||
−0.358014 | + | 0.933716i | \(0.616546\pi\) | |||||||
\(444\) | 46.2412 | + | 26.6974i | 2.19451 | + | 1.26700i | ||||
\(445\) | 6.51712 | − | 11.2880i | 0.308941 | − | 0.535102i | ||||
\(446\) | 4.62050 | + | 8.00293i | 0.218787 | + | 0.378950i | ||||
\(447\) | − | 5.70305i | − | 0.269745i | ||||||
\(448\) | −9.61391 | + | 5.55059i | −0.454215 | + | 0.262241i | ||||
\(449\) | 26.6585 | − | 15.3913i | 1.25809 | − | 0.726360i | 0.285388 | − | 0.958412i | \(-0.407877\pi\) |
0.972703 | + | 0.232052i | \(0.0745441\pi\) | |||||||
\(450\) | 35.5705i | 1.67681i | ||||||||
\(451\) | 5.35559 | + | 9.27616i | 0.252185 | + | 0.436797i | ||||
\(452\) | −6.01371 | + | 10.4160i | −0.282861 | + | 0.489929i | ||||
\(453\) | −31.1370 | − | 17.9770i | −1.46295 | − | 0.844632i | ||||
\(454\) | 28.6166 | 1.34304 | ||||||||
\(455\) | −12.7475 | + | 2.47929i | −0.597614 | + | 0.116231i | ||||
\(456\) | −5.10133 | −0.238892 | ||||||||
\(457\) | −6.71687 | − | 3.87799i | −0.314202 | − | 0.181405i | 0.334603 | − | 0.942359i | \(-0.391398\pi\) |
−0.648805 | + | 0.760955i | \(0.724731\pi\) | |||||||
\(458\) | 17.4214 | − | 30.1748i | 0.814050 | − | 1.40998i | ||||
\(459\) | 4.96373 | + | 8.59743i | 0.231687 | + | 0.401294i | ||||
\(460\) | 34.0422i | 1.58723i | ||||||||
\(461\) | 1.27498 | − | 0.736110i | 0.0593817 | − | 0.0342840i | −0.470015 | − | 0.882658i | \(-0.655752\pi\) |
0.529397 | + | 0.848374i | \(0.322418\pi\) | |||||||
\(462\) | 3.66213 | − | 2.11433i | 0.170378 | − | 0.0983677i | ||||
\(463\) | 14.0366i | 0.652335i | 0.945312 | + | 0.326168i | \(0.105757\pi\) | ||||
−0.945312 | + | 0.326168i | \(0.894243\pi\) | |||||||
\(464\) | 1.85815 | + | 3.21841i | 0.0862625 | + | 0.149411i | ||||
\(465\) | −34.4949 | + | 59.7469i | −1.59966 | + | 2.77070i | ||||
\(466\) | 30.1467 | + | 17.4052i | 1.39652 | + | 0.806281i | ||||
\(467\) | −31.3806 | −1.45212 | −0.726060 | − | 0.687631i | \(-0.758651\pi\) | ||||
−0.726060 | + | 0.687631i | \(0.758651\pi\) | |||||||
\(468\) | 12.2566 | + | 14.0966i | 0.566562 | + | 0.651614i | ||||
\(469\) | −8.42649 | −0.389099 | ||||||||
\(470\) | −19.6225 | − | 11.3291i | −0.905119 | − | 0.522571i | ||||
\(471\) | −14.6816 | + | 25.4293i | −0.676492 | + | 1.17172i | ||||
\(472\) | 3.47399 | + | 6.01713i | 0.159903 | + | 0.276961i | ||||
\(473\) | − | 3.22865i | − | 0.148454i | ||||||
\(474\) | −3.12985 | + | 1.80702i | −0.143759 | + | 0.0829993i | ||||
\(475\) | −16.4246 | + | 9.48277i | −0.753614 | + | 0.435099i | ||||
\(476\) | 12.1500i | 0.556895i | ||||||||
\(477\) | −5.20337 | − | 9.01251i | −0.238246 | − | 0.412654i | ||||
\(478\) | −32.0849 | + | 55.5726i | −1.46753 | + | 2.54183i | ||||
\(479\) | 35.6760 | + | 20.5975i | 1.63008 | + | 0.941125i | 0.984068 | + | 0.177795i | \(0.0568964\pi\) |
0.646009 | + | 0.763330i | \(0.276437\pi\) | |||||||
\(480\) | 65.2598 | 2.97869 | ||||||||
\(481\) | 26.2243 | − | 22.8014i | 1.19572 | − | 1.03965i | ||||
\(482\) | −62.2572 | −2.83574 | ||||||||
\(483\) | 7.55745 | + | 4.36330i | 0.343876 | + | 0.198537i | ||||
\(484\) | 12.5101 | − | 21.6681i | 0.568641 | − | 0.984914i | ||||
\(485\) | 0.834351 | + | 1.44514i | 0.0378859 | + | 0.0656204i | ||||
\(486\) | 39.2002i | 1.77816i | ||||||||
\(487\) | 24.5314 | − | 14.1632i | 1.11163 | − | 0.641798i | 0.172376 | − | 0.985031i | \(-0.444856\pi\) |
0.939250 | + | 0.343234i | \(0.111522\pi\) | |||||||
\(488\) | −1.26400 | + | 0.729774i | −0.0572188 | + | 0.0330353i | ||||
\(489\) | − | 5.24584i | − | 0.237225i | ||||||
\(490\) | −3.79878 | − | 6.57967i | −0.171611 | − | 0.297239i | ||||
\(491\) | 17.3931 | − | 30.1258i | 0.784941 | − | 1.35956i | −0.144094 | − | 0.989564i | \(-0.546027\pi\) |
0.929034 | − | 0.369993i | \(-0.120640\pi\) | |||||||
\(492\) | −57.9765 | − | 33.4728i | −2.61378 | − | 1.50907i | ||||
\(493\) | 6.35879 | 0.286386 | ||||||||
\(494\) | −5.88828 | + | 17.1068i | −0.264926 | + | 0.769670i | ||||
\(495\) | −6.75244 | −0.303499 | ||||||||
\(496\) | 21.2621 | + | 12.2757i | 0.954695 | + | 0.551194i | ||||
\(497\) | 3.22444 | − | 5.58490i | 0.144636 | − | 0.250517i | ||||
\(498\) | 11.3725 | + | 19.6978i | 0.509615 | + | 0.882680i | ||||
\(499\) | 0.0694885i | 0.00311073i | 0.999999 | + | 0.00155537i | \(0.000495089\pi\) | ||||
−0.999999 | + | 0.00155537i | \(0.999505\pi\) | |||||||
\(500\) | −22.7142 | + | 13.1140i | −1.01581 | + | 0.586477i | ||||
\(501\) | 27.0133 | − | 15.5961i | 1.20686 | − | 0.696783i | ||||
\(502\) | − | 27.3855i | − | 1.22228i | ||||||
\(503\) | −12.8686 | − | 22.2891i | −0.573782 | − | 0.993820i | −0.996173 | − | 0.0874060i | \(-0.972142\pi\) |
0.422391 | − | 0.906414i | \(-0.361191\pi\) | |||||||
\(504\) | −1.00276 | + | 1.73683i | −0.0446664 | + | 0.0773646i | ||||
\(505\) | −18.1634 | − | 10.4866i | −0.808260 | − | 0.466649i | ||||
\(506\) | −7.21437 | −0.320718 | ||||||||
\(507\) | 27.2582 | − | 11.0198i | 1.21058 | − | 0.489407i | ||||
\(508\) | −30.1540 | −1.33787 | ||||||||
\(509\) | −6.09682 | − | 3.52000i | −0.270237 | − | 0.156021i | 0.358759 | − | 0.933430i | \(-0.383200\pi\) |
−0.628995 | + | 0.777409i | \(0.716533\pi\) | |||||||
\(510\) | 42.6152 | − | 73.8117i | 1.88703 | − | 3.26844i | ||||
\(511\) | −3.57430 | − | 6.19086i | −0.158118 | − | 0.273868i | ||||
\(512\) | − | 28.7215i | − | 1.26932i | ||||||
\(513\) | −4.12312 | + | 2.38049i | −0.182040 | + | 0.105101i | ||||
\(514\) | −8.37619 | + | 4.83599i | −0.369458 | + | 0.213307i | ||||
\(515\) | 29.6746i | 1.30762i | ||||||||
\(516\) | 10.0896 | + | 17.4758i | 0.444171 | + | 0.769327i | ||||
\(517\) | 1.32173 | − | 2.28930i | 0.0581295 | − | 0.100683i | ||||
\(518\) | 17.6068 | + | 10.1653i | 0.773597 | + | 0.446636i | ||||
\(519\) | 8.33263 | 0.365762 | ||||||||
\(520\) | −4.00775 | + | 11.6434i | −0.175752 | + | 0.510597i | ||||
\(521\) | 16.3253 | 0.715225 | 0.357613 | − | 0.933870i | \(-0.383591\pi\) | ||||
0.357613 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(522\) | 4.95322 | + | 2.85974i | 0.216796 | + | 0.125167i | ||||
\(523\) | 3.54473 | − | 6.13965i | 0.155000 | − | 0.268468i | −0.778059 | − | 0.628191i | \(-0.783796\pi\) |
0.933059 | + | 0.359723i | \(0.117129\pi\) | |||||||
\(524\) | −10.0463 | − | 17.4007i | −0.438874 | − | 0.760152i | ||||
\(525\) | 18.0317i | 0.786968i | ||||||||
\(526\) | 4.86836 | − | 2.81075i | 0.212271 | − | 0.122555i | ||||
\(527\) | 36.3805 | − | 21.0043i | 1.58476 | − | 0.914963i | ||||
\(528\) | 5.81138i | 0.252908i | ||||||||
\(529\) | 4.05594 | + | 7.02510i | 0.176345 | + | 0.305439i | ||||
\(530\) | 18.6912 | − | 32.3741i | 0.811894 | − | 1.40624i | ||||
\(531\) | −13.4216 | − | 7.74899i | −0.582449 | − | 0.336277i | ||||
\(532\) | −5.82686 | −0.252626 | ||||||||
\(533\) | −32.8796 | + | 28.5880i | −1.42417 | + | 1.23828i | ||||
\(534\) | −17.2644 | −0.747102 | ||||||||
\(535\) | −11.9548 | − | 6.90209i | −0.516850 | − | 0.298403i | ||||
\(536\) | −3.99505 | + | 6.91963i | −0.172560 | + | 0.298882i | ||||
\(537\) | −6.66368 | − | 11.5418i | −0.287559 | − | 0.498067i | ||||
\(538\) | − | 25.1558i | − | 1.08454i | ||||||
\(539\) | 0.767631 | − | 0.443192i | 0.0330642 | − | 0.0190896i | ||||
\(540\) | −15.2922 | + | 8.82897i | −0.658073 | + | 0.379938i | ||||
\(541\) | 25.5162i | 1.09703i | 0.836141 | + | 0.548515i | \(0.184806\pi\) | ||||
−0.836141 | + | 0.548515i | \(0.815194\pi\) | |||||||
\(542\) | −13.7409 | − | 23.7999i | −0.590222 | − | 1.02229i | ||||
\(543\) | 2.39218 | − | 4.14338i | 0.102658 | − | 0.177809i | ||||
\(544\) | −34.4136 | − | 19.8687i | −1.47547 | − | 0.851864i | ||||
\(545\) | −37.5235 | −1.60733 | ||||||||
\(546\) | 11.2863 | + | 12.9805i | 0.483007 | + | 0.555516i | ||||
\(547\) | −13.3073 | −0.568978 | −0.284489 | − | 0.958679i | \(-0.591824\pi\) | ||||
−0.284489 | + | 0.958679i | \(0.591824\pi\) | |||||||
\(548\) | 15.8158 | + | 9.13126i | 0.675618 | + | 0.390068i | ||||
\(549\) | 1.62781 | − | 2.81945i | 0.0694733 | − | 0.120331i | ||||
\(550\) | −7.45350 | − | 12.9098i | −0.317818 | − | 0.550478i | ||||
\(551\) | 3.04952i | 0.129914i | ||||||||
\(552\) | 7.16607 | − | 4.13733i | 0.305008 | − | 0.176096i | ||||
\(553\) | −0.656058 | + | 0.378775i | −0.0278984 | + | 0.0161072i | ||||
\(554\) | 45.0669i | 1.91471i | ||||||||
\(555\) | −39.2559 | − | 67.9932i | −1.66632 | − | 2.88615i | ||||
\(556\) | 20.4297 | − | 35.3852i | 0.866412 | − | 1.50067i | ||||
\(557\) | −14.7285 | − | 8.50353i | −0.624069 | − | 0.360306i | 0.154383 | − | 0.988011i | \(-0.450661\pi\) |
−0.778451 | + | 0.627705i | \(0.783994\pi\) | |||||||
\(558\) | 37.7851 | 1.59957 | ||||||||
\(559\) | 12.8916 | − | 2.50732i | 0.545259 | − | 0.106048i | ||||
\(560\) | 10.4412 | 0.441220 | ||||||||
\(561\) | 8.61140 | + | 4.97179i | 0.363573 | + | 0.209909i | ||||
\(562\) | 18.2122 | − | 31.5445i | 0.768235 | − | 1.33062i | ||||
\(563\) | −12.4596 | − | 21.5807i | −0.525111 | − | 0.909519i | −0.999572 | − | 0.0292428i | \(-0.990690\pi\) |
0.474461 | − | 0.880276i | \(-0.342643\pi\) | |||||||
\(564\) | 16.5218i | 0.695691i | ||||||||
\(565\) | 15.3158 | − | 8.84257i | 0.644340 | − | 0.372010i | ||||
\(566\) | −38.8013 | + | 22.4019i | −1.63094 | + | 0.941623i | ||||
\(567\) | 10.8717i | 0.456569i | ||||||||
\(568\) | −3.05745 | − | 5.29566i | −0.128288 | − | 0.222201i | ||||
\(569\) | 2.94065 | − | 5.09335i | 0.123278 | − | 0.213524i | −0.797780 | − | 0.602948i | \(-0.793993\pi\) |
0.921059 | + | 0.389424i | \(0.127326\pi\) | |||||||
\(570\) | 35.3983 | + | 20.4372i | 1.48267 | + | 0.856022i | ||||
\(571\) | −8.92622 | −0.373551 | −0.186775 | − | 0.982403i | \(-0.559804\pi\) | ||||
−0.186775 | + | 0.982403i | \(0.559804\pi\) | |||||||
\(572\) | −7.40220 | − | 2.54789i | −0.309501 | − | 0.106533i | ||||
\(573\) | −25.7074 | −1.07394 | ||||||||
\(574\) | −22.0751 | − | 12.7451i | −0.921397 | − | 0.531969i | ||||
\(575\) | 15.3816 | − | 26.6417i | 0.641457 | − | 1.11104i | ||||
\(576\) | −11.7398 | − | 20.3339i | −0.489158 | − | 0.847247i | ||||
\(577\) | − | 36.1933i | − | 1.50675i | −0.657592 | − | 0.753374i | \(-0.728425\pi\) | ||
0.657592 | − | 0.753374i | \(-0.271575\pi\) | |||||||
\(578\) | −13.8894 | + | 8.01905i | −0.577723 | + | 0.333549i | ||||
\(579\) | −27.5961 | + | 15.9326i | −1.14685 | + | 0.662136i | ||||
\(580\) | 11.3104i | 0.469638i | ||||||||
\(581\) | 2.38383 | + | 4.12892i | 0.0988980 | + | 0.171296i | ||||
\(582\) | 1.10513 | − | 1.91414i | 0.0458091 | − | 0.0793437i | ||||
\(583\) | 3.77699 | + | 2.18065i | 0.156427 | + | 0.0903132i | ||||
\(584\) | −6.77838 | −0.280491 | ||||||||
\(585\) | −5.24383 | − | 26.9617i | −0.216806 | − | 1.11473i | ||||
\(586\) | −0.886069 | −0.0366032 | ||||||||
\(587\) | 31.6008 | + | 18.2447i | 1.30431 | + | 0.753041i | 0.981139 | − | 0.193301i | \(-0.0619195\pi\) |
0.323166 | + | 0.946342i | \(0.395253\pi\) | |||||||
\(588\) | −2.76998 | + | 4.79774i | −0.114232 | + | 0.197855i | ||||
\(589\) | 10.0732 | + | 17.4472i | 0.415058 | + | 0.718901i | ||||
\(590\) | − | 55.6708i | − | 2.29193i | ||||||
\(591\) | 44.9649 | − | 25.9605i | 1.84961 | − | 1.06787i | ||||
\(592\) | −24.1967 | + | 13.9699i | −0.994476 | + | 0.574161i | ||||
\(593\) | 34.9930i | 1.43699i | 0.695533 | + | 0.718495i | \(0.255168\pi\) | ||||
−0.695533 | + | 0.718495i | \(0.744832\pi\) | |||||||
\(594\) | −1.87107 | − | 3.24079i | −0.0767711 | − | 0.132971i | ||||
\(595\) | 8.93270 | − | 15.4719i | 0.366205 | − | 0.634286i | ||||
\(596\) | −5.34926 | − | 3.08839i | −0.219114 | − | 0.126506i | ||||
\(597\) | 7.12385 | 0.291560 | ||||||||
\(598\) | −5.60256 | − | 28.8062i | −0.229106 | − | 1.17797i | ||||
\(599\) | −32.5052 | −1.32812 | −0.664062 | − | 0.747677i | \(-0.731169\pi\) | ||||
−0.664062 | + | 0.747677i | \(0.731169\pi\) | |||||||
\(600\) | 14.8072 | + | 8.54894i | 0.604501 | + | 0.349009i | ||||
\(601\) | −10.0390 | + | 17.3881i | −0.409500 | + | 0.709275i | −0.994834 | − | 0.101518i | \(-0.967630\pi\) |
0.585334 | + | 0.810792i | \(0.300963\pi\) | |||||||
\(602\) | 3.84172 | + | 6.65406i | 0.156577 | + | 0.271199i | ||||
\(603\) | − | 17.8225i | − | 0.725788i | ||||||
\(604\) | −33.7235 | + | 19.4703i | −1.37219 | + | 0.792235i | ||||
\(605\) | −31.8608 | + | 18.3949i | −1.29533 | + | 0.747858i | ||||
\(606\) | 27.7799i | 1.12848i | ||||||||
\(607\) | −4.85800 | − | 8.41431i | −0.197180 | − | 0.341526i | 0.750433 | − | 0.660947i | \(-0.229845\pi\) |
−0.947613 | + | 0.319420i | \(0.896512\pi\) | |||||||
\(608\) | 9.52856 | − | 16.5039i | 0.386434 | − | 0.669323i | ||||
\(609\) | 2.51093 | + | 1.44969i | 0.101748 | + | 0.0587442i | ||||
\(610\) | 11.6946 | 0.473502 | ||||||||
\(611\) | 10.1674 | + | 3.49968i | 0.411327 | + | 0.141582i | ||||
\(612\) | −25.6979 | −1.03878 | ||||||||
\(613\) | −10.2898 | − | 5.94080i | −0.415600 | − | 0.239947i | 0.277593 | − | 0.960699i | \(-0.410463\pi\) |
−0.693193 | + | 0.720752i | \(0.743797\pi\) | |||||||
\(614\) | −14.8508 | + | 25.7224i | −0.599331 | + | 1.03807i | ||||
\(615\) | 49.2184 | + | 85.2488i | 1.98468 | + | 3.43756i | ||||
\(616\) | − | 0.840480i | − | 0.0338639i | ||||||
\(617\) | −17.3105 | + | 9.99422i | −0.696895 | + | 0.402352i | −0.806190 | − | 0.591657i | \(-0.798474\pi\) |
0.109295 | + | 0.994009i | \(0.465141\pi\) | |||||||
\(618\) | 34.0393 | − | 19.6526i | 1.36926 | − | 0.790543i | ||||
\(619\) | 41.7176i | 1.67677i | 0.545078 | + | 0.838386i | \(0.316500\pi\) | ||||
−0.545078 | + | 0.838386i | \(0.683500\pi\) | |||||||
\(620\) | 37.3603 | + | 64.7100i | 1.50043 | + | 2.59882i | ||||
\(621\) | 3.86129 | − | 6.68794i | 0.154948 | − | 0.268378i | ||||
\(622\) | −18.9708 | − | 10.9528i | −0.760659 | − | 0.439166i | ||||
\(623\) | −3.61884 | −0.144986 | ||||||||
\(624\) | −23.2042 | + | 4.51302i | −0.928911 | + | 0.180665i | ||||
\(625\) | −1.29828 | −0.0519312 | ||||||||
\(626\) | 12.5091 | + | 7.22211i | 0.499963 | + | 0.288654i | ||||
\(627\) | −2.38435 | + | 4.12982i | −0.0952219 | + | 0.164929i | ||||
\(628\) | 15.9012 | + | 27.5416i | 0.634526 | + | 1.09903i | ||||
\(629\) | 47.8066i | 1.90618i | ||||||||
\(630\) | 13.9164 | − | 8.03461i | 0.554441 | − | 0.320107i | ||||
\(631\) | 15.2780 | − | 8.82074i | 0.608206 | − | 0.351148i | −0.164057 | − | 0.986451i | \(-0.552458\pi\) |
0.772263 | + | 0.635303i | \(0.219125\pi\) | |||||||
\(632\) | 0.718319i | 0.0285732i | ||||||||
\(633\) | 16.8084 | + | 29.1130i | 0.668073 | + | 1.15714i | ||||
\(634\) | 0.739603 | − | 1.28103i | 0.0293734 | − | 0.0508762i | ||||
\(635\) | 38.3982 | + | 22.1692i | 1.52379 | + | 0.879759i | ||||
\(636\) | −27.2584 | −1.08086 | ||||||||
\(637\) | 2.36575 | + | 2.72089i | 0.0937343 | + | 0.107806i | ||||
\(638\) | −2.39694 | −0.0948958 | ||||||||
\(639\) | 11.8124 | + | 6.81987i | 0.467290 | + | 0.269790i | ||||
\(640\) | 13.3159 | − | 23.0639i | 0.526359 | − | 0.911680i | ||||
\(641\) | −5.46012 | − | 9.45721i | −0.215662 | − | 0.373537i | 0.737815 | − | 0.675003i | \(-0.235858\pi\) |
−0.953477 | + | 0.301465i | \(0.902524\pi\) | |||||||
\(642\) | 18.2842i | 0.721618i | ||||||||
\(643\) | 15.2725 | − | 8.81757i | 0.602288 | − | 0.347731i | −0.167653 | − | 0.985846i | \(-0.553619\pi\) |
0.769941 | + | 0.638115i | \(0.220286\pi\) | |||||||
\(644\) | 8.18524 | − | 4.72575i | 0.322544 | − | 0.186221i | ||||
\(645\) | − | 29.6716i | − | 1.16832i | ||||||
\(646\) | −12.4445 | − | 21.5544i | −0.489620 | − | 0.848048i | ||||
\(647\) | 8.33632 | − | 14.4389i | 0.327735 | − | 0.567653i | −0.654327 | − | 0.756211i | \(-0.727048\pi\) |
0.982062 | + | 0.188558i | \(0.0603815\pi\) | |||||||
\(648\) | 8.92758 | + | 5.15434i | 0.350708 | + | 0.202482i | ||||
\(649\) | 6.49495 | 0.254949 | ||||||||
\(650\) | 45.7593 | − | 39.7866i | 1.79483 | − | 1.56056i | ||||
\(651\) | 19.1544 | 0.750719 | ||||||||
\(652\) | −4.92042 | − | 2.84080i | −0.192698 | − | 0.111254i | ||||
\(653\) | 3.38664 | − | 5.86584i | 0.132530 | − | 0.229548i | −0.792121 | − | 0.610364i | \(-0.791023\pi\) |
0.924651 | + | 0.380816i | \(0.124357\pi\) | |||||||
\(654\) | 24.8506 | + | 43.0426i | 0.971737 | + | 1.68310i | ||||
\(655\) | 29.5441i | 1.15439i | ||||||||
\(656\) | 30.3374 | − | 17.5153i | 1.18448 | − | 0.683858i | ||||
\(657\) | 13.0940 | − | 7.55983i | 0.510846 | − | 0.294937i | ||||
\(658\) | 6.29081i | 0.245241i | ||||||||
\(659\) | −16.7680 | − | 29.0431i | −0.653190 | − | 1.13136i | −0.982344 | − | 0.187082i | \(-0.940097\pi\) |
0.329154 | − | 0.944276i | \(-0.393236\pi\) | |||||||
\(660\) | −8.84332 | + | 15.3171i | −0.344226 | + | 0.596216i | ||||
\(661\) | −21.7945 | − | 12.5830i | −0.847707 | − | 0.489424i | 0.0121696 | − | 0.999926i | \(-0.496126\pi\) |
−0.859876 | + | 0.510502i | \(0.829460\pi\) | |||||||
\(662\) | 8.85657 | 0.344221 | ||||||||
\(663\) | −13.1643 | + | 38.2454i | −0.511261 | + | 1.48533i | ||||
\(664\) | 4.52075 | 0.175439 | ||||||||
\(665\) | 7.41995 | + | 4.28391i | 0.287733 | + | 0.166123i | ||||
\(666\) | −21.5001 | + | 37.2393i | −0.833112 | + | 1.44299i | ||||
\(667\) | −2.47325 | − | 4.28380i | −0.0957647 | − | 0.165869i | ||||
\(668\) | − | 33.7833i | − | 1.30712i | ||||||
\(669\) | −8.58060 | + | 4.95401i | −0.331745 | + | 0.191533i | ||||
\(670\) | 55.4436 | − | 32.0104i | 2.14197 | − | 1.23667i | ||||
\(671\) | 1.36438i | 0.0526713i | ||||||||
\(672\) | −9.05939 | − | 15.6913i | −0.349473 | − | 0.605306i | ||||
\(673\) | −0.927341 | + | 1.60620i | −0.0357464 | + | 0.0619145i | −0.883345 | − | 0.468723i | \(-0.844714\pi\) |
0.847599 | + | 0.530638i | \(0.178048\pi\) | |||||||
\(674\) | −37.3172 | − | 21.5451i | −1.43741 | − | 0.829887i | ||||
\(675\) | 15.9571 | 0.614189 | ||||||||
\(676\) | 4.42503 | − | 31.5348i | 0.170194 | − | 1.21288i | ||||
\(677\) | −14.7209 | −0.565770 | −0.282885 | − | 0.959154i | \(-0.591291\pi\) | ||||
−0.282885 | + | 0.959154i | \(0.591291\pi\) | |||||||
\(678\) | −20.2863 | − | 11.7123i | −0.779092 | − | 0.449809i | ||||
\(679\) | 0.231650 | − | 0.401229i | 0.00888990 | − | 0.0153978i | ||||
\(680\) | −8.47009 | − | 14.6706i | −0.324813 | − | 0.562593i | ||||
\(681\) | 30.6822i | 1.17575i | ||||||||
\(682\) | −13.7136 | + | 7.91756i | −0.525122 | + | 0.303179i | ||||
\(683\) | 6.87930 | − | 3.97177i | 0.263229 | − | 0.151975i | −0.362578 | − | 0.931954i | \(-0.618103\pi\) |
0.625807 | + | 0.779978i | \(0.284770\pi\) | |||||||
\(684\) | − | 12.3241i | − | 0.471224i | ||||||
\(685\) | −13.4266 | − | 23.2556i | −0.513005 | − | 0.888551i | ||||
\(686\) | −1.05469 | + | 1.82678i | −0.0402684 | + | 0.0697469i | ||||
\(687\) | 32.3529 | + | 18.6790i | 1.23434 | + | 0.712647i | ||||
\(688\) | −10.5592 | −0.402566 | ||||||||
\(689\) | −5.77394 | + | 16.7746i | −0.219969 | + | 0.639060i | ||||
\(690\) | −66.3008 | −2.52403 | ||||||||
\(691\) | 8.86002 | + | 5.11534i | 0.337051 | + | 0.194597i | 0.658967 | − | 0.752172i | \(-0.270994\pi\) |
−0.321916 | + | 0.946768i | \(0.604327\pi\) | |||||||
\(692\) | 4.51240 | − | 7.81571i | 0.171536 | − | 0.297109i | ||||
\(693\) | 0.937375 | + | 1.62358i | 0.0356079 | + | 0.0616748i | ||||
\(694\) | − | 16.8118i | − | 0.638168i | ||||||
\(695\) | −52.0306 | + | 30.0399i | −1.97363 | + | 1.13948i | ||||
\(696\) | 2.38089 | − | 1.37461i | 0.0902475 | − | 0.0521044i | ||||
\(697\) | − | 59.9392i | − | 2.27036i | ||||||
\(698\) | 22.7785 | + | 39.4535i | 0.862178 | + | 1.49334i | ||||
\(699\) | −18.6616 | + | 32.3228i | −0.705845 | + | 1.22256i | ||||
\(700\) | 16.9131 | + | 9.76479i | 0.639255 | + | 0.369074i | ||||
\(701\) | −16.5978 | −0.626891 | −0.313445 | − | 0.949606i | \(-0.601483\pi\) | ||||
−0.313445 | + | 0.949606i | \(0.601483\pi\) | |||||||
\(702\) | 11.4871 | − | 9.98773i | 0.433552 | − | 0.376963i | ||||
\(703\) | −22.9269 | −0.864706 | ||||||||
\(704\) | 8.52162 | + | 4.91996i | 0.321171 | + | 0.185428i | ||||
\(705\) | 12.1468 | − | 21.0389i | 0.457475 | − | 0.792371i | ||||
\(706\) | 22.8000 | + | 39.4907i | 0.858088 | + | 1.48625i | ||||
\(707\) | 5.82303i | 0.218998i | ||||||||
\(708\) | −35.1552 | + | 20.2969i | −1.32121 | + | 0.762804i | ||||
\(709\) | 41.4531 | − | 23.9329i | 1.55680 | − | 0.898820i | 0.559242 | − | 0.829004i | \(-0.311092\pi\) |
0.997560 | − | 0.0698158i | \(-0.0222412\pi\) | |||||||
\(710\) | 48.9957i | 1.83878i | ||||||||
\(711\) | −0.801130 | − | 1.38760i | −0.0300447 | − | 0.0520390i | ||||
\(712\) | −1.71571 | + | 2.97170i | −0.0642990 | + | 0.111369i | ||||
\(713\) | −28.3004 | − | 16.3393i | −1.05986 | − | 0.611910i | ||||
\(714\) | −23.6634 | −0.885581 | ||||||||
\(715\) | 7.55279 | + | 8.68661i | 0.282458 | + | 0.324861i | ||||
\(716\) | −14.4344 | −0.539441 | ||||||||
\(717\) | −59.5840 | − | 34.4008i | −2.22520 | − | 1.28472i | ||||
\(718\) | 14.4318 | − | 24.9965i | 0.538588 | − | 0.932862i | ||||
\(719\) | −19.0461 | − | 32.9888i | −0.710300 | − | 1.23028i | −0.964744 | − | 0.263188i | \(-0.915226\pi\) |
0.254444 | − | 0.967087i | \(-0.418107\pi\) | |||||||
\(720\) | 22.0836i | 0.823009i | ||||||||
\(721\) | 7.13508 | − | 4.11944i | 0.265724 | − | 0.153416i | ||||
\(722\) | −24.3719 | + | 14.0711i | −0.907028 | + | 0.523673i | ||||
\(723\) | − | 66.7511i | − | 2.48250i | ||||||
\(724\) | −2.59089 | − | 4.48756i | −0.0962898 | − | 0.166779i | ||||
\(725\) | 5.11047 | − | 8.85159i | 0.189798 | − | 0.328740i | ||||
\(726\) | 42.2009 | + | 24.3647i | 1.56622 | + | 0.904259i | ||||
\(727\) | 15.4059 | 0.571374 | 0.285687 | − | 0.958323i | \(-0.407778\pi\) | ||||
0.285687 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(728\) | 3.35594 | − | 0.652702i | 0.124379 | − | 0.0241908i | ||||
\(729\) | −9.41460 | −0.348689 | ||||||||
\(730\) | 47.0354 | + | 27.1559i | 1.74086 | + | 1.00508i | ||||
\(731\) | −9.03369 | + | 15.6468i | −0.334123 | + | 0.578718i | ||||
\(732\) | −4.26372 | − | 7.38498i | −0.157592 | − | 0.272957i | ||||
\(733\) | 11.6298i | 0.429557i | 0.976663 | + | 0.214778i | \(0.0689029\pi\) | ||||
−0.976663 | + | 0.214778i | \(0.931097\pi\) | |||||||
\(734\) | 20.8487 | − | 12.0370i | 0.769538 | − | 0.444293i | ||||
\(735\) | 7.05461 | − | 4.07298i | 0.260213 | − | 0.150234i | ||||
\(736\) | 30.9117i | 1.13942i | ||||||||
\(737\) | 3.73456 | + | 6.46844i | 0.137564 | + | 0.238268i | ||||
\(738\) | 26.9565 | − | 46.6900i | 0.992282 | − | 1.71868i | ||||
\(739\) | 2.32875 | + | 1.34451i | 0.0856645 | + | 0.0494584i | 0.542220 | − | 0.840236i | \(-0.317584\pi\) |
−0.456556 | + | 0.889695i | \(0.650917\pi\) | |||||||
\(740\) | −85.0336 | −3.12590 | ||||||||
\(741\) | −18.3416 | − | 6.31331i | −0.673794 | − | 0.231925i | ||||
\(742\) | −10.3789 | −0.381020 | ||||||||
\(743\) | −2.13665 | − | 1.23360i | −0.0783862 | − | 0.0452563i | 0.460295 | − | 0.887766i | \(-0.347744\pi\) |
−0.538681 | + | 0.842510i | \(0.681077\pi\) | |||||||
\(744\) | 9.08120 | − | 15.7291i | 0.332933 | − | 0.576657i | ||||
\(745\) | 4.54118 | + | 7.86556i | 0.166376 | + | 0.288172i | ||||
\(746\) | 65.9835i | 2.41583i | ||||||||
\(747\) | −8.73288 | + | 5.04193i | −0.319519 | + | 0.184475i | ||||
\(748\) | 9.32673 | − | 5.38479i | 0.341019 | − | 0.196887i | ||||
\(749\) | 3.83260i | 0.140040i | ||||||||
\(750\) | −25.5409 | − | 44.2382i | −0.932623 | − | 1.61535i | ||||
\(751\) | −18.9592 | + | 32.8383i | −0.691832 | + | 1.19829i | 0.279405 | + | 0.960173i | \(0.409863\pi\) |
−0.971237 | + | 0.238115i | \(0.923471\pi\) | |||||||
\(752\) | −7.48709 | − | 4.32267i | −0.273026 | − | 0.157632i | ||||
\(753\) | 29.3623 | 1.07002 | ||||||||
\(754\) | −1.86142 | − | 9.57072i | −0.0677890 | − | 0.348545i | ||||
\(755\) | 57.2583 | 2.08384 | ||||||||
\(756\) | 4.24574 | + | 2.45128i | 0.154416 | + | 0.0891522i | ||||
\(757\) | −17.3225 | + | 30.0035i | −0.629598 | + | 1.09050i | 0.358034 | + | 0.933709i | \(0.383447\pi\) |
−0.987632 | + | 0.156788i | \(0.949886\pi\) | |||||||
\(758\) | 28.9145 | + | 50.0814i | 1.05022 | + | 1.81904i | ||||
\(759\) | − | 7.73512i | − | 0.280767i | ||||||
\(760\) | 7.03569 | − | 4.06206i | 0.255211 | − | 0.147346i | ||||
\(761\) | 19.7969 | − | 11.4297i | 0.717636 | − | 0.414328i | −0.0962458 | − | 0.995358i | \(-0.530683\pi\) |
0.813882 | + | 0.581030i | \(0.197350\pi\) | |||||||
\(762\) | − | 58.7280i | − | 2.12749i | ||||||
\(763\) | 5.20902 | + | 9.02229i | 0.188579 | + | 0.326629i | ||||
\(764\) | −13.9214 | + | 24.1126i | −0.503659 | + | 0.872363i | ||||
\(765\) | 32.7239 | + | 18.8931i | 1.18313 | + | 0.683083i | ||||
\(766\) | 33.9625 | 1.22712 | ||||||||
\(767\) | 5.04386 | + | 25.9336i | 0.182123 | + | 0.936408i | ||||
\(768\) | 14.9390 | 0.539065 | ||||||||
\(769\) | −44.8839 | − | 25.9137i | −1.61855 | − | 0.934473i | −0.987294 | − | 0.158902i | \(-0.949205\pi\) |
−0.631260 | − | 0.775571i | \(-0.717462\pi\) | |||||||
\(770\) | −3.36718 | + | 5.83212i | −0.121345 | + | 0.210175i | ||||
\(771\) | −5.18507 | − | 8.98080i | −0.186736 | − | 0.323436i | ||||
\(772\) | 34.5122i | 1.24212i | ||||||||
\(773\) | −4.93605 | + | 2.84983i | −0.177538 | + | 0.102501i | −0.586135 | − | 0.810213i | \(-0.699351\pi\) |
0.408598 | + | 0.912715i | \(0.366018\pi\) | |||||||
\(774\) | −14.0737 | + | 8.12545i | −0.505868 | + | 0.292063i | ||||
\(775\) | − | 67.5234i | − | 2.42551i | ||||||
\(776\) | −0.219653 | − | 0.380450i | −0.00788508 | − | 0.0136574i | ||||
\(777\) | −10.8990 | + | 18.8777i | −0.391000 | + | 0.677232i | ||||
\(778\) | −38.6146 | − | 22.2941i | −1.38440 | − | 0.799283i | ||||
\(779\) | 28.7454 | 1.02991 | ||||||||
\(780\) | −68.0269 | − | 23.4154i | −2.43576 | − | 0.838406i | ||||
\(781\) | −5.71619 | −0.204541 | ||||||||
\(782\) | 34.9625 | + | 20.1856i | 1.25026 | + | 0.721836i | ||||
\(783\) | 1.28289 | − | 2.22204i | 0.0458469 | − | 0.0794092i | ||||
\(784\) | −1.44945 | − | 2.51051i | −0.0517659 | − | 0.0896612i | ||||
\(785\) | − | 46.7622i | − | 1.66902i | ||||||
\(786\) | 33.8896 | − | 19.5662i | 1.20880 | − | 0.697902i | ||||
\(787\) | −14.5614 | + | 8.40705i | −0.519059 | + | 0.299679i | −0.736550 | − | 0.676384i | \(-0.763546\pi\) |
0.217490 | + | 0.976062i | \(0.430213\pi\) | |||||||
\(788\) | − | 56.2340i | − | 2.00325i | ||||||
\(789\) | 3.01364 | + | 5.21977i | 0.107288 | + | 0.185829i | ||||
\(790\) | 2.87777 | − | 4.98444i | 0.102386 | − | 0.177338i | ||||
\(791\) | −4.25228 | − | 2.45505i | −0.151194 | − | 0.0872917i | ||||
\(792\) | 1.77766 | 0.0631664 | ||||||||
\(793\) | −5.44781 | + | 1.05955i | −0.193457 | + | 0.0376258i | ||||
\(794\) | 27.6296 | 0.980539 | ||||||||
\(795\) | 34.7109 | + | 20.0404i | 1.23107 | + | 0.710759i | ||||
\(796\) | 3.85781 | − | 6.68192i | 0.136736 | − | 0.236834i | ||||
\(797\) | 21.0651 | + | 36.4858i | 0.746163 | + | 1.29239i | 0.949650 | + | 0.313314i | \(0.101439\pi\) |
−0.203487 | + | 0.979078i | \(0.565227\pi\) | |||||||
\(798\) | − | 11.3484i | − | 0.401729i | ||||||
\(799\) | −12.8108 | + | 7.39632i | −0.453214 | + | 0.261663i | ||||
\(800\) | −55.3154 | + | 31.9364i | −1.95570 | + | 1.12912i | ||||
\(801\) | − | 7.65403i | − | 0.270442i | ||||||
\(802\) | 20.5082 | + | 35.5213i | 0.724171 | + | 1.25430i | ||||
\(803\) | −3.16820 | + | 5.48748i | −0.111803 | + | 0.193649i | ||||
\(804\) | −40.4281 | − | 23.3412i | −1.42579 | − | 0.823180i | ||||
\(805\) | −13.8975 | −0.489823 | ||||||||
\(806\) | −42.2637 | − | 48.6083i | −1.48868 | − | 1.71215i | ||||
\(807\) | 26.9716 | 0.949445 | ||||||||
\(808\) | 4.78173 | + | 2.76073i | 0.168221 | + | 0.0971223i | ||||
\(809\) | 15.0843 | − | 26.1268i | 0.530336 | − | 0.918569i | −0.469037 | − | 0.883178i | \(-0.655399\pi\) |
0.999374 | − | 0.0353910i | \(-0.0112677\pi\) | |||||||
\(810\) | −41.2992 | − | 71.5323i | −1.45111 | − | 2.51339i | ||||
\(811\) | − | 23.7929i | − | 0.835480i | −0.908567 | − | 0.417740i | \(-0.862822\pi\) | ||
0.908567 | − | 0.417740i | \(-0.137178\pi\) | |||||||
\(812\) | 2.71951 | − | 1.57011i | 0.0954360 | − | 0.0551000i | ||||
\(813\) | 25.5178 | − | 14.7327i | 0.894950 | − | 0.516699i | ||||
\(814\) | − | 18.0207i | − | 0.631624i | ||||||
\(815\) | 4.17712 | + | 7.23499i | 0.146318 | + | 0.253431i | ||||
\(816\) | 16.2601 | − | 28.1633i | 0.569217 | − | 0.985913i | ||||
\(817\) | −7.50384 | − | 4.33234i | −0.262526 | − | 0.151569i | ||||
\(818\) | 50.7432 | 1.77419 | ||||||||
\(819\) | −5.75483 | + | 5.00368i | −0.201090 | + | 0.174843i | ||||
\(820\) | 106.614 | 3.72312 | ||||||||
\(821\) | −31.0771 | − | 17.9424i | −1.08460 | − | 0.626193i | −0.152465 | − | 0.988309i | \(-0.548721\pi\) |
−0.932133 | + | 0.362116i | \(0.882054\pi\) | |||||||
\(822\) | −17.7841 | + | 30.8029i | −0.620291 | + | 1.07438i | ||||
\(823\) | −6.11728 | − | 10.5954i | −0.213235 | − | 0.369334i | 0.739490 | − | 0.673167i | \(-0.235067\pi\) |
−0.952725 | + | 0.303833i | \(0.901733\pi\) | |||||||
\(824\) | − | 7.81220i | − | 0.272151i | ||||||
\(825\) | 13.8417 | − | 7.99151i | 0.481906 | − | 0.278229i | ||||
\(826\) | −13.3857 | + | 7.72823i | −0.465748 | + | 0.268900i | ||||
\(827\) | 27.3474i | 0.950962i | 0.879726 | + | 0.475481i | \(0.157726\pi\) | ||||
−0.879726 | + | 0.475481i | \(0.842274\pi\) | |||||||
\(828\) | 9.99521 | + | 17.3122i | 0.347358 | + | 0.601641i | ||||
\(829\) | 11.7869 | − | 20.4155i | 0.409376 | − | 0.709060i | −0.585444 | − | 0.810713i | \(-0.699080\pi\) |
0.994820 | + | 0.101653i | \(0.0324132\pi\) | |||||||
\(830\) | −31.3697 | − | 18.1113i | −1.08886 | − | 0.628652i | ||||
\(831\) | −48.3199 | −1.67620 | ||||||||
\(832\) | −13.0271 | + | 37.8466i | −0.451634 | + | 1.31210i | ||||
\(833\) | −4.96016 | −0.171859 | ||||||||
\(834\) | 68.9165 | + | 39.7889i | 2.38638 | + | 1.37778i | ||||
\(835\) | −24.8376 | + | 43.0199i | −0.859539 | + | 1.48877i | ||||
\(836\) | 2.58242 | + | 4.47288i | 0.0893148 | + | 0.154698i | ||||
\(837\) | − | 16.9506i | − | 0.585898i | ||||||
\(838\) | −71.2880 | + | 41.1582i | −2.46260 | + | 1.42179i | ||||
\(839\) | 9.16975 | − | 5.29416i | 0.316575 | − | 0.182775i | −0.333290 | − | 0.942824i | \(-0.608159\pi\) |
0.649865 | + | 0.760050i | \(0.274825\pi\) | |||||||
\(840\) | − | 7.72409i | − | 0.266507i | ||||||
\(841\) | 13.6783 | + | 23.6915i | 0.471665 | + | 0.816947i | ||||
\(842\) | −23.2332 | + | 40.2411i | −0.800669 | + | 1.38680i | ||||
\(843\) | 33.8214 | + | 19.5268i | 1.16487 | + | 0.672538i | ||||
\(844\) | 36.4092 | 1.25326 | ||||||||
\(845\) | −28.8193 | + | 36.9033i | −0.991414 | + | 1.26951i | ||||
\(846\) | −13.3054 | −0.457449 | ||||||||
\(847\) | 8.84586 | + | 5.10716i | 0.303947 | + | 0.175484i | ||||
\(848\) | 7.13174 | − | 12.3525i | 0.244905 | − | 0.424188i | ||||
\(849\) | −24.0189 | − | 41.6020i | −0.824328 | − | 1.42778i | ||||
\(850\) | 83.4188i | 2.86124i | ||||||||
\(851\) | 32.2065 | − | 18.5944i | 1.10402 | − | 0.637408i | ||||
\(852\) | 30.9401 | − | 17.8633i | 1.05999 | − | 0.611985i | ||||
\(853\) | 21.3925i | 0.732464i | 0.930524 | + | 0.366232i | \(0.119352\pi\) | ||||
−0.930524 | + | 0.366232i | \(0.880648\pi\) | |||||||
\(854\) | −1.62345 | − | 2.81190i | −0.0555534 | − | 0.0962213i | ||||
\(855\) | −9.06070 | + | 15.6936i | −0.309870 | + | 0.536710i | ||||
\(856\) | 3.14724 | + | 1.81706i | 0.107570 | + | 0.0621058i | ||||
\(857\) | −7.22129 | −0.246675 | −0.123337 | − | 0.992365i | \(-0.539360\pi\) | ||||
−0.123337 | + | 0.992365i | \(0.539360\pi\) | |||||||
\(858\) | 4.96229 | − | 14.4166i | 0.169410 | − | 0.492173i | ||||
\(859\) | 57.1073 | 1.94848 | 0.974238 | − | 0.225524i | \(-0.0724095\pi\) | ||||
0.974238 | + | 0.225524i | \(0.0724095\pi\) | |||||||
\(860\) | −27.8309 | − | 16.0682i | −0.949027 | − | 0.547921i | ||||
\(861\) | 13.6650 | − | 23.6685i | 0.465703 | − | 0.806621i | ||||
\(862\) | −37.8421 | − | 65.5444i | −1.28891 | − | 2.23245i | ||||
\(863\) | − | 51.3361i | − | 1.74750i | −0.486374 | − | 0.873751i | \(-0.661681\pi\) | ||
0.486374 | − | 0.873751i | \(-0.338319\pi\) | |||||||
\(864\) | −13.8860 | + | 8.01707i | −0.472411 | + | 0.272746i | ||||
\(865\) | −11.4922 | + | 6.63505i | −0.390748 | + | 0.225598i | ||||
\(866\) | 25.7631i | 0.875467i | ||||||||
\(867\) | −8.59788 | − | 14.8920i | −0.291999 | − | 0.505758i | ||||
\(868\) | 10.3727 | − | 17.9661i | 0.352074 | − | 0.609810i | ||||
\(869\) | 0.581520 | + | 0.335741i | 0.0197267 | + | 0.0113892i | ||||
\(870\) | −22.0281 | −0.746823 | ||||||||
\(871\) | −22.9276 | + | 19.9349i | −0.776871 | + | 0.675470i | ||||
\(872\) | 9.87851 | 0.334528 | ||||||||
\(873\) | 0.848621 | + | 0.489952i | 0.0287215 | + | 0.0165824i | ||||
\(874\) | −9.68055 | + | 16.7672i | −0.327449 | + | 0.567159i | ||||
\(875\) | −5.35371 | − | 9.27291i | −0.180989 | − | 0.313481i | ||||
\(876\) | − | 39.6029i | − | 1.33806i | ||||||
\(877\) | −18.5570 | + | 10.7139i | −0.626624 | + | 0.361781i | −0.779443 | − | 0.626473i | \(-0.784498\pi\) |
0.152820 | + | 0.988254i | \(0.451165\pi\) | |||||||
\(878\) | −28.7815 | + | 16.6170i | −0.971330 | + | 0.560798i | ||||
\(879\) | − | 0.950027i | − | 0.0320436i | ||||||
\(880\) | −4.62745 | − | 8.01497i | −0.155991 | − | 0.270185i | ||||
\(881\) | 14.5309 | − | 25.1683i | 0.489560 | − | 0.847943i | −0.510368 | − | 0.859956i | \(-0.670491\pi\) |
0.999928 | + | 0.0120134i | \(0.00382406\pi\) | |||||||
\(882\) | −3.86375 | − | 2.23073i | −0.130099 | − | 0.0751127i | ||||
\(883\) | 4.83594 | 0.162742 | 0.0813711 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813711 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(884\) | 28.7438 | + | 33.0589i | 0.966760 | + | 1.11189i | ||||
\(885\) | 59.6892 | 2.00643 | ||||||||
\(886\) | −27.5308 | − | 15.8949i | −0.924916 | − | 0.534000i | ||||
\(887\) | 12.4949 | − | 21.6418i | 0.419538 | − | 0.726660i | −0.576355 | − | 0.817199i | \(-0.695526\pi\) |
0.995893 | + | 0.0905387i | \(0.0288589\pi\) | |||||||
\(888\) | 10.3346 | + | 17.9000i | 0.346806 | + | 0.600685i | ||||
\(889\) | − | 12.3102i | − | 0.412869i | ||||||
\(890\) | 23.8108 | − | 13.7471i | 0.798138 | − | 0.460805i | ||||
\(891\) | 8.34546 | − | 4.81826i | 0.279584 | − | 0.161418i | ||||
\(892\) | 10.7311i | 0.359303i | ||||||||
\(893\) | −3.54710 | − | 6.14376i | −0.118699 | − | 0.205593i | ||||
\(894\) | 6.01497 | − | 10.4182i | 0.201171 | − | 0.348438i | ||||
\(895\) | 18.3809 | + | 10.6122i | 0.614406 | + | 0.354727i | ||||
\(896\) | −7.39409 | −0.247019 | ||||||||
\(897\) | 30.8855 | − | 6.00696i | 1.03124 | − | 0.200567i | ||||
\(898\) | 64.9324 | 2.16682 | ||||||||
\(899\) | −9.40269 | − | 5.42865i | −0.313597 | − | 0.181055i | ||||
\(900\) | −20.6530 | + | 35.7721i | −0.688435 | + | 1.19240i | ||||
\(901\) | −12.2028 | − | 21.1359i | −0.406534 | − | 0.704138i | ||||
\(902\) | 22.5940i | 0.752300i | ||||||||
\(903\) | −7.13436 | + | 4.11902i | −0.237417 | + | 0.137073i | ||||
\(904\) | −4.03206 | + | 2.32791i | −0.134104 | + | 0.0774252i | ||||
\(905\) | 7.61931i | 0.253274i | ||||||||
\(906\) | −37.9204 | − | 65.6801i | −1.25982 | − | 2.18208i | ||||
\(907\) | 7.52060 | − | 13.0261i | 0.249717 | − | 0.432523i | −0.713730 | − | 0.700421i | \(-0.752996\pi\) |
0.963447 | + | 0.267898i | \(0.0863290\pi\) | |||||||
\(908\) | 28.7789 | + | 16.6155i | 0.955060 | + | 0.551404i | ||||
\(909\) | −12.3160 | −0.408497 | ||||||||
\(910\) | −25.9019 | − | 8.91563i | −0.858639 | − | 0.295550i | ||||
\(911\) | −9.22150 | −0.305522 | −0.152761 | − | 0.988263i | \(-0.548816\pi\) | ||||
−0.152761 | + | 0.988263i | \(0.548816\pi\) | |||||||
\(912\) | 13.5065 | + | 7.79795i | 0.447243 | + | 0.258216i | ||||
\(913\) | 2.11299 | − | 3.65981i | 0.0699298 | − | 0.121122i | ||||
\(914\) | −8.18018 | − | 14.1685i | −0.270576 | − | 0.468652i | ||||
\(915\) | 12.5388i | 0.414519i | ||||||||
\(916\) | 35.0404 | − | 20.2306i | 1.15777 | − | 0.668437i | ||||
\(917\) | 7.10371 | − | 4.10133i | 0.234585 | − | 0.135438i | ||||
\(918\) | 20.9409i | 0.691151i | ||||||||
\(919\) | 22.5402 | + | 39.0407i | 0.743531 | + | 1.28783i | 0.950878 | + | 0.309567i | \(0.100184\pi\) |
−0.207346 | + | 0.978268i | \(0.566483\pi\) | |||||||
\(920\) | −6.58889 | + | 11.4123i | −0.217229 | + | 0.376252i | ||||
\(921\) | −27.5791 | − | 15.9228i | −0.908762 | − | 0.524674i | ||||
\(922\) | 3.10548 | 0.102274 | ||||||||
\(923\) | −4.43910 | − | 22.8241i | −0.146115 | − | 0.751265i | ||||
\(924\) | 4.91053 | 0.161544 | ||||||||
\(925\) | 66.5480 | + | 38.4215i | 2.18808 | + | 1.26329i | ||||
\(926\) | −14.8043 | + | 25.6418i | −0.486499 | + | 0.842642i | ||||
\(927\) | 8.71284 | + | 15.0911i | 0.286167 | + | 0.495656i | ||||
\(928\) | 10.2703i | 0.337139i | ||||||||
\(929\) | −40.6313 | + | 23.4585i | −1.33307 | + | 0.769647i | −0.985769 | − | 0.168107i | \(-0.946235\pi\) |
−0.347300 | + | 0.937754i | \(0.612901\pi\) | |||||||
\(930\) | −126.030 | + | 72.7632i | −4.13267 | + | 2.38600i | ||||
\(931\) | − | 2.37878i | − | 0.0779612i | ||||||
\(932\) | 20.2117 | + | 35.0078i | 0.662058 | + | 1.14672i | ||||
\(933\) | 11.7434 | − | 20.3401i | 0.384461 | − | 0.665906i | ||||
\(934\) | −57.3256 | − | 33.0969i | −1.87575 | − | 1.08296i | ||||
\(935\) | −15.8356 | −0.517880 | ||||||||
\(936\) | 1.38050 | + | 7.09800i | 0.0451231 | + | 0.232005i | ||||
\(937\) | −28.3912 | −0.927501 | −0.463750 | − | 0.885966i | \(-0.653497\pi\) | ||||
−0.463750 | + | 0.885966i | \(0.653497\pi\) | |||||||
\(938\) | −15.3934 | − | 8.88737i | −0.502612 | − | 0.290183i | ||||
\(939\) | −7.74342 | + | 13.4120i | −0.252697 | + | 0.437684i | ||||
\(940\) | −13.1558 | − | 22.7866i | −0.429096 | − | 0.743216i | ||||
\(941\) | − | 17.8718i | − | 0.582603i | −0.956631 | − | 0.291302i | \(-0.905912\pi\) | ||
0.956631 | − | 0.291302i | \(-0.0940883\pi\) | |||||||
\(942\) | −53.6402 | + | 30.9692i | −1.74769 | + | 1.00903i | ||||
\(943\) | −40.3800 | + | 23.3134i | −1.31495 | + | 0.759188i | ||||
\(944\) | − | 21.2415i | − | 0.691353i | ||||||
\(945\) | −3.60437 | − | 6.24295i | −0.117250 | − | 0.203083i | ||||
\(946\) | 3.40524 | − | 5.89805i | 0.110714 | − | 0.191762i | ||||
\(947\) | 8.24659 | + | 4.76117i | 0.267978 | + | 0.154717i | 0.627969 | − | 0.778239i | \(-0.283887\pi\) |
−0.359990 | + | 0.932956i | \(0.617220\pi\) | |||||||
\(948\) | −4.19680 | −0.136306 | ||||||||
\(949\) | −24.3713 | − | 8.38878i | −0.791125 | − | 0.272311i | ||||
\(950\) | −40.0057 | −1.29796 | ||||||||
\(951\) | 1.37350 | + | 0.792989i | 0.0445387 | + | 0.0257144i | ||||
\(952\) | −2.35164 | + | 4.07316i | −0.0762171 | + | 0.132012i | ||||
\(953\) | −6.70900 | − | 11.6203i | −0.217326 | − | 0.376419i | 0.736664 | − | 0.676259i | \(-0.236400\pi\) |
−0.953990 | + | 0.299840i | \(0.903067\pi\) | |||||||
\(954\) | − | 21.9519i | − | 0.710718i | ||||||
\(955\) | 35.4552 | − | 20.4701i | 1.14730 | − | 0.662397i | ||||
\(956\) | −64.5335 | + | 37.2584i | −2.08716 | + | 1.20502i | ||||
\(957\) | − | 2.56996i | − | 0.0830749i | ||||||
\(958\) | 43.4482 | + | 75.2545i | 1.40375 | + | 2.43136i | ||||
\(959\) | −3.72778 | + | 6.45670i | −0.120376 | + | 0.208498i | ||||
\(960\) | 78.3145 | + | 45.2149i | 2.52759 | + | 1.45931i | ||||
\(961\) | −40.7275 | −1.31379 | ||||||||
\(962\) | 71.9545 | − | 13.9946i | 2.31991 | − | 0.451202i | ||||
\(963\) | −8.10615 | −0.261217 | ||||||||
\(964\) | −62.6102 | − | 36.1480i | −2.01654 | − | 1.16425i | ||||
\(965\) | 25.3734 | − | 43.9480i | 0.816798 | − | 1.41474i | ||||
\(966\) | 9.20389 | + | 15.9416i | 0.296130 | + | 0.512913i | ||||
\(967\) | 12.9316i | 0.415851i | 0.978145 | + | 0.207926i | \(0.0666712\pi\) | ||||
−0.978145 | + | 0.207926i | \(0.933329\pi\) | |||||||
\(968\) | 8.38775 | − | 4.84267i | 0.269593 | − | 0.155649i | ||||
\(969\) | 23.1103 | − | 13.3427i | 0.742409 | − | 0.428630i | ||||
\(970\) | 3.51994i | 0.113019i | ||||||||
\(971\) | −23.7607 | − | 41.1547i | −0.762516 | − | 1.32072i | −0.941550 | − | 0.336874i | \(-0.890630\pi\) |
0.179034 | − | 0.983843i | \(-0.442703\pi\) | |||||||
\(972\) | −22.7605 | + | 39.4224i | −0.730044 | + | 1.26447i | ||||
\(973\) | 14.4458 | + | 8.34028i | 0.463111 | + | 0.267377i | ||||
\(974\) | 59.7515 | 1.91456 | ||||||||
\(975\) | 42.6584 | + | 49.0623i | 1.36616 | + | 1.57125i | ||||
\(976\) | 4.46216 | 0.142830 | ||||||||
\(977\) | 31.6049 | + | 18.2471i | 1.01113 | + | 0.583776i | 0.911522 | − | 0.411251i | \(-0.134908\pi\) |
0.0996074 | + | 0.995027i | \(0.468241\pi\) | |||||||
\(978\) | 5.53276 | − | 9.58302i | 0.176918 | − | 0.306431i | ||||
\(979\) | 1.60384 | + | 2.77793i | 0.0512589 | + | 0.0887831i | ||||
\(980\) | − | 8.82263i | − | 0.281829i | ||||||
\(981\) | −19.0826 | + | 11.0174i | −0.609261 | + | 0.351757i | ||||
\(982\) | 63.5470 | − | 36.6889i | 2.02787 | − | 1.17079i | ||||
\(983\) | − | 44.1843i | − | 1.40926i | −0.709576 | − | 0.704629i | \(-0.751113\pi\) | ||
0.709576 | − | 0.704629i | \(-0.248887\pi\) | |||||||
\(984\) | −12.9573 | − | 22.4428i | −0.413065 | − | 0.715449i | ||||
\(985\) | −41.3433 | + | 71.6087i | −1.31731 | + | 2.28164i | ||||
\(986\) | 11.6161 | + | 6.70658i | 0.369933 | + | 0.213581i | ||||
\(987\) | −6.74490 | −0.214692 | ||||||||
\(988\) | −15.8542 | + | 13.7849i | −0.504391 | + | 0.438555i | ||||
\(989\) | 14.0546 | 0.446911 | ||||||||
\(990\) | −12.3352 | − | 7.12176i | −0.392040 | − | 0.226344i | ||||
\(991\) | 25.3549 | − | 43.9159i | 0.805424 | − | 1.39504i | −0.110581 | − | 0.993867i | \(-0.535271\pi\) |
0.916005 | − | 0.401168i | \(-0.131396\pi\) | |||||||
\(992\) | 33.9247 | + | 58.7594i | 1.07711 | + | 1.86561i | ||||
\(993\) | 9.49586i | 0.301342i | ||||||||
\(994\) | 11.7807 | − | 6.80160i | 0.373662 | − | 0.215734i | ||||
\(995\) | −9.82511 | + | 5.67253i | −0.311477 | + | 0.179831i | ||||
\(996\) | 26.4126i | 0.836916i | ||||||||
\(997\) | 25.1384 | + | 43.5410i | 0.796141 | + | 1.37896i | 0.922112 | + | 0.386923i | \(0.126462\pi\) |
−0.125971 | + | 0.992034i | \(0.540205\pi\) | |||||||
\(998\) | −0.0732891 | + | 0.126940i | −0.00231993 | + | 0.00401823i | ||||
\(999\) | 16.7057 | + | 9.64505i | 0.528546 | + | 0.305156i |
(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 | 91.2.q.a.43.6 | yes | 12 | |
3.2 | odd | 2 | 819.2.ct.a.316.1 | 12 | |||
4.3 | odd | 2 | 1456.2.cc.c.225.5 | 12 | |||
7.2 | even | 3 | 637.2.k.h.459.1 | 12 | |||
7.3 | odd | 6 | 637.2.u.i.30.1 | 12 | |||
7.4 | even | 3 | 637.2.u.h.30.1 | 12 | |||
7.5 | odd | 6 | 637.2.k.g.459.1 | 12 | |||
7.6 | odd | 2 | 637.2.q.h.589.6 | 12 | |||
13.4 | even | 6 | 1183.2.c.i.337.11 | 12 | |||
13.6 | odd | 12 | 1183.2.a.m.1.2 | 6 | |||
13.7 | odd | 12 | 1183.2.a.p.1.5 | 6 | |||
13.9 | even | 3 | 1183.2.c.i.337.2 | 12 | |||
13.10 | even | 6 | inner | 91.2.q.a.36.6 | ✓ | 12 | |
39.23 | odd | 6 | 819.2.ct.a.127.1 | 12 | |||
52.23 | odd | 6 | 1456.2.cc.c.673.5 | 12 | |||
91.6 | even | 12 | 8281.2.a.by.1.2 | 6 | |||
91.10 | odd | 6 | 637.2.k.g.569.6 | 12 | |||
91.20 | even | 12 | 8281.2.a.ch.1.5 | 6 | |||
91.23 | even | 6 | 637.2.u.h.361.1 | 12 | |||
91.62 | odd | 6 | 637.2.q.h.491.6 | 12 | |||
91.75 | odd | 6 | 637.2.u.i.361.1 | 12 | |||
91.88 | even | 6 | 637.2.k.h.569.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.6 | ✓ | 12 | 13.10 | even | 6 | inner | |
91.2.q.a.43.6 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.k.g.459.1 | 12 | 7.5 | odd | 6 | |||
637.2.k.g.569.6 | 12 | 91.10 | odd | 6 | |||
637.2.k.h.459.1 | 12 | 7.2 | even | 3 | |||
637.2.k.h.569.6 | 12 | 91.88 | even | 6 | |||
637.2.q.h.491.6 | 12 | 91.62 | odd | 6 | |||
637.2.q.h.589.6 | 12 | 7.6 | odd | 2 | |||
637.2.u.h.30.1 | 12 | 7.4 | even | 3 | |||
637.2.u.h.361.1 | 12 | 91.23 | even | 6 | |||
637.2.u.i.30.1 | 12 | 7.3 | odd | 6 | |||
637.2.u.i.361.1 | 12 | 91.75 | odd | 6 | |||
819.2.ct.a.127.1 | 12 | 39.23 | odd | 6 | |||
819.2.ct.a.316.1 | 12 | 3.2 | odd | 2 | |||
1183.2.a.m.1.2 | 6 | 13.6 | odd | 12 | |||
1183.2.a.p.1.5 | 6 | 13.7 | odd | 12 | |||
1183.2.c.i.337.2 | 12 | 13.9 | even | 3 | |||
1183.2.c.i.337.11 | 12 | 13.4 | even | 6 | |||
1456.2.cc.c.225.5 | 12 | 4.3 | odd | 2 | |||
1456.2.cc.c.673.5 | 12 | 52.23 | odd | 6 | |||
8281.2.a.by.1.2 | 6 | 91.6 | even | 12 | |||
8281.2.a.ch.1.5 | 6 | 91.20 | even | 12 |