Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(91,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Character | \(\chi\) | \(=\) | 460.91 |
Dual form | 460.2.e.b.91.1 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39466 | + | 0.234385i | −0.986170 | + | 0.165735i | ||||
\(3\) | 1.37989i | 0.796677i | 0.917238 | + | 0.398339i | \(0.130413\pi\) | ||||
−0.917238 | + | 0.398339i | \(0.869587\pi\) | |||||||
\(4\) | 1.89013 | − | 0.653773i | 0.945064 | − | 0.326886i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −0.323424 | − | 1.92446i | −0.132037 | − | 0.785659i | ||||
\(7\) | −2.31854 | −0.876325 | −0.438162 | − | 0.898896i | \(-0.644371\pi\) | ||||
−0.438162 | + | 0.898896i | \(0.644371\pi\) | |||||||
\(8\) | −2.48284 | + | 1.35481i | −0.877817 | + | 0.478996i | ||||
\(9\) | 1.09592 | 0.365306 | ||||||||
\(10\) | −0.234385 | − | 1.39466i | −0.0741191 | − | 0.441029i | ||||
\(11\) | −1.65400 | −0.498701 | −0.249350 | − | 0.968413i | \(-0.580217\pi\) | ||||
−0.249350 | + | 0.968413i | \(0.580217\pi\) | |||||||
\(12\) | 0.902131 | + | 2.60816i | 0.260423 | + | 0.752910i | ||||
\(13\) | −3.48270 | −0.965928 | −0.482964 | − | 0.875640i | \(-0.660440\pi\) | ||||
−0.482964 | + | 0.875640i | \(0.660440\pi\) | |||||||
\(14\) | 3.23356 | − | 0.543431i | 0.864206 | − | 0.145238i | ||||
\(15\) | −1.37989 | −0.356285 | ||||||||
\(16\) | 3.14516 | − | 2.47143i | 0.786291 | − | 0.617857i | ||||
\(17\) | 5.56745i | 1.35031i | 0.737678 | + | 0.675153i | \(0.235922\pi\) | ||||
−0.737678 | + | 0.675153i | \(0.764078\pi\) | |||||||
\(18\) | −1.52843 | + | 0.256867i | −0.360254 | + | 0.0605440i | ||||
\(19\) | −6.63011 | −1.52105 | −0.760526 | − | 0.649307i | \(-0.775059\pi\) | ||||
−0.760526 | + | 0.649307i | \(0.775059\pi\) | |||||||
\(20\) | 0.653773 | + | 1.89013i | 0.146188 | + | 0.422645i | ||||
\(21\) | − | 3.19932i | − | 0.698148i | ||||||
\(22\) | 2.30676 | − | 0.387673i | 0.491804 | − | 0.0826523i | ||||
\(23\) | 0.716404 | − | 4.74202i | 0.149381 | − | 0.988780i | ||||
\(24\) | −1.86948 | − | 3.42604i | −0.381605 | − | 0.699337i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 4.85717 | − | 0.816294i | 0.952570 | − | 0.160088i | ||||
\(27\) | 5.65189i | 1.08771i | ||||||||
\(28\) | −4.38233 | + | 1.51580i | −0.828183 | + | 0.286459i | ||||
\(29\) | 4.94862 | 0.918935 | 0.459468 | − | 0.888194i | \(-0.348040\pi\) | ||||
0.459468 | + | 0.888194i | \(0.348040\pi\) | |||||||
\(30\) | 1.92446 | − | 0.323424i | 0.351357 | − | 0.0590489i | ||||
\(31\) | 3.53020i | 0.634042i | 0.948419 | + | 0.317021i | \(0.102683\pi\) | ||||
−0.948419 | + | 0.317021i | \(0.897317\pi\) | |||||||
\(32\) | −3.80715 | + | 4.18397i | −0.673016 | + | 0.739628i | ||||
\(33\) | − | 2.28233i | − | 0.397303i | ||||||
\(34\) | −1.30493 | − | 7.76468i | −0.223793 | − | 1.33163i | ||||
\(35\) | − | 2.31854i | − | 0.391904i | ||||||
\(36\) | 2.07142 | − | 0.716481i | 0.345237 | − | 0.119413i | ||||
\(37\) | − | 9.38162i | − | 1.54233i | −0.636636 | − | 0.771164i | \(-0.719675\pi\) | ||
0.636636 | − | 0.771164i | \(-0.280325\pi\) | |||||||
\(38\) | 9.24672 | − | 1.55400i | 1.50002 | − | 0.252092i | ||||
\(39\) | − | 4.80573i | − | 0.769533i | ||||||
\(40\) | −1.35481 | − | 2.48284i | −0.214213 | − | 0.392572i | ||||
\(41\) | −6.37131 | −0.995031 | −0.497516 | − | 0.867455i | \(-0.665754\pi\) | ||||
−0.497516 | + | 0.867455i | \(0.665754\pi\) | |||||||
\(42\) | 0.749872 | + | 4.46194i | 0.115708 | + | 0.688493i | ||||
\(43\) | −12.8813 | −1.96438 | −0.982188 | − | 0.187900i | \(-0.939832\pi\) | ||||
−0.982188 | + | 0.187900i | \(0.939832\pi\) | |||||||
\(44\) | −3.12628 | + | 1.08134i | −0.471304 | + | 0.163018i | ||||
\(45\) | 1.09592i | 0.163370i | ||||||||
\(46\) | 0.112322 | + | 6.78140i | 0.0165609 | + | 0.999863i | ||||
\(47\) | 8.60850i | 1.25568i | 0.778343 | + | 0.627840i | \(0.216061\pi\) | ||||
−0.778343 | + | 0.627840i | \(0.783939\pi\) | |||||||
\(48\) | 3.41029 | + | 4.33996i | 0.492232 | + | 0.626420i | ||||
\(49\) | −1.62438 | −0.232055 | ||||||||
\(50\) | 1.39466 | − | 0.234385i | 0.197234 | − | 0.0331470i | ||||
\(51\) | −7.68244 | −1.07576 | ||||||||
\(52\) | −6.58275 | + | 2.27690i | −0.912864 | + | 0.315749i | ||||
\(53\) | − | 2.04707i | − | 0.281187i | −0.990067 | − | 0.140594i | \(-0.955099\pi\) | ||
0.990067 | − | 0.140594i | \(-0.0449011\pi\) | |||||||
\(54\) | −1.32472 | − | 7.88245i | −0.180271 | − | 1.07267i | ||||
\(55\) | − | 1.65400i | − | 0.223026i | ||||||
\(56\) | 5.75656 | − | 3.14117i | 0.769253 | − | 0.419756i | ||||
\(57\) | − | 9.14879i | − | 1.21179i | ||||||
\(58\) | −6.90162 | + | 1.15988i | −0.906227 | + | 0.152300i | ||||
\(59\) | − | 9.50571i | − | 1.23754i | −0.785573 | − | 0.618769i | \(-0.787632\pi\) | ||
0.785573 | − | 0.618769i | \(-0.212368\pi\) | |||||||
\(60\) | −2.60816 | + | 0.902131i | −0.336712 | + | 0.116465i | ||||
\(61\) | 3.86641i | 0.495043i | 0.968882 | + | 0.247521i | \(0.0796161\pi\) | ||||
−0.968882 | + | 0.247521i | \(0.920384\pi\) | |||||||
\(62\) | −0.827425 | − | 4.92341i | −0.105083 | − | 0.625273i | ||||
\(63\) | −2.54093 | −0.320127 | ||||||||
\(64\) | 4.32901 | − | 6.72753i | 0.541126 | − | 0.840942i | ||||
\(65\) | − | 3.48270i | − | 0.431976i | ||||||
\(66\) | 0.534945 | + | 3.18307i | 0.0658472 | + | 0.391809i | ||||
\(67\) | −4.67720 | −0.571411 | −0.285705 | − | 0.958318i | \(-0.592228\pi\) | ||||
−0.285705 | + | 0.958318i | \(0.592228\pi\) | |||||||
\(68\) | 3.63985 | + | 10.5232i | 0.441396 | + | 1.27612i | ||||
\(69\) | 6.54344 | + | 0.988556i | 0.787738 | + | 0.119008i | ||||
\(70\) | 0.543431 | + | 3.23356i | 0.0649524 | + | 0.386484i | ||||
\(71\) | 10.9401i | 1.29835i | 0.760639 | + | 0.649175i | \(0.224886\pi\) | ||||
−0.760639 | + | 0.649175i | \(0.775114\pi\) | |||||||
\(72\) | −2.72099 | + | 1.48475i | −0.320672 | + | 0.174980i | ||||
\(73\) | 6.51430 | 0.762441 | 0.381220 | − | 0.924484i | \(-0.375504\pi\) | ||||
0.381220 | + | 0.924484i | \(0.375504\pi\) | |||||||
\(74\) | 2.19891 | + | 13.0841i | 0.255618 | + | 1.52100i | ||||
\(75\) | − | 1.37989i | − | 0.159335i | ||||||
\(76\) | −12.5318 | + | 4.33459i | −1.43749 | + | 0.497211i | ||||
\(77\) | 3.83487 | 0.437024 | ||||||||
\(78\) | 1.12639 | + | 6.70234i | 0.127539 | + | 0.758891i | ||||
\(79\) | 4.23483 | 0.476456 | 0.238228 | − | 0.971209i | \(-0.423434\pi\) | ||||
0.238228 | + | 0.971209i | \(0.423434\pi\) | |||||||
\(80\) | 2.47143 | + | 3.14516i | 0.276314 | + | 0.351640i | ||||
\(81\) | −4.51121 | −0.501246 | ||||||||
\(82\) | 8.88578 | − | 1.49334i | 0.981270 | − | 0.164912i | ||||
\(83\) | 5.44089 | 0.597215 | 0.298608 | − | 0.954376i | \(-0.403478\pi\) | ||||
0.298608 | + | 0.954376i | \(0.403478\pi\) | |||||||
\(84\) | −2.09163 | − | 6.04711i | −0.228215 | − | 0.659794i | ||||
\(85\) | −5.56745 | −0.603875 | ||||||||
\(86\) | 17.9649 | − | 3.01918i | 1.93721 | − | 0.325566i | ||||
\(87\) | 6.82852i | 0.732095i | ||||||||
\(88\) | 4.10663 | − | 2.24085i | 0.437768 | − | 0.238876i | ||||
\(89\) | 7.48765i | 0.793689i | 0.917886 | + | 0.396845i | \(0.129895\pi\) | ||||
−0.917886 | + | 0.396845i | \(0.870105\pi\) | |||||||
\(90\) | −0.256867 | − | 1.52843i | −0.0270761 | − | 0.161110i | ||||
\(91\) | 8.07478 | 0.846467 | ||||||||
\(92\) | −1.74611 | − | 9.43139i | −0.182044 | − | 0.983290i | ||||
\(93\) | −4.87126 | −0.505127 | ||||||||
\(94\) | −2.01770 | − | 12.0059i | −0.208110 | − | 1.23831i | ||||
\(95\) | − | 6.63011i | − | 0.680235i | ||||||
\(96\) | −5.77340 | − | 5.25343i | −0.589245 | − | 0.536176i | ||||
\(97\) | 19.0123i | 1.93040i | 0.261509 | + | 0.965201i | \(0.415780\pi\) | ||||
−0.261509 | + | 0.965201i | \(0.584220\pi\) | |||||||
\(98\) | 2.26545 | − | 0.380731i | 0.228845 | − | 0.0384596i | ||||
\(99\) | −1.81265 | −0.182178 | ||||||||
\(100\) | −1.89013 | + | 0.653773i | −0.189013 | + | 0.0653773i | ||||
\(101\) | 4.06769 | 0.404750 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(102\) | 10.7144 | − | 1.80065i | 1.06088 | − | 0.178291i | ||||
\(103\) | 15.5279 | 1.53001 | 0.765005 | − | 0.644025i | \(-0.222737\pi\) | ||||
0.765005 | + | 0.644025i | \(0.222737\pi\) | |||||||
\(104\) | 8.64700 | − | 4.71839i | 0.847908 | − | 0.462676i | ||||
\(105\) | 3.19932 | 0.312221 | ||||||||
\(106\) | 0.479803 | + | 2.85496i | 0.0466026 | + | 0.277298i | ||||
\(107\) | 16.9678 | 1.64034 | 0.820168 | − | 0.572123i | \(-0.193880\pi\) | ||||
0.820168 | + | 0.572123i | \(0.193880\pi\) | |||||||
\(108\) | 3.69505 | + | 10.6828i | 0.355557 | + | 1.02795i | ||||
\(109\) | − | 4.30718i | − | 0.412553i | −0.978494 | − | 0.206276i | \(-0.933865\pi\) | ||
0.978494 | − | 0.206276i | \(-0.0661346\pi\) | |||||||
\(110\) | 0.387673 | + | 2.30676i | 0.0369632 | + | 0.219941i | ||||
\(111\) | 12.9456 | 1.22874 | ||||||||
\(112\) | −7.29218 | + | 5.73010i | −0.689046 | + | 0.541443i | ||||
\(113\) | 5.36983i | 0.505151i | 0.967577 | + | 0.252575i | \(0.0812776\pi\) | ||||
−0.967577 | + | 0.252575i | \(0.918722\pi\) | |||||||
\(114\) | 2.14434 | + | 12.7594i | 0.200836 | + | 1.19503i | ||||
\(115\) | 4.74202 | + | 0.716404i | 0.442196 | + | 0.0668050i | ||||
\(116\) | 9.35352 | − | 3.23527i | 0.868452 | − | 0.300387i | ||||
\(117\) | −3.81676 | −0.352859 | ||||||||
\(118\) | 2.22800 | + | 13.2572i | 0.205104 | + | 1.22042i | ||||
\(119\) | − | 12.9083i | − | 1.18331i | ||||||
\(120\) | 3.42604 | − | 1.86948i | 0.312753 | − | 0.170659i | ||||
\(121\) | −8.26427 | −0.751298 | ||||||||
\(122\) | −0.906228 | − | 5.39231i | −0.0820460 | − | 0.488196i | ||||
\(123\) | − | 8.79167i | − | 0.792718i | ||||||
\(124\) | 2.30795 | + | 6.67252i | 0.207260 | + | 0.599210i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.54372 | − | 0.595555i | 0.315699 | − | 0.0530562i | ||||
\(127\) | − | 2.29388i | − | 0.203549i | −0.994808 | − | 0.101774i | \(-0.967548\pi\) | ||
0.994808 | − | 0.101774i | \(-0.0324520\pi\) | |||||||
\(128\) | −4.46064 | + | 10.3972i | −0.394268 | + | 0.918995i | ||||
\(129\) | − | 17.7747i | − | 1.56497i | ||||||
\(130\) | 0.816294 | + | 4.85717i | 0.0715937 | + | 0.426002i | ||||
\(131\) | 13.9868i | 1.22203i | 0.791619 | + | 0.611015i | \(0.209239\pi\) | ||||
−0.791619 | + | 0.611015i | \(0.790761\pi\) | |||||||
\(132\) | −1.49213 | − | 4.31390i | −0.129873 | − | 0.375477i | ||||
\(133\) | 15.3722 | 1.33294 | ||||||||
\(134\) | 6.52308 | − | 1.09627i | 0.563508 | − | 0.0947029i | ||||
\(135\) | −5.65189 | −0.486438 | ||||||||
\(136\) | −7.54281 | − | 13.8231i | −0.646791 | − | 1.18532i | ||||
\(137\) | 12.2230i | 1.04428i | 0.852860 | + | 0.522139i | \(0.174866\pi\) | ||||
−0.852860 | + | 0.522139i | \(0.825134\pi\) | |||||||
\(138\) | −9.35755 | + | 0.154991i | −0.796568 | + | 0.0131937i | ||||
\(139\) | − | 1.61414i | − | 0.136910i | −0.997654 | − | 0.0684549i | \(-0.978193\pi\) | ||
0.997654 | − | 0.0684549i | \(-0.0218069\pi\) | |||||||
\(140\) | −1.51580 | − | 4.38233i | −0.128108 | − | 0.370375i | ||||
\(141\) | −11.8787 | −1.00037 | ||||||||
\(142\) | −2.56419 | − | 15.2577i | −0.215182 | − | 1.28039i | ||||
\(143\) | 5.76040 | 0.481709 | ||||||||
\(144\) | 3.44684 | − | 2.70848i | 0.287236 | − | 0.225707i | ||||
\(145\) | 4.94862i | 0.410960i | ||||||||
\(146\) | −9.08520 | + | 1.52685i | −0.751897 | + | 0.126363i | ||||
\(147\) | − | 2.24146i | − | 0.184873i | ||||||
\(148\) | −6.13344 | − | 17.7325i | −0.504166 | − | 1.45760i | ||||
\(149\) | 4.80668i | 0.393779i | 0.980426 | + | 0.196889i | \(0.0630840\pi\) | ||||
−0.980426 | + | 0.196889i | \(0.936916\pi\) | |||||||
\(150\) | 0.323424 | + | 1.92446i | 0.0264075 | + | 0.157132i | ||||
\(151\) | 9.37662i | 0.763059i | 0.924357 | + | 0.381529i | \(0.124602\pi\) | ||||
−0.924357 | + | 0.381529i | \(0.875398\pi\) | |||||||
\(152\) | 16.4615 | − | 8.98251i | 1.33521 | − | 0.728578i | ||||
\(153\) | 6.10147i | 0.493274i | ||||||||
\(154\) | −5.34832 | + | 0.898836i | −0.430980 | + | 0.0724302i | ||||
\(155\) | −3.53020 | −0.283552 | ||||||||
\(156\) | −3.14186 | − | 9.08344i | −0.251550 | − | 0.727258i | ||||
\(157\) | − | 14.5957i | − | 1.16486i | −0.812879 | − | 0.582432i | \(-0.802101\pi\) | ||
0.812879 | − | 0.582432i | \(-0.197899\pi\) | |||||||
\(158\) | −5.90613 | + | 0.992581i | −0.469866 | + | 0.0789655i | ||||
\(159\) | 2.82472 | 0.224015 | ||||||||
\(160\) | −4.18397 | − | 3.80715i | −0.330772 | − | 0.300982i | ||||
\(161\) | −1.66101 | + | 10.9946i | −0.130906 | + | 0.866492i | ||||
\(162\) | 6.29159 | − | 1.05736i | 0.494314 | − | 0.0830741i | ||||
\(163\) | − | 5.23715i | − | 0.410205i | −0.978740 | − | 0.205103i | \(-0.934247\pi\) | ||
0.978740 | − | 0.205103i | \(-0.0657529\pi\) | |||||||
\(164\) | −12.0426 | + | 4.16539i | −0.940368 | + | 0.325262i | ||||
\(165\) | 2.28233 | 0.177679 | ||||||||
\(166\) | −7.58817 | + | 1.27526i | −0.588956 | + | 0.0989796i | ||||
\(167\) | 2.65734i | 0.205631i | 0.994700 | + | 0.102816i | \(0.0327852\pi\) | ||||
−0.994700 | + | 0.102816i | \(0.967215\pi\) | |||||||
\(168\) | 4.33445 | + | 7.94339i | 0.334410 | + | 0.612846i | ||||
\(169\) | −0.870770 | −0.0669823 | ||||||||
\(170\) | 7.76468 | − | 1.30493i | 0.595524 | − | 0.100083i | ||||
\(171\) | −7.26606 | −0.555649 | ||||||||
\(172\) | −24.3473 | + | 8.42143i | −1.85646 | + | 0.642128i | ||||
\(173\) | −8.91998 | −0.678173 | −0.339087 | − | 0.940755i | \(-0.610118\pi\) | ||||
−0.339087 | + | 0.940755i | \(0.610118\pi\) | |||||||
\(174\) | −1.60050 | − | 9.52344i | −0.121334 | − | 0.721970i | ||||
\(175\) | 2.31854 | 0.175265 | ||||||||
\(176\) | −5.20211 | + | 4.08775i | −0.392124 | + | 0.308126i | ||||
\(177\) | 13.1168 | 0.985918 | ||||||||
\(178\) | −1.75499 | − | 10.4427i | −0.131542 | − | 0.782713i | ||||
\(179\) | 1.37963i | 0.103119i | 0.998670 | + | 0.0515593i | \(0.0164191\pi\) | ||||
−0.998670 | + | 0.0515593i | \(0.983581\pi\) | |||||||
\(180\) | 0.716481 | + | 2.07142i | 0.0534033 | + | 0.154395i | ||||
\(181\) | 20.6166i | 1.53242i | 0.642592 | + | 0.766208i | \(0.277859\pi\) | ||||
−0.642592 | + | 0.766208i | \(0.722141\pi\) | |||||||
\(182\) | −11.2615 | + | 1.89261i | −0.834761 | + | 0.140289i | ||||
\(183\) | −5.33520 | −0.394389 | ||||||||
\(184\) | 4.64580 | + | 12.7443i | 0.342493 | + | 0.939521i | ||||
\(185\) | 9.38162 | 0.689750 | ||||||||
\(186\) | 6.79373 | − | 1.14175i | 0.498141 | − | 0.0837173i | ||||
\(187\) | − | 9.20858i | − | 0.673398i | ||||||
\(188\) | 5.62800 | + | 16.2712i | 0.410464 | + | 1.18670i | ||||
\(189\) | − | 13.1041i | − | 0.953185i | ||||||
\(190\) | 1.55400 | + | 9.24672i | 0.112739 | + | 0.670828i | ||||
\(191\) | 7.65350 | 0.553788 | 0.276894 | − | 0.960901i | \(-0.410695\pi\) | ||||
0.276894 | + | 0.960901i | \(0.410695\pi\) | |||||||
\(192\) | 9.28322 | + | 5.97353i | 0.669959 | + | 0.431102i | ||||
\(193\) | −3.72049 | −0.267807 | −0.133904 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133904 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(194\) | −4.45619 | − | 26.5155i | −0.319936 | − | 1.90371i | ||||
\(195\) | 4.80573 | 0.344146 | ||||||||
\(196\) | −3.07029 | + | 1.06198i | −0.219306 | + | 0.0758555i | ||||
\(197\) | 2.90083 | 0.206675 | 0.103338 | − | 0.994646i | \(-0.467048\pi\) | ||||
0.103338 | + | 0.994646i | \(0.467048\pi\) | |||||||
\(198\) | 2.52802 | − | 0.424858i | 0.179659 | − | 0.0301933i | ||||
\(199\) | 12.0631 | 0.855130 | 0.427565 | − | 0.903985i | \(-0.359372\pi\) | ||||
0.427565 | + | 0.903985i | \(0.359372\pi\) | |||||||
\(200\) | 2.48284 | − | 1.35481i | 0.175563 | − | 0.0957992i | ||||
\(201\) | − | 6.45400i | − | 0.455230i | ||||||
\(202\) | −5.67303 | + | 0.953406i | −0.399153 | + | 0.0670814i | ||||
\(203\) | −11.4736 | −0.805286 | ||||||||
\(204\) | −14.5208 | + | 5.02257i | −1.01666 | + | 0.351650i | ||||
\(205\) | − | 6.37131i | − | 0.444991i | ||||||
\(206\) | −21.6561 | + | 3.63951i | −1.50885 | + | 0.253576i | ||||
\(207\) | 0.785120 | − | 5.19686i | 0.0545696 | − | 0.361207i | ||||
\(208\) | −10.9537 | + | 8.60725i | −0.759500 | + | 0.596805i | ||||
\(209\) | 10.9662 | 0.758550 | ||||||||
\(210\) | −4.46194 | + | 0.749872i | −0.307903 | + | 0.0517461i | ||||
\(211\) | 14.7717i | 1.01692i | 0.861084 | + | 0.508462i | \(0.169786\pi\) | ||||
−0.861084 | + | 0.508462i | \(0.830214\pi\) | |||||||
\(212\) | −1.33832 | − | 3.86923i | −0.0919162 | − | 0.265740i | ||||
\(213\) | −15.0961 | −1.03437 | ||||||||
\(214\) | −23.6642 | + | 3.97699i | −1.61765 | + | 0.271862i | ||||
\(215\) | − | 12.8813i | − | 0.878496i | ||||||
\(216\) | −7.65722 | − | 14.0328i | −0.521008 | − | 0.954808i | ||||
\(217\) | − | 8.18489i | − | 0.555627i | ||||||
\(218\) | 1.00954 | + | 6.00703i | 0.0683746 | + | 0.406847i | ||||
\(219\) | 8.98898i | 0.607419i | ||||||||
\(220\) | −1.08134 | − | 3.12628i | −0.0729040 | − | 0.210773i | ||||
\(221\) | − | 19.3898i | − | 1.30430i | ||||||
\(222\) | −18.0546 | + | 3.03424i | −1.21174 | + | 0.203645i | ||||
\(223\) | − | 23.6624i | − | 1.58455i | −0.610164 | − | 0.792275i | \(-0.708896\pi\) | ||
0.610164 | − | 0.792275i | \(-0.291104\pi\) | |||||||
\(224\) | 8.82703 | − | 9.70069i | 0.589781 | − | 0.648155i | ||||
\(225\) | −1.09592 | −0.0730611 | ||||||||
\(226\) | −1.25861 | − | 7.48906i | −0.0837213 | − | 0.498165i | ||||
\(227\) | −26.1645 | −1.73660 | −0.868298 | − | 0.496042i | \(-0.834786\pi\) | ||||
−0.868298 | + | 0.496042i | \(0.834786\pi\) | |||||||
\(228\) | −5.98123 | − | 17.2924i | −0.396117 | − | 1.14522i | ||||
\(229\) | 19.1863i | 1.26787i | 0.773387 | + | 0.633934i | \(0.218561\pi\) | ||||
−0.773387 | + | 0.633934i | \(0.781439\pi\) | |||||||
\(230\) | −6.78140 | + | 0.112322i | −0.447152 | + | 0.00740627i | ||||
\(231\) | 5.29168i | 0.348167i | ||||||||
\(232\) | −12.2866 | + | 6.70441i | −0.806657 | + | 0.440166i | ||||
\(233\) | 27.4651 | 1.79930 | 0.899651 | − | 0.436611i | \(-0.143821\pi\) | ||||
0.899651 | + | 0.436611i | \(0.143821\pi\) | |||||||
\(234\) | 5.32306 | − | 0.894590i | 0.347979 | − | 0.0584812i | ||||
\(235\) | −8.60850 | −0.561557 | ||||||||
\(236\) | −6.21458 | − | 17.9670i | −0.404534 | − | 1.16955i | ||||
\(237\) | 5.84358i | 0.379581i | ||||||||
\(238\) | 3.02552 | + | 18.0027i | 0.196116 | + | 1.16694i | ||||
\(239\) | − | 0.599617i | − | 0.0387860i | −0.999812 | − | 0.0193930i | \(-0.993827\pi\) | ||
0.999812 | − | 0.0193930i | \(-0.00617337\pi\) | |||||||
\(240\) | −4.33996 | + | 3.41029i | −0.280143 | + | 0.220133i | ||||
\(241\) | − | 14.3108i | − | 0.921840i | −0.887442 | − | 0.460920i | \(-0.847519\pi\) | ||
0.887442 | − | 0.460920i | \(-0.152481\pi\) | |||||||
\(242\) | 11.5258 | − | 1.93702i | 0.740907 | − | 0.124517i | ||||
\(243\) | 10.7307i | 0.688377i | ||||||||
\(244\) | 2.52775 | + | 7.30800i | 0.161823 | + | 0.467847i | ||||
\(245\) | − | 1.62438i | − | 0.103778i | ||||||
\(246\) | 2.06064 | + | 12.2614i | 0.131381 | + | 0.781755i | ||||
\(247\) | 23.0907 | 1.46923 | ||||||||
\(248\) | −4.78273 | − | 8.76492i | −0.303703 | − | 0.556573i | ||||
\(249\) | 7.50780i | 0.475788i | ||||||||
\(250\) | 0.234385 | + | 1.39466i | 0.0148238 | + | 0.0882058i | ||||
\(251\) | 18.5184 | 1.16887 | 0.584437 | − | 0.811439i | \(-0.301315\pi\) | ||||
0.584437 | + | 0.811439i | \(0.301315\pi\) | |||||||
\(252\) | −4.80267 | + | 1.66119i | −0.302540 | + | 0.104645i | ||||
\(253\) | −1.18493 | + | 7.84332i | −0.0744962 | + | 0.493105i | ||||
\(254\) | 0.537650 | + | 3.19917i | 0.0337352 | + | 0.200734i | ||||
\(255\) | − | 7.68244i | − | 0.481093i | ||||||
\(256\) | 3.78410 | − | 15.5461i | 0.236506 | − | 0.971630i | ||||
\(257\) | −20.7306 | −1.29314 | −0.646569 | − | 0.762855i | \(-0.723797\pi\) | ||||
−0.646569 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(258\) | 4.16612 | + | 24.7896i | 0.259371 | + | 1.54333i | ||||
\(259\) | 21.7516i | 1.35158i | ||||||||
\(260\) | −2.27690 | − | 6.58275i | −0.141207 | − | 0.408245i | ||||
\(261\) | 5.42328 | 0.335692 | ||||||||
\(262\) | −3.27829 | − | 19.5067i | −0.202534 | − | 1.20513i | ||||
\(263\) | −8.63352 | −0.532366 | −0.266183 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266183 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(264\) | 3.09212 | + | 5.66667i | 0.190307 | + | 0.348760i | ||||
\(265\) | 2.04707 | 0.125751 | ||||||||
\(266\) | −21.4389 | + | 3.60301i | −1.31450 | + | 0.220914i | ||||
\(267\) | −10.3321 | −0.632314 | ||||||||
\(268\) | −8.84050 | + | 3.05782i | −0.540019 | + | 0.186786i | ||||
\(269\) | −29.2749 | −1.78492 | −0.892461 | − | 0.451125i | \(-0.851023\pi\) | ||||
−0.892461 | + | 0.451125i | \(0.851023\pi\) | |||||||
\(270\) | 7.88245 | − | 1.32472i | 0.479710 | − | 0.0806199i | ||||
\(271\) | 7.04520i | 0.427966i | 0.976837 | + | 0.213983i | \(0.0686437\pi\) | ||||
−0.976837 | + | 0.213983i | \(0.931356\pi\) | |||||||
\(272\) | 13.7596 | + | 17.5105i | 0.834295 | + | 1.06173i | ||||
\(273\) | 11.1423i | 0.674361i | ||||||||
\(274\) | −2.86488 | − | 17.0468i | −0.173074 | − | 1.02984i | ||||
\(275\) | 1.65400 | 0.0997401 | ||||||||
\(276\) | 13.0142 | − | 2.40943i | 0.783365 | − | 0.145031i | ||||
\(277\) | −17.7450 | −1.06619 | −0.533095 | − | 0.846055i | \(-0.678971\pi\) | ||||
−0.533095 | + | 0.846055i | \(0.678971\pi\) | |||||||
\(278\) | 0.378331 | + | 2.25117i | 0.0226908 | + | 0.135016i | ||||
\(279\) | 3.86880i | 0.231619i | ||||||||
\(280\) | 3.14117 | + | 5.75656i | 0.187721 | + | 0.344020i | ||||
\(281\) | − | 12.8863i | − | 0.768735i | −0.923180 | − | 0.384367i | \(-0.874420\pi\) | ||
0.923180 | − | 0.384367i | \(-0.125580\pi\) | |||||||
\(282\) | 16.5668 | − | 2.78420i | 0.986536 | − | 0.165797i | ||||
\(283\) | 4.81508 | 0.286227 | 0.143113 | − | 0.989706i | \(-0.454289\pi\) | ||||
0.143113 | + | 0.989706i | \(0.454289\pi\) | |||||||
\(284\) | 7.15233 | + | 20.6782i | 0.424413 | + | 1.22702i | ||||
\(285\) | 9.14879 | 0.541928 | ||||||||
\(286\) | −8.03378 | + | 1.35015i | −0.475047 | + | 0.0798362i | ||||
\(287\) | 14.7721 | 0.871971 | ||||||||
\(288\) | −4.17232 | + | 4.58528i | −0.245857 | + | 0.270190i | ||||
\(289\) | −13.9965 | −0.823325 | ||||||||
\(290\) | −1.15988 | − | 6.90162i | −0.0681106 | − | 0.405277i | ||||
\(291\) | −26.2347 | −1.53791 | ||||||||
\(292\) | 12.3129 | − | 4.25887i | 0.720555 | − | 0.249232i | ||||
\(293\) | − | 13.6754i | − | 0.798926i | −0.916749 | − | 0.399463i | \(-0.869197\pi\) | ||
0.916749 | − | 0.399463i | \(-0.130803\pi\) | |||||||
\(294\) | 0.525365 | + | 3.12607i | 0.0306399 | + | 0.182316i | ||||
\(295\) | 9.50571 | 0.553444 | ||||||||
\(296\) | 12.7103 | + | 23.2931i | 0.738769 | + | 1.35388i | ||||
\(297\) | − | 9.34825i | − | 0.542440i | ||||||
\(298\) | −1.12661 | − | 6.70367i | −0.0652630 | − | 0.388333i | ||||
\(299\) | −2.49502 | + | 16.5151i | −0.144291 | + | 0.955090i | ||||
\(300\) | −0.902131 | − | 2.60816i | −0.0520846 | − | 0.150582i | ||||
\(301\) | 29.8657 | 1.72143 | ||||||||
\(302\) | −2.19774 | − | 13.0772i | −0.126466 | − | 0.752506i | ||||
\(303\) | 5.61294i | 0.322455i | ||||||||
\(304\) | −20.8528 | + | 16.3858i | −1.19599 | + | 0.939793i | ||||
\(305\) | −3.86641 | −0.221390 | ||||||||
\(306\) | −1.43009 | − | 8.50944i | −0.0817529 | − | 0.486452i | ||||
\(307\) | − | 8.25398i | − | 0.471079i | −0.971865 | − | 0.235540i | \(-0.924314\pi\) | ||
0.971865 | − | 0.235540i | \(-0.0756858\pi\) | |||||||
\(308\) | 7.24839 | − | 2.50713i | 0.413015 | − | 0.142857i | ||||
\(309\) | 21.4267i | 1.21892i | ||||||||
\(310\) | 4.92341 | − | 0.827425i | 0.279631 | − | 0.0469946i | ||||
\(311\) | 1.09686i | 0.0621970i | 0.999516 | + | 0.0310985i | \(0.00990055\pi\) | ||||
−0.999516 | + | 0.0310985i | \(0.990099\pi\) | |||||||
\(312\) | 6.51083 | + | 11.9319i | 0.368603 | + | 0.675509i | ||||
\(313\) | − | 30.9986i | − | 1.75214i | −0.482180 | − | 0.876072i | \(-0.660155\pi\) | ||
0.482180 | − | 0.876072i | \(-0.339845\pi\) | |||||||
\(314\) | 3.42101 | + | 20.3560i | 0.193059 | + | 1.14875i | ||||
\(315\) | − | 2.54093i | − | 0.143165i | ||||||
\(316\) | 8.00437 | − | 2.76862i | 0.450281 | − | 0.155747i | ||||
\(317\) | −8.23636 | −0.462600 | −0.231300 | − | 0.972882i | \(-0.574298\pi\) | ||||
−0.231300 | + | 0.972882i | \(0.574298\pi\) | |||||||
\(318\) | −3.93952 | + | 0.662073i | −0.220917 | + | 0.0371272i | ||||
\(319\) | −8.18503 | −0.458274 | ||||||||
\(320\) | 6.72753 | + | 4.32901i | 0.376081 | + | 0.241999i | ||||
\(321\) | 23.4136i | 1.30682i | ||||||||
\(322\) | −0.260422 | − | 15.7229i | −0.0145128 | − | 0.876205i | ||||
\(323\) | − | 36.9128i | − | 2.05389i | ||||||
\(324\) | −8.52677 | + | 2.94931i | −0.473709 | + | 0.163850i | ||||
\(325\) | 3.48270 | 0.193186 | ||||||||
\(326\) | 1.22751 | + | 7.30402i | 0.0679855 | + | 0.404532i | ||||
\(327\) | 5.94341 | 0.328671 | ||||||||
\(328\) | 15.8190 | − | 8.63188i | 0.873455 | − | 0.476616i | ||||
\(329\) | − | 19.9591i | − | 1.10038i | ||||||
\(330\) | −3.18307 | + | 0.534945i | −0.175222 | + | 0.0294477i | ||||
\(331\) | − | 8.65040i | − | 0.475469i | −0.971330 | − | 0.237734i | \(-0.923595\pi\) | ||
0.971330 | − | 0.237734i | \(-0.0764048\pi\) | |||||||
\(332\) | 10.2840 | − | 3.55711i | 0.564407 | − | 0.195222i | ||||
\(333\) | − | 10.2815i | − | 0.563421i | ||||||
\(334\) | −0.622841 | − | 3.70608i | −0.0340804 | − | 0.202787i | ||||
\(335\) | − | 4.67720i | − | 0.255543i | ||||||
\(336\) | −7.90688 | − | 10.0624i | −0.431355 | − | 0.548947i | ||||
\(337\) | − | 4.60244i | − | 0.250711i | −0.992112 | − | 0.125356i | \(-0.959993\pi\) | ||
0.992112 | − | 0.125356i | \(-0.0400071\pi\) | |||||||
\(338\) | 1.21442 | − | 0.204096i | 0.0660560 | − | 0.0111013i | ||||
\(339\) | −7.40974 | −0.402442 | ||||||||
\(340\) | −10.5232 | + | 3.63985i | −0.570700 | + | 0.197398i | ||||
\(341\) | − | 5.83895i | − | 0.316197i | ||||||
\(342\) | 10.1336 | − | 1.70305i | 0.547965 | − | 0.0920906i | ||||
\(343\) | 19.9960 | 1.07968 | ||||||||
\(344\) | 31.9822 | − | 17.4516i | 1.72436 | − | 0.940928i | ||||
\(345\) | −0.988556 | + | 6.54344i | −0.0532220 | + | 0.352287i | ||||
\(346\) | 12.4403 | − | 2.09071i | 0.668794 | − | 0.112397i | ||||
\(347\) | 27.6570i | 1.48471i | 0.670008 | + | 0.742354i | \(0.266291\pi\) | ||||
−0.670008 | + | 0.742354i | \(0.733709\pi\) | |||||||
\(348\) | 4.46430 | + | 12.9068i | 0.239312 | + | 0.691876i | ||||
\(349\) | 0.443757 | 0.0237538 | 0.0118769 | − | 0.999929i | \(-0.496219\pi\) | ||||
0.0118769 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(350\) | −3.23356 | + | 0.543431i | −0.172841 | + | 0.0290476i | ||||
\(351\) | − | 19.6839i | − | 1.05065i | ||||||
\(352\) | 6.29704 | − | 6.92030i | 0.335633 | − | 0.368853i | ||||
\(353\) | −3.85949 | −0.205420 | −0.102710 | − | 0.994711i | \(-0.532751\pi\) | ||||
−0.102710 | + | 0.994711i | \(0.532751\pi\) | |||||||
\(354\) | −18.2934 | + | 3.07438i | −0.972283 | + | 0.163401i | ||||
\(355\) | −10.9401 | −0.580640 | ||||||||
\(356\) | 4.89522 | + | 14.1526i | 0.259446 | + | 0.750087i | ||||
\(357\) | 17.8120 | 0.942713 | ||||||||
\(358\) | −0.323365 | − | 1.92411i | −0.0170904 | − | 0.101693i | ||||
\(359\) | 16.8300 | 0.888253 | 0.444127 | − | 0.895964i | \(-0.353514\pi\) | ||||
0.444127 | + | 0.895964i | \(0.353514\pi\) | |||||||
\(360\) | −1.48475 | − | 2.72099i | −0.0782534 | − | 0.143409i | ||||
\(361\) | 24.9584 | 1.31360 | ||||||||
\(362\) | −4.83221 | − | 28.7530i | −0.253975 | − | 1.51122i | ||||
\(363\) | − | 11.4037i | − | 0.598542i | ||||||
\(364\) | 15.2624 | − | 5.27907i | 0.799965 | − | 0.276699i | ||||
\(365\) | 6.51430i | 0.340974i | ||||||||
\(366\) | 7.44076 | − | 1.25049i | 0.388935 | − | 0.0653642i | ||||
\(367\) | 2.40164 | 0.125365 | 0.0626824 | − | 0.998034i | \(-0.480034\pi\) | ||||
0.0626824 | + | 0.998034i | \(0.480034\pi\) | |||||||
\(368\) | −9.46635 | − | 16.6850i | −0.493468 | − | 0.869764i | ||||
\(369\) | −6.98243 | −0.363491 | ||||||||
\(370\) | −13.0841 | + | 2.19891i | −0.680211 | + | 0.114316i | ||||
\(371\) | 4.74621i | 0.246411i | ||||||||
\(372\) | −9.20731 | + | 3.18470i | −0.477377 | + | 0.165119i | ||||
\(373\) | 0.740895i | 0.0383621i | 0.999816 | + | 0.0191810i | \(0.00610589\pi\) | ||||
−0.999816 | + | 0.0191810i | \(0.993894\pi\) | |||||||
\(374\) | 2.15835 | + | 12.8428i | 0.111606 | + | 0.664085i | ||||
\(375\) | 1.37989 | 0.0712570 | ||||||||
\(376\) | −11.6628 | − | 21.3736i | −0.601465 | − | 1.10226i | ||||
\(377\) | −17.2346 | −0.887626 | ||||||||
\(378\) | 3.07141 | + | 18.2757i | 0.157976 | + | 0.940003i | ||||
\(379\) | 13.8734 | 0.712631 | 0.356316 | − | 0.934366i | \(-0.384033\pi\) | ||||
0.356316 | + | 0.934366i | \(0.384033\pi\) | |||||||
\(380\) | −4.33459 | − | 12.5318i | −0.222360 | − | 0.642866i | ||||
\(381\) | 3.16529 | 0.162163 | ||||||||
\(382\) | −10.6740 | + | 1.79387i | −0.546129 | + | 0.0917821i | ||||
\(383\) | −11.6143 | −0.593463 | −0.296732 | − | 0.954961i | \(-0.595897\pi\) | ||||
−0.296732 | + | 0.954961i | \(0.595897\pi\) | |||||||
\(384\) | −14.3470 | − | 6.15517i | −0.732142 | − | 0.314105i | ||||
\(385\) | 3.83487i | 0.195443i | ||||||||
\(386\) | 5.18881 | − | 0.872028i | 0.264103 | − | 0.0443851i | ||||
\(387\) | −14.1168 | −0.717598 | ||||||||
\(388\) | 12.4297 | + | 35.9356i | 0.631022 | + | 1.82435i | ||||
\(389\) | 5.88082i | 0.298170i | 0.988824 | + | 0.149085i | \(0.0476327\pi\) | ||||
−0.988824 | + | 0.149085i | \(0.952367\pi\) | |||||||
\(390\) | −6.70234 | + | 1.12639i | −0.339386 | + | 0.0570371i | ||||
\(391\) | 26.4010 | + | 3.98855i | 1.33515 | + | 0.201709i | ||||
\(392\) | 4.03308 | − | 2.20072i | 0.203702 | − | 0.111153i | ||||
\(393\) | −19.3002 | −0.973564 | ||||||||
\(394\) | −4.04566 | + | 0.679911i | −0.203817 | + | 0.0342534i | ||||
\(395\) | 4.23483i | 0.213077i | ||||||||
\(396\) | −3.42614 | + | 1.18506i | −0.172170 | + | 0.0595516i | ||||
\(397\) | 25.6253 | 1.28610 | 0.643049 | − | 0.765825i | \(-0.277669\pi\) | ||||
0.643049 | + | 0.765825i | \(0.277669\pi\) | |||||||
\(398\) | −16.8239 | + | 2.82741i | −0.843303 | + | 0.141725i | ||||
\(399\) | 21.2118i | 1.06192i | ||||||||
\(400\) | −3.14516 | + | 2.47143i | −0.157258 | + | 0.123571i | ||||
\(401\) | 12.3949i | 0.618972i | 0.950904 | + | 0.309486i | \(0.100157\pi\) | ||||
−0.950904 | + | 0.309486i | \(0.899843\pi\) | |||||||
\(402\) | 1.51272 | + | 9.00110i | 0.0754476 | + | 0.448934i | ||||
\(403\) | − | 12.2946i | − | 0.612439i | ||||||
\(404\) | 7.68845 | − | 2.65934i | 0.382515 | − | 0.132307i | ||||
\(405\) | − | 4.51121i | − | 0.224164i | ||||||
\(406\) | 16.0017 | − | 2.68923i | 0.794149 | − | 0.133464i | ||||
\(407\) | 15.5172i | 0.769160i | ||||||||
\(408\) | 19.0743 | − | 10.4082i | 0.944318 | − | 0.515283i | ||||
\(409\) | 3.15508 | 0.156009 | 0.0780043 | − | 0.996953i | \(-0.475145\pi\) | ||||
0.0780043 | + | 0.996953i | \(0.475145\pi\) | |||||||
\(410\) | 1.49334 | + | 8.88578i | 0.0737508 | + | 0.438837i | ||||
\(411\) | −16.8663 | −0.831953 | ||||||||
\(412\) | 29.3497 | − | 10.1517i | 1.44596 | − | 0.500139i | ||||
\(413\) | 22.0394i | 1.08449i | ||||||||
\(414\) | 0.123095 | + | 7.43185i | 0.00604980 | + | 0.365256i | ||||
\(415\) | 5.44089i | 0.267083i | ||||||||
\(416\) | 13.2592 | − | 14.5715i | 0.650085 | − | 0.714428i | ||||
\(417\) | 2.22733 | 0.109073 | ||||||||
\(418\) | −15.2941 | + | 2.57032i | −0.748059 | + | 0.125718i | ||||
\(419\) | 0.845711 | 0.0413157 | 0.0206578 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206578 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(420\) | 6.04711 | − | 2.09163i | 0.295069 | − | 0.102061i | ||||
\(421\) | − | 26.0162i | − | 1.26795i | −0.773354 | − | 0.633975i | \(-0.781422\pi\) | ||
0.773354 | − | 0.633975i | \(-0.218578\pi\) | |||||||
\(422\) | −3.46226 | − | 20.6014i | −0.168540 | − | 1.00286i | ||||
\(423\) | 9.43421i | 0.458707i | ||||||||
\(424\) | 2.77338 | + | 5.08256i | 0.134687 | + | 0.246831i | ||||
\(425\) | − | 5.56745i | − | 0.270061i | ||||||
\(426\) | 21.0538 | − | 3.53829i | 1.02006 | − | 0.171431i | ||||
\(427\) | − | 8.96441i | − | 0.433818i | ||||||
\(428\) | 32.0712 | − | 11.0931i | 1.55022 | − | 0.536204i | ||||
\(429\) | 7.94869i | 0.383767i | ||||||||
\(430\) | 3.01918 | + | 17.9649i | 0.145598 | + | 0.866347i | ||||
\(431\) | −15.1645 | −0.730447 | −0.365224 | − | 0.930920i | \(-0.619007\pi\) | ||||
−0.365224 | + | 0.930920i | \(0.619007\pi\) | |||||||
\(432\) | 13.9682 | + | 17.7761i | 0.672048 | + | 0.855254i | ||||
\(433\) | 4.87293i | 0.234178i | 0.993121 | + | 0.117089i | \(0.0373563\pi\) | ||||
−0.993121 | + | 0.117089i | \(0.962644\pi\) | |||||||
\(434\) | 1.91842 | + | 11.4151i | 0.0920869 | + | 0.547943i | ||||
\(435\) | −6.82852 | −0.327403 | ||||||||
\(436\) | −2.81592 | − | 8.14112i | −0.134858 | − | 0.389889i | ||||
\(437\) | −4.74984 | + | 31.4401i | −0.227216 | + | 1.50399i | ||||
\(438\) | −2.10688 | − | 12.5365i | −0.100671 | − | 0.599019i | ||||
\(439\) | − | 20.7315i | − | 0.989460i | −0.869047 | − | 0.494730i | \(-0.835267\pi\) | ||
0.869047 | − | 0.494730i | \(-0.164733\pi\) | |||||||
\(440\) | 2.24085 | + | 4.10663i | 0.106828 | + | 0.195776i | ||||
\(441\) | −1.78019 | −0.0847709 | ||||||||
\(442\) | 4.54468 | + | 27.0421i | 0.216168 | + | 1.28626i | ||||
\(443\) | − | 19.8054i | − | 0.940984i | −0.882404 | − | 0.470492i | \(-0.844076\pi\) | ||
0.882404 | − | 0.470492i | \(-0.155924\pi\) | |||||||
\(444\) | 24.4687 | − | 8.46345i | 1.16124 | − | 0.401658i | ||||
\(445\) | −7.48765 | −0.354949 | ||||||||
\(446\) | 5.54611 | + | 33.0009i | 0.262616 | + | 1.56264i | ||||
\(447\) | −6.63267 | −0.313715 | ||||||||
\(448\) | −10.0370 | + | 15.5980i | −0.474202 | + | 0.736938i | ||||
\(449\) | 7.22437 | 0.340939 | 0.170470 | − | 0.985363i | \(-0.445472\pi\) | ||||
0.170470 | + | 0.985363i | \(0.445472\pi\) | |||||||
\(450\) | 1.52843 | − | 0.256867i | 0.0720507 | − | 0.0121088i | ||||
\(451\) | 10.5382 | 0.496223 | ||||||||
\(452\) | 3.51065 | + | 10.1497i | 0.165127 | + | 0.477400i | ||||
\(453\) | −12.9387 | −0.607911 | ||||||||
\(454\) | 36.4904 | − | 6.13256i | 1.71258 | − | 0.287815i | ||||
\(455\) | 8.07478i | 0.378552i | ||||||||
\(456\) | 12.3948 | + | 22.7150i | 0.580441 | + | 1.06373i | ||||
\(457\) | 37.5343i | 1.75578i | 0.478861 | + | 0.877891i | \(0.341050\pi\) | ||||
−0.478861 | + | 0.877891i | \(0.658950\pi\) | |||||||
\(458\) | −4.49699 | − | 26.7583i | −0.210131 | − | 1.25033i | ||||
\(459\) | −31.4667 | −1.46874 | ||||||||
\(460\) | 9.43139 | − | 1.74611i | 0.439741 | − | 0.0814127i | ||||
\(461\) | 12.1716 | 0.566889 | 0.283444 | − | 0.958989i | \(-0.408523\pi\) | ||||
0.283444 | + | 0.958989i | \(0.408523\pi\) | |||||||
\(462\) | −1.24029 | − | 7.38007i | −0.0577035 | − | 0.343352i | ||||
\(463\) | − | 2.25366i | − | 0.104736i | −0.998628 | − | 0.0523681i | \(-0.983323\pi\) | ||
0.998628 | − | 0.0523681i | \(-0.0166769\pi\) | |||||||
\(464\) | 15.5642 | − | 12.2302i | 0.722550 | − | 0.567770i | ||||
\(465\) | − | 4.87126i | − | 0.225899i | ||||||
\(466\) | −38.3044 | + | 6.43742i | −1.77442 | + | 0.298208i | ||||
\(467\) | −4.35631 | −0.201586 | −0.100793 | − | 0.994907i | \(-0.532138\pi\) | ||||
−0.100793 | + | 0.994907i | \(0.532138\pi\) | |||||||
\(468\) | −7.21415 | + | 2.49529i | −0.333474 | + | 0.115345i | ||||
\(469\) | 10.8443 | 0.500741 | ||||||||
\(470\) | 12.0059 | − | 2.01770i | 0.553791 | − | 0.0930698i | ||||
\(471\) | 20.1404 | 0.928020 | ||||||||
\(472\) | 12.8784 | + | 23.6012i | 0.592776 | + | 1.08633i | ||||
\(473\) | 21.3057 | 0.979636 | ||||||||
\(474\) | −1.36965 | − | 8.14978i | −0.0629100 | − | 0.374332i | ||||
\(475\) | 6.63011 | 0.304210 | ||||||||
\(476\) | −8.43912 | − | 24.3984i | −0.386807 | − | 1.11830i | ||||
\(477\) | − | 2.24342i | − | 0.102719i | ||||||
\(478\) | 0.140541 | + | 0.836260i | 0.00642821 | + | 0.0382496i | ||||
\(479\) | −36.1090 | −1.64986 | −0.824932 | − | 0.565232i | \(-0.808787\pi\) | ||||
−0.824932 | + | 0.565232i | \(0.808787\pi\) | |||||||
\(480\) | 5.25343 | − | 5.77340i | 0.239785 | − | 0.263518i | ||||
\(481\) | 32.6734i | 1.48978i | ||||||||
\(482\) | 3.35424 | + | 19.9586i | 0.152781 | + | 0.909091i | ||||
\(483\) | −15.1712 | − | 2.29200i | −0.690315 | − | 0.104290i | ||||
\(484\) | −15.6205 | + | 5.40296i | −0.710024 | + | 0.245589i | ||||
\(485\) | −19.0123 | −0.863302 | ||||||||
\(486\) | −2.51512 | − | 14.9657i | −0.114088 | − | 0.678856i | ||||
\(487\) | − | 18.1513i | − | 0.822514i | −0.911519 | − | 0.411257i | \(-0.865090\pi\) | ||
0.911519 | − | 0.411257i | \(-0.134910\pi\) | |||||||
\(488\) | −5.23823 | − | 9.59968i | −0.237123 | − | 0.434557i | ||||
\(489\) | 7.22667 | 0.326801 | ||||||||
\(490\) | 0.380731 | + | 2.26545i | 0.0171997 | + | 0.102343i | ||||
\(491\) | 22.6804i | 1.02355i | 0.859119 | + | 0.511776i | \(0.171012\pi\) | ||||
−0.859119 | + | 0.511776i | \(0.828988\pi\) | |||||||
\(492\) | −5.74776 | − | 16.6174i | −0.259129 | − | 0.749169i | ||||
\(493\) | 27.5512i | 1.24084i | ||||||||
\(494\) | −32.2036 | + | 5.41212i | −1.44891 | + | 0.243503i | ||||
\(495\) | − | 1.81265i | − | 0.0814726i | ||||||
\(496\) | 8.72462 | + | 11.1030i | 0.391747 | + | 0.498541i | ||||
\(497\) | − | 25.3650i | − | 1.13778i | ||||||
\(498\) | −1.75972 | − | 10.4708i | −0.0788548 | − | 0.469208i | ||||
\(499\) | 31.4754i | 1.40903i | 0.709688 | + | 0.704516i | \(0.248836\pi\) | ||||
−0.709688 | + | 0.704516i | \(0.751164\pi\) | |||||||
\(500\) | −0.653773 | − | 1.89013i | −0.0292376 | − | 0.0845291i | ||||
\(501\) | −3.66683 | −0.163822 | ||||||||
\(502\) | −25.8268 | + | 4.34045i | −1.15271 | + | 0.193724i | ||||
\(503\) | 13.7449 | 0.612853 | 0.306426 | − | 0.951894i | \(-0.400867\pi\) | ||||
0.306426 | + | 0.951894i | \(0.400867\pi\) | |||||||
\(504\) | 6.30872 | − | 3.44246i | 0.281013 | − | 0.153339i | ||||
\(505\) | 4.06769i | 0.181010i | ||||||||
\(506\) | −0.185780 | − | 11.2165i | −0.00825894 | − | 0.498632i | ||||
\(507\) | − | 1.20156i | − | 0.0533633i | ||||||
\(508\) | −1.49967 | − | 4.33572i | −0.0665373 | − | 0.192366i | ||||
\(509\) | −14.8818 | −0.659625 | −0.329813 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329813 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(510\) | 1.80065 | + | 10.7144i | 0.0797341 | + | 0.474440i | ||||
\(511\) | −15.1036 | −0.668146 | ||||||||
\(512\) | −1.63374 | + | 22.5684i | −0.0722018 | + | 0.997390i | ||||
\(513\) | − | 37.4727i | − | 1.65446i | ||||||
\(514\) | 28.9120 | − | 4.85894i | 1.27525 | − | 0.214319i | ||||
\(515\) | 15.5279i | 0.684241i | ||||||||
\(516\) | −11.6206 | − | 33.5964i | −0.511568 | − | 1.47900i | ||||
\(517\) | − | 14.2385i | − | 0.626208i | ||||||
\(518\) | −5.09826 | − | 30.3360i | −0.224005 | − | 1.33289i | ||||
\(519\) | − | 12.3085i | − | 0.540285i | ||||||
\(520\) | 4.71839 | + | 8.64700i | 0.206915 | + | 0.379196i | ||||
\(521\) | − | 14.8702i | − | 0.651476i | −0.945460 | − | 0.325738i | \(-0.894387\pi\) | ||
0.945460 | − | 0.325738i | \(-0.105613\pi\) | |||||||
\(522\) | −7.56360 | + | 1.27113i | −0.331050 | + | 0.0556361i | ||||
\(523\) | −2.95573 | −0.129245 | −0.0646226 | − | 0.997910i | \(-0.520584\pi\) | ||||
−0.0646226 | + | 0.997910i | \(0.520584\pi\) | |||||||
\(524\) | 9.14418 | + | 26.4368i | 0.399465 | + | 1.15490i | ||||
\(525\) | 3.19932i | 0.139630i | ||||||||
\(526\) | 12.0408 | − | 2.02357i | 0.525003 | − | 0.0882317i | ||||
\(527\) | −19.6542 | −0.856150 | ||||||||
\(528\) | −5.64062 | − | 7.17831i | −0.245477 | − | 0.312396i | ||||
\(529\) | −21.9735 | − | 6.79441i | −0.955371 | − | 0.295409i | ||||
\(530\) | −2.85496 | + | 0.479803i | −0.124012 | + | 0.0208413i | ||||
\(531\) | − | 10.4175i | − | 0.452080i | ||||||
\(532\) | 29.0554 | − | 10.0499i | 1.25971 | − | 0.435719i | ||||
\(533\) | 22.1894 | 0.961129 | ||||||||
\(534\) | 14.4097 | − | 2.42169i | 0.623569 | − | 0.104797i | ||||
\(535\) | 16.9678i | 0.733581i | ||||||||
\(536\) | 11.6127 | − | 6.33669i | 0.501594 | − | 0.273703i | ||||
\(537\) | −1.90374 | −0.0821523 | ||||||||
\(538\) | 40.8284 | − | 6.86160i | 1.76024 | − | 0.295824i | ||||
\(539\) | 2.68673 | 0.115726 | ||||||||
\(540\) | −10.6828 | + | 3.69505i | −0.459715 | + | 0.159010i | ||||
\(541\) | −24.8102 | −1.06667 | −0.533337 | − | 0.845903i | \(-0.679062\pi\) | ||||
−0.533337 | + | 0.845903i | \(0.679062\pi\) | |||||||
\(542\) | −1.65129 | − | 9.82563i | −0.0709290 | − | 0.422047i | ||||
\(543\) | −28.4485 | −1.22084 | ||||||||
\(544\) | −23.2940 | − | 21.1961i | −0.998724 | − | 0.908777i | ||||
\(545\) | 4.30718 | 0.184499 | ||||||||
\(546\) | −2.61158 | − | 15.5396i | −0.111765 | − | 0.665035i | ||||
\(547\) | − | 14.3225i | − | 0.612386i | −0.951969 | − | 0.306193i | \(-0.900945\pi\) | ||
0.951969 | − | 0.306193i | \(-0.0990553\pi\) | |||||||
\(548\) | 7.99104 | + | 23.1030i | 0.341360 | + | 0.986910i | ||||
\(549\) | 4.23726i | 0.180842i | ||||||||
\(550\) | −2.30676 | + | 0.387673i | −0.0983607 | + | 0.0165305i | ||||
\(551\) | −32.8099 | −1.39775 | ||||||||
\(552\) | −17.5856 | + | 6.41066i | −0.748494 | + | 0.272856i | ||||
\(553\) | −9.81861 | −0.417530 | ||||||||
\(554\) | 24.7481 | − | 4.15915i | 1.05145 | − | 0.176705i | ||||
\(555\) | 12.9456i | 0.549508i | ||||||||
\(556\) | −1.05528 | − | 3.05094i | −0.0447539 | − | 0.129388i | ||||
\(557\) | − | 39.1149i | − | 1.65735i | −0.559730 | − | 0.828675i | \(-0.689095\pi\) | ||
0.559730 | − | 0.828675i | \(-0.310905\pi\) | |||||||
\(558\) | −0.906789 | − | 5.39565i | −0.0383875 | − | 0.228416i | ||||
\(559\) | 44.8617 | 1.89745 | ||||||||
\(560\) | −5.73010 | − | 7.29218i | −0.242141 | − | 0.308151i | ||||
\(561\) | 12.7068 | 0.536481 | ||||||||
\(562\) | 3.02037 | + | 17.9720i | 0.127406 | + | 0.758104i | ||||
\(563\) | −35.3742 | −1.49085 | −0.745423 | − | 0.666592i | \(-0.767753\pi\) | ||||
−0.745423 | + | 0.666592i | \(0.767753\pi\) | |||||||
\(564\) | −22.4523 | + | 7.76600i | −0.945414 | + | 0.327008i | ||||
\(565\) | −5.36983 | −0.225910 | ||||||||
\(566\) | −6.71537 | + | 1.12858i | −0.282268 | + | 0.0474378i | ||||
\(567\) | 10.4594 | 0.439254 | ||||||||
\(568\) | −14.8217 | − | 27.1625i | −0.621905 | − | 1.13971i | ||||
\(569\) | − | 8.98709i | − | 0.376758i | −0.982096 | − | 0.188379i | \(-0.939677\pi\) | ||
0.982096 | − | 0.188379i | \(-0.0603234\pi\) | |||||||
\(570\) | −12.7594 | + | 2.14434i | −0.534433 | + | 0.0898165i | ||||
\(571\) | −16.6329 | −0.696067 | −0.348034 | − | 0.937482i | \(-0.613151\pi\) | ||||
−0.348034 | + | 0.937482i | \(0.613151\pi\) | |||||||
\(572\) | 10.8879 | − | 3.76599i | 0.455246 | − | 0.157464i | ||||
\(573\) | 10.5609i | 0.441190i | ||||||||
\(574\) | −20.6020 | + | 3.46236i | −0.859912 | + | 0.144516i | ||||
\(575\) | −0.716404 | + | 4.74202i | −0.0298761 | + | 0.197756i | ||||
\(576\) | 4.74423 | − | 7.37282i | 0.197676 | − | 0.307201i | ||||
\(577\) | −20.6514 | −0.859729 | −0.429865 | − | 0.902893i | \(-0.641439\pi\) | ||||
−0.429865 | + | 0.902893i | \(0.641439\pi\) | |||||||
\(578\) | 19.5203 | − | 3.28057i | 0.811938 | − | 0.136454i | ||||
\(579\) | − | 5.13385i | − | 0.213356i | ||||||
\(580\) | 3.23527 | + | 9.35352i | 0.134337 | + | 0.388384i | ||||
\(581\) | −12.6149 | −0.523355 | ||||||||
\(582\) | 36.5884 | − | 6.14903i | 1.51664 | − | 0.254885i | ||||
\(583\) | 3.38586i | 0.140228i | ||||||||
\(584\) | −16.1740 | + | 8.82560i | −0.669284 | + | 0.365206i | ||||
\(585\) | − | 3.81676i | − | 0.157803i | ||||||
\(586\) | 3.20531 | + | 19.0725i | 0.132410 | + | 0.787877i | ||||
\(587\) | 40.9822i | 1.69152i | 0.533566 | + | 0.845759i | \(0.320852\pi\) | ||||
−0.533566 | + | 0.845759i | \(0.679148\pi\) | |||||||
\(588\) | −1.46541 | − | 4.23665i | −0.0604323 | − | 0.174716i | ||||
\(589\) | − | 23.4056i | − | 0.964411i | ||||||
\(590\) | −13.2572 | + | 2.22800i | −0.545790 | + | 0.0917252i | ||||
\(591\) | 4.00281i | 0.164654i | ||||||||
\(592\) | −23.1860 | − | 29.5067i | −0.952938 | − | 1.21272i | ||||
\(593\) | 26.5118 | 1.08871 | 0.544354 | − | 0.838855i | \(-0.316775\pi\) | ||||
0.544354 | + | 0.838855i | \(0.316775\pi\) | |||||||
\(594\) | 2.19109 | + | 13.0376i | 0.0899015 | + | 0.534939i | ||||
\(595\) | 12.9083 | 0.529191 | ||||||||
\(596\) | 3.14248 | + | 9.08524i | 0.128721 | + | 0.372146i | ||||
\(597\) | 16.6457i | 0.681262i | ||||||||
\(598\) | −0.391183 | − | 23.6176i | −0.0159967 | − | 0.965796i | ||||
\(599\) | − | 1.77018i | − | 0.0723276i | −0.999346 | − | 0.0361638i | \(-0.988486\pi\) | ||
0.999346 | − | 0.0361638i | \(-0.0115138\pi\) | |||||||
\(600\) | 1.86948 | + | 3.42604i | 0.0763210 | + | 0.139867i | ||||
\(601\) | −46.2673 | −1.88728 | −0.943641 | − | 0.330970i | \(-0.892624\pi\) | ||||
−0.943641 | + | 0.330970i | \(0.892624\pi\) | |||||||
\(602\) | −41.6524 | + | 7.00008i | −1.69763 | + | 0.285302i | ||||
\(603\) | −5.12582 | −0.208740 | ||||||||
\(604\) | 6.13018 | + | 17.7230i | 0.249433 | + | 0.721139i | ||||
\(605\) | − | 8.26427i | − | 0.335991i | ||||||
\(606\) | −1.31559 | − | 7.82812i | −0.0534422 | − | 0.317996i | ||||
\(607\) | − | 39.0068i | − | 1.58324i | −0.611015 | − | 0.791619i | \(-0.709239\pi\) | ||
0.611015 | − | 0.791619i | \(-0.290761\pi\) | |||||||
\(608\) | 25.2419 | − | 27.7402i | 1.02369 | − | 1.12501i | ||||
\(609\) | − | 15.8322i | − | 0.641553i | ||||||
\(610\) | 5.39231 | − | 0.906228i | 0.218328 | − | 0.0366921i | ||||
\(611\) | − | 29.9809i | − | 1.21290i | ||||||
\(612\) | 3.98897 | + | 11.5325i | 0.161245 | + | 0.466176i | ||||
\(613\) | − | 0.0667318i | − | 0.00269527i | −0.999999 | − | 0.00134764i | \(-0.999571\pi\) | ||
0.999999 | − | 0.00134764i | \(-0.000428966\pi\) | |||||||
\(614\) | 1.93461 | + | 11.5115i | 0.0780744 | + | 0.464564i | ||||
\(615\) | 8.79167 | 0.354514 | ||||||||
\(616\) | −9.52137 | + | 5.19550i | −0.383627 | + | 0.209333i | ||||
\(617\) | − | 13.1473i | − | 0.529291i | −0.964346 | − | 0.264645i | \(-0.914745\pi\) | ||
0.964346 | − | 0.264645i | \(-0.0852549\pi\) | |||||||
\(618\) | −5.02210 | − | 29.8829i | −0.202019 | − | 1.20207i | ||||
\(619\) | 19.6605 | 0.790220 | 0.395110 | − | 0.918634i | \(-0.370706\pi\) | ||||
0.395110 | + | 0.918634i | \(0.370706\pi\) | |||||||
\(620\) | −6.67252 | + | 2.30795i | −0.267975 | + | 0.0926893i | ||||
\(621\) | 26.8014 | + | 4.04904i | 1.07550 | + | 0.162482i | ||||
\(622\) | −0.257087 | − | 1.52974i | −0.0103082 | − | 0.0613368i | ||||
\(623\) | − | 17.3604i | − | 0.695530i | ||||||
\(624\) | −11.8770 | − | 15.1148i | −0.475461 | − | 0.605077i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.26561 | + | 43.2324i | 0.290392 | + | 1.72791i | ||||
\(627\) | 15.1321i | 0.604319i | ||||||||
\(628\) | −9.54227 | − | 27.5877i | −0.380778 | − | 1.10087i | ||||
\(629\) | 52.2317 | 2.08261 | ||||||||
\(630\) | 0.595555 | + | 3.54372i | 0.0237275 | + | 0.141185i | ||||
\(631\) | −3.93430 | −0.156622 | −0.0783111 | − | 0.996929i | \(-0.524953\pi\) | ||||
−0.0783111 | + | 0.996929i | \(0.524953\pi\) | |||||||
\(632\) | −10.5144 | + | 5.73737i | −0.418241 | + | 0.228220i | ||||
\(633\) | −20.3832 | −0.810161 | ||||||||
\(634\) | 11.4869 | − | 1.93048i | 0.456203 | − | 0.0766691i | ||||
\(635\) | 2.29388 | 0.0910297 | ||||||||
\(636\) | 5.33909 | − | 1.84673i | 0.211709 | − | 0.0732275i | ||||
\(637\) | 5.65724 | 0.224148 | ||||||||
\(638\) | 11.4153 | − | 1.91845i | 0.451936 | − | 0.0759521i | ||||
\(639\) | 11.9894i | 0.474295i | ||||||||
\(640\) | −10.3972 | − | 4.46064i | −0.410987 | − | 0.176322i | ||||
\(641\) | − | 17.7243i | − | 0.700067i | −0.936737 | − | 0.350033i | \(-0.886170\pi\) | ||
0.936737 | − | 0.350033i | \(-0.113830\pi\) | |||||||
\(642\) | −5.48779 | − | 32.6539i | −0.216586 | − | 1.28875i | ||||
\(643\) | 4.97285 | 0.196110 | 0.0980551 | − | 0.995181i | \(-0.468738\pi\) | ||||
0.0980551 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(644\) | 4.04842 | + | 21.8670i | 0.159530 | + | 0.861682i | ||||
\(645\) | 17.7747 | 0.699877 | ||||||||
\(646\) | 8.65182 | + | 51.4807i | 0.340401 | + | 2.02548i | ||||
\(647\) | 36.1791i | 1.42235i | 0.703016 | + | 0.711174i | \(0.251836\pi\) | ||||
−0.703016 | + | 0.711174i | \(0.748164\pi\) | |||||||
\(648\) | 11.2006 | − | 6.11182i | 0.440002 | − | 0.240095i | ||||
\(649\) | 15.7225i | 0.617161i | ||||||||
\(650\) | −4.85717 | + | 0.816294i | −0.190514 | + | 0.0320177i | ||||
\(651\) | 11.2942 | 0.442655 | ||||||||
\(652\) | −3.42391 | − | 9.89889i | −0.134091 | − | 0.387670i | ||||
\(653\) | −20.9627 | −0.820332 | −0.410166 | − | 0.912011i | \(-0.634529\pi\) | ||||
−0.410166 | + | 0.912011i | \(0.634529\pi\) | |||||||
\(654\) | −8.28901 | + | 1.39305i | −0.324126 | + | 0.0544724i | ||||
\(655\) | −13.9868 | −0.546509 | ||||||||
\(656\) | −20.0388 | + | 15.7462i | −0.782384 | + | 0.614787i | ||||
\(657\) | 7.13913 | 0.278524 | ||||||||
\(658\) | 4.67812 | + | 27.8361i | 0.182372 | + | 1.08517i | ||||
\(659\) | −26.4259 | −1.02941 | −0.514703 | − | 0.857368i | \(-0.672098\pi\) | ||||
−0.514703 | + | 0.857368i | \(0.672098\pi\) | |||||||
\(660\) | 4.31390 | − | 1.49213i | 0.167918 | − | 0.0580810i | ||||
\(661\) | 4.30861i | 0.167586i | 0.996483 | + | 0.0837928i | \(0.0267034\pi\) | ||||
−0.996483 | + | 0.0837928i | \(0.973297\pi\) | |||||||
\(662\) | 2.02752 | + | 12.0643i | 0.0788020 | + | 0.468893i | ||||
\(663\) | 26.7557 | 1.03910 | ||||||||
\(664\) | −13.5089 | + | 7.37135i | −0.524246 | + | 0.286064i | ||||
\(665\) | 15.3722i | 0.596107i | ||||||||
\(666\) | 2.40982 | + | 14.3391i | 0.0933788 | + | 0.555629i | ||||
\(667\) | 3.54521 | − | 23.4665i | 0.137271 | − | 0.908625i | ||||
\(668\) | 1.73730 | + | 5.02271i | 0.0672181 | + | 0.194335i | ||||
\(669\) | 32.6514 | 1.26238 | ||||||||
\(670\) | 1.09627 | + | 6.52308i | 0.0423524 | + | 0.252009i | ||||
\(671\) | − | 6.39505i | − | 0.246878i | ||||||
\(672\) | 13.3858 | + | 12.1803i | 0.516370 | + | 0.469865i | ||||
\(673\) | 41.2693 | 1.59081 | 0.795407 | − | 0.606075i | \(-0.207257\pi\) | ||||
0.795407 | + | 0.606075i | \(0.207257\pi\) | |||||||
\(674\) | 1.07874 | + | 6.41882i | 0.0415517 | + | 0.247244i | ||||
\(675\) | − | 5.65189i | − | 0.217542i | ||||||
\(676\) | −1.64587 | + | 0.569286i | −0.0633026 | + | 0.0218956i | ||||
\(677\) | 37.9054i | 1.45682i | 0.685139 | + | 0.728412i | \(0.259741\pi\) | ||||
−0.685139 | + | 0.728412i | \(0.740259\pi\) | |||||||
\(678\) | 10.3340 | − | 1.73673i | 0.396876 | − | 0.0666988i | ||||
\(679\) | − | 44.0806i | − | 1.69166i | ||||||
\(680\) | 13.8231 | − | 7.54281i | 0.530092 | − | 0.289254i | ||||
\(681\) | − | 36.1040i | − | 1.38351i | ||||||
\(682\) | 1.36856 | + | 8.14333i | 0.0524050 | + | 0.311824i | ||||
\(683\) | − | 30.0463i | − | 1.14969i | −0.818262 | − | 0.574845i | \(-0.805062\pi\) | ||
0.818262 | − | 0.574845i | \(-0.194938\pi\) | |||||||
\(684\) | −13.7338 | + | 4.75035i | −0.525124 | + | 0.181634i | ||||
\(685\) | −12.2230 | −0.467016 | ||||||||
\(686\) | −27.8875 | + | 4.68675i | −1.06475 | + | 0.178941i | ||||
\(687\) | −26.4749 | −1.01008 | ||||||||
\(688\) | −40.5137 | + | 31.8351i | −1.54457 | + | 1.21370i | ||||
\(689\) | 7.12935i | 0.271607i | ||||||||
\(690\) | −0.154991 | − | 9.35755i | −0.00590041 | − | 0.356236i | ||||
\(691\) | 31.4123i | 1.19498i | 0.801876 | + | 0.597491i | \(0.203835\pi\) | ||||
−0.801876 | + | 0.597491i | \(0.796165\pi\) | |||||||
\(692\) | −16.8599 | + | 5.83164i | −0.640917 | + | 0.221686i | ||||
\(693\) | 4.20270 | 0.159647 | ||||||||
\(694\) | −6.48239 | − | 38.5720i | −0.246068 | − | 1.46417i | ||||
\(695\) | 1.61414 | 0.0612279 | ||||||||
\(696\) | −9.25132 | − | 16.9541i | −0.350670 | − | 0.642645i | ||||
\(697\) | − | 35.4720i | − | 1.34360i | ||||||
\(698\) | −0.618888 | + | 0.104010i | −0.0234253 | + | 0.00393684i | ||||
\(699\) | 37.8987i | 1.43346i | ||||||||
\(700\) | 4.38233 | − | 1.51580i | 0.165637 | − | 0.0572917i | ||||
\(701\) | 27.3698i | 1.03374i | 0.856063 | + | 0.516871i | \(0.172903\pi\) | ||||
−0.856063 | + | 0.516871i | \(0.827097\pi\) | |||||||
\(702\) | 4.61361 | + | 27.4522i | 0.174129 | + | 1.03612i | ||||
\(703\) | 62.2012i | 2.34596i | ||||||||
\(704\) | −7.16019 | + | 11.1274i | −0.269860 | + | 0.419378i | ||||
\(705\) | − | 11.8787i | − | 0.447379i | ||||||
\(706\) | 5.38266 | − | 0.904606i | 0.202579 | − | 0.0340453i | ||||
\(707\) | −9.43109 | −0.354693 | ||||||||
\(708\) | 24.7924 | − | 8.57540i | 0.931756 | − | 0.322283i | ||||
\(709\) | − | 46.7346i | − | 1.75515i | −0.479436 | − | 0.877577i | \(-0.659159\pi\) | ||
0.479436 | − | 0.877577i | \(-0.340841\pi\) | |||||||
\(710\) | 15.2577 | − | 2.56419i | 0.572610 | − | 0.0962325i | ||||
\(711\) | 4.64102 | 0.174052 | ||||||||
\(712\) | −10.1443 | − | 18.5906i | −0.380174 | − | 0.696714i | ||||
\(713\) | 16.7403 | + | 2.52905i | 0.626928 | + | 0.0947136i | ||||
\(714\) | −24.8417 | + | 4.17487i | −0.929675 | + | 0.156241i | ||||
\(715\) | 5.76040i | 0.215427i | ||||||||
\(716\) | 0.901967 | + | 2.60768i | 0.0337081 | + | 0.0974537i | ||||
\(717\) | 0.827403 | 0.0308999 | ||||||||
\(718\) | −23.4720 | + | 3.94470i | −0.875969 | + | 0.147215i | ||||
\(719\) | − | 23.8230i | − | 0.888447i | −0.895916 | − | 0.444223i | \(-0.853480\pi\) | ||
0.895916 | − | 0.444223i | \(-0.146520\pi\) | |||||||
\(720\) | 2.70848 | + | 3.44684i | 0.100939 | + | 0.128456i | ||||
\(721\) | −36.0020 | −1.34079 | ||||||||
\(722\) | −34.8084 | + | 5.84988i | −1.29543 | + | 0.217710i | ||||
\(723\) | 19.7473 | 0.734409 | ||||||||
\(724\) | 13.4785 | + | 38.9679i | 0.500926 | + | 1.44823i | ||||
\(725\) | −4.94862 | −0.183787 | ||||||||
\(726\) | 2.67287 | + | 15.9043i | 0.0991994 | + | 0.590264i | ||||
\(727\) | 24.5081 | 0.908956 | 0.454478 | − | 0.890758i | \(-0.349826\pi\) | ||||
0.454478 | + | 0.890758i | \(0.349826\pi\) | |||||||
\(728\) | −20.0484 | + | 10.9398i | −0.743043 | + | 0.405454i | ||||
\(729\) | −28.3408 | −1.04966 | ||||||||
\(730\) | −1.52685 | − | 9.08520i | −0.0565114 | − | 0.336258i | ||||
\(731\) | − | 71.7159i | − | 2.65251i | ||||||
\(732\) | −10.0842 | + | 3.48801i | −0.372723 | + | 0.128920i | ||||
\(733\) | 14.8727i | 0.549337i | 0.961539 | + | 0.274669i | \(0.0885681\pi\) | ||||
−0.961539 | + | 0.274669i | \(0.911432\pi\) | |||||||
\(734\) | −3.34947 | + | 0.562910i | −0.123631 | + | 0.0207774i | ||||
\(735\) | 2.24146 | 0.0826775 | ||||||||
\(736\) | 17.1130 | + | 21.0510i | 0.630794 | + | 0.775951i | ||||
\(737\) | 7.73610 | 0.284963 | ||||||||
\(738\) | 9.73808 | − | 1.63658i | 0.358464 | − | 0.0602432i | ||||
\(739\) | 25.8160i | 0.949658i | 0.880078 | + | 0.474829i | \(0.157490\pi\) | ||||
−0.880078 | + | 0.474829i | \(0.842510\pi\) | |||||||
\(740\) | 17.7325 | − | 6.13344i | 0.651858 | − | 0.225470i | ||||
\(741\) | 31.8625i | 1.17050i | ||||||||
\(742\) | −1.11244 | − | 6.61933i | −0.0408390 | − | 0.243003i | ||||
\(743\) | 26.3405 | 0.966339 | 0.483170 | − | 0.875527i | \(-0.339485\pi\) | ||||
0.483170 | + | 0.875527i | \(0.339485\pi\) | |||||||
\(744\) | 12.0946 | − | 6.59961i | 0.443409 | − | 0.241954i | ||||
\(745\) | −4.80668 | −0.176103 | ||||||||
\(746\) | −0.173655 | − | 1.03329i | −0.00635795 | − | 0.0378316i | ||||
\(747\) | 5.96277 | 0.218166 | ||||||||
\(748\) | −6.02032 | − | 17.4054i | −0.220125 | − | 0.636404i | ||||
\(749\) | −39.3404 | −1.43747 | ||||||||
\(750\) | −1.92446 | + | 0.323424i | −0.0702715 | + | 0.0118098i | ||||
\(751\) | 27.2225 | 0.993364 | 0.496682 | − | 0.867933i | \(-0.334551\pi\) | ||||
0.496682 | + | 0.867933i | \(0.334551\pi\) | |||||||
\(752\) | 21.2753 | + | 27.0751i | 0.775830 | + | 0.987329i | ||||
\(753\) | 25.5533i | 0.931215i | ||||||||
\(754\) | 24.0363 | − | 4.03953i | 0.875350 | − | 0.147111i | ||||
\(755\) | −9.37662 | −0.341250 | ||||||||
\(756\) | −8.56712 | − | 24.7685i | −0.311583 | − | 0.900821i | ||||
\(757\) | 28.6707i | 1.04205i | 0.853540 | + | 0.521027i | \(0.174451\pi\) | ||||
−0.853540 | + | 0.521027i | \(0.825549\pi\) | |||||||
\(758\) | −19.3487 | + | 3.25173i | −0.702776 | + | 0.118108i | ||||
\(759\) | −10.8229 | − | 1.63507i | −0.392845 | − | 0.0593494i | ||||
\(760\) | 8.98251 | + | 16.4615i | 0.325830 | + | 0.597122i | ||||
\(761\) | −23.3091 | −0.844953 | −0.422476 | − | 0.906374i | \(-0.638839\pi\) | ||||
−0.422476 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(762\) | −4.41448 | + | 0.741896i | −0.159920 | + | 0.0268761i | ||||
\(763\) | 9.98636i | 0.361530i | ||||||||
\(764\) | 14.4661 | − | 5.00365i | 0.523365 | − | 0.181026i | ||||
\(765\) | −6.10147 | −0.220599 | ||||||||
\(766\) | 16.1980 | − | 2.72222i | 0.585256 | − | 0.0983578i | ||||
\(767\) | 33.1056i | 1.19537i | ||||||||
\(768\) | 21.4518 | + | 5.22162i | 0.774075 | + | 0.188419i | ||||
\(769\) | 48.0354i | 1.73220i | 0.499871 | + | 0.866100i | \(0.333381\pi\) | ||||
−0.499871 | + | 0.866100i | \(0.666619\pi\) | |||||||
\(770\) | −0.898836 | − | 5.34832i | −0.0323918 | − | 0.192740i | ||||
\(771\) | − | 28.6058i | − | 1.03021i | ||||||
\(772\) | −7.03221 | + | 2.43236i | −0.253095 | + | 0.0875425i | ||||
\(773\) | − | 20.1340i | − | 0.724170i | −0.932145 | − | 0.362085i | \(-0.882065\pi\) | ||
0.932145 | − | 0.362085i | \(-0.117935\pi\) | |||||||
\(774\) | 19.6881 | − | 3.30877i | 0.707674 | − | 0.118931i | ||||
\(775\) | − | 3.53020i | − | 0.126808i | ||||||
\(776\) | −25.7579 | − | 47.2044i | −0.924655 | − | 1.69454i | ||||
\(777\) | −30.0148 | −1.07677 | ||||||||
\(778\) | −1.37838 | − | 8.20172i | −0.0494172 | − | 0.294046i | ||||
\(779\) | 42.2425 | 1.51349 | ||||||||
\(780\) | 9.08344 | − | 3.14186i | 0.325239 | − | 0.112496i | ||||
\(781\) | − | 18.0949i | − | 0.647488i | ||||||
\(782\) | −37.7551 | + | 0.625345i | −1.35012 | + | 0.0223623i | ||||
\(783\) | 27.9691i | 0.999533i | ||||||||
\(784\) | −5.10895 | + | 4.01454i | −0.182462 | + | 0.143377i | ||||
\(785\) | 14.5957 | 0.520943 | ||||||||
\(786\) | 26.9171 | − | 4.52367i | 0.960100 | − | 0.161354i | ||||
\(787\) | 7.68977 | 0.274111 | 0.137055 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137055 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(788\) | 5.48294 | − | 1.89648i | 0.195321 | − | 0.0675594i | ||||
\(789\) | − | 11.9133i | − | 0.424123i | ||||||
\(790\) | −0.992581 | − | 5.90613i | −0.0353144 | − | 0.210131i | ||||
\(791\) | − | 12.4501i | − | 0.442676i | ||||||
\(792\) | 4.50052 | − | 2.45579i | 0.159919 | − | 0.0872626i | ||||
\(793\) | − | 13.4656i | − | 0.478176i | ||||||
\(794\) | −35.7385 | + | 6.00619i | −1.26831 | + | 0.213152i | ||||
\(795\) | 2.82472i | 0.100183i | ||||||||
\(796\) | 22.8008 | − | 7.88652i | 0.808152 | − | 0.279530i | ||||
\(797\) | − | 3.88875i | − | 0.137747i | −0.997625 | − | 0.0688734i | \(-0.978060\pi\) | ||
0.997625 | − | 0.0688734i | \(-0.0219404\pi\) | |||||||
\(798\) | −4.97173 | − | 29.5832i | −0.175997 | − | 1.04723i | ||||
\(799\) | −47.9274 | −1.69555 | ||||||||
\(800\) | 3.80715 | − | 4.18397i | 0.134603 | − | 0.147926i | ||||
\(801\) | 8.20584i | 0.289939i | ||||||||
\(802\) | −2.90518 | − | 17.2866i | −0.102586 | − | 0.610412i | ||||
\(803\) | −10.7747 | −0.380230 | ||||||||
\(804\) | −4.21945 | − | 12.1989i | −0.148808 | − | 0.430221i | ||||
\(805\) | −10.9946 | − | 1.66101i | −0.387507 | − | 0.0585429i | ||||
\(806\) | 2.88168 | + | 17.1468i | 0.101503 | + | 0.603969i | ||||
\(807\) | − | 40.3960i | − | 1.42201i | ||||||
\(808\) | −10.0994 | + | 5.51093i | −0.355297 | + | 0.193874i | ||||
\(809\) | −19.8128 | −0.696581 | −0.348290 | − | 0.937387i | \(-0.613238\pi\) | ||||
−0.348290 | + | 0.937387i | \(0.613238\pi\) | |||||||
\(810\) | 1.05736 | + | 6.29159i | 0.0371519 | + | 0.221064i | ||||
\(811\) | − | 44.4156i | − | 1.55964i | −0.626003 | − | 0.779821i | \(-0.715310\pi\) | ||
0.626003 | − | 0.779821i | \(-0.284690\pi\) | |||||||
\(812\) | −21.6865 | + | 7.50110i | −0.761046 | + | 0.263237i | ||||
\(813\) | −9.72157 | −0.340950 | ||||||||
\(814\) | −3.63700 | − | 21.6412i | −0.127477 | − | 0.758523i | ||||
\(815\) | 5.23715 | 0.183449 | ||||||||
\(816\) | −24.1625 | + | 18.9866i | −0.845858 | + | 0.664664i | ||||
\(817\) | 85.4043 | 2.98792 | ||||||||
\(818\) | −4.40024 | + | 0.739503i | −0.153851 | + | 0.0258561i | ||||
\(819\) | 8.84929 | 0.309219 | ||||||||
\(820\) | −4.16539 | − | 12.0426i | −0.145462 | − | 0.420545i | ||||
\(821\) | 36.9381 | 1.28915 | 0.644575 | − | 0.764541i | \(-0.277034\pi\) | ||||
0.644575 | + | 0.764541i | \(0.277034\pi\) | |||||||
\(822\) | 23.5227 | − | 3.95321i | 0.820447 | − | 0.137884i | ||||
\(823\) | 9.38371i | 0.327096i | 0.986535 | + | 0.163548i | \(0.0522938\pi\) | ||||
−0.986535 | + | 0.163548i | \(0.947706\pi\) | |||||||
\(824\) | −38.5533 | + | 21.0373i | −1.34307 | + | 0.732868i | ||||
\(825\) | 2.28233i | 0.0794607i | ||||||||
\(826\) | −5.16569 | − | 30.7373i | −0.179738 | − | 1.06949i | ||||
\(827\) | 34.4624 | 1.19837 | 0.599187 | − | 0.800609i | \(-0.295491\pi\) | ||||
0.599187 | + | 0.800609i | \(0.295491\pi\) | |||||||
\(828\) | −1.91359 | − | 10.3360i | −0.0665019 | − | 0.359202i | ||||
\(829\) | 18.3378 | 0.636897 | 0.318449 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318449 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(830\) | −1.27526 | − | 7.58817i | −0.0442650 | − | 0.263389i | ||||
\(831\) | − | 24.4860i | − | 0.849410i | ||||||
\(832\) | −15.0766 | + | 23.4300i | −0.522689 | + | 0.812289i | ||||
\(833\) | − | 9.04367i | − | 0.313345i | ||||||
\(834\) | −3.10636 | + | 0.522053i | −0.107564 | + | 0.0180772i | ||||
\(835\) | −2.65734 | −0.0919611 | ||||||||
\(836\) | 20.7276 | − | 7.16942i | 0.716878 | − | 0.247960i | ||||
\(837\) | −19.9523 | −0.689652 | ||||||||
\(838\) | −1.17948 | + | 0.198222i | −0.0407443 | + | 0.00684746i | ||||
\(839\) | −28.6022 | −0.987456 | −0.493728 | − | 0.869616i | \(-0.664366\pi\) | ||||
−0.493728 | + | 0.869616i | \(0.664366\pi\) | |||||||
\(840\) | −7.94339 | + | 4.33445i | −0.274073 | + | 0.149553i | ||||
\(841\) | −4.51118 | −0.155558 | ||||||||
\(842\) | 6.09780 | + | 36.2836i | 0.210144 | + | 1.25041i | ||||
\(843\) | 17.7817 | 0.612433 | ||||||||
\(844\) | 9.65732 | + | 27.9204i | 0.332419 | + | 0.961059i | ||||
\(845\) | − | 0.870770i | − | 0.0299554i | ||||||
\(846\) | −2.21124 | − | 13.1575i | −0.0760239 | − | 0.452363i | ||||
\(847\) | 19.1610 | 0.658381 | ||||||||
\(848\) | −5.05919 | − | 6.43838i | −0.173733 | − | 0.221095i | ||||
\(849\) | 6.64425i | 0.228030i | ||||||||
\(850\) | 1.30493 | + | 7.76468i | 0.0447586 | + | 0.266326i | ||||
\(851\) | −44.4878 | − | 6.72103i | −1.52502 | − | 0.230394i | ||||
\(852\) | −28.5335 | + | 9.86940i | −0.977542 | + | 0.338120i | ||||
\(853\) | −15.5290 | −0.531701 | −0.265851 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265851 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(854\) | 2.10112 | + | 12.5023i | 0.0718990 | + | 0.427819i | ||||
\(855\) | − | 7.26606i | − | 0.248494i | ||||||
\(856\) | −42.1283 | + | 22.9880i | −1.43992 | + | 0.785714i | ||||
\(857\) | 5.90572 | 0.201736 | 0.100868 | − | 0.994900i | \(-0.467838\pi\) | ||||
0.100868 | + | 0.994900i | \(0.467838\pi\) | |||||||
\(858\) | −1.86305 | − | 11.0857i | −0.0636036 | − | 0.378459i | ||||
\(859\) | − | 11.1944i | − | 0.381947i | −0.981595 | − | 0.190973i | \(-0.938836\pi\) | ||
0.981595 | − | 0.190973i | \(-0.0611644\pi\) | |||||||
\(860\) | −8.42143 | − | 24.3473i | −0.287168 | − | 0.830235i | ||||
\(861\) | 20.3838i | 0.694679i | ||||||||
\(862\) | 21.1492 | − | 3.55433i | 0.720345 | − | 0.121061i | ||||
\(863\) | 57.7691i | 1.96648i | 0.182310 | + | 0.983241i | \(0.441643\pi\) | ||||
−0.182310 | + | 0.983241i | \(0.558357\pi\) | |||||||
\(864\) | −23.6473 | − | 21.5176i | −0.804499 | − | 0.732044i | ||||
\(865\) | − | 8.91998i | − | 0.303288i | ||||||
\(866\) | −1.14214 | − | 6.79606i | −0.0388116 | − | 0.230939i | ||||
\(867\) | − | 19.3136i | − | 0.655924i | ||||||
\(868\) | −5.35106 | − | 15.4705i | −0.181627 | − | 0.525103i | ||||
\(869\) | −7.00442 | −0.237609 | ||||||||
\(870\) | 9.52344 | − | 1.60050i | 0.322875 | − | 0.0542622i | ||||
\(871\) | 16.2893 | 0.551942 | ||||||||
\(872\) | 5.83539 | + | 10.6940i | 0.197611 | + | 0.362146i | ||||
\(873\) | 20.8359i | 0.705187i | ||||||||
\(874\) | −0.744705 | − | 44.9615i | −0.0251900 | − | 1.52084i | ||||
\(875\) | 2.31854i | 0.0783809i | ||||||||
\(876\) | 5.87675 | + | 16.9903i | 0.198557 | + | 0.574050i | ||||
\(877\) | 17.2151 | 0.581312 | 0.290656 | − | 0.956828i | \(-0.406127\pi\) | ||||
0.290656 | + | 0.956828i | \(0.406127\pi\) | |||||||
\(878\) | 4.85915 | + | 28.9133i | 0.163988 | + | 0.975776i | ||||
\(879\) | 18.8705 | 0.636486 | ||||||||
\(880\) | −4.08775 | − | 5.20211i | −0.137798 | − | 0.175363i | ||||
\(881\) | 1.23909i | 0.0417461i | 0.999782 | + | 0.0208730i | \(0.00664457\pi\) | ||||
−0.999782 | + | 0.0208730i | \(0.993355\pi\) | |||||||
\(882\) | 2.48275 | − | 0.417250i | 0.0835985 | − | 0.0140495i | ||||
\(883\) | 57.4856i | 1.93454i | 0.253742 | + | 0.967272i | \(0.418339\pi\) | ||||
−0.253742 | + | 0.967272i | \(0.581661\pi\) | |||||||
\(884\) | −12.6765 | − | 36.6492i | −0.426357 | − | 1.23264i | ||||
\(885\) | 13.1168i | 0.440916i | ||||||||
\(886\) | 4.64210 | + | 27.6217i | 0.155954 | + | 0.927971i | ||||
\(887\) | 3.53645i | 0.118742i | 0.998236 | + | 0.0593712i | \(0.0189096\pi\) | ||||
−0.998236 | + | 0.0593712i | \(0.981090\pi\) | |||||||
\(888\) | −32.1418 | + | 17.5387i | −1.07861 | + | 0.588560i | ||||
\(889\) | 5.31844i | 0.178375i | ||||||||
\(890\) | 10.4427 | − | 1.75499i | 0.350040 | − | 0.0588275i | ||||
\(891\) | 7.46156 | 0.249972 | ||||||||
\(892\) | −15.4698 | − | 44.7249i | −0.517968 | − | 1.49750i | ||||
\(893\) | − | 57.0754i | − | 1.90995i | ||||||
\(894\) | 9.25029 | − | 1.55460i | 0.309376 | − | 0.0519936i | ||||
\(895\) | −1.37963 | −0.0461161 | ||||||||
\(896\) | 10.3422 | − | 24.1064i | 0.345507 | − | 0.805338i | ||||
\(897\) | −22.7889 | − | 3.44285i | −0.760899 | − | 0.114953i | ||||
\(898\) | −10.0755 | + | 1.69328i | −0.336224 | + | 0.0565056i | ||||
\(899\) | 17.4696i | 0.582643i | ||||||||
\(900\) | −2.07142 | + | 0.716481i | −0.0690474 | + | 0.0238827i | ||||
\(901\) | 11.3970 | 0.379688 | ||||||||
\(902\) | −14.6971 | + | 2.46999i | −0.489360 | + | 0.0822416i | ||||
\(903\) | 41.2113i | 1.37143i | ||||||||
\(904\) | −7.27507 | − | 13.3324i | −0.241965 | − | 0.443430i | ||||
\(905\) | −20.6166 | −0.685318 | ||||||||
\(906\) | 18.0450 | − | 3.03263i | 0.599504 | − | 0.100752i | ||||
\(907\) | −47.5207 | −1.57790 | −0.788949 | − | 0.614458i | \(-0.789375\pi\) | ||||
−0.788949 | + | 0.614458i | \(0.789375\pi\) | |||||||
\(908\) | −49.4542 | + | 17.1056i | −1.64119 | + | 0.567670i | ||||
\(909\) | 4.45785 | 0.147858 | ||||||||
\(910\) | −1.89261 | − | 11.2615i | −0.0627393 | − | 0.373316i | ||||
\(911\) | 2.29768 | 0.0761255 | 0.0380628 | − | 0.999275i | \(-0.487881\pi\) | ||||
0.0380628 | + | 0.999275i | \(0.487881\pi\) | |||||||
\(912\) | −22.6106 | − | 28.7744i | −0.748711 | − | 0.952817i | ||||
\(913\) | −8.99925 | −0.297832 | ||||||||
\(914\) | −8.79748 | − | 52.3474i | −0.290995 | − | 1.73150i | ||||
\(915\) | − | 5.33520i | − | 0.176376i | ||||||
\(916\) | 12.5435 | + | 36.2646i | 0.414449 | + | 1.19822i | ||||
\(917\) | − | 32.4289i | − | 1.07090i | ||||||
\(918\) | 43.8851 | − | 7.37531i | 1.44843 | − | 0.243422i | ||||
\(919\) | 11.6989 | 0.385910 | 0.192955 | − | 0.981208i | \(-0.438193\pi\) | ||||
0.192955 | + | 0.981208i | \(0.438193\pi\) | |||||||
\(920\) | −12.7443 | + | 4.64580i | −0.420166 | + | 0.153167i | ||||
\(921\) | 11.3895 | 0.375298 | ||||||||
\(922\) | −16.9752 | + | 2.85284i | −0.559049 | + | 0.0939534i | ||||
\(923\) | − | 38.1011i | − | 1.25411i | ||||||
\(924\) | 3.45955 | + | 10.0019i | 0.113811 | + | 0.329040i | ||||
\(925\) | 9.38162i | 0.308466i | ||||||||
\(926\) | 0.528223 | + | 3.14307i | 0.0173585 | + | 0.103288i | ||||
\(927\) | 17.0173 | 0.558921 | ||||||||
\(928\) | −18.8401 | + | 20.7049i | −0.618458 | + | 0.679670i | ||||
\(929\) | 22.6705 | 0.743796 | 0.371898 | − | 0.928274i | \(-0.378707\pi\) | ||||
0.371898 | + | 0.928274i | \(0.378707\pi\) | |||||||
\(930\) | 1.14175 | + | 6.79373i | 0.0374395 | + | 0.222775i | ||||
\(931\) | 10.7698 | 0.352967 | ||||||||
\(932\) | 51.9126 | − | 17.9560i | 1.70045 | − | 0.588167i | ||||
\(933\) | −1.51353 | −0.0495509 | ||||||||
\(934\) | 6.07555 | − | 1.02105i | 0.198798 | − | 0.0334099i | ||||
\(935\) | 9.20858 | 0.301153 | ||||||||
\(936\) | 9.47640 | − | 5.17096i | 0.309746 | − | 0.169018i | ||||
\(937\) | 21.3724i | 0.698206i | 0.937084 | + | 0.349103i | \(0.113514\pi\) | ||||
−0.937084 | + | 0.349103i | \(0.886486\pi\) | |||||||
\(938\) | −15.1240 | + | 2.54173i | −0.493816 | + | 0.0829905i | ||||
\(939\) | 42.7745 | 1.39589 | ||||||||
\(940\) | −16.2712 | + | 5.62800i | −0.530707 | + | 0.183565i | ||||
\(941\) | − | 19.2671i | − | 0.628091i | −0.949408 | − | 0.314045i | \(-0.898316\pi\) | ||
0.949408 | − | 0.314045i | \(-0.101684\pi\) | |||||||
\(942\) | −28.0889 | + | 4.72061i | −0.915186 | + | 0.153806i | ||||
\(943\) | −4.56443 | + | 30.2129i | −0.148638 | + | 0.983867i | ||||
\(944\) | −23.4927 | − | 29.8970i | −0.764622 | − | 0.973065i | ||||
\(945\) | 13.1041 | 0.426277 | ||||||||
\(946\) | −29.7141 | + | 4.99373i | −0.966088 | + | 0.162360i | ||||
\(947\) | 1.73836i | 0.0564891i | 0.999601 | + | 0.0282446i | \(0.00899172\pi\) | ||||
−0.999601 | + | 0.0282446i | \(0.991008\pi\) | |||||||
\(948\) | 3.82037 | + | 11.0451i | 0.124080 | + | 0.358728i | ||||
\(949\) | −22.6874 | −0.736463 | ||||||||
\(950\) | −9.24672 | + | 1.55400i | −0.300003 | + | 0.0504184i | ||||
\(951\) | − | 11.3652i | − | 0.368543i | ||||||
\(952\) | 17.4883 | + | 32.0494i | 0.566799 | + | 1.03873i | ||||
\(953\) | 49.8435i | 1.61459i | 0.590149 | + | 0.807295i | \(0.299069\pi\) | ||||
−0.590149 | + | 0.807295i | \(0.700931\pi\) | |||||||
\(954\) | 0.525824 | + | 3.12880i | 0.0170242 | + | 0.101299i | ||||
\(955\) | 7.65350i | 0.247661i | ||||||||
\(956\) | −0.392013 | − | 1.13335i | −0.0126786 | − | 0.0366553i | ||||
\(957\) | − | 11.2944i | − | 0.365096i | ||||||
\(958\) | 50.3597 | − | 8.46342i | 1.62705 | − | 0.273441i | ||||
\(959\) | − | 28.3394i | − | 0.915127i | ||||||
\(960\) | −5.97353 | + | 9.28322i | −0.192795 | + | 0.299615i | ||||
\(961\) | 18.5377 | 0.597991 | ||||||||
\(962\) | −7.65816 | − | 45.5681i | −0.246909 | − | 1.46918i | ||||
\(963\) | 18.5953 | 0.599224 | ||||||||
\(964\) | −9.35602 | − | 27.0493i | −0.301337 | − | 0.871198i | ||||
\(965\) | − | 3.72049i | − | 0.119767i | ||||||
\(966\) | 21.6958 | − | 0.359352i | 0.698052 | − | 0.0115620i | ||||
\(967\) | − | 48.8626i | − | 1.57131i | −0.618662 | − | 0.785657i | \(-0.712325\pi\) | ||
0.618662 | − | 0.785657i | \(-0.287675\pi\) | |||||||
\(968\) | 20.5189 | − | 11.1965i | 0.659502 | − | 0.359869i | ||||
\(969\) | 50.9355 | 1.63628 | ||||||||
\(970\) | 26.5155 | − | 4.45619i | 0.851363 | − | 0.143080i | ||||
\(971\) | 48.9550 | 1.57104 | 0.785520 | − | 0.618837i | \(-0.212396\pi\) | ||||
0.785520 | + | 0.618837i | \(0.212396\pi\) | |||||||
\(972\) | 7.01546 | + | 20.2824i | 0.225021 | + | 0.650560i | ||||
\(973\) | 3.74245i | 0.119977i | ||||||||
\(974\) | 4.25439 | + | 25.3148i | 0.136320 | + | 0.811139i | ||||
\(975\) | 4.80573i | 0.153907i | ||||||||
\(976\) | 9.55555 | + | 12.1605i | 0.305866 | + | 0.389248i | ||||
\(977\) | 28.3251i | 0.906201i | 0.891459 | + | 0.453100i | \(0.149682\pi\) | ||||
−0.891459 | + | 0.453100i | \(0.850318\pi\) | |||||||
\(978\) | −10.0787 | + | 1.69382i | −0.322282 | + | 0.0541625i | ||||
\(979\) | − | 12.3846i | − | 0.395813i | ||||||
\(980\) | −1.06198 | − | 3.07029i | −0.0339236 | − | 0.0980768i | ||||
\(981\) | − | 4.72031i | − | 0.150708i | ||||||
\(982\) | −5.31594 | − | 31.6313i | −0.169639 | − | 1.00940i | ||||
\(983\) | 11.9527 | 0.381233 | 0.190617 | − | 0.981665i | \(-0.438951\pi\) | ||||
0.190617 | + | 0.981665i | \(0.438951\pi\) | |||||||
\(984\) | 11.9110 | + | 21.8283i | 0.379709 | + | 0.695862i | ||||
\(985\) | 2.90083i | 0.0924281i | ||||||||
\(986\) | −6.45759 | − | 38.4244i | −0.205651 | − | 1.22368i | ||||
\(987\) | 27.5413 | 0.876650 | ||||||||
\(988\) | 43.6444 | − | 15.0961i | 1.38851 | − | 0.480270i | ||||
\(989\) | −9.22820 | + | 61.0833i | −0.293440 | + | 1.94234i | ||||
\(990\) | 0.424858 | + | 2.52802i | 0.0135029 | + | 0.0803458i | ||||
\(991\) | 42.6367i | 1.35440i | 0.735800 | + | 0.677199i | \(0.236806\pi\) | ||||
−0.735800 | + | 0.677199i | \(0.763194\pi\) | |||||||
\(992\) | −14.7702 | − | 13.4400i | −0.468955 | − | 0.426720i | ||||
\(993\) | 11.9366 | 0.378795 | ||||||||
\(994\) | 5.94518 | + | 35.3755i | 0.188570 | + | 1.12204i | ||||
\(995\) | 12.0631i | 0.382426i | ||||||||
\(996\) | 4.90840 | + | 14.1907i | 0.155529 | + | 0.449650i | ||||
\(997\) | −4.21192 | −0.133393 | −0.0666964 | − | 0.997773i | \(-0.521246\pi\) | ||||
−0.0666964 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(998\) | −7.37736 | − | 43.8973i | −0.233526 | − | 1.38955i | ||||
\(999\) | 53.0239 | 1.67760 |
(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 | 460.2.e.b.91.4 | yes | 32 | |
4.3 | odd | 2 | inner | 460.2.e.b.91.2 | yes | 32 | |
23.22 | odd | 2 | inner | 460.2.e.b.91.3 | yes | 32 | |
92.91 | even | 2 | inner | 460.2.e.b.91.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.e.b.91.1 | ✓ | 32 | 92.91 | even | 2 | inner | |
460.2.e.b.91.2 | yes | 32 | 4.3 | odd | 2 | inner | |
460.2.e.b.91.3 | yes | 32 | 23.22 | odd | 2 | inner | |
460.2.e.b.91.4 | yes | 32 | 1.1 | even | 1 | trivial |