Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [357,2,Mod(16,357)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(357, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("357.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 357 = 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 357.p (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: | \(2.85065935216\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 16.16 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.16 |
$q$-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 \(\left(\mathbb{Z}/357\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(190\) | \(239\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.262370 | − | 0.454438i | 0.185523 | − | 0.321336i | −0.758229 | − | 0.651988i | \(-0.773935\pi\) |
0.943753 | + | 0.330652i | \(0.107269\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.862324 | + | 1.49359i | 0.431162 | + | 0.746795i | ||||
\(5\) | −3.41917 | − | 1.97406i | −1.52910 | − | 0.882826i | −0.999400 | − | 0.0346402i | \(-0.988971\pi\) |
−0.529699 | − | 0.848186i | \(-0.677695\pi\) | |||||||
\(6\) | − | 0.524739i | − | 0.214224i | ||||||
\(7\) | 2.63978 | − | 0.177717i | 0.997741 | − | 0.0671707i | ||||
\(8\) | 1.95447 | 0.691009 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.79417 | + | 1.03587i | −0.567367 | + | 0.327570i | ||||
\(11\) | 2.72471 | − | 1.57311i | 0.821530 | − | 0.474311i | −0.0294136 | − | 0.999567i | \(-0.509364\pi\) |
0.850944 | + | 0.525257i | \(0.176031\pi\) | |||||||
\(12\) | 1.49359 | + | 0.862324i | 0.431162 | + | 0.248932i | ||||
\(13\) | 0.881206 | 0.244402 | 0.122201 | − | 0.992505i | \(-0.461005\pi\) | ||||
0.122201 | + | 0.992505i | \(0.461005\pi\) | |||||||
\(14\) | 0.611836 | − | 1.24624i | 0.163520 | − | 0.333072i | ||||
\(15\) | −3.94812 | −1.01940 | ||||||||
\(16\) | −1.21186 | + | 2.09899i | −0.302964 | + | 0.524749i | ||||
\(17\) | 1.84188 | − | 3.68883i | 0.446721 | − | 0.894673i | ||||
\(18\) | −0.262370 | − | 0.454438i | −0.0618411 | − | 0.107112i | ||||
\(19\) | 1.76691 | − | 3.06038i | 0.405357 | − | 0.702099i | −0.589006 | − | 0.808129i | \(-0.700481\pi\) |
0.994363 | + | 0.106030i | \(0.0338138\pi\) | |||||||
\(20\) | − | 6.80911i | − | 1.52256i | ||||||
\(21\) | 2.19725 | − | 1.47380i | 0.479480 | − | 0.321608i | ||||
\(22\) | − | 1.65095i | − | 0.351983i | ||||||
\(23\) | −2.87027 | − | 1.65715i | −0.598492 | − | 0.345540i | 0.169956 | − | 0.985452i | \(-0.445638\pi\) |
−0.768448 | + | 0.639912i | \(0.778971\pi\) | |||||||
\(24\) | 1.69262 | − | 0.977235i | 0.345505 | − | 0.199477i | ||||
\(25\) | 5.29381 | + | 9.16915i | 1.05876 | + | 1.83383i | ||||
\(26\) | 0.231202 | − | 0.400453i | 0.0453424 | − | 0.0785353i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.54178 | + | 3.78949i | 0.480351 | + | 0.716147i | ||||
\(29\) | 8.73480i | 1.62201i | 0.585038 | + | 0.811006i | \(0.301080\pi\) | ||||
−0.585038 | + | 0.811006i | \(0.698920\pi\) | |||||||
\(30\) | −1.03587 | + | 1.79417i | −0.189122 | + | 0.327570i | ||||
\(31\) | −3.05508 | + | 1.76385i | −0.548708 | + | 0.316797i | −0.748601 | − | 0.663021i | \(-0.769274\pi\) |
0.199893 | + | 0.979818i | \(0.435941\pi\) | |||||||
\(32\) | 2.59038 | + | 4.48667i | 0.457918 | + | 0.793138i | ||||
\(33\) | 1.57311 | − | 2.72471i | 0.273843 | − | 0.474311i | ||||
\(34\) | −1.19309 | − | 1.80486i | −0.204613 | − | 0.309530i | ||||
\(35\) | −9.37666 | − | 4.60343i | −1.58495 | − | 0.778121i | ||||
\(36\) | 1.72465 | 0.287441 | ||||||||
\(37\) | −10.3688 | − | 5.98645i | −1.70463 | − | 0.984167i | −0.940935 | − | 0.338586i | \(-0.890051\pi\) |
−0.763692 | − | 0.645581i | \(-0.776615\pi\) | |||||||
\(38\) | −0.927167 | − | 1.60590i | −0.150406 | − | 0.260512i | ||||
\(39\) | 0.763146 | − | 0.440603i | 0.122201 | − | 0.0705529i | ||||
\(40\) | −6.68266 | − | 3.85824i | −1.05662 | − | 0.610041i | ||||
\(41\) | 6.52657i | 1.01928i | 0.860388 | + | 0.509640i | \(0.170221\pi\) | ||||
−0.860388 | + | 0.509640i | \(0.829779\pi\) | |||||||
\(42\) | −0.0932550 | − | 1.38519i | −0.0143896 | − | 0.213740i | ||||
\(43\) | 3.56197 | 0.543195 | 0.271598 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271598 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(44\) | 4.69916 | + | 2.71306i | 0.708426 | + | 0.409010i | ||||
\(45\) | −3.41917 | + | 1.97406i | −0.509700 | + | 0.294275i | ||||
\(46\) | −1.50614 | + | 0.869572i | −0.222069 | + | 0.128211i | ||||
\(47\) | −4.34796 | + | 7.53089i | −0.634215 | + | 1.09849i | 0.352466 | + | 0.935825i | \(0.385343\pi\) |
−0.986681 | + | 0.162668i | \(0.947990\pi\) | |||||||
\(48\) | 2.42371i | 0.349832i | ||||||||
\(49\) | 6.93683 | − | 0.938266i | 0.990976 | − | 0.134038i | ||||
\(50\) | 5.55574 | 0.785701 | ||||||||
\(51\) | −0.249302 | − | 4.11556i | −0.0349093 | − | 0.576294i | ||||
\(52\) | 0.759885 | + | 1.31616i | 0.105377 | + | 0.182518i | ||||
\(53\) | 2.38577 | + | 4.13228i | 0.327711 | + | 0.567612i | 0.982057 | − | 0.188583i | \(-0.0603894\pi\) |
−0.654346 | + | 0.756195i | \(0.727056\pi\) | |||||||
\(54\) | −0.454438 | − | 0.262370i | −0.0618411 | − | 0.0357040i | ||||
\(55\) | −12.4216 | −1.67493 | ||||||||
\(56\) | 5.15936 | − | 0.347342i | 0.689449 | − | 0.0464156i | ||||
\(57\) | − | 3.53382i | − | 0.468066i | ||||||
\(58\) | 3.96942 | + | 2.29175i | 0.521211 | + | 0.300921i | ||||
\(59\) | −6.39036 | − | 11.0684i | −0.831953 | − | 1.44099i | −0.896487 | − | 0.443070i | \(-0.853889\pi\) |
0.0645336 | − | 0.997916i | \(-0.479444\pi\) | |||||||
\(60\) | −3.40456 | − | 5.89687i | −0.439526 | − | 0.761282i | ||||
\(61\) | 6.80373 | + | 3.92813i | 0.871128 | + | 0.502946i | 0.867723 | − | 0.497048i | \(-0.165583\pi\) |
0.00340495 | + | 0.999994i | \(0.498916\pi\) | |||||||
\(62\) | 1.85112i | 0.235093i | ||||||||
\(63\) | 1.16598 | − | 2.37497i | 0.146900 | − | 0.299218i | ||||
\(64\) | −2.12888 | −0.266109 | ||||||||
\(65\) | −3.01299 | − | 1.73955i | −0.373716 | − | 0.215765i | ||||
\(66\) | −0.825473 | − | 1.42976i | −0.101609 | − | 0.175991i | ||||
\(67\) | −1.65233 | − | 2.86192i | −0.201865 | − | 0.349640i | 0.747265 | − | 0.664527i | \(-0.231367\pi\) |
−0.949129 | + | 0.314887i | \(0.898033\pi\) | |||||||
\(68\) | 7.09790 | − | 0.429959i | 0.860747 | − | 0.0521402i | ||||
\(69\) | −3.31430 | −0.398995 | ||||||||
\(70\) | −4.55212 | + | 3.05331i | −0.544083 | + | 0.364940i | ||||
\(71\) | 4.10813i | 0.487545i | 0.969832 | + | 0.243772i | \(0.0783850\pi\) | ||||
−0.969832 | + | 0.243772i | \(0.921615\pi\) | |||||||
\(72\) | 0.977235 | − | 1.69262i | 0.115168 | − | 0.199477i | ||||
\(73\) | −9.52688 | + | 5.50035i | −1.11504 | + | 0.643767i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) |
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(74\) | −5.44094 | + | 3.14133i | −0.632496 | + | 0.365172i | ||||
\(75\) | 9.16915 | + | 5.29381i | 1.05876 | + | 0.611277i | ||||
\(76\) | 6.09460 | 0.699099 | ||||||||
\(77\) | 6.91305 | − | 4.63689i | 0.787815 | − | 0.528422i | ||||
\(78\) | − | 0.462403i | − | 0.0523569i | ||||||
\(79\) | 3.03542 | + | 1.75250i | 0.341512 | + | 0.197172i | 0.660940 | − | 0.750439i | \(-0.270158\pi\) |
−0.319429 | + | 0.947610i | \(0.603491\pi\) | |||||||
\(80\) | 8.28708 | − | 4.78455i | 0.926523 | − | 0.534929i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.96592 | + | 1.71237i | 0.327531 | + | 0.189100i | ||||
\(83\) | −10.1912 | −1.11863 | −0.559314 | − | 0.828956i | \(-0.688935\pi\) | ||||
−0.559314 | + | 0.828956i | \(0.688935\pi\) | |||||||
\(84\) | 4.09599 | + | 2.01091i | 0.446909 | + | 0.219408i | ||||
\(85\) | −13.5797 | + | 8.97677i | −1.47292 | + | 0.973667i | ||||
\(86\) | 0.934553 | − | 1.61869i | 0.100775 | − | 0.174548i | ||||
\(87\) | 4.36740 | + | 7.56456i | 0.468234 | + | 0.811006i | ||||
\(88\) | 5.32536 | − | 3.07460i | 0.567685 | − | 0.327753i | ||||
\(89\) | 0.556702 | − | 0.964235i | 0.0590103 | − | 0.102209i | −0.835011 | − | 0.550233i | \(-0.814539\pi\) |
0.894021 | + | 0.448024i | \(0.147872\pi\) | |||||||
\(90\) | 2.07173i | 0.218380i | ||||||||
\(91\) | 2.32619 | − | 0.156605i | 0.243850 | − | 0.0164167i | ||||
\(92\) | − | 5.71601i | − | 0.595935i | ||||||
\(93\) | −1.76385 | + | 3.05508i | −0.182903 | + | 0.316797i | ||||
\(94\) | 2.28155 | + | 3.95175i | 0.235323 | + | 0.407592i | ||||
\(95\) | −12.0827 | + | 6.97597i | −1.23966 | + | 0.715719i | ||||
\(96\) | 4.48667 | + | 2.59038i | 0.457918 | + | 0.264379i | ||||
\(97\) | 4.98168i | 0.505813i | 0.967491 | + | 0.252907i | \(0.0813866\pi\) | ||||
−0.967491 | + | 0.252907i | \(0.918613\pi\) | |||||||
\(98\) | 1.39363 | − | 3.39853i | 0.140778 | − | 0.343303i | ||||
\(99\) | − | 3.14622i | − | 0.316207i | ||||||
\(100\) | −9.12997 | + | 15.8136i | −0.912997 | + | 1.58136i | ||||
\(101\) | 5.22082 | + | 9.04272i | 0.519491 | + | 0.899784i | 0.999743 | + | 0.0226541i | \(0.00721164\pi\) |
−0.480253 | + | 0.877130i | \(0.659455\pi\) | |||||||
\(102\) | −1.93568 | − | 0.966506i | −0.191660 | − | 0.0956984i | ||||
\(103\) | 1.96640 | − | 3.40591i | 0.193756 | − | 0.335595i | −0.752736 | − | 0.658322i | \(-0.771266\pi\) |
0.946492 | + | 0.322728i | \(0.104600\pi\) | |||||||
\(104\) | 1.72229 | 0.168884 | ||||||||
\(105\) | −10.4221 | + | 0.701647i | −1.01710 | + | 0.0684737i | ||||
\(106\) | 2.50382 | 0.243192 | ||||||||
\(107\) | 1.66112 | + | 0.959050i | 0.160587 | + | 0.0927148i | 0.578140 | − | 0.815938i | \(-0.303779\pi\) |
−0.417553 | + | 0.908653i | \(0.637112\pi\) | |||||||
\(108\) | 1.49359 | − | 0.862324i | 0.143721 | − | 0.0829772i | ||||
\(109\) | −8.20123 | + | 4.73498i | −0.785535 | + | 0.453529i | −0.838388 | − | 0.545073i | \(-0.816502\pi\) |
0.0528532 | + | 0.998602i | \(0.483168\pi\) | |||||||
\(110\) | −3.25906 | + | 5.64486i | −0.310740 | + | 0.538217i | ||||
\(111\) | −11.9729 | −1.13642 | ||||||||
\(112\) | −2.82600 | + | 5.75624i | −0.267032 | + | 0.543914i | ||||
\(113\) | − | 6.18373i | − | 0.581717i | −0.956766 | − | 0.290858i | \(-0.906059\pi\) | ||
0.956766 | − | 0.290858i | \(-0.0939409\pi\) | |||||||
\(114\) | −1.60590 | − | 0.927167i | −0.150406 | − | 0.0868372i | ||||
\(115\) | 6.54262 | + | 11.3322i | 0.610103 | + | 1.05673i | ||||
\(116\) | −13.0462 | + | 7.53223i | −1.21131 | + | 0.699350i | ||||
\(117\) | 0.440603 | − | 0.763146i | 0.0407337 | − | 0.0705529i | ||||
\(118\) | −6.70654 | −0.617387 | ||||||||
\(119\) | 4.20658 | − | 10.0650i | 0.385616 | − | 0.922659i | ||||
\(120\) | −7.71647 | −0.704414 | ||||||||
\(121\) | −0.550645 | + | 0.953746i | −0.0500587 | + | 0.0867042i | ||||
\(122\) | 3.57018 | − | 2.06125i | 0.323229 | − | 0.186616i | ||||
\(123\) | 3.26329 | + | 5.65218i | 0.294241 | + | 0.509640i | ||||
\(124\) | −5.26894 | − | 3.04202i | −0.473164 | − | 0.273182i | ||||
\(125\) | − | 22.0606i | − | 1.97316i | ||||||
\(126\) | −0.773358 | − | 1.15299i | −0.0688962 | − | 0.102716i | ||||
\(127\) | 19.4346 | 1.72454 | 0.862272 | − | 0.506446i | \(-0.169041\pi\) | ||||
0.862272 | + | 0.506446i | \(0.169041\pi\) | |||||||
\(128\) | −5.73931 | + | 9.94077i | −0.507288 | + | 0.878648i | ||||
\(129\) | 3.08476 | − | 1.78098i | 0.271598 | − | 0.156807i | ||||
\(130\) | −1.58103 | + | 0.912811i | −0.138666 | + | 0.0800588i | ||||
\(131\) | 4.97882 | + | 2.87452i | 0.435001 | + | 0.251148i | 0.701475 | − | 0.712694i | \(-0.252525\pi\) |
−0.266474 | + | 0.963842i | \(0.585859\pi\) | |||||||
\(132\) | 5.42613 | 0.472284 | ||||||||
\(133\) | 4.12037 | − | 8.39273i | 0.357281 | − | 0.727742i | ||||
\(134\) | −1.73409 | −0.149802 | ||||||||
\(135\) | −1.97406 | + | 3.41917i | −0.169900 | + | 0.294275i | ||||
\(136\) | 3.59990 | − | 7.20971i | 0.308689 | − | 0.618228i | ||||
\(137\) | −5.68727 | − | 9.85064i | −0.485896 | − | 0.841597i | 0.513973 | − | 0.857807i | \(-0.328173\pi\) |
−0.999869 | + | 0.0162100i | \(0.994840\pi\) | |||||||
\(138\) | −0.869572 | + | 1.50614i | −0.0740229 | + | 0.128211i | ||||
\(139\) | 1.61965i | 0.137377i | 0.997638 | + | 0.0686886i | \(0.0218815\pi\) | ||||
−0.997638 | + | 0.0686886i | \(0.978119\pi\) | |||||||
\(140\) | −1.21009 | − | 17.9745i | −0.102272 | − | 1.51913i | ||||
\(141\) | 8.69592i | 0.732329i | ||||||||
\(142\) | 1.86689 | + | 1.07785i | 0.156666 | + | 0.0904509i | ||||
\(143\) | 2.40103 | − | 1.38623i | 0.200784 | − | 0.115923i | ||||
\(144\) | 1.21186 | + | 2.09899i | 0.100988 | + | 0.174916i | ||||
\(145\) | 17.2430 | − | 29.8658i | 1.43195 | − | 2.48022i | ||||
\(146\) | 5.77250i | 0.477735i | ||||||||
\(147\) | 5.53834 | − | 4.28098i | 0.456795 | − | 0.353089i | ||||
\(148\) | − | 20.6491i | − | 1.69734i | ||||||
\(149\) | 2.43008 | − | 4.20902i | 0.199080 | − | 0.344816i | −0.749150 | − | 0.662400i | \(-0.769538\pi\) |
0.948230 | + | 0.317583i | \(0.102871\pi\) | |||||||
\(150\) | 4.81142 | − | 2.77787i | 0.392850 | − | 0.226812i | ||||
\(151\) | 5.63671 | + | 9.76307i | 0.458709 | + | 0.794507i | 0.998893 | − | 0.0470396i | \(-0.0149787\pi\) |
−0.540184 | + | 0.841547i | \(0.681645\pi\) | |||||||
\(152\) | 3.45337 | − | 5.98142i | 0.280106 | − | 0.485157i | ||||
\(153\) | −2.27368 | − | 3.43953i | −0.183816 | − | 0.278070i | ||||
\(154\) | −0.293401 | − | 4.35813i | −0.0236429 | − | 0.351188i | ||||
\(155\) | 13.9278 | 1.11871 | ||||||||
\(156\) | 1.31616 | + | 0.759885i | 0.105377 | + | 0.0608395i | ||||
\(157\) | −11.6010 | − | 20.0936i | −0.925863 | − | 1.60364i | −0.790168 | − | 0.612890i | \(-0.790007\pi\) |
−0.135695 | − | 0.990751i | \(-0.543327\pi\) | |||||||
\(158\) | 1.59280 | − | 0.919606i | 0.126717 | − | 0.0731600i | ||||
\(159\) | 4.13228 | + | 2.38577i | 0.327711 | + | 0.189204i | ||||
\(160\) | − | 20.4542i | − | 1.61705i | ||||||
\(161\) | −7.87137 | − | 3.86441i | −0.620351 | − | 0.304558i | ||||
\(162\) | −0.524739 | −0.0412274 | ||||||||
\(163\) | 2.53868 | + | 1.46571i | 0.198845 | + | 0.114803i | 0.596117 | − | 0.802898i | \(-0.296710\pi\) |
−0.397272 | + | 0.917701i | \(0.630043\pi\) | |||||||
\(164\) | −9.74802 | + | 5.62802i | −0.761192 | + | 0.439475i | ||||
\(165\) | −10.7575 | + | 6.21082i | −0.837467 | + | 0.483512i | ||||
\(166\) | −2.67386 | + | 4.63126i | −0.207532 | + | 0.359455i | ||||
\(167\) | 3.85772i | 0.298519i | 0.988798 | + | 0.149260i | \(0.0476890\pi\) | ||||
−0.988798 | + | 0.149260i | \(0.952311\pi\) | |||||||
\(168\) | 4.29447 | − | 2.88049i | 0.331325 | − | 0.222234i | ||||
\(169\) | −12.2235 | −0.940267 | ||||||||
\(170\) | 0.516488 | + | 8.52634i | 0.0396128 | + | 0.653940i | ||||
\(171\) | −1.76691 | − | 3.06038i | −0.135119 | − | 0.234033i | ||||
\(172\) | 3.07157 | + | 5.32012i | 0.234205 | + | 0.405655i | ||||
\(173\) | 14.7421 | + | 8.51133i | 1.12082 | + | 0.647104i | 0.941610 | − | 0.336707i | \(-0.109313\pi\) |
0.179208 | + | 0.983811i | \(0.442646\pi\) | |||||||
\(174\) | 4.58349 | 0.347474 | ||||||||
\(175\) | 15.6040 | + | 23.2637i | 1.17955 | + | 1.75857i | ||||
\(176\) | 7.62553i | 0.574796i | ||||||||
\(177\) | −11.0684 | − | 6.39036i | −0.831953 | − | 0.480329i | ||||
\(178\) | −0.292123 | − | 0.505972i | −0.0218956 | − | 0.0379242i | ||||
\(179\) | −4.48115 | − | 7.76157i | −0.334937 | − | 0.580127i | 0.648536 | − | 0.761184i | \(-0.275382\pi\) |
−0.983473 | + | 0.181057i | \(0.942048\pi\) | |||||||
\(180\) | −5.89687 | − | 3.40456i | −0.439526 | − | 0.253761i | ||||
\(181\) | − | 17.4488i | − | 1.29696i | −0.761231 | − | 0.648481i | \(-0.775405\pi\) | ||
0.761231 | − | 0.648481i | \(-0.224595\pi\) | |||||||
\(182\) | 0.539153 | − | 1.09819i | 0.0399647 | − | 0.0814036i | ||||
\(183\) | 7.85627 | 0.580752 | ||||||||
\(184\) | −5.60985 | − | 3.23885i | −0.413564 | − | 0.238771i | ||||
\(185\) | 23.6352 | + | 40.9374i | 1.73770 | + | 3.00978i | ||||
\(186\) | 0.925561 | + | 1.60312i | 0.0678655 | + | 0.117546i | ||||
\(187\) | −0.784360 | − | 12.9485i | −0.0573581 | − | 0.946886i | ||||
\(188\) | −14.9974 | −1.09380 | ||||||||
\(189\) | −0.177717 | − | 2.63978i | −0.0129270 | − | 0.192015i | ||||
\(190\) | 7.32113i | 0.531131i | ||||||||
\(191\) | −1.05824 | + | 1.83293i | −0.0765719 | + | 0.132626i | −0.901769 | − | 0.432219i | \(-0.857731\pi\) |
0.825197 | + | 0.564845i | \(0.191064\pi\) | |||||||
\(192\) | −1.84366 | + | 1.06444i | −0.133055 | + | 0.0768192i | ||||
\(193\) | 20.5920 | − | 11.8888i | 1.48225 | − | 0.855776i | 0.482451 | − | 0.875923i | \(-0.339747\pi\) |
0.999797 | + | 0.0201469i | \(0.00641340\pi\) | |||||||
\(194\) | 2.26386 | + | 1.30704i | 0.162536 | + | 0.0938402i | ||||
\(195\) | −3.47910 | −0.249144 | ||||||||
\(196\) | 7.38318 | + | 9.55169i | 0.527370 | + | 0.682264i | ||||
\(197\) | − | 20.3392i | − | 1.44911i | −0.689219 | − | 0.724553i | \(-0.742046\pi\) | ||
0.689219 | − | 0.724553i | \(-0.257954\pi\) | |||||||
\(198\) | −1.42976 | − | 0.825473i | −0.101609 | − | 0.0586638i | ||||
\(199\) | −15.5463 | + | 8.97568i | −1.10205 | + | 0.636269i | −0.936759 | − | 0.349976i | \(-0.886190\pi\) |
−0.165291 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(200\) | 10.3466 | + | 17.9208i | 0.731615 | + | 1.26719i | ||||
\(201\) | −2.86192 | − | 1.65233i | −0.201865 | − | 0.116547i | ||||
\(202\) | 5.47914 | 0.385511 | ||||||||
\(203\) | 1.55232 | + | 23.0579i | 0.108952 | + | 1.61835i | ||||
\(204\) | 5.93198 | − | 3.92130i | 0.415322 | − | 0.274546i | ||||
\(205\) | 12.8838 | − | 22.3155i | 0.899846 | − | 1.55858i | ||||
\(206\) | −1.03185 | − | 1.78722i | −0.0718924 | − | 0.124521i | ||||
\(207\) | −2.87027 | + | 1.65715i | −0.199497 | + | 0.115180i | ||||
\(208\) | −1.06789 | + | 1.84965i | −0.0740451 | + | 0.128250i | ||||
\(209\) | − | 11.1182i | − | 0.769061i | ||||||
\(210\) | −2.41560 | + | 4.92030i | −0.166692 | + | 0.339533i | ||||
\(211\) | − | 1.86073i | − | 0.128098i | −0.997947 | − | 0.0640489i | \(-0.979599\pi\) | ||
0.997947 | − | 0.0640489i | \(-0.0204014\pi\) | |||||||
\(212\) | −4.11462 | + | 7.12673i | −0.282593 | + | 0.489466i | ||||
\(213\) | 2.05406 | + | 3.55774i | 0.140742 | + | 0.243772i | ||||
\(214\) | 0.871656 | − | 0.503251i | 0.0595852 | − | 0.0344015i | ||||
\(215\) | −12.1790 | − | 7.03154i | −0.830599 | − | 0.479547i | ||||
\(216\) | − | 1.95447i | − | 0.132985i | ||||||
\(217\) | −7.75126 | + | 5.19911i | −0.526189 | + | 0.352938i | ||||
\(218\) | 4.96926i | 0.336561i | ||||||||
\(219\) | −5.50035 | + | 9.52688i | −0.371679 | + | 0.643767i | ||||
\(220\) | −10.7115 | − | 18.5528i | −0.722169 | − | 1.25083i | ||||
\(221\) | 1.62307 | − | 3.25062i | 0.109180 | − | 0.218660i | ||||
\(222\) | −3.14133 | + | 5.44094i | −0.210832 | + | 0.365172i | ||||
\(223\) | −6.89198 | −0.461521 | −0.230761 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230761 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(224\) | 7.63537 | + | 11.3834i | 0.510160 | + | 0.760588i | ||||
\(225\) | 10.5876 | 0.705842 | ||||||||
\(226\) | −2.81012 | − | 1.62242i | −0.186926 | − | 0.107922i | ||||
\(227\) | 3.13873 | − | 1.81215i | 0.208325 | − | 0.120276i | −0.392208 | − | 0.919877i | \(-0.628289\pi\) |
0.600533 | + | 0.799600i | \(0.294955\pi\) | |||||||
\(228\) | 5.27808 | − | 3.04730i | 0.349549 | − | 0.201812i | ||||
\(229\) | −5.92085 | + | 10.2552i | −0.391261 | + | 0.677683i | −0.992616 | − | 0.121298i | \(-0.961294\pi\) |
0.601355 | + | 0.798982i | \(0.294628\pi\) | |||||||
\(230\) | 6.86634 | 0.452753 | ||||||||
\(231\) | 3.66843 | − | 7.47219i | 0.241365 | − | 0.491634i | ||||
\(232\) | 17.0719i | 1.12083i | ||||||||
\(233\) | 3.86669 | + | 2.23243i | 0.253315 | + | 0.146252i | 0.621281 | − | 0.783588i | \(-0.286612\pi\) |
−0.367966 | + | 0.929839i | \(0.619946\pi\) | |||||||
\(234\) | −0.231202 | − | 0.400453i | −0.0151141 | − | 0.0261784i | ||||
\(235\) | 29.7328 | − | 17.1663i | 1.93956 | − | 1.11980i | ||||
\(236\) | 11.0211 | − | 19.0891i | 0.717414 | − | 1.24260i | ||||
\(237\) | 3.50500 | 0.227674 | ||||||||
\(238\) | −3.47025 | − | 4.55238i | −0.224943 | − | 0.295087i | ||||
\(239\) | 0.597778 | 0.0386670 | 0.0193335 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193335 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(240\) | 4.78455 | − | 8.28708i | 0.308841 | − | 0.534929i | ||||
\(241\) | −1.77806 | + | 1.02656i | −0.114535 | + | 0.0661267i | −0.556173 | − | 0.831067i | \(-0.687731\pi\) |
0.441638 | + | 0.897193i | \(0.354397\pi\) | |||||||
\(242\) | 0.288945 | + | 0.500468i | 0.0185741 | + | 0.0321713i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 13.5493i | 0.867405i | ||||||||
\(245\) | −25.5704 | − | 10.4856i | −1.63363 | − | 0.669902i | ||||
\(246\) | 3.42475 | 0.218354 | ||||||||
\(247\) | 1.55701 | − | 2.69682i | 0.0990703 | − | 0.171595i | ||||
\(248\) | −5.97106 | + | 3.44739i | −0.379162 | + | 0.218910i | ||||
\(249\) | −8.82582 | + | 5.09559i | −0.559314 | + | 0.322920i | ||||
\(250\) | −10.0252 | − | 5.78803i | −0.634047 | − | 0.366067i | ||||
\(251\) | 5.98660 | 0.377871 | 0.188936 | − | 0.981989i | \(-0.439496\pi\) | ||||
0.188936 | + | 0.981989i | \(0.439496\pi\) | |||||||
\(252\) | 4.55269 | − | 0.306499i | 0.286792 | − | 0.0193076i | ||||
\(253\) | −10.4275 | −0.655573 | ||||||||
\(254\) | 5.09905 | − | 8.83182i | 0.319943 | − | 0.554158i | ||||
\(255\) | −7.27195 | + | 14.5639i | −0.455387 | + | 0.912029i | ||||
\(256\) | 0.882765 | + | 1.52899i | 0.0551728 | + | 0.0955621i | ||||
\(257\) | −4.21568 | + | 7.30178i | −0.262967 | + | 0.455472i | −0.967029 | − | 0.254666i | \(-0.918034\pi\) |
0.704062 | + | 0.710139i | \(0.251368\pi\) | |||||||
\(258\) | − | 1.86911i | − | 0.116365i | ||||||
\(259\) | −28.4353 | − | 13.9602i | −1.76688 | − | 0.867443i | ||||
\(260\) | − | 6.00023i | − | 0.372118i | ||||||
\(261\) | 7.56456 | + | 4.36740i | 0.468234 | + | 0.270335i | ||||
\(262\) | 2.61258 | − | 1.50837i | 0.161406 | − | 0.0931877i | ||||
\(263\) | 3.08641 | + | 5.34582i | 0.190316 | + | 0.329637i | 0.945355 | − | 0.326043i | \(-0.105715\pi\) |
−0.755039 | + | 0.655680i | \(0.772382\pi\) | |||||||
\(264\) | 3.07460 | − | 5.32536i | 0.189228 | − | 0.327753i | ||||
\(265\) | − | 18.8386i | − | 1.15725i | ||||||
\(266\) | −2.73291 | − | 4.07445i | −0.167565 | − | 0.249820i | ||||
\(267\) | − | 1.11340i | − | 0.0681392i | ||||||
\(268\) | 2.84969 | − | 4.93581i | 0.174073 | − | 0.301503i | ||||
\(269\) | −6.69495 | + | 3.86533i | −0.408199 | + | 0.235674i | −0.690015 | − | 0.723795i | \(-0.742396\pi\) |
0.281817 | + | 0.959468i | \(0.409063\pi\) | |||||||
\(270\) | 1.03587 | + | 1.79417i | 0.0630408 | + | 0.109190i | ||||
\(271\) | −3.69428 | + | 6.39869i | −0.224412 | + | 0.388693i | −0.956143 | − | 0.292901i | \(-0.905379\pi\) |
0.731731 | + | 0.681593i | \(0.238713\pi\) | |||||||
\(272\) | 5.51075 | + | 8.33642i | 0.334138 | + | 0.505470i | ||||
\(273\) | 1.93623 | − | 1.29872i | 0.117186 | − | 0.0786019i | ||||
\(274\) | −5.96867 | −0.360580 | ||||||||
\(275\) | 28.8482 | + | 16.6555i | 1.73961 | + | 1.00437i | ||||
\(276\) | −2.85800 | − | 4.95021i | −0.172032 | − | 0.297967i | ||||
\(277\) | 19.8730 | − | 11.4737i | 1.19405 | − | 0.689388i | 0.234831 | − | 0.972036i | \(-0.424546\pi\) |
0.959224 | + | 0.282649i | \(0.0912130\pi\) | |||||||
\(278\) | 0.736031 | + | 0.424948i | 0.0441442 | + | 0.0254867i | ||||
\(279\) | 3.52770i | 0.211198i | ||||||||
\(280\) | −18.3264 | − | 8.99726i | −1.09521 | − | 0.537689i | ||||
\(281\) | −29.9362 | −1.78584 | −0.892922 | − | 0.450212i | \(-0.851349\pi\) | ||||
−0.892922 | + | 0.450212i | \(0.851349\pi\) | |||||||
\(282\) | 3.95175 | + | 2.28155i | 0.235323 | + | 0.135864i | ||||
\(283\) | 25.3699 | − | 14.6473i | 1.50808 | − | 0.870693i | 0.508128 | − | 0.861282i | \(-0.330338\pi\) |
0.999956 | − | 0.00941090i | \(-0.00299563\pi\) | |||||||
\(284\) | −6.13585 | + | 3.54254i | −0.364096 | + | 0.210211i | ||||
\(285\) | −6.97597 | + | 12.0827i | −0.413221 | + | 0.715719i | ||||
\(286\) | − | 1.45482i | − | 0.0860255i | ||||||
\(287\) | 1.15988 | + | 17.2287i | 0.0684657 | + | 1.01698i | ||||
\(288\) | 5.18076 | 0.305279 | ||||||||
\(289\) | −10.2150 | − | 13.5888i | −0.600880 | − | 0.799339i | ||||
\(290\) | −9.04808 | − | 15.6717i | −0.531322 | − | 0.920276i | ||||
\(291\) | 2.49084 | + | 4.31427i | 0.146016 | + | 0.252907i | ||||
\(292\) | −16.4305 | − | 9.48617i | −0.961524 | − | 0.555136i | ||||
\(293\) | 1.29200 | 0.0754792 | 0.0377396 | − | 0.999288i | \(-0.487984\pi\) | ||||
0.0377396 | + | 0.999288i | \(0.487984\pi\) | |||||||
\(294\) | −0.492345 | − | 3.64003i | −0.0287141 | − | 0.212291i | ||||
\(295\) | 50.4597i | 2.93788i | ||||||||
\(296\) | −20.2656 | − | 11.7003i | −1.17791 | − | 0.680069i | ||||
\(297\) | −1.57311 | − | 2.72471i | −0.0912811 | − | 0.158104i | ||||
\(298\) | −1.27516 | − | 2.20864i | −0.0738679 | − | 0.127943i | ||||
\(299\) | −2.52930 | − | 1.46029i | −0.146273 | − | 0.0844508i | ||||
\(300\) | 18.2599i | 1.05424i | ||||||||
\(301\) | 9.40280 | − | 0.633022i | 0.541968 | − | 0.0364868i | ||||
\(302\) | 5.91561 | 0.340405 | ||||||||
\(303\) | 9.04272 | + | 5.22082i | 0.519491 | + | 0.299928i | ||||
\(304\) | 4.28248 | + | 7.41747i | 0.245617 | + | 0.425421i | ||||
\(305\) | −15.5087 | − | 26.8619i | −0.888027 | − | 1.53811i | ||||
\(306\) | −2.15960 | + | 0.130819i | −0.123456 | + | 0.00747841i | ||||
\(307\) | 27.3475 | 1.56080 | 0.780402 | − | 0.625278i | \(-0.215014\pi\) | ||||
0.780402 | + | 0.625278i | \(0.215014\pi\) | |||||||
\(308\) | 12.8869 | + | 6.32676i | 0.734299 | + | 0.360501i | ||||
\(309\) | − | 3.93281i | − | 0.223730i | ||||||
\(310\) | 3.65422 | − | 6.32930i | 0.207546 | − | 0.359480i | ||||
\(311\) | −1.52215 | + | 0.878811i | −0.0863129 | + | 0.0498328i | −0.542535 | − | 0.840033i | \(-0.682536\pi\) |
0.456222 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(312\) | 1.49155 | − | 0.861145i | 0.0844422 | − | 0.0487527i | ||||
\(313\) | −5.77045 | − | 3.33157i | −0.326165 | − | 0.188311i | 0.327972 | − | 0.944687i | \(-0.393635\pi\) |
−0.654137 | + | 0.756376i | \(0.726968\pi\) | |||||||
\(314\) | −12.1750 | −0.687076 | ||||||||
\(315\) | −8.67502 | + | 5.81872i | −0.488782 | + | 0.327848i | ||||
\(316\) | 6.04490i | 0.340052i | ||||||||
\(317\) | −7.67483 | − | 4.43106i | −0.431061 | − | 0.248873i | 0.268737 | − | 0.963213i | \(-0.413394\pi\) |
−0.699799 | + | 0.714340i | \(0.746727\pi\) | |||||||
\(318\) | 2.16837 | − | 1.25191i | 0.121596 | − | 0.0702036i | ||||
\(319\) | 13.7408 | + | 23.7998i | 0.769338 | + | 1.33253i | ||||
\(320\) | 7.27899 | + | 4.20252i | 0.406908 | + | 0.234928i | ||||
\(321\) | 1.91810 | 0.107058 | ||||||||
\(322\) | −3.82134 | + | 2.56314i | −0.212955 | + | 0.142838i | ||||
\(323\) | −8.03479 | − | 12.1547i | −0.447068 | − | 0.676305i | ||||
\(324\) | 0.862324 | − | 1.49359i | 0.0479069 | − | 0.0829772i | ||||
\(325\) | 4.66494 | + | 8.07991i | 0.258764 | + | 0.448193i | ||||
\(326\) | 1.33215 | − | 0.769116i | 0.0737808 | − | 0.0425974i | ||||
\(327\) | −4.73498 | + | 8.20123i | −0.261845 | + | 0.453529i | ||||
\(328\) | 12.7560i | 0.704331i | ||||||||
\(329\) | −10.1393 | + | 20.6526i | −0.558996 | + | 1.13861i | ||||
\(330\) | 6.51813i | 0.358811i | ||||||||
\(331\) | 6.58321 | − | 11.4025i | 0.361846 | − | 0.626736i | −0.626419 | − | 0.779487i | \(-0.715480\pi\) |
0.988265 | + | 0.152751i | \(0.0488132\pi\) | |||||||
\(332\) | −8.78811 | − | 15.2214i | −0.482310 | − | 0.835385i | ||||
\(333\) | −10.3688 | + | 5.98645i | −0.568209 | + | 0.328056i | ||||
\(334\) | 1.75309 | + | 1.01215i | 0.0959249 | + | 0.0553823i | ||||
\(335\) | 13.0472i | 0.712845i | ||||||||
\(336\) | 0.430734 | + | 6.39805i | 0.0234985 | + | 0.349042i | ||||
\(337\) | 18.5405i | 1.00997i | 0.863129 | + | 0.504983i | \(0.168501\pi\) | ||||
−0.863129 | + | 0.504983i | \(0.831499\pi\) | |||||||
\(338\) | −3.20707 | + | 5.55481i | −0.174442 | + | 0.302142i | ||||
\(339\) | −3.09187 | − | 5.35527i | −0.167927 | − | 0.290858i | ||||
\(340\) | −25.1177 | − | 12.5416i | −1.36220 | − | 0.680162i | ||||
\(341\) | −5.54946 | + | 9.61195i | −0.300520 | + | 0.520516i | ||||
\(342\) | −1.85433 | −0.100271 | ||||||||
\(343\) | 18.1449 | − | 3.70960i | 0.979735 | − | 0.200300i | ||||
\(344\) | 6.96176 | 0.375353 | ||||||||
\(345\) | 11.3322 | + | 6.54262i | 0.610103 | + | 0.352243i | ||||
\(346\) | 7.73573 | − | 4.46623i | 0.415876 | − | 0.240106i | ||||
\(347\) | −21.4320 | + | 12.3737i | −1.15053 | + | 0.664257i | −0.949016 | − | 0.315229i | \(-0.897919\pi\) |
−0.201512 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(348\) | −7.53223 | + | 13.0462i | −0.403770 | + | 0.699350i | ||||
\(349\) | −23.1652 | −1.24001 | −0.620003 | − | 0.784599i | \(-0.712869\pi\) | ||||
−0.620003 | + | 0.784599i | \(0.712869\pi\) | |||||||
\(350\) | 14.6659 | − | 0.987350i | 0.783926 | − | 0.0527761i | ||||
\(351\) | − | 0.881206i | − | 0.0470353i | ||||||
\(352\) | 14.1160 | + | 8.14990i | 0.752388 | + | 0.434391i | ||||
\(353\) | 11.2072 | + | 19.4114i | 0.596498 | + | 1.03316i | 0.993334 | + | 0.115275i | \(0.0367748\pi\) |
−0.396836 | + | 0.917890i | \(0.629892\pi\) | |||||||
\(354\) | −5.80803 | + | 3.35327i | −0.308694 | + | 0.178224i | ||||
\(355\) | 8.10968 | − | 14.0464i | 0.430417 | − | 0.745504i | ||||
\(356\) | 1.92023 | 0.101772 | ||||||||
\(357\) | −1.38951 | − | 10.8199i | −0.0735405 | − | 0.572647i | ||||
\(358\) | −4.70287 | −0.248554 | ||||||||
\(359\) | −14.0101 | + | 24.2662i | −0.739424 | + | 1.28072i | 0.213331 | + | 0.976980i | \(0.431569\pi\) |
−0.952755 | + | 0.303740i | \(0.901764\pi\) | |||||||
\(360\) | −6.68266 | + | 3.85824i | −0.352207 | + | 0.203347i | ||||
\(361\) | 3.25605 | + | 5.63965i | 0.171371 | + | 0.296824i | ||||
\(362\) | −7.92941 | − | 4.57805i | −0.416760 | − | 0.240617i | ||||
\(363\) | 1.10129i | 0.0578028i | ||||||||
\(364\) | 2.23983 | + | 3.33932i | 0.117399 | + | 0.175028i | ||||
\(365\) | 43.4320 | 2.27334 | ||||||||
\(366\) | 2.06125 | − | 3.57018i | 0.107743 | − | 0.186616i | ||||
\(367\) | −14.2493 | + | 8.22682i | −0.743806 | + | 0.429436i | −0.823451 | − | 0.567387i | \(-0.807954\pi\) |
0.0796457 | + | 0.996823i | \(0.474621\pi\) | |||||||
\(368\) | 6.95670 | − | 4.01645i | 0.362643 | − | 0.209372i | ||||
\(369\) | 5.65218 | + | 3.26329i | 0.294241 | + | 0.169880i | ||||
\(370\) | 24.8047 | 1.28953 | ||||||||
\(371\) | 7.03228 | + | 10.4843i | 0.365098 | + | 0.544318i | ||||
\(372\) | −6.08404 | −0.315443 | ||||||||
\(373\) | −6.59906 | + | 11.4299i | −0.341686 | + | 0.591818i | −0.984746 | − | 0.173998i | \(-0.944331\pi\) |
0.643060 | + | 0.765816i | \(0.277665\pi\) | |||||||
\(374\) | −6.09006 | − | 3.04084i | −0.314910 | − | 0.157238i | ||||
\(375\) | −11.0303 | − | 19.1050i | −0.569602 | − | 0.986580i | ||||
\(376\) | −8.49796 | + | 14.7189i | −0.438249 | + | 0.759069i | ||||
\(377\) | 7.69716i | 0.396424i | ||||||||
\(378\) | −1.24624 | − | 0.611836i | −0.0640997 | − | 0.0314694i | ||||
\(379\) | − | 7.07128i | − | 0.363227i | −0.983370 | − | 0.181614i | \(-0.941868\pi\) | ||
0.983370 | − | 0.181614i | \(-0.0581320\pi\) | |||||||
\(380\) | −20.8385 | − | 12.0311i | −1.06899 | − | 0.617182i | ||||
\(381\) | 16.8309 | − | 9.71731i | 0.862272 | − | 0.497833i | ||||
\(382\) | 0.555302 | + | 0.961812i | 0.0284117 | + | 0.0492106i | ||||
\(383\) | 9.14863 | − | 15.8459i | 0.467473 | − | 0.809687i | −0.531836 | − | 0.846847i | \(-0.678498\pi\) |
0.999309 | + | 0.0371601i | \(0.0118312\pi\) | |||||||
\(384\) | 11.4786i | 0.585766i | ||||||||
\(385\) | −32.7904 | + | 2.20754i | −1.67115 | + | 0.112507i | ||||
\(386\) | − | 12.4771i | − | 0.635066i | ||||||
\(387\) | 1.78098 | − | 3.08476i | 0.0905326 | − | 0.156807i | ||||
\(388\) | −7.44059 | + | 4.29583i | −0.377739 | + | 0.218088i | ||||
\(389\) | −10.3759 | − | 17.9716i | −0.526079 | − | 0.911195i | −0.999538 | − | 0.0303794i | \(-0.990328\pi\) |
0.473460 | − | 0.880815i | \(-0.343005\pi\) | |||||||
\(390\) | −0.912811 | + | 1.58103i | −0.0462220 | + | 0.0800588i | ||||
\(391\) | −11.3996 | + | 7.53567i | −0.576504 | + | 0.381095i | ||||
\(392\) | 13.5578 | − | 1.83381i | 0.684774 | − | 0.0926215i | ||||
\(393\) | 5.74904 | 0.290001 | ||||||||
\(394\) | −9.24288 | − | 5.33638i | −0.465650 | − | 0.268843i | ||||
\(395\) | −6.91908 | − | 11.9842i | −0.348137 | − | 0.602991i | ||||
\(396\) | 4.69916 | − | 2.71306i | 0.236142 | − | 0.136337i | ||||
\(397\) | 7.04005 | + | 4.06457i | 0.353330 | + | 0.203995i | 0.666151 | − | 0.745817i | \(-0.267941\pi\) |
−0.312821 | + | 0.949812i | \(0.601274\pi\) | |||||||
\(398\) | 9.41978i | 0.472171i | ||||||||
\(399\) | −0.628020 | − | 9.32850i | −0.0314403 | − | 0.467009i | ||||
\(400\) | −25.6613 | −1.28307 | ||||||||
\(401\) | 25.1535 | + | 14.5224i | 1.25611 | + | 0.725214i | 0.972316 | − | 0.233672i | \(-0.0750740\pi\) |
0.283792 | + | 0.958886i | \(0.408407\pi\) | |||||||
\(402\) | −1.50176 | + | 0.867044i | −0.0749012 | + | 0.0432442i | ||||
\(403\) | −2.69215 | + | 1.55431i | −0.134106 | + | 0.0774259i | ||||
\(404\) | −9.00407 | + | 15.5955i | −0.447969 | + | 0.775906i | ||||
\(405\) | 3.94812i | 0.196184i | ||||||||
\(406\) | 10.8857 | + | 5.34426i | 0.540246 | + | 0.265231i | ||||
\(407\) | −37.6694 | −1.86720 | ||||||||
\(408\) | −0.487254 | − | 8.04374i | −0.0241227 | − | 0.398224i | ||||
\(409\) | −9.92796 | − | 17.1957i | −0.490906 | − | 0.850274i | 0.509039 | − | 0.860743i | \(-0.330001\pi\) |
−0.999945 | + | 0.0104691i | \(0.996668\pi\) | |||||||
\(410\) | −6.76065 | − | 11.7098i | −0.333885 | − | 0.578306i | ||||
\(411\) | −9.85064 | − | 5.68727i | −0.485896 | − | 0.280532i | ||||
\(412\) | 6.78271 | 0.334160 | ||||||||
\(413\) | −18.8362 | − | 28.0825i | −0.926866 | − | 1.38185i | ||||
\(414\) | 1.73914i | 0.0854743i | ||||||||
\(415\) | 34.8454 | + | 20.1180i | 1.71049 | + | 0.987553i | ||||
\(416\) | 2.28266 | + | 3.95367i | 0.111916 | + | 0.193845i | ||||
\(417\) | 0.809826 | + | 1.40266i | 0.0396574 | + | 0.0686886i | ||||
\(418\) | −5.05252 | − | 2.91707i | −0.247127 | − | 0.142679i | ||||
\(419\) | − | 9.95587i | − | 0.486376i | −0.969979 | − | 0.243188i | \(-0.921807\pi\) | ||
0.969979 | − | 0.243188i | \(-0.0781932\pi\) | |||||||
\(420\) | −10.0352 | − | 14.9614i | −0.489670 | − | 0.730040i | ||||
\(421\) | 19.7581 | 0.962950 | 0.481475 | − | 0.876460i | \(-0.340101\pi\) | ||||
0.481475 | + | 0.876460i | \(0.340101\pi\) | |||||||
\(422\) | −0.845584 | − | 0.488198i | −0.0411624 | − | 0.0237651i | ||||
\(423\) | 4.34796 | + | 7.53089i | 0.211405 | + | 0.366164i | ||||
\(424\) | 4.66292 | + | 8.07641i | 0.226451 | + | 0.392225i | ||||
\(425\) | 43.5740 | − | 2.63952i | 2.11365 | − | 0.128036i | ||||
\(426\) | 2.15569 | 0.104444 | ||||||||
\(427\) | 18.6584 | + | 9.16025i | 0.902944 | + | 0.443296i | ||||
\(428\) | 3.30805i | 0.159901i | ||||||||
\(429\) | 1.38623 | − | 2.40103i | 0.0669280 | − | 0.115923i | ||||
\(430\) | −6.39079 | + | 3.68972i | −0.308191 | + | 0.177934i | ||||
\(431\) | 23.2412 | − | 13.4183i | 1.11949 | − | 0.646337i | 0.178219 | − | 0.983991i | \(-0.442967\pi\) |
0.941270 | + | 0.337654i | \(0.109633\pi\) | |||||||
\(432\) | 2.09899 | + | 1.21186i | 0.100988 | + | 0.0583054i | ||||
\(433\) | −14.8038 | −0.711424 | −0.355712 | − | 0.934596i | \(-0.615762\pi\) | ||||
−0.355712 | + | 0.934596i | \(0.615762\pi\) | |||||||
\(434\) | 0.328976 | + | 4.88655i | 0.0157913 | + | 0.234562i | ||||
\(435\) | − | 34.4860i | − | 1.65348i | ||||||
\(436\) | −14.1442 | − | 8.16618i | −0.677386 | − | 0.391089i | ||||
\(437\) | −10.1430 | + | 5.85607i | −0.485206 | + | 0.280134i | ||||
\(438\) | 2.88625 | + | 4.99913i | 0.137910 | + | 0.238868i | ||||
\(439\) | −15.7900 | − | 9.11635i | −0.753615 | − | 0.435100i | 0.0733838 | − | 0.997304i | \(-0.476620\pi\) |
−0.826998 | + | 0.562204i | \(0.809954\pi\) | |||||||
\(440\) | −24.2777 | −1.15740 | ||||||||
\(441\) | 2.65585 | − | 6.47661i | 0.126469 | − | 0.308410i | ||||
\(442\) | −1.05136 | − | 1.59045i | −0.0500080 | − | 0.0756500i | ||||
\(443\) | 11.6806 | − | 20.2314i | 0.554963 | − | 0.961224i | −0.442944 | − | 0.896549i | \(-0.646066\pi\) |
0.997906 | − | 0.0646742i | \(-0.0206008\pi\) | |||||||
\(444\) | −10.3245 | − | 17.8826i | −0.489981 | − | 0.848671i | ||||
\(445\) | −3.80691 | + | 2.19792i | −0.180465 | + | 0.104192i | ||||
\(446\) | −1.80825 | + | 3.13197i | −0.0856229 | + | 0.148303i | ||||
\(447\) | − | 4.86016i | − | 0.229878i | ||||||
\(448\) | −5.61975 | + | 0.378337i | −0.265508 | + | 0.0178747i | ||||
\(449\) | 20.7793i | 0.980635i | 0.871544 | + | 0.490317i | \(0.163119\pi\) | ||||
−0.871544 | + | 0.490317i | \(0.836881\pi\) | |||||||
\(450\) | 2.77787 | − | 4.81142i | 0.130950 | − | 0.226812i | ||||
\(451\) | 10.2670 | + | 17.7830i | 0.483455 | + | 0.837369i | ||||
\(452\) | 9.23596 | − | 5.33239i | 0.434423 | − | 0.250814i | ||||
\(453\) | 9.76307 | + | 5.63671i | 0.458709 | + | 0.264836i | ||||
\(454\) | − | 1.90181i | − | 0.0892563i | ||||||
\(455\) | −8.26277 | − | 4.05657i | −0.387365 | − | 0.190175i | ||||
\(456\) | − | 6.90675i | − | 0.323438i | ||||||
\(457\) | 9.08014 | − | 15.7273i | 0.424751 | − | 0.735690i | −0.571646 | − | 0.820500i | \(-0.693695\pi\) |
0.996397 | + | 0.0848098i | \(0.0270283\pi\) | |||||||
\(458\) | 3.10690 | + | 5.38131i | 0.145176 | + | 0.251452i | ||||
\(459\) | −3.68883 | − | 1.84188i | −0.172180 | − | 0.0859715i | ||||
\(460\) | −11.2837 | + | 19.5440i | −0.526107 | + | 0.911243i | ||||
\(461\) | 23.4048 | 1.09007 | 0.545035 | − | 0.838413i | \(-0.316516\pi\) | ||||
0.545035 | + | 0.838413i | \(0.316516\pi\) | |||||||
\(462\) | −2.43316 | − | 3.62755i | −0.113201 | − | 0.168769i | ||||
\(463\) | 11.3279 | 0.526450 | 0.263225 | − | 0.964734i | \(-0.415214\pi\) | ||||
0.263225 | + | 0.964734i | \(0.415214\pi\) | |||||||
\(464\) | −18.3343 | − | 10.5853i | −0.851149 | − | 0.491411i | ||||
\(465\) | 12.0618 | − | 6.96389i | 0.559353 | − | 0.322942i | ||||
\(466\) | 2.02900 | − | 1.17145i | 0.0939918 | − | 0.0542662i | ||||
\(467\) | −19.9227 | + | 34.5071i | −0.921912 | + | 1.59680i | −0.125459 | + | 0.992099i | \(0.540040\pi\) |
−0.796453 | + | 0.604700i | \(0.793293\pi\) | |||||||
\(468\) | 1.51977 | 0.0702514 | ||||||||
\(469\) | −4.87040 | − | 7.26119i | −0.224894 | − | 0.335291i | ||||
\(470\) | − | 18.0156i | − | 0.830999i | ||||||
\(471\) | −20.0936 | − | 11.6010i | −0.925863 | − | 0.534547i | ||||
\(472\) | −12.4898 | − | 21.6329i | −0.574888 | − | 0.995734i | ||||
\(473\) | 9.70533 | − | 5.60337i | 0.446251 | − | 0.257643i | ||||
\(474\) | 0.919606 | − | 1.59280i | 0.0422389 | − | 0.0731600i | ||||
\(475\) | 37.4148 | 1.71671 | ||||||||
\(476\) | 18.6604 | − | 2.39641i | 0.855300 | − | 0.109839i | ||||
\(477\) | 4.77155 | 0.218474 | ||||||||
\(478\) | 0.156839 | − | 0.271653i | 0.00717364 | − | 0.0124251i | ||||
\(479\) | 12.9347 | − | 7.46784i | 0.591000 | − | 0.341214i | −0.174493 | − | 0.984658i | \(-0.555829\pi\) |
0.765493 | + | 0.643444i | \(0.222495\pi\) | |||||||
\(480\) | −10.2271 | − | 17.7139i | −0.466802 | − | 0.808524i | ||||
\(481\) | −9.13708 | − | 5.27530i | −0.416615 | − | 0.240533i | ||||
\(482\) | 1.07736i | 0.0490722i | ||||||||
\(483\) | −8.74901 | + | 0.589007i | −0.398094 | + | 0.0268008i | ||||
\(484\) | −1.89934 | −0.0863336 | ||||||||
\(485\) | 9.83414 | − | 17.0332i | 0.446545 | − | 0.773439i | ||||
\(486\) | −0.454438 | + | 0.262370i | −0.0206137 | + | 0.0119013i | ||||
\(487\) | −2.20905 | + | 1.27540i | −0.100102 | + | 0.0577937i | −0.549215 | − | 0.835681i | \(-0.685073\pi\) |
0.449113 | + | 0.893475i | \(0.351740\pi\) | |||||||
\(488\) | 13.2977 | + | 7.67742i | 0.601957 | + | 0.347540i | ||||
\(489\) | 2.93142 | 0.132563 | ||||||||
\(490\) | −11.4740 | + | 8.86904i | −0.518341 | + | 0.400662i | ||||
\(491\) | 8.42710 | 0.380310 | 0.190155 | − | 0.981754i | \(-0.439101\pi\) | ||||
0.190155 | + | 0.981754i | \(0.439101\pi\) | |||||||
\(492\) | −5.62802 | + | 9.74802i | −0.253731 | + | 0.439475i | ||||
\(493\) | 32.2212 | + | 16.0884i | 1.45117 | + | 0.724587i | ||||
\(494\) | −0.817025 | − | 1.41513i | −0.0367597 | − | 0.0636697i | ||||
\(495\) | −6.21082 | + | 10.7575i | −0.279156 | + | 0.483512i | ||||
\(496\) | − | 8.55012i | − | 0.383912i | ||||||
\(497\) | 0.730083 | + | 10.8445i | 0.0327487 | + | 0.486444i | ||||
\(498\) | 5.34771i | 0.239637i | ||||||||
\(499\) | −30.6923 | − | 17.7202i | −1.37397 | − | 0.793264i | −0.382548 | − | 0.923936i | \(-0.624953\pi\) |
−0.991426 | + | 0.130671i | \(0.958287\pi\) | |||||||
\(500\) | 32.9495 | − | 19.0234i | 1.47355 | − | 0.850752i | ||||
\(501\) | 1.92886 | + | 3.34088i | 0.0861751 | + | 0.149260i | ||||
\(502\) | 1.57070 | − | 2.72054i | 0.0701039 | − | 0.121424i | ||||
\(503\) | 22.9796i | 1.02461i | 0.858803 | + | 0.512306i | \(0.171209\pi\) | ||||
−0.858803 | + | 0.512306i | \(0.828791\pi\) | |||||||
\(504\) | 2.27887 | − | 4.64181i | 0.101509 | − | 0.206763i | ||||
\(505\) | − | 41.2248i | − | 1.83448i | ||||||
\(506\) | −2.73587 | + | 4.73866i | −0.121624 | + | 0.210659i | ||||
\(507\) | −10.5858 | + | 6.11174i | −0.470134 | + | 0.271432i | ||||
\(508\) | 16.7589 | + | 29.0273i | 0.743558 | + | 1.28788i | ||||
\(509\) | 3.24495 | − | 5.62042i | 0.143830 | − | 0.249121i | −0.785106 | − | 0.619362i | \(-0.787391\pi\) |
0.928936 | + | 0.370241i | \(0.120725\pi\) | |||||||
\(510\) | 4.71046 | + | 7.12578i | 0.208583 | + | 0.315535i | ||||
\(511\) | −24.1713 | + | 16.2128i | −1.06928 | + | 0.717211i | ||||
\(512\) | −22.0308 | −0.973632 | ||||||||
\(513\) | −3.06038 | − | 1.76691i | −0.135119 | − | 0.0780110i | ||||
\(514\) | 2.21213 | + | 3.83153i | 0.0975731 | + | 0.169001i | ||||
\(515\) | −13.4469 | + | 7.76359i | −0.592543 | + | 0.342105i | ||||
\(516\) | 5.32012 | + | 3.07157i | 0.234205 | + | 0.135218i | ||||
\(517\) | 27.3593i | 1.20326i | ||||||||
\(518\) | −13.8046 | + | 9.25935i | −0.606539 | + | 0.406832i | ||||
\(519\) | 17.0227 | 0.747212 | ||||||||
\(520\) | −5.88880 | − | 3.39990i | −0.258241 | − | 0.149095i | ||||
\(521\) | −7.41911 | + | 4.28343i | −0.325037 | + | 0.187660i | −0.653636 | − | 0.756809i | \(-0.726757\pi\) |
0.328598 | + | 0.944470i | \(0.393424\pi\) | |||||||
\(522\) | 3.96942 | − | 2.29175i | 0.173737 | − | 0.100307i | ||||
\(523\) | −14.2665 | + | 24.7103i | −0.623830 | + | 1.08051i | 0.364935 | + | 0.931033i | \(0.381091\pi\) |
−0.988766 | + | 0.149473i | \(0.952242\pi\) | |||||||
\(524\) | 9.91508i | 0.433142i | ||||||||
\(525\) | 25.1453 | + | 12.3450i | 1.09743 | + | 0.538779i | ||||
\(526\) | 3.23912 | 0.141232 | ||||||||
\(527\) | 0.879464 | + | 14.5185i | 0.0383100 | + | 0.632434i | ||||
\(528\) | 3.81276 | + | 6.60390i | 0.165929 | + | 0.287398i | ||||
\(529\) | −6.00770 | − | 10.4056i | −0.261204 | − | 0.452419i | ||||
\(530\) | −8.56098 | − | 4.94268i | −0.371865 | − | 0.214696i | ||||
\(531\) | −12.7807 | −0.554636 | ||||||||
\(532\) | 16.0884 | − | 1.08311i | 0.697520 | − | 0.0469589i | ||||
\(533\) | 5.75125i | 0.249114i | ||||||||
\(534\) | −0.505972 | − | 0.292123i | −0.0218956 | − | 0.0126414i | ||||
\(535\) | −3.78644 | − | 6.55831i | −0.163702 | − | 0.283540i | ||||
\(536\) | −3.22943 | − | 5.59354i | −0.139490 | − | 0.241604i | ||||
\(537\) | −7.76157 | − | 4.48115i | −0.334937 | − | 0.193376i | ||||
\(538\) | 4.05659i | 0.174892i | ||||||||
\(539\) | 17.4248 | − | 13.4689i | 0.750541 | − | 0.580147i | ||||
\(540\) | −6.80911 | −0.293018 | ||||||||
\(541\) | −14.2027 | − | 8.19993i | −0.610622 | − | 0.352543i | 0.162587 | − | 0.986694i | \(-0.448016\pi\) |
−0.773209 | + | 0.634152i | \(0.781349\pi\) | |||||||
\(542\) | 1.93854 | + | 3.35764i | 0.0832672 | + | 0.144223i | ||||
\(543\) | −8.72442 | − | 15.1111i | −0.374401 | − | 0.648481i | ||||
\(544\) | 21.3217 | − | 1.29157i | 0.914161 | − | 0.0553758i | ||||
\(545\) | 37.3885 | 1.60155 | ||||||||
\(546\) | −0.0821769 | − | 1.22064i | −0.00351684 | − | 0.0522386i | ||||
\(547\) | − | 15.8926i | − | 0.679519i | −0.940512 | − | 0.339759i | \(-0.889654\pi\) | ||
0.940512 | − | 0.339759i | \(-0.110346\pi\) | |||||||
\(548\) | 9.80854 | − | 16.9889i | 0.419000 | − | 0.725729i | ||||
\(549\) | 6.80373 | − | 3.92813i | 0.290376 | − | 0.167649i | ||||
\(550\) | 15.1378 | − | 8.73980i | 0.645477 | − | 0.372666i | ||||
\(551\) | 26.7318 | + | 15.4336i | 1.13881 | + | 0.657494i | ||||
\(552\) | −6.47770 | −0.275709 | ||||||||
\(553\) | 8.32428 | + | 4.08677i | 0.353984 | + | 0.173787i | ||||
\(554\) | − | 12.0414i | − | 0.511590i | ||||||
\(555\) | 40.9374 | + | 23.6352i | 1.73770 | + | 1.00326i | ||||
\(556\) | −2.41910 | + | 1.39667i | −0.102593 | + | 0.0592318i | ||||
\(557\) | −9.45205 | − | 16.3714i | −0.400496 | − | 0.693680i | 0.593290 | − | 0.804989i | \(-0.297829\pi\) |
−0.993786 | + | 0.111309i | \(0.964496\pi\) | |||||||
\(558\) | 1.60312 | + | 0.925561i | 0.0678655 | + | 0.0391821i | ||||
\(559\) | 3.13883 | 0.132758 | ||||||||
\(560\) | 21.0257 | − | 14.1029i | 0.888499 | − | 0.595956i | ||||
\(561\) | −7.15351 | − | 10.8215i | −0.302021 | − | 0.456885i | ||||
\(562\) | −7.85435 | + | 13.6041i | −0.331316 | + | 0.573856i | ||||
\(563\) | 0.762601 | + | 1.32086i | 0.0321398 | + | 0.0556678i | 0.881648 | − | 0.471908i | \(-0.156434\pi\) |
−0.849508 | + | 0.527576i | \(0.823101\pi\) | |||||||
\(564\) | −12.9881 | + | 7.49871i | −0.546899 | + | 0.315752i | ||||
\(565\) | −12.2071 | + | 21.1432i | −0.513555 | + | 0.889503i | ||||
\(566\) | − | 15.3720i | − | 0.646135i | ||||||
\(567\) | −1.47380 | − | 2.19725i | −0.0618936 | − | 0.0922760i | ||||
\(568\) | 8.02921i | 0.336898i | ||||||||
\(569\) | 18.0752 | − | 31.3072i | 0.757753 | − | 1.31247i | −0.186241 | − | 0.982504i | \(-0.559631\pi\) |
0.943994 | − | 0.329962i | \(-0.107036\pi\) | |||||||
\(570\) | 3.66057 | + | 6.34029i | 0.153324 | + | 0.265565i | ||||
\(571\) | 4.95620 | − | 2.86147i | 0.207411 | − | 0.119749i | −0.392697 | − | 0.919668i | \(-0.628458\pi\) |
0.600107 | + | 0.799919i | \(0.295124\pi\) | |||||||
\(572\) | 4.14093 | + | 2.39077i | 0.173141 | + | 0.0999630i | ||||
\(573\) | 2.11649i | 0.0884176i | ||||||||
\(574\) | 8.13368 | + | 3.99319i | 0.339493 | + | 0.166673i | ||||
\(575\) | − | 35.0906i | − | 1.46338i | ||||||
\(576\) | −1.06444 | + | 1.84366i | −0.0443516 | + | 0.0768192i | ||||
\(577\) | 7.35989 | + | 12.7477i | 0.306396 | + | 0.530694i | 0.977571 | − | 0.210605i | \(-0.0675434\pi\) |
−0.671175 | + | 0.741299i | \(0.734210\pi\) | |||||||
\(578\) | −8.85534 | + | 1.07679i | −0.368334 | + | 0.0447884i | ||||
\(579\) | 11.8888 | − | 20.5920i | 0.494083 | − | 0.855776i | ||||
\(580\) | 59.4763 | 2.46962 | ||||||||
\(581\) | −26.9024 | + | 1.81115i | −1.11610 | + | 0.0751390i | ||||
\(582\) | 2.61409 | 0.108357 | ||||||||
\(583\) | 13.0011 | + | 7.50617i | 0.538449 | + | 0.310874i | ||||
\(584\) | −18.6200 | + | 10.7503i | −0.770501 | + | 0.444849i | ||||
\(585\) | −3.01299 | + | 1.73955i | −0.124572 | + | 0.0719216i | ||||
\(586\) | 0.338980 | − | 0.587131i | 0.0140031 | − | 0.0242542i | ||||
\(587\) | 0.254477 | 0.0105034 | 0.00525170 | − | 0.999986i | \(-0.498328\pi\) | ||||
0.00525170 | + | 0.999986i | \(0.498328\pi\) | |||||||
\(588\) | 11.1699 | + | 4.58042i | 0.460638 | + | 0.188893i | ||||
\(589\) | 12.4663i | 0.513663i | ||||||||
\(590\) | 22.9308 | + | 13.2391i | 0.944046 | + | 0.545045i | ||||
\(591\) | −10.1696 | − | 17.6142i | −0.418321 | − | 0.724553i | ||||
\(592\) | 25.1311 | − | 14.5094i | 1.03288 | − | 0.596334i | ||||
\(593\) | 5.80934 | − | 10.0621i | 0.238561 | − | 0.413200i | −0.721741 | − | 0.692164i | \(-0.756658\pi\) |
0.960302 | + | 0.278964i | \(0.0899910\pi\) | |||||||
\(594\) | −1.65095 | −0.0677391 | ||||||||
\(595\) | −34.2520 | + | 26.1100i | −1.40419 | + | 1.07041i | ||||
\(596\) | 8.38207 | 0.343343 | ||||||||
\(597\) | −8.97568 | + | 15.5463i | −0.367350 | + | 0.636269i | ||||
\(598\) | −1.32722 | + | 0.766272i | −0.0542741 | + | 0.0313352i | ||||
\(599\) | −0.898032 | − | 1.55544i | −0.0366926 | − | 0.0635534i | 0.847096 | − | 0.531440i | \(-0.178349\pi\) |
−0.883789 | + | 0.467887i | \(0.845016\pi\) | |||||||
\(600\) | 17.9208 | + | 10.3466i | 0.731615 | + | 0.422398i | ||||
\(601\) | − | 21.7215i | − | 0.886038i | −0.896512 | − | 0.443019i | \(-0.853907\pi\) | ||
0.896512 | − | 0.443019i | \(-0.146093\pi\) | |||||||
\(602\) | 2.17934 | − | 4.43907i | 0.0888233 | − | 0.180923i | ||||
\(603\) | −3.30467 | −0.134576 | ||||||||
\(604\) | −9.72135 | + | 16.8379i | −0.395556 | + | 0.685123i | ||||
\(605\) | 3.76550 | − | 2.17401i | 0.153089 | − | 0.0883862i | ||||
\(606\) | 4.74507 | − | 2.73957i | 0.192755 | − | 0.111287i | ||||
\(607\) | −6.57697 | − | 3.79722i | −0.266951 | − | 0.154124i | 0.360550 | − | 0.932740i | \(-0.382589\pi\) |
−0.627501 | + | 0.778615i | \(0.715922\pi\) | |||||||
\(608\) | 18.3079 | 0.742482 | ||||||||
\(609\) | 12.8733 | + | 19.1926i | 0.521653 | + | 0.777723i | ||||
\(610\) | −16.2761 | −0.658999 | ||||||||
\(611\) | −3.83145 | + | 6.63626i | −0.155004 | + | 0.268474i | ||||
\(612\) | 3.17659 | − | 6.36194i | 0.128406 | − | 0.257166i | ||||
\(613\) | −17.6575 | − | 30.5837i | −0.713180 | − | 1.23526i | −0.963657 | − | 0.267141i | \(-0.913921\pi\) |
0.250478 | − | 0.968122i | \(-0.419412\pi\) | |||||||
\(614\) | 7.17515 | − | 12.4277i | 0.289566 | − | 0.501542i | ||||
\(615\) | − | 25.7677i | − | 1.03905i | ||||||
\(616\) | 13.5113 | − | 9.06265i | 0.544388 | − | 0.365145i | ||||
\(617\) | − | 28.3849i | − | 1.14273i | −0.820695 | − | 0.571367i | \(-0.806413\pi\) | ||
0.820695 | − | 0.571367i | \(-0.193587\pi\) | |||||||
\(618\) | −1.78722 | − | 1.03185i | −0.0718924 | − | 0.0415071i | ||||
\(619\) | −37.9247 | + | 21.8959i | −1.52432 | + | 0.880069i | −0.524739 | + | 0.851263i | \(0.675837\pi\) |
−0.999585 | + | 0.0288058i | \(0.990830\pi\) | |||||||
\(620\) | 12.0103 | + | 20.8024i | 0.482344 | + | 0.835444i | ||||
\(621\) | −1.65715 | + | 2.87027i | −0.0664992 | + | 0.115180i | ||||
\(622\) | 0.922293i | 0.0369806i | ||||||||
\(623\) | 1.29821 | − | 2.64430i | 0.0520115 | − | 0.105942i | ||||
\(624\) | 2.13579i | 0.0854999i | ||||||||
\(625\) | −17.0799 | + | 29.5832i | −0.683194 | + | 1.18333i | ||||
\(626\) | −3.02798 | + | 1.74820i | −0.121022 | + | 0.0698723i | ||||
\(627\) | −5.55909 | − | 9.62863i | −0.222009 | − | 0.384530i | ||||
\(628\) | 20.0077 | − | 34.6543i | 0.798394 | − | 1.38286i | ||||
\(629\) | −41.1812 | + | 27.2226i | −1.64200 | + | 1.08544i | ||||
\(630\) | 0.368182 | + | 5.46891i | 0.0146687 | + | 0.217887i | ||||
\(631\) | −35.7358 | −1.42262 | −0.711309 | − | 0.702879i | \(-0.751897\pi\) | ||||
−0.711309 | + | 0.702879i | \(0.751897\pi\) | |||||||
\(632\) | 5.93264 | + | 3.42521i | 0.235988 | + | 0.136248i | ||||
\(633\) | −0.930363 | − | 1.61144i | −0.0369786 | − | 0.0640489i | ||||
\(634\) | −4.02728 | + | 2.32515i | −0.159944 | + | 0.0923436i | ||||
\(635\) | −66.4503 | − | 38.3651i | −2.63700 | − | 1.52247i | ||||
\(636\) | 8.22924i | 0.326311i | ||||||||
\(637\) | 6.11278 | − | 0.826805i | 0.242197 | − | 0.0327592i | ||||
\(638\) | 14.4207 | 0.570920 | ||||||||
\(639\) | 3.55774 | + | 2.05406i | 0.140742 | + | 0.0812575i | ||||
\(640\) | 39.2473 | − | 22.6595i | 1.55139 | − | 0.895694i | ||||
\(641\) | 33.1558 | − | 19.1425i | 1.30958 | − | 0.756084i | 0.327550 | − | 0.944834i | \(-0.393777\pi\) |
0.982025 | + | 0.188750i | \(0.0604437\pi\) | |||||||
\(642\) | 0.503251 | − | 0.871656i | 0.0198617 | − | 0.0344015i | ||||
\(643\) | − | 28.8295i | − | 1.13692i | −0.822709 | − | 0.568462i | \(-0.807539\pi\) | ||
0.822709 | − | 0.568462i | \(-0.192461\pi\) | |||||||
\(644\) | −1.01583 | − | 15.0890i | −0.0400293 | − | 0.594589i | ||||
\(645\) | −14.0631 | −0.553733 | ||||||||
\(646\) | −7.63163 | + | 0.462290i | −0.300262 | + | 0.0181886i | ||||
\(647\) | −16.8078 | − | 29.1119i | −0.660782 | − | 1.14451i | −0.980410 | − | 0.196965i | \(-0.936891\pi\) |
0.319628 | − | 0.947543i | \(-0.396442\pi\) | |||||||
\(648\) | −0.977235 | − | 1.69262i | −0.0383894 | − | 0.0664924i | ||||
\(649\) | −34.8237 | − | 20.1055i | −1.36695 | − | 0.789209i | ||||
\(650\) | 4.89575 | 0.192027 | ||||||||
\(651\) | −4.11323 | + | 8.37819i | −0.161210 | + | 0.328367i | ||||
\(652\) | 5.05567i | 0.197995i | ||||||||
\(653\) | −4.62911 | − | 2.67262i | −0.181151 | − | 0.104588i | 0.406682 | − | 0.913570i | \(-0.366686\pi\) |
−0.587833 | + | 0.808982i | \(0.700019\pi\) | |||||||
\(654\) | 2.48463 | + | 4.30351i | 0.0971567 | + | 0.168280i | ||||
\(655\) | −11.3489 | − | 19.6570i | −0.443440 | − | 0.768061i | ||||
\(656\) | −13.6992 | − | 7.90926i | −0.534865 | − | 0.308805i | ||||
\(657\) | 11.0007i | 0.429178i | ||||||||
\(658\) | 6.72506 | + | 10.0263i | 0.262170 | + | 0.390865i | ||||
\(659\) | 18.7631 | 0.730905 | 0.365453 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365453 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(660\) | −18.5528 | − | 10.7115i | −0.722169 | − | 0.416944i | ||||
\(661\) | −1.34834 | − | 2.33540i | −0.0524444 | − | 0.0908364i | 0.838611 | − | 0.544730i | \(-0.183368\pi\) |
−0.891056 | + | 0.453894i | \(0.850035\pi\) | |||||||
\(662\) | −3.45447 | − | 5.98332i | −0.134262 | − | 0.232548i | ||||
\(663\) | −0.219687 | − | 3.62666i | −0.00853192 | − | 0.140848i | ||||
\(664\) | −19.9184 | −0.772982 | ||||||||
\(665\) | −30.6560 | + | 20.5623i | −1.18879 | + | 0.797372i | ||||
\(666\) | 6.28266i | 0.243448i | ||||||||
\(667\) | 14.4749 | − | 25.0712i | 0.560470 | − | 0.970762i | ||||
\(668\) | −5.76185 | + | 3.32661i | −0.222933 | + | 0.128710i | ||||
\(669\) | −5.96863 | + | 3.44599i | −0.230761 | + | 0.133230i | ||||
\(670\) | 5.92914 | + | 3.42319i | 0.229063 | + | 0.132249i | ||||
\(671\) | 24.7176 | 0.954210 | ||||||||
\(672\) | 12.3041 | + | 6.04066i | 0.474643 | + | 0.233024i | ||||
\(673\) | 25.0509i | 0.965642i | 0.875719 | + | 0.482821i | \(0.160388\pi\) | ||||
−0.875719 | + | 0.482821i | \(0.839612\pi\) | |||||||
\(674\) | 8.42551 | + | 4.86447i | 0.324539 | + | 0.187372i | ||||
\(675\) | 9.16915 | − | 5.29381i | 0.352921 | − | 0.203759i | ||||
\(676\) | −10.5406 | − | 18.2569i | −0.405408 | − | 0.702187i | ||||
\(677\) | −26.6177 | − | 15.3677i | −1.02300 | − | 0.590630i | −0.108029 | − | 0.994148i | \(-0.534454\pi\) |
−0.914972 | + | 0.403518i | \(0.867787\pi\) | |||||||
\(678\) | −3.24485 | −0.124618 | ||||||||
\(679\) | 0.885330 | + | 13.1505i | 0.0339758 | + | 0.504671i | ||||
\(680\) | −26.5410 | + | 17.5448i | −1.01780 | + | 0.672813i | ||||
\(681\) | 1.81215 | − | 3.13873i | 0.0694416 | − | 0.120276i | ||||
\(682\) | 2.91202 | + | 5.04377i | 0.111507 | + | 0.193136i | ||||
\(683\) | 32.4078 | − | 18.7107i | 1.24005 | − | 0.715944i | 0.270946 | − | 0.962594i | \(-0.412663\pi\) |
0.969104 | + | 0.246651i | \(0.0793300\pi\) | |||||||
\(684\) | 3.04730 | − | 5.27808i | 0.116516 | − | 0.201812i | ||||
\(685\) | 44.9080i | 1.71585i | ||||||||
\(686\) | 3.07490 | − | 9.21903i | 0.117400 | − | 0.351984i | ||||
\(687\) | 11.8417i | 0.451789i | ||||||||
\(688\) | −4.31659 | + | 7.47656i | −0.164569 | + | 0.285041i | ||||
\(689\) | 2.10236 | + | 3.64139i | 0.0800934 | + | 0.138726i | ||||
\(690\) | 5.94643 | − | 3.43317i | 0.226377 | − | 0.130699i | ||||
\(691\) | 43.7189 | + | 25.2411i | 1.66315 | + | 0.960218i | 0.971199 | + | 0.238268i | \(0.0765798\pi\) |
0.691946 | + | 0.721949i | \(0.256754\pi\) | |||||||
\(692\) | 29.3581i | 1.11603i | ||||||||
\(693\) | −0.559137 | − | 8.30532i | −0.0212398 | − | 0.315493i | ||||
\(694\) | 12.9860i | 0.492941i | ||||||||
\(695\) | 3.19729 | − | 5.53787i | 0.121280 | − | 0.210063i | ||||
\(696\) | 8.53595 | + | 14.7847i | 0.323554 | + | 0.560413i | ||||
\(697\) | 24.0754 | + | 12.0212i | 0.911922 | + | 0.455334i | ||||
\(698\) | −6.07785 | + | 10.5271i | −0.230050 | + | 0.398458i | ||||
\(699\) | 4.46487 | 0.168877 | ||||||||
\(700\) | −21.2907 | + | 43.3668i | −0.804714 | + | 1.63911i | ||||
\(701\) | −13.7310 | −0.518613 | −0.259306 | − | 0.965795i | \(-0.583494\pi\) | ||||
−0.259306 | + | 0.965795i | \(0.583494\pi\) | |||||||
\(702\) | −0.400453 | − | 0.231202i | −0.0151141 | − | 0.00872614i | ||||
\(703\) | −36.6416 | + | 21.1551i | −1.38197 | + | 0.797878i | ||||
\(704\) | −5.80056 | + | 3.34896i | −0.218617 | + | 0.126219i | ||||
\(705\) | 17.1663 | − | 29.7328i | 0.646519 | − | 1.11980i | ||||
\(706\) | 11.7617 | 0.442657 | ||||||||
\(707\) | 15.3888 | + | 22.9429i | 0.578757 | + | 0.862858i | ||||
\(708\) | − | 22.0422i | − | 0.828398i | ||||||
\(709\) | −1.47125 | − | 0.849427i | −0.0552540 | − | 0.0319009i | 0.472119 | − | 0.881535i | \(-0.343489\pi\) |
−0.527373 | + | 0.849634i | \(0.676823\pi\) | |||||||
\(710\) | −4.25547 | − | 7.37069i | −0.159705 | − | 0.276617i | ||||
\(711\) | 3.03542 | − | 1.75250i | 0.113837 | − | 0.0657239i | ||||
\(712\) | 1.08806 | − | 1.88457i | 0.0407766 | − | 0.0706272i | ||||
\(713\) | 11.6919 | 0.437864 | ||||||||
\(714\) | −5.28151 | − | 2.20736i | −0.197656 | − | 0.0826083i | ||||
\(715\) | −10.9460 | −0.409358 | ||||||||
\(716\) | 7.72840 | − | 13.3860i | 0.288824 | − | 0.500258i | ||||
\(717\) | 0.517691 | − | 0.298889i | 0.0193335 | − | 0.0111622i | ||||
\(718\) | 7.35164 | + | 12.7334i | 0.274361 | + | 0.475207i | ||||
\(719\) | −21.0367 | − | 12.1455i | −0.784535 | − | 0.452951i | 0.0535001 | − | 0.998568i | \(-0.482962\pi\) |
−0.838035 | + | 0.545616i | \(0.816296\pi\) | |||||||
\(720\) | − | 9.56909i | − | 0.356619i | ||||||
\(721\) | 4.58558 | − | 9.34031i | 0.170776 | − | 0.347851i | ||||
\(722\) | 3.41716 | 0.127173 | ||||||||
\(723\) | −1.02656 | + | 1.77806i | −0.0381783 | + | 0.0661267i | ||||
\(724\) | 26.0614 | − | 15.0466i | 0.968565 | − | 0.559201i | ||||
\(725\) | −80.0907 | + | 46.2404i | −2.97450 | + | 1.71733i | ||||
\(726\) | 0.500468 | + | 0.288945i | 0.0185741 | + | 0.0107238i | ||||
\(727\) | −21.9394 | −0.813689 | −0.406844 | − | 0.913497i | \(-0.633371\pi\) | ||||
−0.406844 | + | 0.913497i | \(0.633371\pi\) | |||||||
\(728\) | 4.54646 | − | 0.306080i | 0.168503 | − | 0.0113441i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 11.3952 | − | 19.7371i | 0.421757 | − | 0.730505i | ||||
\(731\) | 6.56072 | − | 13.1395i | 0.242657 | − | 0.485982i | ||||
\(732\) | 6.77465 | + | 11.7340i | 0.250398 | + | 0.433702i | ||||
\(733\) | 3.31674 | − | 5.74476i | 0.122507 | − | 0.212188i | −0.798249 | − | 0.602328i | \(-0.794240\pi\) |
0.920756 | + | 0.390140i | \(0.127573\pi\) | |||||||
\(734\) | 8.63387i | 0.318682i | ||||||||
\(735\) | −27.3874 | + | 3.70438i | −1.01020 | + | 0.136638i | ||||
\(736\) | − | 17.1706i | − | 0.632916i | ||||||
\(737\) | −9.00425 | − | 5.19860i | −0.331676 | − | 0.191493i | ||||
\(738\) | 2.96592 | − | 1.71237i | 0.109177 | − | 0.0630334i | ||||
\(739\) | 11.1509 | + | 19.3140i | 0.410194 | + | 0.710477i | 0.994911 | − | 0.100761i | \(-0.0321276\pi\) |
−0.584717 | + | 0.811238i | \(0.698794\pi\) | |||||||
\(740\) | −40.7625 | + | 70.6026i | −1.49846 | + | 2.59540i | ||||
\(741\) | − | 3.11402i | − | 0.114397i | ||||||
\(742\) | 6.60952 | − | 0.444971i | 0.242643 | − | 0.0163354i | ||||
\(743\) | 31.1925i | 1.14434i | 0.820134 | + | 0.572171i | \(0.193899\pi\) | ||||
−0.820134 | + | 0.572171i | \(0.806101\pi\) | |||||||
\(744\) | −3.44739 | + | 5.97106i | −0.126387 | + | 0.218910i | ||||
\(745\) | −16.6177 | + | 9.59424i | −0.608826 | + | 0.351506i | ||||
\(746\) | 3.46279 | + | 5.99772i | 0.126782 | + | 0.219592i | ||||
\(747\) | −5.09559 | + | 8.82582i | −0.186438 | + | 0.322920i | ||||
\(748\) | 18.6633 | − | 12.3373i | 0.682399 | − | 0.451096i | ||||
\(749\) | 4.55543 | + | 2.23647i | 0.166452 | + | 0.0817187i | ||||
\(750\) | −11.5761 | −0.422698 | ||||||||
\(751\) | −8.02312 | − | 4.63215i | −0.292768 | − | 0.169030i | 0.346422 | − | 0.938079i | \(-0.387397\pi\) |
−0.639189 | + | 0.769049i | \(0.720730\pi\) | |||||||
\(752\) | −10.5382 | − | 18.2527i | −0.384289 | − | 0.665607i | ||||
\(753\) | 5.18455 | − | 2.99330i | 0.188936 | − | 0.109082i | ||||
\(754\) | 3.49788 | + | 2.01950i | 0.127385 | + | 0.0735458i | ||||
\(755\) | − | 44.5088i | − | 1.61984i | ||||||
\(756\) | 3.78949 | − | 2.54178i | 0.137822 | − | 0.0924436i | ||||
\(757\) | −26.2641 | −0.954584 | −0.477292 | − | 0.878745i | \(-0.658382\pi\) | ||||
−0.477292 | + | 0.878745i | \(0.658382\pi\) | |||||||
\(758\) | −3.21345 | − | 1.85529i | −0.116718 | − | 0.0673871i | ||||
\(759\) | −9.03050 | + | 5.21376i | −0.327786 | + | 0.189248i | ||||
\(760\) | −23.6153 | + | 13.6343i | −0.856618 | + | 0.494569i | ||||
\(761\) | −1.27087 | + | 2.20122i | −0.0460691 | + | 0.0797940i | −0.888140 | − | 0.459572i | \(-0.848003\pi\) |
0.842071 | + | 0.539366i | \(0.181336\pi\) | |||||||
\(762\) | − | 10.1981i | − | 0.369439i | ||||||
\(763\) | −20.8079 | + | 13.9568i | −0.753297 | + | 0.505270i | ||||
\(764\) | −3.65020 | −0.132060 | ||||||||
\(765\) | 0.984275 | + | 16.2487i | 0.0355865 | + | 0.587474i | ||||
\(766\) | −4.80064 | − | 8.31496i | −0.173454 | − | 0.300432i | ||||
\(767\) | −5.63122 | − | 9.75355i | −0.203331 | − | 0.352180i | ||||
\(768\) | 1.52899 | + | 0.882765i | 0.0551728 | + | 0.0318540i | ||||
\(769\) | 20.9202 | 0.754403 | 0.377201 | − | 0.926131i | \(-0.376886\pi\) | ||||
0.377201 | + | 0.926131i | \(0.376886\pi\) | |||||||
\(770\) | −7.60001 | + | 15.4804i | −0.273885 | + | 0.557874i | ||||
\(771\) | 8.43136i | 0.303648i | ||||||||
\(772\) | 35.5140 | + | 20.5040i | 1.27818 | + | 0.737957i | ||||
\(773\) | 1.92270 | + | 3.33021i | 0.0691546 | + | 0.119779i | 0.898529 | − | 0.438913i | \(-0.144636\pi\) |
−0.829375 | + | 0.558693i | \(0.811303\pi\) | |||||||
\(774\) | −0.934553 | − | 1.61869i | −0.0335918 | − | 0.0581827i | ||||
\(775\) | −32.3460 | − | 18.6750i | −1.16190 | − | 0.670825i | ||||
\(776\) | 9.73655i | 0.349522i | ||||||||
\(777\) | −31.6058 | + | 2.12779i | −1.13385 | + | 0.0763340i | ||||
\(778\) | −10.8893 | −0.390399 | ||||||||
\(779\) | 19.9738 | + | 11.5319i | 0.715635 | + | 0.413172i | ||||
\(780\) | −3.00011 | − | 5.19635i | −0.107421 | − | 0.186059i | ||||
\(781\) | 6.46254 | + | 11.1934i | 0.231248 | + | 0.400533i | ||||
\(782\) | 0.433573 | + | 7.15755i | 0.0155045 | + | 0.255954i | ||||
\(783\) | 8.73480 | 0.312156 | ||||||||
\(784\) | −6.43702 | + | 15.6974i | −0.229894 | + | 0.560622i | ||||
\(785\) | 91.6044i | 3.26950i | ||||||||
\(786\) | 1.50837 | − | 2.61258i | 0.0538019 | − | 0.0931877i | ||||
\(787\) | −4.32323 | + | 2.49602i | −0.154107 | + | 0.0889735i | −0.575070 | − | 0.818104i | \(-0.695025\pi\) |
0.420964 | + | 0.907077i | \(0.361692\pi\) | |||||||
\(788\) | 30.3784 | − | 17.5390i | 1.08218 | − | 0.624800i | ||||
\(789\) | 5.34582 | + | 3.08641i | 0.190316 | + | 0.109879i | ||||
\(790\) | −7.26143 | −0.258350 | ||||||||
\(791\) | −1.09895 | − | 16.3237i | −0.0390743 | − | 0.580403i | ||||
\(792\) | − | 6.14919i | − | 0.218502i | ||||||
\(793\) | 5.99548 | + | 3.46149i | 0.212906 | + | 0.122921i | ||||
\(794\) | 3.69419 | − | 2.13284i | 0.131102 | − | 0.0756917i | ||||
\(795\) | −9.41931 | − | 16.3147i | −0.334068 | − | 0.578624i | ||||
\(796\) | −26.8120 | − | 15.4799i | −0.950324 | − | 0.548670i | ||||
\(797\) | 9.44898 | 0.334700 | 0.167350 | − | 0.985898i | \(-0.446479\pi\) | ||||
0.167350 | + | 0.985898i | \(0.446479\pi\) | |||||||
\(798\) | −4.40399 | − | 2.16212i | −0.155900 | − | 0.0765382i | ||||
\(799\) | 19.7718 | + | 29.9099i | 0.699475 | + | 1.05814i | ||||
\(800\) | −27.4260 | + | 47.5031i | −0.969654 | + | 1.67949i | ||||
\(801\) | −0.556702 | − | 0.964235i | −0.0196701 | − | 0.0340696i | ||||
\(802\) | 13.1991 | − | 7.62048i | 0.466075 | − | 0.269088i | ||||
\(803\) | −17.3053 | + | 29.9737i | −0.610691 | + | 1.05775i | ||||
\(804\) | − | 5.69939i | − | 0.201002i | ||||||
\(805\) | 19.2850 | + | 28.7516i | 0.679706 | + | 1.01336i | ||||
\(806\) | 1.63122i | 0.0574573i | ||||||||
\(807\) | −3.86533 | + | 6.69495i | −0.136066 | + | 0.235674i | ||||
\(808\) | 10.2039 | + | 17.6737i | 0.358973 | + | 0.621759i | ||||
\(809\) | 11.0705 | − | 6.39154i | 0.389217 | − | 0.224714i | −0.292604 | − | 0.956234i | \(-0.594522\pi\) |
0.681821 | + | 0.731519i | \(0.261188\pi\) | |||||||
\(810\) | 1.79417 | + | 1.03587i | 0.0630408 | + | 0.0363966i | ||||
\(811\) | 39.3249i | 1.38088i | 0.723388 | + | 0.690442i | \(0.242584\pi\) | ||||
−0.723388 | + | 0.690442i | \(0.757416\pi\) | |||||||
\(812\) | −33.1005 | + | 22.2019i | −1.16160 | + | 0.779135i | ||||
\(813\) | 7.38857i | 0.259128i | ||||||||
\(814\) | −9.88331 | + | 17.1184i | −0.346410 | + | 0.600000i | ||||
\(815\) | −5.78680 | − | 10.0230i | −0.202703 | − | 0.351091i | ||||
\(816\) | 8.94066 | + | 4.46418i | 0.312986 | + | 0.156278i | ||||
\(817\) | 6.29368 | − | 10.9010i | 0.220188 | − | 0.381377i | ||||
\(818\) | −10.4192 | −0.364298 | ||||||||
\(819\) | 1.02747 | − | 2.09284i | 0.0359027 | − | 0.0731297i | ||||
\(820\) | 44.4402 | 1.55192 | ||||||||
\(821\) | −16.3585 | − | 9.44460i | −0.570917 | − | 0.329619i | 0.186599 | − | 0.982436i | \(-0.440254\pi\) |
−0.757515 | + | 0.652817i | \(0.773587\pi\) | |||||||
\(822\) | −5.16902 | + | 2.98433i | −0.180290 | + | 0.104091i | ||||
\(823\) | 4.20168 | − | 2.42584i | 0.146461 | − | 0.0845595i | −0.424979 | − | 0.905203i | \(-0.639718\pi\) |
0.571440 | + | 0.820644i | \(0.306385\pi\) | |||||||
\(824\) | 3.84328 | − | 6.65675i | 0.133887 | − | 0.231899i | ||||
\(825\) | 33.3110 | 1.15974 | ||||||||
\(826\) | −17.7038 | + | 1.19187i | −0.615993 | + | 0.0414703i | ||||
\(827\) | − | 33.5279i | − | 1.16588i | −0.812516 | − | 0.582939i | \(-0.801903\pi\) | ||
0.812516 | − | 0.582939i | \(-0.198097\pi\) | |||||||
\(828\) | −4.95021 | − | 2.85800i | −0.172032 | − | 0.0993225i | ||||
\(829\) | −18.2842 | − | 31.6692i | −0.635036 | − | 1.09992i | −0.986507 | − | 0.163717i | \(-0.947652\pi\) |
0.351471 | − | 0.936199i | \(-0.385682\pi\) | |||||||
\(830\) | 18.2847 | − | 10.5567i | 0.634673 | − | 0.366428i | ||||
\(831\) | 11.4737 | − | 19.8730i | 0.398018 | − | 0.689388i | ||||
\(832\) | −1.87598 | −0.0650378 | ||||||||
\(833\) | 9.31570 | − | 27.3170i | 0.322770 | − | 0.946477i | ||||
\(834\) | 0.849895 | 0.0294295 | ||||||||
\(835\) | 7.61536 | − | 13.1902i | 0.263540 | − | 0.456466i | ||||
\(836\) | 16.6060 | − | 9.58748i | 0.574331 | − | 0.331590i | ||||
\(837\) | 1.76385 | + | 3.05508i | 0.0609676 | + | 0.105599i | ||||
\(838\) | −4.52432 | − | 2.61212i | −0.156290 | − | 0.0902341i | ||||
\(839\) | 3.39453i | 0.117192i | 0.998282 | + | 0.0585961i | \(0.0186624\pi\) | ||||
−0.998282 | + | 0.0585961i | \(0.981338\pi\) | |||||||
\(840\) | −20.3698 | + | 1.37135i | −0.702824 | + | 0.0473160i | ||||
\(841\) | −47.2967 | −1.63092 | ||||||||
\(842\) | 5.18392 | − | 8.97881i | 0.178650 | − | 0.309430i | ||||
\(843\) | −25.9255 | + | 14.9681i | −0.892922 | + | 0.515529i | ||||
\(844\) | 2.77916 | − | 1.60455i | 0.0956627 | − | 0.0552309i | ||||
\(845\) | 41.7941 | + | 24.1299i | 1.43776 | + | 0.830092i | ||||
\(846\) | 4.56309 | 0.156882 | ||||||||
\(847\) | −1.28408 | + | 2.61553i | −0.0441216 | + | 0.0898708i | ||||
\(848\) | −11.5648 | −0.397138 | ||||||||
\(849\) | 14.6473 | − | 25.3699i | 0.502695 | − | 0.870693i | ||||
\(850\) | 10.2330 | − | 20.4942i | 0.350989 | − | 0.702945i | ||||
\(851\) | 19.8409 | + | 34.3655i | 0.680138 | + | 1.17803i | ||||
\(852\) | −3.54254 | + | 6.13585i | −0.121365 | + | 0.210211i | ||||
\(853\) | − | 55.1187i | − | 1.88723i | −0.331048 | − | 0.943614i | \(-0.607402\pi\) | ||
0.331048 | − | 0.943614i | \(-0.392598\pi\) | |||||||
\(854\) | 9.05816 | − | 6.07571i | 0.309964 | − | 0.207906i | ||||
\(855\) | 13.9519i | 0.477146i | ||||||||
\(856\) | 3.24661 | + | 1.87443i | 0.110967 | + | 0.0640668i | ||||
\(857\) | 30.7761 | − | 17.7686i | 1.05129 | − | 0.606964i | 0.128282 | − | 0.991738i | \(-0.459054\pi\) |
0.923011 | + | 0.384774i | \(0.125720\pi\) | |||||||
\(858\) | −0.727411 | − | 1.25991i | −0.0248334 | − | 0.0430127i | ||||
\(859\) | 8.85048 | − | 15.3295i | 0.301975 | − | 0.523035i | −0.674609 | − | 0.738176i | \(-0.735688\pi\) |
0.976583 | + | 0.215140i | \(0.0690209\pi\) | |||||||
\(860\) | − | 24.2539i | − | 0.827050i | ||||||
\(861\) | 9.61883 | + | 14.3405i | 0.327809 | + | 0.488724i | ||||
\(862\) | − | 14.0822i | − | 0.479643i | ||||||
\(863\) | 21.1654 | − | 36.6596i | 0.720479 | − | 1.24791i | −0.240329 | − | 0.970691i | \(-0.577255\pi\) |
0.960808 | − | 0.277215i | \(-0.0894113\pi\) | |||||||
\(864\) | 4.48667 | − | 2.59038i | 0.152639 | − | 0.0881264i | ||||
\(865\) | −33.6037 | − | 58.2034i | −1.14256 | − | 1.97897i | ||||
\(866\) | −3.88406 | + | 6.72739i | −0.131986 | + | 0.228606i | ||||
\(867\) | −15.6408 | − | 6.66073i | −0.531189 | − | 0.226210i | ||||
\(868\) | −14.4494 | − | 7.09388i | −0.490446 | − | 0.240782i | ||||
\(869\) | 11.0275 | 0.374083 | ||||||||
\(870\) | −15.6717 | − | 9.04808i | −0.531322 | − | 0.306759i | ||||
\(871\) | −1.45604 | − | 2.52194i | −0.0493362 | − | 0.0854528i | ||||
\(872\) | −16.0290 | + | 9.25438i | −0.542812 | + | 0.313393i | ||||
\(873\) | 4.31427 | + | 2.49084i | 0.146016 | + | 0.0843022i | ||||
\(874\) | 6.14582i | 0.207886i | ||||||||
\(875\) | −3.92054 | − | 58.2351i | −0.132539 | − | 1.96870i | ||||
\(876\) | −18.9723 | −0.641016 | ||||||||
\(877\) | 12.4124 | + | 7.16629i | 0.419136 | + | 0.241988i | 0.694708 | − | 0.719292i | \(-0.255534\pi\) |
−0.275571 | + | 0.961281i | \(0.588867\pi\) | |||||||
\(878\) | −8.28562 | + | 4.78371i | −0.279626 | + | 0.161442i | ||||
\(879\) | 1.11890 | − | 0.645998i | 0.0377396 | − | 0.0217890i | ||||
\(880\) | 15.0532 | − | 26.0730i | 0.507445 | − | 0.878920i | ||||
\(881\) | 23.7723i | 0.800910i | 0.916317 | + | 0.400455i | \(0.131148\pi\) | ||||
−0.916317 | + | 0.400455i | \(0.868852\pi\) | |||||||
\(882\) | −2.24640 | − | 2.90619i | −0.0756401 | − | 0.0978563i | ||||
\(883\) | 52.7233 | 1.77428 | 0.887141 | − | 0.461499i | \(-0.152688\pi\) | ||||
0.887141 | + | 0.461499i | \(0.152688\pi\) | |||||||
\(884\) | 6.25471 | − | 0.378882i | 0.210369 | − | 0.0127432i | ||||
\(885\) | 25.2299 | + | 43.6994i | 0.848093 | + | 1.46894i | ||||
\(886\) | −6.12928 | − | 10.6162i | −0.205917 | − | 0.356659i | ||||
\(887\) | 14.7128 | + | 8.49445i | 0.494008 | + | 0.285216i | 0.726236 | − | 0.687446i | \(-0.241268\pi\) |
−0.232228 | + | 0.972661i | \(0.574601\pi\) | |||||||
\(888\) | −23.4007 | −0.785276 | ||||||||
\(889\) | 51.3030 | − | 3.45386i | 1.72065 | − | 0.115839i | ||||
\(890\) | 2.30667i | 0.0773199i | ||||||||
\(891\) | −2.72471 | − | 1.57311i | −0.0912811 | − | 0.0527012i | ||||
\(892\) | −5.94312 | − | 10.2938i | −0.198990 | − | 0.344662i | ||||
\(893\) | 15.3649 | + | 26.6128i | 0.514167 | + | 0.890564i | ||||
\(894\) | −2.20864 | − | 1.27516i | −0.0738679 | − | 0.0426477i | ||||
\(895\) | 35.3842i | 1.18276i | ||||||||
\(896\) | −13.3838 | + | 27.2614i | −0.447123 | + | 0.910739i | ||||
\(897\) | −2.92058 | −0.0975154 | ||||||||
\(898\) | 9.44288 | + | 5.45185i | 0.315113 | + | 0.181931i | ||||
\(899\) | −15.4069 | − | 26.6855i | −0.513848 | − | 0.890011i | ||||
\(900\) | 9.12997 | + | 15.8136i | 0.304332 | + | 0.527119i | ||||
\(901\) | 19.6376 | − | 1.18956i | 0.654223 | − | 0.0396299i | ||||
\(902\) | 10.7750 | 0.358769 | ||||||||
\(903\) | 7.82655 | − | 5.24961i | 0.260451 | − | 0.174696i | ||||
\(904\) | − | 12.0859i | − | 0.401972i | ||||||
\(905\) | −34.4450 | + | 59.6605i | −1.14499 | + | 1.98318i | ||||
\(906\) | 5.12307 | − | 2.95780i | 0.170202 | − | 0.0982664i | ||||
\(907\) | 19.0038 | − | 10.9719i | 0.631012 | − | 0.364315i | −0.150132 | − | 0.988666i | \(-0.547970\pi\) |
0.781144 | + | 0.624351i | \(0.214637\pi\) | |||||||
\(908\) | 5.41321 | + | 3.12532i | 0.179644 | + | 0.103717i | ||||
\(909\) | 10.4416 | 0.346327 | ||||||||
\(910\) | −4.01136 | + | 2.69059i | −0.132975 | + | 0.0891923i | ||||
\(911\) | 12.2367i | 0.405421i | 0.979239 | + | 0.202711i | \(0.0649751\pi\) | ||||
−0.979239 | + | 0.202711i | \(0.935025\pi\) | |||||||
\(912\) | 7.41747 | + | 4.28248i | 0.245617 | + | 0.141807i | ||||
\(913\) | −27.7680 | + | 16.0319i | −0.918986 | + | 0.530577i | ||||
\(914\) | −4.76471 | − | 8.25271i | −0.157602 | − | 0.272976i | ||||
\(915\) | −26.8619 | − | 15.5087i | −0.888027 | − | 0.512703i | ||||
\(916\) | −20.4228 | −0.674787 | ||||||||
\(917\) | 13.6538 | + | 6.70327i | 0.450889 | + | 0.221362i | ||||
\(918\) | −1.80486 | + | 1.19309i | −0.0595691 | + | 0.0393779i | ||||
\(919\) | 12.4392 | − | 21.5454i | 0.410332 | − | 0.710717i | −0.584594 | − | 0.811326i | \(-0.698746\pi\) |
0.994926 | + | 0.100610i | \(0.0320793\pi\) | |||||||
\(920\) | 12.7874 | + | 22.1484i | 0.421587 | + | 0.730210i | ||||
\(921\) | 23.6836 | − | 13.6737i | 0.780402 | − | 0.450565i | ||||
\(922\) | 6.14071 | − | 10.6360i | 0.202233 | − | 0.350279i | ||||
\(923\) | 3.62010i | 0.119157i | ||||||||
\(924\) | 14.3238 | − | 0.964314i | 0.471217 | − | 0.0317236i | ||||
\(925\) | − | 126.765i | − | 4.16800i | ||||||
\(926\) | 2.97209 | − | 5.14780i | 0.0976688 | − | 0.169167i | ||||
\(927\) | −1.96640 | − | 3.40591i | −0.0645852 | − | 0.111865i | ||||
\(928\) | −39.1901 | + | 22.6264i | −1.28648 | + | 0.742749i | ||||
\(929\) | −11.5459 | − | 6.66604i | −0.378809 | − | 0.218706i | 0.298491 | − | 0.954412i | \(-0.403517\pi\) |
−0.677300 | + | 0.735707i | \(0.736850\pi\) | |||||||
\(930\) | − | 7.30845i | − | 0.239653i | ||||||
\(931\) | 9.38532 | − | 22.8872i | 0.307591 | − | 0.750097i | ||||
\(932\) | 7.70033i | 0.252233i | ||||||||
\(933\) | −0.878811 | + | 1.52215i | −0.0287710 | + | 0.0498328i | ||||
\(934\) | 10.4542 | + | 18.1072i | 0.342073 | + | 0.592487i | ||||
\(935\) | −22.8792 | + | 45.8214i | −0.748229 | + | 1.49852i | ||||
\(936\) | 0.861145 | − | 1.49155i | 0.0281474 | − | 0.0487527i | ||||
\(937\) | −1.81301 | −0.0592285 | −0.0296142 | − | 0.999561i | \(-0.509428\pi\) | ||||
−0.0296142 | + | 0.999561i | \(0.509428\pi\) | |||||||
\(938\) | −4.57760 | + | 0.308177i | −0.149464 | + | 0.0100623i | ||||
\(939\) | −6.66314 | −0.217443 | ||||||||
\(940\) | 51.2787 | + | 29.6058i | 1.67253 | + | 0.965634i | ||||
\(941\) | 15.7681 | − | 9.10373i | 0.514026 | − | 0.296773i | −0.220461 | − | 0.975396i | \(-0.570756\pi\) |
0.734487 | + | 0.678623i | \(0.237423\pi\) | |||||||
\(942\) | −10.5439 | + | 6.08751i | −0.343538 | + | 0.198342i | ||||
\(943\) | 10.8155 | − | 18.7330i | 0.352202 | − | 0.610031i | ||||
\(944\) | 30.9767 | 1.00821 | ||||||||
\(945\) | −4.60343 | + | 9.37666i | −0.149750 | + | 0.305023i | ||||
\(946\) | − | 5.88062i | − | 0.191195i | ||||||
\(947\) | −45.3198 | − | 26.1654i | −1.47270 | − | 0.850262i | −0.473168 | − | 0.880972i | \(-0.656890\pi\) |
−0.999528 | + | 0.0307102i | \(0.990223\pi\) | |||||||
\(948\) | 3.02245 | + | 5.23504i | 0.0981646 | + | 0.170026i | ||||
\(949\) | −8.39514 | + | 4.84694i | −0.272518 | + | 0.157338i | ||||
\(950\) | 9.81650 | − | 17.0027i | 0.318489 | − | 0.551640i | ||||
\(951\) | −8.86213 | −0.287374 | ||||||||
\(952\) | 8.22163 | − | 19.6718i | 0.266465 | − | 0.637566i | ||||
\(953\) | 14.5346 | 0.470823 | 0.235411 | − | 0.971896i | \(-0.424356\pi\) | ||||
0.235411 | + | 0.971896i | \(0.424356\pi\) | |||||||
\(954\) | 1.25191 | − | 2.16837i | 0.0405320 | − | 0.0702036i | ||||
\(955\) | 7.23663 | − | 4.17807i | 0.234172 | − | 0.135199i | ||||
\(956\) | 0.515478 | + | 0.892835i | 0.0166718 | + | 0.0288763i | ||||
\(957\) | 23.7998 | + | 13.7408i | 0.769338 | + | 0.444177i | ||||
\(958\) | − | 7.83733i | − | 0.253213i | ||||||
\(959\) | −16.7637 | − | 24.9927i | −0.541329 | − | 0.807058i | ||||
\(960\) | 8.40505 | 0.271272 | ||||||||
\(961\) | −9.27767 | + | 16.0694i | −0.299280 | + | 0.518367i | ||||
\(962\) | −4.79459 | + | 2.76816i | −0.154584 | + | 0.0892489i | ||||
\(963\) | 1.66112 | − | 0.959050i | 0.0535289 | − | 0.0309049i | ||||
\(964\) | −3.06653 | − | 1.77046i | −0.0987662 | − | 0.0570227i | ||||
\(965\) | −93.8769 | −3.02201 | ||||||||
\(966\) | −2.02781 | + | 4.13042i | −0.0652437 | + | 0.132894i | ||||
\(967\) | 33.4397 | 1.07535 | 0.537673 | − | 0.843153i | \(-0.319303\pi\) | ||||
0.537673 | + | 0.843153i | \(0.319303\pi\) | |||||||
\(968\) | −1.07622 | + | 1.86407i | −0.0345910 | + | 0.0599134i | ||||
\(969\) | −13.0357 | − | 6.50887i | −0.418766 | − | 0.209095i | ||||
\(970\) | −5.16036 | − | 8.93800i | −0.165689 | − | 0.286982i | ||||
\(971\) | −9.35752 | + | 16.2077i | −0.300297 | + | 0.520130i | −0.976203 | − | 0.216858i | \(-0.930419\pi\) |
0.675906 | + | 0.736988i | \(0.263753\pi\) | |||||||
\(972\) | − | 1.72465i | − | 0.0553181i | ||||||
\(973\) | 0.287840 | + | 4.27552i | 0.00922771 | + | 0.137067i | ||||
\(974\) | 1.33850i | 0.0428883i | ||||||||
\(975\) | 8.07991 | + | 4.66494i | 0.258764 | + | 0.149398i | ||||
\(976\) | −16.4903 | + | 9.52066i | −0.527840 | + | 0.304749i | ||||
\(977\) | 5.92714 | + | 10.2661i | 0.189626 | + | 0.328442i | 0.945126 | − | 0.326707i | \(-0.105939\pi\) |
−0.755499 | + | 0.655149i | \(0.772606\pi\) | |||||||
\(978\) | 0.769116 | − | 1.33215i | 0.0245936 | − | 0.0425974i | ||||
\(979\) | − | 3.50301i | − | 0.111957i | ||||||
\(980\) | −6.38876 | − | 47.2337i | −0.204081 | − | 1.50883i | ||||
\(981\) | 9.46996i | 0.302353i | ||||||||
\(982\) | 2.21102 | − | 3.82959i | 0.0705564 | − | 0.122207i | ||||
\(983\) | 14.8167 | − | 8.55441i | 0.472578 | − | 0.272843i | −0.244740 | − | 0.969589i | \(-0.578703\pi\) |
0.717318 | + | 0.696745i | \(0.245369\pi\) | |||||||
\(984\) | 6.37799 | + | 11.0470i | 0.203323 | + | 0.352166i | ||||
\(985\) | −40.1507 | + | 69.5431i | −1.27931 | + | 2.21583i | ||||
\(986\) | 15.7651 | − | 10.4214i | 0.502062 | − | 0.331885i | ||||
\(987\) | 1.54541 | + | 22.9553i | 0.0491910 | + | 0.730675i | ||||
\(988\) | 5.37060 | 0.170861 | ||||||||
\(989\) | −10.2238 | − | 5.90272i | −0.325098 | − | 0.187696i | ||||
\(990\) | 3.25906 | + | 5.64486i | 0.103580 | + | 0.179406i | ||||
\(991\) | −18.6242 | + | 10.7527i | −0.591616 | + | 0.341570i | −0.765736 | − | 0.643155i | \(-0.777625\pi\) |
0.174120 | + | 0.984724i | \(0.444292\pi\) | |||||||
\(992\) | −15.8276 | − | 9.13808i | −0.502527 | − | 0.290134i | ||||
\(993\) | − | 13.1664i | − | 0.417824i | ||||||
\(994\) | 5.11971 | + | 2.51350i | 0.162387 | + | 0.0797233i | ||||
\(995\) | 70.8740 | 2.24686 | ||||||||
\(996\) | −15.2214 | − | 8.78811i | −0.482310 | − | 0.278462i | ||||
\(997\) | 14.2408 | − | 8.22193i | 0.451011 | − | 0.260391i | −0.257246 | − | 0.966346i | \(-0.582815\pi\) |
0.708257 | + | 0.705955i | \(0.249482\pi\) | |||||||
\(998\) | −16.1054 | + | 9.29848i | −0.509809 | + | 0.294338i | ||||
\(999\) | −5.98645 | + | 10.3688i | −0.189403 | + | 0.328056i |
(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 | 357.2.p.a.16.16 | yes | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.15 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.15 | ✓ | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.16 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.15 | ✓ | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.16.16 | yes | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.67.15 | yes | 48 | 7.4 | even | 3 | inner | |
357.2.p.a.67.16 | yes | 48 | 119.67 | even | 6 | inner |