Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(117,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.117");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.j (of order \(6\), degree \(2\), not 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.5 | ||
Character | \(\chi\) | \(=\) | 392.325 |
Dual form | 392.3.j.e.117.5 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33557 | + | 1.48871i | −0.667786 | + | 0.744353i | ||||
\(3\) | −1.70138 | + | 2.94687i | −0.567126 | + | 0.982291i | 0.429722 | + | 0.902961i | \(0.358612\pi\) |
−0.996848 | + | 0.0793303i | \(0.974722\pi\) | |||||||
\(4\) | −0.432496 | − | 3.97655i | −0.108124 | − | 0.994137i | ||||
\(5\) | 2.15858 | + | 3.73877i | 0.431716 | + | 0.747754i | 0.997021 | − | 0.0771275i | \(-0.0245748\pi\) |
−0.565305 | + | 0.824882i | \(0.691242\pi\) | |||||||
\(6\) | −2.11472 | − | 6.46862i | −0.352453 | − | 1.07810i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.49755 | + | 4.66711i | 0.812193 | + | 0.583389i | ||||
\(9\) | −1.28938 | − | 2.23327i | −0.143264 | − | 0.248141i | ||||
\(10\) | −8.44888 | − | 1.77990i | −0.844888 | − | 0.177990i | ||||
\(11\) | 15.4899 | + | 8.94308i | 1.40817 | + | 0.813007i | 0.995212 | − | 0.0977432i | \(-0.0311624\pi\) |
0.412958 | + | 0.910750i | \(0.364496\pi\) | |||||||
\(12\) | 12.4542 | + | 5.49111i | 1.03785 | + | 0.457592i | ||||
\(13\) | 3.25607 | 0.250467 | 0.125233 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125233 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.6903 | −0.979350 | ||||||||
\(16\) | −15.6259 | + | 3.43968i | −0.976618 | + | 0.214980i | ||||
\(17\) | 13.6263 | + | 7.86717i | 0.801550 | + | 0.462775i | 0.844013 | − | 0.536323i | \(-0.180187\pi\) |
−0.0424631 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(18\) | 5.04674 | + | 1.06319i | 0.280375 | + | 0.0590659i | ||||
\(19\) | 0.778522 | + | 1.34844i | 0.0409748 | + | 0.0709705i | 0.885786 | − | 0.464095i | \(-0.153620\pi\) |
−0.844811 | + | 0.535065i | \(0.820287\pi\) | |||||||
\(20\) | 13.9338 | − | 10.2007i | 0.696692 | − | 0.510035i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −34.0014 | + | 11.1157i | −1.54552 | + | 0.505261i | ||||
\(23\) | 20.7069 | + | 35.8655i | 0.900301 | + | 1.55937i | 0.827103 | + | 0.562050i | \(0.189987\pi\) |
0.0731984 | + | 0.997317i | \(0.476679\pi\) | |||||||
\(24\) | −24.8082 | + | 11.2069i | −1.03367 | + | 0.466956i | ||||
\(25\) | 3.18105 | − | 5.50975i | 0.127242 | − | 0.220390i | ||||
\(26\) | −4.34871 | + | 4.84733i | −0.167258 | + | 0.186436i | ||||
\(27\) | −21.8499 | −0.809257 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.74374i | 0.129095i | 0.997915 | + | 0.0645473i | \(0.0205603\pi\) | ||||
−0.997915 | + | 0.0645473i | \(0.979440\pi\) | |||||||
\(30\) | 19.6199 | − | 21.8695i | 0.653996 | − | 0.728983i | ||||
\(31\) | 0.0145172 | + | 0.00838150i | 0.000468296 | + | 0.000270371i | 0.500234 | − | 0.865890i | \(-0.333247\pi\) |
−0.499766 | + | 0.866161i | \(0.666581\pi\) | |||||||
\(32\) | 15.7488 | − | 27.8563i | 0.492151 | − | 0.870510i | ||||
\(33\) | −52.7082 | + | 30.4311i | −1.59722 | + | 0.922155i | ||||
\(34\) | −29.9109 | + | 9.77845i | −0.879732 | + | 0.287602i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.32306 | + | 6.09316i | −0.231196 | + | 0.169254i | ||||
\(37\) | 1.16774 | − | 0.674194i | 0.0315605 | − | 0.0182215i | −0.484137 | − | 0.874992i | \(-0.660866\pi\) |
0.515697 | + | 0.856771i | \(0.327533\pi\) | |||||||
\(38\) | −3.04720 | − | 0.641947i | −0.0801895 | − | 0.0168933i | ||||
\(39\) | −5.53981 | + | 9.59523i | −0.142046 | + | 0.246031i | ||||
\(40\) | −3.42377 | + | 34.3672i | −0.0855944 | + | 0.859179i | ||||
\(41\) | − | 70.3018i | − | 1.71468i | −0.514753 | − | 0.857339i | \(-0.672116\pi\) | ||
0.514753 | − | 0.857339i | \(-0.327884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13.0380i | − | 0.303210i | −0.988441 | − | 0.151605i | \(-0.951556\pi\) | ||
0.988441 | − | 0.151605i | \(-0.0484442\pi\) | |||||||
\(44\) | 28.8633 | − | 65.4641i | 0.655984 | − | 1.48782i | ||||
\(45\) | 5.56646 | − | 9.64139i | 0.123699 | − | 0.214253i | ||||
\(46\) | −81.0487 | − | 17.0743i | −1.76193 | − | 0.371181i | ||||
\(47\) | −30.9797 | + | 17.8862i | −0.659144 | + | 0.380557i | −0.791951 | − | 0.610585i | \(-0.790934\pi\) |
0.132807 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(48\) | 16.4493 | − | 51.8998i | 0.342693 | − | 1.08124i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.95387 | + | 12.0943i | 0.0790774 | + | 0.241886i | ||||
\(51\) | −46.3671 | + | 26.7701i | −0.909160 | + | 0.524904i | ||||
\(52\) | −1.40824 | − | 12.9479i | −0.0270815 | − | 0.248998i | ||||
\(53\) | −39.7989 | − | 22.9779i | −0.750923 | − | 0.433546i | 0.0751042 | − | 0.997176i | \(-0.476071\pi\) |
−0.826027 | + | 0.563630i | \(0.809404\pi\) | |||||||
\(54\) | 29.1821 | − | 32.5281i | 0.540410 | − | 0.602373i | ||||
\(55\) | 77.2174i | 1.40395i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.29824 | −0.0929516 | ||||||||
\(58\) | −5.57333 | − | 5.00004i | −0.0960920 | − | 0.0862075i | ||||
\(59\) | −34.3509 | + | 59.4974i | −0.582218 | + | 1.00843i | 0.412998 | + | 0.910732i | \(0.364482\pi\) |
−0.995216 | + | 0.0976993i | \(0.968852\pi\) | |||||||
\(60\) | 6.35348 | + | 58.4165i | 0.105891 | + | 0.973609i | ||||
\(61\) | −48.0386 | − | 83.2052i | −0.787517 | − | 1.36402i | −0.927484 | − | 0.373864i | \(-0.878033\pi\) |
0.139966 | − | 0.990156i | \(-0.455301\pi\) | |||||||
\(62\) | −0.0318663 | + | 0.0104177i | −0.000513973 | + | 0.000168028i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 20.4362 | + | 60.6495i | 0.319316 | + | 0.947648i | ||||
\(65\) | 7.02849 | + | 12.1737i | 0.108131 | + | 0.187288i | ||||
\(66\) | 25.0926 | − | 119.110i | 0.380191 | − | 1.80470i | ||||
\(67\) | −12.0808 | − | 6.97484i | −0.180310 | − | 0.104102i | 0.407128 | − | 0.913371i | \(-0.366530\pi\) |
−0.587438 | + | 0.809269i | \(0.699864\pi\) | |||||||
\(68\) | 25.3909 | − | 57.5883i | 0.373395 | − | 0.846887i | ||||
\(69\) | −140.921 | −2.04234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −75.7095 | −1.06633 | −0.533166 | − | 0.846011i | \(-0.678998\pi\) | ||||
−0.533166 | + | 0.846011i | \(0.678998\pi\) | |||||||
\(72\) | 2.04511 | − | 20.5284i | 0.0284044 | − | 0.285117i | ||||
\(73\) | 46.0282 | + | 26.5744i | 0.630523 | + | 0.364033i | 0.780955 | − | 0.624588i | \(-0.214733\pi\) |
−0.150432 | + | 0.988620i | \(0.548066\pi\) | |||||||
\(74\) | −0.555921 | + | 2.63886i | −0.00751245 | + | 0.0356602i | ||||
\(75\) | 10.8244 | + | 18.7483i | 0.144325 | + | 0.249978i | ||||
\(76\) | 5.02543 | − | 3.67902i | 0.0661240 | − | 0.0484082i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.88567 | − | 21.0623i | −0.0882778 | − | 0.270029i | ||||
\(79\) | 11.6744 | + | 20.2206i | 0.147777 | + | 0.255957i | 0.930406 | − | 0.366532i | \(-0.119455\pi\) |
−0.782628 | + | 0.622489i | \(0.786122\pi\) | |||||||
\(80\) | −46.5900 | − | 50.9968i | −0.582374 | − | 0.637460i | ||||
\(81\) | 48.7794 | − | 84.4884i | 0.602215 | − | 1.04307i | ||||
\(82\) | 104.659 | + | 93.8931i | 1.27633 | + | 1.14504i | ||||
\(83\) | 102.487 | 1.23479 | 0.617393 | − | 0.786655i | \(-0.288189\pi\) | ||||
0.617393 | + | 0.786655i | \(0.288189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 67.9277i | 0.799150i | ||||||||
\(86\) | 19.4098 | + | 17.4132i | 0.225696 | + | 0.202480i | ||||
\(87\) | −11.0323 | − | 6.36952i | −0.126808 | − | 0.0732129i | ||||
\(88\) | 58.9078 | + | 130.401i | 0.669407 | + | 1.48183i | ||||
\(89\) | 76.6985 | − | 44.2819i | 0.861781 | − | 0.497549i | −0.00282755 | − | 0.999996i | \(-0.500900\pi\) |
0.864608 | + | 0.502447i | \(0.167567\pi\) | |||||||
\(90\) | 6.91880 | + | 21.1636i | 0.0768755 | + | 0.235151i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 133.665 | − | 97.8538i | 1.45288 | − | 1.06363i | ||||
\(93\) | −0.0493984 | + | 0.0285202i | −0.000531166 | + | 0.000306669i | ||||
\(94\) | 14.7484 | − | 70.0080i | 0.156898 | − | 0.744766i | ||||
\(95\) | −3.36100 | + | 5.82143i | −0.0353790 | + | 0.0612782i | ||||
\(96\) | 55.2944 | + | 93.8040i | 0.575983 | + | 0.977125i | ||||
\(97\) | 140.869i | 1.45226i | 0.687558 | + | 0.726130i | \(0.258683\pi\) | ||||
−0.687558 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 46.1241i | − | 0.465900i | ||||||
\(100\) | −23.2856 | − | 10.2667i | −0.232856 | − | 0.102667i | ||||
\(101\) | 17.6988 | − | 30.6553i | 0.175236 | − | 0.303518i | −0.765007 | − | 0.644022i | \(-0.777265\pi\) |
0.940243 | + | 0.340504i | \(0.110598\pi\) | |||||||
\(102\) | 22.0738 | − | 104.780i | 0.216410 | − | 1.02726i | ||||
\(103\) | −87.1651 | + | 50.3248i | −0.846263 | + | 0.488590i | −0.859388 | − | 0.511324i | \(-0.829155\pi\) |
0.0131250 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(104\) | 21.1565 | + | 15.1964i | 0.203427 | + | 0.146119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 87.3617 | − | 28.5603i | 0.824167 | − | 0.269437i | ||||
\(107\) | −92.6215 | + | 53.4751i | −0.865622 | + | 0.499767i | −0.865891 | − | 0.500233i | \(-0.833248\pi\) |
0.000269099 | 1.00000i | \(0.499914\pi\) | ||||||||
\(108\) | 9.45000 | + | 86.8873i | 0.0875000 | + | 0.804512i | ||||
\(109\) | −45.5799 | − | 26.3156i | −0.418165 | − | 0.241427i | 0.276127 | − | 0.961121i | \(-0.410949\pi\) |
−0.694292 | + | 0.719694i | \(0.744282\pi\) | |||||||
\(110\) | −114.954 | − | 103.129i | −1.04504 | − | 0.937540i | ||||
\(111\) | 4.58824i | 0.0413355i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 45.4346 | 0.402076 | 0.201038 | − | 0.979583i | \(-0.435568\pi\) | ||||
0.201038 | + | 0.979583i | \(0.435568\pi\) | |||||||
\(114\) | 7.07618 | − | 7.88753i | 0.0620718 | − | 0.0691888i | ||||
\(115\) | −89.3952 | + | 154.837i | −0.777350 | + | 1.34641i | ||||
\(116\) | 14.8872 | − | 1.61915i | 0.128338 | − | 0.0139582i | ||||
\(117\) | −4.19831 | − | 7.27168i | −0.0358830 | − | 0.0621511i | ||||
\(118\) | −42.6962 | − | 130.601i | −0.361832 | − | 1.10679i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −95.4506 | − | 68.5610i | −0.795422 | − | 0.571342i | ||||
\(121\) | 99.4572 | + | 172.265i | 0.821961 | + | 1.42368i | ||||
\(122\) | 188.027 | + | 39.6112i | 1.54121 | + | 0.324682i | ||||
\(123\) | 207.171 | + | 119.610i | 1.68431 | + | 0.972439i | ||||
\(124\) | 0.0270508 | − | 0.0613532i | 0.000218152 | − | 0.000494784i | ||||
\(125\) | 135.395 | 1.08316 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 125.695 | 0.989723 | 0.494861 | − | 0.868972i | \(-0.335219\pi\) | ||||
0.494861 | + | 0.868972i | \(0.335219\pi\) | |||||||
\(128\) | −117.583 | − | 50.5782i | −0.918620 | − | 0.395143i | ||||
\(129\) | 38.4215 | + | 22.1827i | 0.297841 | + | 0.171959i | ||||
\(130\) | −27.5101 | − | 5.79549i | −0.211616 | − | 0.0445807i | ||||
\(131\) | −56.6504 | − | 98.1214i | −0.432446 | − | 0.749018i | 0.564638 | − | 0.825339i | \(-0.309016\pi\) |
−0.997083 | + | 0.0763210i | \(0.975683\pi\) | |||||||
\(132\) | 143.807 | + | 196.436i | 1.08945 | + | 1.48815i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 26.5182 | − | 8.66933i | 0.197897 | − | 0.0646965i | ||||
\(135\) | −47.1648 | − | 81.6919i | −0.349369 | − | 0.605125i | ||||
\(136\) | 51.8208 | + | 114.713i | 0.381036 | + | 0.843477i | ||||
\(137\) | −39.1679 | + | 67.8408i | −0.285897 | + | 0.495188i | −0.972826 | − | 0.231536i | \(-0.925625\pi\) |
0.686929 | + | 0.726724i | \(0.258958\pi\) | |||||||
\(138\) | 188.211 | − | 209.791i | 1.36384 | − | 1.52022i | ||||
\(139\) | 149.038 | 1.07222 | 0.536109 | − | 0.844149i | \(-0.319894\pi\) | ||||
0.536109 | + | 0.844149i | \(0.319894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 121.725i | − | 0.863295i | ||||||
\(142\) | 101.115 | − | 112.709i | 0.712081 | − | 0.793727i | ||||
\(143\) | 50.4361 | + | 29.1193i | 0.352700 | + | 0.203631i | ||||
\(144\) | 27.8294 | + | 30.4618i | 0.193260 | + | 0.211540i | ||||
\(145\) | −13.9970 | + | 8.08117i | −0.0965310 | + | 0.0557322i | ||||
\(146\) | −101.035 | + | 33.0305i | −0.692023 | + | 0.226236i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.18601 | − | 4.35198i | −0.0215271 | − | 0.0294053i | ||||
\(149\) | −73.8369 | + | 42.6298i | −0.495550 | + | 0.286106i | −0.726874 | − | 0.686771i | \(-0.759028\pi\) |
0.231324 | + | 0.972877i | \(0.425694\pi\) | |||||||
\(150\) | −42.3675 | − | 8.92545i | −0.282450 | − | 0.0595030i | ||||
\(151\) | −65.9012 | + | 114.144i | −0.436432 | + | 0.755922i | −0.997411 | − | 0.0719076i | \(-0.977091\pi\) |
0.560979 | + | 0.827830i | \(0.310425\pi\) | |||||||
\(152\) | −1.23483 | + | 12.3950i | −0.00812389 | + | 0.0815460i | ||||
\(153\) | − | 40.5751i | − | 0.265197i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0723686i | 0.000466894i | ||||||||
\(156\) | 40.5518 | + | 17.8794i | 0.259948 | + | 0.114612i | ||||
\(157\) | 122.552 | − | 212.267i | 0.780589 | − | 1.35202i | −0.151010 | − | 0.988532i | \(-0.548253\pi\) |
0.931599 | − | 0.363487i | \(-0.118414\pi\) | |||||||
\(158\) | −45.6946 | − | 9.62637i | −0.289206 | − | 0.0609264i | ||||
\(159\) | 135.426 | − | 78.1883i | 0.851737 | − | 0.491750i | ||||
\(160\) | 138.144 | − | 1.24885i | 0.863397 | − | 0.00780534i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 60.6301 | + | 185.459i | 0.374260 | + | 1.14481i | ||||
\(163\) | 208.089 | − | 120.140i | 1.27662 | − | 0.737057i | 0.300395 | − | 0.953815i | \(-0.402882\pi\) |
0.976225 | + | 0.216758i | \(0.0695482\pi\) | |||||||
\(164\) | −279.559 | + | 30.4052i | −1.70463 | + | 0.185398i | ||||
\(165\) | −227.550 | − | 131.376i | −1.37909 | − | 0.796219i | ||||
\(166\) | −136.879 | + | 152.573i | −0.824573 | + | 0.919117i | ||||
\(167\) | − | 73.1965i | − | 0.438302i | −0.975691 | − | 0.219151i | \(-0.929671\pi\) | ||
0.975691 | − | 0.219151i | \(-0.0703288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −158.398 | −0.937266 | ||||||||
\(170\) | −101.124 | − | 90.7224i | −0.594850 | − | 0.533661i | ||||
\(171\) | 2.00762 | − | 3.47730i | 0.0117405 | − | 0.0203351i | ||||
\(172\) | −51.8464 | + | 5.63890i | −0.301433 | + | 0.0327843i | ||||
\(173\) | −18.5246 | − | 32.0855i | −0.107078 | − | 0.185465i | 0.807507 | − | 0.589858i | \(-0.200816\pi\) |
−0.914585 | + | 0.404393i | \(0.867483\pi\) | |||||||
\(174\) | 24.2168 | − | 7.91696i | 0.139177 | − | 0.0454998i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −272.804 | − | 86.4634i | −1.55002 | − | 0.491269i | ||||
\(177\) | −116.888 | − | 202.455i | −0.660382 | − | 1.14382i | ||||
\(178\) | −36.5136 | + | 173.323i | −0.205132 | + | 0.973726i | ||||
\(179\) | 205.982 | + | 118.924i | 1.15074 | + | 0.664379i | 0.949067 | − | 0.315074i | \(-0.102029\pi\) |
0.201672 | + | 0.979453i | \(0.435363\pi\) | |||||||
\(180\) | −40.7469 | − | 17.9654i | −0.226372 | − | 0.0998080i | ||||
\(181\) | −292.553 | −1.61631 | −0.808157 | − | 0.588966i | \(-0.799535\pi\) | ||||
−0.808157 | + | 0.588966i | \(0.799535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 326.927 | 1.78649 | ||||||||
\(184\) | −32.8437 | + | 329.679i | −0.178499 | + | 1.79173i | ||||
\(185\) | 5.04132 | + | 2.91061i | 0.0272504 | + | 0.0157330i | ||||
\(186\) | 0.0235169 | − | 0.111631i | 0.000126435 | − | 0.000600164i | ||||
\(187\) | 140.713 | + | 243.723i | 0.752478 | + | 1.30333i | ||||
\(188\) | 84.5238 | + | 115.457i | 0.449595 | + | 0.614132i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.17754 | − | 12.7785i | −0.0219871 | − | 0.0672552i | ||||
\(191\) | −70.6135 | − | 122.306i | −0.369704 | − | 0.640346i | 0.619815 | − | 0.784748i | \(-0.287208\pi\) |
−0.989519 | + | 0.144402i | \(0.953874\pi\) | |||||||
\(192\) | −213.496 | − | 42.9648i | −1.11196 | − | 0.223775i | ||||
\(193\) | 32.9799 | − | 57.1229i | 0.170880 | − | 0.295973i | −0.767848 | − | 0.640633i | \(-0.778672\pi\) |
0.938728 | + | 0.344659i | \(0.112006\pi\) | |||||||
\(194\) | −209.713 | − | 188.141i | −1.08099 | − | 0.969798i | ||||
\(195\) | −47.8325 | −0.245295 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 199.421i | − | 1.01229i | −0.862448 | − | 0.506145i | \(-0.831070\pi\) | ||
0.862448 | − | 0.506145i | \(-0.168930\pi\) | |||||||
\(198\) | 68.6652 | + | 61.6020i | 0.346794 | + | 0.311121i | ||||
\(199\) | −58.6230 | − | 33.8460i | −0.294588 | − | 0.170080i | 0.345421 | − | 0.938448i | \(-0.387736\pi\) |
−0.640009 | + | 0.768367i | \(0.721069\pi\) | |||||||
\(200\) | 46.3836 | − | 20.9535i | 0.231918 | − | 0.104768i | ||||
\(201\) | 41.1079 | − | 23.7337i | 0.204517 | − | 0.118078i | ||||
\(202\) | 21.9987 | + | 67.2907i | 0.108904 | + | 0.333122i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 126.506 | + | 172.803i | 0.620128 | + | 0.847075i | ||||
\(205\) | 262.842 | − | 151.752i | 1.28216 | − | 0.740254i | ||||
\(206\) | 41.4964 | − | 196.976i | 0.201439 | − | 0.956193i | ||||
\(207\) | 53.3982 | − | 92.4884i | 0.257962 | − | 0.446804i | ||||
\(208\) | −50.8790 | + | 11.1998i | −0.244611 | + | 0.0538454i | ||||
\(209\) | 27.8495i | 0.133251i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 62.1464i | − | 0.294533i | −0.989097 | − | 0.147266i | \(-0.952953\pi\) | ||
0.989097 | − | 0.147266i | \(-0.0470475\pi\) | |||||||
\(212\) | −74.1600 | + | 168.200i | −0.349811 | + | 0.793398i | ||||
\(213\) | 128.811 | − | 223.106i | 0.604744 | − | 1.04745i | ||||
\(214\) | 44.0940 | − | 209.306i | 0.206047 | − | 0.978066i | ||||
\(215\) | 48.7463 | − | 28.1437i | 0.226727 | − | 0.130901i | ||||
\(216\) | −141.971 | − | 101.976i | −0.657273 | − | 0.472111i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 100.051 | − | 32.7088i | 0.458952 | − | 0.150040i | ||||
\(219\) | −156.623 | + | 90.4261i | −0.715172 | + | 0.412905i | ||||
\(220\) | 307.059 | − | 33.3962i | 1.39572 | − | 0.151801i | ||||
\(221\) | 44.3683 | + | 25.6161i | 0.200762 | + | 0.115910i | ||||
\(222\) | −6.83054 | − | 6.12792i | −0.0307682 | − | 0.0276033i | ||||
\(223\) | − | 115.525i | − | 0.518050i | −0.965871 | − | 0.259025i | \(-0.916599\pi\) | ||
0.965871 | − | 0.259025i | \(-0.0834012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.4063 | −0.0729171 | ||||||||
\(226\) | −60.6812 | + | 67.6388i | −0.268501 | + | 0.299287i | ||||
\(227\) | 28.2532 | − | 48.9360i | 0.124463 | − | 0.215577i | −0.797060 | − | 0.603901i | \(-0.793612\pi\) |
0.921523 | + | 0.388324i | \(0.126946\pi\) | |||||||
\(228\) | 2.29147 | + | 21.0687i | 0.0100503 | + | 0.0924067i | ||||
\(229\) | 59.1696 | + | 102.485i | 0.258383 | + | 0.447532i | 0.965809 | − | 0.259255i | \(-0.0834771\pi\) |
−0.707426 | + | 0.706787i | \(0.750144\pi\) | |||||||
\(230\) | −111.113 | − | 339.879i | −0.483101 | − | 1.47774i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.4724 | + | 24.3251i | −0.0753123 | + | 0.104850i | ||||
\(233\) | 12.3403 | + | 21.3740i | 0.0529625 | + | 0.0917337i | 0.891291 | − | 0.453431i | \(-0.149800\pi\) |
−0.838329 | + | 0.545165i | \(0.816467\pi\) | |||||||
\(234\) | 16.4325 | + | 3.46180i | 0.0702245 | + | 0.0147940i | ||||
\(235\) | −133.745 | − | 77.2175i | −0.569126 | − | 0.328585i | ||||
\(236\) | 251.451 | + | 110.866i | 1.06547 | + | 0.469769i | ||||
\(237\) | −79.4503 | −0.335233 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −251.189 | −1.05100 | −0.525499 | − | 0.850794i | \(-0.676121\pi\) | ||||
−0.525499 | + | 0.850794i | \(0.676121\pi\) | |||||||
\(240\) | 229.548 | − | 50.5298i | 0.956452 | − | 0.210541i | ||||
\(241\) | −97.3782 | − | 56.2213i | −0.404059 | − | 0.233283i | 0.284175 | − | 0.958772i | \(-0.408280\pi\) |
−0.688234 | + | 0.725489i | \(0.741614\pi\) | |||||||
\(242\) | −389.284 | − | 82.0096i | −1.60861 | − | 0.338883i | ||||
\(243\) | 67.6598 | + | 117.190i | 0.278436 | + | 0.482265i | ||||
\(244\) | −310.093 | + | 227.014i | −1.27087 | + | 0.930384i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −454.755 | + | 148.668i | −1.84860 | + | 0.604343i | ||||
\(247\) | 2.53492 | + | 4.39061i | 0.0102628 | + | 0.0177758i | ||||
\(248\) | 0.0552087 | + | 0.122212i | 0.000222616 | + | 0.000492792i | ||||
\(249\) | −174.370 | + | 302.017i | −0.700280 | + | 1.21292i | ||||
\(250\) | −180.830 | + | 201.564i | −0.723321 | + | 0.806256i | ||||
\(251\) | 121.248 | 0.483059 | 0.241529 | − | 0.970394i | \(-0.422351\pi\) | ||||
0.241529 | + | 0.970394i | \(0.422351\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 740.735i | 2.92781i | ||||||||
\(254\) | −167.874 | + | 187.123i | −0.660923 | + | 0.736704i | ||||
\(255\) | −200.174 | − | 115.571i | −0.784998 | − | 0.453219i | ||||
\(256\) | 232.337 | − | 107.496i | 0.907567 | − | 0.419907i | ||||
\(257\) | 90.7377 | − | 52.3874i | 0.353065 | − | 0.203842i | −0.312969 | − | 0.949763i | \(-0.601324\pi\) |
0.666034 | + | 0.745921i | \(0.267990\pi\) | |||||||
\(258\) | −84.3381 | + | 27.5718i | −0.326892 | + | 0.106867i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 45.3695 | − | 33.2142i | 0.174498 | − | 0.127747i | ||||
\(261\) | 8.36079 | − | 4.82710i | 0.0320337 | − | 0.0184946i | ||||
\(262\) | 221.735 | + | 46.7123i | 0.846315 | + | 0.178291i | ||||
\(263\) | 52.3392 | − | 90.6542i | 0.199008 | − | 0.344693i | −0.749199 | − | 0.662345i | \(-0.769561\pi\) |
0.948207 | + | 0.317653i | \(0.102895\pi\) | |||||||
\(264\) | −484.500 | − | 48.2675i | −1.83523 | − | 0.182831i | ||||
\(265\) | − | 198.399i | − | 0.748675i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 301.361i | 1.12869i | ||||||||
\(268\) | −22.5109 | + | 51.0564i | −0.0839959 | + | 0.190509i | ||||
\(269\) | −152.466 | + | 264.079i | −0.566789 | + | 0.981707i | 0.430092 | + | 0.902785i | \(0.358481\pi\) |
−0.996881 | + | 0.0789222i | \(0.974852\pi\) | |||||||
\(270\) | 184.607 | + | 38.8908i | 0.683731 | + | 0.144040i | ||||
\(271\) | −88.8942 | + | 51.3231i | −0.328023 | + | 0.189384i | −0.654963 | − | 0.755661i | \(-0.727316\pi\) |
0.326940 | + | 0.945045i | \(0.393982\pi\) | |||||||
\(272\) | −239.984 | − | 76.0613i | −0.882295 | − | 0.279637i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −48.6835 | − | 148.916i | −0.177677 | − | 0.543488i | ||||
\(275\) | 98.5482 | − | 56.8968i | 0.358357 | − | 0.206898i | ||||
\(276\) | 60.9479 | + | 560.381i | 0.220826 | + | 2.03036i | ||||
\(277\) | −14.4235 | − | 8.32739i | −0.0520703 | − | 0.0300628i | 0.473739 | − | 0.880665i | \(-0.342904\pi\) |
−0.525809 | + | 0.850603i | \(0.676237\pi\) | |||||||
\(278\) | −199.051 | + | 221.874i | −0.716012 | + | 0.798109i | ||||
\(279\) | − | 0.0432277i | − | 0.000154938i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 75.8291 | 0.269855 | 0.134927 | − | 0.990856i | \(-0.456920\pi\) | ||||
0.134927 | + | 0.990856i | \(0.456920\pi\) | |||||||
\(282\) | 181.212 | + | 162.572i | 0.642596 | + | 0.576496i | ||||
\(283\) | 43.6656 | − | 75.6311i | 0.154296 | − | 0.267248i | −0.778507 | − | 0.627636i | \(-0.784023\pi\) |
0.932802 | + | 0.360389i | \(0.117356\pi\) | |||||||
\(284\) | 32.7441 | + | 301.063i | 0.115296 | + | 1.06008i | ||||
\(285\) | −11.4367 | − | 19.8089i | −0.0401287 | − | 0.0695050i | ||||
\(286\) | −110.711 | + | 36.1936i | −0.387102 | + | 0.126551i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82.5169 | + | 0.745975i | −0.286517 | + | 0.00259019i | ||||
\(289\) | −20.7152 | − | 35.8798i | −0.0716789 | − | 0.124151i | ||||
\(290\) | 6.66350 | − | 31.6304i | 0.0229776 | − | 0.109070i | ||||
\(291\) | −415.124 | − | 239.672i | −1.42654 | − | 0.823614i | ||||
\(292\) | 85.7673 | − | 194.527i | 0.293724 | − | 0.666187i | ||||
\(293\) | 27.5057 | 0.0938760 | 0.0469380 | − | 0.998898i | \(-0.485054\pi\) | ||||
0.0469380 | + | 0.998898i | \(0.485054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −296.597 | −1.00541 | ||||||||
\(296\) | 10.7340 | + | 1.06935i | 0.0362634 | + | 0.00361268i | ||||
\(297\) | −338.452 | − | 195.406i | −1.13957 | − | 0.657931i | ||||
\(298\) | 35.1513 | − | 166.857i | 0.117957 | − | 0.559922i | ||||
\(299\) | 67.4232 | + | 116.780i | 0.225496 | + | 0.390570i | ||||
\(300\) | 69.8722 | − | 51.1522i | 0.232907 | − | 0.170507i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −81.9115 | − | 250.555i | −0.271230 | − | 0.829654i | ||||
\(303\) | 60.2248 | + | 104.312i | 0.198762 | + | 0.344266i | ||||
\(304\) | −16.8033 | − | 18.3927i | −0.0552740 | − | 0.0605023i | ||||
\(305\) | 207.390 | − | 359.211i | 0.679968 | − | 1.17774i | ||||
\(306\) | 60.4044 | + | 54.1909i | 0.197400 | + | 0.177095i | ||||
\(307\) | 247.996 | 0.807805 | 0.403902 | − | 0.914802i | \(-0.367654\pi\) | ||||
0.403902 | + | 0.914802i | \(0.367654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 342.486i | − | 1.10837i | ||||||
\(310\) | −0.107736 | − | 0.0966534i | −0.000347534 | − | 0.000311785i | ||||
\(311\) | −378.484 | − | 218.518i | −1.21699 | − | 0.702630i | −0.252717 | − | 0.967540i | \(-0.581324\pi\) |
−0.964273 | + | 0.264910i | \(0.914658\pi\) | |||||||
\(312\) | −80.7771 | + | 36.4905i | −0.258901 | + | 0.116957i | ||||
\(313\) | 71.7330 | − | 41.4151i | 0.229179 | − | 0.132317i | −0.381014 | − | 0.924569i | \(-0.624425\pi\) |
0.610193 | + | 0.792253i | \(0.291092\pi\) | |||||||
\(314\) | 152.326 | + | 465.943i | 0.485114 | + | 1.48389i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 75.3593 | − | 55.1691i | 0.238479 | − | 0.174586i | ||||
\(317\) | 211.775 | − | 122.268i | 0.668059 | − | 0.385704i | −0.127282 | − | 0.991867i | \(-0.540625\pi\) |
0.795341 | + | 0.606162i | \(0.207292\pi\) | |||||||
\(318\) | −64.4718 | + | 306.036i | −0.202742 | + | 0.962377i | ||||
\(319\) | −33.4806 | + | 57.9900i | −0.104955 | + | 0.181787i | ||||
\(320\) | −182.641 | + | 207.323i | −0.570755 | + | 0.647885i | ||||
\(321\) | − | 363.925i | − | 1.13372i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.4991i | 0.0758485i | ||||||||
\(324\) | −357.069 | − | 157.433i | −1.10207 | − | 0.485904i | ||||
\(325\) | 10.3577 | − | 17.9401i | 0.0318699 | − | 0.0552004i | ||||
\(326\) | −99.0643 | + | 470.240i | −0.303878 | + | 1.44245i | ||||
\(327\) | 155.097 | − | 89.5456i | 0.474304 | − | 0.273840i | ||||
\(328\) | 328.106 | − | 456.789i | 1.00032 | − | 1.39265i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 499.490 | − | 163.293i | 1.51361 | − | 0.494828i | ||||
\(331\) | 66.2919 | − | 38.2736i | 0.200278 | − | 0.115630i | −0.396507 | − | 0.918032i | \(-0.629778\pi\) |
0.596785 | + | 0.802401i | \(0.296445\pi\) | |||||||
\(332\) | −44.3253 | − | 407.546i | −0.133510 | − | 1.22755i | ||||
\(333\) | −3.01132 | − | 1.73858i | −0.00904299 | − | 0.00522097i | ||||
\(334\) | 108.968 | + | 97.7592i | 0.326252 | + | 0.292692i | ||||
\(335\) | − | 60.2230i | − | 0.179770i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −38.2520 | −0.113507 | −0.0567537 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567537 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(338\) | 211.552 | − | 235.808i | 0.625893 | − | 0.697657i | ||||
\(339\) | −77.3015 | + | 133.890i | −0.228028 | + | 0.394956i | ||||
\(340\) | 270.118 | − | 29.3785i | 0.794465 | − | 0.0864072i | ||||
\(341\) | 0.149913 | + | 0.259656i | 0.000439627 | + | 0.000761456i | ||||
\(342\) | 2.49536 | + | 7.63294i | 0.00729637 | + | 0.0223185i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 60.8500 | − | 84.7153i | 0.176889 | − | 0.246265i | ||||
\(345\) | −304.190 | − | 526.873i | −0.881711 | − | 1.52717i | ||||
\(346\) | 72.5068 | + | 15.2748i | 0.209557 | + | 0.0441469i | ||||
\(347\) | 208.395 | + | 120.317i | 0.600561 | + | 0.346734i | 0.769262 | − | 0.638933i | \(-0.220624\pi\) |
−0.168701 | + | 0.985667i | \(0.553957\pi\) | |||||||
\(348\) | −20.5573 | + | 46.6254i | −0.0590727 | + | 0.133981i | ||||
\(349\) | 430.367 | 1.23314 | 0.616572 | − | 0.787298i | \(-0.288521\pi\) | ||||
0.616572 | + | 0.787298i | \(0.288521\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −71.1449 | −0.202692 | ||||||||
\(352\) | 493.068 | − | 290.648i | 1.40076 | − | 0.825703i | ||||
\(353\) | 265.950 | + | 153.546i | 0.753399 | + | 0.434975i | 0.826921 | − | 0.562318i | \(-0.190090\pi\) |
−0.0735214 | + | 0.997294i | \(0.523424\pi\) | |||||||
\(354\) | 457.509 | + | 96.3822i | 1.29240 | + | 0.272266i | ||||
\(355\) | −163.425 | − | 283.061i | −0.460353 | − | 0.797354i | ||||
\(356\) | −209.261 | − | 285.844i | −0.587811 | − | 0.802931i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −452.147 | + | 147.816i | −1.26298 | + | 0.412893i | ||||
\(359\) | −230.880 | − | 399.896i | −0.643120 | − | 1.11392i | −0.984732 | − | 0.174075i | \(-0.944306\pi\) |
0.341613 | − | 0.939841i | \(-0.389027\pi\) | |||||||
\(360\) | 81.1657 | − | 36.6661i | 0.225460 | − | 0.101850i | ||||
\(361\) | 179.288 | − | 310.536i | 0.496642 | − | 0.860209i | ||||
\(362\) | 390.726 | − | 435.526i | 1.07935 | − | 1.20311i | ||||
\(363\) | −676.858 | −1.86462 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 229.452i | 0.628635i | ||||||||
\(366\) | −436.635 | + | 486.699i | −1.19299 | + | 1.32978i | ||||
\(367\) | 542.949 | + | 313.471i | 1.47942 | + | 0.854146i | 0.999729 | − | 0.0232895i | \(-0.00741394\pi\) |
0.479695 | + | 0.877435i | \(0.340747\pi\) | |||||||
\(368\) | −446.930 | − | 489.205i | −1.21448 | − | 1.32936i | ||||
\(369\) | −157.003 | + | 90.6457i | −0.425482 | + | 0.245652i | ||||
\(370\) | −11.0661 | + | 3.61772i | −0.0299083 | + | 0.00977762i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.134777 | + | 0.184100i | 0.000362303 | + | 0.000494894i | ||||
\(373\) | −357.317 | + | 206.297i | −0.957953 | + | 0.553075i | −0.895543 | − | 0.444976i | \(-0.853212\pi\) |
−0.0624108 | + | 0.998051i | \(0.519879\pi\) | |||||||
\(374\) | −550.765 | − | 116.028i | −1.47263 | − | 0.310236i | ||||
\(375\) | −230.359 | + | 398.993i | −0.614290 | + | 1.06398i | ||||
\(376\) | −284.769 | − | 28.3697i | −0.757364 | − | 0.0754512i | ||||
\(377\) | 12.1899i | 0.0323339i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 327.118i | − | 0.863107i | −0.902087 | − | 0.431554i | \(-0.857966\pi\) | ||
0.902087 | − | 0.431554i | \(-0.142034\pi\) | |||||||
\(380\) | 24.6028 | + | 10.8475i | 0.0647443 | + | 0.0285459i | ||||
\(381\) | −213.854 | + | 370.407i | −0.561298 | + | 0.972196i | ||||
\(382\) | 276.387 | + | 58.2259i | 0.723527 | + | 0.152424i | ||||
\(383\) | 215.523 | − | 124.432i | 0.562724 | − | 0.324889i | −0.191514 | − | 0.981490i | \(-0.561340\pi\) |
0.754238 | + | 0.656601i | \(0.228006\pi\) | |||||||
\(384\) | 349.102 | − | 260.451i | 0.909119 | − | 0.678257i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.9922 | + | 125.389i | 0.106197 | + | 0.324842i | ||||
\(387\) | −29.1175 | + | 16.8110i | −0.0752390 | + | 0.0434392i | ||||
\(388\) | 560.173 | − | 60.9253i | 1.44375 | − | 0.157024i | ||||
\(389\) | 326.728 | + | 188.637i | 0.839918 | + | 0.484927i | 0.857236 | − | 0.514923i | \(-0.172179\pi\) |
−0.0173181 | + | 0.999850i | \(0.505513\pi\) | |||||||
\(390\) | 63.8837 | − | 71.2086i | 0.163804 | − | 0.182586i | ||||
\(391\) | 651.620i | 1.66655i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 385.535 | 0.981005 | ||||||||
\(394\) | 296.880 | + | 266.341i | 0.753502 | + | 0.675994i | ||||
\(395\) | −50.4003 | + | 87.2958i | −0.127596 | + | 0.221002i | ||||
\(396\) | −183.415 | + | 19.9485i | −0.463168 | + | 0.0503749i | ||||
\(397\) | 335.874 | + | 581.752i | 0.846031 | + | 1.46537i | 0.884723 | + | 0.466118i | \(0.154348\pi\) |
−0.0386913 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(398\) | 128.682 | − | 42.0687i | 0.323322 | − | 0.105700i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −30.7550 | + | 97.0365i | −0.0768876 | + | 0.242591i | ||||
\(401\) | 235.200 | + | 407.378i | 0.586534 | + | 1.01591i | 0.994682 | + | 0.102991i | \(0.0328411\pi\) |
−0.408149 | + | 0.912915i | \(0.633826\pi\) | |||||||
\(402\) | −19.5701 | + | 92.8957i | −0.0486819 | + | 0.231084i | ||||
\(403\) | 0.0472689 | + | 0.0272907i | 0.000117293 | + | 6.77189e-5i | ||||
\(404\) | −129.557 | − | 57.1220i | −0.320685 | − | 0.141391i | ||||
\(405\) | 421.177 | 1.03994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.1175 | 0.0592567 | ||||||||
\(408\) | −426.211 | − | 42.4606i | −1.04464 | − | 0.104070i | ||||
\(409\) | 57.7400 | + | 33.3362i | 0.141174 | + | 0.0815067i | 0.568923 | − | 0.822391i | \(-0.307360\pi\) |
−0.427750 | + | 0.903897i | \(0.640693\pi\) | |||||||
\(410\) | −125.130 | + | 593.971i | −0.305196 | + | 1.44871i | ||||
\(411\) | −133.279 | − | 230.846i | −0.324279 | − | 0.561669i | ||||
\(412\) | 237.818 | + | 324.851i | 0.577227 | + | 0.788474i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 66.3709 | + | 203.019i | 0.160316 | + | 0.490384i | ||||
\(415\) | 221.227 | + | 383.177i | 0.533077 | + | 0.923317i | ||||
\(416\) | 51.2793 | − | 90.7021i | 0.123267 | − | 0.218034i | ||||
\(417\) | −253.571 | + | 439.197i | −0.608083 | + | 1.05323i | ||||
\(418\) | −41.4598 | − | 37.1950i | −0.0991860 | − | 0.0889833i | ||||
\(419\) | −437.380 | −1.04387 | −0.521933 | − | 0.852986i | \(-0.674789\pi\) | ||||
−0.521933 | + | 0.852986i | \(0.674789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 703.800i | − | 1.67173i | −0.548933 | − | 0.835867i | \(-0.684966\pi\) | ||
0.548933 | − | 0.835867i | \(-0.315034\pi\) | |||||||
\(422\) | 92.5178 | + | 83.0010i | 0.219236 | + | 0.196685i | ||||
\(423\) | 79.8893 | + | 46.1241i | 0.188864 | + | 0.109040i | ||||
\(424\) | −151.355 | − | 335.046i | −0.356969 | − | 0.790203i | ||||
\(425\) | 86.6923 | − | 50.0518i | 0.203982 | − | 0.117769i | ||||
\(426\) | 160.104 | + | 489.736i | 0.375832 | + | 1.14961i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 252.705 | + | 345.186i | 0.590431 | + | 0.806510i | ||||
\(429\) | −171.622 | + | 99.0858i | −0.400051 | + | 0.230969i | ||||
\(430\) | −23.2065 | + | 110.157i | −0.0539686 | + | 0.256179i | ||||
\(431\) | 274.869 | − | 476.087i | 0.637747 | − | 1.10461i | −0.348178 | − | 0.937428i | \(-0.613200\pi\) |
0.985926 | − | 0.167183i | \(-0.0534670\pi\) | |||||||
\(432\) | 341.425 | − | 75.1568i | 0.790335 | − | 0.173974i | ||||
\(433\) | 355.012i | 0.819890i | 0.912110 | + | 0.409945i | \(0.134452\pi\) | ||||
−0.912110 | + | 0.409945i | \(0.865548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 54.9965i | − | 0.126429i | ||||||
\(436\) | −84.9321 | + | 192.632i | −0.194798 | + | 0.441817i | ||||
\(437\) | −32.2416 | + | 55.8441i | −0.0737794 | + | 0.127790i | ||||
\(438\) | 74.5628 | − | 353.936i | 0.170235 | − | 0.808073i | ||||
\(439\) | −477.032 | + | 275.415i | −1.08663 | + | 0.627369i | −0.932678 | − | 0.360709i | \(-0.882535\pi\) |
−0.153956 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(440\) | −360.382 | + | 501.724i | −0.819050 | + | 1.14028i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −97.3919 | + | 31.8393i | −0.220344 | + | 0.0720347i | ||||
\(443\) | 234.027 | − | 135.116i | 0.528278 | − | 0.305001i | −0.212037 | − | 0.977262i | \(-0.568010\pi\) |
0.740315 | + | 0.672260i | \(0.234676\pi\) | |||||||
\(444\) | 18.2454 | − | 1.98439i | 0.0410932 | − | 0.00446936i | ||||
\(445\) | 331.120 | + | 191.172i | 0.744089 | + | 0.429600i | ||||
\(446\) | 171.983 | + | 154.292i | 0.385612 | + | 0.345947i | ||||
\(447\) | − | 290.117i | − | 0.649032i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 455.397 | 1.01425 | 0.507124 | − | 0.861873i | \(-0.330709\pi\) | ||||
0.507124 | + | 0.861873i | \(0.330709\pi\) | |||||||
\(450\) | 21.9118 | − | 24.4242i | 0.0486930 | − | 0.0542761i | ||||
\(451\) | 628.714 | − | 1088.96i | 1.39404 | − | 2.41456i | ||||
\(452\) | −19.6503 | − | 180.673i | −0.0434741 | − | 0.399719i | ||||
\(453\) | −224.246 | − | 388.405i | −0.495024 | − | 0.857406i | ||||
\(454\) | 35.1171 | + | 107.418i | 0.0773505 | + | 0.236604i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −34.4256 | − | 24.7275i | −0.0754947 | − | 0.0542269i | ||||
\(457\) | 84.3172 | + | 146.042i | 0.184501 | + | 0.319566i | 0.943408 | − | 0.331633i | \(-0.107600\pi\) |
−0.758907 | + | 0.651199i | \(0.774266\pi\) | |||||||
\(458\) | −231.595 | − | 48.7896i | −0.505666 | − | 0.106528i | ||||
\(459\) | −297.735 | − | 171.897i | −0.648659 | − | 0.374504i | ||||
\(460\) | 654.380 | + | 288.518i | 1.42257 | + | 0.627213i | ||||
\(461\) | 265.062 | 0.574971 | 0.287485 | − | 0.957785i | \(-0.407181\pi\) | ||||
0.287485 | + | 0.957785i | \(0.407181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 97.4735 | 0.210526 | 0.105263 | − | 0.994444i | \(-0.466432\pi\) | ||||
0.105263 | + | 0.994444i | \(0.466432\pi\) | |||||||
\(464\) | −12.8773 | − | 58.4993i | −0.0277528 | − | 0.126076i | ||||
\(465\) | −0.213261 | − | 0.123126i | −0.000458626 | − | 0.000264788i | ||||
\(466\) | −48.3009 | − | 10.1754i | −0.103650 | − | 0.0218357i | ||||
\(467\) | −37.0997 | − | 64.2586i | −0.0794427 | − | 0.137599i | 0.823567 | − | 0.567219i | \(-0.191981\pi\) |
−0.903010 | + | 0.429620i | \(0.858647\pi\) | |||||||
\(468\) | −27.1005 | + | 19.8398i | −0.0579070 | + | 0.0423926i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 293.580 | − | 95.9770i | 0.624638 | − | 0.204206i | ||||
\(471\) | 417.016 | + | 722.293i | 0.885385 | + | 1.53353i | ||||
\(472\) | −500.877 | + | 226.268i | −1.06118 | + | 0.479382i | ||||
\(473\) | 116.600 | − | 201.958i | 0.246512 | − | 0.426972i | ||||
\(474\) | 106.112 | − | 118.278i | 0.223864 | − | 0.249532i | ||||
\(475\) | 9.90608 | 0.0208549 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 118.509i | 0.248447i | ||||||||
\(478\) | 335.480 | − | 373.946i | 0.701842 | − | 0.782314i | ||||
\(479\) | 475.220 | + | 274.368i | 0.992108 | + | 0.572794i | 0.905904 | − | 0.423484i | \(-0.139193\pi\) |
0.0862043 | + | 0.996277i | \(0.472526\pi\) | |||||||
\(480\) | −231.354 | + | 409.216i | −0.481988 | + | 0.852534i | ||||
\(481\) | 3.80224 | − | 2.19522i | 0.00790486 | − | 0.00456387i | ||||
\(482\) | 213.753 | − | 69.8799i | 0.443470 | − | 0.144979i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 642.006 | − | 470.001i | 1.32646 | − | 0.971076i | ||||
\(485\) | −526.678 | + | 304.078i | −1.08593 | + | 0.626964i | ||||
\(486\) | −264.827 | − | 55.7904i | −0.544911 | − | 0.114795i | ||||
\(487\) | −283.938 | + | 491.795i | −0.583034 | + | 1.00985i | 0.412083 | + | 0.911146i | \(0.364801\pi\) |
−0.995117 | + | 0.0986990i | \(0.968532\pi\) | |||||||
\(488\) | 76.1951 | − | 764.831i | 0.156137 | − | 1.56728i | ||||
\(489\) | 817.617i | 1.67202i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 78.8005i | 0.160490i | 0.996775 | + | 0.0802449i | \(0.0255702\pi\) | ||||
−0.996775 | + | 0.0802449i | \(0.974430\pi\) | |||||||
\(492\) | 386.035 | − | 875.555i | 0.784623 | − | 1.77958i | ||||
\(493\) | −29.4527 | + | 51.0135i | −0.0597417 | + | 0.103476i | ||||
\(494\) | −9.92190 | − | 2.09022i | −0.0200848 | − | 0.00423122i | ||||
\(495\) | 172.447 | − | 99.5626i | 0.348379 | − | 0.201136i | ||||
\(496\) | −0.255674 | − | 0.0810339i | −0.000515471 | − | 0.000163375i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −216.732 | − | 662.951i | −0.435204 | − | 1.33123i | ||||
\(499\) | −290.932 | + | 167.970i | −0.583030 | + | 0.336612i | −0.762337 | − | 0.647181i | \(-0.775948\pi\) |
0.179307 | + | 0.983793i | \(0.442615\pi\) | |||||||
\(500\) | −58.5579 | − | 538.406i | −0.117116 | − | 1.07681i | ||||
\(501\) | 215.701 | + | 124.535i | 0.430541 | + | 0.248573i | ||||
\(502\) | −161.935 | + | 180.502i | −0.322580 | + | 0.359566i | ||||
\(503\) | − | 274.052i | − | 0.544836i | −0.962179 | − | 0.272418i | \(-0.912177\pi\) | ||
0.962179 | − | 0.272418i | \(-0.0878233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 152.817 | 0.302609 | ||||||||
\(506\) | −1102.74 | − | 989.304i | −2.17932 | − | 1.95515i | ||||
\(507\) | 269.495 | − | 466.779i | 0.531548 | − | 0.920669i | ||||
\(508\) | −54.3625 | − | 499.832i | −0.107013 | − | 0.983921i | ||||
\(509\) | −168.009 | − | 291.000i | −0.330076 | − | 0.571709i | 0.652450 | − | 0.757831i | \(-0.273741\pi\) |
−0.982526 | + | 0.186123i | \(0.940408\pi\) | |||||||
\(510\) | 439.398 | − | 143.648i | 0.861566 | − | 0.281663i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −150.273 | + | 489.451i | −0.293501 | + | 0.955959i | ||||
\(513\) | −17.0106 | − | 29.4633i | −0.0331591 | − | 0.0574333i | ||||
\(514\) | −43.1972 | + | 205.049i | −0.0840412 | + | 0.398928i | ||||
\(515\) | −376.306 | − | 217.260i | −0.730691 | − | 0.421865i | ||||
\(516\) | 71.5933 | − | 162.379i | 0.138747 | − | 0.314688i | ||||
\(517\) | −639.829 | −1.23758 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 126.069 | 0.242908 | ||||||||
\(520\) | −11.1480 | + | 111.902i | −0.0214385 | + | 0.215196i | ||||
\(521\) | 547.572 | + | 316.141i | 1.05100 | + | 0.606796i | 0.922930 | − | 0.384969i | \(-0.125788\pi\) |
0.128072 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(522\) | −3.98029 | + | 18.8937i | −0.00762508 | + | 0.0361948i | ||||
\(523\) | −389.623 | − | 674.847i | −0.744977 | − | 1.29034i | −0.950206 | − | 0.311624i | \(-0.899127\pi\) |
0.205229 | − | 0.978714i | \(-0.434206\pi\) | |||||||
\(524\) | −365.683 | + | 267.710i | −0.697869 | + | 0.510897i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 65.0547 | + | 198.993i | 0.123678 | + | 0.378314i | ||||
\(527\) | 0.131877 | + | 0.228418i | 0.000250242 | + | 0.000433431i | ||||
\(528\) | 718.940 | − | 656.813i | 1.36163 | − | 1.24396i | ||||
\(529\) | −593.054 | + | 1027.20i | −1.12109 | + | 1.94178i | ||||
\(530\) | 295.358 | + | 264.976i | 0.557279 | + | 0.499955i | ||||
\(531\) | 177.165 | 0.333644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 228.907i | − | 0.429470i | ||||||
\(534\) | −448.638 | − | 402.489i | −0.840146 | − | 0.753725i | ||||
\(535\) | −399.862 | − | 230.861i | −0.747406 | − | 0.431515i | ||||
\(536\) | −45.9431 | − | 101.702i | −0.0857146 | − | 0.189742i | ||||
\(537\) | −700.908 | + | 404.669i | −1.30523 | + | 0.753574i | ||||
\(538\) | −189.507 | − | 579.674i | −0.352243 | − | 1.07746i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −304.453 | + | 222.885i | −0.563802 | + | 0.412750i | ||||
\(541\) | 583.617 | − | 336.952i | 1.07878 | − | 0.622831i | 0.148209 | − | 0.988956i | \(-0.452649\pi\) |
0.930566 | + | 0.366125i | \(0.119316\pi\) | |||||||
\(542\) | 42.3195 | − | 200.883i | 0.0780803 | − | 0.370633i | ||||
\(543\) | 497.743 | − | 862.117i | 0.916655 | − | 1.58769i | ||||
\(544\) | 433.749 | − | 255.681i | 0.797333 | − | 0.470002i | ||||
\(545\) | − | 227.217i | − | 0.416913i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 52.5329i | − | 0.0960382i | −0.998846 | − | 0.0480191i | \(-0.984709\pi\) | ||
0.998846 | − | 0.0480191i | \(-0.0152908\pi\) | |||||||
\(548\) | 286.712 | + | 126.412i | 0.523198 | + | 0.230679i | ||||
\(549\) | −123.880 | + | 214.566i | −0.225646 | + | 0.390831i | ||||
\(550\) | −46.9155 | + | 222.699i | −0.0853009 | + | 0.404907i | ||||
\(551\) | −5.04821 | + | 2.91458i | −0.00916190 | + | 0.00528963i | ||||
\(552\) | −915.643 | − | 657.695i | −1.65877 | − | 1.19148i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 31.6606 | − | 10.3505i | 0.0571491 | − | 0.0186832i | ||||
\(555\) | −17.1544 | + | 9.90409i | −0.0309088 | + | 0.0178452i | ||||
\(556\) | −64.4585 | − | 592.658i | −0.115933 | − | 1.06593i | ||||
\(557\) | 678.123 | + | 391.515i | 1.21746 | + | 0.702899i | 0.964373 | − | 0.264546i | \(-0.0852220\pi\) |
0.253083 | + | 0.967445i | \(0.418555\pi\) | |||||||
\(558\) | 0.0643534 | + | 0.0577337i | 0.000115329 | + | 0.000103465i | ||||
\(559\) | − | 42.4528i | − | 0.0759441i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −957.628 | −1.70700 | ||||||||
\(562\) | −101.275 | + | 112.887i | −0.180205 | + | 0.200867i | ||||
\(563\) | −446.202 | + | 772.844i | −0.792543 | + | 1.37272i | 0.131845 | + | 0.991270i | \(0.457910\pi\) |
−0.924388 | + | 0.381454i | \(0.875423\pi\) | |||||||
\(564\) | −484.044 | + | 52.6454i | −0.858234 | + | 0.0933429i | ||||
\(565\) | 98.0743 | + | 169.870i | 0.173583 | + | 0.300654i | ||||
\(566\) | 54.2739 | + | 166.016i | 0.0958903 | + | 0.293315i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −491.926 | − | 353.345i | −0.866067 | − | 0.622085i | ||||
\(569\) | 148.722 | + | 257.593i | 0.261373 | + | 0.452712i | 0.966607 | − | 0.256263i | \(-0.0824912\pi\) |
−0.705234 | + | 0.708975i | \(0.749158\pi\) | |||||||
\(570\) | 44.7642 | + | 9.43036i | 0.0785337 | + | 0.0165445i | ||||
\(571\) | −218.885 | − | 126.373i | −0.383335 | − | 0.221319i | 0.295933 | − | 0.955209i | \(-0.404369\pi\) |
−0.679268 | + | 0.733890i | \(0.737703\pi\) | |||||||
\(572\) | 93.9808 | − | 213.155i | 0.164302 | − | 0.372649i | ||||
\(573\) | 480.561 | 0.838676 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 263.479 | 0.458225 | ||||||||
\(576\) | 109.097 | − | 123.840i | 0.189404 | − | 0.215000i | ||||
\(577\) | −764.454 | − | 441.358i | −1.32488 | − | 0.764918i | −0.340375 | − | 0.940290i | \(-0.610554\pi\) |
−0.984502 | + | 0.175371i | \(0.943887\pi\) | |||||||
\(578\) | 81.0811 | + | 17.0812i | 0.140279 | + | 0.0295522i | ||||
\(579\) | 112.223 | + | 194.375i | 0.193821 | + | 0.335709i | ||||
\(580\) | 38.1888 | + | 52.1647i | 0.0658428 | + | 0.0899391i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 911.229 | − | 297.899i | 1.56568 | − | 0.511853i | ||||
\(583\) | −410.987 | − | 711.850i | −0.704951 | − | 1.22101i | ||||
\(584\) | 175.045 | + | 387.487i | 0.299734 | + | 0.663504i | ||||
\(585\) | 18.1248 | − | 31.3930i | 0.0309825 | − | 0.0536633i | ||||
\(586\) | −36.7358 | + | 40.9479i | −0.0626890 | + | 0.0698769i | ||||
\(587\) | 66.7814 | 0.113767 | 0.0568836 | − | 0.998381i | \(-0.481884\pi\) | ||||
0.0568836 | + | 0.998381i | \(0.481884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0261007i | 4.43136e-5i | ||||||||
\(590\) | 396.126 | − | 441.545i | 0.671400 | − | 0.748382i | ||||
\(591\) | 587.670 | + | 339.291i | 0.994365 | + | 0.574097i | ||||
\(592\) | −15.9279 | + | 14.5515i | −0.0269053 | + | 0.0245803i | ||||
\(593\) | 311.911 | − | 180.082i | 0.525989 | − | 0.303680i | −0.213393 | − | 0.976967i | \(-0.568451\pi\) |
0.739381 | + | 0.673287i | \(0.235118\pi\) | |||||||
\(594\) | 742.929 | − | 242.878i | 1.25072 | − | 0.408886i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 201.454 | + | 275.179i | 0.338009 | + | 0.461710i | ||||
\(597\) | 199.480 | − | 115.170i | 0.334137 | − | 0.192914i | ||||
\(598\) | −263.900 | − | 55.5952i | −0.441305 | − | 0.0929686i | ||||
\(599\) | 99.0219 | − | 171.511i | 0.165312 | − | 0.286329i | −0.771454 | − | 0.636285i | \(-0.780470\pi\) |
0.936766 | + | 0.349956i | \(0.113804\pi\) | |||||||
\(600\) | −17.1688 | + | 172.337i | −0.0286146 | + | 0.287228i | ||||
\(601\) | 373.907i | 0.622141i | 0.950387 | + | 0.311071i | \(0.100688\pi\) | ||||
−0.950387 | + | 0.311071i | \(0.899312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.9728i | 0.0596565i | ||||||||
\(604\) | 482.402 | + | 212.692i | 0.798679 | + | 0.352140i | ||||
\(605\) | −429.373 | + | 743.696i | −0.709708 | + | 1.22925i | ||||
\(606\) | −235.725 | − | 49.6597i | −0.388986 | − | 0.0819466i | ||||
\(607\) | −200.164 | + | 115.565i | −0.329760 | + | 0.190387i | −0.655735 | − | 0.754992i | \(-0.727641\pi\) |
0.325975 | + | 0.945379i | \(0.394308\pi\) | |||||||
\(608\) | 49.8234 | − | 0.450416i | 0.0819463 | − | 0.000740816i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 257.775 | + | 788.495i | 0.422581 | + | 1.29261i | ||||
\(611\) | −100.872 | + | 58.2386i | −0.165094 | + | 0.0953168i | ||||
\(612\) | −161.349 | + | 17.5486i | −0.263642 | + | 0.0286741i | ||||
\(613\) | −444.718 | − | 256.758i | −0.725479 | − | 0.418855i | 0.0912873 | − | 0.995825i | \(-0.470902\pi\) |
−0.816766 | + | 0.576969i | \(0.804235\pi\) | |||||||
\(614\) | −331.217 | + | 369.193i | −0.539441 | + | 0.601292i | ||||
\(615\) | 1032.75i | 1.67927i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1119.01 | −1.81363 | −0.906815 | − | 0.421529i | \(-0.861493\pi\) | ||||
−0.906815 | + | 0.421529i | \(0.861493\pi\) | |||||||
\(618\) | 509.862 | + | 457.415i | 0.825019 | + | 0.740154i | ||||
\(619\) | −64.1019 | + | 111.028i | −0.103557 | + | 0.179366i | −0.913148 | − | 0.407629i | \(-0.866356\pi\) |
0.809591 | + | 0.586995i | \(0.199689\pi\) | |||||||
\(620\) | 0.287777 | − | 0.0312991i | 0.000464157 | − | 5.04824e-5i | ||||
\(621\) | −452.445 | − | 783.658i | −0.728575 | − | 1.26193i | ||||
\(622\) | 830.802 | − | 271.605i | 1.33569 | − | 0.436665i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 53.5599 | − | 168.989i | 0.0858332 | − | 0.270816i | ||||
\(625\) | 212.735 | + | 368.469i | 0.340377 | + | 0.589550i | ||||
\(626\) | −34.1497 | + | 162.102i | −0.0545522 | + | 0.258949i | ||||
\(627\) | −82.0690 | − | 47.3826i | −0.130892 | − | 0.0755703i | ||||
\(628\) | −897.094 | − | 395.531i | −1.42849 | − | 0.629827i | ||||
\(629\) | 21.2160 | 0.0337297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 313.995 | 0.497615 | 0.248808 | − | 0.968553i | \(-0.419961\pi\) | ||||
0.248808 | + | 0.968553i | \(0.419961\pi\) | |||||||
\(632\) | −18.5170 | + | 185.870i | −0.0292991 | + | 0.294098i | ||||
\(633\) | 183.138 | + | 105.735i | 0.289317 | + | 0.167037i | ||||
\(634\) | −100.819 | + | 478.569i | −0.159020 | + | 0.754840i | ||||
\(635\) | 271.322 | + | 469.944i | 0.427279 | + | 0.740070i | ||||
\(636\) | −369.491 | − | 504.713i | −0.580961 | − | 0.793573i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −41.6145 | − | 127.293i | −0.0652264 | − | 0.199518i | ||||
\(639\) | 97.6183 | + | 169.080i | 0.152767 | + | 0.264601i | ||||
\(640\) | −64.7127 | − | 548.795i | −0.101114 | − | 0.857492i | ||||
\(641\) | 115.594 | − | 200.215i | 0.180334 | − | 0.312348i | −0.761660 | − | 0.647977i | \(-0.775615\pi\) |
0.941994 | + | 0.335629i | \(0.108949\pi\) | |||||||
\(642\) | 541.778 | + | 486.048i | 0.843891 | + | 0.757085i | ||||
\(643\) | −637.869 | −0.992020 | −0.496010 | − | 0.868317i | \(-0.665202\pi\) | ||||
−0.496010 | + | 0.868317i | \(0.665202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 191.532i | 0.296949i | ||||||||
\(646\) | −36.4719 | − | 32.7203i | −0.0564581 | − | 0.0506505i | ||||
\(647\) | 586.461 | + | 338.594i | 0.906432 | + | 0.523329i | 0.879281 | − | 0.476303i | \(-0.158023\pi\) |
0.0271505 | + | 0.999631i | \(0.491357\pi\) | |||||||
\(648\) | 711.263 | − | 321.309i | 1.09763 | − | 0.495847i | ||||
\(649\) | −1064.18 | + | 614.405i | −1.63972 | + | 0.946695i | ||||
\(650\) | 12.8741 | + | 39.3799i | 0.0198063 | + | 0.0605845i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −567.742 | − | 775.517i | −0.870769 | − | 1.18944i | ||||
\(653\) | −916.022 | + | 528.865i | −1.40279 | + | 0.809901i | −0.994678 | − | 0.103031i | \(-0.967146\pi\) |
−0.408112 | + | 0.912932i | \(0.633813\pi\) | |||||||
\(654\) | −73.8367 | + | 350.489i | −0.112900 | + | 0.535916i | ||||
\(655\) | 244.569 | − | 423.606i | 0.373388 | − | 0.646726i | ||||
\(656\) | 241.816 | + | 1098.53i | 0.368622 | + | 1.67459i | ||||
\(657\) | − | 137.058i | − | 0.208612i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 644.502i | 0.978000i | 0.872284 | + | 0.489000i | \(0.162638\pi\) | ||||
−0.872284 | + | 0.489000i | \(0.837362\pi\) | |||||||
\(660\) | −424.009 | + | 961.684i | −0.642438 | + | 1.45710i | ||||
\(661\) | −560.069 | + | 970.068i | −0.847306 | + | 1.46758i | 0.0362979 | + | 0.999341i | \(0.488443\pi\) |
−0.883604 | + | 0.468236i | \(0.844890\pi\) | |||||||
\(662\) | −31.5593 | + | 149.806i | −0.0476727 | + | 0.226294i | ||||
\(663\) | −150.975 | + | 87.1652i | −0.227714 | + | 0.131471i | ||||
\(664\) | 665.916 | + | 478.319i | 1.00289 | + | 0.720360i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.61007 | − | 2.16096i | 0.00992503 | − | 0.00324469i | ||||
\(667\) | −134.271 | + | 77.5214i | −0.201306 | + | 0.116224i | ||||
\(668\) | −291.070 | + | 31.6572i | −0.435733 | + | 0.0473910i | ||||
\(669\) | 340.438 | + | 196.552i | 0.508876 | + | 0.293800i | ||||
\(670\) | 89.6544 | + | 80.4322i | 0.133813 | + | 0.120048i | ||||
\(671\) | − | 1718.45i | − | 2.56103i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −307.811 | −0.457371 | −0.228686 | − | 0.973500i | \(-0.573443\pi\) | ||||
−0.228686 | + | 0.973500i | \(0.573443\pi\) | |||||||
\(674\) | 51.0883 | − | 56.9460i | 0.0757987 | − | 0.0844897i | ||||
\(675\) | −69.5058 | + | 120.388i | −0.102972 | + | 0.178352i | ||||
\(676\) | 68.5065 | + | 629.878i | 0.101341 | + | 0.931772i | ||||
\(677\) | 507.773 | + | 879.488i | 0.750033 | + | 1.29910i | 0.947806 | + | 0.318848i | \(0.103296\pi\) |
−0.197773 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(678\) | −96.0814 | − | 293.899i | −0.141713 | − | 0.433479i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −317.026 | + | 441.364i | −0.466215 | + | 0.649064i | ||||
\(681\) | 96.1388 | + | 166.517i | 0.141173 | + | 0.244519i | ||||
\(682\) | −0.586772 | − | 0.123614i | −0.000860369 | − | 0.000181252i | ||||
\(683\) | −840.220 | − | 485.102i | −1.23019 | − | 0.710251i | −0.263121 | − | 0.964763i | \(-0.584752\pi\) |
−0.967070 | + | 0.254512i | \(0.918085\pi\) | |||||||
\(684\) | −14.6959 | − | 6.47948i | −0.0214853 | − | 0.00947293i | ||||
\(685\) | −338.188 | −0.493706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −402.680 | −0.586143 | ||||||||
\(688\) | 44.8467 | + | 203.731i | 0.0651842 | + | 0.296121i | ||||
\(689\) | −129.588 | − | 74.8177i | −0.188081 | − | 0.108589i | ||||
\(690\) | 1190.63 | + | 250.827i | 1.72555 | + | 0.363517i | ||||
\(691\) | −274.581 | − | 475.588i | −0.397367 | − | 0.688260i | 0.596033 | − | 0.802960i | \(-0.296743\pi\) |
−0.993400 | + | 0.114700i | \(0.963409\pi\) | |||||||
\(692\) | −119.578 | + | 87.5407i | −0.172800 | + | 0.126504i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −457.442 | + | 149.547i | −0.659138 | + | 0.215485i | ||||
\(695\) | 321.711 | + | 557.221i | 0.462894 | + | 0.801756i | ||||
\(696\) | −41.9559 | − | 92.8754i | −0.0602814 | − | 0.133442i | ||||
\(697\) | 553.076 | − | 957.956i | 0.793510 | − | 1.37440i | ||||
\(698\) | −574.786 | + | 640.691i | −0.823476 | + | 0.917895i | ||||
\(699\) | −83.9818 | −0.120146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 452.665i | − | 0.645742i | −0.946443 | − | 0.322871i | \(-0.895352\pi\) | ||
0.946443 | − | 0.322871i | \(-0.104648\pi\) | |||||||
\(702\) | 95.0191 | − | 105.914i | 0.135355 | − | 0.150874i | ||||
\(703\) | 1.81822 | + | 1.04975i | 0.00258637 | + | 0.00149324i | ||||
\(704\) | −225.839 | + | 1122.21i | −0.320794 | + | 1.59406i | ||||
\(705\) | 455.100 | − | 262.752i | 0.645533 | − | 0.372698i | ||||
\(706\) | −583.781 | + | 190.849i | −0.826885 | + | 0.270325i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −754.520 | + | 552.371i | −1.06571 | + | 0.780185i | ||||
\(709\) | −609.174 | + | 351.707i | −0.859202 | + | 0.496060i | −0.863745 | − | 0.503929i | \(-0.831887\pi\) |
0.00454321 | + | 0.999990i | \(0.498554\pi\) | |||||||
\(710\) | 639.660 | + | 134.756i | 0.900930 | + | 0.189797i | ||||
\(711\) | 30.1054 | − | 52.1442i | 0.0423424 | − | 0.0733392i | ||||
\(712\) | 705.020 | + | 70.2365i | 0.990197 | + | 0.0986468i | ||||
\(713\) | 0.694220i | 0.000973661i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 251.425i | 0.351644i | ||||||||
\(716\) | 383.820 | − | 870.533i | 0.536062 | − | 1.21583i | ||||
\(717\) | 427.367 | − | 740.221i | 0.596049 | − | 1.03239i | ||||
\(718\) | 903.684 | + | 190.377i | 1.25861 | + | 0.265149i | ||||
\(719\) | −54.1160 | + | 31.2439i | −0.0752656 | + | 0.0434546i | −0.537161 | − | 0.843480i | \(-0.680503\pi\) |
0.461895 | + | 0.886935i | \(0.347170\pi\) | |||||||
\(720\) | −53.8176 | + | 169.802i | −0.0747467 | + | 0.235836i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 222.845 | + | 681.650i | 0.308649 | + | 0.944113i | ||||
\(723\) | 331.354 | − | 191.307i | 0.458305 | − | 0.264602i | ||||
\(724\) | 126.528 | + | 1163.35i | 0.174762 | + | 1.60684i | ||||
\(725\) | 20.6271 | + | 11.9090i | 0.0284511 | + | 0.0164263i | ||||
\(726\) | 903.992 | − | 1007.64i | 1.24517 | − | 1.38794i | ||||
\(727\) | − | 889.995i | − | 1.22420i | −0.790779 | − | 0.612101i | \(-0.790324\pi\) | ||
0.790779 | − | 0.612101i | \(-0.209676\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 417.569 | 0.572797 | ||||||||
\(730\) | −341.586 | − | 306.449i | −0.467927 | − | 0.419794i | ||||
\(731\) | 102.573 | − | 177.661i | 0.140318 | − | 0.243038i | ||||
\(732\) | −141.395 | − | 1300.04i | −0.193162 | − | 1.77601i | ||||
\(733\) | 456.127 | + | 790.035i | 0.622274 | + | 1.07781i | 0.989061 | + | 0.147505i | \(0.0471243\pi\) |
−0.366787 | + | 0.930305i | \(0.619542\pi\) | |||||||
\(734\) | −1191.81 | + | 389.628i | −1.62372 | + | 0.530828i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1325.19 | − | 11.9801i | 1.80053 | − | 0.0162773i | ||||
\(737\) | −124.753 | − | 216.079i | −0.169271 | − | 0.293187i | ||||
\(738\) | 74.7438 | − | 354.795i | 0.101279 | − | 0.480752i | ||||
\(739\) | 1081.52 | + | 624.415i | 1.46349 | + | 0.844946i | 0.999171 | − | 0.0407224i | \(-0.0129659\pi\) |
0.464319 | + | 0.885668i | \(0.346299\pi\) | |||||||
\(740\) | 9.39382 | − | 21.3059i | 0.0126944 | − | 0.0287917i | ||||
\(741\) | −17.2514 | −0.0232813 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −305.880 | −0.411682 | −0.205841 | − | 0.978585i | \(-0.565993\pi\) | ||||
−0.205841 | + | 0.978585i | \(0.565993\pi\) | |||||||
\(744\) | −0.454075 | − | 0.0452365i | −0.000610316 | − | 6.08018e-5i | ||||
\(745\) | −318.766 | − | 184.040i | −0.427874 | − | 0.247033i | ||||
\(746\) | 170.106 | − | 807.464i | 0.228025 | − | 1.08239i | ||||
\(747\) | −132.145 | − | 228.882i | −0.176901 | − | 0.306401i | ||||
\(748\) | 908.318 | − | 664.963i | 1.21433 | − | 0.888988i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −286.323 | − | 875.820i | −0.381764 | − | 1.16776i | ||||
\(751\) | −258.895 | − | 448.420i | −0.344734 | − | 0.597097i | 0.640571 | − | 0.767899i | \(-0.278698\pi\) |
−0.985305 | + | 0.170802i | \(0.945364\pi\) | |||||||
\(752\) | 422.564 | − | 386.048i | 0.561920 | − | 0.513362i | ||||
\(753\) | −206.288 | + | 357.302i | −0.273955 | + | 0.474504i | ||||
\(754\) | −18.1472 | − | 16.2805i | −0.0240678 | − | 0.0215921i | ||||
\(755\) | −569.012 | −0.753659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 939.898i | 1.24161i | 0.783965 | + | 0.620804i | \(0.213194\pi\) | ||||
−0.783965 | + | 0.620804i | \(0.786806\pi\) | |||||||
\(758\) | 486.982 | + | 436.889i | 0.642457 | + | 0.576371i | ||||
\(759\) | −2182.85 | − | 1260.27i | −2.87596 | − | 1.66044i | ||||
\(760\) | −49.0075 | + | 22.1388i | −0.0644836 | + | 0.0291301i | ||||
\(761\) | 976.757 | − | 563.931i | 1.28352 | − | 0.741039i | 0.306028 | − | 0.952022i | \(-0.401000\pi\) |
0.977490 | + | 0.210983i | \(0.0676665\pi\) | |||||||
\(762\) | −265.809 | − | 813.072i | −0.348831 | − | 1.06702i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −455.816 | + | 333.695i | −0.596618 | + | 0.436773i | ||||
\(765\) | 151.701 | − | 87.5846i | 0.198302 | − | 0.114490i | ||||
\(766\) | −102.603 | + | 487.039i | −0.133947 | + | 0.635821i | ||||
\(767\) | −111.849 | + | 193.728i | −0.145826 | + | 0.252579i | ||||
\(768\) | −78.5156 | + | 867.560i | −0.102234 | + | 1.12964i | ||||
\(769\) | − | 300.115i | − | 0.390267i | −0.980777 | − | 0.195133i | \(-0.937486\pi\) | ||
0.980777 | − | 0.195133i | \(-0.0625139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 356.524i | 0.462417i | ||||||||
\(772\) | −241.416 | − | 106.441i | −0.312714 | − | 0.137877i | ||||
\(773\) | 375.120 | − | 649.727i | 0.485278 | − | 0.840527i | −0.514579 | − | 0.857443i | \(-0.672052\pi\) |
0.999857 | + | 0.0169165i | \(0.00538495\pi\) | |||||||
\(774\) | 13.8619 | − | 65.7997i | 0.0179094 | − | 0.0850125i | ||||
\(775\) | 0.0923598 | − | 0.0533240i | 0.000119174 | − | 6.88051e-5i | ||||
\(776\) | −657.452 | + | 915.304i | −0.847231 | + | 1.17952i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −717.194 | + | 234.465i | −0.921843 | + | 0.301369i | ||||
\(779\) | 94.7977 | − | 54.7315i | 0.121691 | − | 0.0702586i | ||||
\(780\) | 20.6874 | + | 190.208i | 0.0265222 | + | 0.243857i | ||||
\(781\) | −1172.73 | − | 677.076i | −1.50158 | − | 0.866935i | ||||
\(782\) | −970.071 | − | 870.285i | −1.24050 | − | 1.11290i | ||||
\(783\) | − | 81.8005i | − | 0.104471i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1058.16 | 1.34797 | ||||||||
\(786\) | −514.910 | + | 573.949i | −0.655102 | + | 0.730215i | ||||
\(787\) | 144.776 | − | 250.760i | 0.183960 | − | 0.318627i | −0.759266 | − | 0.650781i | \(-0.774442\pi\) |
0.943225 | + | 0.332153i | \(0.107775\pi\) | |||||||
\(788\) | −793.009 | + | 86.2489i | −1.00636 | + | 0.109453i | ||||
\(789\) | 178.098 | + | 308.474i | 0.225726 | + | 0.390969i | ||||
\(790\) | −62.6447 | − | 191.621i | −0.0792971 | − | 0.242558i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 215.266 | − | 299.693i | 0.271801 | − | 0.378401i | ||||
\(793\) | −156.417 | − | 270.922i | −0.197247 | − | 0.341642i | ||||
\(794\) | −1314.64 | − | 276.952i | −1.65572 | − | 0.348807i | ||||
\(795\) | 584.657 | + | 337.552i | 0.735417 | + | 0.424593i | ||||
\(796\) | −109.236 | + | 247.756i | −0.137231 | + | 0.311251i | ||||
\(797\) | 1086.57 | 1.36332 | 0.681659 | − | 0.731670i | \(-0.261259\pi\) | ||||
0.681659 | + | 0.731670i | \(0.261259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −562.854 | −0.704448 | ||||||||
\(800\) | −103.383 | − | 175.384i | −0.129229 | − | 0.219231i | ||||
\(801\) | −197.787 | − | 114.192i | −0.246925 | − | 0.142562i | ||||
\(802\) | −920.593 | − | 193.939i | −1.14787 | − | 0.241819i | ||||
\(803\) | 475.313 | + | 823.267i | 0.591922 | + | 1.02524i | ||||
\(804\) | −112.157 | − | 153.203i | −0.139499 | − | 0.190551i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.103759 | + | 0.0339208i | −0.000128733 | + | 4.20854e-5i | ||||
\(807\) | −518.806 | − | 898.598i | −0.642882 | − | 1.11350i | ||||
\(808\) | 258.070 | − | 116.582i | 0.319394 | − | 0.144284i | ||||
\(809\) | −90.9745 | + | 157.572i | −0.112453 | + | 0.194774i | −0.916759 | − | 0.399441i | \(-0.869204\pi\) |
0.804306 | + | 0.594216i | \(0.202537\pi\) | |||||||
\(810\) | −562.513 | + | 627.010i | −0.694460 | + | 0.774086i | ||||
\(811\) | 1005.31 | 1.23960 | 0.619799 | − | 0.784760i | \(-0.287214\pi\) | ||||
0.619799 | + | 0.784760i | \(0.287214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 349.280i | − | 0.429619i | ||||||
\(814\) | −32.2106 | + | 35.9039i | −0.0395708 | + | 0.0441079i | ||||
\(815\) | 898.355 | + | 518.665i | 1.10228 | + | 0.636399i | ||||
\(816\) | 632.447 | − | 577.795i | 0.775058 | − | 0.708082i | ||||
\(817\) | 17.5810 | − | 10.1504i | 0.0215190 | − | 0.0124240i | ||||
\(818\) | −126.744 | + | 41.4351i | −0.154944 | + | 0.0506541i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −717.128 | − | 979.573i | −0.874546 | − | 1.19460i | ||||
\(821\) | 851.009 | − | 491.330i | 1.03655 | − | 0.598453i | 0.117697 | − | 0.993050i | \(-0.462449\pi\) |
0.918855 | + | 0.394596i | \(0.129115\pi\) | |||||||
\(822\) | 521.665 | + | 109.898i | 0.634629 | + | 0.133696i | ||||
\(823\) | −742.505 | + | 1286.06i | −0.902194 | + | 1.56265i | −0.0775532 | + | 0.996988i | \(0.524711\pi\) |
−0.824641 | + | 0.565657i | \(0.808623\pi\) | |||||||
\(824\) | −801.231 | − | 79.8213i | −0.972367 | − | 0.0968705i | ||||
\(825\) | 387.212i | 0.469348i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 708.113i | − | 0.856243i | −0.903721 | − | 0.428121i | \(-0.859176\pi\) | ||
0.903721 | − | 0.428121i | \(-0.140824\pi\) | |||||||
\(828\) | −390.879 | − | 172.340i | −0.472076 | − | 0.208140i | ||||
\(829\) | 75.0164 | − | 129.932i | 0.0904902 | − | 0.156734i | −0.817227 | − | 0.576316i | \(-0.804490\pi\) |
0.907718 | + | 0.419582i | \(0.137823\pi\) | |||||||
\(830\) | −865.902 | − | 182.418i | −1.04326 | − | 0.219780i | ||||
\(831\) | 49.0796 | − | 28.3361i | 0.0590609 | − | 0.0340988i | ||||
\(832\) | 66.5417 | + | 197.479i | 0.0799780 | + | 0.237354i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −315.174 | − | 964.072i | −0.377907 | − | 1.15596i | ||||
\(835\) | 273.665 | − | 158.001i | 0.327743 | − | 0.189222i | ||||
\(836\) | 110.745 | − | 12.0448i | 0.132470 | − | 0.0144077i | ||||
\(837\) | −0.317199 | − | 0.183135i | −0.000378972 | − | 0.000218799i | ||||
\(838\) | 584.152 | − | 651.130i | 0.697079 | − | 0.777005i | ||||
\(839\) | 1106.41i | 1.31873i | 0.751824 | + | 0.659364i | \(0.229174\pi\) | ||||
−0.751824 | + | 0.659364i | \(0.770826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 826.984 | 0.983335 | ||||||||
\(842\) | 1047.75 | + | 939.975i | 1.24436 | + | 1.11636i | ||||
\(843\) | −129.014 | + | 223.459i | −0.153042 | + | 0.265076i | ||||
\(844\) | −247.128 | + | 26.8781i | −0.292806 | + | 0.0318461i | ||||
\(845\) | −341.915 | − | 592.214i | −0.404633 | − | 0.700845i | ||||
\(846\) | −175.363 | + | 57.3297i | −0.207285 | + | 0.0677656i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 700.931 | + | 222.155i | 0.826569 | + | 0.261975i | ||||
\(849\) | 148.584 | + | 257.354i | 0.175010 | + | 0.303126i | ||||
\(850\) | −41.2713 | + | 195.907i | −0.0485544 | + | 0.230479i | ||||
\(851\) | 48.3606 | + | 27.9210i | 0.0568279 | + | 0.0328096i | ||||
\(852\) | −942.904 | − | 415.729i | −1.10669 | − | 0.487945i | ||||
\(853\) | −1243.82 | −1.45817 | −0.729086 | − | 0.684423i | \(-0.760054\pi\) | ||||
−0.729086 | + | 0.684423i | \(0.760054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.3344 | 0.0202742 | ||||||||
\(856\) | −851.386 | − | 84.8180i | −0.994610 | − | 0.0990864i | ||||
\(857\) | −245.650 | − | 141.826i | −0.286639 | − | 0.165491i | 0.349786 | − | 0.936830i | \(-0.386254\pi\) |
−0.636425 | + | 0.771339i | \(0.719588\pi\) | |||||||
\(858\) | 81.7033 | − | 387.831i | 0.0952253 | − | 0.452017i | ||||
\(859\) | −455.900 | − | 789.641i | −0.530733 | − | 0.919256i | −0.999357 | − | 0.0358586i | \(-0.988583\pi\) |
0.468624 | − | 0.883398i | \(-0.344750\pi\) | |||||||
\(860\) | −132.997 | − | 181.670i | −0.154648 | − | 0.211244i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 341.647 | + | 1045.05i | 0.396342 | + | 1.21235i | ||||
\(863\) | 436.908 | + | 756.747i | 0.506266 | + | 0.876879i | 0.999974 | + | 0.00725099i | \(0.00230808\pi\) |
−0.493707 | + | 0.869628i | \(0.664359\pi\) | |||||||
\(864\) | −344.111 | + | 608.659i | −0.398276 | + | 0.704466i | ||||
\(865\) | 79.9735 | − | 138.518i | 0.0924550 | − | 0.160137i | ||||
\(866\) | −528.509 | − | 474.145i | −0.610288 | − | 0.547511i | ||||
\(867\) | 140.978 | 0.162604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 417.620i | 0.480575i | ||||||||
\(870\) | 81.8737 | + | 73.4518i | 0.0941077 | + | 0.0844274i | ||||
\(871\) | −39.3358 | − | 22.7105i | −0.0451617 | − | 0.0260741i | ||||
\(872\) | −173.340 | − | 383.713i | −0.198784 | − | 0.440038i | ||||
\(873\) | 314.599 | − | 181.634i | 0.360365 | − | 0.208057i | ||||
\(874\) | −40.0745 | − | 122.582i | −0.0458518 | − | 0.140254i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 427.323 | + | 583.709i | 0.487811 | + | 0.666334i | ||||
\(877\) | 549.476 | − | 317.240i | 0.626540 | − | 0.361733i | −0.152871 | − | 0.988246i | \(-0.548852\pi\) |
0.779411 | + | 0.626513i | \(0.215518\pi\) | |||||||
\(878\) | 227.099 | − | 1078.00i | 0.258655 | − | 1.22779i | ||||
\(879\) | −46.7975 | + | 81.0557i | −0.0532395 | + | 0.0922136i | ||||
\(880\) | −265.603 | − | 1206.59i | −0.301822 | − | 1.37113i | ||||
\(881\) | − | 670.044i | − | 0.760549i | −0.924874 | − | 0.380274i | \(-0.875830\pi\) | ||
0.924874 | − | 0.380274i | \(-0.124170\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 875.514i | − | 0.991522i | −0.868459 | − | 0.495761i | \(-0.834889\pi\) | ||
0.868459 | − | 0.495761i | \(-0.165111\pi\) | |||||||
\(884\) | 82.6744 | − | 187.512i | 0.0935231 | − | 0.212117i | ||||
\(885\) | 504.623 | − | 874.033i | 0.570196 | − | 0.987608i | ||||
\(886\) | −111.412 | + | 528.854i | −0.125748 | + | 0.596901i | ||||
\(887\) | −854.152 | + | 493.145i | −0.962967 | + | 0.555969i | −0.897085 | − | 0.441858i | \(-0.854319\pi\) |
−0.0658820 | + | 0.997827i | \(0.520986\pi\) | |||||||
\(888\) | −21.4138 | + | 29.8123i | −0.0241146 | + | 0.0335724i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −726.833 | + | 237.616i | −0.816667 | + | 0.266985i | ||||
\(891\) | 1511.17 | − | 872.476i | 1.69604 | − | 0.979210i | ||||
\(892\) | −459.392 | + | 49.9642i | −0.515013 | + | 0.0560136i | ||||
\(893\) | −48.2368 | − | 27.8495i | −0.0540166 | − | 0.0311865i | ||||
\(894\) | 431.900 | + | 387.473i | 0.483109 | + | 0.433415i | ||||
\(895\) | 1026.83i | 1.14729i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −458.850 | −0.511538 | ||||||||
\(898\) | −608.216 | + | 677.953i | −0.677301 | + | 0.754959i | ||||
\(899\) | −0.0313782 | + | 0.0543486i | −3.49034e−5 | + | 6.04545e-5i | ||||
\(900\) | 7.09567 | + | 65.2406i | 0.00788408 | + | 0.0724896i | ||||
\(901\) | −361.543 | − | 626.210i | −0.401268 | − | 0.695017i | ||||
\(902\) | 781.457 | + | 2390.36i | 0.866360 | + | 2.65007i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 295.213 | + | 212.048i | 0.326564 | + | 0.234567i | ||||
\(905\) | −631.499 | − | 1093.79i | −0.697789 | − | 1.20861i | ||||
\(906\) | 877.718 | + | 184.907i | 0.968783 | + | 0.204091i | ||||
\(907\) | −750.592 | − | 433.355i | −0.827555 | − | 0.477789i | 0.0254599 | − | 0.999676i | \(-0.491895\pi\) |
−0.853015 | + | 0.521887i | \(0.825228\pi\) | |||||||
\(908\) | −206.816 | − | 91.1856i | −0.227771 | − | 0.100425i | ||||
\(909\) | −91.2820 | −0.100420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −128.713 | −0.141288 | −0.0706438 | − | 0.997502i | \(-0.522505\pi\) | ||||
−0.0706438 | + | 0.997502i | \(0.522505\pi\) | |||||||
\(912\) | 82.7898 | − | 18.2243i | 0.0907782 | − | 0.0199827i | ||||
\(913\) | 1587.51 | + | 916.552i | 1.73879 | + | 1.00389i | ||||
\(914\) | −330.025 | − | 69.5255i | −0.361077 | − | 0.0760673i | ||||
\(915\) | 705.699 | + | 1222.31i | 0.771256 | + | 1.33585i | ||||
\(916\) | 381.945 | − | 279.615i | 0.416971 | − | 0.305257i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 653.550 | − | 213.659i | 0.711929 | − | 0.232743i | ||||
\(919\) | −430.087 | − | 744.933i | −0.467995 | − | 0.810591i | 0.531336 | − | 0.847161i | \(-0.321690\pi\) |
−0.999331 | + | 0.0365701i | \(0.988357\pi\) | |||||||
\(920\) | −1303.49 | + | 588.844i | −1.41684 | + | 0.640047i | ||||
\(921\) | −421.935 | + | 730.813i | −0.458127 | + | 0.793500i | ||||
\(922\) | −354.009 | + | 394.599i | −0.383957 | + | 0.427982i | ||||
\(923\) | −246.515 | −0.267081 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.57859i | − | 0.00927415i | ||||||
\(926\) | −130.183 | + | 145.109i | −0.140586 | + | 0.156706i | ||||
\(927\) | 224.778 | + | 129.776i | 0.242479 | + | 0.139995i | ||||
\(928\) | 104.287 | + | 58.9595i | 0.112378 | + | 0.0635340i | ||||
\(929\) | −202.025 | + | 116.639i | −0.217465 | + | 0.125554i | −0.604776 | − | 0.796396i | \(-0.706737\pi\) |
0.387311 | + | 0.921949i | \(0.373404\pi\) | |||||||
\(930\) | 0.468124 | − | 0.153039i | 0.000503360 | − | 0.000164558i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 79.6575 | − | 58.3158i | 0.0854694 | − | 0.0625706i | ||||
\(933\) | 1287.89 | − | 743.563i | 1.38037 | − | 0.796960i | ||||
\(934\) | 145.212 | + | 30.5914i | 0.155473 | + | 0.0327531i | ||||
\(935\) | −607.483 | + | 1052.19i | −0.649714 | + | 1.12534i | ||||
\(936\) | 6.65903 | − | 66.8420i | 0.00711435 | − | 0.0714124i | ||||
\(937\) | − | 1426.29i | − | 1.52219i | −0.648641 | − | 0.761095i | \(-0.724662\pi\) | ||
0.648641 | − | 0.761095i | \(-0.275338\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 281.851i | 0.300161i | ||||||||
\(940\) | −249.215 | + | 565.238i | −0.265123 | + | 0.601317i | ||||
\(941\) | 635.425 | − | 1100.59i | 0.675265 | − | 1.16959i | −0.301126 | − | 0.953584i | \(-0.597362\pi\) |
0.976391 | − | 0.216010i | \(-0.0693043\pi\) | |||||||
\(942\) | −1632.24 | − | 343.860i | −1.73274 | − | 0.365031i | ||||
\(943\) | 2521.41 | − | 1455.73i | 2.67381 | − | 1.54373i | ||||
\(944\) | 332.111 | − | 1047.86i | 0.351812 | − | 1.11002i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 144.928 | + | 443.312i | 0.153200 | + | 0.468618i | ||||
\(947\) | −1413.50 | + | 816.086i | −1.49261 | + | 0.861759i | −0.999964 | − | 0.00847064i | \(-0.997304\pi\) |
−0.492646 | + | 0.870230i | \(0.663970\pi\) | |||||||
\(948\) | 34.3619 | + | 315.938i | 0.0362467 | + | 0.333268i | ||||
\(949\) | 149.871 | + | 86.5280i | 0.157925 | + | 0.0911781i | ||||
\(950\) | −13.2303 | + | 14.7472i | −0.0139266 | + | 0.0155234i | ||||
\(951\) | 832.098i | 0.874972i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 95.9158 | 0.100646 | 0.0503231 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503231 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(954\) | −176.425 | − | 158.277i | −0.184932 | − | 0.165909i | ||||
\(955\) | 304.850 | − | 528.015i | 0.319215 | − | 0.552896i | ||||
\(956\) | 108.638 | + | 998.864i | 0.113638 | + | 1.04484i | ||||
\(957\) | −113.926 | − | 197.326i | −0.119045 | − | 0.206192i | ||||
\(958\) | −1043.14 | + | 341.024i | −1.08888 | + | 0.355975i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −300.213 | − | 890.957i | −0.312722 | − | 0.928080i | ||||
\(961\) | −480.500 | − | 832.250i | −0.500000 | − | 0.866025i | ||||
\(962\) | −1.81012 | + | 8.59229i | −0.00188162 | + | 0.00893170i | ||||
\(963\) | 238.849 | + | 137.899i | 0.248025 | + | 0.143198i | ||||
\(964\) | −181.451 | + | 411.545i | −0.188227 | + | 0.426914i | ||||
\(965\) | 284.759 | 0.295087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1419.97 | 1.46843 | 0.734216 | − | 0.678916i | \(-0.237550\pi\) | ||||
0.734216 | + | 0.678916i | \(0.237550\pi\) | |||||||
\(968\) | −157.751 | + | 1583.48i | −0.162966 | + | 1.63582i | ||||
\(969\) | −72.1956 | − | 41.6822i | −0.0745053 | − | 0.0430157i | ||||
\(970\) | 250.734 | − | 1190.19i | 0.258488 | − | 1.22700i | ||||
\(971\) | 329.817 | + | 571.261i | 0.339668 | + | 0.588322i | 0.984370 | − | 0.176112i | \(-0.0563520\pi\) |
−0.644702 | + | 0.764434i | \(0.723019\pi\) | |||||||
\(972\) | 436.750 | − | 319.737i | 0.449332 | − | 0.328948i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −352.919 | − | 1079.53i | −0.362340 | − | 1.10834i | ||||
\(975\) | 35.2448 | + | 61.0459i | 0.0361486 | + | 0.0626111i | ||||
\(976\) | 1036.85 | + | 1134.92i | 1.06234 | + | 1.16283i | ||||
\(977\) | 957.151 | − | 1657.83i | 0.979683 | − | 1.69686i | 0.316160 | − | 0.948706i | \(-0.397606\pi\) |
0.663523 | − | 0.748156i | \(-0.269060\pi\) | |||||||
\(978\) | −1217.19 | − | 1091.99i | −1.24457 | − | 1.11655i | ||||
\(979\) | 1584.07 | 1.61804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 135.723i | 0.138352i | ||||||||
\(982\) | −117.311 | − | 105.244i | −0.119461 | − | 0.107173i | ||||
\(983\) | −193.655 | − | 111.806i | −0.197004 | − | 0.113740i | 0.398253 | − | 0.917275i | \(-0.369616\pi\) |
−0.595257 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(984\) | 787.867 | + | 1744.06i | 0.800678 | + | 1.77242i | ||||
\(985\) | 745.591 | − | 430.467i | 0.756945 | − | 0.437022i | ||||
\(986\) | −36.6080 | − | 111.979i | −0.0371278 | − | 0.113569i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.3631 | − | 11.9792i | 0.0165619 | − | 0.0121247i | ||||
\(989\) | 467.616 | − | 269.978i | 0.472816 | − | 0.272981i | ||||
\(990\) | −82.0964 | + | 389.697i | −0.0829257 | + | 0.393633i | ||||
\(991\) | 736.371 | − | 1275.43i | 0.743058 | − | 1.28701i | −0.208038 | − | 0.978121i | \(-0.566708\pi\) |
0.951096 | − | 0.308894i | \(-0.0999589\pi\) | |||||||
\(992\) | 0.462106 | − | 0.272396i | 0.000465833 | − | 0.000274593i | ||||
\(993\) | 260.472i | 0.262308i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 292.237i | − | 0.293706i | ||||||
\(996\) | 1276.40 | + | 562.768i | 1.28153 | + | 0.565029i | ||||
\(997\) | 53.4480 | − | 92.5746i | 0.0536088 | − | 0.0928532i | −0.837976 | − | 0.545708i | \(-0.816261\pi\) |
0.891584 | + | 0.452854i | \(0.149594\pi\) | |||||||
\(998\) | 138.503 | − | 657.448i | 0.138781 | − | 0.658765i | ||||
\(999\) | −25.5150 | + | 14.7311i | −0.0255405 | + | 0.0147458i |
(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 | 392.3.j.e.325.5 | 28 | ||
7.2 | even | 3 | 56.3.j.a.5.14 | yes | 28 | ||
7.3 | odd | 6 | 392.3.h.a.293.9 | 28 | |||
7.4 | even | 3 | 392.3.h.a.293.10 | 28 | |||
7.5 | odd | 6 | inner | 392.3.j.e.117.14 | 28 | ||
7.6 | odd | 2 | 56.3.j.a.45.5 | yes | 28 | ||
8.5 | even | 2 | inner | 392.3.j.e.325.14 | 28 | ||
28.3 | even | 6 | 1568.3.h.a.881.22 | 28 | |||
28.11 | odd | 6 | 1568.3.h.a.881.8 | 28 | |||
28.23 | odd | 6 | 224.3.n.a.145.11 | 28 | |||
28.27 | even | 2 | 224.3.n.a.17.4 | 28 | |||
56.3 | even | 6 | 1568.3.h.a.881.7 | 28 | |||
56.5 | odd | 6 | inner | 392.3.j.e.117.5 | 28 | ||
56.11 | odd | 6 | 1568.3.h.a.881.21 | 28 | |||
56.13 | odd | 2 | 56.3.j.a.45.14 | yes | 28 | ||
56.27 | even | 2 | 224.3.n.a.17.11 | 28 | |||
56.37 | even | 6 | 56.3.j.a.5.5 | ✓ | 28 | ||
56.45 | odd | 6 | 392.3.h.a.293.12 | 28 | |||
56.51 | odd | 6 | 224.3.n.a.145.4 | 28 | |||
56.53 | even | 6 | 392.3.h.a.293.11 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.5 | ✓ | 28 | 56.37 | even | 6 | ||
56.3.j.a.5.14 | yes | 28 | 7.2 | even | 3 | ||
56.3.j.a.45.5 | yes | 28 | 7.6 | odd | 2 | ||
56.3.j.a.45.14 | yes | 28 | 56.13 | odd | 2 | ||
224.3.n.a.17.4 | 28 | 28.27 | even | 2 | |||
224.3.n.a.17.11 | 28 | 56.27 | even | 2 | |||
224.3.n.a.145.4 | 28 | 56.51 | odd | 6 | |||
224.3.n.a.145.11 | 28 | 28.23 | odd | 6 | |||
392.3.h.a.293.9 | 28 | 7.3 | odd | 6 | |||
392.3.h.a.293.10 | 28 | 7.4 | even | 3 | |||
392.3.h.a.293.11 | 28 | 56.53 | even | 6 | |||
392.3.h.a.293.12 | 28 | 56.45 | odd | 6 | |||
392.3.j.e.117.5 | 28 | 56.5 | odd | 6 | inner | ||
392.3.j.e.117.14 | 28 | 7.5 | odd | 6 | inner | ||
392.3.j.e.325.5 | 28 | 1.1 | even | 1 | trivial | ||
392.3.j.e.325.14 | 28 | 8.5 | even | 2 | inner | ||
1568.3.h.a.881.7 | 28 | 56.3 | even | 6 | |||
1568.3.h.a.881.8 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.21 | 28 | 56.11 | odd | 6 | |||
1568.3.h.a.881.22 | 28 | 28.3 | even | 6 |