Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Character | \(\chi\) | \(=\) | 1050.649 |
Dual form | 1050.3.q.e.199.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 4.01037 | + | 5.73733i | 0.572910 | + | 0.819618i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.69259 | + | 15.0560i | 0.790236 | + | 1.36873i | 0.925821 | + | 0.377963i | \(0.123375\pi\) |
−0.135585 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(12\) | −1.73205 | + | 3.00000i | −0.144338 | + | 0.250000i | ||||
\(13\) | 7.22559 | 0.555815 | 0.277907 | − | 0.960608i | \(-0.410359\pi\) | ||||
0.277907 | + | 0.960608i | \(0.410359\pi\) | |||||||
\(14\) | −0.854777 | − | 9.86252i | −0.0610555 | − | 0.704466i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.32600 | − | 2.29669i | −0.0779998 | − | 0.135100i | 0.824387 | − | 0.566027i | \(-0.191520\pi\) |
−0.902387 | + | 0.430927i | \(0.858187\pi\) | |||||||
\(18\) | 3.67423 | − | 2.12132i | 0.204124 | − | 0.117851i | ||||
\(19\) | −2.20128 | − | 1.27091i | −0.115857 | − | 0.0668900i | 0.440952 | − | 0.897531i | \(-0.354641\pi\) |
−0.556809 | + | 0.830641i | \(0.687974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.13291 | + | 10.9842i | −0.244424 | + | 0.523058i | ||||
\(22\) | − | 24.5864i | − | 1.11756i | ||||||
\(23\) | 34.7289 | + | 20.0507i | 1.50995 | + | 0.871771i | 0.999933 | + | 0.0116074i | \(0.00369482\pi\) |
0.510019 | + | 0.860163i | \(0.329639\pi\) | |||||||
\(24\) | 4.24264 | − | 2.44949i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.84951 | − | 5.10926i | −0.340366 | − | 0.196510i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −5.92697 | + | 12.6835i | −0.211678 | + | 0.452982i | ||||
\(29\) | −47.0080 | −1.62096 | −0.810482 | − | 0.585763i | \(-0.800795\pi\) | ||||
−0.810482 | + | 0.585763i | \(0.800795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.9025 | − | 20.1510i | 1.12589 | − | 0.650031i | 0.182990 | − | 0.983115i | \(-0.441422\pi\) |
0.942897 | + | 0.333084i | \(0.108089\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −15.0560 | + | 26.0778i | −0.456243 | + | 0.790236i | ||||
\(34\) | 3.75049i | 0.110308i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −28.1482 | − | 16.2514i | −0.760762 | − | 0.439226i | 0.0688071 | − | 0.997630i | \(-0.478081\pi\) |
−0.829569 | + | 0.558404i | \(0.811414\pi\) | |||||||
\(38\) | 1.79734 | + | 3.11308i | 0.0472984 | + | 0.0819232i | ||||
\(39\) | 6.25755 | + | 10.8384i | 0.160450 | + | 0.277907i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.6679i | 1.72361i | 0.507241 | + | 0.861804i | \(0.330665\pi\) | ||||
−0.507241 | + | 0.861804i | \(0.669335\pi\) | |||||||
\(42\) | 14.0535 | − | 9.82336i | 0.334608 | − | 0.233890i | ||||
\(43\) | − | 37.3732i | − | 0.869144i | −0.900637 | − | 0.434572i | \(-0.856900\pi\) | ||
0.900637 | − | 0.434572i | \(-0.143100\pi\) | |||||||
\(44\) | −17.3852 | + | 30.1120i | −0.395118 | + | 0.684364i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −28.3560 | − | 49.1141i | −0.616435 | − | 1.06770i | ||||
\(47\) | 16.7242 | − | 28.9672i | 0.355835 | − | 0.616324i | −0.631426 | − | 0.775436i | \(-0.717530\pi\) |
0.987260 | + | 0.159113i | \(0.0508633\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | −16.8339 | + | 46.0176i | −0.343548 | + | 0.939135i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.29669 | − | 3.97799i | 0.0450332 | − | 0.0779998i | ||||
\(52\) | 7.22559 | + | 12.5151i | 0.138954 | + | 0.240675i | ||||
\(53\) | 61.3911 | − | 35.4442i | 1.15832 | − | 0.668758i | 0.207422 | − | 0.978252i | \(-0.433493\pi\) |
0.950902 | + | 0.309493i | \(0.100159\pi\) | |||||||
\(54\) | 6.36396 | + | 3.67423i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.2276 | − | 11.3430i | 0.289779 | − | 0.202554i | ||||
\(57\) | − | 4.40256i | − | 0.0772379i | ||||||
\(58\) | 57.5728 | + | 33.2397i | 0.992634 | + | 0.573098i | ||||
\(59\) | −87.0863 | + | 50.2793i | −1.47604 | + | 0.852192i | −0.999635 | − | 0.0270340i | \(-0.991394\pi\) |
−0.476405 | + | 0.879226i | \(0.658060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1621 | − | 6.44446i | −0.182986 | − | 0.105647i | 0.405709 | − | 0.914002i | \(-0.367025\pi\) |
−0.588695 | + | 0.808355i | \(0.700358\pi\) | |||||||
\(62\) | −56.9955 | −0.919283 | ||||||||
\(63\) | −20.9216 | + | 1.81326i | −0.332088 | + | 0.0287819i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 36.8795 | − | 21.2924i | 0.558781 | − | 0.322612i | ||||
\(67\) | 81.4689 | − | 47.0361i | 1.21595 | − | 0.702031i | 0.251904 | − | 0.967752i | \(-0.418943\pi\) |
0.964050 | + | 0.265721i | \(0.0856100\pi\) | |||||||
\(68\) | 2.65199 | − | 4.59339i | 0.0389999 | − | 0.0675498i | ||||
\(69\) | 69.4578i | 1.00663i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5793 | −0.163088 | −0.0815440 | − | 0.996670i | \(-0.525985\pi\) | ||||
−0.0815440 | + | 0.996670i | \(0.525985\pi\) | |||||||
\(72\) | 7.34847 | + | 4.24264i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 11.3345 | + | 19.6320i | 0.155267 | + | 0.268931i | 0.933156 | − | 0.359471i | \(-0.117043\pi\) |
−0.777889 | + | 0.628402i | \(0.783709\pi\) | |||||||
\(74\) | 22.9829 | + | 39.8076i | 0.310580 | + | 0.537940i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.08364i | − | 0.0668900i | ||||||
\(77\) | −51.5208 | + | 110.252i | −0.669101 | + | 1.43185i | ||||
\(78\) | − | 17.6990i | − | 0.226910i | ||||||
\(79\) | −12.0542 | + | 20.8785i | −0.152585 | + | 0.264285i | −0.932177 | − | 0.362003i | \(-0.882093\pi\) |
0.779592 | + | 0.626287i | \(0.215426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 49.9698 | − | 86.5502i | 0.609388 | − | 1.05549i | ||||
\(83\) | −111.664 | −1.34535 | −0.672676 | − | 0.739937i | \(-0.734855\pi\) | ||||
−0.672676 | + | 0.739937i | \(0.734855\pi\) | |||||||
\(84\) | −24.1581 | + | 2.09377i | −0.287597 | + | 0.0249258i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −26.4268 | + | 45.7726i | −0.307289 | + | 0.532240i | ||||
\(87\) | −40.7101 | − | 70.5120i | −0.467932 | − | 0.810482i | ||||
\(88\) | 42.5848 | − | 24.5864i | 0.483919 | − | 0.279390i | ||||
\(89\) | 110.770 | + | 63.9533i | 1.24461 | + | 0.718577i | 0.970030 | − | 0.242987i | \(-0.0781272\pi\) |
0.274582 | + | 0.961564i | \(0.411460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.9773 | + | 41.4556i | 0.318432 | + | 0.455556i | ||||
\(92\) | 80.2029i | 0.871771i | ||||||||
\(93\) | 60.4529 | + | 34.9025i | 0.650031 | + | 0.375296i | ||||
\(94\) | −40.9658 | + | 23.6516i | −0.435807 | + | 0.251613i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −7.48256 | −0.0771398 | −0.0385699 | − | 0.999256i | \(-0.512280\pi\) | ||||
−0.0385699 | + | 0.999256i | \(0.512280\pi\) | |||||||
\(98\) | 53.1566 | − | 44.4565i | 0.542414 | − | 0.453638i | ||||
\(99\) | −52.1556 | −0.526824 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −81.9228 | + | 47.2982i | −0.811117 | + | 0.468299i | −0.847344 | − | 0.531045i | \(-0.821799\pi\) |
0.0362267 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(102\) | −5.62573 | + | 3.24802i | −0.0551542 | + | 0.0318433i | ||||
\(103\) | −29.9109 | + | 51.8072i | −0.290397 | + | 0.502982i | −0.973904 | − | 0.226962i | \(-0.927121\pi\) |
0.683507 | + | 0.729944i | \(0.260454\pi\) | |||||||
\(104\) | − | 20.4371i | − | 0.196510i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.251 | −0.945767 | ||||||||
\(107\) | −5.59592 | − | 3.23081i | −0.0522983 | − | 0.0301945i | 0.473623 | − | 0.880728i | \(-0.342946\pi\) |
−0.525921 | + | 0.850533i | \(0.676279\pi\) | |||||||
\(108\) | −5.19615 | − | 9.00000i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −81.9201 | − | 141.890i | −0.751560 | − | 1.30174i | −0.947066 | − | 0.321038i | \(-0.895968\pi\) |
0.195506 | − | 0.980703i | \(-0.437365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 56.2964i | − | 0.507175i | ||||||
\(112\) | −27.8954 | + | 2.41768i | −0.249066 | + | 0.0215864i | ||||
\(113\) | 105.434i | 0.933040i | 0.884511 | + | 0.466520i | \(0.154492\pi\) | ||||
−0.884511 | + | 0.466520i | \(0.845508\pi\) | |||||||
\(114\) | −3.11308 | + | 5.39202i | −0.0273077 | + | 0.0472984i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −47.0080 | − | 81.4202i | −0.405241 | − | 0.701898i | ||||
\(117\) | −10.8384 | + | 18.7726i | −0.0926358 | + | 0.160450i | ||||
\(118\) | 142.211 | 1.20518 | ||||||||
\(119\) | 7.85915 | − | 16.8183i | 0.0660433 | − | 0.141330i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −90.6223 | + | 156.962i | −0.748945 | + | 1.29721i | ||||
\(122\) | 9.11384 | + | 15.7856i | 0.0747036 | + | 0.129391i | ||||
\(123\) | −106.002 | + | 61.2002i | −0.861804 | + | 0.497563i | ||||
\(124\) | 69.8050 | + | 40.3019i | 0.562944 | + | 0.325016i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 26.9058 | + | 12.5730i | 0.213538 | + | 0.0997858i | ||||
\(127\) | 53.7033i | 0.422860i | 0.977393 | + | 0.211430i | \(0.0678121\pi\) | ||||
−0.977393 | + | 0.211430i | \(0.932188\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 56.0598 | − | 32.3661i | 0.434572 | − | 0.250900i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50.6489 | − | 29.2421i | −0.386632 | − | 0.223222i | 0.294068 | − | 0.955785i | \(-0.404991\pi\) |
−0.680700 | + | 0.732562i | \(0.738324\pi\) | |||||||
\(132\) | −60.2240 | −0.456243 | ||||||||
\(133\) | −1.53632 | − | 17.7263i | −0.0115513 | − | 0.133280i | ||||
\(134\) | −133.038 | −0.992822 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.49603 | + | 3.75049i | −0.0477650 | + | 0.0275771i | ||||
\(137\) | −10.4936 | + | 6.05848i | −0.0765956 | + | 0.0442225i | −0.537809 | − | 0.843067i | \(-0.680748\pi\) |
0.461213 | + | 0.887289i | \(0.347414\pi\) | |||||||
\(138\) | 49.1141 | − | 85.0680i | 0.355899 | − | 0.616435i | ||||
\(139\) | 45.2562i | 0.325584i | 0.986660 | + | 0.162792i | \(0.0520500\pi\) | ||||
−0.986660 | + | 0.162792i | \(0.947950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57.9344 | 0.410882 | ||||||||
\(142\) | 14.1816 | + | 8.18777i | 0.0998706 | + | 0.0576603i | ||||
\(143\) | 62.8091 | + | 108.789i | 0.439225 | + | 0.760759i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 32.0589i | − | 0.219581i | ||||||
\(147\) | −83.6050 | + | 14.6016i | −0.568741 | + | 0.0993309i | ||||
\(148\) | − | 65.0055i | − | 0.439226i | ||||||
\(149\) | −25.4474 | + | 44.0762i | −0.170788 | + | 0.295814i | −0.938696 | − | 0.344747i | \(-0.887965\pi\) |
0.767908 | + | 0.640561i | \(0.221298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 78.8476 | + | 136.568i | 0.522169 | + | 0.904424i | 0.999667 | + | 0.0257911i | \(0.00821047\pi\) |
−0.477498 | + | 0.878633i | \(0.658456\pi\) | |||||||
\(152\) | −3.59468 | + | 6.22616i | −0.0236492 | + | 0.0409616i | ||||
\(153\) | 7.95598 | 0.0519999 | ||||||||
\(154\) | 141.060 | − | 98.6004i | 0.915974 | − | 0.640263i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.5151 | + | 21.6768i | −0.0802249 | + | 0.138954i | ||||
\(157\) | 83.9231 | + | 145.359i | 0.534542 | + | 0.925854i | 0.999185 | + | 0.0403562i | \(0.0128493\pi\) |
−0.464643 | + | 0.885498i | \(0.653817\pi\) | |||||||
\(158\) | 29.5266 | − | 17.0472i | 0.186877 | − | 0.107894i | ||||
\(159\) | 106.333 | + | 61.3911i | 0.668758 | + | 0.386108i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.2381 | + | 279.662i | 0.150547 | + | 1.73703i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | 239.517 | + | 138.285i | 1.46943 | + | 0.848374i | 0.999412 | − | 0.0342839i | \(-0.0109150\pi\) |
0.470015 | + | 0.882658i | \(0.344248\pi\) | |||||||
\(164\) | −122.400 | + | 70.6679i | −0.746344 | + | 0.430902i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 136.760 | + | 78.9586i | 0.823857 | + | 0.475654i | ||||
\(167\) | −48.4258 | −0.289975 | −0.144987 | − | 0.989433i | \(-0.546314\pi\) | ||||
−0.144987 | + | 0.989433i | \(0.546314\pi\) | |||||||
\(168\) | 31.0681 | + | 14.5181i | 0.184929 | + | 0.0864170i | ||||
\(169\) | −116.791 | −0.691070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.60384 | − | 3.81273i | 0.0386190 | − | 0.0222967i | ||||
\(172\) | 64.7323 | − | 37.3732i | 0.376351 | − | 0.217286i | ||||
\(173\) | −56.4843 | + | 97.8337i | −0.326499 | + | 0.565513i | −0.981815 | − | 0.189842i | \(-0.939202\pi\) |
0.655316 | + | 0.755355i | \(0.272536\pi\) | |||||||
\(174\) | 115.146i | 0.661756i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −69.5407 | −0.395118 | ||||||||
\(177\) | −150.838 | − | 87.0863i | −0.852192 | − | 0.492013i | ||||
\(178\) | −90.4437 | − | 156.653i | −0.508111 | − | 0.880073i | ||||
\(179\) | 165.708 | + | 287.015i | 0.925744 | + | 1.60344i | 0.790360 | + | 0.612642i | \(0.209893\pi\) |
0.135384 | + | 0.990793i | \(0.456773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 213.328i | − | 1.17861i | −0.807912 | − | 0.589303i | \(-0.799402\pi\) | ||
0.807912 | − | 0.589303i | \(-0.200598\pi\) | |||||||
\(182\) | −6.17627 | − | 71.2626i | −0.0339356 | − | 0.391553i | ||||
\(183\) | − | 22.3243i | − | 0.121991i | ||||||
\(184\) | 56.7120 | − | 98.2281i | 0.308218 | − | 0.533848i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −49.3596 | − | 85.4933i | −0.265374 | − | 0.459642i | ||||
\(187\) | 23.0527 | − | 39.9285i | 0.123277 | − | 0.213521i | ||||
\(188\) | 66.8969 | 0.355835 | ||||||||
\(189\) | −20.8385 | − | 29.8120i | −0.110257 | − | 0.157736i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 33.4517 | − | 57.9400i | 0.175140 | − | 0.303351i | −0.765070 | − | 0.643947i | \(-0.777296\pi\) |
0.940210 | + | 0.340596i | \(0.110629\pi\) | |||||||
\(192\) | −6.92820 | − | 12.0000i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 97.5179 | − | 56.3020i | 0.505274 | − | 0.291720i | −0.225615 | − | 0.974217i | \(-0.572439\pi\) |
0.730889 | + | 0.682497i | \(0.239106\pi\) | |||||||
\(194\) | 9.16422 | + | 5.29097i | 0.0472383 | + | 0.0272730i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −96.5387 | + | 16.8605i | −0.492544 | + | 0.0860231i | ||||
\(197\) | − | 61.0211i | − | 0.309752i | −0.987934 | − | 0.154876i | \(-0.950502\pi\) | ||
0.987934 | − | 0.154876i | \(-0.0494978\pi\) | |||||||
\(198\) | 63.8772 | + | 36.8795i | 0.322612 | + | 0.186260i | ||||
\(199\) | 165.554 | − | 95.5826i | 0.831929 | − | 0.480314i | −0.0225837 | − | 0.999745i | \(-0.507189\pi\) |
0.854513 | + | 0.519431i | \(0.173856\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 141.108 | + | 81.4689i | 0.702031 | + | 0.405318i | ||||
\(202\) | 133.779 | 0.662274 | ||||||||
\(203\) | −188.519 | − | 269.700i | −0.928667 | − | 1.32857i | ||||
\(204\) | 9.18678 | 0.0450332 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 73.2664 | − | 42.3004i | 0.355662 | − | 0.205342i | ||||
\(207\) | −104.187 | + | 60.1522i | −0.503317 | + | 0.290590i | ||||
\(208\) | −14.4512 | + | 25.0302i | −0.0694768 | + | 0.120337i | ||||
\(209\) | − | 44.1900i | − | 0.211435i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 280.115 | 1.32756 | 0.663781 | − | 0.747927i | \(-0.268951\pi\) | ||||
0.663781 | + | 0.747927i | \(0.268951\pi\) | |||||||
\(212\) | 122.782 | + | 70.8884i | 0.579162 | + | 0.334379i | ||||
\(213\) | −10.0279 | − | 17.3689i | −0.0470795 | − | 0.0815440i | ||||
\(214\) | 4.56905 | + | 7.91383i | 0.0213507 | + | 0.0369805i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 255.585 | + | 119.434i | 1.17781 | + | 0.550388i | ||||
\(218\) | 231.705i | 1.06287i | ||||||||
\(219\) | −19.6320 | + | 34.0036i | −0.0896437 | + | 0.155267i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.58111 | − | 16.5950i | −0.0433535 | − | 0.0750904i | ||||
\(222\) | −39.8076 | + | 68.9487i | −0.179313 | + | 0.310580i | ||||
\(223\) | −272.759 | −1.22313 | −0.611567 | − | 0.791192i | \(-0.709461\pi\) | ||||
−0.611567 | + | 0.791192i | \(0.709461\pi\) | |||||||
\(224\) | 35.8743 | + | 16.7640i | 0.160153 | + | 0.0748393i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 74.5528 | − | 129.129i | 0.329879 | − | 0.571368i | ||||
\(227\) | 8.03620 | + | 13.9191i | 0.0354018 | + | 0.0613176i | 0.883183 | − | 0.469028i | \(-0.155396\pi\) |
−0.847782 | + | 0.530345i | \(0.822062\pi\) | |||||||
\(228\) | 7.62546 | − | 4.40256i | 0.0334450 | − | 0.0193095i | ||||
\(229\) | −128.261 | − | 74.0517i | −0.560093 | − | 0.323370i | 0.193090 | − | 0.981181i | \(-0.438149\pi\) |
−0.753183 | + | 0.657811i | \(0.771482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −209.997 | + | 18.2003i | −0.909078 | + | 0.0787891i | ||||
\(232\) | 132.959i | 0.573098i | ||||||||
\(233\) | −259.044 | − | 149.559i | −1.11178 | − | 0.641885i | −0.172488 | − | 0.985012i | \(-0.555181\pi\) |
−0.939289 | + | 0.343127i | \(0.888514\pi\) | |||||||
\(234\) | 26.5485 | − | 15.3278i | 0.113455 | − | 0.0655034i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −174.173 | − | 100.559i | −0.738020 | − | 0.426096i | ||||
\(237\) | −41.7570 | −0.176190 | ||||||||
\(238\) | −21.5178 | + | 15.0408i | −0.0904108 | + | 0.0631968i | ||||
\(239\) | 114.253 | 0.478046 | 0.239023 | − | 0.971014i | \(-0.423173\pi\) | ||||
0.239023 | + | 0.971014i | \(0.423173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −118.162 | + | 68.2209i | −0.490299 | + | 0.283074i | −0.724699 | − | 0.689066i | \(-0.758021\pi\) |
0.234399 | + | 0.972140i | \(0.424688\pi\) | |||||||
\(242\) | 221.978 | − | 128.159i | 0.917266 | − | 0.529584i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | − | 25.7778i | − | 0.105647i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 173.100 | 0.703660 | ||||||||
\(247\) | −15.9056 | − | 9.18308i | −0.0643950 | − | 0.0371785i | ||||
\(248\) | −56.9955 | − | 98.7192i | −0.229821 | − | 0.398061i | ||||
\(249\) | −96.7041 | − | 167.496i | −0.388370 | − | 0.672676i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 457.024i | − | 1.82081i | −0.413717 | − | 0.910406i | \(-0.635770\pi\) | ||
0.413717 | − | 0.910406i | \(-0.364230\pi\) | |||||||
\(252\) | −24.0622 | − | 34.4240i | −0.0954850 | − | 0.136603i | ||||
\(253\) | 697.171i | 2.75562i | ||||||||
\(254\) | 37.9739 | − | 65.7728i | 0.149504 | − | 0.258948i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −24.9991 | + | 43.2997i | −0.0972726 | + | 0.168481i | −0.910555 | − | 0.413388i | \(-0.864345\pi\) |
0.813282 | + | 0.581869i | \(0.197679\pi\) | |||||||
\(258\) | −91.5453 | −0.354827 | ||||||||
\(259\) | −19.6453 | − | 226.669i | −0.0758505 | − | 0.875172i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 70.5120 | − | 122.130i | 0.270161 | − | 0.467932i | ||||
\(262\) | 41.3546 | + | 71.6283i | 0.157842 | + | 0.273390i | ||||
\(263\) | −157.857 | + | 91.1388i | −0.600217 | + | 0.346535i | −0.769127 | − | 0.639096i | \(-0.779309\pi\) |
0.168910 | + | 0.985631i | \(0.445975\pi\) | |||||||
\(264\) | 73.7591 | + | 42.5848i | 0.279390 | + | 0.161306i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.6528 | + | 22.7965i | −0.0400480 | + | 0.0857012i | ||||
\(267\) | 221.541i | 0.829741i | ||||||||
\(268\) | 162.938 | + | 94.0722i | 0.607977 | + | 0.351016i | ||||
\(269\) | 32.5814 | − | 18.8109i | 0.121120 | − | 0.0699289i | −0.438216 | − | 0.898870i | \(-0.644389\pi\) |
0.559336 | + | 0.828941i | \(0.311056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 175.576 | + | 101.369i | 0.647880 | + | 0.374054i | 0.787644 | − | 0.616131i | \(-0.211301\pi\) |
−0.139763 | + | 0.990185i | \(0.544634\pi\) | |||||||
\(272\) | 10.6080 | 0.0389999 | ||||||||
\(273\) | −37.0883 | + | 79.3675i | −0.135855 | + | 0.290724i | ||||
\(274\) | 17.1360 | 0.0625401 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −120.304 | + | 69.4578i | −0.435885 | + | 0.251659i | ||||
\(277\) | 221.912 | − | 128.121i | 0.801126 | − | 0.462530i | −0.0427390 | − | 0.999086i | \(-0.513608\pi\) |
0.843865 | + | 0.536556i | \(0.180275\pi\) | |||||||
\(278\) | 32.0010 | − | 55.4273i | 0.115111 | − | 0.199379i | ||||
\(279\) | 120.906i | 0.433354i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −141.462 | −0.503423 | −0.251711 | − | 0.967802i | \(-0.580993\pi\) | ||||
−0.251711 | + | 0.967802i | \(0.580993\pi\) | |||||||
\(282\) | −70.9549 | − | 40.9658i | −0.251613 | − | 0.145269i | ||||
\(283\) | −271.684 | − | 470.571i | −0.960014 | − | 1.66279i | −0.722452 | − | 0.691421i | \(-0.756985\pi\) |
−0.237562 | − | 0.971372i | \(-0.576348\pi\) | |||||||
\(284\) | −11.5793 | − | 20.0559i | −0.0407720 | − | 0.0706192i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 177.651i | − | 0.621157i | ||||||
\(287\) | −405.445 | + | 283.405i | −1.41270 | + | 0.987472i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 140.983 | − | 244.191i | 0.487832 | − | 0.844950i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.48008 | − | 11.2238i | −0.0222683 | − | 0.0385699i | ||||
\(292\) | −22.6690 | + | 39.2639i | −0.0776337 | + | 0.134466i | ||||
\(293\) | 375.289 | 1.28085 | 0.640424 | − | 0.768021i | \(-0.278759\pi\) | ||||
0.640424 | + | 0.768021i | \(0.278759\pi\) | |||||||
\(294\) | 112.720 | + | 41.2344i | 0.383400 | + | 0.140253i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −45.9658 | + | 79.6151i | −0.155290 | + | 0.268970i | ||||
\(297\) | −45.1680 | − | 78.2333i | −0.152081 | − | 0.263412i | ||||
\(298\) | 62.3332 | − | 35.9881i | 0.209172 | − | 0.120765i | ||||
\(299\) | 250.937 | + | 144.878i | 0.839253 | + | 0.484543i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 214.422 | − | 149.880i | 0.712367 | − | 0.497942i | ||||
\(302\) | − | 223.015i | − | 0.738459i | ||||||
\(303\) | −141.894 | − | 81.9228i | −0.468299 | − | 0.270372i | ||||
\(304\) | 8.80512 | − | 5.08364i | 0.0289642 | − | 0.0167225i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.74405 | − | 5.62573i | −0.0318433 | − | 0.0183847i | ||||
\(307\) | 41.3436 | 0.134670 | 0.0673349 | − | 0.997730i | \(-0.478550\pi\) | ||||
0.0673349 | + | 0.997730i | \(0.478550\pi\) | |||||||
\(308\) | −242.484 | + | 21.0159i | −0.787284 | + | 0.0682333i | ||||
\(309\) | −103.614 | −0.335321 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −126.924 | + | 73.2794i | −0.408115 | + | 0.235625i | −0.689979 | − | 0.723829i | \(-0.742380\pi\) |
0.281865 | + | 0.959454i | \(0.409047\pi\) | |||||||
\(312\) | 30.6556 | − | 17.6990i | 0.0982551 | − | 0.0567276i | ||||
\(313\) | 112.435 | − | 194.744i | 0.359218 | − | 0.622184i | −0.628612 | − | 0.777719i | \(-0.716377\pi\) |
0.987830 | + | 0.155535i | \(0.0497100\pi\) | |||||||
\(314\) | − | 237.370i | − | 0.755957i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.2168 | −0.152585 | ||||||||
\(317\) | 195.918 | + | 113.113i | 0.618038 | + | 0.356825i | 0.776105 | − | 0.630604i | \(-0.217193\pi\) |
−0.158067 | + | 0.987428i | \(0.550526\pi\) | |||||||
\(318\) | −86.8202 | − | 150.377i | −0.273019 | − | 0.472884i | ||||
\(319\) | −408.621 | − | 707.753i | −1.28094 | − | 2.21866i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11.1918i | − | 0.0348656i | ||||||
\(322\) | 168.065 | − | 359.653i | 0.521942 | − | 1.11694i | ||||
\(323\) | 6.74089i | 0.0208696i | ||||||||
\(324\) | 9.00000 | − | 15.5885i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −195.565 | − | 338.728i | −0.599891 | − | 1.03904i | ||||
\(327\) | 141.890 | − | 245.760i | 0.433914 | − | 0.751560i | ||||
\(328\) | 199.879 | 0.609388 | ||||||||
\(329\) | 233.265 | − | 20.2169i | 0.709011 | − | 0.0614495i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −69.9082 | + | 121.085i | −0.211203 | + | 0.365814i | −0.952091 | − | 0.305814i | \(-0.901071\pi\) |
0.740888 | + | 0.671628i | \(0.234405\pi\) | |||||||
\(332\) | −111.664 | − | 193.408i | −0.336338 | − | 0.582555i | ||||
\(333\) | 84.4446 | − | 48.7541i | 0.253587 | − | 0.146409i | ||||
\(334\) | 59.3093 | + | 34.2422i | 0.177573 | + | 0.102522i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −27.7847 | − | 39.7494i | −0.0826924 | − | 0.118302i | ||||
\(337\) | 30.1128i | 0.0893556i | 0.999001 | + | 0.0446778i | \(0.0142261\pi\) | ||||
−0.999001 | + | 0.0446778i | \(0.985774\pi\) | |||||||
\(338\) | 143.039 | + | 82.5836i | 0.423192 | + | 0.244330i | ||||
\(339\) | −158.150 | + | 91.3081i | −0.466520 | + | 0.269345i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 606.786 | + | 350.328i | 1.77943 | + | 1.02736i | ||||
\(342\) | −10.7840 | −0.0315323 | ||||||||
\(343\) | −331.528 | + | 87.9664i | −0.966554 | + | 0.256462i | ||||
\(344\) | −105.707 | −0.307289 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 138.358 | − | 79.8809i | 0.399878 | − | 0.230870i | ||||
\(347\) | −360.186 | + | 207.954i | −1.03800 | + | 0.599290i | −0.919266 | − | 0.393636i | \(-0.871217\pi\) |
−0.118734 | + | 0.992926i | \(0.537884\pi\) | |||||||
\(348\) | 81.4202 | − | 141.024i | 0.233966 | − | 0.405241i | ||||
\(349\) | − | 594.950i | − | 1.70473i | −0.522950 | − | 0.852363i | \(-0.675169\pi\) | ||
0.522950 | − | 0.852363i | \(-0.324831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.5453 | −0.106967 | ||||||||
\(352\) | 85.1697 | + | 49.1727i | 0.241959 | + | 0.139695i | ||||
\(353\) | −182.159 | − | 315.509i | −0.516031 | − | 0.893793i | −0.999827 | − | 0.0186116i | \(-0.994075\pi\) |
0.483795 | − | 0.875181i | \(-0.339258\pi\) | |||||||
\(354\) | 123.159 | + | 213.317i | 0.347906 | + | 0.602591i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 255.813i | 0.718577i | ||||||||
\(357\) | 32.0336 | − | 2.77633i | 0.0897301 | − | 0.00777684i | ||||
\(358\) | − | 468.693i | − | 1.30920i | ||||||
\(359\) | −306.381 | + | 530.668i | −0.853430 | + | 1.47818i | 0.0246647 | + | 0.999696i | \(0.492148\pi\) |
−0.878094 | + | 0.478488i | \(0.841185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −177.270 | − | 307.040i | −0.491051 | − | 0.850526i | ||||
\(362\) | −150.846 | + | 261.272i | −0.416700 | + | 0.721746i | ||||
\(363\) | −313.925 | −0.864807 | ||||||||
\(364\) | −42.8259 | + | 91.6457i | −0.117654 | + | 0.251774i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15.7856 | + | 27.3415i | −0.0431302 | + | 0.0747036i | ||||
\(367\) | −246.509 | − | 426.967i | −0.671687 | − | 1.16340i | −0.977425 | − | 0.211281i | \(-0.932236\pi\) |
0.305738 | − | 0.952116i | \(-0.401097\pi\) | |||||||
\(368\) | −138.916 | + | 80.2029i | −0.377488 | + | 0.217943i | ||||
\(369\) | −183.601 | − | 106.002i | −0.497563 | − | 0.287268i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 449.556 | + | 210.077i | 1.21174 | + | 0.566245i | ||||
\(372\) | 139.610i | 0.375296i | ||||||||
\(373\) | 143.243 | + | 82.7013i | 0.384029 | + | 0.221719i | 0.679570 | − | 0.733611i | \(-0.262166\pi\) |
−0.295541 | + | 0.955330i | \(0.595500\pi\) | |||||||
\(374\) | −56.4674 | + | 32.6015i | −0.150982 | + | 0.0871697i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −81.9317 | − | 47.3033i | −0.217903 | − | 0.125807i | ||||
\(377\) | −339.660 | −0.900956 | ||||||||
\(378\) | 4.44155 | + | 51.2472i | 0.0117501 | + | 0.135575i | ||||
\(379\) | 179.349 | 0.473215 | 0.236608 | − | 0.971605i | \(-0.423964\pi\) | ||||
0.236608 | + | 0.971605i | \(0.423964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −80.5549 | + | 46.5084i | −0.211430 | + | 0.122069i | ||||
\(382\) | −81.9395 | + | 47.3078i | −0.214501 | + | 0.123842i | ||||
\(383\) | 134.585 | − | 233.108i | 0.351396 | − | 0.608636i | −0.635098 | − | 0.772432i | \(-0.719040\pi\) |
0.986494 | + | 0.163795i | \(0.0523736\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −159.246 | −0.412554 | ||||||||
\(387\) | 97.0984 | + | 56.0598i | 0.250900 | + | 0.144857i | ||||
\(388\) | −7.48256 | − | 12.9602i | −0.0192849 | − | 0.0334025i | ||||
\(389\) | −236.874 | − | 410.277i | −0.608930 | − | 1.05470i | −0.991417 | − | 0.130737i | \(-0.958266\pi\) |
0.382487 | − | 0.923961i | \(-0.375068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 106.349i | − | 0.271992i | ||||||
\(392\) | 130.157 | + | 47.6133i | 0.332034 | + | 0.121463i | ||||
\(393\) | − | 101.298i | − | 0.257755i | ||||||
\(394\) | −43.1484 | + | 74.7353i | −0.109514 | + | 0.189683i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −52.1556 | − | 90.3361i | −0.131706 | − | 0.228121i | ||||
\(397\) | 256.967 | − | 445.080i | 0.647271 | − | 1.12111i | −0.336500 | − | 0.941683i | \(-0.609243\pi\) |
0.983772 | − | 0.179424i | \(-0.0574233\pi\) | |||||||
\(398\) | −270.348 | −0.679267 | ||||||||
\(399\) | 25.2589 | − | 17.6559i | 0.0633056 | − | 0.0442504i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 203.367 | − | 352.242i | 0.507150 | − | 0.878410i | −0.492816 | − | 0.870134i | \(-0.664032\pi\) |
0.999966 | − | 0.00827591i | \(-0.00263433\pi\) | |||||||
\(402\) | −115.214 | − | 199.557i | −0.286603 | − | 0.496411i | ||||
\(403\) | 252.191 | − | 145.603i | 0.625785 | − | 0.361297i | ||||
\(404\) | −163.846 | − | 94.5963i | −0.405558 | − | 0.234149i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.1814 | + | 463.617i | 0.0989689 | + | 1.14191i | ||||
\(407\) | − | 565.066i | − | 1.38837i | ||||||
\(408\) | −11.2515 | − | 6.49603i | −0.0275771 | − | 0.0159217i | ||||
\(409\) | 422.173 | − | 243.742i | 1.03221 | − | 0.595946i | 0.114592 | − | 0.993413i | \(-0.463444\pi\) |
0.917617 | + | 0.397467i | \(0.130111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.1755 | − | 10.4936i | −0.0442225 | − | 0.0255319i | ||||
\(412\) | −119.643 | −0.290397 | ||||||||
\(413\) | −637.717 | − | 298.004i | −1.54411 | − | 0.721560i | ||||
\(414\) | 170.136 | 0.410957 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.3980 | − | 20.4371i | 0.0850914 | − | 0.0491275i | ||||
\(417\) | −67.8843 | + | 39.1930i | −0.162792 | + | 0.0939881i | ||||
\(418\) | −31.2471 | + | 54.1215i | −0.0747537 | + | 0.129477i | ||||
\(419\) | − | 552.257i | − | 1.31804i | −0.752127 | − | 0.659018i | \(-0.770972\pi\) | ||
0.752127 | − | 0.659018i | \(-0.229028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −74.6870 | −0.177404 | −0.0887019 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887019 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(422\) | −343.070 | − | 198.072i | −0.812962 | − | 0.469364i | ||||
\(423\) | 50.1727 | + | 86.9016i | 0.118612 | + | 0.205441i | ||||
\(424\) | −100.251 | − | 173.640i | −0.236442 | − | 0.409529i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 28.3633i | 0.0665804i | ||||||||
\(427\) | −7.79031 | − | 89.8855i | −0.0182443 | − | 0.210505i | ||||
\(428\) | − | 12.9232i | − | 0.0301945i | ||||||
\(429\) | −108.789 | + | 188.427i | −0.253586 | + | 0.439225i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −242.339 | − | 419.743i | −0.562271 | − | 0.973881i | −0.997298 | − | 0.0734641i | \(-0.976595\pi\) |
0.435027 | − | 0.900417i | \(-0.356739\pi\) | |||||||
\(432\) | 10.3923 | − | 18.0000i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −458.196 | −1.05819 | −0.529094 | − | 0.848563i | \(-0.677468\pi\) | ||||
−0.529094 | + | 0.848563i | \(0.677468\pi\) | |||||||
\(434\) | −228.573 | − | 327.002i | −0.526667 | − | 0.753461i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 163.840 | − | 283.779i | 0.375780 | − | 0.650870i | ||||
\(437\) | −50.9653 | − | 88.2746i | −0.116626 | − | 0.202001i | ||||
\(438\) | 48.0883 | − | 27.7638i | 0.109791 | − | 0.0633877i | ||||
\(439\) | −121.167 | − | 69.9559i | −0.276007 | − | 0.159353i | 0.355607 | − | 0.934635i | \(-0.384274\pi\) |
−0.631614 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −94.3065 | − | 112.762i | −0.213847 | − | 0.255696i | ||||
\(442\) | 27.0995i | 0.0613110i | ||||||||
\(443\) | −13.9364 | − | 8.04616i | −0.0314591 | − | 0.0181629i | 0.484188 | − | 0.874964i | \(-0.339115\pi\) |
−0.515647 | + | 0.856801i | \(0.672448\pi\) | |||||||
\(444\) | 97.5082 | − | 56.2964i | 0.219613 | − | 0.126794i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 334.060 | + | 192.870i | 0.749014 | + | 0.432444i | ||||
\(447\) | −88.1524 | −0.197209 | ||||||||
\(448\) | −32.0830 | − | 45.8986i | −0.0716138 | − | 0.102452i | ||||
\(449\) | 329.314 | 0.733439 | 0.366720 | − | 0.930332i | \(-0.380481\pi\) | ||||
0.366720 | + | 0.930332i | \(0.380481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1063.98 | + | 614.288i | −2.35915 | + | 1.36206i | ||||
\(452\) | −182.616 | + | 105.434i | −0.404018 | + | 0.233260i | ||||
\(453\) | −136.568 | + | 236.543i | −0.301475 | + | 0.522169i | ||||
\(454\) | − | 22.7298i | − | 0.0500657i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4523 | −0.0273077 | ||||||||
\(457\) | 771.557 | + | 445.459i | 1.68831 | + | 0.974745i | 0.955814 | + | 0.293972i | \(0.0949772\pi\) |
0.732494 | + | 0.680773i | \(0.238356\pi\) | |||||||
\(458\) | 104.725 | + | 181.389i | 0.228657 | + | 0.396046i | ||||
\(459\) | 6.89008 | + | 11.9340i | 0.0150111 | + | 0.0259999i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 534.019i | 1.15839i | 0.815188 | + | 0.579196i | \(0.196633\pi\) | ||||
−0.815188 | + | 0.579196i | \(0.803367\pi\) | |||||||
\(462\) | 270.062 | + | 126.200i | 0.584550 | + | 0.273159i | ||||
\(463\) | − | 158.679i | − | 0.342719i | −0.985209 | − | 0.171359i | \(-0.945184\pi\) | ||
0.985209 | − | 0.171359i | \(-0.0548159\pi\) | |||||||
\(464\) | 94.0160 | − | 162.840i | 0.202621 | − | 0.350949i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 211.509 | + | 366.344i | 0.453881 | + | 0.786145i | ||||
\(467\) | 56.0995 | − | 97.1671i | 0.120127 | − | 0.208067i | −0.799690 | − | 0.600413i | \(-0.795003\pi\) |
0.919818 | + | 0.392346i | \(0.128336\pi\) | |||||||
\(468\) | −43.3535 | −0.0926358 | ||||||||
\(469\) | 596.582 | + | 278.782i | 1.27203 | + | 0.594417i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −145.359 | + | 251.769i | −0.308618 | + | 0.534542i | ||||
\(472\) | 142.211 | + | 246.317i | 0.301295 | + | 0.521859i | ||||
\(473\) | 562.691 | − | 324.870i | 1.18962 | − | 0.686829i | ||||
\(474\) | 51.1416 | + | 29.5266i | 0.107894 | + | 0.0622925i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 36.9893 | − | 3.20583i | 0.0777085 | − | 0.00673494i | ||||
\(477\) | 212.665i | 0.445839i | ||||||||
\(478\) | −139.931 | − | 80.7891i | −0.292742 | − | 0.169015i | ||||
\(479\) | 598.669 | − | 345.642i | 1.24983 | − | 0.721590i | 0.278755 | − | 0.960362i | \(-0.410078\pi\) |
0.971076 | + | 0.238772i | \(0.0767450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −203.387 | − | 117.426i | −0.422843 | − | 0.244128i | ||||
\(482\) | 192.958 | 0.400328 | ||||||||
\(483\) | −398.502 | + | 278.551i | −0.825056 | + | 0.576711i | ||||
\(484\) | −362.489 | −0.748945 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 624.248 | − | 360.410i | 1.28182 | − | 0.740062i | 0.304643 | − | 0.952467i | \(-0.401463\pi\) |
0.977182 | + | 0.212405i | \(0.0681297\pi\) | |||||||
\(488\) | −18.2277 | + | 31.5713i | −0.0373518 | + | 0.0646953i | ||||
\(489\) | 479.033i | 0.979618i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 589.995 | 1.20162 | 0.600809 | − | 0.799392i | \(-0.294845\pi\) | ||||
0.600809 | + | 0.799392i | \(0.294845\pi\) | |||||||
\(492\) | −212.004 | − | 122.400i | −0.430902 | − | 0.248781i | ||||
\(493\) | 62.3325 | + | 107.963i | 0.126435 | + | 0.218992i | ||||
\(494\) | 12.9868 | + | 22.4939i | 0.0262891 | + | 0.0455341i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 161.208i | 0.325016i | ||||||||
\(497\) | −46.4371 | − | 66.4340i | −0.0934348 | − | 0.133670i | ||||
\(498\) | 273.521i | 0.549238i | ||||||||
\(499\) | −437.845 | + | 758.370i | −0.877445 | + | 1.51978i | −0.0233104 | + | 0.999728i | \(0.507421\pi\) |
−0.854135 | + | 0.520052i | \(0.825913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.9380 | − | 72.6387i | −0.0837085 | − | 0.144987i | ||||
\(502\) | −323.165 | + | 559.737i | −0.643754 | + | 1.11501i | ||||
\(503\) | 817.809 | 1.62586 | 0.812931 | − | 0.582360i | \(-0.197871\pi\) | ||||
0.812931 | + | 0.582360i | \(0.197871\pi\) | |||||||
\(504\) | 5.12866 | + | 59.1751i | 0.0101759 | + | 0.117411i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 492.974 | − | 853.857i | 0.974258 | − | 1.68746i | ||||
\(507\) | −101.144 | − | 175.186i | −0.199495 | − | 0.345535i | ||||
\(508\) | −93.0168 | + | 53.7033i | −0.183104 | + | 0.105715i | ||||
\(509\) | 657.585 | + | 379.657i | 1.29191 | + | 0.745887i | 0.978993 | − | 0.203892i | \(-0.0653591\pi\) |
0.312921 | + | 0.949779i | \(0.398692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −67.1794 | + | 143.761i | −0.131467 | + | 0.281333i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 11.4382 | + | 6.60384i | 0.0222967 | + | 0.0128730i | ||||
\(514\) | 61.2350 | − | 35.3540i | 0.119134 | − | 0.0687821i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 112.120 | + | 64.7323i | 0.217286 | + | 0.125450i | ||||
\(517\) | 581.508 | 1.12477 | ||||||||
\(518\) | −136.219 | + | 291.504i | −0.262971 | + | 0.562748i | ||||
\(519\) | −195.667 | −0.377009 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −153.671 | + | 88.7220i | −0.294954 | + | 0.170292i | −0.640174 | − | 0.768230i | \(-0.721138\pi\) |
0.345220 | + | 0.938522i | \(0.387804\pi\) | |||||||
\(522\) | −172.718 | + | 99.7190i | −0.330878 | + | 0.191033i | ||||
\(523\) | 52.6094 | − | 91.1221i | 0.100592 | − | 0.174230i | −0.811337 | − | 0.584579i | \(-0.801260\pi\) |
0.911929 | + | 0.410349i | \(0.134593\pi\) | |||||||
\(524\) | − | 116.969i | − | 0.223222i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 257.780 | 0.490075 | ||||||||
\(527\) | −92.5612 | − | 53.4403i | −0.175638 | − | 0.101405i | ||||
\(528\) | −60.2240 | − | 104.311i | −0.114061 | − | 0.197559i | ||||
\(529\) | 539.563 | + | 934.551i | 1.01997 | + | 1.76664i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 301.676i | − | 0.568128i | ||||||
\(532\) | 29.1665 | − | 20.3873i | 0.0548243 | − | 0.0383220i | ||||
\(533\) | 510.618i | 0.958007i | ||||||||
\(534\) | 156.653 | − | 271.331i | 0.293358 | − | 0.508111i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −133.038 | − | 230.429i | −0.248206 | − | 0.429905i | ||||
\(537\) | −287.015 | + | 497.125i | −0.534479 | + | 0.925744i | ||||
\(538\) | −53.2051 | −0.0988943 | ||||||||
\(539\) | −839.172 | + | 146.562i | −1.55690 | + | 0.271914i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 138.181 | − | 239.337i | 0.255419 | − | 0.442398i | −0.709591 | − | 0.704614i | \(-0.751120\pi\) |
0.965009 | + | 0.262216i | \(0.0844534\pi\) | |||||||
\(542\) | −143.357 | − | 248.301i | −0.264496 | − | 0.458121i | ||||
\(543\) | 319.992 | − | 184.747i | 0.589303 | − | 0.340234i | ||||
\(544\) | −12.9921 | − | 7.50097i | −0.0238825 | − | 0.0137886i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 101.545 | − | 70.9796i | 0.185980 | − | 0.129999i | ||||
\(547\) | 918.409i | 1.67899i | 0.543366 | + | 0.839496i | \(0.317150\pi\) | ||||
−0.543366 | + | 0.839496i | \(0.682850\pi\) | |||||||
\(548\) | −20.9872 | − | 12.1170i | −0.0382978 | − | 0.0221113i | ||||
\(549\) | 33.4864 | − | 19.3334i | 0.0609953 | − | 0.0352156i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 103.478 | + | 59.7429i | 0.187800 | + | 0.108426i | ||||
\(552\) | 196.456 | 0.355899 | ||||||||
\(553\) | −168.128 | + | 14.5716i | −0.304030 | + | 0.0263500i | ||||
\(554\) | −362.380 | −0.654116 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −78.3861 | + | 45.2562i | −0.140982 | + | 0.0813961i | ||||
\(557\) | 636.538 | − | 367.505i | 1.14280 | − | 0.659794i | 0.195675 | − | 0.980669i | \(-0.437310\pi\) |
0.947122 | + | 0.320875i | \(0.103977\pi\) | |||||||
\(558\) | 85.4933 | − | 148.079i | 0.153214 | − | 0.265374i | ||||
\(559\) | − | 270.044i | − | 0.483083i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 79.8569 | 0.142347 | ||||||||
\(562\) | 173.255 | + | 100.029i | 0.308282 | + | 0.177987i | ||||
\(563\) | −413.283 | − | 715.827i | −0.734073 | − | 1.27145i | −0.955129 | − | 0.296191i | \(-0.904284\pi\) |
0.221056 | − | 0.975261i | \(-0.429050\pi\) | |||||||
\(564\) | 57.9344 | + | 100.345i | 0.102721 | + | 0.177917i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 768.438i | 1.35767i | ||||||||
\(567\) | 26.6714 | − | 57.0757i | 0.0470395 | − | 0.100663i | ||||
\(568\) | 32.7511i | 0.0576603i | ||||||||
\(569\) | −216.546 | + | 375.069i | −0.380573 | + | 0.659172i | −0.991144 | − | 0.132790i | \(-0.957607\pi\) |
0.610571 | + | 0.791961i | \(0.290940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −240.036 | − | 415.754i | −0.420378 | − | 0.728116i | 0.575598 | − | 0.817733i | \(-0.304769\pi\) |
−0.995976 | + | 0.0896166i | \(0.971436\pi\) | |||||||
\(572\) | −125.618 | + | 217.577i | −0.219612 | + | 0.380380i | ||||
\(573\) | 115.880 | 0.202234 | ||||||||
\(574\) | 696.964 | − | 60.4054i | 1.21422 | − | 0.105236i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −43.5695 | − | 75.4646i | −0.0755104 | − | 0.130788i | 0.825798 | − | 0.563966i | \(-0.190725\pi\) |
−0.901308 | + | 0.433179i | \(0.857392\pi\) | |||||||
\(578\) | −345.338 | + | 199.381i | −0.597470 | + | 0.344949i | ||||
\(579\) | 168.906 | + | 97.5179i | 0.291720 | + | 0.168425i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −447.815 | − | 640.655i | −0.770766 | − | 1.10268i | ||||
\(582\) | 18.3284i | 0.0314922i | ||||||||
\(583\) | 1067.30 | + | 616.204i | 1.83070 | + | 1.05695i | ||||
\(584\) | 55.5276 | − | 32.0589i | 0.0950815 | − | 0.0548953i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −459.633 | − | 265.369i | −0.784356 | − | 0.452848i | ||||
\(587\) | 104.332 | 0.177737 | 0.0888687 | − | 0.996043i | \(-0.471675\pi\) | ||||
0.0888687 | + | 0.996043i | \(0.471675\pi\) | |||||||
\(588\) | −108.896 | − | 130.206i | −0.185197 | − | 0.221439i | ||||
\(589\) | −102.440 | −0.173922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 91.5316 | − | 52.8458i | 0.154876 | − | 0.0894176i | ||||
\(592\) | 112.593 | − | 65.0055i | 0.190191 | − | 0.109807i | ||||
\(593\) | 145.735 | − | 252.421i | 0.245760 | − | 0.425668i | −0.716585 | − | 0.697499i | \(-0.754296\pi\) |
0.962345 | + | 0.271831i | \(0.0876293\pi\) | |||||||
\(594\) | 127.754i | 0.215075i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −101.790 | −0.170788 | ||||||||
\(597\) | 286.748 | + | 165.554i | 0.480314 | + | 0.277310i | ||||
\(598\) | −204.889 | − | 354.878i | −0.342624 | − | 0.593442i | ||||
\(599\) | 298.839 | + | 517.604i | 0.498896 | + | 0.864114i | 0.999999 | − | 0.00127378i | \(-0.000405456\pi\) |
−0.501103 | + | 0.865388i | \(0.667072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 447.444i | − | 0.744499i | −0.928133 | − | 0.372250i | \(-0.878587\pi\) | ||
0.928133 | − | 0.372250i | \(-0.121413\pi\) | |||||||
\(602\) | −368.594 | + | 31.9458i | −0.612283 | + | 0.0530661i | ||||
\(603\) | 282.217i | 0.468021i | ||||||||
\(604\) | −157.695 | + | 273.136i | −0.261085 | + | 0.452212i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 115.856 | + | 200.669i | 0.191182 | + | 0.331137i | ||||
\(607\) | −308.155 | + | 533.739i | −0.507668 | + | 0.879307i | 0.492293 | + | 0.870430i | \(0.336159\pi\) |
−0.999961 | + | 0.00887709i | \(0.997174\pi\) | |||||||
\(608\) | −14.3787 | −0.0236492 | ||||||||
\(609\) | 241.288 | − | 516.346i | 0.396203 | − | 0.847859i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 120.842 | − | 209.305i | 0.197778 | − | 0.342562i | ||||
\(612\) | 7.95598 | + | 13.7802i | 0.0130000 | + | 0.0225166i | ||||
\(613\) | 110.052 | − | 63.5384i | 0.179530 | − | 0.103651i | −0.407542 | − | 0.913186i | \(-0.633614\pi\) |
0.587072 | + | 0.809535i | \(0.300281\pi\) | |||||||
\(614\) | −50.6354 | − | 29.2344i | −0.0824681 | − | 0.0476130i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 311.841 | + | 145.723i | 0.506235 | + | 0.236563i | ||||
\(617\) | 68.5630i | 0.111123i | 0.998455 | + | 0.0555616i | \(0.0176949\pi\) | ||||
−0.998455 | + | 0.0555616i | \(0.982305\pi\) | |||||||
\(618\) | 126.901 | + | 73.2664i | 0.205342 | + | 0.118554i | ||||
\(619\) | −833.529 | + | 481.238i | −1.34657 | + | 0.777445i | −0.987763 | − | 0.155965i | \(-0.950151\pi\) |
−0.358812 | + | 0.933410i | \(0.616818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −180.457 | − | 104.187i | −0.290590 | − | 0.167772i | ||||
\(622\) | 207.265 | 0.333224 | ||||||||
\(623\) | 77.3092 | + | 892.003i | 0.124092 | + | 1.43179i | ||||
\(624\) | −50.0604 | −0.0802249 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −275.409 | + | 159.008i | −0.439951 | + | 0.254006i | ||||
\(627\) | 66.2850 | − | 38.2697i | 0.105718 | − | 0.0610362i | ||||
\(628\) | −167.846 | + | 290.718i | −0.267271 | + | 0.462927i | ||||
\(629\) | 86.1971i | 0.137038i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 412.586 | 0.653860 | 0.326930 | − | 0.945048i | \(-0.393986\pi\) | ||||
0.326930 | + | 0.945048i | \(0.393986\pi\) | |||||||
\(632\) | 59.0533 | + | 34.0944i | 0.0934387 | + | 0.0539469i | ||||
\(633\) | 242.587 | + | 420.173i | 0.383234 | + | 0.663781i | ||||
\(634\) | −159.966 | − | 277.070i | −0.252313 | − | 0.437019i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 245.565i | 0.386108i | ||||||||
\(637\) | −121.635 | + | 332.504i | −0.190949 | + | 0.521985i | ||||
\(638\) | 1155.76i | 1.81153i | ||||||||
\(639\) | 17.3689 | − | 30.0838i | 0.0271813 | − | 0.0470795i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 71.3374 | + | 123.560i | 0.111291 | + | 0.192761i | 0.916291 | − | 0.400513i | \(-0.131168\pi\) |
−0.805000 | + | 0.593275i | \(0.797835\pi\) | |||||||
\(642\) | −7.91383 | + | 13.7072i | −0.0123268 | + | 0.0213507i | ||||
\(643\) | 239.942 | 0.373160 | 0.186580 | − | 0.982440i | \(-0.440260\pi\) | ||||
0.186580 | + | 0.982440i | \(0.440260\pi\) | |||||||
\(644\) | −460.150 | + | 321.643i | −0.714519 | + | 0.499446i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.76653 | − | 8.25588i | 0.00737853 | − | 0.0127800i | ||||
\(647\) | −74.3724 | − | 128.817i | −0.114950 | − | 0.199098i | 0.802810 | − | 0.596235i | \(-0.203337\pi\) |
−0.917760 | + | 0.397136i | \(0.870004\pi\) | |||||||
\(648\) | −22.0454 | + | 12.7279i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −1514.01 | − | 874.115i | −2.33284 | − | 1.34686i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 42.1915 | + | 486.810i | 0.0648102 | + | 0.747788i | ||||
\(652\) | 553.140i | 0.848374i | ||||||||
\(653\) | 249.434 | + | 144.011i | 0.381982 | + | 0.220537i | 0.678680 | − | 0.734434i | \(-0.262552\pi\) |
−0.296698 | + | 0.954971i | \(0.595886\pi\) | |||||||
\(654\) | −347.557 | + | 200.662i | −0.531433 | + | 0.306823i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −244.801 | − | 141.336i | −0.373172 | − | 0.215451i | ||||
\(657\) | −68.0071 | −0.103512 | ||||||||
\(658\) | −299.985 | − | 140.183i | −0.455905 | − | 0.213043i | ||||
\(659\) | 175.647 | 0.266536 | 0.133268 | − | 0.991080i | \(-0.457453\pi\) | ||||
0.133268 | + | 0.991080i | \(0.457453\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −615.015 | + | 355.079i | −0.930432 | + | 0.537185i | −0.886948 | − | 0.461869i | \(-0.847179\pi\) |
−0.0434835 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(662\) | 171.239 | − | 98.8651i | 0.258670 | − | 0.149343i | ||||
\(663\) | 16.5950 | − | 28.7433i | 0.0250301 | − | 0.0433535i | ||||
\(664\) | 315.834i | 0.475654i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −137.897 | −0.207053 | ||||||||
\(667\) | −1632.53 | − | 942.544i | −2.44758 | − | 1.41311i | ||||
\(668\) | −48.4258 | − | 83.8760i | −0.0724937 | − | 0.125563i | ||||
\(669\) | −236.216 | − | 409.139i | −0.353089 | − | 0.611567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 224.076i | − | 0.333944i | ||||||
\(672\) | 5.92207 | + | 68.3296i | 0.00881261 | + | 0.101681i | ||||
\(673\) | 1173.04i | 1.74301i | 0.490389 | + | 0.871504i | \(0.336855\pi\) | ||||
−0.490389 | + | 0.871504i | \(0.663145\pi\) | |||||||
\(674\) | 21.2930 | − | 36.8806i | 0.0315920 | − | 0.0547189i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −116.791 | − | 202.288i | −0.172768 | − | 0.299242i | ||||
\(677\) | −338.731 | + | 586.699i | −0.500341 | + | 0.866616i | 0.499659 | + | 0.866222i | \(0.333459\pi\) |
−1.00000 | 0.000393478i | \(0.999875\pi\) | ||||||||
\(678\) | 258.258 | 0.380912 | ||||||||
\(679\) | −30.0078 | − | 42.9299i | −0.0441941 | − | 0.0632252i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.9191 | + | 24.1086i | −0.0204392 | + | 0.0354018i | ||||
\(682\) | −495.439 | − | 858.126i | −0.726450 | − | 1.25825i | ||||
\(683\) | 719.691 | − | 415.514i | 1.05372 | − | 0.608366i | 0.130032 | − | 0.991510i | \(-0.458492\pi\) |
0.923689 | + | 0.383144i | \(0.125159\pi\) | |||||||
\(684\) | 13.2077 | + | 7.62546i | 0.0193095 | + | 0.0111483i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 468.239 | + | 126.689i | 0.682564 | + | 0.184679i | ||||
\(687\) | − | 256.523i | − | 0.373395i | ||||||
\(688\) | 129.465 | + | 74.7464i | 0.188175 | + | 0.108643i | ||||
\(689\) | 443.587 | − | 256.105i | 0.643813 | − | 0.371706i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 541.436 | + | 312.598i | 0.783554 | + | 0.452385i | 0.837688 | − | 0.546149i | \(-0.183907\pi\) |
−0.0541345 | + | 0.998534i | \(0.517240\pi\) | |||||||
\(692\) | −225.937 | −0.326499 | ||||||||
\(693\) | −209.163 | − | 299.233i | −0.301823 | − | 0.431794i | ||||
\(694\) | 588.181 | 0.847524 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −199.438 | + | 115.146i | −0.286549 | + | 0.165439i | ||||
\(697\) | 162.303 | − | 93.7055i | 0.232859 | − | 0.134441i | ||||
\(698\) | −420.693 | + | 728.661i | −0.602712 | + | 1.04393i | ||||
\(699\) | − | 518.088i | − | 0.741185i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1030.02 | 1.46936 | 0.734678 | − | 0.678416i | \(-0.237333\pi\) | ||||
0.734678 | + | 0.678416i | \(0.237333\pi\) | |||||||
\(702\) | 45.9834 | + | 26.5485i | 0.0655034 | + | 0.0378184i | ||||
\(703\) | 41.3081 | + | 71.5477i | 0.0587597 | + | 0.101775i | ||||
\(704\) | −69.5407 | − | 120.448i | −0.0987795 | − | 0.171091i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 515.224i | 0.729779i | ||||||||
\(707\) | −599.906 | − | 280.335i | −0.848523 | − | 0.396513i | ||||
\(708\) | − | 348.345i | − | 0.492013i | ||||||
\(709\) | −329.126 | + | 570.062i | −0.464211 | + | 0.804037i | −0.999166 | − | 0.0408438i | \(-0.986995\pi\) |
0.534955 | + | 0.844881i | \(0.320329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.1626 | − | 62.6354i | −0.0508616 | − | 0.0880949i | ||||
\(712\) | 180.887 | − | 313.306i | 0.254055 | − | 0.440037i | ||||
\(713\) | 1616.17 | 2.26671 | ||||||||
\(714\) | −41.1962 | − | 19.2509i | −0.0576978 | − | 0.0269621i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −331.416 | + | 574.030i | −0.462872 | + | 0.801718i | ||||
\(717\) | 98.9461 | + | 171.380i | 0.138000 | + | 0.239023i | ||||
\(718\) | 750.478 | − | 433.288i | 1.04523 | − | 0.603466i | ||||
\(719\) | 1166.99 | + | 673.760i | 1.62307 | + | 0.937079i | 0.986093 | + | 0.166195i | \(0.0531481\pi\) |
0.636975 | + | 0.770884i | \(0.280185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −417.188 | + | 36.1574i | −0.578625 | + | 0.0501490i | ||||
\(722\) | 501.394i | 0.694452i | ||||||||
\(723\) | −204.663 | − | 118.162i | −0.283074 | − | 0.163433i | ||||
\(724\) | 369.495 | − | 213.328i | 0.510352 | − | 0.294652i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 384.478 | + | 221.978i | 0.529584 | + | 0.305755i | ||||
\(727\) | −1126.18 | −1.54907 | −0.774536 | − | 0.632530i | \(-0.782017\pi\) | ||||
−0.774536 | + | 0.632530i | \(0.782017\pi\) | |||||||
\(728\) | 117.254 | − | 81.9602i | 0.161063 | − | 0.112583i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −85.8348 | + | 49.5568i | −0.117421 | + | 0.0677931i | ||||
\(732\) | 38.6668 | − | 22.3243i | 0.0528235 | − | 0.0304976i | ||||
\(733\) | 303.337 | − | 525.395i | 0.413829 | − | 0.716773i | −0.581476 | − | 0.813564i | \(-0.697524\pi\) |
0.995305 | + | 0.0967907i | \(0.0308577\pi\) | |||||||
\(734\) | 697.233i | 0.949909i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 226.848 | 0.308218 | ||||||||
\(737\) | 1416.35 | + | 817.731i | 1.92178 | + | 1.10954i | ||||
\(738\) | 149.909 | + | 259.651i | 0.203129 | + | 0.351830i | ||||
\(739\) | 461.084 | + | 798.622i | 0.623930 | + | 1.08068i | 0.988747 | + | 0.149599i | \(0.0477984\pi\) |
−0.364817 | + | 0.931079i | \(0.618868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 31.8111i | − | 0.0429300i | ||||||
\(742\) | −402.045 | − | 575.175i | −0.541840 | − | 0.775168i | ||||
\(743\) | − | 13.3994i | − | 0.0180342i | −0.999959 | − | 0.00901712i | \(-0.997130\pi\) | ||
0.999959 | − | 0.00901712i | \(-0.00287028\pi\) | |||||||
\(744\) | 98.7192 | − | 170.987i | 0.132687 | − | 0.229821i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −116.957 | − | 202.576i | −0.156779 | − | 0.271550i | ||||
\(747\) | 167.496 | − | 290.112i | 0.224225 | − | 0.388370i | ||||
\(748\) | 92.2108 | 0.123277 | ||||||||
\(749\) | −3.90552 | − | 45.0624i | −0.00521431 | − | 0.0601634i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −538.071 | + | 931.967i | −0.716473 | + | 1.24097i | 0.245916 | + | 0.969291i | \(0.420911\pi\) |
−0.962389 | + | 0.271676i | \(0.912422\pi\) | |||||||
\(752\) | 66.8969 | + | 115.869i | 0.0889587 | + | 0.154081i | ||||
\(753\) | 685.536 | − | 395.794i | 0.910406 | − | 0.525623i | ||||
\(754\) | 415.997 | + | 240.176i | 0.551721 | + | 0.318536i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 30.7975 | − | 65.9054i | 0.0407374 | − | 0.0871764i | ||||
\(757\) | − | 254.117i | − | 0.335690i | −0.985813 | − | 0.167845i | \(-0.946319\pi\) | ||
0.985813 | − | 0.167845i | \(-0.0536807\pi\) | |||||||
\(758\) | −219.656 | − | 126.819i | −0.289784 | − | 0.167307i | ||||
\(759\) | −1045.76 | + | 603.768i | −1.37781 | + | 0.795478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −685.095 | − | 395.540i | −0.900256 | − | 0.519763i | −0.0229729 | − | 0.999736i | \(-0.507313\pi\) |
−0.877283 | + | 0.479973i | \(0.840646\pi\) | |||||||
\(762\) | 131.546 | 0.172632 | ||||||||
\(763\) | 485.538 | − | 1039.03i | 0.636354 | − | 1.36177i | ||||
\(764\) | 133.807 | 0.175140 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −329.664 | + | 190.332i | −0.430371 | + | 0.248475i | ||||
\(767\) | −629.250 | + | 363.298i | −0.820405 | + | 0.473661i | ||||
\(768\) | 13.8564 | − | 24.0000i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 464.403i | 0.603905i | 0.953323 | + | 0.301952i | \(0.0976384\pi\) | ||||
−0.953323 | + | 0.301952i | \(0.902362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −86.5993 | −0.112321 | ||||||||
\(772\) | 195.036 | + | 112.604i | 0.252637 | + | 0.145860i | ||||
\(773\) | −390.063 | − | 675.608i | −0.504609 | − | 0.874008i | −0.999986 | − | 0.00533002i | \(-0.998303\pi\) |
0.495377 | − | 0.868678i | \(-0.335030\pi\) | |||||||
\(774\) | −79.2805 | − | 137.318i | −0.102430 | − | 0.177413i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21.1639i | 0.0272730i | ||||||||
\(777\) | 322.991 | − | 225.769i | 0.415690 | − | 0.290566i | ||||
\(778\) | 669.980i | 0.861157i | ||||||||
\(779\) | 89.8126 | − | 155.560i | 0.115292 | − | 0.199692i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −100.654 | − | 174.337i | −0.128878 | − | 0.223223i | ||||
\(782\) | −75.2000 | + | 130.250i | −0.0961637 | + | 0.166560i | ||||
\(783\) | 244.261 | 0.311955 | ||||||||
\(784\) | −125.742 | − | 150.349i | −0.160385 | − | 0.191772i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −71.6283 | + | 124.064i | −0.0911302 | + | 0.157842i | ||||
\(787\) | 576.402 | + | 998.358i | 0.732404 | + | 1.26856i | 0.955853 | + | 0.293845i | \(0.0949351\pi\) |
−0.223449 | + | 0.974716i | \(0.571732\pi\) | |||||||
\(788\) | 105.692 | − | 61.0211i | 0.134126 | − | 0.0774379i | ||||
\(789\) | −273.416 | − | 157.857i | −0.346535 | − | 0.200072i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −604.907 | + | 422.827i | −0.764737 | + | 0.534548i | ||||
\(792\) | 147.518i | 0.186260i | ||||||||
\(793\) | −80.6530 | − | 46.5650i | −0.101706 | − | 0.0587201i | ||||
\(794\) | −629.437 | + | 363.406i | −0.792742 | + | 0.457690i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 331.108 | + | 191.165i | 0.415964 | + | 0.240157i | ||||
\(797\) | 1475.63 | 1.85148 | 0.925742 | − | 0.378156i | \(-0.123442\pi\) | ||||
0.925742 | + | 0.378156i | \(0.123442\pi\) | |||||||
\(798\) | −43.4204 | + | 3.76321i | −0.0544115 | + | 0.00471580i | ||||
\(799\) | −88.7051 | −0.111020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −332.311 | + | 191.860i | −0.414871 | + | 0.239526i | ||||
\(802\) | −498.146 | + | 287.605i | −0.621129 | + | 0.358609i | ||||
\(803\) | −197.053 | + | 341.305i | −0.245396 | + | 0.425038i | ||||
\(804\) | 325.876i | 0.405318i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −411.827 | −0.510951 | ||||||||
\(807\) | 56.4326 | + | 32.5814i | 0.0699289 | + | 0.0403734i | ||||
\(808\) | 133.779 | + | 231.713i | 0.165569 | + | 0.286773i | ||||
\(809\) | −6.88050 | − | 11.9174i | −0.00850495 | − | 0.0147310i | 0.861742 | − | 0.507347i | \(-0.169374\pi\) |
−0.870247 | + | 0.492616i | \(0.836041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1274.65i | − | 1.57170i | −0.618416 | − | 0.785851i | \(-0.712225\pi\) | ||
0.618416 | − | 0.785851i | \(-0.287775\pi\) | |||||||
\(812\) | 278.615 | − | 596.225i | 0.343122 | − | 0.734268i | ||||
\(813\) | 351.151i | 0.431920i | ||||||||
\(814\) | −399.562 | + | 692.062i | −0.490863 | + | 0.850199i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.18678 | + | 15.9120i | 0.0112583 | + | 0.0195000i | ||||
\(817\) | −47.4980 | + | 82.2689i | −0.0581371 | + | 0.100696i | ||||
\(818\) | −689.406 | −0.842795 | ||||||||
\(819\) | −151.171 | + | 13.1019i | −0.184580 | + | 0.0159974i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −292.249 | + | 506.190i | −0.355967 | + | 0.616553i | −0.987283 | − | 0.158973i | \(-0.949182\pi\) |
0.631316 | + | 0.775526i | \(0.282515\pi\) | |||||||
\(822\) | 14.8402 | + | 25.7040i | 0.0180538 | + | 0.0312700i | ||||
\(823\) | 70.1196 | − | 40.4835i | 0.0851999 | − | 0.0491902i | −0.456795 | − | 0.889572i | \(-0.651003\pi\) |
0.541995 | + | 0.840382i | \(0.317669\pi\) | |||||||
\(824\) | 146.533 | + | 84.6007i | 0.177831 | + | 0.102671i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 570.320 | + | 815.913i | 0.690461 | + | 0.987789i | ||||
\(827\) | − | 1628.46i | − | 1.96911i | −0.175072 | − | 0.984556i | \(-0.556016\pi\) | ||
0.175072 | − | 0.984556i | \(-0.443984\pi\) | |||||||
\(828\) | −208.373 | − | 120.304i | −0.251659 | − | 0.145295i | ||||
\(829\) | 761.982 | − | 439.931i | 0.919158 | − | 0.530676i | 0.0357920 | − | 0.999359i | \(-0.488605\pi\) |
0.883366 | + | 0.468683i | \(0.155271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 384.362 | + | 221.912i | 0.462530 | + | 0.267042i | ||||
\(832\) | −57.8047 | −0.0694768 | ||||||||
\(833\) | 128.010 | − | 22.3570i | 0.153674 | − | 0.0268391i | ||||
\(834\) | 110.855 | 0.132919 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 76.5394 | − | 44.1900i | 0.0915543 | − | 0.0528589i | ||||
\(837\) | −181.359 | + | 104.708i | −0.216677 | + | 0.125099i | ||||
\(838\) | −390.505 | + | 676.374i | −0.465996 | + | 0.807129i | ||||
\(839\) | 647.389i | 0.771619i | 0.922578 | + | 0.385810i | \(0.126078\pi\) | ||||
−0.922578 | + | 0.385810i | \(0.873922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1368.75 | 1.62753 | ||||||||
\(842\) | 91.4725 | + | 52.8117i | 0.108637 | + | 0.0627217i | ||||
\(843\) | −122.510 | − | 212.193i | −0.145326 | − | 0.251711i | ||||
\(844\) | 280.115 | + | 485.174i | 0.331890 | + | 0.574851i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 141.910i | − | 0.167742i | ||||||
\(847\) | −1263.97 | + | 109.548i | −1.49230 | + | 0.129336i | ||||
\(848\) | 283.554i | 0.334379i | ||||||||
\(849\) | 470.571 | − | 815.052i | 0.554264 | − | 0.960014i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −651.704 | − | 1128.78i | −0.765809 | − | 1.32642i | ||||
\(852\) | 20.0559 | − | 34.7378i | 0.0235397 | − | 0.0407720i | ||||
\(853\) | 569.518 | 0.667665 | 0.333833 | − | 0.942632i | \(-0.391658\pi\) | ||||
0.333833 | + | 0.942632i | \(0.391658\pi\) | |||||||
\(854\) | −54.0175 | + | 115.595i | −0.0632524 | + | 0.135358i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.13810 | + | 15.8277i | −0.0106754 | + | 0.0184903i | ||||
\(857\) | 319.299 | + | 553.041i | 0.372577 | + | 0.645322i | 0.989961 | − | 0.141339i | \(-0.0451409\pi\) |
−0.617384 | + | 0.786662i | \(0.711808\pi\) | |||||||
\(858\) | 266.477 | − | 153.850i | 0.310579 | − | 0.179313i | ||||
\(859\) | −1097.36 | − | 633.562i | −1.27749 | − | 0.737558i | −0.301102 | − | 0.953592i | \(-0.597355\pi\) |
−0.976386 | + | 0.216034i | \(0.930688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −776.233 | − | 362.732i | −0.901548 | − | 0.421292i | ||||
\(862\) | 685.437i | 0.795171i | ||||||||
\(863\) | −178.430 | − | 103.017i | −0.206756 | − | 0.119371i | 0.393047 | − | 0.919518i | \(-0.371421\pi\) |
−0.599803 | + | 0.800148i | \(0.704754\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 561.173 | + | 323.993i | 0.648006 | + | 0.374126i | ||||
\(867\) | 488.381 | 0.563300 | ||||||||
\(868\) | 48.7185 | + | 562.120i | 0.0561273 | + | 0.647604i | ||||
\(869\) | −419.129 | −0.482312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 588.661 | − | 339.864i | 0.675845 | − | 0.390199i | ||||
\(872\) | −401.325 | + | 231.705i | −0.460235 | + | 0.265717i | ||||
\(873\) | 11.2238 | − | 19.4403i | 0.0128566 | − | 0.0222683i | ||||
\(874\) | 144.152i | 0.164933i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −78.5279 | −0.0896437 | ||||||||
\(877\) | −714.076 | − | 412.272i | −0.814226 | − | 0.470093i | 0.0341955 | − | 0.999415i | \(-0.489113\pi\) |
−0.848421 | + | 0.529322i | \(0.822446\pi\) | |||||||
\(878\) | 98.9325 | + | 171.356i | 0.112679 | + | 0.195167i | ||||
\(879\) | 325.009 | + | 562.933i | 0.369749 | + | 0.640424i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 416.337i | 0.472574i | 0.971683 | + | 0.236287i | \(0.0759305\pi\) | ||||
−0.971683 | + | 0.236287i | \(0.924070\pi\) | |||||||
\(882\) | 35.7666 | + | 204.790i | 0.0405517 | + | 0.232188i | ||||
\(883\) | − | 650.529i | − | 0.736726i | −0.929682 | − | 0.368363i | \(-0.879918\pi\) | ||
0.929682 | − | 0.368363i | \(-0.120082\pi\) | |||||||
\(884\) | 19.1622 | − | 33.1900i | 0.0216767 | − | 0.0375452i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.3790 | + | 19.7090i | 0.0128431 | + | 0.0222449i | ||||
\(887\) | 173.198 | − | 299.987i | 0.195262 | − | 0.338204i | −0.751724 | − | 0.659478i | \(-0.770777\pi\) |
0.946987 | + | 0.321273i | \(0.104111\pi\) | |||||||
\(888\) | −159.230 | −0.179313 | ||||||||
\(889\) | −308.113 | + | 215.370i | −0.346584 | + | 0.242261i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 78.2333 | − | 135.504i | 0.0878040 | − | 0.152081i | ||||
\(892\) | −272.759 | − | 472.433i | −0.305784 | − | 0.529633i | ||||
\(893\) | −73.6295 | + | 42.5100i | −0.0824518 | + | 0.0476036i | ||||
\(894\) | 107.964 | + | 62.3332i | 0.120765 | + | 0.0697239i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.83822 | + | 78.9002i | 0.00763194 | + | 0.0880582i | ||||
\(897\) | 501.873i | 0.559502i | ||||||||
\(898\) | −403.326 | − | 232.860i | −0.449138 | − | 0.259310i | ||||
\(899\) | −1640.70 | + | 947.256i | −1.82502 | + | 1.05368i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −162.809 | − | 93.9978i | −0.180698 | − | 0.104326i | ||||
\(902\) | 1737.47 | 1.92624 | ||||||||
\(903\) | 410.516 | + | 191.833i | 0.454613 | + | 0.212440i | ||||
\(904\) | 298.211 | 0.329879 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 334.522 | − | 193.136i | 0.369230 | − | 0.213175i | ||||
\(907\) | 363.888 | − | 210.091i | 0.401199 | − | 0.231633i | −0.285802 | − | 0.958289i | \(-0.592260\pi\) |
0.687001 | + | 0.726656i | \(0.258927\pi\) | |||||||
\(908\) | −16.0724 | + | 27.8382i | −0.0177009 | + | 0.0306588i | ||||
\(909\) | − | 283.789i | − | 0.312199i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 717.087 | 0.787142 | 0.393571 | − | 0.919294i | \(-0.371239\pi\) | ||||
0.393571 | + | 0.919294i | \(0.371239\pi\) | |||||||
\(912\) | 15.2509 | + | 8.80512i | 0.0167225 | + | 0.00965474i | ||||
\(913\) | −970.652 | − | 1681.22i | −1.06315 | − | 1.84142i | ||||
\(914\) | −629.974 | − | 1091.15i | −0.689249 | − | 1.19381i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 296.207i | − | 0.323370i | ||||||
\(917\) | −35.3490 | − | 407.861i | −0.0385485 | − | 0.444777i | ||||
\(918\) | − | 19.4881i | − | 0.0212289i | ||||||
\(919\) | −59.5137 | + | 103.081i | −0.0647592 | + | 0.112166i | −0.896587 | − | 0.442867i | \(-0.853961\pi\) |
0.831828 | + | 0.555034i | \(0.187295\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.8046 | + | 62.0154i | 0.0388758 | + | 0.0673349i | ||||
\(922\) | 377.608 | − | 654.037i | 0.409553 | − | 0.709367i | ||||
\(923\) | −83.6669 | −0.0906467 | ||||||||
\(924\) | −241.521 | − | 345.525i | −0.261386 | − | 0.373945i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −112.203 | + | 194.341i | −0.121169 | + | 0.209872i | ||||
\(927\) | −89.7326 | − | 155.421i | −0.0967989 | − | 0.167661i | ||||
\(928\) | −230.291 | + | 132.959i | −0.248159 | + | 0.143274i | ||||
\(929\) | −328.049 | − | 189.399i | −0.353121 | − | 0.203874i | 0.312938 | − | 0.949773i | \(-0.398687\pi\) |
−0.666059 | + | 0.745899i | \(0.732020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95.5403 | − | 79.9034i | 0.102621 | − | 0.0858253i | ||||
\(932\) | − | 598.237i | − | 0.641885i | ||||||
\(933\) | −219.838 | − | 126.924i | −0.235625 | − | 0.136038i | ||||
\(934\) | −137.415 | + | 79.3366i | −0.147125 | + | 0.0849429i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 53.0970 | + | 30.6556i | 0.0567276 | + | 0.0327517i | ||||
\(937\) | −365.585 | −0.390165 | −0.195083 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195083 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(938\) | −533.532 | − | 763.284i | −0.568798 | − | 0.813735i | ||||
\(939\) | 389.487 | 0.414790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1193.22 | + | 688.903i | −1.26803 | + | 0.732097i | −0.974615 | − | 0.223889i | \(-0.928125\pi\) |
−0.293414 | + | 0.955985i | \(0.594791\pi\) | |||||||
\(942\) | 356.056 | − | 205.569i | 0.377978 | − | 0.218226i | ||||
\(943\) | −1416.94 | + | 2454.22i | −1.50259 | + | 2.60256i | ||||
\(944\) | − | 402.235i | − | 0.426096i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −918.871 | −0.971323 | ||||||||
\(947\) | −411.218 | − | 237.417i | −0.434232 | − | 0.250704i | 0.266916 | − | 0.963720i | \(-0.413995\pi\) |
−0.701148 | + | 0.713016i | \(0.747329\pi\) | |||||||
\(948\) | −41.7570 | − | 72.3252i | −0.0440474 | − | 0.0762924i | ||||
\(949\) | 81.8986 | + | 141.853i | 0.0862999 | + | 0.149476i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 391.836i | 0.412025i | ||||||||
\(952\) | −47.5693 | − | 22.2290i | −0.0499677 | − | 0.0233498i | ||||
\(953\) | 172.839i | 0.181363i | 0.995880 | + | 0.0906813i | \(0.0289045\pi\) | ||||
−0.995880 | + | 0.0906813i | \(0.971096\pi\) | |||||||
\(954\) | 150.377 | − | 260.461i | 0.157628 | − | 0.273019i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 114.253 | + | 197.892i | 0.119512 | + | 0.207000i | ||||
\(957\) | 707.753 | − | 1225.86i | 0.739554 | − | 1.28094i | ||||
\(958\) | −977.622 | −1.02048 | ||||||||
\(959\) | −76.8427 | − | 35.9085i | −0.0801280 | − | 0.0374437i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 331.623 | − | 574.388i | 0.345081 | − | 0.597698i | ||||
\(962\) | 166.065 | + | 287.633i | 0.172625 | + | 0.298995i | ||||
\(963\) | 16.7878 | − | 9.69242i | 0.0174328 | − | 0.0100648i | ||||
\(964\) | −236.324 | − | 136.442i | −0.245150 | − | 0.141537i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 685.029 | − | 59.3709i | 0.709139 | − | 0.0614606i | ||||
\(967\) | − | 1209.88i | − | 1.25117i | −0.780158 | − | 0.625583i | \(-0.784861\pi\) | ||
0.780158 | − | 0.625583i | \(-0.215139\pi\) | |||||||
\(968\) | 443.957 | + | 256.319i | 0.458633 | + | 0.264792i | ||||
\(969\) | −10.1113 | + | 5.83779i | −0.0104348 | + | 0.00602455i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −675.990 | − | 390.283i | −0.696180 | − | 0.401939i | 0.109743 | − | 0.993960i | \(-0.464997\pi\) |
−0.805923 | + | 0.592020i | \(0.798330\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −259.650 | + | 181.494i | −0.266855 | + | 0.186531i | ||||
\(974\) | −1019.39 | −1.04661 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.6485 | − | 25.7778i | 0.0457465 | − | 0.0264117i | ||||
\(977\) | 1376.86 | − | 794.931i | 1.40927 | − | 0.813644i | 0.413955 | − | 0.910297i | \(-0.364147\pi\) |
0.995318 | + | 0.0966527i | \(0.0308136\pi\) | |||||||
\(978\) | 338.728 | − | 586.694i | 0.346347 | − | 0.599891i | ||||
\(979\) | 2223.68i | 2.27138i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 491.520 | 0.501040 | ||||||||
\(982\) | −722.593 | − | 417.189i | −0.735838 | − | 0.424836i | ||||
\(983\) | −350.785 | − | 607.577i | −0.356851 | − | 0.618084i | 0.630582 | − | 0.776123i | \(-0.282816\pi\) |
−0.987433 | + | 0.158039i | \(0.949483\pi\) | |||||||
\(984\) | 173.100 | + | 299.819i | 0.175915 | + | 0.304694i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 176.303i | − | 0.178806i | ||||||
\(987\) | 232.339 | + | 332.389i | 0.235399 | + | 0.336767i | ||||
\(988\) | − | 36.7323i | − | 0.0371785i | ||||||
\(989\) | 749.360 | − | 1297.93i | 0.757695 | − | 1.31237i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −203.359 | − | 352.228i | −0.205206 | − | 0.355427i | 0.744992 | − | 0.667073i | \(-0.232453\pi\) |
−0.950198 | + | 0.311646i | \(0.899120\pi\) | |||||||
\(992\) | 113.991 | − | 197.438i | 0.114910 | − | 0.199031i | ||||
\(993\) | −242.169 | −0.243876 | ||||||||
\(994\) | 9.89768 | + | 114.201i | 0.00995743 | + | 0.114890i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 193.408 | − | 334.993i | 0.194185 | − | 0.336338i | ||||
\(997\) | −378.379 | − | 655.372i | −0.379518 | − | 0.657344i | 0.611474 | − | 0.791264i | \(-0.290577\pi\) |
−0.990992 | + | 0.133920i | \(0.957243\pi\) | |||||||
\(998\) | 1072.50 | − | 619.207i | 1.07465 | − | 0.620448i | ||||
\(999\) | 146.262 | + | 84.4446i | 0.146409 | + | 0.0845291i |
(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 | 1050.3.q.e.649.2 | 32 | ||
5.2 | odd | 4 | 1050.3.p.i.901.5 | 16 | |||
5.3 | odd | 4 | 210.3.o.b.61.2 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.q.e.649.15 | 32 | ||
7.3 | odd | 6 | inner | 1050.3.q.e.199.15 | 32 | ||
15.8 | even | 4 | 630.3.v.c.271.8 | 16 | |||
35.3 | even | 12 | 210.3.o.b.31.2 | ✓ | 16 | ||
35.17 | even | 12 | 1050.3.p.i.451.5 | 16 | |||
35.23 | odd | 12 | 1470.3.f.d.391.11 | 16 | |||
35.24 | odd | 6 | inner | 1050.3.q.e.199.2 | 32 | ||
35.33 | even | 12 | 1470.3.f.d.391.13 | 16 | |||
105.38 | odd | 12 | 630.3.v.c.451.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.2 | ✓ | 16 | 35.3 | even | 12 | ||
210.3.o.b.61.2 | yes | 16 | 5.3 | odd | 4 | ||
630.3.v.c.271.8 | 16 | 15.8 | even | 4 | |||
630.3.v.c.451.8 | 16 | 105.38 | odd | 12 | |||
1050.3.p.i.451.5 | 16 | 35.17 | even | 12 | |||
1050.3.p.i.901.5 | 16 | 5.2 | odd | 4 | |||
1050.3.q.e.199.2 | 32 | 35.24 | odd | 6 | inner | ||
1050.3.q.e.199.15 | 32 | 7.3 | odd | 6 | inner | ||
1050.3.q.e.649.2 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.q.e.649.15 | 32 | 5.4 | even | 2 | inner | ||
1470.3.f.d.391.11 | 16 | 35.23 | odd | 12 | |||
1470.3.f.d.391.13 | 16 | 35.33 | even | 12 |