Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Character | \(\chi\) | \(=\) | 76.9 |
Dual form | 76.4.i.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.65540 | + | 1.38904i | −0.318581 | + | 0.267321i | −0.788028 | − | 0.615639i | \(-0.788898\pi\) |
0.469447 | + | 0.882961i | \(0.344453\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.99353 | + | 3.27338i | 0.804406 | + | 0.292780i | 0.711311 | − | 0.702878i | \(-0.248102\pi\) |
0.0930948 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0466734 | + | 0.0808407i | −0.00252013 | + | 0.00436499i | −0.867283 | − | 0.497816i | \(-0.834136\pi\) |
0.864763 | + | 0.502181i | \(0.167469\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.87760 | + | 21.9910i | −0.143615 | + | 0.814481i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.3982 | + | 24.9384i | 0.394656 | + | 0.683564i | 0.993057 | − | 0.117632i | \(-0.0375304\pi\) |
−0.598401 | + | 0.801197i | \(0.704197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.7744 | + | 51.8349i | 1.31793 | + | 1.10588i | 0.986739 | + | 0.162315i | \(0.0518960\pi\) |
0.331194 | + | 0.943563i | \(0.392548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −19.4347 | + | 7.07365i | −0.334535 | + | 0.121761i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.24768 | + | 12.7472i | 0.0320672 | + | 0.181862i | 0.996634 | − | 0.0819754i | \(-0.0261229\pi\) |
−0.964567 | + | 0.263837i | \(0.915012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.98203 | − | 82.3306i | −0.108454 | − | 0.994102i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0350282 | − | 0.198655i | −0.000363989 | − | 0.00206428i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −31.6580 | + | 11.5226i | −0.287006 | + | 0.104462i | −0.481512 | − | 0.876440i | \(-0.659912\pi\) |
0.194505 | + | 0.980901i | \(0.437690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.5870 | − | 21.4700i | −0.204696 | − | 0.171760i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.3005 | − | 92.3191i | −0.379914 | − | 0.658030i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.33650 | − | 52.9499i | 0.0597843 | − | 0.339053i | −0.940215 | − | 0.340583i | \(-0.889376\pi\) |
0.999999 | + | 0.00152923i | \(0.000486771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.3029 | − | 35.1657i | 0.117630 | − | 0.203740i | −0.801198 | − | 0.598399i | \(-0.795804\pi\) |
0.918828 | + | 0.394659i | \(0.129137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −58.4752 | − | 21.2832i | −0.308461 | − | 0.112271i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.684380 | + | 0.574263i | −0.00330518 | + | 0.00277338i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.12775 | 0.0361133 | 0.0180567 | − | 0.999837i | \(-0.494252\pi\) | ||||
0.0180567 | + | 0.999837i | \(0.494252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −174.262 | −0.715493 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 196.821 | − | 165.152i | 0.749714 | − | 0.629085i | −0.185713 | − | 0.982604i | \(-0.559459\pi\) |
0.935427 | + | 0.353519i | \(0.115015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −418.967 | − | 152.492i | −1.48586 | − | 0.540808i | −0.533502 | − | 0.845799i | \(-0.679124\pi\) |
−0.952355 | + | 0.304991i | \(0.901347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −106.858 | + | 185.084i | −0.353988 | + | 0.613125i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 64.4398 | − | 365.456i | 0.199990 | − | 1.13420i | −0.705142 | − | 0.709066i | \(-0.749117\pi\) |
0.905132 | − | 0.425131i | \(-0.139772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 171.496 | + | 297.039i | 0.499987 | + | 0.866003i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.4272 | − | 17.9796i | −0.0588316 | − | 0.0493655i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 423.366 | − | 154.093i | 1.09724 | − | 0.399363i | 0.270943 | − | 0.962596i | \(-0.412665\pi\) |
0.826299 | + | 0.563232i | \(0.190442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 47.8578 | + | 271.415i | 0.117330 | + | 0.665410i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 129.229 | + | 123.813i | 0.300296 | + | 0.287710i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 35.0142 | + | 198.575i | 0.0772620 | + | 0.438175i | 0.998760 | + | 0.0497908i | \(0.0158555\pi\) |
−0.921498 | + | 0.388384i | \(0.873033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −209.354 | + | 76.1986i | −0.439427 | + | 0.159938i | −0.552253 | − | 0.833677i | \(-0.686232\pi\) |
0.112827 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.59678 | − | 1.33986i | −0.00319327 | − | 0.00267947i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 385.895 | + | 668.389i | 0.736375 | + | 1.27544i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26.2614 | + | 148.936i | −0.0478858 | + | 0.271574i | −0.999344 | − | 0.0362028i | \(-0.988474\pi\) |
0.951459 | + | 0.307776i | \(0.0995849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36.4012 | − | 63.0486i | 0.0635099 | − | 0.110002i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 341.051 | + | 124.132i | 0.570075 | + | 0.207490i | 0.610943 | − | 0.791674i | \(-0.290790\pi\) |
−0.0408687 | + | 0.999165i | \(0.513013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.86543 | + | 2.40438i | −0.00459416 | + | 0.00385496i | −0.645082 | − | 0.764114i | \(-0.723177\pi\) |
0.640488 | + | 0.767968i | \(0.278732\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 72.1794 | 0.111127 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.68805 | −0.00397833 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −573.251 | + | 481.015i | −0.816403 | + | 0.685043i | −0.952127 | − | 0.305703i | \(-0.901108\pi\) |
0.135724 | + | 0.990747i | \(0.456664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −350.087 | − | 127.421i | −0.480230 | − | 0.174789i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 355.657 | − | 616.017i | 0.470343 | − | 0.814658i | −0.529082 | − | 0.848571i | \(-0.677464\pi\) |
0.999425 | + | 0.0339128i | \(0.0107969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.5119 | + | 122.000i | −0.0274505 | + | 0.155679i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 58.0940 | + | 100.622i | 0.0715901 | + | 0.123998i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 605.237 | + | 507.854i | 0.720843 | + | 0.604859i | 0.927618 | − | 0.373530i | \(-0.121853\pi\) |
−0.206776 | + | 0.978388i | \(0.566297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.07358 | + | 2.57457i | −0.00814850 | + | 0.00296581i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.2373 | + | 86.4148i | 0.0169896 | + | 0.0963526i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 188.719 | − | 769.844i | 0.203812 | − | 0.831414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −176.963 | − | 1003.61i | −0.185236 | − | 1.05052i | −0.925652 | − | 0.378375i | \(-0.876483\pi\) |
0.740417 | − | 0.672148i | \(-0.234628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −604.250 | + | 219.929i | −0.613429 | + | 0.223270i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1282.37 | − | 1076.04i | −1.26338 | − | 1.06010i | −0.995314 | − | 0.0966975i | \(-0.969172\pi\) |
−0.268063 | − | 0.963401i | \(-0.586383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 262.718 | + | 455.041i | 0.251324 | + | 0.435307i | 0.963891 | − | 0.266298i | \(-0.0858006\pi\) |
−0.712566 | + | 0.701605i | \(0.752467\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.335244 | − | 1.90127i | 0.000311586 | − | 0.00176709i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 908.450 | − | 1573.48i | 0.820777 | − | 1.42163i | −0.0843270 | − | 0.996438i | \(-0.526874\pi\) |
0.905104 | − | 0.425190i | \(-0.139793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1651.34 | − | 601.040i | −1.45110 | − | 0.528157i | −0.508202 | − | 0.861238i | \(-0.669690\pi\) |
−0.942898 | + | 0.333081i | \(0.891912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.4546 | + | 11.2898i | −0.0115050 | + | 0.00965386i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 898.636 | 0.748111 | 0.374055 | − | 0.927406i | \(-0.377967\pi\) | ||||
0.374055 | + | 0.927406i | \(0.377967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −322.435 | −0.261454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1379.44 | + | 1157.48i | −1.08999 | + | 0.914611i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.13540 | − | 0.413252i | −0.000874638 | − | 0.000318342i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 250.884 | − | 434.545i | 0.188493 | − | 0.326480i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −96.4130 | + | 546.785i | −0.0706770 | + | 0.400829i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −758.007 | − | 1312.91i | −0.542386 | − | 0.939440i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −269.896 | − | 226.469i | −0.188578 | − | 0.158235i | 0.543611 | − | 0.839337i | \(-0.317057\pi\) |
−0.732189 | + | 0.681102i | \(0.761501\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 905.373 | − | 329.529i | 0.617935 | − | 0.224910i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 474.362 | + | 2690.24i | 0.316375 | + | 1.79425i | 0.564402 | + | 0.825500i | \(0.309107\pi\) |
−0.248027 | + | 0.968753i | \(0.579782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.07488 | + | 3.11653i | 0.00461256 | + | 0.00203186i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −177.164 | − | 1004.75i | −0.112947 | − | 0.640554i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2083.77 | − | 758.431i | 1.29948 | − | 0.472972i | 0.402653 | − | 0.915353i | \(-0.368088\pi\) |
0.896827 | + | 0.442381i | \(0.145866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 587.348 | + | 492.843i | 0.358404 | + | 0.300737i | 0.804154 | − | 0.594421i | \(-0.202619\pi\) |
−0.445750 | + | 0.895157i | \(0.647063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 400.961 | + | 694.484i | 0.239482 | + | 0.414795i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −403.239 | + | 2286.88i | −0.235808 | + | 1.33733i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 257.293 | − | 445.645i | 0.147359 | − | 0.255233i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −696.493 | − | 253.503i | −0.390788 | − | 0.142235i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1020.29 | + | 856.123i | −0.560975 | + | 0.470714i | −0.878637 | − | 0.477490i | \(-0.841547\pi\) |
0.317662 | + | 0.948204i | \(0.397102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2504.18 | 1.34959 | 0.674793 | − | 0.738007i | \(-0.264233\pi\) | ||||
0.674793 | + | 0.738007i | \(0.264233\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −289.039 | −0.152728 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 297.706 | − | 249.805i | 0.154273 | − | 0.129450i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2735.55 | − | 995.659i | −1.39058 | − | 0.506129i | −0.465210 | − | 0.885200i | \(-0.654021\pi\) |
−0.925367 | + | 0.379072i | \(0.876243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −486.797 | + | 843.157i | −0.242802 | + | 0.420545i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.546093 | − | 3.09705i | 0.000267318 | − | 0.00151603i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 476.727 | + | 825.716i | 0.229081 | + | 0.396780i | 0.957536 | − | 0.288314i | \(-0.0930947\pi\) |
−0.728455 | + | 0.685093i | \(0.759761\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −456.230 | − | 382.822i | −0.215257 | − | 0.180622i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3219.48 | − | 1171.80i | 1.49180 | − | 0.542972i | 0.537879 | − | 0.843022i | \(-0.319226\pi\) |
0.953923 | + | 0.300051i | \(0.0970036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 747.717 | + | 4240.51i | 0.340335 | + | 1.93014i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1845.36 | + | 121.722i | 0.825252 | + | 0.0544345i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −183.470 | − | 1040.51i | −0.0806299 | − | 0.457275i | −0.998214 | − | 0.0597340i | \(-0.980975\pi\) |
0.917584 | − | 0.397541i | \(-0.130136\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.92988 | − | 1.06639i | 0.00126559 | − | 0.000460637i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −333.792 | − | 280.085i | −0.141748 | − | 0.118940i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1458.78 | + | 2526.69i | 0.609132 | + | 1.05505i | 0.991384 | + | 0.130990i | \(0.0418154\pi\) |
−0.382252 | + | 0.924058i | \(0.624851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −86.6876 | + | 491.630i | −0.0355991 | + | 0.201893i | −0.997420 | − | 0.0717872i | \(-0.977130\pi\) |
0.961821 | + | 0.273680i | \(0.0882409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 240.720 | − | 416.940i | 0.0972381 | − | 0.168421i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 73.0971 | + | 26.6052i | 0.0290498 | + | 0.0105733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −285.533 | + | 239.590i | −0.111659 | + | 0.0936929i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.95085 | 0.00382972 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3954.16 | −1.49797 | −0.748987 | − | 0.662584i | \(-0.769460\pi\) | ||||
−0.748987 | + | 0.662584i | \(0.769460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2456.20 | + | 2060.99i | −0.916067 | + | 0.768671i | −0.973263 | − | 0.229692i | \(-0.926228\pi\) |
0.0571967 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1567.23 | − | 570.425i | −0.575547 | − | 0.209482i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2385.34 | − | 4131.53i | 0.862683 | − | 1.49421i | −0.00664619 | − | 0.999978i | \(-0.502116\pi\) |
0.869329 | − | 0.494233i | \(-0.164551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −154.510 | + | 876.271i | −0.0550399 | + | 0.312147i | −0.999882 | − | 0.0153802i | \(-0.995104\pi\) |
0.944842 | + | 0.327527i | \(0.106215\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −163.405 | − | 283.026i | −0.0573419 | − | 0.0993191i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.84474 | + | 3.22612i | 0.00132930 | + | 0.00111541i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2310.72 | − | 841.034i | 0.787258 | − | 0.286538i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −130.635 | − | 740.870i | −0.0438637 | − | 0.248763i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1923.87 | − | 1409.41i | 0.636730 | − | 0.466463i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −893.500 | − | 5067.29i | −0.291522 | − | 1.65330i | −0.681013 | − | 0.732271i | \(-0.738460\pi\) |
0.389491 | − | 0.921030i | \(-0.372651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −736.999 | + | 268.246i | −0.237082 | + | 0.0862906i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3268.83 | − | 2742.87i | −1.03689 | − | 0.870058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.89521 | + | 3.28261i | 0.000592882 | + | 0.00102690i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.40364 | − | 7.96041i | 0.000433100 | − | 0.00245623i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −521.901 | + | 903.959i | −0.158855 | + | 0.275144i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2658.51 | − | 967.619i | −0.798328 | − | 0.290568i | −0.0895346 | − | 0.995984i | \(-0.528538\pi\) |
−0.708794 | + | 0.705416i | \(0.750760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 571.363 | − | 479.431i | 0.169293 | − | 0.142054i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3211.84 | −0.939107 | −0.469554 | − | 0.882904i | \(-0.655585\pi\) | ||||
−0.469554 | + | 0.882904i | \(0.655585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3296.93 | −0.951386 | −0.475693 | − | 0.879611i | \(-0.657803\pi\) | ||||
−0.475693 | + | 0.879611i | \(0.657803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.44978 | − | 3.73381i | 0.00126742 | − | 0.00106349i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −313.608 | − | 114.144i | −0.0881766 | − | 0.0320937i | 0.297555 | − | 0.954705i | \(-0.403829\pi\) |
−0.385732 | + | 0.922611i | \(0.626051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1775.82 | − | 3075.81i | 0.492943 | − | 0.853802i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 280.808 | − | 1592.54i | 0.0769638 | − | 0.436484i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1485.26 | + | 2572.54i | 0.401981 | + | 0.696251i | 0.993965 | − | 0.109698i | \(-0.0349885\pi\) |
−0.591984 | + | 0.805950i | \(0.701655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3859.37 | + | 3238.39i | 1.03155 | + | 0.865574i | 0.991035 | − | 0.133605i | \(-0.0426554\pi\) |
0.0405159 | + | 0.999179i | \(0.487100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3461.17 | − | 1259.76i | 0.913722 | − | 0.332568i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 570.030 | + | 3232.80i | 0.148644 | + | 0.843004i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3712.74 | − | 5551.50i | 0.956420 | − | 1.43010i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 266.919 | + | 1513.77i | 0.0679330 | + | 0.385267i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6502.67 | + | 2366.78i | −1.63524 | + | 0.595178i | −0.986197 | − | 0.165575i | \(-0.947052\pi\) |
−0.649041 | + | 0.760753i | \(0.724830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −743.172 | − | 623.595i | −0.184675 | − | 0.154961i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −133.852 | − | 231.839i | −0.0328712 | − | 0.0569346i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 59.9734 | − | 340.126i | 0.0145566 | − | 0.0825544i | −0.976664 | − | 0.214773i | \(-0.931099\pi\) |
0.991221 | + | 0.132218i | \(0.0422100\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.379349 | + | 0.657052i | −9.10101e−5 | + | 0.000157634i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1128.22 | + | 410.638i | 0.267567 | + | 0.0973863i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3191.15 | + | 2677.69i | −0.748192 | + | 0.627808i | −0.935024 | − | 0.354584i | \(-0.884623\pi\) |
0.186832 | + | 0.982392i | \(0.440178\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4311.96 | 0.999552 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1707.34 | −0.391338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4483.60 | + | 3762.19i | −1.01625 | + | 0.852731i | −0.989151 | − | 0.146902i | \(-0.953070\pi\) |
−0.0270942 | + | 0.999633i | \(0.508625\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1408.80 | − | 512.760i | −0.315787 | − | 0.114937i | 0.179264 | − | 0.983801i | \(-0.442628\pi\) |
−0.495051 | + | 0.868864i | \(0.664851\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.13339 | − | 14.0874i | 0.00180313 | − | 0.00312312i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 167.022 | − | 947.228i | 0.0366247 | − | 0.207709i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 864.040 | + | 1496.56i | 0.187419 | + | 0.324620i | 0.944389 | − | 0.328830i | \(-0.106654\pi\) |
−0.756970 | + | 0.653450i | \(0.773321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 694.602 | + | 582.840i | 0.149049 | + | 0.125067i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4756.56 | − | 1731.25i | 1.00980 | − | 0.367536i | 0.216442 | − | 0.976295i | \(-0.430555\pi\) |
0.793355 | + | 0.608760i | \(0.208333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1290.93 | + | 7321.24i | 0.271159 | + | 1.53782i | 0.750905 | + | 0.660410i | \(0.229618\pi\) |
−0.479746 | + | 0.877407i | \(0.659271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 756.941 | + | 1536.53i | 0.157324 | + | 0.319356i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.16473 | + | 23.6194i | 0.000856573 | + | 0.00485787i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4459.27 | − | 1623.04i | 0.907647 | − | 0.330357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1686.99 | + | 1415.56i | 0.339840 | + | 0.285159i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1969.27 | + | 3410.87i | 0.392648 | + | 0.680087i | 0.992798 | − | 0.119801i | \(-0.0382256\pi\) |
−0.600150 | + | 0.799888i | \(0.704892\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −335.111 | + | 1900.51i | −0.0661387 | + | 0.375091i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1534.86 | − | 2658.46i | 0.299871 | − | 0.519391i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2552.92 | − | 929.188i | −0.493777 | − | 0.179720i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.8821 | − | 26.7523i | 0.00610517 | − | 0.00512284i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3617.50 | 0.685875 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2132.26 | −0.400304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5529.57 | − | 4639.86i | 1.02798 | − | 0.862577i | 0.0373697 | − | 0.999302i | \(-0.488102\pi\) |
0.990609 | + | 0.136725i | \(0.0436576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1066.97 | − | 388.347i | −0.196434 | − | 0.0714961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3445.54 | + | 5967.85i | −0.628227 | + | 1.08812i | 0.359680 | + | 0.933076i | \(0.382886\pi\) |
−0.987907 | + | 0.155045i | \(0.950448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −878.282 | + | 4980.99i | −0.158605 | + | 0.899495i | 0.796810 | + | 0.604230i | \(0.206519\pi\) |
−0.955415 | + | 0.295265i | \(0.904592\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.97486 | − | 17.2770i | −0.00178419 | − | 0.00309031i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3261.03 | − | 2736.33i | −0.577785 | − | 0.484819i | 0.306434 | − | 0.951892i | \(-0.400864\pi\) |
−0.884219 | + | 0.467073i | \(0.845309\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1454.91 | − | 529.545i | 0.255359 | − | 0.0929431i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 681.787 | + | 3866.61i | 0.118547 | + | 0.672315i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1029.30 | − | 299.548i | 0.177311 | − | 0.0516016i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −467.724 | − | 2652.60i | −0.0798298 | − | 0.452737i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3568.49 | − | 1298.83i | 0.603481 | − | 0.219649i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.5361 | + | 22.2664i | 0.00444676 | + | 0.00373127i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1746.01 | − | 3024.18i | −0.289938 | − | 0.502187i | 0.683857 | − | 0.729616i | \(-0.260301\pi\) |
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −31.5162 | + | 178.737i | −0.00518641 | + | 0.0294136i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −723.707 | + | 1253.50i | −0.118031 | + | 0.204435i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4238.55 | − | 1542.71i | −0.685130 | − | 0.249367i | −0.0240813 | − | 0.999710i | \(-0.507666\pi\) |
−0.661049 | + | 0.750343i | \(0.729888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1487.60 | + | 1248.24i | −0.238334 | + | 0.199986i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1169.30 | 0.185693 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −64.0351 | −0.0100804 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 533.757 | − | 447.875i | 0.0832942 | − | 0.0698921i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10159.4 | − | 3697.74i | −1.57172 | − | 0.572060i | −0.598339 | − | 0.801243i | \(-0.704172\pi\) |
−0.973383 | + | 0.229183i | \(0.926395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.1386 | + | 50.4695i | −0.00446921 | + | 0.00774089i | −0.868251 | − | 0.496125i | \(-0.834756\pi\) |
0.863782 | + | 0.503865i | \(0.168089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1492.75 | − | 8465.78i | 0.227000 | − | 1.28738i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2072.14 | − | 3589.05i | −0.312433 | − | 0.541150i | 0.666455 | − | 0.745545i | \(-0.267811\pi\) |
−0.978889 | + | 0.204395i | \(0.934477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2660.92 | + | 2232.78i | 0.397822 | + | 0.333813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.45356 | − | 0.893023i | 0.000363743 | − | 0.000132392i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −273.150 | − | 1549.11i | −0.0401568 | − | 0.227741i | 0.958124 | − | 0.286354i | \(-0.0924433\pi\) |
−0.998281 | + | 0.0586132i | \(0.981332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6697.65 | + | 1478.99i | −0.976476 | + | 0.215628i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 188.288 | + | 1067.83i | 0.0272246 | + | 0.154398i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.6408 | + | 12.2443i | −0.00482422 | + | 0.00175587i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2906.84 | − | 2439.13i | −0.413449 | − | 0.346925i | 0.412215 | − | 0.911086i | \(-0.364755\pi\) |
−0.825665 | + | 0.564161i | \(0.809200\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2868.67 | + | 4968.68i | 0.404707 | + | 0.700974i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.30297 | + | 41.4172i | −0.00102197 | + | 0.00579589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5536.77 | − | 9589.97i | 0.768588 | − | 1.33123i | −0.169741 | − | 0.985489i | \(-0.554293\pi\) |
0.938329 | − | 0.345744i | \(-0.112373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3078.49 | + | 1120.48i | 0.423926 | + | 0.154296i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3321.41 | − | 2786.99i | 0.453743 | − | 0.380736i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1803.87 | −0.244481 | −0.122241 | − | 0.992500i | \(-0.539008\pi\) | ||||
−0.122241 | + | 0.992500i | \(0.539008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 761.360 | 0.102377 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7497.92 | + | 6291.50i | −1.00033 | + | 0.839375i | −0.987030 | − | 0.160536i | \(-0.948678\pi\) |
−0.0132985 | + | 0.999912i | \(0.504233\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.1750 | − | 8.79899i | −0.00320019 | − | 0.00116477i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4978.03 | − | 8622.20i | 0.653869 | − | 1.13253i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1250.09 | + | 7089.63i | −0.162936 | + | 0.924058i | 0.788230 | + | 0.615380i | \(0.210998\pi\) |
−0.951167 | + | 0.308678i | \(0.900114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −218.037 | − | 377.652i | −0.0282011 | − | 0.0488457i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4522.11 | − | 3794.50i | −0.580433 | − | 0.487041i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6730.10 | + | 2449.56i | −0.857286 | + | 0.312027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1394.61 | − | 7909.22i | −0.176306 | − | 0.999880i | −0.936626 | − | 0.350331i | \(-0.886069\pi\) |
0.760320 | − | 0.649549i | \(-0.225042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.0407 | + | 4.66821i | −0.00201263 | + | 0.000585721i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2306.73 | − | 13082.1i | −0.287263 | − | 1.62915i | −0.697087 | − | 0.716987i | \(-0.745521\pi\) |
0.409824 | − | 0.912165i | \(-0.365590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3077.01 | − | 1119.94i | 0.380340 | − | 0.138432i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2731.42 | − | 2291.94i | −0.335125 | − | 0.281203i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 117.025 | + | 202.693i | 0.0142523 | + | 0.0246858i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1448.04 | + | 8212.22i | −0.175063 | + | 0.992831i | 0.763008 | + | 0.646389i | \(0.223722\pi\) |
−0.938071 | + | 0.346442i | \(0.887390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2395.98 | + | 4149.95i | −0.287554 | + | 0.498058i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.6872 | − | 6.43761i | −0.00210734 | − | 0.000767008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5215.07 | − | 4375.96i | 0.616862 | − | 0.517609i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1656.87 | −0.194574 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11382.8 | 1.32718 | 0.663588 | − | 0.748098i | \(-0.269033\pi\) | ||||
0.663588 | + | 0.748098i | \(0.269033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2016.27 | + | 1691.85i | −0.233413 | + | 0.195857i | −0.751991 | − | 0.659174i | \(-0.770906\pi\) |
0.518578 | + | 0.855031i | \(0.326462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7786.87 | + | 2834.19i | 0.895061 | + | 0.325775i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 216.172 | − | 374.421i | 0.0246726 | − | 0.0427343i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.61131 | − | 20.4808i | 0.000409282 | − | 0.00232115i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2509.05 | − | 4345.81i | −0.282374 | − | 0.489086i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6860.32 | + | 5756.50i | 0.766706 | + | 0.643343i | 0.939863 | − | 0.341552i | \(-0.110952\pi\) |
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13082.0 | + | 4761.47i | −1.45192 | + | 0.528457i | −0.943128 | − | 0.332431i | \(-0.892131\pi\) |
−0.508795 | + | 0.860887i | \(0.669909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 193.097 | + | 1095.11i | 0.0212835 | + | 0.120704i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1233.01 | + | 2502.92i | 0.134972 | + | 0.273984i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2544.55 | + | 14430.8i | 0.276639 | + | 1.56890i | 0.733706 | + | 0.679467i | \(0.237789\pi\) |
−0.457067 | + | 0.889432i | \(0.651100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7197.18 | + | 2619.56i | −0.777149 | + | 0.282859i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2073.61 | + | 1739.96i | 0.222393 | + | 0.186610i | 0.747176 | − | 0.664626i | \(-0.231409\pi\) |
−0.524783 | + | 0.851236i | \(0.675854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3780.82 | + | 6548.57i | 0.402760 | + | 0.697600i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 499.789 | − | 2834.45i | 0.0528842 | − | 0.299921i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1598.46 | − | 2768.61i | 0.168009 | − | 0.291000i | −0.769711 | − | 0.638393i | \(-0.779600\pi\) |
0.937720 | + | 0.347393i | \(0.112933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6952.50 | + | 2530.50i | 0.725899 | + | 0.264206i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4145.41 | + | 3478.41i | −0.429952 | + | 0.360773i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −72.0440 | −0.00742303 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6844.40 | 0.700585 | 0.350293 | − | 0.936640i | \(-0.386082\pi\) | ||||
0.350293 | + | 0.936640i | \(0.386082\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1057.01 | − | 886.936i | 0.107488 | − | 0.0901931i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13372.5 | + | 4867.18i | 1.35101 | + | 0.491729i | 0.913264 | − | 0.407368i | \(-0.133553\pi\) |
0.437750 | + | 0.899097i | \(0.355775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3164.48 | + | 5481.04i | −0.317637 | + | 0.550163i | −0.979995 | − | 0.199024i | \(-0.936223\pi\) |
0.662357 | + | 0.749188i | \(0.269556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −145.831 | + | 827.051i | −0.0145436 | + | 0.0824808i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7250.01 | + | 12557.4i | 0.718395 | + | 1.24430i | 0.961636 | + | 0.274330i | \(0.0884562\pi\) |
−0.243241 | + | 0.969966i | \(0.578210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8144 | − | 9.07434i | −0.00106474 | − | 0.000893420i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5911.43 | − | 2151.58i | 0.578311 | − | 0.210488i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2229.47 | − | 12644.0i | −0.216726 | − | 1.22911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1537.82 | + | 2299.44i | −0.148547 | + | 0.222117i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1747.00 | + | 9907.74i | 0.167693 | + | 0.951036i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9427.46 | + | 3431.31i | −0.899273 | + | 0.327309i | −0.749961 | − | 0.661482i | \(-0.769928\pi\) |
−0.149311 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 502.087 | + | 421.301i | 0.0475950 | + | 0.0399369i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.39793 | + | 5.88539i | 0.000320106 | + | 0.000554440i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1693.66 | − | 9605.22i | 0.158567 | − | 0.899280i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1367.77 | + | 2369.04i | −0.127268 | + | 0.220434i | −0.922617 | − | 0.385717i | \(-0.873954\pi\) |
0.795349 | + | 0.606151i | \(0.207287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1936.13 | − | 704.692i | −0.179048 | − | 0.0651683i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5834.67 | − | 4895.87i | 0.536283 | − | 0.449995i | −0.333981 | − | 0.942580i | \(-0.608392\pi\) |
0.870264 | + | 0.492585i | \(0.163948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 695.949 | 0.0635780 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6154.25 | −0.558814 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9529 | + | 21.7771i | −0.00234235 | + | 0.00196547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1646.96 | + | 599.444i | 0.147752 | + | 0.0537772i | 0.414837 | − | 0.909896i | \(-0.363838\pi\) |
−0.267086 | + | 0.963673i | \(0.586061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3701.84 | + | 6411.78i | −0.330112 | + | 0.571771i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1141.90 | − | 6476.04i | 0.101222 | − | 0.574060i | −0.891440 | − | 0.453139i | \(-0.850304\pi\) |
0.992662 | − | 0.120921i | \(-0.0385848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8010.79 | − | 13875.1i | −0.705892 | − | 1.22264i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7128.02 | − | 5981.11i | −0.624391 | − | 0.523926i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −322.286 | + | 117.302i | −0.0280650 | + | 0.0102148i | −0.356014 | − | 0.934480i | \(-0.615865\pi\) |
0.327950 | + | 0.944695i | \(0.393642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0606325 | − | 0.343864i | −5.24897e−6 | − | 2.97684e-5i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7121.94 | + | 5217.47i | −0.612946 | + | 0.449039i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 873.243 | + | 4952.40i | 0.0747178 | + | 0.423746i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10041.7 | − | 3654.88i | 0.854224 | − | 0.310912i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1749.03 | + | 1467.61i | 0.147926 | + | 0.124125i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2564.96 | − | 4442.64i | −0.215687 | − | 0.373581i | 0.737798 | − | 0.675022i | \(-0.235866\pi\) |
−0.953485 | + | 0.301441i | \(0.902532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 997.974 | − | 5659.79i | 0.0834385 | − | 0.473203i | −0.914244 | − | 0.405164i | \(-0.867214\pi\) |
0.997683 | − | 0.0680396i | \(-0.0216744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.36885 | + | 5.83503i | −0.000280055 | + | 0.000485070i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 493.899 | + | 179.765i | 0.0408247 | + | 0.0148590i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8451.00 | + | 7091.23i | −0.694584 | + | 0.582825i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4502.64 | −0.367981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20719.2 | 1.68376 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13320.8 | − | 11177.5i | 1.07646 | − | 0.903259i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5924.54 | − | 2156.36i | −0.476095 | − | 0.173284i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4938.45 | + | 8553.65i | −0.394646 | + | 0.683547i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 926.670 | − | 5255.41i | 0.0736426 | − | 0.417648i | −0.925592 | − | 0.378523i | \(-0.876432\pi\) |
0.999234 | − | 0.0391247i | \(-0.0124570\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −539.392 | − | 934.255i | −0.0426290 | − | 0.0738356i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12884.0 | − | 10810.9i | −1.01264 | − | 0.849706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3133.63 | + | 1140.55i | −0.244944 | + | 0.0891522i | −0.461575 | − | 0.887101i | \(-0.652715\pi\) |
0.216631 | + | 0.976254i | \(0.430493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −863.890 | − | 4899.37i | −0.0671584 | − | 0.380874i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4443.26 | − | 293.082i | −0.343537 | − | 0.0226601i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1300 | − | 68.7926i | −0.000932767 | − | 0.00528998i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −157.960 | + | 57.4929i | −0.0120812 | + | 0.00439718i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14826.8 | + | 12441.2i | 1.12788 | + | 0.946407i | 0.998976 | − | 0.0452495i | \(-0.0144083\pi\) |
0.128908 | + | 0.991657i | \(0.458853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17977.1 | − | 31137.2i | −1.36019 | − | 2.35593i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 139.868 | − | 793.233i | 0.0105263 | − | 0.0596976i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7945.72 | + | 13762.4i | −0.594800 | + | 1.03022i | 0.398775 | + | 0.917049i | \(0.369435\pi\) |
−0.993575 | + | 0.113175i | \(0.963898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8081.90 | + | 2941.57i | 0.601785 | + | 0.219032i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.6406 | − | 22.3541i | 0.00197319 | − | 0.00165570i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 105.009 | 0.00773674 | 0.00386837 | − | 0.999993i | \(-0.498769\pi\) | ||||
0.00386837 | + | 0.999993i | \(0.498769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22895.9 | −1.67805 | −0.839024 | − | 0.544095i | \(-0.816873\pi\) | ||||
−0.839024 | + | 0.544095i | \(0.816873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6545.70 | − | 5492.50i | 0.477226 | − | 0.400440i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1057.42 | + | 384.870i | 0.0766914 | + | 0.0279134i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3092.06 | + | 5355.61i | −0.223092 | + | 0.386407i | −0.955745 | − | 0.294195i | \(-0.904949\pi\) |
0.732653 | + | 0.680602i | \(0.238282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1203.17 | − | 6823.52i | 0.0863593 | − | 0.489768i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.1995 | + | 57.5032i | 0.00237065 | + | 0.00410608i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9938.52 | + | 8339.41i | 0.706023 | + | 0.592424i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16194.9 | + | 5894.46i | −1.14457 | + | 0.416591i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3635.15 | − | 20616.0i | −0.255603 | − | 1.44960i | −0.794521 | − | 0.607237i | \(-0.792278\pi\) |
0.538918 | − | 0.842358i | \(-0.318833\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3077.57 | − | 1355.69i | −0.215296 | − | 0.0948393i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1790.19 | + | 10152.7i | 0.124600 | + | 0.706641i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6568.39 | − | 2390.70i | 0.454859 | − | 0.165555i | −0.104422 | − | 0.994533i | \(-0.533299\pi\) |
0.559281 | + | 0.828978i | \(0.311077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.85852 | − | 7.43318i | −0.000610360 | − | 0.000512153i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −961.402 | − | 1665.20i | −0.0659088 | − | 0.114157i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4674.76 | − | 26511.9i | 0.318874 | − | 1.80843i | −0.230749 | − | 0.973013i | \(-0.574118\pi\) |
0.549624 | − | 0.835412i | \(-0.314771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4059.07 | + | 7030.52i | −0.275496 | + | 0.477173i | −0.970260 | − | 0.242065i | \(-0.922175\pi\) |
0.694764 | + | 0.719238i | \(0.255509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3173.42 | − | 1155.03i | −0.214314 | − | 0.0780041i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3678.76 | − | 3086.85i | 0.247212 | − | 0.207435i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26841.4 | −1.79482 | −0.897411 | − | 0.441195i | \(-0.854555\pi\) | ||||
−0.897411 | + | 0.441195i | \(0.854555\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.8458 | −0.000721664 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22924.1 | − | 19235.6i | 1.51786 | − | 1.27363i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11582.1 | + | 4215.55i | 0.763128 | + | 0.277756i | 0.694119 | − | 0.719860i | \(-0.255794\pi\) |
0.0690088 | + | 0.997616i | \(0.478016\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2656.93 | + | 4601.93i | −0.174208 | + | 0.301736i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1470.10 | + | 8337.33i | −0.0959220 | + | 0.544000i | 0.898539 | + | 0.438894i | \(0.144630\pi\) |
−0.994461 | + | 0.105107i | \(0.966482\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10519.2 | + | 18219.8i | 0.683040 | + | 1.18306i | 0.974048 | + | 0.226340i | \(0.0726760\pi\) |
−0.291008 | + | 0.956721i | \(0.593991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2751.14 | + | 2308.48i | 0.177777 | + | 0.149172i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −69.3037 | + | 25.2245i | −0.00445681 | + | 0.00162215i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1794.51 | − | 10177.2i | −0.114849 | − | 0.651338i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1227.03 | + | 5005.46i | −0.0781547 | + | 0.318818i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.2686 | + | 103.606i | 0.00115805 | + | 0.00656764i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3881.74 | + | 1412.84i | −0.244897 | + | 0.0891351i | −0.461552 | − | 0.887113i | \(-0.652707\pi\) |
0.216656 | + | 0.976248i | \(0.430485\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8517.77 | + | 7147.26i | 0.534836 | + | 0.448781i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1686.00 | − | 2920.23i | −0.105365 | − | 0.182497i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4802.95 | + | 27238.9i | −0.298744 | + | 1.69426i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4052.25 | + | 7018.71i | −0.250868 | + | 0.434516i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23825.3 | + | 8671.68i | 1.46808 | + | 0.534338i | 0.947579 | − | 0.319521i | \(-0.103522\pi\) |
0.520503 | + | 0.853860i | \(0.325744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14347.8 | − | 12039.3i | 0.879975 | − | 0.738386i | −0.0861993 | − | 0.996278i | \(-0.527472\pi\) |
0.966174 | + | 0.257892i | \(0.0830277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9221.17 | 0.562920 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10979.6 | 0.667160 | 0.333580 | − | 0.942722i | \(-0.391743\pi\) | ||||
0.333580 | + | 0.942722i | \(0.391743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4448.01 | + | 3732.32i | −0.269029 | + | 0.225742i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.69700 | − | 2.80148i | −0.000463394 | − | 0.000168662i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6995.50 | − | 12116.6i | 0.419227 | − | 0.726122i | −0.576635 | − | 0.817002i | \(-0.695635\pi\) |
0.995862 | + | 0.0908798i | \(0.0289679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4539.98 | + | 25747.5i | −0.270827 | + | 1.53594i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −41.7637 | − | 72.3369i | −0.00248000 | − | 0.00429548i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6586.19 | + | 5526.47i | 0.389319 | + | 0.326678i | 0.816348 | − | 0.577560i | \(-0.195995\pi\) |
−0.427029 | + | 0.904238i | \(0.640440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30322.9 | + | 11036.6i | −1.78430 | + | 0.649433i | −0.784742 | + | 0.619822i | \(0.787205\pi\) |
−0.999561 | + | 0.0296112i | \(0.990573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −391.684 | − | 2221.35i | −0.0229438 | − | 0.130121i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53.4265 | + | 51.1874i | 0.00311548 | + | 0.00298490i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 314.544 | + | 1783.87i | 0.0182597 | + | 0.103556i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5744.95 | − | 2090.99i | 0.332007 | − | 0.120841i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4914.59 | − | 4123.83i | −0.282750 | − | 0.237256i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5398.45 | − | 9350.38i | −0.309205 | − | 0.535558i | 0.668984 | − | 0.743277i | \(-0.266729\pi\) |
−0.978189 | + | 0.207719i | \(0.933396\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −618.296 | + | 3506.53i | −0.0352566 | + | 0.199950i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8537.64 | + | 14787.6i | −0.484680 | + | 0.839490i | −0.999845 | − | 0.0176007i | \(-0.994397\pi\) |
0.515165 | + | 0.857091i | \(0.327731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 89.3916 | + | 32.5359i | 0.00505234 | + | 0.00183890i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5316.87 | − | 4461.38i | 0.299182 | − | 0.251043i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23053.3 | −1.29152 | −0.645762 | − | 0.763538i | \(-0.723460\pi\) | ||||
−0.645762 | + | 0.763538i | \(0.723460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21223.1 | 1.18379 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5457.72 | − | 4579.57i | 0.303093 | − | 0.254326i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34140.5 | + | 12426.1i | 1.88774 | + | 0.687080i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1222.32 | + | 2117.13i | −0.0672929 | + | 0.116555i | −0.897709 | − | 0.440589i | \(-0.854770\pi\) |
0.830416 | + | 0.557144i | \(0.188103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4232 | − | 59.1128i | 0.000571348 | − | 0.00324027i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3669.07 | + | 6355.01i | 0.200253 | + | 0.346848i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2547.62 | + | 2137.71i | 0.138448 | + | 0.116172i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 677.696 | − | 246.661i | 0.0366707 | − | 0.0133470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1013.54 | − | 5748.05i | −0.0546088 | − | 0.309702i | 0.945253 | − | 0.326339i | \(-0.105815\pi\) |
−0.999862 | + | 0.0166372i | \(0.994704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −73.0036 | − | 669.162i | −0.00391662 | − | 0.0359003i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1332.74 | + | 7558.36i | 0.0711972 | + | 0.403779i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 146.841 | − | 53.4456i | 0.00781118 | − | 0.00284304i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9627.24 | + | 8078.21i | 0.509956 | + | 0.427903i | 0.861114 | − | 0.508413i | \(-0.169768\pi\) |
−0.351158 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8355.15 | − | 14471.5i | −0.440707 | − | 0.763327i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −237.551 | + | 1347.22i | −0.0124773 | + | 0.0707625i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11112.4 | + | 19247.2i | −0.581229 | + | 1.00672i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6032.06 | − | 2195.49i | −0.314186 | − | 0.114354i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12046.4 | + | 10108.1i | −0.624832 | + | 0.524296i | −0.899318 | − | 0.437295i | \(-0.855937\pi\) |
0.274486 | + | 0.961591i | \(0.411492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49.0478 | −0.00253348 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10887.0 | −0.560019 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1375.73 | + | 1154.37i | −0.0704735 | + | 0.0591343i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14496.9 | + | 5276.45i | 0.739562 | + | 0.269178i | 0.684207 | − | 0.729288i | \(-0.260149\pi\) |
0.0553552 | + | 0.998467i | \(0.482371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1049.75 | − | 1818.22i | 0.0533328 | − | 0.0923752i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1002.14 | − | 5683.41i | 0.0507051 | − | 0.287563i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12280.5 | − | 21270.5i | −0.618814 | − | 1.07182i | −0.989702 | − | 0.143140i | \(-0.954280\pi\) |
0.370888 | − | 0.928678i | \(-0.379053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5434.12 | − | 4559.77i | −0.272708 | − | 0.228829i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4092.34 | + | 1489.49i | −0.204537 | + | 0.0744452i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6302.25 | − | 35741.8i | −0.313711 | − | 1.77914i | −0.579361 | − | 0.815071i | \(-0.696698\pi\) |
0.265650 | − | 0.964070i | \(-0.414413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1565.22 | + | 14347.1i | 0.0775978 | + | 0.711273i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 798.473 | + | 4528.37i | 0.0394255 | + | 0.223593i | 0.998154 | − | 0.0607291i | \(-0.0193426\pi\) |
−0.958729 | + | 0.284322i | \(0.908231\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11978.4 | + | 4359.78i | −0.589067 | + | 0.214403i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12167.7 | + | 10209.9i | 0.595975 | + | 0.500082i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 84.8009 | + | 146.879i | 0.00413692 | + | 0.00716536i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6559.85 | − | 37202.7i | 0.318738 | − | 1.80765i | −0.231712 | − | 0.972785i | \(-0.574433\pi\) |
0.550450 | − | 0.834868i | \(-0.314456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7476.94 | − | 12950.4i | 0.361852 | − | 0.626746i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22521.4 | + | 8197.13i | 1.08561 | + | 0.395131i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3645.48 | − | 3058.92i | 0.175029 | − | 0.146867i | −0.551065 | − | 0.834463i | \(-0.685778\pi\) |
0.726094 | + | 0.687596i | \(0.241334\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2096.44 | 0.100258 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16224.0 | 0.772825 | 0.386413 | − | 0.922326i | \(-0.373714\pi\) | ||||
0.386413 | + | 0.922326i | \(0.373714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 125.662 | − | 105.443i | 0.00596235 | − | 0.00500301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2599.48 | − | 946.135i | −0.122856 | − | 0.0447158i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8130.15 | + | 14081.8i | −0.382741 | + | 0.662927i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4203.82 | − | 23841.1i | 0.197131 | − | 1.11799i | −0.712220 | − | 0.701956i | \(-0.752310\pi\) |
0.909351 | − | 0.416029i | \(-0.136579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 373.170 | + | 646.349i | 0.0174311 | + | 0.0301916i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32244.3 | − | 27056.2i | −1.50032 | − | 1.25892i | −0.880382 | − | 0.474265i | \(-0.842714\pi\) |
−0.619937 | − | 0.784652i | \(-0.712842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1274.50 | + | 463.880i | −0.0590728 | + | 0.0215007i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.284700 | − | 1.61461i | −1.31449e−5 | − | 7.45482e-5i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15365.0 | − | 14721.0i | −0.706684 | − | 0.677066i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1814.85 | + | 10292.5i | 0.0831505 | + | 0.471570i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5385.93 | + | 1960.32i | −0.245820 | + | 0.0894713i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21343.1 | − | 17909.0i | −0.970404 | − | 0.814266i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1059.61 | + | 1835.30i | 0.0479937 | + | 0.0831275i | 0.889024 | − | 0.457860i | \(-0.151384\pi\) |
−0.841031 | + | 0.540988i | \(0.818051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1563.19 | − | 8865.28i | 0.0705335 | − | 0.400015i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.9424 | + | 72.6463i | −0.00188533 | + | 0.00326549i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16882.5 | − | 6144.71i | −0.756007 | − | 0.275164i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7137.99 | + | 5989.49i | −0.318438 | + | 0.267202i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15388.2 | −0.683911 | −0.341955 | − | 0.939716i | \(-0.611089\pi\) | ||||
−0.341955 | + | 0.939716i | \(0.611089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4803.39 | 0.212681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13515.1 | + | 11340.5i | −0.596170 | + | 0.500246i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −101.218 | − | 36.8405i | −0.00444822 | − | 0.00161902i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0491 | − | 26.0658i | 0.000658896 | − | 0.00114124i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2196.30 | − | 12455.8i | 0.0958034 | − | 0.543328i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21524.0 | − | 37280.7i | −0.935408 | − | 1.62017i | −0.773905 | − | 0.633301i | \(-0.781699\pi\) |
−0.161502 | − | 0.986872i | \(-0.551634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15389.8 | − | 12913.6i | −0.666349 | − | 0.559133i | 0.245633 | − | 0.969363i | \(-0.421004\pi\) |
−0.911982 | + | 0.410230i | \(0.865449\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3044.36 | − | 1108.06i | 0.131329 | − | 0.0477998i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1584.58 | + | 8986.61i | 0.0681049 | + | 0.386242i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8791.54 | + | 35863.5i | −0.376471 | + | 1.53575i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.1889 | − | 165.538i | −0.00124535 | − | 0.00706273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26070.6 | − | 9488.93i | 1.10825 | − | 0.403369i | 0.277897 | − | 0.960611i | \(-0.410363\pi\) |
0.830350 | + | 0.557242i | \(0.188140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22760.5 | + | 19098.3i | 0.964011 | + | 0.808902i | 0.981601 | − | 0.190944i | \(-0.0611548\pi\) |
−0.0175896 | + | 0.999845i | \(0.505599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1039.25 | + | 1800.04i | 0.0438571 | + | 0.0759627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3476.25 | + | 19714.8i | −0.146168 | + | 0.828962i | 0.820253 | + | 0.572000i | \(0.193832\pi\) |
−0.966422 | + | 0.256961i | \(0.917279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13793.1 | − | 23890.3i | 0.577869 | − | 1.00090i | −0.417855 | − | 0.908514i | \(-0.637218\pi\) |
0.995723 | − | 0.0923842i | \(-0.0294488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3509.11 | − | 1277.21i | −0.146486 | − | 0.0533165i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3400.95 | + | 2853.74i | −0.141460 | + | 0.118699i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32790.2 | 1.35899 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4328.62 | −0.178756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19091.1 | − | 16019.3i | 0.785575 | − | 0.659176i | −0.159071 | − | 0.987267i | \(-0.550850\pi\) |
0.944646 | + | 0.328092i | \(0.106405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20201.6 | + | 7352.80i | 0.828310 | + | 0.301480i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5469.22 | + | 9472.97i | −0.223452 | + | 0.387030i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7156.18 | + | 40584.7i | −0.291337 | + | 1.65226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.4192 | + | 40.5633i | 0.000950053 | + | 0.00164554i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12306.5 | − | 10326.4i | −0.497477 | − | 0.417433i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −257.308 | + | 93.6524i | −0.0103648 | + | 0.00377246i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1123.74 | − | 6373.04i | −0.0451068 | − | 0.255813i | 0.953913 | − | 0.300084i | \(-0.0970147\pi\) |
−0.999020 | + | 0.0442706i | \(0.985904\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16197.8 | + | 7135.26i | 0.647900 | + | 0.285404i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −830.583 | − | 4710.47i | −0.0331064 | − | 0.187756i | 0.963770 | − | 0.266735i | \(-0.0859449\pi\) |
−0.996876 | + | 0.0789795i | \(0.974834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2874.73 | + | 1046.32i | −0.114185 | + | 0.0415598i | −0.398481 | − | 0.917177i | \(-0.630462\pi\) |
0.284296 | + | 0.958737i | \(0.408240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.7026 | − | 33.3144i | −0.00157150 | − | 0.00131864i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8221.71 | + | 14240.4i | 0.324299 | + | 0.561703i | 0.981370 | − | 0.192126i | \(-0.0615382\pi\) |
−0.657071 | + | 0.753829i | \(0.728205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1755.94 | − | 9958.43i | 0.0690217 | − | 0.391441i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5127.38 | + | 8880.89i | −0.200848 | + | 0.347879i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20249.5 | − | 7370.22i | −0.790470 | − | 0.287707i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9342.37 | + | 7839.18i | −0.363437 | + | 0.304960i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22756.5 | 0.882234 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 141.515 | 0.00546752 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19700.2 | + | 16530.4i | −0.758526 | + | 0.636479i | −0.937743 | − | 0.347331i | \(-0.887088\pi\) |
0.179217 | + | 0.983810i | \(0.442644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7997.77 | − | 2910.95i | −0.306892 | − | 0.111700i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7182.33 | + | 12440.2i | −0.274664 | + | 0.475731i | −0.970050 | − | 0.242904i | \(-0.921900\pi\) |
0.695387 | + | 0.718636i | \(0.255233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2856.53 | − | 16200.2i | 0.108867 | − | 0.617417i | −0.880738 | − | 0.473605i | \(-0.842953\pi\) |
0.989605 | − | 0.143813i | \(-0.0459363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2085.14 | − | 3611.58i | −0.0791993 | − | 0.137177i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34311.4 | + | 28790.7i | 1.29883 | + | 1.08985i | 0.990346 | + | 0.138620i | \(0.0442668\pi\) |
0.308486 | + | 0.951229i | \(0.400178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.9049 | − | 11.2485i | 0.00116594 | − | 0.000424366i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1862.94 | − | 10565.3i | −0.0700458 | − | 0.397250i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30667.0 | − | 2022.83i | −1.14920 | − | 0.0758022i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4848.81 | + | 27499.0i | 0.181093 | + | 1.02703i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5516.78 | − | 2007.94i | 0.205351 | − | 0.0747416i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1672.46 | − | 1403.36i | −0.0620465 | − | 0.0520632i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2915.84 | + | 5050.39i | 0.107814 | + | 0.186740i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.6175 | + | 88.5712i | −0.000575546 | + | 0.00326408i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2388.92 | + | 4137.73i | −0.0877462 | + | 0.151981i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42023.3 | + | 15295.2i | 1.53844 | + | 0.559945i | 0.965669 | − | 0.259774i | \(-0.0836481\pi\) |
0.572766 | + | 0.819719i | \(0.305870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28635.7 | − | 24028.2i | 1.04487 | − | 0.876750i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29208.6 | −1.06227 | −0.531133 | − | 0.847288i | \(-0.678234\pi\) | ||||
−0.531133 | + | 0.847288i | \(0.678234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20483.3 | 0.742495 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3529.73 | − | 2961.79i | 0.127529 | − | 0.107010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −239.621 | − | 87.2148i | −0.00862919 | − | 0.00314077i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18170.8 | − | 31472.8i | 0.652231 | − | 1.12970i | −0.330349 | − | 0.943859i | \(-0.607166\pi\) |
0.982580 | − | 0.185839i | \(-0.0595002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2708.67 | + | 15361.6i | −0.0969095 | + | 0.549601i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14633.8 | + | 25346.5i | 0.521862 | + | 0.903891i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −207.965 | − | 174.503i | −0.00739225 | − | 0.00620284i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11025.5 | + | 4012.96i | −0.390643 | + | 0.142182i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3470.02 | + | 19679.4i | 0.122549 | + | 0.695007i | 0.982734 | + | 0.185025i | \(0.0592367\pi\) |
−0.860185 | + | 0.509982i | \(0.829652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22915.0 | − | 16787.3i | 0.806670 | − | 0.590959i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2585.86 | − | 14665.1i | −0.0907366 | − | 0.514593i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3352.21 | + | 1220.11i | −0.117250 | + | 0.0426757i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7274.24 | − | 6103.81i | −0.253617 | − | 0.212810i | 0.507111 | − | 0.861881i | \(-0.330713\pi\) |
−0.760728 | + | 0.649071i | \(0.775158\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5464.89 | − | 9465.47i | −0.189925 | − | 0.328961i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6026.29 | + | 34176.8i | −0.208769 | + | 1.18399i | 0.682629 | + | 0.730765i | \(0.260836\pi\) |
−0.891398 | + | 0.453221i | \(0.850275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4327.98 | + | 7496.28i | −0.149457 | + | 0.258868i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 89.4933 | + | 32.5729i | 0.00308065 | + | 0.00112127i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13221.9 | + | 11094.5i | −0.453699 | + | 0.380699i | −0.840806 | − | 0.541336i | \(-0.817919\pi\) |
0.387107 | + | 0.922035i | \(0.373474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −301.641 | −0.0103179 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9199.18 | 0.313674 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1948.33 | + | 1634.84i | −0.0662250 | + | 0.0555694i | −0.675299 | − | 0.737544i | \(-0.735986\pi\) |
0.609074 | + | 0.793113i | \(0.291541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35561.9 | − | 12943.5i | −1.20498 | − | 0.438577i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1672.90 | + | 2897.54i | −0.0565069 | + | 0.0978728i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.9446 | + | 203.852i | −0.00121034 | + | 0.00686416i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14071.1 | + | 24371.8i | 0.472327 | + | 0.818094i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31079.8 | + | 26079.0i | 1.04001 | + | 0.872674i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28836.3 | + | 10495.5i | −0.961941 | + | 0.350118i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3948.75 | + | 22394.5i | 0.131317 | + | 0.744733i | 0.977354 | + | 0.211610i | \(0.0678707\pi\) |
−0.846038 | + | 0.533123i | \(0.821018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1287.81 | + | 1925.61i | −0.0426939 | + | 0.0638384i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5503.23 | − | 31210.4i | −0.181882 | − | 1.03150i | −0.929897 | − | 0.367820i | \(-0.880104\pi\) |
0.748015 | − | 0.663681i | \(-0.231007\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67.2553 | + | 24.4789i | −0.00221594 | + | 0.000806535i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4458.84 | + | 3741.41i | 0.146459 | + | 0.122893i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14690.8 | + | 25445.3i | 0.481066 | + | 0.833231i | 0.999764 | − | 0.0217266i | \(-0.00691634\pi\) |
−0.518698 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3950.75 | + | 22405.8i | −0.128975 | + | 0.731454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19620.7 | − | 33984.1i | 0.638574 | − | 1.10604i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7117.62 | − | 2590.60i | −0.230943 | − | 0.0840564i | 0.223957 | − | 0.974599i | \(-0.428103\pi\) |
−0.454900 | + | 0.890543i | \(0.650325\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34976.7 | − | 29348.9i | 1.13142 | − | 0.949376i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −74.8568 | −0.00241410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15020.7 | 0.482944 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9195.90 | + | 7716.28i | −0.294770 | + | 0.247342i | −0.778164 | − | 0.628062i | \(-0.783849\pi\) |
0.483393 | + | 0.875403i | \(0.339404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7091.05 | + | 2580.93i | 0.226614 | + | 0.0824807i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4257.96 | + | 7375.00i | −0.135665 | + | 0.234978i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.3793 | − | 194.974i | 0.00109208 | − | 0.00619348i | −0.984257 | − | 0.176744i | \(-0.943444\pi\) |
0.985349 | + | 0.170551i | \(0.0545546\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −433.213 | − | 750.346i | −0.0137200 | − | 0.0237637i |
(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 | 76.4.i.a.9.2 | ✓ | 30 | |
19.6 | even | 9 | 1444.4.a.j.1.6 | 15 | |||
19.13 | odd | 18 | 1444.4.a.k.1.10 | 15 | |||
19.17 | even | 9 | inner | 76.4.i.a.17.2 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.i.a.9.2 | ✓ | 30 | 1.1 | even | 1 | trivial | |
76.4.i.a.17.2 | yes | 30 | 19.17 | even | 9 | inner | |
1444.4.a.j.1.6 | 15 | 19.6 | even | 9 | |||
1444.4.a.k.1.10 | 15 | 19.13 | odd | 18 |