Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(373,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.373");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 373.15 | ||
Character | \(\chi\) | \(=\) | 684.373 |
Dual form | 684.3.bl.a.673.15 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.43106 | + | 2.63668i | −0.477018 | + | 0.878893i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.52048 | 1.10410 | 0.552048 | − | 0.833812i | \(-0.313846\pi\) | ||||
0.552048 | + | 0.833812i | \(0.313846\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.838417 | + | 1.45218i | 0.119774 | + | 0.207454i | 0.919678 | − | 0.392673i | \(-0.128450\pi\) |
−0.799904 | + | 0.600128i | \(0.795116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.90416 | − | 7.54647i | −0.544907 | − | 0.838497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.764365 | + | 1.32392i | 0.0694877 | + | 0.120356i | 0.898676 | − | 0.438613i | \(-0.144530\pi\) |
−0.829188 | + | 0.558970i | \(0.811197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.9605 | + | 10.3695i | −1.38157 | + | 0.797652i | −0.992346 | − | 0.123490i | \(-0.960591\pi\) |
−0.389227 | + | 0.921142i | \(0.627258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.90012 | + | 14.5557i | −0.526675 | + | 0.970383i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.66839 | + | 16.7462i | 0.568729 | + | 0.985068i | 0.996692 | + | 0.0812714i | \(0.0258980\pi\) |
−0.427963 | + | 0.903796i | \(0.640769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.1509 | − | 10.0074i | −0.850047 | − | 0.526707i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.02876 | + | 0.132486i | −0.239465 | + | 0.00630885i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.35650 | − | 12.7418i | −0.319848 | − | 0.553993i | 0.660608 | − | 0.750731i | \(-0.270299\pi\) |
−0.980456 | + | 0.196738i | \(0.936965\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47574 | 0.219030 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.9158 | − | 2.13128i | 0.996880 | − | 0.0789365i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.8226i | 1.40768i | 0.710360 | + | 0.703838i | \(0.248532\pi\) | ||||
−0.710360 | + | 0.703838i | \(0.751468\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.1199 | + | 13.3483i | 0.745803 | + | 0.430590i | 0.824176 | − | 0.566334i | \(-0.191639\pi\) |
−0.0783722 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.58460 | + | 0.120784i | −0.138927 | + | 0.00366013i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.62847 | + | 8.01674i | 0.132242 | + | 0.229050i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 59.7594i | 1.61512i | 0.589787 | + | 0.807559i | \(0.299212\pi\) | ||||
−0.589787 | + | 0.807559i | \(0.700788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.63857 | − | 62.1953i | −0.0420147 | − | 1.59475i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 36.9438i | 0.901067i | 0.892759 | + | 0.450534i | \(0.148766\pi\) | ||||
−0.892759 | + | 0.450534i | \(0.851234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38108 | − | 4.12414i | 0.0553738 | − | 0.0959103i | −0.837010 | − | 0.547188i | \(-0.815698\pi\) |
0.892384 | + | 0.451278i | \(0.149032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.0733 | − | 41.6602i | −0.601630 | − | 0.925781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −54.0607 | −1.15023 | −0.575114 | − | 0.818073i | \(-0.695042\pi\) | ||||
−0.575114 | + | 0.818073i | \(0.695042\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.0941 | − | 40.0002i | 0.471308 | − | 0.816330i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −57.9902 | + | 1.52779i | −1.13706 | + | 0.0299567i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −17.5032 | − | 10.1055i | −0.330250 | − | 0.190670i | 0.325702 | − | 0.945472i | \(-0.394399\pi\) |
−0.655952 | + | 0.754803i | \(0.727733\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.21966 | + | 7.30867i | 0.0767211 | + | 0.132885i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 49.4992 | − | 28.2635i | 0.868407 | − | 0.495852i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 98.9167i | − | 1.67655i | −0.545245 | − | 0.838277i | \(-0.683563\pi\) | ||
0.545245 | − | 0.838277i | \(-0.316437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −87.2069 | −1.42962 | −0.714811 | − | 0.699318i | \(-0.753487\pi\) | ||||
−0.714811 | + | 0.699318i | \(0.753487\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.84711 | − | 13.4488i | 0.108684 | − | 0.213473i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −99.1504 | + | 57.2445i | −1.52539 | + | 0.880685i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −74.7887 | + | 43.1793i | −1.11625 | + | 0.644467i | −0.940441 | − | 0.339958i | \(-0.889587\pi\) |
−0.175808 | + | 0.984424i | \(0.556254\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 44.1237 | − | 1.16247i | 0.639474 | − | 0.0168474i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −76.0630 | + | 43.9150i | −1.07131 | + | 0.618521i | −0.928539 | − | 0.371234i | \(-0.878935\pi\) |
−0.142771 | + | 0.989756i | \(0.545601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.5689 | + | 52.9469i | 0.418752 | + | 0.725300i | 0.995814 | − | 0.0914003i | \(-0.0291343\pi\) |
−0.577062 | + | 0.816700i | \(0.695801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.83609 | + | 14.4378i | −0.104481 | + | 0.192504i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.28171 | + | 2.21999i | −0.0166456 | + | 0.0288311i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.1924 | − | 18.0089i | −0.394840 | − | 0.227961i | 0.289415 | − | 0.957204i | \(-0.406539\pi\) |
−0.684255 | + | 0.729243i | \(0.739873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −32.8984 | + | 74.0182i | −0.406153 | + | 0.913805i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.38181 | + | 7.58953i | 0.0527930 | + | 0.0914401i | 0.891214 | − | 0.453583i | \(-0.149854\pi\) |
−0.838421 | + | 0.545023i | \(0.816521\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 53.3742 | + | 92.4469i | 0.627932 | + | 1.08761i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −107.636 | − | 58.4194i | −1.23720 | − | 0.671488i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 63.7489 | + | 36.8055i | 0.716280 | + | 0.413544i | 0.813382 | − | 0.581730i | \(-0.197624\pi\) |
−0.0971020 | + | 0.995274i | \(0.530957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.1167 | − | 17.3879i | −0.330953 | − | 0.191076i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −68.2810 | + | 41.8577i | −0.734204 | + | 0.450082i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −89.1607 | − | 55.2459i | −0.938534 | − | 0.581535i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −41.8517 | − | 24.1631i | −0.431461 | − | 0.249104i | 0.268508 | − | 0.963277i | \(-0.413469\pi\) |
−0.699969 | + | 0.714173i | \(0.746803\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.24234 | − | 12.2610i | 0.0630540 | − | 0.123848i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28.1075 | −0.278292 | −0.139146 | − | 0.990272i | \(-0.544436\pi\) | ||||
−0.139146 | + | 0.990272i | \(0.544436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.8268 | + | 44.3560i | 0.745891 | + | 0.430641i | 0.824207 | − | 0.566288i | \(-0.191621\pi\) |
−0.0783160 | + | 0.996929i | \(0.524954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.7612 | + | 0.731386i | −0.264392 | + | 0.00696558i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.6565i | − | 0.118285i | −0.998250 | − | 0.0591424i | \(-0.981163\pi\) | ||
0.998250 | − | 0.0591424i | \(-0.0188366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.232 | − | 57.8690i | 0.919560 | − | 0.530908i | 0.0360650 | − | 0.999349i | \(-0.488518\pi\) |
0.883495 | + | 0.468442i | \(0.155184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −157.566 | − | 85.5190i | −1.41952 | − | 0.770441i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 100.398 | + | 57.9648i | 0.888477 | + | 0.512963i | 0.873444 | − | 0.486924i | \(-0.161881\pi\) |
0.0150332 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −40.6115 | − | 70.3411i | −0.353143 | − | 0.611662i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 166.334 | + | 84.6845i | 1.42166 | + | 0.723799i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.2123 | + | 28.0805i | −0.136238 | + | 0.235971i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.3315 | − | 102.765i | 0.490343 | − | 0.849299i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −97.4089 | − | 52.8686i | −0.791942 | − | 0.429826i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −107.783 | −0.862267 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.8993 | + | 54.2128i | 0.739364 | + | 0.426872i | 0.821838 | − | 0.569721i | \(-0.192949\pi\) |
−0.0824738 | + | 0.996593i | \(0.526282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46659 | + | 12.1800i | 0.0578806 | + | 0.0944187i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −161.825 | −1.23531 | −0.617653 | − | 0.786451i | \(-0.711916\pi\) | ||||
−0.617653 | + | 0.786451i | \(0.711916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.991416 | − | 31.8444i | 0.00745426 | − | 0.239432i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 148.588 | − | 11.7657i | 1.10065 | − | 0.0871535i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −140.521 | −1.02570 | −0.512851 | − | 0.858478i | \(-0.671411\pi\) | ||||
−0.512851 | + | 0.858478i | \(0.671411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97.7068 | + | 169.233i | 0.702926 | + | 1.21750i | 0.967435 | + | 0.253121i | \(0.0814570\pi\) |
−0.264508 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.3639 | − | 142.541i | 0.548680 | − | 1.01093i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.4567 | − | 15.8521i | −0.192005 | − | 0.110854i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 225.361i | 1.55421i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72.4187 | + | 118.134i | 0.492644 | + | 0.803634i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −62.0000 | −0.416107 | −0.208054 | − | 0.978117i | \(-0.566713\pi\) | ||||
−0.208054 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 198.836 | − | 114.798i | 1.31680 | − | 0.760252i | 0.333584 | − | 0.942720i | \(-0.391742\pi\) |
0.983212 | + | 0.182468i | \(0.0584086\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 78.9590 | − | 155.088i | 0.516072 | − | 1.01365i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 127.633 | + | 73.6890i | 0.823439 | + | 0.475413i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 151.432 | 0.964538 | 0.482269 | − | 0.876023i | \(-0.339813\pi\) | ||||
0.482269 | + | 0.876023i | \(0.339813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 51.6931 | − | 31.6889i | 0.325114 | − | 0.199301i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.3356 | − | 21.3659i | 0.0766188 | − | 0.132708i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 224.865 | 1.37954 | 0.689770 | − | 0.724029i | \(-0.257712\pi\) | ||||
0.689770 | + | 0.724029i | \(0.257712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.3092 | + | 0.666787i | −0.153389 | + | 0.00404113i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 89.5358 | − | 51.6935i | 0.536143 | − | 0.309542i | −0.207372 | − | 0.978262i | \(-0.566491\pi\) |
0.743514 | + | 0.668720i | \(0.233158\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 130.552 | − | 226.123i | 0.772496 | − | 1.33800i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.68580 | + | 170.960i | 0.0215544 | + | 0.999768i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −205.008 | − | 118.361i | −1.18502 | − | 0.684170i | −0.227848 | − | 0.973697i | \(-0.573169\pi\) |
−0.957170 | + | 0.289527i | \(0.906502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.59095 | + | 7.95177i | 0.0262340 | + | 0.0454387i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 260.812 | + | 141.555i | 1.47351 | + | 0.799747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 165.052i | − | 0.922081i | −0.887379 | − | 0.461040i | \(-0.847476\pi\) | ||
0.887379 | − | 0.461040i | \(-0.152524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.86440 | + | 5.69521i | 0.0544994 | + | 0.0314653i | 0.527002 | − | 0.849864i | \(-0.323316\pi\) |
−0.472503 | + | 0.881329i | \(0.656649\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 124.798 | − | 229.937i | 0.681956 | − | 1.25648i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 329.901i | 1.78325i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7804 | + | 25.6003i | −0.0790393 | + | 0.136900i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.6616 | + | 37.2996i | 0.135776 | + | 0.197353i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 139.076 | + | 240.886i | 0.728146 | + | 1.26119i | 0.957666 | + | 0.287882i | \(0.0929510\pi\) |
−0.229520 | + | 0.973304i | \(0.573716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 292.808i | 1.51714i | 0.651592 | + | 0.758570i | \(0.274102\pi\) | ||||
−0.651592 | + | 0.758570i | \(0.725898\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.04572 | − | 343.348i | −0.0463883 | − | 1.76076i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 200.140 | 1.01594 | 0.507971 | − | 0.861374i | \(-0.330396\pi\) | ||||
0.507971 | + | 0.861374i | \(0.330396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.26766 | + | 5.65976i | −0.0164204 | + | 0.0284410i | −0.874119 | − | 0.485712i | \(-0.838560\pi\) |
0.857698 | + | 0.514153i | \(0.171894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.82315 | − | 258.986i | −0.0339460 | − | 1.28849i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −59.2818 | + | 34.2264i | −0.292029 | + | 0.168603i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 203.947i | 0.994866i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60.0784 | + | 118.004i | −0.290234 | + | 0.570066i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.903850 | − | 29.0318i | 0.00432464 | − | 0.138908i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 213.884i | − | 1.01367i | −0.862043 | − | 0.506835i | \(-0.830815\pi\) | ||
0.862043 | − | 0.506835i | \(-0.169185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.93941 | − | 263.399i | −0.0325794 | − | 1.23661i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.1447 | − | 22.7673i | 0.0611381 | − | 0.105894i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 44.7657i | 0.206294i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −183.350 | + | 4.83047i | −0.837214 | + | 0.0220569i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −347.297 | − | 200.512i | −1.57148 | − | 0.907295i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 300.535 | + | 173.514i | 1.34769 | + | 0.778090i | 0.987922 | − | 0.154952i | \(-0.0495223\pi\) |
0.359769 | + | 0.933042i | \(0.382856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.8539 | − | 41.3225i | −0.119351 | − | 0.183656i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −324.621 | + | 187.420i | −1.43005 | + | 0.825640i | −0.997124 | − | 0.0757900i | \(-0.975852\pi\) |
−0.432926 | + | 0.901430i | \(0.642519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.6607 | + | 27.1251i | −0.0683872 | + | 0.118450i | −0.898191 | − | 0.439604i | \(-0.855119\pi\) |
0.829804 | + | 0.558054i | \(0.188452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.01920 | − | 6.55640i | −0.0173992 | − | 0.0283827i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.2550 | + | 52.4032i | 0.129850 | + | 0.224907i | 0.923618 | − | 0.383314i | \(-0.125217\pi\) |
−0.793768 | + | 0.608220i | \(0.791884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −298.441 | −1.26996 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 92.1218 | − | 56.4725i | 0.388699 | − | 0.238281i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 96.9628 | − | 167.944i | 0.405702 | − | 0.702696i | −0.588701 | − | 0.808351i | \(-0.700360\pi\) |
0.994403 | + | 0.105655i | \(0.0336938\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 195.379i | 0.810700i | 0.914162 | + | 0.405350i | \(0.132850\pi\) | ||||
−0.914162 | + | 0.405350i | \(0.867150\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −148.083 | − | 192.667i | −0.609394 | − | 0.792867i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 127.491 | − | 220.820i | 0.520370 | − | 0.901308i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 393.849 | + | 12.2618i | 1.59453 | + | 0.0496427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.2818 | + | 0.692410i | −0.105549 | + | 0.00278076i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.93929 | + | 6.82305i | −0.0156944 | + | 0.0271835i | −0.873766 | − | 0.486347i | \(-0.838329\pi\) |
0.858072 | + | 0.513530i | \(0.171663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2461 | − | 19.4788i | 0.0444510 | − | 0.0769914i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −320.134 | + | 8.43414i | −1.25543 | + | 0.0330751i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 437.956 | − | 252.854i | 1.70411 | − | 0.983867i | 0.762602 | − | 0.646867i | \(-0.223921\pi\) |
0.941505 | − | 0.336999i | \(-0.109412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −86.7814 | + | 50.1033i | −0.335063 | + | 0.193449i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 308.067 | − | 200.201i | 1.18033 | − | 0.767053i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −132.636 | + | 229.733i | −0.504321 | + | 0.873509i | 0.495667 | + | 0.868513i | \(0.334924\pi\) |
−0.999988 | + | 0.00499640i | \(0.998410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −96.6264 | − | 55.7873i | −0.364628 | − | 0.210518i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −188.272 | + | 115.415i | −0.705140 | + | 0.432265i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 55.3986 | − | 31.9844i | 0.205943 | − | 0.118901i | −0.393482 | − | 0.919332i | \(-0.628730\pi\) |
0.599424 | + | 0.800431i | \(0.295396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −261.759 | − | 453.380i | −0.965901 | − | 1.67299i | −0.707175 | − | 0.707038i | \(-0.750031\pi\) |
−0.258726 | − | 0.965951i | \(-0.583303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 88.9449 | − | 54.5251i | 0.325806 | − | 0.199725i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.18546 | + | 7.24943i | 0.0152199 | + | 0.0263616i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −38.1732 | − | 66.1179i | −0.137809 | − | 0.238693i | 0.788858 | − | 0.614576i | \(-0.210673\pi\) |
−0.926667 | + | 0.375883i | \(0.877339\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.6513 | − | 239.936i | −0.0453452 | − | 0.859985i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 458.998i | 1.63344i | 0.577031 | + | 0.816722i | \(0.304211\pi\) | ||||
−0.577031 | + | 0.816722i | \(0.695789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 126.719 | 0.447770 | 0.223885 | − | 0.974616i | \(-0.428126\pi\) | ||||
0.223885 | + | 0.974616i | \(0.428126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 273.260 | − | 156.028i | 0.958806 | − | 0.547468i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −53.6490 | + | 30.9743i | −0.186930 | + | 0.107924i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −42.4557 | + | 73.5354i | −0.146906 | + | 0.254448i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 123.602 | − | 75.7708i | 0.424751 | − | 0.260381i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 142.675 | + | 82.3734i | 0.486945 | + | 0.281138i | 0.723306 | − | 0.690527i | \(-0.242621\pi\) |
−0.236361 | + | 0.971665i | \(0.575955\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 546.068i | − | 1.85108i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.3951 | + | 34.0052i | 0.0787714 | + | 0.114496i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 264.252 | + | 152.566i | 0.883787 | + | 0.510255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.98534 | 0.0265294 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 40.2234 | − | 74.1105i | 0.132750 | − | 0.244589i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −481.424 | −1.57844 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −143.939 | + | 83.1031i | −0.468856 | + | 0.270694i | −0.715761 | − | 0.698346i | \(-0.753920\pi\) |
0.246905 | + | 0.969040i | \(0.420587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −226.896 | + | 139.092i | −0.734291 | + | 0.450135i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 129.031 | − | 223.488i | 0.414891 | − | 0.718612i | −0.580526 | − | 0.814241i | \(-0.697153\pi\) |
0.995417 | + | 0.0956298i | \(0.0304865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 268.054 | 0.856404 | 0.428202 | − | 0.903683i | \(-0.359147\pi\) | ||||
0.428202 | + | 0.903683i | \(0.359147\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 37.7993 | − | 74.2440i | 0.119998 | − | 0.235695i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 534.558i | 1.68630i | 0.537675 | + | 0.843152i | \(0.319303\pi\) | ||||
−0.537675 | + | 0.843152i | \(0.680697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.0458 | + | 31.2034i | −0.169423 | + | 0.0978162i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.3711 | + | 18.1121i | 0.103960 | + | 0.0564241i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4327 | − | 367.221i | 0.0353955 | − | 1.13691i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −98.3468 | + | 56.7805i | −0.302606 | + | 0.174709i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.14440 | + | 347.093i | 0.0279645 | + | 1.06145i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −45.3254 | − | 78.5060i | −0.137767 | − | 0.238620i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −255.142 | + | 147.306i | −0.770821 | + | 0.445034i | −0.833168 | − | 0.553021i | \(-0.813475\pi\) |
0.0623461 | + | 0.998055i | \(0.480142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 450.972 | − | 293.070i | 1.35427 | − | 0.880089i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −412.870 | + | 238.370i | −1.23245 | + | 0.711554i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 234.469i | − | 0.695754i | −0.937540 | − | 0.347877i | \(-0.886903\pi\) | ||
0.937540 | − | 0.347877i | \(-0.113097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −296.510 | + | 181.766i | −0.874660 | + | 0.536184i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.8118i | 0.119683i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 159.615 | 0.465349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 243.584 | − | 6.41738i | 0.706041 | − | 0.0186011i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 588.236 | 1.69520 | 0.847602 | − | 0.530633i | \(-0.178046\pi\) | ||||
0.847602 | + | 0.530633i | \(0.178046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 230.931 | + | 399.985i | 0.661695 | + | 1.14609i | 0.980170 | + | 0.198158i | \(0.0634958\pi\) |
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −461.319 | + | 317.381i | −1.31430 | + | 0.904219i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −225.135 | − | 389.946i | −0.637777 | − | 1.10466i | −0.985919 | − | 0.167221i | \(-0.946521\pi\) |
0.348142 | − | 0.937442i | \(-0.386813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −419.905 | + | 242.432i | −1.18283 | + | 0.682907i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −50.8386 | − | 82.9314i | −0.142405 | − | 0.232301i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 91.4010 | + | 158.311i | 0.254599 | + | 0.440978i | 0.964786 | − | 0.263034i | \(-0.0847232\pi\) |
−0.710188 | + | 0.704012i | \(0.751390\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 160.703 | + | 323.258i | 0.445160 | + | 0.895451i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 186.052 | + | 303.501i | 0.512540 | + | 0.836090i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 168.755 | + | 292.292i | 0.462343 | + | 0.800801i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 80.8772 | 0.220374 | 0.110187 | − | 0.993911i | \(-0.464855\pi\) | ||||
0.110187 | + | 0.993911i | \(0.464855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 278.795 | − | 181.178i | 0.755542 | − | 0.490998i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 33.8905i | − | 0.0913491i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 129.659 | + | 74.8584i | 0.347610 | + | 0.200693i | 0.663632 | − | 0.748059i | \(-0.269014\pi\) |
−0.316022 | + | 0.948752i | \(0.602347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 154.244 | − | 284.190i | 0.411317 | − | 0.757841i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −423.309 | − | 733.193i | −1.12284 | − | 1.94481i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 454.252i | 1.19855i | 0.800542 | + | 0.599277i | \(0.204545\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −277.317 | + | 170.001i | −0.727866 | + | 0.446196i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 98.3469i | 0.256781i | 0.991724 | + | 0.128390i | \(0.0409810\pi\) | ||||
−0.991724 | + | 0.128390i | \(0.959019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.07567 | + | 12.2554i | −0.0183784 | + | 0.0318323i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −42.7999 | + | 2.25675i | −0.110594 | + | 0.00583139i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 336.895 | 0.866054 | 0.433027 | − | 0.901381i | \(-0.357445\pi\) | ||||
0.433027 | + | 0.901381i | \(0.357445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 142.251 | − | 246.386i | 0.363814 | − | 0.630144i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 231.580 | − | 426.681i | 0.589263 | − | 1.08570i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −172.197 | − | 99.4180i | −0.435942 | − | 0.251691i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −140.690 | − | 243.683i | −0.354384 | − | 0.613811i | 0.632628 | − | 0.774455i | \(-0.281976\pi\) |
−0.987012 | + | 0.160645i | \(0.948643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 82.5448 | + | 48.1852i | 0.206879 | + | 0.120765i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 260.401i | − | 0.649378i | −0.945821 | − | 0.324689i | \(-0.894740\pi\) | ||
0.945821 | − | 0.324689i | \(-0.105260\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −553.659 | −1.37384 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −181.615 | + | 408.616i | −0.448433 | + | 1.00893i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −79.1165 | + | 45.6779i | −0.194389 | + | 0.112231i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −160.526 | + | 92.6800i | −0.392485 | + | 0.226601i | −0.683236 | − | 0.730197i | \(-0.739428\pi\) |
0.290751 | + | 0.956799i | \(0.406095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 201.094 | − | 370.509i | 0.489279 | − | 0.901483i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 143.645 | − | 82.9334i | 0.347809 | − | 0.200807i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.1897 | + | 41.8979i | 0.0582885 | + | 0.100959i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −586.037 | + | 15.4395i | −1.40537 | + | 0.0370253i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 42.6325 | − | 73.8416i | 0.101748 | − | 0.176233i | −0.810657 | − | 0.585522i | \(-0.800890\pi\) |
0.912405 | + | 0.409289i | \(0.134223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 526.755 | + | 304.122i | 1.25120 | + | 0.722381i | 0.971348 | − | 0.237662i | \(-0.0763812\pi\) |
0.279852 | + | 0.960043i | \(0.409715\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 265.123 | + | 407.968i | 0.626767 | + | 0.964463i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 52.9416 | + | 91.6976i | 0.124569 | + | 0.215759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −73.1158 | − | 126.640i | −0.171231 | − | 0.296581i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 81.0890 | − | 49.7092i | 0.189019 | − | 0.115872i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 79.3761 | + | 45.8278i | 0.184167 | + | 0.106329i | 0.589249 | − | 0.807951i | \(-0.299424\pi\) |
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 547.653 | + | 316.188i | 1.26479 | + | 0.730225i | 0.973997 | − | 0.226561i | \(-0.0727484\pi\) |
0.290791 | + | 0.956787i | \(0.406082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −594.204 | − | 322.504i | −1.36599 | − | 0.741388i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.69896 | + | 279.412i | −0.0199061 | + | 0.639386i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −348.320 | − | 201.103i | −0.793440 | − | 0.458093i | 0.0477324 | − | 0.998860i | \(-0.484801\pi\) |
−0.841172 | + | 0.540768i | \(0.818134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −415.117 | + | 21.8883i | −0.941309 | + | 0.0496333i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −118.638 | −0.267807 | −0.133903 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133903 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 351.925 | + | 203.184i | 0.790842 | + | 0.456593i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 88.7254 | − | 163.474i | 0.198491 | − | 0.365714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 217.699i | 0.484853i | 0.970170 | + | 0.242426i | \(0.0779433\pi\) | ||||
−0.970170 | + | 0.242426i | \(0.922057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.9105 | + | 28.2385i | −0.108449 | + | 0.0626131i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.1403 | + | 688.550i | 0.0400448 | + | 1.51998i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −166.259 | − | 95.9895i | −0.365404 | − | 0.210966i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8170 | − | 49.9125i | −0.0630568 | − | 0.109218i | 0.832774 | − | 0.553614i | \(-0.186752\pi\) |
−0.895830 | + | 0.444396i | \(0.853418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 295.923 | + | 430.129i | 0.644712 | + | 0.937100i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −232.941 | + | 403.466i | −0.505295 | + | 0.875197i | 0.494686 | + | 0.869072i | \(0.335283\pi\) |
−0.999981 | + | 0.00612534i | \(0.998050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −46.1604 | + | 79.9521i | −0.0996984 | + | 0.172683i | −0.911560 | − | 0.411168i | \(-0.865121\pi\) |
0.811861 | + | 0.583850i | \(0.198454\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −376.944 | + | 231.074i | −0.810633 | + | 0.496934i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −601.527 | −1.28807 | −0.644033 | − | 0.764998i | \(-0.722740\pi\) | ||||
−0.644033 | + | 0.764998i | \(0.722740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −125.408 | − | 72.4045i | −0.267395 | − | 0.154381i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −216.708 | + | 399.279i | −0.460102 | + | 0.847726i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.28004 | 0.0153912 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −88.4381 | − | 54.7981i | −0.186185 | − | 0.115364i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.57785 | + | 181.647i | 0.0200793 | + | 0.380811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −372.868 | −0.778430 | −0.389215 | − | 0.921147i | \(-0.627254\pi\) | ||||
−0.389215 | + | 0.921147i | \(0.627254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −619.673 | − | 1073.31i | −1.28830 | − | 2.23140i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.6822 | + | 63.1010i | 0.0800873 | + | 0.130644i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −231.042 | − | 133.392i | −0.476374 | − | 0.275035i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 733.353i | − | 1.50586i | −0.658102 | − | 0.752929i | \(-0.728640\pi\) | ||
0.658102 | − | 0.752929i | \(-0.271360\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −321.794 | + | 592.897i | −0.658066 | + | 1.21247i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −45.9359 | −0.0935559 | −0.0467779 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467779 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −683.622 | + | 394.689i | −1.38666 | + | 0.800587i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.4608 | − | 67.6864i | 0.0696177 | − | 0.136740i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −127.545 | − | 73.6382i | −0.256630 | − | 0.148165i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 345.818 | 0.693023 | 0.346511 | − | 0.938046i | \(-0.387366\pi\) | ||||
0.346511 | + | 0.938046i | \(0.387366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.16856 | + | 310.054i | 0.0163045 | + | 0.618870i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −293.370 | + | 508.133i | −0.583242 | + | 1.01020i | 0.411851 | + | 0.911251i | \(0.364883\pi\) |
−0.995092 | + | 0.0989526i | \(0.968451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −155.167 | −0.307261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 409.386 | + | 667.817i | 0.807467 | + | 1.31719i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 104.974 | − | 60.6066i | 0.206235 | − | 0.119070i | −0.393325 | − | 0.919399i | \(-0.628675\pi\) |
0.599561 | + | 0.800329i | \(0.295342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.2590 | + | 88.7832i | −0.100311 | + | 0.173744i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −456.042 | − | 234.935i | −0.888971 | − | 0.457964i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 424.121 | + | 244.866i | 0.823536 | + | 0.475469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.3221 | − | 71.5720i | −0.0799267 | − | 0.138437i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 605.459 | − | 371.159i | 1.16659 | − | 0.715142i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 462.527i | − | 0.887768i | −0.896084 | − | 0.443884i | \(-0.853600\pi\) | ||
0.896084 | − | 0.443884i | \(-0.146400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −720.329 | − | 415.882i | −1.37730 | − | 0.795185i | −0.385467 | − | 0.922721i | \(-0.625960\pi\) |
−0.991834 | + | 0.127536i | \(0.959293\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −27.5362 | + | 0.725458i | −0.0524499 | + | 0.00138183i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 516.226i | 0.979556i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 156.264 | − | 270.657i | 0.295395 | − | 0.511638i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −746.472 | + | 485.103i | −1.40579 | + | 0.913566i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −383.087 | − | 663.527i | −0.718738 | − | 1.24489i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 69.8699i | − | 0.130598i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 435.191 | + | 236.199i | 0.810411 | + | 0.439850i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 70.6093 | 0.131001 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −208.868 | + | 361.769i | −0.386077 | + | 0.668705i | −0.991918 | − | 0.126881i | \(-0.959503\pi\) |
0.605841 | + | 0.795586i | \(0.292837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.1330 | + | 17.8591i | −0.0536519 | + | 0.0328897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 553.329 | − | 319.465i | 1.01528 | − | 0.586174i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 514.242i | − | 0.940114i | −0.882636 | − | 0.470057i | \(-0.844233\pi\) | ||
0.882636 | − | 0.470057i | \(-0.155767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 427.677 | + | 658.104i | 0.779010 | + | 1.19873i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 408.530 | − | 659.322i | 0.741433 | − | 1.19659i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 60.3959i | − | 0.109215i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −869.842 | − | 472.106i | −1.56728 | − | 0.850642i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −331.389 | + | 573.982i | −0.594953 | + | 1.03049i | 0.398600 | + | 0.917125i | \(0.369496\pi\) |
−0.993553 | + | 0.113364i | \(0.963837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 98.7620i | 0.176676i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46.3484 | − | 75.6066i | −0.0826174 | − | 0.134771i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 700.676 | + | 404.536i | 1.24454 | + | 0.718536i | 0.970015 | − | 0.243044i | \(-0.0781460\pi\) |
0.274525 | + | 0.961580i | \(0.411479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 554.245 | + | 319.994i | 0.980965 | + | 0.566360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −135.070 | + | 14.2837i | −0.238219 | + | 0.0251917i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −173.823 | + | 100.357i | −0.305488 | + | 0.176374i | −0.644906 | − | 0.764262i | \(-0.723103\pi\) |
0.339418 | + | 0.940636i | \(0.389770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 174.282 | − | 301.865i | 0.305222 | − | 0.528660i | −0.672089 | − | 0.740471i | \(-0.734603\pi\) |
0.977311 | + | 0.211811i | \(0.0679360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −834.166 | + | 21.9766i | −1.45579 | + | 0.0383536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.2823 | − | 69.7710i | −0.0700562 | − | 0.121341i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −102.187 | −0.177101 | −0.0885503 | − | 0.996072i | \(-0.528223\pi\) | ||||
−0.0885503 | + | 0.996072i | \(0.528223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −772.041 | − | 419.024i | −1.33340 | − | 0.723704i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.34758 | + | 12.7264i | −0.0126464 | + | 0.0219043i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 30.8972i | − | 0.0529968i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 918.243 | + | 467.499i | 1.56965 | + | 0.799144i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 284.222 | − | 492.288i | 0.484195 | − | 0.838650i | −0.515640 | − | 0.856805i | \(-0.672446\pi\) |
0.999835 | + | 0.0181550i | \(0.00577925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −239.825 | − | 446.958i | −0.407173 | − | 0.758841i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −286.412 | + | 527.706i | −0.484623 | + | 0.892904i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 551.047 | − | 954.441i | 0.929252 | − | 1.60951i | 0.144677 | − | 0.989479i | \(-0.453786\pi\) |
0.784576 | − | 0.620033i | \(-0.212881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −89.4997 | + | 155.018i | −0.150420 | + | 0.260534i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.2468 | − | 16.7152i | −0.0171638 | − | 0.0279987i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 504.389 | − | 291.209i | 0.842051 | − | 0.486159i | −0.0159097 | − | 0.999873i | \(-0.505064\pi\) |
0.857961 | + | 0.513715i | \(0.171731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −462.788 | + | 267.191i | −0.770031 | + | 0.444577i | −0.832886 | − | 0.553445i | \(-0.813313\pi\) |
0.0628549 | + | 0.998023i | \(0.479979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 692.627 | + | 352.633i | 1.14863 | + | 0.584797i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 327.539 | − | 567.313i | 0.541386 | − | 0.937708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −549.907 | − | 317.489i | −0.905942 | − | 0.523046i | −0.0268186 | − | 0.999640i | \(-0.508538\pi\) |
−0.879123 | + | 0.476595i | \(0.841871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.40842 | − | 205.287i | −0.00888082 | − | 0.337089i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 970.955 | − | 560.581i | 1.58913 | − | 0.917482i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −73.8570 | − | 127.924i | −0.120484 | − | 0.208685i | 0.799474 | − | 0.600700i | \(-0.205111\pi\) |
−0.919959 | + | 0.392015i | \(0.871778\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −537.744 | − | 291.860i | −0.874381 | − | 0.474569i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −212.890 | − | 368.736i | −0.345040 | − | 0.597627i | 0.640321 | − | 0.768108i | \(-0.278801\pi\) |
−0.985361 | + | 0.170480i | \(0.945468\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −294.086 | − | 509.373i | −0.475099 | − | 0.822896i | 0.524494 | − | 0.851414i | \(-0.324255\pi\) |
−0.999593 | + | 0.0285181i | \(0.990921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −225.162 | − | 327.277i | −0.362580 | − | 0.527017i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 123.433i | 0.198127i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −731.910 | −1.17106 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 75.2541 | + | 43.9293i | 0.120022 | + | 0.0700626i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1000.74 | + | 577.777i | −1.59100 | + | 0.918565i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 249.213 | − | 431.649i | 0.394949 | − | 0.684071i | −0.598146 | − | 0.801387i | \(-0.704096\pi\) |
0.993095 | + | 0.117316i | \(0.0374290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 563.944 | + | 306.080i | 0.890907 | + | 0.483539i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 518.369 | + | 299.281i | 0.816330 | + | 0.471308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 957.895i | 1.50376i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 704.429 | + | 358.641i | 1.10239 | + | 0.561254i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −418.804 | − | 241.797i | −0.653361 | − | 0.377218i | 0.136382 | − | 0.990656i | \(-0.456453\pi\) |
−0.789743 | + | 0.613438i | \(0.789786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 919.540 | 1.43008 | 0.715039 | − | 0.699085i | \(-0.246409\pi\) | ||||
0.715039 | + | 0.699085i | \(0.246409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.2192 | + | 67.2395i | 0.0639058 | + | 0.104247i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 917.882 | 1.41867 | 0.709337 | − | 0.704869i | \(-0.248994\pi\) | ||||
0.709337 | + | 0.704869i | \(0.248994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 130.958 | − | 75.6084i | 0.201784 | − | 0.116500i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −118.033 | − | 64.0622i | −0.181310 | − | 0.0984059i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −188.112 | + | 325.820i | −0.288074 | + | 0.498958i | −0.973350 | − | 0.229325i | \(-0.926348\pi\) |
0.685276 | + | 0.728283i | \(0.259681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −893.352 | −1.36390 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 249.647 | − | 490.347i | 0.379981 | − | 0.746343i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 862.027i | 1.30808i | 0.756458 | + | 0.654042i | \(0.226928\pi\) | ||||
−0.756458 | + | 0.654042i | \(0.773072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1005.25 | + | 580.382i | −1.52080 | + | 0.878037i | −0.521106 | + | 0.853492i | \(0.674480\pi\) |
−0.999699 | + | 0.0245451i | \(0.992186\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1025.69 | − | 628.768i | 1.54704 | − | 0.948368i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.47310 | − | 175.797i | 0.00823022 | − | 0.264356i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 520.155 | − | 300.312i | 0.779843 | − | 0.450243i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −887.583 | + | 544.106i | −1.32673 | + | 0.813313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −66.6579 | − | 115.455i | −0.0993411 | − | 0.172064i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 793.000 | − | 457.839i | 1.17831 | − | 0.680296i | 0.222685 | − | 0.974891i | \(-0.428518\pi\) |
0.955622 | + | 0.294595i | \(0.0951847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 147.384 | − | 11.6704i | 0.218346 | − | 0.0172894i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 499.660 | − | 288.479i | 0.738051 | − | 0.426114i | −0.0833095 | − | 0.996524i | \(-0.526549\pi\) |
0.821360 | + | 0.570410i | \(0.193216\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 81.0350i | − | 0.119345i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.6160 | − | 1124.13i | −0.0434889 | − | 1.65071i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 110.380i | 0.161611i | 0.996730 | + | 0.0808054i | \(0.0257492\pi\) | ||||
−0.996730 | + | 0.0808054i | \(0.974251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −775.745 | −1.13247 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −49.1088 | − | 80.1096i | −0.0714830 | − | 0.116608i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 419.155 | 0.608353 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 316.990 | + | 549.043i | 0.458741 | + | 0.794564i | 0.998895 | − | 0.0470031i | \(-0.0149671\pi\) |
−0.540153 | + | 0.841567i | \(0.681634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.0388 | − | 1.21479i | 0.0332451 | − | 0.00175294i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 539.389 | + | 934.249i | 0.776099 | + | 1.34424i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −618.666 | + | 357.187i | −0.887612 | + | 0.512463i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −181.467 | + | 4.78087i | −0.259610 | + | 0.00683958i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −314.952 | − | 545.513i | −0.449290 | − | 0.778192i | 0.549050 | − | 0.835789i | \(-0.314990\pi\) |
−0.998340 | + | 0.0575969i | \(0.981656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 598.038 | − | 965.167i | 0.850694 | − | 1.37293i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 427.086 | − | 786.895i | 0.605796 | − | 1.11616i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.5658 | − | 40.8172i | −0.0333321 | − | 0.0577329i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 634.859 | 0.895429 | 0.447714 | − | 0.894177i | \(-0.352238\pi\) | ||||
0.447714 | + | 0.894177i | \(0.352238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.0686 | + | 323.711i | 0.0240065 | + | 0.455290i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 392.787i | − | 0.550893i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −151.574 | − | 87.5113i | −0.211992 | − | 0.122393i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 304.057 | + | 495.998i | 0.424068 | + | 0.691768i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −426.697 | − | 739.061i | −0.593459 | − | 1.02790i | −0.993762 | − | 0.111518i | \(-0.964429\pi\) |
0.400304 | − | 0.916383i | \(-0.368905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 148.755i | 0.206318i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −515.151 | − | 279.598i | −0.712519 | − | 0.386719i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 223.534i | 0.308323i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −320.492 | + | 555.108i | −0.440842 | + | 0.763560i | −0.997752 | − | 0.0670123i | \(-0.978653\pi\) |
0.556910 | + | 0.830573i | \(0.311987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 719.915 | − | 114.730i | 0.987538 | − | 0.157380i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 92.0847 | 0.125971 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −460.500 | + | 797.610i | −0.628241 | + | 1.08814i | 0.359664 | + | 0.933082i | \(0.382891\pi\) |
−0.987905 | + | 0.155063i | \(0.950442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 399.786 | + | 652.158i | 0.543927 | + | 0.887290i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −114.332 | − | 66.0094i | −0.155131 | − | 0.0895650i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.6756 | − | 37.5432i | −0.0293310 | − | 0.0508027i | 0.850987 | − | 0.525186i | \(-0.176004\pi\) |
−0.880318 | + | 0.474384i | \(0.842671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −595.950 | + | 1020.91i | −0.804251 | + | 1.37774i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 971.585i | 1.30765i | 0.756645 | + | 0.653826i | \(0.226837\pi\) | ||||
−0.756645 | + | 0.653826i | \(0.773163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −342.270 | −0.459423 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.7850 | − | 70.2875i | 0.0479050 | − | 0.0940930i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3795 | − | 10.6114i | 0.0245387 | − | 0.0141674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −815.627 | + | 470.903i | −1.08605 | + | 0.627034i | −0.932523 | − | 0.361110i | \(-0.882398\pi\) |
−0.153532 | + | 0.988144i | \(0.549065\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.3529 | − | 20.1508i | −0.0164049 | − | 0.0267607i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1097.67 | − | 633.741i | 1.45387 | − | 0.839392i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 147.926 | + | 256.215i | 0.195411 | + | 0.338461i | 0.947035 | − | 0.321130i | \(-0.104063\pi\) |
−0.751624 | + | 0.659591i | \(0.770729\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 35.2656 | + | 57.5276i | 0.0464633 | + | 0.0757940i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.8819 | + | 82.9339i | −0.0629198 | + | 0.108980i | −0.895769 | − | 0.444519i | \(-0.853375\pi\) |
0.832850 | + | 0.553499i | \(0.186708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 168.072 | + | 97.0366i | 0.220278 | + | 0.127178i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 435.892 | − | 856.161i | 0.569793 | − | 1.11916i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1025.71 | + | 1776.59i | 1.33731 | + | 2.31628i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 283.214 | + | 490.542i | 0.368289 | + | 0.637896i | 0.989298 | − | 0.145908i | \(-0.0466103\pi\) |
−0.621009 | + | 0.783803i | \(0.713277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.9557 | + | 1516.60i | 0.0518232 | + | 1.96705i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −667.545 | − | 385.407i | −0.863577 | − | 0.498587i | 0.00163121 | − | 0.999999i | \(-0.499481\pi\) |
−0.865209 | + | 0.501412i | \(0.832814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 126.599 | + | 73.0917i | 0.163353 | + | 0.0943119i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.91727 | − | 300.515i | −0.0101895 | − | 0.386764i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 369.712 | − | 596.675i | 0.474598 | − | 0.765950i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −116.280 | − | 67.1342i | −0.148886 | − | 0.0859592i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 87.0046 | + | 1098.77i | 0.111117 | + | 1.40328i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 835.980 | 1.06494 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 536.750 | + | 309.893i | 0.682020 | + | 0.393764i | 0.800616 | − | 0.599178i | \(-0.204506\pi\) |
−0.118596 | + | 0.992943i | \(0.537839\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −415.922 | − | 678.480i | −0.527151 | − | 0.859924i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 194.395i | 0.245758i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1566.28 | − | 904.290i | 1.97513 | − | 1.14034i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 285.371 | − | 174.938i | 0.358957 | − | 0.220048i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 323.319 | + | 186.669i | 0.405670 | + | 0.234214i | 0.688928 | − | 0.724830i | \(-0.258082\pi\) |
−0.283257 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −522.681 | − | 905.309i | −0.654168 | − | 1.13305i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.8837 | − | 661.579i | −0.0435502 | − | 0.825942i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.7316 | + | 80.9415i | −0.0581962 | + | 0.100799i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 68.0987 | − | 117.950i | 0.0845946 | − | 0.146522i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.05414 | + | 191.840i | 0.00626288 | + | 0.237720i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −398.989 | −0.493188 | −0.246594 | − | 0.969119i | \(-0.579311\pi\) | ||||
−0.246594 | + | 0.969119i | \(0.579311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −492.099 | − | 284.113i | −0.606780 | − | 0.350325i | 0.164924 | − | 0.986306i | \(-0.447262\pi\) |
−0.771704 | + | 0.635982i | \(0.780595\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1570.01 | − | 41.3629i | 1.93113 | − | 0.0508769i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1241.36 | 1.52315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −79.7286 | + | 42.7801i | −0.0975870 | + | 0.0523625i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.4800 | + | 312.548i | 0.0201221 | + | 0.381621i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 319.131 | 0.388710 | 0.194355 | − | 0.980931i | \(-0.437739\pi\) | ||||
0.194355 | + | 0.980931i | \(0.437739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −413.122 | − | 715.548i | −0.501971 | − | 0.869438i | −0.999997 | − | 0.00227688i | \(-0.999275\pi\) |
0.498027 | − | 0.867162i | \(-0.334058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.1041 | + | 0.661383i | −0.0304292 | + | 0.000801676i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −640.947 | − | 370.051i | −0.775026 | − | 0.447462i | 0.0596384 | − | 0.998220i | \(-0.481005\pi\) |
−0.834665 | + | 0.550758i | \(0.814339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1430.53i | − | 1.72561i | −0.505539 | − | 0.862804i | \(-0.668706\pi\) | ||
0.505539 | − | 0.862804i | \(-0.331294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 228.960 | − | 6.03209i | 0.275523 | − | 0.00725883i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 893.132 | 1.07219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 494.281 | − | 285.373i | 0.591953 | − | 0.341764i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 650.739 | + | 310.004i | 0.777465 | + | 0.370375i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 235.161 | + | 135.771i | 0.280288 | + | 0.161824i | 0.633554 | − | 0.773699i | \(-0.281596\pi\) |
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −825.487 | −0.981554 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1210.23 | − | 656.852i | −1.43562 | − | 0.779183i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 720.710 | − | 1248.31i | 0.852911 | − | 1.47728i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 198.978 | 0.234921 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −181.342 | + | 334.117i | −0.213594 | + | 0.393542i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 761.444 | − | 439.620i | 0.894764 | − | 0.516592i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6469 | − | 49.6180i | 0.0335838 | − | 0.0581688i | −0.848745 | − | 0.528802i | \(-0.822641\pi\) |
0.882329 | + | 0.470634i | \(0.155975\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.3474 | + | 943.783i | 0.0237981 | + | 1.10384i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −475.737 | − | 274.667i | −0.555119 | − | 0.320498i | 0.196065 | − | 0.980591i | \(-0.437184\pi\) |
−0.751184 | + | 0.660093i | \(0.770517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 124.904 | + | 216.339i | 0.145406 | + | 0.251850i | 0.929524 | − | 0.368761i | \(-0.120218\pi\) |
−0.784119 | + | 0.620611i | \(0.786885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.89453 | − | 185.781i | −0.00568470 | − | 0.215774i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 33.3471i | − | 0.0386409i | −0.999813 | − | 0.0193204i | \(-0.993850\pi\) | ||
0.999813 | − | 0.0193204i | \(-0.00615027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1131.74 | − | 653.412i | −1.30837 | − | 0.755390i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −133.133 | − | 217.175i | −0.153556 | − | 0.250491i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 55.0615i | − | 0.0633619i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 895.493 | − | 1551.04i | 1.02812 | − | 1.78076i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9014 | + | 434.332i | 0.0262330 | + | 0.497517i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −90.3674 | − | 156.521i | −0.103277 | − | 0.178881i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 895.620i | 1.02123i | 0.859809 | + | 0.510616i | \(0.170583\pi\) | ||||
−0.859809 | + | 0.510616i | \(0.829417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −421.368 | + | 258.307i | −0.479372 | + | 0.293865i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −449.443 | −0.510151 | −0.255075 | − | 0.966921i | \(-0.582100\pi\) | ||||
−0.255075 | + | 0.966921i | \(0.582100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −432.651 | + | 749.374i | −0.489979 | + | 0.848669i | −0.999933 | − | 0.0115329i | \(-0.996329\pi\) |
0.509954 | + | 0.860201i | \(0.329662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1439.81 | + | 781.454i | 1.62690 | + | 0.882998i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 806.404 | − | 465.577i | 0.909136 | − | 0.524890i | 0.0289829 | − | 0.999580i | \(-0.490773\pi\) |
0.880153 | + | 0.474690i | \(0.157440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 181.812i | 0.204513i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −123.140 | + | 13.0221i | −0.138205 | + | 0.0146151i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 873.129 | + | 541.009i | 0.977748 | + | 0.605833i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 911.170i | − | 1.01807i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −780.428 | + | 478.418i | −0.870042 | + | 0.533353i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −544.912 | + | 943.815i | −0.606131 | + | 1.04985i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 390.816i | − | 0.433758i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4275 | + | 21.0548i | −0.0126550 | + | 0.0233165i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.4563 | + | 31.4403i | 0.0601727 | + | 0.0347407i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 217.224 | + | 125.414i | 0.239497 | + | 0.138274i | 0.614946 | − | 0.788569i | \(-0.289178\pi\) |
−0.375448 | + | 0.926843i | \(0.622511\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 137.844 | + | 212.112i | 0.151643 | + | 0.233347i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −680.835 | + | 393.080i | −0.747349 | + | 0.431482i | −0.824735 | − | 0.565519i | \(-0.808676\pi\) |
0.0773862 | + | 0.997001i | \(0.475343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.69861 | + | 11.6023i | −0.00733692 | + | 0.0127079i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 688.945 | − | 1269.36i | 0.752945 | − | 1.38728i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −135.677 | − | 234.999i | −0.147957 | − | 0.256269i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 668.462 | 0.727380 | 0.363690 | − | 0.931520i | \(-0.381517\pi\) | ||||
0.363690 | + | 0.931520i | \(0.381517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.1319 | − | 498.446i | −0.0142583 | − | 0.541201i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 910.751 | − | 1577.47i | 0.986729 | − | 1.70907i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 327.227i | 0.353759i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.0400 | − | 797.300i | −0.0453505 | − | 0.860086i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 786.563 | − | 1362.37i | 0.846677 | − | 1.46649i | −0.0374806 | − | 0.999297i | \(-0.511933\pi\) |
0.884157 | − | 0.467190i | \(-0.154733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −773.290 | + | 414.926i | −0.830601 | + | 0.445678i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 404.616 | + | 660.037i | 0.433672 | + | 0.707436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −81.5947 | + | 141.326i | −0.0872671 | + | 0.151151i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −351.661 | + | 609.095i | −0.375305 | + | 0.650048i | −0.990373 | − | 0.138427i | \(-0.955795\pi\) |
0.615067 | + | 0.788475i | \(0.289129\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −383.601 | + | 706.774i | −0.408520 | + | 0.752688i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1043.02 | + | 602.186i | −1.10841 | + | 0.639943i | −0.938418 | − | 0.345502i | \(-0.887709\pi\) |
−0.169996 | + | 0.985445i | \(0.554375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 470.731 | − | 271.777i | 0.499185 | − | 0.288205i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 141.665 | + | 205.912i | 0.149910 | + | 0.217896i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 402.675 | − | 697.454i | 0.425211 | − | 0.736487i | −0.571229 | − | 0.820791i | \(-0.693533\pi\) |
0.996440 | + | 0.0843034i | \(0.0268665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1098.06 | − | 633.967i | −1.15707 | − | 0.668037i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1409.46 | − | 764.983i | −1.48208 | − | 0.804398i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.1016 | + | 11.0283i | −0.0200437 | + | 0.0115722i | −0.509988 | − | 0.860181i | \(-0.670350\pi\) |
0.489945 | + | 0.871754i | \(0.337017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 767.766 | + | 1329.81i | 0.803943 | + | 1.39247i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.93073 | − | 187.155i | −0.00515228 | − | 0.195565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −117.815 | − | 204.062i | −0.122852 | − | 0.212786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −124.147 | − | 215.028i | −0.129185 | − | 0.223755i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −95.5117 | + | 62.0694i | −0.0991814 | + | 0.0644542i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1616.44i | 1.67507i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1102.89 | 1.14052 | 0.570261 | − | 0.821463i | \(-0.306842\pi\) | ||||
0.570261 | + | 0.821463i | \(0.306842\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 951.883 | + | 555.658i | 0.982336 | + | 0.573435i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1145.08 | + | 661.109i | −1.17927 | + | 0.680854i | −0.955847 | − | 0.293866i | \(-0.905058\pi\) |
−0.223427 | + | 0.974721i | \(0.571725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −163.838 | + | 283.776i | −0.168384 | + | 0.291650i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.97241 | − | 340.565i | −0.00920247 | − | 0.349298i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1364.73 | − | 787.927i | −1.39686 | − | 0.806476i | −0.402795 | − | 0.915290i | \(-0.631961\pi\) |
−0.994062 | + | 0.108814i | \(0.965295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 112.531i | 0.114945i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −928.260 | − | 472.599i | −0.946239 | − | 0.481752i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −181.250 | − | 104.645i | −0.184384 | − | 0.106454i | 0.404967 | − | 0.914331i | \(-0.367283\pi\) |
−0.589351 | + | 0.807877i | \(0.700616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1104.87 | 1.12170 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 271.858 | − | 7.16228i | 0.275439 | − | 0.00725662i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.0655 | −0.0708448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 117.245 | − | 67.6913i | 0.118310 | − | 0.0683061i | −0.439677 | − | 0.898156i | \(-0.644907\pi\) |
0.557987 | + | 0.829850i | \(0.311574\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.2772 | − | 883.531i | −0.0234413 | − | 0.889759i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.0391 | + | 31.2446i | −0.0181297 | + | 0.0314016i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1087.30 | −1.09057 | −0.545285 | − | 0.838251i | \(-0.683579\pi\) | ||||
−0.545285 | + | 0.838251i | \(0.683579\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 127.364 | + | 1608.47i | 0.127492 | + | 1.61008i |
(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 | 684.3.bl.a.373.15 | yes | 80 | |
3.2 | odd | 2 | 2052.3.bl.a.145.9 | 80 | |||
9.2 | odd | 6 | 2052.3.s.a.829.32 | 80 | |||
9.7 | even | 3 | 684.3.s.a.601.1 | yes | 80 | ||
19.8 | odd | 6 | 684.3.s.a.445.1 | ✓ | 80 | ||
57.8 | even | 6 | 2052.3.s.a.901.32 | 80 | |||
171.65 | even | 6 | 2052.3.bl.a.1585.9 | 80 | |||
171.160 | odd | 6 | inner | 684.3.bl.a.673.15 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.1 | ✓ | 80 | 19.8 | odd | 6 | ||
684.3.s.a.601.1 | yes | 80 | 9.7 | even | 3 | ||
684.3.bl.a.373.15 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.bl.a.673.15 | yes | 80 | 171.160 | odd | 6 | inner | |
2052.3.s.a.829.32 | 80 | 9.2 | odd | 6 | |||
2052.3.s.a.901.32 | 80 | 57.8 | even | 6 | |||
2052.3.bl.a.145.9 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.1585.9 | 80 | 171.65 | even | 6 |