Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (of order \(2\), degree \(1\), 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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.36 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.35 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39960 | 1.19980 | 0.599901 | − | 0.800075i | \(-0.295207\pi\) | ||||
0.599901 | + | 0.800075i | \(0.295207\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 1.75809 | 0.439523 | ||||||||
\(5\) | 1.89961i | 0.379923i | 0.981792 | + | 0.189961i | \(0.0608363\pi\) | ||||
−0.981792 | + | 0.189961i | \(0.939164\pi\) | |||||||
\(6\) | −4.15623 | −0.692706 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −5.37969 | −0.672461 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 4.55832i | 0.455832i | ||||||||
\(11\) | − | 11.7870i | − | 1.07155i | −0.844362 | − | 0.535773i | \(-0.820020\pi\) | ||
0.844362 | − | 0.535773i | \(-0.179980\pi\) | |||||||
\(12\) | −3.04511 | −0.253759 | ||||||||
\(13\) | −9.50541 | −0.731185 | −0.365593 | − | 0.930775i | \(-0.619134\pi\) | ||||
−0.365593 | + | 0.930775i | \(0.619134\pi\) | |||||||
\(14\) | − | 6.34875i | − | 0.453482i | ||||||
\(15\) | − | 3.29023i | − | 0.219349i | ||||||
\(16\) | −19.9415 | −1.24634 | ||||||||
\(17\) | − | 23.2236i | − | 1.36610i | −0.730374 | − | 0.683048i | \(-0.760654\pi\) | ||
0.730374 | − | 0.683048i | \(-0.239346\pi\) | |||||||
\(18\) | 7.19881 | 0.399934 | ||||||||
\(19\) | − | 20.1037i | − | 1.05809i | −0.848594 | − | 0.529044i | \(-0.822550\pi\) | ||
0.848594 | − | 0.529044i | \(-0.177450\pi\) | |||||||
\(20\) | 3.33970i | 0.166985i | ||||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | − | 28.2841i | − | 1.28564i | ||||||
\(23\) | 21.2213 | + | 8.86874i | 0.922667 | + | 0.385597i | ||||
\(24\) | 9.31789 | 0.388245 | ||||||||
\(25\) | 21.3915 | 0.855659 | ||||||||
\(26\) | −22.8092 | −0.877277 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 4.65148i | − | 0.166124i | ||||||
\(29\) | −22.9320 | −0.790757 | −0.395379 | − | 0.918518i | \(-0.629387\pi\) | ||||
−0.395379 | + | 0.918518i | \(0.629387\pi\) | |||||||
\(30\) | − | 7.89524i | − | 0.263175i | ||||||
\(31\) | −27.0399 | −0.872256 | −0.436128 | − | 0.899885i | \(-0.643651\pi\) | ||||
−0.436128 | + | 0.899885i | \(0.643651\pi\) | |||||||
\(32\) | −26.3329 | −0.822902 | ||||||||
\(33\) | 20.4157i | 0.618657i | ||||||||
\(34\) | − | 55.7275i | − | 1.63904i | ||||||
\(35\) | 5.02591 | 0.143597 | ||||||||
\(36\) | 5.27428 | 0.146508 | ||||||||
\(37\) | − | 36.2524i | − | 0.979795i | −0.871780 | − | 0.489897i | \(-0.837034\pi\) | ||
0.871780 | − | 0.489897i | \(-0.162966\pi\) | |||||||
\(38\) | − | 48.2409i | − | 1.26950i | ||||||
\(39\) | 16.4639 | 0.422150 | ||||||||
\(40\) | − | 10.2193i | − | 0.255483i | ||||||
\(41\) | −50.4211 | −1.22978 | −0.614891 | − | 0.788612i | \(-0.710800\pi\) | ||||
−0.614891 | + | 0.788612i | \(0.710800\pi\) | |||||||
\(42\) | 10.9964i | 0.261818i | ||||||||
\(43\) | − | 12.8026i | − | 0.297734i | −0.988857 | − | 0.148867i | \(-0.952437\pi\) | ||
0.988857 | − | 0.148867i | \(-0.0475626\pi\) | |||||||
\(44\) | − | 20.7226i | − | 0.470969i | ||||||
\(45\) | 5.69884i | 0.126641i | ||||||||
\(46\) | 50.9228 | + | 21.2815i | 1.10702 | + | 0.462640i | ||||
\(47\) | −35.2976 | −0.751013 | −0.375507 | − | 0.926820i | \(-0.622531\pi\) | ||||
−0.375507 | + | 0.926820i | \(0.622531\pi\) | |||||||
\(48\) | 34.5397 | 0.719576 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 51.3310 | 1.02662 | ||||||||
\(51\) | 40.2245i | 0.788716i | ||||||||
\(52\) | −16.7114 | −0.321373 | ||||||||
\(53\) | − | 43.6619i | − | 0.823810i | −0.911227 | − | 0.411905i | \(-0.864863\pi\) | ||
0.911227 | − | 0.411905i | \(-0.135137\pi\) | |||||||
\(54\) | −12.4687 | −0.230902 | ||||||||
\(55\) | 22.3908 | 0.407105 | ||||||||
\(56\) | 14.2333i | 0.254166i | ||||||||
\(57\) | 34.8206i | 0.610888i | ||||||||
\(58\) | −55.0276 | −0.948752 | ||||||||
\(59\) | 21.5090 | 0.364559 | 0.182279 | − | 0.983247i | \(-0.441652\pi\) | ||||
0.182279 | + | 0.983247i | \(0.441652\pi\) | |||||||
\(60\) | − | 5.78452i | − | 0.0964087i | ||||||
\(61\) | 88.3762i | 1.44879i | 0.689385 | + | 0.724395i | \(0.257881\pi\) | ||||
−0.689385 | + | 0.724395i | \(0.742119\pi\) | |||||||
\(62\) | −64.8851 | −1.04653 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | 16.5775 | 0.259023 | ||||||||
\(65\) | − | 18.0566i | − | 0.277794i | ||||||
\(66\) | 48.9896i | 0.742266i | ||||||||
\(67\) | − | 19.2677i | − | 0.287577i | −0.989608 | − | 0.143788i | \(-0.954072\pi\) | ||
0.989608 | − | 0.143788i | \(-0.0459285\pi\) | |||||||
\(68\) | − | 40.8293i | − | 0.600431i | ||||||
\(69\) | −36.7564 | − | 15.3611i | −0.532702 | − | 0.222625i | ||||
\(70\) | 12.0602 | 0.172288 | ||||||||
\(71\) | 116.730 | 1.64409 | 0.822044 | − | 0.569424i | \(-0.192834\pi\) | ||||
0.822044 | + | 0.569424i | \(0.192834\pi\) | |||||||
\(72\) | −16.1391 | −0.224154 | ||||||||
\(73\) | −24.8834 | −0.340868 | −0.170434 | − | 0.985369i | \(-0.554517\pi\) | ||||
−0.170434 | + | 0.985369i | \(0.554517\pi\) | |||||||
\(74\) | − | 86.9914i | − | 1.17556i | ||||||
\(75\) | −37.0511 | −0.494015 | ||||||||
\(76\) | − | 35.3441i | − | 0.465054i | ||||||
\(77\) | −31.1855 | −0.405006 | ||||||||
\(78\) | 39.5067 | 0.506496 | ||||||||
\(79\) | 26.1733i | 0.331308i | 0.986184 | + | 0.165654i | \(0.0529735\pi\) | ||||
−0.986184 | + | 0.165654i | \(0.947027\pi\) | |||||||
\(80\) | − | 37.8811i | − | 0.473514i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −120.991 | −1.47549 | ||||||||
\(83\) | 64.1905i | 0.773380i | 0.922210 | + | 0.386690i | \(0.126382\pi\) | ||||
−0.922210 | + | 0.386690i | \(0.873618\pi\) | |||||||
\(84\) | 8.05659i | 0.0959118i | ||||||||
\(85\) | 44.1159 | 0.519011 | ||||||||
\(86\) | − | 30.7211i | − | 0.357222i | ||||||
\(87\) | 39.7193 | 0.456544 | ||||||||
\(88\) | 63.4104i | 0.720573i | ||||||||
\(89\) | 99.9201i | 1.12270i | 0.827579 | + | 0.561349i | \(0.189717\pi\) | ||||
−0.827579 | + | 0.561349i | \(0.810283\pi\) | |||||||
\(90\) | 13.6750i | 0.151944i | ||||||||
\(91\) | 25.1490i | 0.276362i | ||||||||
\(92\) | 37.3091 | + | 15.5921i | 0.405534 | + | 0.169479i | ||||
\(93\) | 46.8345 | 0.503597 | ||||||||
\(94\) | −84.7003 | −0.901067 | ||||||||
\(95\) | 38.1892 | 0.401992 | ||||||||
\(96\) | 45.6099 | 0.475103 | ||||||||
\(97\) | 49.1664i | 0.506870i | 0.967352 | + | 0.253435i | \(0.0815605\pi\) | ||||
−0.967352 | + | 0.253435i | \(0.918440\pi\) | |||||||
\(98\) | −16.7972 | −0.171400 | ||||||||
\(99\) | − | 35.3610i | − | 0.357182i | ||||||
\(100\) | 37.6082 | 0.376082 | ||||||||
\(101\) | −6.46798 | −0.0640394 | −0.0320197 | − | 0.999487i | \(-0.510194\pi\) | ||||
−0.0320197 | + | 0.999487i | \(0.510194\pi\) | |||||||
\(102\) | 96.5228i | 0.946302i | ||||||||
\(103\) | − | 67.3537i | − | 0.653919i | −0.945038 | − | 0.326960i | \(-0.893976\pi\) | ||
0.945038 | − | 0.326960i | \(-0.106024\pi\) | |||||||
\(104\) | 51.1361 | 0.491694 | ||||||||
\(105\) | −8.70512 | −0.0829060 | ||||||||
\(106\) | − | 104.771i | − | 0.988409i | ||||||
\(107\) | 97.3074i | 0.909415i | 0.890641 | + | 0.454708i | \(0.150256\pi\) | ||||
−0.890641 | + | 0.454708i | \(0.849744\pi\) | |||||||
\(108\) | −9.13532 | −0.0845863 | ||||||||
\(109\) | − | 149.211i | − | 1.36891i | −0.729056 | − | 0.684454i | \(-0.760041\pi\) | ||
0.729056 | − | 0.684454i | \(-0.239959\pi\) | |||||||
\(110\) | 53.7289 | 0.488445 | ||||||||
\(111\) | 62.7910i | 0.565685i | ||||||||
\(112\) | 52.7602i | 0.471073i | ||||||||
\(113\) | − | 16.3063i | − | 0.144304i | −0.997394 | − | 0.0721519i | \(-0.977013\pi\) | ||
0.997394 | − | 0.0721519i | \(-0.0229866\pi\) | |||||||
\(114\) | 83.5556i | 0.732944i | ||||||||
\(115\) | −16.8472 | + | 40.3124i | −0.146497 | + | 0.350542i | ||||
\(116\) | −40.3165 | −0.347556 | ||||||||
\(117\) | −28.5162 | −0.243728 | ||||||||
\(118\) | 51.6130 | 0.437398 | ||||||||
\(119\) | −61.4439 | −0.516336 | ||||||||
\(120\) | 17.7004i | 0.147503i | ||||||||
\(121\) | −17.9335 | −0.148211 | ||||||||
\(122\) | 212.068i | 1.73826i | ||||||||
\(123\) | 87.3319 | 0.710015 | ||||||||
\(124\) | −47.5387 | −0.383377 | ||||||||
\(125\) | 88.1259i | 0.705007i | ||||||||
\(126\) | − | 19.0463i | − | 0.151161i | ||||||
\(127\) | 148.405 | 1.16854 | 0.584270 | − | 0.811559i | \(-0.301381\pi\) | ||||
0.584270 | + | 0.811559i | \(0.301381\pi\) | |||||||
\(128\) | 145.111 | 1.13368 | ||||||||
\(129\) | 22.1747i | 0.171897i | ||||||||
\(130\) | − | 43.3287i | − | 0.333298i | ||||||
\(131\) | −36.7507 | −0.280540 | −0.140270 | − | 0.990113i | \(-0.544797\pi\) | ||||
−0.140270 | + | 0.990113i | \(0.544797\pi\) | |||||||
\(132\) | 35.8927i | 0.271914i | ||||||||
\(133\) | −53.1894 | −0.399920 | ||||||||
\(134\) | − | 46.2347i | − | 0.345035i | ||||||
\(135\) | − | 9.87068i | − | 0.0731162i | ||||||
\(136\) | 124.936i | 0.918646i | ||||||||
\(137\) | 78.8141i | 0.575286i | 0.957738 | + | 0.287643i | \(0.0928716\pi\) | ||||
−0.957738 | + | 0.287643i | \(0.907128\pi\) | |||||||
\(138\) | −88.2009 | − | 36.8606i | −0.639137 | − | 0.267106i | ||||
\(139\) | 72.4952 | 0.521548 | 0.260774 | − | 0.965400i | \(-0.416022\pi\) | ||||
0.260774 | + | 0.965400i | \(0.416022\pi\) | |||||||
\(140\) | 8.83601 | 0.0631143 | ||||||||
\(141\) | 61.1373 | 0.433598 | ||||||||
\(142\) | 280.106 | 1.97258 | ||||||||
\(143\) | 112.040i | 0.783499i | ||||||||
\(144\) | −59.8244 | −0.415448 | ||||||||
\(145\) | − | 43.5619i | − | 0.300427i | ||||||
\(146\) | −59.7102 | −0.408974 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | − | 63.7351i | − | 0.430642i | ||||||
\(149\) | − | 208.161i | − | 1.39706i | −0.715583 | − | 0.698528i | \(-0.753839\pi\) | ||
0.715583 | − | 0.698528i | \(-0.246161\pi\) | |||||||
\(150\) | −88.9079 | −0.592720 | ||||||||
\(151\) | −5.35118 | −0.0354383 | −0.0177191 | − | 0.999843i | \(-0.505640\pi\) | ||||
−0.0177191 | + | 0.999843i | \(0.505640\pi\) | |||||||
\(152\) | 108.152i | 0.711523i | ||||||||
\(153\) | − | 69.6709i | − | 0.455365i | ||||||
\(154\) | −74.8328 | −0.485927 | ||||||||
\(155\) | − | 51.3654i | − | 0.331390i | ||||||
\(156\) | 28.9450 | 0.185545 | ||||||||
\(157\) | − | 160.794i | − | 1.02416i | −0.858937 | − | 0.512082i | \(-0.828874\pi\) | ||
0.858937 | − | 0.512082i | \(-0.171126\pi\) | |||||||
\(158\) | 62.8056i | 0.397504i | ||||||||
\(159\) | 75.6247i | 0.475627i | ||||||||
\(160\) | − | 50.0223i | − | 0.312639i | ||||||
\(161\) | 23.4645 | − | 56.1464i | 0.145742 | − | 0.348735i | ||||
\(162\) | 21.5964 | 0.133311 | ||||||||
\(163\) | −219.889 | −1.34901 | −0.674506 | − | 0.738270i | \(-0.735643\pi\) | ||||
−0.674506 | + | 0.738270i | \(0.735643\pi\) | |||||||
\(164\) | −88.6449 | −0.540518 | ||||||||
\(165\) | −38.7819 | −0.235042 | ||||||||
\(166\) | 154.032i | 0.927902i | ||||||||
\(167\) | 165.497 | 0.990997 | 0.495499 | − | 0.868609i | \(-0.334985\pi\) | ||||
0.495499 | + | 0.868609i | \(0.334985\pi\) | |||||||
\(168\) | − | 24.6528i | − | 0.146743i | ||||||
\(169\) | −78.6472 | −0.465368 | ||||||||
\(170\) | 105.861 | 0.622710 | ||||||||
\(171\) | − | 60.3111i | − | 0.352696i | ||||||
\(172\) | − | 22.5081i | − | 0.130861i | ||||||
\(173\) | −192.854 | −1.11476 | −0.557382 | − | 0.830256i | \(-0.688194\pi\) | ||||
−0.557382 | + | 0.830256i | \(0.688194\pi\) | |||||||
\(174\) | 95.3106 | 0.547762 | ||||||||
\(175\) | − | 56.5965i | − | 0.323409i | ||||||
\(176\) | 235.050i | 1.33551i | ||||||||
\(177\) | −37.2546 | −0.210478 | ||||||||
\(178\) | 239.769i | 1.34701i | ||||||||
\(179\) | −59.6812 | −0.333415 | −0.166707 | − | 0.986006i | \(-0.553314\pi\) | ||||
−0.166707 | + | 0.986006i | \(0.553314\pi\) | |||||||
\(180\) | 10.0191i | 0.0556616i | ||||||||
\(181\) | − | 357.591i | − | 1.97564i | −0.155605 | − | 0.987819i | \(-0.549733\pi\) | ||
0.155605 | − | 0.987819i | \(-0.450267\pi\) | |||||||
\(182\) | 60.3475i | 0.331580i | ||||||||
\(183\) | − | 153.072i | − | 0.836459i | ||||||
\(184\) | −114.164 | − | 47.7111i | −0.620458 | − | 0.259299i | ||||
\(185\) | 68.8656 | 0.372246 | ||||||||
\(186\) | 112.384 | 0.604217 | ||||||||
\(187\) | −273.737 | −1.46383 | ||||||||
\(188\) | −62.0565 | −0.330088 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 91.6390 | 0.482311 | ||||||||
\(191\) | 83.7639i | 0.438555i | 0.975663 | + | 0.219277i | \(0.0703700\pi\) | ||||
−0.975663 | + | 0.219277i | \(0.929630\pi\) | |||||||
\(192\) | −28.7130 | −0.149547 | ||||||||
\(193\) | −203.616 | −1.05500 | −0.527501 | − | 0.849554i | \(-0.676871\pi\) | ||||
−0.527501 | + | 0.849554i | \(0.676871\pi\) | |||||||
\(194\) | 117.980i | 0.608144i | ||||||||
\(195\) | 31.2750i | 0.160384i | ||||||||
\(196\) | −12.3066 | −0.0627890 | ||||||||
\(197\) | 308.447 | 1.56572 | 0.782861 | − | 0.622196i | \(-0.213759\pi\) | ||||
0.782861 | + | 0.622196i | \(0.213759\pi\) | |||||||
\(198\) | − | 84.8524i | − | 0.428547i | ||||||
\(199\) | − | 336.923i | − | 1.69308i | −0.532326 | − | 0.846539i | \(-0.678682\pi\) | ||
0.532326 | − | 0.846539i | \(-0.321318\pi\) | |||||||
\(200\) | −115.079 | −0.575397 | ||||||||
\(201\) | 33.3726i | 0.166033i | ||||||||
\(202\) | −15.5206 | −0.0768346 | ||||||||
\(203\) | 60.6723i | 0.298878i | ||||||||
\(204\) | 70.7184i | 0.346659i | ||||||||
\(205\) | − | 95.7806i | − | 0.467222i | ||||||
\(206\) | − | 161.622i | − | 0.784573i | ||||||
\(207\) | 63.6640 | + | 26.6062i | 0.307556 | + | 0.128532i | ||||
\(208\) | 189.552 | 0.911307 | ||||||||
\(209\) | −236.962 | −1.13379 | ||||||||
\(210\) | −20.8888 | −0.0994707 | ||||||||
\(211\) | 214.467 | 1.01643 | 0.508215 | − | 0.861230i | \(-0.330305\pi\) | ||||
0.508215 | + | 0.861230i | \(0.330305\pi\) | |||||||
\(212\) | − | 76.7617i | − | 0.362084i | ||||||
\(213\) | −202.183 | −0.949214 | ||||||||
\(214\) | 233.499i | 1.09112i | ||||||||
\(215\) | 24.3199 | 0.113116 | ||||||||
\(216\) | 27.9537 | 0.129415 | ||||||||
\(217\) | 71.5410i | 0.329682i | ||||||||
\(218\) | − | 358.047i | − | 1.64242i | ||||||
\(219\) | 43.0992 | 0.196800 | ||||||||
\(220\) | 39.3650 | 0.178932 | ||||||||
\(221\) | 220.750i | 0.998869i | ||||||||
\(222\) | 150.673i | 0.678709i | ||||||||
\(223\) | 22.7824 | 0.102163 | 0.0510816 | − | 0.998694i | \(-0.483733\pi\) | ||||
0.0510816 | + | 0.998694i | \(0.483733\pi\) | |||||||
\(224\) | 69.6702i | 0.311028i | ||||||||
\(225\) | 64.1744 | 0.285220 | ||||||||
\(226\) | − | 39.1287i | − | 0.173136i | ||||||
\(227\) | 57.0590i | 0.251361i | 0.992071 | + | 0.125681i | \(0.0401114\pi\) | ||||
−0.992071 | + | 0.125681i | \(0.959889\pi\) | |||||||
\(228\) | 61.2178i | 0.268499i | ||||||||
\(229\) | − | 350.946i | − | 1.53252i | −0.642533 | − | 0.766258i | \(-0.722117\pi\) | ||
0.642533 | − | 0.766258i | \(-0.277883\pi\) | |||||||
\(230\) | −40.4265 | + | 96.7336i | −0.175768 | + | 0.420581i | ||||
\(231\) | 54.0149 | 0.233831 | ||||||||
\(232\) | 123.367 | 0.531753 | ||||||||
\(233\) | 197.772 | 0.848805 | 0.424402 | − | 0.905474i | \(-0.360484\pi\) | ||||
0.424402 | + | 0.905474i | \(0.360484\pi\) | |||||||
\(234\) | −68.4276 | −0.292426 | ||||||||
\(235\) | − | 67.0519i | − | 0.285327i | ||||||
\(236\) | 37.8147 | 0.160232 | ||||||||
\(237\) | − | 45.3335i | − | 0.191281i | ||||||
\(238\) | −147.441 | −0.619500 | ||||||||
\(239\) | 16.7669 | 0.0701542 | 0.0350771 | − | 0.999385i | \(-0.488832\pi\) | ||||
0.0350771 | + | 0.999385i | \(0.488832\pi\) | |||||||
\(240\) | 65.6120i | 0.273383i | ||||||||
\(241\) | − | 300.467i | − | 1.24675i | −0.781922 | − | 0.623376i | \(-0.785760\pi\) | ||
0.781922 | − | 0.623376i | \(-0.214240\pi\) | |||||||
\(242\) | −43.0334 | −0.177824 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 155.373i | 0.636777i | ||||||||
\(245\) | − | 13.2973i | − | 0.0542747i | ||||||
\(246\) | 209.562 | 0.851877 | ||||||||
\(247\) | 191.094i | 0.773659i | ||||||||
\(248\) | 145.466 | 0.586558 | ||||||||
\(249\) | − | 111.181i | − | 0.446511i | ||||||
\(250\) | 211.467i | 0.845868i | ||||||||
\(251\) | 175.805i | 0.700418i | 0.936672 | + | 0.350209i | \(0.113889\pi\) | ||||
−0.936672 | + | 0.350209i | \(0.886111\pi\) | |||||||
\(252\) | − | 13.9544i | − | 0.0553747i | ||||||
\(253\) | 104.536 | − | 250.136i | 0.413185 | − | 0.988680i | ||||
\(254\) | 356.112 | 1.40202 | ||||||||
\(255\) | −76.4110 | −0.299651 | ||||||||
\(256\) | 281.899 | 1.10117 | ||||||||
\(257\) | −258.428 | −1.00556 | −0.502779 | − | 0.864415i | \(-0.667689\pi\) | ||||
−0.502779 | + | 0.864415i | \(0.667689\pi\) | |||||||
\(258\) | 53.2105i | 0.206242i | ||||||||
\(259\) | −95.9149 | −0.370328 | ||||||||
\(260\) | − | 31.7452i | − | 0.122097i | ||||||
\(261\) | −68.7959 | −0.263586 | ||||||||
\(262\) | −88.1871 | −0.336592 | ||||||||
\(263\) | 513.701i | 1.95324i | 0.214981 | + | 0.976618i | \(0.431031\pi\) | ||||
−0.214981 | + | 0.976618i | \(0.568969\pi\) | |||||||
\(264\) | − | 109.830i | − | 0.416023i | ||||||
\(265\) | 82.9408 | 0.312984 | ||||||||
\(266\) | −127.633 | −0.479825 | ||||||||
\(267\) | − | 173.067i | − | 0.648190i | ||||||
\(268\) | − | 33.8743i | − | 0.126397i | ||||||
\(269\) | 328.407 | 1.22085 | 0.610423 | − | 0.792076i | \(-0.291000\pi\) | ||||
0.610423 | + | 0.792076i | \(0.291000\pi\) | |||||||
\(270\) | − | 23.6857i | − | 0.0877249i | ||||||
\(271\) | −524.797 | −1.93652 | −0.968260 | − | 0.249946i | \(-0.919587\pi\) | ||||
−0.968260 | + | 0.249946i | \(0.919587\pi\) | |||||||
\(272\) | 463.114i | 1.70262i | ||||||||
\(273\) | − | 43.5593i | − | 0.159558i | ||||||
\(274\) | 189.123i | 0.690228i | ||||||||
\(275\) | − | 252.141i | − | 0.916878i | ||||||
\(276\) | −64.6212 | − | 27.0063i | −0.234135 | − | 0.0978487i | ||||
\(277\) | −258.121 | −0.931846 | −0.465923 | − | 0.884825i | \(-0.654278\pi\) | ||||
−0.465923 | + | 0.884825i | \(0.654278\pi\) | |||||||
\(278\) | 173.960 | 0.625754 | ||||||||
\(279\) | −81.1198 | −0.290752 | ||||||||
\(280\) | −27.0378 | −0.0965636 | ||||||||
\(281\) | 362.403i | 1.28969i | 0.764313 | + | 0.644845i | \(0.223078\pi\) | ||||
−0.764313 | + | 0.644845i | \(0.776922\pi\) | |||||||
\(282\) | 146.705 | 0.520231 | ||||||||
\(283\) | 33.3103i | 0.117704i | 0.998267 | + | 0.0588521i | \(0.0187440\pi\) | ||||
−0.998267 | + | 0.0588521i | \(0.981256\pi\) | |||||||
\(284\) | 205.222 | 0.722614 | ||||||||
\(285\) | −66.1457 | −0.232090 | ||||||||
\(286\) | 268.852i | 0.940043i | ||||||||
\(287\) | 133.402i | 0.464814i | ||||||||
\(288\) | −78.9986 | −0.274301 | ||||||||
\(289\) | −250.337 | −0.866218 | ||||||||
\(290\) | − | 104.531i | − | 0.360452i | ||||||
\(291\) | − | 85.1588i | − | 0.292642i | ||||||
\(292\) | −43.7472 | −0.149819 | ||||||||
\(293\) | − | 413.973i | − | 1.41288i | −0.707774 | − | 0.706439i | \(-0.750300\pi\) | ||
0.707774 | − | 0.706439i | \(-0.249700\pi\) | |||||||
\(294\) | 29.0936 | 0.0989579 | ||||||||
\(295\) | 40.8587i | 0.138504i | ||||||||
\(296\) | 195.027i | 0.658874i | ||||||||
\(297\) | 61.2471i | 0.206219i | ||||||||
\(298\) | − | 499.504i | − | 1.67619i | ||||||
\(299\) | −201.718 | − | 84.3010i | −0.674641 | − | 0.281943i | ||||
\(300\) | −65.1393 | −0.217131 | ||||||||
\(301\) | −33.8724 | −0.112533 | ||||||||
\(302\) | −12.8407 | −0.0425189 | ||||||||
\(303\) | 11.2029 | 0.0369732 | ||||||||
\(304\) | 400.897i | 1.31874i | ||||||||
\(305\) | −167.881 | −0.550428 | ||||||||
\(306\) | − | 167.182i | − | 0.546348i | ||||||
\(307\) | 322.114 | 1.04923 | 0.524616 | − | 0.851339i | \(-0.324209\pi\) | ||||
0.524616 | + | 0.851339i | \(0.324209\pi\) | |||||||
\(308\) | −54.8270 | −0.178010 | ||||||||
\(309\) | 116.660i | 0.377540i | ||||||||
\(310\) | − | 123.257i | − | 0.397602i | ||||||
\(311\) | 546.043 | 1.75577 | 0.877883 | − | 0.478876i | \(-0.158955\pi\) | ||||
0.877883 | + | 0.478876i | \(0.158955\pi\) | |||||||
\(312\) | −88.5704 | −0.283879 | ||||||||
\(313\) | 159.579i | 0.509836i | 0.966963 | + | 0.254918i | \(0.0820485\pi\) | ||||
−0.966963 | + | 0.254918i | \(0.917952\pi\) | |||||||
\(314\) | − | 385.841i | − | 1.22879i | ||||||
\(315\) | 15.0777 | 0.0478658 | ||||||||
\(316\) | 46.0151i | 0.145617i | ||||||||
\(317\) | 498.849 | 1.57366 | 0.786829 | − | 0.617172i | \(-0.211722\pi\) | ||||
0.786829 | + | 0.617172i | \(0.211722\pi\) | |||||||
\(318\) | 181.469i | 0.570658i | ||||||||
\(319\) | 270.299i | 0.847333i | ||||||||
\(320\) | 31.4908i | 0.0984088i | ||||||||
\(321\) | − | 168.541i | − | 0.525051i | ||||||
\(322\) | 56.3054 | − | 134.729i | 0.174862 | − | 0.418413i | ||||
\(323\) | −466.881 | −1.44545 | ||||||||
\(324\) | 15.8228 | 0.0488359 | ||||||||
\(325\) | −203.335 | −0.625645 | ||||||||
\(326\) | −527.646 | −1.61855 | ||||||||
\(327\) | 258.441i | 0.790340i | ||||||||
\(328\) | 271.250 | 0.826981 | ||||||||
\(329\) | 93.3887i | 0.283856i | ||||||||
\(330\) | −93.0612 | −0.282004 | ||||||||
\(331\) | 83.6420 | 0.252695 | 0.126347 | − | 0.991986i | \(-0.459675\pi\) | ||||
0.126347 | + | 0.991986i | \(0.459675\pi\) | |||||||
\(332\) | 112.853i | 0.339918i | ||||||||
\(333\) | − | 108.757i | − | 0.326598i | ||||||
\(334\) | 397.126 | 1.18900 | ||||||||
\(335\) | 36.6011 | 0.109257 | ||||||||
\(336\) | − | 91.3833i | − | 0.271974i | ||||||
\(337\) | − | 382.659i | − | 1.13549i | −0.823205 | − | 0.567744i | \(-0.807816\pi\) | ||
0.823205 | − | 0.567744i | \(-0.192184\pi\) | |||||||
\(338\) | −188.722 | −0.558349 | ||||||||
\(339\) | 28.2434i | 0.0833139i | ||||||||
\(340\) | 77.5599 | 0.228117 | ||||||||
\(341\) | 318.720i | 0.934663i | ||||||||
\(342\) | − | 144.723i | − | 0.423165i | ||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 68.8738i | 0.200215i | ||||||||
\(345\) | 29.1802 | − | 69.8231i | 0.0845802 | − | 0.202386i | ||||
\(346\) | −462.774 | −1.33750 | ||||||||
\(347\) | −297.380 | −0.857003 | −0.428502 | − | 0.903541i | \(-0.640958\pi\) | ||||
−0.428502 | + | 0.903541i | \(0.640958\pi\) | |||||||
\(348\) | 69.8302 | 0.200662 | ||||||||
\(349\) | 330.611 | 0.947309 | 0.473654 | − | 0.880711i | \(-0.342935\pi\) | ||||
0.473654 | + | 0.880711i | \(0.342935\pi\) | |||||||
\(350\) | − | 135.809i | − | 0.388026i | ||||||
\(351\) | 49.3916 | 0.140717 | ||||||||
\(352\) | 310.386i | 0.881778i | ||||||||
\(353\) | 435.318 | 1.23320 | 0.616598 | − | 0.787278i | \(-0.288510\pi\) | ||||
0.616598 | + | 0.787278i | \(0.288510\pi\) | |||||||
\(354\) | −89.3963 | −0.252532 | ||||||||
\(355\) | 221.742i | 0.624626i | ||||||||
\(356\) | 175.669i | 0.493452i | ||||||||
\(357\) | 106.424 | 0.298107 | ||||||||
\(358\) | −143.211 | −0.400031 | ||||||||
\(359\) | − | 455.565i | − | 1.26898i | −0.772930 | − | 0.634491i | \(-0.781210\pi\) | ||
0.772930 | − | 0.634491i | \(-0.218790\pi\) | |||||||
\(360\) | − | 30.6580i | − | 0.0851611i | ||||||
\(361\) | −43.1583 | −0.119552 | ||||||||
\(362\) | − | 858.075i | − | 2.37037i | ||||||
\(363\) | 31.0618 | 0.0855697 | ||||||||
\(364\) | 44.2142i | 0.121468i | ||||||||
\(365\) | − | 47.2688i | − | 0.129503i | ||||||
\(366\) | − | 367.312i | − | 1.00358i | ||||||
\(367\) | − | 64.4735i | − | 0.175677i | −0.996135 | − | 0.0878385i | \(-0.972004\pi\) | ||
0.996135 | − | 0.0878385i | \(-0.0279960\pi\) | |||||||
\(368\) | −423.185 | − | 176.856i | −1.14996 | − | 0.480586i | ||||
\(369\) | −151.263 | −0.409928 | ||||||||
\(370\) | 165.250 | 0.446622 | ||||||||
\(371\) | −115.519 | −0.311371 | ||||||||
\(372\) | 82.3395 | 0.221343 | ||||||||
\(373\) | − | 317.319i | − | 0.850721i | −0.905024 | − | 0.425360i | \(-0.860147\pi\) | ||
0.905024 | − | 0.425360i | \(-0.139853\pi\) | |||||||
\(374\) | −656.860 | −1.75631 | ||||||||
\(375\) | − | 152.638i | − | 0.407036i | ||||||
\(376\) | 189.890 | 0.505027 | ||||||||
\(377\) | 217.978 | 0.578190 | ||||||||
\(378\) | 32.9891i | 0.0872727i | ||||||||
\(379\) | − | 463.183i | − | 1.22212i | −0.791585 | − | 0.611059i | \(-0.790744\pi\) | ||
0.791585 | − | 0.611059i | \(-0.209256\pi\) | |||||||
\(380\) | 67.1402 | 0.176685 | ||||||||
\(381\) | −257.044 | −0.674657 | ||||||||
\(382\) | 201.000i | 0.526178i | ||||||||
\(383\) | − | 94.3791i | − | 0.246421i | −0.992381 | − | 0.123210i | \(-0.960681\pi\) | ||
0.992381 | − | 0.123210i | \(-0.0393190\pi\) | |||||||
\(384\) | −251.339 | −0.654530 | ||||||||
\(385\) | − | 59.2404i | − | 0.153871i | ||||||
\(386\) | −488.596 | −1.26579 | ||||||||
\(387\) | − | 38.4077i | − | 0.0992447i | ||||||
\(388\) | 86.4391i | 0.222781i | ||||||||
\(389\) | − | 609.706i | − | 1.56737i | −0.621161 | − | 0.783683i | \(-0.713339\pi\) | ||
0.621161 | − | 0.783683i | \(-0.286661\pi\) | |||||||
\(390\) | 75.0475i | 0.192429i | ||||||||
\(391\) | 205.964 | − | 492.837i | 0.526763 | − | 1.26045i | ||||
\(392\) | 37.6578 | 0.0960658 | ||||||||
\(393\) | 63.6541 | 0.161970 | ||||||||
\(394\) | 740.151 | 1.87856 | ||||||||
\(395\) | −49.7192 | −0.125871 | ||||||||
\(396\) | − | 62.1679i | − | 0.156990i | ||||||
\(397\) | −197.643 | −0.497842 | −0.248921 | − | 0.968524i | \(-0.580076\pi\) | ||||
−0.248921 | + | 0.968524i | \(0.580076\pi\) | |||||||
\(398\) | − | 808.480i | − | 2.03136i | ||||||
\(399\) | 92.1267 | 0.230894 | ||||||||
\(400\) | −426.578 | −1.06644 | ||||||||
\(401\) | − | 145.916i | − | 0.363880i | −0.983310 | − | 0.181940i | \(-0.941762\pi\) | ||
0.983310 | − | 0.181940i | \(-0.0582377\pi\) | |||||||
\(402\) | 80.0809i | 0.199206i | ||||||||
\(403\) | 257.026 | 0.637781 | ||||||||
\(404\) | −11.3713 | −0.0281468 | ||||||||
\(405\) | 17.0965i | 0.0422136i | ||||||||
\(406\) | 145.589i | 0.358594i | ||||||||
\(407\) | −427.307 | −1.04990 | ||||||||
\(408\) | − | 216.395i | − | 0.530381i | ||||||
\(409\) | −210.872 | −0.515578 | −0.257789 | − | 0.966201i | \(-0.582994\pi\) | ||||
−0.257789 | + | 0.966201i | \(0.582994\pi\) | |||||||
\(410\) | − | 229.835i | − | 0.560574i | ||||||
\(411\) | − | 136.510i | − | 0.332141i | ||||||
\(412\) | − | 118.414i | − | 0.287413i | ||||||
\(413\) | − | 56.9074i | − | 0.137790i | ||||||
\(414\) | 152.768 | + | 63.8444i | 0.369006 | + | 0.154213i | ||||
\(415\) | −121.937 | −0.293825 | ||||||||
\(416\) | 250.305 | 0.601694 | ||||||||
\(417\) | −125.565 | −0.301116 | ||||||||
\(418\) | −568.615 | −1.36032 | ||||||||
\(419\) | 509.278i | 1.21546i | 0.794143 | + | 0.607731i | \(0.207920\pi\) | ||||
−0.794143 | + | 0.607731i | \(0.792080\pi\) | |||||||
\(420\) | −15.3044 | −0.0364391 | ||||||||
\(421\) | 642.060i | 1.52508i | 0.646940 | + | 0.762541i | \(0.276048\pi\) | ||||
−0.646940 | + | 0.762541i | \(0.723952\pi\) | |||||||
\(422\) | 514.635 | 1.21951 | ||||||||
\(423\) | −105.893 | −0.250338 | ||||||||
\(424\) | 234.888i | 0.553980i | ||||||||
\(425\) | − | 496.788i | − | 1.16891i | ||||||
\(426\) | −485.158 | −1.13887 | ||||||||
\(427\) | 233.821 | 0.547591 | ||||||||
\(428\) | 171.075i | 0.399709i | ||||||||
\(429\) | − | 194.060i | − | 0.452353i | ||||||
\(430\) | 58.3582 | 0.135717 | ||||||||
\(431\) | − | 203.279i | − | 0.471645i | −0.971796 | − | 0.235822i | \(-0.924222\pi\) | ||
0.971796 | − | 0.235822i | \(-0.0757784\pi\) | |||||||
\(432\) | 103.619 | 0.239859 | ||||||||
\(433\) | − | 279.424i | − | 0.645321i | −0.946515 | − | 0.322661i | \(-0.895423\pi\) | ||
0.946515 | − | 0.322661i | \(-0.104577\pi\) | |||||||
\(434\) | 171.670i | 0.395553i | ||||||||
\(435\) | 75.4514i | 0.173451i | ||||||||
\(436\) | − | 262.327i | − | 0.601667i | ||||||
\(437\) | 178.294 | − | 426.627i | 0.407996 | − | 0.976264i | ||||
\(438\) | 103.421 | 0.236121 | ||||||||
\(439\) | 63.9956 | 0.145776 | 0.0728880 | − | 0.997340i | \(-0.476778\pi\) | ||||
0.0728880 | + | 0.997340i | \(0.476778\pi\) | |||||||
\(440\) | −120.455 | −0.273762 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 529.713i | 1.19844i | ||||||||
\(443\) | 602.496 | 1.36004 | 0.680018 | − | 0.733195i | \(-0.261972\pi\) | ||||
0.680018 | + | 0.733195i | \(0.261972\pi\) | |||||||
\(444\) | 110.392i | 0.248632i | ||||||||
\(445\) | −189.810 | −0.426539 | ||||||||
\(446\) | 54.6687 | 0.122576 | ||||||||
\(447\) | 360.546i | 0.806590i | ||||||||
\(448\) | − | 43.8599i | − | 0.0979015i | ||||||
\(449\) | −757.082 | −1.68615 | −0.843075 | − | 0.537796i | \(-0.819257\pi\) | ||||
−0.843075 | + | 0.537796i | \(0.819257\pi\) | |||||||
\(450\) | 153.993 | 0.342207 | ||||||||
\(451\) | 594.314i | 1.31777i | ||||||||
\(452\) | − | 28.6680i | − | 0.0634249i | ||||||
\(453\) | 9.26851 | 0.0204603 | ||||||||
\(454\) | 136.919i | 0.301583i | ||||||||
\(455\) | −47.7733 | −0.104996 | ||||||||
\(456\) | − | 187.324i | − | 0.410798i | ||||||
\(457\) | 466.080i | 1.01987i | 0.860213 | + | 0.509935i | \(0.170330\pi\) | ||||
−0.860213 | + | 0.509935i | \(0.829670\pi\) | |||||||
\(458\) | − | 842.131i | − | 1.83871i | ||||||
\(459\) | 120.674i | 0.262905i | ||||||||
\(460\) | −29.6189 | + | 70.8729i | −0.0643889 | + | 0.154071i | ||||
\(461\) | −512.022 | −1.11068 | −0.555339 | − | 0.831624i | \(-0.687411\pi\) | ||||
−0.555339 | + | 0.831624i | \(0.687411\pi\) | |||||||
\(462\) | 129.614 | 0.280550 | ||||||||
\(463\) | −236.851 | −0.511557 | −0.255779 | − | 0.966735i | \(-0.582332\pi\) | ||||
−0.255779 | + | 0.966735i | \(0.582332\pi\) | |||||||
\(464\) | 457.297 | 0.985554 | ||||||||
\(465\) | 88.9676i | 0.191328i | ||||||||
\(466\) | 474.573 | 1.01840 | ||||||||
\(467\) | 455.178i | 0.974685i | 0.873211 | + | 0.487343i | \(0.162034\pi\) | ||||
−0.873211 | + | 0.487343i | \(0.837966\pi\) | |||||||
\(468\) | −50.1342 | −0.107124 | ||||||||
\(469\) | −50.9774 | −0.108694 | ||||||||
\(470\) | − | 160.898i | − | 0.342336i | ||||||
\(471\) | 278.503i | 0.591301i | ||||||||
\(472\) | −115.712 | −0.245152 | ||||||||
\(473\) | −150.904 | −0.319036 | ||||||||
\(474\) | − | 108.782i | − | 0.229499i | ||||||
\(475\) | − | 430.047i | − | 0.905363i | ||||||
\(476\) | −108.024 | −0.226941 | ||||||||
\(477\) | − | 130.986i | − | 0.274603i | ||||||
\(478\) | 40.2338 | 0.0841711 | ||||||||
\(479\) | − | 5.78512i | − | 0.0120775i | −0.999982 | − | 0.00603874i | \(-0.998078\pi\) | ||
0.999982 | − | 0.00603874i | \(-0.00192220\pi\) | |||||||
\(480\) | 86.6412i | 0.180502i | ||||||||
\(481\) | 344.594i | 0.716412i | ||||||||
\(482\) | − | 721.002i | − | 1.49586i | ||||||
\(483\) | −40.6417 | + | 97.2484i | −0.0841443 | + | 0.201342i | ||||
\(484\) | −31.5288 | −0.0651422 | ||||||||
\(485\) | −93.3972 | −0.192572 | ||||||||
\(486\) | −37.4061 | −0.0769673 | ||||||||
\(487\) | −286.687 | −0.588680 | −0.294340 | − | 0.955701i | \(-0.595100\pi\) | ||||
−0.294340 | + | 0.955701i | \(0.595100\pi\) | |||||||
\(488\) | − | 475.436i | − | 0.974254i | ||||||
\(489\) | 380.859 | 0.778852 | ||||||||
\(490\) | − | 31.9082i | − | 0.0651188i | ||||||
\(491\) | −81.5009 | −0.165990 | −0.0829948 | − | 0.996550i | \(-0.526448\pi\) | ||||
−0.0829948 | + | 0.996550i | \(0.526448\pi\) | |||||||
\(492\) | 153.538 | 0.312068 | ||||||||
\(493\) | 532.563i | 1.08025i | ||||||||
\(494\) | 458.549i | 0.928237i | ||||||||
\(495\) | 67.1723 | 0.135702 | ||||||||
\(496\) | 539.216 | 1.08713 | ||||||||
\(497\) | − | 308.839i | − | 0.621407i | ||||||
\(498\) | − | 266.791i | − | 0.535724i | ||||||
\(499\) | 821.224 | 1.64574 | 0.822870 | − | 0.568230i | \(-0.192372\pi\) | ||||
0.822870 | + | 0.568230i | \(0.192372\pi\) | |||||||
\(500\) | 154.933i | 0.309867i | ||||||||
\(501\) | −286.648 | −0.572152 | ||||||||
\(502\) | 421.862i | 0.840362i | ||||||||
\(503\) | 596.272i | 1.18543i | 0.805412 | + | 0.592716i | \(0.201944\pi\) | ||||
−0.805412 | + | 0.592716i | \(0.798056\pi\) | |||||||
\(504\) | 42.6999i | 0.0847221i | ||||||||
\(505\) | − | 12.2867i | − | 0.0243300i | ||||||
\(506\) | 250.845 | − | 600.227i | 0.495740 | − | 1.18622i | ||||
\(507\) | 136.221 | 0.268680 | ||||||||
\(508\) | 260.909 | 0.513600 | ||||||||
\(509\) | 145.511 | 0.285876 | 0.142938 | − | 0.989732i | \(-0.454345\pi\) | ||||
0.142938 | + | 0.989732i | \(0.454345\pi\) | |||||||
\(510\) | −183.356 | −0.359522 | ||||||||
\(511\) | 65.8352i | 0.128836i | ||||||||
\(512\) | 96.0009 | 0.187502 | ||||||||
\(513\) | 104.462i | 0.203629i | ||||||||
\(514\) | −620.125 | −1.20647 | ||||||||
\(515\) | 127.946 | 0.248439 | ||||||||
\(516\) | 38.9852i | 0.0755526i | ||||||||
\(517\) | 416.053i | 0.804745i | ||||||||
\(518\) | −230.158 | −0.444320 | ||||||||
\(519\) | 334.033 | 0.643610 | ||||||||
\(520\) | 97.1389i | 0.186806i | ||||||||
\(521\) | − | 757.208i | − | 1.45337i | −0.686968 | − | 0.726687i | \(-0.741059\pi\) | ||
0.686968 | − | 0.726687i | \(-0.258941\pi\) | |||||||
\(522\) | −165.083 | −0.316251 | ||||||||
\(523\) | 291.346i | 0.557066i | 0.960427 | + | 0.278533i | \(0.0898482\pi\) | ||||
−0.960427 | + | 0.278533i | \(0.910152\pi\) | |||||||
\(524\) | −64.6111 | −0.123304 | ||||||||
\(525\) | 98.0280i | 0.186720i | ||||||||
\(526\) | 1232.68i | 2.34350i | ||||||||
\(527\) | 627.966i | 1.19159i | ||||||||
\(528\) | − | 407.119i | − | 0.771059i | ||||||
\(529\) | 371.691 | + | 376.413i | 0.702629 | + | 0.711556i | ||||
\(530\) | 199.025 | 0.375519 | ||||||||
\(531\) | 64.5269 | 0.121520 | ||||||||
\(532\) | −93.5118 | −0.175774 | ||||||||
\(533\) | 479.273 | 0.899199 | ||||||||
\(534\) | − | 415.291i | − | 0.777699i | ||||||
\(535\) | −184.847 | −0.345508 | ||||||||
\(536\) | 103.654i | 0.193384i | ||||||||
\(537\) | 103.371 | 0.192497 | ||||||||
\(538\) | 788.047 | 1.46477 | ||||||||
\(539\) | 82.5090i | 0.153078i | ||||||||
\(540\) | − | 17.3536i | − | 0.0321362i | ||||||
\(541\) | −361.351 | −0.667931 | −0.333966 | − | 0.942585i | \(-0.608387\pi\) | ||||
−0.333966 | + | 0.942585i | \(0.608387\pi\) | |||||||
\(542\) | −1259.30 | −2.32344 | ||||||||
\(543\) | 619.365i | 1.14064i | ||||||||
\(544\) | 611.545i | 1.12416i | ||||||||
\(545\) | 283.443 | 0.520080 | ||||||||
\(546\) | − | 104.525i | − | 0.191438i | ||||||
\(547\) | 536.912 | 0.981558 | 0.490779 | − | 0.871284i | \(-0.336712\pi\) | ||||
0.490779 | + | 0.871284i | \(0.336712\pi\) | |||||||
\(548\) | 138.562i | 0.252851i | ||||||||
\(549\) | 265.129i | 0.482930i | ||||||||
\(550\) | − | 605.039i | − | 1.10007i | ||||||
\(551\) | 461.017i | 0.836691i | ||||||||
\(552\) | 197.738 | + | 82.6380i | 0.358221 | + | 0.149706i | ||||
\(553\) | 69.2481 | 0.125223 | ||||||||
\(554\) | −619.389 | −1.11803 | ||||||||
\(555\) | −119.279 | −0.214917 | ||||||||
\(556\) | 127.453 | 0.229233 | ||||||||
\(557\) | 915.897i | 1.64434i | 0.569242 | + | 0.822170i | \(0.307237\pi\) | ||||
−0.569242 | + | 0.822170i | \(0.692763\pi\) | |||||||
\(558\) | −194.655 | −0.348845 | ||||||||
\(559\) | 121.694i | 0.217699i | ||||||||
\(560\) | −100.224 | −0.178971 | ||||||||
\(561\) | 474.127 | 0.845145 | ||||||||
\(562\) | 869.623i | 1.54737i | ||||||||
\(563\) | 676.872i | 1.20226i | 0.799152 | + | 0.601130i | \(0.205282\pi\) | ||||
−0.799152 | + | 0.601130i | \(0.794718\pi\) | |||||||
\(564\) | 107.485 | 0.190576 | ||||||||
\(565\) | 30.9757 | 0.0548243 | ||||||||
\(566\) | 79.9314i | 0.141222i | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | −627.972 | −1.10558 | ||||||||
\(569\) | − | 726.413i | − | 1.27665i | −0.769767 | − | 0.638325i | \(-0.779628\pi\) | ||
0.769767 | − | 0.638325i | \(-0.220372\pi\) | |||||||
\(570\) | −158.723 | −0.278462 | ||||||||
\(571\) | 281.192i | 0.492455i | 0.969212 | + | 0.246227i | \(0.0791910\pi\) | ||||
−0.969212 | + | 0.246227i | \(0.920809\pi\) | |||||||
\(572\) | 196.977i | 0.344366i | ||||||||
\(573\) | − | 145.083i | − | 0.253200i | ||||||
\(574\) | 320.111i | 0.557685i | ||||||||
\(575\) | 453.956 | + | 189.715i | 0.789488 | + | 0.329940i | ||||
\(576\) | 49.7324 | 0.0863410 | ||||||||
\(577\) | 962.280 | 1.66773 | 0.833865 | − | 0.551969i | \(-0.186123\pi\) | ||||
0.833865 | + | 0.551969i | \(0.186123\pi\) | |||||||
\(578\) | −600.709 | −1.03929 | ||||||||
\(579\) | 352.673 | 0.609106 | ||||||||
\(580\) | − | 76.5858i | − | 0.132044i | ||||||
\(581\) | 169.832 | 0.292310 | ||||||||
\(582\) | − | 204.347i | − | 0.351112i | ||||||
\(583\) | −514.644 | −0.882751 | ||||||||
\(584\) | 133.865 | 0.229220 | ||||||||
\(585\) | − | 54.1698i | − | 0.0925980i | ||||||
\(586\) | − | 993.372i | − | 1.69517i | ||||||
\(587\) | −105.339 | −0.179452 | −0.0897262 | − | 0.995966i | \(-0.528599\pi\) | ||||
−0.0897262 | + | 0.995966i | \(0.528599\pi\) | |||||||
\(588\) | 21.3157 | 0.0362513 | ||||||||
\(589\) | 543.603i | 0.922925i | ||||||||
\(590\) | 98.0447i | 0.166177i | ||||||||
\(591\) | −534.247 | −0.903970 | ||||||||
\(592\) | 722.927i | 1.22116i | ||||||||
\(593\) | 28.3074 | 0.0477359 | 0.0238680 | − | 0.999715i | \(-0.492402\pi\) | ||||
0.0238680 | + | 0.999715i | \(0.492402\pi\) | |||||||
\(594\) | 146.969i | 0.247422i | ||||||||
\(595\) | − | 116.720i | − | 0.196168i | ||||||
\(596\) | − | 365.967i | − | 0.614038i | ||||||
\(597\) | 583.567i | 0.977499i | ||||||||
\(598\) | −484.042 | − | 202.289i | −0.809435 | − | 0.338276i | ||||
\(599\) | −175.103 | −0.292325 | −0.146162 | − | 0.989261i | \(-0.546692\pi\) | ||||
−0.146162 | + | 0.989261i | \(0.546692\pi\) | |||||||
\(600\) | 199.323 | 0.332206 | ||||||||
\(601\) | 155.499 | 0.258734 | 0.129367 | − | 0.991597i | \(-0.458705\pi\) | ||||
0.129367 | + | 0.991597i | \(0.458705\pi\) | |||||||
\(602\) | −81.2803 | −0.135017 | ||||||||
\(603\) | − | 57.8030i | − | 0.0958590i | ||||||
\(604\) | −9.40786 | −0.0155759 | ||||||||
\(605\) | − | 34.0668i | − | 0.0563087i | ||||||
\(606\) | 26.8824 | 0.0443605 | ||||||||
\(607\) | 562.737 | 0.927079 | 0.463540 | − | 0.886076i | \(-0.346579\pi\) | ||||
0.463540 | + | 0.886076i | \(0.346579\pi\) | |||||||
\(608\) | 529.388i | 0.870704i | ||||||||
\(609\) | − | 105.087i | − | 0.172557i | ||||||
\(610\) | −402.847 | −0.660404 | ||||||||
\(611\) | 335.518 | 0.549130 | ||||||||
\(612\) | − | 122.488i | − | 0.200144i | ||||||
\(613\) | − | 1112.46i | − | 1.81478i | −0.420288 | − | 0.907391i | \(-0.638071\pi\) | ||
0.420288 | − | 0.907391i | \(-0.361929\pi\) | |||||||
\(614\) | 772.947 | 1.25887 | ||||||||
\(615\) | 165.897i | 0.269751i | ||||||||
\(616\) | 167.768 | 0.272351 | ||||||||
\(617\) | 670.161i | 1.08616i | 0.839681 | + | 0.543080i | \(0.182742\pi\) | ||||
−0.839681 | + | 0.543080i | \(0.817258\pi\) | |||||||
\(618\) | 279.938i | 0.452974i | ||||||||
\(619\) | 631.709i | 1.02053i | 0.860017 | + | 0.510266i | \(0.170453\pi\) | ||||
−0.860017 | + | 0.510266i | \(0.829547\pi\) | |||||||
\(620\) | − | 90.3052i | − | 0.145654i | ||||||
\(621\) | −110.269 | − | 46.0833i | −0.177567 | − | 0.0742083i | ||||
\(622\) | 1310.29 | 2.10657 | ||||||||
\(623\) | 264.364 | 0.424340 | ||||||||
\(624\) | −328.314 | −0.526144 | ||||||||
\(625\) | 367.382 | 0.587810 | ||||||||
\(626\) | 382.925i | 0.611702i | ||||||||
\(627\) | 410.431 | 0.654595 | ||||||||
\(628\) | − | 282.690i | − | 0.450144i | ||||||
\(629\) | −841.913 | −1.33849 | ||||||||
\(630\) | 36.1805 | 0.0574294 | ||||||||
\(631\) | 7.16238i | 0.0113508i | 0.999984 | + | 0.00567542i | \(0.00180655\pi\) | ||||
−0.999984 | + | 0.00567542i | \(0.998193\pi\) | |||||||
\(632\) | − | 140.804i | − | 0.222792i | ||||||
\(633\) | −371.467 | −0.586836 | ||||||||
\(634\) | 1197.04 | 1.88808 | ||||||||
\(635\) | 281.911i | 0.443955i | ||||||||
\(636\) | 132.955i | 0.209049i | ||||||||
\(637\) | 66.5379 | 0.104455 | ||||||||
\(638\) | 648.611i | 1.01663i | ||||||||
\(639\) | 350.191 | 0.548029 | ||||||||
\(640\) | 275.655i | 0.430710i | ||||||||
\(641\) | 857.091i | 1.33711i | 0.743661 | + | 0.668557i | \(0.233088\pi\) | ||||
−0.743661 | + | 0.668557i | \(0.766912\pi\) | |||||||
\(642\) | − | 404.432i | − | 0.629957i | ||||||
\(643\) | − | 582.061i | − | 0.905227i | −0.891707 | − | 0.452613i | \(-0.850492\pi\) | ||
0.891707 | − | 0.452613i | \(-0.149508\pi\) | |||||||
\(644\) | 41.2527 | − | 98.7106i | 0.0640570 | − | 0.153277i | ||||
\(645\) | −42.1234 | −0.0653075 | ||||||||
\(646\) | −1120.33 | −1.73425 | ||||||||
\(647\) | 798.806 | 1.23463 | 0.617315 | − | 0.786716i | \(-0.288220\pi\) | ||||
0.617315 | + | 0.786716i | \(0.288220\pi\) | |||||||
\(648\) | −48.4172 | −0.0747179 | ||||||||
\(649\) | − | 253.526i | − | 0.390641i | ||||||
\(650\) | −487.922 | −0.750650 | ||||||||
\(651\) | − | 123.913i | − | 0.190342i | ||||||
\(652\) | −386.585 | −0.592921 | ||||||||
\(653\) | −429.160 | −0.657213 | −0.328607 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328607 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(654\) | 620.156i | 0.948251i | ||||||||
\(655\) | − | 69.8121i | − | 0.106583i | ||||||
\(656\) | 1005.47 | 1.53273 | ||||||||
\(657\) | −74.6501 | −0.113623 | ||||||||
\(658\) | 224.096i | 0.340571i | ||||||||
\(659\) | − | 799.463i | − | 1.21315i | −0.795028 | − | 0.606573i | \(-0.792544\pi\) | ||
0.795028 | − | 0.606573i | \(-0.207456\pi\) | |||||||
\(660\) | −68.1822 | −0.103306 | ||||||||
\(661\) | − | 112.845i | − | 0.170718i | −0.996350 | − | 0.0853590i | \(-0.972796\pi\) | ||
0.996350 | − | 0.0853590i | \(-0.0272037\pi\) | |||||||
\(662\) | 200.707 | 0.303183 | ||||||||
\(663\) | − | 382.350i | − | 0.576698i | ||||||
\(664\) | − | 345.325i | − | 0.520068i | ||||||
\(665\) | − | 101.039i | − | 0.151939i | ||||||
\(666\) | − | 260.974i | − | 0.391853i | ||||||
\(667\) | −486.647 | − | 203.378i | −0.729606 | − | 0.304914i | ||||
\(668\) | 290.958 | 0.435566 | ||||||||
\(669\) | −39.4603 | −0.0589839 | ||||||||
\(670\) | 87.8281 | 0.131087 | ||||||||
\(671\) | 1041.69 | 1.55244 | ||||||||
\(672\) | − | 120.672i | − | 0.179572i | ||||||
\(673\) | −32.4266 | −0.0481822 | −0.0240911 | − | 0.999710i | \(-0.507669\pi\) | ||||
−0.0240911 | + | 0.999710i | \(0.507669\pi\) | |||||||
\(674\) | − | 918.230i | − | 1.36236i | ||||||
\(675\) | −111.153 | −0.164672 | ||||||||
\(676\) | −138.269 | −0.204540 | ||||||||
\(677\) | 621.675i | 0.918279i | 0.888364 | + | 0.459139i | \(0.151842\pi\) | ||||
−0.888364 | + | 0.459139i | \(0.848158\pi\) | |||||||
\(678\) | 67.7729i | 0.0999601i | ||||||||
\(679\) | 130.082 | 0.191579 | ||||||||
\(680\) | −237.330 | −0.349015 | ||||||||
\(681\) | − | 98.8290i | − | 0.145123i | ||||||
\(682\) | 764.801i | 1.12141i | ||||||||
\(683\) | 111.256 | 0.162894 | 0.0814468 | − | 0.996678i | \(-0.474046\pi\) | ||||
0.0814468 | + | 0.996678i | \(0.474046\pi\) | |||||||
\(684\) | − | 106.032i | − | 0.155018i | ||||||
\(685\) | −149.716 | −0.218564 | ||||||||
\(686\) | 44.4413i | 0.0647832i | ||||||||
\(687\) | 607.856i | 0.884798i | ||||||||
\(688\) | 255.302i | 0.371079i | ||||||||
\(689\) | 415.025i | 0.602358i | ||||||||
\(690\) | 70.0208 | − | 167.548i | 0.101479 | − | 0.242823i | ||||
\(691\) | 123.165 | 0.178242 | 0.0891209 | − | 0.996021i | \(-0.471594\pi\) | ||||
0.0891209 | + | 0.996021i | \(0.471594\pi\) | |||||||
\(692\) | −339.056 | −0.489965 | ||||||||
\(693\) | −93.5565 | −0.135002 | ||||||||
\(694\) | −713.594 | −1.02823 | ||||||||
\(695\) | 137.713i | 0.198148i | ||||||||
\(696\) | −213.678 | −0.307008 | ||||||||
\(697\) | 1170.96i | 1.68000i | ||||||||
\(698\) | 793.334 | 1.13658 | ||||||||
\(699\) | −342.550 | −0.490058 | ||||||||
\(700\) | − | 99.5019i | − | 0.142146i | ||||||
\(701\) | − | 1207.42i | − | 1.72242i | −0.508247 | − | 0.861211i | \(-0.669706\pi\) | ||
0.508247 | − | 0.861211i | \(-0.330294\pi\) | |||||||
\(702\) | 118.520 | 0.168832 | ||||||||
\(703\) | −728.807 | −1.03671 | ||||||||
\(704\) | − | 195.399i | − | 0.277555i | ||||||
\(705\) | 116.137i | 0.164734i | ||||||||
\(706\) | 1044.59 | 1.47959 | ||||||||
\(707\) | 17.1127i | 0.0242046i | ||||||||
\(708\) | −65.4971 | −0.0925100 | ||||||||
\(709\) | 1165.00i | 1.64315i | 0.570098 | + | 0.821576i | \(0.306905\pi\) | ||||
−0.570098 | + | 0.821576i | \(0.693095\pi\) | |||||||
\(710\) | 532.093i | 0.749427i | ||||||||
\(711\) | 78.5200i | 0.110436i | ||||||||
\(712\) | − | 537.539i | − | 0.754970i | ||||||
\(713\) | −573.824 | − | 239.810i | −0.804802 | − | 0.336340i | ||||
\(714\) | 255.375 | 0.357669 | ||||||||
\(715\) | −212.833 | −0.297669 | ||||||||
\(716\) | −104.925 | −0.146543 | ||||||||
\(717\) | −29.0410 | −0.0405035 | ||||||||
\(718\) | − | 1093.17i | − | 1.52253i | ||||||
\(719\) | −341.047 | −0.474335 | −0.237167 | − | 0.971469i | \(-0.576219\pi\) | ||||
−0.237167 | + | 0.971469i | \(0.576219\pi\) | |||||||
\(720\) | − | 113.643i | − | 0.157838i | ||||||
\(721\) | −178.201 | −0.247158 | ||||||||
\(722\) | −103.563 | −0.143439 | ||||||||
\(723\) | 520.425i | 0.719813i | ||||||||
\(724\) | − | 628.677i | − | 0.868339i | ||||||
\(725\) | −490.548 | −0.676618 | ||||||||
\(726\) | 74.5360 | 0.102667 | ||||||||
\(727\) | 970.051i | 1.33432i | 0.744914 | + | 0.667160i | \(0.232490\pi\) | ||||
−0.744914 | + | 0.667160i | \(0.767510\pi\) | |||||||
\(728\) | − | 135.293i | − | 0.185843i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 113.426i | − | 0.155378i | ||||||
\(731\) | −297.322 | −0.406733 | ||||||||
\(732\) | − | 269.115i | − | 0.367643i | ||||||
\(733\) | − | 399.314i | − | 0.544766i | −0.962189 | − | 0.272383i | \(-0.912188\pi\) | ||
0.962189 | − | 0.272383i | \(-0.0878118\pi\) | |||||||
\(734\) | − | 154.711i | − | 0.210778i | ||||||
\(735\) | 23.0316i | 0.0313355i | ||||||||
\(736\) | −558.819 | − | 233.539i | −0.759265 | − | 0.317309i | ||||
\(737\) | −227.108 | −0.308152 | ||||||||
\(738\) | −362.972 | −0.491832 | ||||||||
\(739\) | −352.600 | −0.477131 | −0.238565 | − | 0.971126i | \(-0.576677\pi\) | ||||
−0.238565 | + | 0.971126i | \(0.576677\pi\) | |||||||
\(740\) | 121.072 | 0.163611 | ||||||||
\(741\) | − | 330.984i | − | 0.446672i | ||||||
\(742\) | −277.199 | −0.373583 | ||||||||
\(743\) | 1220.21i | 1.64228i | 0.570727 | + | 0.821140i | \(0.306661\pi\) | ||||
−0.570727 | + | 0.821140i | \(0.693339\pi\) | |||||||
\(744\) | −251.955 | −0.338650 | ||||||||
\(745\) | 395.426 | 0.530773 | ||||||||
\(746\) | − | 761.439i | − | 1.02070i | ||||||
\(747\) | 192.572i | 0.257793i | ||||||||
\(748\) | −481.255 | −0.643389 | ||||||||
\(749\) | 257.451 | 0.343727 | ||||||||
\(750\) | − | 366.272i | − | 0.488362i | ||||||
\(751\) | − | 966.244i | − | 1.28661i | −0.765610 | − | 0.643305i | \(-0.777563\pi\) | ||
0.765610 | − | 0.643305i | \(-0.222437\pi\) | |||||||
\(752\) | 703.887 | 0.936020 | ||||||||
\(753\) | − | 304.503i | − | 0.404386i | ||||||
\(754\) | 523.060 | 0.693713 | ||||||||
\(755\) | − | 10.1652i | − | 0.0134638i | ||||||
\(756\) | 24.1698i | 0.0319706i | ||||||||
\(757\) | − | 426.679i | − | 0.563644i | −0.959467 | − | 0.281822i | \(-0.909061\pi\) | ||
0.959467 | − | 0.281822i | \(-0.0909388\pi\) | |||||||
\(758\) | − | 1111.45i | − | 1.46630i | ||||||
\(759\) | −181.062 | + | 433.248i | −0.238553 | + | 0.570815i | ||||
\(760\) | −205.446 | −0.270324 | ||||||||
\(761\) | 10.0740 | 0.0132379 | 0.00661894 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661894 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(762\) | −616.804 | −0.809454 | ||||||||
\(763\) | −394.775 | −0.517399 | ||||||||
\(764\) | 147.265i | 0.192755i | ||||||||
\(765\) | 132.348 | 0.173004 | ||||||||
\(766\) | − | 226.472i | − | 0.295656i | ||||||
\(767\) | −204.452 | −0.266560 | ||||||||
\(768\) | −488.263 | −0.635759 | ||||||||
\(769\) | − | 242.409i | − | 0.315226i | −0.987501 | − | 0.157613i | \(-0.949620\pi\) | ||
0.987501 | − | 0.157613i | \(-0.0503799\pi\) | |||||||
\(770\) | − | 142.153i | − | 0.184615i | ||||||
\(771\) | 447.611 | 0.580559 | ||||||||
\(772\) | −357.975 | −0.463698 | ||||||||
\(773\) | − | 826.460i | − | 1.06916i | −0.845118 | − | 0.534579i | \(-0.820470\pi\) | ||
0.845118 | − | 0.534579i | \(-0.179530\pi\) | |||||||
\(774\) | − | 92.1632i | − | 0.119074i | ||||||
\(775\) | −578.424 | −0.746354 | ||||||||
\(776\) | − | 264.500i | − | 0.340851i | ||||||
\(777\) | 166.129 | 0.213809 | ||||||||
\(778\) | − | 1463.05i | − | 1.88053i | ||||||
\(779\) | 1013.65i | 1.30122i | ||||||||
\(780\) | 54.9843i | 0.0704927i | ||||||||
\(781\) | − | 1375.90i | − | 1.76172i | ||||||
\(782\) | 494.233 | − | 1182.61i | 0.632011 | − | 1.51229i | ||||
\(783\) | 119.158 | 0.152181 | ||||||||
\(784\) | 139.590 | 0.178049 | ||||||||
\(785\) | 305.446 | 0.389103 | ||||||||
\(786\) | 152.744 | 0.194331 | ||||||||
\(787\) | − | 1271.91i | − | 1.61614i | −0.589084 | − | 0.808072i | \(-0.700511\pi\) | ||
0.589084 | − | 0.808072i | \(-0.299489\pi\) | |||||||
\(788\) | 542.279 | 0.688171 | ||||||||
\(789\) | − | 889.757i | − | 1.12770i | ||||||
\(790\) | −119.306 | −0.151021 | ||||||||
\(791\) | −43.1425 | −0.0545417 | ||||||||
\(792\) | 190.231i | 0.240191i | ||||||||
\(793\) | − | 840.052i | − | 1.05933i | ||||||
\(794\) | −474.266 | −0.597312 | ||||||||
\(795\) | −143.658 | −0.180702 | ||||||||
\(796\) | − | 592.341i | − | 0.744147i | ||||||
\(797\) | 322.055i | 0.404084i | 0.979377 | + | 0.202042i | \(0.0647578\pi\) | ||||
−0.979377 | + | 0.202042i | \(0.935242\pi\) | |||||||
\(798\) | 221.067 | 0.277027 | ||||||||
\(799\) | 819.739i | 1.02596i | ||||||||
\(800\) | −563.299 | −0.704124 | ||||||||
\(801\) | 299.760i | 0.374233i | ||||||||
\(802\) | − | 350.140i | − | 0.436584i | ||||||
\(803\) | 293.300i | 0.365256i | ||||||||
\(804\) | 58.6720i | 0.0729752i | ||||||||
\(805\) | 106.656 | + | 44.5735i | 0.132493 | + | 0.0553708i | ||||
\(806\) | 616.760 | 0.765210 | ||||||||
\(807\) | −568.818 | −0.704855 | ||||||||
\(808\) | 34.7957 | 0.0430640 | ||||||||
\(809\) | −906.479 | −1.12049 | −0.560246 | − | 0.828326i | \(-0.689294\pi\) | ||||
−0.560246 | + | 0.828326i | \(0.689294\pi\) | |||||||
\(810\) | 41.0249i | 0.0506480i | ||||||||
\(811\) | −37.9719 | −0.0468211 | −0.0234106 | − | 0.999726i | \(-0.507452\pi\) | ||||
−0.0234106 | + | 0.999726i | \(0.507452\pi\) | |||||||
\(812\) | 106.667i | 0.131364i | ||||||||
\(813\) | 908.975 | 1.11805 | ||||||||
\(814\) | −1025.37 | −1.25967 | ||||||||
\(815\) | − | 417.704i | − | 0.512520i | ||||||
\(816\) | − | 802.136i | − | 0.983010i | ||||||
\(817\) | −257.379 | −0.315029 | ||||||||
\(818\) | −506.008 | −0.618592 | ||||||||
\(819\) | 75.4469i | 0.0921207i | ||||||||
\(820\) | − | 168.391i | − | 0.205355i | ||||||
\(821\) | −401.596 | −0.489154 | −0.244577 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244577 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(822\) | − | 327.570i | − | 0.398503i | ||||||
\(823\) | 92.9808 | 0.112978 | 0.0564889 | − | 0.998403i | \(-0.482009\pi\) | ||||
0.0564889 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(824\) | 362.342i | 0.439735i | ||||||||
\(825\) | 436.722i | 0.529360i | ||||||||
\(826\) | − | 136.555i | − | 0.165321i | ||||||
\(827\) | − | 23.9802i | − | 0.0289966i | −0.999895 | − | 0.0144983i | \(-0.995385\pi\) | ||
0.999895 | − | 0.0144983i | \(-0.00461512\pi\) | |||||||
\(828\) | 111.927 | + | 46.7762i | 0.135178 | + | 0.0564930i | ||||
\(829\) | 984.055 | 1.18704 | 0.593519 | − | 0.804820i | \(-0.297738\pi\) | ||||
0.593519 | + | 0.804820i | \(0.297738\pi\) | |||||||
\(830\) | −292.601 | −0.352531 | ||||||||
\(831\) | 447.079 | 0.538002 | ||||||||
\(832\) | −157.576 | −0.189394 | ||||||||
\(833\) | 162.565i | 0.195157i | ||||||||
\(834\) | −301.307 | −0.361279 | ||||||||
\(835\) | 314.379i | 0.376502i | ||||||||
\(836\) | −416.602 | −0.498327 | ||||||||
\(837\) | 140.504 | 0.167866 | ||||||||
\(838\) | 1222.07i | 1.45831i | ||||||||
\(839\) | − | 640.165i | − | 0.763010i | −0.924367 | − | 0.381505i | \(-0.875406\pi\) | ||
0.924367 | − | 0.381505i | \(-0.124594\pi\) | |||||||
\(840\) | 46.8308 | 0.0557510 | ||||||||
\(841\) | −315.125 | −0.374703 | ||||||||
\(842\) | 1540.69i | 1.82980i | ||||||||
\(843\) | − | 627.700i | − | 0.744603i | ||||||
\(844\) | 377.053 | 0.446745 | ||||||||
\(845\) | − | 149.399i | − | 0.176804i | ||||||
\(846\) | −254.101 | −0.300356 | ||||||||
\(847\) | 47.4477i | 0.0560185i | ||||||||
\(848\) | 870.684i | 1.02675i | ||||||||
\(849\) | − | 57.6951i | − | 0.0679565i | ||||||
\(850\) | − | 1192.09i | − | 1.40246i | ||||||
\(851\) | 321.513 | − | 769.325i | 0.377806 | − | 0.904025i | ||||
\(852\) | −355.456 | −0.417202 | ||||||||
\(853\) | 677.711 | 0.794503 | 0.397252 | − | 0.917710i | \(-0.369964\pi\) | ||||
0.397252 | + | 0.917710i | \(0.369964\pi\) | |||||||
\(854\) | 561.078 | 0.657000 | ||||||||
\(855\) | 114.568 | 0.133997 | ||||||||
\(856\) | − | 523.484i | − | 0.611546i | ||||||
\(857\) | 194.493 | 0.226946 | 0.113473 | − | 0.993541i | \(-0.463802\pi\) | ||||
0.113473 | + | 0.993541i | \(0.463802\pi\) | |||||||
\(858\) | − | 465.666i | − | 0.542734i | ||||||
\(859\) | −894.039 | −1.04079 | −0.520395 | − | 0.853926i | \(-0.674215\pi\) | ||||
−0.520395 | + | 0.853926i | \(0.674215\pi\) | |||||||
\(860\) | 42.7567 | 0.0497171 | ||||||||
\(861\) | − | 231.058i | − | 0.268361i | ||||||
\(862\) | − | 487.789i | − | 0.565880i | ||||||
\(863\) | 190.049 | 0.220219 | 0.110109 | − | 0.993919i | \(-0.464880\pi\) | ||||
0.110109 | + | 0.993919i | \(0.464880\pi\) | |||||||
\(864\) | 136.830 | 0.158368 | ||||||||
\(865\) | − | 366.349i | − | 0.423524i | ||||||
\(866\) | − | 670.507i | − | 0.774257i | ||||||
\(867\) | 433.596 | 0.500111 | ||||||||
\(868\) | 125.776i | 0.144903i | ||||||||
\(869\) | 308.505 | 0.355012 | ||||||||
\(870\) | 181.053i | 0.208107i | ||||||||
\(871\) | 183.147i | 0.210272i | ||||||||
\(872\) | 802.709i | 0.920538i | ||||||||
\(873\) | 147.499i | 0.168957i | ||||||||
\(874\) | 427.836 | − | 1023.74i | 0.489515 | − | 1.17132i | ||||
\(875\) | 233.159 | 0.266468 | ||||||||
\(876\) | 75.7724 | 0.0864982 | ||||||||
\(877\) | −849.024 | −0.968101 | −0.484050 | − | 0.875040i | \(-0.660835\pi\) | ||||
−0.484050 | + | 0.875040i | \(0.660835\pi\) | |||||||
\(878\) | 153.564 | 0.174902 | ||||||||
\(879\) | 717.023i | 0.815726i | ||||||||
\(880\) | −446.505 | −0.507392 | ||||||||
\(881\) | 1068.08i | 1.21235i | 0.795330 | + | 0.606176i | \(0.207297\pi\) | ||||
−0.795330 | + | 0.606176i | \(0.792703\pi\) | |||||||
\(882\) | −50.3917 | −0.0571334 | ||||||||
\(883\) | −14.2405 | −0.0161274 | −0.00806368 | − | 0.999967i | \(-0.502567\pi\) | ||||
−0.00806368 | + | 0.999967i | \(0.502567\pi\) | |||||||
\(884\) | 388.099i | 0.439026i | ||||||||
\(885\) | − | 70.7694i | − | 0.0799654i | ||||||
\(886\) | 1445.75 | 1.63177 | ||||||||
\(887\) | 608.195 | 0.685676 | 0.342838 | − | 0.939395i | \(-0.388612\pi\) | ||||
0.342838 | + | 0.939395i | \(0.388612\pi\) | |||||||
\(888\) | − | 337.796i | − | 0.380401i | ||||||
\(889\) | − | 392.642i | − | 0.441667i | ||||||
\(890\) | −455.468 | −0.511761 | ||||||||
\(891\) | − | 106.083i | − | 0.119061i | ||||||
\(892\) | 40.0535 | 0.0449031 | ||||||||
\(893\) | 709.613i | 0.794639i | ||||||||
\(894\) | 865.167i | 0.967748i | ||||||||
\(895\) | − | 113.371i | − | 0.126672i | ||||||
\(896\) | − | 383.927i | − | 0.428490i | ||||||
\(897\) | 349.385 | + | 146.014i | 0.389504 | + | 0.162780i | ||||
\(898\) | −1816.69 | −2.02305 | ||||||||
\(899\) | 620.079 | 0.689743 | ||||||||
\(900\) | 112.825 | 0.125361 | ||||||||
\(901\) | −1013.99 | −1.12540 | ||||||||
\(902\) | 1426.12i | 1.58106i | ||||||||
\(903\) | 58.6687 | 0.0649709 | ||||||||
\(904\) | 87.7230i | 0.0970387i | ||||||||
\(905\) | 679.284 | 0.750590 | ||||||||
\(906\) | 22.2407 | 0.0245483 | ||||||||
\(907\) | − | 256.082i | − | 0.282339i | −0.989985 | − | 0.141170i | \(-0.954914\pi\) | ||
0.989985 | − | 0.141170i | \(-0.0450863\pi\) | |||||||
\(908\) | 100.315i | 0.110479i | ||||||||
\(909\) | −19.4039 | −0.0213465 | ||||||||
\(910\) | −114.637 | −0.125975 | ||||||||
\(911\) | − | 358.680i | − | 0.393721i | −0.980431 | − | 0.196861i | \(-0.936925\pi\) | ||
0.980431 | − | 0.196861i | \(-0.0630746\pi\) | |||||||
\(912\) | − | 694.375i | − | 0.761376i | ||||||
\(913\) | 756.614 | 0.828712 | ||||||||
\(914\) | 1118.41i | 1.22364i | ||||||||
\(915\) | 290.778 | 0.317790 | ||||||||
\(916\) | − | 616.996i | − | 0.673576i | ||||||
\(917\) | 97.2332i | 0.106034i | ||||||||
\(918\) | 289.568i | 0.315434i | ||||||||
\(919\) | 852.534i | 0.927676i | 0.885920 | + | 0.463838i | \(0.153528\pi\) | ||||
−0.885920 | + | 0.463838i | \(0.846472\pi\) | |||||||
\(920\) | 90.6326 | − | 216.868i | 0.0985137 | − | 0.235726i | ||||
\(921\) | −557.919 | −0.605775 | ||||||||
\(922\) | −1228.65 | −1.33259 | ||||||||
\(923\) | −1109.57 | −1.20213 | ||||||||
\(924\) | 94.9631 | 0.102774 | ||||||||
\(925\) | − | 775.492i | − | 0.838370i | ||||||
\(926\) | −568.348 | −0.613767 | ||||||||
\(927\) | − | 202.061i | − | 0.217973i | ||||||
\(928\) | 603.864 | 0.650716 | ||||||||
\(929\) | −1365.22 | −1.46956 | −0.734781 | − | 0.678304i | \(-0.762715\pi\) | ||||
−0.734781 | + | 0.678304i | \(0.762715\pi\) | |||||||
\(930\) | 213.487i | 0.229556i | ||||||||
\(931\) | 140.726i | 0.151156i | ||||||||
\(932\) | 347.701 | 0.373069 | ||||||||
\(933\) | −945.774 | −1.01369 | ||||||||
\(934\) | 1092.25i | 1.16943i | ||||||||
\(935\) | − | 519.995i | − | 0.556144i | ||||||
\(936\) | 153.408 | 0.163898 | ||||||||
\(937\) | 849.124i | 0.906215i | 0.891456 | + | 0.453108i | \(0.149685\pi\) | ||||
−0.891456 | + | 0.453108i | \(0.850315\pi\) | |||||||
\(938\) | −122.326 | −0.130411 | ||||||||
\(939\) | − | 276.398i | − | 0.294354i | ||||||
\(940\) | − | 117.883i | − | 0.125408i | ||||||
\(941\) | − | 1017.42i | − | 1.08122i | −0.841275 | − | 0.540608i | \(-0.818194\pi\) | ||
0.841275 | − | 0.540608i | \(-0.181806\pi\) | |||||||
\(942\) | 668.296i | 0.709444i | ||||||||
\(943\) | −1070.00 | − | 447.172i | −1.13468 | − | 0.474201i | ||||
\(944\) | −428.921 | −0.454365 | ||||||||
\(945\) | −26.1154 | −0.0276353 | ||||||||
\(946\) | −362.109 | −0.382780 | ||||||||
\(947\) | 139.135 | 0.146922 | 0.0734610 | − | 0.997298i | \(-0.476596\pi\) | ||||
0.0734610 | + | 0.997298i | \(0.476596\pi\) | |||||||
\(948\) | − | 79.7005i | − | 0.0840723i | ||||||
\(949\) | 236.527 | 0.249238 | ||||||||
\(950\) | − | 1031.94i | − | 1.08626i | ||||||
\(951\) | −864.032 | −0.908551 | ||||||||
\(952\) | 330.549 | 0.347216 | ||||||||
\(953\) | − | 1583.35i | − | 1.66143i | −0.556694 | − | 0.830717i | \(-0.687931\pi\) | ||
0.556694 | − | 0.830717i | \(-0.312069\pi\) | |||||||
\(954\) | − | 314.314i | − | 0.329470i | ||||||
\(955\) | −159.119 | −0.166617 | ||||||||
\(956\) | 29.4777 | 0.0308344 | ||||||||
\(957\) | − | 468.172i | − | 0.489208i | ||||||
\(958\) | − | 13.8820i | − | 0.0144906i | ||||||
\(959\) | 208.523 | 0.217437 | ||||||||
\(960\) | − | 54.5437i | − | 0.0568163i | ||||||
\(961\) | −229.842 | −0.239169 | ||||||||
\(962\) | 826.889i | 0.859552i | ||||||||
\(963\) | 291.922i | 0.303138i | ||||||||
\(964\) | − | 528.249i | − | 0.547977i | ||||||
\(965\) | − | 386.791i | − | 0.400820i | ||||||
\(966\) | −97.5239 | + | 233.358i | −0.100956 | + | 0.241571i | ||||
\(967\) | 1209.98 | 1.25127 | 0.625636 | − | 0.780115i | \(-0.284840\pi\) | ||||
0.625636 | + | 0.780115i | \(0.284840\pi\) | |||||||
\(968\) | 96.4768 | 0.0996661 | ||||||||
\(969\) | 808.661 | 0.834531 | ||||||||
\(970\) | −224.116 | −0.231048 | ||||||||
\(971\) | − | 361.766i | − | 0.372570i | −0.982496 | − | 0.186285i | \(-0.940355\pi\) | ||
0.982496 | − | 0.186285i | \(-0.0596448\pi\) | |||||||
\(972\) | −27.4059 | −0.0281954 | ||||||||
\(973\) | − | 191.804i | − | 0.197127i | ||||||
\(974\) | −687.935 | −0.706299 | ||||||||
\(975\) | 352.186 | 0.361216 | ||||||||
\(976\) | − | 1762.35i | − | 1.80569i | ||||||
\(977\) | 467.002i | 0.477995i | 0.971020 | + | 0.238998i | \(0.0768189\pi\) | ||||
−0.971020 | + | 0.238998i | \(0.923181\pi\) | |||||||
\(978\) | 913.909 | 0.934467 | ||||||||
\(979\) | 1177.76 | 1.20302 | ||||||||
\(980\) | − | 23.3779i | − | 0.0238550i | ||||||
\(981\) | − | 447.633i | − | 0.456303i | ||||||
\(982\) | −195.570 | −0.199155 | ||||||||
\(983\) | 1055.40i | 1.07365i | 0.843695 | + | 0.536824i | \(0.180376\pi\) | ||||
−0.843695 | + | 0.536824i | \(0.819624\pi\) | |||||||
\(984\) | −469.818 | −0.477458 | ||||||||
\(985\) | 585.931i | 0.594854i | ||||||||
\(986\) | 1277.94i | 1.29609i | ||||||||
\(987\) | − | 161.754i | − | 0.163885i | ||||||
\(988\) | 335.961i | 0.340041i | ||||||||
\(989\) | 113.543 | − | 271.688i | 0.114806 | − | 0.274709i | ||||
\(990\) | 161.187 | 0.162815 | ||||||||
\(991\) | 1049.02 | 1.05855 | 0.529276 | − | 0.848450i | \(-0.322464\pi\) | ||||
0.529276 | + | 0.848450i | \(0.322464\pi\) | |||||||
\(992\) | 712.039 | 0.717782 | ||||||||
\(993\) | −144.872 | −0.145893 | ||||||||
\(994\) | − | 741.091i | − | 0.745564i | ||||||
\(995\) | 640.023 | 0.643239 | ||||||||
\(996\) | − | 195.467i | − | 0.196252i | ||||||
\(997\) | 1636.68 | 1.64160 | 0.820802 | − | 0.571212i | \(-0.193527\pi\) | ||||
0.820802 | + | 0.571212i | \(0.193527\pi\) | |||||||
\(998\) | 1970.61 | 1.97456 | ||||||||
\(999\) | 188.373i | 0.188562i |
(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 | 483.3.f.a.22.36 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.35 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.35 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.36 | yes | 48 | 1.1 | even | 1 | trivial |