Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,3,Mod(736,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.736");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.b (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: | \(31.4714705336\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 736.13 | ||
Character | \(\chi\) | \(=\) | 1155.736 |
Dual form | 1155.3.b.a.736.84 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.25995i | − | 1.62998i | −0.579477 | − | 0.814988i | \(-0.696743\pi\) | ||
0.579477 | − | 0.814988i | \(-0.303257\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −6.62729 | −1.65682 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | − | 5.64640i | − | 0.941067i | ||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 8.56486i | 1.07061i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 7.28948i | − | 0.728948i | ||||||
\(11\) | −6.99198 | + | 8.49189i | −0.635634 | + | 0.771990i | ||||
\(12\) | −11.4788 | −0.956567 | ||||||||
\(13\) | 11.8404i | 0.910801i | 0.890287 | + | 0.455401i | \(0.150504\pi\) | ||||
−0.890287 | + | 0.455401i | \(0.849496\pi\) | |||||||
\(14\) | 8.62503 | 0.616073 | ||||||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | 1.41185 | 0.0882406 | ||||||||
\(17\) | 0.714799i | 0.0420470i | 0.999779 | + | 0.0210235i | \(0.00669248\pi\) | ||||
−0.999779 | + | 0.0210235i | \(0.993308\pi\) | |||||||
\(18\) | − | 9.77986i | − | 0.543326i | ||||||
\(19\) | 9.50856i | 0.500451i | 0.968188 | + | 0.250225i | \(0.0805047\pi\) | ||||
−0.968188 | + | 0.250225i | \(0.919495\pi\) | |||||||
\(20\) | −14.8191 | −0.740954 | ||||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | 27.6832 | + | 22.7935i | 1.25833 | + | 1.03607i | ||||
\(23\) | 5.30292 | 0.230562 | 0.115281 | − | 0.993333i | \(-0.463223\pi\) | ||||
0.115281 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(24\) | 14.8348i | 0.618115i | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 38.5992 | 1.48458 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 17.5342i | − | 0.626220i | ||||||
\(29\) | − | 18.2527i | − | 0.629405i | −0.949190 | − | 0.314702i | \(-0.898095\pi\) | ||
0.949190 | − | 0.314702i | \(-0.101905\pi\) | |||||||
\(30\) | − | 12.6257i | − | 0.420858i | ||||||
\(31\) | 15.1227 | 0.487829 | 0.243914 | − | 0.969797i | \(-0.421568\pi\) | ||||
0.243914 | + | 0.969797i | \(0.421568\pi\) | |||||||
\(32\) | 29.6569i | 0.926777i | ||||||||
\(33\) | −12.1105 | + | 14.7084i | −0.366984 | + | 0.445709i | ||||
\(34\) | 2.33021 | 0.0685357 | ||||||||
\(35\) | 5.91608i | 0.169031i | ||||||||
\(36\) | −19.8819 | −0.552275 | ||||||||
\(37\) | 21.2978 | 0.575616 | 0.287808 | − | 0.957688i | \(-0.407074\pi\) | ||||
0.287808 | + | 0.957688i | \(0.407074\pi\) | |||||||
\(38\) | 30.9975 | 0.815723 | ||||||||
\(39\) | 20.5082i | 0.525851i | ||||||||
\(40\) | 19.1516i | 0.478790i | ||||||||
\(41\) | 34.2854i | 0.836230i | 0.908394 | + | 0.418115i | \(0.137309\pi\) | ||||
−0.908394 | + | 0.418115i | \(0.862691\pi\) | |||||||
\(42\) | 14.9390 | 0.355690 | ||||||||
\(43\) | 60.6984i | 1.41159i | 0.708416 | + | 0.705796i | \(0.249410\pi\) | ||||
−0.708416 | + | 0.705796i | \(0.750590\pi\) | |||||||
\(44\) | 46.3379 | − | 56.2783i | 1.05313 | − | 1.27905i | ||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | − | 17.2873i | − | 0.375810i | ||||||
\(47\) | 69.4507 | 1.47767 | 0.738837 | − | 0.673884i | \(-0.235375\pi\) | ||||
0.738837 | + | 0.673884i | \(0.235375\pi\) | |||||||
\(48\) | 2.44540 | 0.0509458 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | − | 16.2998i | − | 0.325995i | ||||||
\(51\) | 1.23807i | 0.0242759i | ||||||||
\(52\) | − | 78.4699i | − | 1.50904i | ||||||
\(53\) | 76.9151 | 1.45123 | 0.725615 | − | 0.688101i | \(-0.241556\pi\) | ||||
0.725615 | + | 0.688101i | \(0.241556\pi\) | |||||||
\(54\) | − | 16.9392i | − | 0.313689i | ||||||
\(55\) | −15.6345 | + | 18.9885i | −0.284264 | + | 0.345245i | ||||
\(56\) | −22.6605 | −0.404651 | ||||||||
\(57\) | 16.4693i | 0.288935i | ||||||||
\(58\) | −59.5031 | −1.02591 | ||||||||
\(59\) | −90.6691 | −1.53676 | −0.768382 | − | 0.639991i | \(-0.778938\pi\) | ||||
−0.768382 | + | 0.639991i | \(0.778938\pi\) | |||||||
\(60\) | −25.6674 | −0.427790 | ||||||||
\(61\) | 117.263i | 1.92235i | 0.275947 | + | 0.961173i | \(0.411008\pi\) | ||||
−0.275947 | + | 0.961173i | \(0.588992\pi\) | |||||||
\(62\) | − | 49.2993i | − | 0.795149i | ||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | 102.327 | 1.59886 | ||||||||
\(65\) | 26.4760i | 0.407323i | ||||||||
\(66\) | 47.9487 | + | 39.4795i | 0.726495 | + | 0.598175i | ||||
\(67\) | −64.3561 | −0.960539 | −0.480270 | − | 0.877121i | \(-0.659461\pi\) | ||||
−0.480270 | + | 0.877121i | \(0.659461\pi\) | |||||||
\(68\) | − | 4.73719i | − | 0.0696645i | ||||||
\(69\) | 9.18492 | 0.133115 | ||||||||
\(70\) | 19.2861 | 0.275516 | ||||||||
\(71\) | 116.263 | 1.63751 | 0.818754 | − | 0.574145i | \(-0.194665\pi\) | ||||
0.818754 | + | 0.574145i | \(0.194665\pi\) | |||||||
\(72\) | 25.6946i | 0.356869i | ||||||||
\(73\) | 57.1670i | 0.783110i | 0.920155 | + | 0.391555i | \(0.128063\pi\) | ||||
−0.920155 | + | 0.391555i | \(0.871937\pi\) | |||||||
\(74\) | − | 69.4298i | − | 0.938240i | ||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | − | 63.0161i | − | 0.829159i | ||||||
\(77\) | −22.4674 | − | 18.4990i | −0.291785 | − | 0.240247i | ||||
\(78\) | 66.8558 | 0.857125 | ||||||||
\(79\) | − | 78.9922i | − | 0.999902i | −0.866054 | − | 0.499951i | \(-0.833351\pi\) | ||
0.866054 | − | 0.499951i | \(-0.166649\pi\) | |||||||
\(80\) | 3.15699 | 0.0394624 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 111.769 | 1.36303 | ||||||||
\(83\) | 50.1381i | 0.604073i | 0.953296 | + | 0.302036i | \(0.0976664\pi\) | ||||
−0.953296 | + | 0.302036i | \(0.902334\pi\) | |||||||
\(84\) | − | 30.3701i | − | 0.361549i | ||||||
\(85\) | 1.59834i | 0.0188040i | ||||||||
\(86\) | 197.874 | 2.30086 | ||||||||
\(87\) | − | 31.6147i | − | 0.363387i | ||||||
\(88\) | −72.7318 | − | 59.8853i | −0.826498 | − | 0.680514i | ||||
\(89\) | 72.2902 | 0.812249 | 0.406125 | − | 0.913818i | \(-0.366880\pi\) | ||||
0.406125 | + | 0.913818i | \(0.366880\pi\) | |||||||
\(90\) | − | 21.8684i | − | 0.242983i | ||||||
\(91\) | −31.3268 | −0.344251 | ||||||||
\(92\) | −35.1440 | −0.382000 | ||||||||
\(93\) | 26.1933 | 0.281648 | ||||||||
\(94\) | − | 226.406i | − | 2.40857i | ||||||
\(95\) | 21.2618i | 0.223808i | ||||||||
\(96\) | 51.3672i | 0.535075i | ||||||||
\(97\) | −53.1639 | −0.548082 | −0.274041 | − | 0.961718i | \(-0.588360\pi\) | ||||
−0.274041 | + | 0.961718i | \(0.588360\pi\) | |||||||
\(98\) | 22.8197i | 0.232854i | ||||||||
\(99\) | −20.9759 | + | 25.4757i | −0.211878 | + | 0.257330i | ||||
\(100\) | −33.1365 | −0.331365 | ||||||||
\(101\) | − | 36.0469i | − | 0.356900i | −0.983949 | − | 0.178450i | \(-0.942892\pi\) | ||
0.983949 | − | 0.178450i | \(-0.0571082\pi\) | |||||||
\(102\) | 4.03605 | 0.0395691 | ||||||||
\(103\) | 1.48598 | 0.0144270 | 0.00721349 | − | 0.999974i | \(-0.497704\pi\) | ||||
0.00721349 | + | 0.999974i | \(0.497704\pi\) | |||||||
\(104\) | −101.411 | −0.975110 | ||||||||
\(105\) | 10.2470i | 0.0975900i | ||||||||
\(106\) | − | 250.740i | − | 2.36547i | ||||||
\(107\) | − | 60.2073i | − | 0.562685i | −0.959607 | − | 0.281342i | \(-0.909220\pi\) | ||
0.959607 | − | 0.281342i | \(-0.0907797\pi\) | |||||||
\(108\) | −34.4364 | −0.318856 | ||||||||
\(109\) | − | 102.947i | − | 0.944468i | −0.881473 | − | 0.472234i | \(-0.843448\pi\) | ||
0.881473 | − | 0.472234i | \(-0.156552\pi\) | |||||||
\(110\) | 61.9015 | + | 50.9679i | 0.562741 | + | 0.463344i | ||||
\(111\) | 36.8889 | 0.332332 | ||||||||
\(112\) | 3.73540i | 0.0333518i | ||||||||
\(113\) | −68.8910 | −0.609655 | −0.304827 | − | 0.952408i | \(-0.598599\pi\) | ||||
−0.304827 | + | 0.952408i | \(0.598599\pi\) | |||||||
\(114\) | 53.6892 | 0.470958 | ||||||||
\(115\) | 11.8577 | 0.103110 | ||||||||
\(116\) | 120.966i | 1.04281i | ||||||||
\(117\) | 35.5213i | 0.303600i | ||||||||
\(118\) | 295.577i | 2.50489i | ||||||||
\(119\) | −1.89118 | −0.0158923 | ||||||||
\(120\) | 33.1715i | 0.276430i | ||||||||
\(121\) | −23.2245 | − | 118.750i | −0.191938 | − | 0.981407i | ||||
\(122\) | 382.272 | 3.13338 | ||||||||
\(123\) | 59.3841i | 0.482797i | ||||||||
\(124\) | −100.222 | −0.808246 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 25.8751 | 0.205358 | ||||||||
\(127\) | − | 4.54268i | − | 0.0357691i | −0.999840 | − | 0.0178846i | \(-0.994307\pi\) | ||
0.999840 | − | 0.0178846i | \(-0.00569313\pi\) | |||||||
\(128\) | − | 214.955i | − | 1.67934i | ||||||
\(129\) | 105.133i | 0.814983i | ||||||||
\(130\) | 86.3104 | 0.663927 | ||||||||
\(131\) | 70.1980i | 0.535863i | 0.963438 | + | 0.267931i | \(0.0863401\pi\) | ||||
−0.963438 | + | 0.267931i | \(0.913660\pi\) | |||||||
\(132\) | 80.2596 | − | 97.4768i | 0.608027 | − | 0.738461i | ||||
\(133\) | −25.1573 | −0.189153 | ||||||||
\(134\) | 209.798i | 1.56566i | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | −6.12215 | −0.0450158 | ||||||||
\(137\) | 57.1217 | 0.416947 | 0.208473 | − | 0.978028i | \(-0.433151\pi\) | ||||
0.208473 | + | 0.978028i | \(0.433151\pi\) | |||||||
\(138\) | − | 29.9424i | − | 0.216974i | ||||||
\(139\) | − | 118.088i | − | 0.849558i | −0.905297 | − | 0.424779i | \(-0.860352\pi\) | ||
0.905297 | − | 0.424779i | \(-0.139648\pi\) | |||||||
\(140\) | − | 39.2076i | − | 0.280054i | ||||||
\(141\) | 120.292 | 0.853135 | ||||||||
\(142\) | − | 379.012i | − | 2.66910i | ||||||
\(143\) | −100.548 | − | 82.7879i | −0.703130 | − | 0.578937i | ||||
\(144\) | 4.23555 | 0.0294135 | ||||||||
\(145\) | − | 40.8144i | − | 0.281478i | ||||||
\(146\) | 186.362 | 1.27645 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | −141.147 | −0.953694 | ||||||||
\(149\) | 108.058i | 0.725221i | 0.931941 | + | 0.362610i | \(0.118114\pi\) | ||||
−0.931941 | + | 0.362610i | \(0.881886\pi\) | |||||||
\(150\) | − | 28.2320i | − | 0.188213i | ||||||
\(151\) | − | 15.9008i | − | 0.105303i | −0.998613 | − | 0.0526516i | \(-0.983233\pi\) | ||
0.998613 | − | 0.0526516i | \(-0.0167673\pi\) | |||||||
\(152\) | −81.4395 | −0.535786 | ||||||||
\(153\) | 2.14440i | 0.0140157i | ||||||||
\(154\) | −60.3060 | + | 73.2428i | −0.391597 | + | 0.475603i | ||||
\(155\) | 33.8154 | 0.218164 | ||||||||
\(156\) | − | 135.914i | − | 0.871243i | ||||||
\(157\) | −57.6377 | −0.367119 | −0.183560 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183560 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(158\) | −257.511 | −1.62982 | ||||||||
\(159\) | 133.221 | 0.837868 | ||||||||
\(160\) | 66.3147i | 0.414467i | ||||||||
\(161\) | 14.0302i | 0.0871441i | ||||||||
\(162\) | − | 29.3396i | − | 0.181109i | ||||||
\(163\) | −306.244 | −1.87880 | −0.939398 | − | 0.342827i | \(-0.888615\pi\) | ||||
−0.939398 | + | 0.342827i | \(0.888615\pi\) | |||||||
\(164\) | − | 227.219i | − | 1.38548i | ||||||
\(165\) | −27.0798 | + | 32.8890i | −0.164120 | + | 0.199327i | ||||
\(166\) | 163.448 | 0.984625 | ||||||||
\(167\) | 282.882i | 1.69391i | 0.531668 | + | 0.846953i | \(0.321565\pi\) | ||||
−0.531668 | + | 0.846953i | \(0.678435\pi\) | |||||||
\(168\) | −39.2491 | −0.233626 | ||||||||
\(169\) | 28.8045 | 0.170441 | ||||||||
\(170\) | 5.21051 | 0.0306501 | ||||||||
\(171\) | 28.5257i | 0.166817i | ||||||||
\(172\) | − | 402.266i | − | 2.33876i | ||||||
\(173\) | 205.611i | 1.18850i | 0.804279 | + | 0.594251i | \(0.202552\pi\) | ||||
−0.804279 | + | 0.594251i | \(0.797448\pi\) | |||||||
\(174\) | −103.062 | −0.592312 | ||||||||
\(175\) | 13.2288i | 0.0755929i | ||||||||
\(176\) | −9.87162 | + | 11.9893i | −0.0560888 | + | 0.0681209i | ||||
\(177\) | −157.044 | −0.887252 | ||||||||
\(178\) | − | 235.663i | − | 1.32395i | ||||||
\(179\) | −337.861 | −1.88749 | −0.943745 | − | 0.330674i | \(-0.892724\pi\) | ||||
−0.943745 | + | 0.330674i | \(0.892724\pi\) | |||||||
\(180\) | −44.4572 | −0.246985 | ||||||||
\(181\) | −57.0926 | −0.315429 | −0.157714 | − | 0.987485i | \(-0.550413\pi\) | ||||
−0.157714 | + | 0.987485i | \(0.550413\pi\) | |||||||
\(182\) | 102.124i | 0.561120i | ||||||||
\(183\) | 203.106i | 1.10987i | ||||||||
\(184\) | 45.4187i | 0.246841i | ||||||||
\(185\) | 47.6233 | 0.257423 | ||||||||
\(186\) | − | 85.3888i | − | 0.459080i | ||||||
\(187\) | −6.07000 | − | 4.99786i | −0.0324599 | − | 0.0267265i | ||||
\(188\) | −460.270 | −2.44824 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 69.3125 | 0.364802 | ||||||||
\(191\) | 63.7145 | 0.333584 | 0.166792 | − | 0.985992i | \(-0.446659\pi\) | ||||
0.166792 | + | 0.985992i | \(0.446659\pi\) | |||||||
\(192\) | 177.236 | 0.923105 | ||||||||
\(193\) | − | 164.827i | − | 0.854024i | −0.904246 | − | 0.427012i | \(-0.859566\pi\) | ||
0.904246 | − | 0.427012i | \(-0.140434\pi\) | |||||||
\(194\) | 173.312i | 0.893360i | ||||||||
\(195\) | 45.8577i | 0.235168i | ||||||||
\(196\) | 46.3911 | 0.236689 | ||||||||
\(197\) | − | 344.225i | − | 1.74734i | −0.486523 | − | 0.873668i | \(-0.661735\pi\) | ||
0.486523 | − | 0.873668i | \(-0.338265\pi\) | |||||||
\(198\) | 83.0495 | + | 68.3806i | 0.419442 | + | 0.345356i | ||||
\(199\) | 149.135 | 0.749423 | 0.374711 | − | 0.927142i | \(-0.377742\pi\) | ||||
0.374711 | + | 0.927142i | \(0.377742\pi\) | |||||||
\(200\) | 42.8243i | 0.214121i | ||||||||
\(201\) | −111.468 | −0.554568 | ||||||||
\(202\) | −117.511 | −0.581738 | ||||||||
\(203\) | 48.2922 | 0.237893 | ||||||||
\(204\) | − | 8.20505i | − | 0.0402208i | ||||||
\(205\) | 76.6645i | 0.373973i | ||||||||
\(206\) | − | 4.84422i | − | 0.0235156i | ||||||
\(207\) | 15.9088 | 0.0768539 | ||||||||
\(208\) | 16.7169i | 0.0803697i | ||||||||
\(209\) | −80.7457 | − | 66.4837i | −0.386343 | − | 0.318104i | ||||
\(210\) | 33.4046 | 0.159069 | ||||||||
\(211\) | 314.317i | 1.48965i | 0.667257 | + | 0.744827i | \(0.267468\pi\) | ||||
−0.667257 | + | 0.744827i | \(0.732532\pi\) | |||||||
\(212\) | −509.739 | −2.40443 | ||||||||
\(213\) | 201.374 | 0.945416 | ||||||||
\(214\) | −196.273 | −0.917163 | ||||||||
\(215\) | 135.726i | 0.631283i | ||||||||
\(216\) | 44.5043i | 0.206038i | ||||||||
\(217\) | 40.0109i | 0.184382i | ||||||||
\(218\) | −335.602 | −1.53946 | ||||||||
\(219\) | 99.0162i | 0.452129i | ||||||||
\(220\) | 103.615 | − | 125.842i | 0.470976 | − | 0.572009i | ||||
\(221\) | −8.46352 | −0.0382965 | ||||||||
\(222\) | − | 120.256i | − | 0.541693i | ||||||
\(223\) | −369.689 | −1.65780 | −0.828900 | − | 0.559397i | \(-0.811033\pi\) | ||||
−0.828900 | + | 0.559397i | \(0.811033\pi\) | |||||||
\(224\) | −78.4647 | −0.350289 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 224.581i | 0.993723i | ||||||||
\(227\) | − | 154.248i | − | 0.679507i | −0.940514 | − | 0.339754i | \(-0.889656\pi\) | ||
0.940514 | − | 0.339754i | \(-0.110344\pi\) | |||||||
\(228\) | − | 109.147i | − | 0.478715i | ||||||
\(229\) | 131.904 | 0.575999 | 0.288000 | − | 0.957631i | \(-0.407010\pi\) | ||||
0.288000 | + | 0.957631i | \(0.407010\pi\) | |||||||
\(230\) | − | 38.6555i | − | 0.168067i | ||||||
\(231\) | −38.9147 | − | 32.0413i | −0.168462 | − | 0.138707i | ||||
\(232\) | 156.332 | 0.673845 | ||||||||
\(233\) | 65.4028i | 0.280699i | 0.990102 | + | 0.140349i | \(0.0448226\pi\) | ||||
−0.990102 | + | 0.140349i | \(0.955177\pi\) | |||||||
\(234\) | 115.798 | 0.494862 | ||||||||
\(235\) | 155.296 | 0.660836 | ||||||||
\(236\) | 600.891 | 2.54615 | ||||||||
\(237\) | − | 136.819i | − | 0.577293i | ||||||
\(238\) | 6.16516i | 0.0259040i | ||||||||
\(239\) | 275.468i | 1.15259i | 0.817243 | + | 0.576293i | \(0.195501\pi\) | ||||
−0.817243 | + | 0.576293i | \(0.804499\pi\) | |||||||
\(240\) | 5.46807 | 0.0227836 | ||||||||
\(241\) | − | 4.09092i | − | 0.0169748i | −0.999964 | − | 0.00848739i | \(-0.997298\pi\) | ||
0.999964 | − | 0.00848739i | \(-0.00270165\pi\) | |||||||
\(242\) | −387.120 | + | 75.7108i | −1.59967 | + | 0.312855i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 777.137i | − | 3.18499i | ||||||
\(245\) | −15.6525 | −0.0638877 | ||||||||
\(246\) | 193.589 | 0.786948 | ||||||||
\(247\) | −112.585 | −0.455811 | ||||||||
\(248\) | 129.524i | 0.522273i | ||||||||
\(249\) | 86.8417i | 0.348762i | ||||||||
\(250\) | − | 36.4474i | − | 0.145790i | ||||||
\(251\) | −9.82343 | −0.0391372 | −0.0195686 | − | 0.999809i | \(-0.506229\pi\) | ||||
−0.0195686 | + | 0.999809i | \(0.506229\pi\) | |||||||
\(252\) | − | 52.6025i | − | 0.208740i | ||||||
\(253\) | −37.0779 | + | 45.0318i | −0.146553 | + | 0.177991i | ||||
\(254\) | −14.8089 | −0.0583028 | ||||||||
\(255\) | 2.76841i | 0.0108565i | ||||||||
\(256\) | −291.434 | −1.13841 | ||||||||
\(257\) | −103.472 | −0.402615 | −0.201308 | − | 0.979528i | \(-0.564519\pi\) | ||||
−0.201308 | + | 0.979528i | \(0.564519\pi\) | |||||||
\(258\) | 342.728 | 1.32840 | ||||||||
\(259\) | 56.3487i | 0.217562i | ||||||||
\(260\) | − | 175.464i | − | 0.674862i | ||||||
\(261\) | − | 54.7582i | − | 0.209802i | ||||||
\(262\) | 228.842 | 0.873444 | ||||||||
\(263\) | − | 385.813i | − | 1.46697i | −0.679705 | − | 0.733485i | \(-0.737892\pi\) | ||
0.679705 | − | 0.733485i | \(-0.262108\pi\) | |||||||
\(264\) | −125.975 | − | 103.724i | −0.477179 | − | 0.392895i | ||||
\(265\) | 171.987 | 0.649009 | ||||||||
\(266\) | 82.0116i | 0.308314i | ||||||||
\(267\) | 125.210 | 0.468952 | ||||||||
\(268\) | 426.507 | 1.59144 | ||||||||
\(269\) | 88.0610 | 0.327364 | 0.163682 | − | 0.986513i | \(-0.447663\pi\) | ||||
0.163682 | + | 0.986513i | \(0.447663\pi\) | |||||||
\(270\) | − | 37.8772i | − | 0.140286i | ||||||
\(271\) | − | 254.661i | − | 0.939709i | −0.882744 | − | 0.469855i | \(-0.844306\pi\) | ||
0.882744 | − | 0.469855i | \(-0.155694\pi\) | |||||||
\(272\) | 1.00919i | 0.00371026i | ||||||||
\(273\) | −54.2596 | −0.198753 | ||||||||
\(274\) | − | 186.214i | − | 0.679614i | ||||||
\(275\) | −34.9599 | + | 42.4595i | −0.127127 | + | 0.154398i | ||||
\(276\) | −60.8712 | −0.220548 | ||||||||
\(277\) | − | 322.903i | − | 1.16572i | −0.812574 | − | 0.582858i | \(-0.801934\pi\) | ||
0.812574 | − | 0.582858i | \(-0.198066\pi\) | |||||||
\(278\) | −384.963 | −1.38476 | ||||||||
\(279\) | 45.3681 | 0.162610 | ||||||||
\(280\) | −50.6704 | −0.180966 | ||||||||
\(281\) | 365.333i | 1.30012i | 0.759884 | + | 0.650059i | \(0.225256\pi\) | ||||
−0.759884 | + | 0.650059i | \(0.774744\pi\) | |||||||
\(282\) | − | 392.147i | − | 1.39059i | ||||||
\(283\) | 30.2357i | 0.106840i | 0.998572 | + | 0.0534199i | \(0.0170122\pi\) | ||||
−0.998572 | + | 0.0534199i | \(0.982988\pi\) | |||||||
\(284\) | −770.509 | −2.71306 | ||||||||
\(285\) | 36.8265i | 0.129216i | ||||||||
\(286\) | −269.885 | + | 327.780i | −0.943653 | + | 1.14609i | ||||
\(287\) | −90.7107 | −0.316065 | ||||||||
\(288\) | 88.9706i | 0.308926i | ||||||||
\(289\) | 288.489 | 0.998232 | ||||||||
\(290\) | −133.053 | −0.458803 | ||||||||
\(291\) | −92.0826 | −0.316435 | ||||||||
\(292\) | − | 378.863i | − | 1.29748i | ||||||
\(293\) | 166.153i | 0.567074i | 0.958961 | + | 0.283537i | \(0.0915080\pi\) | ||||
−0.958961 | + | 0.283537i | \(0.908492\pi\) | |||||||
\(294\) | 39.5248i | 0.134438i | ||||||||
\(295\) | −202.742 | −0.687262 | ||||||||
\(296\) | 182.412i | 0.616258i | ||||||||
\(297\) | −36.3314 | + | 44.1252i | −0.122328 | + | 0.148570i | ||||
\(298\) | 352.264 | 1.18209 | ||||||||
\(299\) | 62.7888i | 0.209996i | ||||||||
\(300\) | −57.3940 | −0.191313 | ||||||||
\(301\) | −160.593 | −0.533531 | ||||||||
\(302\) | −51.8358 | −0.171642 | ||||||||
\(303\) | − | 62.4350i | − | 0.206056i | ||||||
\(304\) | 13.4247i | 0.0441601i | ||||||||
\(305\) | 262.208i | 0.859699i | ||||||||
\(306\) | 6.99064 | 0.0228452 | ||||||||
\(307\) | − | 275.260i | − | 0.896612i | −0.893880 | − | 0.448306i | \(-0.852027\pi\) | ||
0.893880 | − | 0.448306i | \(-0.147973\pi\) | |||||||
\(308\) | 148.898 | + | 122.599i | 0.483436 | + | 0.398047i | ||||
\(309\) | 2.57379 | 0.00832942 | ||||||||
\(310\) | − | 110.236i | − | 0.355602i | ||||||
\(311\) | 4.61508 | 0.0148395 | 0.00741974 | − | 0.999972i | \(-0.497638\pi\) | ||||
0.00741974 | + | 0.999972i | \(0.497638\pi\) | |||||||
\(312\) | −175.650 | −0.562980 | ||||||||
\(313\) | 191.204 | 0.610874 | 0.305437 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305437 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(314\) | 187.896i | 0.598396i | ||||||||
\(315\) | 17.7482i | 0.0563436i | ||||||||
\(316\) | 523.505i | 1.65666i | ||||||||
\(317\) | 227.156 | 0.716581 | 0.358291 | − | 0.933610i | \(-0.383360\pi\) | ||||
0.358291 | + | 0.933610i | \(0.383360\pi\) | |||||||
\(318\) | − | 434.294i | − | 1.36570i | ||||||
\(319\) | 155.000 | + | 127.623i | 0.485894 | + | 0.400071i | ||||
\(320\) | 228.811 | 0.715034 | ||||||||
\(321\) | − | 104.282i | − | 0.324866i | ||||||
\(322\) | 45.7378 | 0.142043 | ||||||||
\(323\) | −6.79672 | −0.0210425 | ||||||||
\(324\) | −59.6456 | −0.184092 | ||||||||
\(325\) | 59.2021i | 0.182160i | ||||||||
\(326\) | 998.341i | 3.06239i | ||||||||
\(327\) | − | 178.309i | − | 0.545289i | ||||||
\(328\) | −293.650 | −0.895273 | ||||||||
\(329\) | 183.749i | 0.558508i | ||||||||
\(330\) | 107.216 | + | 88.2789i | 0.324898 | + | 0.267512i | ||||
\(331\) | −215.320 | −0.650515 | −0.325257 | − | 0.945626i | \(-0.605451\pi\) | ||||
−0.325257 | + | 0.945626i | \(0.605451\pi\) | |||||||
\(332\) | − | 332.280i | − | 1.00084i | ||||||
\(333\) | 63.8934 | 0.191872 | ||||||||
\(334\) | 922.183 | 2.76103 | ||||||||
\(335\) | −143.905 | −0.429566 | ||||||||
\(336\) | 6.46991i | 0.0192557i | ||||||||
\(337\) | − | 10.2677i | − | 0.0304679i | −0.999884 | − | 0.0152339i | \(-0.995151\pi\) | ||
0.999884 | − | 0.0152339i | \(-0.00484930\pi\) | |||||||
\(338\) | − | 93.9014i | − | 0.277815i | ||||||
\(339\) | −119.323 | −0.351984 | ||||||||
\(340\) | − | 10.5927i | − | 0.0311549i | ||||||
\(341\) | −105.737 | + | 128.420i | −0.310081 | + | 0.376599i | ||||
\(342\) | 92.9924 | 0.271908 | ||||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | −519.873 | −1.51126 | ||||||||
\(345\) | 20.5381 | 0.0595308 | ||||||||
\(346\) | 670.282 | 1.93723 | ||||||||
\(347\) | 89.6958i | 0.258489i | 0.991613 | + | 0.129245i | \(0.0412553\pi\) | ||||
−0.991613 | + | 0.129245i | \(0.958745\pi\) | |||||||
\(348\) | 209.520i | 0.602068i | ||||||||
\(349\) | 421.491i | 1.20771i | 0.797094 | + | 0.603855i | \(0.206369\pi\) | ||||
−0.797094 | + | 0.603855i | \(0.793631\pi\) | |||||||
\(350\) | 43.1251 | 0.123215 | ||||||||
\(351\) | 61.5246i | 0.175284i | ||||||||
\(352\) | −251.843 | − | 207.360i | −0.715463 | − | 0.589091i | ||||
\(353\) | 89.5009 | 0.253544 | 0.126772 | − | 0.991932i | \(-0.459538\pi\) | ||||
0.126772 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(354\) | 511.955i | 1.44620i | ||||||||
\(355\) | 259.972 | 0.732316 | ||||||||
\(356\) | −479.088 | −1.34575 | ||||||||
\(357\) | −3.27562 | −0.00917541 | ||||||||
\(358\) | 1101.41i | 3.07656i | ||||||||
\(359\) | 242.680i | 0.675989i | 0.941148 | + | 0.337995i | \(0.109749\pi\) | ||||
−0.941148 | + | 0.337995i | \(0.890251\pi\) | |||||||
\(360\) | 57.4548i | 0.159597i | ||||||||
\(361\) | 270.587 | 0.749549 | ||||||||
\(362\) | 186.119i | 0.514142i | ||||||||
\(363\) | −40.2260 | − | 205.681i | −0.110816 | − | 0.566616i | ||||
\(364\) | 207.612 | 0.570362 | ||||||||
\(365\) | 127.829i | 0.350217i | ||||||||
\(366\) | 662.115 | 1.80906 | ||||||||
\(367\) | 151.072 | 0.411640 | 0.205820 | − | 0.978590i | \(-0.434014\pi\) | ||||
0.205820 | + | 0.978590i | \(0.434014\pi\) | |||||||
\(368\) | 7.48693 | 0.0203449 | ||||||||
\(369\) | 102.856i | 0.278743i | ||||||||
\(370\) | − | 155.250i | − | 0.419594i | ||||||
\(371\) | 203.498i | 0.548513i | ||||||||
\(372\) | −173.590 | −0.466641 | ||||||||
\(373\) | 340.987i | 0.914174i | 0.889422 | + | 0.457087i | \(0.151107\pi\) | ||||
−0.889422 | + | 0.457087i | \(0.848893\pi\) | |||||||
\(374\) | −16.2928 | + | 19.7879i | −0.0435636 | + | 0.0529089i | ||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 594.835i | 1.58201i | ||||||||
\(377\) | 216.120 | 0.573263 | ||||||||
\(378\) | 44.8169 | 0.118563 | ||||||||
\(379\) | 182.264 | 0.480909 | 0.240454 | − | 0.970660i | \(-0.422704\pi\) | ||||
0.240454 | + | 0.970660i | \(0.422704\pi\) | |||||||
\(380\) | − | 140.908i | − | 0.370811i | ||||||
\(381\) | − | 7.86815i | − | 0.0206513i | ||||||
\(382\) | − | 207.706i | − | 0.543733i | ||||||
\(383\) | 687.344 | 1.79463 | 0.897316 | − | 0.441389i | \(-0.145514\pi\) | ||||
0.897316 | + | 0.441389i | \(0.145514\pi\) | |||||||
\(384\) | − | 372.313i | − | 0.969565i | ||||||
\(385\) | −50.2387 | − | 41.3651i | −0.130490 | − | 0.107442i | ||||
\(386\) | −537.327 | −1.39204 | ||||||||
\(387\) | 182.095i | 0.470530i | ||||||||
\(388\) | 352.333 | 0.908074 | ||||||||
\(389\) | −418.402 | −1.07558 | −0.537792 | − | 0.843077i | \(-0.680741\pi\) | ||||
−0.537792 | + | 0.843077i | \(0.680741\pi\) | |||||||
\(390\) | 149.494 | 0.383318 | ||||||||
\(391\) | 3.79052i | 0.00969443i | ||||||||
\(392\) | − | 59.9540i | − | 0.152944i | ||||||
\(393\) | 121.587i | 0.309381i | ||||||||
\(394\) | −1122.16 | −2.84812 | ||||||||
\(395\) | − | 176.632i | − | 0.447170i | ||||||
\(396\) | 139.014 | − | 168.835i | 0.351045 | − | 0.426351i | ||||
\(397\) | 14.2376 | 0.0358629 | 0.0179314 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179314 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(398\) | − | 486.173i | − | 1.22154i | ||||||
\(399\) | −43.5737 | −0.109207 | ||||||||
\(400\) | 7.05925 | 0.0176481 | ||||||||
\(401\) | 714.683 | 1.78225 | 0.891125 | − | 0.453757i | \(-0.149917\pi\) | ||||
0.891125 | + | 0.453757i | \(0.149917\pi\) | |||||||
\(402\) | 363.381i | 0.903932i | ||||||||
\(403\) | 179.059i | 0.444315i | ||||||||
\(404\) | 238.893i | 0.591320i | ||||||||
\(405\) | 20.1246 | 0.0496904 | ||||||||
\(406\) | − | 157.430i | − | 0.387759i | ||||||
\(407\) | −148.914 | + | 180.859i | −0.365881 | + | 0.444370i | ||||
\(408\) | −10.6039 | −0.0259899 | ||||||||
\(409\) | − | 258.746i | − | 0.632630i | −0.948654 | − | 0.316315i | \(-0.897554\pi\) | ||
0.948654 | − | 0.316315i | \(-0.102446\pi\) | |||||||
\(410\) | 249.923 | 0.609568 | ||||||||
\(411\) | 98.9377 | 0.240724 | ||||||||
\(412\) | −9.84802 | −0.0239030 | ||||||||
\(413\) | − | 239.888i | − | 0.580843i | ||||||
\(414\) | − | 51.8618i | − | 0.125270i | ||||||
\(415\) | 112.112i | 0.270150i | ||||||||
\(416\) | −351.150 | −0.844110 | ||||||||
\(417\) | − | 204.535i | − | 0.490492i | ||||||
\(418\) | −216.734 | + | 263.227i | −0.518502 | + | 0.629730i | ||||
\(419\) | 624.763 | 1.49108 | 0.745540 | − | 0.666461i | \(-0.232192\pi\) | ||||
0.745540 | + | 0.666461i | \(0.232192\pi\) | |||||||
\(420\) | − | 67.9096i | − | 0.161689i | ||||||
\(421\) | −549.214 | −1.30455 | −0.652274 | − | 0.757984i | \(-0.726185\pi\) | ||||
−0.652274 | + | 0.757984i | \(0.726185\pi\) | |||||||
\(422\) | 1024.66 | 2.42810 | ||||||||
\(423\) | 208.352 | 0.492558 | ||||||||
\(424\) | 658.767i | 1.55370i | ||||||||
\(425\) | 3.57400i | 0.00840940i | ||||||||
\(426\) | − | 656.468i | − | 1.54101i | ||||||
\(427\) | −310.249 | −0.726578 | ||||||||
\(428\) | 399.011i | 0.932269i | ||||||||
\(429\) | −174.153 | − | 143.393i | −0.405952 | − | 0.334249i | ||||
\(430\) | 442.460 | 1.02898 | ||||||||
\(431\) | 399.513i | 0.926944i | 0.886112 | + | 0.463472i | \(0.153396\pi\) | ||||
−0.886112 | + | 0.463472i | \(0.846604\pi\) | |||||||
\(432\) | 7.33619 | 0.0169819 | ||||||||
\(433\) | 231.226 | 0.534009 | 0.267004 | − | 0.963695i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963695i | \(0.413966\pi\) | |||||||
\(434\) | 130.434 | 0.300538 | ||||||||
\(435\) | − | 70.6925i | − | 0.162512i | ||||||
\(436\) | 682.260i | 1.56482i | ||||||||
\(437\) | 50.4231i | 0.115385i | ||||||||
\(438\) | 322.788 | 0.736959 | ||||||||
\(439\) | − | 308.759i | − | 0.703322i | −0.936127 | − | 0.351661i | \(-0.885617\pi\) | ||
0.936127 | − | 0.351661i | \(-0.114383\pi\) | |||||||
\(440\) | −162.633 | − | 133.908i | −0.369621 | − | 0.304335i | ||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 27.5907i | 0.0624224i | ||||||||
\(443\) | 165.492 | 0.373571 | 0.186786 | − | 0.982401i | \(-0.440193\pi\) | ||||
0.186786 | + | 0.982401i | \(0.440193\pi\) | |||||||
\(444\) | −244.473 | −0.550615 | ||||||||
\(445\) | 161.646 | 0.363249 | ||||||||
\(446\) | 1205.17i | 2.70217i | ||||||||
\(447\) | 187.162i | 0.418706i | ||||||||
\(448\) | 270.733i | 0.604314i | ||||||||
\(449\) | −586.467 | −1.30616 | −0.653081 | − | 0.757288i | \(-0.726524\pi\) | ||||
−0.653081 | + | 0.757288i | \(0.726524\pi\) | |||||||
\(450\) | − | 48.8993i | − | 0.108665i | ||||||
\(451\) | −291.148 | − | 239.723i | −0.645561 | − | 0.531536i | ||||
\(452\) | 456.561 | 1.01009 | ||||||||
\(453\) | − | 27.5409i | − | 0.0607968i | ||||||
\(454\) | −502.842 | −1.10758 | ||||||||
\(455\) | −70.0489 | −0.153954 | ||||||||
\(456\) | −141.057 | −0.309336 | ||||||||
\(457\) | 347.355i | 0.760076i | 0.924971 | + | 0.380038i | \(0.124089\pi\) | ||||
−0.924971 | + | 0.380038i | \(0.875911\pi\) | |||||||
\(458\) | − | 430.000i | − | 0.938865i | ||||||
\(459\) | 3.71421i | 0.00809195i | ||||||||
\(460\) | −78.5844 | −0.170836 | ||||||||
\(461\) | − | 177.402i | − | 0.384820i | −0.981315 | − | 0.192410i | \(-0.938370\pi\) | ||
0.981315 | − | 0.192410i | \(-0.0616303\pi\) | |||||||
\(462\) | −104.453 | + | 126.860i | −0.226089 | + | 0.274589i | ||||
\(463\) | −530.403 | −1.14558 | −0.572790 | − | 0.819702i | \(-0.694139\pi\) | ||||
−0.572790 | + | 0.819702i | \(0.694139\pi\) | |||||||
\(464\) | − | 25.7701i | − | 0.0555391i | ||||||
\(465\) | 58.5699 | 0.125957 | ||||||||
\(466\) | 213.210 | 0.457532 | ||||||||
\(467\) | −562.622 | −1.20476 | −0.602379 | − | 0.798210i | \(-0.705780\pi\) | ||||
−0.602379 | + | 0.798210i | \(0.705780\pi\) | |||||||
\(468\) | − | 235.410i | − | 0.503012i | ||||||
\(469\) | − | 170.270i | − | 0.363050i | ||||||
\(470\) | − | 506.259i | − | 1.07715i | ||||||
\(471\) | −99.8315 | −0.211956 | ||||||||
\(472\) | − | 776.568i | − | 1.64527i | ||||||
\(473\) | −515.445 | − | 424.402i | −1.08973 | − | 0.897256i | ||||
\(474\) | −446.022 | −0.940975 | ||||||||
\(475\) | 47.5428i | 0.100090i | ||||||||
\(476\) | 12.5334 | 0.0263307 | ||||||||
\(477\) | 230.745 | 0.483743 | ||||||||
\(478\) | 898.012 | 1.87869 | ||||||||
\(479\) | 715.033i | 1.49276i | 0.665519 | + | 0.746381i | \(0.268210\pi\) | ||||
−0.665519 | + | 0.746381i | \(0.731790\pi\) | |||||||
\(480\) | 114.861i | 0.239293i | ||||||||
\(481\) | 252.175i | 0.524272i | ||||||||
\(482\) | −13.3362 | −0.0276685 | ||||||||
\(483\) | 24.3010i | 0.0503127i | ||||||||
\(484\) | 153.916 | + | 786.993i | 0.318008 | + | 1.62602i | ||||
\(485\) | −118.878 | −0.245110 | ||||||||
\(486\) | − | 50.8176i | − | 0.104563i | ||||||
\(487\) | −742.123 | −1.52387 | −0.761933 | − | 0.647655i | \(-0.775750\pi\) | ||||
−0.761933 | + | 0.647655i | \(0.775750\pi\) | |||||||
\(488\) | −1004.34 | −2.05808 | ||||||||
\(489\) | −530.430 | −1.08472 | ||||||||
\(490\) | 51.0263i | 0.104135i | ||||||||
\(491\) | − | 339.593i | − | 0.691635i | −0.938302 | − | 0.345818i | \(-0.887602\pi\) | ||
0.938302 | − | 0.345818i | \(-0.112398\pi\) | |||||||
\(492\) | − | 393.556i | − | 0.799910i | ||||||
\(493\) | 13.0470 | 0.0264646 | ||||||||
\(494\) | 367.023i | 0.742962i | ||||||||
\(495\) | −46.9036 | + | 56.9654i | −0.0947548 | + | 0.115082i | ||||
\(496\) | 21.3510 | 0.0430463 | ||||||||
\(497\) | 307.603i | 0.618920i | ||||||||
\(498\) | 283.100 | 0.568473 | ||||||||
\(499\) | 587.144 | 1.17664 | 0.588320 | − | 0.808628i | \(-0.299789\pi\) | ||||
0.588320 | + | 0.808628i | \(0.299789\pi\) | |||||||
\(500\) | −74.0954 | −0.148191 | ||||||||
\(501\) | 489.966i | 0.977977i | ||||||||
\(502\) | 32.0239i | 0.0637927i | ||||||||
\(503\) | 349.582i | 0.694993i | 0.937681 | + | 0.347497i | \(0.112968\pi\) | ||||
−0.937681 | + | 0.347497i | \(0.887032\pi\) | |||||||
\(504\) | −67.9814 | −0.134884 | ||||||||
\(505\) | − | 80.6032i | − | 0.159610i | ||||||
\(506\) | 146.802 | + | 120.872i | 0.290122 | + | 0.238878i | ||||
\(507\) | 49.8909 | 0.0984041 | ||||||||
\(508\) | 30.1057i | 0.0592631i | ||||||||
\(509\) | 202.587 | 0.398010 | 0.199005 | − | 0.979998i | \(-0.436229\pi\) | ||||
0.199005 | + | 0.979998i | \(0.436229\pi\) | |||||||
\(510\) | 9.02487 | 0.0176958 | ||||||||
\(511\) | −151.250 | −0.295988 | ||||||||
\(512\) | 90.2402i | 0.176250i | ||||||||
\(513\) | 49.4080i | 0.0963118i | ||||||||
\(514\) | 337.314i | 0.656254i | ||||||||
\(515\) | 3.32275 | 0.00645194 | ||||||||
\(516\) | − | 696.746i | − | 1.35028i | ||||||
\(517\) | −485.598 | + | 589.768i | −0.939260 | + | 1.14075i | ||||
\(518\) | 183.694 | 0.354622 | ||||||||
\(519\) | 356.129i | 0.686182i | ||||||||
\(520\) | −226.763 | −0.436083 | ||||||||
\(521\) | −288.271 | −0.553304 | −0.276652 | − | 0.960970i | \(-0.589225\pi\) | ||||
−0.276652 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(522\) | −178.509 | −0.341972 | ||||||||
\(523\) | − | 609.078i | − | 1.16459i | −0.812979 | − | 0.582293i | \(-0.802156\pi\) | ||
0.812979 | − | 0.582293i | \(-0.197844\pi\) | |||||||
\(524\) | − | 465.223i | − | 0.887830i | ||||||
\(525\) | 22.9129i | 0.0436436i | ||||||||
\(526\) | −1257.73 | −2.39113 | ||||||||
\(527\) | 10.8097i | 0.0205117i | ||||||||
\(528\) | −17.0982 | + | 20.7660i | −0.0323829 | + | 0.0393296i | ||||
\(529\) | −500.879 | −0.946841 | ||||||||
\(530\) | − | 560.671i | − | 1.05787i | ||||||
\(531\) | −272.007 | −0.512255 | ||||||||
\(532\) | 166.725 | 0.313392 | ||||||||
\(533\) | −405.954 | −0.761639 | ||||||||
\(534\) | − | 408.180i | − | 0.764381i | ||||||
\(535\) | − | 134.628i | − | 0.251640i | ||||||
\(536\) | − | 551.201i | − | 1.02836i | ||||||
\(537\) | −585.192 | −1.08974 | ||||||||
\(538\) | − | 287.075i | − | 0.533596i | ||||||
\(539\) | 48.9438 | − | 59.4433i | 0.0908049 | − | 0.110284i | ||||
\(540\) | −77.0022 | −0.142597 | ||||||||
\(541\) | − | 636.893i | − | 1.17725i | −0.808406 | − | 0.588625i | \(-0.799669\pi\) | ||
0.808406 | − | 0.588625i | \(-0.200331\pi\) | |||||||
\(542\) | −830.184 | −1.53170 | ||||||||
\(543\) | −98.8873 | −0.182113 | ||||||||
\(544\) | −21.1987 | −0.0389682 | ||||||||
\(545\) | − | 230.196i | − | 0.422379i | ||||||
\(546\) | 176.884i | 0.323963i | ||||||||
\(547\) | 196.340i | 0.358939i | 0.983764 | + | 0.179469i | \(0.0574381\pi\) | ||||
−0.983764 | + | 0.179469i | \(0.942562\pi\) | |||||||
\(548\) | −378.562 | −0.690807 | ||||||||
\(549\) | 351.789i | 0.640782i | ||||||||
\(550\) | 138.416 | + | 113.968i | 0.251665 | + | 0.207214i | ||||
\(551\) | 173.557 | 0.314986 | ||||||||
\(552\) | 78.6675i | 0.142514i | ||||||||
\(553\) | 208.994 | 0.377927 | ||||||||
\(554\) | −1052.65 | −1.90009 | ||||||||
\(555\) | 82.4860 | 0.148623 | ||||||||
\(556\) | 782.607i | 1.40757i | ||||||||
\(557\) | − | 72.6355i | − | 0.130405i | −0.997872 | − | 0.0652024i | \(-0.979231\pi\) | ||
0.997872 | − | 0.0652024i | \(-0.0207693\pi\) | |||||||
\(558\) | − | 147.898i | − | 0.265050i | ||||||
\(559\) | −718.695 | −1.28568 | ||||||||
\(560\) | 8.35262i | 0.0149154i | ||||||||
\(561\) | −10.5135 | − | 8.65655i | −0.0187407 | − | 0.0154306i | ||||
\(562\) | 1190.97 | 2.11916 | ||||||||
\(563\) | − | 632.420i | − | 1.12330i | −0.827373 | − | 0.561652i | \(-0.810166\pi\) | ||
0.827373 | − | 0.561652i | \(-0.189834\pi\) | |||||||
\(564\) | −797.211 | −1.41349 | ||||||||
\(565\) | −154.045 | −0.272646 | ||||||||
\(566\) | 98.5669 | 0.174146 | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | 995.776i | 1.75313i | ||||||||
\(569\) | − | 190.350i | − | 0.334535i | −0.985912 | − | 0.167267i | \(-0.946506\pi\) | ||
0.985912 | − | 0.167267i | \(-0.0534943\pi\) | |||||||
\(570\) | 120.053 | 0.210619 | ||||||||
\(571\) | 561.099i | 0.982660i | 0.870973 | + | 0.491330i | \(0.163489\pi\) | ||||
−0.870973 | + | 0.491330i | \(0.836511\pi\) | |||||||
\(572\) | 666.358 | + | 548.660i | 1.16496 | + | 0.959196i | ||||
\(573\) | 110.357 | 0.192595 | ||||||||
\(574\) | 295.713i | 0.515179i | ||||||||
\(575\) | 26.5146 | 0.0461123 | ||||||||
\(576\) | 306.982 | 0.532955 | ||||||||
\(577\) | 812.560 | 1.40825 | 0.704125 | − | 0.710076i | \(-0.251340\pi\) | ||||
0.704125 | + | 0.710076i | \(0.251340\pi\) | |||||||
\(578\) | − | 940.461i | − | 1.62709i | ||||||
\(579\) | − | 285.488i | − | 0.493071i | ||||||
\(580\) | 270.489i | 0.466360i | ||||||||
\(581\) | −132.653 | −0.228318 | ||||||||
\(582\) | 300.185i | 0.515782i | ||||||||
\(583\) | −537.789 | + | 653.155i | −0.922451 | + | 1.12033i | ||||
\(584\) | −489.627 | −0.838403 | ||||||||
\(585\) | 79.4279i | 0.135774i | ||||||||
\(586\) | 541.650 | 0.924318 | ||||||||
\(587\) | −364.939 | −0.621701 | −0.310851 | − | 0.950459i | \(-0.600614\pi\) | ||||
−0.310851 | + | 0.950459i | \(0.600614\pi\) | |||||||
\(588\) | 80.3517 | 0.136652 | ||||||||
\(589\) | 143.795i | 0.244134i | ||||||||
\(590\) | 660.931i | 1.12022i | ||||||||
\(591\) | − | 596.215i | − | 1.00882i | ||||||
\(592\) | 30.0693 | 0.0507927 | ||||||||
\(593\) | − | 417.866i | − | 0.704665i | −0.935875 | − | 0.352332i | \(-0.885389\pi\) | ||
0.935875 | − | 0.352332i | \(-0.114611\pi\) | |||||||
\(594\) | 143.846 | + | 118.439i | 0.242165 | + | 0.199392i | ||||
\(595\) | −4.22881 | −0.00710724 | ||||||||
\(596\) | − | 716.131i | − | 1.20156i | ||||||
\(597\) | 258.310 | 0.432679 | ||||||||
\(598\) | 204.688 | 0.342288 | ||||||||
\(599\) | 1132.05 | 1.88990 | 0.944952 | − | 0.327209i | \(-0.106108\pi\) | ||||
0.944952 | + | 0.327209i | \(0.106108\pi\) | |||||||
\(600\) | 74.1738i | 0.123623i | ||||||||
\(601\) | − | 657.422i | − | 1.09388i | −0.837172 | − | 0.546940i | \(-0.815793\pi\) | ||
0.837172 | − | 0.546940i | \(-0.184207\pi\) | |||||||
\(602\) | 523.525i | 0.869644i | ||||||||
\(603\) | −193.068 | −0.320180 | ||||||||
\(604\) | 105.379i | 0.174469i | ||||||||
\(605\) | −51.9316 | − | 265.534i | −0.0858373 | − | 0.438899i | ||||
\(606\) | −203.535 | −0.335867 | ||||||||
\(607\) | − | 678.467i | − | 1.11774i | −0.829256 | − | 0.558869i | \(-0.811236\pi\) | ||
0.829256 | − | 0.558869i | \(-0.188764\pi\) | |||||||
\(608\) | −281.994 | −0.463806 | ||||||||
\(609\) | 83.6445 | 0.137347 | ||||||||
\(610\) | 854.786 | 1.40129 | ||||||||
\(611\) | 822.325i | 1.34587i | ||||||||
\(612\) | − | 14.2116i | − | 0.0232215i | ||||||
\(613\) | − | 30.6052i | − | 0.0499269i | −0.999688 | − | 0.0249635i | \(-0.992053\pi\) | ||
0.999688 | − | 0.0249635i | \(-0.00794694\pi\) | |||||||
\(614\) | −897.334 | −1.46146 | ||||||||
\(615\) | 132.787i | 0.215914i | ||||||||
\(616\) | 158.442 | − | 192.430i | 0.257210 | − | 0.312387i | ||||
\(617\) | 871.930 | 1.41318 | 0.706588 | − | 0.707625i | \(-0.250233\pi\) | ||||
0.706588 | + | 0.707625i | \(0.250233\pi\) | |||||||
\(618\) | − | 8.39044i | − | 0.0135768i | ||||||
\(619\) | 675.320 | 1.09099 | 0.545493 | − | 0.838115i | \(-0.316342\pi\) | ||||
0.545493 | + | 0.838115i | \(0.316342\pi\) | |||||||
\(620\) | −224.104 | −0.361459 | ||||||||
\(621\) | 27.5548 | 0.0443716 | ||||||||
\(622\) | − | 15.0449i | − | 0.0241880i | ||||||
\(623\) | 191.262i | 0.307001i | ||||||||
\(624\) | 28.9545i | 0.0464015i | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 623.314i | − | 0.995710i | ||||||
\(627\) | −139.856 | − | 115.153i | −0.223055 | − | 0.183657i | ||||
\(628\) | 381.982 | 0.608252 | ||||||||
\(629\) | 15.2236i | 0.0242029i | ||||||||
\(630\) | 57.8584 | 0.0918388 | ||||||||
\(631\) | 435.147 | 0.689614 | 0.344807 | − | 0.938674i | \(-0.387944\pi\) | ||||
0.344807 | + | 0.938674i | \(0.387944\pi\) | |||||||
\(632\) | 676.557 | 1.07050 | ||||||||
\(633\) | 544.413i | 0.860053i | ||||||||
\(634\) | − | 740.519i | − | 1.16801i | ||||||
\(635\) | − | 10.1577i | − | 0.0159964i | ||||||
\(636\) | −882.894 | −1.38820 | ||||||||
\(637\) | − | 82.8829i | − | 0.130114i | ||||||
\(638\) | 416.044 | − | 505.294i | 0.652107 | − | 0.791996i | ||||
\(639\) | 348.789 | 0.545836 | ||||||||
\(640\) | − | 480.654i | − | 0.751022i | ||||||
\(641\) | 349.206 | 0.544784 | 0.272392 | − | 0.962186i | \(-0.412185\pi\) | ||||
0.272392 | + | 0.962186i | \(0.412185\pi\) | |||||||
\(642\) | −339.955 | −0.529524 | ||||||||
\(643\) | −1140.87 | −1.77429 | −0.887144 | − | 0.461493i | \(-0.847314\pi\) | ||||
−0.887144 | + | 0.461493i | \(0.847314\pi\) | |||||||
\(644\) | − | 92.9823i | − | 0.144382i | ||||||
\(645\) | 235.084i | 0.364471i | ||||||||
\(646\) | 22.1570i | 0.0342987i | ||||||||
\(647\) | 830.684 | 1.28390 | 0.641950 | − | 0.766746i | \(-0.278125\pi\) | ||||
0.641950 | + | 0.766746i | \(0.278125\pi\) | |||||||
\(648\) | 77.0837i | 0.118956i | ||||||||
\(649\) | 633.957 | − | 769.953i | 0.976820 | − | 1.18637i | ||||
\(650\) | 192.996 | 0.296917 | ||||||||
\(651\) | 69.3009i | 0.106453i | ||||||||
\(652\) | 2029.57 | 3.11283 | ||||||||
\(653\) | 551.009 | 0.843812 | 0.421906 | − | 0.906640i | \(-0.361361\pi\) | ||||
0.421906 | + | 0.906640i | \(0.361361\pi\) | |||||||
\(654\) | −581.280 | −0.888808 | ||||||||
\(655\) | 156.968i | 0.239645i | ||||||||
\(656\) | 48.4059i | 0.0737894i | ||||||||
\(657\) | 171.501i | 0.261037i | ||||||||
\(658\) | 599.014 | 0.910355 | ||||||||
\(659\) | − | 193.074i | − | 0.292980i | −0.989212 | − | 0.146490i | \(-0.953202\pi\) | ||
0.989212 | − | 0.146490i | \(-0.0467976\pi\) | |||||||
\(660\) | 179.466 | − | 217.965i | 0.271918 | − | 0.330250i | ||||
\(661\) | −1047.86 | −1.58527 | −0.792634 | − | 0.609698i | \(-0.791291\pi\) | ||||
−0.792634 | + | 0.609698i | \(0.791291\pi\) | |||||||
\(662\) | 701.934i | 1.06032i | ||||||||
\(663\) | −14.6593 | −0.0221105 | ||||||||
\(664\) | −429.425 | −0.646725 | ||||||||
\(665\) | −56.2534 | −0.0845916 | ||||||||
\(666\) | − | 208.289i | − | 0.312747i | ||||||
\(667\) | − | 96.7928i | − | 0.145117i | ||||||
\(668\) | − | 1874.74i | − | 2.80650i | ||||||
\(669\) | −640.321 | −0.957131 | ||||||||
\(670\) | 469.123i | 0.700183i | ||||||||
\(671\) | −995.786 | − | 819.901i | −1.48403 | − | 1.22191i | ||||
\(672\) | −135.905 | −0.202239 | ||||||||
\(673\) | 164.660i | 0.244666i | 0.992489 | + | 0.122333i | \(0.0390376\pi\) | ||||
−0.992489 | + | 0.122333i | \(0.960962\pi\) | |||||||
\(674\) | −33.4721 | −0.0496619 | ||||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | −190.896 | −0.282391 | ||||||||
\(677\) | − | 1335.05i | − | 1.97201i | −0.166727 | − | 0.986003i | \(-0.553320\pi\) | ||
0.166727 | − | 0.986003i | \(-0.446680\pi\) | |||||||
\(678\) | 388.986i | 0.573726i | ||||||||
\(679\) | − | 140.658i | − | 0.207155i | ||||||
\(680\) | −13.6896 | −0.0201317 | ||||||||
\(681\) | − | 267.166i | − | 0.392314i | ||||||
\(682\) | 418.644 | + | 344.699i | 0.613848 | + | 0.505424i | ||||
\(683\) | −226.154 | −0.331118 | −0.165559 | − | 0.986200i | \(-0.552943\pi\) | ||||
−0.165559 | + | 0.986200i | \(0.552943\pi\) | |||||||
\(684\) | − | 189.048i | − | 0.276386i | ||||||
\(685\) | 127.728 | 0.186464 | ||||||||
\(686\) | −60.3752 | −0.0880105 | ||||||||
\(687\) | 228.464 | 0.332553 | ||||||||
\(688\) | 85.6971i | 0.124560i | ||||||||
\(689\) | 910.707i | 1.32178i | ||||||||
\(690\) | − | 66.9533i | − | 0.0970338i | ||||||
\(691\) | −514.860 | −0.745094 | −0.372547 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372547 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(692\) | − | 1362.64i | − | 1.96914i | ||||||
\(693\) | −67.4023 | − | 55.4971i | −0.0972616 | − | 0.0800824i | ||||
\(694\) | 292.404 | 0.421332 | ||||||||
\(695\) | − | 264.054i | − | 0.379934i | ||||||
\(696\) | 270.775 | 0.389045 | ||||||||
\(697\) | −24.5072 | −0.0351610 | ||||||||
\(698\) | 1374.04 | 1.96854 | ||||||||
\(699\) | 113.281i | 0.162062i | ||||||||
\(700\) | − | 87.6709i | − | 0.125244i | ||||||
\(701\) | − | 1123.33i | − | 1.60247i | −0.598350 | − | 0.801235i | \(-0.704177\pi\) | ||
0.598350 | − | 0.801235i | \(-0.295823\pi\) | |||||||
\(702\) | 200.567 | 0.285708 | ||||||||
\(703\) | 202.511i | 0.288067i | ||||||||
\(704\) | −715.471 | + | 868.953i | −1.01629 | + | 1.23431i | ||||
\(705\) | 268.981 | 0.381534 | ||||||||
\(706\) | − | 291.769i | − | 0.413270i | ||||||
\(707\) | 95.3710 | 0.134895 | ||||||||
\(708\) | 1040.77 | 1.47002 | ||||||||
\(709\) | −849.866 | −1.19868 | −0.599341 | − | 0.800494i | \(-0.704571\pi\) | ||||
−0.599341 | + | 0.800494i | \(0.704571\pi\) | |||||||
\(710\) | − | 847.497i | − | 1.19366i | ||||||
\(711\) | − | 236.977i | − | 0.333301i | ||||||
\(712\) | 619.155i | 0.869599i | ||||||||
\(713\) | 80.1944 | 0.112475 | ||||||||
\(714\) | 10.6784i | 0.0149557i | ||||||||
\(715\) | −224.831 | − | 185.119i | −0.314449 | − | 0.258908i | ||||
\(716\) | 2239.10 | 3.12724 | ||||||||
\(717\) | 477.124i | 0.665445i | ||||||||
\(718\) | 791.126 | 1.10185 | ||||||||
\(719\) | 171.596 | 0.238659 | 0.119330 | − | 0.992855i | \(-0.461925\pi\) | ||||
0.119330 | + | 0.992855i | \(0.461925\pi\) | |||||||
\(720\) | 9.47098 | 0.0131541 | ||||||||
\(721\) | 3.93153i | 0.00545289i | ||||||||
\(722\) | − | 882.102i | − | 1.22175i | ||||||
\(723\) | − | 7.08568i | − | 0.00980039i | ||||||
\(724\) | 378.370 | 0.522610 | ||||||||
\(725\) | − | 91.2637i | − | 0.125881i | ||||||
\(726\) | −670.512 | + | 131.135i | −0.923570 | + | 0.180627i | ||||
\(727\) | 550.052 | 0.756605 | 0.378303 | − | 0.925682i | \(-0.376508\pi\) | ||||
0.378303 | + | 0.925682i | \(0.376508\pi\) | |||||||
\(728\) | − | 268.310i | − | 0.368557i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 416.718 | 0.570846 | ||||||||
\(731\) | −43.3872 | −0.0593532 | ||||||||
\(732\) | − | 1346.04i | − | 1.83885i | ||||||
\(733\) | − | 719.483i | − | 0.981559i | −0.871284 | − | 0.490780i | \(-0.836712\pi\) | ||
0.871284 | − | 0.490780i | \(-0.163288\pi\) | |||||||
\(734\) | − | 492.488i | − | 0.670964i | ||||||
\(735\) | −27.1109 | −0.0368856 | ||||||||
\(736\) | 157.268i | 0.213679i | ||||||||
\(737\) | 449.977 | − | 546.506i | 0.610552 | − | 0.741527i | ||||
\(738\) | 335.306 | 0.454345 | ||||||||
\(739\) | 784.036i | 1.06094i | 0.847703 | + | 0.530471i | \(0.177985\pi\) | ||||
−0.847703 | + | 0.530471i | \(0.822015\pi\) | |||||||
\(740\) | −315.614 | −0.426505 | ||||||||
\(741\) | −195.004 | −0.263163 | ||||||||
\(742\) | 663.395 | 0.894063 | ||||||||
\(743\) | − | 1364.56i | − | 1.83655i | −0.395940 | − | 0.918276i | \(-0.629581\pi\) | ||
0.395940 | − | 0.918276i | \(-0.370419\pi\) | |||||||
\(744\) | 224.342i | 0.301534i | ||||||||
\(745\) | 241.625i | 0.324328i | ||||||||
\(746\) | 1111.60 | 1.49008 | ||||||||
\(747\) | 150.414i | 0.201358i | ||||||||
\(748\) | 40.2277 | + | 33.1223i | 0.0537803 | + | 0.0442811i | ||||
\(749\) | 159.293 | 0.212675 | ||||||||
\(750\) | − | 63.1287i | − | 0.0841716i | ||||||
\(751\) | −561.098 | −0.747134 | −0.373567 | − | 0.927603i | \(-0.621865\pi\) | ||||
−0.373567 | + | 0.927603i | \(0.621865\pi\) | |||||||
\(752\) | 98.0539 | 0.130391 | ||||||||
\(753\) | −17.0147 | −0.0225958 | ||||||||
\(754\) | − | 704.541i | − | 0.934404i | ||||||
\(755\) | − | 35.5552i | − | 0.0470930i | ||||||
\(756\) | − | 91.1102i | − | 0.120516i | ||||||
\(757\) | 1015.88 | 1.34199 | 0.670993 | − | 0.741463i | \(-0.265868\pi\) | ||||
0.670993 | + | 0.741463i | \(0.265868\pi\) | |||||||
\(758\) | − | 594.173i | − | 0.783870i | ||||||
\(759\) | −64.2208 | + | 77.9974i | −0.0846124 | + | 0.102763i | ||||
\(760\) | −182.104 | −0.239611 | ||||||||
\(761\) | 380.426i | 0.499903i | 0.968258 | + | 0.249951i | \(0.0804146\pi\) | ||||
−0.968258 | + | 0.249951i | \(0.919585\pi\) | |||||||
\(762\) | −25.6498 | −0.0336611 | ||||||||
\(763\) | 272.372 | 0.356975 | ||||||||
\(764\) | −422.254 | −0.552689 | ||||||||
\(765\) | 4.79502i | 0.00626800i | ||||||||
\(766\) | − | 2240.71i | − | 2.92521i | ||||||
\(767\) | − | 1073.56i | − | 1.39969i | ||||||
\(768\) | −504.778 | −0.657263 | ||||||||
\(769\) | − | 258.509i | − | 0.336163i | −0.985773 | − | 0.168081i | \(-0.946243\pi\) | ||
0.985773 | − | 0.168081i | \(-0.0537572\pi\) | |||||||
\(770\) | −134.848 | + | 163.776i | −0.175128 | + | 0.212696i | ||||
\(771\) | −179.219 | −0.232450 | ||||||||
\(772\) | 1092.35i | 1.41497i | ||||||||
\(773\) | −934.303 | −1.20867 | −0.604336 | − | 0.796730i | \(-0.706562\pi\) | ||||
−0.604336 | + | 0.796730i | \(0.706562\pi\) | |||||||
\(774\) | 593.622 | 0.766954 | ||||||||
\(775\) | 75.6134 | 0.0975657 | ||||||||
\(776\) | − | 455.341i | − | 0.586780i | ||||||
\(777\) | 97.5987i | 0.125610i | ||||||||
\(778\) | 1363.97i | 1.75318i | ||||||||
\(779\) | −326.005 | −0.418492 | ||||||||
\(780\) | − | 303.913i | − | 0.389632i | ||||||
\(781\) | −812.909 | + | 987.293i | −1.04086 | + | 1.26414i | ||||
\(782\) | 12.3569 | 0.0158017 | ||||||||
\(783\) | − | 94.8440i | − | 0.121129i | ||||||
\(784\) | −9.88295 | −0.0126058 | ||||||||
\(785\) | −128.882 | −0.164181 | ||||||||
\(786\) | 396.367 | 0.504283 | ||||||||
\(787\) | 602.118i | 0.765080i | 0.923939 | + | 0.382540i | \(0.124951\pi\) | ||||
−0.923939 | + | 0.382540i | \(0.875049\pi\) | |||||||
\(788\) | 2281.28i | 2.89503i | ||||||||
\(789\) | − | 668.248i | − | 0.846956i | ||||||
\(790\) | −575.812 | −0.728876 | ||||||||
\(791\) | − | 182.268i | − | 0.230428i | ||||||
\(792\) | −218.196 | − | 179.656i | −0.275499 | − | 0.226838i | ||||
\(793\) | −1388.44 | −1.75087 | ||||||||
\(794\) | − | 46.4138i | − | 0.0584557i | ||||||
\(795\) | 297.891 | 0.374706 | ||||||||
\(796\) | −988.362 | −1.24166 | ||||||||
\(797\) | −39.9447 | −0.0501189 | −0.0250594 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250594 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(798\) | 142.048i | 0.178005i | ||||||||
\(799\) | 49.6433i | 0.0621318i | ||||||||
\(800\) | 148.284i | 0.185355i | ||||||||
\(801\) | 216.870 | 0.270750 | ||||||||
\(802\) | − | 2329.83i | − | 2.90503i | ||||||
\(803\) | −485.456 | − | 399.711i | −0.604553 | − | 0.497772i | ||||
\(804\) | 738.732 | 0.918821 | ||||||||
\(805\) | 31.3725i | 0.0389720i | ||||||||
\(806\) | 583.724 | 0.724223 | ||||||||
\(807\) | 152.526 | 0.189004 | ||||||||
\(808\) | 308.736 | 0.382099 | ||||||||
\(809\) | − | 538.906i | − | 0.666139i | −0.942902 | − | 0.333069i | \(-0.891916\pi\) | ||
0.942902 | − | 0.333069i | \(-0.108084\pi\) | |||||||
\(810\) | − | 65.6053i | − | 0.0809942i | ||||||
\(811\) | − | 747.119i | − | 0.921232i | −0.887599 | − | 0.460616i | \(-0.847628\pi\) | ||
0.887599 | − | 0.460616i | \(-0.152372\pi\) | |||||||
\(812\) | −320.047 | −0.394146 | ||||||||
\(813\) | − | 441.086i | − | 0.542541i | ||||||
\(814\) | 589.590 | + | 485.452i | 0.724313 | + | 0.596378i | ||||
\(815\) | −684.782 | −0.840224 | ||||||||
\(816\) | 1.74797i | 0.00214212i | ||||||||
\(817\) | −577.155 | −0.706432 | ||||||||
\(818\) | −843.499 | −1.03117 | ||||||||
\(819\) | −93.9804 | −0.114750 | ||||||||
\(820\) | − | 508.078i | − | 0.619608i | ||||||
\(821\) | − | 477.472i | − | 0.581574i | −0.956788 | − | 0.290787i | \(-0.906083\pi\) | ||
0.956788 | − | 0.290787i | \(-0.0939171\pi\) | |||||||
\(822\) | − | 322.532i | − | 0.392375i | ||||||
\(823\) | −150.719 | −0.183134 | −0.0915668 | − | 0.995799i | \(-0.529187\pi\) | ||||
−0.0915668 | + | 0.995799i | \(0.529187\pi\) | |||||||
\(824\) | 12.7272i | 0.0154456i | ||||||||
\(825\) | −60.5523 | + | 73.5420i | −0.0733967 | + | 0.0891418i | ||||
\(826\) | −782.024 | −0.946760 | ||||||||
\(827\) | − | 1258.20i | − | 1.52140i | −0.649103 | − | 0.760701i | \(-0.724856\pi\) | ||
0.649103 | − | 0.760701i | \(-0.275144\pi\) | |||||||
\(828\) | −105.432 | −0.127333 | ||||||||
\(829\) | −305.944 | −0.369051 | −0.184526 | − | 0.982828i | \(-0.559075\pi\) | ||||
−0.184526 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(830\) | 365.480 | 0.440338 | ||||||||
\(831\) | − | 559.285i | − | 0.673026i | ||||||
\(832\) | 1211.60i | 1.45625i | ||||||||
\(833\) | − | 5.00360i | − | 0.00600672i | ||||||
\(834\) | −666.775 | −0.799491 | ||||||||
\(835\) | 632.544i | 0.757538i | ||||||||
\(836\) | 535.126 | + | 440.607i | 0.640102 | + | 0.527042i | ||||
\(837\) | 78.5798 | 0.0938827 | ||||||||
\(838\) | − | 2036.70i | − | 2.43043i | ||||||
\(839\) | 925.604 | 1.10322 | 0.551611 | − | 0.834101i | \(-0.314013\pi\) | ||||
0.551611 | + | 0.834101i | \(0.314013\pi\) | |||||||
\(840\) | −87.7637 | −0.104481 | ||||||||
\(841\) | 507.838 | 0.603850 | ||||||||
\(842\) | 1790.41i | 2.12638i | ||||||||
\(843\) | 632.775i | 0.750623i | ||||||||
\(844\) | − | 2083.07i | − | 2.46810i | ||||||
\(845\) | 64.4089 | 0.0762235 | ||||||||
\(846\) | − | 679.218i | − | 0.802858i | ||||||
\(847\) | 314.184 | − | 61.4463i | 0.370937 | − | 0.0725458i | ||||
\(848\) | 108.593 | 0.128057 | ||||||||
\(849\) | 52.3697i | 0.0616840i | ||||||||
\(850\) | 11.6511 | 0.0137071 | ||||||||
\(851\) | 112.940 | 0.132715 | ||||||||
\(852\) | −1334.56 | −1.56639 | ||||||||
\(853\) | − | 1249.50i | − | 1.46483i | −0.680858 | − | 0.732415i | \(-0.738393\pi\) | ||
0.680858 | − | 0.732415i | \(-0.261607\pi\) | |||||||
\(854\) | 1011.40i | 1.18431i | ||||||||
\(855\) | 63.7854i | 0.0746028i | ||||||||
\(856\) | 515.667 | 0.602414 | ||||||||
\(857\) | 1327.44i | 1.54894i | 0.632612 | + | 0.774469i | \(0.281983\pi\) | ||||
−0.632612 | + | 0.774469i | \(0.718017\pi\) | |||||||
\(858\) | −467.454 | + | 567.732i | −0.544818 | + | 0.661693i | ||||
\(859\) | 589.495 | 0.686258 | 0.343129 | − | 0.939288i | \(-0.388513\pi\) | ||||
0.343129 | + | 0.939288i | \(0.388513\pi\) | |||||||
\(860\) | − | 899.495i | − | 1.04592i | ||||||
\(861\) | −157.115 | −0.182480 | ||||||||
\(862\) | 1302.39 | 1.51090 | ||||||||
\(863\) | 456.664 | 0.529159 | 0.264579 | − | 0.964364i | \(-0.414767\pi\) | ||||
0.264579 | + | 0.964364i | \(0.414767\pi\) | |||||||
\(864\) | 154.102i | 0.178358i | ||||||||
\(865\) | 459.760i | 0.531515i | ||||||||
\(866\) | − | 753.785i | − | 0.870422i | ||||||
\(867\) | 499.678 | 0.576330 | ||||||||
\(868\) | − | 265.164i | − | 0.305488i | ||||||
\(869\) | 670.794 | + | 552.312i | 0.771914 | + | 0.635572i | ||||
\(870\) | −230.454 | −0.264890 | ||||||||
\(871\) | − | 762.004i | − | 0.874861i | ||||||
\(872\) | 881.726 | 1.01115 | ||||||||
\(873\) | −159.492 | −0.182694 | ||||||||
\(874\) | 164.377 | 0.188074 | ||||||||
\(875\) | 29.5804i | 0.0338062i | ||||||||
\(876\) | − | 656.210i | − | 0.749098i | ||||||
\(877\) | 50.3291i | 0.0573878i | 0.999588 | + | 0.0286939i | \(0.00913481\pi\) | ||||
−0.999588 | + | 0.0286939i | \(0.990865\pi\) | |||||||
\(878\) | −1006.54 | −1.14640 | ||||||||
\(879\) | 287.785i | 0.327401i | ||||||||
\(880\) | −22.0736 | + | 26.8088i | −0.0250837 | + | 0.0304646i | ||||
\(881\) | 192.520 | 0.218524 | 0.109262 | − | 0.994013i | \(-0.465151\pi\) | ||||
0.109262 | + | 0.994013i | \(0.465151\pi\) | |||||||
\(882\) | 68.4590i | 0.0776179i | ||||||||
\(883\) | −913.532 | −1.03458 | −0.517289 | − | 0.855811i | \(-0.673059\pi\) | ||||
−0.517289 | + | 0.855811i | \(0.673059\pi\) | |||||||
\(884\) | 56.0903 | 0.0634505 | ||||||||
\(885\) | −351.160 | −0.396791 | ||||||||
\(886\) | − | 539.496i | − | 0.608912i | ||||||
\(887\) | 1484.18i | 1.67326i | 0.547771 | + | 0.836628i | \(0.315476\pi\) | ||||
−0.547771 | + | 0.836628i | \(0.684524\pi\) | |||||||
\(888\) | 315.948i | 0.355797i | ||||||||
\(889\) | 12.0188 | 0.0135195 | ||||||||
\(890\) | − | 526.957i | − | 0.592087i | ||||||
\(891\) | −62.9278 | + | 76.4270i | −0.0706260 | + | 0.0857767i | ||||
\(892\) | 2450.04 | 2.74668 | ||||||||
\(893\) | 660.376i | 0.739503i | ||||||||
\(894\) | 610.138 | 0.682481 | ||||||||
\(895\) | −755.480 | −0.844111 | ||||||||
\(896\) | 568.717 | 0.634729 | ||||||||
\(897\) | 108.753i | 0.121241i | ||||||||
\(898\) | 1911.85i | 2.12901i | ||||||||
\(899\) | − | 276.030i | − | 0.307042i | ||||||
\(900\) | −99.4094 | −0.110455 | ||||||||
\(901\) | 54.9789i | 0.0610199i | ||||||||
\(902\) | −781.485 | + | 949.129i | −0.866391 | + | 1.05225i | ||||
\(903\) | −278.155 | −0.308034 | ||||||||
\(904\) | − | 590.041i | − | 0.652701i | ||||||
\(905\) | −127.663 | −0.141064 | ||||||||
\(906\) | −89.7822 | −0.0990973 | ||||||||
\(907\) | −932.895 | −1.02855 | −0.514275 | − | 0.857625i | \(-0.671939\pi\) | ||||
−0.514275 | + | 0.857625i | \(0.671939\pi\) | |||||||
\(908\) | 1022.25i | 1.12582i | ||||||||
\(909\) | − | 108.141i | − | 0.118967i | ||||||
\(910\) | 228.356i | 0.250941i | ||||||||
\(911\) | 502.091 | 0.551142 | 0.275571 | − | 0.961281i | \(-0.411133\pi\) | ||||
0.275571 | + | 0.961281i | \(0.411133\pi\) | |||||||
\(912\) | 23.2522i | 0.0254958i | ||||||||
\(913\) | −425.767 | − | 350.564i | −0.466338 | − | 0.383969i | ||||
\(914\) | 1132.36 | 1.23891 | ||||||||
\(915\) | 454.158i | 0.496347i | ||||||||
\(916\) | −874.165 | −0.954329 | ||||||||
\(917\) | −185.727 | −0.202537 | ||||||||
\(918\) | 12.1081 | 0.0131897 | ||||||||
\(919\) | 532.086i | 0.578984i | 0.957180 | + | 0.289492i | \(0.0934864\pi\) | ||||
−0.957180 | + | 0.289492i | \(0.906514\pi\) | |||||||
\(920\) | 101.559i | 0.110391i | ||||||||
\(921\) | − | 476.764i | − | 0.517659i | ||||||
\(922\) | −578.322 | −0.627247 | ||||||||
\(923\) | 1376.60i | 1.49144i | ||||||||
\(924\) | 257.899 | + | 212.347i | 0.279112 | + | 0.229813i | ||||
\(925\) | 106.489 | 0.115123 | ||||||||
\(926\) | 1729.09i | 1.86727i | ||||||||
\(927\) | 4.45794 | 0.00480899 | ||||||||
\(928\) | 541.319 | 0.583318 | ||||||||
\(929\) | 1099.03 | 1.18302 | 0.591510 | − | 0.806298i | \(-0.298532\pi\) | ||||
0.591510 | + | 0.806298i | \(0.298532\pi\) | |||||||
\(930\) | − | 190.935i | − | 0.205307i | ||||||
\(931\) | − | 66.5600i | − | 0.0714930i | ||||||
\(932\) | − | 433.444i | − | 0.465068i | ||||||
\(933\) | 7.99355 | 0.00856758 | ||||||||
\(934\) | 1834.12i | 1.96373i | ||||||||
\(935\) | −13.5729 | − | 11.1756i | −0.0145165 | − | 0.0119525i | ||||
\(936\) | −304.234 | −0.325037 | ||||||||
\(937\) | − | 1167.21i | − | 1.24568i | −0.782348 | − | 0.622842i | \(-0.785978\pi\) | ||
0.782348 | − | 0.622842i | \(-0.214022\pi\) | |||||||
\(938\) | −555.073 | −0.591763 | ||||||||
\(939\) | 331.174 | 0.352688 | ||||||||
\(940\) | −1029.20 | −1.09489 | ||||||||
\(941\) | 1057.61i | 1.12392i | 0.827166 | + | 0.561958i | \(0.189952\pi\) | ||||
−0.827166 | + | 0.561958i | \(0.810048\pi\) | |||||||
\(942\) | 325.446i | 0.345484i | ||||||||
\(943\) | 181.813i | 0.192802i | ||||||||
\(944\) | −128.011 | −0.135605 | ||||||||
\(945\) | 30.7409i | 0.0325300i | ||||||||
\(946\) | −1383.53 | + | 1680.33i | −1.46251 | + | 1.77624i | ||||
\(947\) | 59.2468 | 0.0625626 | 0.0312813 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312813 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(948\) | 906.737i | 0.956473i | ||||||||
\(949\) | −676.882 | −0.713258 | ||||||||
\(950\) | 154.987 | 0.163145 | ||||||||
\(951\) | 393.446 | 0.413718 | ||||||||
\(952\) | − | 16.1977i | − | 0.0170144i | ||||||
\(953\) | − | 231.973i | − | 0.243414i | −0.992566 | − | 0.121707i | \(-0.961163\pi\) | ||
0.992566 | − | 0.121707i | \(-0.0388368\pi\) | |||||||
\(954\) | − | 752.219i | − | 0.788490i | ||||||
\(955\) | 142.470 | 0.149183 | ||||||||
\(956\) | − | 1825.61i | − | 1.90963i | ||||||
\(957\) | 268.468 | + | 221.049i | 0.280531 | + | 0.230981i | ||||
\(958\) | 2330.97 | 2.43317 | ||||||||
\(959\) | 151.130i | 0.157591i | ||||||||
\(960\) | 396.312 | 0.412825 | ||||||||
\(961\) | −732.304 | −0.762023 | ||||||||
\(962\) | 822.078 | 0.854551 | ||||||||
\(963\) | − | 180.622i | − | 0.187562i | ||||||
\(964\) | 27.1117i | 0.0281242i | ||||||||
\(965\) | − | 368.563i | − | 0.381931i | ||||||
\(966\) | 79.2202 | 0.0820085 | ||||||||
\(967\) | − | 90.1447i | − | 0.0932210i | −0.998913 | − | 0.0466105i | \(-0.985158\pi\) | ||
0.998913 | − | 0.0466105i | \(-0.0148420\pi\) | |||||||
\(968\) | 1017.08 | − | 198.915i | 1.05070 | − | 0.205490i | ||||
\(969\) | −11.7723 | −0.0121489 | ||||||||
\(970\) | 387.537i | 0.399523i | ||||||||
\(971\) | −276.170 | −0.284418 | −0.142209 | − | 0.989837i | \(-0.545421\pi\) | ||||
−0.142209 | + | 0.989837i | \(0.545421\pi\) | |||||||
\(972\) | −103.309 | −0.106285 | ||||||||
\(973\) | 312.433 | 0.321103 | ||||||||
\(974\) | 2419.29i | 2.48387i | ||||||||
\(975\) | 102.541i | 0.105170i | ||||||||
\(976\) | 165.558i | 0.169629i | ||||||||
\(977\) | −101.200 | −0.103582 | −0.0517911 | − | 0.998658i | \(-0.516493\pi\) | ||||
−0.0517911 | + | 0.998658i | \(0.516493\pi\) | |||||||
\(978\) | 1729.18i | 1.76807i | ||||||||
\(979\) | −505.451 | + | 613.880i | −0.516293 | + | 0.627048i | ||||
\(980\) | 103.734 | 0.105851 | ||||||||
\(981\) | − | 308.841i | − | 0.314823i | ||||||
\(982\) | −1107.06 | −1.12735 | ||||||||
\(983\) | −1714.69 | −1.74435 | −0.872173 | − | 0.489198i | \(-0.837290\pi\) | ||||
−0.872173 | + | 0.489198i | \(0.837290\pi\) | |||||||
\(984\) | −508.616 | −0.516886 | ||||||||
\(985\) | − | 769.711i | − | 0.781432i | ||||||
\(986\) | − | 42.5327i | − | 0.0431367i | ||||||
\(987\) | 318.263i | 0.322455i | ||||||||
\(988\) | 746.136 | 0.755199 | ||||||||
\(989\) | 321.879i | 0.325459i | ||||||||
\(990\) | 185.704 | + | 152.904i | 0.187580 | + | 0.154448i | ||||
\(991\) | 345.608 | 0.348746 | 0.174373 | − | 0.984680i | \(-0.444210\pi\) | ||||
0.174373 | + | 0.984680i | \(0.444210\pi\) | |||||||
\(992\) | 448.491i | 0.452108i | ||||||||
\(993\) | −372.946 | −0.375575 | ||||||||
\(994\) | 1002.77 | 1.00882 | ||||||||
\(995\) | 333.476 | 0.335152 | ||||||||
\(996\) | − | 575.525i | − | 0.577837i | ||||||
\(997\) | − | 1286.97i | − | 1.29085i | −0.763825 | − | 0.645424i | \(-0.776681\pi\) | ||
0.763825 | − | 0.645424i | \(-0.223319\pi\) | |||||||
\(998\) | − | 1914.06i | − | 1.91790i | ||||||
\(999\) | 110.667 | 0.110777 |
(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 | 1155.3.b.a.736.13 | ✓ | 96 | |
11.10 | odd | 2 | inner | 1155.3.b.a.736.84 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.3.b.a.736.13 | ✓ | 96 | 1.1 | even | 1 | trivial | |
1155.3.b.a.736.84 | yes | 96 | 11.10 | odd | 2 | inner |