Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,3,Mod(209,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5177896084\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.20 | ||
Character | \(\chi\) | \(=\) | 1120.209 |
Dual form | 1120.3.c.g.209.19 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.26463i | 1.75488i | 0.479689 | + | 0.877439i | \(0.340750\pi\) | ||||
−0.479689 | + | 0.877439i | \(0.659250\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.99643 | + | 0.188883i | 0.999286 | + | 0.0377767i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.12587 | − | 3.38729i | 0.875124 | − | 0.483899i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.7163 | −2.07959 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.50793i | − | 0.864357i | −0.901788 | − | 0.432179i | \(-0.857745\pi\) | ||
0.901788 | − | 0.432179i | \(-0.142255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 16.8405i | − | 1.29542i | −0.761886 | − | 0.647711i | \(-0.775727\pi\) | ||
0.761886 | − | 0.647711i | \(-0.224273\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.994401 | + | 26.3044i | −0.0662934 | + | 1.75362i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.7673 | 1.28043 | 0.640213 | − | 0.768197i | \(-0.278846\pi\) | ||||
0.640213 | + | 0.768197i | \(0.278846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.78431 | −0.409701 | −0.204850 | − | 0.978793i | \(-0.565671\pi\) | ||||
−0.204850 | + | 0.978793i | \(0.565671\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.8328 | + | 32.2504i | 0.849182 | + | 1.53574i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.3018i | 0.752250i | 0.926569 | + | 0.376125i | \(0.122744\pi\) | ||||
−0.926569 | + | 0.376125i | \(0.877256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9286 | + | 1.88748i | 0.997146 | + | 0.0754994i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 51.1530i | − | 1.89456i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.7974i | 0.372325i | 0.982519 | + | 0.186162i | \(0.0596051\pi\) | ||||
−0.982519 | + | 0.186162i | \(0.940395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 52.3486i | 1.68866i | 0.535820 | + | 0.844332i | \(0.320002\pi\) | ||||
−0.535820 | + | 0.844332i | \(0.679998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 50.0558 | 1.51684 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.2473 | − | 15.7673i | 0.892780 | − | 0.450494i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.3938 | 0.443075 | 0.221537 | − | 0.975152i | \(-0.428892\pi\) | ||||
0.221537 | + | 0.975152i | \(0.428892\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 88.6589 | 2.27331 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.8696i | 1.31389i | 0.753938 | + | 0.656946i | \(0.228152\pi\) | ||||
−0.753938 | + | 0.656946i | \(0.771848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.63054 | 0.154199 | 0.0770993 | − | 0.997023i | \(-0.475434\pi\) | ||||
0.0770993 | + | 0.997023i | \(0.475434\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −93.5149 | − | 3.53520i | −2.07811 | − | 0.0785601i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 69.6204 | 1.48128 | 0.740642 | − | 0.671899i | \(-0.234521\pi\) | ||||
0.740642 | + | 0.671899i | \(0.234521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26.0525 | − | 41.5002i | 0.531684 | − | 0.846943i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 114.597i | 2.24699i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.7961 | 1.35464 | 0.677322 | − | 0.735687i | \(-0.263140\pi\) | ||||
0.677322 | + | 0.735687i | \(0.263140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79589 | − | 47.5057i | 0.0326525 | − | 0.863740i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 40.9815i | − | 0.718974i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.57383 | −0.0605734 | −0.0302867 | − | 0.999541i | \(-0.509642\pi\) | ||||
−0.0302867 | + | 0.999541i | \(0.509642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.8212 | 0.456086 | 0.228043 | − | 0.973651i | \(-0.426767\pi\) | ||||
0.228043 | + | 0.973651i | \(0.426767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −114.654 | + | 63.3977i | −1.81990 | + | 1.00631i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.18088 | − | 84.1423i | 0.0489367 | − | 1.29450i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.1210 | −0.927180 | −0.463590 | − | 0.886050i | \(-0.653439\pi\) | ||||
−0.463590 | + | 0.886050i | \(0.653439\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −91.0874 | −1.32011 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78.8867 | −1.11108 | −0.555540 | − | 0.831490i | \(-0.687489\pi\) | ||||
−0.555540 | + | 0.831490i | \(0.687489\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26.1926 | −0.358803 | −0.179401 | − | 0.983776i | \(-0.557416\pi\) | ||||
−0.179401 | + | 0.983776i | \(0.557416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.93691 | + | 131.240i | −0.132492 | + | 1.74987i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −32.2061 | − | 58.2443i | −0.418261 | − | 0.756420i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 55.3047 | 0.700060 | 0.350030 | − | 0.936739i | \(-0.386171\pi\) | ||||
0.350030 | + | 0.936739i | \(0.386171\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 100.855 | 1.24512 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 62.8573i | − | 0.757316i | −0.925537 | − | 0.378658i | \(-0.876386\pi\) | ||
0.925537 | − | 0.378658i | \(-0.123614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 108.759 | + | 4.11147i | 1.27951 | + | 0.0483702i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −56.8445 | −0.653385 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 53.9148i | − | 0.605784i | −0.953025 | − | 0.302892i | \(-0.902048\pi\) | ||
0.953025 | − | 0.302892i | \(-0.0979522\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −57.0436 | − | 103.163i | −0.626852 | − | 1.13365i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −275.596 | −2.96340 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.8938 | − | 1.47033i | −0.409408 | − | 0.0154771i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.1560 | −0.176866 | −0.0884331 | − | 0.996082i | \(-0.528186\pi\) | ||||
−0.0884331 | + | 0.996082i | \(0.528186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 177.954i | 1.79751i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49.3961 | 0.489071 | 0.244535 | − | 0.969640i | \(-0.421365\pi\) | ||||
0.244535 | + | 0.969640i | \(0.421365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 35.5249 | 0.344902 | 0.172451 | − | 0.985018i | \(-0.444831\pi\) | ||||
0.172451 | + | 0.985018i | \(0.444831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 83.0089 | + | 164.505i | 0.790561 | + | 1.56672i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 150.957 | 1.41081 | 0.705405 | − | 0.708804i | \(-0.250765\pi\) | ||||
0.705405 | + | 0.708804i | \(0.250765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.49558i | − | 0.0137209i | −0.999976 | − | 0.00686044i | \(-0.997816\pi\) | ||
0.999976 | − | 0.00686044i | \(-0.00218376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.3072i | 0.777542i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 184.712i | 1.63462i | 0.576197 | + | 0.817311i | \(0.304536\pi\) | ||||
−0.576197 | + | 0.817311i | \(0.695464\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.26801 | + | 86.4470i | −0.0284175 | + | 0.751713i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 315.192i | 2.69395i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 133.343 | − | 73.7320i | 1.12053 | − | 0.619597i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.5992 | 0.252886 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −283.604 | −2.30572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 124.198 | + | 14.1393i | 0.993582 | + | 0.113114i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 48.9383i | − | 0.385341i | −0.981264 | − | 0.192670i | \(-0.938285\pi\) | ||
0.981264 | − | 0.192670i | \(-0.0617148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 34.9073i | 0.270599i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −121.072 | −0.924214 | −0.462107 | − | 0.886824i | \(-0.652906\pi\) | ||||
−0.462107 | + | 0.886824i | \(0.652906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −47.6857 | + | 26.3677i | −0.358539 | + | 0.198254i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.66194 | − | 255.582i | 0.0715699 | − | 1.89320i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 202.587i | − | 1.47874i | −0.673300 | − | 0.739369i | \(-0.735124\pi\) | ||
0.673300 | − | 0.739369i | \(-0.264876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −176.207 | −1.26768 | −0.633840 | − | 0.773465i | \(-0.718522\pi\) | ||||
−0.633840 | + | 0.773465i | \(0.718522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 366.526i | 2.59947i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160.118 | −1.11971 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.03945 | + | 53.9486i | −0.0140652 | + | 0.372059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 218.483 | + | 137.157i | 1.48628 | + | 0.933041i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.331i | 0.861281i | 0.902524 | + | 0.430640i | \(0.141712\pi\) | ||||
−0.902524 | + | 0.430640i | \(0.858288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 189.463 | 1.25472 | 0.627361 | − | 0.778729i | \(-0.284135\pi\) | ||||
0.627361 | + | 0.778729i | \(0.284135\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −407.403 | −2.66277 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.88777 | + | 261.556i | −0.0637921 | + | 1.68746i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.0847i | − | 0.127928i | −0.997952 | − | 0.0639641i | \(-0.979626\pi\) | ||
0.997952 | − | 0.0639641i | \(-0.0203743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 377.980i | 2.37723i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 58.6061 | + | 105.988i | 0.364013 | + | 0.658312i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −186.675 | −1.14524 | −0.572622 | − | 0.819819i | \(-0.694074\pi\) | ||||
−0.572622 | + | 0.819819i | \(0.694074\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 250.100 | + | 9.45469i | 1.51576 | + | 0.0573012i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 36.8456 | 0.220632 | 0.110316 | − | 0.993897i | \(-0.464814\pi\) | ||||
0.110316 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −114.602 | −0.678117 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 145.694 | 0.852011 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 193.813i | − | 1.12031i | −0.828389 | − | 0.560153i | \(-0.810742\pi\) | ||
0.828389 | − | 0.560153i | \(-0.189258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 159.103 | − | 72.8781i | 0.909160 | − | 0.416446i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 18.8149i | − | 0.106299i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 185.148i | − | 1.03435i | −0.855880 | − | 0.517175i | \(-0.826984\pi\) | ||
0.855880 | − | 0.517175i | \(-0.173016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −96.1838 | −0.531402 | −0.265701 | − | 0.964055i | \(-0.585603\pi\) | ||||
−0.265701 | + | 0.964055i | \(0.585603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 146.469i | 0.800375i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 81.9103 | + | 3.09651i | 0.442759 | + | 0.0167379i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 206.962i | − | 1.10675i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −173.270 | − | 313.357i | −0.916772 | − | 1.65797i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −216.967 | −1.13595 | −0.567977 | − | 0.823044i | \(-0.692274\pi\) | ||||
−0.567977 | + | 0.823044i | \(0.692274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 364.330i | 1.88772i | 0.330346 | + | 0.943860i | \(0.392835\pi\) | ||||
−0.330346 | + | 0.943860i | \(0.607165\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 442.978 | + | 16.7462i | 2.27168 | + | 0.0858779i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −53.5832 | −0.271996 | −0.135998 | − | 0.990709i | \(-0.543424\pi\) | ||||
−0.135998 | + | 0.990709i | \(0.543424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 306.342i | − | 1.53941i | −0.638401 | − | 0.769704i | \(-0.720404\pi\) | ||
0.638401 | − | 0.769704i | \(-0.279596\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 327.044i | − | 1.62709i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 36.5740 | + | 66.1436i | 0.180168 | + | 0.325831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1751 | + | 269.156i | −0.0496344 | + | 1.31295i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 323.826i | − | 1.56438i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 74.0127i | 0.354128i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.57377i | − | 0.0358946i | −0.999839 | − | 0.0179473i | \(-0.994287\pi\) | ||
0.999839 | − | 0.0179473i | \(-0.00571311\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 415.310i | − | 1.94981i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33.1290 | + | 1.25240i | 0.154088 | + | 0.00582510i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 177.320 | + | 320.681i | 0.817142 | + | 1.47779i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 137.894i | − | 0.629655i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 366.571i | − | 1.65869i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 365.812 | 1.64041 | 0.820207 | − | 0.572067i | \(-0.193858\pi\) | ||||
0.820207 | + | 0.572067i | \(0.193858\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −466.573 | − | 35.3268i | −2.07366 | − | 0.157008i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 320.799i | − | 1.41321i | −0.707608 | − | 0.706605i | \(-0.750226\pi\) | ||
0.707608 | − | 0.706605i | \(-0.249774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −202.193 | −0.882937 | −0.441469 | − | 0.897277i | \(-0.645542\pi\) | ||||
−0.441469 | + | 0.897277i | \(0.645542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 306.635 | − | 169.553i | 1.32742 | − | 0.733997i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2649i | 0.0698065i | 0.999391 | + | 0.0349032i | \(0.0111123\pi\) | ||||
−0.999391 | + | 0.0349032i | \(0.988888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 347.853 | + | 13.1501i | 1.48023 | + | 0.0559580i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 291.159i | 1.22852i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −332.222 | −1.39005 | −0.695025 | − | 0.718986i | \(-0.744607\pi\) | ||||
−0.695025 | + | 0.718986i | \(0.744607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 324.579i | − | 1.34680i | −0.739278 | − | 0.673400i | \(-0.764833\pi\) | ||
0.739278 | − | 0.673400i | \(-0.235167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 70.5850i | 0.290473i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 138.008 | − | 202.432i | 0.563300 | − | 0.826253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 131.092i | 0.530735i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 330.920 | 1.32900 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −302.261 | −1.20423 | −0.602113 | − | 0.798411i | \(-0.705675\pi\) | ||||
−0.602113 | + | 0.798411i | \(0.705675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 164.504 | 0.650213 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.6454 | + | 572.574i | −0.0848838 | + | 2.24539i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.7241 | 0.103985 | 0.0519924 | − | 0.998647i | \(-0.483443\pi\) | ||||
0.0519924 | + | 0.998647i | \(0.483443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100.426 | − | 55.5304i | 0.387746 | − | 0.214403i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 202.088i | − | 0.774285i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 159.326i | 0.605800i | 0.953022 | + | 0.302900i | \(0.0979549\pi\) | ||||
−0.953022 | + | 0.302900i | \(0.902045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 358.724 | + | 13.5611i | 1.35368 | + | 0.0511739i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 283.842 | 1.06308 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 120.174 | 0.446744 | 0.223372 | − | 0.974733i | \(-0.428293\pi\) | ||||
0.223372 | + | 0.974733i | \(0.428293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110.800i | 0.408854i | 0.978882 | + | 0.204427i | \(0.0655331\pi\) | ||||
−0.978882 | + | 0.204427i | \(0.934467\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 543.113 | − | 300.313i | 1.98942 | − | 1.10005i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.9461 | − | 237.020i | 0.0652584 | − | 0.861890i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −406.197 | −1.46641 | −0.733207 | − | 0.680006i | \(-0.761977\pi\) | ||||
−0.733207 | + | 0.680006i | \(0.761977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 979.774i | − | 3.51174i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −283.218 | −1.00789 | −0.503946 | − | 0.863735i | \(-0.668119\pi\) | ||||
−0.503946 | + | 0.863735i | \(0.668119\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 244.520i | − | 0.864027i | −0.901867 | − | 0.432014i | \(-0.857803\pi\) | ||
0.901867 | − | 0.432014i | \(-0.142197\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.74073 | − | 204.761i | 0.0271604 | − | 0.718461i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 182.472 | + | 329.998i | 0.635790 | + | 1.14982i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 184.813 | 0.639492 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 90.3202i | − | 0.310379i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.5005i | 0.0938584i | 0.998898 | + | 0.0469292i | \(0.0149435\pi\) | ||||
−0.998898 | + | 0.0469292i | \(0.985056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8564 | − | 0.675037i | −0.0605302 | − | 0.00228826i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −486.359 | −1.63757 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 291.370 | 0.974481 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.6178 | − | 22.4595i | 0.134943 | − | 0.0746164i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 260.052i | 0.858259i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 139.007 | + | 5.25497i | 0.455760 | + | 0.0172294i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 135.158i | − | 0.440254i | −0.975471 | − | 0.220127i | \(-0.929353\pi\) | ||
0.975471 | − | 0.220127i | \(-0.0706472\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 187.026i | 0.605261i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.13693i | − | 0.0229483i | −0.999934 | − | 0.0114742i | \(-0.996348\pi\) | ||
0.999934 | − | 0.0114742i | \(-0.00365242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −367.602 | −1.17445 | −0.587224 | − | 0.809424i | \(-0.699779\pi\) | ||||
−0.587224 | + | 0.809424i | \(0.699779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −584.835 | + | 295.106i | −1.85662 | + | 0.936844i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 438.224 | 1.38241 | 0.691206 | − | 0.722658i | \(-0.257080\pi\) | ||||
0.691206 | + | 0.722658i | \(0.257080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 102.661 | 0.321822 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 794.731i | 2.47580i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −169.443 | −0.524592 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.7861 | − | 419.810i | 0.0978035 | − | 1.29172i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.87366 | 0.0240785 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 426.485 | − | 235.824i | 1.29631 | − | 0.716791i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 239.131i | 0.722450i | 0.932479 | + | 0.361225i | \(0.117641\pi\) | ||||
−0.932479 | + | 0.361225i | \(0.882359\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −306.832 | −0.921416 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −310.383 | − | 11.7336i | −0.926518 | − | 0.0350257i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 247.164i | 0.733425i | 0.930334 | + | 0.366713i | \(0.119517\pi\) | ||||
−0.930334 | + | 0.366713i | \(0.880483\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −972.442 | −2.86856 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 497.727 | 1.45961 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0213 | − | 342.472i | 0.0554557 | − | 0.998461i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −455.112 | − | 17.2049i | −1.31916 | − | 0.0498692i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −217.690 | −0.627348 | −0.313674 | − | 0.949531i | \(-0.601560\pi\) | ||||
−0.313674 | + | 0.949531i | \(0.601560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 117.972 | 0.338029 | 0.169015 | − | 0.985614i | \(-0.445941\pi\) | ||||
0.169015 | + | 0.985614i | \(0.445941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −861.441 | −2.45425 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 361.591 | 1.02434 | 0.512168 | − | 0.858885i | \(-0.328842\pi\) | ||||
0.512168 | + | 0.858885i | \(0.328842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −394.152 | − | 14.9004i | −1.11029 | − | 0.0419729i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 388.172 | + | 702.004i | 1.08732 | + | 1.96640i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −317.055 | −0.883163 | −0.441581 | − | 0.897221i | \(-0.645582\pi\) | ||||
−0.441581 | + | 0.897221i | \(0.645582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −300.404 | −0.832145 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 161.094i | 0.443784i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −130.870 | − | 4.94734i | −0.358547 | − | 0.0135544i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −148.629 | −0.404983 | −0.202492 | − | 0.979284i | \(-0.564904\pi\) | ||||
−0.202492 | + | 0.979284i | \(0.564904\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1008.24i | − | 2.73236i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 439.814 | − | 243.194i | 1.18548 | − | 0.655510i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 172.124 | 0.461458 | 0.230729 | − | 0.973018i | \(-0.425889\pi\) | ||||
0.230729 | + | 0.973018i | \(0.425889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −74.4381 | + | 653.855i | −0.198502 | + | 1.74361i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 181.834 | 0.482318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 323.133i | − | 0.852592i | −0.904584 | − | 0.426296i | \(-0.859818\pi\) | ||
0.904584 | − | 0.426296i | \(-0.140182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 257.642 | 0.676226 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 156.518 | 0.408662 | 0.204331 | − | 0.978902i | \(-0.434498\pi\) | ||||
0.204331 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −149.914 | − | 297.097i | −0.389388 | − | 0.771681i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −124.099 | −0.320670 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 424.478i | − | 1.09120i | −0.838045 | − | 0.545602i | \(-0.816301\pi\) | ||
0.838045 | − | 0.545602i | \(-0.183699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 376.612i | 0.963201i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 637.399i | − | 1.62188i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 276.326 | + | 10.4461i | 0.699560 | + | 0.0264459i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 125.289i | − | 0.315590i | −0.987472 | − | 0.157795i | \(-0.949562\pi\) | ||
0.987472 | − | 0.157795i | \(-0.0504385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −138.816 | − | 251.047i | −0.347911 | − | 0.629192i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −498.995 | −1.24438 | −0.622189 | − | 0.782867i | \(-0.713756\pi\) | ||||
−0.622189 | + | 0.782867i | \(0.713756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 881.575 | 2.18753 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 503.913 | + | 19.0497i | 1.24423 | + | 0.0470364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 155.871i | − | 0.382975i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 371.026i | 0.907155i | 0.891217 | + | 0.453577i | \(0.149852\pi\) | ||||
−0.891217 | + | 0.453577i | \(0.850148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1066.55 | 2.59500 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.8928 | + | 12.1056i | −0.0530093 | + | 0.0293114i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8727 | − | 314.062i | 0.0286089 | − | 0.756776i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 927.667i | − | 2.22462i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 298.761 | 0.713033 | 0.356516 | − | 0.934289i | \(-0.383964\pi\) | ||||
0.356516 | + | 0.934289i | \(0.383964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 39.1981i | − | 0.0931070i | −0.998916 | − | 0.0465535i | \(-0.985176\pi\) | ||
0.998916 | − | 0.0465535i | \(-0.0148238\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1303.04 | −3.08047 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 542.628 | + | 41.0853i | 1.27677 | + | 0.0966714i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 170.429 | − | 94.2386i | 0.399132 | − | 0.220699i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 842.963i | − | 1.96495i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 336.264 | 0.780196 | 0.390098 | − | 0.920773i | \(-0.372441\pi\) | ||||
0.390098 | + | 0.920773i | \(0.372441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −295.132 | −0.681597 | −0.340799 | − | 0.940136i | \(-0.610697\pi\) | ||||
−0.340799 | + | 0.940136i | \(0.610697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −284.019 | − | 10.7370i | −0.652918 | − | 0.0246827i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 134.682i | − | 0.308197i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 104.219i | 0.237400i | 0.992930 | + | 0.118700i | \(0.0378727\pi\) | ||||
−0.992930 | + | 0.118700i | \(0.962127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −487.608 | + | 776.732i | −1.10569 | + | 1.76130i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −219.958 | −0.496518 | −0.248259 | − | 0.968694i | \(-0.579858\pi\) | ||||
−0.248259 | + | 0.968694i | \(0.579858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1836 | − | 269.382i | 0.0228845 | − | 0.605352i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −675.615 | −1.51144 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −274.759 | −0.611936 | −0.305968 | − | 0.952042i | \(-0.598980\pi\) | ||||
−0.305968 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 512.188 | 1.13567 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 997.453i | 2.20188i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −265.529 | − | 526.219i | −0.583579 | − | 1.15653i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 172.854i | 0.378237i | 0.981954 | + | 0.189119i | \(0.0605630\pi\) | ||||
−0.981954 | + | 0.189119i | \(0.939437\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1113.46i | − | 2.42584i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −741.040 | −1.60746 | −0.803731 | − | 0.594993i | \(-0.797155\pi\) | ||||
−0.803731 | + | 0.594993i | \(0.797155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 153.903i | − | 0.332404i | −0.986092 | − | 0.166202i | \(-0.946850\pi\) | ||
0.986092 | − | 0.166202i | \(-0.0531504\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1377.00 | − | 52.0555i | −2.96128 | − | 0.111947i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 695.292i | 1.48885i | 0.667708 | + | 0.744423i | \(0.267276\pi\) | ||||
−0.667708 | + | 0.744423i | \(0.732724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −380.545 | + | 210.422i | −0.811397 | + | 0.448661i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 105.739 | 0.224498 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 63.0427i | − | 0.133283i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −194.052 | − | 14.6928i | −0.408531 | − | 0.0309321i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1343.76 | −2.81711 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 205.463i | − | 0.428942i | −0.976730 | − | 0.214471i | \(-0.931197\pi\) | ||
0.976730 | − | 0.214471i | \(-0.0688028\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 276.079i | − | 0.573969i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −557.989 | + | 308.539i | −1.15526 | + | 0.638798i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −85.7189 | − | 3.24049i | −0.176740 | − | 0.00668141i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 117.450i | − | 0.241171i | −0.992703 | − | 0.120586i | \(-0.961523\pi\) | ||
0.992703 | − | 0.120586i | \(-0.0384772\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 982.775i | − | 2.00976i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 324.679i | 0.661261i | 0.943760 | + | 0.330631i | \(0.107261\pi\) | ||||
−0.943760 | + | 0.330631i | \(0.892739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 235.030i | 0.476735i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −33.6125 | + | 889.134i | −0.0679040 | + | 1.79623i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −483.250 | + | 267.212i | −0.972334 | + | 0.537650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 684.255i | 1.37125i | 0.727954 | + | 0.685626i | \(0.240471\pi\) | ||||
−0.727954 | + | 0.685626i | \(0.759529\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 193.979i | 0.387183i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 628.664 | 1.24983 | 0.624915 | − | 0.780693i | \(-0.285134\pi\) | ||||
0.624915 | + | 0.780693i | \(0.285134\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 246.804 | + | 9.33010i | 0.488722 | + | 0.0184755i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 603.336i | − | 1.19001i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −554.759 | −1.08990 | −0.544950 | − | 0.838469i | \(-0.683451\pi\) | ||||
−0.544950 | + | 0.838469i | \(0.683451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −160.452 | + | 88.7219i | −0.313997 | + | 0.173624i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 398.191i | 0.776200i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 177.498 | + | 6.71007i | 0.344656 | + | 0.0130293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 661.946i | − | 1.28036i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1020.35 | 1.96600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 255.396i | − | 0.490204i | −0.969497 | − | 0.245102i | \(-0.921178\pi\) | ||
0.969497 | − | 0.245102i | \(-0.0788215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 849.106i | 1.62353i | 0.583985 | + | 0.811765i | \(0.301493\pi\) | ||||
−0.583985 | + | 0.811765i | \(0.698507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 383.676 | + | 837.619i | 0.730812 | + | 1.59546i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1139.48i | 2.16221i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 229.649 | 0.434120 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 66.8891 | 0.125968 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 907.189 | 1.70204 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 754.245 | + | 28.5132i | 1.40980 | + | 0.0532957i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 974.739 | 1.81516 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −394.581 | − | 247.706i | −0.732061 | − | 0.459565i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 654.500i | 1.20980i | 0.796303 | + | 0.604899i | \(0.206786\pi\) | ||||
−0.796303 | + | 0.604899i | \(0.793214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 506.372i | − | 0.932546i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.282489 | − | 7.47254i | 0.000518329 | − | 0.0137111i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −388.810 | −0.710805 | −0.355402 | − | 0.934713i | \(-0.615656\pi\) | ||||
−0.355402 | + | 0.934713i | \(0.615656\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −520.712 | −0.948474 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 84.0505i | − | 0.152542i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 338.790 | − | 187.333i | 0.612639 | − | 0.338758i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.3020 | + | 431.228i | −0.0293729 | + | 0.776987i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −942.596 | −1.69227 | −0.846137 | − | 0.532966i | \(-0.821077\pi\) | ||||
−0.846137 | + | 0.532966i | \(0.821077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 111.661i | − | 0.199752i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1089.58 | 1.94220 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 364.114i | − | 0.646739i | −0.946273 | − | 0.323370i | \(-0.895184\pi\) | ||
0.946273 | − | 0.323370i | \(-0.104816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.8891 | + | 922.902i | −0.0617506 | + | 1.63346i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 617.822 | − | 341.623i | 1.08963 | − | 0.602511i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −350.135 | −0.615352 | −0.307676 | − | 0.951491i | \(-0.599551\pi\) | ||||
−0.307676 | + | 0.951491i | \(0.599551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 800.701i | 1.40228i | 0.713025 | + | 0.701139i | \(0.247325\pi\) | ||||
−0.713025 | + | 0.701139i | \(0.752675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1142.25i | − | 1.99346i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.6568 | + | 431.309i | −0.0567944 | + | 0.750103i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −546.338 | −0.946859 | −0.473429 | − | 0.880832i | \(-0.656984\pi\) | ||||
−0.473429 | + | 0.880832i | \(0.656984\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1918.06 | −3.31272 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −212.916 | − | 385.055i | −0.366464 | − | 0.662746i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 682.633i | − | 1.17090i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −59.5345 | + | 1574.84i | −0.101768 | + | 2.69203i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 547.924i | − | 0.933430i | −0.884408 | − | 0.466715i | \(-0.845437\pi\) | ||
0.884408 | − | 0.466715i | \(-0.154563\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 407.498i | − | 0.691847i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 282.096i | − | 0.477320i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 826.816 | 1.39429 | 0.697147 | − | 0.716928i | \(-0.254452\pi\) | ||||
0.697147 | + | 0.716928i | \(0.254452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 680.167 | − | 343.210i | 1.14314 | − | 0.576824i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1612.78 | 2.70147 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −66.8880 | −0.111666 | −0.0558331 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558331 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 796.784i | 1.32576i | 0.748724 | + | 0.662882i | \(0.230667\pi\) | ||||
−0.748724 | + | 0.662882i | \(0.769333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1162.68 | 1.92816 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 152.887 | + | 5.77968i | 0.252706 | + | 0.00955319i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 697.222 | 1.14864 | 0.574318 | − | 0.818632i | \(-0.305267\pi\) | ||||
0.574318 | + | 0.818632i | \(0.305267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −348.222 | + | 192.549i | −0.571793 | + | 0.316172i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1172.44i | − | 1.91889i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 772.158 | 1.25964 | 0.629819 | − | 0.776742i | \(-0.283129\pi\) | ||||
0.629819 | + | 0.776742i | \(0.283129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1417.01 | − | 53.5680i | −2.30407 | − | 0.0871024i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 672.411i | − | 1.08981i | −0.838499 | − | 0.544904i | \(-0.816566\pi\) | ||
0.838499 | − | 0.544904i | \(-0.183434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 511.593 | 0.826483 | 0.413242 | − | 0.910621i | \(-0.364396\pi\) | ||||
0.413242 | + | 0.910621i | \(0.364396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 885.037 | 1.42518 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −182.625 | − | 330.275i | −0.293138 | − | 0.530136i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 617.875 | + | 94.1049i | 0.988600 | + | 0.150568i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −389.650 | −0.621451 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 356.847 | 0.567325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 286.544 | 0.454110 | 0.227055 | − | 0.973882i | \(-0.427090\pi\) | ||||
0.227055 | + | 0.973882i | \(0.427090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.8731 | 0.0629907 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.24362 | − | 244.517i | 0.0145569 | − | 0.385066i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −698.883 | − | 438.737i | −1.09715 | − | 0.688755i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1476.47 | 2.31060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −963.812 | −1.50361 | −0.751804 | − | 0.659387i | \(-0.770816\pi\) | ||||
−0.751804 | + | 0.659387i | \(0.770816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 207.379i | − | 0.322517i | −0.986912 | − | 0.161259i | \(-0.948445\pi\) | ||
0.986912 | − | 0.161259i | \(-0.0515553\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.59341 | + | 174.412i | −0.0102223 | + | 0.270406i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 309.166 | 0.477846 | 0.238923 | − | 0.971038i | \(-0.423206\pi\) | ||||
0.238923 | + | 0.971038i | \(0.423206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.9797i | 0.0523571i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1688.26 | + | 933.523i | −2.59334 | + | 1.43398i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −155.495 | −0.238124 | −0.119062 | − | 0.992887i | \(-0.537989\pi\) | ||||
−0.119062 | + | 0.992887i | \(0.537989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −604.928 | − | 22.8685i | −0.923554 | − | 0.0349137i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 490.230 | 0.746164 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 245.819i | − | 0.373018i | −0.982453 | − | 0.186509i | \(-0.940283\pi\) | ||
0.982453 | − | 0.186509i | \(-0.0597173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −81.2555 | −0.122928 | −0.0614640 | − | 0.998109i | \(-0.519577\pi\) | ||||
−0.0614640 | + | 0.998109i | \(0.519577\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1929.86 | 2.91080 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −243.239 | + | 122.737i | −0.365772 | + | 0.184568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −186.814 | −0.280082 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1925.87i | 2.87872i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 264.522i | − | 0.394221i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 883.945i | 1.31344i | 0.754134 | + | 0.656720i | \(0.228057\pi\) | ||||
−0.754134 | + | 0.656720i | \(0.771943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 96.5505 | − | 1275.17i | 0.143038 | − | 1.88915i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.0368i | − | 0.0236880i | −0.999930 | − | 0.0118440i | \(-0.996230\pi\) | ||
0.999930 | − | 0.0118440i | \(-0.00377016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −105.096 | + | 58.1124i | −0.154780 | + | 0.0855853i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1688.89 | 2.48001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 242.497 | 0.355046 | 0.177523 | − | 0.984117i | \(-0.443192\pi\) | ||||
0.177523 | + | 0.984117i | \(0.443192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.2653 | − | 1012.21i | 0.0558618 | − | 1.47768i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1064.47i | − | 1.54945i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1209.08i | − | 1.75483i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 283.360 | 0.410072 | 0.205036 | − | 0.978754i | \(-0.434269\pi\) | ||||
0.205036 | + | 0.978754i | \(0.434269\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 602.781 | + | 1090.12i | 0.869814 | + | 1.57305i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −880.408 | − | 33.2826i | −1.26677 | − | 0.0478887i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1172.59i | 1.68234i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −85.6288 | −0.122502 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1231.40i | − | 1.75664i | −0.478074 | − | 0.878320i | \(-0.658665\pi\) | ||
0.478074 | − | 0.878320i | \(-0.341335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −127.614 | −0.181528 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −69.2306 | + | 1831.32i | −0.0981994 | + | 2.59762i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 302.594 | − | 167.319i | 0.427998 | − | 0.236661i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 473.151i | − | 0.667349i | −0.942688 | − | 0.333675i | \(-0.891711\pi\) | ||
0.942688 | − | 0.333675i | \(-0.108289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1035.10 | −1.45584 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −905.722 | −1.27030 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −800.019 | − | 30.2436i | −1.11891 | − | 0.0422988i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1749.03i | − | 2.43937i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 345.700i | − | 0.480807i | −0.970673 | − | 0.240403i | \(-0.922720\pi\) | ||
0.970673 | − | 0.240403i | \(-0.0772797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 217.621 | − | 120.333i | 0.301832 | − | 0.166898i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1708.79 | 2.36347 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.3800 | + | 269.165i | −0.0281103 | + | 0.371262i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −691.369 | −0.950989 | −0.475495 | − | 0.879719i | \(-0.657731\pi\) | ||||
−0.475495 | + | 0.879719i | \(0.657731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 536.087 | 0.735372 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 144.329 | 0.197440 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 388.815i | 0.530443i | 0.964188 | + | 0.265221i | \(0.0854451\pi\) | ||||
−0.964188 | + | 0.265221i | \(0.914555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1065.73 | + | 726.563i | 1.44997 | + | 0.988522i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 590.643i | 0.801415i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1153.58i | 1.56100i | 0.625154 | + | 0.780501i | \(0.285036\pi\) | ||||
−0.625154 | + | 0.780501i | \(0.714964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −690.149 | −0.931375 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 100.750i | − | 0.135599i | −0.997699 | − | 0.0677993i | \(-0.978402\pi\) | ||
0.997699 | − | 0.0677993i | \(-0.0215977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.2396 | + | 641.196i | −0.0325363 | + | 0.860666i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1176.46i | 1.57491i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 924.741 | − | 511.334i | 1.23463 | − | 0.682689i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 239.295 | 0.318635 | 0.159317 | − | 0.987227i | \(-0.449071\pi\) | ||||
0.159317 | + | 0.987227i | \(0.449071\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1591.29i | − | 2.11327i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 946.639 | + | 35.7864i | 1.25383 | + | 0.0473992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 549.057 | 0.725307 | 0.362653 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362653 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 866.053i | 1.14104i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1103.71i | − | 1.45035i | −0.688567 | − | 0.725173i | \(-0.741760\pi\) | ||
0.688567 | − | 0.725173i | \(-0.258240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.06595 | − | 9.16170i | −0.00663951 | − | 0.0120075i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2035.56 | − | 76.9517i | −2.66087 | − | 0.100590i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 60.1850i | 0.0784681i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 994.764i | 1.29358i | 0.762668 | + | 0.646790i | \(0.223889\pi\) | ||||
−0.762668 | + | 0.646790i | \(0.776111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 140.693i | 0.182481i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 184.516i | − | 0.238701i | −0.992852 | − | 0.119350i | \(-0.961919\pi\) | ||
0.992852 | − | 0.119350i | \(-0.0380812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −98.8071 | + | 1304.98i | −0.127493 | + | 1.68384i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 292.347 | + | 528.706i | 0.376251 | + | 0.680446i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 419.338i | − | 0.538302i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 750.050i | 0.960371i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 552.321 | 0.705390 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.79367 | − | 100.352i | 0.00483270 | − | 0.127837i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 303.686i | 0.385878i | 0.981211 | + | 0.192939i | \(0.0618019\pi\) | ||||
−0.981211 | + | 0.192939i | \(0.938198\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −838.790 | −1.06311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 625.674 | + | 1131.52i | 0.790991 | + | 1.43050i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 468.523i | − | 0.590823i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −71.3941 | + | 1888.55i | −0.0898039 | + | 2.37554i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 407.980i | 0.511895i | 0.966691 | + | 0.255947i | \(0.0823874\pi\) | ||||
−0.966691 | + | 0.255947i | \(0.917613\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1515.44 | 1.89668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1009.09i | 1.25979i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 249.037i | 0.310134i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 272.802 | + | 540.633i | 0.338884 | + | 0.671594i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 632.673i | 0.783982i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −570.551 | −0.705255 | −0.352627 | − | 0.935764i | \(-0.614712\pi\) | ||||
−0.352627 | + | 0.935764i | \(0.614712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1192.22 | −1.47006 | −0.735030 | − | 0.678034i | \(-0.762832\pi\) | ||||
−0.735030 | + | 0.678034i | \(0.762832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −583.319 | −0.717489 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −932.708 | − | 35.2598i | −1.14443 | − | 0.0432635i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.6142 | −0.0631752 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1067.65 | + | 1930.83i | 1.30360 | + | 2.35754i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1244.34i | 1.51563i | 0.652467 | + | 0.757817i | \(0.273734\pi\) | ||||
−0.652467 | + | 0.757817i | \(0.726266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 630.742i | 0.766393i | 0.923667 | + | 0.383197i | \(0.125177\pi\) | ||||
−0.923667 | + | 0.383197i | \(0.874823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1247.82 | + | 94.4795i | 1.51251 | + | 0.114521i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −627.976 | −0.759343 | −0.379671 | − | 0.925121i | \(-0.623963\pi\) | ||||
−0.379671 | + | 0.925121i | \(0.623963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1417.09 | −1.70940 | −0.854698 | − | 0.519126i | \(-0.826257\pi\) | ||||
−0.854698 | + | 0.519126i | \(0.826257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2138.48i | − | 2.57338i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 567.092 | − | 903.345i | 0.680783 | − | 1.08445i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 184.097 | + | 6.95952i | 0.220475 | + | 0.00833475i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2677.79 | 3.19927 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 507.188i | 0.604515i | 0.953226 | + | 0.302257i | \(0.0977402\pi\) | ||||
−0.953226 | + | 0.302257i | \(0.902260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 724.416 | 0.861374 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1491.04i | − | 1.76873i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −572.599 | − | 21.6463i | −0.677632 | − | 0.0256170i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 187.447 | − | 103.648i | 0.221307 | − | 0.122371i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1287.31 | 1.51626 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 283.641i | 0.333303i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1385.60i | 1.62438i | 0.583392 | + | 0.812190i | \(0.301725\pi\) | ||||
−0.583392 | + | 0.812190i | \(0.698275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 727.949 | + | 27.5191i | 0.851403 | + | 0.0321861i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1618.95 | −1.88909 | −0.944547 | − | 0.328377i | \(-0.893498\pi\) | ||||
−0.944547 | + | 0.328377i | \(0.893498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 254.737 | 0.296551 | 0.148276 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148276 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1737.32 | + | 960.647i | −2.01779 | + | 1.11573i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1022.78i | − | 1.18515i | −0.805517 | − | 0.592573i | \(-0.798112\pi\) | ||
0.805517 | − | 0.592573i | \(-0.201888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.6080 | − | 968.373i | 0.0423214 | − | 1.11951i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 972.974i | 1.12223i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 525.834i | − | 0.605102i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1046.15i | 1.20109i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 321.098 | 0.367810 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 808.713 | − | 334.078i | 0.924243 | − | 0.381804i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1060.41 | −1.20913 | −0.604566 | − | 0.796555i | \(-0.706654\pi\) | ||||
−0.604566 | + | 0.796555i | \(0.706654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −144.780 | −0.164710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 852.759i | − | 0.967944i | −0.875083 | − | 0.483972i | \(-0.839194\pi\) | ||
0.875083 | − | 0.483972i | \(-0.160806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.04631 | 0.0102450 | 0.00512249 | − | 0.999987i | \(-0.498369\pi\) | ||||
0.00512249 | + | 0.999987i | \(0.498369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.55382 | − | 94.0074i | 0.00401562 | − | 0.106223i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1630.46 | −1.83818 | −0.919089 | − | 0.394051i | \(-0.871073\pi\) | ||||
−0.919089 | + | 0.394051i | \(0.871073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −165.768 | − | 299.789i | −0.186466 | − | 0.337221i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 958.918i | − | 1.07623i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −541.947 | −0.606883 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.9714 | − | 925.082i | 0.0390742 | − | 1.03361i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1533.95i | 1.71009i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −565.230 | −0.628732 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1562.80 | 1.73452 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 118.241 | + | 213.838i | 0.130943 | + | 0.236808i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −480.576 | − | 18.1675i | −0.531023 | − | 0.0200746i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1121.12 | −1.23608 | −0.618040 | − | 0.786147i | \(-0.712073\pi\) | ||||
−0.618040 | + | 0.786147i | \(0.712073\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −924.515 | −1.01707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1192.51 | 1.30901 | 0.654507 | − | 0.756056i | \(-0.272876\pi\) | ||||
0.654507 | + | 0.756056i | \(0.272876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −597.642 | −0.654592 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.6655 | + | 731.820i | −0.0302355 | + | 0.799803i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −741.671 | + | 410.106i | −0.808802 | + | 0.447226i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1193.80 | −1.29902 | −0.649510 | − | 0.760353i | \(-0.725026\pi\) | ||||
−0.649510 | + | 0.760353i | \(0.725026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 711.557 | 0.772591 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1328.49i | 1.43932i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 408.675 | + | 30.9430i | 0.441810 | + | 0.0334519i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −664.897 | −0.717257 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1193.64i | 1.28487i | 0.766341 | + | 0.642434i | \(0.222075\pi\) | ||||
−0.766341 | + | 0.642434i | \(0.777925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −202.801 | + | 323.050i | −0.217831 | + | 0.346993i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.5733 | 0.0402715 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.0916 | − | 1034.07i | 0.0418092 | − | 1.10596i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −233.497 | −0.249196 | −0.124598 | − | 0.992207i | \(-0.539764\pi\) | ||||
−0.124598 | + | 0.992207i | \(0.539764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1935.29i | − | 2.06101i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 582.111 | 0.618609 | 0.309304 | − | 0.950963i | \(-0.399904\pi\) | ||||
0.309304 | + | 0.950963i | \(0.399904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −932.038 | −0.988376 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −806.544 | − | 1598.39i | −0.853485 | − | 1.69142i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1490.42 | −1.57384 | −0.786918 | − | 0.617057i | \(-0.788325\pi\) | ||||
−0.786918 | + | 0.617057i | \(0.788325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 441.096i | 0.464801i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2307.09i | 2.42596i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 674.661i | − | 0.707934i | −0.935258 | − | 0.353967i | \(-0.884833\pi\) | ||
0.935258 | − | 0.353967i | \(-0.115167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1084.06 | − | 40.9815i | −1.13514 | − | 0.0429125i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 540.473i | 0.564758i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −686.221 | − | 1241.02i | −0.715559 | − | 1.29408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1779.37 | −1.85159 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2825.36 | −2.93391 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −68.8158 | + | 1820.35i | −0.0713117 | + | 1.88637i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 316.851i | 0.327664i | 0.986488 | + | 0.163832i | \(0.0523855\pi\) | ||||
−0.986488 | + | 0.163832i | \(0.947615\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 892.055i | − | 0.920594i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1735.31 | 1.78714 | 0.893569 | − | 0.448925i | \(-0.148193\pi\) | ||||
0.893569 | + | 0.448925i | \(0.148193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1079.42 | + | 596.865i | −1.10938 | + | 0.613428i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2210.15 | + | 167.342i | 2.26682 | + | 0.171633i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 216.917i | − | 0.222024i | −0.993819 | − | 0.111012i | \(-0.964591\pi\) | ||
0.993819 | − | 0.111012i | \(-0.0354092\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −512.618 | −0.523614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.9917i | 0.0285339i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −971.105 | −0.987899 | −0.493950 | − | 0.869491i | \(-0.664447\pi\) | ||||
−0.493950 | + | 0.869491i | \(0.664447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −267.725 | − | 10.1210i | −0.271802 | − | 0.0102751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1241.53 | + | 2245.29i | 1.25788 | + | 2.27486i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 114.720i | 0.115996i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 869.891 | 0.877791 | 0.438896 | − | 0.898538i | \(-0.355370\pi\) | ||||
0.438896 | + | 0.898538i | \(0.355370\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1258.94 | −1.26781 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.8629 | − | 1530.62i | 0.0581537 | − | 1.53831i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 666.914i | 0.668921i | 0.942410 | + | 0.334461i | \(0.108554\pi\) | ||||
−0.942410 | + | 0.334461i | \(0.891446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 838.590i | − | 0.839430i |
(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 | 1120.3.c.g.209.20 | 80 | ||
4.3 | odd | 2 | 280.3.c.g.69.57 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.3.c.g.209.77 | 80 | ||
7.6 | odd | 2 | inner | 1120.3.c.g.209.65 | 80 | ||
8.3 | odd | 2 | 280.3.c.g.69.22 | yes | 80 | ||
8.5 | even | 2 | inner | 1120.3.c.g.209.59 | 80 | ||
20.19 | odd | 2 | 280.3.c.g.69.24 | yes | 80 | ||
28.27 | even | 2 | 280.3.c.g.69.58 | yes | 80 | ||
35.34 | odd | 2 | inner | 1120.3.c.g.209.60 | 80 | ||
40.19 | odd | 2 | 280.3.c.g.69.59 | yes | 80 | ||
40.29 | even | 2 | inner | 1120.3.c.g.209.66 | 80 | ||
56.13 | odd | 2 | inner | 1120.3.c.g.209.78 | 80 | ||
56.27 | even | 2 | 280.3.c.g.69.21 | ✓ | 80 | ||
140.139 | even | 2 | 280.3.c.g.69.23 | yes | 80 | ||
280.69 | odd | 2 | inner | 1120.3.c.g.209.19 | 80 | ||
280.139 | even | 2 | 280.3.c.g.69.60 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.3.c.g.69.21 | ✓ | 80 | 56.27 | even | 2 | ||
280.3.c.g.69.22 | yes | 80 | 8.3 | odd | 2 | ||
280.3.c.g.69.23 | yes | 80 | 140.139 | even | 2 | ||
280.3.c.g.69.24 | yes | 80 | 20.19 | odd | 2 | ||
280.3.c.g.69.57 | yes | 80 | 4.3 | odd | 2 | ||
280.3.c.g.69.58 | yes | 80 | 28.27 | even | 2 | ||
280.3.c.g.69.59 | yes | 80 | 40.19 | odd | 2 | ||
280.3.c.g.69.60 | yes | 80 | 280.139 | even | 2 | ||
1120.3.c.g.209.19 | 80 | 280.69 | odd | 2 | inner | ||
1120.3.c.g.209.20 | 80 | 1.1 | even | 1 | trivial | ||
1120.3.c.g.209.59 | 80 | 8.5 | even | 2 | inner | ||
1120.3.c.g.209.60 | 80 | 35.34 | odd | 2 | inner | ||
1120.3.c.g.209.65 | 80 | 7.6 | odd | 2 | inner | ||
1120.3.c.g.209.66 | 80 | 40.29 | even | 2 | inner | ||
1120.3.c.g.209.77 | 80 | 5.4 | even | 2 | inner | ||
1120.3.c.g.209.78 | 80 | 56.13 | odd | 2 | inner |