Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.52 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.25 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.23497i | 0.808742i | 0.914595 | + | 0.404371i | \(0.132510\pi\) | ||||
−0.914595 | + | 0.404371i | \(0.867490\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.53498 | 0.345936 | ||||||||
\(5\) | − 9.83059i | − 0.393224i | −0.980481 | − | 0.196612i | \(-0.937006\pi\) | ||||
0.980481 | − | 0.196612i | \(-0.0629939\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −84.9856 | −1.73440 | −0.867200 | − | 0.497960i | \(-0.834083\pi\) | ||||
−0.867200 | + | 0.497960i | \(0.834083\pi\) | |||||||
\(8\) | 69.6650i | 1.08852i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 31.8017 | 0.318017 | ||||||||
\(11\) | 4.98375i | 0.0411880i | 0.999788 | + | 0.0205940i | \(0.00655574\pi\) | ||||
−0.999788 | + | 0.0205940i | \(0.993444\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 170.315 | 1.00778 | 0.503891 | − | 0.863767i | \(-0.331901\pi\) | ||||
0.503891 | + | 0.863767i | \(0.331901\pi\) | |||||||
\(14\) | − 274.926i | − 1.40268i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −136.804 | −0.534392 | ||||||||
\(17\) | − 209.426i | − 0.724658i | −0.932050 | − | 0.362329i | \(-0.881982\pi\) | ||||
0.932050 | − | 0.362329i | \(-0.118018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −96.6592 | −0.267754 | −0.133877 | − | 0.990998i | \(-0.542743\pi\) | ||||
−0.133877 | + | 0.990998i | \(0.542743\pi\) | |||||||
\(20\) | − 54.4121i | − 0.136030i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.1223 | −0.0333105 | ||||||||
\(23\) | − 778.979i | − 1.47255i | −0.676682 | − | 0.736275i | \(-0.736583\pi\) | ||||
0.676682 | − | 0.736275i | \(-0.263417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 528.359 | 0.845375 | ||||||||
\(26\) | 550.964i | 0.815036i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −470.393 | −0.599991 | ||||||||
\(29\) | 357.930i | 0.425601i | 0.977096 | + | 0.212801i | \(0.0682585\pi\) | ||||
−0.977096 | + | 0.212801i | \(0.931742\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 74.8477 | 0.0778852 | 0.0389426 | − | 0.999241i | \(-0.487601\pi\) | ||||
0.0389426 | + | 0.999241i | \(0.487601\pi\) | |||||||
\(32\) | 672.082i | 0.656330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 677.487 | 0.586062 | ||||||||
\(35\) | 835.459i | 0.682007i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1846.48 | −1.34878 | −0.674391 | − | 0.738375i | \(-0.735594\pi\) | ||||
−0.674391 | + | 0.738375i | \(0.735594\pi\) | |||||||
\(38\) | − 312.690i | − 0.216544i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 684.848 | 0.428030 | ||||||||
\(41\) | − 627.641i | − 0.373374i | −0.982419 | − | 0.186687i | \(-0.940225\pi\) | ||||
0.982419 | − | 0.186687i | \(-0.0597750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2902.85 | 1.56995 | 0.784977 | − | 0.619525i | \(-0.212675\pi\) | ||||
0.784977 | + | 0.619525i | \(0.212675\pi\) | |||||||
\(44\) | 27.5849i | 0.0142484i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2519.97 | 1.19091 | ||||||||
\(47\) | 2788.16i | 1.26218i | 0.775708 | + | 0.631092i | \(0.217393\pi\) | ||||
−0.775708 | + | 0.631092i | \(0.782607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4821.55 | 2.00814 | ||||||||
\(50\) | 1709.23i | 0.683691i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 942.691 | 0.348628 | ||||||||
\(53\) | 1856.53i | 0.660921i | 0.943820 | + | 0.330461i | \(0.107204\pi\) | ||||
−0.943820 | + | 0.330461i | \(0.892796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48.9932 | 0.0161961 | ||||||||
\(56\) | − 5920.52i | − 1.88792i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1157.89 | −0.344202 | ||||||||
\(59\) | − 453.188i | − 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3752.57 | 1.00848 | 0.504242 | − | 0.863562i | \(-0.331772\pi\) | ||||
0.504242 | + | 0.863562i | \(0.331772\pi\) | |||||||
\(62\) | 242.130i | 0.0629890i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4363.03 | −1.06519 | ||||||||
\(65\) | − 1674.30i | − 0.396284i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7055.01 | 1.57162 | 0.785811 | − | 0.618467i | \(-0.212246\pi\) | ||||
0.785811 | + | 0.618467i | \(0.212246\pi\) | |||||||
\(68\) | − 1159.17i | − 0.250685i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2702.68 | −0.551568 | ||||||||
\(71\) | − 8612.42i | − 1.70847i | −0.519883 | − | 0.854237i | \(-0.674025\pi\) | ||||
0.519883 | − | 0.854237i | \(-0.325975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3578.48 | 0.671510 | 0.335755 | − | 0.941949i | \(-0.391009\pi\) | ||||
0.335755 | + | 0.941949i | \(0.391009\pi\) | |||||||
\(74\) | − 5973.31i | − 1.09082i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −535.007 | −0.0926258 | ||||||||
\(77\) | − 423.547i | − 0.0714365i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3518.38 | 0.563752 | 0.281876 | − | 0.959451i | \(-0.409043\pi\) | ||||
0.281876 | + | 0.959451i | \(0.409043\pi\) | |||||||
\(80\) | 1344.87i | 0.210136i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2030.40 | 0.301963 | ||||||||
\(83\) | − 7820.57i | − 1.13523i | −0.823296 | − | 0.567613i | \(-0.807867\pi\) | ||||
0.823296 | − | 0.567613i | \(-0.192133\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2058.78 | −0.284953 | ||||||||
\(86\) | 9390.61i | 1.26969i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −347.193 | −0.0448338 | ||||||||
\(89\) | 11047.1i | 1.39466i | 0.716752 | + | 0.697328i | \(0.245628\pi\) | ||||
−0.716752 | + | 0.697328i | \(0.754372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14474.3 | −1.74790 | ||||||||
\(92\) | − 4311.63i | − 0.509408i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9019.63 | −1.02078 | ||||||||
\(95\) | 950.217i | 0.105287i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17797.5 | 1.89154 | 0.945772 | − | 0.324831i | \(-0.105307\pi\) | ||||
0.945772 | + | 0.324831i | \(0.105307\pi\) | |||||||
\(98\) | 15597.6i | 1.62407i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2924.46 | 0.292446 | ||||||||
\(101\) | − 10178.1i | − 0.997757i | −0.866672 | − | 0.498879i | \(-0.833745\pi\) | ||||
0.866672 | − | 0.498879i | \(-0.166255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12961.9 | 1.22179 | 0.610893 | − | 0.791713i | \(-0.290811\pi\) | ||||
0.610893 | + | 0.791713i | \(0.290811\pi\) | |||||||
\(104\) | 11865.0i | 1.09699i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6005.81 | −0.534515 | ||||||||
\(107\) | 8348.89i | 0.729224i | 0.931159 | + | 0.364612i | \(0.118798\pi\) | ||||
−0.931159 | + | 0.364612i | \(0.881202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18152.6 | 1.52787 | 0.763935 | − | 0.645294i | \(-0.223265\pi\) | ||||
0.763935 | + | 0.645294i | \(0.223265\pi\) | |||||||
\(110\) | 158.491i | 0.0130985i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11626.4 | 0.926850 | ||||||||
\(113\) | 13979.2i | 1.09478i | 0.836879 | + | 0.547389i | \(0.184378\pi\) | ||||
−0.836879 | + | 0.547389i | \(0.815622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7657.83 | −0.579042 | ||||||||
\(116\) | 1981.14i | 0.147231i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1466.05 | 0.105289 | ||||||||
\(119\) | 17798.2i | 1.25685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14616.2 | 0.998304 | ||||||||
\(122\) | 12139.5i | 0.815604i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 414.280 | 0.0269433 | ||||||||
\(125\) | − 11338.2i | − 0.725645i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −23300.1 | −1.44461 | −0.722304 | − | 0.691576i | \(-0.756917\pi\) | ||||
−0.722304 | + | 0.691576i | \(0.756917\pi\) | |||||||
\(128\) | − 3360.97i | − 0.205137i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5416.31 | 0.320492 | ||||||||
\(131\) | − 558.954i | − 0.0325712i | −0.999867 | − | 0.0162856i | \(-0.994816\pi\) | ||||
0.999867 | − | 0.0162856i | \(-0.00518409\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8214.64 | 0.464393 | ||||||||
\(134\) | 22822.7i | 1.27104i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14589.7 | 0.788802 | ||||||||
\(137\) | − 5606.38i | − 0.298704i | −0.988784 | − | 0.149352i | \(-0.952281\pi\) | ||||
0.988784 | − | 0.149352i | \(-0.0477188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21532.7 | 1.11447 | 0.557235 | − | 0.830355i | \(-0.311862\pi\) | ||||
0.557235 | + | 0.830355i | \(0.311862\pi\) | |||||||
\(140\) | 4624.24i | 0.235931i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27860.9 | 1.38172 | ||||||||
\(143\) | 848.808i | 0.0415086i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3518.67 | 0.167356 | ||||||||
\(146\) | 11576.3i | 0.543079i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10220.2 | −0.466592 | ||||||||
\(149\) | 26085.3i | 1.17496i | 0.809238 | + | 0.587481i | \(0.199880\pi\) | ||||
−0.809238 | + | 0.587481i | \(0.800120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17430.2 | −0.764448 | −0.382224 | − | 0.924070i | \(-0.624842\pi\) | ||||
−0.382224 | + | 0.924070i | \(0.624842\pi\) | |||||||
\(152\) | − 6733.76i | − 0.291454i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1370.16 | 0.0577737 | ||||||||
\(155\) | − 735.797i | − 0.0306263i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16653.9 | −0.675640 | −0.337820 | − | 0.941211i | \(-0.609690\pi\) | ||||
−0.337820 | + | 0.941211i | \(0.609690\pi\) | |||||||
\(158\) | 11381.8i | 0.455930i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6606.96 | 0.258084 | ||||||||
\(161\) | 66202.0i | 2.55399i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 811.917 | 0.0305588 | 0.0152794 | − | 0.999883i | \(-0.495136\pi\) | ||||
0.0152794 | + | 0.999883i | \(0.495136\pi\) | |||||||
\(164\) | − 3473.98i | − 0.129163i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25299.3 | 0.918105 | ||||||||
\(167\) | − 34611.4i | − 1.24104i | −0.784191 | − | 0.620520i | \(-0.786922\pi\) | ||||
0.784191 | − | 0.620520i | \(-0.213078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 446.280 | 0.0156255 | ||||||||
\(170\) | − 6660.10i | − 0.230453i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16067.2 | 0.543104 | ||||||||
\(173\) | 8414.35i | 0.281144i | 0.990070 | + | 0.140572i | \(0.0448941\pi\) | ||||
−0.990070 | + | 0.140572i | \(0.955106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −44902.9 | −1.46622 | ||||||||
\(176\) | − 681.799i | − 0.0220105i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −35736.9 | −1.12792 | ||||||||
\(179\) | − 47015.1i | − 1.46734i | −0.679506 | − | 0.733670i | \(-0.737806\pi\) | ||||
0.679506 | − | 0.733670i | \(-0.262194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12837.7 | −0.391860 | −0.195930 | − | 0.980618i | \(-0.562772\pi\) | ||||
−0.195930 | + | 0.980618i | \(0.562772\pi\) | |||||||
\(182\) | − 46824.0i | − 1.41360i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 54267.6 | 1.60289 | ||||||||
\(185\) | 18152.0i | 0.530373i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1043.73 | 0.0298472 | ||||||||
\(188\) | 15432.4i | 0.436635i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3073.92 | −0.0851502 | ||||||||
\(191\) | − 60775.0i | − 1.66594i | −0.553321 | − | 0.832968i | \(-0.686640\pi\) | ||||
0.553321 | − | 0.832968i | \(-0.313360\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22371.4 | −0.600590 | −0.300295 | − | 0.953846i | \(-0.597085\pi\) | ||||
−0.300295 | + | 0.953846i | \(0.597085\pi\) | |||||||
\(194\) | 57574.5i | 1.52977i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26687.2 | 0.694689 | ||||||||
\(197\) | − 31702.4i | − 0.816882i | −0.912785 | − | 0.408441i | \(-0.866073\pi\) | ||||
0.912785 | − | 0.408441i | \(-0.133927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −52481.1 | −1.32525 | −0.662624 | − | 0.748953i | \(-0.730557\pi\) | ||||
−0.662624 | + | 0.748953i | \(0.730557\pi\) | |||||||
\(200\) | 36808.2i | 0.920204i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32925.9 | 0.806928 | ||||||||
\(203\) | − 30418.9i | − 0.738162i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6170.08 | −0.146819 | ||||||||
\(206\) | 41931.4i | 0.988110i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −23299.9 | −0.538551 | ||||||||
\(209\) | − 481.725i | − 0.0110283i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8850.73 | 0.198799 | 0.0993994 | − | 0.995048i | \(-0.468308\pi\) | ||||
0.0993994 | + | 0.995048i | \(0.468308\pi\) | |||||||
\(212\) | 10275.8i | 0.228637i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27008.4 | −0.589755 | ||||||||
\(215\) | − 28536.7i | − 0.617343i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6360.97 | −0.135084 | ||||||||
\(218\) | 58723.1i | 1.23565i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 271.176 | 0.00560281 | ||||||||
\(221\) | − 35668.5i | − 0.730298i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17012.2 | −0.342097 | −0.171049 | − | 0.985263i | \(-0.554716\pi\) | ||||
−0.171049 | + | 0.985263i | \(0.554716\pi\) | |||||||
\(224\) | − 57117.3i | − 1.13834i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −45222.3 | −0.885393 | ||||||||
\(227\) | 50453.0i | 0.979118i | 0.871970 | + | 0.489559i | \(0.162842\pi\) | ||||
−0.871970 | + | 0.489559i | \(0.837158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23301.6 | 0.444340 | 0.222170 | − | 0.975008i | \(-0.428686\pi\) | ||||
0.222170 | + | 0.975008i | \(0.428686\pi\) | |||||||
\(230\) | − 24772.8i | − 0.468295i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24935.2 | −0.463273 | ||||||||
\(233\) | 31693.0i | 0.583783i | 0.956451 | + | 0.291892i | \(0.0942846\pi\) | ||||
−0.956451 | + | 0.291892i | \(0.905715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27409.3 | 0.496321 | ||||||||
\(236\) | − 2508.38i | − 0.0450370i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −57576.7 | −1.01647 | ||||||||
\(239\) | 26482.9i | 0.463628i | 0.972760 | + | 0.231814i | \(0.0744661\pi\) | ||||
−0.972760 | + | 0.231814i | \(0.925534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24512.4 | −0.422038 | −0.211019 | − | 0.977482i | \(-0.567678\pi\) | ||||
−0.211019 | + | 0.977482i | \(0.567678\pi\) | |||||||
\(242\) | 47282.8i | 0.807370i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20770.4 | 0.348871 | ||||||||
\(245\) | − 47398.7i | − 0.789649i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16462.5 | −0.269838 | ||||||||
\(248\) | 5214.26i | 0.0847792i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 36678.7 | 0.586860 | ||||||||
\(251\) | − 67859.2i | − 1.07711i | −0.842589 | − | 0.538557i | \(-0.818970\pi\) | ||||
0.842589 | − | 0.538557i | \(-0.181030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3882.24 | 0.0606514 | ||||||||
\(254\) | − 75375.0i | − 1.16831i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −58935.9 | −0.899291 | ||||||||
\(257\) | 63829.7i | 0.966399i | 0.875510 | + | 0.483200i | \(0.160525\pi\) | ||||
−0.875510 | + | 0.483200i | \(0.839475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 156924. | 2.33933 | ||||||||
\(260\) | − 9267.21i | − 0.137089i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1808.20 | 0.0263417 | ||||||||
\(263\) | − 45119.3i | − 0.652305i | −0.945317 | − | 0.326153i | \(-0.894248\pi\) | ||||
0.945317 | − | 0.326153i | \(-0.105752\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18250.8 | 0.259890 | ||||||||
\(266\) | 26574.1i | 0.375574i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 39049.3 | 0.543681 | ||||||||
\(269\) | − 48160.9i | − 0.665565i | −0.943004 | − | 0.332782i | \(-0.892013\pi\) | ||||
0.943004 | − | 0.332782i | \(-0.107987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 48564.2 | 0.661269 | 0.330634 | − | 0.943759i | \(-0.392737\pi\) | ||||
0.330634 | + | 0.943759i | \(0.392737\pi\) | |||||||
\(272\) | 28650.4i | 0.387252i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18136.5 | 0.241575 | ||||||||
\(275\) | 2633.21i | 0.0348193i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 92108.4 | 1.20044 | 0.600219 | − | 0.799836i | \(-0.295080\pi\) | ||||
0.600219 | + | 0.799836i | \(0.295080\pi\) | |||||||
\(278\) | 69657.6i | 0.901319i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −58202.2 | −0.742375 | ||||||||
\(281\) | − 79561.8i | − 1.00761i | −0.863818 | − | 0.503804i | \(-0.831933\pi\) | ||||
0.863818 | − | 0.503804i | \(-0.168067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −124898. | −1.55948 | −0.779742 | − | 0.626101i | \(-0.784650\pi\) | ||||
−0.779742 | + | 0.626101i | \(0.784650\pi\) | |||||||
\(284\) | − 47669.5i | − 0.591023i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2745.87 | −0.0335697 | ||||||||
\(287\) | 53340.5i | 0.647579i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39661.6 | 0.474870 | ||||||||
\(290\) | 11382.8i | 0.135348i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19806.8 | 0.232300 | ||||||||
\(293\) | − 38846.3i | − 0.452496i | −0.974070 | − | 0.226248i | \(-0.927354\pi\) | ||||
0.974070 | − | 0.226248i | \(-0.0726459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4455.10 | −0.0511934 | ||||||||
\(296\) | − 128635.i | − 1.46817i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −84385.2 | −0.950241 | ||||||||
\(299\) | − 132672.i | − 1.48401i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −246700. | −2.72293 | ||||||||
\(302\) | − 56386.1i | − 0.618242i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13223.4 | 0.143086 | ||||||||
\(305\) | − 36890.0i | − 0.396560i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −53031.7 | −0.562677 | −0.281338 | − | 0.959609i | \(-0.590778\pi\) | ||||
−0.281338 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(308\) | − 2344.32i | − 0.0247125i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2380.28 | 0.0247688 | ||||||||
\(311\) | − 127407.i | − 1.31726i | −0.752465 | − | 0.658632i | \(-0.771135\pi\) | ||||
0.752465 | − | 0.658632i | \(-0.228865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34530.6 | 0.352464 | 0.176232 | − | 0.984349i | \(-0.443609\pi\) | ||||
0.176232 | + | 0.984349i | \(0.443609\pi\) | |||||||
\(314\) | − 53874.7i | − 0.546419i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19474.1 | 0.195022 | ||||||||
\(317\) | 15699.4i | 0.156230i | 0.996944 | + | 0.0781150i | \(0.0248901\pi\) | ||||
−0.996944 | + | 0.0781150i | \(0.975110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1783.84 | −0.0175297 | ||||||||
\(320\) | 42891.2i | 0.418859i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −214161. | −2.06552 | ||||||||
\(323\) | 20243.0i | 0.194030i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 89987.7 | 0.851954 | ||||||||
\(326\) | 2626.53i | 0.0247142i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 43724.6 | 0.406423 | ||||||||
\(329\) | − 236954.i | − 2.18913i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −141162. | −1.28843 | −0.644216 | − | 0.764844i | \(-0.722816\pi\) | ||||
−0.644216 | + | 0.764844i | \(0.722816\pi\) | |||||||
\(332\) | − 43286.7i | − 0.392715i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 111967. | 1.00368 | ||||||||
\(335\) | − 69354.9i | − 0.617999i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 38060.4 | 0.335130 | 0.167565 | − | 0.985861i | \(-0.446410\pi\) | ||||
0.167565 | + | 0.985861i | \(0.446410\pi\) | |||||||
\(338\) | 1443.70i | 0.0126370i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11395.3 | −0.0985755 | ||||||||
\(341\) | 373.022i | 0.00320794i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −205712. | −1.74852 | ||||||||
\(344\) | 202227.i | 1.70892i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27220.2 | −0.227373 | ||||||||
\(347\) | − 139688.i | − 1.16011i | −0.814577 | − | 0.580055i | \(-0.803031\pi\) | ||||
0.814577 | − | 0.580055i | \(-0.196969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 169472. | 1.39138 | 0.695691 | − | 0.718341i | \(-0.255098\pi\) | ||||
0.695691 | + | 0.718341i | \(0.255098\pi\) | |||||||
\(350\) | − 145260.i | − 1.18579i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3349.49 | −0.0270329 | ||||||||
\(353\) | 145139.i | 1.16475i | 0.812919 | + | 0.582377i | \(0.197877\pi\) | ||||
−0.812919 | + | 0.582377i | \(0.802123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −84665.2 | −0.671813 | ||||||||
\(356\) | 61145.3i | 0.482462i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 152092. | 1.18670 | ||||||||
\(359\) | 200226.i | 1.55358i | 0.629762 | + | 0.776788i | \(0.283152\pi\) | ||||
−0.629762 | + | 0.776788i | \(0.716848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −120978. | −0.928308 | ||||||||
\(362\) | − 41529.6i | − 0.316913i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −80115.1 | −0.604661 | ||||||||
\(365\) | − 35178.6i | − 0.264054i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 38293.8 | 0.284313 | 0.142157 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142157 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(368\) | 106568.i | 0.786919i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −58721.2 | −0.428935 | ||||||||
\(371\) | − 157778.i | − 1.14630i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −150209. | −1.07964 | −0.539818 | − | 0.841782i | \(-0.681507\pi\) | ||||
−0.539818 | + | 0.841782i | \(0.681507\pi\) | |||||||
\(374\) | 3376.43i | 0.0241387i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −194237. | −1.37391 | ||||||||
\(377\) | 60961.0i | 0.428913i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −47965.7 | −0.333928 | −0.166964 | − | 0.985963i | \(-0.553396\pi\) | ||||
−0.166964 | + | 0.985963i | \(0.553396\pi\) | |||||||
\(380\) | 5259.43i | 0.0364227i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 196605. | 1.34731 | ||||||||
\(383\) | 151408.i | 1.03217i | 0.856537 | + | 0.516086i | \(0.172612\pi\) | ||||
−0.856537 | + | 0.516086i | \(0.827388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4163.72 | −0.0280905 | ||||||||
\(386\) | − 72370.7i | − 0.485723i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 98509.0 | 0.654353 | ||||||||
\(389\) | 261549.i | 1.72844i | 0.503117 | + | 0.864218i | \(0.332186\pi\) | ||||
−0.503117 | + | 0.864218i | \(0.667814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −163139. | −1.06710 | ||||||||
\(392\) | 335893.i | 2.18589i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 102556. | 0.660647 | ||||||||
\(395\) | − 34587.7i | − 0.221681i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 269644. | 1.71084 | 0.855421 | − | 0.517933i | \(-0.173298\pi\) | ||||
0.855421 | + | 0.517933i | \(0.173298\pi\) | |||||||
\(398\) | − 169775.i | − 1.07178i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −72281.9 | −0.451762 | ||||||||
\(401\) | − 95186.4i | − 0.591952i | −0.955195 | − | 0.295976i | \(-0.904355\pi\) | ||||
0.955195 | − | 0.295976i | \(-0.0956448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12747.7 | 0.0784913 | ||||||||
\(404\) | − 56335.7i | − 0.345160i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 98404.3 | 0.596983 | ||||||||
\(407\) | − 9202.40i | − 0.0555536i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 69543.9 | 0.415731 | 0.207866 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207866 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(410\) | − 19960.0i | − 0.118739i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 71744.0 | 0.422660 | ||||||||
\(413\) | 38514.4i | 0.225800i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −76880.8 | −0.446398 | ||||||||
\(416\) | 114466.i | 0.661438i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1558.37 | 0.00891902 | ||||||||
\(419\) | 19338.6i | 0.110153i | 0.998482 | + | 0.0550766i | \(0.0175403\pi\) | ||||
−0.998482 | + | 0.0550766i | \(0.982460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25467.9 | −0.143691 | −0.0718454 | − | 0.997416i | \(-0.522889\pi\) | ||||
−0.0718454 | + | 0.997416i | \(0.522889\pi\) | |||||||
\(422\) | 28631.8i | 0.160777i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −129335. | −0.719423 | ||||||||
\(425\) | − 110652.i | − 0.612608i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −318915. | −1.74912 | ||||||||
\(428\) | 46210.9i | 0.252265i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 92315.3 | 0.499271 | ||||||||
\(431\) | − 177704.i | − 0.956627i | −0.878189 | − | 0.478314i | \(-0.841248\pi\) | ||||
0.878189 | − | 0.478314i | \(-0.158752\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −118232. | −0.630606 | −0.315303 | − | 0.948991i | \(-0.602106\pi\) | ||||
−0.315303 | + | 0.948991i | \(0.602106\pi\) | |||||||
\(434\) | − 20577.6i | − 0.109248i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 100474. | 0.528545 | ||||||||
\(437\) | 75295.5i | 0.394281i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 148789. | 0.772045 | 0.386022 | − | 0.922489i | \(-0.373849\pi\) | ||||
0.386022 | + | 0.922489i | \(0.373849\pi\) | |||||||
\(440\) | 3413.11i | 0.0176297i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 115386. | 0.590623 | ||||||||
\(443\) | − 317446.i | − 1.61757i | −0.588105 | − | 0.808784i | \(-0.700126\pi\) | ||||
0.588105 | − | 0.808784i | \(-0.299874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 108599. | 0.548412 | ||||||||
\(446\) | − 55033.8i | − 0.276668i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 370795. | 1.84747 | ||||||||
\(449\) | − 267391.i | − 1.32634i | −0.748469 | − | 0.663169i | \(-0.769211\pi\) | ||||
0.748469 | − | 0.663169i | \(-0.230789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3128.01 | 0.0153785 | ||||||||
\(452\) | 77374.6i | 0.378723i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −163214. | −0.791854 | ||||||||
\(455\) | 142291.i | 0.687315i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 58479.0 | 0.280006 | 0.140003 | − | 0.990151i | \(-0.455289\pi\) | ||||
0.140003 | + | 0.990151i | \(0.455289\pi\) | |||||||
\(458\) | 75380.0i | 0.359356i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −42385.9 | −0.200311 | ||||||||
\(461\) | 164100.i | 0.772160i | 0.922465 | + | 0.386080i | \(0.126171\pi\) | ||||
−0.922465 | + | 0.386080i | \(0.873829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −105301. | −0.491216 | −0.245608 | − | 0.969369i | \(-0.578988\pi\) | ||||
−0.245608 | + | 0.969369i | \(0.578988\pi\) | |||||||
\(464\) | − 48966.5i | − 0.227438i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −102526. | −0.472130 | ||||||||
\(467\) | 385404.i | 1.76718i | 0.468257 | + | 0.883592i | \(0.344882\pi\) | ||||
−0.468257 | + | 0.883592i | \(0.655118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −599574. | −2.72582 | ||||||||
\(470\) | 88668.3i | 0.401395i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 31571.3 | 0.141713 | ||||||||
\(473\) | 14467.1i | 0.0646633i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51070.8 | −0.226353 | ||||||||
\(476\) | 98512.7i | 0.434789i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −85671.4 | −0.374956 | ||||||||
\(479\) | 230440.i | 1.00435i | 0.864765 | + | 0.502176i | \(0.167467\pi\) | ||||
−0.864765 | + | 0.502176i | \(0.832533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −314484. | −1.35928 | ||||||||
\(482\) | − 79296.8i | − 0.341320i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 80900.1 | 0.345349 | ||||||||
\(485\) | − 174960.i | − 0.743800i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −48164.1 | −0.203079 | −0.101540 | − | 0.994832i | \(-0.532377\pi\) | ||||
−0.101540 | + | 0.994832i | \(0.532377\pi\) | |||||||
\(488\) | 261423.i | 1.09775i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 153333. | 0.638623 | ||||||||
\(491\) | − 211675.i | − 0.878022i | −0.898482 | − | 0.439011i | \(-0.855329\pi\) | ||||
0.898482 | − | 0.439011i | \(-0.144671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 74960.0 | 0.308415 | ||||||||
\(494\) | − 53255.8i | − 0.218229i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10239.5 | −0.0416212 | ||||||||
\(497\) | 731932.i | 2.96318i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 375387. | 1.50757 | 0.753786 | − | 0.657120i | \(-0.228226\pi\) | ||||
0.753786 | + | 0.657120i | \(0.228226\pi\) | |||||||
\(500\) | − 62756.7i | − 0.251027i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 219522. | 0.871107 | ||||||||
\(503\) | 69030.8i | 0.272839i | 0.990651 | + | 0.136420i | \(0.0435595\pi\) | ||||
−0.990651 | + | 0.136420i | \(0.956440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −100057. | −0.392342 | ||||||||
\(506\) | 12558.9i | 0.0490514i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −128965. | −0.499742 | ||||||||
\(509\) | − 231705.i | − 0.894332i | −0.894451 | − | 0.447166i | \(-0.852433\pi\) | ||||
0.894451 | − | 0.447166i | \(-0.147567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −304119. | −1.16467 | ||||||||
\(512\) | − 244431.i | − 0.932432i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −206487. | −0.781568 | ||||||||
\(515\) | − 127423.i | − 0.480435i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13895.5 | −0.0519868 | ||||||||
\(518\) | 507645.i | 1.89191i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 116640. | 0.431361 | ||||||||
\(521\) | − 63854.4i | − 0.235242i | −0.993059 | − | 0.117621i | \(-0.962473\pi\) | ||||
0.993059 | − | 0.117621i | \(-0.0375268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 364579. | 1.33287 | 0.666435 | − | 0.745563i | \(-0.267819\pi\) | ||||
0.666435 | + | 0.745563i | \(0.267819\pi\) | |||||||
\(524\) | − 3093.80i | − 0.0112675i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 145960. | 0.527547 | ||||||||
\(527\) | − 15675.1i | − 0.0564402i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −326968. | −1.16841 | ||||||||
\(530\) | 59040.7i | 0.210184i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 45467.9 | 0.160650 | ||||||||
\(533\) | − 106897.i | − 0.376279i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 82074.5 | 0.286748 | ||||||||
\(536\) | 491487.i | 1.71073i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 155799. | 0.538270 | ||||||||
\(539\) | 24029.4i | 0.0827114i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 287660. | 0.982844 | 0.491422 | − | 0.870922i | \(-0.336477\pi\) | ||||
0.491422 | + | 0.870922i | \(0.336477\pi\) | |||||||
\(542\) | 157104.i | 0.534796i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 140752. | 0.475615 | ||||||||
\(545\) | − 178451.i | − 0.600794i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40922.4 | 0.136768 | 0.0683842 | − | 0.997659i | \(-0.478216\pi\) | ||||
0.0683842 | + | 0.997659i | \(0.478216\pi\) | |||||||
\(548\) | − 31031.2i | − 0.103333i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8518.35 | −0.0281599 | ||||||||
\(551\) | − 34597.3i | − 0.113956i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −299011. | −0.977771 | ||||||||
\(554\) | 297968.i | 0.970845i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 119183. | 0.385536 | ||||||||
\(557\) | 6420.57i | 0.0206949i | 0.999946 | + | 0.0103475i | \(0.00329375\pi\) | ||||
−0.999946 | + | 0.0103475i | \(0.996706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 494399. | 1.58217 | ||||||||
\(560\) | − 114294.i | − 0.364459i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 257380. | 0.814896 | ||||||||
\(563\) | − 33869.4i | − 0.106854i | −0.998572 | − | 0.0534269i | \(-0.982986\pi\) | ||||
0.998572 | − | 0.0534269i | \(-0.0170144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 137424. | 0.430492 | ||||||||
\(566\) | − 404040.i | − 1.26122i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 599984. | 1.85970 | ||||||||
\(569\) | − 549854.i | − 1.69833i | −0.528126 | − | 0.849166i | \(-0.677105\pi\) | ||||
0.528126 | − | 0.849166i | \(-0.322895\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 629932. | 1.93206 | 0.966032 | − | 0.258423i | \(-0.0832029\pi\) | ||||
0.966032 | + | 0.258423i | \(0.0832029\pi\) | |||||||
\(572\) | 4698.13i | 0.0143593i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −172555. | −0.523725 | ||||||||
\(575\) | − 411581.i | − 1.24486i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −563046. | −1.69119 | −0.845594 | − | 0.533826i | \(-0.820754\pi\) | ||||
−0.845594 | + | 0.533826i | \(0.820754\pi\) | |||||||
\(578\) | 128304.i | 0.384048i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19475.7 | 0.0578946 | ||||||||
\(581\) | 664636.i | 1.96894i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9252.47 | −0.0272220 | ||||||||
\(584\) | 249295.i | 0.730949i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 125667. | 0.365952 | ||||||||
\(587\) | 520388.i | 1.51026i | 0.655576 | + | 0.755129i | \(0.272426\pi\) | ||||
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7234.72 | −0.0208541 | ||||||||
\(590\) | − 14412.1i | − 0.0414022i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 252607. | 0.720778 | ||||||||
\(593\) | 41999.5i | 0.119436i | 0.998215 | + | 0.0597179i | \(0.0190201\pi\) | ||||
−0.998215 | + | 0.0597179i | \(0.980980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 174967. | 0.494222 | ||||||||
\(596\) | 144382.i | 0.406461i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 429190. | 1.20018 | ||||||||
\(599\) | − 39343.2i | − 0.109652i | −0.998496 | − | 0.0548260i | \(-0.982540\pi\) | ||||
0.998496 | − | 0.0548260i | \(-0.0174604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −80632.4 | −0.223234 | −0.111617 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111617 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(602\) | − 798067.i | − 2.20215i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −96475.7 | −0.264450 | ||||||||
\(605\) | − 143686.i | − 0.392557i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −424244. | −1.15143 | −0.575717 | − | 0.817649i | \(-0.695277\pi\) | ||||
−0.575717 | + | 0.817649i | \(0.695277\pi\) | |||||||
\(608\) | − 64962.9i | − 0.175735i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 119338. | 0.320715 | ||||||||
\(611\) | 474867.i | 1.27201i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 283622. | 0.754777 | 0.377388 | − | 0.926055i | \(-0.376822\pi\) | ||||
0.377388 | + | 0.926055i | \(0.376822\pi\) | |||||||
\(614\) | − 171556.i | − 0.455060i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 29506.4 | 0.0777597 | ||||||||
\(617\) | 491931.i | 1.29221i | 0.763247 | + | 0.646106i | \(0.223604\pi\) | ||||
−0.763247 | + | 0.646106i | \(0.776396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −312185. | −0.814762 | −0.407381 | − | 0.913258i | \(-0.633558\pi\) | ||||
−0.407381 | + | 0.913258i | \(0.633558\pi\) | |||||||
\(620\) | − 4072.62i | − 0.0105947i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 412158. | 1.06533 | ||||||||
\(623\) | − 938842.i | − 2.41889i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 218763. | 0.560034 | ||||||||
\(626\) | 111705.i | 0.285053i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −92178.7 | −0.233728 | ||||||||
\(629\) | 386702.i | 0.977405i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 70824.4 | 0.177879 | 0.0889395 | − | 0.996037i | \(-0.471652\pi\) | ||||
0.0889395 | + | 0.996037i | \(0.471652\pi\) | |||||||
\(632\) | 245108.i | 0.613653i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −50787.1 | −0.126350 | ||||||||
\(635\) | 229053.i | 0.568054i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 821184. | 2.02377 | ||||||||
\(638\) | − 5770.65i | − 0.0141770i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −33040.3 | −0.0806649 | ||||||||
\(641\) | − 486066.i | − 1.18298i | −0.806311 | − | 0.591492i | \(-0.798539\pi\) | ||||
0.806311 | − | 0.591492i | \(-0.201461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 472005. | 1.14163 | 0.570814 | − | 0.821079i | \(-0.306628\pi\) | ||||
0.570814 | + | 0.821079i | \(0.306628\pi\) | |||||||
\(644\) | 366427.i | 0.883518i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −65485.4 | −0.156920 | ||||||||
\(647\) | − 296340.i | − 0.707917i | −0.935261 | − | 0.353958i | \(-0.884835\pi\) | ||||
0.935261 | − | 0.353958i | \(-0.115165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2258.57 | 0.00536222 | ||||||||
\(650\) | 291107.i | 0.689011i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4493.94 | 0.0105714 | ||||||||
\(653\) | 242277.i | 0.568180i | 0.958798 | + | 0.284090i | \(0.0916914\pi\) | ||||
−0.958798 | + | 0.284090i | \(0.908309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5494.85 | −0.0128078 | ||||||||
\(656\) | 85864.1i | 0.199528i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 766538. | 1.77044 | ||||||||
\(659\) | − 247436.i | − 0.569760i | −0.958563 | − | 0.284880i | \(-0.908046\pi\) | ||||
0.958563 | − | 0.284880i | \(-0.0919537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −427955. | −0.979480 | −0.489740 | − | 0.871869i | \(-0.662908\pi\) | ||||
−0.489740 | + | 0.871869i | \(0.662908\pi\) | |||||||
\(662\) | − 456654.i | − 1.04201i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 544820. | 1.23571 | ||||||||
\(665\) | − 80754.8i | − 0.182610i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 278820. | 0.626719 | ||||||||
\(668\) | − 191573.i | − 0.429321i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 224361. | 0.499802 | ||||||||
\(671\) | 18701.9i | 0.0415375i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 517331. | 1.14219 | 0.571095 | − | 0.820884i | \(-0.306519\pi\) | ||||
0.571095 | + | 0.820884i | \(0.306519\pi\) | |||||||
\(674\) | 123124.i | 0.271034i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2470.15 | 0.00540543 | ||||||||
\(677\) | 280479.i | 0.611959i | 0.952038 | + | 0.305980i | \(0.0989840\pi\) | ||||
−0.952038 | + | 0.305980i | \(0.901016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.51253e6 | −3.28069 | ||||||||
\(680\) | − 143425.i | − 0.310175i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1206.71 | −0.00259439 | ||||||||
\(683\) | 242148.i | 0.519086i | 0.965732 | + | 0.259543i | \(0.0835720\pi\) | ||||
−0.965732 | + | 0.259543i | \(0.916428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55114.1 | −0.117458 | ||||||||
\(686\) | − 665472.i | − 1.41410i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −397122. | −0.838971 | ||||||||
\(689\) | 316195.i | 0.666065i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41284.0 | −0.0864621 | −0.0432310 | − | 0.999065i | \(-0.513765\pi\) | ||||
−0.0432310 | + | 0.999065i | \(0.513765\pi\) | |||||||
\(692\) | 46573.3i | 0.0972578i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 451885. | 0.938230 | ||||||||
\(695\) | − 211679.i | − 0.438236i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −131445. | −0.270568 | ||||||||
\(698\) | 548236.i | 1.12527i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −248537. | −0.507218 | ||||||||
\(701\) | − 897088.i | − 1.82557i | −0.408438 | − | 0.912786i | \(-0.633926\pi\) | ||||
0.408438 | − | 0.912786i | \(-0.366074\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 178479. | 0.361142 | ||||||||
\(704\) | − 21744.3i | − 0.0438732i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −469520. | −0.941986 | ||||||||
\(707\) | 864994.i | 1.73051i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 304280. | 0.605314 | 0.302657 | − | 0.953100i | \(-0.402126\pi\) | ||||
0.302657 | + | 0.953100i | \(0.402126\pi\) | |||||||
\(710\) | − 273889.i | − 0.543323i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −769594. | −1.51810 | ||||||||
\(713\) | − 58304.8i | − 0.114690i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8344.29 | 0.0163221 | ||||||||
\(716\) | − 260227.i | − 0.507606i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −647726. | −1.25644 | ||||||||
\(719\) | 761954.i | 1.47391i | 0.675942 | + | 0.736955i | \(0.263737\pi\) | ||||
−0.675942 | + | 0.736955i | \(0.736263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.10158e6 | −2.11907 | ||||||||
\(722\) | − 391360.i | − 0.750762i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −71056.4 | −0.135558 | ||||||||
\(725\) | 189116.i | 0.359793i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −101145. | −0.191370 | −0.0956852 | − | 0.995412i | \(-0.530504\pi\) | ||||
−0.0956852 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(728\) | − 1.00835e6i | − 1.90261i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 113802. | 0.213551 | ||||||||
\(731\) | − 607932.i | − 1.13768i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 216085. | 0.402176 | 0.201088 | − | 0.979573i | \(-0.435552\pi\) | ||||
0.201088 | + | 0.979573i | \(0.435552\pi\) | |||||||
\(734\) | 123879.i | 0.229936i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 523538. | 0.966479 | ||||||||
\(737\) | 35160.4i | 0.0647320i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −633797. | −1.16054 | −0.580272 | − | 0.814423i | \(-0.697054\pi\) | ||||
−0.580272 | + | 0.814423i | \(0.697054\pi\) | |||||||
\(740\) | 100471.i | 0.183475i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 510407. | 0.927063 | ||||||||
\(743\) | 282503.i | 0.511735i | 0.966712 | + | 0.255868i | \(0.0823611\pi\) | ||||
−0.966712 | + | 0.255868i | \(0.917639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 256434. | 0.462023 | ||||||||
\(746\) | − 485920.i | − 0.873146i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5777.01 | 0.0103252 | ||||||||
\(749\) | − 709535.i | − 1.26477i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 870392. | 1.54325 | 0.771623 | − | 0.636080i | \(-0.219445\pi\) | ||||
0.771623 | + | 0.636080i | \(0.219445\pi\) | |||||||
\(752\) | − 381433.i | − 0.674501i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −197207. | −0.346880 | ||||||||
\(755\) | 171349.i | 0.300599i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −709614. | −1.23831 | −0.619157 | − | 0.785267i | \(-0.712525\pi\) | ||||
−0.619157 | + | 0.785267i | \(0.712525\pi\) | |||||||
\(758\) | − 155168.i | − 0.270061i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −66196.9 | −0.114607 | ||||||||
\(761\) | 345513.i | 0.596615i | 0.954470 | + | 0.298308i | \(0.0964222\pi\) | ||||
−0.954470 | + | 0.298308i | \(0.903578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.54271e6 | −2.64994 | ||||||||
\(764\) | − 336388.i | − 0.576308i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −489801. | −0.834762 | ||||||||
\(767\) | − 77184.8i | − 0.131202i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 96909.7 | 0.163876 | 0.0819379 | − | 0.996637i | \(-0.473889\pi\) | ||||
0.0819379 | + | 0.996637i | \(0.473889\pi\) | |||||||
\(770\) | − 13469.5i | − 0.0227180i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −123825. | −0.207766 | ||||||||
\(773\) | 826181.i | 1.38266i | 0.722538 | + | 0.691331i | \(0.242975\pi\) | ||||
−0.722538 | + | 0.691331i | \(0.757025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39546.5 | 0.0658422 | ||||||||
\(776\) | 1.23987e6i | 2.05897i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −846102. | −1.39786 | ||||||||
\(779\) | 60667.3i | 0.0999723i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42922.1 | 0.0703687 | ||||||||
\(782\) | − 527749.i | − 0.863006i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −659609. | −1.07314 | ||||||||
\(785\) | 163717.i | 0.265678i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 794567. | 1.28287 | 0.641433 | − | 0.767179i | \(-0.278340\pi\) | ||||
0.641433 | + | 0.767179i | \(0.278340\pi\) | |||||||
\(788\) | − 175472.i | − 0.282589i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 111890. | 0.179282 | ||||||||
\(791\) | − 1.18803e6i | − 1.89878i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 639120. | 1.01633 | ||||||||
\(794\) | 872290.i | 1.38363i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −290482. | −0.458451 | ||||||||
\(797\) | 779274.i | 1.22680i | 0.789773 | + | 0.613400i | \(0.210198\pi\) | ||||
−0.789773 | + | 0.613400i | \(0.789802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 583915. | 0.914652 | ||||||||
\(800\) | 355101.i | 0.554845i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 307925. | 0.478736 | ||||||||
\(803\) | 17834.2i | 0.0276582i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 650805. | 1.00429 | ||||||||
\(806\) | 41238.4i | 0.0634793i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 709059. | 1.08607 | ||||||||
\(809\) | 169320.i | 0.258709i | 0.991598 | + | 0.129354i | \(0.0412905\pi\) | ||||
−0.991598 | + | 0.129354i | \(0.958710\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 157589. | 0.239598 | 0.119799 | − | 0.992798i | \(-0.461775\pi\) | ||||
0.119799 | + | 0.992798i | \(0.461775\pi\) | |||||||
\(812\) | − 168368.i | − 0.255357i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29769.5 | 0.0449285 | ||||||||
\(815\) | − 7981.63i | − 0.0120165i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −280587. | −0.420362 | ||||||||
\(818\) | 224972.i | 0.336219i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34151.3 | −0.0507901 | ||||||||
\(821\) | − 436652.i | − 0.647812i | −0.946089 | − | 0.323906i | \(-0.895004\pi\) | ||||
0.946089 | − | 0.323906i | \(-0.104996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −787170. | −1.16217 | −0.581084 | − | 0.813844i | \(-0.697371\pi\) | ||||
−0.581084 | + | 0.813844i | \(0.697371\pi\) | |||||||
\(824\) | 902992.i | 1.32993i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −124593. | −0.182614 | ||||||||
\(827\) | 545449.i | 0.797523i | 0.917055 | + | 0.398762i | \(0.130560\pi\) | ||||
−0.917055 | + | 0.398762i | \(0.869440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −450871. | −0.656060 | −0.328030 | − | 0.944667i | \(-0.606385\pi\) | ||||
−0.328030 | + | 0.944667i | \(0.606385\pi\) | |||||||
\(830\) | − 248707.i | − 0.361021i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −743091. | −1.07348 | ||||||||
\(833\) | − 1.00976e6i | − 1.45522i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −340250. | −0.488006 | ||||||||
\(836\) | − 2666.34i | − 0.00381507i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −62559.8 | −0.0890855 | ||||||||
\(839\) | − 555172.i | − 0.788686i | −0.918963 | − | 0.394343i | \(-0.870972\pi\) | ||||
0.918963 | − | 0.394343i | \(-0.129028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 579167. | 0.818864 | ||||||||
\(842\) | − 82387.9i | − 0.116209i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 48988.6 | 0.0687717 | ||||||||
\(845\) | − 4387.20i | − 0.00614432i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24216e6 | −1.73146 | ||||||||
\(848\) | − 253981.i | − 0.353191i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 357957. | 0.495442 | ||||||||
\(851\) | 1.43837e6i | 1.98615i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.20523e6 | −1.65643 | −0.828215 | − | 0.560410i | \(-0.810644\pi\) | ||||
−0.828215 | + | 0.560410i | \(0.810644\pi\) | |||||||
\(854\) | − 1.03168e6i | − 1.41458i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −581625. | −0.793772 | ||||||||
\(857\) | − 972072.i | − 1.32354i | −0.749708 | − | 0.661769i | \(-0.769806\pi\) | ||||
0.749708 | − | 0.661769i | \(-0.230194\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 854142. | 1.15756 | 0.578780 | − | 0.815484i | \(-0.303529\pi\) | ||||
0.578780 | + | 0.815484i | \(0.303529\pi\) | |||||||
\(860\) | − 157950.i | − 0.213561i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 574867. | 0.773665 | ||||||||
\(863\) | − 126040.i | − 0.169233i | −0.996414 | − | 0.0846166i | \(-0.973033\pi\) | ||||
0.996414 | − | 0.0846166i | \(-0.0269666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 82718.1 | 0.110552 | ||||||||
\(866\) | − 382476.i | − 0.509998i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −35207.8 | −0.0467305 | ||||||||
\(869\) | 17534.7i | 0.0232198i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.20158e6 | 1.58385 | ||||||||
\(872\) | 1.26460e6i | 1.66311i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −243579. | −0.318872 | ||||||||
\(875\) | 963584.i | 1.25856i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −167079. | −0.217232 | −0.108616 | − | 0.994084i | \(-0.534642\pi\) | ||||
−0.108616 | + | 0.994084i | \(0.534642\pi\) | |||||||
\(878\) | 481329.i | 0.624385i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6702.48 | −0.00865507 | ||||||||
\(881\) | − 501079.i | − 0.645586i | −0.946470 | − | 0.322793i | \(-0.895378\pi\) | ||||
0.946470 | − | 0.322793i | \(-0.104622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 219320. | 0.281292 | 0.140646 | − | 0.990060i | \(-0.455082\pi\) | ||||
0.140646 | + | 0.990060i | \(0.455082\pi\) | |||||||
\(884\) | − 197424.i | − 0.252636i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.02693e6 | 1.30820 | ||||||||
\(887\) | − 733514.i | − 0.932311i | −0.884703 | − | 0.466156i | \(-0.845639\pi\) | ||||
0.884703 | − | 0.466156i | \(-0.154361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.98017e6 | 2.50553 | ||||||||
\(890\) | 351315.i | 0.443524i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −94161.9 | −0.118344 | ||||||||
\(893\) | − 269502.i | − 0.337955i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −462186. | −0.576993 | ||||||||
\(896\) | 285634.i | 0.355790i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 865002. | 1.07267 | ||||||||
\(899\) | 26790.3i | 0.0331480i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 388806. | 0.478942 | ||||||||
\(902\) | 10119.0i | 0.0124373i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −973862. | −1.19168 | ||||||||
\(905\) | 126202.i | 0.154088i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −917159. | −1.11489 | −0.557443 | − | 0.830215i | \(-0.688217\pi\) | ||||
−0.557443 | + | 0.830215i | \(0.688217\pi\) | |||||||
\(908\) | 279256.i | 0.338712i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −460308. | −0.555860 | ||||||||
\(911\) | − 148683.i | − 0.179153i | −0.995980 | − | 0.0895765i | \(-0.971449\pi\) | ||||
0.995980 | − | 0.0895765i | \(-0.0285513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38975.8 | 0.0467577 | ||||||||
\(914\) | 189178.i | 0.226453i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 128974. | 0.153713 | ||||||||
\(917\) | 47503.0i | 0.0564914i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −180189. | −0.213353 | −0.106676 | − | 0.994294i | \(-0.534021\pi\) | ||||
−0.106676 | + | 0.994294i | \(0.534021\pi\) | |||||||
\(920\) | − 533482.i | − 0.630296i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −530859. | −0.624478 | ||||||||
\(923\) | − 1.46683e6i | − 1.72177i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −975606. | −1.14023 | ||||||||
\(926\) | − 340647.i | − 0.397267i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −240559. | −0.279335 | ||||||||
\(929\) | − 1.13809e6i | − 1.31869i | −0.751839 | − | 0.659347i | \(-0.770833\pi\) | ||||
0.751839 | − | 0.659347i | \(-0.229167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −466047. | −0.537688 | ||||||||
\(932\) | 175420.i | 0.201952i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.24677e6 | −1.42920 | ||||||||
\(935\) | − 10260.5i | − 0.0117366i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −308142. | −0.350971 | −0.175486 | − | 0.984482i | \(-0.556150\pi\) | ||||
−0.175486 | + | 0.984482i | \(0.556150\pi\) | |||||||
\(938\) | − 1.93960e6i | − 2.20449i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 151710. | 0.171695 | ||||||||
\(941\) | 899640.i | 1.01599i | 0.861360 | + | 0.507995i | \(0.169613\pi\) | ||||
−0.861360 | + | 0.507995i | \(0.830387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −488919. | −0.549812 | ||||||||
\(944\) | 61998.1i | 0.0695719i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46800.5 | −0.0522959 | ||||||||
\(947\) | 599889.i | 0.668915i | 0.942411 | + | 0.334457i | \(0.108553\pi\) | ||||
−0.942411 | + | 0.334457i | \(0.891447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 609469. | 0.676736 | ||||||||
\(950\) | − 165213.i | − 0.183061i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.23991e6 | −1.36810 | ||||||||
\(953\) | 1.14195e6i | 1.25737i | 0.777662 | + | 0.628683i | \(0.216406\pi\) | ||||
−0.777662 | + | 0.628683i | \(0.783594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −597455. | −0.655086 | ||||||||
\(956\) | 146582.i | 0.160386i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −745465. | −0.812262 | ||||||||
\(959\) | 476462.i | 0.518073i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −917919. | −0.993934 | ||||||||
\(962\) | − 1.01735e6i | − 1.09931i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −135675. | −0.145998 | ||||||||
\(965\) | 219924.i | 0.236166i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.07074e6 | −1.14507 | −0.572533 | − | 0.819882i | \(-0.694039\pi\) | ||||
−0.572533 | + | 0.819882i | \(0.694039\pi\) | |||||||
\(968\) | 1.01823e6i | 1.08667i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 565991. | 0.601542 | ||||||||
\(971\) | 505487.i | 0.536132i | 0.963401 | + | 0.268066i | \(0.0863846\pi\) | ||||
−0.963401 | + | 0.268066i | \(0.913615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.82997e6 | −1.93294 | ||||||||
\(974\) | − 155809.i | − 0.164239i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −513368. | −0.538926 | ||||||||
\(977\) | 650673.i | 0.681669i | 0.940123 | + | 0.340835i | \(0.110710\pi\) | ||||
−0.940123 | + | 0.340835i | \(0.889290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55055.8 | −0.0574431 | ||||||||
\(980\) | − 262351.i | − 0.273168i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 684760. | 0.710094 | ||||||||
\(983\) | 1.60271e6i | 1.65863i | 0.558784 | + | 0.829313i | \(0.311268\pi\) | ||||
−0.558784 | + | 0.829313i | \(0.688732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −311653. | −0.321217 | ||||||||
\(986\) | 242493.i | 0.249429i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −91119.8 | −0.0933467 | ||||||||
\(989\) | − 2.26126e6i | − 2.31184i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41952.2 | 0.0427177 | 0.0213588 | − | 0.999772i | \(-0.493201\pi\) | ||||
0.0213588 | + | 0.999772i | \(0.493201\pi\) | |||||||
\(992\) | 50303.8i | 0.0511184i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.36778e6 | −2.39645 | ||||||||
\(995\) | 515920.i | 0.521119i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 634831. | 0.638657 | 0.319328 | − | 0.947644i | \(-0.396543\pi\) | ||||
0.319328 | + | 0.947644i | \(0.396543\pi\) | |||||||
\(998\) | 1.21436e6i | 1.21924i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.b.a.296.52 | yes | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.25 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.25 | ✓ | 76 | 3.2 | odd | 2 | inner | |
531.5.b.a.296.52 | yes | 76 | 1.1 | even | 1 | trivial |