Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
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([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (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: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.23 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.18 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07792i | 0.269480i | 0.990881 | + | 0.134740i | \(0.0430199\pi\) | ||||
−0.990881 | + | 0.134740i | \(0.956980\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.8381 | 0.927380 | ||||||||
\(5\) | −26.1400 | −1.04560 | −0.522801 | − | 0.852455i | \(-0.675113\pi\) | ||||
−0.522801 | + | 0.852455i | \(0.675113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.1298 | 1.00265 | 0.501325 | − | 0.865259i | \(-0.332846\pi\) | ||||
0.501325 | + | 0.865259i | \(0.332846\pi\) | |||||||
\(8\) | 33.2410i | 0.519391i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 28.1769i | − | 0.281769i | ||||||
\(11\) | 190.415i | 1.57368i | 0.617158 | + | 0.786839i | \(0.288284\pi\) | ||||
−0.617158 | + | 0.786839i | \(0.711716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 198.277i | 1.17323i | 0.809864 | + | 0.586617i | \(0.199541\pi\) | ||||
−0.809864 | + | 0.586617i | \(0.800459\pi\) | |||||||
\(14\) | 52.9580i | 0.270194i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 201.578 | 0.787415 | ||||||||
\(17\) | 81.6050 | 0.282370 | 0.141185 | − | 0.989983i | \(-0.454909\pi\) | ||||
0.141185 | + | 0.989983i | \(0.454909\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −590.362 | −1.63535 | −0.817676 | − | 0.575678i | \(-0.804738\pi\) | ||||
−0.817676 | + | 0.575678i | \(0.804738\pi\) | |||||||
\(20\) | −387.868 | −0.969671 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −205.252 | −0.424075 | ||||||||
\(23\) | − | 808.730i | − | 1.52879i | −0.644748 | − | 0.764395i | \(-0.723038\pi\) | ||
0.644748 | − | 0.764395i | \(-0.276962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 58.3017 | 0.0932828 | ||||||||
\(26\) | −213.726 | −0.316163 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 728.992 | 0.929837 | ||||||||
\(29\) | 714.690 | 0.849809 | 0.424905 | − | 0.905238i | \(-0.360308\pi\) | ||||
0.424905 | + | 0.905238i | \(0.360308\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1370.46i | − | 1.42607i | −0.701126 | − | 0.713037i | \(-0.747319\pi\) | ||
0.701126 | − | 0.713037i | \(-0.252681\pi\) | |||||||
\(32\) | 749.141i | 0.731583i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 87.9637i | 0.0760932i | ||||||||
\(35\) | −1284.26 | −1.04837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2106.01i | 1.53835i | 0.639036 | + | 0.769177i | \(0.279334\pi\) | ||||
−0.639036 | + | 0.769177i | \(0.720666\pi\) | |||||||
\(38\) | − | 636.363i | − | 0.440695i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 868.921i | − | 0.543076i | ||||||
\(41\) | −1132.48 | −0.673694 | −0.336847 | − | 0.941559i | \(-0.609360\pi\) | ||||
−0.336847 | + | 0.941559i | \(0.609360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 349.669i | 0.189113i | 0.995520 | + | 0.0945563i | \(0.0301432\pi\) | ||||
−0.995520 | + | 0.0945563i | \(0.969857\pi\) | |||||||
\(44\) | 2825.40i | 1.45940i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 871.746 | 0.411978 | ||||||||
\(47\) | 2257.08i | 1.02176i | 0.859651 | + | 0.510882i | \(0.170681\pi\) | ||||
−0.859651 | + | 0.510882i | \(0.829319\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.7381 | 0.00530533 | ||||||||
\(50\) | 62.8446i | 0.0251378i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2942.05i | 1.08803i | ||||||||
\(53\) | −4733.28 | −1.68504 | −0.842520 | − | 0.538665i | \(-0.818929\pi\) | ||||
−0.842520 | + | 0.538665i | \(0.818929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4977.46i | − | 1.64544i | ||||||
\(56\) | 1633.12i | 0.520767i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 770.378i | 0.229007i | ||||||||
\(59\) | 3019.48 | + | 1732.08i | 0.867417 | + | 0.497582i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1500.86i | − | 0.403349i | −0.979453 | − | 0.201675i | \(-0.935362\pi\) | ||
0.979453 | − | 0.201675i | \(-0.0646384\pi\) | |||||||
\(62\) | 1477.24 | 0.384298 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2417.74 | 0.590268 | ||||||||
\(65\) | − | 5182.96i | − | 1.22674i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 233.568i | − | 0.0520312i | −0.999662 | − | 0.0260156i | \(-0.991718\pi\) | ||
0.999662 | − | 0.0260156i | \(-0.00828195\pi\) | |||||||
\(68\) | 1210.86 | 0.261865 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 1384.32i | − | 0.282515i | ||||||
\(71\) | −2664.24 | −0.528515 | −0.264258 | − | 0.964452i | \(-0.585127\pi\) | ||||
−0.264258 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9123.79i | 1.71210i | 0.516892 | + | 0.856051i | \(0.327089\pi\) | ||||
−0.516892 | + | 0.856051i | \(0.672911\pi\) | |||||||
\(74\) | −2270.11 | −0.414556 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8759.85 | −1.51659 | ||||||||
\(77\) | 9355.06i | 1.57785i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8286.52 | −1.32776 | −0.663878 | − | 0.747841i | \(-0.731090\pi\) | ||||
−0.663878 | + | 0.747841i | \(0.731090\pi\) | |||||||
\(80\) | −5269.26 | −0.823323 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1220.72i | − | 0.181547i | ||||||
\(83\) | − | 7478.73i | − | 1.08560i | −0.839860 | − | 0.542802i | \(-0.817363\pi\) | ||
0.839860 | − | 0.542802i | \(-0.182637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2133.16 | −0.295247 | ||||||||
\(86\) | −376.915 | −0.0509621 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6329.59 | −0.817354 | ||||||||
\(89\) | 10590.0i | 1.33696i | 0.743732 | + | 0.668478i | \(0.233054\pi\) | ||||
−0.743732 | + | 0.668478i | \(0.766946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9741.29i | 1.17634i | ||||||||
\(92\) | − | 12000.0i | − | 1.41777i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2432.95 | −0.275345 | ||||||||
\(95\) | 15432.1 | 1.70993 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15056.8i | 1.60025i | 0.599833 | + | 0.800125i | \(0.295234\pi\) | ||||
−0.599833 | + | 0.800125i | \(0.704766\pi\) | |||||||
\(98\) | 13.7306i | 0.00142968i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 865.086 | 0.0865086 | ||||||||
\(101\) | − | 7157.42i | − | 0.701639i | −0.936443 | − | 0.350819i | \(-0.885903\pi\) | ||
0.936443 | − | 0.350819i | \(-0.114097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10141.1i | − | 0.955896i | −0.878388 | − | 0.477948i | \(-0.841381\pi\) | ||
0.878388 | − | 0.477948i | \(-0.158619\pi\) | |||||||
\(104\) | −6590.91 | −0.609367 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 5102.10i | − | 0.454085i | ||||||
\(107\) | −3578.48 | −0.312558 | −0.156279 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156279 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2420.34i | 0.203716i | 0.994799 | + | 0.101858i | \(0.0324787\pi\) | ||||
−0.994799 | + | 0.101858i | \(0.967521\pi\) | |||||||
\(110\) | 5365.30 | 0.443413 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9903.50 | 0.789501 | ||||||||
\(113\) | − | 1468.79i | − | 0.115028i | −0.998345 | − | 0.0575140i | \(-0.981683\pi\) | ||
0.998345 | − | 0.0575140i | \(-0.0183174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21140.2i | 1.59851i | ||||||||
\(116\) | 10604.6 | 0.788097 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1867.05 | + | 3254.76i | −0.134089 | + | 0.233752i | ||||
\(119\) | 4009.24 | 0.283118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21616.9 | −1.47646 | ||||||||
\(122\) | 1617.81 | 0.108695 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 20335.0i | − | 1.32251i | ||||||
\(125\) | 14813.5 | 0.948065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −23012.3 | −1.42677 | −0.713383 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713383 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(128\) | 14592.4i | 0.890649i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5586.82 | 0.330581 | ||||||||
\(131\) | − | 16089.2i | − | 0.937543i | −0.883319 | − | 0.468772i | \(-0.844697\pi\) | ||
0.883319 | − | 0.468772i | \(-0.155303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29004.4 | −1.63968 | ||||||||
\(134\) | 251.768 | 0.0140214 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2712.63i | 0.146661i | ||||||||
\(137\) | 4170.90 | 0.222223 | 0.111111 | − | 0.993808i | \(-0.464559\pi\) | ||||
0.111111 | + | 0.993808i | \(0.464559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22317.2 | 1.15508 | 0.577538 | − | 0.816364i | \(-0.304014\pi\) | ||||
0.577538 | + | 0.816364i | \(0.304014\pi\) | |||||||
\(140\) | −19055.9 | −0.972239 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2871.84i | − | 0.142424i | ||||||
\(143\) | −37754.9 | −1.84629 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18682.0 | −0.888562 | ||||||||
\(146\) | −9834.72 | −0.461377 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31249.1i | 1.42664i | ||||||||
\(149\) | 20688.1i | 0.931853i | 0.884823 | + | 0.465927i | \(0.154279\pi\) | ||||
−0.884823 | + | 0.465927i | \(0.845721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30416.0i | 1.33397i | 0.745069 | + | 0.666987i | \(0.232417\pi\) | ||||
−0.745069 | + | 0.666987i | \(0.767583\pi\) | |||||||
\(152\) | − | 19624.2i | − | 0.849387i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10084.0 | −0.425198 | ||||||||
\(155\) | 35823.8i | 1.49111i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 37967.4i | − | 1.54032i | −0.637849 | − | 0.770162i | \(-0.720175\pi\) | ||
0.637849 | − | 0.770162i | \(-0.279825\pi\) | |||||||
\(158\) | − | 8932.21i | − | 0.357804i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 19582.6i | − | 0.764945i | ||||||
\(161\) | − | 39732.7i | − | 1.53284i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25366.6 | −0.954745 | −0.477372 | − | 0.878701i | \(-0.658411\pi\) | ||||
−0.477372 | + | 0.878701i | \(0.658411\pi\) | |||||||
\(164\) | −16803.8 | −0.624770 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8061.48 | 0.292549 | ||||||||
\(167\) | −33472.9 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10752.6 | −0.376479 | ||||||||
\(170\) | − | 2299.38i | − | 0.0795632i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5188.42i | 0.175379i | ||||||||
\(173\) | 23093.0i | 0.771594i | 0.922584 | + | 0.385797i | \(0.126073\pi\) | ||||
−0.922584 | + | 0.385797i | \(0.873927\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2864.35 | 0.0935299 | ||||||||
\(176\) | 38383.5i | 1.23914i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11415.2 | −0.360283 | ||||||||
\(179\) | 49281.4i | 1.53807i | 0.639205 | + | 0.769036i | \(0.279264\pi\) | ||||
−0.639205 | + | 0.769036i | \(0.720736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 52984.7 | 1.61731 | 0.808656 | − | 0.588282i | \(-0.200196\pi\) | ||||
0.808656 | + | 0.588282i | \(0.200196\pi\) | |||||||
\(182\) | −10500.3 | −0.317001 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26883.0 | 0.794039 | ||||||||
\(185\) | − | 55051.1i | − | 1.60851i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15538.8i | 0.444360i | ||||||||
\(188\) | 33490.7i | 0.947565i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16634.6i | 0.460791i | ||||||||
\(191\) | 31600.3i | 0.866213i | 0.901343 | + | 0.433106i | \(0.142583\pi\) | ||||
−0.901343 | + | 0.433106i | \(0.857417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6662.77 | −0.178871 | −0.0894355 | − | 0.995993i | \(-0.528506\pi\) | ||||
−0.0894355 | + | 0.995993i | \(0.528506\pi\) | |||||||
\(194\) | −16230.0 | −0.431236 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 189.009 | 0.00492006 | ||||||||
\(197\) | 3249.83 | 0.0837391 | 0.0418696 | − | 0.999123i | \(-0.486669\pi\) | ||||
0.0418696 | + | 0.999123i | \(0.486669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −39419.7 | −0.995421 | −0.497710 | − | 0.867343i | \(-0.665826\pi\) | ||||
−0.497710 | + | 0.867343i | \(0.665826\pi\) | |||||||
\(200\) | 1938.01i | 0.0484502i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7715.12 | 0.189078 | ||||||||
\(203\) | 35112.6 | 0.852061 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29603.0 | 0.704415 | ||||||||
\(206\) | 10931.3 | 0.257595 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 39968.3i | 0.923822i | ||||||||
\(209\) | − | 112414.i | − | 2.57352i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8215.58i | 0.184533i | 0.995734 | + | 0.0922663i | \(0.0294111\pi\) | ||||
−0.995734 | + | 0.0922663i | \(0.970589\pi\) | |||||||
\(212\) | −70232.8 | −1.56267 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 3857.31i | − | 0.0842281i | ||||||
\(215\) | − | 9140.37i | − | 0.197736i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 67330.3i | − | 1.42985i | ||||||
\(218\) | −2608.94 | −0.0548973 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 73856.0i | − | 1.52595i | ||||||
\(221\) | 16180.4i | 0.331287i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24717.2 | 0.497037 | 0.248519 | − | 0.968627i | \(-0.420056\pi\) | ||||
0.248519 | + | 0.968627i | \(0.420056\pi\) | |||||||
\(224\) | 36805.2i | 0.733521i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1583.24 | 0.0309978 | ||||||||
\(227\) | − | 22950.1i | − | 0.445382i | −0.974889 | − | 0.222691i | \(-0.928516\pi\) | ||
0.974889 | − | 0.222691i | \(-0.0714842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26740.2i | 0.509911i | 0.966953 | + | 0.254955i | \(0.0820608\pi\) | ||||
−0.966953 | + | 0.254955i | \(0.917939\pi\) | |||||||
\(230\) | −22787.5 | −0.430765 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23757.0i | 0.441383i | ||||||||
\(233\) | 29499.8i | 0.543385i | 0.962384 | + | 0.271693i | \(0.0875834\pi\) | ||||
−0.962384 | + | 0.271693i | \(0.912417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 59000.1i | − | 1.06836i | ||||||
\(236\) | 44803.3 | + | 25700.8i | 0.804425 | + | 0.461448i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4321.64i | 0.0762948i | ||||||||
\(239\) | −37689.9 | −0.659825 | −0.329913 | − | 0.944011i | \(-0.607019\pi\) | ||||
−0.329913 | + | 0.944011i | \(0.607019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 49193.4 | 0.846979 | 0.423489 | − | 0.905901i | \(-0.360805\pi\) | ||||
0.423489 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(242\) | − | 23301.3i | − | 0.397877i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 22269.9i | − | 0.374058i | ||||||
\(245\) | −332.974 | −0.00554726 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 117055.i | − | 1.91865i | ||||||
\(248\) | 45555.4 | 0.740689 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15967.8i | 0.255485i | ||||||||
\(251\) | 67494.9 | 1.07133 | 0.535666 | − | 0.844430i | \(-0.320061\pi\) | ||||
0.535666 | + | 0.844430i | \(0.320061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 153994. | 2.40582 | ||||||||
\(254\) | − | 24805.4i | − | 0.384485i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 22954.4 | 0.350256 | ||||||||
\(257\) | 94378.9 | 1.42892 | 0.714461 | − | 0.699675i | \(-0.246672\pi\) | ||||
0.714461 | + | 0.699675i | \(0.246672\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 103468.i | 1.54243i | ||||||||
\(260\) | − | 76905.2i | − | 1.13765i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17342.8 | 0.252649 | ||||||||
\(263\) | 96817.8 | 1.39973 | 0.699864 | − | 0.714276i | \(-0.253244\pi\) | ||||
0.699864 | + | 0.714276i | \(0.253244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 123728. | 1.76188 | ||||||||
\(266\) | − | 31264.4i | − | 0.441862i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 3465.70i | − | 0.0482527i | ||||||
\(269\) | − | 56566.9i | − | 0.781732i | −0.920448 | − | 0.390866i | \(-0.872176\pi\) | ||
0.920448 | − | 0.390866i | \(-0.127824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17865.0 | −0.243257 | −0.121628 | − | 0.992576i | \(-0.538812\pi\) | ||||
−0.121628 | + | 0.992576i | \(0.538812\pi\) | |||||||
\(272\) | 16449.8 | 0.222343 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4495.90i | 0.0598846i | ||||||||
\(275\) | 11101.5i | 0.146797i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −86629.0 | −1.12902 | −0.564512 | − | 0.825425i | \(-0.690936\pi\) | ||||
−0.564512 | + | 0.825425i | \(0.690936\pi\) | |||||||
\(278\) | 24056.2i | 0.311270i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 42689.9i | − | 0.544514i | ||||||
\(281\) | 84063.8 | 1.06462 | 0.532312 | − | 0.846548i | \(-0.321323\pi\) | ||||
0.532312 | + | 0.846548i | \(0.321323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10026.8i | − | 0.125195i | −0.998039 | − | 0.0625977i | \(-0.980062\pi\) | ||
0.998039 | − | 0.0625977i | \(-0.0199385\pi\) | |||||||
\(284\) | −39532.3 | −0.490135 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 40696.7i | − | 0.497539i | ||||||
\(287\) | −55638.5 | −0.675478 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −76861.6 | −0.920267 | ||||||||
\(290\) | − | 20137.7i | − | 0.239450i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 135380.i | 1.58777i | ||||||||
\(293\) | 68620.8 | 0.799319 | 0.399660 | − | 0.916664i | \(-0.369128\pi\) | ||||
0.399660 | + | 0.916664i | \(0.369128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −78929.3 | − | 45276.8i | −0.906972 | − | 0.520273i | ||||
\(296\) | −70005.8 | −0.799007 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22300.1 | −0.251116 | ||||||||
\(299\) | 160352. | 1.79363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17179.2i | 0.189614i | ||||||||
\(302\) | −32786.0 | −0.359480 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −119004. | −1.28770 | ||||||||
\(305\) | 39232.6i | 0.421743i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 158352. | 1.68014 | 0.840072 | − | 0.542475i | \(-0.182513\pi\) | ||||
0.840072 | + | 0.542475i | \(0.182513\pi\) | |||||||
\(308\) | 138811.i | 1.46326i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −38615.2 | −0.401823 | ||||||||
\(311\) | −58229.0 | −0.602030 | −0.301015 | − | 0.953619i | \(-0.597325\pi\) | ||||
−0.301015 | + | 0.953619i | \(0.597325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 38385.1i | 0.391808i | 0.980623 | + | 0.195904i | \(0.0627642\pi\) | ||||
−0.980623 | + | 0.195904i | \(0.937236\pi\) | |||||||
\(314\) | 40925.9 | 0.415086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −122956. | −1.23133 | ||||||||
\(317\) | −25846.8 | −0.257210 | −0.128605 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128605 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 136088.i | 1.33733i | ||||||||
\(320\) | −63199.8 | −0.617185 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42828.7 | 0.413070 | ||||||||
\(323\) | −48176.5 | −0.461775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11559.9i | 0.109443i | ||||||||
\(326\) | − | 27343.2i | − | 0.257285i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 37644.7i | − | 0.349910i | ||||||
\(329\) | 110890.i | 1.02447i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 127603. | 1.16467 | 0.582337 | − | 0.812947i | \(-0.302138\pi\) | ||||
0.582337 | + | 0.812947i | \(0.302138\pi\) | |||||||
\(332\) | − | 110970.i | − | 1.00677i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 36081.2i | − | 0.323435i | ||||||
\(335\) | 6105.48i | 0.0544039i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 55504.5i | − | 0.488730i | −0.969683 | − | 0.244365i | \(-0.921421\pi\) | ||
0.969683 | − | 0.244365i | \(-0.0785794\pi\) | |||||||
\(338\) | − | 11590.5i | − | 0.101454i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31652.0 | −0.273806 | ||||||||
\(341\) | 260956. | 2.24418 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117335. | −0.997330 | ||||||||
\(344\) | −11623.4 | −0.0982233 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24892.5 | −0.207929 | ||||||||
\(347\) | 84690.6i | 0.703358i | 0.936121 | + | 0.351679i | \(0.114389\pi\) | ||||
−0.936121 | + | 0.351679i | \(0.885611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 74255.3i | − | 0.609645i | −0.952409 | − | 0.304822i | \(-0.901403\pi\) | ||
0.952409 | − | 0.304822i | \(-0.0985971\pi\) | |||||||
\(350\) | 3087.54i | 0.0252044i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −142648. | −1.15128 | ||||||||
\(353\) | − | 221926.i | − | 1.78098i | −0.455001 | − | 0.890491i | \(-0.650361\pi\) | ||
0.455001 | − | 0.890491i | \(-0.349639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 69643.5 | 0.552616 | ||||||||
\(356\) | 157136.i | 1.23987i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −53121.4 | −0.414480 | ||||||||
\(359\) | −55048.5 | −0.427127 | −0.213563 | − | 0.976929i | \(-0.568507\pi\) | ||||
−0.213563 | + | 0.976929i | \(0.568507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 218207. | 1.67438 | ||||||||
\(362\) | 57113.3i | 0.435833i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 144542.i | 1.09092i | ||||||||
\(365\) | − | 238496.i | − | 1.79018i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 146662.i | − | 1.08889i | −0.838796 | − | 0.544446i | \(-0.816740\pi\) | ||
0.838796 | − | 0.544446i | \(-0.183260\pi\) | |||||||
\(368\) | − | 163022.i | − | 1.20379i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 59340.7 | 0.433460 | ||||||||
\(371\) | −232545. | −1.68950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 166279. | 1.19515 | 0.597573 | − | 0.801815i | \(-0.296132\pi\) | ||||
0.597573 | + | 0.801815i | \(0.296132\pi\) | |||||||
\(374\) | −16749.6 | −0.119746 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −75027.5 | −0.530695 | ||||||||
\(377\) | 141706.i | 0.997025i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 60758.9 | 0.422991 | 0.211496 | − | 0.977379i | \(-0.432167\pi\) | ||||
0.211496 | + | 0.977379i | \(0.432167\pi\) | |||||||
\(380\) | 228983. | 1.58575 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −34062.6 | −0.233427 | ||||||||
\(383\) | −120080. | −0.818601 | −0.409300 | − | 0.912400i | \(-0.634227\pi\) | ||||
−0.409300 | + | 0.912400i | \(0.634227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 244542.i | − | 1.64980i | ||||||
\(386\) | − | 7181.93i | − | 0.0482022i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 223413.i | 1.48404i | ||||||||
\(389\) | −184834. | −1.22147 | −0.610735 | − | 0.791835i | \(-0.709126\pi\) | ||||
−0.610735 | + | 0.791835i | \(0.709126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 65996.4i | − | 0.431685i | ||||||
\(392\) | 423.427i | 0.00275554i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3503.06i | 0.0225660i | ||||||||
\(395\) | 216610. | 1.38830 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 170314.i | 1.08061i | 0.841469 | + | 0.540306i | \(0.181692\pi\) | ||||
−0.841469 | + | 0.540306i | \(0.818308\pi\) | |||||||
\(398\) | − | 42491.2i | − | 0.268246i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11752.4 | 0.0734523 | ||||||||
\(401\) | 32629.9i | 0.202921i | 0.994840 | + | 0.101461i | \(0.0323516\pi\) | ||||
−0.994840 | + | 0.101461i | \(0.967648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 271730. | 1.67312 | ||||||||
\(404\) | − | 106202.i | − | 0.650686i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 37848.5i | 0.229613i | ||||||||
\(407\) | −401015. | −2.42087 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 278424.i | − | 1.66441i | −0.554468 | − | 0.832205i | \(-0.687078\pi\) | ||
0.554468 | − | 0.832205i | \(-0.312922\pi\) | |||||||
\(410\) | 31909.7i | 0.189826i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 150475.i | − | 0.886480i | ||||||
\(413\) | 148346. | + | 85097.0i | 0.869715 | + | 0.498901i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 195494.i | 1.13511i | ||||||||
\(416\) | −148537. | −0.858319 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 121173. | 0.693512 | ||||||||
\(419\) | − | 99149.5i | − | 0.564758i | −0.959303 | − | 0.282379i | \(-0.908876\pi\) | ||
0.959303 | − | 0.282379i | \(-0.0911236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 124249.i | − | 0.701015i | −0.936560 | − | 0.350508i | \(-0.886009\pi\) | ||
0.936560 | − | 0.350508i | \(-0.113991\pi\) | |||||||
\(422\) | −8855.74 | −0.0497279 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 157339.i | − | 0.875194i | ||||||
\(425\) | 4757.72 | 0.0263403 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 73737.1i | − | 0.404418i | ||||||
\(428\) | −53097.7 | −0.289860 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9852.59 | 0.0532860 | ||||||||
\(431\) | − | 80751.0i | − | 0.434704i | −0.976093 | − | 0.217352i | \(-0.930258\pi\) | ||
0.976093 | − | 0.217352i | \(-0.0697419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 267478. | 1.42663 | 0.713317 | − | 0.700841i | \(-0.247192\pi\) | ||||
0.713317 | + | 0.700841i | \(0.247192\pi\) | |||||||
\(434\) | 72576.7 | 0.385317 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35913.3i | 0.188922i | ||||||||
\(437\) | 477444.i | 2.50011i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 244540. | 1.26888 | 0.634441 | − | 0.772971i | \(-0.281230\pi\) | ||||
0.634441 | + | 0.772971i | \(0.281230\pi\) | |||||||
\(440\) | 165456. | 0.854626 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17441.1 | −0.0892751 | ||||||||
\(443\) | 303375.i | 1.54587i | 0.634487 | + | 0.772933i | \(0.281211\pi\) | ||||
−0.634487 | + | 0.772933i | \(0.718789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 276824.i | − | 1.39792i | ||||||
\(446\) | 26643.1i | 0.133942i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 118783. | 0.591832 | ||||||||
\(449\) | 265110. | 1.31503 | 0.657513 | − | 0.753444i | \(-0.271609\pi\) | ||||
0.657513 | + | 0.753444i | \(0.271609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 215641.i | − | 1.06018i | ||||||
\(452\) | − | 21794.1i | − | 0.106675i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24738.4 | 0.120022 | ||||||||
\(455\) | − | 254638.i | − | 1.22999i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 351393.i | 1.68252i | 0.540628 | + | 0.841262i | \(0.318187\pi\) | ||||
−0.540628 | + | 0.841262i | \(0.681813\pi\) | |||||||
\(458\) | −28823.8 | −0.137411 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 313681.i | 1.48242i | ||||||||
\(461\) | −96578.1 | −0.454440 | −0.227220 | − | 0.973843i | \(-0.572964\pi\) | ||||
−0.227220 | + | 0.973843i | \(0.572964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 247348.i | − | 1.15384i | −0.816800 | − | 0.576922i | \(-0.804254\pi\) | ||
0.816800 | − | 0.576922i | \(-0.195746\pi\) | |||||||
\(464\) | 144066. | 0.669153 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31798.5 | −0.146432 | ||||||||
\(467\) | − | 233363.i | − | 1.07004i | −0.844841 | − | 0.535018i | \(-0.820305\pi\) | ||
0.844841 | − | 0.535018i | \(-0.179695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11475.1i | − | 0.0521690i | ||||||
\(470\) | 63597.4 | 0.287901 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −57576.2 | + | 100370.i | −0.258440 | + | 0.450528i | ||||
\(473\) | −66582.3 | −0.297602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34419.1 | −0.152550 | ||||||||
\(476\) | 59489.5 | 0.262559 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 40626.7i | − | 0.177810i | ||||||
\(479\) | −254275. | −1.10824 | −0.554119 | − | 0.832438i | \(-0.686945\pi\) | ||||
−0.554119 | + | 0.832438i | \(0.686945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −417572. | −1.80485 | ||||||||
\(482\) | 53026.5i | 0.228244i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −320753. | −1.36924 | ||||||||
\(485\) | − | 393584.i | − | 1.67322i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 221313. | 0.933146 | 0.466573 | − | 0.884483i | \(-0.345488\pi\) | ||||
0.466573 | + | 0.884483i | \(0.345488\pi\) | |||||||
\(488\) | 49890.2 | 0.209496 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 358.920i | − | 0.00149488i | ||||||
\(491\) | −20143.2 | −0.0835537 | −0.0417769 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417769 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58322.3 | 0.239961 | ||||||||
\(494\) | 126176. | 0.517038 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 276254.i | − | 1.12291i | ||||||
\(497\) | −130894. | −0.529915 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −142382. | −0.571813 | −0.285907 | − | 0.958258i | \(-0.592295\pi\) | ||||
−0.285907 | + | 0.958258i | \(0.592295\pi\) | |||||||
\(500\) | 219804. | 0.879217 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 72754.1i | 0.288702i | ||||||||
\(503\) | − | 61029.3i | − | 0.241214i | −0.992700 | − | 0.120607i | \(-0.961516\pi\) | ||
0.992700 | − | 0.120607i | \(-0.0384841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 187095.i | 0.733635i | ||||||||
\(506\) | 165994.i | 0.648321i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −341459. | −1.32315 | ||||||||
\(509\) | 119724.i | 0.462111i | 0.972941 | + | 0.231056i | \(0.0742179\pi\) | ||||
−0.972941 | + | 0.231056i | \(0.925782\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 448250.i | 1.71664i | ||||||||
\(512\) | 258221.i | 0.985036i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 101733.i | 0.385066i | ||||||||
\(515\) | 265089.i | 0.999487i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −429782. | −1.60793 | ||||||||
\(518\) | −111530. | −0.415654 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 172287. | 0.637155 | ||||||||
\(521\) | −526245. | −1.93871 | −0.969355 | − | 0.245663i | \(-0.920994\pi\) | ||||
−0.969355 | + | 0.245663i | \(0.920994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43580.1 | 0.159325 | 0.0796626 | − | 0.996822i | \(-0.474616\pi\) | ||||
0.0796626 | + | 0.996822i | \(0.474616\pi\) | |||||||
\(524\) | − | 238733.i | − | 0.869459i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 104362.i | 0.377199i | ||||||||
\(527\) | − | 111836.i | − | 0.402681i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −374203. | −1.33720 | ||||||||
\(530\) | 133369.i | 0.474792i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −430370. | −1.52061 | ||||||||
\(533\) | − | 224544.i | − | 0.790400i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 93541.5 | 0.326811 | ||||||||
\(536\) | 7764.03 | 0.0270245 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 60974.6 | 0.210661 | ||||||||
\(539\) | 2425.52i | 0.00834888i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 318207.i | 1.08721i | 0.839340 | + | 0.543606i | \(0.182942\pi\) | ||||
−0.839340 | + | 0.543606i | \(0.817058\pi\) | |||||||
\(542\) | − | 19257.1i | − | 0.0655529i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 61133.7i | 0.206577i | ||||||||
\(545\) | − | 63267.9i | − | 0.213005i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −151057. | −0.504856 | −0.252428 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252428 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(548\) | 61888.2 | 0.206085 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11966.6 | −0.0395589 | ||||||||
\(551\) | −421926. | −1.38974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −407115. | −1.33127 | ||||||||
\(554\) | − | 93379.1i | − | 0.304250i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 331145. | 1.07119 | ||||||||
\(557\) | 439612. | 1.41697 | 0.708483 | − | 0.705728i | \(-0.249380\pi\) | ||||
0.708483 | + | 0.705728i | \(0.249380\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −69331.2 | −0.221873 | ||||||||
\(560\) | −258878. | −0.825504 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 90614.0i | 0.286895i | ||||||||
\(563\) | 468132.i | 1.47690i | 0.674308 | + | 0.738450i | \(0.264442\pi\) | ||||
−0.674308 | + | 0.738450i | \(0.735558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38394.3i | 0.120274i | ||||||||
\(566\) | 10808.1 | 0.0337376 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 88562.2i | − | 0.274506i | ||||||
\(569\) | 156283.i | 0.482711i | 0.970437 | + | 0.241356i | \(0.0775920\pi\) | ||||
−0.970437 | + | 0.241356i | \(0.922408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 214333.i | − | 0.657379i | −0.944438 | − | 0.328690i | \(-0.893393\pi\) | ||
0.944438 | − | 0.328690i | \(-0.106607\pi\) | |||||||
\(572\) | −560210. | −1.71222 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 59973.8i | − | 0.182028i | ||||||
\(575\) | − | 47150.4i | − | 0.142610i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −83530.0 | −0.250894 | −0.125447 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125447 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(578\) | − | 82850.7i | − | 0.247994i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −277205. | −0.824035 | ||||||||
\(581\) | − | 367429.i | − | 1.08848i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 901288.i | − | 2.65171i | ||||||
\(584\) | −303284. | −0.889249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 73967.7i | 0.215401i | ||||||||
\(587\) | 65804.0i | 0.190975i | 0.995431 | + | 0.0954873i | \(0.0304409\pi\) | ||||
−0.995431 | + | 0.0954873i | \(0.969559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 809066.i | 2.33213i | ||||||||
\(590\) | 48804.7 | − | 85079.5i | 0.140203 | − | 0.244411i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 424525.i | 1.21132i | ||||||||
\(593\) | 180576. | 0.513511 | 0.256756 | − | 0.966476i | \(-0.417346\pi\) | ||||
0.256756 | + | 0.966476i | \(0.417346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −104802. | −0.296029 | ||||||||
\(596\) | 306971.i | 0.864183i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 172847.i | 0.483347i | ||||||||
\(599\) | 121500. | 0.338629 | 0.169314 | − | 0.985562i | \(-0.445845\pi\) | ||||
0.169314 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 246152.i | 0.681483i | 0.940157 | + | 0.340742i | \(0.110678\pi\) | ||||
−0.940157 | + | 0.340742i | \(0.889322\pi\) | |||||||
\(602\) | −18517.8 | −0.0510971 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 451315.i | 1.23710i | ||||||||
\(605\) | 565067. | 1.54379 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 91016.6 | 0.247026 | 0.123513 | − | 0.992343i | \(-0.460584\pi\) | ||||
0.123513 | + | 0.992343i | \(0.460584\pi\) | |||||||
\(608\) | − | 442265.i | − | 1.19640i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −42289.6 | −0.113651 | ||||||||
\(611\) | −447526. | −1.19877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 165519.i | 0.440481i | 0.975446 | + | 0.220240i | \(0.0706842\pi\) | ||||
−0.975446 | + | 0.220240i | \(0.929316\pi\) | |||||||
\(614\) | 170691.i | 0.452765i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −310971. | −0.819519 | ||||||||
\(617\) | 337650. | 0.886945 | 0.443472 | − | 0.896288i | \(-0.353746\pi\) | ||||
0.443472 | + | 0.896288i | \(0.353746\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −158426. | −0.413470 | −0.206735 | − | 0.978397i | \(-0.566284\pi\) | ||||
−0.206735 | + | 0.978397i | \(0.566284\pi\) | |||||||
\(620\) | 531557.i | 1.38282i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 62766.2i | − | 0.162235i | ||||||
\(623\) | 520286.i | 1.34050i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −423664. | −1.08458 | ||||||||
\(626\) | −41376.1 | −0.105585 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 563364.i | − | 1.42847i | ||||||
\(629\) | 171861.i | 0.434386i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 563902. | 1.41627 | 0.708133 | − | 0.706080i | \(-0.249538\pi\) | ||||
0.708133 | + | 0.706080i | \(0.249538\pi\) | |||||||
\(632\) | − | 275452.i | − | 0.689624i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 27860.7i | − | 0.0693129i | ||||||
\(635\) | 601543. | 1.49183 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2525.66i | 0.00622439i | ||||||||
\(638\) | −146692. | −0.360383 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 381446.i | − | 0.931264i | ||||||
\(641\) | 46995.0 | 0.114376 | 0.0571881 | − | 0.998363i | \(-0.481787\pi\) | ||||
0.0571881 | + | 0.998363i | \(0.481787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 357241. | 0.864050 | 0.432025 | − | 0.901862i | \(-0.357799\pi\) | ||||
0.432025 | + | 0.901862i | \(0.357799\pi\) | |||||||
\(644\) | − | 589558.i | − | 1.42153i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 51930.5i | − | 0.124439i | ||||||
\(647\) | 146425. | 0.349790 | 0.174895 | − | 0.984587i | \(-0.444041\pi\) | ||||
0.174895 | + | 0.984587i | \(0.444041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −329815. | + | 574954.i | −0.783035 | + | 1.36503i | ||||
\(650\) | −12460.6 | −0.0294926 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −376392. | −0.885412 | ||||||||
\(653\) | 149895. | 0.351529 | 0.175764 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175764 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 420572.i | 0.980297i | ||||||||
\(656\) | −228283. | −0.530477 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −119530. | −0.276075 | ||||||||
\(659\) | 561285.i | 1.29245i | 0.763148 | + | 0.646223i | \(0.223653\pi\) | ||||
−0.763148 | + | 0.646223i | \(0.776347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −158811. | −0.363478 | −0.181739 | − | 0.983347i | \(-0.558173\pi\) | ||||
−0.181739 | + | 0.983347i | \(0.558173\pi\) | |||||||
\(662\) | 137546.i | 0.313856i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 248600. | 0.563853 | ||||||||
\(665\) | 758176. | 1.71446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 577991.i | − | 1.29918i | ||||||
\(668\) | −496674. | −1.11306 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6581.22 | −0.0146608 | ||||||||
\(671\) | 285787. | 0.634742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 468994.i | 1.03547i | 0.855541 | + | 0.517735i | \(0.173225\pi\) | ||||
−0.855541 | + | 0.517735i | \(0.826775\pi\) | |||||||
\(674\) | 59829.5 | 0.131703 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −159548. | −0.349139 | ||||||||
\(677\) | 560613. | 1.22317 | 0.611584 | − | 0.791180i | \(-0.290533\pi\) | ||||
0.611584 | + | 0.791180i | \(0.290533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 739736.i | 1.60449i | ||||||||
\(680\) | − | 70908.3i | − | 0.153348i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 281289.i | 0.604762i | ||||||||
\(683\) | − | 39053.9i | − | 0.0837188i | −0.999124 | − | 0.0418594i | \(-0.986672\pi\) | ||
0.999124 | − | 0.0418594i | \(-0.0133282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −109027. | −0.232356 | ||||||||
\(686\) | − | 126478.i | − | 0.268760i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 70485.7i | 0.148910i | ||||||||
\(689\) | − | 938499.i | − | 1.97695i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 138810.i | − | 0.290714i | −0.989379 | − | 0.145357i | \(-0.953567\pi\) | ||
0.989379 | − | 0.145357i | \(-0.0464330\pi\) | |||||||
\(692\) | 342657.i | 0.715561i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −91289.7 | −0.189541 | ||||||||
\(695\) | −583373. | −1.20775 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −92416.0 | −0.190231 | ||||||||
\(698\) | 80041.3 | 0.164287 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 42501.5 | 0.0867378 | ||||||||
\(701\) | − | 399850.i | − | 0.813695i | −0.913496 | − | 0.406847i | \(-0.866628\pi\) | ||
0.913496 | − | 0.406847i | \(-0.133372\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.24331e6i | − | 2.51575i | ||||||
\(704\) | 460374.i | 0.928892i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 239219. | 0.479939 | ||||||||
\(707\) | − | 351642.i | − | 0.703497i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −572973. | −1.13983 | −0.569917 | − | 0.821702i | \(-0.693025\pi\) | ||||
−0.569917 | + | 0.821702i | \(0.693025\pi\) | |||||||
\(710\) | 75070.1i | 0.148919i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −352023. | −0.694402 | ||||||||
\(713\) | −1.10833e6 | −2.18017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 986913. | 1.93049 | ||||||||
\(716\) | 731242.i | 1.42638i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 59337.9i | − | 0.115102i | ||||||
\(719\) | − | 655458.i | − | 1.26791i | −0.773372 | − | 0.633953i | \(-0.781431\pi\) | ||
0.773372 | − | 0.633953i | \(-0.218569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 498231.i | − | 0.958429i | ||||||
\(722\) | 235209.i | 0.451211i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 786192. | 1.49986 | ||||||||
\(725\) | 41667.6 | 0.0792726 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 438565. | 0.829785 | 0.414892 | − | 0.909870i | \(-0.363819\pi\) | ||||
0.414892 | + | 0.909870i | \(0.363819\pi\) | |||||||
\(728\) | −323810. | −0.610981 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 257080. | 0.482417 | ||||||||
\(731\) | 28534.8i | 0.0533998i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 524612. | 0.976406 | 0.488203 | − | 0.872730i | \(-0.337653\pi\) | ||||
0.488203 | + | 0.872730i | \(0.337653\pi\) | |||||||
\(734\) | 158090. | 0.293435 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 605853. | 1.11844 | ||||||||
\(737\) | 44474.9 | 0.0818803 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 354679.i | − | 0.649451i | −0.945808 | − | 0.324725i | \(-0.894728\pi\) | ||
0.945808 | − | 0.324725i | \(-0.105272\pi\) | |||||||
\(740\) | − | 816853.i | − | 1.49170i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 250665.i | − | 0.455288i | ||||||
\(743\) | 9241.58 | 0.0167405 | 0.00837025 | − | 0.999965i | \(-0.497336\pi\) | ||||
0.00837025 | + | 0.999965i | \(0.497336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 540787.i | − | 0.974347i | ||||||
\(746\) | 179236.i | 0.322068i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 230567.i | 0.412091i | ||||||||
\(749\) | −175810. | −0.313386 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.07245e6i | − | 1.90150i | −0.309962 | − | 0.950749i | \(-0.600316\pi\) | ||
0.309962 | − | 0.950749i | \(-0.399684\pi\) | |||||||
\(752\) | 454978.i | 0.804553i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −152748. | −0.268678 | ||||||||
\(755\) | − | 795074.i | − | 1.39481i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 513889. | 0.896762 | 0.448381 | − | 0.893842i | \(-0.352001\pi\) | ||||
0.448381 | + | 0.893842i | \(0.352001\pi\) | |||||||
\(758\) | 65493.2i | 0.113988i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 512978.i | 0.888120i | ||||||||
\(761\) | −300411. | −0.518736 | −0.259368 | − | 0.965779i | \(-0.583514\pi\) | ||||
−0.259368 | + | 0.965779i | \(0.583514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 118911.i | 0.204255i | ||||||||
\(764\) | 468888.i | 0.803309i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 129436.i | − | 0.220597i | ||||||
\(767\) | −343432. | + | 598692.i | −0.583781 | + | 1.01768i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 690998.i | − | 1.16849i | −0.811579 | − | 0.584243i | \(-0.801391\pi\) | ||
0.811579 | − | 0.584243i | \(-0.198609\pi\) | |||||||
\(770\) | 263596. | 0.444588 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −98862.7 | −0.165882 | ||||||||
\(773\) | 312549.i | 0.523069i | 0.965194 | + | 0.261534i | \(0.0842285\pi\) | ||||
−0.965194 | + | 0.261534i | \(0.915771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 79900.0i | − | 0.133028i | ||||||
\(776\) | −500502. | −0.831155 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 199236.i | − | 0.329162i | ||||||
\(779\) | 668573. | 1.10173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 507312.i | − | 0.831713i | ||||||
\(782\) | 71138.9 | 0.116331 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2567.72 | 0.00417749 | ||||||||
\(785\) | 992470.i | 1.61056i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 858686. | 1.38639 | 0.693194 | − | 0.720751i | \(-0.256203\pi\) | ||||
0.693194 | + | 0.720751i | \(0.256203\pi\) | |||||||
\(788\) | 48221.3 | 0.0776580 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 233488.i | 0.374120i | ||||||||
\(791\) | − | 72161.5i | − | 0.115333i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 297586. | 0.473223 | ||||||||
\(794\) | −183585. | −0.291203 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −584912. | −0.923134 | ||||||||
\(797\) | − | 795885.i | − | 1.25295i | −0.779442 | − | 0.626475i | \(-0.784497\pi\) | ||
0.779442 | − | 0.626475i | \(-0.215503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 184189.i | 0.288516i | ||||||||
\(800\) | 43676.2i | 0.0682441i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35172.5 | −0.0546832 | ||||||||
\(803\) | −1.73731e6 | −2.69430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.03862e6i | 1.60274i | ||||||||
\(806\) | 292903.i | 0.450872i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 237920. | 0.364425 | ||||||||
\(809\) | 610886.i | 0.933390i | 0.884418 | + | 0.466695i | \(0.154555\pi\) | ||||
−0.884418 | + | 0.466695i | \(0.845445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.12919e6i | 1.71682i | 0.512967 | + | 0.858408i | \(0.328546\pi\) | ||||
−0.512967 | + | 0.858408i | \(0.671454\pi\) | |||||||
\(812\) | 521003. | 0.790184 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 432263.i | − | 0.652377i | ||||||
\(815\) | 663084. | 0.998283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 206431.i | − | 0.309266i | ||||||
\(818\) | 300119. | 0.448525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 439253. | 0.653261 | ||||||||
\(821\) | 458260.i | 0.679869i | 0.940449 | + | 0.339935i | \(0.110405\pi\) | ||||
−0.940449 | + | 0.339935i | \(0.889595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 749847.i | 1.10707i | 0.832828 | + | 0.553533i | \(0.186721\pi\) | ||||
−0.832828 | + | 0.553533i | \(0.813279\pi\) | |||||||
\(824\) | 337100. | 0.496484 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −91727.7 | + | 159906.i | −0.134444 | + | 0.234371i | ||||
\(827\) | 241049. | 0.352447 | 0.176223 | − | 0.984350i | \(-0.443612\pi\) | ||||
0.176223 | + | 0.984350i | \(0.443612\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −459844. | −0.669116 | −0.334558 | − | 0.942375i | \(-0.608587\pi\) | ||||
−0.334558 | + | 0.942375i | \(0.608587\pi\) | |||||||
\(830\) | −210727. | −0.305890 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 479381.i | 0.692523i | ||||||||
\(833\) | 1039.49 | 0.00149807 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 874984. | 1.25495 | ||||||||
\(836\) | − | 1.66801e6i | − | 2.38663i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 106875. | 0.152191 | ||||||||
\(839\) | − | 614502.i | − | 0.872970i | −0.899712 | − | 0.436485i | \(-0.856223\pi\) | ||
0.899712 | − | 0.436485i | \(-0.143777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −196500. | −0.277824 | ||||||||
\(842\) | 133930. | 0.188910 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 121903.i | 0.171132i | ||||||||
\(845\) | 281074. | 0.393647 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.06203e6 | −1.48037 | ||||||||
\(848\) | −954126. | −1.32683 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5128.44i | 0.00709818i | ||||||||
\(851\) | 1.70319e6 | 2.35182 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 124975. | 0.171761 | 0.0858805 | − | 0.996305i | \(-0.472630\pi\) | ||||
0.0858805 | + | 0.996305i | \(0.472630\pi\) | |||||||
\(854\) | 79482.7 | 0.108983 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 118952.i | − | 0.162340i | ||||||
\(857\) | 250279.i | 0.340771i | 0.985377 | + | 0.170386i | \(0.0545014\pi\) | ||||
−0.985377 | + | 0.170386i | \(0.945499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 223143.i | 0.302411i | 0.988502 | + | 0.151206i | \(0.0483155\pi\) | ||||
−0.988502 | + | 0.151206i | \(0.951684\pi\) | |||||||
\(860\) | − | 135626.i | − | 0.183377i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 87043.1 | 0.117144 | ||||||||
\(863\) | 719881.i | 0.966583i | 0.875459 | + | 0.483292i | \(0.160559\pi\) | ||||
−0.875459 | + | 0.483292i | \(0.839441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 603653.i | − | 0.806780i | ||||||
\(866\) | 288320.i | 0.384450i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 999053.i | − | 1.32602i | ||||||
\(869\) | − | 1.57788e6i | − | 2.08946i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46311.1 | 0.0610448 | ||||||||
\(872\) | −80454.7 | −0.105808 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −514646. | −0.673730 | ||||||||
\(875\) | 727785. | 0.950577 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −191233. | −0.248636 | −0.124318 | − | 0.992242i | \(-0.539674\pi\) | ||||
−0.124318 | + | 0.992242i | \(0.539674\pi\) | |||||||
\(878\) | 263595.i | 0.341939i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1.00335e6i | − | 1.29564i | ||||||
\(881\) | − | 253450.i | − | 0.326543i | −0.986581 | − | 0.163272i | \(-0.947795\pi\) | ||
0.986581 | − | 0.163272i | \(-0.0522047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 499438. | 0.640560 | 0.320280 | − | 0.947323i | \(-0.396223\pi\) | ||||
0.320280 | + | 0.947323i | \(0.396223\pi\) | |||||||
\(884\) | 240086.i | 0.307229i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −327014. | −0.416580 | ||||||||
\(887\) | 941595.i | 1.19679i | 0.801202 | + | 0.598393i | \(0.204194\pi\) | ||||
−0.801202 | + | 0.598393i | \(0.795806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.13059e6 | −1.43055 | ||||||||
\(890\) | 298394. | 0.376712 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 366755. | 0.460942 | ||||||||
\(893\) | − | 1.33249e6i | − | 1.67095i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.28822e6i | − | 1.60821i | ||||||
\(896\) | 716921.i | 0.893008i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 285768.i | 0.354373i | ||||||||
\(899\) | − | 979451.i | − | 1.21189i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −386259. | −0.475806 | ||||||||
\(902\) | 232444. | 0.285697 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 48824.2 | 0.0597445 | ||||||||
\(905\) | −1.38502e6 | −1.69106 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 965170. | 1.17325 | 0.586623 | − | 0.809860i | \(-0.300457\pi\) | ||||
0.586623 | + | 0.809860i | \(0.300457\pi\) | |||||||
\(908\) | − | 340536.i | − | 0.413039i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 274479. | 0.331457 | ||||||||
\(911\) | −720113. | −0.867689 | −0.433845 | − | 0.900988i | \(-0.642843\pi\) | ||||
−0.433845 | + | 0.900988i | \(0.642843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.42406e6 | 1.70839 | ||||||||
\(914\) | −378774. | −0.453406 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 396774.i | 0.472881i | ||||||||
\(917\) | − | 790458.i | − | 0.940027i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.34142e6i | 1.58831i | 0.607716 | + | 0.794155i | \(0.292086\pi\) | ||||
−0.607716 | + | 0.794155i | \(0.707914\pi\) | |||||||
\(920\) | −702722. | −0.830249 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 104104.i | − | 0.122463i | ||||||
\(923\) | − | 528257.i | − | 0.620072i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 122784.i | 0.143502i | ||||||||
\(926\) | 266622. | 0.310938 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 535403.i | 0.621706i | ||||||||
\(929\) | 1.26115e6i | 1.46128i | 0.682761 | + | 0.730642i | \(0.260779\pi\) | ||||
−0.682761 | + | 0.730642i | \(0.739221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7520.09 | −0.00867608 | ||||||||
\(932\) | 437721.i | 0.503925i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 251547. | 0.288353 | ||||||||
\(935\) | − | 406186.i | − | 0.464624i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 251396.i | 0.286338i | 0.989698 | + | 0.143169i | \(0.0457293\pi\) | ||||
−0.989698 | + | 0.143169i | \(0.954271\pi\) | |||||||
\(938\) | 12369.3 | 0.0140585 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 875449.i | − | 0.990775i | ||||||
\(941\) | 766362.i | 0.865475i | 0.901520 | + | 0.432737i | \(0.142452\pi\) | ||||
−0.901520 | + | 0.432737i | \(0.857548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 915870.i | 1.02994i | ||||||||
\(944\) | 608661. | + | 349151.i | 0.683017 | + | 0.391804i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 71770.4i | − | 0.0801979i | ||||||
\(947\) | 2912.67 | 0.00324782 | 0.00162391 | − | 0.999999i | \(-0.499483\pi\) | ||||
0.00162391 | + | 0.999999i | \(0.499483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.80903e6 | −2.00870 | ||||||||
\(950\) | − | 37101.1i | − | 0.0411092i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 133271.i | 0.147049i | ||||||||
\(953\) | 1.10603e6 | 1.21782 | 0.608910 | − | 0.793240i | \(-0.291607\pi\) | ||||
0.608910 | + | 0.793240i | \(0.291607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 826033.i | − | 0.905714i | ||||||
\(956\) | −559246. | −0.611909 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 274088.i | − | 0.298648i | ||||||
\(959\) | 204915. | 0.222811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −954632. | −1.03369 | ||||||||
\(962\) | − | 450109.i | − | 0.486371i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 729936. | 0.785472 | ||||||||
\(965\) | 174165. | 0.187028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 165920.i | 0.177438i | 0.996057 | + | 0.0887188i | \(0.0282772\pi\) | ||||
−0.996057 | + | 0.0887188i | \(0.971723\pi\) | |||||||
\(968\) | − | 718567.i | − | 0.766861i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 424252. | 0.450901 | ||||||||
\(971\) | −236926. | −0.251290 | −0.125645 | − | 0.992075i | \(-0.540100\pi\) | ||||
−0.125645 | + | 0.992075i | \(0.540100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09644e6 | 1.15814 | ||||||||
\(974\) | 238558.i | 0.251464i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 302541.i | − | 0.317603i | ||||||
\(977\) | − | 904625.i | − | 0.947719i | −0.880600 | − | 0.473860i | \(-0.842860\pi\) | ||
0.880600 | − | 0.473860i | \(-0.157140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.01650e6 | −2.10394 | ||||||||
\(980\) | −4940.70 | −0.00514442 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 21712.8i | − | 0.0225161i | ||||||
\(983\) | − | 902770.i | − | 0.934265i | −0.884187 | − | 0.467133i | \(-0.845287\pi\) | ||
0.884187 | − | 0.467133i | \(-0.154713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −84950.7 | −0.0875578 | ||||||||
\(986\) | 62866.8i | 0.0646647i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.73687e6i | − | 1.77932i | ||||||
\(989\) | 282788. | 0.289113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 480106.i | − | 0.488866i | −0.969666 | − | 0.244433i | \(-0.921398\pi\) | ||
0.969666 | − | 0.244433i | \(-0.0786018\pi\) | |||||||
\(992\) | 1.02667e6 | 1.04329 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 141093.i | − | 0.142802i | ||||||
\(995\) | 1.03043e6 | 1.04081 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −144762. | −0.145635 | −0.0728173 | − | 0.997345i | \(-0.523199\pi\) | ||||
−0.0728173 | + | 0.997345i | \(0.523199\pi\) | |||||||
\(998\) | − | 153476.i | − | 0.154092i | ||||||
\(999\) | 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.c.d.235.23 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.18 | ✓ | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.18 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.23 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.18 | ✓ | 40 | 3.2 | odd | 2 | ||
177.5.c.a.58.23 | yes | 40 | 177.176 | even | 2 | ||
531.5.c.d.235.18 | 40 | 59.58 | odd | 2 | inner | ||
531.5.c.d.235.23 | 40 | 1.1 | even | 1 | trivial |