Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,5,Mod(80,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.80");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.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: | \(8.37296700979\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.39400128.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{9} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 80.4 | ||
Root | \(-0.102534 - 0.177594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.80 |
Dual form | 81.5.b.a.80.3 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.355188i | 0.0887969i | 0.999014 | + | 0.0443984i | \(0.0141371\pi\) | ||||
−0.999014 | + | 0.0443984i | \(0.985863\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.8738 | 0.992115 | ||||||||
\(5\) | 34.7338i | 1.38935i | 0.719323 | + | 0.694676i | \(0.244452\pi\) | ||||
−0.719323 | + | 0.694676i | \(0.755548\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.2109 | −0.636956 | −0.318478 | − | 0.947930i | \(-0.603172\pi\) | ||||
−0.318478 | + | 0.947930i | \(0.603172\pi\) | |||||||
\(8\) | 11.3212i | 0.176894i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.3370 | −0.123370 | ||||||||
\(11\) | 57.7314i | 0.477119i | 0.971128 | + | 0.238559i | \(0.0766752\pi\) | ||||
−0.971128 | + | 0.238559i | \(0.923325\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73.2956 | −0.433702 | −0.216851 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216851 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(14\) | − 11.0857i | − 0.0565597i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 249.960 | 0.976408 | ||||||||
\(17\) | 386.985i | 1.33905i | 0.742791 | + | 0.669524i | \(0.233502\pi\) | ||||
−0.742791 | + | 0.669524i | \(0.766498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 115.791 | 0.320750 | 0.160375 | − | 0.987056i | \(-0.448730\pi\) | ||||
0.160375 | + | 0.987056i | \(0.448730\pi\) | |||||||
\(20\) | 551.359i | 1.37840i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.5055 | −0.0423667 | ||||||||
\(23\) | 548.312i | 1.03651i | 0.855227 | + | 0.518253i | \(0.173417\pi\) | ||||
−0.855227 | + | 0.518253i | \(0.826583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −581.437 | −0.930299 | ||||||||
\(26\) | − 26.0337i | − 0.0385113i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −495.436 | −0.631934 | ||||||||
\(29\) | − 785.291i | − 0.933758i | −0.884321 | − | 0.466879i | \(-0.845378\pi\) | ||||
0.884321 | − | 0.466879i | \(-0.154622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 544.734 | 0.566840 | 0.283420 | − | 0.958996i | \(-0.408531\pi\) | ||||
0.283420 | + | 0.958996i | \(0.408531\pi\) | |||||||
\(32\) | 269.922i | 0.263596i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −137.452 | −0.118903 | ||||||||
\(35\) | − 1084.07i | − 0.884957i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 898.827 | 0.656557 | 0.328279 | − | 0.944581i | \(-0.393532\pi\) | ||||
0.328279 | + | 0.944581i | \(0.393532\pi\) | |||||||
\(38\) | 41.1275i | 0.0284816i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −393.228 | −0.245768 | ||||||||
\(41\) | − 2588.85i | − 1.54007i | −0.638003 | − | 0.770034i | \(-0.720239\pi\) | ||||
0.638003 | − | 0.770034i | \(-0.279761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2000.11 | 1.08172 | 0.540862 | − | 0.841111i | \(-0.318098\pi\) | ||||
0.540862 | + | 0.841111i | \(0.318098\pi\) | |||||||
\(44\) | 916.419i | 0.473357i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −194.753 | −0.0920385 | ||||||||
\(47\) | − 811.345i | − 0.367291i | −0.982993 | − | 0.183645i | \(-0.941210\pi\) | ||||
0.982993 | − | 0.183645i | \(-0.0587898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1426.88 | −0.594287 | ||||||||
\(50\) | − 206.519i | − 0.0826077i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1163.48 | −0.430282 | ||||||||
\(53\) | − 2221.00i | − 0.790672i | −0.918537 | − | 0.395336i | \(-0.870628\pi\) | ||||
0.918537 | − | 0.395336i | \(-0.129372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2005.23 | −0.662886 | ||||||||
\(56\) | − 353.344i | − 0.112674i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 278.926 | 0.0829148 | ||||||||
\(59\) | − 1512.26i | − 0.434432i | −0.976124 | − | 0.217216i | \(-0.930302\pi\) | ||||
0.976124 | − | 0.217216i | \(-0.0696976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1902.56 | −0.511304 | −0.255652 | − | 0.966769i | \(-0.582290\pi\) | ||||
−0.255652 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(62\) | 193.483i | 0.0503337i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3903.49 | 0.953001 | ||||||||
\(65\) | − 2545.83i | − 0.602564i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4507.09 | 1.00403 | 0.502015 | − | 0.864859i | \(-0.332592\pi\) | ||||
0.502015 | + | 0.864859i | \(0.332592\pi\) | |||||||
\(68\) | 6142.93i | 1.32849i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 385.049 | 0.0785814 | ||||||||
\(71\) | − 3993.54i | − 0.792213i | −0.918205 | − | 0.396106i | \(-0.870361\pi\) | ||||
0.918205 | − | 0.396106i | \(-0.129639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3436.70 | −0.644905 | −0.322452 | − | 0.946586i | \(-0.604507\pi\) | ||||
−0.322452 | + | 0.946586i | \(0.604507\pi\) | |||||||
\(74\) | 319.252i | 0.0583002i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1838.05 | 0.318221 | ||||||||
\(77\) | − 1801.85i | − 0.303904i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1202.78 | 0.192722 | 0.0963608 | − | 0.995346i | \(-0.469280\pi\) | ||||
0.0963608 | + | 0.995346i | \(0.469280\pi\) | |||||||
\(80\) | 8682.07i | 1.35657i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 919.529 | 0.136753 | ||||||||
\(83\) | 9256.34i | 1.34364i | 0.740714 | + | 0.671820i | \(0.234487\pi\) | ||||
−0.740714 | + | 0.671820i | \(0.765513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13441.4 | −1.86041 | ||||||||
\(86\) | 710.413i | 0.0960537i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −653.588 | −0.0843993 | ||||||||
\(89\) | 8929.99i | 1.12738i | 0.825986 | + | 0.563691i | \(0.190619\pi\) | ||||
−0.825986 | + | 0.563691i | \(0.809381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2287.62 | 0.276249 | ||||||||
\(92\) | 8703.81i | 1.02833i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 288.180 | 0.0326143 | ||||||||
\(95\) | 4021.86i | 0.445635i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6670.29 | 0.708926 | 0.354463 | − | 0.935070i | \(-0.384664\pi\) | ||||
0.354463 | + | 0.935070i | \(0.384664\pi\) | |||||||
\(98\) | − 506.811i | − 0.0527708i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9229.64 | −0.922964 | ||||||||
\(101\) | − 9150.06i | − 0.896977i | −0.893789 | − | 0.448489i | \(-0.851962\pi\) | ||||
0.893789 | − | 0.448489i | \(-0.148038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15312.4 | 1.44334 | 0.721670 | − | 0.692237i | \(-0.243375\pi\) | ||||
0.721670 | + | 0.692237i | \(0.243375\pi\) | |||||||
\(104\) | − 829.793i | − 0.0767190i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 788.870 | 0.0702092 | ||||||||
\(107\) | − 6099.28i | − 0.532735i | −0.963872 | − | 0.266367i | \(-0.914177\pi\) | ||||
0.963872 | − | 0.266367i | \(-0.0858234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15169.5 | 1.27679 | 0.638393 | − | 0.769710i | \(-0.279599\pi\) | ||||
0.638393 | + | 0.769710i | \(0.279599\pi\) | |||||||
\(110\) | − 712.233i | − 0.0588622i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7801.48 | −0.621929 | ||||||||
\(113\) | 1373.06i | 0.107531i | 0.998554 | + | 0.0537655i | \(0.0171224\pi\) | ||||
−0.998554 | + | 0.0537655i | \(0.982878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19045.0 | −1.44007 | ||||||||
\(116\) | − 12465.6i | − 0.926396i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 537.135 | 0.0385762 | ||||||||
\(119\) | − 12078.1i | − 0.852914i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11308.1 | 0.772358 | ||||||||
\(122\) | − 675.767i | − 0.0454022i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8647.01 | 0.562371 | ||||||||
\(125\) | 1513.10i | 0.0968386i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19152.4 | −1.18745 | −0.593726 | − | 0.804667i | \(-0.702344\pi\) | ||||
−0.593726 | + | 0.804667i | \(0.702344\pi\) | |||||||
\(128\) | 5705.22i | 0.348219i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 904.248 | 0.0535058 | ||||||||
\(131\) | 3020.00i | 0.175980i | 0.996121 | + | 0.0879902i | \(0.0280444\pi\) | ||||
−0.996121 | + | 0.0879902i | \(0.971956\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3613.93 | −0.204304 | ||||||||
\(134\) | 1600.86i | 0.0891548i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4381.13 | −0.236869 | ||||||||
\(137\) | − 10147.9i | − 0.540671i | −0.962766 | − | 0.270336i | \(-0.912865\pi\) | ||||
0.962766 | − | 0.270336i | \(-0.0871346\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −35126.4 | −1.81804 | −0.909021 | − | 0.416751i | \(-0.863169\pi\) | ||||
−0.909021 | + | 0.416751i | \(0.863169\pi\) | |||||||
\(140\) | − 17208.4i | − 0.877979i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1418.46 | 0.0703460 | ||||||||
\(143\) | − 4231.45i | − 0.206927i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27276.1 | 1.29732 | ||||||||
\(146\) | − 1220.67i | − 0.0572656i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14267.8 | 0.651380 | ||||||||
\(149\) | − 37382.0i | − 1.68380i | −0.539636 | − | 0.841899i | \(-0.681438\pi\) | ||||
0.539636 | − | 0.841899i | \(-0.318562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 33270.0 | 1.45915 | 0.729573 | − | 0.683903i | \(-0.239719\pi\) | ||||
0.729573 | + | 0.683903i | \(0.239719\pi\) | |||||||
\(152\) | 1310.89i | 0.0567387i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 639.993 | 0.0269857 | ||||||||
\(155\) | 18920.7i | 0.787541i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8080.33 | 0.327816 | 0.163908 | − | 0.986476i | \(-0.447590\pi\) | ||||
0.163908 | + | 0.986476i | \(0.447590\pi\) | |||||||
\(158\) | 427.211i | 0.0171131i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9375.41 | −0.366227 | ||||||||
\(161\) | − 17113.3i | − 0.660209i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25427.1 | −0.957022 | −0.478511 | − | 0.878081i | \(-0.658823\pi\) | ||||
−0.478511 | + | 0.878081i | \(0.658823\pi\) | |||||||
\(164\) | − 41095.0i | − 1.52792i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3287.74 | −0.119311 | ||||||||
\(167\) | 35052.8i | 1.25687i | 0.777863 | + | 0.628434i | \(0.216304\pi\) | ||||
−0.777863 | + | 0.628434i | \(0.783696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23188.8 | −0.811903 | ||||||||
\(170\) | − 4774.24i | − 0.165198i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 31749.4 | 1.07319 | ||||||||
\(173\) | 14700.5i | 0.491177i | 0.969374 | + | 0.245589i | \(0.0789813\pi\) | ||||
−0.969374 | + | 0.245589i | \(0.921019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18147.2 | 0.592560 | ||||||||
\(176\) | 14430.6i | 0.465862i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3171.82 | −0.100108 | ||||||||
\(179\) | 37052.5i | 1.15641i | 0.815892 | + | 0.578205i | \(0.196247\pi\) | ||||
−0.815892 | + | 0.578205i | \(0.803753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −39664.7 | −1.21073 | −0.605365 | − | 0.795948i | \(-0.706973\pi\) | ||||
−0.605365 | + | 0.795948i | \(0.706973\pi\) | |||||||
\(182\) | 812.533i | 0.0245300i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6207.54 | −0.183351 | ||||||||
\(185\) | 31219.7i | 0.912189i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22341.2 | −0.638885 | ||||||||
\(188\) | − 12879.2i | − 0.364395i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1428.51 | −0.0395710 | ||||||||
\(191\) | 57637.0i | 1.57992i | 0.613160 | + | 0.789959i | \(0.289898\pi\) | ||||
−0.613160 | + | 0.789959i | \(0.710102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4179.63 | 0.112208 | 0.0561039 | − | 0.998425i | \(-0.482132\pi\) | ||||
0.0561039 | + | 0.998425i | \(0.482132\pi\) | |||||||
\(194\) | 2369.20i | 0.0629504i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22650.1 | −0.589601 | ||||||||
\(197\) | 22191.5i | 0.571812i | 0.958258 | + | 0.285906i | \(0.0922945\pi\) | ||||
−0.958258 | + | 0.285906i | \(0.907705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 50608.7 | 1.27797 | 0.638983 | − | 0.769221i | \(-0.279355\pi\) | ||||
0.638983 | + | 0.769221i | \(0.279355\pi\) | |||||||
\(200\) | − 6582.56i | − 0.164564i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3249.99 | 0.0796488 | ||||||||
\(203\) | 24509.6i | 0.594763i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 89920.7 | 2.13970 | ||||||||
\(206\) | 5438.77i | 0.128164i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18321.0 | −0.423469 | ||||||||
\(209\) | 6684.77i | 0.153036i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8918.05 | −0.200311 | −0.100156 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100156 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(212\) | − 35255.7i | − 0.784437i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2166.39 | 0.0473052 | ||||||||
\(215\) | 69471.4i | 1.50290i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17001.6 | −0.361052 | ||||||||
\(218\) | 5388.02i | 0.113375i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −31830.7 | −0.657659 | ||||||||
\(221\) | − 28364.3i | − 0.580747i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8497.53 | −0.170877 | −0.0854384 | − | 0.996343i | \(-0.527229\pi\) | ||||
−0.0854384 | + | 0.996343i | \(0.527229\pi\) | |||||||
\(224\) | − 8424.49i | − 0.167899i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −487.695 | −0.00954842 | ||||||||
\(227\) | 19102.8i | 0.370719i | 0.982671 | + | 0.185360i | \(0.0593450\pi\) | ||||
−0.982671 | + | 0.185360i | \(0.940655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10723.0 | −0.204478 | −0.102239 | − | 0.994760i | \(-0.532601\pi\) | ||||
−0.102239 | + | 0.994760i | \(0.532601\pi\) | |||||||
\(230\) | − 6764.53i | − 0.127874i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8890.43 | 0.165176 | ||||||||
\(233\) | − 102200.i | − 1.88251i | −0.337694 | − | 0.941256i | \(-0.609647\pi\) | ||||
0.337694 | − | 0.941256i | \(-0.390353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28181.1 | 0.510296 | ||||||||
\(236\) | − 24005.3i | − 0.431006i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4290.00 | 0.0757362 | ||||||||
\(239\) | − 15520.2i | − 0.271707i | −0.990729 | − | 0.135854i | \(-0.956622\pi\) | ||||
0.990729 | − | 0.135854i | \(-0.0433777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −71957.8 | −1.23892 | −0.619461 | − | 0.785028i | \(-0.712649\pi\) | ||||
−0.619461 | + | 0.785028i | \(0.712649\pi\) | |||||||
\(242\) | 4016.49i | 0.0685830i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −30201.0 | −0.507272 | ||||||||
\(245\) | − 49561.1i | − 0.825674i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8486.96 | −0.139110 | ||||||||
\(248\) | 6167.03i | 0.100270i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −537.435 | −0.00859897 | ||||||||
\(251\) | 41487.8i | 0.658526i | 0.944238 | + | 0.329263i | \(0.106800\pi\) | ||||
−0.944238 | + | 0.329263i | \(0.893200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31654.8 | −0.494537 | ||||||||
\(254\) | − 6802.70i | − 0.105442i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 60429.5 | 0.922080 | ||||||||
\(257\) | 72529.3i | 1.09811i | 0.835785 | + | 0.549057i | \(0.185013\pi\) | ||||
−0.835785 | + | 0.549057i | \(0.814987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28053.1 | −0.418198 | ||||||||
\(260\) | − 40412.2i | − 0.597813i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1072.67 | −0.0156265 | ||||||||
\(263\) | − 85890.2i | − 1.24174i | −0.783912 | − | 0.620872i | \(-0.786779\pi\) | ||||
0.783912 | − | 0.620872i | \(-0.213221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 77143.7 | 1.09852 | ||||||||
\(266\) | − 1283.62i | − 0.0181416i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 71544.9 | 0.996114 | ||||||||
\(269\) | − 88967.6i | − 1.22950i | −0.788724 | − | 0.614748i | \(-0.789258\pi\) | ||||
0.788724 | − | 0.614748i | \(-0.210742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 96541.6 | 1.31455 | 0.657273 | − | 0.753652i | \(-0.271710\pi\) | ||||
0.657273 | + | 0.753652i | \(0.271710\pi\) | |||||||
\(272\) | 96730.8i | 1.30746i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3604.39 | 0.0480099 | ||||||||
\(275\) | − 33567.2i | − 0.443863i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23541.6 | −0.306815 | −0.153407 | − | 0.988163i | \(-0.549025\pi\) | ||||
−0.153407 | + | 0.988163i | \(0.549025\pi\) | |||||||
\(278\) | − 12476.5i | − 0.161436i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12273.0 | 0.156543 | ||||||||
\(281\) | − 58409.9i | − 0.739731i | −0.929085 | − | 0.369865i | \(-0.879404\pi\) | ||||
0.929085 | − | 0.369865i | \(-0.120596\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −76117.3 | −0.950408 | −0.475204 | − | 0.879876i | \(-0.657626\pi\) | ||||
−0.475204 | + | 0.879876i | \(0.657626\pi\) | |||||||
\(284\) | − 63392.9i | − 0.785966i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1502.96 | 0.0183745 | ||||||||
\(287\) | 80800.3i | 0.980956i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −66236.1 | −0.793047 | ||||||||
\(290\) | 9688.14i | 0.115198i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −54553.6 | −0.639820 | ||||||||
\(293\) | − 139911.i | − 1.62973i | −0.579649 | − | 0.814866i | \(-0.696810\pi\) | ||||
0.579649 | − | 0.814866i | \(-0.303190\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 52526.4 | 0.603579 | ||||||||
\(296\) | 10175.8i | 0.116141i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13277.6 | 0.149516 | ||||||||
\(299\) | − 40188.8i | − 0.449534i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −62425.1 | −0.689011 | ||||||||
\(302\) | 11817.1i | 0.129568i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 28943.1 | 0.313183 | ||||||||
\(305\) | − 66083.2i | − 0.710381i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −81796.8 | −0.867880 | −0.433940 | − | 0.900942i | \(-0.642877\pi\) | ||||
−0.433940 | + | 0.900942i | \(0.642877\pi\) | |||||||
\(308\) | − 28602.2i | − 0.301508i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6720.39 | −0.0699312 | ||||||||
\(311\) | 1702.71i | 0.0176043i | 0.999961 | + | 0.00880216i | \(0.00280185\pi\) | ||||
−0.999961 | + | 0.00880216i | \(0.997198\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −69960.1 | −0.714105 | −0.357052 | − | 0.934084i | \(-0.616218\pi\) | ||||
−0.357052 | + | 0.934084i | \(0.616218\pi\) | |||||||
\(314\) | 2870.03i | 0.0291090i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19092.7 | 0.191202 | ||||||||
\(317\) | 116629.i | 1.16062i | 0.814397 | + | 0.580309i | \(0.197068\pi\) | ||||
−0.814397 | + | 0.580309i | \(0.802932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45335.9 | 0.445514 | ||||||||
\(320\) | 135583.i | 1.32405i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6078.42 | 0.0586245 | ||||||||
\(323\) | 44809.3i | 0.429500i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42616.8 | 0.403472 | ||||||||
\(326\) | − 9031.40i | − 0.0849806i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29308.9 | 0.272428 | ||||||||
\(329\) | 25322.8i | 0.233948i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 100836. | 0.920366 | 0.460183 | − | 0.887824i | \(-0.347784\pi\) | ||||
0.460183 | + | 0.887824i | \(0.347784\pi\) | |||||||
\(332\) | 146934.i | 1.33305i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12450.3 | −0.111606 | ||||||||
\(335\) | 156549.i | 1.39495i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 40094.5 | 0.353041 | 0.176520 | − | 0.984297i | \(-0.443516\pi\) | ||||
0.176520 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(338\) | − 8236.36i | − 0.0720945i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −213367. | −1.84574 | ||||||||
\(341\) | 31448.2i | 0.270450i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 119471. | 1.01549 | ||||||||
\(344\) | 22643.6i | 0.191350i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5221.42 | −0.0436150 | ||||||||
\(347\) | 226362.i | 1.87994i | 0.341254 | + | 0.939971i | \(0.389148\pi\) | ||||
−0.341254 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 79598.3 | 0.653511 | 0.326755 | − | 0.945109i | \(-0.394045\pi\) | ||||
0.326755 | + | 0.945109i | \(0.394045\pi\) | |||||||
\(350\) | 6445.64i | 0.0526175i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15583.0 | −0.125766 | ||||||||
\(353\) | − 139919.i | − 1.12286i | −0.827523 | − | 0.561431i | \(-0.810251\pi\) | ||||
0.827523 | − | 0.561431i | \(-0.189749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 138711. | 1.10066 | ||||||||
\(356\) | 141753.i | 1.11849i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13160.6 | −0.102686 | ||||||||
\(359\) | − 211616.i | − 1.64195i | −0.570963 | − | 0.820976i | \(-0.693430\pi\) | ||||
0.570963 | − | 0.820976i | \(-0.306570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −116913. | −0.897119 | ||||||||
\(362\) | − 14088.4i | − 0.107509i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 36313.3 | 0.274071 | ||||||||
\(365\) | − 119370.i | − 0.896000i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31993.6 | −0.237537 | −0.118769 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118769 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(368\) | 137056.i | 1.01205i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11088.8 | −0.0809995 | ||||||||
\(371\) | 69319.2i | 0.503623i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −123148. | −0.885133 | −0.442567 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442567 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(374\) | − 7935.30i | − 0.0567310i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9185.40 | 0.0649714 | ||||||||
\(377\) | 57558.3i | 0.404972i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −116524. | −0.811218 | −0.405609 | − | 0.914047i | \(-0.632941\pi\) | ||||
−0.405609 | + | 0.914047i | \(0.632941\pi\) | |||||||
\(380\) | 63842.4i | 0.442122i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20471.9 | −0.140292 | ||||||||
\(383\) | − 181112.i | − 1.23467i | −0.786701 | − | 0.617334i | \(-0.788213\pi\) | ||||
0.786701 | − | 0.617334i | \(-0.211787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 62585.0 | 0.422229 | ||||||||
\(386\) | 1484.55i | 0.00996371i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 105883. | 0.703336 | ||||||||
\(389\) | − 50827.4i | − 0.335892i | −0.985796 | − | 0.167946i | \(-0.946287\pi\) | ||||
0.985796 | − | 0.167946i | \(-0.0537134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −212188. | −1.38793 | ||||||||
\(392\) | − 16154.0i | − 0.105126i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7882.13 | −0.0507751 | ||||||||
\(395\) | 41777.0i | 0.267758i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 228710. | 1.45112 | 0.725561 | − | 0.688158i | \(-0.241580\pi\) | ||||
0.725561 | + | 0.688158i | \(0.241580\pi\) | |||||||
\(398\) | 17975.6i | 0.113479i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −145336. | −0.908351 | ||||||||
\(401\) | − 188930.i | − 1.17493i | −0.809250 | − | 0.587465i | \(-0.800126\pi\) | ||||
0.809250 | − | 0.587465i | \(-0.199874\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39926.5 | −0.245840 | ||||||||
\(404\) | − 145247.i | − 0.889904i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8705.50 | −0.0528131 | ||||||||
\(407\) | 51890.5i | 0.313256i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 277427. | 1.65845 | 0.829223 | − | 0.558918i | \(-0.188783\pi\) | ||||
0.829223 | + | 0.558918i | \(0.188783\pi\) | |||||||
\(410\) | 31938.7i | 0.189998i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 243067. | 1.43196 | ||||||||
\(413\) | 47198.8i | 0.276714i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −321508. | −1.86679 | ||||||||
\(416\) | − 19784.1i | − 0.114322i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2374.35 | −0.0135891 | ||||||||
\(419\) | 102422.i | 0.583397i | 0.956510 | + | 0.291699i | \(0.0942205\pi\) | ||||
−0.956510 | + | 0.291699i | \(0.905780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 47135.8 | 0.265942 | 0.132971 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132971 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(422\) | − 3167.58i | − 0.0177870i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25144.3 | 0.139865 | ||||||||
\(425\) | − 225007.i | − 1.24571i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 59380.6 | 0.325678 | ||||||||
\(428\) | − 96819.0i | − 0.528534i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24675.4 | −0.133452 | ||||||||
\(431\) | − 45556.1i | − 0.245240i | −0.992454 | − | 0.122620i | \(-0.960870\pi\) | ||||
0.992454 | − | 0.122620i | \(-0.0391297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 209599. | 1.11793 | 0.558965 | − | 0.829192i | \(-0.311199\pi\) | ||||
0.558965 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(434\) | − 6038.76i | − 0.0320603i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 240798. | 1.26672 | ||||||||
\(437\) | 63489.5i | 0.332460i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −183684. | −0.953110 | −0.476555 | − | 0.879145i | \(-0.658115\pi\) | ||||
−0.476555 | + | 0.879145i | \(0.658115\pi\) | |||||||
\(440\) | − 22701.6i | − 0.117260i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10074.6 | 0.0515685 | ||||||||
\(443\) | − 115943.i | − 0.590795i | −0.955374 | − | 0.295398i | \(-0.904548\pi\) | ||||
0.955374 | − | 0.295398i | \(-0.0954521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −310172. | −1.56633 | ||||||||
\(446\) | − 3018.22i | − 0.0151733i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −121831. | −0.607020 | ||||||||
\(449\) | − 328940.i | − 1.63164i | −0.578305 | − | 0.815820i | \(-0.696286\pi\) | ||||
0.578305 | − | 0.815820i | \(-0.303714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 149458. | 0.734795 | ||||||||
\(452\) | 21795.8i | 0.106683i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6785.07 | −0.0329187 | ||||||||
\(455\) | 79457.6i | 0.383807i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −212737. | −1.01862 | −0.509308 | − | 0.860584i | \(-0.670099\pi\) | ||||
−0.509308 | + | 0.860584i | \(0.670099\pi\) | |||||||
\(458\) | − 3808.68i | − 0.0181570i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −302317. | −1.42872 | ||||||||
\(461\) | − 48448.1i | − 0.227968i | −0.993483 | − | 0.113984i | \(-0.963639\pi\) | ||||
0.993483 | − | 0.113984i | \(-0.0363613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 169101. | 0.788832 | 0.394416 | − | 0.918932i | \(-0.370947\pi\) | ||||
0.394416 | + | 0.918932i | \(0.370947\pi\) | |||||||
\(464\) | − 196292.i | − 0.911729i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36300.1 | 0.167161 | ||||||||
\(467\) | 54646.4i | 0.250569i | 0.992121 | + | 0.125285i | \(0.0399844\pi\) | ||||
−0.992121 | + | 0.125285i | \(0.960016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −140670. | −0.639524 | ||||||||
\(470\) | 10009.6i | 0.0453127i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17120.6 | 0.0768482 | ||||||||
\(473\) | 115469.i | 0.516111i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −67325.1 | −0.298394 | ||||||||
\(476\) | − 191726.i | − 0.846189i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5512.58 | 0.0241268 | ||||||||
\(479\) | − 138577.i | − 0.603978i | −0.953311 | − | 0.301989i | \(-0.902349\pi\) | ||||
0.953311 | − | 0.301989i | \(-0.0976506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −65880.0 | −0.284750 | ||||||||
\(482\) | − 25558.5i | − 0.110012i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 179503. | 0.766268 | ||||||||
\(485\) | 231684.i | 0.984948i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23464.1 | 0.0989340 | 0.0494670 | − | 0.998776i | \(-0.484248\pi\) | ||||
0.0494670 | + | 0.998776i | \(0.484248\pi\) | |||||||
\(488\) | − 21539.3i | − 0.0904464i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17603.5 | 0.0733172 | ||||||||
\(491\) | − 74326.7i | − 0.308306i | −0.988047 | − | 0.154153i | \(-0.950735\pi\) | ||||
0.988047 | − | 0.154153i | \(-0.0492649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 303895. | 1.25035 | ||||||||
\(494\) | − 3014.46i | − 0.0123525i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 136162. | 0.553467 | ||||||||
\(497\) | 124642.i | 0.504605i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18972.0 | −0.0761925 | −0.0380963 | − | 0.999274i | \(-0.512129\pi\) | ||||
−0.0380963 | + | 0.999274i | \(0.512129\pi\) | |||||||
\(500\) | 24018.8i | 0.0960750i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14735.9 | −0.0584751 | ||||||||
\(503\) | 117856.i | 0.465818i | 0.972498 | + | 0.232909i | \(0.0748245\pi\) | ||||
−0.972498 | + | 0.232909i | \(0.925175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 317816. | 1.24622 | ||||||||
\(506\) | − 11243.4i | − 0.0439133i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −304022. | −1.17809 | ||||||||
\(509\) | − 183460.i | − 0.708120i | −0.935223 | − | 0.354060i | \(-0.884801\pi\) | ||||
0.935223 | − | 0.354060i | \(-0.115199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 107262. | 0.410776 | ||||||||
\(512\) | 112747.i | 0.430097i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25761.5 | −0.0975091 | ||||||||
\(515\) | 531858.i | 2.00531i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46840.1 | 0.175241 | ||||||||
\(518\) | − 9964.13i | − 0.0371347i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 28821.9 | 0.106590 | ||||||||
\(521\) | 409498.i | 1.50861i | 0.656526 | + | 0.754303i | \(0.272025\pi\) | ||||
−0.656526 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −211852. | −0.774513 | −0.387256 | − | 0.921972i | \(-0.626577\pi\) | ||||
−0.387256 | + | 0.921972i | \(0.626577\pi\) | |||||||
\(524\) | 47939.0i | 0.174593i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30507.1 | 0.110263 | ||||||||
\(527\) | 210804.i | 0.759026i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20804.7 | −0.0743448 | ||||||||
\(530\) | 27400.5i | 0.0975453i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −57367.0 | −0.202693 | ||||||||
\(533\) | 189751.i | 0.667930i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 211851. | 0.740156 | ||||||||
\(536\) | 51025.7i | 0.177607i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31600.2 | 0.109175 | ||||||||
\(539\) | − 82375.9i | − 0.283545i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44016.5 | 0.150391 | 0.0751954 | − | 0.997169i | \(-0.476042\pi\) | ||||
0.0751954 | + | 0.997169i | \(0.476042\pi\) | |||||||
\(542\) | 34290.4i | 0.116728i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −104456. | −0.352967 | ||||||||
\(545\) | 526894.i | 1.77391i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42859.1 | −0.143241 | −0.0716207 | − | 0.997432i | \(-0.522817\pi\) | ||||
−0.0716207 | + | 0.997432i | \(0.522817\pi\) | |||||||
\(548\) | − 161085.i | − 0.536408i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11922.6 | 0.0394137 | ||||||||
\(551\) | − 90929.5i | − 0.299503i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37539.6 | −0.122755 | ||||||||
\(554\) | − 8361.69i | − 0.0272442i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −557591. | −1.80371 | ||||||||
\(557\) | 311007.i | 1.00244i | 0.865319 | + | 0.501222i | \(0.167116\pi\) | ||||
−0.865319 | + | 0.501222i | \(0.832884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −146599. | −0.469145 | ||||||||
\(560\) | − 270975.i | − 0.864078i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20746.5 | 0.0656858 | ||||||||
\(563\) | 285768.i | 0.901563i | 0.892634 | + | 0.450782i | \(0.148855\pi\) | ||||
−0.892634 | + | 0.450782i | \(0.851145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −47691.7 | −0.149398 | ||||||||
\(566\) | − 27035.9i | − 0.0843933i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 45211.7 | 0.140137 | ||||||||
\(569\) | − 136683.i | − 0.422171i | −0.977468 | − | 0.211086i | \(-0.932300\pi\) | ||||
0.977468 | − | 0.211086i | \(-0.0676999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28510.0 | −0.0874431 | −0.0437215 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437215 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(572\) | − 67169.4i | − 0.205296i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28699.3 | −0.0871058 | ||||||||
\(575\) | − 318809.i | − 0.964261i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −293742. | −0.882297 | −0.441149 | − | 0.897434i | \(-0.645429\pi\) | ||||
−0.441149 | + | 0.897434i | \(0.645429\pi\) | |||||||
\(578\) | − 23526.2i | − 0.0704201i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 432977. | 1.28709 | ||||||||
\(581\) | − 288898.i | − 0.855840i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 128221. | 0.377244 | ||||||||
\(584\) | − 38907.5i | − 0.114080i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 49694.6 | 0.144715 | ||||||||
\(587\) | 386055.i | 1.12040i | 0.828357 | + | 0.560200i | \(0.189276\pi\) | ||||
−0.828357 | + | 0.560200i | \(0.810724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 63075.2 | 0.181814 | ||||||||
\(590\) | 18656.7i | 0.0535959i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 224671. | 0.641067 | ||||||||
\(593\) | − 305581.i | − 0.868995i | −0.900673 | − | 0.434497i | \(-0.856926\pi\) | ||||
0.900673 | − | 0.434497i | \(-0.143074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 419519. | 1.18500 | ||||||||
\(596\) | − 593396.i | − 1.67052i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14274.6 | 0.0399172 | ||||||||
\(599\) | − 264738.i | − 0.737840i | −0.929461 | − | 0.368920i | \(-0.879728\pi\) | ||||
0.929461 | − | 0.368920i | \(-0.120272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −132203. | −0.366009 | −0.183005 | − | 0.983112i | \(-0.558582\pi\) | ||||
−0.183005 | + | 0.983112i | \(0.558582\pi\) | |||||||
\(602\) | − 22172.6i | − 0.0611820i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 528123. | 1.44764 | ||||||||
\(605\) | 392773.i | 1.07308i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −254146. | −0.689772 | −0.344886 | − | 0.938645i | \(-0.612082\pi\) | ||||
−0.344886 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(608\) | 31254.5i | 0.0845484i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23471.9 | 0.0630797 | ||||||||
\(611\) | 59468.0i | 0.159295i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −492878. | −1.31165 | −0.655826 | − | 0.754912i | \(-0.727680\pi\) | ||||
−0.655826 | + | 0.754912i | \(0.727680\pi\) | |||||||
\(614\) | − 29053.2i | − 0.0770650i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20399.0 | 0.0537587 | ||||||||
\(617\) | 121278.i | 0.318574i | 0.987232 | + | 0.159287i | \(0.0509195\pi\) | ||||
−0.987232 | + | 0.159287i | \(0.949081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 307364. | 0.802180 | 0.401090 | − | 0.916039i | \(-0.368631\pi\) | ||||
0.401090 | + | 0.916039i | \(0.368631\pi\) | |||||||
\(620\) | 300344.i | 0.781331i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −604.780 | −0.00156321 | ||||||||
\(623\) | − 278713.i | − 0.718092i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −415954. | −1.06484 | ||||||||
\(626\) | − 24849.0i | − 0.0634103i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 128266. | 0.325231 | ||||||||
\(629\) | 347832.i | 0.879161i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −254196. | −0.638425 | −0.319212 | − | 0.947683i | \(-0.603418\pi\) | ||||
−0.319212 | + | 0.947683i | \(0.603418\pi\) | |||||||
\(632\) | 13616.9i | 0.0340912i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41425.3 | −0.103059 | ||||||||
\(635\) | − 665236.i | − 1.64979i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 104584. | 0.257743 | ||||||||
\(638\) | 16102.8i | 0.0395602i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −198164. | −0.483799 | ||||||||
\(641\) | 365987.i | 0.890736i | 0.895348 | + | 0.445368i | \(0.146927\pi\) | ||||
−0.895348 | + | 0.445368i | \(0.853073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 230783. | 0.558189 | 0.279094 | − | 0.960264i | \(-0.409966\pi\) | ||||
0.279094 | + | 0.960264i | \(0.409966\pi\) | |||||||
\(644\) | − 271653.i | − 0.655003i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15915.7 | −0.0381383 | ||||||||
\(647\) | − 278596.i | − 0.665529i | −0.943010 | − | 0.332764i | \(-0.892019\pi\) | ||||
0.943010 | − | 0.332764i | \(-0.107981\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 87304.7 | 0.207276 | ||||||||
\(650\) | 15136.9i | 0.0358271i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −403626. | −0.949476 | ||||||||
\(653\) | 78506.8i | 0.184111i | 0.995754 | + | 0.0920557i | \(0.0293438\pi\) | ||||
−0.995754 | + | 0.0920557i | \(0.970656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −104896. | −0.244499 | ||||||||
\(656\) | − 647111.i | − 1.50373i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8994.34 | −0.0207739 | ||||||||
\(659\) | − 857273.i | − 1.97401i | −0.160703 | − | 0.987003i | \(-0.551376\pi\) | ||||
0.160703 | − | 0.987003i | \(-0.448624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22344.0 | 0.0511396 | 0.0255698 | − | 0.999673i | \(-0.491860\pi\) | ||||
0.0255698 | + | 0.999673i | \(0.491860\pi\) | |||||||
\(662\) | 35815.8i | 0.0817257i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −104793. | −0.237681 | ||||||||
\(665\) | − 125526.i | − 0.283850i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 430584. | 0.967846 | ||||||||
\(668\) | 556423.i | 1.24696i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −55604.1 | −0.123867 | ||||||||
\(671\) | − 109838.i | − 0.243953i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −663478. | −1.46486 | −0.732430 | − | 0.680842i | \(-0.761614\pi\) | ||||
−0.732430 | + | 0.680842i | \(0.761614\pi\) | |||||||
\(674\) | 14241.1i | 0.0313489i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −368095. | −0.805501 | ||||||||
\(677\) | − 228121.i | − 0.497722i | −0.968539 | − | 0.248861i | \(-0.919944\pi\) | ||||
0.968539 | − | 0.248861i | \(-0.0800563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −208185. | −0.451555 | ||||||||
\(680\) | − 152173.i | − 0.329094i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11170.0 | −0.0240151 | ||||||||
\(683\) | − 53606.6i | − 0.114915i | −0.998348 | − | 0.0574575i | \(-0.981701\pi\) | ||||
0.998348 | − | 0.0574575i | \(-0.0182994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 352474. | 0.751182 | ||||||||
\(686\) | 42434.8i | 0.0901724i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 499948. | 1.05620 | ||||||||
\(689\) | 162789.i | 0.342915i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 757326. | 1.58609 | 0.793043 | − | 0.609166i | \(-0.208496\pi\) | ||||
0.793043 | + | 0.609166i | \(0.208496\pi\) | |||||||
\(692\) | 233353.i | 0.487305i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80400.9 | −0.166933 | ||||||||
\(695\) | − 1.22007e6i | − 2.52590i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00185e6 | 2.06222 | ||||||||
\(698\) | 28272.3i | 0.0580297i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 288065. | 0.587888 | ||||||||
\(701\) | − 506359.i | − 1.03044i | −0.857058 | − | 0.515220i | \(-0.827710\pi\) | ||||
0.857058 | − | 0.515220i | \(-0.172290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 104076. | 0.210591 | ||||||||
\(704\) | 225354.i | 0.454695i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 49697.4 | 0.0997067 | ||||||||
\(707\) | 285581.i | 0.571335i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −651243. | −1.29554 | −0.647770 | − | 0.761836i | \(-0.724298\pi\) | ||||
−0.647770 | + | 0.761836i | \(0.724298\pi\) | |||||||
\(710\) | 49268.4i | 0.0977354i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −101098. | −0.199427 | ||||||||
\(713\) | 298684.i | 0.587533i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 146974. | 0.287495 | ||||||||
\(716\) | 588166.i | 1.14729i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 75163.5 | 0.145800 | ||||||||
\(719\) | 69724.6i | 0.134874i | 0.997724 | + | 0.0674370i | \(0.0214822\pi\) | ||||
−0.997724 | + | 0.0674370i | \(0.978518\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −477913. | −0.919345 | ||||||||
\(722\) | − 41526.2i | − 0.0796614i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −629631. | −1.20118 | ||||||||
\(725\) | 456597.i | 0.868675i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −747728. | −1.41473 | −0.707367 | − | 0.706846i | \(-0.750117\pi\) | ||||
−0.707367 | + | 0.706846i | \(0.750117\pi\) | |||||||
\(728\) | 25898.6i | 0.0488667i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 42398.6 | 0.0795620 | ||||||||
\(731\) | 774011.i | 1.44848i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 65738.5 | 0.122352 | 0.0611761 | − | 0.998127i | \(-0.480515\pi\) | ||||
0.0611761 | + | 0.998127i | \(0.480515\pi\) | |||||||
\(734\) | − 11363.7i | − 0.0210925i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −148001. | −0.273218 | ||||||||
\(737\) | 260201.i | 0.479042i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 977921. | 1.79067 | 0.895334 | − | 0.445395i | \(-0.146937\pi\) | ||||
0.895334 | + | 0.445395i | \(0.146937\pi\) | |||||||
\(740\) | 495576.i | 0.904996i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24621.3 | −0.0447202 | ||||||||
\(743\) | − 504874.i | − 0.914545i | −0.889327 | − | 0.457272i | \(-0.848826\pi\) | ||||
0.889327 | − | 0.457272i | \(-0.151174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.29842e6 | 2.33939 | ||||||||
\(746\) | − 43740.5i | − 0.0785971i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −354640. | −0.633847 | ||||||||
\(749\) | 190364.i | 0.339329i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −532791. | −0.944663 | −0.472332 | − | 0.881421i | \(-0.656588\pi\) | ||||
−0.472332 | + | 0.881421i | \(0.656588\pi\) | |||||||
\(752\) | − 202804.i | − 0.358626i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20444.0 | −0.0359603 | ||||||||
\(755\) | 1.15559e6i | 2.02727i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −293571. | −0.512297 | −0.256148 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256148 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(758\) | − 41388.0i | − 0.0720337i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −45532.2 | −0.0788301 | ||||||||
\(761\) | 25691.2i | 0.0443624i | 0.999754 | + | 0.0221812i | \(0.00706108\pi\) | ||||
−0.999754 | + | 0.0221812i | \(0.992939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −473453. | −0.813257 | ||||||||
\(764\) | 914920.i | 1.56746i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 64328.9 | 0.109635 | ||||||||
\(767\) | 110842.i | 0.188414i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −647144. | −1.09433 | −0.547165 | − | 0.837025i | \(-0.684293\pi\) | ||||
−0.547165 | + | 0.837025i | \(0.684293\pi\) | |||||||
\(770\) | 22229.4i | 0.0374927i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 66346.8 | 0.111323 | ||||||||
\(773\) | − 610238.i | − 1.02127i | −0.859798 | − | 0.510634i | \(-0.829411\pi\) | ||||
0.859798 | − | 0.510634i | \(-0.170589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −316728. | −0.527331 | ||||||||
\(776\) | 75515.6i | 0.125405i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18053.3 | 0.0298261 | ||||||||
\(779\) | − 299766.i | − 0.493977i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 230553. | 0.377980 | ||||||||
\(782\) | − 75366.6i | − 0.123244i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −356664. | −0.580266 | ||||||||
\(785\) | 280661.i | 0.455451i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −580321. | −0.936955 | −0.468477 | − | 0.883475i | \(-0.655197\pi\) | ||||
−0.468477 | + | 0.883475i | \(0.655197\pi\) | |||||||
\(788\) | 352264.i | 0.567303i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14838.7 | −0.0237761 | ||||||||
\(791\) | − 42854.5i | − 0.0684926i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 139449. | 0.221753 | ||||||||
\(794\) | 81234.9i | 0.128855i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 803355. | 1.26789 | ||||||||
\(797\) | 1.05714e6i | 1.66424i | 0.554598 | + | 0.832118i | \(0.312872\pi\) | ||||
−0.554598 | + | 0.832118i | \(0.687128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 313978. | 0.491820 | ||||||||
\(800\) | − 156943.i | − 0.245223i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 67105.5 | 0.104330 | ||||||||
\(803\) | − 198405.i | − 0.307696i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 594409. | 0.917263 | ||||||||
\(806\) | − 14181.4i | − 0.0218298i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 103590. | 0.158670 | ||||||||
\(809\) | 355969.i | 0.543895i | 0.962312 | + | 0.271947i | \(0.0876677\pi\) | ||||
−0.962312 | + | 0.271947i | \(0.912332\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −136417. | −0.207409 | −0.103704 | − | 0.994608i | \(-0.533070\pi\) | ||||
−0.103704 | + | 0.994608i | \(0.533070\pi\) | |||||||
\(812\) | 389061.i | 0.590074i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18430.9 | −0.0278161 | ||||||||
\(815\) | − 883181.i | − 1.32964i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 231594. | 0.346964 | ||||||||
\(818\) | 98538.4i | 0.147265i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.42739e6 | 2.12282 | ||||||||
\(821\) | − 455979.i | − 0.676485i | −0.941059 | − | 0.338243i | \(-0.890168\pi\) | ||||
0.941059 | − | 0.338243i | \(-0.109832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 503590. | 0.743494 | 0.371747 | − | 0.928334i | \(-0.378759\pi\) | ||||
0.371747 | + | 0.928334i | \(0.378759\pi\) | |||||||
\(824\) | 173355.i | 0.255318i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16764.4 | −0.0245713 | ||||||||
\(827\) | − 551861.i | − 0.806898i | −0.915002 | − | 0.403449i | \(-0.867811\pi\) | ||||
0.915002 | − | 0.403449i | \(-0.132189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −182308. | −0.265275 | −0.132638 | − | 0.991165i | \(-0.542345\pi\) | ||||
−0.132638 | + | 0.991165i | \(0.542345\pi\) | |||||||
\(830\) | − 114196.i | − 0.165765i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −286109. | −0.413318 | ||||||||
\(833\) | − 552182.i | − 0.795778i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.21752e6 | −1.74623 | ||||||||
\(836\) | 106113.i | 0.151829i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36379.0 | −0.0518039 | ||||||||
\(839\) | − 415684.i | − 0.590526i | −0.955416 | − | 0.295263i | \(-0.904593\pi\) | ||||
0.955416 | − | 0.295263i | \(-0.0954073\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 90599.4 | 0.128095 | ||||||||
\(842\) | 16742.1i | 0.0236148i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −141564. | −0.198732 | ||||||||
\(845\) | − 805434.i | − 1.12802i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −352935. | −0.491958 | ||||||||
\(848\) | − 555161.i | − 0.772018i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 79919.8 | 0.110616 | ||||||||
\(851\) | 492837.i | 0.680525i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 150271. | 0.206527 | 0.103263 | − | 0.994654i | \(-0.467072\pi\) | ||||
0.103263 | + | 0.994654i | \(0.467072\pi\) | |||||||
\(854\) | 21091.3i | 0.0289192i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 69051.1 | 0.0942374 | ||||||||
\(857\) | 144768.i | 0.197111i | 0.995132 | + | 0.0985554i | \(0.0314222\pi\) | ||||
−0.995132 | + | 0.0985554i | \(0.968578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 333897. | 0.452508 | 0.226254 | − | 0.974068i | \(-0.427352\pi\) | ||||
0.226254 | + | 0.974068i | \(0.427352\pi\) | |||||||
\(860\) | 1.10278e6i | 1.49105i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16180.9 | 0.0217766 | ||||||||
\(863\) | − 1.13280e6i | − 1.52101i | −0.649330 | − | 0.760507i | \(-0.724951\pi\) | ||||
0.649330 | − | 0.760507i | \(-0.275049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −510603. | −0.682418 | ||||||||
\(866\) | 74447.1i | 0.0992686i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −269881. | −0.358206 | ||||||||
\(869\) | 69437.9i | 0.0919511i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −330350. | −0.435450 | ||||||||
\(872\) | 171737.i | 0.225855i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −22550.7 | −0.0295214 | ||||||||
\(875\) | − 47225.2i | − 0.0616820i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 496541. | 0.645589 | 0.322795 | − | 0.946469i | \(-0.395378\pi\) | ||||
0.322795 | + | 0.946469i | \(0.395378\pi\) | |||||||
\(878\) | − 65242.4i | − 0.0846332i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −501228. | −0.647247 | ||||||||
\(881\) | 1.21533e6i | 1.56583i | 0.622131 | + | 0.782913i | \(0.286267\pi\) | ||||
−0.622131 | + | 0.782913i | \(0.713733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −999070. | −1.28137 | −0.640685 | − | 0.767804i | \(-0.721349\pi\) | ||||
−0.640685 | + | 0.767804i | \(0.721349\pi\) | |||||||
\(884\) | − 450250.i | − 0.576168i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41181.5 | 0.0524608 | ||||||||
\(887\) | − 1.08316e6i | − 1.37672i | −0.725367 | − | 0.688362i | \(-0.758330\pi\) | ||||
0.725367 | − | 0.688362i | \(-0.241670\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 597763. | 0.756355 | ||||||||
\(890\) | − 110169.i | − 0.139085i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −134888. | −0.169529 | ||||||||
\(893\) | − 93946.4i | − 0.117809i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.28698e6 | −1.60666 | ||||||||
\(896\) | − 178065.i | − 0.221800i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 116836. | 0.144885 | ||||||||
\(899\) | − 427774.i | − 0.529292i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 859491. | 1.05875 | ||||||||
\(902\) | 53085.6i | 0.0652475i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15544.7 | −0.0190216 | ||||||||
\(905\) | − 1.37771e6i | − 1.68213i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.27685e6 | 1.55212 | 0.776061 | − | 0.630658i | \(-0.217215\pi\) | ||||
0.776061 | + | 0.630658i | \(0.217215\pi\) | |||||||
\(908\) | 303235.i | 0.367796i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28222.4 | −0.0340809 | ||||||||
\(911\) | 273486.i | 0.329532i | 0.986333 | + | 0.164766i | \(0.0526869\pi\) | ||||
−0.986333 | + | 0.164766i | \(0.947313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −534381. | −0.641076 | ||||||||
\(914\) | − 75561.6i | − 0.0904500i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −170215. | −0.202865 | ||||||||
\(917\) | − 94256.7i | − 0.112092i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.15882e6 | 1.37210 | 0.686051 | − | 0.727553i | \(-0.259343\pi\) | ||||
0.686051 | + | 0.727553i | \(0.259343\pi\) | |||||||
\(920\) | − 215612.i | − 0.254740i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17208.1 | 0.0202429 | ||||||||
\(923\) | 292709.i | 0.343584i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −522611. | −0.610795 | ||||||||
\(926\) | 60062.6i | 0.0700459i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 211967. | 0.246135 | ||||||||
\(929\) | 852706.i | 0.988025i | 0.869455 | + | 0.494012i | \(0.164470\pi\) | ||||
−0.869455 | + | 0.494012i | \(0.835530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −165220. | −0.190618 | ||||||||
\(932\) | − 1.62230e6i | − 1.86767i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19409.7 | −0.0222498 | ||||||||
\(935\) | − 775993.i | − 0.887636i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 629989. | 0.717552 | 0.358776 | − | 0.933424i | \(-0.383194\pi\) | ||||
0.358776 | + | 0.933424i | \(0.383194\pi\) | |||||||
\(938\) | − 49964.3i | − 0.0567877i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 447343. | 0.506273 | ||||||||
\(941\) | 423252.i | 0.477991i | 0.971021 | + | 0.238996i | \(0.0768182\pi\) | ||||
−0.971021 | + | 0.238996i | \(0.923182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.41950e6 | 1.59629 | ||||||||
\(944\) | − 378004.i | − 0.424182i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41013.1 | −0.0458290 | ||||||||
\(947\) | − 1.39444e6i | − 1.55489i | −0.628952 | − | 0.777444i | \(-0.716516\pi\) | ||||
0.628952 | − | 0.777444i | \(-0.283484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 251895. | 0.279696 | ||||||||
\(950\) | − 23913.1i | − 0.0264965i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 136739. | 0.150875 | ||||||||
\(953\) | − 24001.0i | − 0.0264267i | −0.999913 | − | 0.0132134i | \(-0.995794\pi\) | ||||
0.999913 | − | 0.0132134i | \(-0.00420607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00195e6 | −2.19506 | ||||||||
\(956\) | − 246365.i | − 0.269565i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 49220.9 | 0.0536314 | ||||||||
\(959\) | 316723.i | 0.344384i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −626786. | −0.678692 | ||||||||
\(962\) | − 23399.8i | − 0.0252849i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.14225e6 | −1.22915 | ||||||||
\(965\) | 145174.i | 0.155896i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.04406e6 | 1.11654 | 0.558268 | − | 0.829660i | \(-0.311466\pi\) | ||||
0.558268 | + | 0.829660i | \(0.311466\pi\) | |||||||
\(968\) | 128021.i | 0.136625i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −82291.4 | −0.0874603 | ||||||||
\(971\) | 605213.i | 0.641904i | 0.947096 | + | 0.320952i | \(0.104003\pi\) | ||||
−0.947096 | + | 0.320952i | \(0.895997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09632e6 | 1.15801 | ||||||||
\(974\) | 8334.15i | 0.00878503i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −475565. | −0.499241 | ||||||||
\(977\) | − 48105.1i | − 0.0503967i | −0.999682 | − | 0.0251983i | \(-0.991978\pi\) | ||||
0.999682 | − | 0.0251983i | \(-0.00802173\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −515540. | −0.537895 | ||||||||
\(980\) | − 786724.i | − 0.819163i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26399.9 | 0.0273766 | ||||||||
\(983\) | − 123883.i | − 0.128205i | −0.997943 | − | 0.0641024i | \(-0.979582\pi\) | ||||
0.997943 | − | 0.0641024i | \(-0.0204184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −770794. | −0.794448 | ||||||||
\(986\) | 107940.i | 0.111027i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −134721. | −0.138013 | ||||||||
\(989\) | 1.09668e6i | 1.12121i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 851418. | 0.866953 | 0.433477 | − | 0.901165i | \(-0.357287\pi\) | ||||
0.433477 | + | 0.901165i | \(0.357287\pi\) | |||||||
\(992\) | 147036.i | 0.149417i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −44271.3 | −0.0448073 | ||||||||
\(995\) | 1.75783e6i | 1.77555i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.60305e6 | −1.61271 | −0.806355 | − | 0.591432i | \(-0.798563\pi\) | ||||
−0.806355 | + | 0.591432i | \(0.798563\pi\) | |||||||
\(998\) | − 6738.62i | − 0.00676566i | ||||||||
\(999\) | 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 | 81.5.b.a.80.4 | 6 | ||
3.2 | odd | 2 | inner | 81.5.b.a.80.3 | 6 | ||
4.3 | odd | 2 | 1296.5.e.c.161.6 | 6 | |||
9.2 | odd | 6 | 27.5.d.a.17.2 | 6 | |||
9.4 | even | 3 | 27.5.d.a.8.2 | 6 | |||
9.5 | odd | 6 | 9.5.d.a.2.2 | ✓ | 6 | ||
9.7 | even | 3 | 9.5.d.a.5.2 | yes | 6 | ||
12.11 | even | 2 | 1296.5.e.c.161.1 | 6 | |||
36.7 | odd | 6 | 144.5.q.a.113.1 | 6 | |||
36.11 | even | 6 | 432.5.q.a.17.3 | 6 | |||
36.23 | even | 6 | 144.5.q.a.65.1 | 6 | |||
36.31 | odd | 6 | 432.5.q.a.305.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.2 | ✓ | 6 | 9.5 | odd | 6 | ||
9.5.d.a.5.2 | yes | 6 | 9.7 | even | 3 | ||
27.5.d.a.8.2 | 6 | 9.4 | even | 3 | |||
27.5.d.a.17.2 | 6 | 9.2 | odd | 6 | |||
81.5.b.a.80.3 | 6 | 3.2 | odd | 2 | inner | ||
81.5.b.a.80.4 | 6 | 1.1 | even | 1 | trivial | ||
144.5.q.a.65.1 | 6 | 36.23 | even | 6 | |||
144.5.q.a.113.1 | 6 | 36.7 | odd | 6 | |||
432.5.q.a.17.3 | 6 | 36.11 | even | 6 | |||
432.5.q.a.305.3 | 6 | 36.31 | odd | 6 | |||
1296.5.e.c.161.1 | 6 | 12.11 | even | 2 | |||
1296.5.e.c.161.6 | 6 | 4.3 | odd | 2 |