Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,5,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("144.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8852746841\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-0.102534 - 0.177594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.65 |
Dual form | 144.5.q.a.113.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.32172 | − | 3.42768i | −0.924635 | − | 0.380854i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −30.0804 | + | 17.3669i | −1.20321 | + | 0.694676i | −0.961268 | − | 0.275614i | \(-0.911119\pi\) |
−0.241946 | + | 0.970290i | \(0.577786\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.6054 | + | 27.0294i | −0.318478 | + | 0.551620i | −0.980171 | − | 0.198155i | \(-0.936505\pi\) |
0.661693 | + | 0.749775i | \(0.269838\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 57.5020 | + | 57.0484i | 0.709901 | + | 0.704301i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −49.9968 | − | 28.8657i | −0.413197 | − | 0.238559i | 0.278965 | − | 0.960301i | \(-0.410009\pi\) |
−0.692162 | + | 0.721742i | \(0.743342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.6478 | + | 63.4758i | 0.216851 | + | 0.375597i | 0.953844 | − | 0.300304i | \(-0.0970882\pi\) |
−0.736993 | + | 0.675901i | \(0.763755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 309.848 | − | 41.4165i | 1.37710 | − | 0.184074i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 386.985i | − | 1.33905i | −0.742791 | − | 0.669524i | \(-0.766498\pi\) | ||
0.742791 | − | 0.669524i | \(-0.233502\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −115.791 | −0.320750 | −0.160375 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160375 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 222.512 | − | 171.441i | 0.504563 | − | 0.388754i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 474.852 | − | 274.156i | 0.897641 | − | 0.518253i | 0.0212066 | − | 0.999775i | \(-0.493249\pi\) |
0.876434 | + | 0.481522i | \(0.159916\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 290.719 | − | 503.539i | 0.465150 | − | 0.805663i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −282.971 | − | 671.839i | −0.388164 | − | 0.921590i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −680.082 | − | 392.645i | −0.808658 | − | 0.466879i | 0.0378313 | − | 0.999284i | \(-0.487955\pi\) |
−0.846490 | + | 0.532405i | \(0.821288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 272.367 | + | 471.753i | 0.283420 | + | 0.490898i | 0.972225 | − | 0.234049i | \(-0.0751976\pi\) |
−0.688805 | + | 0.724947i | \(0.741864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 317.117 | + | 411.585i | 0.291200 | + | 0.377948i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1084.07i | − | 0.884957i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 898.827 | 0.656557 | 0.328279 | − | 0.944581i | \(-0.393532\pi\) | ||||
0.328279 | + | 0.944581i | \(0.393532\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −87.3975 | − | 653.845i | −0.0574606 | − | 0.429878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2242.01 | − | 1294.43i | 1.33374 | − | 0.770034i | 0.347867 | − | 0.937544i | \(-0.386906\pi\) |
0.985870 | + | 0.167510i | \(0.0535727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1000.05 | − | 1732.14i | 0.540862 | − | 0.936801i | −0.457993 | − | 0.888956i | \(-0.651431\pi\) |
0.998855 | − | 0.0478447i | \(-0.0152352\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2720.43 | − | 717.406i | −1.34342 | − | 0.354274i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 702.646 | + | 405.673i | 0.318083 | + | 0.183645i | 0.650538 | − | 0.759474i | \(-0.274544\pi\) |
−0.332455 | + | 0.943119i | \(0.607877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 713.441 | + | 1235.72i | 0.297143 | + | 0.514667i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1326.46 | + | 3220.38i | −0.509981 | + | 1.23813i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2221.00i | 0.790672i | 0.918537 | + | 0.395336i | \(0.129372\pi\) | ||||
−0.918537 | + | 0.395336i | \(0.870628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2005.23 | 0.662886 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 963.579 | + | 396.895i | 0.296577 | + | 0.122159i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1309.65 | + | 756.128i | −0.376229 | + | 0.217216i | −0.676176 | − | 0.736740i | \(-0.736364\pi\) |
0.299947 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 951.281 | − | 1647.67i | 0.255652 | − | 0.442802i | −0.709420 | − | 0.704786i | \(-0.751043\pi\) |
0.965072 | + | 0.261983i | \(0.0843765\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2439.33 | + | 663.979i | −0.614595 | + | 0.167291i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2204.76 | − | 1272.92i | −0.521836 | − | 0.301282i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2253.55 | + | 3903.26i | 0.502015 | + | 0.869516i | 0.999997 | + | 0.00232883i | \(0.000741290\pi\) |
−0.497982 | + | 0.867187i | \(0.665925\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4891.30 | + | 653.806i | −1.02737 | + | 0.137325i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 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 | \(0.604507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4145.25 | + | 3193.82i | −0.736934 | + | 0.567790i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1560.44 | − | 900.923i | 0.263188 | − | 0.151952i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 601.388 | − | 1041.63i | 0.0963608 | − | 0.166902i | −0.813815 | − | 0.581124i | \(-0.802613\pi\) |
0.910176 | + | 0.414222i | \(0.135946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 51.9555 | + | 6560.79i | 0.00791883 | + | 0.999969i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8016.22 | − | 4628.17i | −1.16363 | − | 0.671820i | −0.211456 | − | 0.977387i | \(-0.567821\pi\) |
−0.952170 | + | 0.305567i | \(0.901154\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6720.72 | + | 11640.6i | 0.930204 | + | 1.61116i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4313.58 | + | 5598.59i | 0.569902 | + | 0.739673i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8929.99i | − | 1.12738i | −0.825986 | − | 0.563691i | \(-0.809381\pi\) | ||
0.825986 | − | 0.563691i | \(-0.190619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2287.62 | −0.276249 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −649.539 | − | 4859.38i | −0.0751000 | − | 0.561843i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3483.03 | − | 2010.93i | 0.385932 | − | 0.222818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3335.14 | + | 5776.64i | −0.354463 | + | 0.613948i | −0.987026 | − | 0.160561i | \(-0.948670\pi\) |
0.632563 | + | 0.774509i | \(0.282003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1228.18 | − | 4512.07i | −0.125311 | − | 0.460369i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7924.19 | − | 4575.03i | −0.776805 | − | 0.448489i | 0.0584918 | − | 0.998288i | \(-0.481371\pi\) |
−0.835297 | + | 0.549799i | \(0.814704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7656.20 | + | 13260.9i | 0.721670 | + | 1.24997i | 0.960330 | + | 0.278866i | \(0.0899586\pi\) |
−0.238660 | + | 0.971103i | \(0.576708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3715.85 | + | 9021.34i | −0.337039 | + | 0.818262i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 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 | \(0.279599\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7479.78 | − | 3080.89i | −0.607076 | − | 0.250052i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1189.11 | + | 686.532i | −0.0931246 | + | 0.0537655i | −0.545839 | − | 0.837890i | \(-0.683789\pi\) |
0.452714 | + | 0.891656i | \(0.350456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9522.48 | + | 16493.4i | −0.720036 | + | 1.24714i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1513.88 | + | 5740.68i | −0.110591 | + | 0.419365i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10460.0 | + | 6039.06i | 0.738646 | + | 0.426457i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5654.04 | − | 9793.09i | −0.386179 | − | 0.668881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23094.3 | + | 3086.94i | −1.52649 | + | 0.204042i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1513.10i | − | 0.0968386i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19152.4 | 1.18745 | 0.593726 | − | 0.804667i | \(-0.297656\pi\) | ||||
0.593726 | + | 0.804667i | \(0.297656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14259.4 | + | 10986.5i | −0.856884 | + | 0.660210i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2615.39 | − | 1510.00i | 0.152403 | − | 0.0879902i | −0.421859 | − | 0.906661i | \(-0.638622\pi\) |
0.574262 | + | 0.818671i | \(0.305289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1806.97 | − | 3129.76i | 0.102152 | − | 0.176932i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20179.6 | + | 15294.8i | 1.10725 | + | 0.839223i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8788.30 | − | 5073.93i | −0.468235 | − | 0.270336i | 0.247266 | − | 0.968948i | \(-0.420468\pi\) |
−0.715501 | + | 0.698612i | \(0.753801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17563.2 | − | 30420.3i | −0.909021 | − | 1.57447i | −0.815427 | − | 0.578860i | \(-0.803498\pi\) |
−0.0935938 | − | 0.995610i | \(-0.529835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4456.70 | − | 5784.34i | −0.224169 | − | 0.290948i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4231.45i | − | 0.206927i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27276.1 | 1.29732 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1701.41 | − | 12728.7i | −0.0787363 | − | 0.589048i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 32373.7 | − | 18691.0i | 1.45821 | − | 0.841899i | 0.459288 | − | 0.888288i | \(-0.348105\pi\) |
0.998923 | + | 0.0463890i | \(0.0147714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16635.0 | − | 28812.7i | 0.729573 | − | 1.26366i | −0.227490 | − | 0.973780i | \(-0.573052\pi\) |
0.957064 | − | 0.289878i | \(-0.0936146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22076.9 | − | 22252.4i | 0.943093 | − | 0.950591i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16385.8 | − | 9460.33i | −0.682030 | − | 0.393770i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4040.16 | − | 6997.77i | −0.163908 | − | 0.283897i | 0.772359 | − | 0.635186i | \(-0.219077\pi\) |
−0.936267 | + | 0.351289i | \(0.885743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7612.87 | − | 18482.5i | 0.301130 | − | 0.731083i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17113.3i | 0.660209i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25427.1 | 0.957022 | 0.478511 | − | 0.878081i | \(-0.341177\pi\) | ||||
0.478511 | + | 0.878081i | \(0.341177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16687.0 | − | 6873.29i | −0.612928 | − | 0.252463i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 30356.6 | − | 17526.4i | 1.08848 | − | 0.628434i | 0.155309 | − | 0.987866i | \(-0.450363\pi\) |
0.933171 | + | 0.359432i | \(0.117029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11594.4 | − | 20082.1i | 0.405951 | − | 0.703129i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6658.21 | − | 6605.69i | −0.227701 | − | 0.225905i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12731.0 | + | 7350.23i | 0.425372 | + | 0.245589i | 0.697373 | − | 0.716708i | \(-0.254352\pi\) |
−0.272001 | + | 0.962297i | \(0.587685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9073.58 | + | 15715.9i | 0.296280 | + | 0.513172i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13490.3 | − | 1803.21i | 0.430602 | − | 0.0575573i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.706973\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13564.0 | + | 10450.7i | −0.405028 | + | 0.312065i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27037.0 | + | 15609.8i | −0.789979 | + | 0.456094i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11170.6 | + | 19348.0i | −0.319442 | + | 0.553290i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22575.3 | + | 2835.80i | 0.631990 | + | 0.0793874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −49915.1 | − | 28818.5i | −1.36825 | − | 0.789959i | −0.377545 | − | 0.925991i | \(-0.623232\pi\) |
−0.990704 | + | 0.136032i | \(0.956565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2089.81 | − | 3619.67i | −0.0561039 | − | 0.0971748i | 0.836609 | − | 0.547800i | \(-0.184534\pi\) |
−0.892713 | + | 0.450625i | \(0.851201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13984.2 | + | 18150.1i | 0.367763 | + | 0.477319i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22191.5i | − | 0.571812i | −0.958258 | − | 0.285906i | \(-0.907705\pi\) | ||
0.958258 | − | 0.285906i | \(-0.0922945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −50608.7 | −1.27797 | −0.638983 | − | 0.769221i | \(-0.720645\pi\) | ||||
−0.638983 | + | 0.769221i | \(0.720645\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5374.25 | − | 40206.3i | −0.133023 | − | 0.995180i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21225.9 | − | 12254.8i | 0.515080 | − | 0.297382i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −44960.4 | + | 77873.6i | −1.06985 | + | 1.85303i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 42945.1 | + | 11325.0i | 1.00224 | + | 0.264301i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5789.18 | + | 3342.38i | 0.132533 | + | 0.0765180i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4459.02 | − | 7723.26i | −0.100156 | − | 0.173474i | 0.811593 | − | 0.584223i | \(-0.198601\pi\) |
−0.911749 | + | 0.410749i | \(0.865267\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13688.6 | + | 33233.1i | −0.301717 | + | 0.732508i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 69471.4i | 1.50290i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17001.6 | −0.361052 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28599.2 | + | 11779.9i | 0.596302 | + | 0.245614i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24564.2 | − | 14182.1i | 0.502941 | − | 0.290373i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4248.76 | + | 7359.07i | −0.0854384 | + | 0.147984i | −0.905578 | − | 0.424180i | \(-0.860562\pi\) |
0.820140 | + | 0.572164i | \(0.193896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 45443.0 | − | 12369.5i | 0.897640 | − | 0.244335i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16543.5 | − | 9551.40i | −0.321052 | − | 0.185360i | 0.330809 | − | 0.943698i | \(-0.392678\pi\) |
−0.651862 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5361.51 | + | 9286.40i | 0.102239 | + | 0.177083i | 0.912607 | − | 0.408839i | \(-0.134066\pi\) |
−0.810368 | + | 0.585921i | \(0.800733\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16073.7 | + | 2148.52i | −0.301225 | + | 0.0402638i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 102200.i | 1.88251i | 0.337694 | + | 0.941256i | \(0.390353\pi\) | ||||
−0.337694 | + | 0.941256i | \(0.609647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28181.1 | −0.510296 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8574.97 | + | 6606.82i | −0.152664 | + | 0.117624i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13440.9 | + | 7760.09i | −0.235305 | + | 0.135854i | −0.613017 | − | 0.790070i | \(-0.710044\pi\) |
0.377712 | + | 0.925923i | \(0.376711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 35978.9 | − | 62317.3i | 0.619461 | − | 1.07294i | −0.370123 | − | 0.928983i | \(-0.620685\pi\) |
0.989584 | − | 0.143955i | \(-0.0459820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22056.0 | − | 54775.2i | 0.373520 | − | 0.927622i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42921.1 | − | 24780.5i | −0.715054 | − | 0.412837i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4243.48 | − | 7349.92i | −0.0695550 | − | 0.120473i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 50844.9 | + | 65991.4i | 0.820065 | + | 1.06436i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16027.6 | − | 119907.i | −0.246483 | − | 1.84401i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −62812.2 | + | 36264.6i | −0.950994 | + | 0.549057i | −0.893390 | − | 0.449283i | \(-0.851680\pi\) |
−0.0576045 | + | 0.998339i | \(0.518346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14026.6 | + | 24294.7i | −0.209099 | + | 0.362170i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16706.2 | − | 61375.5i | −0.245244 | − | 0.900977i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 74383.1 | + | 42945.1i | 1.07538 | + | 0.620872i | 0.929647 | − | 0.368451i | \(-0.120112\pi\) |
0.145735 | + | 0.989324i | \(0.453445\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38571.8 | − | 66808.4i | −0.549261 | − | 0.951347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30609.2 | + | 74312.8i | −0.429367 | + | 1.04242i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 88967.6i | 1.22950i | 0.788724 | + | 0.614748i | \(0.210742\pi\) | ||||
−0.788724 | + | 0.614748i | \(0.789258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −96541.6 | −1.31455 | −0.657273 | − | 0.753652i | \(-0.728290\pi\) | ||||
−0.657273 | + | 0.753652i | \(0.728290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19036.9 | + | 7841.23i | 0.255429 | + | 0.105210i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29070.0 | + | 16783.6i | −0.384397 | + | 0.221932i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11770.8 | − | 20387.6i | 0.153407 | − | 0.265710i | −0.779071 | − | 0.626936i | \(-0.784309\pi\) |
0.932478 | + | 0.361227i | \(0.117642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11251.1 | + | 42664.8i | −0.144540 | + | 0.548102i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −50584.4 | − | 29204.9i | −0.640626 | − | 0.369865i | 0.144230 | − | 0.989544i | \(-0.453930\pi\) |
−0.784855 | + | 0.619679i | \(0.787263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −38058.6 | − | 65919.5i | −0.475204 | − | 0.823078i | 0.524393 | − | 0.851477i | \(-0.324292\pi\) |
−0.999597 | + | 0.0283989i | \(0.990959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −35877.6 | + | 4795.66i | −0.441707 | + | 0.0590417i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 80800.3i | 0.980956i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −66236.1 | −0.793047 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 47554.6 | − | 36639.7i | 0.561573 | − | 0.432680i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 121166. | − | 69955.5i | 1.41139 | − | 0.814866i | 0.415871 | − | 0.909424i | \(-0.363477\pi\) |
0.995519 | + | 0.0945573i | \(0.0301436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26263.2 | − | 45489.2i | 0.301789 | − | 0.522714i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5245.43 | + | 41758.0i | −0.0594660 | + | 0.473399i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34804.5 | + | 20094.4i | 0.389308 | + | 0.224767i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31212.5 | + | 54061.7i | 0.344505 | + | 0.596701i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 50261.1 | + | 65233.7i | 0.547453 | + | 0.710537i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 66083.2i | 0.710381i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 81796.8 | 0.867880 | 0.433940 | − | 0.900942i | \(-0.357123\pi\) | ||||
0.433940 | + | 0.900942i | \(0.357123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18258.5 | − | 136597.i | −0.191226 | − | 1.43062i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1474.59 | − | 851.354i | 0.0152458 | − | 0.00880216i | −0.492358 | − | 0.870393i | \(-0.663865\pi\) |
0.507604 | + | 0.861591i | \(0.330531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34980.1 | − | 60587.3i | 0.357052 | − | 0.618433i | −0.630415 | − | 0.776259i | \(-0.717115\pi\) |
0.987467 | + | 0.157826i | \(0.0504484\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 61844.6 | − | 62336.3i | 0.623276 | − | 0.628232i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 101004. | + | 58314.7i | 1.00512 | + | 0.580309i | 0.909760 | − | 0.415134i | \(-0.136265\pi\) |
0.0953639 | + | 0.995442i | \(0.469599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22668.0 | + | 39262.1i | 0.222757 | + | 0.385826i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20906.4 | + | 50756.5i | −0.202894 | + | 0.492585i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 44809.3i | 0.429500i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42616.8 | 0.403472 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −126236. | − | 51996.2i | −1.18056 | − | 0.486269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21930.2 | + | 12661.4i | −0.202605 | + | 0.116974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 50418.1 | − | 87326.8i | 0.460183 | − | 0.797061i | −0.538787 | − | 0.842442i | \(-0.681117\pi\) |
0.998970 | + | 0.0453817i | \(0.0144504\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51684.3 | + | 51276.6i | 0.466090 | + | 0.462414i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −135575. | − | 78274.3i | −1.20806 | − | 0.697476i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20047.2 | − | 34722.8i | −0.176520 | − | 0.305742i | 0.764166 | − | 0.645020i | \(-0.223151\pi\) |
−0.940686 | + | 0.339277i | \(0.889817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12248.6 | − | 1637.24i | 0.106583 | − | 0.0142466i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 31448.2i | − | 0.270450i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −119471. | −1.01549 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 135778. | − | 104613.i | 1.14075 | − | 0.878920i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 196035. | − | 113181.i | 1.62808 | − | 0.939971i | 0.643412 | − | 0.765520i | \(-0.277518\pi\) |
0.984666 | − | 0.174451i | \(-0.0558150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −39799.1 | + | 68934.1i | −0.326755 | + | 0.565957i | −0.981866 | − | 0.189576i | \(-0.939289\pi\) |
0.655111 | + | 0.755533i | \(0.272622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32275.3 | − | 42583.3i | 0.261973 | − | 0.345641i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −121173. | − | 69959.4i | −0.972427 | − | 0.561431i | −0.0724520 | − | 0.997372i | \(-0.523082\pi\) |
−0.899975 | + | 0.435941i | \(0.856416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 69355.5 | + | 120127.i | 0.550331 | + | 0.953202i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −66344.9 | − | 86108.8i | −0.520560 | − | 0.675633i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13483.7 | + | 100876.i | 0.102329 | + | 0.765549i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 103377. | − | 59684.8i | 0.775959 | − | 0.448000i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15996.8 | + | 27707.3i | −0.118769 | + | 0.205713i | −0.919280 | − | 0.393604i | \(-0.871228\pi\) |
0.800511 | + | 0.599318i | \(0.204561\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 202765. | + | 53471.2i | 1.48916 | + | 0.392706i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60032.2 | − | 34659.6i | −0.436151 | − | 0.251812i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 61573.9 | + | 106649.i | 0.442567 | + | 0.766548i | 0.997879 | − | 0.0650938i | \(-0.0207347\pi\) |
−0.555312 | + | 0.831642i | \(0.687401\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5186.44 | + | 12591.6i | −0.0368813 | + | 0.0895404i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 57558.3i | − | 0.404972i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 116524. | 0.811218 | 0.405609 | − | 0.914047i | \(-0.367059\pi\) | ||||
0.405609 | + | 0.914047i | \(0.367059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −159381. | − | 65648.4i | −1.09796 | − | 0.452246i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −156848. | + | 90556.2i | −1.06925 | + | 0.617334i | −0.927978 | − | 0.372636i | \(-0.878454\pi\) |
−0.141277 | + | 0.989970i | \(0.545121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31292.5 | + | 54200.2i | −0.211115 | + | 0.365661i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 156321. | − | 42550.2i | 1.04375 | − | 0.284106i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −44017.9 | − | 25413.7i | −0.290891 | − | 0.167946i | 0.347453 | − | 0.937697i | \(-0.387047\pi\) |
−0.638343 | + | 0.769752i | \(0.720380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −106094. | − | 183760.i | −0.693965 | − | 1.20198i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26940.4 | + | 3601.04i | −0.174429 | + | 0.0233154i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41777.0i | 0.267758i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 228710. | 1.45112 | 0.725561 | − | 0.688158i | \(-0.241580\pi\) | ||||
0.725561 | + | 0.688158i | \(0.241580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25764.9 | + | 19851.3i | −0.161839 | + | 0.124693i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 163618. | − | 94464.9i | 1.01752 | − | 0.587465i | 0.104134 | − | 0.994563i | \(-0.466793\pi\) |
0.913384 | + | 0.407099i | \(0.133459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19963.3 | + | 34577.4i | −0.122920 | + | 0.212903i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −115504. | − | 196449.i | −0.704182 | − | 1.19768i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44938.5 | − | 25945.2i | −0.271287 | − | 0.156628i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −138713. | − | 240258.i | −0.829223 | − | 1.43626i | −0.898649 | − | 0.438669i | \(-0.855450\pi\) |
0.0694256 | − | 0.997587i | \(-0.477883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 55741.9 | + | 72347.3i | 0.329988 | + | 0.428291i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 47198.8i | − | 0.276714i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 321508. | 1.86679 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41884.6 | + | 313351.i | 0.240870 | + | 1.80201i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 88699.9 | − | 51210.9i | 0.505237 | − | 0.291699i | −0.225637 | − | 0.974212i | \(-0.572446\pi\) |
0.730874 | + | 0.682513i | \(0.239113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23567.9 | + | 40820.8i | −0.132971 | + | 0.230312i | −0.924821 | − | 0.380404i | \(-0.875785\pi\) |
0.791850 | + | 0.610716i | \(0.209118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17260.5 | + | 63411.8i | 0.0964658 | + | 0.354397i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −194862. | − | 112504.i | −1.07882 | − | 0.622857i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29690.3 | + | 51425.1i | 0.162839 | + | 0.282046i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14504.1 | + | 35213.0i | −0.0788090 | + | 0.191332i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 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 | \(0.311199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −226984. | − | 93493.9i | −1.19955 | − | 0.494089i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54983.5 | + | 31744.8i | −0.287919 | + | 0.166230i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −91842.1 | + | 159075.i | −0.476555 | + | 0.825417i | −0.999639 | − | 0.0268637i | \(-0.991448\pi\) |
0.523084 | + | 0.852281i | \(0.324781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29471.4 | + | 111757.i | −0.151539 | + | 0.574641i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 100410. | + | 57971.5i | 0.511644 | + | 0.295398i | 0.733509 | − | 0.679680i | \(-0.237881\pi\) |
−0.221865 | + | 0.975077i | \(0.571215\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 155086. | + | 268617.i | 0.783165 | + | 1.35648i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −333472. | + | 44574.2i | −1.66895 | + | 0.223084i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 328940.i | 1.63164i | 0.578305 | + | 0.815820i | \(0.303714\pi\) | ||||
−0.578305 | + | 0.815820i | \(0.696286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −149458. | −0.734795 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −237192. | + | 182751.i | −1.15586 | + | 0.890562i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 68812.3 | − | 39728.8i | 0.332387 | − | 0.191904i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 106369. | − | 184236.i | 0.509308 | − | 0.882148i | −0.490634 | − | 0.871366i | \(-0.663235\pi\) |
0.999942 | − | 0.0107819i | \(-0.00343204\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −259992. | + | 109506.i | −1.23405 | + | 0.519770i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41957.2 | − | 24224.0i | −0.197426 | − | 0.113984i | 0.398028 | − | 0.917373i | \(-0.369695\pi\) |
−0.595454 | + | 0.803389i | \(0.703028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 84550.6 | + | 146446.i | 0.394416 | + | 0.683149i | 0.993026 | − | 0.117892i | \(-0.0376135\pi\) |
−0.598610 | + | 0.801040i | \(0.704280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 103931. | + | 134891.i | 0.480660 | + | 0.623848i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9634.97 | + | 72081.9i | 0.0434319 | + | 0.324926i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −99999.1 | + | 57734.5i | −0.446965 | + | 0.258055i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33662.6 | + | 58305.3i | −0.149197 | + | 0.258417i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −126704. | + | 127712.i | −0.556871 | + | 0.561299i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 120011. | + | 69288.6i | 0.523060 | + | 0.301989i | 0.738186 | − | 0.674597i | \(-0.235683\pi\) |
−0.215126 | + | 0.976586i | \(0.569016\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32940.0 | + | 57053.7i | 0.142375 | + | 0.246601i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 58658.9 | − | 142412.i | 0.251443 | − | 0.610453i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 231684.i | − | 0.984948i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23464.1 | −0.0989340 | −0.0494670 | − | 0.998776i | \(-0.515752\pi\) | ||||
−0.0494670 | + | 0.998776i | \(0.515752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −211597. | − | 87156.1i | −0.884897 | − | 0.364485i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −64368.8 | + | 37163.4i | −0.267001 | + | 0.154153i | −0.627524 | − | 0.778597i | \(-0.715932\pi\) |
0.360523 | + | 0.932750i | \(0.382598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −151948. | + | 263181.i | −0.625173 | + | 1.08283i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 115305. | + | 114395.i | 0.470583 | + | 0.466872i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 107943. | + | 62321.0i | 0.437001 | + | 0.252302i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9486.01 | − | 16430.2i | −0.0380963 | − | 0.0659847i | 0.846349 | − | 0.532629i | \(-0.178796\pi\) |
−0.884445 | + | 0.466645i | \(0.845463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −312694. | + | 41796.9i | −1.24579 | + | 0.166521i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −165320. | + | 127375.i | −0.643146 | + | 0.495529i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 158881. | − | 91730.2i | 0.613250 | − | 0.354060i | −0.160986 | − | 0.986957i | \(-0.551468\pi\) |
0.774236 | + | 0.632897i | \(0.218134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53631.2 | − | 92891.9i | 0.205388 | − | 0.355743i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32765.5 | + | 77792.9i | 0.124504 | + | 0.295601i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −460602. | − | 265929.i | −1.73665 | − | 1.00265i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23420.0 | − | 40564.7i | −0.0876207 | − | 0.151763i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −80749.2 | − | 104804.i | −0.299781 | − | 0.389085i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 409498.i | − | 1.50861i | −0.656526 | − | 0.754303i | \(-0.727975\pi\) | ||
0.656526 | − | 0.754303i | \(-0.272025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 211852. | 0.774513 | 0.387256 | − | 0.921972i | \(-0.373423\pi\) | ||||
0.387256 | + | 0.921972i | \(0.373423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21638.6 | − | 161885.i | −0.0785075 | − | 0.587336i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 182561. | − | 105402.i | 0.657336 | − | 0.379513i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10402.4 | − | 18017.4i | 0.0371724 | − | 0.0643845i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −118444. | − | 31234.7i | −0.420071 | − | 0.110777i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 164330. | + | 94875.7i | 0.578444 | + | 0.333965i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 105926. | + | 183468.i | 0.370078 | + | 0.640994i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 127004. | − | 308341.i | 0.440423 | − | 1.06926i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 82375.9i | − | 0.283545i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44016.5 | 0.150391 | 0.0751954 | − | 0.997169i | \(-0.476042\pi\) | ||||
0.0751954 | + | 0.997169i | \(0.476042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 330078. | + | 135958.i | 1.11948 | + | 0.461111i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −456304. | + | 263447.i | −1.53625 | + | 0.886953i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21429.6 | + | 37117.1i | −0.0716207 | + | 0.124051i | −0.899612 | − | 0.436691i | \(-0.856150\pi\) |
0.827991 | + | 0.560741i | \(0.189484\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 148697. | − | 40475.0i | 0.493354 | − | 0.134290i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 78747.3 | + | 45464.8i | 0.259378 | + | 0.149752i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18769.8 | + | 32510.3i | 0.0613776 | + | 0.106309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 278500. | − | 37226.3i | 0.904148 | − | 0.120855i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 311007.i | − | 1.00244i | −0.865319 | − | 0.501222i | \(-0.832884\pi\) | ||
0.865319 | − | 0.501222i | \(-0.167116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 146599. | 0.469145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 159277. | − | 122719.i | 0.506090 | − | 0.389931i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 247482. | − | 142884.i | 0.780777 | − | 0.450782i | −0.0559288 | − | 0.998435i | \(-0.517812\pi\) |
0.836705 | + | 0.547653i | \(0.184479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23845.9 | − | 41302.2i | 0.0746992 | − | 0.129383i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −178145. | − | 100980.i | −0.554125 | − | 0.314100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −118371. | − | 68341.3i | −0.365611 | − | 0.211086i | 0.305928 | − | 0.952055i | \(-0.401033\pi\) |
−0.671539 | + | 0.740969i | \(0.734367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14255.0 | − | 24690.4i | −0.0437215 | − | 0.0757279i | 0.843337 | − | 0.537386i | \(-0.180588\pi\) |
−0.887058 | + | 0.461658i | \(0.847255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 316599. | + | 410912.i | 0.964273 | + | 1.25153i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 318809.i | − | 0.964261i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −293742. | −0.882297 | −0.441149 | − | 0.897434i | \(-0.645429\pi\) | ||||
−0.441149 | + | 0.897434i | \(0.645429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4983.78 | + | 37285.1i | 0.0148663 | + | 0.111219i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 250193. | − | 144449.i | 0.741179 | − | 0.427920i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64110.6 | − | 111043.i | 0.188622 | − | 0.326703i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −54160.0 | − | 198973.i | −0.158258 | − | 0.581410i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −334334. | − | 193028.i | −0.970295 | − | 0.560200i | −0.0709687 | − | 0.997479i | \(-0.522609\pi\) |
−0.899326 | + | 0.437279i | \(0.855942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31537.6 | − | 54624.7i | −0.0909072 | − | 0.157456i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −76065.3 | + | 184671.i | −0.217777 | + | 0.528718i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 305581.i | 0.868995i | 0.900673 | + | 0.434497i | \(0.143074\pi\) | ||||
−0.900673 | + | 0.434497i | \(0.856926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −419519. | −1.18500 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 421152. | + | 173471.i | 1.18165 | + | 0.486718i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −229270. | + | 132369.i | −0.638988 | + | 0.368920i | −0.784225 | − | 0.620477i | \(-0.786939\pi\) |
0.145236 | + | 0.989397i | \(0.453606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 66101.5 | − | 114491.i | 0.183005 | − | 0.316973i | −0.759898 | − | 0.650043i | \(-0.774751\pi\) |
0.942902 | + | 0.333069i | \(0.108084\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −93091.3 | + | 353006.i | −0.256020 | + | 0.970841i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 340151. | + | 196386.i | 0.929312 | + | 0.536538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −127073. | − | 220097.i | −0.344886 | − | 0.597360i | 0.640447 | − | 0.768002i | \(-0.278749\pi\) |
−0.985333 | + | 0.170642i | \(0.945416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −218642. | + | 29225.2i | −0.589520 | + | 0.0787994i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59468.0i | 0.159295i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −492878. | −1.31165 | −0.655826 | − | 0.754912i | \(-0.727680\pi\) | ||||
−0.655826 | + | 0.754912i | \(0.727680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 641074. | − | 493933.i | 1.69495 | − | 1.30592i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −105029. | + | 60638.8i | −0.275893 | + | 0.159287i | −0.631563 | − | 0.775325i | \(-0.717586\pi\) |
0.355670 | + | 0.934612i | \(0.384253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 153682. | − | 266185.i | 0.401090 | − | 0.694709i | −0.592768 | − | 0.805374i | \(-0.701965\pi\) |
0.993858 | + | 0.110665i | \(0.0352981\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −318558. | − | 241446.i | −0.826049 | − | 0.626090i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 241372. | + | 139356.i | 0.621886 | + | 0.359046i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 207977. | + | 360227.i | 0.532421 | + | 0.922181i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −36719.3 | − | 47657.9i | −0.0934026 | − | 0.121227i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 347832.i | − | 0.879161i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 254196. | 0.638425 | 0.319212 | − | 0.947683i | \(-0.396582\pi\) | ||||
0.319212 | + | 0.947683i | \(0.396582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10633.9 | + | 79554.9i | 0.0265390 | + | 0.198545i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −576112. | + | 332618.i | −1.42876 | + | 0.824895i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −52292.1 | + | 90572.5i | −0.128872 | + | 0.223212i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 227825. | − | 229637.i | 0.557957 | − | 0.562393i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 316954. | + | 182993.i | 0.771400 | + | 0.445368i | 0.833374 | − | 0.552710i | \(-0.186406\pi\) |
−0.0619737 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 115391. | + | 199864.i | 0.279094 | + | 0.483406i | 0.971160 | − | 0.238429i | \(-0.0766324\pi\) |
−0.692066 | + | 0.721835i | \(0.743299\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 238126. | − | 578121.i | 0.572383 | − | 1.38963i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 141483. | + | 58276.1i | 0.333842 | + | 0.137508i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −67988.8 | + | 39253.4i | −0.159445 | + | 0.0920557i | −0.577600 | − | 0.816320i | \(-0.696010\pi\) |
0.418154 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52448.0 | + | 90842.6i | −0.122249 | + | 0.211742i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −197617. | − | 196058.i | −0.457819 | − | 0.454208i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 742420. | + | 428637.i | 1.70954 | + | 0.987003i | 0.935121 | + | 0.354328i | \(0.115290\pi\) |
0.774418 | + | 0.632675i | \(0.218043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11172.0 | − | 19350.4i | −0.0255698 | − | 0.0442882i | 0.852957 | − | 0.521981i | \(-0.174807\pi\) |
−0.878527 | + | 0.477692i | \(0.841473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −253028. | + | 33821.5i | −0.575627 | + | 0.0769424i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 125526.i | 0.283850i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −430584. | −0.967846 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60581.6 | − | 46676.7i | 0.135359 | − | 0.104291i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −95122.1 | + | 54918.8i | −0.211269 | + | 0.121976i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 331739. | − | 574588.i | 0.732430 | − | 1.26861i | −0.223412 | − | 0.974724i | \(-0.571719\pi\) |
0.955842 | − | 0.293882i | \(-0.0949472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −420563. | − | 52829.0i | −0.923046 | − | 0.115948i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −197558. | − | 114060.i | −0.431040 | − | 0.248861i | 0.268749 | − | 0.963210i | \(-0.413390\pi\) |
−0.699790 | + | 0.714349i | \(0.746723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −104093. | − | 180294.i | −0.225777 | − | 0.391058i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 104931. | + | 136190.i | 0.226261 | + | 0.293664i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12786.1 | − | 95656.4i | −0.0270910 | − | 0.202675i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −140980. | + | 81394.6i | −0.296974 | + | 0.171458i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 378663. | − | 655863.i | 0.793043 | − | 1.37359i | −0.131031 | − | 0.991378i | \(-0.541829\pi\) |
0.924074 | − | 0.382213i | \(-0.124838\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 141125. | + | 37216.0i | 0.293858 | + | 0.0774932i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.05661e6 | + | 610036.i | 2.18749 | + | 1.26295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −500923. | − | 867624.i | −1.03111 | − | 1.78594i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 350308. | − | 850477.i | 0.716962 | − | 1.74064i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 506359.i | 1.03044i | 0.857058 | + | 0.515220i | \(0.172290\pi\) | ||||
−0.857058 | + | 0.515220i | \(0.827710\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −104076. | −0.210591 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 234515. | + | 96595.9i | 0.471838 | + | 0.194348i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 247321. | − | 142791.i | 0.494791 | − | 0.285668i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 325622. | − | 563993.i | 0.647770 | − | 1.12197i | −0.335885 | − | 0.941903i | \(-0.609035\pi\) |
0.983654 | − | 0.180067i | \(-0.0576314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 94004.6 | − | 25587.8i | 0.185956 | − | 0.0506167i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 258668. | + | 149342.i | 0.508819 | + | 0.293767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 73487.2 | + | 127284.i | 0.143747 | + | 0.248978i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 138450. | − | 18506.3i | 0.269312 | − | 0.0359981i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −513010. | + | 395263.i | −0.981407 | + | 0.756152i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −395425. | + | 228299.i | −0.752294 | + | 0.434337i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −373864. | + | 647552.i | −0.707367 | + | 1.22520i | 0.258463 | + | 0.966021i | \(0.416784\pi\) |
−0.965830 | + | 0.259175i | \(0.916549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −371295. | + | 380223.i | −0.698658 | + | 0.715456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −670313. | − | 387006.i | −1.25442 | − | 0.724240i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32869.3 | − | 56931.2i | −0.0611761 | − | 0.105960i | 0.833815 | − | 0.552044i | \(-0.186152\pi\) |
−0.894991 | + | 0.446083i | \(0.852818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 272238. | + | 353337.i | 0.503934 | + | 0.654054i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 260201.i | − | 0.479042i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −977921. | −1.79067 | −0.895334 | − | 0.445395i | \(-0.853063\pi\) | ||||
−0.895334 | + | 0.445395i | \(0.853063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10119.8 | + | 75709.3i | 0.0184305 | + | 0.137884i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −437233. | + | 252437.i | −0.792019 | + | 0.457272i | −0.840673 | − | 0.541543i | \(-0.817840\pi\) |
0.0486539 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −649209. | + | 1.12446e6i | −1.16969 | + | 2.02597i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −196919. | − | 723442.i | −0.352896 | − | 1.29647i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 164860. | + | 95181.9i | 0.293867 | + | 0.169664i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −266395. | − | 461411.i | −0.472332 | − | 0.818102i | 0.527167 | − | 0.849762i | \(-0.323254\pi\) |
−0.999499 | + | 0.0316593i | \(0.989921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 142207. | − | 345250.i | 0.250802 | − | 0.608896i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.15559e6i | 2.02727i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −293571. | −0.512297 | −0.256148 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256148 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 263422. | + | 108503.i | 0.457266 | + | 0.188346i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22249.2 | + | 12845.6i | −0.0384190 | + | 0.0221812i | −0.519086 | − | 0.854722i | \(-0.673728\pi\) |
0.480667 | + | 0.876903i | \(0.340394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −236727. | + | 410022.i | −0.406629 | + | 0.704301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −277625. | + | 1.05277e6i | −0.474390 | + | 1.79891i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −95991.7 | − | 55420.9i | −0.163171 | − | 0.0942069i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 323572. | + | 560443.i | 0.547165 | + | 0.947717i | 0.998467 | + | 0.0553463i | \(0.0176263\pi\) |
−0.451302 | + | 0.892371i | \(0.649040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 647009. | − | 86483.8i | 1.08843 | − | 0.145488i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 610238.i | 1.02127i | 0.859798 | + | 0.510634i | \(0.170589\pi\) | ||||
−0.859798 | + | 0.510634i | \(0.829411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 316728. | 0.527331 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 200000. | − | 154095.i | 0.331274 | − | 0.255239i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −259605. | + | 149883.i | −0.427797 | + | 0.246989i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −115276. | + | 199665.i | −0.188990 | + | 0.327340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −71351.0 | + | 568013.i | −0.116379 | + | 0.926477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 243059. | + | 140330.i | 0.394432 | + | 0.227726i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −290160. | − | 502572.i | −0.468477 | − | 0.811427i | 0.530874 | − | 0.847451i | \(-0.321864\pi\) |
−0.999351 | + | 0.0360244i | \(0.988531\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −471793. | − | 612339.i | −0.757875 | − | 0.983644i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 42854.5i | − | 0.0684926i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 139449. | 0.221753 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 91986.0 | + | 688172.i | 0.145542 | + | 1.08884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −915508. | + | 528569.i | −1.44127 | + | 0.832118i | −0.997935 | − | 0.0642373i | \(-0.979539\pi\) |
−0.443336 | + | 0.896355i | \(0.646205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 156989. | − | 271913.i | 0.245910 | − | 0.425928i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 509442. | − | 513492.i | 0.794016 | − | 0.800329i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 171824. | + | 99202.7i | 0.266473 | + | 0.153848i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −297205. | − | 514774.i | −0.458631 | − | 0.794373i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 304953. | − | 740363.i | 0.468258 | − | 1.13684i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 355969.i | − | 0.543895i | −0.962312 | − | 0.271947i | \(-0.912332\pi\) | ||
0.962312 | − | 0.271947i | \(-0.0876677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 136417. | 0.207409 | 0.103704 | − | 0.994608i | \(-0.466930\pi\) | ||||
0.103704 | + | 0.994608i | \(0.466930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 803392. | + | 330914.i | 1.21548 | + | 0.500650i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −764857. | + | 441590.i | −1.15150 | + | 0.664820i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −115797. | + | 200567.i | −0.173482 | + | 0.300479i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −131543. | − | 130505.i | −0.196109 | − | 0.194563i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −394889. | − | 227989.i | −0.585854 | − | 0.338243i | 0.177603 | − | 0.984102i | \(-0.443166\pi\) |
−0.763456 | + | 0.645860i | \(0.776499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 251795. | + | 436122.i | 0.371747 | + | 0.643885i | 0.989834 | − | 0.142225i | \(-0.0454255\pi\) |
−0.618087 | + | 0.786109i | \(0.712092\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 299441. | − | 40025.4i | 0.439951 | − | 0.0588069i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | \(0.542345\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −167836. | + | 129314.i | −0.243042 | + | 0.187259i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 478203. | − | 276091.i | 0.689164 | − | 0.397889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −608759. | + | 1.05440e6i | −0.873117 | + | 1.51228i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 239870. | − | 316479.i | 0.342394 | − | 0.451746i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 359993. | + | 207842.i | 0.511410 | + | 0.295263i | 0.733413 | − | 0.679783i | \(-0.237926\pi\) |
−0.222003 | + | 0.975046i | \(0.571259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −45299.7 | − | 78461.4i | −0.0640477 | − | 0.110934i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 320844. | + | 416423.i | 0.451480 | + | 0.585975i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 805434.i | 1.12802i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 352935. | 0.491958 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 90762.1 | + | 679016.i | 0.125918 | + | 0.942030i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 426809. | − | 246419.i | 0.589352 | − | 0.340263i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −75135.3 | + | 130138.i | −0.103263 | + | 0.178857i | −0.913027 | − | 0.407898i | \(-0.866262\pi\) |
0.809764 | + | 0.586756i | \(0.199595\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 315002. | + | 83069.1i | 0.430904 | + | 0.113634i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 125373. | + | 72383.9i | 0.170703 | + | 0.0985554i | 0.582917 | − | 0.812532i | \(-0.301911\pi\) |
−0.412214 | + | 0.911087i | \(0.635245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 166948. | + | 289163.i | 0.226254 | + | 0.391883i | 0.956695 | − | 0.291093i | \(-0.0940188\pi\) |
−0.730441 | + | 0.682976i | \(0.760685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 276958. | − | 672398.i | 0.373601 | − | 0.907026i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 551198. | + | 227036.i | 0.733279 | + | 0.302035i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60135.0 | + | 34718.9i | −0.0796320 | + | 0.0459755i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −165175. | + | 286092.i | −0.217725 | + | 0.377111i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −521325. | + | 141903.i | −0.684038 | + | 0.186193i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40898.3 | + | 23612.6i | 0.0534181 | + | 0.0308410i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −248271. | − | 430017.i | −0.322795 | − | 0.559097i | 0.658269 | − | 0.752783i | \(-0.271289\pi\) |
−0.981064 | + | 0.193686i | \(0.937956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.24810e6 | + | 166830.i | −1.61537 | + | 0.215921i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.21533e6i | − | 1.56583i | −0.622131 | − | 0.782913i | \(-0.713733\pi\) | ||
0.622131 | − | 0.782913i | \(-0.286267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 999070. | 1.28137 | 0.640685 | − | 0.767804i | \(-0.278651\pi\) | ||||
0.640685 | + | 0.767804i | \(0.278651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −374478. | + | 288527.i | −0.478123 | + | 0.368383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −938048. | + | 541582.i | −1.19228 | + | 0.688362i | −0.958823 | − | 0.284005i | \(-0.908337\pi\) |
−0.233456 | + | 0.972367i | \(0.575003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −298882. | + | 517678.i | −0.378178 | + | 0.655023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 186784. | − | 329519.i | 0.235280 | − | 0.415073i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −81360.0 | − | 46973.2i | −0.102025 | − | 0.0589044i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −643488. | − | 1.11455e6i | −0.803330 | − | 1.39141i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −220756. | − | 286519.i | −0.274365 | − | 0.356097i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 427774.i | − | 0.529292i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 859491. | 1.05875 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −74435.6 | − | 556873.i | −0.0912862 | − | 0.682937i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.19313e6 | − | 688853.i | 1.45677 | − | 0.841065i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 638426. | − | 1.10579e6i | 0.776061 | − | 1.34418i | −0.158135 | − | 0.987417i | \(-0.550548\pi\) |
0.934196 | − | 0.356760i | \(-0.116118\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −194658. | − | 715136.i | −0.235583 | − | 0.865487i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −236846. | − | 136743.i | −0.285383 | − | 0.164766i | 0.350475 | − | 0.936572i | \(-0.386020\pi\) |
−0.635858 | + | 0.771806i | \(0.719354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 267191. | + | 462788.i | 0.320538 | + | 0.555188i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 226512. | − | 549926.i | 0.270551 | − | 0.656844i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 94256.7i | 0.112092i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.15882e6 | −1.37210 | −0.686051 | − | 0.727553i | \(-0.740657\pi\) | ||||
−0.686051 | + | 0.727553i | \(0.740657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −680690. | − | 280373.i | −0.802472 | − | 0.330535i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 253493. | − | 146355.i | 0.297552 | − | 0.171792i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 261306. | − | 452595.i | 0.305397 | − | 0.528964i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −316268. | + | 1.19930e6i | −0.368041 | + | 1.39563i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 738465. | + | 426353.i | 0.855655 | + | 0.494012i | 0.862555 | − | 0.505964i | \(-0.168863\pi\) |
−0.00690018 | + | 0.999976i | \(0.502196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −82610.0 | − | 143085.i | −0.0953089 | − | 0.165080i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15189.3 | + | 2030.31i | −0.0174491 | + | 0.00233237i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 775993.i | − | 0.887636i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 629989. | 0.717552 | 0.358776 | − | 0.933424i | \(-0.383194\pi\) | ||||
0.358776 | + | 0.933424i | \(0.383194\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −498768. | + | 384290.i | −0.565676 | + | 0.435840i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −366547. | + | 211626.i | −0.413953 | + | 0.238996i | −0.692487 | − | 0.721431i | \(-0.743485\pi\) |
0.278534 | + | 0.960426i | \(0.410152\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 709749. | − | 1.22932e6i | 0.798145 | − | 1.38243i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −728322. | + | 306761.i | −0.815568 | + | 0.343508i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.20762e6 | + | 697219.i | 1.34657 | + | 0.777444i | 0.987762 | − | 0.155967i | \(-0.0498493\pi\) |
0.358810 | + | 0.933411i | \(0.383183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −125947. | − | 218147.i | −0.139848 | − | 0.242224i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −640642. | − | 831488.i | −0.708361 | − | 0.919379i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24001.0i | 0.0264267i | 0.999913 | + | 0.0132134i | \(0.00420607\pi\) | ||||
−0.999913 | + | 0.0132134i | \(0.995794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.00195e6 | 2.19506 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −54058.5 | − | 404426.i | −0.0590255 | − | 0.441586i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 274290. | − | 158362.i | 0.298245 | − | 0.172192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 313393. | − | 542813.i | 0.339346 | − | 0.587765i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 347954. | − | 350721.i | 0.375206 | − | 0.378189i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 125725. | + | 72587.2i | 0.135010 | + | 0.0779481i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 522031. | + | 904183.i | 0.558268 | + | 0.966949i | 0.997641 | + | 0.0686443i | \(0.0218673\pi\) |
−0.439373 | + | 0.898305i | \(0.644799\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 153592. | − | 372890.i | 0.163577 | − | 0.397131i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −354645. | − | 146077.i | −0.373065 | − | 0.153664i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41660.2 | − | 24052.5i | 0.0436448 | − | 0.0251983i | −0.478019 | − | 0.878350i | \(-0.658645\pi\) |
0.521664 | + | 0.853151i | \(0.325312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −257770. | + | 446471.i | −0.268947 | + | 0.465831i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 872276. | + | 865396.i | 0.906392 | + | 0.899243i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 107286. | + | 61941.5i | 0.111029 | + | 0.0641024i | 0.554486 | − | 0.832193i | \(-0.312915\pi\) |
−0.443457 | + | 0.896295i | \(0.646248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 385397. | + | 667527.i | 0.397224 | + | 0.688012i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 225896. | − | 30194.9i | 0.231886 | − | 0.0309955i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.09668e6i | − | 1.12121i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −851418. | −0.866953 | −0.433477 | − | 0.901165i | \(-0.642713\pi\) | ||||
−0.433477 | + | 0.901165i | \(0.642713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −718894. | + | 553891.i | −0.729065 | + | 0.561728i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.52233e6 | − | 878917.i | 1.53767 | − | 0.887773i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 801524. | − | 1.38828e6i | 0.806355 | − | 1.39665i | −0.109018 | − | 0.994040i | \(-0.534771\pi\) |
0.915373 | − | 0.402607i | \(-0.131896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −254342. | − | 603867.i | −0.254852 | − | 0.605077i |
(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 | 144.5.q.a.65.1 | 6 | ||
3.2 | odd | 2 | 432.5.q.a.305.3 | 6 | |||
4.3 | odd | 2 | 9.5.d.a.2.2 | ✓ | 6 | ||
9.2 | odd | 6 | 1296.5.e.c.161.6 | 6 | |||
9.4 | even | 3 | 432.5.q.a.17.3 | 6 | |||
9.5 | odd | 6 | inner | 144.5.q.a.113.1 | 6 | ||
9.7 | even | 3 | 1296.5.e.c.161.1 | 6 | |||
12.11 | even | 2 | 27.5.d.a.8.2 | 6 | |||
36.7 | odd | 6 | 81.5.b.a.80.3 | 6 | |||
36.11 | even | 6 | 81.5.b.a.80.4 | 6 | |||
36.23 | even | 6 | 9.5.d.a.5.2 | yes | 6 | ||
36.31 | odd | 6 | 27.5.d.a.17.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.2 | ✓ | 6 | 4.3 | odd | 2 | ||
9.5.d.a.5.2 | yes | 6 | 36.23 | even | 6 | ||
27.5.d.a.8.2 | 6 | 12.11 | even | 2 | |||
27.5.d.a.17.2 | 6 | 36.31 | odd | 6 | |||
81.5.b.a.80.3 | 6 | 36.7 | odd | 6 | |||
81.5.b.a.80.4 | 6 | 36.11 | even | 6 | |||
144.5.q.a.65.1 | 6 | 1.1 | even | 1 | trivial | ||
144.5.q.a.113.1 | 6 | 9.5 | odd | 6 | inner | ||
432.5.q.a.17.3 | 6 | 9.4 | even | 3 | |||
432.5.q.a.305.3 | 6 | 3.2 | odd | 2 | |||
1296.5.e.c.161.1 | 6 | 9.7 | even | 3 | |||
1296.5.e.c.161.6 | 6 | 9.2 | odd | 6 |