Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.o.361.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | − | 3.46410i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | − | 6.92820i | −0.500000 | − | 0.866025i | ||||
\(5\) | 9.00000 | − | 15.5885i | 0.804984 | − | 1.39427i | −0.111317 | − | 0.993785i | \(-0.535507\pi\) |
0.916302 | − | 0.400489i | \(-0.131160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −36.0000 | − | 62.3538i | −1.13842 | − | 1.97180i | ||||
\(11\) | −25.0000 | − | 43.3013i | −0.685253 | − | 1.18689i | −0.973357 | − | 0.229294i | \(-0.926358\pi\) |
0.288104 | − | 0.957599i | \(-0.406975\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.0000 | −0.768046 | −0.384023 | − | 0.923323i | \(-0.625462\pi\) | ||||
−0.384023 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 32.0000 | − | 55.4256i | 0.500000 | − | 0.866025i | ||||
\(17\) | 63.0000 | + | 109.119i | 0.898808 | + | 1.55678i | 0.829019 | + | 0.559220i | \(0.188899\pi\) |
0.0697893 | + | 0.997562i | \(0.477767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.0000 | − | 62.3538i | 0.434682 | − | 0.752892i | −0.562587 | − | 0.826738i | \(-0.690194\pi\) |
0.997270 | + | 0.0738459i | \(0.0235273\pi\) | |||||||
\(20\) | −144.000 | −1.60997 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −200.000 | −1.93819 | ||||||||
\(23\) | 7.00000 | − | 12.1244i | 0.0634609 | − | 0.109918i | −0.832549 | − | 0.553951i | \(-0.813120\pi\) |
0.896010 | + | 0.444033i | \(0.146453\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | − | 172.339i | −0.796000 | − | 1.37871i | ||||
\(26\) | −72.0000 | + | 124.708i | −0.543091 | + | 0.940661i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −158.000 | −1.01172 | −0.505860 | − | 0.862616i | \(-0.668825\pi\) | ||||
−0.505860 | + | 0.862616i | \(0.668825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | + | 31.1769i | 0.104287 | + | 0.180630i | 0.913447 | − | 0.406958i | \(-0.133411\pi\) |
−0.809160 | + | 0.587589i | \(0.800077\pi\) | |||||||
\(32\) | −128.000 | − | 221.703i | −0.707107 | − | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 504.000 | 2.54221 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.0000 | − | 140.296i | 0.359900 | − | 0.623366i | −0.628043 | − | 0.778178i | \(-0.716144\pi\) |
0.987944 | + | 0.154812i | \(0.0494773\pi\) | |||||||
\(38\) | −144.000 | − | 249.415i | −0.614734 | − | 1.06475i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 270.000 | 1.02846 | 0.514231 | − | 0.857652i | \(-0.328078\pi\) | ||||
0.514231 | + | 0.857652i | \(0.328078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −324.000 | −1.14906 | −0.574529 | − | 0.818484i | \(-0.694815\pi\) | ||||
−0.574529 | + | 0.818484i | \(0.694815\pi\) | |||||||
\(44\) | −200.000 | + | 346.410i | −0.685253 | + | 1.18689i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −28.0000 | − | 48.4974i | −0.0897473 | − | 0.155447i | ||||
\(47\) | −36.0000 | + | 62.3538i | −0.111726 | + | 0.193516i | −0.916466 | − | 0.400112i | \(-0.868971\pi\) |
0.804740 | + | 0.593627i | \(0.202305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −796.000 | −2.25143 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 144.000 | + | 249.415i | 0.384023 | + | 0.665148i | ||||
\(53\) | −11.0000 | − | 19.0526i | −0.0285088 | − | 0.0493787i | 0.851419 | − | 0.524486i | \(-0.175743\pi\) |
−0.879928 | + | 0.475107i | \(0.842409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −900.000 | −2.20647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −316.000 | + | 547.328i | −0.715394 | + | 1.23910i | ||||
\(59\) | 234.000 | + | 405.300i | 0.516342 | + | 0.894331i | 0.999820 | + | 0.0189746i | \(0.00604016\pi\) |
−0.483478 | + | 0.875357i | \(0.660627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −396.000 | + | 685.892i | −0.831190 | + | 1.43966i | 0.0659047 | + | 0.997826i | \(0.479007\pi\) |
−0.897095 | + | 0.441838i | \(0.854327\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −324.000 | + | 561.184i | −0.618265 | + | 1.07087i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −116.000 | − | 200.918i | −0.211517 | − | 0.366359i | 0.740672 | − | 0.671866i | \(-0.234507\pi\) |
−0.952190 | + | 0.305508i | \(0.901174\pi\) | |||||||
\(68\) | 504.000 | − | 872.954i | 0.898808 | − | 1.55678i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 734.000 | 1.22690 | 0.613449 | − | 0.789734i | \(-0.289782\pi\) | ||||
0.613449 | + | 0.789734i | \(0.289782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −90.0000 | − | 155.885i | −0.144297 | − | 0.249930i | 0.784813 | − | 0.619732i | \(-0.212759\pi\) |
−0.929111 | + | 0.369802i | \(0.879425\pi\) | |||||||
\(74\) | −324.000 | − | 561.184i | −0.508976 | − | 0.881573i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −576.000 | −0.869365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −118.000 | + | 204.382i | −0.168051 | + | 0.291073i | −0.937735 | − | 0.347353i | \(-0.887081\pi\) |
0.769683 | + | 0.638426i | \(0.220414\pi\) | |||||||
\(80\) | −576.000 | − | 997.661i | −0.804984 | − | 1.39427i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 540.000 | − | 935.307i | 0.727232 | − | 1.25960i | ||||
\(83\) | −36.0000 | −0.0476086 | −0.0238043 | − | 0.999717i | \(-0.507578\pi\) | ||||
−0.0238043 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2268.00 | 2.89411 | ||||||||
\(86\) | −648.000 | + | 1122.37i | −0.812507 | + | 1.40730i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 117.000 | − | 202.650i | 0.139348 | − | 0.241358i | −0.787902 | − | 0.615801i | \(-0.788833\pi\) |
0.927250 | + | 0.374443i | \(0.122166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −112.000 | −0.126922 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 144.000 | + | 249.415i | 0.158005 | + | 0.273673i | ||||
\(95\) | −648.000 | − | 1122.37i | −0.699825 | − | 1.21213i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 468.000 | 0.489878 | 0.244939 | − | 0.969538i | \(-0.421232\pi\) | ||||
0.244939 | + | 0.969538i | \(0.421232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −796.000 | + | 1378.71i | −0.796000 | + | 1.37871i | ||||
\(101\) | −333.000 | − | 576.773i | −0.328067 | − | 0.568228i | 0.654061 | − | 0.756441i | \(-0.273064\pi\) |
−0.982128 | + | 0.188213i | \(0.939730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 126.000 | − | 218.238i | 0.120535 | − | 0.208773i | −0.799444 | − | 0.600741i | \(-0.794872\pi\) |
0.919979 | + | 0.391968i | \(0.128206\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −88.0000 | −0.0806351 | ||||||||
\(107\) | 335.000 | − | 580.237i | 0.302670 | − | 0.524240i | −0.674070 | − | 0.738668i | \(-0.735455\pi\) |
0.976740 | + | 0.214428i | \(0.0687887\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.0000 | − | 140.296i | −0.0711779 | − | 0.123284i | 0.828240 | − | 0.560374i | \(-0.189342\pi\) |
−0.899418 | + | 0.437090i | \(0.856009\pi\) | |||||||
\(110\) | −1800.00 | + | 3117.69i | −1.56021 | + | 2.70237i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1390.00 | 1.15717 | 0.578585 | − | 0.815622i | \(-0.303605\pi\) | ||||
0.578585 | + | 0.815622i | \(0.303605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −126.000 | − | 218.238i | −0.102170 | − | 0.176964i | ||||
\(116\) | 632.000 | + | 1094.66i | 0.505860 | + | 0.876175i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1872.00 | 1.46044 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −584.500 | + | 1012.38i | −0.439144 | + | 0.760619i | ||||
\(122\) | 1584.00 | + | 2743.57i | 1.17548 | + | 2.03599i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 144.000 | − | 249.415i | 0.104287 | − | 0.180630i | ||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 916.000 | 0.640015 | 0.320007 | − | 0.947415i | \(-0.396315\pi\) | ||||
0.320007 | + | 0.947415i | \(0.396315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1296.00 | + | 2244.74i | 0.874359 | + | 1.51443i | ||||
\(131\) | 1134.00 | − | 1964.15i | 0.756321 | − | 1.30999i | −0.188394 | − | 0.982094i | \(-0.560328\pi\) |
0.944715 | − | 0.327893i | \(-0.106338\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −928.000 | −0.598261 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 403.000 | + | 698.016i | 0.251318 | + | 0.435296i | 0.963889 | − | 0.266304i | \(-0.0858026\pi\) |
−0.712571 | + | 0.701600i | \(0.752469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2628.00 | 1.60363 | 0.801813 | − | 0.597575i | \(-0.203869\pi\) | ||||
0.801813 | + | 0.597575i | \(0.203869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1468.00 | − | 2542.65i | 0.867548 | − | 1.50264i | ||||
\(143\) | 900.000 | + | 1558.85i | 0.526306 | + | 0.911589i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1422.00 | + | 2462.98i | −0.814418 | + | 1.41061i | ||||
\(146\) | −720.000 | −0.408134 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1296.00 | −0.719801 | ||||||||
\(149\) | −1195.00 | + | 2069.80i | −0.657035 | + | 1.13802i | 0.324344 | + | 0.945939i | \(0.394856\pi\) |
−0.981379 | + | 0.192079i | \(0.938477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1620.00 | − | 2805.92i | −0.873071 | − | 1.51220i | −0.858803 | − | 0.512305i | \(-0.828792\pi\) |
−0.0142676 | − | 0.999898i | \(-0.504542\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 648.000 | 0.335798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1512.00 | − | 2618.86i | −0.768603 | − | 1.33126i | −0.938320 | − | 0.345767i | \(-0.887619\pi\) |
0.169717 | − | 0.985493i | \(-0.445715\pi\) | |||||||
\(158\) | 472.000 | + | 817.528i | 0.237660 | + | 0.411639i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4608.00 | −2.27684 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 892.000 | − | 1544.99i | 0.428631 | − | 0.742410i | −0.568121 | − | 0.822945i | \(-0.692329\pi\) |
0.996752 | + | 0.0805346i | \(0.0256628\pi\) | |||||||
\(164\) | −1080.00 | − | 1870.61i | −0.514231 | − | 0.890674i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −72.0000 | + | 124.708i | −0.0336644 | + | 0.0583084i | ||||
\(167\) | 3024.00 | 1.40122 | 0.700611 | − | 0.713543i | \(-0.252911\pi\) | ||||
0.700611 | + | 0.713543i | \(0.252911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −901.000 | −0.410105 | ||||||||
\(170\) | 4536.00 | − | 7856.58i | 2.04644 | − | 3.54454i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1296.00 | + | 2244.74i | 0.574529 | + | 0.995114i | ||||
\(173\) | 783.000 | − | 1356.20i | 0.344106 | − | 0.596010i | −0.641085 | − | 0.767470i | \(-0.721515\pi\) |
0.985191 | + | 0.171461i | \(0.0548486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3200.00 | −1.37051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −468.000 | − | 810.600i | −0.197068 | − | 0.341332i | ||||
\(179\) | 1901.00 | + | 3292.63i | 0.793784 | + | 1.37487i | 0.923608 | + | 0.383338i | \(0.125226\pi\) |
−0.129824 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −468.000 | −0.192189 | −0.0960944 | − | 0.995372i | \(-0.530635\pi\) | ||||
−0.0960944 | + | 0.995372i | \(0.530635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1458.00 | − | 2525.33i | −0.579429 | − | 1.00360i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3150.00 | − | 5455.96i | 1.23182 | − | 2.13358i | ||||
\(188\) | 576.000 | 0.223453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5184.00 | −1.97940 | ||||||||
\(191\) | 241.000 | − | 417.424i | 0.0912992 | − | 0.158135i | −0.816759 | − | 0.576979i | \(-0.804231\pi\) |
0.908058 | + | 0.418844i | \(0.137565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 405.000 | + | 701.481i | 0.151049 | + | 0.261625i | 0.931614 | − | 0.363450i | \(-0.118401\pi\) |
−0.780564 | + | 0.625076i | \(0.785068\pi\) | |||||||
\(194\) | 936.000 | − | 1621.20i | 0.346396 | − | 0.599976i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2462.00 | 0.890407 | 0.445204 | − | 0.895429i | \(-0.353131\pi\) | ||||
0.445204 | + | 0.895429i | \(0.353131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2268.00 | + | 3928.29i | 0.807911 | + | 1.39934i | 0.914308 | + | 0.405019i | \(0.132735\pi\) |
−0.106397 | + | 0.994324i | \(0.533932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2664.00 | −0.927913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2430.00 | − | 4208.88i | 0.827895 | − | 1.43396i | ||||
\(206\) | −504.000 | − | 872.954i | −0.170463 | − | 0.295250i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1152.00 | + | 1995.32i | −0.384023 | + | 0.665148i | ||||
\(209\) | −3600.00 | −1.19147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2916.00 | 0.951402 | 0.475701 | − | 0.879607i | \(-0.342195\pi\) | ||||
0.475701 | + | 0.879607i | \(0.342195\pi\) | |||||||
\(212\) | −88.0000 | + | 152.420i | −0.0285088 | + | 0.0493787i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1340.00 | − | 2320.95i | −0.428040 | − | 0.741387i | ||||
\(215\) | −2916.00 | + | 5050.66i | −0.924975 | + | 1.60210i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −648.000 | −0.201322 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3600.00 | + | 6235.38i | 1.10324 | + | 1.91086i | ||||
\(221\) | −2268.00 | − | 3928.29i | −0.690327 | − | 1.19568i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1080.00 | −0.324315 | −0.162157 | − | 0.986765i | \(-0.551845\pi\) | ||||
−0.162157 | + | 0.986765i | \(0.551845\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2780.00 | − | 4815.10i | 0.818243 | − | 1.41724i | ||||
\(227\) | −666.000 | − | 1153.55i | −0.194731 | − | 0.337284i | 0.752081 | − | 0.659070i | \(-0.229050\pi\) |
−0.946812 | + | 0.321786i | \(0.895717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −810.000 | + | 1402.96i | −0.233739 | + | 0.404848i | −0.958906 | − | 0.283725i | \(-0.908430\pi\) |
0.725166 | + | 0.688574i | \(0.241763\pi\) | |||||||
\(230\) | −1008.00 | −0.288981 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3359.00 | − | 5817.96i | 0.944444 | − | 1.63582i | 0.187583 | − | 0.982249i | \(-0.439935\pi\) |
0.756861 | − | 0.653576i | \(-0.226732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 648.000 | + | 1122.37i | 0.179876 | + | 0.311554i | ||||
\(236\) | 1872.00 | − | 3242.40i | 0.516342 | − | 0.894331i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3578.00 | 0.968375 | 0.484187 | − | 0.874964i | \(-0.339115\pi\) | ||||
0.484187 | + | 0.874964i | \(0.339115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 378.000 | + | 654.715i | 0.101034 | + | 0.174995i | 0.912111 | − | 0.409944i | \(-0.134452\pi\) |
−0.811077 | + | 0.584939i | \(0.801118\pi\) | |||||||
\(242\) | 2338.00 | + | 4049.53i | 0.621043 | + | 1.07568i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6336.00 | 1.66238 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1296.00 | + | 2244.74i | −0.333856 | + | 0.578256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2664.00 | + | 4614.18i | −0.673945 | + | 1.16731i | ||||
\(251\) | 6516.00 | 1.63859 | 0.819295 | − | 0.573372i | \(-0.194365\pi\) | ||||
0.819295 | + | 0.573372i | \(0.194365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −700.000 | −0.173947 | ||||||||
\(254\) | 1832.00 | − | 3173.12i | 0.452559 | − | 0.783855i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2048.00 | − | 3547.24i | −0.500000 | − | 0.866025i | ||||
\(257\) | −3015.00 | + | 5222.13i | −0.731792 | + | 1.26750i | 0.224325 | + | 0.974514i | \(0.427982\pi\) |
−0.956117 | + | 0.292986i | \(0.905351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5184.00 | 1.23653 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4536.00 | − | 7856.58i | −1.06960 | − | 1.85260i | ||||
\(263\) | 295.000 | + | 510.955i | 0.0691653 | + | 0.119798i | 0.898534 | − | 0.438904i | \(-0.144633\pi\) |
−0.829369 | + | 0.558702i | \(0.811300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −396.000 | −0.0917966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −928.000 | + | 1607.34i | −0.211517 | + | 0.366359i | ||||
\(269\) | −495.000 | − | 857.365i | −0.112196 | − | 0.194329i | 0.804459 | − | 0.594008i | \(-0.202455\pi\) |
−0.916655 | + | 0.399679i | \(0.869122\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1710.00 | − | 2961.81i | 0.383303 | − | 0.663900i | −0.608229 | − | 0.793761i | \(-0.708120\pi\) |
0.991532 | + | 0.129861i | \(0.0414532\pi\) | |||||||
\(272\) | 8064.00 | 1.79762 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3224.00 | 0.710836 | ||||||||
\(275\) | −4975.00 | + | 8616.95i | −1.09092 | + | 1.88953i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1367.00 | + | 2367.71i | 0.296516 | + | 0.513582i | 0.975337 | − | 0.220723i | \(-0.0708417\pi\) |
−0.678820 | + | 0.734305i | \(0.737508\pi\) | |||||||
\(278\) | 5256.00 | − | 9103.66i | 1.13394 | − | 1.96403i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −598.000 | −0.126953 | −0.0634763 | − | 0.997983i | \(-0.520219\pi\) | ||||
−0.0634763 | + | 0.997983i | \(0.520219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1800.00 | − | 3117.69i | −0.378088 | − | 0.654868i | 0.612696 | − | 0.790319i | \(-0.290085\pi\) |
−0.990784 | + | 0.135451i | \(0.956752\pi\) | |||||||
\(284\) | −2936.00 | − | 5085.30i | −0.613449 | − | 1.06253i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7200.00 | 1.48862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5481.50 | + | 9494.24i | −1.11571 | + | 1.93247i | ||||
\(290\) | 5688.00 | + | 9851.90i | 1.15176 | + | 1.99491i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −720.000 | + | 1247.08i | −0.144297 | + | 0.249930i | ||||
\(293\) | −7902.00 | −1.57556 | −0.787781 | − | 0.615955i | \(-0.788770\pi\) | ||||
−0.787781 | + | 0.615955i | \(0.788770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8424.00 | 1.66259 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4780.00 | + | 8279.20i | 0.929188 | + | 1.60940i | ||||
\(299\) | −252.000 | + | 436.477i | −0.0487409 | + | 0.0844218i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12960.0 | −2.46942 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2304.00 | − | 3990.65i | −0.434682 | − | 0.752892i | ||||
\(305\) | 7128.00 | + | 12346.1i | 1.33819 | + | 2.31781i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10224.0 | −1.90070 | −0.950349 | − | 0.311185i | \(-0.899274\pi\) | ||||
−0.950349 | + | 0.311185i | \(0.899274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1296.00 | − | 2244.74i | 0.237445 | − | 0.411266i | ||||
\(311\) | 1944.00 | + | 3367.11i | 0.354451 | + | 0.613926i | 0.987024 | − | 0.160574i | \(-0.0513346\pi\) |
−0.632573 | + | 0.774501i | \(0.718001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2556.00 | + | 4427.12i | −0.461577 | + | 0.799475i | −0.999040 | − | 0.0438124i | \(-0.986050\pi\) |
0.537463 | + | 0.843288i | \(0.319383\pi\) | |||||||
\(314\) | −12096.0 | −2.17394 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | −5051.00 | + | 8748.59i | −0.894929 | + | 1.55006i | −0.0610361 | + | 0.998136i | \(0.519440\pi\) |
−0.833893 | + | 0.551927i | \(0.813893\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3950.00 | + | 6841.60i | 0.693284 | + | 1.20080i | ||||
\(320\) | −4608.00 | + | 7981.29i | −0.804984 | + | 1.39427i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9072.00 | 1.56279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3582.00 | + | 6204.21i | 0.611365 | + | 1.05892i | ||||
\(326\) | −3568.00 | − | 6179.96i | −0.606176 | − | 1.04993i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2754.00 | + | 4770.07i | −0.457322 | + | 0.792105i | −0.998818 | − | 0.0485983i | \(-0.984525\pi\) |
0.541497 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(332\) | 144.000 | + | 249.415i | 0.0238043 | + | 0.0412303i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6048.00 | − | 10475.4i | 0.990814 | − | 1.71614i | ||||
\(335\) | −4176.00 | −0.681072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9234.00 | −1.49261 | −0.746303 | − | 0.665607i | \(-0.768173\pi\) | ||||
−0.746303 | + | 0.665607i | \(0.768173\pi\) | |||||||
\(338\) | −1802.00 | + | 3121.16i | −0.289988 | + | 0.502274i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9072.00 | − | 15713.2i | −1.44705 | − | 2.50637i | ||||
\(341\) | 900.000 | − | 1558.85i | 0.142926 | − | 0.247555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3132.00 | − | 5424.78i | −0.486640 | − | 0.842885i | ||||
\(347\) | −3247.00 | − | 5623.97i | −0.502329 | − | 0.870059i | −0.999996 | − | 0.00269115i | \(-0.999143\pi\) |
0.497668 | − | 0.867368i | \(-0.334190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10080.0 | 1.54605 | 0.773023 | − | 0.634378i | \(-0.218744\pi\) | ||||
0.773023 | + | 0.634378i | \(0.218744\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6400.00 | + | 11085.1i | −0.969094 | + | 1.67852i | ||||
\(353\) | −369.000 | − | 639.127i | −0.0556371 | − | 0.0963662i | 0.836865 | − | 0.547409i | \(-0.184386\pi\) |
−0.892503 | + | 0.451042i | \(0.851052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6606.00 | − | 11441.9i | 0.987634 | − | 1.71063i | ||||
\(356\) | −1872.00 | −0.278696 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15208.0 | 2.24516 | ||||||||
\(359\) | 97.0000 | − | 168.009i | 0.0142603 | − | 0.0246996i | −0.858807 | − | 0.512299i | \(-0.828794\pi\) |
0.873068 | + | 0.487599i | \(0.162127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 837.500 | + | 1450.59i | 0.122102 | + | 0.211487i | ||||
\(362\) | −936.000 | + | 1621.20i | −0.135898 | + | 0.235382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3240.00 | −0.464628 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2376.00 | + | 4115.35i | 0.337946 | + | 0.585340i | 0.984046 | − | 0.177913i | \(-0.0569345\pi\) |
−0.646100 | + | 0.763253i | \(0.723601\pi\) | |||||||
\(368\) | −448.000 | − | 775.959i | −0.0634609 | − | 0.109918i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11664.0 | −1.63887 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1153.00 | − | 1997.05i | 0.160054 | − | 0.277221i | −0.774834 | − | 0.632165i | \(-0.782167\pi\) |
0.934888 | + | 0.354943i | \(0.115500\pi\) | |||||||
\(374\) | −12600.0 | − | 21823.8i | −1.74206 | − | 3.01734i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5688.00 | 0.777047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7452.00 | −1.00998 | −0.504991 | − | 0.863124i | \(-0.668504\pi\) | ||||
−0.504991 | + | 0.863124i | \(0.668504\pi\) | |||||||
\(380\) | −5184.00 | + | 8978.95i | −0.699825 | + | 1.21213i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −964.000 | − | 1669.70i | −0.129117 | − | 0.223636i | ||||
\(383\) | −576.000 | + | 997.661i | −0.0768465 | + | 0.133102i | −0.901888 | − | 0.431970i | \(-0.857818\pi\) |
0.825041 | + | 0.565073i | \(0.191152\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3240.00 | 0.427232 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1872.00 | − | 3242.40i | −0.244939 | − | 0.424247i | ||||
\(389\) | 947.000 | + | 1640.25i | 0.123431 | + | 0.213789i | 0.921119 | − | 0.389282i | \(-0.127277\pi\) |
−0.797687 | + | 0.603071i | \(0.793943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1764.00 | 0.228157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4924.00 | − | 8528.62i | 0.629613 | − | 1.09052i | ||||
\(395\) | 2124.00 | + | 3678.88i | 0.270557 | + | 0.468619i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4608.00 | + | 7981.29i | −0.582541 | + | 1.00899i | 0.412636 | + | 0.910896i | \(0.364608\pi\) |
−0.995177 | + | 0.0980950i | \(0.968725\pi\) | |||||||
\(398\) | 18144.0 | 2.28512 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12736.0 | −1.59200 | ||||||||
\(401\) | −5825.00 | + | 10089.2i | −0.725403 | + | 1.25643i | 0.233405 | + | 0.972380i | \(0.425013\pi\) |
−0.958808 | + | 0.284055i | \(0.908320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −648.000 | − | 1122.37i | −0.0800972 | − | 0.138732i | ||||
\(404\) | −2664.00 | + | 4614.18i | −0.328067 | + | 0.568228i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8100.00 | −0.986492 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3762.00 | + | 6515.98i | 0.454814 | + | 0.787761i | 0.998677 | − | 0.0514127i | \(-0.0163724\pi\) |
−0.543863 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(410\) | −9720.00 | − | 16835.5i | −1.17082 | − | 2.02792i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2016.00 | −0.241071 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −324.000 | + | 561.184i | −0.0383242 | + | 0.0663794i | ||||
\(416\) | 4608.00 | + | 7981.29i | 0.543091 | + | 0.940661i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7200.00 | + | 12470.8i | −0.842496 | + | 1.45925i | ||||
\(419\) | 3852.00 | 0.449123 | 0.224561 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224561 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10402.0 | 1.20419 | 0.602093 | − | 0.798426i | \(-0.294334\pi\) | ||||
0.602093 | + | 0.798426i | \(0.294334\pi\) | |||||||
\(422\) | 5832.00 | − | 10101.3i | 0.672742 | − | 1.16522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12537.0 | − | 21714.7i | 1.43090 | − | 2.47840i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5360.00 | −0.605340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11664.0 | + | 20202.6i | 1.30811 | + | 2.26572i | ||||
\(431\) | −5195.00 | − | 8998.00i | −0.580590 | − | 1.00561i | −0.995409 | − | 0.0957078i | \(-0.969489\pi\) |
0.414819 | − | 0.909904i | \(-0.363845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11232.0 | 1.24659 | 0.623297 | − | 0.781985i | \(-0.285793\pi\) | ||||
0.623297 | + | 0.781985i | \(0.285793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −648.000 | + | 1122.37i | −0.0711779 | + | 0.123284i | ||||
\(437\) | −504.000 | − | 872.954i | −0.0551707 | − | 0.0955584i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7308.00 | + | 12657.8i | −0.794514 | + | 1.37614i | 0.128633 | + | 0.991692i | \(0.458941\pi\) |
−0.923147 | + | 0.384447i | \(0.874392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18144.0 | −1.95254 | ||||||||
\(443\) | 5969.00 | − | 10338.6i | 0.640171 | − | 1.10881i | −0.345223 | − | 0.938521i | \(-0.612197\pi\) |
0.985394 | − | 0.170288i | \(-0.0544698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2106.00 | − | 3647.70i | −0.224346 | − | 0.388579i | ||||
\(446\) | −2160.00 | + | 3741.23i | −0.229325 | + | 0.397203i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8186.00 | −0.860404 | −0.430202 | − | 0.902733i | \(-0.641558\pi\) | ||||
−0.430202 | + | 0.902733i | \(0.641558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6750.00 | − | 11691.3i | −0.704756 | − | 1.22067i | ||||
\(452\) | −5560.00 | − | 9630.20i | −0.578585 | − | 1.00214i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5328.00 | −0.550783 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1053.00 | + | 1823.85i | −0.107784 | + | 0.186687i | −0.914872 | − | 0.403744i | \(-0.867709\pi\) |
0.807088 | + | 0.590431i | \(0.201042\pi\) | |||||||
\(458\) | 3240.00 | + | 5611.84i | 0.330557 | + | 0.572542i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1008.00 | + | 1745.91i | −0.102170 | + | 0.176964i | ||||
\(461\) | −9486.00 | −0.958367 | −0.479183 | − | 0.877715i | \(-0.659067\pi\) | ||||
−0.479183 | + | 0.877715i | \(0.659067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12652.0 | −1.26995 | −0.634977 | − | 0.772531i | \(-0.718990\pi\) | ||||
−0.634977 | + | 0.772531i | \(0.718990\pi\) | |||||||
\(464\) | −5056.00 | + | 8757.25i | −0.505860 | + | 0.876175i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13436.0 | − | 23271.8i | −1.33565 | − | 2.31341i | ||||
\(467\) | −1854.00 | + | 3211.22i | −0.183711 | + | 0.318196i | −0.943141 | − | 0.332392i | \(-0.892144\pi\) |
0.759431 | + | 0.650588i | \(0.225478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5184.00 | 0.508766 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8100.00 | + | 14029.6i | 0.787396 | + | 1.36381i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14328.0 | −1.38403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7156.00 | − | 12394.6i | 0.684744 | − | 1.18601i | ||||
\(479\) | −4032.00 | − | 6983.63i | −0.384607 | − | 0.666159i | 0.607108 | − | 0.794620i | \(-0.292330\pi\) |
−0.991715 | + | 0.128461i | \(0.958996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2916.00 | + | 5050.66i | −0.276420 | + | 0.478774i | ||||
\(482\) | 3024.00 | 0.285766 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9352.00 | 0.878287 | ||||||||
\(485\) | 4212.00 | − | 7295.40i | 0.394344 | − | 0.683025i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5832.00 | + | 10101.3i | 0.542655 | + | 0.939907i | 0.998750 | + | 0.0499756i | \(0.0159143\pi\) |
−0.456095 | + | 0.889931i | \(0.650752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9814.00 | 0.902036 | 0.451018 | − | 0.892515i | \(-0.351061\pi\) | ||||
0.451018 | + | 0.892515i | \(0.351061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9954.00 | − | 17240.8i | −0.909342 | − | 1.57503i | ||||
\(494\) | 5184.00 | + | 8978.95i | 0.472144 | + | 0.817778i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2304.00 | 0.208574 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7614.00 | − | 13187.8i | 0.683065 | − | 1.18310i | −0.290976 | − | 0.956730i | \(-0.593980\pi\) |
0.974041 | − | 0.226373i | \(-0.0726868\pi\) | |||||||
\(500\) | 5328.00 | + | 9228.37i | 0.476551 | + | 0.825410i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13032.0 | − | 22572.1i | 1.15866 | − | 2.00686i | ||||
\(503\) | 11088.0 | 0.982882 | 0.491441 | − | 0.870911i | \(-0.336470\pi\) | ||||
0.491441 | + | 0.870911i | \(0.336470\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11988.0 | −1.05635 | ||||||||
\(506\) | −1400.00 | + | 2424.87i | −0.122999 | + | 0.213041i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3664.00 | − | 6346.23i | −0.320007 | − | 0.554269i | ||||
\(509\) | −2907.00 | + | 5035.07i | −0.253144 | + | 0.438459i | −0.964390 | − | 0.264485i | \(-0.914798\pi\) |
0.711245 | + | 0.702944i | \(0.248131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16384.0 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12060.0 | + | 20888.5i | 1.03491 | + | 1.79252i | ||||
\(515\) | −2268.00 | − | 3928.29i | −0.194058 | − | 0.336119i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3600.00 | 0.306243 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5841.00 | − | 10116.9i | −0.491169 | − | 0.850729i | 0.508780 | − | 0.860897i | \(-0.330097\pi\) |
−0.999948 | + | 0.0101677i | \(0.996763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1494.00 | − | 2587.68i | 0.124910 | − | 0.216351i | −0.796788 | − | 0.604259i | \(-0.793469\pi\) |
0.921698 | + | 0.387909i | \(0.126802\pi\) | |||||||
\(524\) | −18144.0 | −1.51264 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2360.00 | 0.195629 | ||||||||
\(527\) | −2268.00 | + | 3928.29i | −0.187468 | + | 0.324704i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5985.50 | + | 10367.2i | 0.491945 | + | 0.852074i | ||||
\(530\) | −792.000 | + | 1371.78i | −0.0649100 | + | 0.112427i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9720.00 | −0.789906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6030.00 | − | 10444.3i | −0.487289 | − | 0.844009i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3960.00 | −0.317338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3565.00 | + | 6174.76i | −0.283311 | + | 0.490709i | −0.972198 | − | 0.234159i | \(-0.924766\pi\) |
0.688887 | + | 0.724869i | \(0.258100\pi\) | |||||||
\(542\) | −6840.00 | − | 11847.2i | −0.542072 | − | 0.938897i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16128.0 | − | 27934.5i | 1.27111 | − | 2.20162i | ||||
\(545\) | −2916.00 | −0.229188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5488.00 | −0.428976 | −0.214488 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214488 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(548\) | 3224.00 | − | 5584.13i | 0.251318 | − | 0.435296i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19900.0 | + | 34467.8i | 1.54280 | + | 2.67220i | ||||
\(551\) | −5688.00 | + | 9851.90i | −0.439777 | + | 0.761716i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10936.0 | 0.838675 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10512.0 | − | 18207.3i | −0.801813 | − | 1.38878i | ||||
\(557\) | 2873.00 | + | 4976.18i | 0.218551 | + | 0.378541i | 0.954365 | − | 0.298642i | \(-0.0965337\pi\) |
−0.735814 | + | 0.677183i | \(0.763200\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11664.0 | 0.882531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1196.00 | + | 2071.53i | −0.0897691 | + | 0.155485i | ||||
\(563\) | 6534.00 | + | 11317.2i | 0.489121 | + | 0.847183i | 0.999922 | − | 0.0125165i | \(-0.00398422\pi\) |
−0.510800 | + | 0.859699i | \(0.670651\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12510.0 | − | 21668.0i | 0.931504 | − | 1.61341i | ||||
\(566\) | −14400.0 | −1.06939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −565.000 | + | 978.609i | −0.0416275 | + | 0.0721009i | −0.886088 | − | 0.463516i | \(-0.846588\pi\) |
0.844461 | + | 0.535617i | \(0.179921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8432.00 | − | 14604.7i | −0.617983 | − | 1.07038i | −0.989853 | − | 0.142093i | \(-0.954617\pi\) |
0.371870 | − | 0.928285i | \(-0.378717\pi\) | |||||||
\(572\) | 7200.00 | − | 12470.8i | 0.526306 | − | 0.911589i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2786.00 | −0.202060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1044.00 | + | 1808.26i | 0.0753246 | + | 0.130466i | 0.901227 | − | 0.433347i | \(-0.142667\pi\) |
−0.825903 | + | 0.563813i | \(0.809334\pi\) | |||||||
\(578\) | 21926.0 | + | 37976.9i | 1.57786 | + | 2.73293i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22752.0 | 1.62884 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −550.000 | + | 952.628i | −0.0390715 | + | 0.0676738i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15804.0 | + | 27373.3i | −1.11409 | + | 1.92966i | ||||
\(587\) | −10260.0 | −0.721423 | −0.360712 | − | 0.932677i | \(-0.617466\pi\) | ||||
−0.360712 | + | 0.932677i | \(0.617466\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2592.00 | 0.181327 | ||||||||
\(590\) | 16848.0 | − | 29181.6i | 1.17563 | − | 2.03625i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5184.00 | − | 8978.95i | −0.359900 | − | 0.623366i | ||||
\(593\) | 1791.00 | − | 3102.10i | 0.124026 | − | 0.214820i | −0.797326 | − | 0.603549i | \(-0.793753\pi\) |
0.921352 | + | 0.388730i | \(0.127086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19120.0 | 1.31407 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1008.00 | + | 1745.91i | 0.0689301 | + | 0.119390i | ||||
\(599\) | 3517.00 | + | 6091.62i | 0.239901 | + | 0.415521i | 0.960686 | − | 0.277638i | \(-0.0895517\pi\) |
−0.720785 | + | 0.693159i | \(0.756218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18072.0 | −1.22658 | −0.613288 | − | 0.789859i | \(-0.710154\pi\) | ||||
−0.613288 | + | 0.789859i | \(0.710154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12960.0 | + | 22447.4i | −0.873071 | + | 1.51220i | ||||
\(605\) | 10521.0 | + | 18222.9i | 0.707007 | + | 1.22457i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14292.0 | + | 24754.5i | −0.955674 | + | 1.65528i | −0.222857 | + | 0.974851i | \(0.571538\pi\) |
−0.732817 | + | 0.680426i | \(0.761795\pi\) | |||||||
\(608\) | −18432.0 | −1.22947 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 57024.0 | 3.78497 | ||||||||
\(611\) | 1296.00 | − | 2244.74i | 0.0858110 | − | 0.148629i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5455.00 | + | 9448.34i | 0.359421 | + | 0.622536i | 0.987864 | − | 0.155320i | \(-0.0496407\pi\) |
−0.628443 | + | 0.777856i | \(0.716307\pi\) | |||||||
\(614\) | −20448.0 | + | 35417.0i | −1.34400 | + | 2.32787i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5522.00 | 0.360304 | 0.180152 | − | 0.983639i | \(-0.442341\pi\) | ||||
0.180152 | + | 0.983639i | \(0.442341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1206.00 | − | 2088.85i | −0.0783089 | − | 0.135635i | 0.824211 | − | 0.566282i | \(-0.191619\pi\) |
−0.902520 | + | 0.430647i | \(0.858285\pi\) | |||||||
\(620\) | −2592.00 | − | 4489.48i | −0.167899 | − | 0.290809i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15552.0 | 1.00254 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 449.500 | − | 778.557i | 0.0287680 | − | 0.0498276i | ||||
\(626\) | 10224.0 | + | 17708.5i | 0.652769 | + | 1.13063i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12096.0 | + | 20950.9i | −0.768603 | + | 1.33126i | ||||
\(629\) | 20412.0 | 1.29393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24676.0 | 1.55679 | 0.778396 | − | 0.627773i | \(-0.216034\pi\) | ||||
0.778396 | + | 0.627773i | \(0.216034\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20204.0 | + | 34994.4i | 1.26562 | + | 2.19212i | ||||
\(635\) | 8244.00 | − | 14279.0i | 0.515202 | − | 0.892356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31600.0 | 1.96090 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13741.0 | − | 23800.1i | −0.846703 | − | 1.46653i | −0.884134 | − | 0.467234i | \(-0.845251\pi\) |
0.0374303 | − | 0.999299i | \(-0.488083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22752.0 | −1.39541 | −0.697707 | − | 0.716383i | \(-0.745796\pi\) | ||||
−0.697707 | + | 0.716383i | \(0.745796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18144.0 | − | 31426.3i | 1.10506 | − | 1.91401i | ||||
\(647\) | 7416.00 | + | 12844.9i | 0.450623 | + | 0.780502i | 0.998425 | − | 0.0561063i | \(-0.0178686\pi\) |
−0.547802 | + | 0.836608i | \(0.684535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11700.0 | − | 20265.0i | 0.707650 | − | 1.22569i | ||||
\(650\) | 28656.0 | 1.72920 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14272.0 | −0.857262 | ||||||||
\(653\) | 1411.00 | − | 2443.92i | 0.0845585 | − | 0.146460i | −0.820645 | − | 0.571439i | \(-0.806385\pi\) |
0.905203 | + | 0.424979i | \(0.139719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20412.0 | − | 35354.6i | −1.21765 | − | 2.10904i | ||||
\(656\) | 8640.00 | − | 14964.9i | 0.514231 | − | 0.890674i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15826.0 | 0.935498 | 0.467749 | − | 0.883861i | \(-0.345065\pi\) | ||||
0.467749 | + | 0.883861i | \(0.345065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11916.0 | + | 20639.1i | 0.701178 | + | 1.21448i | 0.968053 | + | 0.250745i | \(0.0806755\pi\) |
−0.266875 | + | 0.963731i | \(0.585991\pi\) | |||||||
\(662\) | 11016.0 | + | 19080.3i | 0.646751 | + | 1.12021i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1106.00 | + | 1915.65i | −0.0642046 | + | 0.111206i | ||||
\(668\) | −12096.0 | − | 20950.9i | −0.700611 | − | 1.21349i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8352.00 | + | 14466.1i | −0.481591 | + | 0.834140i | ||||
\(671\) | 39600.0 | 2.27830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13770.0 | 0.788699 | 0.394350 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394350 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(674\) | −18468.0 | + | 31987.5i | −1.05543 | + | 1.82806i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3604.00 | + | 6242.31i | 0.205052 | + | 0.355161i | ||||
\(677\) | 4167.00 | − | 7217.46i | 0.236560 | − | 0.409733i | −0.723165 | − | 0.690675i | \(-0.757313\pi\) |
0.959725 | + | 0.280942i | \(0.0906468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3600.00 | − | 6235.38i | −0.202128 | − | 0.350096i | ||||
\(683\) | −9299.00 | − | 16106.3i | −0.520961 | − | 0.902331i | −0.999703 | − | 0.0243752i | \(-0.992240\pi\) |
0.478742 | − | 0.877956i | \(-0.341093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14508.0 | 0.809229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10368.0 | + | 17957.9i | −0.574529 | + | 0.995114i | ||||
\(689\) | 396.000 | + | 685.892i | 0.0218961 | + | 0.0379251i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4482.00 | + | 7763.05i | −0.246749 | + | 0.427381i | −0.962622 | − | 0.270849i | \(-0.912696\pi\) |
0.715873 | + | 0.698230i | \(0.246029\pi\) | |||||||
\(692\) | −12528.0 | −0.688213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25976.0 | −1.42080 | ||||||||
\(695\) | 23652.0 | − | 40966.5i | 1.29089 | − | 2.23589i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17010.0 | + | 29462.2i | 0.924390 | + | 1.60109i | ||||
\(698\) | 20160.0 | − | 34918.1i | 1.09322 | − | 1.89351i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3542.00 | −0.190841 | −0.0954205 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954205 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5832.00 | − | 10101.3i | −0.312885 | − | 0.541932i | ||||
\(704\) | 12800.0 | + | 22170.3i | 0.685253 | + | 1.18689i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2952.00 | −0.157365 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 243.000 | − | 420.888i | 0.0128717 | − | 0.0222945i | −0.859518 | − | 0.511106i | \(-0.829236\pi\) |
0.872390 | + | 0.488811i | \(0.162569\pi\) | |||||||
\(710\) | −26424.0 | − | 45767.7i | −1.39673 | − | 2.41920i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 504.000 | 0.0264726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32400.0 | 1.69467 | ||||||||
\(716\) | 15208.0 | − | 26341.0i | 0.793784 | − | 1.37487i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −388.000 | − | 672.036i | −0.0201672 | − | 0.0349306i | ||||
\(719\) | −13464.0 | + | 23320.3i | −0.698362 | + | 1.20960i | 0.270672 | + | 0.962672i | \(0.412754\pi\) |
−0.969034 | + | 0.246927i | \(0.920579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6700.00 | 0.345358 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1872.00 | + | 3242.40i | 0.0960944 | + | 0.166440i | ||||
\(725\) | 15721.0 | + | 27229.6i | 0.805329 | + | 1.39487i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20628.0 | 1.05234 | 0.526169 | − | 0.850380i | \(-0.323628\pi\) | ||||
0.526169 | + | 0.850380i | \(0.323628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6480.00 | + | 11223.7i | −0.328542 | + | 0.569051i | ||||
\(731\) | −20412.0 | − | 35354.6i | −1.03278 | − | 1.78883i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4878.00 | − | 8448.94i | 0.245802 | − | 0.425742i | −0.716555 | − | 0.697531i | \(-0.754282\pi\) |
0.962357 | + | 0.271789i | \(0.0876153\pi\) | |||||||
\(734\) | 19008.0 | 0.955856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3584.00 | −0.179495 | ||||||||
\(737\) | −5800.00 | + | 10045.9i | −0.289886 | + | 0.502097i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9532.00 | − | 16509.9i | −0.474479 | − | 0.821822i | 0.525094 | − | 0.851045i | \(-0.324030\pi\) |
−0.999573 | + | 0.0292221i | \(0.990697\pi\) | |||||||
\(740\) | −11664.0 | + | 20202.6i | −0.579429 | + | 1.00360i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3766.00 | 0.185950 | 0.0929752 | − | 0.995668i | \(-0.470362\pi\) | ||||
0.0929752 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21510.0 | + | 37256.4i | 1.05781 | + | 1.83217i | ||||
\(746\) | −4612.00 | − | 7988.22i | −0.226350 | − | 0.392050i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50400.0 | −2.46365 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5832.00 | − | 10101.3i | 0.283372 | − | 0.490815i | −0.688841 | − | 0.724913i | \(-0.741880\pi\) |
0.972213 | + | 0.234097i | \(0.0752134\pi\) | |||||||
\(752\) | 2304.00 | + | 3990.65i | 0.111726 | + | 0.193516i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11376.0 | − | 19703.8i | 0.549456 | − | 0.951685i | ||||
\(755\) | −58320.0 | −2.81123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34182.0 | −1.64117 | −0.820585 | − | 0.571524i | \(-0.806352\pi\) | ||||
−0.820585 | + | 0.571524i | \(0.806352\pi\) | |||||||
\(758\) | −14904.0 | + | 25814.5i | −0.714166 | + | 1.23697i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2367.00 | + | 4099.76i | −0.112751 | + | 0.195291i | −0.916879 | − | 0.399166i | \(-0.869300\pi\) |
0.804127 | + | 0.594457i | \(0.202633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3856.00 | −0.182598 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2304.00 | + | 3990.65i | 0.108677 | + | 0.188235i | ||||
\(767\) | −8424.00 | − | 14590.8i | −0.396575 | − | 0.686888i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30240.0 | −1.41805 | −0.709026 | − | 0.705182i | \(-0.750865\pi\) | ||||
−0.709026 | + | 0.705182i | \(0.750865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3240.00 | − | 5611.84i | 0.151049 | − | 0.261625i | ||||
\(773\) | 13851.0 | + | 23990.6i | 0.644484 | + | 1.11628i | 0.984421 | + | 0.175830i | \(0.0562609\pi\) |
−0.339937 | + | 0.940448i | \(0.610406\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3582.00 | − | 6204.21i | 0.166025 | − | 0.287563i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7576.00 | 0.349117 | ||||||||
\(779\) | 9720.00 | − | 16835.5i | 0.447054 | − | 0.774320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18350.0 | − | 31783.1i | −0.840736 | − | 1.45620i | ||||
\(782\) | 3528.00 | − | 6110.68i | 0.161331 | − | 0.279434i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54432.0 | −2.47486 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11322.0 | + | 19610.3i | 0.512815 | + | 0.888222i | 0.999890 | + | 0.0148617i | \(0.00473080\pi\) |
−0.487074 | + | 0.873361i | \(0.661936\pi\) | |||||||
\(788\) | −9848.00 | − | 17057.2i | −0.445204 | − | 0.771115i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16992.0 | 0.765251 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14256.0 | − | 24692.1i | 0.638393 | − | 1.10573i | ||||
\(794\) | 18432.0 | + | 31925.2i | 0.823838 | + | 1.42693i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18144.0 | − | 31426.3i | 0.807911 | − | 1.39934i | ||||
\(797\) | −30150.0 | −1.33998 | −0.669992 | − | 0.742368i | \(-0.733703\pi\) | ||||
−0.669992 | + | 0.742368i | \(0.733703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9072.00 | −0.401682 | ||||||||
\(800\) | −25472.0 | + | 44118.8i | −1.12571 | + | 1.94979i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23300.0 | + | 40356.8i | 1.02587 | + | 1.77687i | ||||
\(803\) | −4500.00 | + | 7794.23i | −0.197760 | + | 0.342531i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5184.00 | −0.226549 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5659.00 | − | 9801.68i | −0.245933 | − | 0.425969i | 0.716460 | − | 0.697628i | \(-0.245761\pi\) |
−0.962394 | + | 0.271659i | \(0.912428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29628.0 | −1.28284 | −0.641418 | − | 0.767192i | \(-0.721653\pi\) | ||||
−0.641418 | + | 0.767192i | \(0.721653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16200.0 | + | 28059.2i | −0.697555 | + | 1.20820i | ||||
\(815\) | −16056.0 | − | 27809.8i | −0.690082 | − | 1.19526i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11664.0 | + | 20202.6i | −0.499476 | + | 0.865117i | ||||
\(818\) | 30096.0 | 1.28641 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38880.0 | −1.65579 | ||||||||
\(821\) | 8885.00 | − | 15389.3i | 0.377696 | − | 0.654189i | −0.613030 | − | 0.790059i | \(-0.710050\pi\) |
0.990727 | + | 0.135870i | \(0.0433830\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3934.00 | − | 6813.89i | −0.166623 | − | 0.288599i | 0.770608 | − | 0.637310i | \(-0.219953\pi\) |
−0.937230 | + | 0.348711i | \(0.886620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35726.0 | −1.50219 | −0.751097 | − | 0.660192i | \(-0.770475\pi\) | ||||
−0.751097 | + | 0.660192i | \(0.770475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13554.0 | − | 23476.2i | −0.567853 | − | 0.983550i | −0.996778 | − | 0.0802098i | \(-0.974441\pi\) |
0.428925 | − | 0.903340i | \(-0.358892\pi\) | |||||||
\(830\) | 1296.00 | + | 2244.74i | 0.0541986 | + | 0.0938747i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18432.0 | 0.768046 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27216.0 | − | 47139.5i | 1.12796 | − | 1.95369i | ||||
\(836\) | 14400.0 | + | 24941.5i | 0.595735 | + | 1.03184i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7704.00 | − | 13343.7i | 0.317578 | − | 0.550061i | ||||
\(839\) | −23256.0 | −0.956956 | −0.478478 | − | 0.878099i | \(-0.658811\pi\) | ||||
−0.478478 | + | 0.878099i | \(0.658811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 575.000 | 0.0235762 | ||||||||
\(842\) | 20804.0 | − | 36033.6i | 0.851488 | − | 1.47482i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11664.0 | − | 20202.6i | −0.475701 | − | 0.823938i | ||||
\(845\) | −8109.00 | + | 14045.2i | −0.330128 | + | 0.571798i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1408.00 | −0.0570176 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −50148.0 | − | 86858.9i | −2.02360 | − | 3.50498i | ||||
\(851\) | −1134.00 | − | 1964.15i | −0.0456792 | − | 0.0791187i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35280.0 | 1.41614 | 0.708068 | − | 0.706144i | \(-0.249567\pi\) | ||||
0.708068 | + | 0.706144i | \(0.249567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9855.00 | − | 17069.4i | −0.392813 | − | 0.680371i | 0.600007 | − | 0.799995i | \(-0.295165\pi\) |
−0.992819 | + | 0.119624i | \(0.961831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1944.00 | + | 3367.11i | −0.0772159 | + | 0.133742i | −0.902048 | − | 0.431636i | \(-0.857936\pi\) |
0.824832 | + | 0.565378i | \(0.191270\pi\) | |||||||
\(860\) | 46656.0 | 1.84995 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41560.0 | −1.64216 | ||||||||
\(863\) | −18317.0 | + | 31726.0i | −0.722500 | + | 1.25141i | 0.237494 | + | 0.971389i | \(0.423674\pi\) |
−0.959995 | + | 0.280019i | \(0.909659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14094.0 | − | 24411.5i | −0.554000 | − | 0.959557i | ||||
\(866\) | 22464.0 | − | 38908.8i | 0.881476 | − | 1.52676i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11800.0 | 0.460630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4176.00 | + | 7233.04i | 0.162455 | + | 0.281380i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4032.00 | −0.156046 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −613.000 | + | 1061.75i | −0.0236027 | + | 0.0408810i | −0.877585 | − | 0.479420i | \(-0.840847\pi\) |
0.853983 | + | 0.520301i | \(0.174180\pi\) | |||||||
\(878\) | 29232.0 | + | 50631.3i | 1.12361 | + | 1.94615i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −28800.0 | + | 49883.1i | −1.10324 | + | 1.91086i | ||||
\(881\) | 38538.0 | 1.47376 | 0.736878 | − | 0.676026i | \(-0.236299\pi\) | ||||
0.736878 | + | 0.676026i | \(0.236299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37260.0 | −1.42004 | −0.710022 | − | 0.704180i | \(-0.751315\pi\) | ||||
−0.710022 | + | 0.704180i | \(0.751315\pi\) | |||||||
\(884\) | −18144.0 | + | 31426.3i | −0.690327 | + | 1.19568i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23876.0 | − | 41354.4i | −0.905338 | − | 1.56809i | ||||
\(887\) | 13320.0 | − | 23070.9i | 0.504219 | − | 0.873332i | −0.495770 | − | 0.868454i | \(-0.665114\pi\) |
0.999988 | − | 0.00487800i | \(-0.00155272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16848.0 | −0.634546 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4320.00 | + | 7482.46i | 0.162157 | + | 0.280865i | ||||
\(893\) | 2592.00 | + | 4489.48i | 0.0971310 | + | 0.168236i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68436.0 | 2.55594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16372.0 | + | 28357.1i | −0.608397 | + | 1.05377i | ||||
\(899\) | −2844.00 | − | 4925.95i | −0.105509 | − | 0.182747i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1386.00 | − | 2400.62i | 0.0512479 | − | 0.0887640i | ||||
\(902\) | −54000.0 | −1.99335 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4212.00 | + | 7295.40i | −0.154709 | + | 0.267964i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6318.00 | + | 10943.1i | 0.231296 | + | 0.400617i | 0.958190 | − | 0.286133i | \(-0.0923700\pi\) |
−0.726894 | + | 0.686750i | \(0.759037\pi\) | |||||||
\(908\) | −5328.00 | + | 9228.37i | −0.194731 | + | 0.337284i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33638.0 | 1.22336 | 0.611678 | − | 0.791107i | \(-0.290495\pi\) | ||||
0.611678 | + | 0.791107i | \(0.290495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 900.000 | + | 1558.85i | 0.0326239 | + | 0.0565063i | ||||
\(914\) | 4212.00 | + | 7295.40i | 0.152430 | + | 0.264016i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12960.0 | 0.467479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18468.0 | + | 31987.5i | −0.662898 | + | 1.14817i | 0.316953 | + | 0.948441i | \(0.397340\pi\) |
−0.979851 | + | 0.199731i | \(0.935993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18972.0 | + | 32860.5i | −0.677668 | + | 1.17375i | ||||
\(923\) | −26424.0 | −0.942315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32238.0 | −1.14592 | ||||||||
\(926\) | −25304.0 | + | 43827.8i | −0.897992 | + | 1.55537i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20224.0 | + | 35029.0i | 0.715394 | + | 1.23910i | ||||
\(929\) | −11151.0 | + | 19314.1i | −0.393813 | + | 0.682104i | −0.992949 | − | 0.118543i | \(-0.962178\pi\) |
0.599136 | + | 0.800647i | \(0.295511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −53744.0 | −1.88889 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7416.00 | + | 12844.9i | 0.259806 | + | 0.449997i | ||||
\(935\) | −56700.0 | − | 98207.3i | −1.98320 | − | 3.43500i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13824.0 | 0.481975 | 0.240987 | − | 0.970528i | \(-0.422529\pi\) | ||||
0.240987 | + | 0.970528i | \(0.422529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5184.00 | − | 8978.95i | 0.179876 | − | 0.311554i | ||||
\(941\) | 6777.00 | + | 11738.1i | 0.234776 | + | 0.406643i | 0.959207 | − | 0.282703i | \(-0.0912311\pi\) |
−0.724432 | + | 0.689346i | \(0.757898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1890.00 | − | 3273.58i | 0.0652671 | − | 0.113046i | ||||
\(944\) | 29952.0 | 1.03268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64800.0 | 2.22709 | ||||||||
\(947\) | 22439.0 | − | 38865.5i | 0.769978 | − | 1.33364i | −0.167596 | − | 0.985856i | \(-0.553600\pi\) |
0.937574 | − | 0.347786i | \(-0.113066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3240.00 | + | 5611.84i | 0.110827 | + | 0.191958i | ||||
\(950\) | −28656.0 | + | 49633.6i | −0.978656 | + | 1.69508i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38362.0 | −1.30395 | −0.651976 | − | 0.758239i | \(-0.726060\pi\) | ||||
−0.651976 | + | 0.758239i | \(0.726060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4338.00 | − | 7513.64i | −0.146989 | − | 0.254592i | ||||
\(956\) | −14312.0 | − | 24789.1i | −0.484187 | − | 0.838637i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32256.0 | −1.08783 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14247.5 | − | 24677.4i | 0.478248 | − | 0.828351i | ||||
\(962\) | 11664.0 | + | 20202.6i | 0.390917 | + | 0.677089i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3024.00 | − | 5237.72i | 0.101034 | − | 0.174995i | ||||
\(965\) | 14580.0 | 0.486370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26444.0 | 0.879402 | 0.439701 | − | 0.898144i | \(-0.355084\pi\) | ||||
0.439701 | + | 0.898144i | \(0.355084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16848.0 | − | 29181.6i | −0.557687 | − | 0.965943i | ||||
\(971\) | 8910.00 | − | 15432.6i | 0.294475 | − | 0.510046i | −0.680387 | − | 0.732853i | \(-0.738188\pi\) |
0.974863 | + | 0.222806i | \(0.0715218\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 46656.0 | 1.53486 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25344.0 | + | 43897.1i | 0.831190 | + | 1.43966i | ||||
\(977\) | 17219.0 | + | 29824.2i | 0.563853 | + | 0.976622i | 0.997155 | + | 0.0753737i | \(0.0240150\pi\) |
−0.433302 | + | 0.901249i | \(0.642652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11700.0 | −0.381955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19628.0 | − | 33996.7i | 0.637836 | − | 1.10476i | ||||
\(983\) | 13032.0 | + | 22572.1i | 0.422845 | + | 0.732388i | 0.996216 | − | 0.0869069i | \(-0.0276983\pi\) |
−0.573372 | + | 0.819295i | \(0.694365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22158.0 | − | 38378.8i | 0.716764 | − | 1.24147i | ||||
\(986\) | −79632.0 | −2.57201 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20736.0 | 0.667713 | ||||||||
\(989\) | −2268.00 | + | 3928.29i | −0.0729203 | + | 0.126302i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16848.0 | − | 29181.6i | −0.540055 | − | 0.935402i | −0.998900 | − | 0.0468863i | \(-0.985070\pi\) |
0.458845 | − | 0.888516i | \(-0.348263\pi\) | |||||||
\(992\) | 4608.00 | − | 7981.29i | 0.147484 | − | 0.255450i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 81648.0 | 2.60142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18036.0 | − | 31239.3i | −0.572925 | − | 0.992335i | −0.996264 | − | 0.0863632i | \(-0.972475\pi\) |
0.423339 | − | 0.905971i | \(-0.360858\pi\) | |||||||
\(998\) | −30456.0 | − | 52751.3i | −0.966000 | − | 1.67316i | ||||
\(999\) | 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 | 441.4.e.o.226.1 | 2 | ||
3.2 | odd | 2 | 147.4.e.a.79.1 | 2 | |||
7.2 | even | 3 | 441.4.a.a.1.1 | 1 | |||
7.3 | odd | 6 | 441.4.e.l.361.1 | 2 | |||
7.4 | even | 3 | inner | 441.4.e.o.361.1 | 2 | ||
7.5 | odd | 6 | 441.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 441.4.e.l.226.1 | 2 | |||
21.2 | odd | 6 | 147.4.a.h.1.1 | yes | 1 | ||
21.5 | even | 6 | 147.4.a.f.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 147.4.e.a.67.1 | 2 | |||
21.17 | even | 6 | 147.4.e.d.67.1 | 2 | |||
21.20 | even | 2 | 147.4.e.d.79.1 | 2 | |||
84.23 | even | 6 | 2352.4.a.s.1.1 | 1 | |||
84.47 | odd | 6 | 2352.4.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.f.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
147.4.a.h.1.1 | yes | 1 | 21.2 | odd | 6 | ||
147.4.e.a.67.1 | 2 | 21.11 | odd | 6 | |||
147.4.e.a.79.1 | 2 | 3.2 | odd | 2 | |||
147.4.e.d.67.1 | 2 | 21.17 | even | 6 | |||
147.4.e.d.79.1 | 2 | 21.20 | even | 2 | |||
441.4.a.a.1.1 | 1 | 7.2 | even | 3 | |||
441.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
441.4.e.l.226.1 | 2 | 7.6 | odd | 2 | |||
441.4.e.l.361.1 | 2 | 7.3 | odd | 6 | |||
441.4.e.o.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.o.361.1 | 2 | 7.4 | even | 3 | inner | ||
2352.4.a.s.1.1 | 1 | 84.23 | even | 6 | |||
2352.4.a.t.1.1 | 1 | 84.47 | odd | 6 |