Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(8.67328077084\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.4.e.d.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −4.00000 | + | 6.92820i | −0.500000 | + | 0.866025i | ||||
\(5\) | 9.00000 | + | 15.5885i | 0.804984 | + | 1.39427i | 0.916302 | + | 0.400489i | \(0.131160\pi\) |
−0.111317 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(6\) | −12.0000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 36.0000 | − | 62.3538i | 1.13842 | − | 1.97180i | ||||
\(11\) | 25.0000 | − | 43.3013i | 0.685253 | − | 1.18689i | −0.288104 | − | 0.957599i | \(-0.593025\pi\) |
0.973357 | − | 0.229294i | \(-0.0736417\pi\) | |||||||
\(12\) | 12.0000 | + | 20.7846i | 0.288675 | + | 0.500000i | ||||
\(13\) | 36.0000 | 0.768046 | 0.384023 | − | 0.923323i | \(-0.374538\pi\) | ||||
0.384023 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000 | 0.929516 | ||||||||
\(16\) | 32.0000 | + | 55.4256i | 0.500000 | + | 0.866025i | ||||
\(17\) | 63.0000 | − | 109.119i | 0.898808 | − | 1.55678i | 0.0697893 | − | 0.997562i | \(-0.477767\pi\) |
0.829019 | − | 0.559220i | \(-0.188899\pi\) | |||||||
\(18\) | −18.0000 | + | 31.1769i | −0.235702 | + | 0.408248i | ||||
\(19\) | −36.0000 | − | 62.3538i | −0.434682 | − | 0.752892i | 0.562587 | − | 0.826738i | \(-0.309806\pi\) |
−0.997270 | + | 0.0738459i | \(0.976473\pi\) | |||||||
\(20\) | −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 | \(-0.186880\pi\) |
−0.896010 | + | 0.444033i | \(0.853547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | + | 172.339i | −0.796000 | + | 1.37871i | ||||
\(26\) | −72.0000 | − | 124.708i | −0.543091 | − | 0.940661i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.000 | 1.01172 | 0.505860 | − | 0.862616i | \(-0.331175\pi\) | ||||
0.505860 | + | 0.862616i | \(0.331175\pi\) | |||||||
\(30\) | −108.000 | − | 187.061i | −0.657267 | − | 1.13842i | ||||
\(31\) | −18.0000 | + | 31.1769i | −0.104287 | + | 0.180630i | −0.913447 | − | 0.406958i | \(-0.866589\pi\) |
0.809160 | + | 0.587589i | \(0.199923\pi\) | |||||||
\(32\) | 128.000 | − | 221.703i | 0.707107 | − | 1.22474i | ||||
\(33\) | −75.0000 | − | 129.904i | −0.395631 | − | 0.685253i | ||||
\(34\) | −504.000 | −2.54221 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 72.0000 | 0.333333 | ||||||||
\(37\) | 81.0000 | + | 140.296i | 0.359900 | + | 0.623366i | 0.987944 | − | 0.154812i | \(-0.0494773\pi\) |
−0.628043 | + | 0.778178i | \(0.716144\pi\) | |||||||
\(38\) | −144.000 | + | 249.415i | −0.614734 | + | 1.06475i | ||||
\(39\) | 54.0000 | − | 93.5307i | 0.221716 | − | 0.384023i | ||||
\(40\) | 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 | ||||
\(45\) | 81.0000 | − | 140.296i | 0.268328 | − | 0.464758i | ||||
\(46\) | −28.0000 | + | 48.4974i | −0.0897473 | + | 0.155447i | ||||
\(47\) | −36.0000 | − | 62.3538i | −0.111726 | − | 0.193516i | 0.804740 | − | 0.593627i | \(-0.202305\pi\) |
−0.916466 | + | 0.400112i | \(0.868971\pi\) | |||||||
\(48\) | 192.000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 796.000 | 2.25143 | ||||||||
\(51\) | −189.000 | − | 327.358i | −0.518927 | − | 0.898808i | ||||
\(52\) | −144.000 | + | 249.415i | −0.384023 | + | 0.665148i | ||||
\(53\) | 11.0000 | − | 19.0526i | 0.0285088 | − | 0.0493787i | −0.851419 | − | 0.524486i | \(-0.824257\pi\) |
0.879928 | + | 0.475107i | \(0.157591\pi\) | |||||||
\(54\) | 54.0000 | + | 93.5307i | 0.136083 | + | 0.235702i | ||||
\(55\) | 900.000 | 2.20647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −216.000 | −0.501928 | ||||||||
\(58\) | −316.000 | − | 547.328i | −0.715394 | − | 1.23910i | ||||
\(59\) | 234.000 | − | 405.300i | 0.516342 | − | 0.894331i | −0.483478 | − | 0.875357i | \(-0.660627\pi\) |
0.999820 | − | 0.0189746i | \(-0.00604016\pi\) | |||||||
\(60\) | −216.000 | + | 374.123i | −0.464758 | + | 0.804984i | ||||
\(61\) | 396.000 | + | 685.892i | 0.831190 | + | 1.43966i | 0.897095 | + | 0.441838i | \(0.145673\pi\) |
−0.0659047 | + | 0.997826i | \(0.520993\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 324.000 | + | 561.184i | 0.618265 | + | 1.07087i | ||||
\(66\) | −300.000 | + | 519.615i | −0.559507 | + | 0.969094i | ||||
\(67\) | −116.000 | + | 200.918i | −0.211517 | + | 0.366359i | −0.952190 | − | 0.305508i | \(-0.901174\pi\) |
0.740672 | + | 0.671866i | \(0.234507\pi\) | |||||||
\(68\) | 504.000 | + | 872.954i | 0.898808 | + | 1.55678i | ||||
\(69\) | −42.0000 | −0.0732783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −734.000 | −1.22690 | −0.613449 | − | 0.789734i | \(-0.710218\pi\) | ||||
−0.613449 | + | 0.789734i | \(0.710218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.0000 | − | 155.885i | 0.144297 | − | 0.249930i | −0.784813 | − | 0.619732i | \(-0.787241\pi\) |
0.929111 | + | 0.369802i | \(0.120575\pi\) | |||||||
\(74\) | 324.000 | − | 561.184i | 0.508976 | − | 0.881573i | ||||
\(75\) | 298.500 | + | 517.017i | 0.459571 | + | 0.796000i | ||||
\(76\) | 576.000 | 0.869365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −432.000 | −0.627107 | ||||||||
\(79\) | −118.000 | − | 204.382i | −0.168051 | − | 0.291073i | 0.769683 | − | 0.638426i | \(-0.220414\pi\) |
−0.937735 | + | 0.347353i | \(0.887081\pi\) | |||||||
\(80\) | −576.000 | + | 997.661i | −0.804984 | + | 1.39427i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −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 | ||||
\(87\) | 237.000 | − | 410.496i | 0.292058 | − | 0.505860i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 117.000 | + | 202.650i | 0.139348 | + | 0.241358i | 0.927250 | − | 0.374443i | \(-0.122166\pi\) |
−0.787902 | + | 0.615801i | \(0.788833\pi\) | |||||||
\(90\) | −648.000 | −0.758947 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 112.000 | 0.126922 | ||||||||
\(93\) | 54.0000 | + | 93.5307i | 0.0602101 | + | 0.104287i | ||||
\(94\) | −144.000 | + | 249.415i | −0.158005 | + | 0.273673i | ||||
\(95\) | 648.000 | − | 1122.37i | 0.699825 | − | 1.21213i | ||||
\(96\) | −384.000 | − | 665.108i | −0.408248 | − | 0.707107i | ||||
\(97\) | −468.000 | −0.489878 | −0.244939 | − | 0.969538i | \(-0.578768\pi\) | ||||
−0.244939 | + | 0.969538i | \(0.578768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −450.000 | −0.456835 | ||||||||
\(100\) | −796.000 | − | 1378.71i | −0.796000 | − | 1.37871i | ||||
\(101\) | −333.000 | + | 576.773i | −0.328067 | + | 0.568228i | −0.982128 | − | 0.188213i | \(-0.939730\pi\) |
0.654061 | + | 0.756441i | \(0.273064\pi\) | |||||||
\(102\) | −756.000 | + | 1309.43i | −0.733874 | + | 1.27111i | ||||
\(103\) | −126.000 | − | 218.238i | −0.120535 | − | 0.208773i | 0.799444 | − | 0.600741i | \(-0.205128\pi\) |
−0.919979 | + | 0.391968i | \(0.871794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −88.0000 | −0.0806351 | ||||||||
\(107\) | −335.000 | − | 580.237i | −0.302670 | − | 0.524240i | 0.674070 | − | 0.738668i | \(-0.264545\pi\) |
−0.976740 | + | 0.214428i | \(0.931211\pi\) | |||||||
\(108\) | 108.000 | − | 187.061i | 0.0962250 | − | 0.166667i | ||||
\(109\) | −81.0000 | + | 140.296i | −0.0711779 | + | 0.123284i | −0.899418 | − | 0.437090i | \(-0.856009\pi\) |
0.828240 | + | 0.560374i | \(0.189342\pi\) | |||||||
\(110\) | −1800.00 | − | 3117.69i | −1.56021 | − | 2.70237i | ||||
\(111\) | 486.000 | 0.415577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1390.00 | −1.15717 | −0.578585 | − | 0.815622i | \(-0.696395\pi\) | ||||
−0.578585 | + | 0.815622i | \(0.696395\pi\) | |||||||
\(114\) | 432.000 | + | 748.246i | 0.354917 | + | 0.614734i | ||||
\(115\) | 126.000 | − | 218.238i | 0.102170 | − | 0.176964i | ||||
\(116\) | −632.000 | + | 1094.66i | −0.505860 | + | 0.876175i | ||||
\(117\) | −162.000 | − | 280.592i | −0.128008 | − | 0.221716i | ||||
\(118\) | −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 | ||||
\(123\) | 405.000 | − | 701.481i | 0.296891 | − | 0.514231i | ||||
\(124\) | −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 | ||||||||
\(129\) | −486.000 | + | 841.777i | −0.331705 | + | 0.574529i | ||||
\(130\) | 1296.00 | − | 2244.74i | 0.874359 | − | 1.51443i | ||||
\(131\) | 1134.00 | + | 1964.15i | 0.756321 | + | 1.30999i | 0.944715 | + | 0.327893i | \(0.106338\pi\) |
−0.188394 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(132\) | 1200.00 | 0.791262 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 928.000 | 0.598261 | ||||||||
\(135\) | −243.000 | − | 420.888i | −0.154919 | − | 0.268328i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −403.000 | + | 698.016i | −0.251318 | + | 0.435296i | −0.963889 | − | 0.266304i | \(-0.914197\pi\) |
0.712571 | + | 0.701600i | \(0.247531\pi\) | |||||||
\(138\) | 84.0000 | + | 145.492i | 0.0518156 | + | 0.0897473i | ||||
\(139\) | −2628.00 | −1.60363 | −0.801813 | − | 0.597575i | \(-0.796131\pi\) | ||||
−0.801813 | + | 0.597575i | \(0.796131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −216.000 | −0.129011 | ||||||||
\(142\) | 1468.00 | + | 2542.65i | 0.867548 | + | 1.50264i | ||||
\(143\) | 900.000 | − | 1558.85i | 0.526306 | − | 0.911589i | ||||
\(144\) | 288.000 | − | 498.831i | 0.166667 | − | 0.288675i | ||||
\(145\) | 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 | 0.981379 | + | 0.192079i | \(0.0615230\pi\) |
−0.324344 | + | 0.945939i | \(0.605144\pi\) | |||||||
\(150\) | 1194.00 | − | 2068.07i | 0.649931 | − | 1.12571i | ||||
\(151\) | −1620.00 | + | 2805.92i | −0.873071 | + | 1.51220i | −0.0142676 | + | 0.999898i | \(0.504542\pi\) |
−0.858803 | + | 0.512305i | \(0.828792\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1134.00 | −0.599206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −648.000 | −0.335798 | ||||||||
\(156\) | 432.000 | + | 748.246i | 0.221716 | + | 0.384023i | ||||
\(157\) | 1512.00 | − | 2618.86i | 0.768603 | − | 1.33126i | −0.169717 | − | 0.985493i | \(-0.554285\pi\) |
0.938320 | − | 0.345767i | \(-0.112381\pi\) | |||||||
\(158\) | −472.000 | + | 817.528i | −0.237660 | + | 0.411639i | ||||
\(159\) | −33.0000 | − | 57.1577i | −0.0164596 | − | 0.0285088i | ||||
\(160\) | 4608.00 | 2.27684 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 324.000 | 0.157135 | ||||||||
\(163\) | 892.000 | + | 1544.99i | 0.428631 | + | 0.742410i | 0.996752 | − | 0.0805346i | \(-0.0256628\pi\) |
−0.568121 | + | 0.822945i | \(0.692329\pi\) | |||||||
\(164\) | −1080.00 | + | 1870.61i | −0.514231 | + | 0.890674i | ||||
\(165\) | 1350.00 | − | 2338.27i | 0.636954 | − | 1.10324i | ||||
\(166\) | 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 | ||||
\(171\) | −324.000 | + | 561.184i | −0.144894 | + | 0.250964i | ||||
\(172\) | 1296.00 | − | 2244.74i | 0.574529 | − | 0.995114i | ||||
\(173\) | 783.000 | + | 1356.20i | 0.344106 | + | 0.596010i | 0.985191 | − | 0.171461i | \(-0.0548486\pi\) |
−0.641085 | + | 0.767470i | \(0.721515\pi\) | |||||||
\(174\) | −1896.00 | −0.826065 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3200.00 | 1.37051 | ||||||||
\(177\) | −702.000 | − | 1215.90i | −0.298110 | − | 0.516342i | ||||
\(178\) | 468.000 | − | 810.600i | 0.197068 | − | 0.341332i | ||||
\(179\) | −1901.00 | + | 3292.63i | −0.793784 | + | 1.37487i | 0.129824 | + | 0.991537i | \(0.458559\pi\) |
−0.923608 | + | 0.383338i | \(0.874774\pi\) | |||||||
\(180\) | 648.000 | + | 1122.37i | 0.268328 | + | 0.464758i | ||||
\(181\) | 468.000 | 0.192189 | 0.0960944 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960944 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2376.00 | 0.959776 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1458.00 | + | 2525.33i | −0.579429 | + | 1.00360i | ||||
\(186\) | 216.000 | − | 374.123i | 0.0851499 | − | 0.147484i | ||||
\(187\) | −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 | \(-0.195769\pi\) |
−0.908058 | + | 0.418844i | \(0.862435\pi\) | |||||||
\(192\) | −768.000 | + | 1330.22i | −0.288675 | + | 0.500000i | ||||
\(193\) | 405.000 | − | 701.481i | 0.151049 | − | 0.261625i | −0.780564 | − | 0.625076i | \(-0.785068\pi\) |
0.931614 | + | 0.363450i | \(0.118401\pi\) | |||||||
\(194\) | 936.000 | + | 1621.20i | 0.346396 | + | 0.599976i | ||||
\(195\) | 1944.00 | 0.713911 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2462.00 | −0.890407 | −0.445204 | − | 0.895429i | \(-0.646869\pi\) | ||||
−0.445204 | + | 0.895429i | \(0.646869\pi\) | |||||||
\(198\) | 900.000 | + | 1558.85i | 0.323031 | + | 0.559507i | ||||
\(199\) | −2268.00 | + | 3928.29i | −0.807911 | + | 1.39934i | 0.106397 | + | 0.994324i | \(0.466068\pi\) |
−0.914308 | + | 0.405019i | \(0.867265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 348.000 | + | 602.754i | 0.122120 | + | 0.211517i | ||||
\(202\) | 2664.00 | 0.927913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3024.00 | 1.03785 | ||||||||
\(205\) | 2430.00 | + | 4208.88i | 0.827895 | + | 1.43396i | ||||
\(206\) | −504.000 | + | 872.954i | −0.170463 | + | 0.295250i | ||||
\(207\) | −63.0000 | + | 109.119i | −0.0211536 | + | 0.0366392i | ||||
\(208\) | 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 | ||||
\(213\) | −1101.00 | + | 1906.99i | −0.354175 | + | 0.613449i | ||||
\(214\) | −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 | ||||||||
\(219\) | −270.000 | − | 467.654i | −0.0833101 | − | 0.144297i | ||||
\(220\) | −3600.00 | + | 6235.38i | −1.10324 | + | 1.91086i | ||||
\(221\) | 2268.00 | − | 3928.29i | 0.690327 | − | 1.19568i | ||||
\(222\) | −972.000 | − | 1683.55i | −0.293858 | − | 0.508976i | ||||
\(223\) | 1080.00 | 0.324315 | 0.162157 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162157 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 2780.00 | + | 4815.10i | 0.818243 | + | 1.41724i | ||||
\(227\) | −666.000 | + | 1153.55i | −0.194731 | + | 0.337284i | −0.946812 | − | 0.321786i | \(-0.895717\pi\) |
0.752081 | + | 0.659070i | \(0.229050\pi\) | |||||||
\(228\) | 864.000 | − | 1496.49i | 0.250964 | − | 0.434682i | ||||
\(229\) | 810.000 | + | 1402.96i | 0.233739 | + | 0.404848i | 0.958906 | − | 0.283725i | \(-0.0915704\pi\) |
−0.725166 | + | 0.688574i | \(0.758237\pi\) | |||||||
\(230\) | −1008.00 | −0.288981 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3359.00 | − | 5817.96i | −0.944444 | − | 1.63582i | −0.756861 | − | 0.653576i | \(-0.773268\pi\) |
−0.187583 | − | 0.982249i | \(-0.560065\pi\) | |||||||
\(234\) | −648.000 | + | 1122.37i | −0.181030 | + | 0.313554i | ||||
\(235\) | 648.000 | − | 1122.37i | 0.179876 | − | 0.311554i | ||||
\(236\) | 1872.00 | + | 3242.40i | 0.516342 | + | 0.894331i | ||||
\(237\) | −708.000 | −0.194049 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3578.00 | −0.968375 | −0.484187 | − | 0.874964i | \(-0.660885\pi\) | ||||
−0.484187 | + | 0.874964i | \(0.660885\pi\) | |||||||
\(240\) | 1728.00 | + | 2992.98i | 0.464758 | + | 0.804984i | ||||
\(241\) | −378.000 | + | 654.715i | −0.101034 | + | 0.174995i | −0.912111 | − | 0.409944i | \(-0.865548\pi\) |
0.811077 | + | 0.584939i | \(0.198882\pi\) | |||||||
\(242\) | −2338.00 | + | 4049.53i | −0.621043 | + | 1.07568i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −6336.00 | −1.66238 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3240.00 | −0.839735 | ||||||||
\(247\) | −1296.00 | − | 2244.74i | −0.333856 | − | 0.578256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −54.0000 | + | 93.5307i | −0.0137434 | + | 0.0238043i | ||||
\(250\) | 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 | ||||
\(255\) | 3402.00 | − | 5892.44i | 0.835457 | − | 1.44705i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3015.00 | − | 5222.13i | −0.731792 | − | 1.26750i | −0.956117 | − | 0.292986i | \(-0.905351\pi\) |
0.224325 | − | 0.974514i | \(-0.427982\pi\) | |||||||
\(258\) | 3888.00 | 0.938203 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5184.00 | −1.23653 | ||||||||
\(261\) | −711.000 | − | 1231.49i | −0.168620 | − | 0.292058i | ||||
\(262\) | 4536.00 | − | 7856.58i | 1.06960 | − | 1.85260i | ||||
\(263\) | −295.000 | + | 510.955i | −0.0691653 | + | 0.119798i | −0.898534 | − | 0.438904i | \(-0.855367\pi\) |
0.829369 | + | 0.558702i | \(0.188700\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 396.000 | 0.0917966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 702.000 | 0.160905 | ||||||||
\(268\) | −928.000 | − | 1607.34i | −0.211517 | − | 0.366359i | ||||
\(269\) | −495.000 | + | 857.365i | −0.112196 | + | 0.194329i | −0.916655 | − | 0.399679i | \(-0.869122\pi\) |
0.804459 | + | 0.594008i | \(0.202455\pi\) | |||||||
\(270\) | −972.000 | + | 1683.55i | −0.219089 | + | 0.379473i | ||||
\(271\) | −1710.00 | − | 2961.81i | −0.383303 | − | 0.663900i | 0.608229 | − | 0.793761i | \(-0.291880\pi\) |
−0.991532 | + | 0.129861i | \(0.958547\pi\) | |||||||
\(272\) | 8064.00 | 1.79762 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3224.00 | 0.710836 | ||||||||
\(275\) | 4975.00 | + | 8616.95i | 1.09092 | + | 1.88953i | ||||
\(276\) | 168.000 | − | 290.985i | 0.0366392 | − | 0.0634609i | ||||
\(277\) | 1367.00 | − | 2367.71i | 0.296516 | − | 0.513582i | −0.678820 | − | 0.734305i | \(-0.737508\pi\) |
0.975337 | + | 0.220723i | \(0.0708417\pi\) | |||||||
\(278\) | 5256.00 | + | 9103.66i | 1.13394 | + | 1.96403i | ||||
\(279\) | 324.000 | 0.0695246 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 598.000 | 0.126953 | 0.0634763 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634763 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(282\) | 432.000 | + | 748.246i | 0.0912242 | + | 0.158005i | ||||
\(283\) | 1800.00 | − | 3117.69i | 0.378088 | − | 0.654868i | −0.612696 | − | 0.790319i | \(-0.709915\pi\) |
0.990784 | + | 0.135451i | \(0.0432484\pi\) | |||||||
\(284\) | 2936.00 | − | 5085.30i | 0.613449 | − | 1.06253i | ||||
\(285\) | −1944.00 | − | 3367.11i | −0.404044 | − | 0.699825i | ||||
\(286\) | −7200.00 | −1.48862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2304.00 | −0.471405 | ||||||||
\(289\) | −5481.50 | − | 9494.24i | −1.11571 | − | 1.93247i | ||||
\(290\) | 5688.00 | − | 9851.90i | 1.15176 | − | 1.99491i | ||||
\(291\) | −702.000 | + | 1215.90i | −0.141416 | + | 0.244939i | ||||
\(292\) | 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 | ||||||||
\(297\) | −675.000 | + | 1169.13i | −0.131877 | + | 0.228418i | ||||
\(298\) | 4780.00 | − | 8279.20i | 0.929188 | − | 1.60940i | ||||
\(299\) | −252.000 | − | 436.477i | −0.0487409 | − | 0.0844218i | ||||
\(300\) | −4776.00 | −0.919142 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12960.0 | 2.46942 | ||||||||
\(303\) | 999.000 | + | 1730.32i | 0.189409 | + | 0.328067i | ||||
\(304\) | 2304.00 | − | 3990.65i | 0.434682 | − | 0.752892i | ||||
\(305\) | −7128.00 | + | 12346.1i | −1.33819 | + | 2.31781i | ||||
\(306\) | 2268.00 | + | 3928.29i | 0.423702 | + | 0.733874i | ||||
\(307\) | 10224.0 | 1.90070 | 0.950349 | − | 0.311185i | \(-0.100726\pi\) | ||||
0.950349 | + | 0.311185i | \(0.100726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −756.000 | −0.139182 | ||||||||
\(310\) | 1296.00 | + | 2244.74i | 0.237445 | + | 0.411266i | ||||
\(311\) | 1944.00 | − | 3367.11i | 0.354451 | − | 0.613926i | −0.632573 | − | 0.774501i | \(-0.718001\pi\) |
0.987024 | + | 0.160574i | \(0.0513346\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2556.00 | + | 4427.12i | 0.461577 | + | 0.799475i | 0.999040 | − | 0.0438124i | \(-0.0139504\pi\) |
−0.537463 | + | 0.843288i | \(0.680617\pi\) | |||||||
\(314\) | −12096.0 | −2.17394 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | 5051.00 | + | 8748.59i | 0.894929 | + | 1.55006i | 0.833893 | + | 0.551927i | \(0.186107\pi\) |
0.0610361 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(318\) | −132.000 | + | 228.631i | −0.0232773 | + | 0.0403175i | ||||
\(319\) | 3950.00 | − | 6841.60i | 0.693284 | − | 1.20080i | ||||
\(320\) | −4608.00 | − | 7981.29i | −0.804984 | − | 1.39427i | ||||
\(321\) | −2010.00 | −0.349493 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9072.00 | −1.56279 | ||||||||
\(324\) | −324.000 | − | 561.184i | −0.0555556 | − | 0.0962250i | ||||
\(325\) | −3582.00 | + | 6204.21i | −0.611365 | + | 1.05892i | ||||
\(326\) | 3568.00 | − | 6179.96i | 0.606176 | − | 1.04993i | ||||
\(327\) | 243.000 | + | 420.888i | 0.0410946 | + | 0.0711779i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10800.0 | −1.80158 | ||||||||
\(331\) | −2754.00 | − | 4770.07i | −0.457322 | − | 0.792105i | 0.541497 | − | 0.840703i | \(-0.317858\pi\) |
−0.998818 | + | 0.0485983i | \(0.984525\pi\) | |||||||
\(332\) | 144.000 | − | 249.415i | 0.0238043 | − | 0.0412303i | ||||
\(333\) | 729.000 | − | 1262.67i | 0.119967 | − | 0.207789i | ||||
\(334\) | −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 | ||||
\(339\) | −2085.00 | + | 3611.33i | −0.334046 | + | 0.578585i | ||||
\(340\) | −9072.00 | + | 15713.2i | −1.44705 | + | 2.50637i | ||||
\(341\) | 900.000 | + | 1558.85i | 0.142926 | + | 0.247555i | ||||
\(342\) | 2592.00 | 0.409823 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −378.000 | − | 654.715i | −0.0589879 | − | 0.102170i | ||||
\(346\) | 3132.00 | − | 5424.78i | 0.486640 | − | 0.842885i | ||||
\(347\) | 3247.00 | − | 5623.97i | 0.502329 | − | 0.870059i | −0.497668 | − | 0.867368i | \(-0.665810\pi\) |
0.999996 | − | 0.00269115i | \(-0.000856622\pi\) | |||||||
\(348\) | 1896.00 | + | 3283.97i | 0.292058 | + | 0.505860i | ||||
\(349\) | −10080.0 | −1.54605 | −0.773023 | − | 0.634378i | \(-0.781256\pi\) | ||||
−0.773023 | + | 0.634378i | \(0.781256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −972.000 | −0.147811 | ||||||||
\(352\) | −6400.00 | − | 11085.1i | −0.969094 | − | 1.67852i | ||||
\(353\) | −369.000 | + | 639.127i | −0.0556371 | + | 0.0963662i | −0.892503 | − | 0.451042i | \(-0.851052\pi\) |
0.836865 | + | 0.547409i | \(0.184386\pi\) | |||||||
\(354\) | −2808.00 | + | 4863.60i | −0.421592 | + | 0.730219i | ||||
\(355\) | −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 | \(-0.171206\pi\) |
−0.873068 | + | 0.487599i | \(0.837873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 837.500 | − | 1450.59i | 0.122102 | − | 0.211487i | ||||
\(362\) | −936.000 | − | 1621.20i | −0.135898 | − | 0.235382i | ||||
\(363\) | −3507.00 | −0.507079 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3240.00 | 0.464628 | ||||||||
\(366\) | −4752.00 | − | 8230.71i | −0.678664 | − | 1.17548i | ||||
\(367\) | −2376.00 | + | 4115.35i | −0.337946 | + | 0.585340i | −0.984046 | − | 0.177913i | \(-0.943065\pi\) |
0.646100 | + | 0.763253i | \(0.276399\pi\) | |||||||
\(368\) | 448.000 | − | 775.959i | 0.0634609 | − | 0.109918i | ||||
\(369\) | −1215.00 | − | 2104.44i | −0.171410 | − | 0.296891i | ||||
\(370\) | 11664.0 | 1.63887 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −864.000 | −0.120420 | ||||||||
\(373\) | 1153.00 | + | 1997.05i | 0.160054 | + | 0.277221i | 0.934888 | − | 0.354943i | \(-0.115500\pi\) |
−0.774834 | + | 0.632165i | \(0.782167\pi\) | |||||||
\(374\) | −12600.0 | + | 21823.8i | −1.74206 | + | 3.01734i | ||||
\(375\) | −1998.00 | + | 3460.64i | −0.275137 | + | 0.476551i | ||||
\(376\) | 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 | ||||
\(381\) | 1374.00 | − | 2379.84i | 0.184756 | − | 0.320007i | ||||
\(382\) | −964.000 | + | 1669.70i | −0.129117 | + | 0.223636i | ||||
\(383\) | −576.000 | − | 997.661i | −0.0768465 | − | 0.133102i | 0.825041 | − | 0.565073i | \(-0.191152\pi\) |
−0.901888 | + | 0.431970i | \(0.857818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3240.00 | −0.427232 | ||||||||
\(387\) | 1458.00 | + | 2525.33i | 0.191510 | + | 0.331705i | ||||
\(388\) | 1872.00 | − | 3242.40i | 0.244939 | − | 0.424247i | ||||
\(389\) | −947.000 | + | 1640.25i | −0.123431 | + | 0.213789i | −0.921119 | − | 0.389282i | \(-0.872723\pi\) |
0.797687 | + | 0.603071i | \(0.206057\pi\) | |||||||
\(390\) | −3888.00 | − | 6734.21i | −0.504812 | − | 0.874359i | ||||
\(391\) | −1764.00 | −0.228157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6804.00 | 0.873324 | ||||||||
\(394\) | 4924.00 | + | 8528.62i | 0.629613 | + | 1.09052i | ||||
\(395\) | 2124.00 | − | 3678.88i | 0.270557 | − | 0.468619i | ||||
\(396\) | 1800.00 | − | 3117.69i | 0.228418 | − | 0.395631i | ||||
\(397\) | 4608.00 | + | 7981.29i | 0.582541 | + | 1.00899i | 0.995177 | + | 0.0980950i | \(0.0312749\pi\) |
−0.412636 | + | 0.910896i | \(0.635392\pi\) | |||||||
\(398\) | 18144.0 | 2.28512 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12736.0 | −1.59200 | ||||||||
\(401\) | 5825.00 | + | 10089.2i | 0.725403 | + | 1.25643i | 0.958808 | + | 0.284055i | \(0.0916799\pi\) |
−0.233405 | + | 0.972380i | \(0.574987\pi\) | |||||||
\(402\) | 1392.00 | − | 2411.01i | 0.172703 | − | 0.299131i | ||||
\(403\) | −648.000 | + | 1122.37i | −0.0800972 | + | 0.138732i | ||||
\(404\) | −2664.00 | − | 4614.18i | −0.328067 | − | 0.568228i | ||||
\(405\) | −1458.00 | −0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8100.00 | 0.986492 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3762.00 | + | 6515.98i | −0.454814 | + | 0.787761i | −0.998677 | − | 0.0514127i | \(-0.983628\pi\) |
0.543863 | + | 0.839174i | \(0.316961\pi\) | |||||||
\(410\) | 9720.00 | − | 16835.5i | 1.17082 | − | 2.02792i | ||||
\(411\) | 1209.00 | + | 2094.05i | 0.145099 | + | 0.251318i | ||||
\(412\) | 2016.00 | 0.241071 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 504.000 | 0.0598315 | ||||||||
\(415\) | −324.000 | − | 561.184i | −0.0383242 | − | 0.0663794i | ||||
\(416\) | 4608.00 | − | 7981.29i | 0.543091 | − | 0.940661i | ||||
\(417\) | −3942.00 | + | 6827.74i | −0.462927 | + | 0.801813i | ||||
\(418\) | 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 | ||||
\(423\) | −324.000 | + | 561.184i | −0.0372421 | + | 0.0645053i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12537.0 | + | 21714.7i | 1.43090 | + | 2.47840i | ||||
\(426\) | 8808.00 | 1.00176 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5360.00 | 0.605340 | ||||||||
\(429\) | −2700.00 | − | 4676.54i | −0.303863 | − | 0.526306i | ||||
\(430\) | −11664.0 | + | 20202.6i | −1.30811 | + | 2.26572i | ||||
\(431\) | 5195.00 | − | 8998.00i | 0.580590 | − | 1.00561i | −0.414819 | − | 0.909904i | \(-0.636155\pi\) |
0.995409 | − | 0.0957078i | \(-0.0305114\pi\) | |||||||
\(432\) | −864.000 | − | 1496.49i | −0.0962250 | − | 0.166667i | ||||
\(433\) | −11232.0 | −1.24659 | −0.623297 | − | 0.781985i | \(-0.714207\pi\) | ||||
−0.623297 | + | 0.781985i | \(0.714207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8532.00 | 0.940409 | ||||||||
\(436\) | −648.000 | − | 1122.37i | −0.0711779 | − | 0.123284i | ||||
\(437\) | −504.000 | + | 872.954i | −0.0551707 | + | 0.0955584i | ||||
\(438\) | −1080.00 | + | 1870.61i | −0.117818 | + | 0.204067i | ||||
\(439\) | 7308.00 | + | 12657.8i | 0.794514 | + | 1.37614i | 0.923147 | + | 0.384447i | \(0.125608\pi\) |
−0.128633 | + | 0.991692i | \(0.541059\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18144.0 | −1.95254 | ||||||||
\(443\) | −5969.00 | − | 10338.6i | −0.640171 | − | 1.10881i | −0.985394 | − | 0.170288i | \(-0.945530\pi\) |
0.345223 | − | 0.938521i | \(-0.387803\pi\) | |||||||
\(444\) | −1944.00 | + | 3367.11i | −0.207789 | + | 0.359900i | ||||
\(445\) | −2106.00 | + | 3647.70i | −0.224346 | + | 0.388579i | ||||
\(446\) | −2160.00 | − | 3741.23i | −0.229325 | − | 0.397203i | ||||
\(447\) | 7170.00 | 0.758679 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8186.00 | 0.860404 | 0.430202 | − | 0.902733i | \(-0.358442\pi\) | ||||
0.430202 | + | 0.902733i | \(0.358442\pi\) | |||||||
\(450\) | −3582.00 | − | 6204.21i | −0.375238 | − | 0.649931i | ||||
\(451\) | 6750.00 | − | 11691.3i | 0.704756 | − | 1.22067i | ||||
\(452\) | 5560.00 | − | 9630.20i | 0.578585 | − | 1.00214i | ||||
\(453\) | 4860.00 | + | 8417.77i | 0.504068 | + | 0.873071i | ||||
\(454\) | 5328.00 | 0.550783 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1053.00 | − | 1823.85i | −0.107784 | − | 0.186687i | 0.807088 | − | 0.590431i | \(-0.201042\pi\) |
−0.914872 | + | 0.403744i | \(0.867709\pi\) | |||||||
\(458\) | 3240.00 | − | 5611.84i | 0.330557 | − | 0.572542i | ||||
\(459\) | −1701.00 | + | 2946.22i | −0.172976 | + | 0.299603i | ||||
\(460\) | 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 | ||||
\(465\) | −972.000 | + | 1683.55i | −0.0969364 | + | 0.167899i | ||||
\(466\) | −13436.0 | + | 23271.8i | −1.33565 | + | 2.31341i | ||||
\(467\) | −1854.00 | − | 3211.22i | −0.183711 | − | 0.318196i | 0.759431 | − | 0.650588i | \(-0.225478\pi\) |
−0.943141 | + | 0.332392i | \(0.892144\pi\) | |||||||
\(468\) | 2592.00 | 0.256015 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5184.00 | −0.508766 | ||||||||
\(471\) | −4536.00 | − | 7856.58i | −0.443753 | − | 0.768603i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8100.00 | + | 14029.6i | −0.787396 | + | 1.36381i | ||||
\(474\) | 1416.00 | + | 2452.58i | 0.137213 | + | 0.237660i | ||||
\(475\) | 14328.0 | 1.38403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −198.000 | −0.0190059 | ||||||||
\(478\) | 7156.00 | + | 12394.6i | 0.684744 | + | 1.18601i | ||||
\(479\) | −4032.00 | + | 6983.63i | −0.384607 | + | 0.666159i | −0.991715 | − | 0.128461i | \(-0.958996\pi\) |
0.607108 | + | 0.794620i | \(0.292330\pi\) | |||||||
\(480\) | 6912.00 | − | 11971.9i | 0.657267 | − | 1.13842i | ||||
\(481\) | 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 | ||||
\(486\) | 486.000 | − | 841.777i | 0.0453609 | − | 0.0785674i | ||||
\(487\) | 5832.00 | − | 10101.3i | 0.542655 | − | 0.939907i | −0.456095 | − | 0.889931i | \(-0.650752\pi\) |
0.998750 | − | 0.0499756i | \(-0.0159143\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5352.00 | 0.494940 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9814.00 | −0.902036 | −0.451018 | − | 0.892515i | \(-0.648939\pi\) | ||||
−0.451018 | + | 0.892515i | \(0.648939\pi\) | |||||||
\(492\) | 3240.00 | + | 5611.84i | 0.296891 | + | 0.514231i | ||||
\(493\) | 9954.00 | − | 17240.8i | 0.909342 | − | 1.57503i | ||||
\(494\) | −5184.00 | + | 8978.95i | −0.472144 | + | 0.817778i | ||||
\(495\) | −4050.00 | − | 7014.81i | −0.367745 | − | 0.636954i | ||||
\(496\) | −2304.00 | −0.208574 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 432.000 | 0.0388723 | ||||||||
\(499\) | 7614.00 | + | 13187.8i | 0.683065 | + | 1.18310i | 0.974041 | + | 0.226373i | \(0.0726868\pi\) |
−0.290976 | + | 0.956730i | \(0.593980\pi\) | |||||||
\(500\) | 5328.00 | − | 9228.37i | 0.476551 | − | 0.825410i | ||||
\(501\) | 4536.00 | − | 7856.58i | 0.404498 | − | 0.700611i | ||||
\(502\) | −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 | ||||
\(507\) | −1351.50 | + | 2340.87i | −0.118387 | + | 0.205052i | ||||
\(508\) | −3664.00 | + | 6346.23i | −0.320007 | + | 0.554269i | ||||
\(509\) | −2907.00 | − | 5035.07i | −0.253144 | − | 0.438459i | 0.711245 | − | 0.702944i | \(-0.248131\pi\) |
−0.964390 | + | 0.264485i | \(0.914798\pi\) | |||||||
\(510\) | −27216.0 | −2.36303 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16384.0 | 1.41421 | ||||||||
\(513\) | 972.000 | + | 1683.55i | 0.0836547 | + | 0.144894i | ||||
\(514\) | −12060.0 | + | 20888.5i | −1.03491 | + | 1.79252i | ||||
\(515\) | 2268.00 | − | 3928.29i | 0.194058 | − | 0.336119i | ||||
\(516\) | −3888.00 | − | 6734.21i | −0.331705 | − | 0.574529i | ||||
\(517\) | −3600.00 | −0.306243 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4698.00 | 0.397340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5841.00 | + | 10116.9i | −0.491169 | + | 0.850729i | −0.999948 | − | 0.0101677i | \(-0.996763\pi\) |
0.508780 | + | 0.860897i | \(0.330097\pi\) | |||||||
\(522\) | −2844.00 | + | 4925.95i | −0.238465 | + | 0.413033i | ||||
\(523\) | −1494.00 | − | 2587.68i | −0.124910 | − | 0.216351i | 0.796788 | − | 0.604259i | \(-0.206531\pi\) |
−0.921698 | + | 0.387909i | \(0.873198\pi\) | |||||||
\(524\) | −18144.0 | −1.51264 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2360.00 | 0.195629 | ||||||||
\(527\) | 2268.00 | + | 3928.29i | 0.187468 | + | 0.324704i | ||||
\(528\) | 4800.00 | − | 8313.84i | 0.395631 | − | 0.685253i | ||||
\(529\) | 5985.50 | − | 10367.2i | 0.491945 | − | 0.852074i | ||||
\(530\) | −792.000 | − | 1371.78i | −0.0649100 | − | 0.112427i | ||||
\(531\) | −4212.00 | −0.344228 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9720.00 | 0.789906 | ||||||||
\(534\) | −1404.00 | − | 2431.80i | −0.113777 | − | 0.197068i | ||||
\(535\) | 6030.00 | − | 10444.3i | 0.487289 | − | 0.844009i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5703.00 | + | 9877.89i | 0.458292 | + | 0.793784i | ||||
\(538\) | 3960.00 | 0.317338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3888.00 | 0.309839 | ||||||||
\(541\) | −3565.00 | − | 6174.76i | −0.283311 | − | 0.490709i | 0.688887 | − | 0.724869i | \(-0.258100\pi\) |
−0.972198 | + | 0.234159i | \(0.924766\pi\) | |||||||
\(542\) | −6840.00 | + | 11847.2i | −0.542072 | + | 0.938897i | ||||
\(543\) | 702.000 | − | 1215.90i | 0.0554801 | − | 0.0960944i | ||||
\(544\) | −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 | ||||
\(549\) | 3564.00 | − | 6173.03i | 0.277063 | − | 0.479888i | ||||
\(550\) | 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 | ||||||||
\(555\) | 4374.00 | + | 7575.99i | 0.334533 | + | 0.579429i | ||||
\(556\) | 10512.0 | − | 18207.3i | 0.801813 | − | 1.38878i | ||||
\(557\) | −2873.00 | + | 4976.18i | −0.218551 | + | 0.378541i | −0.954365 | − | 0.298642i | \(-0.903466\pi\) |
0.735814 | + | 0.677183i | \(0.236800\pi\) | |||||||
\(558\) | −648.000 | − | 1122.37i | −0.0491613 | − | 0.0851499i | ||||
\(559\) | −11664.0 | −0.882531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18900.0 | −1.42239 | ||||||||
\(562\) | −1196.00 | − | 2071.53i | −0.0897691 | − | 0.155485i | ||||
\(563\) | 6534.00 | − | 11317.2i | 0.489121 | − | 0.847183i | −0.510800 | − | 0.859699i | \(-0.670651\pi\) |
0.999922 | + | 0.0125165i | \(0.00398422\pi\) | |||||||
\(564\) | 864.000 | − | 1496.49i | 0.0645053 | − | 0.111726i | ||||
\(565\) | −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 | \(-0.153412\pi\) |
−0.844461 | + | 0.535617i | \(0.820079\pi\) | |||||||
\(570\) | −7776.00 | + | 13468.4i | −0.571405 | + | 0.989702i | ||||
\(571\) | −8432.00 | + | 14604.7i | −0.617983 | + | 1.07038i | 0.371870 | + | 0.928285i | \(0.378717\pi\) |
−0.989853 | + | 0.142093i | \(0.954617\pi\) | |||||||
\(572\) | 7200.00 | + | 12470.8i | 0.526306 | + | 0.911589i | ||||
\(573\) | −1446.00 | −0.105423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2786.00 | 0.202060 | ||||||||
\(576\) | 2304.00 | + | 3990.65i | 0.166667 | + | 0.288675i | ||||
\(577\) | −1044.00 | + | 1808.26i | −0.0753246 | + | 0.130466i | −0.901227 | − | 0.433347i | \(-0.857333\pi\) |
0.825903 | + | 0.563813i | \(0.190666\pi\) | |||||||
\(578\) | −21926.0 | + | 37976.9i | −1.57786 | + | 2.73293i | ||||
\(579\) | −1215.00 | − | 2104.44i | −0.0872084 | − | 0.151049i | ||||
\(580\) | −22752.0 | −1.62884 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5616.00 | 0.399984 | ||||||||
\(583\) | −550.000 | − | 952.628i | −0.0390715 | − | 0.0676738i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2916.00 | − | 5050.66i | 0.206088 | − | 0.356956i | ||||
\(586\) | 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 | ||||
\(591\) | −3693.00 | + | 6396.46i | −0.257038 | + | 0.445204i | ||||
\(592\) | −5184.00 | + | 8978.95i | −0.359900 | + | 0.623366i | ||||
\(593\) | 1791.00 | + | 3102.10i | 0.124026 | + | 0.214820i | 0.921352 | − | 0.388730i | \(-0.127086\pi\) |
−0.797326 | + | 0.603549i | \(0.793753\pi\) | |||||||
\(594\) | 5400.00 | 0.373005 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19120.0 | −1.31407 | ||||||||
\(597\) | 6804.00 | + | 11784.9i | 0.466448 | + | 0.807911i | ||||
\(598\) | −1008.00 | + | 1745.91i | −0.0689301 | + | 0.119390i | ||||
\(599\) | −3517.00 | + | 6091.62i | −0.239901 | + | 0.415521i | −0.960686 | − | 0.277638i | \(-0.910448\pi\) |
0.720785 | + | 0.693159i | \(0.243782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18072.0 | 1.22658 | 0.613288 | − | 0.789859i | \(-0.289846\pi\) | ||||
0.613288 | + | 0.789859i | \(0.289846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2088.00 | 0.141011 | ||||||||
\(604\) | −12960.0 | − | 22447.4i | −0.873071 | − | 1.51220i | ||||
\(605\) | 10521.0 | − | 18222.9i | 0.707007 | − | 1.22457i | ||||
\(606\) | 3996.00 | − | 6921.28i | 0.267865 | − | 0.463956i | ||||
\(607\) | 14292.0 | + | 24754.5i | 0.955674 | + | 1.65528i | 0.732817 | + | 0.680426i | \(0.238205\pi\) |
0.222857 | + | 0.974851i | \(0.428462\pi\) | |||||||
\(608\) | −18432.0 | −1.22947 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 57024.0 | 3.78497 | ||||||||
\(611\) | −1296.00 | − | 2244.74i | −0.0858110 | − | 0.148629i | ||||
\(612\) | 4536.00 | − | 7856.58i | 0.299603 | − | 0.518927i | ||||
\(613\) | 5455.00 | − | 9448.34i | 0.359421 | − | 0.622536i | −0.628443 | − | 0.777856i | \(-0.716307\pi\) |
0.987864 | + | 0.155320i | \(0.0496407\pi\) | |||||||
\(614\) | −20448.0 | − | 35417.0i | −1.34400 | − | 2.32787i | ||||
\(615\) | 14580.0 | 0.955971 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5522.00 | −0.360304 | −0.180152 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180152 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(618\) | 1512.00 | + | 2618.86i | 0.0984168 | + | 0.170463i | ||||
\(619\) | 1206.00 | − | 2088.85i | 0.0783089 | − | 0.135635i | −0.824211 | − | 0.566282i | \(-0.808381\pi\) |
0.902520 | + | 0.430647i | \(0.141715\pi\) | |||||||
\(620\) | 2592.00 | − | 4489.48i | 0.167899 | − | 0.290809i | ||||
\(621\) | 189.000 | + | 327.358i | 0.0122131 | + | 0.0211536i | ||||
\(622\) | −15552.0 | −1.00254 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6912.00 | 0.443432 | ||||||||
\(625\) | 449.500 | + | 778.557i | 0.0287680 | + | 0.0498276i | ||||
\(626\) | 10224.0 | − | 17708.5i | 0.652769 | − | 1.13063i | ||||
\(627\) | −5400.00 | + | 9353.07i | −0.343948 | + | 0.595735i | ||||
\(628\) | 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 | ||||||||
\(633\) | 4374.00 | − | 7575.99i | 0.274646 | − | 0.475701i | ||||
\(634\) | 20204.0 | − | 34994.4i | 1.26562 | − | 2.19212i | ||||
\(635\) | 8244.00 | + | 14279.0i | 0.515202 | + | 0.892356i | ||||
\(636\) | 528.000 | 0.0329191 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −31600.0 | −1.96090 | ||||||||
\(639\) | 3303.00 | + | 5720.96i | 0.204483 | + | 0.354175i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13741.0 | − | 23800.1i | 0.846703 | − | 1.46653i | −0.0374303 | − | 0.999299i | \(-0.511917\pi\) |
0.884134 | − | 0.467234i | \(-0.154749\pi\) | |||||||
\(642\) | 4020.00 | + | 6962.84i | 0.247129 | + | 0.428040i | ||||
\(643\) | 22752.0 | 1.39541 | 0.697707 | − | 0.716383i | \(-0.254204\pi\) | ||||
0.697707 | + | 0.716383i | \(0.254204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17496.0 | −1.06807 | ||||||||
\(646\) | 18144.0 | + | 31426.3i | 1.10506 | + | 1.91401i | ||||
\(647\) | 7416.00 | − | 12844.9i | 0.450623 | − | 0.780502i | −0.547802 | − | 0.836608i | \(-0.684535\pi\) |
0.998425 | + | 0.0561063i | \(0.0178686\pi\) | |||||||
\(648\) | 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 | \(-0.193615\pi\) |
−0.905203 | + | 0.424979i | \(0.860281\pi\) | |||||||
\(654\) | 972.000 | − | 1683.55i | 0.0581165 | − | 0.100661i | ||||
\(655\) | −20412.0 | + | 35354.6i | −1.21765 | + | 2.10904i | ||||
\(656\) | 8640.00 | + | 14964.9i | 0.514231 | + | 0.890674i | ||||
\(657\) | −1620.00 | −0.0961982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15826.0 | −0.935498 | −0.467749 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(660\) | 10800.0 | + | 18706.1i | 0.636954 | + | 1.10324i | ||||
\(661\) | −11916.0 | + | 20639.1i | −0.701178 | + | 1.21448i | 0.266875 | + | 0.963731i | \(0.414009\pi\) |
−0.968053 | + | 0.250745i | \(0.919324\pi\) | |||||||
\(662\) | −11016.0 | + | 19080.3i | −0.646751 | + | 1.12021i | ||||
\(663\) | −6804.00 | − | 11784.9i | −0.398560 | − | 0.690327i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5832.00 | −0.339317 | ||||||||
\(667\) | −1106.00 | − | 1915.65i | −0.0642046 | − | 0.111206i | ||||
\(668\) | −12096.0 | + | 20950.9i | −0.700611 | + | 1.21349i | ||||
\(669\) | 1620.00 | − | 2805.92i | 0.0936216 | − | 0.162157i | ||||
\(670\) | 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 | ||||
\(675\) | 2686.50 | − | 4653.15i | 0.153190 | − | 0.265333i | ||||
\(676\) | 3604.00 | − | 6242.31i | 0.205052 | − | 0.355161i | ||||
\(677\) | 4167.00 | + | 7217.46i | 0.236560 | + | 0.409733i | 0.959725 | − | 0.280942i | \(-0.0906468\pi\) |
−0.723165 | + | 0.690675i | \(0.757313\pi\) | |||||||
\(678\) | 16680.0 | 0.944825 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1998.00 | + | 3460.64i | 0.112428 | + | 0.194731i | ||||
\(682\) | 3600.00 | − | 6235.38i | 0.202128 | − | 0.350096i | ||||
\(683\) | 9299.00 | − | 16106.3i | 0.520961 | − | 0.902331i | −0.478742 | − | 0.877956i | \(-0.658907\pi\) |
0.999703 | − | 0.0243752i | \(-0.00775963\pi\) | |||||||
\(684\) | −2592.00 | − | 4489.48i | −0.144894 | − | 0.250964i | ||||
\(685\) | −14508.0 | −0.809229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4860.00 | 0.269899 | ||||||||
\(688\) | −10368.0 | − | 17957.9i | −0.574529 | − | 0.995114i | ||||
\(689\) | 396.000 | − | 685.892i | 0.0218961 | − | 0.0379251i | ||||
\(690\) | −1512.00 | + | 2618.86i | −0.0834215 | + | 0.144490i | ||||
\(691\) | 4482.00 | + | 7763.05i | 0.246749 | + | 0.427381i | 0.962622 | − | 0.270849i | \(-0.0873045\pi\) |
−0.715873 | + | 0.698230i | \(0.753971\pi\) | |||||||
\(692\) | −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 | ||||
\(699\) | −20154.0 | −1.09055 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3542.00 | 0.190841 | 0.0954205 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954205 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(702\) | 1944.00 | + | 3367.11i | 0.104518 | + | 0.181030i | ||||
\(703\) | 5832.00 | − | 10101.3i | 0.312885 | − | 0.541932i | ||||
\(704\) | −12800.0 | + | 22170.3i | −0.685253 | + | 1.18689i | ||||
\(705\) | −1944.00 | − | 3367.11i | −0.103851 | − | 0.179876i | ||||
\(706\) | 2952.00 | 0.157365 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11232.0 | 0.596221 | ||||||||
\(709\) | 243.000 | + | 420.888i | 0.0128717 | + | 0.0222945i | 0.872390 | − | 0.488811i | \(-0.162569\pi\) |
−0.859518 | + | 0.511106i | \(0.829236\pi\) | |||||||
\(710\) | −26424.0 | + | 45767.7i | −1.39673 | + | 2.41920i | ||||
\(711\) | −1062.00 | + | 1839.44i | −0.0560170 | + | 0.0970244i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 504.000 | 0.0264726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32400.0 | 1.69467 | ||||||||
\(716\) | −15208.0 | − | 26341.0i | −0.793784 | − | 1.37487i | ||||
\(717\) | −5367.00 | + | 9295.92i | −0.279546 | + | 0.484187i | ||||
\(718\) | −388.000 | + | 672.036i | −0.0201672 | + | 0.0349306i | ||||
\(719\) | −13464.0 | − | 23320.3i | −0.698362 | − | 1.20960i | −0.969034 | − | 0.246927i | \(-0.920579\pi\) |
0.270672 | − | 0.962672i | \(-0.412754\pi\) | |||||||
\(720\) | 10368.0 | 0.536656 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6700.00 | −0.345358 | ||||||||
\(723\) | 1134.00 | + | 1964.15i | 0.0583318 | + | 0.101034i | ||||
\(724\) | −1872.00 | + | 3242.40i | −0.0960944 | + | 0.166440i | ||||
\(725\) | −15721.0 | + | 27229.6i | −0.805329 | + | 1.39487i | ||||
\(726\) | 7014.00 | + | 12148.6i | 0.358559 | + | 0.621043i | ||||
\(727\) | −20628.0 | −1.05234 | −0.526169 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526169 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −6480.00 | − | 11223.7i | −0.328542 | − | 0.569051i | ||||
\(731\) | −20412.0 | + | 35354.6i | −1.03278 | + | 1.78883i | ||||
\(732\) | −9504.00 | + | 16461.4i | −0.479888 | + | 0.831190i | ||||
\(733\) | −4878.00 | − | 8448.94i | −0.245802 | − | 0.425742i | 0.716555 | − | 0.697531i | \(-0.245718\pi\) |
−0.962357 | + | 0.271789i | \(0.912385\pi\) | |||||||
\(734\) | 19008.0 | 0.955856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3584.00 | −0.179495 | ||||||||
\(737\) | 5800.00 | + | 10045.9i | 0.289886 | + | 0.502097i | ||||
\(738\) | −4860.00 | + | 8417.77i | −0.242411 | + | 0.419868i | ||||
\(739\) | −9532.00 | + | 16509.9i | −0.474479 | + | 0.821822i | −0.999573 | − | 0.0292221i | \(-0.990697\pi\) |
0.525094 | + | 0.851045i | \(0.324030\pi\) | |||||||
\(740\) | −11664.0 | − | 20202.6i | −0.579429 | − | 1.00360i | ||||
\(741\) | −7776.00 | −0.385504 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3766.00 | −0.185950 | −0.0929752 | − | 0.995668i | \(-0.529638\pi\) | ||||
−0.0929752 | + | 0.995668i | \(0.529638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21510.0 | + | 37256.4i | −1.05781 | + | 1.83217i | ||||
\(746\) | 4612.00 | − | 7988.22i | 0.226350 | − | 0.392050i | ||||
\(747\) | 162.000 | + | 280.592i | 0.00793477 | + | 0.0137434i | ||||
\(748\) | 50400.0 | 2.46365 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15984.0 | 0.778204 | ||||||||
\(751\) | 5832.00 | + | 10101.3i | 0.283372 | + | 0.490815i | 0.972213 | − | 0.234097i | \(-0.0752134\pi\) |
−0.688841 | + | 0.724913i | \(0.741880\pi\) | |||||||
\(752\) | 2304.00 | − | 3990.65i | 0.111726 | − | 0.193516i | ||||
\(753\) | 9774.00 | − | 16929.1i | 0.473020 | − | 0.819295i | ||||
\(754\) | −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 | ||||
\(759\) | −1050.00 | + | 1818.65i | −0.0502142 | + | 0.0869736i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2367.00 | − | 4099.76i | −0.112751 | − | 0.195291i | 0.804127 | − | 0.594457i | \(-0.202633\pi\) |
−0.916879 | + | 0.399166i | \(0.869300\pi\) | |||||||
\(762\) | −10992.0 | −0.522570 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3856.00 | 0.182598 | ||||||||
\(765\) | −10206.0 | − | 17677.3i | −0.482351 | − | 0.835457i | ||||
\(766\) | −2304.00 | + | 3990.65i | −0.108677 | + | 0.188235i | ||||
\(767\) | 8424.00 | − | 14590.8i | 0.396575 | − | 0.686888i | ||||
\(768\) | 6144.00 | + | 10641.7i | 0.288675 | + | 0.500000i | ||||
\(769\) | 30240.0 | 1.41805 | 0.709026 | − | 0.705182i | \(-0.249135\pi\) | ||||
0.709026 | + | 0.705182i | \(0.249135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18090.0 | −0.845001 | ||||||||
\(772\) | 3240.00 | + | 5611.84i | 0.151049 | + | 0.261625i | ||||
\(773\) | 13851.0 | − | 23990.6i | 0.644484 | − | 1.11628i | −0.339937 | − | 0.940448i | \(-0.610406\pi\) |
0.984421 | − | 0.175830i | \(-0.0562609\pi\) | |||||||
\(774\) | 5832.00 | − | 10101.3i | 0.270836 | − | 0.469101i | ||||
\(775\) | −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 | ||||
\(780\) | −7776.00 | + | 13468.4i | −0.356956 | + | 0.618265i | ||||
\(781\) | −18350.0 | + | 31783.1i | −0.840736 | + | 1.45620i | ||||
\(782\) | 3528.00 | + | 6110.68i | 0.161331 | + | 0.279434i | ||||
\(783\) | −4266.00 | −0.194705 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54432.0 | 2.47486 | ||||||||
\(786\) | −13608.0 | − | 23569.7i | −0.617533 | − | 1.06960i | ||||
\(787\) | −11322.0 | + | 19610.3i | −0.512815 | + | 0.888222i | 0.487074 | + | 0.873361i | \(0.338064\pi\) |
−0.999890 | + | 0.0148617i | \(0.995269\pi\) | |||||||
\(788\) | 9848.00 | − | 17057.2i | 0.445204 | − | 0.771115i | ||||
\(789\) | 885.000 | + | 1532.86i | 0.0399326 | + | 0.0691653i | ||||
\(790\) | −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 | ||||
\(795\) | 594.000 | − | 1028.84i | 0.0264994 | − | 0.0458983i | ||||
\(796\) | −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 | ||||
\(801\) | 1053.00 | − | 1823.85i | 0.0464493 | − | 0.0804526i | ||||
\(802\) | 23300.0 | − | 40356.8i | 1.02587 | − | 1.77687i | ||||
\(803\) | −4500.00 | − | 7794.23i | −0.197760 | − | 0.342531i | ||||
\(804\) | −5568.00 | −0.244239 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5184.00 | 0.226549 | ||||||||
\(807\) | 1485.00 | + | 2572.10i | 0.0647763 | + | 0.112196i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5659.00 | − | 9801.68i | 0.245933 | − | 0.425969i | −0.716460 | − | 0.697628i | \(-0.754239\pi\) |
0.962394 | + | 0.271659i | \(0.0875723\pi\) | |||||||
\(810\) | 2916.00 | + | 5050.66i | 0.126491 | + | 0.219089i | ||||
\(811\) | 29628.0 | 1.28284 | 0.641418 | − | 0.767192i | \(-0.278347\pi\) | ||||
0.641418 | + | 0.767192i | \(0.278347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10260.0 | −0.442600 | ||||||||
\(814\) | −16200.0 | − | 28059.2i | −0.697555 | − | 1.20820i | ||||
\(815\) | −16056.0 | + | 27809.8i | −0.690082 | + | 1.19526i | ||||
\(816\) | 12096.0 | − | 20950.9i | 0.518927 | − | 0.898808i | ||||
\(817\) | 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 | \(-0.289950\pi\) |
−0.990727 | + | 0.135870i | \(0.956617\pi\) | |||||||
\(822\) | 4836.00 | − | 8376.20i | 0.205201 | − | 0.355418i | ||||
\(823\) | −3934.00 | + | 6813.89i | −0.166623 | + | 0.288599i | −0.937230 | − | 0.348711i | \(-0.886620\pi\) |
0.770608 | + | 0.637310i | \(0.219953\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29850.0 | 1.25969 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35726.0 | 1.50219 | 0.751097 | − | 0.660192i | \(-0.229525\pi\) | ||||
0.751097 | + | 0.660192i | \(0.229525\pi\) | |||||||
\(828\) | −504.000 | − | 872.954i | −0.0211536 | − | 0.0366392i | ||||
\(829\) | 13554.0 | − | 23476.2i | 0.567853 | − | 0.983550i | −0.428925 | − | 0.903340i | \(-0.641108\pi\) |
0.996778 | − | 0.0802098i | \(-0.0255590\pi\) | |||||||
\(830\) | −1296.00 | + | 2244.74i | −0.0541986 | + | 0.0938747i | ||||
\(831\) | −4101.00 | − | 7103.14i | −0.171194 | − | 0.296516i | ||||
\(832\) | −18432.0 | −0.768046 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31536.0 | 1.30936 | ||||||||
\(835\) | 27216.0 | + | 47139.5i | 1.12796 | + | 1.95369i | ||||
\(836\) | 14400.0 | − | 24941.5i | 0.595735 | − | 1.03184i | ||||
\(837\) | 486.000 | − | 841.777i | 0.0200700 | − | 0.0347623i | ||||
\(838\) | −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 | ||||
\(843\) | 897.000 | − | 1553.65i | 0.0366481 | − | 0.0634763i | ||||
\(844\) | −11664.0 | + | 20202.6i | −0.475701 | + | 0.823938i | ||||
\(845\) | −8109.00 | − | 14045.2i | −0.330128 | − | 0.571798i | ||||
\(846\) | 2592.00 | 0.105337 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1408.00 | 0.0570176 | ||||||||
\(849\) | −5400.00 | − | 9353.07i | −0.218289 | − | 0.378088i | ||||
\(850\) | 50148.0 | − | 86858.9i | 2.02360 | − | 3.50498i | ||||
\(851\) | 1134.00 | − | 1964.15i | 0.0456792 | − | 0.0791187i | ||||
\(852\) | −8808.00 | − | 15255.9i | −0.354175 | − | 0.613449i | ||||
\(853\) | −35280.0 | −1.41614 | −0.708068 | − | 0.706144i | \(-0.750433\pi\) | ||||
−0.708068 | + | 0.706144i | \(0.750433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11664.0 | −0.466550 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9855.00 | + | 17069.4i | −0.392813 | + | 0.680371i | −0.992819 | − | 0.119624i | \(-0.961831\pi\) |
0.600007 | + | 0.799995i | \(0.295165\pi\) | |||||||
\(858\) | −10800.0 | + | 18706.1i | −0.429727 | + | 0.744309i | ||||
\(859\) | 1944.00 | + | 3367.11i | 0.0772159 | + | 0.133742i | 0.902048 | − | 0.431636i | \(-0.142064\pi\) |
−0.824832 | + | 0.565378i | \(0.808730\pi\) | |||||||
\(860\) | 46656.0 | 1.84995 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41560.0 | −1.64216 | ||||||||
\(863\) | 18317.0 | + | 31726.0i | 0.722500 | + | 1.25141i | 0.959995 | + | 0.280019i | \(0.0903406\pi\) |
−0.237494 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(864\) | −3456.00 | + | 5985.97i | −0.136083 | + | 0.235702i | ||||
\(865\) | −14094.0 | + | 24411.5i | −0.554000 | + | 0.959557i | ||||
\(866\) | 22464.0 | + | 38908.8i | 0.881476 | + | 1.52676i | ||||
\(867\) | −32889.0 | −1.28831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11800.0 | −0.460630 | ||||||||
\(870\) | −17064.0 | − | 29555.7i | −0.664970 | − | 1.15176i | ||||
\(871\) | −4176.00 | + | 7233.04i | −0.162455 | + | 0.281380i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2106.00 | + | 3647.70i | 0.0816464 | + | 0.141416i | ||||
\(874\) | 4032.00 | 0.156046 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4320.00 | 0.166620 | ||||||||
\(877\) | −613.000 | − | 1061.75i | −0.0236027 | − | 0.0408810i | 0.853983 | − | 0.520301i | \(-0.174180\pi\) |
−0.877585 | + | 0.479420i | \(0.840847\pi\) | |||||||
\(878\) | 29232.0 | − | 50631.3i | 1.12361 | − | 1.94615i | ||||
\(879\) | −11853.0 | + | 20530.0i | −0.454826 | + | 0.787781i | ||||
\(880\) | 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 | ||||
\(885\) | 12636.0 | − | 21886.2i | 0.479949 | − | 0.831295i | ||||
\(886\) | −23876.0 | + | 41354.4i | −0.905338 | + | 1.56809i | ||||
\(887\) | 13320.0 | + | 23070.9i | 0.504219 | + | 0.873332i | 0.999988 | + | 0.00487800i | \(0.00155272\pi\) |
−0.495770 | + | 0.868454i | \(0.665114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16848.0 | 0.634546 | ||||||||
\(891\) | 2025.00 | + | 3507.40i | 0.0761392 | + | 0.131877i | ||||
\(892\) | −4320.00 | + | 7482.46i | −0.162157 | + | 0.280865i | ||||
\(893\) | −2592.00 | + | 4489.48i | −0.0971310 | + | 0.168236i | ||||
\(894\) | −14340.0 | − | 24837.6i | −0.536467 | − | 0.929188i | ||||
\(895\) | −68436.0 | −2.55594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1512.00 | −0.0562812 | ||||||||
\(898\) | −16372.0 | − | 28357.1i | −0.608397 | − | 1.05377i | ||||
\(899\) | −2844.00 | + | 4925.95i | −0.105509 | + | 0.182747i | ||||
\(900\) | −7164.00 | + | 12408.4i | −0.265333 | + | 0.459571i | ||||
\(901\) | −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 | ||||
\(906\) | 19440.0 | − | 33671.1i | 0.712860 | − | 1.23471i | ||||
\(907\) | 6318.00 | − | 10943.1i | 0.231296 | − | 0.400617i | −0.726894 | − | 0.686750i | \(-0.759037\pi\) |
0.958190 | + | 0.286133i | \(0.0923700\pi\) | |||||||
\(908\) | −5328.00 | − | 9228.37i | −0.194731 | − | 0.337284i | ||||
\(909\) | 5994.00 | 0.218711 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33638.0 | −1.22336 | −0.611678 | − | 0.791107i | \(-0.709505\pi\) | ||||
−0.611678 | + | 0.791107i | \(0.709505\pi\) | |||||||
\(912\) | −6912.00 | − | 11971.9i | −0.250964 | − | 0.434682i | ||||
\(913\) | −900.000 | + | 1558.85i | −0.0326239 | + | 0.0565063i | ||||
\(914\) | −4212.00 | + | 7295.40i | −0.152430 | + | 0.264016i | ||||
\(915\) | 21384.0 | + | 37038.2i | 0.772605 | + | 1.33819i | ||||
\(916\) | −12960.0 | −0.467479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13608.0 | 0.489249 | ||||||||
\(919\) | −18468.0 | − | 31987.5i | −0.662898 | − | 1.14817i | −0.979851 | − | 0.199731i | \(-0.935993\pi\) |
0.316953 | − | 0.948441i | \(-0.397340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15336.0 | − | 26562.7i | 0.548684 | − | 0.950349i | ||||
\(922\) | 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 | ||||
\(927\) | −1134.00 | + | 1964.15i | −0.0401785 | + | 0.0695912i | ||||
\(928\) | 20224.0 | − | 35029.0i | 0.715394 | − | 1.23910i | ||||
\(929\) | −11151.0 | − | 19314.1i | −0.393813 | − | 0.682104i | 0.599136 | − | 0.800647i | \(-0.295511\pi\) |
−0.992949 | + | 0.118543i | \(0.962178\pi\) | |||||||
\(930\) | 7776.00 | 0.274178 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 53744.0 | 1.88889 | ||||||||
\(933\) | −5832.00 | − | 10101.3i | −0.204642 | − | 0.354451i | ||||
\(934\) | −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 | \(-0.577471\pi\) | ||||
−0.240987 | + | 0.970528i | \(0.577471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15336.0 | 0.532983 | ||||||||
\(940\) | 5184.00 | + | 8978.95i | 0.179876 | + | 0.311554i | ||||
\(941\) | 6777.00 | − | 11738.1i | 0.234776 | − | 0.406643i | −0.724432 | − | 0.689346i | \(-0.757898\pi\) |
0.959207 | + | 0.282703i | \(0.0912311\pi\) | |||||||
\(942\) | −18144.0 | + | 31426.3i | −0.627562 | + | 1.08697i | ||||
\(943\) | −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 | −0.937574 | − | 0.347786i | \(-0.886934\pi\) |
0.167596 | − | 0.985856i | \(-0.446400\pi\) | |||||||
\(948\) | 2832.00 | − | 4905.17i | 0.0970244 | − | 0.168051i | ||||
\(949\) | 3240.00 | − | 5611.84i | 0.110827 | − | 0.191958i | ||||
\(950\) | −28656.0 | − | 49633.6i | −0.978656 | − | 1.69508i | ||||
\(951\) | 30306.0 | 1.03337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38362.0 | 1.30395 | 0.651976 | − | 0.758239i | \(-0.273940\pi\) | ||||
0.651976 | + | 0.758239i | \(0.273940\pi\) | |||||||
\(954\) | 396.000 | + | 685.892i | 0.0134392 | + | 0.0232773i | ||||
\(955\) | 4338.00 | − | 7513.64i | 0.146989 | − | 0.254592i | ||||
\(956\) | 14312.0 | − | 24789.1i | 0.484187 | − | 0.838637i | ||||
\(957\) | −11850.0 | − | 20524.8i | −0.400268 | − | 0.693284i | ||||
\(958\) | 32256.0 | 1.08783 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27648.0 | −0.929516 | ||||||||
\(961\) | 14247.5 | + | 24677.4i | 0.478248 | + | 0.828351i | ||||
\(962\) | 11664.0 | − | 20202.6i | 0.390917 | − | 0.677089i | ||||
\(963\) | −3015.00 | + | 5222.13i | −0.100890 | + | 0.174747i | ||||
\(964\) | −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 | ||||||||
\(969\) | −13608.0 | + | 23569.7i | −0.451137 | + | 0.781393i | ||||
\(970\) | −16848.0 | + | 29181.6i | −0.557687 | + | 0.965943i | ||||
\(971\) | 8910.00 | + | 15432.6i | 0.294475 | + | 0.510046i | 0.974863 | − | 0.222806i | \(-0.0715218\pi\) |
−0.680387 | + | 0.732853i | \(0.738188\pi\) | |||||||
\(972\) | −1944.00 | −0.0641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −46656.0 | −1.53486 | ||||||||
\(975\) | 10746.0 | + | 18612.6i | 0.352972 | + | 0.611365i | ||||
\(976\) | −25344.0 | + | 43897.1i | −0.831190 | + | 1.43966i | ||||
\(977\) | −17219.0 | + | 29824.2i | −0.563853 | + | 0.976622i | 0.433302 | + | 0.901249i | \(0.357348\pi\) |
−0.997155 | + | 0.0753737i | \(0.975985\pi\) | |||||||
\(978\) | −10704.0 | − | 18539.9i | −0.349976 | − | 0.606176i | ||||
\(979\) | 11700.0 | 0.381955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1458.00 | 0.0474519 | ||||||||
\(982\) | 19628.0 | + | 33996.7i | 0.637836 | + | 1.10476i | ||||
\(983\) | 13032.0 | − | 22572.1i | 0.422845 | − | 0.732388i | −0.573372 | − | 0.819295i | \(-0.694365\pi\) |
0.996216 | + | 0.0869069i | \(0.0276983\pi\) | |||||||
\(984\) | 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 | ||||
\(990\) | −16200.0 | + | 28059.2i | −0.520071 | + | 0.900789i | ||||
\(991\) | −16848.0 | + | 29181.6i | −0.540055 | + | 0.935402i | 0.458845 | + | 0.888516i | \(0.348263\pi\) |
−0.998900 | + | 0.0468863i | \(0.985070\pi\) | |||||||
\(992\) | 4608.00 | + | 7981.29i | 0.147484 | + | 0.255450i | ||||
\(993\) | −16524.0 | −0.528070 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −81648.0 | −2.60142 | ||||||||
\(996\) | −432.000 | − | 748.246i | −0.0137434 | − | 0.0238043i | ||||
\(997\) | 18036.0 | − | 31239.3i | 0.572925 | − | 0.992335i | −0.423339 | − | 0.905971i | \(-0.639142\pi\) |
0.996264 | − | 0.0863632i | \(-0.0275246\pi\) | |||||||
\(998\) | 30456.0 | − | 52751.3i | 0.966000 | − | 1.67316i | ||||
\(999\) | −2187.00 | − | 3788.00i | −0.0692629 | − | 0.119967i |
(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 | 147.4.e.d.67.1 | 2 | ||
3.2 | odd | 2 | 441.4.e.l.361.1 | 2 | |||
7.2 | even | 3 | inner | 147.4.e.d.79.1 | 2 | ||
7.3 | odd | 6 | 147.4.a.h.1.1 | yes | 1 | ||
7.4 | even | 3 | 147.4.a.f.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 147.4.e.a.79.1 | 2 | |||
7.6 | odd | 2 | 147.4.e.a.67.1 | 2 | |||
21.2 | odd | 6 | 441.4.e.l.226.1 | 2 | |||
21.5 | even | 6 | 441.4.e.o.226.1 | 2 | |||
21.11 | odd | 6 | 441.4.a.c.1.1 | 1 | |||
21.17 | even | 6 | 441.4.a.a.1.1 | 1 | |||
21.20 | even | 2 | 441.4.e.o.361.1 | 2 | |||
28.3 | even | 6 | 2352.4.a.s.1.1 | 1 | |||
28.11 | 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 | 7.4 | even | 3 | ||
147.4.a.h.1.1 | yes | 1 | 7.3 | odd | 6 | ||
147.4.e.a.67.1 | 2 | 7.6 | odd | 2 | |||
147.4.e.a.79.1 | 2 | 7.5 | odd | 6 | |||
147.4.e.d.67.1 | 2 | 1.1 | even | 1 | trivial | ||
147.4.e.d.79.1 | 2 | 7.2 | even | 3 | inner | ||
441.4.a.a.1.1 | 1 | 21.17 | even | 6 | |||
441.4.a.c.1.1 | 1 | 21.11 | odd | 6 | |||
441.4.e.l.226.1 | 2 | 21.2 | odd | 6 | |||
441.4.e.l.361.1 | 2 | 3.2 | odd | 2 | |||
441.4.e.o.226.1 | 2 | 21.5 | even | 6 | |||
441.4.e.o.361.1 | 2 | 21.20 | even | 2 | |||
2352.4.a.s.1.1 | 1 | 28.3 | even | 6 | |||
2352.4.a.t.1.1 | 1 | 28.11 | odd | 6 |