Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,5,Mod(127,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.g (of order \(2\), degree \(1\), 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: | \(19.8470329121\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.127 |
Dual form | 192.5.g.b.127.1 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 42.0000 | 1.68000 | 0.840000 | − | 0.542586i | \(-0.182555\pi\) | ||||
0.840000 | + | 0.542586i | \(0.182555\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 76.2102i | 1.55531i | 0.628691 | + | 0.777655i | \(0.283591\pi\) | ||||
−0.628691 | + | 0.777655i | \(0.716409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.7846i | 0.171774i | 0.996305 | + | 0.0858868i | \(0.0273723\pi\) | ||||
−0.996305 | + | 0.0858868i | \(0.972628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 182.000 | 1.07692 | 0.538462 | − | 0.842650i | \(-0.319006\pi\) | ||||
0.538462 | + | 0.842650i | \(0.319006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 218.238i | 0.969948i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −246.000 | −0.851211 | −0.425606 | − | 0.904909i | \(-0.639939\pi\) | ||||
−0.425606 | + | 0.904909i | \(0.639939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 117.779i | 0.326259i | 0.986605 | + | 0.163129i | \(0.0521588\pi\) | ||||
−0.986605 | + | 0.163129i | \(0.947841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −396.000 | −0.897959 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 748.246i | − 1.41445i | −0.706987 | − | 0.707227i | \(-0.749946\pi\) | ||||
0.706987 | − | 0.707227i | \(-0.250054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1139.00 | 1.82240 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 140.296i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −78.0000 | −0.0927467 | −0.0463734 | − | 0.998924i | \(-0.514766\pi\) | ||||
−0.0463734 | + | 0.998924i | \(0.514766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1475.71i | 1.53560i | 0.640692 | + | 0.767798i | \(0.278647\pi\) | ||||
−0.640692 | + | 0.767798i | \(0.721353\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.000 | −0.0991736 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3200.83i | 2.61292i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −530.000 | −0.387144 | −0.193572 | − | 0.981086i | \(-0.562007\pi\) | ||||
−0.193572 | + | 0.981086i | \(0.562007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 945.700i | 0.621762i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −918.000 | −0.546104 | −0.273052 | − | 0.961999i | \(-0.588033\pi\) | ||||
−0.273052 | + | 0.961999i | \(0.588033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 852.169i | 0.460881i | 0.973086 | + | 0.230441i | \(0.0740167\pi\) | ||||
−0.973086 | + | 0.230441i | \(0.925983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1134.00 | −0.560000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3782.80i | 1.71245i | 0.516604 | + | 0.856224i | \(0.327196\pi\) | ||||
−0.516604 | + | 0.856224i | \(0.672804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3407.00 | −1.41899 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1278.25i | − 0.491447i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4626.00 | 1.64685 | 0.823425 | − | 0.567426i | \(-0.192061\pi\) | ||||
0.823425 | + | 0.567426i | \(0.192061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 872.954i | 0.288580i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −612.000 | −0.188366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 228.631i | 0.0656796i | 0.999461 | + | 0.0328398i | \(0.0104551\pi\) | ||||
−0.999461 | + | 0.0328398i | \(0.989545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1346.00 | −0.361731 | −0.180865 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180865 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 2057.68i | − 0.518437i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7644.00 | 1.80923 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1087.73i | − 0.242310i | −0.992634 | − | 0.121155i | \(-0.961340\pi\) | ||||
0.992634 | − | 0.121155i | \(-0.0386597\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3888.00 | 0.816635 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1829.05i | − 0.362834i | −0.983406 | − | 0.181417i | \(-0.941932\pi\) | ||||
0.983406 | − | 0.181417i | \(-0.0580684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −926.000 | −0.173766 | −0.0868831 | − | 0.996219i | \(-0.527691\pi\) | ||||
−0.0868831 | + | 0.996219i | \(0.527691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5918.42i | 1.05216i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1584.00 | −0.267161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 4399.41i | − 0.704921i | −0.935827 | − | 0.352460i | \(-0.885345\pi\) | ||||
0.935827 | − | 0.352460i | \(-0.114655\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 11992.7i | − 1.74085i | −0.492301 | − | 0.870425i | \(-0.663844\pi\) | ||||
0.492301 | − | 0.870425i | \(-0.336156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10332.0 | −1.43003 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 405.300i | − 0.0535473i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11586.0 | 1.46269 | 0.731347 | − | 0.682005i | \(-0.238892\pi\) | ||||
0.731347 | + | 0.682005i | \(0.238892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13870.3i | 1.67495i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7668.00 | −0.886576 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4946.74i | 0.548115i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13118.0 | −1.39420 | −0.697099 | − | 0.716975i | \(-0.745526\pi\) | ||||
−0.697099 | + | 0.716975i | \(0.745526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 561.184i | − 0.0572579i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5490.00 | 0.538183 | 0.269091 | − | 0.963115i | \(-0.413277\pi\) | ||||
0.269091 | + | 0.963115i | \(0.413277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5701.91i | − 0.537460i | −0.963216 | − | 0.268730i | \(-0.913396\pi\) | ||||
0.963216 | − | 0.268730i | \(-0.0866039\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16632.0 | −1.50857 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 10080.5i | − 0.880473i | −0.897882 | − | 0.440237i | \(-0.854895\pi\) | ||||
0.897882 | − | 0.440237i | \(-0.145105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16166.0 | 1.36066 | 0.680330 | − | 0.732906i | \(-0.261836\pi\) | ||||
0.680330 | + | 0.732906i | \(0.261836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 2753.96i | − 0.223518i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1842.00 | 0.144256 | 0.0721278 | − | 0.997395i | \(-0.477021\pi\) | ||||
0.0721278 | + | 0.997395i | \(0.477021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 31426.3i | − 2.37628i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4914.00 | −0.358974 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 18747.7i | − 1.32390i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14209.0 | 0.970494 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4770.07i | − 0.315293i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 21588.0 | 1.38163 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 394.908i | − 0.0244843i | −0.999925 | − | 0.0122422i | \(-0.996103\pi\) | ||||
0.999925 | − | 0.0122422i | \(-0.00389690\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4428.00 | −0.266090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 353.338i | 0.0205896i | 0.999947 | + | 0.0102948i | \(0.00327700\pi\) | ||||
−0.999947 | + | 0.0102948i | \(0.996723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8976.00 | −0.507434 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5892.44i | − 0.323316i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13254.0 | −0.706164 | −0.353082 | − | 0.935592i | \(-0.614866\pi\) | ||||
−0.353082 | + | 0.935592i | \(0.614866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 13212.1i | − 0.683820i | −0.939733 | − | 0.341910i | \(-0.888926\pi\) | ||||
0.939733 | − | 0.341910i | \(-0.111074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19656.0 | −0.988683 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3782.80i | 0.184987i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3276.00 | −0.155815 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 17703.3i | − 0.819255i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −438.000 | −0.0197288 | −0.00986442 | − | 0.999951i | \(-0.503140\pi\) | ||||
−0.00986442 | + | 0.999951i | \(0.503140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 28052.3i | − 1.23031i | −0.788406 | − | 0.615155i | \(-0.789093\pi\) | ||||
0.788406 | − | 0.615155i | \(-0.210907\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6642.00 | 0.283737 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 61979.7i | 2.57980i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19346.0 | −0.784859 | −0.392430 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392430 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24037.4i | 0.950809i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 57024.0 | 2.19992 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 36255.3i | 1.36457i | 0.731086 | + | 0.682286i | \(0.239014\pi\) | ||||
−0.731086 | + | 0.682286i | \(0.760986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4536.00 | −0.166612 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 18747.7i | − 0.672226i | −0.941822 | − | 0.336113i | \(-0.890888\pi\) | ||||
0.941822 | − | 0.336113i | \(-0.109112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4563.00 | 0.159763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3180.05i | − 0.108753i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 34410.0 | 1.14972 | 0.574861 | − | 0.818251i | \(-0.305056\pi\) | ||||
0.574861 | + | 0.818251i | \(0.305056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 86803.5i | 2.83440i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1188.00 | −0.0379201 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 16856.3i | − 0.526086i | −0.964784 | − | 0.263043i | \(-0.915274\pi\) | ||||
0.964784 | − | 0.263043i | \(-0.0847261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15706.0 | −0.479411 | −0.239706 | − | 0.970846i | \(-0.577051\pi\) | ||||
−0.239706 | + | 0.970846i | \(0.577051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6994.02i | − 0.208845i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22260.0 | −0.650402 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5113.01i | − 0.146216i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10692.0 | 0.299320 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2660.43i | 0.0729265i | 0.999335 | + | 0.0364632i | \(0.0116092\pi\) | ||||
−0.999335 | + | 0.0364632i | \(0.988391\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26782.0 | −0.718999 | −0.359500 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359500 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 39719.4i | 1.04456i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 52482.0 | 1.35232 | 0.676158 | − | 0.736757i | \(-0.263644\pi\) | ||||
0.676158 | + | 0.736757i | \(0.263644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 23077.8i | − 0.582759i | −0.956608 | − | 0.291380i | \(-0.905886\pi\) | ||||
0.956608 | − | 0.291380i | \(-0.0941143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5652.00 | 0.139898 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5944.40i | − 0.144250i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38556.0 | −0.917454 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20202.6i | 0.471485i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2448.00 | −0.0560427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 23895.4i | − 0.536721i | −0.963319 | − | 0.268361i | \(-0.913518\pi\) | ||||
0.963319 | − | 0.268361i | \(-0.0864819\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9504.00 | 0.209482 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35791.1i | 0.774280i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −112464. | −2.38833 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4811.64i | − 0.100324i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −44772.0 | −0.916689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 852.169i | 0.0171363i | 0.999963 | + | 0.00856813i | \(0.00272735\pi\) | ||||
−0.999963 | + | 0.00856813i | \(0.997273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30753.0 | −0.607467 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 76175.6i | − 1.47831i | −0.673538 | − | 0.739153i | \(-0.735226\pi\) | ||||
0.673538 | − | 0.739153i | \(-0.264774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 48470.0 | 0.924277 | 0.462138 | − | 0.886808i | \(-0.347082\pi\) | ||||
0.462138 | + | 0.886808i | \(0.347082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 8230.71i | − 0.154246i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 48738.0 | 0.897751 | 0.448875 | − | 0.893594i | \(-0.351825\pi\) | ||||
0.448875 | + | 0.893594i | \(0.351825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 158878.i | 2.87691i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22860.0 | 0.406986 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 71000.2i | 1.24298i | 0.783422 | + | 0.621490i | \(0.213472\pi\) | ||||
−0.783422 | + | 0.621490i | \(0.786528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 73138.0 | 1.25924 | 0.629621 | − | 0.776903i | \(-0.283210\pi\) | ||||
0.629621 | + | 0.776903i | \(0.283210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −143094. | −2.38391 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21435.9i | 0.351356i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 62316.0 | 1.00508 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 91888.8i | 1.45853i | 0.684232 | + | 0.729264i | \(0.260138\pi\) | ||||
−0.684232 | + | 0.729264i | \(0.739862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15552.0 | 0.242966 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 53686.6i | − 0.825631i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −48894.0 | −0.740269 | −0.370134 | − | 0.928978i | \(-0.620688\pi\) | ||||
−0.370134 | + | 0.928978i | \(0.620688\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 40391.4i | − 0.602129i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2106.00 | 0.0309156 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 78191.7i | 1.13044i | 0.824939 | + | 0.565222i | \(0.191210\pi\) | ||||
−0.824939 | + | 0.565222i | \(0.808790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 194292. | 2.76671 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 60202.6i | 0.844487i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 71538.0 | 0.988626 | 0.494313 | − | 0.869284i | \(-0.335420\pi\) | ||||
0.494313 | + | 0.869284i | \(0.335420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 108198.i | − 1.47326i | −0.676296 | − | 0.736630i | \(-0.736416\pi\) | ||||
0.676296 | − | 0.736630i | \(-0.263584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −72072.0 | −0.967033 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23673.7i | 0.313040i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 120518. | 1.57070 | 0.785348 | − | 0.619054i | \(-0.212484\pi\) | ||||
0.785348 | + | 0.619054i | \(0.212484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 39844.1i | − 0.511865i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3054.00 | −0.0386773 | −0.0193387 | − | 0.999813i | \(-0.506156\pi\) | ||||
−0.0193387 | + | 0.999813i | \(0.506156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 132959.i | − 1.66014i | −0.557657 | − | 0.830071i | \(-0.688300\pi\) | ||||
0.557657 | − | 0.830071i | \(-0.311700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25704.0 | −0.316454 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 69961.0i | − 0.849361i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23005.0 | −0.275440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 68163.1i | − 0.804940i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −151662. | −1.76661 | −0.883307 | − | 0.468795i | \(-0.844688\pi\) | ||||
−0.883307 | + | 0.468795i | \(0.844688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9602.49i | 0.110342i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2916.00 | 0.0330579 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 136181.i | − 1.52326i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −64944.0 | −0.716813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28526.9i | 0.310720i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −56532.0 | −0.607708 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5424.78i | 0.0575580i | 0.999586 | + | 0.0287790i | \(0.00916190\pi\) | ||||
−0.999586 | + | 0.0287790i | \(0.990838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29628.0 | 0.310303 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 141127.i | − 1.45912i | −0.683917 | − | 0.729560i | \(-0.739725\pi\) | ||||
0.683917 | − | 0.729560i | \(-0.260275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −128686. | −1.31354 | −0.656769 | − | 0.754092i | \(-0.728077\pi\) | ||||
−0.656769 | + | 0.754092i | \(0.728077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 86422.4i | − 0.870974i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 73986.0 | 0.736260 | 0.368130 | − | 0.929774i | \(-0.379998\pi\) | ||||
0.368130 | + | 0.929774i | \(0.379998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1621.20i | − 0.0159314i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52380.0 | 0.508341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 28973.7i | − 0.277715i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 207298. | 1.96258 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 84001.0i | 0.785577i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −288288. | −2.66339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 57026.0i | − 0.520496i | −0.965542 | − | 0.260248i | \(-0.916196\pi\) | ||||
0.965542 | − | 0.260248i | \(-0.0838043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14310.0 | 0.129048 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 45684.6i | − 0.407080i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 98674.0 | 0.868846 | 0.434423 | − | 0.900709i | \(-0.356952\pi\) | ||||
0.434423 | + | 0.900709i | \(0.356952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9571.31i | 0.0832860i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30672.0 | −0.263775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 76667.5i | − 0.651663i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 163296. | 1.37195 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 56929.0i | − 0.472797i | −0.971656 | − | 0.236399i | \(-0.924033\pi\) | ||||
0.971656 | − | 0.236399i | \(-0.0759671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −181346. | −1.48887 | −0.744436 | − | 0.667694i | \(-0.767281\pi\) | ||||
−0.744436 | + | 0.667694i | \(0.767281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 25533.9i | − 0.207254i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4302.00 | −0.0345240 | −0.0172620 | − | 0.999851i | \(-0.505495\pi\) | ||||
−0.0172620 | + | 0.999851i | \(0.505495\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 76819.9i | − 0.609561i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 97416.0 | 0.764353 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 185232.i | − 1.43724i | −0.695405 | − | 0.718618i | \(-0.744775\pi\) | ||||
0.695405 | − | 0.718618i | \(-0.255225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 116449. | 0.893555 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 73832.1i | 0.560315i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38892.0 | −0.291927 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 182690.i | 1.35638i | 0.734885 | + | 0.678191i | \(0.237236\pi\) | ||||
−0.734885 | + | 0.678191i | \(0.762764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24786.0 | 0.182035 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 352549.i | 2.56136i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −151778. | −1.09092 | −0.545458 | − | 0.838138i | \(-0.683644\pi\) | ||||
−0.545458 | + | 0.838138i | \(0.683644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 112175.i | 0.797686i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14196.0 | −0.0998811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 36005.9i | − 0.250666i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | − | 0.125333i | \(-0.0399999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2052.00 | 0.0141360 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 65346.8i | − 0.445479i | −0.974878 | − | 0.222739i | \(-0.928500\pi\) | ||||
0.974878 | − | 0.222739i | \(-0.0714999\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −66528.0 | −0.448831 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 23008.6i | − 0.153627i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −105750. | −0.698846 | −0.349423 | − | 0.936965i | \(-0.613622\pi\) | ||||
−0.349423 | + | 0.936965i | \(0.613622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 184069.i | 1.20400i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1836.00 | −0.0118874 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 184775.i | − 1.18427i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27934.0 | 0.177236 | 0.0886180 | − | 0.996066i | \(-0.471755\pi\) | ||||
0.0886180 | + | 0.996066i | \(0.471755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 46640.7i | − 0.292967i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 237882. | 1.47936 | 0.739678 | − | 0.672961i | \(-0.234978\pi\) | ||||
0.739678 | + | 0.672961i | \(0.234978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 268579.i | 1.65372i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30618.0 | 0.186667 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 11015.8i | − 0.0665011i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20270.0 | −0.121173 | −0.0605867 | − | 0.998163i | \(-0.519297\pi\) | ||||
−0.0605867 | + | 0.998163i | \(0.519297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 68869.8i | − 0.407704i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17424.0 | −0.102152 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 503694.i | − 2.92463i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 68652.0 | 0.394804 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24089.4i | 0.137214i | 0.997644 | + | 0.0686068i | \(0.0218554\pi\) | ||||
−0.997644 | + | 0.0686068i | \(0.978145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −116698. | −0.658414 | −0.329207 | − | 0.944258i | \(-0.606781\pi\) | ||||
−0.329207 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 102136.i | − 0.570816i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −280194. | −1.55125 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 102579.i | − 0.562604i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19656.0 | −0.106802 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 355542.i | 1.91397i | 0.290132 | + | 0.956986i | \(0.406301\pi\) | ||||
−0.290132 | + | 0.956986i | \(0.593699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −199726. | −1.06527 | −0.532634 | − | 0.846346i | \(-0.678798\pi\) | ||||
−0.532634 | + | 0.846346i | \(0.678798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 17022.6i | − 0.0899595i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 88128.0 | 0.461478 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146469.i | 0.760006i | 0.924985 | + | 0.380003i | \(0.124077\pi\) | ||||
−0.924985 | + | 0.380003i | \(0.875923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 91989.0 | 0.472997 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 50444.2i | − 0.257042i | −0.991707 | − | 0.128521i | \(-0.958977\pi\) | ||||
0.991707 | − | 0.128521i | \(-0.0410230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 486612. | 2.45733 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2275.91i | − 0.0113905i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 149994. | 0.744014 | 0.372007 | − | 0.928230i | \(-0.378670\pi\) | ||||
0.372007 | + | 0.928230i | \(0.378670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 19080.3i | − 0.0938062i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 145764. | 0.710320 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 582551.i | 2.81392i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 284338. | 1.36145 | 0.680726 | − | 0.732538i | \(-0.261664\pi\) | ||||
0.680726 | + | 0.732538i | \(0.261664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34512.8i | 0.163816i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 183402. | 0.862983 | 0.431491 | − | 0.902117i | \(-0.357987\pi\) | ||||
0.431491 | + | 0.902117i | \(0.357987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 172422.i | 0.804324i | 0.915568 | + | 0.402162i | \(0.131741\pi\) | ||||
−0.915568 | + | 0.402162i | \(0.868259\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −322056. | −1.48945 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 68734.7i | 0.315168i | 0.987506 | + | 0.157584i | \(0.0503705\pi\) | ||||
−0.987506 | + | 0.157584i | \(0.949629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 82896.0 | 0.376867 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 100525.i | − 0.453139i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17712.0 | −0.0791672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 134151.i | 0.594574i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −124902. | −0.548950 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 249956.i | − 1.08941i | −0.838627 | − | 0.544706i | \(-0.816641\pi\) | ||||
0.838627 | − | 0.544706i | \(-0.183359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −96460.0 | −0.416924 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 296305.i | 1.27012i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −550956. | −2.34225 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 271108.i | 1.14310i | 0.820568 | + | 0.571549i | \(0.193657\pi\) | ||||
−0.820568 | + | 0.571549i | \(0.806343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −188388. | −0.787835 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 227862.i | 0.945166i | 0.881286 | + | 0.472583i | \(0.156678\pi\) | ||||
−0.881286 | + | 0.472583i | \(0.843322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19188.0 | 0.0789470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 23569.7i | − 0.0961932i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 139392. | 0.564320 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 248854.i | 0.999410i | 0.866196 | + | 0.499705i | \(0.166558\pi\) | ||||
−0.866196 | + | 0.499705i | \(0.833442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 97416.0 | 0.388110 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 446537.i | 1.76490i | 0.470403 | + | 0.882452i | \(0.344109\pi\) | ||||
−0.470403 | + | 0.882452i | \(0.655891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 230580. | 0.904147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23710.0i | 0.0922394i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39330.0 | 0.151806 | 0.0759029 | − | 0.997115i | \(-0.475816\pi\) | ||||
0.0759029 | + | 0.997115i | \(0.475816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 70570.7i | − 0.270260i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16524.0 | 0.0627886 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 239480.i | − 0.902933i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −78624.0 | −0.294154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 178800.i | 0.663792i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −464598. | −1.71160 | −0.855799 | − | 0.517308i | \(-0.826934\pi\) | ||||
−0.855799 | + | 0.517308i | \(0.826934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 135509.i | 0.495409i | 0.968836 | + | 0.247704i | \(0.0796762\pi\) | ||||
−0.968836 | + | 0.247704i | \(0.920324\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −451044. | −1.63644 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 363024.i | − 1.30712i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −280031. | −1.00068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6173.03i | − 0.0218932i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −167076. | −0.588111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 423382.i | − 1.47919i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 87588.0 | 0.303736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 70813.2i | − 0.243745i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −360442. | −1.23152 | −0.615759 | − | 0.787934i | \(-0.711151\pi\) | ||||
−0.615759 | + | 0.787934i | \(0.711151\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 81610.8i | − 0.276788i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 678972. | 2.28591 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 261644.i | 0.874451i | 0.899352 | + | 0.437225i | \(0.144039\pi\) | ||||
−0.899352 | + | 0.437225i | \(0.855961\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36342.0 | 0.120577 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 9186.80i | − 0.0302594i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 335280. | 1.09637 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 115666.i | − 0.375510i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 233274. | 0.751893 | 0.375946 | − | 0.926641i | \(-0.377318\pi\) | ||||
0.375946 | + | 0.926641i | \(0.377318\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 155095.i | 0.496333i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26568.0 | 0.0844176 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 419704.i | − 1.32412i | −0.749453 | − | 0.662058i | \(-0.769683\pi\) | ||||
0.749453 | − | 0.662058i | \(-0.230317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 77364.0 | 0.242349 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 55557.3i | 0.172812i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 470058. | 1.45187 | 0.725934 | − | 0.687765i | \(-0.241408\pi\) | ||||
0.725934 | + | 0.687765i | \(0.241408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 320381.i | − 0.982640i | −0.870979 | − | 0.491320i | \(-0.836515\pi\) | ||||
0.870979 | − | 0.491320i | \(-0.163485\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13824.0 | −0.0421041 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 852252.i | − 2.57770i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −341038. | −1.02436 | −0.512178 | − | 0.858879i | \(-0.671161\pi\) | ||||
−0.512178 | + | 0.858879i | \(0.671161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 139163.i | − 0.415114i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 913968. | 2.70756 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 96149.6i | 0.282885i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −206388. | −0.603077 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 114128.i | 0.331220i | 0.986191 | + | 0.165610i | \(0.0529594\pi\) | ||||
−0.986191 | + | 0.165610i | \(0.947041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −173808. | −0.501002 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 272704.i | 0.780760i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −96846.0 | −0.275405 | −0.137703 | − | 0.990474i | \(-0.543972\pi\) | ||||
−0.137703 | + | 0.990474i | \(0.543972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 787404.i | − 2.22415i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 119916. | 0.336456 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 519782.i | − 1.44866i | −0.689452 | − | 0.724331i | \(-0.742149\pi\) | ||||
0.689452 | − | 0.724331i | \(-0.257851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −627742. | −1.73793 | −0.868965 | − | 0.494874i | \(-0.835214\pi\) | ||||
−0.868965 | + | 0.494874i | \(0.835214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29368.7i | 0.0807699i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 596778. | 1.63043 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 133195.i | − 0.361501i | −0.983529 | − | 0.180751i | \(-0.942147\pi\) | ||||
0.983529 | − | 0.180751i | \(-0.0578527\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30888.0 | 0.0832828 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 688469.i | 1.84418i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −247202. | −0.657856 | −0.328928 | − | 0.944355i | \(-0.606687\pi\) | ||||
−0.328928 | + | 0.944355i | \(0.606687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 200343.i | − 0.529692i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31758.0 | −0.0834224 | −0.0417112 | − | 0.999130i | \(-0.513281\pi\) | ||||
−0.0417112 | + | 0.999130i | \(0.513281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 656094.i | − 1.71232i | −0.516712 | − | 0.856160i | \(-0.672844\pi\) | ||||
0.516712 | − | 0.856160i | \(-0.327156\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −104976. | −0.272212 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 882972.i | 2.27494i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 194821. | 0.498742 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 12720.2i | − 0.0323563i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 130380. | 0.329541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 417736.i | 1.04916i | 0.851360 | + | 0.524582i | \(0.175778\pi\) | ||||
−0.851360 | + | 0.524582i | \(0.824222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 124164. | 0.309876 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 16586.1i | − 0.0411337i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −620074. | −1.52815 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 49384.2i | 0.120945i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −152214. | −0.370458 | −0.185229 | − | 0.982695i | \(-0.559303\pi\) | ||||
−0.185229 | + | 0.982695i | \(0.559303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 714138.i | 1.72727i | 0.504117 | + | 0.863635i | \(0.331818\pi\) | ||||
−0.504117 | + | 0.863635i | \(0.668182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −185976. | −0.447031 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 259558.i | − 0.620049i | −0.950729 | − | 0.310025i | \(-0.899663\pi\) | ||||
0.950729 | − | 0.310025i | \(-0.100337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4752.00 | −0.0112820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 584380.i | − 1.37890i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 330714. | 0.775579 | 0.387790 | − | 0.921748i | \(-0.373239\pi\) | ||||
0.387790 | + | 0.921748i | \(0.373239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14840.2i | 0.0345906i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25002.0 | 0.0579221 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 253884.i | − 0.584608i | −0.956326 | − | 0.292304i | \(-0.905578\pi\) | ||||
0.956326 | − | 0.292304i | \(-0.0944219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 722158. | 1.65283 | 0.826417 | − | 0.563058i | \(-0.190375\pi\) | ||||
0.826417 | + | 0.563058i | \(0.190375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 232642.i | − 0.529251i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −376992. | −0.852489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58363.2i | 0.131186i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4428.00 | −0.00989362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 27976.1i | − 0.0621358i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −552910. | −1.22074 | −0.610372 | − | 0.792115i | \(-0.708980\pi\) | ||||
−0.610372 | + | 0.792115i | \(0.708980\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 159797.i | − 0.350721i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −609030. | −1.32881 | −0.664403 | − | 0.747375i | \(-0.731314\pi\) | ||||
−0.664403 | + | 0.747375i | \(0.731314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 999726.i | − 2.16841i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 395820. | 0.853500 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23715.2i | 0.0508377i | 0.999677 | + | 0.0254189i | \(0.00809195\pi\) | ||||
−0.999677 | + | 0.0254189i | \(0.991908\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −556668. | −1.18636 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 251858.i | 0.533631i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 841932. | 1.77353 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 431842.i | − 0.904417i | −0.891912 | − | 0.452208i | \(-0.850636\pi\) | ||||
0.891912 | − | 0.452208i | \(-0.149364\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42768.0 | 0.0890538 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 554908.i | − 1.14882i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 225828. | 0.464849 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 253250.i | 0.518317i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44958.0 | −0.0914894 | −0.0457447 | − | 0.998953i | \(-0.514566\pi\) | ||||
−0.0457447 | + | 0.998953i | \(0.514566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 62423.1i | − 0.126309i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −825552. | −1.66099 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 418394.i | 0.837041i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −533002. | −1.06032 | −0.530159 | − | 0.847898i | \(-0.677868\pi\) | ||||
−0.530159 | + | 0.847898i | \(0.677868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 118784.i | 0.234974i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.10419e6 | 2.17203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 158878.i | 0.310778i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −368928. | −0.717634 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 292107.i | 0.565046i | 0.959260 | + | 0.282523i | \(0.0911714\pi\) | ||||
−0.959260 | + | 0.282523i | \(0.908829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 434544. | 0.835917 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 380036.i | 0.727023i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −88842.0 | −0.169022 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 755791.i | − 1.42999i | −0.699130 | − | 0.714995i | \(-0.746429\pi\) | ||||
0.699130 | − | 0.714995i | \(-0.253571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 209634.i | − 0.392307i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 832982. | 1.55034 | 0.775171 | − | 0.631751i | \(-0.217664\pi\) | ||||
0.775171 | + | 0.631751i | \(0.217664\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 743538.i | − 1.37635i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22608.0 | 0.0416224 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 698093.i | − 1.27827i | −0.769093 | − | 0.639137i | \(-0.779292\pi\) | ||||
0.769093 | − | 0.639137i | \(-0.220708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −111384. | −0.202855 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 461044.i | 0.835151i | 0.908642 | + | 0.417575i | \(0.137120\pi\) | ||||
−0.908642 | + | 0.417575i | \(0.862880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18396.0 | −0.0331445 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 323803.i | 0.580284i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 768240. | 1.36941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 937060.i | 1.66145i | 0.556682 | + | 0.830726i | \(0.312074\pi\) | ||||
−0.556682 | + | 0.830726i | \(0.687926\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −477468. | −0.842082 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.17820e6i | − 2.06692i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −295786. | −0.516162 | −0.258081 | − | 0.966123i | \(-0.583090\pi\) | ||||
−0.258081 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80810.6i | 0.140276i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.02615e6 | −1.77191 | −0.885955 | − | 0.463772i | \(-0.846496\pi\) | ||||
−0.885955 | + | 0.463772i | \(0.846496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.23201e6i | 2.11625i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 278964. | 0.476678 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41610.8i | 0.0707319i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 362306. | 0.612665 | 0.306332 | − | 0.951925i | \(-0.400898\pi\) | ||||
0.306332 | + | 0.951925i | \(0.400898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 254061.i | − 0.427394i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.02608e6 | −1.71720 | −0.858601 | − | 0.512644i | \(-0.828666\pi\) | ||||
−0.858601 | + | 0.512644i | \(0.828666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.68083e6i | 2.79847i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 209880. | 0.347639 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 108122.i | − 0.178171i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38016.0 | 0.0623253 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10943.1i | 0.0178491i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −812532. | −1.31856 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 850042.i | 1.37243i | 0.727398 | + | 0.686216i | \(0.240730\pi\) | ||||
−0.727398 | + | 0.686216i | \(0.759270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −406296. | −0.652662 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 140379.i | 0.224362i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −244972. | −0.389556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.00957e6i | 1.59736i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −761478. | −1.19878 | −0.599392 | − | 0.800456i | \(-0.704591\pi\) | ||||
−0.599392 | + | 0.800456i | \(0.704591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 930569.i | − 1.45766i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −312822. | −0.487565 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19246.5i | − 0.0298484i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.39501e6 | 3.69586 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 371722.i | 0.570784i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 247674. | 0.378428 | 0.189214 | − | 0.981936i | \(-0.439406\pi\) | ||||
0.189214 | + | 0.981936i | \(0.439406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 920197.i | 1.39907i | 0.714599 | + | 0.699534i | \(0.246609\pi\) | ||||
−0.714599 | + | 0.699534i | \(0.753391\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 562212. | 0.850588 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.52272e6i | 2.29248i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −100368. | −0.150367 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 374497.i | − 0.558317i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 250242. | 0.371256 | 0.185628 | − | 0.982620i | \(-0.440568\pi\) | ||||
0.185628 | + | 0.982620i | \(0.440568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 400762.i | − 0.591680i | −0.955238 | − | 0.295840i | \(-0.904401\pi\) | ||||
0.955238 | − | 0.295840i | \(-0.0955995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −123012. | −0.180734 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17272.0i | 0.0252541i | 0.999920 | + | 0.0126270i | \(0.00401942\pi\) | ||||
−0.999920 | + | 0.0126270i | \(0.995981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15686.0 | 0.0228246 | 0.0114123 | − | 0.999935i | \(-0.496367\pi\) | ||||
0.0114123 | + | 0.999935i | \(0.496367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 626230.i | 0.906842i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 838122. | 1.20786 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 787404.i | − 1.12934i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 207036. | 0.295525 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 115479.i | − 0.164051i | −0.996630 | − | 0.0820257i | \(-0.973861\pi\) | ||||
0.996630 | − | 0.0820257i | \(-0.0261390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −701197. | −0.991398 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 15869.0i | − 0.0223304i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 191646. | 0.268402 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.08287e6i | 1.50942i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 690876. | 0.958484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 396570.i | 0.547597i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −345938. | −0.475445 | −0.237722 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237722 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 133562.i | − 0.182705i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −267990. | −0.364886 | −0.182443 | − | 0.983216i | \(-0.558400\pi\) | ||||
−0.182443 | + | 0.983216i | \(0.558400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 522407.i | 0.707983i | 0.935249 | + | 0.353992i | \(0.115176\pi\) | ||||
−0.935249 | + | 0.353992i | \(0.884824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 363528. | 0.490379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 826895.i | 1.11027i | 0.831760 | + | 0.555135i | \(0.187333\pi\) | ||||
−0.831760 | + | 0.555135i | \(0.812667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.44522e6 | 1.93153 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 119537.i | − 0.159025i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 91440.0 | 0.121087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 197966.i | − 0.260949i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 354186. | 0.464732 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.64523e6i | 2.14887i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.11629e6 | −1.45137 | −0.725685 | − | 0.688028i | \(-0.758477\pi\) | ||||
−0.725685 | + | 0.688028i | \(0.758477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 788059.i | − 1.01995i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19170.0 | 0.0246985 | 0.0123492 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123492 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 568909.i | − 0.729662i | −0.931074 | − | 0.364831i | \(-0.881127\pi\) | ||||
0.931074 | − | 0.364831i | \(-0.118873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49896.0 | −0.0637058 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.09015e6i | − 1.38561i | −0.721126 | − | 0.692804i | \(-0.756375\pi\) | ||||
0.721126 | − | 0.692804i | \(-0.243625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30096.0 | 0.0380807 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15152.0i | 0.0190860i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −445536. | −0.558702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 707965.i | − 0.883824i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 707616. | 0.879453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 115105.i | − 0.142421i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.13800e6 | −1.40182 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 337459.i | − 0.413852i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −659652. | −0.805411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 916193.i | − 1.11371i | −0.830610 | − | 0.556855i | \(-0.812008\pi\) | ||||
0.830610 | − | 0.556855i | \(-0.187992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −148230. | −0.179394 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 995500.i | − 1.19951i | −0.800183 | − | 0.599756i | \(-0.795264\pi\) | ||||
0.800183 | − | 0.599756i | \(-0.204736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 249264. | 0.299032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 293749.i | − 0.350860i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26928.0 | −0.0320233 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 97084.9i | − 0.114953i | −0.998347 | − | 0.0574766i | \(-0.981695\pi\) | ||||
0.998347 | − | 0.0574766i | \(-0.0183054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28188.0 | −0.0332311 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 332886.i | − 0.390744i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −603670. | −0.705531 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 153952.i | 0.179153i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.27882e6 | −1.48176 | −0.740881 | − | 0.671636i | \(-0.765592\pi\) | ||||
−0.740881 | + | 0.671636i | \(0.765592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 401275.i | − 0.462959i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 733320. | 0.842423 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 214747.i | − 0.245642i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −981262. | −1.11765 | −0.558825 | − | 0.829286i | \(-0.688748\pi\) | ||||
−0.558825 | + | 0.829286i | \(0.688748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 668672.i | − 0.758371i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −284406. | −0.321188 | −0.160594 | − | 0.987021i | \(-0.551341\pi\) | ||||
−0.160594 | + | 0.987021i | \(0.551341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 686890.i | 0.772438i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 449064. | 0.502857 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 993109.i | 1.10738i | 0.832722 | + | 0.553691i | \(0.186781\pi\) | ||||
−0.832722 | + | 0.553691i | \(0.813219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −168532. | −0.187133 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 384443.i | 0.425080i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 602922. | 0.663858 | 0.331929 | − | 0.943304i | \(-0.392301\pi\) | ||||
0.331929 | + | 0.943304i | \(0.392301\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 111738.i | 0.122516i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8424.00 | 0.00919802 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1.01009e6i | − 1.09831i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.25419e6 | −1.35805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 272174.i | 0.293491i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.12484e6 | −1.20792 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 575810.i | − 0.615781i | −0.951422 | − | 0.307890i | \(-0.900377\pi\) | ||||
0.951422 | − | 0.307890i | \(-0.0996230\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 150552. | 0.160339 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.23920e6i | 1.31432i | 0.753749 | + | 0.657162i | \(0.228243\pi\) | ||||
−0.753749 | + | 0.657162i | \(0.771757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.00690e6 | 1.06355 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.07715e6i | 1.13310i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.04074e6 | −1.09032 | −0.545160 | − | 0.838332i | \(-0.683531\pi\) | ||||
−0.545160 | + | 0.838332i | \(0.683531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 240810.i | 0.251252i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −436482. | −0.453553 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 948734.i | 0.981833i | 0.871207 | + | 0.490916i | \(0.163338\pi\) | ||||
−0.871207 | + | 0.490916i | \(0.836662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.20424e6 | 2.27189 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.49799e6i | − 1.53771i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 637632. | 0.651895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 616007.i | 0.627247i | 0.949547 | + | 0.313623i | \(0.101543\pi\) | ||||
−0.949547 | + | 0.313623i | \(0.898457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 296316. | 0.300508 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 969269.i | − 0.979035i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 535870. | 0.539100 | 0.269550 | − | 0.962986i | \(-0.413125\pi\) | ||||
0.269550 | + | 0.962986i | \(0.413125\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 74356.9i | 0.0745059i |
(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 | 192.5.g.b.127.2 | 2 | ||
3.2 | odd | 2 | 576.5.g.d.127.2 | 2 | |||
4.3 | odd | 2 | inner | 192.5.g.b.127.1 | 2 | ||
8.3 | odd | 2 | 48.5.g.a.31.2 | yes | 2 | ||
8.5 | even | 2 | 48.5.g.a.31.1 | ✓ | 2 | ||
12.11 | even | 2 | 576.5.g.d.127.1 | 2 | |||
16.3 | odd | 4 | 768.5.b.c.127.3 | 4 | |||
16.5 | even | 4 | 768.5.b.c.127.4 | 4 | |||
16.11 | odd | 4 | 768.5.b.c.127.2 | 4 | |||
16.13 | even | 4 | 768.5.b.c.127.1 | 4 | |||
24.5 | odd | 2 | 144.5.g.f.127.2 | 2 | |||
24.11 | even | 2 | 144.5.g.f.127.1 | 2 | |||
40.3 | even | 4 | 1200.5.j.b.799.2 | 4 | |||
40.13 | odd | 4 | 1200.5.j.b.799.3 | 4 | |||
40.19 | odd | 2 | 1200.5.e.b.751.1 | 2 | |||
40.27 | even | 4 | 1200.5.j.b.799.4 | 4 | |||
40.29 | even | 2 | 1200.5.e.b.751.2 | 2 | |||
40.37 | odd | 4 | 1200.5.j.b.799.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.5.g.a.31.1 | ✓ | 2 | 8.5 | even | 2 | ||
48.5.g.a.31.2 | yes | 2 | 8.3 | odd | 2 | ||
144.5.g.f.127.1 | 2 | 24.11 | even | 2 | |||
144.5.g.f.127.2 | 2 | 24.5 | odd | 2 | |||
192.5.g.b.127.1 | 2 | 4.3 | odd | 2 | inner | ||
192.5.g.b.127.2 | 2 | 1.1 | even | 1 | trivial | ||
576.5.g.d.127.1 | 2 | 12.11 | even | 2 | |||
576.5.g.d.127.2 | 2 | 3.2 | odd | 2 | |||
768.5.b.c.127.1 | 4 | 16.13 | even | 4 | |||
768.5.b.c.127.2 | 4 | 16.11 | odd | 4 | |||
768.5.b.c.127.3 | 4 | 16.3 | odd | 4 | |||
768.5.b.c.127.4 | 4 | 16.5 | even | 4 | |||
1200.5.e.b.751.1 | 2 | 40.19 | odd | 2 | |||
1200.5.e.b.751.2 | 2 | 40.29 | even | 2 | |||
1200.5.j.b.799.1 | 4 | 40.37 | odd | 4 | |||
1200.5.j.b.799.2 | 4 | 40.3 | even | 4 | |||
1200.5.j.b.799.3 | 4 | 40.13 | odd | 4 | |||
1200.5.j.b.799.4 | 4 | 40.27 | even | 4 |