Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(127,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.127 |
Dual form | 768.3.b.f.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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.29253i | 1.65851i | 0.558874 | + | 0.829253i | \(0.311234\pi\) | ||||
−0.558874 | + | 0.829253i | \(0.688766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.55583i | 1.22226i | 0.791529 | + | 0.611131i | \(0.209285\pi\) | ||||
−0.791529 | + | 0.611131i | \(0.790715\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7980 | 1.25436 | 0.627180 | − | 0.778874i | \(-0.284209\pi\) | ||||
0.627180 | + | 0.778874i | \(0.284209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.0693i | 1.31302i | 0.754316 | + | 0.656512i | \(0.227969\pi\) | ||||
−0.754316 | + | 0.656512i | \(0.772031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 14.3631i | − 0.957539i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 20.3246 | 1.19556 | 0.597781 | − | 0.801659i | \(-0.296049\pi\) | ||||
0.597781 | + | 0.801659i | \(0.296049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.4440 | 1.07600 | 0.537999 | − | 0.842946i | \(-0.319181\pi\) | ||||
0.537999 | + | 0.842946i | \(0.319181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 14.8191i | − 0.705673i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.51575i | − 0.239815i | −0.992785 | − | 0.119908i | \(-0.961740\pi\) | ||||
0.992785 | − | 0.119908i | \(-0.0382598\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −43.7660 | −1.75064 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0586i | 1.41581i | 0.706306 | + | 0.707906i | \(0.250360\pi\) | ||||
−0.706306 | + | 0.707906i | \(0.749640\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 22.2953i | − 0.719205i | −0.933106 | − | 0.359602i | \(-0.882912\pi\) | ||||
0.933106 | − | 0.359602i | \(-0.117088\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −23.8988 | −0.724205 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −70.9495 | −2.02713 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6326i | 0.314396i | 0.987567 | + | 0.157198i | \(0.0502461\pi\) | ||||
−0.987567 | + | 0.157198i | \(0.949754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 29.5649i | − 0.758075i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −35.9527 | −0.876894 | −0.438447 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438447 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66.8648 | 1.55499 | 0.777497 | − | 0.628886i | \(-0.216489\pi\) | ||||
0.777497 | + | 0.628886i | \(0.216489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.8776i | 0.552835i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 19.9366i | − 0.424182i | −0.977250 | − | 0.212091i | \(-0.931973\pi\) | ||||
0.977250 | − | 0.212091i | \(-0.0680274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.2023 | −0.493924 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.2032 | −0.690259 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 17.6329i | − 0.332697i | −0.986067 | − | 0.166348i | \(-0.946802\pi\) | ||||
0.986067 | − | 0.166348i | \(-0.0531977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 114.420i | 2.08036i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −35.4100 | −0.621227 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −62.1572 | −1.05351 | −0.526756 | − | 0.850017i | \(-0.676592\pi\) | ||||
−0.526756 | + | 0.850017i | \(0.676592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 47.4836i | − 0.778419i | −0.921149 | − | 0.389210i | \(-0.872748\pi\) | ||||
0.921149 | − | 0.389210i | \(-0.127252\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25.6675i | 0.407421i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −141.548 | −2.17766 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.8105 | 1.11657 | 0.558287 | − | 0.829648i | \(-0.311459\pi\) | ||||
0.558287 | + | 0.829648i | \(0.311459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.55356i | 0.138457i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.9150i | 0.238240i | 0.992880 | + | 0.119120i | \(0.0380073\pi\) | ||||
−0.992880 | + | 0.119120i | \(0.961993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −101.712 | −1.39331 | −0.696657 | − | 0.717404i | \(-0.745330\pi\) | ||||
−0.696657 | + | 0.717404i | \(0.745330\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.8050 | 1.01073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 118.053i | 1.53316i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 0.879320i | − 0.0111306i | −0.999985 | − | 0.00556532i | \(-0.998228\pi\) | ||||
0.999985 | − | 0.00556532i | \(-0.00177151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23.2131 | 0.279676 | 0.139838 | − | 0.990174i | \(-0.455342\pi\) | ||||
0.139838 | + | 0.990174i | \(0.455342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 168.542i | 1.98285i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 71.1155i | − 0.817420i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.3089 | 0.183246 | 0.0916231 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916231 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −146.042 | −1.60486 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 38.6167i | 0.415233i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 169.532i | 1.78455i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 188.307 | 1.94131 | 0.970656 | − | 0.240474i | \(-0.0773028\pi\) | ||||
0.970656 | + | 0.240474i | \(0.0773028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 41.3939 | 0.418120 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66.8468i | 0.661849i | 0.943657 | + | 0.330925i | \(0.107361\pi\) | ||||
−0.943657 | + | 0.330925i | \(0.892639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 166.313i | − 1.61469i | −0.590083 | − | 0.807343i | \(-0.700905\pi\) | ||||
0.590083 | − | 0.807343i | \(-0.299095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 122.888 | 1.17036 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −80.1467 | −0.749035 | −0.374517 | − | 0.927220i | \(-0.622192\pi\) | ||||
−0.374517 | + | 0.927220i | \(0.622192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 26.8781i | 0.246589i | 0.992370 | + | 0.123294i | \(0.0393459\pi\) | ||||
−0.992370 | + | 0.123294i | \(0.960654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 20.1483i | − 0.181516i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −79.0958 | −0.699963 | −0.349981 | − | 0.936757i | \(-0.613812\pi\) | ||||
−0.349981 | + | 0.936757i | \(0.613812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 45.7395 | 0.397735 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 51.2079i | 0.437675i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 173.894i | 1.46129i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69.3837 | 0.573419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 62.2718 | 0.506275 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 155.618i | − 1.24494i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 170.725i | − 1.34429i | −0.740419 | − | 0.672145i | \(-0.765373\pi\) | ||||
0.740419 | − | 0.672145i | \(-0.234627\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −115.813 | −0.897777 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −178.980 | −1.36626 | −0.683129 | − | 0.730297i | \(-0.739381\pi\) | ||||
−0.683129 | + | 0.730297i | \(0.739381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 174.915i | 1.31515i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 43.0892i | − 0.319180i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 93.2075 | 0.680347 | 0.340173 | − | 0.940363i | \(-0.389514\pi\) | ||||
0.340173 | + | 0.940363i | \(0.389514\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −222.476 | −1.60055 | −0.800274 | − | 0.599635i | \(-0.795313\pi\) | ||||
−0.800274 | + | 0.599635i | \(0.795313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.5312i | 0.244902i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 235.522i | 1.64700i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −340.479 | −2.34813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 41.9196 | 0.285167 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 94.0043i | − 0.630901i | −0.948942 | − | 0.315451i | \(-0.897844\pi\) | ||||
0.948942 | − | 0.315451i | \(-0.102156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 82.0081i | − 0.543100i | −0.962424 | − | 0.271550i | \(-0.912464\pi\) | ||||
0.962424 | − | 0.271550i | \(-0.0875362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 60.9737 | 0.398521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 184.885 | 1.19281 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 56.7180i | − 0.361261i | −0.983551 | − | 0.180631i | \(-0.942186\pi\) | ||||
0.983551 | − | 0.180631i | \(-0.0578139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.5411i | 0.192083i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 47.1918 | 0.293117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 189.588 | 1.16312 | 0.581559 | − | 0.813504i | \(-0.302443\pi\) | ||||
0.581559 | + | 0.813504i | \(0.302443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 198.181i | − 1.20110i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 312.777i | − 1.87291i | −0.350783 | − | 0.936457i | \(-0.614084\pi\) | ||||
0.350783 | − | 0.936457i | \(-0.385916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −122.361 | −0.724031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 61.3319 | 0.358666 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 182.538i | − 1.05513i | −0.849514 | − | 0.527567i | \(-0.823104\pi\) | ||||
0.849514 | − | 0.527567i | \(-0.176896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 374.455i | − 2.13974i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 107.659 | 0.608245 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7781 | 0.110492 | 0.0552461 | − | 0.998473i | \(-0.482406\pi\) | ||||
0.0552461 | + | 0.998473i | \(0.482406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 265.750i | − 1.46823i | −0.679023 | − | 0.734117i | \(-0.737597\pi\) | ||||
0.679023 | − | 0.734117i | \(-0.262403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 82.2440i | 0.449421i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −96.4640 | −0.521427 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 280.438 | 1.49967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 44.4574i | − 0.235224i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 288.025i | 1.50799i | 0.656882 | + | 0.753993i | \(0.271875\pi\) | ||||
−0.656882 | + | 0.753993i | \(0.728125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 281.010 | 1.45601 | 0.728005 | − | 0.685572i | \(-0.240448\pi\) | ||||
0.728005 | + | 0.685572i | \(0.240448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 245.168 | 1.25727 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 33.8330i | 0.171741i | 0.996306 | + | 0.0858705i | \(0.0273671\pi\) | ||||
−0.996306 | + | 0.0858705i | \(0.972633\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 84.9700i | − 0.426985i | −0.976945 | − | 0.213493i | \(-0.931516\pi\) | ||||
0.976945 | − | 0.213493i | \(-0.0684839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −129.576 | −0.644654 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −351.290 | −1.73049 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 298.138i | − 1.45433i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 16.5472i | − 0.0799384i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 282.085 | 1.34969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −140.700 | −0.666826 | −0.333413 | − | 0.942781i | \(-0.608200\pi\) | ||||
−0.333413 | + | 0.942781i | \(0.608200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 29.2977i | − 0.137548i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 554.478i | 2.57897i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 190.755 | 0.879057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 176.170 | 0.804431 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 346.926i | 1.56980i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 247.529i | 1.11000i | 0.831851 | + | 0.554999i | \(0.187281\pi\) | ||||
−0.831851 | + | 0.554999i | \(0.812719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −131.298 | −0.583547 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −129.752 | −0.571593 | −0.285797 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285797 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 294.304i | − 1.28517i | −0.766214 | − | 0.642586i | \(-0.777862\pi\) | ||||
0.766214 | − | 0.642586i | \(-0.222138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 204.474i | − 0.885168i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 239.948 | 1.02982 | 0.514911 | − | 0.857244i | \(-0.327825\pi\) | ||||
0.514911 | + | 0.857244i | \(0.327825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 165.325 | 0.703509 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.52303i | 0.00642628i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 425.346i | − 1.77969i | −0.456261 | − | 0.889846i | \(-0.650812\pi\) | ||||
0.456261 | − | 0.889846i | \(-0.349188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 264.493 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 200.698i | − 0.819176i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 348.964i | 1.41281i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −40.2063 | −0.161471 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −221.125 | −0.880976 | −0.440488 | − | 0.897759i | \(-0.645195\pi\) | ||||
−0.440488 | + | 0.897759i | \(0.645195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 76.1061i | − 0.300815i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 291.923i | − 1.14480i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 87.0655 | 0.338776 | 0.169388 | − | 0.985549i | \(-0.445821\pi\) | ||||
0.169388 | + | 0.985549i | \(0.445821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −99.5270 | −0.384274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 123.176i | 0.471937i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 277.324i | 1.05447i | 0.849721 | + | 0.527233i | \(0.176770\pi\) | ||||
−0.849721 | + | 0.527233i | \(0.823230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 146.222 | 0.551780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.2479 | −0.105797 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 49.8005i | − 0.185132i | −0.995707 | − | 0.0925659i | \(-0.970493\pi\) | ||||
0.995707 | − | 0.0925659i | \(-0.0295069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 31.3145i | − 0.115552i | −0.998330 | − | 0.0577758i | \(-0.981599\pi\) | ||||
0.998330 | − | 0.0577758i | \(-0.0184009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 252.952 | 0.926566 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −603.882 | −2.19593 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 79.1431i | 0.285715i | 0.989743 | + | 0.142858i | \(0.0456291\pi\) | ||||
−0.989743 | + | 0.142858i | \(0.954371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 66.8860i | − 0.239735i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 106.190 | 0.377902 | 0.188951 | − | 0.981987i | \(-0.439491\pi\) | ||||
0.188951 | + | 0.981987i | \(0.439491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 270.251 | 0.954949 | 0.477475 | − | 0.878646i | \(-0.341552\pi\) | ||||
0.477475 | + | 0.878646i | \(0.341552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 293.638i | − 1.03031i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 307.605i | − 1.07179i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 124.088 | 0.429371 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −326.158 | −1.12082 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 24.2487i | − 0.0827600i | −0.999143 | − | 0.0413800i | \(-0.986825\pi\) | ||||
0.999143 | − | 0.0413800i | \(-0.0131754\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 515.440i | − 1.74726i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −71.6963 | −0.241402 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 94.1500 | 0.314883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 572.084i | 1.90061i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 115.782i | − 0.382119i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 393.759 | 1.29101 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 122.865 | 0.400211 | 0.200106 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200106 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 288.062i | 0.932239i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 108.808i | 0.349865i | 0.984580 | + | 0.174933i | \(0.0559707\pi\) | ||||
−0.984580 | + | 0.174933i | \(0.944029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 52.2216 | 0.166842 | 0.0834211 | − | 0.996514i | \(-0.473415\pi\) | ||||
0.0834211 | + | 0.996514i | \(0.473415\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −212.848 | −0.675709 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 94.3251i | 0.297555i | 0.988871 | + | 0.148778i | \(0.0475339\pi\) | ||||
−0.988871 | + | 0.148778i | \(0.952466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 566.524i | 1.77594i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 138.818 | 0.432456 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 415.515 | 1.28642 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 747.056i | − 2.29863i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 46.5543i | − 0.142368i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 170.574 | 0.518462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 406.107 | 1.22691 | 0.613454 | − | 0.789730i | \(-0.289780\pi\) | ||||
0.613454 | + | 0.789730i | \(0.289780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34.8979i | 0.104799i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 620.368i | 1.85184i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.4140 | −0.0665105 | −0.0332552 | − | 0.999447i | \(-0.510587\pi\) | ||||
−0.0332552 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 136.998 | 0.404124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 307.630i | − 0.902142i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 212.165i | 0.618557i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −79.2232 | −0.229632 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −458.377 | −1.32097 | −0.660486 | − | 0.750839i | \(-0.729650\pi\) | ||||
−0.660486 | + | 0.750839i | \(0.729650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 282.960i | 0.810774i | 0.914145 | + | 0.405387i | \(0.132863\pi\) | ||||
−0.914145 | + | 0.405387i | \(0.867137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 88.6947i | − 0.252692i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −175.820 | −0.498073 | −0.249036 | − | 0.968494i | \(-0.580114\pi\) | ||||
−0.249036 | + | 0.968494i | \(0.580114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −140.268 | −0.395122 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 301.193i | − 0.843677i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 53.5791i | − 0.149246i | −0.997212 | − | 0.0746228i | \(-0.976225\pi\) | ||||
0.997212 | − | 0.0746228i | \(-0.0237753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 56.9552 | 0.157771 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −120.176 | −0.331063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 843.449i | − 2.31082i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 62.4258i | − 0.170097i | −0.996377 | − | 0.0850487i | \(-0.972895\pi\) | ||||
0.996377 | − | 0.0850487i | \(-0.0271046\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −107.858 | −0.292298 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 150.864 | 0.406643 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 370.552i | 0.993437i | 0.867912 | + | 0.496719i | \(0.165462\pi\) | ||||
−0.867912 | + | 0.496719i | \(0.834538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 269.538i | 0.718768i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −700.841 | −1.85900 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 68.7286 | 0.181342 | 0.0906709 | − | 0.995881i | \(-0.471099\pi\) | ||||
0.0906709 | + | 0.995881i | \(0.471099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 295.704i | 0.776126i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 155.858i | 0.406939i | 0.979081 | + | 0.203470i | \(0.0652218\pi\) | ||||
−0.979081 | + | 0.203470i | \(0.934778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −978.958 | −2.54275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 200.594 | 0.518332 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 481.792i | 1.23854i | 0.785179 | + | 0.619269i | \(0.212571\pi\) | ||||
−0.785179 | + | 0.619269i | \(0.787429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 112.105i | − 0.286714i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 310.002 | 0.788810 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.29179 | 0.0184602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 422.315i | − 1.06377i | −0.846818 | − | 0.531883i | \(-0.821485\pi\) | ||||
0.846818 | − | 0.531883i | \(-0.178515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 302.962i | − 0.759303i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −641.025 | −1.59857 | −0.799283 | − | 0.600955i | \(-0.794787\pi\) | ||||
−0.799283 | + | 0.600955i | \(0.794787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 380.566 | 0.944333 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 74.6328i | 0.184278i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 160.507i | 0.394365i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 278.562 | 0.681081 | 0.340541 | − | 0.940230i | \(-0.389390\pi\) | ||||
0.340541 | + | 0.940230i | \(0.389390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −161.440 | −0.392798 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 531.807i | − 1.28767i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 192.496i | 0.463845i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 385.340 | 0.924077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −505.611 | −1.20671 | −0.603354 | − | 0.797473i | \(-0.706169\pi\) | ||||
−0.603354 | + | 0.797473i | \(0.706169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 179.846i | 0.427189i | 0.976922 | + | 0.213594i | \(0.0685171\pi\) | ||||
−0.976922 | + | 0.213594i | \(0.931483\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 59.8097i | − 0.141394i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −889.526 | −2.09300 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 406.262 | 0.951432 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 407.935i | − 0.950898i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 580.645i | − 1.34720i | −0.739094 | − | 0.673602i | \(-0.764746\pi\) | ||||
0.739094 | − | 0.673602i | \(-0.235254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −425.621 | −0.982959 | −0.491479 | − | 0.870889i | \(-0.663544\pi\) | ||||
−0.491479 | + | 0.870889i | \(0.663544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 589.727 | 1.35570 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 112.764i | − 0.258041i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 129.991i | − 0.296107i | −0.988979 | − | 0.148053i | \(-0.952699\pi\) | ||||
0.988979 | − | 0.148053i | \(-0.0473008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −72.6069 | −0.164641 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −205.564 | −0.464027 | −0.232014 | − | 0.972713i | \(-0.574531\pi\) | ||||
−0.232014 | + | 0.972713i | \(0.574531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 135.242i | 0.303915i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 162.820i | 0.364251i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 415.190 | 0.924698 | 0.462349 | − | 0.886698i | \(-0.347007\pi\) | ||||
0.462349 | + | 0.886698i | \(0.347007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −496.073 | −1.09994 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 142.042i | 0.313559i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1211.06i | − 2.66167i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 598.927 | 1.31056 | 0.655281 | − | 0.755385i | \(-0.272550\pi\) | ||||
0.655281 | + | 0.755385i | \(0.272550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −105.610 | −0.230086 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 376.804i | 0.817361i | 0.912677 | + | 0.408681i | \(0.134011\pi\) | ||||
−0.912677 | + | 0.408681i | \(0.865989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 218.577i | 0.472088i | 0.971742 | + | 0.236044i | \(0.0758510\pi\) | ||||
−0.971742 | + | 0.236044i | \(0.924149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −320.230 | −0.688666 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 443.608 | 0.949911 | 0.474955 | − | 0.880010i | \(-0.342464\pi\) | ||||
0.474955 | + | 0.880010i | \(0.342464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 640.066i | 1.36475i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 98.2385i | 0.208574i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 922.597 | 1.95052 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −894.751 | −1.88369 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 52.8988i | − 0.110899i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 222.133i | 0.463743i | 0.972746 | + | 0.231871i | \(0.0744849\pi\) | ||||
−0.972746 | + | 0.231871i | \(0.925515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −198.561 | −0.412809 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −81.7387 | −0.169231 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1561.54i | 3.21968i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 403.795i | − 0.829148i | −0.910016 | − | 0.414574i | \(-0.863931\pi\) | ||||
0.910016 | − | 0.414574i | \(-0.136069\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −328.376 | −0.671526 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 808.347 | 1.64633 | 0.823164 | − | 0.567803i | \(-0.192207\pi\) | ||||
0.823164 | + | 0.567803i | \(0.192207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 834.498i | 1.69269i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 343.260i | 0.693454i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −144.722 | −0.291192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 132.172 | 0.264874 | 0.132437 | − | 0.991191i | \(-0.457720\pi\) | ||||
0.132437 | + | 0.991191i | \(0.457720\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 541.745i | 1.08133i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 92.8360i | − 0.184565i | −0.995733 | − | 0.0922823i | \(-0.970584\pi\) | ||||
0.995733 | − | 0.0922823i | \(-0.0294162\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −554.329 | −1.09768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 211.936 | 0.418020 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 927.417i | 1.82204i | 0.412366 | + | 0.911018i | \(0.364703\pi\) | ||||
−0.412366 | + | 0.911018i | \(0.635297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 870.231i | − 1.70300i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −106.230 | −0.207076 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1379.15 | 2.67796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 275.084i | − 0.532077i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 316.165i | 0.609182i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −527.145 | −1.01179 | −0.505897 | − | 0.862594i | \(-0.668838\pi\) | ||||
−0.505897 | + | 0.862594i | \(0.668838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −972.249 | −1.85898 | −0.929492 | − | 0.368843i | \(-0.879754\pi\) | ||||
−0.929492 | + | 0.368843i | \(0.879754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 648.575i | 1.23538i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 453.143i | − 0.859854i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 498.577 | 0.942489 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −186.472 | −0.351171 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 613.687i | − 1.15138i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 664.619i | − 1.24228i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.2567 | −0.0637927 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −333.942 | −0.619559 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.66591i | 0.00862461i | 0.999991 | + | 0.00431231i | \(0.00137265\pi\) | ||||
−0.999991 | + | 0.00431231i | \(0.998627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 460.293i | 0.847685i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −222.888 | −0.408968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −386.796 | −0.707123 | −0.353561 | − | 0.935411i | \(-0.615029\pi\) | ||||
−0.353561 | + | 0.935411i | \(0.615029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 142.451i | − 0.259473i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 839.399i | 1.52341i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.52332 | 0.0136046 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 167.081 | 0.301046 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 219.630i | 0.394308i | 0.980373 | + | 0.197154i | \(0.0631699\pi\) | ||||
−0.980373 | + | 0.197154i | \(0.936830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1141.34i | 2.04175i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −485.732 | −0.865833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −266.807 | −0.473902 | −0.236951 | − | 0.971522i | \(-0.576148\pi\) | ||||
−0.236951 | + | 0.971522i | \(0.576148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 655.904i | − 1.16089i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 77.0025i | 0.135807i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 972.046 | 1.70834 | 0.854170 | − | 0.519993i | \(-0.174066\pi\) | ||||
0.854170 | + | 0.519993i | \(0.174066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 340.194 | 0.595786 | 0.297893 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297893 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 498.875i | − 0.870637i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 241.402i | 0.419830i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 65.0584 | 0.112753 | 0.0563764 | − | 0.998410i | \(-0.482045\pi\) | ||||
0.0563764 | + | 0.998410i | \(0.482045\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −486.723 | −0.840628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 198.608i | 0.341838i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 243.299i | − 0.417322i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −424.643 | −0.725886 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 162.144 | 0.276226 | 0.138113 | − | 0.990417i | \(-0.455896\pi\) | ||||
0.138113 | + | 0.990417i | \(0.455896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 455.805i | − 0.773862i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 58.6004i | − 0.0991547i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −793.227 | −1.33765 | −0.668825 | − | 0.743420i | \(-0.733203\pi\) | ||||
−0.668825 | + | 0.743420i | \(0.733203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1442.02 | −2.42356 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 147.172i | 0.246520i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 432.194i | 0.721525i | 0.932658 | + | 0.360763i | \(0.117484\pi\) | ||||
−0.932658 | + | 0.360763i | \(0.882516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −936.310 | −1.55792 | −0.778960 | − | 0.627074i | \(-0.784252\pi\) | ||||
−0.778960 | + | 0.627074i | \(0.784252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 224.431 | 0.372191 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 575.366i | 0.951018i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 223.972i | − 0.368982i | −0.982834 | − | 0.184491i | \(-0.940936\pi\) | ||||
0.982834 | − | 0.184491i | \(-0.0590637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 608.453 | 0.999101 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 340.304 | 0.556962 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1010.40i | 1.64828i | 0.566385 | + | 0.824141i | \(0.308342\pi\) | ||||
−0.566385 | + | 0.824141i | \(0.691658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 516.391i | 0.839660i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 400.206 | 0.648633 | 0.324316 | − | 0.945949i | \(-0.394866\pi\) | ||||
0.324316 | + | 0.945949i | \(0.394866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 417.349 | 0.674231 | 0.337116 | − | 0.941463i | \(-0.390549\pi\) | ||||
0.337116 | + | 0.941463i | \(0.390549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.6607i | 0.0461525i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 139.536i | 0.223975i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 196.315 | 0.314104 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −488.585 | −0.779243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 236.428i | 0.375880i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 718.033i | 1.13793i | 0.822362 | + | 0.568965i | \(0.192656\pi\) | ||||
−0.822362 | + | 0.568965i | \(0.807344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 243.700 | 0.384992 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1415.74 | 2.22951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 413.116i | − 0.648534i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 50.7451i | 0.0794133i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 139.926 | 0.218293 | 0.109146 | − | 0.994026i | \(-0.465188\pi\) | ||||
0.109146 | + | 0.994026i | \(0.465188\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 777.990 | 1.20994 | 0.604969 | − | 0.796249i | \(-0.293186\pi\) | ||||
0.604969 | + | 0.796249i | \(0.293186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 960.384i | − 1.48897i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 673.336i | 1.04070i | 0.853952 | + | 0.520352i | \(0.174199\pi\) | ||||
−0.853952 | + | 0.520352i | \(0.825801\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −857.642 | −1.32148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −330.398 | −0.507524 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 223.410i | 0.342128i | 0.985260 | + | 0.171064i | \(0.0547206\pi\) | ||||
−0.985260 | + | 0.171064i | \(0.945279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1484.20i | − 2.26595i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −305.136 | −0.464438 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −166.367 | −0.252453 | −0.126227 | − | 0.992001i | \(-0.540287\pi\) | ||||
−0.126227 | + | 0.992001i | \(0.540287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 655.773i | 0.992092i | 0.868296 | + | 0.496046i | \(0.165215\pi\) | ||||
−0.868296 | + | 0.496046i | \(0.834785\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 600.894i | − 0.906326i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1450.49 | −2.18119 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 226.469 | 0.339533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 428.734i | − 0.640857i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 655.176i | − 0.976418i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −863.477 | −1.28303 | −0.641513 | − | 0.767112i | \(-0.721693\pi\) | ||||
−0.641513 | + | 0.767112i | \(0.721693\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 227.415 | 0.336911 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 831.520i | − 1.22824i | −0.789212 | − | 0.614121i | \(-0.789511\pi\) | ||||
0.789212 | − | 0.614121i | \(-0.210489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1611.13i | 2.37279i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 224.737 | 0.330010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −308.273 | −0.451351 | −0.225676 | − | 0.974202i | \(-0.572459\pi\) | ||||
−0.225676 | + | 0.974202i | \(0.572459\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 772.926i | 1.12836i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 509.750i | 0.741994i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 300.982 | 0.436839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 666.811 | 0.964994 | 0.482497 | − | 0.875898i | \(-0.339730\pi\) | ||||
0.482497 | + | 0.875898i | \(0.339730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 354.159i | 0.511052i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1844.89i | − 2.65452i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −730.722 | −1.04838 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −415.603 | −0.594568 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 242.205i | 0.345514i | 0.984964 | + | 0.172757i | \(0.0552675\pi\) | ||||
−0.984964 | + | 0.172757i | \(0.944732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 237.817i | 0.338289i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −286.351 | −0.406171 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −571.930 | −0.808953 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1380.24i | − 1.94674i | −0.229237 | − | 0.973371i | \(-0.573623\pi\) | ||||
0.229237 | − | 0.973371i | \(-0.426377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 2.63796i | − 0.00371021i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −122.976 | −0.172476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1953.07 | −2.73157 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 736.722i | 1.02751i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 968.365i | − 1.34682i | −0.739268 | − | 0.673411i | \(-0.764828\pi\) | ||||
0.739268 | − | 0.673411i | \(-0.235172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1422.94 | 1.97357 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −458.115 | −0.633631 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1796.97i | − 2.47858i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1017.52i | 1.39962i | 0.714329 | + | 0.699810i | \(0.246732\pi\) | ||||
−0.714329 | + | 0.699810i | \(0.753268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1359.00 | 1.85909 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1026.22i | − 1.40003i | −0.714127 | − | 0.700016i | \(-0.753176\pi\) | ||||
0.714127 | − | 0.700016i | \(-0.246824\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 347.619i | 0.472952i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1032.23 | 1.40059 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −923.444 | −1.24959 | −0.624793 | − | 0.780791i | \(-0.714817\pi\) | ||||
−0.624793 | + | 0.780791i | \(0.714817\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 604.424i | − 0.815686i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1267.12i | − 1.70542i | −0.522387 | − | 0.852708i | \(-0.674958\pi\) | ||||
0.522387 | − | 0.852708i | \(-0.325042\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 779.533 | 1.04635 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 69.6394 | 0.0932254 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 685.722i | − 0.915517i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 791.442i | 1.05385i | 0.849912 | + | 0.526925i | \(0.176655\pi\) | ||||
−0.849912 | + | 0.526925i | \(0.823345\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 383.000 | 0.508632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 680.054 | 0.900734 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 333.990i | 0.441202i | 0.975364 | + | 0.220601i | \(0.0708019\pi\) | ||||
−0.975364 | + | 0.220601i | \(0.929198\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 131.820i | 0.173675i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −617.122 | −0.810936 | −0.405468 | − | 0.914109i | \(-0.632891\pi\) | ||||
−0.405468 | + | 0.914109i | \(0.632891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −229.965 | −0.301396 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 505.626i | 0.660949i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1060.98i | − 1.38329i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −657.604 | −0.855142 | −0.427571 | − | 0.903982i | \(-0.640631\pi\) | ||||
−0.427571 | + | 0.903982i | \(0.640631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −150.802 | −0.195593 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1314.59i | 1.70064i | 0.526268 | + | 0.850319i | \(0.323591\pi\) | ||||
−0.526268 | + | 0.850319i | \(0.676409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 975.779i | 1.25907i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 172.386 | 0.221861 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −735.015 | −0.943536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 233.393i | 0.298839i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 213.347i | − 0.272473i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 470.336 | 0.599154 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −301.018 | −0.382488 | −0.191244 | − | 0.981542i | \(-0.561252\pi\) | ||||
−0.191244 | + | 0.981542i | \(0.561252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 480.340i | − 0.608796i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 676.731i | − 0.855538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 810.512 | 1.02208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −253.263 | −0.318570 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 476.193i | − 0.597481i | −0.954334 | − | 0.298741i | \(-0.903433\pi\) | ||||
0.954334 | − | 0.298741i | \(-0.0965665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 405.202i | − 0.507137i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.9267 | 0.0610821 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1403.42 | −1.74772 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 391.340i | 0.486136i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 86.2570i | 0.106886i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 692.874 | 0.856457 | 0.428228 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428228 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 785.074 | 0.968032 | 0.484016 | − | 0.875059i | \(-0.339178\pi\) | ||||
0.484016 | + | 0.875059i | \(0.339178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.2383i | 0.0667138i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1572.17i | 1.92904i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1366.98 | 1.67317 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −438.126 | −0.534953 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 527.681i | − 0.642729i | −0.946956 | − | 0.321365i | \(-0.895859\pi\) | ||||
0.946956 | − | 0.321365i | \(-0.104141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 228.552i | − 0.277706i | −0.990313 | − | 0.138853i | \(-0.955658\pi\) | ||||
0.990313 | − | 0.138853i | \(-0.0443416\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1045.95 | 1.26782 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 608.409 | 0.735683 | 0.367841 | − | 0.929889i | \(-0.380097\pi\) | ||||
0.367841 | + | 0.929889i | \(0.380097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 151.637i | − 0.182915i | −0.995809 | − | 0.0914577i | \(-0.970847\pi\) | ||||
0.995809 | − | 0.0914577i | \(-0.0291526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 137.080i | − 0.164958i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −491.901 | −0.590518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2593.71 | 3.10624 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 115.850i | 0.138411i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 653.351i | − 0.778725i | −0.921085 | − | 0.389363i | \(-0.872695\pi\) | ||||
0.921085 | − | 0.389363i | \(-0.127305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −844.805 | −1.00452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −183.927 | −0.218182 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1014.68i | − 1.20081i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 593.635i | 0.700868i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −468.088 | −0.551340 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.1628 | 0.0753969 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1372.25i | 1.60873i | 0.594132 | + | 0.804367i | \(0.297495\pi\) | ||||
−0.594132 | + | 0.804367i | \(0.702505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 508.596i | 0.594849i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1453.61 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 962.466 | 1.12045 | 0.560225 | − | 0.828341i | \(-0.310715\pi\) | ||||
0.560225 | + | 0.828341i | \(0.310715\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 532.787i | 0.618801i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 695.890i | − 0.806362i | −0.915120 | − | 0.403181i | \(-0.867905\pi\) | ||||
0.915120 | − | 0.403181i | \(-0.132095\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1513.70 | 1.74994 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −214.927 | −0.247897 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 12.1328i | − 0.0139618i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1276.96i | 1.46609i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 564.922 | 0.647104 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1331.44 | 1.52165 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 338.191i | − 0.385622i | −0.981236 | − | 0.192811i | \(-0.938240\pi\) | ||||
0.981236 | − | 0.192811i | \(-0.0617605\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.0000i | 0.0477815i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −459.985 | −0.522117 | −0.261058 | − | 0.965323i | \(-0.584072\pi\) | ||||
−0.261058 | + | 0.965323i | \(0.584072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1208.31 | 1.36842 | 0.684209 | − | 0.729286i | \(-0.260147\pi\) | ||||
0.684209 | + | 0.729286i | \(0.260147\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 892.769i | 1.00878i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1500.73i | − 1.69192i | −0.533250 | − | 0.845958i | \(-0.679029\pi\) | ||||
0.533250 | − | 0.845958i | \(-0.320971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1460.69 | 1.64307 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 124.182 | 0.139373 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 407.582i | − 0.456419i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 164.010i | 0.183252i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −163.073 | −0.181798 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 915.415 | 1.01826 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 358.382i | − 0.397760i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 990.878i | − 1.09732i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2203.74 | 2.43507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 665.128 | 0.733328 | 0.366664 | − | 0.930353i | \(-0.380500\pi\) | ||||
0.366664 | + | 0.930353i | \(0.380500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 200.540i | 0.220616i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 345.687i | − 0.379459i | −0.981836 | − | 0.189729i | \(-0.939239\pi\) | ||||
0.981836 | − | 0.189729i | \(-0.0607611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 320.294 | 0.350815 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −682.010 | −0.745367 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1531.32i | − 1.66993i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1102.20i | − 1.19934i | −0.800246 | − | 0.599671i | \(-0.795298\pi\) | ||||
0.800246 | − | 0.599671i | \(-0.204702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −212.808 | −0.231062 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −288.728 | −0.312815 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 509.115i | − 0.550394i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 498.938i | − 0.538228i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1256.03 | −1.35202 | −0.676010 | − | 0.736893i | \(-0.736292\pi\) | ||||
−0.676010 | + | 0.736893i | \(0.736292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −494.790 | −0.531461 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 188.461i | − 0.201995i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2325.54i | 2.48720i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 822.214 | 0.877496 | 0.438748 | − | 0.898610i | \(-0.355422\pi\) | ||||
0.438748 | + | 0.898610i | \(0.355422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −90.4505 | −0.0963264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1185.72i | 1.26006i | 0.776570 | + | 0.630031i | \(0.216958\pi\) | ||||
−0.776570 | + | 0.630031i | \(0.783042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 198.306i | 0.210293i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 368.664 | 0.390121 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1335.34 | 1.41007 | 0.705037 | − | 0.709170i | \(-0.250930\pi\) | ||||
0.705037 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1736.15i | − 1.82945i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 163.376i | − 0.171794i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −663.428 | −0.696147 | −0.348073 | − | 0.937467i | \(-0.613164\pi\) | ||||
−0.348073 | + | 0.937467i | \(0.613164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2388.46 | −2.50100 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 981.249i | − 1.02534i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 797.468i | 0.831562i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 463.918 | 0.482745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −240.440 | −0.249678 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2330.28i | 2.41480i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 155.996i | − 0.161320i | −0.996742 | − | 0.0806600i | \(-0.974297\pi\) | ||||
0.996742 | − | 0.0806600i | \(-0.0257028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −719.692 | −0.742716 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1280.67 | −1.31892 | −0.659460 | − | 0.751740i | \(-0.729215\pi\) | ||||
−0.659460 | + | 0.751740i | \(0.729215\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1903.47i | − 1.95629i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1293.94i | 1.32712i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −217.470 | −0.222590 | −0.111295 | − | 0.993787i | \(-0.535500\pi\) | ||||
−0.111295 | + | 0.993787i | \(0.535500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 225.030 | 0.229857 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 80.6344i | 0.0821962i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1027.63i | − 1.04540i | −0.852515 | − | 0.522702i | \(-0.824924\pi\) | ||||
0.852515 | − | 0.522702i | \(-0.175076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −280.561 | −0.284833 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −295.443 | −0.299334 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 368.809i | − 0.372911i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 797.792i | 0.805038i | 0.915412 | + | 0.402519i | \(0.131865\pi\) | ||||
−0.915412 | + | 0.402519i | \(0.868135\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −703.397 | −0.708356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 704.616 | 0.708157 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1237.58i | − 1.24131i | −0.784085 | − | 0.620654i | \(-0.786867\pi\) | ||||
0.784085 | − | 0.620654i | \(-0.213133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 60.4450i | − 0.0605055i |
(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 | 768.3.b.f.127.4 | 8 | ||
3.2 | odd | 2 | 2304.3.b.q.127.1 | 8 | |||
4.3 | odd | 2 | 768.3.b.e.127.8 | 8 | |||
8.3 | odd | 2 | inner | 768.3.b.f.127.1 | 8 | ||
8.5 | even | 2 | 768.3.b.e.127.5 | 8 | |||
12.11 | even | 2 | 2304.3.b.t.127.1 | 8 | |||
16.3 | odd | 4 | 384.3.g.b.127.8 | yes | 8 | ||
16.5 | even | 4 | 384.3.g.a.127.5 | yes | 8 | ||
16.11 | odd | 4 | 384.3.g.a.127.1 | ✓ | 8 | ||
16.13 | even | 4 | 384.3.g.b.127.4 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.b.t.127.8 | 8 | |||
24.11 | even | 2 | 2304.3.b.q.127.8 | 8 | |||
48.5 | odd | 4 | 1152.3.g.f.127.7 | 8 | |||
48.11 | even | 4 | 1152.3.g.f.127.8 | 8 | |||
48.29 | odd | 4 | 1152.3.g.c.127.1 | 8 | |||
48.35 | even | 4 | 1152.3.g.c.127.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.1 | ✓ | 8 | 16.11 | odd | 4 | ||
384.3.g.a.127.5 | yes | 8 | 16.5 | even | 4 | ||
384.3.g.b.127.4 | yes | 8 | 16.13 | even | 4 | ||
384.3.g.b.127.8 | yes | 8 | 16.3 | odd | 4 | ||
768.3.b.e.127.5 | 8 | 8.5 | even | 2 | |||
768.3.b.e.127.8 | 8 | 4.3 | odd | 2 | |||
768.3.b.f.127.1 | 8 | 8.3 | odd | 2 | inner | ||
768.3.b.f.127.4 | 8 | 1.1 | even | 1 | trivial | ||
1152.3.g.c.127.1 | 8 | 48.29 | odd | 4 | |||
1152.3.g.c.127.2 | 8 | 48.35 | even | 4 | |||
1152.3.g.f.127.7 | 8 | 48.5 | odd | 4 | |||
1152.3.g.f.127.8 | 8 | 48.11 | even | 4 | |||
2304.3.b.q.127.1 | 8 | 3.2 | odd | 2 | |||
2304.3.b.q.127.8 | 8 | 24.11 | even | 2 | |||
2304.3.b.t.127.1 | 8 | 12.11 | even | 2 | |||
2304.3.b.t.127.8 | 8 | 24.5 | odd | 2 |