Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(127,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.g (of order \(2\), degree \(1\), 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: | \(31.3897264543\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.127 |
Dual form | 1152.3.g.c.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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.29253 | −1.65851 | −0.829253 | − | 0.558874i | \(-0.811234\pi\) | ||||
−0.829253 | + | 0.558874i | \(0.811234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.55583i | 1.22226i | 0.791529 | + | 0.611131i | \(0.209285\pi\) | ||||
−0.791529 | + | 0.611131i | \(0.790715\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 13.7980i | − 1.25436i | −0.778874 | − | 0.627180i | \(-0.784209\pi\) | ||||
0.778874 | − | 0.627180i | \(-0.215791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.0693 | −1.31302 | −0.656512 | − | 0.754316i | \(-0.727969\pi\) | ||||
−0.656512 | + | 0.754316i | \(0.727969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.3246 | −1.19556 | −0.597781 | − | 0.801659i | \(-0.703951\pi\) | ||||
−0.597781 | + | 0.801659i | \(0.703951\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 20.4440i | − 1.07600i | −0.842946 | − | 0.537999i | \(-0.819181\pi\) | ||||
0.842946 | − | 0.537999i | \(-0.180819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.51575i | 0.239815i | 0.992785 | + | 0.119908i | \(0.0382598\pi\) | ||||
−0.992785 | + | 0.119908i | \(0.961740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 43.7660 | 1.75064 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0586 | 1.41581 | 0.707906 | − | 0.706306i | \(-0.249640\pi\) | ||||
0.707906 | + | 0.706306i | \(0.249640\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.2953i | 0.719205i | 0.933106 | + | 0.359602i | \(0.117088\pi\) | ||||
−0.933106 | + | 0.359602i | \(0.882912\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 70.9495i | − 2.02713i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6326 | 0.314396 | 0.157198 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157198 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −35.9527 | −0.876894 | −0.438447 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438447 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66.8648i | 1.55499i | 0.628886 | + | 0.777497i | \(0.283511\pi\) | ||||
−0.628886 | + | 0.777497i | \(0.716489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17.6329 | 0.332697 | 0.166348 | − | 0.986067i | \(-0.446802\pi\) | ||||
0.166348 | + | 0.986067i | \(0.446802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 114.420i | 2.08036i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 62.1572i | 1.05351i | 0.850017 | + | 0.526756i | \(0.176592\pi\) | ||||
−0.850017 | + | 0.526756i | \(0.823408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.4836 | 0.778419 | 0.389210 | − | 0.921149i | \(-0.372748\pi\) | ||||
0.389210 | + | 0.921149i | \(0.372748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 141.548 | 2.17766 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 74.8105i | − 1.11657i | −0.829648 | − | 0.558287i | \(-0.811459\pi\) | ||||
0.829648 | − | 0.558287i | \(-0.188541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 16.9150i | − 0.238240i | −0.992880 | − | 0.119120i | \(-0.961993\pi\) | ||||
0.992880 | − | 0.119120i | \(-0.0380073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 101.712 | 1.39331 | 0.696657 | − | 0.717404i | \(-0.254670\pi\) | ||||
0.696657 | + | 0.717404i | \(0.254670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 118.053 | 1.53316 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.879320i | 0.0111306i | 0.999985 | + | 0.00556532i | \(0.00177151\pi\) | ||||
−0.999985 | + | 0.00556532i | \(0.998228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23.2131i | 0.279676i | 0.990174 | + | 0.139838i | \(0.0446582\pi\) | ||||
−0.990174 | + | 0.139838i | \(0.955342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 168.542 | 1.98285 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.3089 | 0.183246 | 0.0916231 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916231 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 146.042i | − 1.60486i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −66.8468 | −0.661849 | −0.330925 | − | 0.943657i | \(-0.607361\pi\) | ||||
−0.330925 | + | 0.943657i | \(0.607361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 166.313i | − 1.61469i | −0.590083 | − | 0.807343i | \(-0.700905\pi\) | ||||
0.590083 | − | 0.807343i | \(-0.299095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 80.1467i | 0.749035i | 0.927220 | + | 0.374517i | \(0.122192\pi\) | ||||
−0.927220 | + | 0.374517i | \(0.877808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −26.8781 | −0.246589 | −0.123294 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123294 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 79.0958 | 0.699963 | 0.349981 | − | 0.936757i | \(-0.386188\pi\) | ||||
0.349981 | + | 0.936757i | \(0.386188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 45.7395i | − 0.397735i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 173.894i | − 1.46129i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −69.3837 | −0.573419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −155.618 | −1.24494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 170.725i | 1.34429i | 0.740419 | + | 0.672145i | \(0.234627\pi\) | ||||
−0.740419 | + | 0.672145i | \(0.765373\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 178.980i | − 1.36626i | −0.730297 | − | 0.683129i | \(-0.760619\pi\) | ||||
0.730297 | − | 0.683129i | \(-0.239381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 174.915 | 1.31515 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 93.2075 | 0.680347 | 0.340173 | − | 0.940363i | \(-0.389514\pi\) | ||||
0.340173 | + | 0.940363i | \(0.389514\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 222.476i | − 1.60055i | −0.599635 | − | 0.800274i | \(-0.704687\pi\) | ||||
0.599635 | − | 0.800274i | \(-0.295313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 235.522i | 1.64700i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −340.479 | −2.34813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.0043 | 0.630901 | 0.315451 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315451 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 82.0081i | − 0.543100i | −0.962424 | − | 0.271550i | \(-0.912464\pi\) | ||||
0.962424 | − | 0.271550i | \(-0.0875362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 184.885i | − 1.19281i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 56.7180 | 0.361261 | 0.180631 | − | 0.983551i | \(-0.442186\pi\) | ||||
0.180631 | + | 0.983551i | \(0.442186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.1918 | −0.293117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 189.588i | − 1.16312i | −0.813504 | − | 0.581559i | \(-0.802443\pi\) | ||||
0.813504 | − | 0.581559i | \(-0.197557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 312.777i | 1.87291i | 0.350783 | + | 0.936457i | \(0.385916\pi\) | ||||
−0.350783 | + | 0.936457i | \(0.614084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 122.361 | 0.724031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −182.538 | −1.05513 | −0.527567 | − | 0.849514i | \(-0.676896\pi\) | ||||
−0.527567 | + | 0.849514i | \(0.676896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 374.455i | 2.13974i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7781i | 0.110492i | 0.998473 | + | 0.0552461i | \(0.0175943\pi\) | ||||
−0.998473 | + | 0.0552461i | \(0.982406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −265.750 | −1.46823 | −0.734117 | − | 0.679023i | \(-0.762403\pi\) | ||||
−0.734117 | + | 0.679023i | \(0.762403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −96.4640 | −0.521427 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 280.438i | 1.49967i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −33.8330 | −0.171741 | −0.0858705 | − | 0.996306i | \(-0.527367\pi\) | ||||
−0.0858705 | + | 0.996306i | \(0.527367\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 84.9700i | − 0.426985i | −0.976945 | − | 0.213493i | \(-0.931516\pi\) | ||||
0.976945 | − | 0.213493i | \(-0.0684839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 351.290i | 1.73049i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 298.138 | 1.45433 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −282.085 | −1.34969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 140.700i | 0.666826i | 0.942781 | + | 0.333413i | \(0.108200\pi\) | ||||
−0.942781 | + | 0.333413i | \(0.891800\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 554.478i | − 2.57897i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −190.755 | −0.879057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 346.926 | 1.56980 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 247.529i | − 1.11000i | −0.831851 | − | 0.554999i | \(-0.812719\pi\) | ||||
0.831851 | − | 0.554999i | \(-0.187281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 129.752i | − 0.571593i | −0.958290 | − | 0.285797i | \(-0.907742\pi\) | ||||
0.958290 | − | 0.285797i | \(-0.0922582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −294.304 | −1.28517 | −0.642586 | − | 0.766214i | \(-0.722138\pi\) | ||||
−0.642586 | + | 0.766214i | \(0.722138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 239.948 | 1.02982 | 0.514911 | − | 0.857244i | \(-0.327825\pi\) | ||||
0.514911 | + | 0.857244i | \(0.327825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 165.325i | 0.703509i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 200.698 | 0.819176 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 348.964i | 1.41281i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.125i | 0.880976i | 0.897759 | + | 0.440488i | \(0.145195\pi\) | ||||
−0.897759 | + | 0.440488i | \(0.854805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 76.1061 | 0.300815 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −87.0655 | −0.338776 | −0.169388 | − | 0.985549i | \(-0.554179\pi\) | ||||
−0.169388 | + | 0.985549i | \(0.554179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 99.5270i | 0.384274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 277.324i | − 1.05447i | −0.849721 | − | 0.527233i | \(-0.823230\pi\) | ||||
0.849721 | − | 0.527233i | \(-0.176770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −146.222 | −0.551780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −49.8005 | −0.185132 | −0.0925659 | − | 0.995707i | \(-0.529507\pi\) | ||||
−0.0925659 | + | 0.995707i | \(0.529507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.3145i | 0.115552i | 0.998330 | + | 0.0577758i | \(0.0184009\pi\) | ||||
−0.998330 | + | 0.0577758i | \(0.981599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 603.882i | − 2.19593i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 79.1431 | 0.285715 | 0.142858 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142858 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 106.190 | 0.377902 | 0.188951 | − | 0.981987i | \(-0.439491\pi\) | ||||
0.188951 | + | 0.981987i | \(0.439491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 270.251i | 0.954949i | 0.878646 | + | 0.477475i | \(0.158448\pi\) | ||||
−0.878646 | + | 0.477475i | \(0.841552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 307.605i | − 1.07179i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 124.088 | 0.429371 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2487 | 0.0827600 | 0.0413800 | − | 0.999143i | \(-0.486825\pi\) | ||||
0.0413800 | + | 0.999143i | \(0.486825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 515.440i | − 1.74726i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 94.1500i | − 0.314883i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −572.084 | −1.90061 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −393.759 | −1.29101 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 122.865i | − 0.400211i | −0.979774 | − | 0.200106i | \(-0.935871\pi\) | ||||
0.979774 | − | 0.200106i | \(-0.0641285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 108.808i | − 0.349865i | −0.984580 | − | 0.174933i | \(-0.944029\pi\) | ||||
0.984580 | − | 0.174933i | \(-0.0559707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −52.2216 | −0.166842 | −0.0834211 | − | 0.996514i | \(-0.526585\pi\) | ||||
−0.0834211 | + | 0.996514i | \(0.526585\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 94.3251 | 0.297555 | 0.148778 | − | 0.988871i | \(-0.452466\pi\) | ||||
0.148778 | + | 0.988871i | \(0.452466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 566.524i | − 1.77594i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 415.515i | 1.28642i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −747.056 | −2.29863 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 170.574 | 0.518462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 406.107i | 1.22691i | 0.789730 | + | 0.613454i | \(0.210220\pi\) | ||||
−0.789730 | + | 0.613454i | \(0.789780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 307.630 | 0.902142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 212.165i | 0.618557i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 458.377i | 1.32097i | 0.750839 | + | 0.660486i | \(0.229650\pi\) | ||||
−0.750839 | + | 0.660486i | \(0.770350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −282.960 | −0.810774 | −0.405387 | − | 0.914145i | \(-0.632863\pi\) | ||||
−0.405387 | + | 0.914145i | \(0.632863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 175.820 | 0.498073 | 0.249036 | − | 0.968494i | \(-0.419886\pi\) | ||||
0.249036 | + | 0.968494i | \(0.419886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 140.268i | 0.395122i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 53.5791i | 0.149246i | 0.997212 | + | 0.0746228i | \(0.0237753\pi\) | ||||
−0.997212 | + | 0.0746228i | \(0.976225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −56.9552 | −0.157771 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −843.449 | −2.31082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 62.4258i | 0.170097i | 0.996377 | + | 0.0850487i | \(0.0271046\pi\) | ||||
−0.996377 | + | 0.0850487i | \(0.972895\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 150.864i | 0.406643i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 370.552 | 0.993437 | 0.496719 | − | 0.867912i | \(-0.334538\pi\) | ||||
0.496719 | + | 0.867912i | \(0.334538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −700.841 | −1.85900 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 68.7286i | 0.181342i | 0.995881 | + | 0.0906709i | \(0.0289012\pi\) | ||||
−0.995881 | + | 0.0906709i | \(0.971099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −481.792 | −1.23854 | −0.619269 | − | 0.785179i | \(-0.712571\pi\) | ||||
−0.619269 | + | 0.785179i | \(0.712571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 112.105i | − 0.286714i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.29179i | − 0.0184602i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 422.315 | 1.06377 | 0.531883 | − | 0.846818i | \(-0.321485\pi\) | ||||
0.531883 | + | 0.846818i | \(0.321485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 641.025 | 1.59857 | 0.799283 | − | 0.600955i | \(-0.205213\pi\) | ||||
0.799283 | + | 0.600955i | \(0.205213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 380.566i | − 0.944333i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 160.507i | − 0.394365i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −278.562 | −0.681081 | −0.340541 | − | 0.940230i | \(-0.610610\pi\) | ||||
−0.340541 | + | 0.940230i | \(0.610610\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −531.807 | −1.28767 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 192.496i | − 0.463845i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 505.611i | − 1.20671i | −0.797473 | − | 0.603354i | \(-0.793831\pi\) | ||||
0.797473 | − | 0.603354i | \(-0.206169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 179.846 | 0.427189 | 0.213594 | − | 0.976922i | \(-0.431483\pi\) | ||||
0.213594 | + | 0.976922i | \(0.431483\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −889.526 | −2.09300 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 406.262i | 0.951432i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 112.764 | 0.258041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 129.991i | − 0.296107i | −0.988979 | − | 0.148053i | \(-0.952699\pi\) | ||||
0.988979 | − | 0.148053i | \(-0.0473008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 205.564i | 0.464027i | 0.972713 | + | 0.232014i | \(0.0745314\pi\) | ||||
−0.972713 | + | 0.232014i | \(0.925469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −135.242 | −0.303915 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −415.190 | −0.924698 | −0.462349 | − | 0.886698i | \(-0.652993\pi\) | ||||
−0.462349 | + | 0.886698i | \(0.652993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 496.073i | 1.09994i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1211.06i | 2.66167i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −598.927 | −1.31056 | −0.655281 | − | 0.755385i | \(-0.727450\pi\) | ||||
−0.655281 | + | 0.755385i | \(0.727450\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 376.804 | 0.817361 | 0.408681 | − | 0.912677i | \(-0.365989\pi\) | ||||
0.408681 | + | 0.912677i | \(0.365989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 218.577i | − 0.472088i | −0.971742 | − | 0.236044i | \(-0.924149\pi\) | ||||
0.971742 | − | 0.236044i | \(-0.0758510\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 443.608i | 0.949911i | 0.880010 | + | 0.474955i | \(0.157536\pi\) | ||||
−0.880010 | + | 0.474955i | \(0.842464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 640.066 | 1.36475 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 922.597 | 1.95052 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 894.751i | − 1.88369i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1561.54 | −3.21968 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 403.795i | − 0.829148i | −0.910016 | − | 0.414574i | \(-0.863931\pi\) | ||||
0.910016 | − | 0.414574i | \(-0.136069\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 808.347i | − 1.64633i | −0.567803 | − | 0.823164i | \(-0.692207\pi\) | ||||
0.567803 | − | 0.823164i | \(-0.307793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −834.498 | −1.69269 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 144.722 | 0.291192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 132.172i | − 0.264874i | −0.991191 | − | 0.132437i | \(-0.957720\pi\) | ||||
0.991191 | − | 0.132437i | \(-0.0422802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 92.8360i | 0.184565i | 0.995733 | + | 0.0922823i | \(0.0294162\pi\) | ||||
−0.995733 | + | 0.0922823i | \(0.970584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 554.329 | 1.09768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 927.417 | 1.82204 | 0.911018 | − | 0.412366i | \(-0.135297\pi\) | ||||
0.911018 | + | 0.412366i | \(0.135297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 870.231i | 1.70300i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1379.15i | 2.67796i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −275.084 | −0.532077 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −527.145 | −1.01179 | −0.505897 | − | 0.862594i | \(-0.668838\pi\) | ||||
−0.505897 | + | 0.862594i | \(0.668838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 972.249i | − 1.85898i | −0.368843 | − | 0.929492i | \(-0.620246\pi\) | ||||
0.368843 | − | 0.929492i | \(-0.379754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 453.143i | − 0.859854i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 498.577 | 0.942489 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 613.687 | 1.15138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 664.619i | − 1.24228i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 333.942i | 0.619559i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.66591 | −0.00862461 | −0.00431231 | − | 0.999991i | \(-0.501373\pi\) | ||||
−0.00431231 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 222.888 | 0.408968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 386.796i | 0.707123i | 0.935411 | + | 0.353561i | \(0.115029\pi\) | ||||
−0.935411 | + | 0.353561i | \(0.884971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 839.399i | − 1.52341i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.52332 | −0.0136046 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 219.630 | 0.394308 | 0.197154 | − | 0.980373i | \(-0.436830\pi\) | ||||
0.197154 | + | 0.980373i | \(0.436830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1141.34i | − 2.04175i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 266.807i | − 0.473902i | −0.971522 | − | 0.236951i | \(-0.923852\pi\) | ||||
0.971522 | − | 0.236951i | \(-0.0761480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −655.904 | −1.16089 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 972.046 | 1.70834 | 0.854170 | − | 0.519993i | \(-0.174066\pi\) | ||||
0.854170 | + | 0.519993i | \(0.174066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 340.194i | 0.595786i | 0.954599 | + | 0.297893i | \(0.0962838\pi\) | ||||
−0.954599 | + | 0.297893i | \(0.903716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −198.608 | −0.341838 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 243.299i | − 0.417322i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 162.144i | − 0.276226i | −0.990417 | − | 0.138113i | \(-0.955896\pi\) | ||||
0.990417 | − | 0.138113i | \(-0.0441036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 455.805 | 0.773862 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 793.227 | 1.33765 | 0.668825 | − | 0.743420i | \(-0.266797\pi\) | ||||
0.668825 | + | 0.743420i | \(0.266797\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1442.02i | 2.42356i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 432.194i | − 0.721525i | −0.932658 | − | 0.360763i | \(-0.882516\pi\) | ||||
0.932658 | − | 0.360763i | \(-0.117484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 936.310 | 1.55792 | 0.778960 | − | 0.627074i | \(-0.215748\pi\) | ||||
0.778960 | + | 0.627074i | \(0.215748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 575.366 | 0.951018 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 223.972i | 0.368982i | 0.982834 | + | 0.184491i | \(0.0590637\pi\) | ||||
−0.982834 | + | 0.184491i | \(0.940936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 340.304i | 0.556962i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1010.40 | 1.64828 | 0.824141 | − | 0.566385i | \(-0.191658\pi\) | ||||
0.824141 | + | 0.566385i | \(0.191658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 400.206 | 0.648633 | 0.324316 | − | 0.945949i | \(-0.394866\pi\) | ||||
0.324316 | + | 0.945949i | \(0.394866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 417.349i | 0.674231i | 0.941463 | + | 0.337116i | \(0.109451\pi\) | ||||
−0.941463 | + | 0.337116i | \(0.890549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 139.536i | 0.223975i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 196.315 | 0.314104 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −236.428 | −0.375880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 718.033i | 1.13793i | 0.822362 | + | 0.568965i | \(0.192656\pi\) | ||||
−0.822362 | + | 0.568965i | \(0.807344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1415.74i | − 2.22951i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 413.116 | 0.648534 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −139.926 | −0.218293 | −0.109146 | − | 0.994026i | \(-0.534812\pi\) | ||||
−0.109146 | + | 0.994026i | \(0.534812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 777.990i | − 1.20994i | −0.796249 | − | 0.604969i | \(-0.793186\pi\) | ||||
0.796249 | − | 0.604969i | \(-0.206814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 673.336i | − 1.04070i | −0.853952 | − | 0.520352i | \(-0.825801\pi\) | ||||
0.853952 | − | 0.520352i | \(-0.174199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 857.642 | 1.32148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 223.410 | 0.342128 | 0.171064 | − | 0.985260i | \(-0.445279\pi\) | ||||
0.171064 | + | 0.985260i | \(0.445279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1484.20i | 2.26595i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 166.367i | − 0.252453i | −0.992001 | − | 0.126227i | \(-0.959713\pi\) | ||||
0.992001 | − | 0.126227i | \(-0.0402866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 655.773 | 0.992092 | 0.496046 | − | 0.868296i | \(-0.334785\pi\) | ||||
0.496046 | + | 0.868296i | \(0.334785\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1450.49 | −2.18119 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 226.469i | 0.339533i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 831.520 | 1.22824 | 0.614121 | − | 0.789212i | \(-0.289511\pi\) | ||||
0.614121 | + | 0.789212i | \(0.289511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1611.13i | 2.37279i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 308.273i | 0.451351i | 0.974202 | + | 0.225676i | \(0.0724590\pi\) | ||||
−0.974202 | + | 0.225676i | \(0.927541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −772.926 | −1.12836 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −300.982 | −0.436839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 666.811i | − 0.964994i | −0.875898 | − | 0.482497i | \(-0.839730\pi\) | ||||
0.875898 | − | 0.482497i | \(-0.160270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1844.89i | 2.65452i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 730.722 | 1.04838 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 242.205 | 0.345514 | 0.172757 | − | 0.984964i | \(-0.444732\pi\) | ||||
0.172757 | + | 0.984964i | \(0.444732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 237.817i | − 0.338289i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 571.930i | − 0.808953i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1380.24 | −1.94674 | −0.973371 | − | 0.229237i | \(-0.926377\pi\) | ||||
−0.973371 | + | 0.229237i | \(0.926377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −122.976 | −0.172476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1953.07i | − 2.73157i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1796.97 | 2.47858 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1017.52i | 1.39962i | 0.714329 | + | 0.699810i | \(0.246732\pi\) | ||||
−0.714329 | + | 0.699810i | \(0.753268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1359.00i | − 1.85909i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1026.22 | 1.40003 | 0.700016 | − | 0.714127i | \(-0.253176\pi\) | ||||
0.700016 | + | 0.714127i | \(0.253176\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1032.23 | −1.40059 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 923.444i | 1.24959i | 0.780791 | + | 0.624793i | \(0.214817\pi\) | ||||
−0.780791 | + | 0.624793i | \(0.785183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1267.12i | 1.70542i | 0.522387 | + | 0.852708i | \(0.325042\pi\) | ||||
−0.522387 | + | 0.852708i | \(0.674958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −779.533 | −1.04635 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −685.722 | −0.915517 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 791.442i | − 1.05385i | −0.849912 | − | 0.526925i | \(-0.823345\pi\) | ||||
0.849912 | − | 0.526925i | \(-0.176655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 680.054i | 0.900734i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 333.990 | 0.441202 | 0.220601 | − | 0.975364i | \(-0.429198\pi\) | ||||
0.220601 | + | 0.975364i | \(0.429198\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −617.122 | −0.810936 | −0.405468 | − | 0.914109i | \(-0.632891\pi\) | ||||
−0.405468 | + | 0.914109i | \(0.632891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 229.965i | − 0.301396i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1314.59 | −1.70064 | −0.850319 | − | 0.526268i | \(-0.823591\pi\) | ||||
−0.850319 | + | 0.526268i | \(0.823591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 975.779i | 1.25907i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 735.015i | 0.943536i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −233.393 | −0.298839 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −470.336 | −0.599154 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 301.018i | 0.382488i | 0.981542 | + | 0.191244i | \(0.0612522\pi\) | ||||
−0.981542 | + | 0.191244i | \(0.938748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 676.731i | 0.855538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −810.512 | −1.02208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −476.193 | −0.597481 | −0.298741 | − | 0.954334i | \(-0.596567\pi\) | ||||
−0.298741 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 405.202i | 0.507137i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1403.42i | − 1.74772i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 391.340 | 0.486136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 692.874 | 0.856457 | 0.428228 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428228 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 785.074i | 0.968032i | 0.875059 | + | 0.484016i | \(0.160822\pi\) | ||||
−0.875059 | + | 0.484016i | \(0.839178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1572.17i | 1.92904i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1366.98 | 1.67317 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 527.681 | 0.642729 | 0.321365 | − | 0.946956i | \(-0.395859\pi\) | ||||
0.321365 | + | 0.946956i | \(0.395859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 228.552i | − 0.277706i | −0.990313 | − | 0.138853i | \(-0.955658\pi\) | ||||
0.990313 | − | 0.138853i | \(-0.0443416\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 608.409i | − 0.735683i | −0.929889 | − | 0.367841i | \(-0.880097\pi\) | ||||
0.929889 | − | 0.367841i | \(-0.119903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 151.637 | 0.182915 | 0.0914577 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914577 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 491.901 | 0.590518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2593.71i | − 3.10624i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 653.351i | 0.778725i | 0.921085 | + | 0.389363i | \(0.127305\pi\) | ||||
−0.921085 | + | 0.389363i | \(0.872695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 844.805 | 1.00452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1014.68 | −1.20081 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 593.635i | − 0.700868i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.1628i | 0.0753969i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1372.25 | 1.60873 | 0.804367 | − | 0.594132i | \(-0.202505\pi\) | ||||
0.804367 | + | 0.594132i | \(0.202505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1453.61 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 962.466i | 1.12045i | 0.828341 | + | 0.560225i | \(0.189285\pi\) | ||||
−0.828341 | + | 0.560225i | \(0.810715\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.1328 | 0.0139618 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1276.96i | 1.46609i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1331.44i | − 1.52165i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 338.191 | 0.385622 | 0.192811 | − | 0.981236i | \(-0.438240\pi\) | ||||
0.192811 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 459.985 | 0.522117 | 0.261058 | − | 0.965323i | \(-0.415928\pi\) | ||||
0.261058 | + | 0.965323i | \(0.415928\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1208.31i | − 1.36842i | −0.729286 | − | 0.684209i | \(-0.760147\pi\) | ||||
0.729286 | − | 0.684209i | \(-0.239853\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1500.73i | 1.69192i | 0.533250 | + | 0.845958i | \(0.320971\pi\) | ||||
−0.533250 | + | 0.845958i | \(0.679029\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1460.69 | −1.64307 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −407.582 | −0.456419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 164.010i | − 0.183252i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 915.415i | 1.01826i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −358.382 | −0.397760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2203.74 | 2.43507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 665.128i | 0.733328i | 0.930353 | + | 0.366664i | \(0.119500\pi\) | ||||
−0.930353 | + | 0.366664i | \(0.880500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1531.32 | 1.66993 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1102.20i | − 1.19934i | −0.800246 | − | 0.599671i | \(-0.795298\pi\) | ||||
0.800246 | − | 0.599671i | \(-0.204702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 288.728i | 0.312815i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 509.115 | 0.550394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1256.03 | 1.35202 | 0.676010 | − | 0.736893i | \(-0.263708\pi\) | ||||
0.676010 | + | 0.736893i | \(0.263708\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 494.790i | 0.531461i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2325.54i | − 2.48720i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −822.214 | −0.877496 | −0.438748 | − | 0.898610i | \(-0.644578\pi\) | ||||
−0.438748 | + | 0.898610i | \(0.644578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1185.72 | 1.26006 | 0.630031 | − | 0.776570i | \(-0.283042\pi\) | ||||
0.630031 | + | 0.776570i | \(0.283042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 198.306i | − 0.210293i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1335.34i | 1.41007i | 0.709170 | + | 0.705037i | \(0.249070\pi\) | ||||
−0.709170 | + | 0.705037i | \(0.750930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1736.15 | −1.82945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −663.428 | −0.696147 | −0.348073 | − | 0.937467i | \(-0.613164\pi\) | ||||
−0.348073 | + | 0.937467i | \(0.613164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2388.46i | − 2.50100i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 797.468i | 0.831562i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 463.918 | 0.482745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2330.28 | −2.41480 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 155.996i | − 0.161320i | −0.996742 | − | 0.0806600i | \(-0.974297\pi\) | ||||
0.996742 | − | 0.0806600i | \(-0.0257028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1280.67i | 1.31892i | 0.751740 | + | 0.659460i | \(0.229215\pi\) | ||||
−0.751740 | + | 0.659460i | \(0.770785\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1903.47 | 1.95629 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 217.470 | 0.222590 | 0.111295 | − | 0.993787i | \(-0.464500\pi\) | ||||
0.111295 | + | 0.993787i | \(0.464500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 225.030i | − 0.229857i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1027.63i | 1.04540i | 0.852515 | + | 0.522702i | \(0.175076\pi\) | ||||
−0.852515 | + | 0.522702i | \(0.824924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 280.561 | 0.284833 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −368.809 | −0.372911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 797.792i | − 0.805038i | −0.915412 | − | 0.402519i | \(-0.868135\pi\) | ||||
0.915412 | − | 0.402519i | \(-0.131865\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 704.616i | 0.708157i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1237.58 | −1.24131 | −0.620654 | − | 0.784085i | \(-0.713133\pi\) | ||||
−0.620654 | + | 0.784085i | \(0.713133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.3.g.c.127.2 | 8 | ||
3.2 | odd | 2 | 384.3.g.b.127.8 | yes | 8 | ||
4.3 | odd | 2 | inner | 1152.3.g.c.127.1 | 8 | ||
8.3 | odd | 2 | 1152.3.g.f.127.7 | 8 | |||
8.5 | even | 2 | 1152.3.g.f.127.8 | 8 | |||
12.11 | even | 2 | 384.3.g.b.127.4 | yes | 8 | ||
16.3 | odd | 4 | 2304.3.b.t.127.8 | 8 | |||
16.5 | even | 4 | 2304.3.b.t.127.1 | 8 | |||
16.11 | odd | 4 | 2304.3.b.q.127.1 | 8 | |||
16.13 | even | 4 | 2304.3.b.q.127.8 | 8 | |||
24.5 | odd | 2 | 384.3.g.a.127.1 | ✓ | 8 | ||
24.11 | even | 2 | 384.3.g.a.127.5 | yes | 8 | ||
48.5 | odd | 4 | 768.3.b.e.127.8 | 8 | |||
48.11 | even | 4 | 768.3.b.f.127.4 | 8 | |||
48.29 | odd | 4 | 768.3.b.f.127.1 | 8 | |||
48.35 | even | 4 | 768.3.b.e.127.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.1 | ✓ | 8 | 24.5 | odd | 2 | ||
384.3.g.a.127.5 | yes | 8 | 24.11 | even | 2 | ||
384.3.g.b.127.4 | yes | 8 | 12.11 | even | 2 | ||
384.3.g.b.127.8 | yes | 8 | 3.2 | odd | 2 | ||
768.3.b.e.127.5 | 8 | 48.35 | even | 4 | |||
768.3.b.e.127.8 | 8 | 48.5 | odd | 4 | |||
768.3.b.f.127.1 | 8 | 48.29 | odd | 4 | |||
768.3.b.f.127.4 | 8 | 48.11 | even | 4 | |||
1152.3.g.c.127.1 | 8 | 4.3 | odd | 2 | inner | ||
1152.3.g.c.127.2 | 8 | 1.1 | even | 1 | trivial | ||
1152.3.g.f.127.7 | 8 | 8.3 | odd | 2 | |||
1152.3.g.f.127.8 | 8 | 8.5 | even | 2 | |||
2304.3.b.q.127.1 | 8 | 16.11 | odd | 4 | |||
2304.3.b.q.127.8 | 8 | 16.13 | even | 4 | |||
2304.3.b.t.127.1 | 8 | 16.5 | even | 4 | |||
2304.3.b.t.127.8 | 8 | 16.3 | odd | 4 |