Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.8 | ||
Root | \(-1.14412 + 1.98168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.l.703.7 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 7.40492 | 1.48098 | 0.740492 | − | 0.672065i | \(-0.234593\pi\) | ||||
0.740492 | + | 0.672065i | \(0.234593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.47802i | 1.35400i | 0.735982 | + | 0.677001i | \(0.236721\pi\) | ||||
−0.735982 | + | 0.677001i | \(0.763279\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.77022i | 0.615475i | 0.951471 | + | 0.307737i | \(0.0995718\pi\) | ||||
−0.951471 | + | 0.307737i | \(0.900428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4164 | 1.10895 | 0.554477 | − | 0.832199i | \(-0.312918\pi\) | ||||
0.554477 | + | 0.832199i | \(0.312918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.8933 | −1.05255 | −0.526274 | − | 0.850315i | \(-0.676411\pi\) | ||||
−0.526274 | + | 0.850315i | \(0.676411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19615i | 0.273482i | 0.990607 | + | 0.136741i | \(0.0436628\pi\) | ||||
−0.990607 | + | 0.136741i | \(0.956337\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.9366i | 1.08420i | 0.840313 | + | 0.542101i | \(0.182371\pi\) | ||||
−0.840313 | + | 0.542101i | \(0.817629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.8328 | 1.19331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.6197 | 1.02137 | 0.510684 | − | 0.859768i | \(-0.329392\pi\) | ||||
0.510684 | + | 0.859768i | \(0.329392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 17.1275i | − 0.552499i | −0.961086 | − | 0.276249i | \(-0.910908\pi\) | ||||
0.961086 | − | 0.276249i | \(-0.0890916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 70.1839i | 2.00526i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.41641 | −0.173416 | −0.0867082 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867082 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.64290 | −0.210803 | −0.105401 | − | 0.994430i | \(-0.533613\pi\) | ||||
−0.105401 | + | 0.994430i | \(0.533613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.1329i | 1.16588i | 0.812514 | + | 0.582941i | \(0.198098\pi\) | ||||
−0.812514 | + | 0.582941i | \(0.801902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.0175i | 1.10676i | 0.832930 | + | 0.553378i | \(0.186661\pi\) | ||||
−0.832930 | + | 0.553378i | \(0.813339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40.8328 | −0.833323 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −82.6921 | −1.56023 | −0.780114 | − | 0.625637i | \(-0.784839\pi\) | ||||
−0.780114 | + | 0.625637i | \(0.784839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.1329i | 0.911508i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 83.7244i | − 1.41906i | −0.704676 | − | 0.709529i | \(-0.748908\pi\) | ||||
0.704676 | − | 0.709529i | \(-0.251092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.41641 | 0.137974 | 0.0689869 | − | 0.997618i | \(-0.478023\pi\) | ||||
0.0689869 | + | 0.997618i | \(0.478023\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 106.752 | 1.64234 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 29.0588i | − 0.433713i | −0.976203 | − | 0.216856i | \(-0.930420\pi\) | ||||
0.976203 | − | 0.216856i | \(-0.0695804\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 113.287i | − 1.59559i | −0.602928 | − | 0.797796i | \(-0.705999\pi\) | ||||
0.602928 | − | 0.797796i | \(-0.294001\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16718 | 0.0296875 | 0.0148437 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148437 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −64.1683 | −0.833354 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 149.485i | 1.89221i | 0.323861 | + | 0.946105i | \(0.395019\pi\) | ||||
−0.323861 | + | 0.946105i | \(0.604981\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 13.5404i | − 0.163138i | −0.996668 | − | 0.0815690i | \(-0.974007\pi\) | ||||
0.996668 | − | 0.0815690i | \(-0.0259931\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −132.498 | −1.55881 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.8933 | −0.201048 | −0.100524 | − | 0.994935i | \(-0.532052\pi\) | ||||
−0.100524 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 136.639i | 1.50153i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38.4771i | 0.405022i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −138.331 | −1.42610 | −0.713048 | − | 0.701115i | \(-0.752686\pi\) | ||||
−0.713048 | + | 0.701115i | \(0.752686\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 97.5019 | 0.965366 | 0.482683 | − | 0.875795i | \(-0.339662\pi\) | ||||
0.482683 | + | 0.875795i | \(0.339662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42.4835i | 0.412461i | 0.978503 | + | 0.206231i | \(0.0661197\pi\) | ||||
−0.978503 | + | 0.206231i | \(0.933880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 97.2648i | − 0.909017i | −0.890742 | − | 0.454509i | \(-0.849815\pi\) | ||||
0.890742 | − | 0.454509i | \(-0.150185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96.8328 | 0.888374 | 0.444187 | − | 0.895934i | \(-0.353493\pi\) | ||||
0.444187 | + | 0.895934i | \(0.353493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −38.8701 | −0.343983 | −0.171991 | − | 0.985098i | \(-0.555020\pi\) | ||||
−0.171991 | + | 0.985098i | \(0.555020\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 184.654i | 1.60568i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 169.593i | − 1.42515i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75.1641 | 0.621191 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 35.7866 | 0.286293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.0165i | 0.779657i | 0.920887 | + | 0.389829i | \(0.127466\pi\) | ||||
−0.920887 | + | 0.389829i | \(0.872534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 54.1618i | 0.413449i | 0.978399 | + | 0.206724i | \(0.0662803\pi\) | ||||
−0.978399 | + | 0.206724i | \(0.933720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −49.2492 | −0.370295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.55944 | 0.0405798 | 0.0202899 | − | 0.999794i | \(-0.493541\pi\) | ||||
0.0202899 | + | 0.999794i | \(0.493541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 152.517i | 1.09724i | 0.836070 | + | 0.548622i | \(0.184847\pi\) | ||||
−0.836070 | + | 0.548622i | \(0.815153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 97.6023i | 0.682534i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 219.331 | 1.51263 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 136.979 | 0.919325 | 0.459663 | − | 0.888094i | \(-0.347970\pi\) | ||||
0.459663 | + | 0.888094i | \(0.347970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 77.9879i | − 0.516476i | −0.966081 | − | 0.258238i | \(-0.916858\pi\) | ||||
0.966081 | − | 0.258238i | \(-0.0831419\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 126.827i | − 0.818242i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 72.1641 | 0.459644 | 0.229822 | − | 0.973233i | \(-0.426186\pi\) | ||||
0.229822 | + | 0.973233i | \(0.426186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −236.350 | −1.46801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 56.5785i | − 0.347108i | −0.984824 | − | 0.173554i | \(-0.944475\pi\) | ||||
0.984824 | − | 0.173554i | \(-0.0555250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 201.637i | − 1.20741i | −0.797208 | − | 0.603705i | \(-0.793691\pi\) | ||||
0.797208 | − | 0.603705i | \(-0.206309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.8328 | 0.229780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 92.5500 | 0.534971 | 0.267485 | − | 0.963562i | \(-0.413807\pi\) | ||||
0.267485 | + | 0.963562i | \(0.413807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 282.756i | 1.61575i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.28851i | 0.0239581i | 0.999928 | + | 0.0119791i | \(0.00381315\pi\) | ||||
−0.999928 | + | 0.0119791i | \(0.996187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 289.748 | 1.60082 | 0.800408 | − | 0.599456i | \(-0.204616\pi\) | ||||
0.800408 | + | 0.599456i | \(0.204616\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −47.5130 | −0.256827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 121.142i | − 0.647816i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 92.6389i | 0.485020i | 0.970149 | + | 0.242510i | \(0.0779708\pi\) | ||||
−0.970149 | + | 0.242510i | \(0.922029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −243.164 | −1.25992 | −0.629959 | − | 0.776629i | \(-0.716928\pi\) | ||||
−0.629959 | + | 0.776629i | \(0.716928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −139.432 | −0.707779 | −0.353890 | − | 0.935287i | \(-0.615141\pi\) | ||||
−0.353890 | + | 0.935287i | \(0.615141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 110.993i | 0.557756i | 0.960327 | + | 0.278878i | \(0.0899624\pi\) | ||||
−0.960327 | + | 0.278878i | \(0.910038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 280.736i | 1.38293i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −64.0000 | −0.312195 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.1791 | −0.168321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 265.095i | 1.25637i | 0.778062 | + | 0.628187i | \(0.216203\pi\) | ||||
−0.778062 | + | 0.628187i | \(0.783797\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 371.230i | 1.72665i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 162.334 | 0.748085 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −257.957 | −1.16723 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 317.925i | 1.42567i | 0.701330 | + | 0.712837i | \(0.252590\pi\) | ||||
−0.701330 | + | 0.712837i | \(0.747410\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 249.366i | 1.09853i | 0.835648 | + | 0.549265i | \(0.185092\pi\) | ||||
−0.835648 | + | 0.549265i | \(0.814908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −152.334 | −0.665216 | −0.332608 | − | 0.943065i | \(-0.607929\pi\) | ||||
−0.332608 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 346.793 | 1.48838 | 0.744191 | − | 0.667966i | \(-0.232835\pi\) | ||||
0.744191 | + | 0.667966i | \(0.232835\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 385.186i | 1.63909i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 104.035i | 0.435293i | 0.976028 | + | 0.217647i | \(0.0698380\pi\) | ||||
−0.976028 | + | 0.217647i | \(0.930162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 281.827 | 1.16940 | 0.584702 | − | 0.811248i | \(-0.301211\pi\) | ||||
0.584702 | + | 0.811248i | \(0.301211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −302.364 | −1.23414 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 74.9099i | 0.303279i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 271.484i | − 1.08161i | −0.841148 | − | 0.540804i | \(-0.818120\pi\) | ||||
0.841148 | − | 0.540804i | \(-0.181880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −168.827 | −0.667299 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 459.105 | 1.78640 | 0.893200 | − | 0.449659i | \(-0.148455\pi\) | ||||
0.893200 | + | 0.449659i | \(0.148455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 60.8148i | − 0.234806i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 203.782i | 0.774835i | 0.921904 | + | 0.387418i | \(0.126633\pi\) | ||||
−0.921904 | + | 0.387418i | \(0.873367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −612.328 | −2.31067 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 323.363 | 1.20209 | 0.601047 | − | 0.799213i | \(-0.294750\pi\) | ||||
0.601047 | + | 0.799213i | \(0.294750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 104.928i | − 0.387190i | −0.981082 | − | 0.193595i | \(-0.937985\pi\) | ||||
0.981082 | − | 0.193595i | \(-0.0620148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 201.975i | 0.734454i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 48.8328 | 0.176292 | 0.0881459 | − | 0.996108i | \(-0.471906\pi\) | ||||
0.0881459 | + | 0.996108i | \(0.471906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.6197 | −0.105408 | −0.0527040 | − | 0.998610i | \(-0.516784\pi\) | ||||
−0.0527040 | + | 0.998610i | \(0.516784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 385.186i | 1.36108i | 0.732711 | + | 0.680540i | \(0.238255\pi\) | ||||
−0.732711 | + | 0.680540i | \(0.761745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 81.9176i | − 0.285427i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.1703 | 0.107856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 281.410 | 0.960443 | 0.480222 | − | 0.877147i | \(-0.340556\pi\) | ||||
0.480222 | + | 0.877147i | \(0.340556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 619.972i | − 2.10160i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 359.497i | 1.20233i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −475.161 | −1.57861 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 62.3228 | 0.204337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 553.961i | − 1.80443i | −0.431282 | − | 0.902217i | \(-0.641939\pi\) | ||||
0.431282 | − | 0.902217i | \(-0.358061\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 15.6847i | − 0.0504331i | −0.999682 | − | 0.0252166i | \(-0.991972\pi\) | ||||
0.999682 | − | 0.0252166i | \(-0.00802753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −308.161 | −0.984540 | −0.492270 | − | 0.870443i | \(-0.663833\pi\) | ||||
−0.492270 | + | 0.870443i | \(0.663833\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −496.107 | −1.56500 | −0.782502 | − | 0.622648i | \(-0.786057\pi\) | ||||
−0.782502 | + | 0.622648i | \(0.786057\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 200.532i | 0.628626i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 92.9763i | − 0.287852i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 430.082 | 1.32333 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −493.023 | −1.49855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 86.5060i | 0.261347i | 0.991425 | + | 0.130674i | \(0.0417140\pi\) | ||||
−0.991425 | + | 0.130674i | \(0.958286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 215.178i | − 0.642322i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 320.659 | 0.951512 | 0.475756 | − | 0.879577i | \(-0.342175\pi\) | ||||
0.475756 | + | 0.879577i | \(0.342175\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 115.957 | 0.340049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 77.4087i | 0.225681i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 674.759i | − 1.94455i | −0.233842 | − | 0.972275i | \(-0.575130\pi\) | ||||
0.233842 | − | 0.972275i | \(-0.424870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −153.918 | −0.441026 | −0.220513 | − | 0.975384i | \(-0.570773\pi\) | ||||
−0.220513 | + | 0.975384i | \(0.570773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −623.228 | −1.76552 | −0.882759 | − | 0.469825i | \(-0.844317\pi\) | ||||
−0.882759 | + | 0.469825i | \(0.844317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 838.881i | − 2.36305i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 160.341i | − 0.446633i | −0.974746 | − | 0.223316i | \(-0.928312\pi\) | ||||
0.974746 | − | 0.223316i | \(-0.0716883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0478 | 0.0439666 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 284.585i | 0.775435i | 0.921778 | + | 0.387717i | \(0.126736\pi\) | ||||
−0.921778 | + | 0.387717i | \(0.873264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 783.757i | − 2.11255i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −301.420 | −0.808095 | −0.404048 | − | 0.914738i | \(-0.632397\pi\) | ||||
−0.404048 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 427.009 | 1.13265 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 248.547i | 0.655796i | 0.944713 | + | 0.327898i | \(0.106340\pi\) | ||||
−0.944713 | + | 0.327898i | \(0.893660\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 488.131i | − 1.27449i | −0.770660 | − | 0.637247i | \(-0.780073\pi\) | ||||
0.770660 | − | 0.637247i | \(-0.219927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −475.161 | −1.23418 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 415.867 | 1.06907 | 0.534534 | − | 0.845147i | \(-0.320487\pi\) | ||||
0.534534 | + | 0.845147i | \(0.320487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 446.199i | − 1.14117i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1106.92i | 2.80233i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 670.827 | 1.68974 | 0.844870 | − | 0.534972i | \(-0.179678\pi\) | ||||
0.844870 | + | 0.534972i | \(0.179678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 114.742 | 0.286139 | 0.143070 | − | 0.989713i | \(-0.454303\pi\) | ||||
0.143070 | + | 0.989713i | \(0.454303\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 246.916i | − 0.612696i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 43.4405i | − 0.106733i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −146.672 | −0.358611 | −0.179305 | − | 0.983793i | \(-0.557385\pi\) | ||||
−0.179305 | + | 0.983793i | \(0.557385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 793.541 | 1.92141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 100.266i | − 0.241605i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 536.872i | − 1.28132i | −0.767825 | − | 0.640659i | \(-0.778661\pi\) | ||||
0.767825 | − | 0.640659i | \(-0.221339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 367.413 | 0.872716 | 0.436358 | − | 0.899773i | \(-0.356268\pi\) | ||||
0.436358 | + | 0.899773i | \(0.356268\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −533.808 | −1.25602 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 79.7709i | 0.186817i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 735.353i | − 1.70616i | −0.521784 | − | 0.853078i | \(-0.674733\pi\) | ||||
0.521784 | − | 0.853078i | \(-0.325267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 765.161 | 1.76712 | 0.883558 | − | 0.468322i | \(-0.155141\pi\) | ||||
0.883558 | + | 0.468322i | \(0.155141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −129.575 | −0.296509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 46.3847i | − 0.105660i | −0.998604 | − | 0.0528299i | \(-0.983176\pi\) | ||||
0.998604 | − | 0.0528299i | \(-0.0168241\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 139.693i | − 0.315334i | −0.987492 | − | 0.157667i | \(-0.949603\pi\) | ||||
0.987492 | − | 0.157667i | \(-0.0503973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −132.498 | −0.297749 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −267.139 | −0.594963 | −0.297482 | − | 0.954728i | \(-0.596147\pi\) | ||||
−0.297482 | + | 0.954728i | \(0.596147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 58.5144i | − 0.129744i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1011.80i | 2.22374i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 237.830 | 0.520415 | 0.260208 | − | 0.965553i | \(-0.416209\pi\) | ||||
0.260208 | + | 0.965553i | \(0.416209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −298.650 | −0.647830 | −0.323915 | − | 0.946086i | \(-0.604999\pi\) | ||||
−0.323915 | + | 0.946086i | \(0.604999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 489.535i | − 1.05731i | −0.848837 | − | 0.528655i | \(-0.822696\pi\) | ||||
0.848837 | − | 0.528655i | \(-0.177304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 454.280i | − 0.972762i | −0.873747 | − | 0.486381i | \(-0.838317\pi\) | ||||
0.873747 | − | 0.486381i | \(-0.161683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 275.420 | 0.587248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −339.411 | −0.717571 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 155.016i | 0.326349i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 3.61359i | − 0.00754403i | −0.999993 | − | 0.00377201i | \(-0.998799\pi\) | ||||
0.999993 | − | 0.00377201i | \(-0.00120067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −92.5016 | −0.192311 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1024.33 | −2.11202 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 874.538i | − 1.79577i | −0.440234 | − | 0.897883i | \(-0.645104\pi\) | ||||
0.440234 | − | 0.897883i | \(-0.354896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 645.196i | 1.31404i | 0.753871 | + | 0.657022i | \(0.228184\pi\) | ||||
−0.753871 | + | 0.657022i | \(0.771816\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −529.994 | −1.07504 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1073.74 | 2.16043 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 564.842i | − 1.13195i | −0.824423 | − | 0.565974i | \(-0.808500\pi\) | ||||
0.824423 | − | 0.565974i | \(-0.191500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 483.048i | − 0.960334i | −0.877177 | − | 0.480167i | \(-0.840576\pi\) | ||||
0.877177 | − | 0.480167i | \(-0.159424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 721.994 | 1.42969 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 216.004 | 0.424369 | 0.212184 | − | 0.977230i | \(-0.431942\pi\) | ||||
0.212184 | + | 0.977230i | \(0.431942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.5406i | 0.0401969i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 314.587i | 0.610848i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −352.170 | −0.681180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 454.806 | 0.872949 | 0.436475 | − | 0.899717i | \(-0.356227\pi\) | ||||
0.436475 | + | 0.899717i | \(0.356227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 325.041i | − 0.621493i | −0.950493 | − | 0.310747i | \(-0.899421\pi\) | ||||
0.950493 | − | 0.310747i | \(-0.100579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 306.467i | 0.581531i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −92.8359 | −0.175493 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −124.600 | −0.233770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 720.238i | − 1.34624i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 276.447i | − 0.512889i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 962.574 | 1.77925 | 0.889625 | − | 0.456692i | \(-0.150966\pi\) | ||||
0.889625 | + | 0.456692i | \(0.150966\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 717.039 | 1.31567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 133.470i | − 0.244003i | −0.992530 | − | 0.122002i | \(-0.961069\pi\) | ||||
0.992530 | − | 0.122002i | \(-0.0389313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 153.908i | 0.279325i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1416.82 | −2.56206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −413.437 | −0.742258 | −0.371129 | − | 0.928581i | \(-0.621029\pi\) | ||||
−0.371129 | + | 0.928581i | \(0.621029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 722.737i | 1.29291i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 516.562i | − 0.917516i | −0.888561 | − | 0.458758i | \(-0.848294\pi\) | ||||
0.888561 | − | 0.458758i | \(-0.151706\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −287.830 | −0.509433 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 468.355 | 0.823120 | 0.411560 | − | 0.911383i | \(-0.364984\pi\) | ||||
0.411560 | + | 0.911383i | \(0.364984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 675.972i | − 1.18384i | −0.805997 | − | 0.591919i | \(-0.798370\pi\) | ||||
0.805997 | − | 0.591919i | \(-0.201630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 743.930i | 1.29379i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −354.823 | −0.614945 | −0.307473 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307473 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 128.337 | 0.220889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 559.844i | − 0.960281i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 220.479i | 0.375603i | 0.982207 | + | 0.187801i | \(0.0601361\pi\) | ||||
−0.982207 | + | 0.187801i | \(0.939864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 88.9969 | 0.151098 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −993.520 | −1.67541 | −0.837707 | − | 0.546121i | \(-0.816104\pi\) | ||||
−0.837707 | + | 0.546121i | \(0.816104\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1255.82i | − 2.11063i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 280.736i | − 0.468674i | −0.972155 | − | 0.234337i | \(-0.924708\pi\) | ||||
0.972155 | − | 0.234337i | \(-0.0752919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 561.830 | 0.934825 | 0.467412 | − | 0.884039i | \(-0.345186\pi\) | ||||
0.467412 | + | 0.884039i | \(0.345186\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 556.584 | 0.919973 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 84.0527i | 0.138472i | 0.997600 | + | 0.0692362i | \(0.0220562\pi\) | ||||
−0.997600 | + | 0.0692362i | \(0.977944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 749.906i | 1.22734i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −730.234 | −1.19125 | −0.595623 | − | 0.803264i | \(-0.703095\pi\) | ||||
−0.595623 | + | 0.803264i | \(0.703095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 549.786 | 0.891064 | 0.445532 | − | 0.895266i | \(-0.353015\pi\) | ||||
0.445532 | + | 0.895266i | \(0.353015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 73.1269i | − 0.118137i | −0.998254 | − | 0.0590685i | \(-0.981187\pi\) | ||||
0.998254 | − | 0.0590685i | \(-0.0188131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 169.593i | − 0.272220i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −480.823 | −0.769318 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 114.811 | 0.182529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 779.849i | − 1.23589i | −0.786220 | − | 0.617947i | \(-0.787965\pi\) | ||||
0.786220 | − | 0.617947i | \(-0.212035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 733.209i | 1.15466i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −588.663 | −0.924117 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −444.341 | −0.693200 | −0.346600 | − | 0.938013i | \(-0.612664\pi\) | ||||
−0.346600 | + | 0.938013i | \(0.612664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 446.199i | − 0.693933i | −0.937878 | − | 0.346966i | \(-0.887212\pi\) | ||||
0.937878 | − | 0.346966i | \(-0.112788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 861.386i | 1.33135i | 0.746240 | + | 0.665677i | \(0.231857\pi\) | ||||
−0.746240 | + | 0.665677i | \(0.768143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 566.833 | 0.873394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −876.302 | −1.34196 | −0.670982 | − | 0.741474i | \(-0.734127\pi\) | ||||
−0.670982 | + | 0.741474i | \(0.734127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 401.064i | 0.612311i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 565.760i | 0.858513i | 0.903183 | + | 0.429257i | \(0.141224\pi\) | ||||
−0.903183 | + | 0.429257i | \(0.858776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −632.580 | −0.957005 | −0.478503 | − | 0.878086i | \(-0.658820\pi\) | ||||
−0.478503 | + | 0.878086i | \(0.658820\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −364.686 | −0.548401 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 738.615i | 1.10737i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.9810i | 0.0849195i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1072.66 | −1.59385 | −0.796924 | − | 0.604080i | \(-0.793541\pi\) | ||||
−0.796924 | + | 0.604080i | \(0.793541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 478.798 | 0.707234 | 0.353617 | − | 0.935390i | \(-0.384952\pi\) | ||||
0.353617 | + | 0.935390i | \(0.384952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1311.11i | − 1.93094i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 318.418i | − 0.466206i | −0.972452 | − | 0.233103i | \(-0.925112\pi\) | ||||
0.972452 | − | 0.233103i | \(-0.0748879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.1672 | 0.0600981 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1192.12 | −1.73022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1121.30i | − 1.62272i | −0.584545 | − | 0.811362i | \(-0.698727\pi\) | ||||
0.584545 | − | 0.811362i | \(-0.301273\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1129.38i | 1.62500i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 154.650 | 0.221880 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −413.437 | −0.589782 | −0.294891 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294891 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 33.3406i | − 0.0474262i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 924.125i | 1.30711i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 682.915 | 0.963209 | 0.481604 | − | 0.876389i | \(-0.340054\pi\) | ||||
0.481604 | + | 0.876389i | \(0.340054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 427.101 | 0.599020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 722.737i | 1.01082i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 286.374i | 0.398295i | 0.979970 | + | 0.199148i | \(0.0638173\pi\) | ||||
−0.979970 | + | 0.199148i | \(0.936183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −402.659 | −0.558474 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 883.638 | 1.21881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 322.923i | − 0.444186i | −0.975026 | − | 0.222093i | \(-0.928711\pi\) | ||||
0.975026 | − | 0.222093i | \(-0.0712888\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 897.044i | − 1.22715i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 521.830 | 0.711910 | 0.355955 | − | 0.934503i | \(-0.384156\pi\) | ||||
0.355955 | + | 0.934503i | \(0.384156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 196.734 | 0.266939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 965.020i | 1.30585i | 0.757424 | + | 0.652923i | \(0.226458\pi\) | ||||
−0.757424 | + | 0.652923i | \(0.773542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1097.33i | − 1.47689i | −0.674312 | − | 0.738447i | \(-0.735560\pi\) | ||||
0.674312 | − | 0.738447i | \(-0.264440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1014.32 | 1.36151 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 921.878 | 1.23081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1381.05i | 1.83894i | 0.393154 | + | 0.919472i | \(0.371384\pi\) | ||||
−0.393154 | + | 0.919472i | \(0.628616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 577.494i | − 0.764892i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 516.252 | 0.681971 | 0.340986 | − | 0.940068i | \(-0.389239\pi\) | ||||
0.340986 | + | 0.940068i | \(0.389239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1216.18 | −1.59814 | −0.799069 | − | 0.601239i | \(-0.794674\pi\) | ||||
−0.799069 | + | 0.601239i | \(0.794674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 917.783i | 1.20286i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1207.00i | − 1.57367i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1004.33 | 1.30601 | 0.653007 | − | 0.757352i | \(-0.273507\pi\) | ||||
0.653007 | + | 0.757352i | \(0.273507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 382.580 | 0.494929 | 0.247464 | − | 0.968897i | \(-0.420403\pi\) | ||||
0.247464 | + | 0.968897i | \(0.420403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 510.960i | − 0.659304i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 44.9098i | − 0.0576506i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 766.978 | 0.982046 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 534.369 | 0.680725 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 477.268i | 0.606440i | 0.952921 | + | 0.303220i | \(0.0980617\pi\) | ||||
−0.952921 | + | 0.303220i | \(0.901938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 368.411i | − 0.465754i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 121.334 | 0.153007 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −514.607 | −0.645680 | −0.322840 | − | 0.946453i | \(-0.604638\pi\) | ||||
−0.322840 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 930.765i | − 1.16491i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6723i | 0.0182719i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1750.15 | −2.17410 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1463.74 | −1.80932 | −0.904662 | − | 0.426129i | \(-0.859877\pi\) | ||||
−0.904662 | + | 0.426129i | \(0.859877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1163.05i | − 1.43410i | −0.697023 | − | 0.717049i | \(-0.745492\pi\) | ||||
0.697023 | − | 0.717049i | \(-0.254508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 418.959i | − 0.514061i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −260.498 | −0.318848 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 392.553 | 0.478140 | 0.239070 | − | 0.971002i | \(-0.423158\pi\) | ||||
0.239070 | + | 0.971002i | \(0.423158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1248.84i | 1.51743i | 0.651424 | + | 0.758714i | \(0.274172\pi\) | ||||
−0.651424 | + | 0.758714i | \(0.725828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1369.15i | − 1.65557i | −0.561049 | − | 0.827783i | \(-0.689602\pi\) | ||||
0.561049 | − | 0.827783i | \(-0.310398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 73.7477 | 0.0889598 | 0.0444799 | − | 0.999010i | \(-0.485837\pi\) | ||||
0.0444799 | + | 0.999010i | \(0.485837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 730.634 | 0.877112 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1493.11i | − 1.78815i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1200.57i | − 1.43096i | −0.698635 | − | 0.715478i | \(-0.746209\pi\) | ||||
0.698635 | − | 0.715478i | \(-0.253791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.3251 | 0.0431927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 287.554 | 0.340300 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 712.406i | 0.841094i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 160.004i | − 0.188018i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 439.079 | 0.514747 | 0.257373 | − | 0.966312i | \(-0.417143\pi\) | ||||
0.257373 | + | 0.966312i | \(0.417143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 510.962 | 0.596222 | 0.298111 | − | 0.954531i | \(-0.403643\pi\) | ||||
0.298111 | + | 0.954531i | \(0.403643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 176.776i | 0.205793i | 0.994692 | + | 0.102897i | \(0.0328111\pi\) | ||||
−0.994692 | + | 0.102897i | \(0.967189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1028.28i | 1.19152i | 0.803163 | + | 0.595759i | \(0.203149\pi\) | ||||
−0.803163 | + | 0.595759i | \(0.796851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 685.325 | 0.792283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1012.04 | −1.16461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 418.923i | − 0.480968i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 339.186i | 0.387641i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 940.915 | 1.07288 | 0.536439 | − | 0.843939i | \(-0.319769\pi\) | ||||
0.536439 | + | 0.843939i | \(0.319769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1065.75 | 1.20970 | 0.604851 | − | 0.796339i | \(-0.293233\pi\) | ||||
0.604851 | + | 0.796339i | \(0.293233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1001.97i | − 1.13474i | −0.823464 | − | 0.567368i | \(-0.807962\pi\) | ||||
0.823464 | − | 0.567368i | \(-0.192038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 674.084i | − 0.759959i | −0.924995 | − | 0.379980i | \(-0.875931\pi\) | ||||
0.924995 | − | 0.379980i | \(-0.124069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −938.480 | −1.05566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −270.291 | −0.302678 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.7561i | 0.0354816i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 507.310i | − 0.564305i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1479.63 | 1.64221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2145.56 | 2.37078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1181.45i | 1.30259i | 0.758826 | + | 0.651293i | \(0.225773\pi\) | ||||
−0.758826 | + | 0.651293i | \(0.774227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1394.43i | 1.53066i | 0.643641 | + | 0.765328i | \(0.277423\pi\) | ||||
−0.643641 | + | 0.765328i | \(0.722577\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 91.6718 | 0.100407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −513.346 | −0.559811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 210.163i | 0.228686i | 0.993441 | + | 0.114343i | \(0.0364763\pi\) | ||||
−0.993441 | + | 0.114343i | \(0.963524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1633.19i | − 1.76944i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −191.420 | −0.206940 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 166.599 | 0.179332 | 0.0896659 | − | 0.995972i | \(-0.471420\pi\) | ||||
0.0896659 | + | 0.995972i | \(0.471420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 212.174i | − 0.227899i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 897.044i | − 0.959405i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 251.158 | 0.268045 | 0.134022 | − | 0.990978i | \(-0.457211\pi\) | ||||
0.134022 | + | 0.990978i | \(0.457211\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 814.564 | 0.865637 | 0.432818 | − | 0.901481i | \(-0.357519\pi\) | ||||
0.432818 | + | 0.901481i | \(0.357519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 215.525i | − 0.228552i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 592.384i | 0.625537i | 0.949829 | + | 0.312769i | \(0.101256\pi\) | ||||
−0.949829 | + | 0.312769i | \(0.898744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2430 | 0.0329220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 844.768 | 0.886430 | 0.443215 | − | 0.896415i | \(-0.353838\pi\) | ||||
0.443215 | + | 0.896415i | \(0.353838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 685.983i | 0.718307i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 52.6925i | 0.0549452i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 667.650 | 0.694745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1800.61 | −1.86592 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 180.173i | 0.186322i | 0.995651 | + | 0.0931611i | \(0.0296971\pi\) | ||||
−0.995651 | + | 0.0931611i | \(0.970303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 411.395i | 0.423682i | 0.977304 | + | 0.211841i | \(0.0679458\pi\) | ||||
−0.977304 | + | 0.211841i | \(0.932054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1445.56 | −1.48567 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1756.25 | −1.79759 | −0.898797 | − | 0.438365i | \(-0.855558\pi\) | ||||
−0.898797 | + | 0.438365i | \(0.855558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 121.142i | − 0.123740i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 803.055i | − 0.816943i | −0.912771 | − | 0.408472i | \(-0.866062\pi\) | ||||
0.912771 | − | 0.408472i | \(-0.133938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1032.49 | −1.04821 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1250.15 | −1.26405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 338.466i | 0.341540i | 0.985311 | + | 0.170770i | \(0.0546254\pi\) | ||||
−0.985311 | + | 0.170770i | \(0.945375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 821.897i | 0.826027i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −591.811 | −0.593592 | −0.296796 | − | 0.954941i | \(-0.595918\pi\) | ||||
−0.296796 | + | 0.954941i | \(0.595918\pi\) | |||||||
\(998\) | 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 | 1728.3.g.l.703.8 | 8 | ||
3.2 | odd | 2 | inner | 1728.3.g.l.703.2 | 8 | ||
4.3 | odd | 2 | inner | 1728.3.g.l.703.7 | 8 | ||
8.3 | odd | 2 | 108.3.d.d.55.4 | yes | 8 | ||
8.5 | even | 2 | 108.3.d.d.55.3 | ✓ | 8 | ||
12.11 | even | 2 | inner | 1728.3.g.l.703.1 | 8 | ||
24.5 | odd | 2 | 108.3.d.d.55.6 | yes | 8 | ||
24.11 | even | 2 | 108.3.d.d.55.5 | yes | 8 | ||
72.5 | odd | 6 | 324.3.f.o.55.1 | 8 | |||
72.11 | even | 6 | 324.3.f.o.271.1 | 8 | |||
72.13 | even | 6 | 324.3.f.o.55.4 | 8 | |||
72.29 | odd | 6 | 324.3.f.p.271.3 | 8 | |||
72.43 | odd | 6 | 324.3.f.o.271.4 | 8 | |||
72.59 | even | 6 | 324.3.f.p.55.4 | 8 | |||
72.61 | even | 6 | 324.3.f.p.271.2 | 8 | |||
72.67 | odd | 6 | 324.3.f.p.55.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.3 | ✓ | 8 | 8.5 | even | 2 | ||
108.3.d.d.55.4 | yes | 8 | 8.3 | odd | 2 | ||
108.3.d.d.55.5 | yes | 8 | 24.11 | even | 2 | ||
108.3.d.d.55.6 | yes | 8 | 24.5 | odd | 2 | ||
324.3.f.o.55.1 | 8 | 72.5 | odd | 6 | |||
324.3.f.o.55.4 | 8 | 72.13 | even | 6 | |||
324.3.f.o.271.1 | 8 | 72.11 | even | 6 | |||
324.3.f.o.271.4 | 8 | 72.43 | odd | 6 | |||
324.3.f.p.55.1 | 8 | 72.67 | odd | 6 | |||
324.3.f.p.55.4 | 8 | 72.59 | even | 6 | |||
324.3.f.p.271.2 | 8 | 72.61 | even | 6 | |||
324.3.f.p.271.3 | 8 | 72.29 | odd | 6 | |||
1728.3.g.l.703.1 | 8 | 12.11 | even | 2 | inner | ||
1728.3.g.l.703.2 | 8 | 3.2 | odd | 2 | inner | ||
1728.3.g.l.703.7 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.g.l.703.8 | 8 | 1.1 | even | 1 | trivial |