Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(1471,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, 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("1568.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.d (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.7 | ||
Root | \(1.92812i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1471 |
Dual form | 1568.3.d.n.1471.2 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.85623i | 1.28541i | 0.766113 | + | 0.642706i | \(0.222188\pi\) | ||||
−0.766113 | + | 0.642706i | \(0.777812\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.490168 | −0.0980336 | −0.0490168 | − | 0.998798i | \(-0.515609\pi\) | ||||
−0.0490168 | + | 0.998798i | \(0.515609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.87054 | −0.652282 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 15.5633i | − 1.41485i | −0.706789 | − | 0.707425i | \(-0.749857\pi\) | ||||
0.706789 | − | 0.707425i | \(-0.250143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50983 | −0.269987 | −0.134994 | − | 0.990846i | \(-0.543101\pi\) | ||||
−0.134994 | + | 0.990846i | \(0.543101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 1.89020i | − 0.126013i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.1463 | 1.42037 | 0.710187 | − | 0.704013i | \(-0.248611\pi\) | ||||
0.710187 | + | 0.704013i | \(0.248611\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56870i | 0.187826i | 0.995580 | + | 0.0939132i | \(0.0299376\pi\) | ||||
−0.995580 | + | 0.0939132i | \(0.970062\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.5741i | 0.851046i | 0.904948 | + | 0.425523i | \(0.139910\pi\) | ||||
−0.904948 | + | 0.425523i | \(0.860090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.7597 | −0.990389 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.0679i | 0.446961i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.9803 | −0.378632 | −0.189316 | − | 0.981916i | \(-0.560627\pi\) | ||||
−0.189316 | + | 0.981916i | \(0.560627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21.1767i | 0.683120i | 0.939860 | + | 0.341560i | \(0.110955\pi\) | ||||
−0.939860 | + | 0.341560i | \(0.889045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 60.0159 | 1.81866 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.4212 | 1.57895 | 0.789475 | − | 0.613783i | \(-0.210353\pi\) | ||||
0.789475 | + | 0.613783i | \(0.210353\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 13.5347i | − 0.347044i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54.1285 | −1.32021 | −0.660103 | − | 0.751175i | \(-0.729487\pi\) | ||||
−0.660103 | + | 0.751175i | \(0.729487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 35.6420i | 0.828884i | 0.910076 | + | 0.414442i | \(0.136023\pi\) | ||||
−0.910076 | + | 0.414442i | \(0.863977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.87755 | 0.0639455 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 64.2248i | 1.36648i | 0.730192 | + | 0.683242i | \(0.239431\pi\) | ||||
−0.730192 | + | 0.683242i | \(0.760569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 93.1140i | 1.82576i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 87.4015 | 1.64908 | 0.824542 | − | 0.565800i | \(-0.191433\pi\) | ||||
0.824542 | + | 0.565800i | \(0.191433\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.62865i | 0.138703i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.7617 | −0.241434 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 66.6954i | 1.13043i | 0.824944 | + | 0.565215i | \(0.191207\pi\) | ||||
−0.824944 | + | 0.565215i | \(0.808793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16.8615 | −0.276418 | −0.138209 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138209 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.72041 | 0.0264678 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 21.2420i | − 0.317045i | −0.987355 | − | 0.158523i | \(-0.949327\pi\) | ||||
0.987355 | − | 0.158523i | \(-0.0506731\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −75.4822 | −1.09394 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64.2140i | 0.904423i | 0.891911 | + | 0.452212i | \(0.149365\pi\) | ||||
−0.891911 | + | 0.452212i | \(0.850635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −99.4587 | −1.36245 | −0.681224 | − | 0.732075i | \(-0.738552\pi\) | ||||
−0.681224 | + | 0.732075i | \(0.738552\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 95.4793i | − 1.27306i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 139.441i | 1.76507i | 0.470243 | + | 0.882537i | \(0.344166\pi\) | ||||
−0.470243 | + | 0.882537i | \(0.655834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −99.3716 | −1.22681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.03134i | 0.0726668i | 0.999340 | + | 0.0363334i | \(0.0115678\pi\) | ||||
−0.999340 | + | 0.0363334i | \(0.988432\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8358 | −0.139244 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 42.3427i | − 0.486698i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 23.9821 | 0.269462 | 0.134731 | − | 0.990882i | \(-0.456983\pi\) | ||||
0.134731 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −81.6624 | −0.878091 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 1.74926i | − 0.0184133i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −171.509 | −1.76813 | −0.884064 | − | 0.467365i | \(-0.845203\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 91.3652i | 0.922881i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 146.427 | 1.44977 | 0.724887 | − | 0.688867i | \(-0.241892\pi\) | ||||
0.724887 | + | 0.688867i | \(0.241892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 118.849i | − 1.15388i | −0.816787 | − | 0.576939i | \(-0.804247\pi\) | ||||
0.816787 | − | 0.576939i | \(-0.195753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 142.434i | − 1.33116i | −0.746326 | − | 0.665581i | \(-0.768184\pi\) | ||||
0.746326 | − | 0.665581i | \(-0.231816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 170.835 | 1.56730 | 0.783649 | − | 0.621204i | \(-0.213356\pi\) | ||||
0.783649 | + | 0.621204i | \(0.213356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 225.286i | 2.02960i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 24.9436 | 0.220740 | 0.110370 | − | 0.993891i | \(-0.464796\pi\) | ||||
0.110370 | + | 0.993891i | \(0.464796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 9.59458i | − 0.0834311i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.6046 | 0.176108 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −121.218 | −1.00180 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 208.732i | − 1.69701i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.3906 | 0.195125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 68.8755i | − 0.542326i | −0.962533 | − | 0.271163i | \(-0.912592\pi\) | ||||
0.962533 | − | 0.271163i | \(-0.0874083\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −137.444 | −1.06546 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 101.326i | − 0.773481i | −0.922189 | − | 0.386741i | \(-0.873601\pi\) | ||||
0.922189 | − | 0.386741i | \(-0.126399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5.91532i | − 0.0438172i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 63.8820 | 0.466292 | 0.233146 | − | 0.972442i | \(-0.425098\pi\) | ||||
0.233146 | + | 0.972442i | \(0.425098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 199.256i | 1.43349i | 0.697333 | + | 0.716747i | \(0.254370\pi\) | ||||
−0.697333 | + | 0.716747i | \(0.745630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −247.666 | −1.75649 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 54.6247i | 0.381991i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.38221 | 0.0371187 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −271.585 | −1.82272 | −0.911359 | − | 0.411612i | \(-0.864966\pi\) | ||||
−0.911359 | + | 0.411612i | \(0.864966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 131.329i | 0.869729i | 0.900496 | + | 0.434864i | \(0.143204\pi\) | ||||
−0.900496 | + | 0.434864i | \(0.856796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −141.752 | −0.926484 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 10.3802i | − 0.0669687i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −133.685 | −0.851494 | −0.425747 | − | 0.904842i | \(-0.639989\pi\) | ||||
−0.425747 | + | 0.904842i | \(0.639989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 337.041i | 2.11975i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 29.8167i | 0.182925i | 0.995809 | + | 0.0914623i | \(0.0291541\pi\) | ||||
−0.995809 | + | 0.0914623i | \(0.970846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.4179 | −0.178290 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 259.708i | 1.55514i | 0.628796 | + | 0.777570i | \(0.283548\pi\) | ||||
−0.628796 | + | 0.777570i | \(0.716452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −156.681 | −0.927107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 20.9502i | − 0.122516i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 84.9760 | 0.491190 | 0.245595 | − | 0.969372i | \(-0.421017\pi\) | ||||
0.245595 | + | 0.969372i | \(0.421017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −257.193 | −1.45307 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.3648i | 0.108183i | 0.998536 | + | 0.0540916i | \(0.0172263\pi\) | ||||
−0.998536 | + | 0.0540916i | \(0.982774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 183.350 | 1.01298 | 0.506491 | − | 0.862245i | \(-0.330942\pi\) | ||||
0.506491 | + | 0.862245i | \(0.330942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 65.0219i | − 0.355311i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.6362 | −0.154790 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 375.798i | − 2.00961i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 93.1822i | 0.487865i | 0.969792 | + | 0.243932i | \(0.0784375\pi\) | ||||
−0.969792 | + | 0.243932i | \(0.921562\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 276.855 | 1.43448 | 0.717242 | − | 0.696824i | \(-0.245404\pi\) | ||||
0.717242 | + | 0.696824i | \(0.245404\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.63429i | 0.0340220i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −177.712 | −0.902089 | −0.451045 | − | 0.892501i | \(-0.648948\pi\) | ||||
−0.451045 | + | 0.892501i | \(0.648948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 227.421i | − 1.14282i | −0.820666 | − | 0.571408i | \(-0.806397\pi\) | ||||
0.820666 | − | 0.571408i | \(-0.193603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 81.9143 | 0.407534 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.5320 | 0.129425 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 114.910i | − 0.555122i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 55.5409 | 0.265746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 325.518i | 1.54274i | 0.636387 | + | 0.771370i | \(0.280428\pi\) | ||||
−0.636387 | + | 0.771370i | \(0.719572\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −247.624 | −1.16256 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 17.4706i | − 0.0812584i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 383.536i | − 1.75131i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −84.7496 | −0.383482 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 106.001i | − 0.475342i | −0.971346 | − | 0.237671i | \(-0.923616\pi\) | ||||
0.971346 | − | 0.237671i | \(-0.0763840\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 145.353 | 0.646013 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.765i | 1.24566i | 0.782357 | + | 0.622830i | \(0.214017\pi\) | ||||
−0.782357 | + | 0.622830i | \(0.785983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −144.716 | −0.631949 | −0.315975 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315975 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 36.9174 | 0.158444 | 0.0792219 | − | 0.996857i | \(-0.474756\pi\) | ||||
0.0792219 | + | 0.996857i | \(0.474756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 31.4809i | − 0.133961i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −537.716 | −2.26885 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 65.5138i | − 0.274116i | −0.990563 | − | 0.137058i | \(-0.956235\pi\) | ||||
0.990563 | − | 0.137058i | \(-0.0437647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 155.844 | 0.646656 | 0.323328 | − | 0.946287i | \(-0.395198\pi\) | ||||
0.323328 | + | 0.946287i | \(0.395198\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 274.589i | − 1.12999i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 12.5255i | − 0.0507107i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.2583 | −0.0934067 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 230.946i | 0.920105i | 0.887892 | + | 0.460052i | \(0.152169\pi\) | ||||
−0.887892 | + | 0.460052i | \(0.847831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 304.638 | 1.20410 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 45.6415i | − 0.178986i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −337.195 | −1.31204 | −0.656022 | − | 0.754742i | \(-0.727762\pi\) | ||||
−0.656022 | + | 0.754742i | \(0.727762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.4605 | 0.246975 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 395.803i | 1.50495i | 0.658619 | + | 0.752476i | \(0.271141\pi\) | ||||
−0.658619 | + | 0.752476i | \(0.728859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.8414 | −0.161666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 92.4806i | 0.346369i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.6881 | −0.117800 | −0.0588998 | − | 0.998264i | \(-0.518759\pi\) | ||||
−0.0588998 | + | 0.998264i | \(0.518759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 69.0163i | 0.254673i | 0.991860 | + | 0.127336i | \(0.0406428\pi\) | ||||
−0.991860 | + | 0.127336i | \(0.959357\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 385.344i | 1.40125i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 54.5783 | 0.197034 | 0.0985168 | − | 0.995135i | \(-0.468590\pi\) | ||||
0.0985168 | + | 0.995135i | \(0.468590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 124.319i | − 0.445587i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −140.453 | −0.499831 | −0.249916 | − | 0.968268i | \(-0.580403\pi\) | ||||
−0.249916 | + | 0.968268i | \(0.580403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 35.7205i | − 0.126221i | −0.998007 | − | 0.0631105i | \(-0.979898\pi\) | ||||
0.998007 | − | 0.0631105i | \(-0.0201021\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.74557 | 0.0236687 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 294.046 | 1.01746 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 661.377i | − 2.27277i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −73.9179 | −0.252279 | −0.126140 | − | 0.992012i | \(-0.540259\pi\) | ||||
−0.126140 | + | 0.992012i | \(0.540259\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 32.6919i | − 0.110820i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 187.817 | 0.632382 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 68.7017i | − 0.229771i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 564.658i | 1.86356i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.26498 | 0.0270983 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 507.360i | − 1.65264i | −0.563202 | − | 0.826319i | \(-0.690431\pi\) | ||||
0.563202 | − | 0.826319i | \(-0.309569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 458.311 | 1.48321 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 242.948i | − 0.781185i | −0.920564 | − | 0.390592i | \(-0.872270\pi\) | ||||
0.920564 | − | 0.390592i | \(-0.127730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 208.239 | 0.665301 | 0.332651 | − | 0.943050i | \(-0.392057\pi\) | ||||
0.332651 | + | 0.943050i | \(0.392057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6307 | −0.0335355 | −0.0167677 | − | 0.999859i | \(-0.505338\pi\) | ||||
−0.0167677 | + | 0.999859i | \(0.505338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 170.891i | 0.535708i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 549.260 | 1.71109 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 86.1711i | 0.266784i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 86.9025 | 0.267392 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 658.781i | 2.01462i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 122.813i | − 0.371035i | −0.982641 | − | 0.185517i | \(-0.940604\pi\) | ||||
0.982641 | − | 0.185517i | \(-0.0593961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −342.964 | −1.02992 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4122i | 0.0310811i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −518.410 | −1.53831 | −0.769154 | − | 0.639063i | \(-0.779322\pi\) | ||||
−0.769154 | + | 0.639063i | \(0.779322\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 96.1885i | 0.283742i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 329.581 | 0.966512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 36.9989 | 0.107243 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 231.720i | 0.667780i | 0.942612 | + | 0.333890i | \(0.108361\pi\) | ||||
−0.942612 | + | 0.333890i | \(0.891639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −170.720 | −0.489169 | −0.244584 | − | 0.969628i | \(-0.578652\pi\) | ||||
−0.244584 | + | 0.969628i | \(0.578652\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 42.3564i | − 0.120674i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 200.237 | 0.567244 | 0.283622 | − | 0.958936i | \(-0.408464\pi\) | ||||
0.283622 | + | 0.958936i | \(0.408464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 31.4757i | − 0.0886638i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 86.9601i | 0.242229i | 0.992639 | + | 0.121114i | \(0.0386468\pi\) | ||||
−0.992639 | + | 0.121114i | \(0.961353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 348.264 | 0.964721 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 467.443i | − 1.28772i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.7515 | 0.133566 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 672.949i | 1.83365i | 0.399290 | + | 0.916825i | \(0.369257\pi\) | ||||
−0.399290 | + | 0.916825i | \(0.630743\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 317.763 | 0.861147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 692.328 | 1.85611 | 0.928053 | − | 0.372448i | \(-0.121481\pi\) | ||||
0.928053 | + | 0.372448i | \(0.121481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 94.0560i | 0.250816i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.5391 | 0.102226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 193.386i | − 0.510253i | −0.966908 | − | 0.255126i | \(-0.917883\pi\) | ||||
0.966908 | − | 0.255126i | \(-0.0821171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 265.600 | 0.697112 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 518.606i | 1.35406i | 0.735954 | + | 0.677031i | \(0.236734\pi\) | ||||
−0.735954 | + | 0.677031i | \(0.763266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 209.238i | − 0.540666i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −531.999 | −1.36761 | −0.683803 | − | 0.729666i | \(-0.739675\pi\) | ||||
−0.683803 | + | 0.729666i | \(0.739675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 472.642i | 1.20880i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 390.737 | 0.994242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 68.3494i | − 0.173036i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 490.068 | 1.23443 | 0.617214 | − | 0.786795i | \(-0.288261\pi\) | ||||
0.617214 | + | 0.786795i | \(0.288261\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 712.938 | 1.77790 | 0.888951 | − | 0.458003i | \(-0.151435\pi\) | ||||
0.888951 | + | 0.458003i | \(0.151435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 74.3268i | − 0.184434i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 48.7088 | 0.120269 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 909.228i | − 2.23398i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 307.818 | 0.752612 | 0.376306 | − | 0.926495i | \(-0.377194\pi\) | ||||
0.376306 | + | 0.926495i | \(0.377194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 246.344i | 0.599377i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.95637i | − 0.00712378i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −768.377 | −1.84263 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 176.023i | − 0.420103i | −0.977690 | − | 0.210051i | \(-0.932637\pi\) | ||||
0.977690 | − | 0.210051i | \(-0.0673631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 263.167 | 0.625101 | 0.312550 | − | 0.949901i | \(-0.398817\pi\) | ||||
0.312550 | + | 0.949901i | \(0.398817\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 377.034i | − 0.891333i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −597.857 | −1.40672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −210.646 | −0.491016 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 256.629i | − 0.595426i | −0.954655 | − | 0.297713i | \(-0.903776\pi\) | ||||
0.954655 | − | 0.297713i | \(-0.0962238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 636.797 | 1.47066 | 0.735331 | − | 0.677708i | \(-0.237027\pi\) | ||||
0.735331 | + | 0.677708i | \(0.237027\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.7551i | 0.0477128i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −69.8540 | −0.159849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 64.4215i | 0.146746i | 0.997305 | + | 0.0733730i | \(0.0233763\pi\) | ||||
−0.997305 | + | 0.0733730i | \(0.976624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 449.411i | − 1.01447i | −0.861807 | − | 0.507236i | \(-0.830667\pi\) | ||||
0.861807 | − | 0.507236i | \(-0.169333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7553 | −0.0264163 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1047.30i | − 2.34294i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 362.900 | 0.808241 | 0.404120 | − | 0.914706i | \(-0.367578\pi\) | ||||
0.404120 | + | 0.914706i | \(0.367578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 842.420i | 1.86789i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −506.435 | −1.11796 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −61.1286 | −0.133761 | −0.0668803 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668803 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 291.397i | 0.634851i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 564.752 | 1.22506 | 0.612530 | − | 0.790448i | \(-0.290152\pi\) | ||||
0.612530 | + | 0.790448i | \(0.290152\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 581.095i | 1.25506i | 0.778590 | + | 0.627532i | \(0.215935\pi\) | ||||
−0.778590 | + | 0.627532i | \(0.784065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 40.0283 | 0.0860824 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 125.780i | − 0.269336i | −0.990891 | − | 0.134668i | \(-0.957003\pi\) | ||||
0.990891 | − | 0.134668i | \(-0.0429968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 515.519i | − 1.09452i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 554.709 | 1.17275 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 88.3601i | − 0.186021i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −513.094 | −1.07567 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 393.505i | − 0.821513i | −0.911745 | − | 0.410756i | \(-0.865265\pi\) | ||||
0.911745 | − | 0.410756i | \(-0.134735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −205.048 | −0.426296 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 84.0680 | 0.173336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 149.606i | 0.307198i | 0.988133 | + | 0.153599i | \(0.0490865\pi\) | ||||
−0.988133 | + | 0.153599i | \(0.950914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −114.980 | −0.235133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 79.1826i | − 0.161268i | −0.996744 | − | 0.0806340i | \(-0.974305\pi\) | ||||
0.996744 | − | 0.0806340i | \(-0.0256945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −265.135 | −0.537799 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 44.7843i | − 0.0904733i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 244.391i | − 0.489762i | −0.969553 | − | 0.244881i | \(-0.921251\pi\) | ||||
0.969553 | − | 0.244881i | \(-0.0787489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1001.50 | −1.99899 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 278.539i | − 0.553755i | −0.960905 | − | 0.276878i | \(-0.910700\pi\) | ||||
0.960905 | − | 0.276878i | \(-0.0892997\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −71.7739 | −0.142127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 604.199i | − 1.19171i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −444.338 | −0.872963 | −0.436481 | − | 0.899713i | \(-0.643775\pi\) | ||||
−0.436481 | + | 0.899713i | \(0.643775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43.0669 | −0.0839510 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 58.2562i | 0.113119i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 999.552 | 1.93337 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 327.687i | 0.631382i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −127.704 | −0.245113 | −0.122557 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122557 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 937.135i | − 1.79184i | −0.444211 | − | 0.895922i | \(-0.646516\pi\) | ||||
0.444211 | − | 0.895922i | \(-0.353484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 511.341i | 0.970286i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 145.856 | 0.275721 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 391.538i | − 0.737359i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 189.982 | 0.356439 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.8167i | 0.130499i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −74.6751 | −0.139060 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −540.845 | −0.999713 | −0.499857 | − | 0.866108i | \(-0.666614\pi\) | ||||
−0.499857 | + | 0.866108i | \(0.666614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 707.040i | 1.30210i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −83.7380 | −0.153648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 667.995i | − 1.22120i | −0.791940 | − | 0.610599i | \(-0.790929\pi\) | ||||
0.791940 | − | 0.610599i | \(-0.209071\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 98.9862 | 0.180303 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 39.1855i | − 0.0711171i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 110.428i | − 0.198969i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 746.470 | 1.34016 | 0.670081 | − | 0.742288i | \(-0.266259\pi\) | ||||
0.670081 | + | 0.742288i | \(0.266259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 125.097i | − 0.223788i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1449.16 | 2.58318 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 518.437i | − 0.920846i | −0.887700 | − | 0.460423i | \(-0.847698\pi\) | ||||
0.887700 | − | 0.460423i | \(-0.152302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2266 | −0.0216399 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −215.471 | −0.378683 | −0.189341 | − | 0.981911i | \(-0.560635\pi\) | ||||
−0.189341 | + | 0.981911i | \(0.560635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.73397i | 0.00829067i | 0.999991 | + | 0.00414534i | \(0.00131951\pi\) | ||||
−0.999991 | + | 0.00414534i | \(0.998680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −359.332 | −0.627107 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 484.649i | − 0.842867i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 72.0226 | 0.124823 | 0.0624113 | − | 0.998051i | \(-0.480121\pi\) | ||||
0.0624113 | + | 0.998051i | \(0.480121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1067.62i | 1.84390i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1360.26i | − 2.33321i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0997 | −0.0172645 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 272.118i | − 0.463575i | −0.972766 | − | 0.231787i | \(-0.925543\pi\) | ||||
0.972766 | − | 0.231787i | \(-0.0744573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −75.5734 | −0.128308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 685.297i | − 1.15956i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −842.019 | −1.41993 | −0.709966 | − | 0.704236i | \(-0.751290\pi\) | ||||
−0.709966 | + | 0.704236i | \(0.751290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 876.987 | 1.46899 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 478.633i | 0.799054i | 0.916721 | + | 0.399527i | \(0.130826\pi\) | ||||
−0.916721 | + | 0.399527i | \(0.869174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −206.471 | −0.343546 | −0.171773 | − | 0.985137i | \(-0.554950\pi\) | ||||
−0.171773 | + | 0.985137i | \(0.554950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 124.702i | 0.206803i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 59.4170 | 0.0982099 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 292.279i | − 0.481514i | −0.970585 | − | 0.240757i | \(-0.922604\pi\) | ||||
0.970585 | − | 0.240757i | \(-0.0773956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 225.418i | − 0.368933i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 827.863 | 1.35051 | 0.675255 | − | 0.737584i | \(-0.264033\pi\) | ||||
0.675255 | + | 0.737584i | \(0.264033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 102.314i | 0.166364i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −667.348 | −1.08160 | −0.540801 | − | 0.841151i | \(-0.681879\pi\) | ||||
−0.540801 | + | 0.841151i | \(0.681879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 750.661i | − 1.21270i | −0.795198 | − | 0.606350i | \(-0.792633\pi\) | ||||
0.795198 | − | 0.606350i | \(-0.207367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −236.219 | −0.380384 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 607.038 | 0.971261 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 214.179i | 0.341593i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1410.66 | 2.24270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1076.70i | − 1.70633i | −0.521637 | − | 0.853167i | \(-0.674679\pi\) | ||||
0.521637 | − | 0.853167i | \(-0.325321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1255.27 | −1.98305 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.7605i | 0.0531662i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 376.971i | − 0.589939i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −298.632 | −0.465885 | −0.232942 | − | 0.972491i | \(-0.574835\pi\) | ||||
−0.232942 | + | 0.972491i | \(0.574835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 504.242i | 0.784202i | 0.919922 | + | 0.392101i | \(0.128252\pi\) | ||||
−0.919922 | + | 0.392101i | \(0.871748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 67.3706 | 0.104451 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 76.2691i | − 0.117881i | −0.998261 | − | 0.0589406i | \(-0.981228\pi\) | ||||
0.998261 | − | 0.0589406i | \(-0.0187723\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1038.00 | 1.59939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −199.148 | −0.304974 | −0.152487 | − | 0.988305i | \(-0.548728\pi\) | ||||
−0.152487 | + | 0.988305i | \(0.548728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.6668i | 0.0758272i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 583.876 | 0.888700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 488.851i | 0.741807i | 0.928671 | + | 0.370904i | \(0.120952\pi\) | ||||
−0.928671 | + | 0.370904i | \(0.879048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 477.111 | 0.721802 | 0.360901 | − | 0.932604i | \(-0.382469\pi\) | ||||
0.360901 | + | 0.932604i | \(0.382469\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 326.814i | − 0.492933i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 214.930i | − 0.322234i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 408.765 | 0.611010 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 262.422i | 0.391090i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −437.908 | −0.650680 | −0.325340 | − | 0.945597i | \(-0.605479\pi\) | ||||
−0.325340 | + | 0.945597i | \(0.605479\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 298.799i | − 0.442665i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −509.653 | −0.752810 | −0.376405 | − | 0.926455i | \(-0.622840\pi\) | ||||
−0.376405 | + | 0.926455i | \(0.622840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1090.41 | −1.60119 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 794.509i | 1.16326i | 0.813452 | + | 0.581632i | \(0.197586\pi\) | ||||
−0.813452 | + | 0.581632i | \(0.802414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.3129 | −0.0457123 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 558.060i | − 0.812315i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −306.765 | −0.445232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 19.0808i | − 0.0276133i | −0.999905 | − | 0.0138066i | \(-0.995605\pi\) | ||||
0.999905 | − | 0.0138066i | \(-0.00439493\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 97.6688i | − 0.140531i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1307.00 | −1.87519 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 142.362i | 0.203665i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 333.075 | 0.475143 | 0.237572 | − | 0.971370i | \(-0.423649\pi\) | ||||
0.237572 | + | 0.971370i | \(0.423649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 208.488i | 0.296568i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 121.398 | 0.172195 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −692.721 | −0.977039 | −0.488519 | − | 0.872553i | \(-0.662463\pi\) | ||||
−0.488519 | + | 0.872553i | \(0.662463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 818.593i | − 1.15133i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −414.515 | −0.581367 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 26.7753i | − 0.0374479i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 252.636 | 0.352352 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 187.332i | − 0.260545i | −0.991478 | − | 0.130272i | \(-0.958415\pi\) | ||||
0.991478 | − | 0.130272i | \(-0.0415852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 600.971i | 0.831219i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 271.870 | 0.374993 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 669.583i | − 0.921022i | −0.887654 | − | 0.460511i | \(-0.847666\pi\) | ||||
0.887654 | − | 0.460511i | \(-0.152334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 164.534 | 0.225698 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 860.624i | 1.17732i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 585.685 | 0.799024 | 0.399512 | − | 0.916728i | \(-0.369180\pi\) | ||||
0.399512 | + | 0.916728i | \(0.369180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −330.597 | −0.448571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 318.797i | − 0.431389i | −0.976461 | − | 0.215695i | \(-0.930798\pi\) | ||||
0.976461 | − | 0.215695i | \(-0.0692016\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.3014 | 0.0651841 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1440.64i | 1.93895i | 0.245185 | + | 0.969476i | \(0.421151\pi\) | ||||
−0.245185 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 133.122 | 0.178688 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 35.4072i | − 0.0473992i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 238.758i | − 0.317920i | −0.987285 | − | 0.158960i | \(-0.949186\pi\) | ||||
0.987285 | − | 0.158960i | \(-0.0508141\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −890.583 | −1.18271 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 64.3733i | − 0.0852626i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −975.208 | −1.28825 | −0.644127 | − | 0.764919i | \(-0.722779\pi\) | ||||
−0.644127 | + | 0.764919i | \(0.722779\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1174.75i | 1.54777i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 135.752 | 0.178386 | 0.0891929 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891929 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 69.4823 | 0.0908265 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 234.090i | − 0.305202i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1375.28 | 1.78841 | 0.894203 | − | 0.447661i | \(-0.147743\pi\) | ||||
0.894203 | + | 0.447661i | \(0.147743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1300.30i | − 1.68652i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 844.987 | 1.09313 | 0.546564 | − | 0.837418i | \(-0.315936\pi\) | ||||
0.546564 | + | 0.837418i | \(0.315936\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 524.330i | − 0.676555i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 193.168i | − 0.247970i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 999.385 | 1.27962 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 132.510i | − 0.169234i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.5279 | 0.0834750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 706.124i | 0.897235i | 0.893724 | + | 0.448617i | \(0.148083\pi\) | ||||
−0.893724 | + | 0.448617i | \(0.851917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1526.31 | −1.93448 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.1811 | 0.0746294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 165.206i | − 0.207807i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1103.57 | −1.38465 | −0.692325 | − | 0.721586i | \(-0.743414\pi\) | ||||
−0.692325 | + | 0.721586i | \(0.743414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1550.79i | 1.94092i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −140.788 | −0.175765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1547.91i | 1.92766i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 122.197i | − 0.151421i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −890.340 | −1.10054 | −0.550272 | − | 0.834986i | \(-0.685476\pi\) | ||||
−0.550272 | + | 0.834986i | \(0.685476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 326.603i | 0.402717i | 0.979518 | + | 0.201358i | \(0.0645356\pi\) | ||||
−0.979518 | + | 0.201358i | \(0.935464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −266.143 | −0.327359 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 14.6152i | − 0.0179328i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −127.196 | −0.155686 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 177.210 | 0.215847 | 0.107924 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107924 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1474.36i | − 1.79144i | −0.444614 | − | 0.895722i | \(-0.646659\pi\) | ||||
0.444614 | − | 0.895722i | \(-0.353341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1485.98 | −1.80118 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 339.749i | − 0.410821i | −0.978676 | − | 0.205411i | \(-0.934147\pi\) | ||||
0.978676 | − | 0.205411i | \(-0.0658530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1063.05 | −1.28233 | −0.641166 | − | 0.767402i | \(-0.721549\pi\) | ||||
−0.641166 | + | 0.767402i | \(0.721549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 210.467i | 0.253269i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 127.301i | − 0.152456i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −255.559 | −0.305328 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 670.497i | 0.799162i | 0.916698 | + | 0.399581i | \(0.130844\pi\) | ||||
−0.916698 | + | 0.399581i | \(0.869156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −720.432 | −0.856638 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 541.618i | − 0.642489i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 76.8000 | 0.0908876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 137.747 | 0.162246 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1143.54i | 1.34376i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 165.395 | 0.193898 | 0.0969489 | − | 0.995289i | \(-0.469092\pi\) | ||||
0.0969489 | + | 0.995289i | \(0.469092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.2691i | 0.0120107i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1088.22 | 1.26981 | 0.634904 | − | 0.772591i | \(-0.281040\pi\) | ||||
0.634904 | + | 0.772591i | \(0.281040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 335.213i | 0.390236i | 0.980780 | + | 0.195118i | \(0.0625091\pi\) | ||||
−0.980780 | + | 0.195118i | \(0.937491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 527.699i | 0.611471i | 0.952117 | + | 0.305735i | \(0.0989023\pi\) | ||||
−0.952117 | + | 0.305735i | \(0.901098\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.6525 | −0.0481532 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1133.91i | 1.30785i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2170.16 | 2.49731 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 74.5560i | 0.0855982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1006.85 | 1.15332 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1257.89 | 1.43431 | 0.717154 | − | 0.696915i | \(-0.245444\pi\) | ||||
0.717154 | + | 0.696915i | \(0.245444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 285.045i | − 0.324283i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1111.12 | −1.26120 | −0.630599 | − | 0.776109i | \(-0.717191\pi\) | ||||
−0.630599 | + | 0.776109i | \(0.717191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 358.772i | 0.406310i | 0.979147 | + | 0.203155i | \(0.0651195\pi\) | ||||
−0.979147 | + | 0.203155i | \(0.934880\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 126.068 | 0.142449 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1570.56i | − 1.77064i | −0.464978 | − | 0.885322i | \(-0.653938\pi\) | ||||
0.464978 | − | 0.885322i | \(-0.346062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1546.55i | 1.73575i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −229.199 | −0.256662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 9.49200i | − 0.0106056i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 264.930 | 0.295351 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 232.528i | − 0.258651i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2110.43 | 2.34232 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −89.8722 | −0.0993063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 901.249i | − 0.993659i | −0.867848 | − | 0.496829i | \(-0.834497\pi\) | ||||
0.867848 | − | 0.496829i | \(-0.165503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −859.607 | −0.945662 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 901.747i | − 0.989843i | −0.868938 | − | 0.494922i | \(-0.835197\pi\) | ||||
0.868938 | − | 0.494922i | \(-0.164803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 93.8678 | 0.102813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.8717i | 0.0348324i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1165.98i | 1.26875i | 0.773025 | + | 0.634375i | \(0.218743\pi\) | ||||
−0.773025 | + | 0.634375i | \(0.781257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1956.50 | 2.12432 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 225.380i | − 0.244183i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1446.49 | −1.56378 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 697.710i | 0.752654i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1400.58 | 1.50762 | 0.753811 | − | 0.657091i | \(-0.228213\pi\) | ||||
0.753811 | + | 0.657091i | \(0.228213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 936.866 | 1.00414 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 184.204i | 0.197010i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1252.37 | −1.33657 | −0.668285 | − | 0.743905i | \(-0.732972\pi\) | ||||
−0.668285 | + | 0.743905i | \(0.732972\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 803.020i | 0.855186i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 335.582 | 0.356622 | 0.178311 | − | 0.983974i | \(-0.442937\pi\) | ||||
0.178311 | + | 0.983974i | \(0.442937\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1059.51i | − 1.12356i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1588.48i | 1.67738i | 0.544610 | + | 0.838689i | \(0.316678\pi\) | ||||
−0.544610 | + | 0.838689i | \(0.683322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 349.083 | 0.367843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 40.9946i | − 0.0431069i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −99.1693 | −0.104060 | −0.0520301 | − | 0.998646i | \(-0.516569\pi\) | ||||
−0.0520301 | + | 0.998646i | \(0.516569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 45.6749i | − 0.0478271i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −658.995 | −0.688605 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 512.546 | 0.533347 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 836.166i | 0.868292i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −135.706 | −0.140628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1322.78i | 1.36792i | 0.729518 | + | 0.683962i | \(0.239744\pi\) | ||||
−0.729518 | + | 0.683962i | \(0.760256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −332.296 | −0.342927 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1571.76i | 1.61870i | 0.587327 | + | 0.809350i | \(0.300180\pi\) | ||||
−0.587327 | + | 0.809350i | \(0.699820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 335.116i | 0.343709i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.9043 | −0.0162787 | −0.00813936 | − | 0.999967i | \(-0.502591\pi\) | ||||
−0.00813936 | + | 0.999967i | \(0.502591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 373.242i | − 0.381248i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1002.90 | −1.02232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 202.919i | 0.206428i | 0.994659 | + | 0.103214i | \(0.0329127\pi\) | ||||
−0.994659 | + | 0.103214i | \(0.967087\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 87.1085 | 0.0884350 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −697.659 | −0.705418 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 760.920i | − 0.767830i | −0.923368 | − | 0.383915i | \(-0.874576\pi\) | ||||
0.923368 | − | 0.383915i | \(-0.125424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 473.594 | 0.476932 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 111.474i | 0.112034i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −860.114 | −0.862702 | −0.431351 | − | 0.902184i | \(-0.641963\pi\) | ||||
−0.431351 | + | 0.902184i | \(0.641963\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 705.023i | 0.705728i |
(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 | 1568.3.d.n.1471.7 | 8 | ||
4.3 | odd | 2 | inner | 1568.3.d.n.1471.2 | 8 | ||
7.6 | odd | 2 | 224.3.d.b.127.2 | ✓ | 8 | ||
21.20 | even | 2 | 2016.3.m.c.127.3 | 8 | |||
28.27 | even | 2 | 224.3.d.b.127.7 | yes | 8 | ||
56.13 | odd | 2 | 448.3.d.e.127.7 | 8 | |||
56.27 | even | 2 | 448.3.d.e.127.2 | 8 | |||
84.83 | odd | 2 | 2016.3.m.c.127.4 | 8 | |||
112.13 | odd | 4 | 1792.3.g.d.127.7 | 8 | |||
112.27 | even | 4 | 1792.3.g.d.127.8 | 8 | |||
112.69 | odd | 4 | 1792.3.g.f.127.2 | 8 | |||
112.83 | even | 4 | 1792.3.g.f.127.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.d.b.127.2 | ✓ | 8 | 7.6 | odd | 2 | ||
224.3.d.b.127.7 | yes | 8 | 28.27 | even | 2 | ||
448.3.d.e.127.2 | 8 | 56.27 | even | 2 | |||
448.3.d.e.127.7 | 8 | 56.13 | odd | 2 | |||
1568.3.d.n.1471.2 | 8 | 4.3 | odd | 2 | inner | ||
1568.3.d.n.1471.7 | 8 | 1.1 | even | 1 | trivial | ||
1792.3.g.d.127.7 | 8 | 112.13 | odd | 4 | |||
1792.3.g.d.127.8 | 8 | 112.27 | even | 4 | |||
1792.3.g.f.127.1 | 8 | 112.83 | even | 4 | |||
1792.3.g.f.127.2 | 8 | 112.69 | odd | 4 | |||
2016.3.m.c.127.3 | 8 | 21.20 | even | 2 | |||
2016.3.m.c.127.4 | 8 | 84.83 | odd | 2 |