Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2017,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.2017");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.c (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1344) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2017.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2017 |
Dual form | 4032.2.c.o.2017.2 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0.732051i | 0.327383i | 0.986512 | + | 0.163692i | \(0.0523402\pi\) | ||||
−0.986512 | + | 0.163692i | \(0.947660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.73205i | − 0.823744i | −0.911242 | − | 0.411872i | \(-0.864875\pi\) | ||||
0.911242 | − | 0.411872i | \(-0.135125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.19615 | −1.01772 | −0.508858 | − | 0.860850i | \(-0.669932\pi\) | ||||
−0.508858 | + | 0.860850i | \(0.669932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.46410i | − 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.73205 | −0.986701 | −0.493350 | − | 0.869831i | \(-0.664228\pi\) | ||||
−0.493350 | + | 0.869831i | \(0.664228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.46410i | − 1.38605i | −0.720914 | − | 0.693024i | \(-0.756278\pi\) | ||||
0.720914 | − | 0.693024i | \(-0.243722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.732051i | 0.123739i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.66025 | −1.50868 | −0.754339 | − | 0.656485i | \(-0.772043\pi\) | ||||
−0.754339 | + | 0.656485i | \(0.772043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.92820i | − 1.36154i | −0.732498 | − | 0.680769i | \(-0.761646\pi\) | ||||
0.732498 | − | 0.680769i | \(-0.238354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.46410i | − 0.475831i | −0.971286 | − | 0.237915i | \(-0.923536\pi\) | ||||
0.971286 | − | 0.237915i | \(-0.0764641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000i | 1.04151i | 0.853706 | + | 0.520756i | \(0.174350\pi\) | ||||
−0.853706 | + | 0.520756i | \(0.825650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.39230i | − 1.07452i | −0.843415 | − | 0.537262i | \(-0.819459\pi\) | ||||
0.843415 | − | 0.537262i | \(-0.180541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.92820 | −0.363199 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.39230i | − 0.780944i | −0.920615 | − | 0.390472i | \(-0.872312\pi\) | ||||
0.920615 | − | 0.390472i | \(-0.127688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.66025 | 0.434392 | 0.217196 | − | 0.976128i | \(-0.430309\pi\) | ||||
0.217196 | + | 0.976128i | \(0.430309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.53590 | −0.999051 | −0.499526 | − | 0.866299i | \(-0.666492\pi\) | ||||
−0.499526 | + | 0.866299i | \(0.666492\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.73205i | − 0.311346i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3923 | 1.39424 | 0.697122 | − | 0.716953i | \(-0.254464\pi\) | ||||
0.697122 | + | 0.716953i | \(0.254464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.53590i | − 0.278351i | −0.990268 | − | 0.139176i | \(-0.955555\pi\) | ||||
0.990268 | − | 0.139176i | \(-0.0444452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.07180i | − 0.333183i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1962 | −1.29279 | −0.646395 | − | 0.763003i | \(-0.723724\pi\) | ||||
−0.646395 | + | 0.763003i | \(0.723724\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000i | 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.53590 | 0.260178 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.39230 | −0.242902 | −0.121451 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121451 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 11.2679i | − 1.12120i | −0.828086 | − | 0.560601i | \(-0.810570\pi\) | ||||
0.828086 | − | 0.560601i | \(-0.189430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.19615i | − 0.792352i | −0.918175 | − | 0.396176i | \(-0.870337\pi\) | ||||
0.918175 | − | 0.396176i | \(-0.129663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9282i | 1.04673i | 0.852108 | + | 0.523366i | \(0.175324\pi\) | ||||
−0.852108 | + | 0.523366i | \(0.824676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.39230 | −0.601337 | −0.300669 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.46410i | − 0.323029i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.19615 | −0.384661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.53590 | 0.321445 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3205 | −1.71442 | −0.857209 | − | 0.514969i | \(-0.827804\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827804\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.39230i | − 0.383757i | −0.981419 | − | 0.191879i | \(-0.938542\pi\) | ||||
0.981419 | − | 0.191879i | \(-0.0614580\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.46410i | − 0.300376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410 | 0.295958 | 0.147979 | − | 0.988990i | \(-0.452723\pi\) | ||||
0.147979 | + | 0.988990i | \(0.452723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 10.9282i | − 0.926918i | −0.886118 | − | 0.463459i | \(-0.846608\pi\) | ||||
0.886118 | − | 0.463459i | \(-0.153392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9282 | 0.913862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.46410 | 0.453769 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.39230i | 0.195985i | 0.995187 | + | 0.0979926i | \(0.0312422\pi\) | ||||
−0.995187 | + | 0.0979926i | \(0.968758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.07180 | 0.0872216 | 0.0436108 | − | 0.999049i | \(-0.486114\pi\) | ||||
0.0436108 | + | 0.999049i | \(0.486114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.46410i | − 0.117599i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.39230i | 0.669779i | 0.942257 | + | 0.334889i | \(0.108699\pi\) | ||||
−0.942257 | + | 0.334889i | \(0.891301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.73205 | −0.372938 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.53590i | − 0.355279i | −0.984096 | − | 0.177639i | \(-0.943154\pi\) | ||||
0.984096 | − | 0.177639i | \(-0.0568461\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.3923 | −1.26847 | −0.634237 | − | 0.773138i | \(-0.718686\pi\) | ||||
−0.634237 | + | 0.773138i | \(0.718686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0526i | 1.22045i | 0.792227 | + | 0.610227i | \(0.208922\pi\) | ||||
−0.792227 | + | 0.610227i | \(0.791078\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.46410 | 0.337454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 20.5885i | − 1.53885i | −0.638735 | − | 0.769427i | \(-0.720542\pi\) | ||||
0.638735 | − | 0.769427i | \(-0.279458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 18.9282i | − 1.40692i | −0.710734 | − | 0.703461i | \(-0.751637\pi\) | ||||
0.710734 | − | 0.703461i | \(-0.248363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.46410 | −0.107643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.4641i | 0.838338i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.7321 | 1.78955 | 0.894774 | − | 0.446519i | \(-0.147336\pi\) | ||||
0.894774 | + | 0.446519i | \(0.147336\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.3923 | −1.75580 | −0.877898 | − | 0.478847i | \(-0.841055\pi\) | ||||
−0.877898 | + | 0.478847i | \(0.841055\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 26.7846i | − 1.90832i | −0.299290 | − | 0.954162i | \(-0.596750\pi\) | ||||
0.299290 | − | 0.954162i | \(-0.403250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.46410i | − 0.523877i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7.07180i | − 0.493916i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.46410 | −0.654646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 0.143594i | − 0.00988539i | −0.999988 | − | 0.00494269i | \(-0.998427\pi\) | ||||
0.999988 | − | 0.00494269i | \(-0.00157331\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.53590 | 0.445745 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 16.7846i | − 1.12906i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.07180 | −0.339633 | −0.169816 | − | 0.985476i | \(-0.554317\pi\) | ||||
−0.169816 | + | 0.985476i | \(0.554317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.3205i | − 0.751369i | −0.926748 | − | 0.375684i | \(-0.877408\pi\) | ||||
0.926748 | − | 0.375684i | \(-0.122592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.9282i | − 0.722156i | −0.932536 | − | 0.361078i | \(-0.882409\pi\) | ||||
0.932536 | − | 0.361078i | \(-0.117591\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9282 | −0.846955 | −0.423477 | − | 0.905907i | \(-0.639191\pi\) | ||||
−0.423477 | + | 0.905907i | \(0.639191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.92820i | 0.191015i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.6603 | 1.78919 | 0.894597 | − | 0.446875i | \(-0.147463\pi\) | ||||
0.894597 | + | 0.446875i | \(0.147463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.46410 | −0.480805 | −0.240403 | − | 0.970673i | \(-0.577279\pi\) | ||||
−0.240403 | + | 0.970673i | \(0.577279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.732051i | 0.0467690i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564 | 0.881662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 23.3205i | − 1.47198i | −0.676994 | − | 0.735989i | \(-0.736718\pi\) | ||||
0.676994 | − | 0.735989i | \(-0.263282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9282i | 0.812789i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.80385 | −0.237277 | −0.118639 | − | 0.992937i | \(-0.537853\pi\) | ||||
−0.118639 | + | 0.992937i | \(0.537853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000i | 0.124274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.19615 | −0.382071 | −0.191036 | − | 0.981583i | \(-0.561185\pi\) | ||||
−0.191036 | + | 0.981583i | \(0.561185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.53590 | 0.155779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.2679i | 1.17479i | 0.809301 | + | 0.587394i | \(0.199846\pi\) | ||||
−0.809301 | + | 0.587394i | \(0.800154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0718 | −0.915546 | −0.457773 | − | 0.889069i | \(-0.651353\pi\) | ||||
−0.457773 | + | 0.889069i | \(0.651353\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 12.1962i | − 0.735456i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.9282i | − 1.01712i | −0.861027 | − | 0.508559i | \(-0.830179\pi\) | ||||
0.861027 | − | 0.508559i | \(-0.169821\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9282 | 1.72571 | 0.862856 | − | 0.505450i | \(-0.168673\pi\) | ||||
0.862856 | + | 0.505450i | \(0.168673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.39230i | − 0.142208i | −0.997469 | − | 0.0711039i | \(-0.977348\pi\) | ||||
0.997469 | − | 0.0711039i | \(-0.0226522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.66025 | −0.570227 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.607695 | 0.0357468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.8038i | − 0.806429i | −0.915105 | − | 0.403215i | \(-0.867893\pi\) | ||||
0.915105 | − | 0.403215i | \(-0.132107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.85641 | −0.340973 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 18.9282i | − 1.09465i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.92820i | − 0.514613i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.14359 | 0.351781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.3205i | 1.44512i | 0.691309 | + | 0.722559i | \(0.257034\pi\) | ||||
−0.691309 | + | 0.722559i | \(0.742966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.7128 | 1.79827 | 0.899134 | − | 0.437673i | \(-0.144197\pi\) | ||||
0.899134 | + | 0.437673i | \(0.144197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.928203 | −0.0524651 | −0.0262326 | − | 0.999656i | \(-0.508351\pi\) | ||||
−0.0262326 | + | 0.999656i | \(0.508351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3923i | 1.03301i | 0.856283 | + | 0.516507i | \(0.172768\pi\) | ||||
−0.856283 | + | 0.516507i | \(0.827232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.3923 | −1.14175 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5359i | 0.808799i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8564i | 0.990495i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9282i | 0.710598i | 0.934753 | + | 0.355299i | \(0.115621\pi\) | ||||
−0.934753 | + | 0.355299i | \(0.884379\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.67949 | 0.255668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.7128 | −1.83645 | −0.918227 | − | 0.396055i | \(-0.870379\pi\) | ||||
−0.918227 | + | 0.396055i | \(0.870379\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.46410i | 0.295898i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2679i | 0.712261i | 0.934436 | + | 0.356130i | \(0.115904\pi\) | ||||
−0.934436 | + | 0.356130i | \(0.884096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 15.3205i | − 0.820088i | −0.912066 | − | 0.410044i | \(-0.865513\pi\) | ||||
0.912066 | − | 0.410044i | \(-0.134487\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3397 | −0.976126 | −0.488063 | − | 0.872808i | \(-0.662296\pi\) | ||||
−0.488063 | + | 0.872808i | \(0.662296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67949i | 0.142213i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.8038 | −1.15076 | −0.575382 | − | 0.817885i | \(-0.695146\pi\) | ||||
−0.575382 | + | 0.817885i | \(0.695146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.24871i | − 0.327072i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8564 | −0.723299 | −0.361649 | − | 0.932314i | \(-0.617786\pi\) | ||||
−0.361649 | + | 0.932314i | \(0.617786\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.46410i | − 0.179847i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.0000i | − 0.621336i | −0.950518 | − | 0.310668i | \(-0.899447\pi\) | ||||
0.950518 | − | 0.310668i | \(-0.100553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.8564 | 1.53768 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.0718i | − 0.774186i | −0.922041 | − | 0.387093i | \(-0.873479\pi\) | ||||
0.922041 | − | 0.387093i | \(-0.126521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3923 | −1.45078 | −0.725390 | − | 0.688339i | \(-0.758340\pi\) | ||||
−0.725390 | + | 0.688339i | \(0.758340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 27.4641i | − 1.39249i | −0.717807 | − | 0.696243i | \(-0.754854\pi\) | ||||
0.717807 | − | 0.696243i | \(-0.245146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8564 | 1.00418 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.07180i | 0.456452i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.3205i | − 0.768914i | −0.923143 | − | 0.384457i | \(-0.874389\pi\) | ||||
0.923143 | − | 0.384457i | \(-0.125611\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3205 | 0.665194 | 0.332597 | − | 0.943069i | \(-0.392075\pi\) | ||||
0.332597 | + | 0.943069i | \(0.392075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.00000i | − 0.398508i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.46410 | 0.270845 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −40.2487 | −1.99017 | −0.995085 | − | 0.0990210i | \(-0.968429\pi\) | ||||
−0.995085 | + | 0.0990210i | \(0.968429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000i | 0.393654i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.85641 | 0.0911274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 22.9282i | − 1.12012i | −0.828453 | − | 0.560058i | \(-0.810779\pi\) | ||||
0.828453 | − | 0.560058i | \(-0.189221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.7846i | 1.89025i | 0.326714 | + | 0.945123i | \(0.394058\pi\) | ||||
−0.326714 | + | 0.945123i | \(0.605942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.7321 | −0.908638 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.39230i | − 0.406132i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.19615 | −0.298458 | −0.149229 | − | 0.988803i | \(-0.547679\pi\) | ||||
−0.149229 | + | 0.988803i | \(0.547679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.7846 | 1.67164 | 0.835821 | − | 0.549002i | \(-0.184992\pi\) | ||||
0.835821 | + | 0.549002i | \(0.184992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3923i | 0.784150i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | 0.661330 | 0.330665 | − | 0.943748i | \(-0.392727\pi\) | ||||
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0526i | 0.477611i | 0.971067 | + | 0.238806i | \(0.0767559\pi\) | ||||
−0.971067 | + | 0.238806i | \(0.923244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 8.92820i | − 0.423237i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.5359 | 0.780377 | 0.390189 | − | 0.920735i | \(-0.372410\pi\) | ||||
0.390189 | + | 0.920735i | \(0.372410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.3923i | 1.24277i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.92820 | −0.137276 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7846 | −0.504483 | −0.252241 | − | 0.967664i | \(-0.581168\pi\) | ||||
−0.252241 | + | 0.967664i | \(0.581168\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7321i | 0.965588i | 0.875734 | + | 0.482794i | \(0.160378\pi\) | ||||
−0.875734 | + | 0.482794i | \(0.839622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1769 | −0.984175 | −0.492087 | − | 0.870546i | \(-0.663766\pi\) | ||||
−0.492087 | + | 0.870546i | \(0.663766\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3923i | 0.943643i | 0.881694 | + | 0.471822i | \(0.156403\pi\) | ||||
−0.881694 | + | 0.471822i | \(0.843597\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.39230i | − 0.295169i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.3923 | −1.12156 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 15.4641i | − 0.709542i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.6410 | 1.40002 | 0.700012 | − | 0.714131i | \(-0.253178\pi\) | ||||
0.700012 | + | 0.714131i | \(0.253178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.75129i | − 0.0795219i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 27.1244i | − 1.22411i | −0.790817 | − | 0.612053i | \(-0.790344\pi\) | ||||
0.790817 | − | 0.612053i | \(-0.209656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.3205i | 1.41060i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.66025 | 0.164185 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 11.8564i | − 0.530766i | −0.964143 | − | 0.265383i | \(-0.914502\pi\) | ||||
0.964143 | − | 0.265383i | \(-0.0854983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.3923 | −0.730897 | −0.365448 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365448 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.24871 | 0.367063 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.5885i | 1.35581i | 0.735150 | + | 0.677905i | \(0.237112\pi\) | ||||
−0.735150 | + | 0.677905i | \(0.762888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.53590 | −0.377606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.2487i | 0.451612i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 10.9282i | − 0.480622i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.80385 | −0.166650 | −0.0833248 | − | 0.996522i | \(-0.526554\pi\) | ||||
−0.0833248 | + | 0.996522i | \(0.526554\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9282i | 0.652765i | 0.945238 | + | 0.326382i | \(0.105830\pi\) | ||||
−0.945238 | + | 0.326382i | \(0.894170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.39230 | 0.365575 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 38.6410i | − 1.67373i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.73205i | − 0.117678i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0000i | 1.11783i | 0.829226 | + | 0.558914i | \(0.188782\pi\) | ||||
−0.829226 | + | 0.558914i | \(0.811218\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 44.2487i | − 1.89194i | −0.324257 | − | 0.945969i | \(-0.605114\pi\) | ||||
0.324257 | − | 0.945969i | \(-0.394886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8564 | −1.10152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3923 | 0.526974 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.5359i | 1.03962i | 0.854282 | + | 0.519810i | \(0.173997\pi\) | ||||
−0.854282 | + | 0.519810i | \(0.826003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.7128 | 1.51049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.6410i | 1.96568i | 0.184448 | + | 0.982842i | \(0.440950\pi\) | ||||
−0.184448 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.67949i | − 0.196868i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.8564 | −1.50318 | −0.751589 | − | 0.659631i | \(-0.770712\pi\) | ||||
−0.751589 | + | 0.659631i | \(0.770712\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.60770i | − 0.0672799i | −0.999434 | − | 0.0336400i | \(-0.989290\pi\) | ||||
0.999434 | − | 0.0336400i | \(-0.0107100\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1244 | −0.880947 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.6410 | 1.85843 | 0.929215 | − | 0.369540i | \(-0.120485\pi\) | ||||
0.929215 | + | 0.369540i | \(0.120485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.53590i | − 0.105207i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.46410 | −0.391963 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.3205i | 1.12764i | 0.825898 | + | 0.563819i | \(0.190668\pi\) | ||||
−0.825898 | + | 0.563819i | \(0.809332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820i | 0.285472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.66025 | −0.0681785 | −0.0340892 | − | 0.999419i | \(-0.510853\pi\) | ||||
−0.0340892 | + | 0.999419i | \(0.510853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.07180i | − 0.125931i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.19615 | −0.0897324 | −0.0448662 | − | 0.998993i | \(-0.514286\pi\) | ||||
−0.0448662 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.58846i | 0.105236i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.6410 | 1.89310 | 0.946550 | − | 0.322556i | \(-0.104542\pi\) | ||||
0.946550 | + | 0.322556i | \(0.104542\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0000i | 0.647291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1436i | 0.571254i | 0.958341 | + | 0.285627i | \(0.0922019\pi\) | ||||
−0.958341 | + | 0.285627i | \(0.907798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5359 | 1.14881 | 0.574406 | − | 0.818571i | \(-0.305233\pi\) | ||||
0.574406 | + | 0.818571i | \(0.305233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 9.85641i | − 0.396162i | −0.980186 | − | 0.198081i | \(-0.936529\pi\) | ||||
0.980186 | − | 0.198081i | \(-0.0634710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.1962 | −0.488629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 8.39230i | − 0.334623i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4641 | −1.17295 | −0.586474 | − | 0.809968i | \(-0.699484\pi\) | ||||
−0.586474 | + | 0.809968i | \(0.699484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 14.1436i | − 0.561271i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000i | 0.158486i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.4641 | 1.71673 | 0.858364 | − | 0.513041i | \(-0.171481\pi\) | ||||
0.858364 | + | 0.513041i | \(0.171481\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.24871i | − 0.325297i | −0.986684 | − | 0.162649i | \(-0.947996\pi\) | ||||
0.986684 | − | 0.162649i | \(-0.0520037\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.1051 | 1.73395 | 0.866976 | − | 0.498351i | \(-0.166061\pi\) | ||||
0.866976 | + | 0.498351i | \(0.166061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.8564 | 0.857939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.8564i | 1.24664i | 0.781968 | + | 0.623319i | \(0.214216\pi\) | ||||
−0.781968 | + | 0.623319i | \(0.785784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.21539 | 0.125636 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1244i | 0.744979i | 0.928036 | + | 0.372490i | \(0.121496\pi\) | ||||
−0.928036 | + | 0.372490i | \(0.878504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.6077i | − 0.762651i | −0.924441 | − | 0.381325i | \(-0.875468\pi\) | ||||
0.924441 | − | 0.381325i | \(-0.124532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.53590 | 0.0983379 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.3205i | 1.36762i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.9282 | −0.885133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.1769 | 0.970499 | 0.485249 | − | 0.874376i | \(-0.338729\pi\) | ||||
0.485249 | + | 0.874376i | \(0.338729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 31.2679i | − 1.20172i | −0.799352 | − | 0.600862i | \(-0.794824\pi\) | ||||
0.799352 | − | 0.600862i | \(-0.205176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.39230 | −0.0918082 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.9090i | 1.22096i | 0.792031 | + | 0.610481i | \(0.209024\pi\) | ||||
−0.792031 | + | 0.610481i | \(0.790976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.53590i | 0.0968917i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8564 | 0.527887 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7846i | 0.942851i | 0.881906 | + | 0.471425i | \(0.156260\pi\) | ||||
−0.881906 | + | 0.471425i | \(0.843740\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.00000 | 0.303457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.5359 | 1.53541 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 33.7128i | − 1.27332i | −0.771147 | − | 0.636658i | \(-0.780316\pi\) | ||||
0.771147 | − | 0.636658i | \(-0.219684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820 | 0.261302 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 11.2679i | − 0.423775i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 2.92820i | − 0.109971i | −0.998487 | − | 0.0549855i | \(-0.982489\pi\) | ||||
0.998487 | − | 0.0549855i | \(-0.0175113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.46410 | 0.354433 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000i | 0.299183i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.4641 | 0.651301 | 0.325651 | − | 0.945490i | \(-0.394417\pi\) | ||||
0.325651 | + | 0.945490i | \(0.394417\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 33.3205i | − 1.23749i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6410 | −0.913885 | −0.456942 | − | 0.889496i | \(-0.651055\pi\) | ||||
−0.456942 | + | 0.889496i | \(0.651055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.4641i | 1.38566i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.9282i | 1.73333i | 0.498888 | + | 0.866666i | \(0.333742\pi\) | ||||
−0.498888 | + | 0.866666i | \(0.666258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.4641 | −0.643298 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3923i | 0.529429i | 0.964327 | + | 0.264715i | \(0.0852778\pi\) | ||||
−0.964327 | + | 0.264715i | \(0.914722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.8038 | −1.09340 | −0.546699 | − | 0.837329i | \(-0.684116\pi\) | ||||
−0.546699 | + | 0.837329i | \(0.684116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.75129 | −0.0641623 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 8.19615i | − 0.299481i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.07180 | 0.185072 | 0.0925362 | − | 0.995709i | \(-0.470503\pi\) | ||||
0.0925362 | + | 0.995709i | \(0.470503\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.784610i | 0.0285549i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16.0000i | − 0.581530i | −0.956795 | − | 0.290765i | \(-0.906090\pi\) | ||||
0.956795 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.2679 | −0.480963 | −0.240481 | − | 0.970654i | \(-0.577305\pi\) | ||||
−0.240481 | + | 0.970654i | \(0.577305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9282i | 0.395628i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.0000 | −1.15545 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.3731i | 0.984541i | 0.870442 | + | 0.492270i | \(0.163833\pi\) | ||||
−0.870442 | + | 0.492270i | \(0.836167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.92820 | −0.320711 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.4641i | 1.19898i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 10.0000i | − 0.357828i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.14359 | −0.219274 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.0718i | − 0.465959i | −0.972482 | − | 0.232980i | \(-0.925152\pi\) | ||||
0.972482 | − | 0.232980i | \(-0.0748475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.39230 | −0.227284 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.5692 | 1.19208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.33975i | 0.153722i | 0.997042 | + | 0.0768608i | \(0.0244897\pi\) | ||||
−0.997042 | + | 0.0768608i | \(0.975510\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.7846 | −0.593797 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.3205i | 0.822963i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.46410i | − 0.122094i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.67949 | −0.234838 | −0.117419 | − | 0.993082i | \(-0.537462\pi\) | ||||
−0.117419 | + | 0.993082i | \(0.537462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7846i | 0.729846i | 0.931038 | + | 0.364923i | \(0.118905\pi\) | ||||
−0.931038 | + | 0.364923i | \(0.881095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.32051 | 0.116312 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.9282 | −1.08204 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.3205i | 1.86090i | 0.366421 | + | 0.930449i | \(0.380583\pi\) | ||||
−0.366421 | + | 0.930449i | \(0.619417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.392305 | −0.0136749 | −0.00683744 | − | 0.999977i | \(-0.502176\pi\) | ||||
−0.00683744 | + | 0.999977i | \(0.502176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.98076i | 0.173198i | 0.996243 | + | 0.0865990i | \(0.0275999\pi\) | ||||
−0.996243 | + | 0.0865990i | \(0.972400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7846i | 1.13866i | 0.822110 | + | 0.569328i | \(0.192797\pi\) | ||||
−0.822110 | + | 0.569328i | \(0.807203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.19615 | −0.145388 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 12.0000i | − 0.415277i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.1051 | −1.10839 | −0.554196 | − | 0.832386i | \(-0.686974\pi\) | ||||
−0.554196 | + | 0.832386i | \(0.686974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7128 | −0.921131 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.19615i | − 0.0755499i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.53590 | 0.121495 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.46410i | − 0.324425i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 18.2487i | − 0.624824i | −0.949947 | − | 0.312412i | \(-0.898863\pi\) | ||||
0.949947 | − | 0.312412i | \(-0.101137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.73205 | 0.0933251 | 0.0466625 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466625 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 51.1769i | − 1.74613i | −0.487600 | − | 0.873067i | \(-0.662128\pi\) | ||||
0.487600 | − | 0.873067i | \(-0.337872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.8756 | −0.914858 | −0.457429 | − | 0.889246i | \(-0.651230\pi\) | ||||
−0.457429 | + | 0.889246i | \(0.651230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.7513 | −0.399556 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 33.8564i | − 1.14850i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5692 | 0.866380 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820i | 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.07180i | 0.306333i | 0.988200 | + | 0.153166i | \(0.0489471\pi\) | ||||
−0.988200 | + | 0.153166i | \(0.951053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.87564 | −0.299028 | −0.149514 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149514 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9282i | 0.435069i | 0.976053 | + | 0.217534i | \(0.0698014\pi\) | ||||
−0.976053 | + | 0.217534i | \(0.930199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.24871 | −0.209811 | −0.104906 | − | 0.994482i | \(-0.533454\pi\) | ||||
−0.104906 | + | 0.994482i | \(0.533454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.3205 | −0.647989 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.8564i | − 0.463687i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0718 | 0.503795 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.9282i | 0.497883i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.5359i | 0.484261i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.8564 | 0.460603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15.8564i | − 0.526503i | −0.964727 | − | 0.263252i | \(-0.915205\pi\) | ||||
0.964727 | − | 0.263252i | \(-0.0847950\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9090 | −1.12345 | −0.561727 | − | 0.827323i | \(-0.689863\pi\) | ||||
−0.561727 | + | 0.827323i | \(0.689863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.92820 | −0.229290 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.39230i | − 0.145047i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.9282 | −0.360488 | −0.180244 | − | 0.983622i | \(-0.557689\pi\) | ||||
−0.180244 | + | 0.983622i | \(0.557689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6410i | 0.481915i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.92820i | 0.293558i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.5885 | 1.46290 | 0.731450 | − | 0.681895i | \(-0.238844\pi\) | ||||
0.731450 | + | 0.681895i | \(0.238844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.46410i | − 0.113531i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.39230 | −0.274458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1436 | −0.396714 | −0.198357 | − | 0.980130i | \(-0.563561\pi\) | ||||
−0.198357 | + | 0.980130i | \(0.563561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.2295i | 1.86563i | 0.360359 | + | 0.932814i | \(0.382654\pi\) | ||||
−0.360359 | + | 0.932814i | \(0.617346\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.7128 | 1.48861 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.58846i | 0.149105i | 0.997217 | + | 0.0745524i | \(0.0237528\pi\) | ||||
−0.997217 | + | 0.0745524i | \(0.976247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 34.1436i | − 1.10835i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.7846 | 0.867639 | 0.433819 | − | 0.901000i | \(-0.357166\pi\) | ||||
0.433819 | + | 0.901000i | \(0.357166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1051i | 0.585868i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.46410 | 0.111862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 17.8564i | − 0.574818i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.5359 | −1.11060 | −0.555300 | − | 0.831650i | \(-0.687396\pi\) | ||||
−0.555300 | + | 0.831650i | \(0.687396\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.78461i | 0.281912i | 0.990016 | + | 0.140956i | \(0.0450175\pi\) | ||||
−0.990016 | + | 0.140956i | \(0.954982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10.9282i | − 0.350342i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.4974 | 1.74353 | 0.871764 | − | 0.489927i | \(-0.162977\pi\) | ||||
0.871764 | + | 0.489927i | \(0.162977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.3205i | 1.06493i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.78461 | 0.152605 | 0.0763027 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763027 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.6077 | 0.624753 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.2487i | 1.34343i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.7846 | −1.67676 | −0.838379 | − | 0.545087i | \(-0.816496\pi\) | ||||
−0.838379 | + | 0.545087i | \(0.816496\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.85641i | 0.185661i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3205i | 0.991930i | 0.868342 | + | 0.495965i | \(0.165186\pi\) | ||||
−0.868342 | + | 0.495965i | \(0.834814\pi\) | |||||||
\(998\) | 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 | 4032.2.c.o.2017.3 | 4 | ||
3.2 | odd | 2 | 1344.2.c.h.673.1 | yes | 4 | ||
4.3 | odd | 2 | 4032.2.c.l.2017.3 | 4 | |||
8.3 | odd | 2 | 4032.2.c.l.2017.2 | 4 | |||
8.5 | even | 2 | inner | 4032.2.c.o.2017.2 | 4 | ||
12.11 | even | 2 | 1344.2.c.e.673.3 | yes | 4 | ||
24.5 | odd | 2 | 1344.2.c.h.673.4 | yes | 4 | ||
24.11 | even | 2 | 1344.2.c.e.673.2 | ✓ | 4 | ||
48.5 | odd | 4 | 5376.2.a.n.1.2 | 2 | |||
48.11 | even | 4 | 5376.2.a.z.1.2 | 2 | |||
48.29 | odd | 4 | 5376.2.a.bd.1.1 | 2 | |||
48.35 | even | 4 | 5376.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.c.e.673.2 | ✓ | 4 | 24.11 | even | 2 | ||
1344.2.c.e.673.3 | yes | 4 | 12.11 | even | 2 | ||
1344.2.c.h.673.1 | yes | 4 | 3.2 | odd | 2 | ||
1344.2.c.h.673.4 | yes | 4 | 24.5 | odd | 2 | ||
4032.2.c.l.2017.2 | 4 | 8.3 | odd | 2 | |||
4032.2.c.l.2017.3 | 4 | 4.3 | odd | 2 | |||
4032.2.c.o.2017.2 | 4 | 8.5 | even | 2 | inner | ||
4032.2.c.o.2017.3 | 4 | 1.1 | even | 1 | trivial | ||
5376.2.a.n.1.2 | 2 | 48.5 | odd | 4 | |||
5376.2.a.t.1.1 | 2 | 48.35 | even | 4 | |||
5376.2.a.z.1.2 | 2 | 48.11 | even | 4 | |||
5376.2.a.bd.1.1 | 2 | 48.29 | odd | 4 |