Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,2,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1911.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.a (trivial) |
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: | yes |
Analytic conductor: | \(15.2594118263\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.375116.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.562376\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0776754 | 0.0549248 | 0.0274624 | − | 0.999623i | \(-0.491257\pi\) | ||||
0.0274624 | + | 0.999623i | \(0.491257\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.99397 | −0.996983 | ||||||||
\(5\) | 2.20243 | 0.984955 | 0.492478 | − | 0.870325i | \(-0.336091\pi\) | ||||
0.492478 | + | 0.870325i | \(0.336091\pi\) | |||||||
\(6\) | 0.0776754 | 0.0317108 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.310233 | −0.109684 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.171074 | 0.0540984 | ||||||||
\(11\) | 2.91629 | 0.879295 | 0.439647 | − | 0.898170i | \(-0.355103\pi\) | ||||
0.439647 | + | 0.898170i | \(0.355103\pi\) | |||||||
\(12\) | −1.99397 | −0.575609 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20243 | 0.568664 | ||||||||
\(16\) | 3.96384 | 0.990959 | ||||||||
\(17\) | 0.393942 | 0.0955449 | 0.0477724 | − | 0.998858i | \(-0.484788\pi\) | ||||
0.0477724 | + | 0.998858i | \(0.484788\pi\) | |||||||
\(18\) | 0.0776754 | 0.0183083 | ||||||||
\(19\) | −0.124751 | −0.0286199 | −0.0143099 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143099 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(20\) | −4.39156 | −0.981984 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.226524 | 0.0482951 | ||||||||
\(23\) | 3.38187 | 0.705170 | 0.352585 | − | 0.935780i | \(-0.385303\pi\) | ||||
0.352585 | + | 0.935780i | \(0.385303\pi\) | |||||||
\(24\) | −0.310233 | −0.0633260 | ||||||||
\(25\) | −0.149317 | −0.0298635 | ||||||||
\(26\) | 0.0776754 | 0.0152334 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.642223 | −0.119258 | −0.0596289 | − | 0.998221i | \(-0.518992\pi\) | ||||
−0.0596289 | + | 0.998221i | \(0.518992\pi\) | |||||||
\(30\) | 0.171074 | 0.0312338 | ||||||||
\(31\) | −5.95780 | −1.07005 | −0.535026 | − | 0.844835i | \(-0.679698\pi\) | ||||
−0.535026 | + | 0.844835i | \(0.679698\pi\) | |||||||
\(32\) | 0.928358 | 0.164112 | ||||||||
\(33\) | 2.91629 | 0.507661 | ||||||||
\(34\) | 0.0305996 | 0.00524778 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.99397 | −0.332328 | ||||||||
\(37\) | 4.18670 | 0.688290 | 0.344145 | − | 0.938917i | \(-0.388169\pi\) | ||||
0.344145 | + | 0.938917i | \(0.388169\pi\) | |||||||
\(38\) | −0.00969009 | −0.00157194 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.683265 | −0.108034 | ||||||||
\(41\) | −0.434984 | −0.0679331 | −0.0339665 | − | 0.999423i | \(-0.510814\pi\) | ||||
−0.0339665 | + | 0.999423i | \(0.510814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.74934 | −1.02927 | −0.514633 | − | 0.857411i | \(-0.672072\pi\) | ||||
−0.514633 | + | 0.857411i | \(0.672072\pi\) | |||||||
\(44\) | −5.81499 | −0.876642 | ||||||||
\(45\) | 2.20243 | 0.328318 | ||||||||
\(46\) | 0.262688 | 0.0387313 | ||||||||
\(47\) | 9.46321 | 1.38035 | 0.690175 | − | 0.723642i | \(-0.257533\pi\) | ||||
0.690175 | + | 0.723642i | \(0.257533\pi\) | |||||||
\(48\) | 3.96384 | 0.572130 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0115983 | −0.00164024 | ||||||||
\(51\) | 0.393942 | 0.0551629 | ||||||||
\(52\) | −1.99397 | −0.276513 | ||||||||
\(53\) | 12.4338 | 1.70792 | 0.853959 | − | 0.520341i | \(-0.174195\pi\) | ||||
0.853959 | + | 0.520341i | \(0.174195\pi\) | |||||||
\(54\) | 0.0776754 | 0.0105703 | ||||||||
\(55\) | 6.42292 | 0.866066 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.124751 | −0.0165237 | ||||||||
\(58\) | −0.0498849 | −0.00655021 | ||||||||
\(59\) | 7.33555 | 0.955007 | 0.477504 | − | 0.878630i | \(-0.341542\pi\) | ||||
0.477504 | + | 0.878630i | \(0.341542\pi\) | |||||||
\(60\) | −4.39156 | −0.566949 | ||||||||
\(61\) | 2.39394 | 0.306513 | 0.153256 | − | 0.988186i | \(-0.451024\pi\) | ||||
0.153256 | + | 0.988186i | \(0.451024\pi\) | |||||||
\(62\) | −0.462775 | −0.0587724 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.85556 | −0.981945 | ||||||||
\(65\) | 2.20243 | 0.273177 | ||||||||
\(66\) | 0.226524 | 0.0278832 | ||||||||
\(67\) | 6.14047 | 0.750178 | 0.375089 | − | 0.926989i | \(-0.377612\pi\) | ||||
0.375089 | + | 0.926989i | \(0.377612\pi\) | |||||||
\(68\) | −0.785507 | −0.0952567 | ||||||||
\(69\) | 3.38187 | 0.407130 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0826 | −1.67129 | −0.835646 | − | 0.549269i | \(-0.814906\pi\) | ||||
−0.835646 | + | 0.549269i | \(0.814906\pi\) | |||||||
\(72\) | −0.310233 | −0.0365613 | ||||||||
\(73\) | 7.55295 | 0.884006 | 0.442003 | − | 0.897014i | \(-0.354268\pi\) | ||||
0.442003 | + | 0.897014i | \(0.354268\pi\) | |||||||
\(74\) | 0.325204 | 0.0378042 | ||||||||
\(75\) | −0.149317 | −0.0172417 | ||||||||
\(76\) | 0.248750 | 0.0285335 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0776754 | 0.00879500 | ||||||||
\(79\) | −2.37472 | −0.267177 | −0.133589 | − | 0.991037i | \(-0.542650\pi\) | ||||
−0.133589 | + | 0.991037i | \(0.542650\pi\) | |||||||
\(80\) | 8.73006 | 0.976050 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.0337875 | −0.00373121 | ||||||||
\(83\) | 9.78804 | 1.07438 | 0.537189 | − | 0.843462i | \(-0.319486\pi\) | ||||
0.537189 | + | 0.843462i | \(0.319486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.867628 | 0.0941074 | ||||||||
\(86\) | −0.524258 | −0.0565322 | ||||||||
\(87\) | −0.642223 | −0.0688535 | ||||||||
\(88\) | −0.904729 | −0.0964445 | ||||||||
\(89\) | 6.40363 | 0.678784 | 0.339392 | − | 0.940645i | \(-0.389779\pi\) | ||||
0.339392 | + | 0.940645i | \(0.389779\pi\) | |||||||
\(90\) | 0.171074 | 0.0180328 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.74335 | −0.703042 | ||||||||
\(93\) | −5.95780 | −0.617795 | ||||||||
\(94\) | 0.735058 | 0.0758155 | ||||||||
\(95\) | −0.274755 | −0.0281893 | ||||||||
\(96\) | 0.928358 | 0.0947502 | ||||||||
\(97\) | −14.9096 | −1.51384 | −0.756919 | − | 0.653509i | \(-0.773296\pi\) | ||||
−0.756919 | + | 0.653509i | \(0.773296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.91629 | 0.293098 | ||||||||
\(100\) | 0.297734 | 0.0297734 | ||||||||
\(101\) | 19.9821 | 1.98829 | 0.994145 | − | 0.108057i | \(-0.0344630\pi\) | ||||
0.994145 | + | 0.108057i | \(0.0344630\pi\) | |||||||
\(102\) | 0.0305996 | 0.00302981 | ||||||||
\(103\) | 14.6745 | 1.44592 | 0.722960 | − | 0.690890i | \(-0.242781\pi\) | ||||
0.722960 | + | 0.690890i | \(0.242781\pi\) | |||||||
\(104\) | −0.310233 | −0.0304208 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.965802 | 0.0938070 | ||||||||
\(107\) | −5.03973 | −0.487209 | −0.243604 | − | 0.969875i | \(-0.578330\pi\) | ||||
−0.243604 | + | 0.969875i | \(0.578330\pi\) | |||||||
\(108\) | −1.99397 | −0.191870 | ||||||||
\(109\) | −0.122682 | −0.0117508 | −0.00587542 | − | 0.999983i | \(-0.501870\pi\) | ||||
−0.00587542 | + | 0.999983i | \(0.501870\pi\) | |||||||
\(110\) | 0.498902 | 0.0475685 | ||||||||
\(111\) | 4.18670 | 0.397384 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.16138 | −0.391470 | −0.195735 | − | 0.980657i | \(-0.562709\pi\) | ||||
−0.195735 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(114\) | −0.00969009 | −0.000907560 0 | ||||||||
\(115\) | 7.44833 | 0.694560 | ||||||||
\(116\) | 1.28057 | 0.118898 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0.569792 | 0.0524536 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.683265 | −0.0623733 | ||||||||
\(121\) | −2.49525 | −0.226841 | ||||||||
\(122\) | 0.185950 | 0.0168352 | ||||||||
\(123\) | −0.434984 | −0.0392212 | ||||||||
\(124\) | 11.8797 | 1.06682 | ||||||||
\(125\) | −11.3410 | −1.01437 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9711 | 1.32847 | 0.664237 | − | 0.747522i | \(-0.268756\pi\) | ||||
0.664237 | + | 0.747522i | \(0.268756\pi\) | |||||||
\(128\) | −2.46690 | −0.218045 | ||||||||
\(129\) | −6.74934 | −0.594246 | ||||||||
\(130\) | 0.171074 | 0.0150042 | ||||||||
\(131\) | −18.7422 | −1.63751 | −0.818755 | − | 0.574143i | \(-0.805335\pi\) | ||||
−0.818755 | + | 0.574143i | \(0.805335\pi\) | |||||||
\(132\) | −5.81499 | −0.506130 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.476964 | 0.0412034 | ||||||||
\(135\) | 2.20243 | 0.189555 | ||||||||
\(136\) | −0.122214 | −0.0104797 | ||||||||
\(137\) | −13.5905 | −1.16111 | −0.580557 | − | 0.814219i | \(-0.697165\pi\) | ||||
−0.580557 | + | 0.814219i | \(0.697165\pi\) | |||||||
\(138\) | 0.262688 | 0.0223615 | ||||||||
\(139\) | 15.7292 | 1.33413 | 0.667066 | − | 0.744999i | \(-0.267550\pi\) | ||||
0.667066 | + | 0.744999i | \(0.267550\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.46321 | 0.796946 | ||||||||
\(142\) | −1.09387 | −0.0917953 | ||||||||
\(143\) | 2.91629 | 0.243873 | ||||||||
\(144\) | 3.96384 | 0.330320 | ||||||||
\(145\) | −1.41445 | −0.117464 | ||||||||
\(146\) | 0.586678 | 0.0485538 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.34815 | −0.686213 | ||||||||
\(149\) | 3.34809 | 0.274286 | 0.137143 | − | 0.990551i | \(-0.456208\pi\) | ||||
0.137143 | + | 0.990551i | \(0.456208\pi\) | |||||||
\(150\) | −0.0115983 | −0.000946995 0 | ||||||||
\(151\) | −20.4476 | −1.66401 | −0.832003 | − | 0.554771i | \(-0.812806\pi\) | ||||
−0.832003 | + | 0.554771i | \(0.812806\pi\) | |||||||
\(152\) | 0.0387019 | 0.00313914 | ||||||||
\(153\) | 0.393942 | 0.0318483 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.1216 | −1.05395 | ||||||||
\(156\) | −1.99397 | −0.159645 | ||||||||
\(157\) | −10.2014 | −0.814158 | −0.407079 | − | 0.913393i | \(-0.633453\pi\) | ||||
−0.407079 | + | 0.913393i | \(0.633453\pi\) | |||||||
\(158\) | −0.184457 | −0.0146746 | ||||||||
\(159\) | 12.4338 | 0.986067 | ||||||||
\(160\) | 2.04464 | 0.161643 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.0776754 | 0.00610275 | ||||||||
\(163\) | 15.5835 | 1.22060 | 0.610299 | − | 0.792171i | \(-0.291049\pi\) | ||||
0.610299 | + | 0.792171i | \(0.291049\pi\) | |||||||
\(164\) | 0.867344 | 0.0677282 | ||||||||
\(165\) | 6.42292 | 0.500023 | ||||||||
\(166\) | 0.760290 | 0.0590099 | ||||||||
\(167\) | −1.53310 | −0.118635 | −0.0593174 | − | 0.998239i | \(-0.518892\pi\) | ||||
−0.0593174 | + | 0.998239i | \(0.518892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.0673933 | 0.00516883 | ||||||||
\(171\) | −0.124751 | −0.00953996 | ||||||||
\(172\) | 13.4580 | 1.02616 | ||||||||
\(173\) | 13.9844 | 1.06322 | 0.531609 | − | 0.846990i | \(-0.321588\pi\) | ||||
0.531609 | + | 0.846990i | \(0.321588\pi\) | |||||||
\(174\) | −0.0498849 | −0.00378176 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.5597 | 0.871345 | ||||||||
\(177\) | 7.33555 | 0.551374 | ||||||||
\(178\) | 0.497404 | 0.0372820 | ||||||||
\(179\) | −21.9304 | −1.63915 | −0.819577 | − | 0.572969i | \(-0.805792\pi\) | ||||
−0.819577 | + | 0.572969i | \(0.805792\pi\) | |||||||
\(180\) | −4.39156 | −0.327328 | ||||||||
\(181\) | −0.955265 | −0.0710043 | −0.0355021 | − | 0.999370i | \(-0.511303\pi\) | ||||
−0.0355021 | + | 0.999370i | \(0.511303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.39394 | 0.176965 | ||||||||
\(184\) | −1.04917 | −0.0773457 | ||||||||
\(185\) | 9.22091 | 0.677934 | ||||||||
\(186\) | −0.462775 | −0.0339323 | ||||||||
\(187\) | 1.14885 | 0.0840121 | ||||||||
\(188\) | −18.8693 | −1.37619 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0213417 | −0.00154829 | ||||||||
\(191\) | 19.6834 | 1.42424 | 0.712121 | − | 0.702056i | \(-0.247735\pi\) | ||||
0.712121 | + | 0.702056i | \(0.247735\pi\) | |||||||
\(192\) | −7.85556 | −0.566926 | ||||||||
\(193\) | 15.0951 | 1.08657 | 0.543283 | − | 0.839550i | \(-0.317181\pi\) | ||||
0.543283 | + | 0.839550i | \(0.317181\pi\) | |||||||
\(194\) | −1.15811 | −0.0831472 | ||||||||
\(195\) | 2.20243 | 0.157719 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0323 | −0.786015 | −0.393008 | − | 0.919535i | \(-0.628565\pi\) | ||||
−0.393008 | + | 0.919535i | \(0.628565\pi\) | |||||||
\(198\) | 0.226524 | 0.0160984 | ||||||||
\(199\) | −7.17701 | −0.508765 | −0.254382 | − | 0.967104i | \(-0.581872\pi\) | ||||
−0.254382 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(200\) | 0.0463231 | 0.00327554 | ||||||||
\(201\) | 6.14047 | 0.433116 | ||||||||
\(202\) | 1.55211 | 0.109206 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.785507 | −0.0549965 | ||||||||
\(205\) | −0.958020 | −0.0669110 | ||||||||
\(206\) | 1.13985 | 0.0794168 | ||||||||
\(207\) | 3.38187 | 0.235057 | ||||||||
\(208\) | 3.96384 | 0.274843 | ||||||||
\(209\) | −0.363811 | −0.0251653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7119 | 1.08165 | 0.540825 | − | 0.841135i | \(-0.318112\pi\) | ||||
0.540825 | + | 0.841135i | \(0.318112\pi\) | |||||||
\(212\) | −24.7926 | −1.70277 | ||||||||
\(213\) | −14.0826 | −0.964921 | ||||||||
\(214\) | −0.391463 | −0.0267598 | ||||||||
\(215\) | −14.8649 | −1.01378 | ||||||||
\(216\) | −0.310233 | −0.0211087 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.00952939 | −0.000645412 0 | ||||||||
\(219\) | 7.55295 | 0.510381 | ||||||||
\(220\) | −12.8071 | −0.863453 | ||||||||
\(221\) | 0.393942 | 0.0264994 | ||||||||
\(222\) | 0.325204 | 0.0218262 | ||||||||
\(223\) | −6.20889 | −0.415778 | −0.207889 | − | 0.978152i | \(-0.566659\pi\) | ||||
−0.207889 | + | 0.978152i | \(0.566659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.149317 | −0.00995449 | ||||||||
\(226\) | −0.323237 | −0.0215014 | ||||||||
\(227\) | −23.6879 | −1.57222 | −0.786111 | − | 0.618085i | \(-0.787909\pi\) | ||||
−0.786111 | + | 0.618085i | \(0.787909\pi\) | |||||||
\(228\) | 0.248750 | 0.0164738 | ||||||||
\(229\) | 9.04226 | 0.597530 | 0.298765 | − | 0.954327i | \(-0.403425\pi\) | ||||
0.298765 | + | 0.954327i | \(0.403425\pi\) | |||||||
\(230\) | 0.578552 | 0.0381486 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.199239 | 0.0130807 | ||||||||
\(233\) | 5.34449 | 0.350129 | 0.175065 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175065 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(234\) | 0.0776754 | 0.00507780 | ||||||||
\(235\) | 20.8420 | 1.35958 | ||||||||
\(236\) | −14.6268 | −0.952126 | ||||||||
\(237\) | −2.37472 | −0.154255 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.2548 | −1.76297 | −0.881484 | − | 0.472215i | \(-0.843455\pi\) | ||||
−0.881484 | + | 0.472215i | \(0.843455\pi\) | |||||||
\(240\) | 8.73006 | 0.563523 | ||||||||
\(241\) | 15.6761 | 1.00979 | 0.504894 | − | 0.863182i | \(-0.331532\pi\) | ||||
0.504894 | + | 0.863182i | \(0.331532\pi\) | |||||||
\(242\) | −0.193819 | −0.0124592 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.77344 | −0.305588 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0337875 | −0.00215422 | ||||||||
\(247\) | −0.124751 | −0.00793773 | ||||||||
\(248\) | 1.84831 | 0.117368 | ||||||||
\(249\) | 9.78804 | 0.620292 | ||||||||
\(250\) | −0.880916 | −0.0557140 | ||||||||
\(251\) | 18.2218 | 1.15015 | 0.575075 | − | 0.818101i | \(-0.304973\pi\) | ||||
0.575075 | + | 0.818101i | \(0.304973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.86253 | 0.620052 | ||||||||
\(254\) | 1.16289 | 0.0729662 | ||||||||
\(255\) | 0.867628 | 0.0543329 | ||||||||
\(256\) | 15.5195 | 0.969969 | ||||||||
\(257\) | −15.0614 | −0.939502 | −0.469751 | − | 0.882799i | \(-0.655656\pi\) | ||||
−0.469751 | + | 0.882799i | \(0.655656\pi\) | |||||||
\(258\) | −0.524258 | −0.0326389 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.39156 | −0.272353 | ||||||||
\(261\) | −0.642223 | −0.0397526 | ||||||||
\(262\) | −1.45580 | −0.0899399 | ||||||||
\(263\) | −27.7916 | −1.71370 | −0.856852 | − | 0.515563i | \(-0.827583\pi\) | ||||
−0.856852 | + | 0.515563i | \(0.827583\pi\) | |||||||
\(264\) | −0.904729 | −0.0556822 | ||||||||
\(265\) | 27.3846 | 1.68222 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.40363 | 0.391896 | ||||||||
\(268\) | −12.2439 | −0.747915 | ||||||||
\(269\) | 8.00809 | 0.488262 | 0.244131 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244131 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(270\) | 0.171074 | 0.0104113 | ||||||||
\(271\) | −20.2645 | −1.23098 | −0.615490 | − | 0.788144i | \(-0.711042\pi\) | ||||
−0.615490 | + | 0.788144i | \(0.711042\pi\) | |||||||
\(272\) | 1.56152 | 0.0946811 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.05565 | −0.0637740 | ||||||||
\(275\) | −0.435453 | −0.0262588 | ||||||||
\(276\) | −6.74335 | −0.405902 | ||||||||
\(277\) | −29.4339 | −1.76851 | −0.884256 | − | 0.467003i | \(-0.845334\pi\) | ||||
−0.884256 | + | 0.467003i | \(0.845334\pi\) | |||||||
\(278\) | 1.22177 | 0.0732769 | ||||||||
\(279\) | −5.95780 | −0.356684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.76735 | −0.224741 | −0.112371 | − | 0.993666i | \(-0.535844\pi\) | ||||
−0.112371 | + | 0.993666i | \(0.535844\pi\) | |||||||
\(282\) | 0.735058 | 0.0437721 | ||||||||
\(283\) | −22.4407 | −1.33396 | −0.666980 | − | 0.745075i | \(-0.732414\pi\) | ||||
−0.666980 | + | 0.745075i | \(0.732414\pi\) | |||||||
\(284\) | 28.0801 | 1.66625 | ||||||||
\(285\) | −0.274755 | −0.0162751 | ||||||||
\(286\) | 0.226524 | 0.0133946 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.928358 | 0.0547040 | ||||||||
\(289\) | −16.8448 | −0.990871 | ||||||||
\(290\) | −0.109868 | −0.00645166 | ||||||||
\(291\) | −14.9096 | −0.874015 | ||||||||
\(292\) | −15.0603 | −0.881339 | ||||||||
\(293\) | −8.13635 | −0.475331 | −0.237665 | − | 0.971347i | \(-0.576382\pi\) | ||||
−0.237665 | + | 0.971347i | \(0.576382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1560 | 0.940639 | ||||||||
\(296\) | −1.29885 | −0.0754943 | ||||||||
\(297\) | 2.91629 | 0.169220 | ||||||||
\(298\) | 0.260064 | 0.0150651 | ||||||||
\(299\) | 3.38187 | 0.195579 | ||||||||
\(300\) | 0.297734 | 0.0171897 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.58828 | −0.0913951 | ||||||||
\(303\) | 19.9821 | 1.14794 | ||||||||
\(304\) | −0.494493 | −0.0283611 | ||||||||
\(305\) | 5.27248 | 0.301901 | ||||||||
\(306\) | 0.0305996 | 0.00174926 | ||||||||
\(307\) | −18.9247 | −1.08009 | −0.540046 | − | 0.841636i | \(-0.681593\pi\) | ||||
−0.540046 | + | 0.841636i | \(0.681593\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6745 | 0.834802 | ||||||||
\(310\) | −1.01923 | −0.0578882 | ||||||||
\(311\) | −11.6189 | −0.658849 | −0.329425 | − | 0.944182i | \(-0.606855\pi\) | ||||
−0.329425 | + | 0.944182i | \(0.606855\pi\) | |||||||
\(312\) | −0.310233 | −0.0175635 | ||||||||
\(313\) | 11.7023 | 0.661455 | 0.330727 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330727 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(314\) | −0.792395 | −0.0447174 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.73512 | 0.266371 | ||||||||
\(317\) | −33.0069 | −1.85385 | −0.926926 | − | 0.375244i | \(-0.877559\pi\) | ||||
−0.926926 | + | 0.375244i | \(0.877559\pi\) | |||||||
\(318\) | 0.965802 | 0.0541595 | ||||||||
\(319\) | −1.87291 | −0.104863 | ||||||||
\(320\) | −17.3013 | −0.967172 | ||||||||
\(321\) | −5.03973 | −0.281290 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0491447 | −0.00273448 | ||||||||
\(324\) | −1.99397 | −0.110776 | ||||||||
\(325\) | −0.149317 | −0.00828263 | ||||||||
\(326\) | 1.21046 | 0.0670411 | ||||||||
\(327\) | −0.122682 | −0.00678435 | ||||||||
\(328\) | 0.134946 | 0.00745116 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.498902 | 0.0274637 | ||||||||
\(331\) | 14.7746 | 0.812085 | 0.406043 | − | 0.913854i | \(-0.366908\pi\) | ||||
0.406043 | + | 0.913854i | \(0.366908\pi\) | |||||||
\(332\) | −19.5170 | −1.07114 | ||||||||
\(333\) | 4.18670 | 0.229430 | ||||||||
\(334\) | −0.119084 | −0.00651599 | ||||||||
\(335\) | 13.5239 | 0.738892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0713 | −0.712041 | −0.356020 | − | 0.934478i | \(-0.615867\pi\) | ||||
−0.356020 | + | 0.934478i | \(0.615867\pi\) | |||||||
\(338\) | 0.0776754 | 0.00422498 | ||||||||
\(339\) | −4.16138 | −0.226015 | ||||||||
\(340\) | −1.73002 | −0.0938235 | ||||||||
\(341\) | −17.3747 | −0.940892 | ||||||||
\(342\) | −0.00969009 | −0.000523980 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.09387 | 0.112894 | ||||||||
\(345\) | 7.44833 | 0.401005 | ||||||||
\(346\) | 1.08625 | 0.0583970 | ||||||||
\(347\) | 6.37950 | 0.342469 | 0.171235 | − | 0.985230i | \(-0.445224\pi\) | ||||
0.171235 | + | 0.985230i | \(0.445224\pi\) | |||||||
\(348\) | 1.28057 | 0.0686458 | ||||||||
\(349\) | 10.3287 | 0.552881 | 0.276441 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276441 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.70736 | 0.144303 | ||||||||
\(353\) | 30.1517 | 1.60481 | 0.802407 | − | 0.596777i | \(-0.203552\pi\) | ||||
0.802407 | + | 0.596777i | \(0.203552\pi\) | |||||||
\(354\) | 0.569792 | 0.0302841 | ||||||||
\(355\) | −31.0158 | −1.64615 | ||||||||
\(356\) | −12.7686 | −0.676736 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.70345 | −0.0900302 | ||||||||
\(359\) | −29.1771 | −1.53991 | −0.769955 | − | 0.638098i | \(-0.779721\pi\) | ||||
−0.769955 | + | 0.638098i | \(0.779721\pi\) | |||||||
\(360\) | −0.683265 | −0.0360112 | ||||||||
\(361\) | −18.9844 | −0.999181 | ||||||||
\(362\) | −0.0742005 | −0.00389989 | ||||||||
\(363\) | −2.49525 | −0.130966 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.6348 | 0.870706 | ||||||||
\(366\) | 0.185950 | 0.00971978 | ||||||||
\(367\) | 4.48431 | 0.234079 | 0.117040 | − | 0.993127i | \(-0.462660\pi\) | ||||
0.117040 | + | 0.993127i | \(0.462660\pi\) | |||||||
\(368\) | 13.4052 | 0.698794 | ||||||||
\(369\) | −0.434984 | −0.0226444 | ||||||||
\(370\) | 0.716237 | 0.0372354 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.8797 | 0.615932 | ||||||||
\(373\) | 23.9891 | 1.24211 | 0.621055 | − | 0.783767i | \(-0.286704\pi\) | ||||
0.621055 | + | 0.783767i | \(0.286704\pi\) | |||||||
\(374\) | 0.0892372 | 0.00461435 | ||||||||
\(375\) | −11.3410 | −0.585646 | ||||||||
\(376\) | −2.93580 | −0.151402 | ||||||||
\(377\) | −0.642223 | −0.0330762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2228 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(380\) | 0.547853 | 0.0281043 | ||||||||
\(381\) | 14.9711 | 0.766995 | ||||||||
\(382\) | 1.52892 | 0.0782262 | ||||||||
\(383\) | 23.0819 | 1.17943 | 0.589714 | − | 0.807612i | \(-0.299240\pi\) | ||||
0.589714 | + | 0.807612i | \(0.299240\pi\) | |||||||
\(384\) | −2.46690 | −0.125888 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.17251 | 0.0596794 | ||||||||
\(387\) | −6.74934 | −0.343088 | ||||||||
\(388\) | 29.7292 | 1.50927 | ||||||||
\(389\) | −33.3369 | −1.69025 | −0.845124 | − | 0.534570i | \(-0.820474\pi\) | ||||
−0.845124 | + | 0.534570i | \(0.820474\pi\) | |||||||
\(390\) | 0.171074 | 0.00866268 | ||||||||
\(391\) | 1.33226 | 0.0673754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.7422 | −0.945417 | ||||||||
\(394\) | −0.856934 | −0.0431717 | ||||||||
\(395\) | −5.23015 | −0.263157 | ||||||||
\(396\) | −5.81499 | −0.292214 | ||||||||
\(397\) | 20.1880 | 1.01321 | 0.506605 | − | 0.862179i | \(-0.330900\pi\) | ||||
0.506605 | + | 0.862179i | \(0.330900\pi\) | |||||||
\(398\) | −0.557477 | −0.0279438 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.591869 | −0.0295935 | ||||||||
\(401\) | −4.21487 | −0.210481 | −0.105240 | − | 0.994447i | \(-0.533561\pi\) | ||||
−0.105240 | + | 0.994447i | \(0.533561\pi\) | |||||||
\(402\) | 0.476964 | 0.0237888 | ||||||||
\(403\) | −5.95780 | −0.296779 | ||||||||
\(404\) | −39.8436 | −1.98229 | ||||||||
\(405\) | 2.20243 | 0.109439 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2096 | 0.605210 | ||||||||
\(408\) | −0.122214 | −0.00605048 | ||||||||
\(409\) | −7.44627 | −0.368195 | −0.184097 | − | 0.982908i | \(-0.558936\pi\) | ||||
−0.184097 | + | 0.982908i | \(0.558936\pi\) | |||||||
\(410\) | −0.0744146 | −0.00367507 | ||||||||
\(411\) | −13.5905 | −0.670370 | ||||||||
\(412\) | −29.2604 | −1.44156 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.262688 | 0.0129104 | ||||||||
\(415\) | 21.5574 | 1.05821 | ||||||||
\(416\) | 0.928358 | 0.0455165 | ||||||||
\(417\) | 15.7292 | 0.770262 | ||||||||
\(418\) | −0.0282591 | −0.00138220 | ||||||||
\(419\) | 12.2817 | 0.600000 | 0.300000 | − | 0.953939i | \(-0.403013\pi\) | ||||
0.300000 | + | 0.953939i | \(0.403013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9884 | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271544\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271544\pi\) | |||||||
\(422\) | 1.22042 | 0.0594093 | ||||||||
\(423\) | 9.46321 | 0.460117 | ||||||||
\(424\) | −3.85738 | −0.187331 | ||||||||
\(425\) | −0.0588223 | −0.00285330 | ||||||||
\(426\) | −1.09387 | −0.0529981 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.0490 | 0.485739 | ||||||||
\(429\) | 2.91629 | 0.140800 | ||||||||
\(430\) | −1.15464 | −0.0556816 | ||||||||
\(431\) | −20.3167 | −0.978621 | −0.489310 | − | 0.872110i | \(-0.662752\pi\) | ||||
−0.489310 | + | 0.872110i | \(0.662752\pi\) | |||||||
\(432\) | 3.96384 | 0.190710 | ||||||||
\(433\) | 9.02891 | 0.433902 | 0.216951 | − | 0.976183i | \(-0.430389\pi\) | ||||
0.216951 | + | 0.976183i | \(0.430389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41445 | −0.0678176 | ||||||||
\(436\) | 0.244624 | 0.0117154 | ||||||||
\(437\) | −0.421893 | −0.0201819 | ||||||||
\(438\) | 0.586678 | 0.0280326 | ||||||||
\(439\) | −10.0349 | −0.478940 | −0.239470 | − | 0.970904i | \(-0.576974\pi\) | ||||
−0.239470 | + | 0.970904i | \(0.576974\pi\) | |||||||
\(440\) | −1.99260 | −0.0949935 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0305996 | 0.00145547 | ||||||||
\(443\) | −33.6409 | −1.59833 | −0.799165 | − | 0.601112i | \(-0.794725\pi\) | ||||
−0.799165 | + | 0.601112i | \(0.794725\pi\) | |||||||
\(444\) | −8.34815 | −0.396185 | ||||||||
\(445\) | 14.1035 | 0.668571 | ||||||||
\(446\) | −0.482278 | −0.0228365 | ||||||||
\(447\) | 3.34809 | 0.158359 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.21577 | 0.0573759 | 0.0286879 | − | 0.999588i | \(-0.490867\pi\) | ||||
0.0286879 | + | 0.999588i | \(0.490867\pi\) | |||||||
\(450\) | −0.0115983 | −0.000546748 0 | ||||||||
\(451\) | −1.26854 | −0.0597332 | ||||||||
\(452\) | 8.29766 | 0.390289 | ||||||||
\(453\) | −20.4476 | −0.960714 | ||||||||
\(454\) | −1.83997 | −0.0863540 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0387019 | 0.00181238 | ||||||||
\(457\) | −28.4334 | −1.33006 | −0.665029 | − | 0.746817i | \(-0.731581\pi\) | ||||
−0.665029 | + | 0.746817i | \(0.731581\pi\) | |||||||
\(458\) | 0.702361 | 0.0328192 | ||||||||
\(459\) | 0.393942 | 0.0183876 | ||||||||
\(460\) | −14.8517 | −0.692465 | ||||||||
\(461\) | −30.9864 | −1.44318 | −0.721590 | − | 0.692320i | \(-0.756588\pi\) | ||||
−0.721590 | + | 0.692320i | \(0.756588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7992 | −0.687779 | −0.343889 | − | 0.939010i | \(-0.611745\pi\) | ||||
−0.343889 | + | 0.939010i | \(0.611745\pi\) | |||||||
\(464\) | −2.54567 | −0.118180 | ||||||||
\(465\) | −13.1216 | −0.608501 | ||||||||
\(466\) | 0.415135 | 0.0192308 | ||||||||
\(467\) | 1.82996 | 0.0846804 | 0.0423402 | − | 0.999103i | \(-0.486519\pi\) | ||||
0.0423402 | + | 0.999103i | \(0.486519\pi\) | |||||||
\(468\) | −1.99397 | −0.0921711 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.61891 | 0.0746748 | ||||||||
\(471\) | −10.2014 | −0.470054 | ||||||||
\(472\) | −2.27573 | −0.104749 | ||||||||
\(473\) | −19.6830 | −0.905027 | ||||||||
\(474\) | −0.184457 | −0.00847241 | ||||||||
\(475\) | 0.0186275 | 0.000854689 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.4338 | 0.569306 | ||||||||
\(478\) | −2.11703 | −0.0968306 | ||||||||
\(479\) | −9.34659 | −0.427057 | −0.213528 | − | 0.976937i | \(-0.568496\pi\) | ||||
−0.213528 | + | 0.976937i | \(0.568496\pi\) | |||||||
\(480\) | 2.04464 | 0.0933246 | ||||||||
\(481\) | 4.18670 | 0.190897 | ||||||||
\(482\) | 1.21765 | 0.0554623 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.97544 | 0.226156 | ||||||||
\(485\) | −32.8372 | −1.49106 | ||||||||
\(486\) | 0.0776754 | 0.00352343 | ||||||||
\(487\) | 23.3739 | 1.05917 | 0.529587 | − | 0.848256i | \(-0.322347\pi\) | ||||
0.529587 | + | 0.848256i | \(0.322347\pi\) | |||||||
\(488\) | −0.742679 | −0.0336195 | ||||||||
\(489\) | 15.5835 | 0.704712 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.4726 | −0.969044 | −0.484522 | − | 0.874779i | \(-0.661007\pi\) | ||||
−0.484522 | + | 0.874779i | \(0.661007\pi\) | |||||||
\(492\) | 0.867344 | 0.0391029 | ||||||||
\(493\) | −0.252998 | −0.0113945 | ||||||||
\(494\) | −0.00969009 | −0.000435978 0 | ||||||||
\(495\) | 6.42292 | 0.288689 | ||||||||
\(496\) | −23.6157 | −1.06038 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.760290 | 0.0340694 | ||||||||
\(499\) | −22.1915 | −0.993427 | −0.496714 | − | 0.867915i | \(-0.665460\pi\) | ||||
−0.496714 | + | 0.867915i | \(0.665460\pi\) | |||||||
\(500\) | 22.6136 | 1.01131 | ||||||||
\(501\) | −1.53310 | −0.0684939 | ||||||||
\(502\) | 1.41539 | 0.0631718 | ||||||||
\(503\) | −17.3231 | −0.772399 | −0.386200 | − | 0.922415i | \(-0.626212\pi\) | ||||
−0.386200 | + | 0.922415i | \(0.626212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.0090 | 1.95838 | ||||||||
\(506\) | 0.766076 | 0.0340562 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −29.8520 | −1.32447 | ||||||||
\(509\) | 26.8613 | 1.19061 | 0.595303 | − | 0.803502i | \(-0.297032\pi\) | ||||
0.595303 | + | 0.803502i | \(0.297032\pi\) | |||||||
\(510\) | 0.0673933 | 0.00298423 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.13928 | 0.271321 | ||||||||
\(513\) | −0.124751 | −0.00550790 | ||||||||
\(514\) | −1.16990 | −0.0516019 | ||||||||
\(515\) | 32.3195 | 1.42417 | ||||||||
\(516\) | 13.4580 | 0.592454 | ||||||||
\(517\) | 27.5975 | 1.21374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9844 | 0.613849 | ||||||||
\(520\) | −0.683265 | −0.0299632 | ||||||||
\(521\) | 10.2029 | 0.446998 | 0.223499 | − | 0.974704i | \(-0.428252\pi\) | ||||
0.223499 | + | 0.974704i | \(0.428252\pi\) | |||||||
\(522\) | −0.0498849 | −0.00218340 | ||||||||
\(523\) | −11.9147 | −0.520992 | −0.260496 | − | 0.965475i | \(-0.583886\pi\) | ||||
−0.260496 | + | 0.965475i | \(0.583886\pi\) | |||||||
\(524\) | 37.3712 | 1.63257 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.15872 | −0.0941248 | ||||||||
\(527\) | −2.34703 | −0.102238 | ||||||||
\(528\) | 11.5597 | 0.503071 | ||||||||
\(529\) | −11.5629 | −0.502736 | ||||||||
\(530\) | 2.12711 | 0.0923957 | ||||||||
\(531\) | 7.33555 | 0.318336 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.434984 | −0.0188412 | ||||||||
\(534\) | 0.497404 | 0.0215248 | ||||||||
\(535\) | −11.0996 | −0.479879 | ||||||||
\(536\) | −1.90498 | −0.0822825 | ||||||||
\(537\) | −21.9304 | −0.946366 | ||||||||
\(538\) | 0.622031 | 0.0268177 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.39156 | −0.188983 | ||||||||
\(541\) | 19.9687 | 0.858520 | 0.429260 | − | 0.903181i | \(-0.358774\pi\) | ||||
0.429260 | + | 0.903181i | \(0.358774\pi\) | |||||||
\(542\) | −1.57405 | −0.0676114 | ||||||||
\(543\) | −0.955265 | −0.0409943 | ||||||||
\(544\) | 0.365719 | 0.0156801 | ||||||||
\(545\) | −0.270199 | −0.0115740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7640 | −0.716778 | −0.358389 | − | 0.933572i | \(-0.616674\pi\) | ||||
−0.358389 | + | 0.933572i | \(0.616674\pi\) | |||||||
\(548\) | 27.0990 | 1.15761 | ||||||||
\(549\) | 2.39394 | 0.102171 | ||||||||
\(550\) | −0.0338239 | −0.00144226 | ||||||||
\(551\) | 0.0801180 | 0.00341314 | ||||||||
\(552\) | −1.04917 | −0.0446556 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.28629 | −0.0971351 | ||||||||
\(555\) | 9.22091 | 0.391406 | ||||||||
\(556\) | −31.3635 | −1.33011 | ||||||||
\(557\) | 23.3797 | 0.990628 | 0.495314 | − | 0.868714i | \(-0.335053\pi\) | ||||
0.495314 | + | 0.868714i | \(0.335053\pi\) | |||||||
\(558\) | −0.462775 | −0.0195908 | ||||||||
\(559\) | −6.74934 | −0.285467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.14885 | 0.0485044 | ||||||||
\(562\) | −0.292630 | −0.0123439 | ||||||||
\(563\) | −42.0038 | −1.77025 | −0.885124 | − | 0.465355i | \(-0.845927\pi\) | ||||
−0.885124 | + | 0.465355i | \(0.845927\pi\) | |||||||
\(564\) | −18.8693 | −0.794542 | ||||||||
\(565\) | −9.16514 | −0.385580 | ||||||||
\(566\) | −1.74309 | −0.0732675 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.36887 | 0.183314 | ||||||||
\(569\) | 12.5796 | 0.527366 | 0.263683 | − | 0.964609i | \(-0.415063\pi\) | ||||
0.263683 | + | 0.964609i | \(0.415063\pi\) | |||||||
\(570\) | −0.0213417 | −0.000893906 0 | ||||||||
\(571\) | −8.79876 | −0.368217 | −0.184108 | − | 0.982906i | \(-0.558940\pi\) | ||||
−0.184108 | + | 0.982906i | \(0.558940\pi\) | |||||||
\(572\) | −5.81499 | −0.243137 | ||||||||
\(573\) | 19.6834 | 0.822287 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.504972 | −0.0210588 | ||||||||
\(576\) | −7.85556 | −0.327315 | ||||||||
\(577\) | −1.41370 | −0.0588531 | −0.0294266 | − | 0.999567i | \(-0.509368\pi\) | ||||
−0.0294266 | + | 0.999567i | \(0.509368\pi\) | |||||||
\(578\) | −1.30843 | −0.0544234 | ||||||||
\(579\) | 15.0951 | 0.627329 | ||||||||
\(580\) | 2.82036 | 0.117109 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.15811 | −0.0480051 | ||||||||
\(583\) | 36.2607 | 1.50176 | ||||||||
\(584\) | −2.34317 | −0.0969612 | ||||||||
\(585\) | 2.20243 | 0.0910591 | ||||||||
\(586\) | −0.631994 | −0.0261074 | ||||||||
\(587\) | 24.3046 | 1.00316 | 0.501580 | − | 0.865111i | \(-0.332752\pi\) | ||||
0.501580 | + | 0.865111i | \(0.332752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.743243 | 0.0306248 | ||||||||
\(590\) | 1.25492 | 0.0516644 | ||||||||
\(591\) | −11.0323 | −0.453806 | ||||||||
\(592\) | 16.5954 | 0.682067 | ||||||||
\(593\) | 26.7063 | 1.09670 | 0.548348 | − | 0.836250i | \(-0.315257\pi\) | ||||
0.548348 | + | 0.836250i | \(0.315257\pi\) | |||||||
\(594\) | 0.226524 | 0.00929439 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.67597 | −0.273459 | ||||||||
\(597\) | −7.17701 | −0.293736 | ||||||||
\(598\) | 0.262688 | 0.0107421 | ||||||||
\(599\) | −33.6537 | −1.37505 | −0.687526 | − | 0.726160i | \(-0.741303\pi\) | ||||
−0.687526 | + | 0.726160i | \(0.741303\pi\) | |||||||
\(600\) | 0.0463231 | 0.00189113 | ||||||||
\(601\) | 12.5737 | 0.512890 | 0.256445 | − | 0.966559i | \(-0.417449\pi\) | ||||
0.256445 | + | 0.966559i | \(0.417449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.14047 | 0.250059 | ||||||||
\(604\) | 40.7719 | 1.65899 | ||||||||
\(605\) | −5.49560 | −0.223428 | ||||||||
\(606\) | 1.55211 | 0.0630503 | ||||||||
\(607\) | −21.4417 | −0.870292 | −0.435146 | − | 0.900360i | \(-0.643303\pi\) | ||||
−0.435146 | + | 0.900360i | \(0.643303\pi\) | |||||||
\(608\) | −0.115814 | −0.00469687 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.409542 | 0.0165819 | ||||||||
\(611\) | 9.46321 | 0.382840 | ||||||||
\(612\) | −0.785507 | −0.0317522 | ||||||||
\(613\) | 30.7261 | 1.24102 | 0.620509 | − | 0.784200i | \(-0.286926\pi\) | ||||
0.620509 | + | 0.784200i | \(0.286926\pi\) | |||||||
\(614\) | −1.46999 | −0.0593238 | ||||||||
\(615\) | −0.958020 | −0.0386311 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.216739 | 0.00872559 | 0.00436279 | − | 0.999990i | \(-0.498611\pi\) | ||||
0.00436279 | + | 0.999990i | \(0.498611\pi\) | |||||||
\(618\) | 1.13985 | 0.0458513 | ||||||||
\(619\) | −30.4980 | −1.22582 | −0.612909 | − | 0.790153i | \(-0.710001\pi\) | ||||
−0.612909 | + | 0.790153i | \(0.710001\pi\) | |||||||
\(620\) | 26.1641 | 1.05077 | ||||||||
\(621\) | 3.38187 | 0.135710 | ||||||||
\(622\) | −0.902505 | −0.0361871 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.96384 | 0.158680 | ||||||||
\(625\) | −24.2311 | −0.969245 | ||||||||
\(626\) | 0.908983 | 0.0363303 | ||||||||
\(627\) | −0.363811 | −0.0145292 | ||||||||
\(628\) | 20.3412 | 0.811702 | ||||||||
\(629\) | 1.64932 | 0.0657626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0505 | −0.559343 | −0.279671 | − | 0.960096i | \(-0.590226\pi\) | ||||
−0.279671 | + | 0.960096i | \(0.590226\pi\) | |||||||
\(632\) | 0.736717 | 0.0293050 | ||||||||
\(633\) | 15.7119 | 0.624490 | ||||||||
\(634\) | −2.56382 | −0.101822 | ||||||||
\(635\) | 32.9729 | 1.30849 | ||||||||
\(636\) | −24.7926 | −0.983092 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.145479 | −0.00575956 | ||||||||
\(639\) | −14.0826 | −0.557097 | ||||||||
\(640\) | −5.43317 | −0.214765 | ||||||||
\(641\) | −18.1731 | −0.717796 | −0.358898 | − | 0.933377i | \(-0.616847\pi\) | ||||
−0.358898 | + | 0.933377i | \(0.616847\pi\) | |||||||
\(642\) | −0.391463 | −0.0154498 | ||||||||
\(643\) | 7.27895 | 0.287054 | 0.143527 | − | 0.989646i | \(-0.454156\pi\) | ||||
0.143527 | + | 0.989646i | \(0.454156\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.8649 | −0.585306 | ||||||||
\(646\) | −0.00381733 | −0.000150191 0 | ||||||||
\(647\) | −17.7797 | −0.698992 | −0.349496 | − | 0.936938i | \(-0.613647\pi\) | ||||
−0.349496 | + | 0.936938i | \(0.613647\pi\) | |||||||
\(648\) | −0.310233 | −0.0121871 | ||||||||
\(649\) | 21.3926 | 0.839733 | ||||||||
\(650\) | −0.0115983 | −0.000454922 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.0731 | −1.21692 | ||||||||
\(653\) | 8.13253 | 0.318251 | 0.159125 | − | 0.987258i | \(-0.449133\pi\) | ||||
0.159125 | + | 0.987258i | \(0.449133\pi\) | |||||||
\(654\) | −0.00952939 | −0.000372629 0 | ||||||||
\(655\) | −41.2782 | −1.61287 | ||||||||
\(656\) | −1.72421 | −0.0673189 | ||||||||
\(657\) | 7.55295 | 0.294669 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0958 | 0.393278 | 0.196639 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196639 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(660\) | −12.8071 | −0.498515 | ||||||||
\(661\) | −24.3455 | −0.946928 | −0.473464 | − | 0.880813i | \(-0.656997\pi\) | ||||
−0.473464 | + | 0.880813i | \(0.656997\pi\) | |||||||
\(662\) | 1.14762 | 0.0446036 | ||||||||
\(663\) | 0.393942 | 0.0152994 | ||||||||
\(664\) | −3.03657 | −0.117842 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.325204 | 0.0126014 | ||||||||
\(667\) | −2.17192 | −0.0840970 | ||||||||
\(668\) | 3.05695 | 0.118277 | ||||||||
\(669\) | −6.20889 | −0.240050 | ||||||||
\(670\) | 1.05048 | 0.0405835 | ||||||||
\(671\) | 6.98143 | 0.269515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4811 | −1.52189 | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(674\) | −1.01532 | −0.0391087 | ||||||||
\(675\) | −0.149317 | −0.00574722 | ||||||||
\(676\) | −1.99397 | −0.0766910 | ||||||||
\(677\) | −17.9830 | −0.691144 | −0.345572 | − | 0.938392i | \(-0.612315\pi\) | ||||
−0.345572 | + | 0.938392i | \(0.612315\pi\) | |||||||
\(678\) | −0.323237 | −0.0124138 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.269167 | −0.0103221 | ||||||||
\(681\) | −23.6879 | −0.907723 | ||||||||
\(682\) | −1.34959 | −0.0516783 | ||||||||
\(683\) | 15.3265 | 0.586452 | 0.293226 | − | 0.956043i | \(-0.405271\pi\) | ||||
0.293226 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(684\) | 0.248750 | 0.00951118 | ||||||||
\(685\) | −29.9321 | −1.14365 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.04226 | 0.344984 | ||||||||
\(688\) | −26.7533 | −1.01996 | ||||||||
\(689\) | 12.4338 | 0.473691 | ||||||||
\(690\) | 0.578552 | 0.0220251 | ||||||||
\(691\) | 25.2599 | 0.960931 | 0.480466 | − | 0.877014i | \(-0.340468\pi\) | ||||
0.480466 | + | 0.877014i | \(0.340468\pi\) | |||||||
\(692\) | −27.8845 | −1.06001 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.495530 | 0.0188101 | ||||||||
\(695\) | 34.6424 | 1.31406 | ||||||||
\(696\) | 0.199239 | 0.00755212 | ||||||||
\(697\) | −0.171358 | −0.00649066 | ||||||||
\(698\) | 0.802283 | 0.0303669 | ||||||||
\(699\) | 5.34449 | 0.202147 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.6169 | 1.42077 | 0.710385 | − | 0.703813i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703813i | \(0.248521\pi\) | |||||||
\(702\) | 0.0776754 | 0.00293167 | ||||||||
\(703\) | −0.522296 | −0.0196988 | ||||||||
\(704\) | −22.9091 | −0.863419 | ||||||||
\(705\) | 20.8420 | 0.784956 | ||||||||
\(706\) | 2.34205 | 0.0881441 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.6268 | −0.549710 | ||||||||
\(709\) | 10.7266 | 0.402847 | 0.201423 | − | 0.979504i | \(-0.435443\pi\) | ||||
0.201423 | + | 0.979504i | \(0.435443\pi\) | |||||||
\(710\) | −2.40916 | −0.0904143 | ||||||||
\(711\) | −2.37472 | −0.0890590 | ||||||||
\(712\) | −1.98662 | −0.0744516 | ||||||||
\(713\) | −20.1485 | −0.754569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.42292 | 0.240203 | ||||||||
\(716\) | 43.7285 | 1.63421 | ||||||||
\(717\) | −27.2548 | −1.01785 | ||||||||
\(718\) | −2.26635 | −0.0845792 | ||||||||
\(719\) | −12.3407 | −0.460230 | −0.230115 | − | 0.973163i | \(-0.573910\pi\) | ||||
−0.230115 | + | 0.973163i | \(0.573910\pi\) | |||||||
\(720\) | 8.73006 | 0.325350 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.47462 | −0.0548798 | ||||||||
\(723\) | 15.6761 | 0.583001 | ||||||||
\(724\) | 1.90477 | 0.0707901 | ||||||||
\(725\) | 0.0958949 | 0.00356145 | ||||||||
\(726\) | −0.193819 | −0.00719330 | ||||||||
\(727\) | −46.5464 | −1.72631 | −0.863155 | − | 0.504939i | \(-0.831515\pi\) | ||||
−0.863155 | + | 0.504939i | \(0.831515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.29212 | 0.0478233 | ||||||||
\(731\) | −2.65885 | −0.0983410 | ||||||||
\(732\) | −4.77344 | −0.176431 | ||||||||
\(733\) | −37.8843 | −1.39929 | −0.699644 | − | 0.714492i | \(-0.746658\pi\) | ||||
−0.699644 | + | 0.714492i | \(0.746658\pi\) | |||||||
\(734\) | 0.348321 | 0.0128568 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.13959 | 0.115727 | ||||||||
\(737\) | 17.9074 | 0.659628 | ||||||||
\(738\) | −0.0337875 | −0.00124374 | ||||||||
\(739\) | 18.9782 | 0.698126 | 0.349063 | − | 0.937099i | \(-0.386500\pi\) | ||||
0.349063 | + | 0.937099i | \(0.386500\pi\) | |||||||
\(740\) | −18.3862 | −0.675889 | ||||||||
\(741\) | −0.124751 | −0.00458285 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2127 | 0.741534 | 0.370767 | − | 0.928726i | \(-0.379095\pi\) | ||||
0.370767 | + | 0.928726i | \(0.379095\pi\) | |||||||
\(744\) | 1.84831 | 0.0677622 | ||||||||
\(745\) | 7.37392 | 0.270159 | ||||||||
\(746\) | 1.86336 | 0.0682226 | ||||||||
\(747\) | 9.78804 | 0.358126 | ||||||||
\(748\) | −2.29077 | −0.0837587 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.880916 | −0.0321665 | ||||||||
\(751\) | −47.1535 | −1.72066 | −0.860328 | − | 0.509742i | \(-0.829741\pi\) | ||||
−0.860328 | + | 0.509742i | \(0.829741\pi\) | |||||||
\(752\) | 37.5106 | 1.36787 | ||||||||
\(753\) | 18.2218 | 0.664040 | ||||||||
\(754\) | −0.0498849 | −0.00181670 | ||||||||
\(755\) | −45.0344 | −1.63897 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.7288 | −0.535327 | −0.267664 | − | 0.963512i | \(-0.586252\pi\) | ||||
−0.267664 | + | 0.963512i | \(0.586252\pi\) | |||||||
\(758\) | 1.57082 | 0.0570546 | ||||||||
\(759\) | 9.86253 | 0.357987 | ||||||||
\(760\) | 0.0852381 | 0.00309191 | ||||||||
\(761\) | −41.7494 | −1.51341 | −0.756706 | − | 0.653755i | \(-0.773193\pi\) | ||||
−0.756706 | + | 0.653755i | \(0.773193\pi\) | |||||||
\(762\) | 1.16289 | 0.0421270 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −39.2481 | −1.41995 | ||||||||
\(765\) | 0.867628 | 0.0313691 | ||||||||
\(766\) | 1.79289 | 0.0647798 | ||||||||
\(767\) | 7.33555 | 0.264871 | ||||||||
\(768\) | 15.5195 | 0.560012 | ||||||||
\(769\) | 34.0121 | 1.22651 | 0.613254 | − | 0.789886i | \(-0.289860\pi\) | ||||
0.613254 | + | 0.789886i | \(0.289860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0614 | −0.542422 | ||||||||
\(772\) | −30.0990 | −1.08329 | ||||||||
\(773\) | 17.0025 | 0.611537 | 0.305769 | − | 0.952106i | \(-0.401087\pi\) | ||||
0.305769 | + | 0.952106i | \(0.401087\pi\) | |||||||
\(774\) | −0.524258 | −0.0188441 | ||||||||
\(775\) | 0.889603 | 0.0319555 | ||||||||
\(776\) | 4.62544 | 0.166044 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.58946 | −0.0928366 | ||||||||
\(779\) | 0.0542648 | 0.00194424 | ||||||||
\(780\) | −4.39156 | −0.157243 | ||||||||
\(781\) | −41.0688 | −1.46956 | ||||||||
\(782\) | 0.103484 | 0.00370058 | ||||||||
\(783\) | −0.642223 | −0.0229512 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.4678 | −0.801909 | ||||||||
\(786\) | −1.45580 | −0.0519268 | ||||||||
\(787\) | 31.1294 | 1.10964 | 0.554822 | − | 0.831969i | \(-0.312786\pi\) | ||||
0.554822 | + | 0.831969i | \(0.312786\pi\) | |||||||
\(788\) | 21.9979 | 0.783644 | ||||||||
\(789\) | −27.7916 | −0.989407 | ||||||||
\(790\) | −0.406254 | −0.0144539 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.904729 | −0.0321482 | ||||||||
\(793\) | 2.39394 | 0.0850114 | ||||||||
\(794\) | 1.56811 | 0.0556503 | ||||||||
\(795\) | 27.3846 | 0.971231 | ||||||||
\(796\) | 14.3107 | 0.507230 | ||||||||
\(797\) | −10.5797 | −0.374752 | −0.187376 | − | 0.982288i | \(-0.559998\pi\) | ||||
−0.187376 | + | 0.982288i | \(0.559998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.72795 | 0.131885 | ||||||||
\(800\) | −0.138620 | −0.00490095 | ||||||||
\(801\) | 6.40363 | 0.226261 | ||||||||
\(802\) | −0.327392 | −0.0115606 | ||||||||
\(803\) | 22.0266 | 0.777302 | ||||||||
\(804\) | −12.2439 | −0.431809 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.462775 | −0.0163005 | ||||||||
\(807\) | 8.00809 | 0.281898 | ||||||||
\(808\) | −6.19909 | −0.218083 | ||||||||
\(809\) | −19.0261 | −0.668924 | −0.334462 | − | 0.942409i | \(-0.608555\pi\) | ||||
−0.334462 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(810\) | 0.171074 | 0.00601094 | ||||||||
\(811\) | 24.9894 | 0.877497 | 0.438748 | − | 0.898610i | \(-0.355422\pi\) | ||||
0.438748 | + | 0.898610i | \(0.355422\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.2645 | −0.710707 | ||||||||
\(814\) | 0.948389 | 0.0332410 | ||||||||
\(815\) | 34.3216 | 1.20223 | ||||||||
\(816\) | 1.56152 | 0.0546641 | ||||||||
\(817\) | 0.841988 | 0.0294574 | ||||||||
\(818\) | −0.578392 | −0.0202230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91026 | 0.0667092 | ||||||||
\(821\) | 45.7000 | 1.59494 | 0.797471 | − | 0.603358i | \(-0.206171\pi\) | ||||
0.797471 | + | 0.603358i | \(0.206171\pi\) | |||||||
\(822\) | −1.05565 | −0.0368199 | ||||||||
\(823\) | −10.3799 | −0.361822 | −0.180911 | − | 0.983499i | \(-0.557905\pi\) | ||||
−0.180911 | + | 0.983499i | \(0.557905\pi\) | |||||||
\(824\) | −4.55250 | −0.158594 | ||||||||
\(825\) | −0.435453 | −0.0151605 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.56239 | −0.332517 | −0.166258 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166258 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(828\) | −6.74335 | −0.234347 | ||||||||
\(829\) | 17.8736 | 0.620777 | 0.310388 | − | 0.950610i | \(-0.399541\pi\) | ||||
0.310388 | + | 0.950610i | \(0.399541\pi\) | |||||||
\(830\) | 1.67448 | 0.0581221 | ||||||||
\(831\) | −29.4339 | −1.02105 | ||||||||
\(832\) | −7.85556 | −0.272343 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.22177 | 0.0423064 | ||||||||
\(835\) | −3.37654 | −0.116850 | ||||||||
\(836\) | 0.725426 | 0.0250894 | ||||||||
\(837\) | −5.95780 | −0.205932 | ||||||||
\(838\) | 0.953985 | 0.0329549 | ||||||||
\(839\) | −33.6620 | −1.16214 | −0.581071 | − | 0.813853i | \(-0.697366\pi\) | ||||
−0.581071 | + | 0.813853i | \(0.697366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5876 | −0.985778 | ||||||||
\(842\) | 2.09633 | 0.0722444 | ||||||||
\(843\) | −3.76735 | −0.129754 | ||||||||
\(844\) | −31.3289 | −1.07839 | ||||||||
\(845\) | 2.20243 | 0.0757658 | ||||||||
\(846\) | 0.735058 | 0.0252718 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 49.2857 | 1.69248 | ||||||||
\(849\) | −22.4407 | −0.770163 | ||||||||
\(850\) | −0.00456904 | −0.000156717 0 | ||||||||
\(851\) | 14.1589 | 0.485361 | ||||||||
\(852\) | 28.0801 | 0.962010 | ||||||||
\(853\) | 45.2796 | 1.55035 | 0.775173 | − | 0.631749i | \(-0.217663\pi\) | ||||
0.775173 | + | 0.631749i | \(0.217663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.274755 | −0.00939643 | ||||||||
\(856\) | 1.56349 | 0.0534389 | ||||||||
\(857\) | 44.5722 | 1.52256 | 0.761278 | − | 0.648425i | \(-0.224572\pi\) | ||||
0.761278 | + | 0.648425i | \(0.224572\pi\) | |||||||
\(858\) | 0.226524 | 0.00773340 | ||||||||
\(859\) | 39.9009 | 1.36140 | 0.680701 | − | 0.732561i | \(-0.261675\pi\) | ||||
0.680701 | + | 0.732561i | \(0.261675\pi\) | |||||||
\(860\) | 29.6402 | 1.01072 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.57811 | −0.0537505 | ||||||||
\(863\) | −3.11045 | −0.105881 | −0.0529406 | − | 0.998598i | \(-0.516859\pi\) | ||||
−0.0529406 | + | 0.998598i | \(0.516859\pi\) | |||||||
\(864\) | 0.928358 | 0.0315834 | ||||||||
\(865\) | 30.7997 | 1.04722 | ||||||||
\(866\) | 0.701324 | 0.0238320 | ||||||||
\(867\) | −16.8448 | −0.572080 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.92538 | −0.234927 | ||||||||
\(870\) | −0.109868 | −0.00372487 | ||||||||
\(871\) | 6.14047 | 0.208062 | ||||||||
\(872\) | 0.0380601 | 0.00128888 | ||||||||
\(873\) | −14.9096 | −0.504613 | ||||||||
\(874\) | −0.0327707 | −0.00110848 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.0603 | −0.508841 | ||||||||
\(877\) | −4.64274 | −0.156774 | −0.0783872 | − | 0.996923i | \(-0.524977\pi\) | ||||
−0.0783872 | + | 0.996923i | \(0.524977\pi\) | |||||||
\(878\) | −0.779466 | −0.0263057 | ||||||||
\(879\) | −8.13635 | −0.274432 | ||||||||
\(880\) | 25.4594 | 0.858236 | ||||||||
\(881\) | 42.8058 | 1.44216 | 0.721082 | − | 0.692850i | \(-0.243645\pi\) | ||||
0.721082 | + | 0.692850i | \(0.243645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.60368 | −0.323190 | −0.161595 | − | 0.986857i | \(-0.551664\pi\) | ||||
−0.161595 | + | 0.986857i | \(0.551664\pi\) | |||||||
\(884\) | −0.785507 | −0.0264194 | ||||||||
\(885\) | 16.1560 | 0.543078 | ||||||||
\(886\) | −2.61307 | −0.0877879 | ||||||||
\(887\) | 10.4937 | 0.352346 | 0.176173 | − | 0.984359i | \(-0.443628\pi\) | ||||
0.176173 | + | 0.984359i | \(0.443628\pi\) | |||||||
\(888\) | −1.29885 | −0.0435866 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.09550 | 0.0367211 | ||||||||
\(891\) | 2.91629 | 0.0976994 | ||||||||
\(892\) | 12.3803 | 0.414524 | ||||||||
\(893\) | −1.18055 | −0.0395055 | ||||||||
\(894\) | 0.260064 | 0.00869784 | ||||||||
\(895\) | −48.3001 | −1.61449 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.38187 | 0.112918 | ||||||||
\(898\) | 0.0944356 | 0.00315136 | ||||||||
\(899\) | 3.82624 | 0.127612 | ||||||||
\(900\) | 0.297734 | 0.00992446 | ||||||||
\(901\) | 4.89820 | 0.163183 | ||||||||
\(902\) | −0.0985343 | −0.00328083 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.29100 | 0.0429380 | ||||||||
\(905\) | −2.10390 | −0.0699360 | ||||||||
\(906\) | −1.58828 | −0.0527670 | ||||||||
\(907\) | 54.3480 | 1.80460 | 0.902298 | − | 0.431113i | \(-0.141879\pi\) | ||||
0.902298 | + | 0.431113i | \(0.141879\pi\) | |||||||
\(908\) | 47.2329 | 1.56748 | ||||||||
\(909\) | 19.9821 | 0.662763 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9548 | 0.992445 | 0.496223 | − | 0.868195i | \(-0.334720\pi\) | ||||
0.496223 | + | 0.868195i | \(0.334720\pi\) | |||||||
\(912\) | −0.494493 | −0.0163743 | ||||||||
\(913\) | 28.5448 | 0.944695 | ||||||||
\(914\) | −2.20858 | −0.0730532 | ||||||||
\(915\) | 5.27248 | 0.174303 | ||||||||
\(916\) | −18.0300 | −0.595727 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0305996 | 0.00100994 | ||||||||
\(919\) | 30.8093 | 1.01631 | 0.508153 | − | 0.861267i | \(-0.330329\pi\) | ||||
0.508153 | + | 0.861267i | \(0.330329\pi\) | |||||||
\(920\) | −2.31072 | −0.0761821 | ||||||||
\(921\) | −18.9247 | −0.623591 | ||||||||
\(922\) | −2.40688 | −0.0792664 | ||||||||
\(923\) | −14.0826 | −0.463533 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.625147 | −0.0205547 | ||||||||
\(926\) | −1.14954 | −0.0377761 | ||||||||
\(927\) | 14.6745 | 0.481973 | ||||||||
\(928\) | −0.596213 | −0.0195716 | ||||||||
\(929\) | 19.8880 | 0.652503 | 0.326252 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326252 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(930\) | −1.01923 | −0.0334218 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.6567 | −0.349073 | ||||||||
\(933\) | −11.6189 | −0.380387 | ||||||||
\(934\) | 0.142143 | 0.00465105 | ||||||||
\(935\) | 2.53025 | 0.0827482 | ||||||||
\(936\) | −0.310233 | −0.0101403 | ||||||||
\(937\) | 50.6240 | 1.65382 | 0.826908 | − | 0.562338i | \(-0.190098\pi\) | ||||
0.826908 | + | 0.562338i | \(0.190098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.7023 | 0.381891 | ||||||||
\(940\) | −41.5583 | −1.35548 | ||||||||
\(941\) | −21.1170 | −0.688394 | −0.344197 | − | 0.938897i | \(-0.611849\pi\) | ||||
−0.344197 | + | 0.938897i | \(0.611849\pi\) | |||||||
\(942\) | −0.792395 | −0.0258176 | ||||||||
\(943\) | −1.47106 | −0.0479044 | ||||||||
\(944\) | 29.0769 | 0.946373 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.52889 | −0.0497084 | ||||||||
\(947\) | 33.0962 | 1.07548 | 0.537741 | − | 0.843110i | \(-0.319278\pi\) | ||||
0.537741 | + | 0.843110i | \(0.319278\pi\) | |||||||
\(948\) | 4.73512 | 0.153789 | ||||||||
\(949\) | 7.55295 | 0.245179 | ||||||||
\(950\) | 0.00144690 | 4.69436e−5 0 | ||||||||
\(951\) | −33.0069 | −1.07032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.06989 | −0.0994436 | −0.0497218 | − | 0.998763i | \(-0.515833\pi\) | ||||
−0.0497218 | + | 0.998763i | \(0.515833\pi\) | |||||||
\(954\) | 0.965802 | 0.0312690 | ||||||||
\(955\) | 43.3513 | 1.40282 | ||||||||
\(956\) | 54.3452 | 1.75765 | ||||||||
\(957\) | −1.87291 | −0.0605425 | ||||||||
\(958\) | −0.726000 | −0.0234560 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −17.3013 | −0.558397 | ||||||||
\(961\) | 4.49541 | 0.145013 | ||||||||
\(962\) | 0.325204 | 0.0104850 | ||||||||
\(963\) | −5.03973 | −0.162403 | ||||||||
\(964\) | −31.2576 | −1.00674 | ||||||||
\(965\) | 33.2457 | 1.07022 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0334 | 0.322651 | 0.161325 | − | 0.986901i | \(-0.448423\pi\) | ||||
0.161325 | + | 0.986901i | \(0.448423\pi\) | |||||||
\(968\) | 0.774107 | 0.0248807 | ||||||||
\(969\) | −0.0491447 | −0.00157875 | ||||||||
\(970\) | −2.55064 | −0.0818963 | ||||||||
\(971\) | 19.4697 | 0.624812 | 0.312406 | − | 0.949949i | \(-0.398865\pi\) | ||||
0.312406 | + | 0.949949i | \(0.398865\pi\) | |||||||
\(972\) | −1.99397 | −0.0639565 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.81558 | 0.0581749 | ||||||||
\(975\) | −0.149317 | −0.00478198 | ||||||||
\(976\) | 9.48919 | 0.303742 | ||||||||
\(977\) | 1.86853 | 0.0597795 | 0.0298898 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298898 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(978\) | 1.21046 | 0.0387062 | ||||||||
\(979\) | 18.6749 | 0.596851 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.122682 | −0.00391694 | ||||||||
\(982\) | −1.66789 | −0.0532246 | ||||||||
\(983\) | −32.2863 | −1.02977 | −0.514886 | − | 0.857258i | \(-0.672166\pi\) | ||||
−0.514886 | + | 0.857258i | \(0.672166\pi\) | |||||||
\(984\) | 0.134946 | 0.00430193 | ||||||||
\(985\) | −24.2977 | −0.774190 | ||||||||
\(986\) | −0.0196517 | −0.000625839 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.248750 | 0.00791378 | ||||||||
\(989\) | −22.8254 | −0.725806 | ||||||||
\(990\) | 0.498902 | 0.0158562 | ||||||||
\(991\) | 56.8365 | 1.80547 | 0.902736 | − | 0.430195i | \(-0.141555\pi\) | ||||
0.902736 | + | 0.430195i | \(0.141555\pi\) | |||||||
\(992\) | −5.53097 | −0.175609 | ||||||||
\(993\) | 14.7746 | 0.468858 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.8068 | −0.501111 | ||||||||
\(996\) | −19.5170 | −0.618421 | ||||||||
\(997\) | 24.1136 | 0.763685 | 0.381843 | − | 0.924227i | \(-0.375290\pi\) | ||||
0.381843 | + | 0.924227i | \(0.375290\pi\) | |||||||
\(998\) | −1.72373 | −0.0545638 | ||||||||
\(999\) | 4.18670 | 0.132461 |
(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 | 1911.2.a.u.1.3 | 5 | ||
3.2 | odd | 2 | 5733.2.a.bp.1.3 | 5 | |||
7.3 | odd | 6 | 273.2.i.e.79.3 | ✓ | 10 | ||
7.5 | odd | 6 | 273.2.i.e.235.3 | yes | 10 | ||
7.6 | odd | 2 | 1911.2.a.t.1.3 | 5 | |||
21.5 | even | 6 | 819.2.j.g.235.3 | 10 | |||
21.17 | even | 6 | 819.2.j.g.352.3 | 10 | |||
21.20 | even | 2 | 5733.2.a.bq.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.i.e.79.3 | ✓ | 10 | 7.3 | odd | 6 | ||
273.2.i.e.235.3 | yes | 10 | 7.5 | odd | 6 | ||
819.2.j.g.235.3 | 10 | 21.5 | even | 6 | |||
819.2.j.g.352.3 | 10 | 21.17 | even | 6 | |||
1911.2.a.t.1.3 | 5 | 7.6 | odd | 2 | |||
1911.2.a.u.1.3 | 5 | 1.1 | even | 1 | trivial | ||
5733.2.a.bp.1.3 | 5 | 3.2 | odd | 2 | |||
5733.2.a.bq.1.3 | 5 | 21.20 | even | 2 |