Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(169,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.t (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: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.2 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 840.169 |
Dual form | 840.2.t.c.169.4 |
$q$-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 \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.47214i | − 1.24035i | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
0.784465 | − | 0.620174i | \(-0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2.23607i | − 0.577350i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.47214i | − 1.56972i | −0.619671 | − | 0.784862i | \(-0.712734\pi\) | ||||
0.619671 | − | 0.784862i | \(-0.287266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.472136 | −0.0847981 | −0.0423991 | − | 0.999101i | \(-0.513500\pi\) | ||||
−0.0423991 | + | 0.999101i | \(0.513500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.23607i | − 0.377964i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.47214i | − 0.406417i | −0.979136 | − | 0.203208i | \(-0.934863\pi\) | ||||
0.979136 | − | 0.203208i | \(-0.0651369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.52786 | −0.550960 | −0.275480 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275480 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.47214i | − 0.376997i | −0.982073 | − | 0.188499i | \(-0.939638\pi\) | ||||
0.982073 | − | 0.188499i | \(-0.0603621\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.23607 | −0.333333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.47214i | − 0.944058i | −0.881583 | − | 0.472029i | \(-0.843522\pi\) | ||||
0.881583 | − | 0.472029i | \(-0.156478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.47214 | −0.603023 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 10.0000i | − 1.24035i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.52786i | − 0.186658i | −0.995635 | − | 0.0933292i | \(-0.970249\pi\) | ||||
0.995635 | − | 0.0933292i | \(-0.0297509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4721 | 1.48017 | 0.740085 | − | 0.672513i | \(-0.234785\pi\) | ||||
0.740085 | + | 0.672513i | \(0.234785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.52786i | 0.881070i | 0.897735 | + | 0.440535i | \(0.145211\pi\) | ||||
−0.897735 | + | 0.440535i | \(0.854789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.00000i | − 0.577350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.94427i | − 0.542704i | −0.962480 | − | 0.271352i | \(-0.912529\pi\) | ||||
0.962480 | − | 0.271352i | \(-0.0874708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 14.4721i | − 1.56972i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 8.47214i | − 0.908308i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.4164 | 1.84614 | 0.923068 | − | 0.384637i | \(-0.125673\pi\) | ||||
0.923068 | + | 0.384637i | \(0.125673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.472136i | 0.0489582i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.47214 | −0.458831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.52786i | − 0.358200i | −0.983831 | − | 0.179100i | \(-0.942681\pi\) | ||||
0.983831 | − | 0.179100i | \(-0.0573186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9443i | 1.27544i | 0.770270 | + | 0.637719i | \(0.220122\pi\) | ||||
−0.770270 | + | 0.637719i | \(0.779878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.23607 | −0.218218 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47214 | −0.234645 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9443i | 1.40584i | 0.711269 | + | 0.702919i | \(0.248121\pi\) | ||||
−0.711269 | + | 0.702919i | \(0.751879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427i | 0.834058i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.47214i | 0.413449i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.47214 | −0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.52786i | 0.318097i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.00000i | − 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.47214 | −0.217659 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8885 | 1.21345 | 0.606724 | − | 0.794913i | \(-0.292483\pi\) | ||||
0.606724 | + | 0.794913i | \(0.292483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000i | 0.173422i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23607i | 0.192450i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.8885i | 1.69919i | 0.527433 | + | 0.849596i | \(0.323154\pi\) | ||||
−0.527433 | + | 0.849596i | \(0.676846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.94427 | 0.249730 | 0.124865 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124865 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.47214 | −0.545052 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427i | 0.747958i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.9443 | 1.57324 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4721 | 1.02176 | 0.510879 | − | 0.859653i | \(-0.329320\pi\) | ||||
0.510879 | + | 0.859653i | \(0.329320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8885 | −1.45575 | −0.727875 | − | 0.685710i | \(-0.759492\pi\) | ||||
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.47214i | 0.523241i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.05573 | −0.0847981 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.41641i | − 0.751511i | −0.926719 | − | 0.375756i | \(-0.877383\pi\) | ||||
0.926719 | − | 0.375756i | \(-0.122617\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.4164i | 1.83411i | 0.398755 | + | 0.917057i | \(0.369442\pi\) | ||||
−0.398755 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.47214i | 0.348155i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 10.4721i | − 0.810358i | −0.914237 | − | 0.405179i | \(-0.867209\pi\) | ||||
0.914237 | − | 0.405179i | \(-0.132791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0000i | 0.912343i | 0.889892 | + | 0.456172i | \(0.150780\pi\) | ||||
−0.889892 | + | 0.456172i | \(0.849220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 5.00000i | − 0.377964i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9443 | 1.71494 | 0.857468 | − | 0.514538i | \(-0.172036\pi\) | ||||
0.857468 | + | 0.514538i | \(0.172036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4721 | 1.22436 | 0.612182 | − | 0.790717i | \(-0.290292\pi\) | ||||
0.612182 | + | 0.790717i | \(0.290292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.52786i | 0.260787i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 5.52786i | − 0.406417i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9443i | 0.946579i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4164 | −1.26021 | −0.630104 | − | 0.776511i | \(-0.716988\pi\) | ||||
−0.630104 | + | 0.776511i | \(0.716988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9443i | 0.931749i | 0.884851 | + | 0.465875i | \(0.154260\pi\) | ||||
−0.884851 | + | 0.465875i | \(0.845740\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.0000 | −0.716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8885i | 1.41700i | 0.705711 | + | 0.708500i | \(0.250628\pi\) | ||||
−0.705711 | + | 0.708500i | \(0.749372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4721 | −1.45123 | −0.725616 | − | 0.688100i | \(-0.758445\pi\) | ||||
−0.725616 | + | 0.688100i | \(0.758445\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52786 | −0.107767 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.47214i | − 0.594627i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.88854 | −0.550960 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 4.00000i | − 0.278019i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.8885 | 1.78224 | 0.891120 | − | 0.453767i | \(-0.149920\pi\) | ||||
0.891120 | + | 0.453767i | \(0.149920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 12.4721i | − 0.854577i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 5.52786i | − 0.376997i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.472136i | 0.0320507i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.52786 | 0.508686 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.9443 | −1.94700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9443i | 1.40253i | 0.712900 | + | 0.701266i | \(0.247382\pi\) | ||||
−0.712900 | + | 0.701266i | \(0.752618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.88854i | 0.656326i | 0.944621 | + | 0.328163i | \(0.106429\pi\) | ||||
−0.944621 | + | 0.328163i | \(0.893571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3607 | 1.74196 | 0.870981 | − | 0.491316i | \(-0.163484\pi\) | ||||
0.870981 | + | 0.491316i | \(0.163484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | 0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2.94427i | − 0.192886i | −0.995339 | − | 0.0964428i | \(-0.969254\pi\) | ||||
0.995339 | − | 0.0964428i | \(-0.0307465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 14.4721i | − 0.944058i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.94427i | 0.580993i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5279 | −1.00441 | −0.502207 | − | 0.864747i | \(-0.667478\pi\) | ||||
−0.502207 | + | 0.864747i | \(0.667478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8885 | −0.765808 | −0.382904 | − | 0.923788i | \(-0.625076\pi\) | ||||
−0.382904 | + | 0.923788i | \(0.625076\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.23607 | −0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427i | 0.569110i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.94427 | −0.313331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 8.00000i | − 0.502956i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.4721 | −0.906280 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 23.4164i | − 1.46068i | −0.683086 | − | 0.730338i | \(-0.739363\pi\) | ||||
0.683086 | − | 0.730338i | \(-0.260637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.47214 | −0.153611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00000i | 0.246651i | 0.992366 | + | 0.123325i | \(0.0393559\pi\) | ||||
−0.992366 | + | 0.123325i | \(0.960644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.47214i | 0.274721i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 17.4164i | − 1.06587i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.3607 | −1.85112 | −0.925562 | − | 0.378597i | \(-0.876407\pi\) | ||||
−0.925562 | + | 0.378597i | \(0.876407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4721 | 1.48658 | 0.743288 | − | 0.668971i | \(-0.233265\pi\) | ||||
0.743288 | + | 0.668971i | \(0.233265\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.47214i | 0.270666i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0000 | −0.603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 23.4164i | − 1.40696i | −0.710717 | − | 0.703478i | \(-0.751629\pi\) | ||||
0.710717 | − | 0.703478i | \(-0.248371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.472136 | 0.0282660 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.94427 | 0.175641 | 0.0878203 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878203 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.9443i | 1.00723i | 0.863927 | + | 0.503616i | \(0.167997\pi\) | ||||
−0.863927 | + | 0.503616i | \(0.832003\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.47214i | 0.264906i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.52786i | 0.208243i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.52786 | −0.206807 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9443i | 1.45726i | 0.684908 | + | 0.728630i | \(0.259843\pi\) | ||||
−0.684908 | + | 0.728630i | \(0.740157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.00000i | − 0.116052i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47214 | −0.142492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.47214i | − 0.256917i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.88854 | −0.451697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 20.0000i | − 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9443 | 0.736374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | 0.907277 | 0.453638 | − | 0.891186i | \(-0.350126\pi\) | ||||
0.453638 | + | 0.891186i | \(0.350126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 25.4164i | − 1.43662i | −0.695723 | − | 0.718310i | \(-0.744916\pi\) | ||||
0.695723 | − | 0.718310i | \(-0.255084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.23607i | 0.125988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.94427i | − 0.390029i | −0.980800 | − | 0.195015i | \(-0.937525\pi\) | ||||
0.980800 | − | 0.195015i | \(-0.0624754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9443 | −0.948697 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.9443i | 0.720239i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 22.3607i | − 1.24035i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.9443i | 0.826420i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.47214 | −0.356820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.8885 | 1.86268 | 0.931341 | − | 0.364147i | \(-0.118639\pi\) | ||||
0.931341 | + | 0.364147i | \(0.118639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.47214i | 0.135472i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 3.41641i | − 0.186658i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0557i | 0.602244i | 0.953586 | + | 0.301122i | \(0.0973611\pi\) | ||||
−0.953586 | + | 0.301122i | \(0.902639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.9443 | 0.811661 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.944272 | 0.0511352 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.94427 | 0.481543 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 30.8328i | − 1.65519i | −0.561324 | − | 0.827596i | \(-0.689708\pi\) | ||||
0.561324 | − | 0.827596i | \(-0.310292\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4164 | −1.36051 | −0.680255 | − | 0.732976i | \(-0.738131\pi\) | ||||
−0.680255 | + | 0.732976i | \(0.738131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5279i | 0.932914i | 0.884544 | + | 0.466457i | \(0.154470\pi\) | ||||
−0.884544 | + | 0.466457i | \(0.845530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.8885 | 1.48017 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.47214i | 0.342542i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8328i | 0.881070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.8885i | 1.35137i | 0.737190 | + | 0.675685i | \(0.236152\pi\) | ||||
−0.737190 | + | 0.675685i | \(0.763848\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52786 | 0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.3607i | − 0.847124i | −0.905867 | − | 0.423562i | \(-0.860780\pi\) | ||||
0.905867 | − | 0.423562i | \(-0.139220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 11.1803i | − 0.577350i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 37.8885i | − 1.95136i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.88854 | 0.302474 | 0.151237 | − | 0.988498i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988498i | \(0.451674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 20.3607i | − 1.04038i | −0.854050 | − | 0.520191i | \(-0.825861\pi\) | ||||
0.854050 | − | 0.520191i | \(-0.174139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.47214i | 0.227921i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.47214i | 0.125666i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.58359 | 0.130993 | 0.0654967 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654967 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8885 | 1.30924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 13.8885i | − 0.700584i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.0000 | −1.00631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.52786i | 0.377813i | 0.981995 | + | 0.188906i | \(0.0604943\pi\) | ||||
−0.981995 | + | 0.188906i | \(0.939506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8885 | −0.793436 | −0.396718 | − | 0.917941i | \(-0.629851\pi\) | ||||
−0.396718 | + | 0.917941i | \(0.629851\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.11146i | 0.105179i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.23607 | 0.111111 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.94427i | 0.245078i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.88854 | 0.390063 | 0.195032 | − | 0.980797i | \(-0.437519\pi\) | ||||
0.195032 | + | 0.980797i | \(0.437519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.8885 | 0.981030 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 11.0557i | − 0.542704i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 2.94427i | − 0.144182i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9443 | −0.533391 | −0.266696 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266696 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.47214i | 0.314686i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 32.3607i | − 1.56972i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.52786i | 0.170725i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.94427 | 0.431834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4164 | −1.03159 | −0.515796 | − | 0.856711i | \(-0.672504\pi\) | ||||
−0.515796 | + | 0.856711i | \(0.672504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4164i | 1.02921i | 0.857428 | + | 0.514603i | \(0.172061\pi\) | ||||
−0.857428 | + | 0.514603i | \(0.827939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 18.9443i | − 0.908308i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.00000i | − 0.382692i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5279 | −1.50474 | −0.752371 | − | 0.658739i | \(-0.771090\pi\) | ||||
−0.752371 | + | 0.658739i | \(0.771090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 36.9443i | − 1.75528i | −0.479325 | − | 0.877638i | \(-0.659118\pi\) | ||||
0.479325 | − | 0.877638i | \(-0.340882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.9443 | 1.84614 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 12.4721i | − 0.589912i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.05573 | 0.427366 | 0.213683 | − | 0.976903i | \(-0.431454\pi\) | ||||
0.213683 | + | 0.976903i | \(0.431454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.05573 | 0.332241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8885i | 0.840477i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.0000 | −0.468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.94427i | 0.418395i | 0.977873 | + | 0.209198i | \(0.0670852\pi\) | ||||
−0.977873 | + | 0.209198i | \(0.932915\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.47214 | 0.302093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4721 | −0.580885 | −0.290443 | − | 0.956892i | \(-0.593803\pi\) | ||||
−0.290443 | + | 0.956892i | \(0.593803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 34.8328i | − 1.61882i | −0.587245 | − | 0.809409i | \(-0.699788\pi\) | ||||
0.587245 | − | 0.809409i | \(-0.300212\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.05573i | 0.0489582i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.0557i | 0.881794i | 0.897558 | + | 0.440897i | \(0.145340\pi\) | ||||
−0.897558 | + | 0.440897i | \(0.854660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.52786 | −0.0705502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.41641 | −0.433885 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.94427i | 0.227338i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.00000i | − 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0557 | −0.504098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.00000i | − 0.182006i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 7.88854i | − 0.358200i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 13.8885i | − 0.629350i | −0.949199 | − | 0.314675i | \(-0.898104\pi\) | ||||
0.949199 | − | 0.314675i | \(-0.101896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.4164 | 1.05893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05573 | 0.0476443 | 0.0238222 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238222 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 54.8328i | − 2.46955i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.47214 | 0.201008 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 12.4721i | − 0.559452i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.88854 | 0.263607 | 0.131804 | − | 0.991276i | \(-0.457923\pi\) | ||||
0.131804 | + | 0.991276i | \(0.457923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.4721 | −0.467861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 39.4164i | − 1.75749i | −0.477291 | − | 0.878745i | \(-0.658381\pi\) | ||||
0.477291 | − | 0.878745i | \(-0.341619\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000i | 0.310881i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5836 | 0.469109 | 0.234555 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234555 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.52786 | 0.333013 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 2.00000i | − 0.0883022i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9443i | 1.27544i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9443i | 0.569288i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.41641 | −0.412540 | −0.206270 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206270 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.05573i | − 0.308525i | −0.988030 | − | 0.154263i | \(-0.950700\pi\) | ||||
0.988030 | − | 0.154263i | \(-0.0493002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.05573i | 0.133110i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.7771i | 0.683382i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 22.9443i | − 0.990118i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9443 | −0.986451 | −0.493226 | − | 0.869901i | \(-0.664182\pi\) | ||||
−0.493226 | + | 0.869901i | \(0.664182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 16.4721i | − 0.706887i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.4164 | −1.43140 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 37.3050i | − 1.59504i | −0.603289 | − | 0.797522i | \(-0.706144\pi\) | ||||
0.603289 | − | 0.797522i | \(-0.293856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.52786 | 0.150566 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.9443 | −0.721850 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.94427i | 0.380349i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.52786 | −0.234645 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.05573i | − 0.214218i | −0.994247 | − | 0.107109i | \(-0.965841\pi\) | ||||
0.994247 | − | 0.107109i | \(-0.0341594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0557 | −0.467607 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.8328i | 1.46803i | 0.679134 | + | 0.734014i | \(0.262355\pi\) | ||||
−0.679134 | + | 0.734014i | \(0.737645\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.4164i | 1.40584i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.00000i | − 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.1115 | −0.423151 | −0.211576 | − | 0.977362i | \(-0.567859\pi\) | ||||
−0.211576 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.4164i | 0.727581i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0000i | 0.834058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 24.4721i | − 1.01879i | −0.860533 | − | 0.509394i | \(-0.829870\pi\) | ||||
0.860533 | − | 0.509394i | \(-0.170130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9443 | 0.537946 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.94427 | −0.205123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.00000i | − 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0000i | 0.413449i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0557i | 0.621416i | 0.950505 | + | 0.310708i | \(0.100566\pi\) | ||||
−0.950505 | + | 0.310708i | \(0.899434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.944272 | 0.0389080 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.8885 | 0.818105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 21.3050i | − 0.874890i | −0.899245 | − | 0.437445i | \(-0.855884\pi\) | ||||
0.899245 | − | 0.437445i | \(-0.144116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4721 | −0.593300 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.4721i | 0.837869i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3607 | −0.750197 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.52786i | 0.0622194i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.6525 | −0.636364 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.94427i | 0.200682i | 0.994953 | + | 0.100341i | \(0.0319933\pi\) | ||||
−0.994953 | + | 0.100341i | \(0.968007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.47214 | −0.343308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.9443 | −1.17096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 7.41641i | − 0.299546i | −0.988720 | − | 0.149773i | \(-0.952146\pi\) | ||||
0.988720 | − | 0.149773i | \(-0.0478543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.88854i | 0.318097i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.8885i | 1.92792i | 0.266047 | + | 0.963960i | \(0.414282\pi\) | ||||
−0.266047 | + | 0.963960i | \(0.585718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8885 | −0.477841 | −0.238920 | − | 0.971039i | \(-0.576794\pi\) | ||||
−0.238920 | + | 0.971039i | \(0.576794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 17.4164i | − 0.697774i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.00000i | − 0.159745i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0557 | 0.917834 | 0.458917 | − | 0.888479i | \(-0.348238\pi\) | ||||
0.458917 | + | 0.888479i | \(0.348238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 25.8885i | − 1.02898i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.94427i | − 0.354943i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214i | 0.177192i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4721 | −0.493390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.05573i | − 0.278251i | −0.990275 | − | 0.139125i | \(-0.955571\pi\) | ||||
0.990275 | − | 0.139125i | \(-0.0444291\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.52786 | −0.217659 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.2492i | 1.50373i | 0.659316 | + | 0.751866i | \(0.270846\pi\) | ||||
−0.659316 | + | 0.751866i | \(0.729154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.472136 | 0.0185045 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.05573i | 0.0413138i | 0.999787 | + | 0.0206569i | \(0.00657577\pi\) | ||||
−0.999787 | + | 0.0206569i | \(0.993424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.0557 | 1.21345 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 7.52786i | − 0.293690i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1115 | 0.471795 | 0.235898 | − | 0.971778i | \(-0.424197\pi\) | ||||
0.235898 | + | 0.971778i | \(0.424197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.2492 | 1.87668 | 0.938339 | − | 0.345717i | \(-0.112364\pi\) | ||||
0.938339 | + | 0.345717i | \(0.112364\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.9443i | 1.12410i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.47214i | 0.173422i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.8885i | 1.31217i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.9443 | 0.809752 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.05573 | 0.272383 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8885i | 0.843741i | 0.906656 | + | 0.421871i | \(0.138626\pi\) | ||||
−0.906656 | + | 0.421871i | \(0.861374\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000i | 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.11146i | − 0.0811499i | −0.999176 | − | 0.0405749i | \(-0.987081\pi\) | ||||
0.999176 | − | 0.0405749i | \(-0.0129189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.88854 | 0.378930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 14.1115i | − 0.539960i | −0.962866 | − | 0.269980i | \(-0.912983\pi\) | ||||
0.962866 | − | 0.269980i | \(-0.0870171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.4721i | 1.69919i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 26.3607i | − 1.00572i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.94427 | 0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.8328 | −1.85769 | −0.928844 | − | 0.370471i | \(-0.879196\pi\) | ||||
−0.928844 | + | 0.370471i | \(0.879196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.00000i | − 0.0759737i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.58359 | 0.249730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.8328i | 0.864855i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.94427 | −0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.472136 | −0.0178323 | −0.00891616 | − | 0.999960i | \(-0.502838\pi\) | ||||
−0.00891616 | + | 0.999960i | \(0.502838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.94427i | 0.186477i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.4721 | −0.545052 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.47214i | − 0.168192i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.8885 | −1.34782 | −0.673911 | − | 0.738812i | \(-0.735387\pi\) | ||||
−0.673911 | + | 0.738812i | \(0.735387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.94427 | 0.335436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.88854i | − 0.0707265i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0000i | 0.747958i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.5279i | 0.579899i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.94427 | −0.333565 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.8885i | 0.442140i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.3607 | 1.57324 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0557i | 0.706738i | 0.935484 | + | 0.353369i | \(0.114964\pi\) | ||||
−0.935484 | + | 0.353369i | \(0.885036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.63932i | − 0.208293i | −0.994562 | − | 0.104147i | \(-0.966789\pi\) | ||||
0.994562 | − | 0.104147i | \(-0.0332111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.23607i | 0.0824786i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.05573i | 0.112559i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.94427 | 0.328576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.83282i | 0.103926i | 0.998649 | + | 0.0519630i | \(0.0165478\pi\) | ||||
−0.998649 | + | 0.0519630i | \(0.983452\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.8885 | 1.02176 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94427i | 0.180901i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8328 | 0.979143 | 0.489572 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489572 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 24.0000i | − 0.874609i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.0000 | −1.45575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.4721i | 1.10753i | 0.832673 | + | 0.553764i | \(0.186809\pi\) | ||||
−0.832673 | + | 0.553764i | \(0.813191\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4721 | −0.887114 | −0.443557 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443557 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.9443i | 0.541019i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.4721i | 0.523241i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05573 | −0.0380705 | −0.0190353 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190353 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.4164 | −0.843321 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 16.9443i | − 0.609443i | −0.952441 | − | 0.304722i | \(-0.901437\pi\) | ||||
0.952441 | − | 0.304722i | \(-0.0985634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.36068 | −0.0847981 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.47214i | 0.0886874i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.05573 | 0.252798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9443 | −0.892576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.47214i | 0.302769i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 21.0557i | − 0.751511i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 36.0000i | − 1.28326i | −0.767014 | − | 0.641631i | \(-0.778258\pi\) | ||||
0.767014 | − | 0.641631i | \(-0.221742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.00000 | 0.142404 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.9443 | 0.531357 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7771i | 0.560261i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.0000i | − 0.991811i | −0.868377 | − | 0.495905i | \(-0.834836\pi\) | ||||
0.868377 | − | 0.495905i | \(-0.165164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.8885 | −1.48191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4164 | −0.615379 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 15.0557i | − 0.531305i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.94427 | 0.315244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.3607i | 1.06875i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.8328 | 0.873075 | 0.436538 | − | 0.899686i | \(-0.356205\pi\) | ||||
0.436538 | + | 0.899686i | \(0.356205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.0557 | 0.458449 | 0.229224 | − | 0.973374i | \(-0.426381\pi\) | ||||
0.229224 | + | 0.973374i | \(0.426381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 24.4721i | − 0.858275i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 52.3607i | 1.83411i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.94427i | 0.172978i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3050 | 0.673747 | 0.336874 | − | 0.941550i | \(-0.390630\pi\) | ||||
0.336874 | + | 0.941550i | \(0.390630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0557i | 0.524810i | 0.964958 | + | 0.262405i | \(0.0845156\pi\) | ||||
−0.964958 | + | 0.262405i | \(0.915484\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.0000i | 0.348155i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.7214i | 1.13783i | 0.822395 | + | 0.568917i | \(0.192637\pi\) | ||||
−0.822395 | + | 0.568917i | \(0.807363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52786 | −0.122528 | −0.0612639 | − | 0.998122i | \(-0.519513\pi\) | ||||
−0.0612639 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.4164 | −0.812306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.47214i | 0.224246i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 23.4164i | − 0.810358i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.472136i | − 0.0163194i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.9443 | −1.13736 | −0.568681 | − | 0.822558i | \(-0.692546\pi\) | ||||
−0.568681 | + | 0.822558i | \(0.692546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.94427i | − 0.101406i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.6525 | −0.538462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9443 | 0.581526 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.88854 | 0.338975 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 31.5279i | − 1.07949i | −0.841827 | − | 0.539747i | \(-0.818520\pi\) | ||||
0.841827 | − | 0.539747i | \(-0.181480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.47214 | 0.152944 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5836i | 0.566485i | 0.959048 | + | 0.283242i | \(0.0914101\pi\) | ||||
−0.959048 | + | 0.283242i | \(0.908590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.0557 | 0.718412 | 0.359206 | − | 0.933258i | \(-0.383048\pi\) | ||||
0.359206 | + | 0.933258i | \(0.383048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.52786 | 0.120229 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.8328i | 0.641077i | 0.947236 | + | 0.320538i | \(0.103864\pi\) | ||||
−0.947236 | + | 0.320538i | \(0.896136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.8328i | 0.912343i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.8885i | 0.845259i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8885 | 0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.83282 | −0.231521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.52786i | 0.119400i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.1803i | − 0.377964i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 49.3050i | − 1.66491i | −0.554093 | − | 0.832455i | \(-0.686935\pi\) | ||||
0.554093 | − | 0.832455i | \(-0.313065\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.9443 | 0.841349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5279 | 0.927437 | 0.463719 | − | 0.885983i | \(-0.346515\pi\) | ||||
0.463719 | + | 0.885983i | \(0.346515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16.3607i | − 0.550581i | −0.961361 | − | 0.275290i | \(-0.911226\pi\) | ||||
0.961361 | − | 0.275290i | \(-0.0887740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.58359i | 0.153902i | 0.997035 | + | 0.0769510i | \(0.0245185\pi\) | ||||
−0.997035 | + | 0.0769510i | \(0.975482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9443i | 0.433164i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.3050 | 1.71494 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 17.8885i | − 0.597281i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9443 | 0.431236 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.47214i | 0.0822675i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.8328 | 1.22436 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3607i | 0.543247i | 0.962404 | + | 0.271624i | \(0.0875606\pi\) | ||||
−0.962404 | + | 0.271624i | \(0.912439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.47214 | −0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.4164 | −0.842083 | −0.421042 | − | 0.907041i | \(-0.638335\pi\) | ||||
−0.421042 | + | 0.907041i | \(0.638335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.88854i | 0.327263i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.88854i | 0.260787i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13.8885i | − 0.458640i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7214 | 1.21133 | 0.605663 | − | 0.795721i | \(-0.292908\pi\) | ||||
0.605663 | + | 0.795721i | \(0.292908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 55.7771i | − 1.83593i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 12.3607i | − 0.406417i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 12.9443i | − 0.425146i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3050 | −0.633375 | −0.316687 | − | 0.948530i | \(-0.602571\pi\) | ||||
−0.316687 | + | 0.948530i | \(0.602571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16.0000i | − 0.523816i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.9443i | 0.946579i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3050i | 0.499991i | 0.968247 | + | 0.249995i | \(0.0804291\pi\) | ||||
−0.968247 | + | 0.249995i | \(0.919571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.4164 | −0.829433 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5279 | 1.15818 | 0.579088 | − | 0.815265i | \(-0.303409\pi\) | ||||
0.579088 | + | 0.815265i | \(0.303409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 14.1115i | − 0.459532i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.23607 | 0.0727393 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0000i | 0.519930i | 0.965618 | + | 0.259965i | \(0.0837111\pi\) | ||||
−0.965618 | + | 0.259965i | \(0.916289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.6656 | 1.09283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.94427 | −0.225183 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000i | 0.583077i | 0.956559 | + | 0.291539i | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.9443 | −1.26021 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9443i | 0.547731i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8885 | 0.642235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7771 | −0.992809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.9443i | 0.931749i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 25.8885i | − 0.832519i | −0.909246 | − | 0.416260i | \(-0.863341\pi\) | ||||
0.909246 | − | 0.416260i | \(-0.136659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.9443 | 0.415830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.8885 | −1.08754 | −0.543768 | − | 0.839236i | \(-0.683003\pi\) | ||||
−0.543768 | + | 0.839236i | \(0.683003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.94427i | − 0.0943890i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.3607 | −0.716115 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.8328i | 1.69027i | 0.534552 | + | 0.845136i | \(0.320480\pi\) | ||||
−0.534552 | + | 0.845136i | \(0.679520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.8328 | −1.11326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.9443 | 0.477134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 25.5279i | − 0.814212i | −0.913381 | − | 0.407106i | \(-0.866538\pi\) | ||||
0.913381 | − | 0.407106i | \(-0.133462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.4721i | 1.41700i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.47214i | 0.206010i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.88854 | 0.314437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.9443 | −1.80889 | −0.904447 | − | 0.426586i | \(-0.859716\pi\) | ||||
−0.904447 | + | 0.426586i | \(0.859716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 33.8885i | − 1.07542i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.7771 | −1.45123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.63932i | 0.178599i | 0.996005 | + | 0.0892995i | \(0.0284628\pi\) | ||||
−0.996005 | + | 0.0892995i | \(0.971537\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.47214 | 0.0782149 |
(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 | 840.2.t.c.169.2 | ✓ | 4 | |
3.2 | odd | 2 | 2520.2.t.f.1009.1 | 4 | |||
4.3 | odd | 2 | 1680.2.t.h.1009.4 | 4 | |||
5.2 | odd | 4 | 4200.2.a.bj.1.1 | 2 | |||
5.3 | odd | 4 | 4200.2.a.bk.1.2 | 2 | |||
5.4 | even | 2 | inner | 840.2.t.c.169.4 | yes | 4 | |
12.11 | even | 2 | 5040.2.t.u.1009.2 | 4 | |||
15.14 | odd | 2 | 2520.2.t.f.1009.2 | 4 | |||
20.3 | even | 4 | 8400.2.a.cz.1.2 | 2 | |||
20.7 | even | 4 | 8400.2.a.db.1.1 | 2 | |||
20.19 | odd | 2 | 1680.2.t.h.1009.2 | 4 | |||
60.59 | even | 2 | 5040.2.t.u.1009.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.c.169.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
840.2.t.c.169.4 | yes | 4 | 5.4 | even | 2 | inner | |
1680.2.t.h.1009.2 | 4 | 20.19 | odd | 2 | |||
1680.2.t.h.1009.4 | 4 | 4.3 | odd | 2 | |||
2520.2.t.f.1009.1 | 4 | 3.2 | odd | 2 | |||
2520.2.t.f.1009.2 | 4 | 15.14 | odd | 2 | |||
4200.2.a.bj.1.1 | 2 | 5.2 | odd | 4 | |||
4200.2.a.bk.1.2 | 2 | 5.3 | odd | 4 | |||
5040.2.t.u.1009.1 | 4 | 60.59 | even | 2 | |||
5040.2.t.u.1009.2 | 4 | 12.11 | even | 2 | |||
8400.2.a.cz.1.2 | 2 | 20.3 | even | 4 | |||
8400.2.a.db.1.1 | 2 | 20.7 | even | 4 |