Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(671,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.h (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.671 |
Dual form | 2240.2.h.a.671.3 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | − | 1.00000i | −0.925820 | − | 0.377964i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000i | 0.516398i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898i | 1.18818i | 0.804400 | + | 0.594089i | \(0.202487\pi\) | ||||
−0.804400 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 4.89898i | −0.436436 | + | 1.06904i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.79796i | 1.81944i | 0.415227 | + | 0.909718i | \(0.363702\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.79796 | −1.75977 | −0.879883 | − | 0.475191i | \(-0.842379\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.44949 | + | 1.00000i | 0.414039 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.89898i | − | 0.805387i | −0.915335 | − | 0.402694i | \(-0.868074\pi\) | ||
0.915335 | − | 0.402694i | \(-0.131926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.89898 | 0.747087 | 0.373544 | − | 0.927613i | \(-0.378143\pi\) | ||||
0.373544 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.89898 | −0.714590 | −0.357295 | − | 0.933992i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933992i | \(0.616301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | + | 4.89898i | 0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.79796 | 1.37199 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.89898i | 0.672927i | 0.941697 | + | 0.336463i | \(0.109231\pi\) | ||||
−0.941697 | + | 0.336463i | \(0.890769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.00000i | − | 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44949 | + | 1.00000i | 0.308607 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.6969 | 1.79552 | 0.897758 | − | 0.440488i | \(-0.145195\pi\) | ||||
0.897758 | + | 0.440488i | \(0.145195\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.0000 | 1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.89898i | − | 0.573382i | −0.958023 | − | 0.286691i | \(-0.907445\pi\) | ||
0.958023 | − | 0.286691i | \(-0.0925553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.00000i | − | 0.230940i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000i | 1.12509i | 0.826767 | + | 0.562544i | \(0.190177\pi\) | ||||
−0.826767 | + | 0.562544i | \(0.809823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.89898i | − | 0.531369i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.5959 | 2.10090 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.79796i | 1.03858i | 0.854598 | + | 0.519291i | \(0.173804\pi\) | ||||
−0.854598 | + | 0.519291i | \(0.826196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.89898 | − | 2.00000i | −0.513553 | − | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.5959i | 2.03200i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.00000i | − | 0.205196i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898 | 0.482711 | 0.241355 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241355 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | − | 4.89898i | 0.195180 | − | 0.478091i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6969 | 1.42081 | 0.710403 | − | 0.703795i | \(-0.248513\pi\) | ||||
0.710403 | + | 0.703795i | \(0.248513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.79796i | 0.938474i | 0.883072 | + | 0.469237i | \(0.155471\pi\) | ||||
−0.883072 | + | 0.469237i | \(0.844529\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.79796 | −0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.00000i | − | 0.559503i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.89898 | − | 12.0000i | 0.449089 | − | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.0000i | − | 0.887357i | −0.896186 | − | 0.443678i | \(-0.853673\pi\) | ||
0.896186 | − | 0.443678i | \(-0.146327\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 9.79796i | − | 0.862662i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.00000i | − | 0.524222i | −0.965038 | − | 0.262111i | \(-0.915581\pi\) | ||
0.965038 | − | 0.262111i | \(-0.0844187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | − | 4.89898i | 0.173422 | − | 0.424795i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000i | 0.344265i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.79796i | 0.825137i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.79796i | − | 0.813676i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.79796 | − | 10.0000i | 0.808122 | − | 0.824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79796i | 0.802680i | 0.915929 | + | 0.401340i | \(0.131455\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.89898i | − | 0.396059i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | 0.786991 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.79796 | 0.777029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 14.6969i | 0.472866 | − | 1.15828i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6969 | −1.15115 | −0.575577 | − | 0.817748i | \(-0.695222\pi\) | ||||
−0.575577 | + | 0.817748i | \(0.695222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.6969 | 1.13728 | 0.568642 | − | 0.822585i | \(-0.307469\pi\) | ||||
0.568642 | + | 0.822585i | \(0.307469\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.00000i | − | 0.152944i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.44949 | − | 1.00000i | −0.185164 | − | 0.0755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | −0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.79796 | −0.732334 | −0.366167 | − | 0.930549i | \(-0.619330\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.0000i | − | 1.47844i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.89898i | 0.360180i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.00000 | + | 9.79796i | −0.290957 | + | 0.712697i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0000i | 1.30243i | 0.758891 | + | 0.651217i | \(0.225741\pi\) | ||||
−0.758891 | + | 0.651217i | \(0.774259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.00000i | 0.286446i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.89898i | − | 0.349038i | −0.984654 | − | 0.174519i | \(-0.944163\pi\) | ||
0.984654 | − | 0.174519i | \(-0.0558370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 29.3939i | − | 2.07328i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.79796 | − | 24.0000i | 0.687682 | − | 1.68447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.89898 | −0.334108 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000 | + | 9.79796i | 1.62923 | + | 0.665129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.79796 | −0.662085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.79796i | 0.659082i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.89898 | 0.328060 | 0.164030 | − | 0.986455i | \(-0.447551\pi\) | ||||
0.164030 | + | 0.986455i | \(0.447551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.0000i | − | 1.19470i | −0.801980 | − | 0.597351i | \(-0.796220\pi\) | ||
0.801980 | − | 0.597351i | \(-0.203780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.89898 | 0.319574 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.0000 | 1.29914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | − | 4.89898i | −0.319438 | − | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000i | 1.13615i | 0.822977 | + | 0.568075i | \(0.192312\pi\) | ||||
−0.822977 | + | 0.568075i | \(0.807688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.79796 | −0.613572 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.4949i | 1.52795i | 0.645246 | + | 0.763975i | \(0.276755\pi\) | ||||
−0.645246 | + | 0.763975i | \(0.723245\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.89898 | + | 12.0000i | −0.304408 | + | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 9.79796i | − | 0.606478i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.89898i | − | 0.300942i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.5959 | 1.19925 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.79796 | −0.595184 | −0.297592 | − | 0.954693i | \(-0.596183\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00000 | + | 9.79796i | −0.242091 | + | 0.592999i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.4949i | − | 1.47176i | −0.677114 | − | 0.735878i | \(-0.736770\pi\) | ||
0.677114 | − | 0.735878i | \(-0.263230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.79796 | 0.586588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000i | 0.832214i | 0.909316 | + | 0.416107i | \(0.136606\pi\) | ||||
−0.909316 | + | 0.416107i | \(0.863394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.79796 | 0.574367 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000i | 0.349334i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000i | 0.693978i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | − | 4.89898i | −0.691669 | − | 0.282372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000i | 0.689382i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0000 | −0.572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 9.79796i | − | 0.557386i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3939 | −1.66677 | −0.833387 | − | 0.552690i | \(-0.813601\pi\) | ||||
−0.833387 | + | 0.552690i | \(0.813601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6969i | 0.830720i | 0.909657 | + | 0.415360i | \(0.136344\pi\) | ||||
−0.909657 | + | 0.415360i | \(0.863656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.44949 | − | 1.00000i | −0.138013 | − | 0.0563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.89898i | − | 0.275154i | −0.990491 | − | 0.137577i | \(-0.956069\pi\) | ||
0.990491 | − | 0.137577i | \(-0.0439315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 29.3939i | − | 1.64061i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.79796 | −0.545173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.5959 | 1.08366 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 4.89898i | 0.661581 | + | 0.270089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5959 | −1.07709 | −0.538545 | − | 0.842597i | \(-0.681026\pi\) | ||||
−0.538545 | + | 0.842597i | \(0.681026\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.89898i | 0.268462i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.6969 | −0.802980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0000 | 1.85210 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 36.0000i | − | 1.95525i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | − | 17.0000i | −0.396780 | − | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0000 | −0.646058 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.4949 | −1.31495 | −0.657477 | − | 0.753474i | \(-0.728377\pi\) | ||||
−0.657477 | + | 0.753474i | \(0.728377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.00000i | − | 0.427008i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.6969i | 0.782239i | 0.920340 | + | 0.391120i | \(0.127912\pi\) | ||||
−0.920340 | + | 0.391120i | \(0.872088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000i | 0.318447i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.0000 | − | 9.79796i | −1.27021 | − | 0.518563i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.0000i | 0.950004i | 0.879985 | + | 0.475002i | \(0.157553\pi\) | ||||
−0.879985 | + | 0.475002i | \(0.842447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0000i | 1.15470i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89898i | 0.256424i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6969 | 0.767174 | 0.383587 | − | 0.923505i | \(-0.374689\pi\) | ||||
0.383587 | + | 0.923505i | \(0.374689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.89898 | − | 12.0000i | 0.254342 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 34.2929i | − | 1.77562i | −0.460213 | − | 0.887808i | \(-0.652227\pi\) | ||
0.460213 | − | 0.887808i | \(-0.347773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000i | 0.103280i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.5959i | 1.00924i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3939 | −1.50986 | −0.754931 | − | 0.655804i | \(-0.772330\pi\) | ||||
−0.754931 | + | 0.655804i | \(0.772330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.0000 | −1.02463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6969 | −0.750978 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.89898 | −0.249029 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.79796i | − | 0.496776i | −0.968661 | − | 0.248388i | \(-0.920099\pi\) | ||
0.968661 | − | 0.248388i | \(-0.0799008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.3939 | −1.48651 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 10.0000i | − | 0.503155i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.79796 | − | 4.00000i | −0.490511 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5959 | −0.976142 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0000 | 0.546594 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.3939i | 1.45343i | 0.686937 | + | 0.726717i | \(0.258955\pi\) | ||||
−0.686937 | + | 0.726717i | \(0.741045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000i | 0.591916i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | + | 14.6969i | −0.295241 | + | 0.723189i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.00000i | − | 0.294528i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000i | 0.879358i | 0.898155 | + | 0.439679i | \(0.144908\pi\) | ||||
−0.898155 | + | 0.439679i | \(0.855092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.5959i | − | 0.955047i | −0.878619 | − | 0.477523i | \(-0.841535\pi\) | ||
0.878619 | − | 0.477523i | \(-0.158465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.89898 | 0.238197 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.89898i | 0.237635i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.4949 | − | 10.0000i | −1.18539 | − | 0.483934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000i | 0.867029i | 0.901146 | + | 0.433515i | \(0.142727\pi\) | ||||
−0.901146 | + | 0.433515i | \(0.857273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2929i | 1.64801i | 0.566583 | + | 0.824005i | \(0.308265\pi\) | ||||
−0.566583 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.5959 | −0.939552 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5959 | −0.935262 | −0.467631 | − | 0.883924i | \(-0.654892\pi\) | ||||
−0.467631 | + | 0.883924i | \(0.654892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.4949 | 1.16379 | 0.581894 | − | 0.813265i | \(-0.302312\pi\) | ||||
0.581894 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.79796i | − | 0.464468i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.5959 | 0.926855 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.0000 | 0.939682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.89898 | + | 2.00000i | 0.229668 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.5959 | 0.914659 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 19.5959i | − | 0.908739i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000i | 0.277647i | 0.990317 | + | 0.138823i | \(0.0443321\pi\) | ||||
−0.990317 | + | 0.138823i | \(0.955668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.0000 | − | 14.6969i | −1.66233 | − | 0.678642i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.0000i | 1.29017i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000i | 0.0917663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.89898i | − | 0.224309i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.1918 | 1.79072 | 0.895360 | − | 0.445342i | \(-0.146918\pi\) | ||||
0.895360 | + | 0.445342i | \(0.146918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.79796i | − | 0.446748i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.3939 | − | 12.0000i | −1.33747 | − | 0.546019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.89898i | − | 0.222451i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.00000i | − | 0.0906287i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453143i | \(-0.0144289\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.3939i | 1.32924i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5959 | −0.884351 | −0.442176 | − | 0.896928i | \(-0.645793\pi\) | ||||
−0.442176 | + | 0.896928i | \(0.645793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.0000 | −2.16181 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 14.6969i | −0.269137 | + | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.79796 | 0.438617 | 0.219308 | − | 0.975656i | \(-0.429620\pi\) | ||||
0.219308 | + | 0.975656i | \(0.429620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 29.3939i | − | 1.31322i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.0000i | 0.799408i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.89898 | + | 12.0000i | −0.216718 | + | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.00000 | 0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.89898 | −0.215875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 36.0000i | − | 1.58022i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.1918i | − | 1.71703i | −0.512792 | − | 0.858513i | \(-0.671389\pi\) | ||
0.512792 | − | 0.858513i | \(-0.328611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.0000i | − | 1.48672i | −0.668894 | − | 0.743358i | \(-0.733232\pi\) | ||
0.668894 | − | 0.743358i | \(-0.266768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | + | 4.89898i | −0.0872872 | + | 0.213809i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 48.0000i | − | 2.09091i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000i | 0.260378i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6969 | −0.635404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.5959i | 0.845626i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5959i | 0.842494i | 0.906946 | + | 0.421247i | \(0.138408\pi\) | ||||
−0.906946 | + | 0.421247i | \(0.861592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 20.0000i | − | 0.858282i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.79796i | − | 0.419698i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.4949 | −1.04733 | −0.523663 | − | 0.851925i | \(-0.675435\pi\) | ||||
−0.523663 | + | 0.851925i | \(0.675435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.5959 | −0.834814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | − | 24.4949i | 0.425243 | − | 1.04163i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.79796 | 0.415900 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.2929i | 1.45303i | 0.687148 | + | 0.726517i | \(0.258862\pi\) | ||||
−0.687148 | + | 0.726517i | \(0.741138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.79796 | 0.414410 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000i | 0.252870i | 0.991975 | + | 0.126435i | \(0.0403535\pi\) | ||||
−0.991975 | + | 0.126435i | \(0.959647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | −0.757266 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9444 | + | 11.0000i | 1.13156 | + | 0.461957i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.0000 | 1.76073 | 0.880366 | − | 0.474295i | \(-0.157297\pi\) | ||||
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.1918 | −1.64013 | −0.820064 | − | 0.572272i | \(-0.806062\pi\) | ||||
−0.820064 | + | 0.572272i | \(0.806062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.0000 | 1.50392 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.89898i | 0.203947i | 0.994787 | + | 0.101974i | \(0.0325157\pi\) | ||||
−0.994787 | + | 0.101974i | \(0.967484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.0000i | 1.16364i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | − | 14.6969i | 0.248922 | − | 0.609732i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0000i | 1.23823i | 0.785299 | + | 0.619116i | \(0.212509\pi\) | ||||
−0.785299 | + | 0.619116i | \(0.787491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 19.5959i | − | 0.807436i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.79796 | −0.403034 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.4949i | − | 1.00588i | −0.864320 | − | 0.502942i | \(-0.832251\pi\) | ||
0.864320 | − | 0.502942i | \(-0.167749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.89898 | + | 12.0000i | −0.200839 | + | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0000i | 0.735460i | 0.929933 | + | 0.367730i | \(0.119865\pi\) | ||||
−0.929933 | + | 0.367730i | \(0.880135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5959i | − | 0.799334i | −0.916660 | − | 0.399667i | \(-0.869126\pi\) | ||
0.916660 | − | 0.399667i | \(-0.130874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.6969 | −0.598506 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.2929 | 1.39190 | 0.695952 | − | 0.718088i | \(-0.254983\pi\) | ||||
0.695952 | + | 0.718088i | \(0.254983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.0000 | − | 19.5959i | −1.94506 | − | 0.794067i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.79796 | −0.396383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.2929i | − | 1.38508i | −0.721382 | − | 0.692538i | \(-0.756493\pi\) | ||
0.721382 | − | 0.692538i | \(-0.243507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.0000i | − | 1.52735i | −0.645601 | − | 0.763674i | \(-0.723393\pi\) | ||
0.645601 | − | 0.763674i | \(-0.276607\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.79796 | − | 24.0000i | 0.392547 | − | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0000i | 1.03504i | 0.855670 | + | 0.517522i | \(0.173145\pi\) | ||||
−0.855670 | + | 0.517522i | \(0.826855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0000i | 0.396838i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0000 | + | 9.79796i | 0.396214 | + | 0.388209i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000i | 0.237356i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0000i | 1.49857i | 0.662246 | + | 0.749287i | \(0.269604\pi\) | ||||
−0.662246 | + | 0.749287i | \(0.730396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.79796i | 0.385794i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.4949 | −0.962994 | −0.481497 | − | 0.876448i | \(-0.659907\pi\) | ||||
−0.481497 | + | 0.876448i | \(0.659907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.5959 | − | 48.0000i | 0.768025 | − | 1.88127i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 34.2929i | − | 1.34198i | −0.741465 | − | 0.670992i | \(-0.765869\pi\) | ||
0.741465 | − | 0.670992i | \(-0.234131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000i | 0.234439i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.89898i | 0.191127i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.9898 | 1.90837 | 0.954186 | − | 0.299215i | \(-0.0967248\pi\) | ||||
0.954186 | + | 0.299215i | \(0.0967248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0000 | −1.78919 | −0.894596 | − | 0.446875i | \(-0.852537\pi\) | ||||
−0.894596 | + | 0.446875i | \(0.852537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.5959 | 0.761042 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | + | 4.89898i | −0.0775567 | + | 0.189974i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −58.7878 | −2.27627 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9.79796i | − | 0.378811i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 4.00000i | − | 0.153960i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000 | 1.61419 | 0.807096 | − | 0.590421i | \(-0.201038\pi\) | ||||
0.807096 | + | 0.590421i | \(0.201038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.89898 | − | 12.0000i | 0.188006 | − | 0.460518i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.0000 | −1.37952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0908 | 1.68709 | 0.843544 | − | 0.537060i | \(-0.180465\pi\) | ||||
0.843544 | + | 0.537060i | \(0.180465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.0000i | 1.06827i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.79796i | 0.373273i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000i | 0.380418i | 0.981744 | + | 0.190209i | \(0.0609166\pi\) | ||||
−0.981744 | + | 0.190209i | \(0.939083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10.0000i | − | 0.379322i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000i | 0.453882i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.79796 | 0.369537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 9.79796i | − | 0.369012i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.6969 | + | 6.00000i | 0.552735 | + | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.9898i | − | 1.83985i | −0.392094 | − | 0.919925i | \(-0.628249\pi\) | ||
0.392094 | − | 0.919925i | \(-0.371751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.0000i | − | 0.375029i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 58.7878i | − | 2.20162i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.0000 | −0.448148 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.1918 | 1.46161 | 0.730804 | − | 0.682587i | \(-0.239145\pi\) | ||||
0.730804 | + | 0.682587i | \(0.239145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | − | 4.89898i | −0.446903 | − | 0.182448i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.79796i | 0.363887i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.89898 | −0.181693 | −0.0908465 | − | 0.995865i | \(-0.528957\pi\) | ||||
−0.0908465 | + | 0.995865i | \(0.528957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000i | 0.887672i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.79796 | + | 10.0000i | −0.361403 | + | 0.368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.3939 | −1.08127 | −0.540636 | − | 0.841257i | \(-0.681816\pi\) | ||||
−0.540636 | + | 0.841257i | \(0.681816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.00000 | 0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.79796i | − | 0.358969i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.00000i | − | 0.219529i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.0000 | − | 14.6969i | −1.31541 | − | 0.537014i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 46.0000i | − | 1.67856i | −0.543696 | − | 0.839282i | \(-0.682976\pi\) | ||
0.543696 | − | 0.839282i | \(-0.317024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 10.0000i | − | 0.363937i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.89898i | − | 0.178056i | −0.996029 | − | 0.0890282i | \(-0.971624\pi\) | ||
0.996029 | − | 0.0890282i | \(-0.0283761\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.5959i | − | 0.710351i | −0.934800 | − | 0.355176i | \(-0.884421\pi\) | ||
0.934800 | − | 0.355176i | \(-0.115579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.79796 | − | 24.0000i | 0.354710 | − | 0.868858i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.89898i | 0.177123i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.0000i | − | 0.433295i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.3939i | − | 1.05997i | −0.848007 | − | 0.529985i | \(-0.822197\pi\) | ||
0.848007 | − | 0.529985i | \(-0.177803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.9898 | 1.76432 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −54.0000 | −1.94225 | −0.971123 | − | 0.238581i | \(-0.923318\pi\) | ||||
−0.971123 | + | 0.238581i | \(0.923318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.79796 | −0.351953 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000 | + | 9.79796i | 0.860995 | + | 0.351500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.1918 | 1.40060 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 26.0000i | − | 0.926800i | −0.886149 | − | 0.463400i | \(-0.846629\pi\) | ||
0.886149 | − | 0.463400i | \(-0.153371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0000 | 0.427211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.0908 | − | 18.0000i | −1.56769 | − | 0.640006i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | 0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.79796 | −0.347498 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.0000i | − | 0.849059i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.79796i | − | 0.346194i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | + | 14.6969i | −0.211472 | + | 0.517999i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 36.0000i | − | 1.26726i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.0000i | 1.75574i | 0.478901 | + | 0.877869i | \(0.341035\pi\) | ||||
−0.478901 | + | 0.877869i | \(0.658965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5959i | 0.687259i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6969 | 0.514811 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.79796i | 0.342787i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.89898 | + | 2.00000i | 0.171184 | + | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5959i | 0.683902i | 0.939718 | + | 0.341951i | \(0.111088\pi\) | ||||
−0.939718 | + | 0.341951i | \(0.888912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0000i | 0.488009i | 0.969774 | + | 0.244005i | \(0.0784612\pi\) | ||||
−0.969774 | + | 0.244005i | \(0.921539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.4949 | −0.851771 | −0.425886 | − | 0.904777i | \(-0.640037\pi\) | ||||
−0.425886 | + | 0.904777i | \(0.640037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.9898 | −1.69944 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.0000 | + | 24.4949i | −0.831551 | + | 0.848698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6969 | −0.508609 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.1918i | 1.35467i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5959 | 0.676526 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −67.0000 | −2.31034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000i | 0.413302i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.9444 | + | 11.0000i | 0.925820 | + | 0.377964i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3939 | 1.00761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000i | 0.0683986i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4949i | 0.836730i | 0.908279 | + | 0.418365i | \(0.137397\pi\) | ||||
−0.908279 | + | 0.418365i | \(0.862603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000i | 0.341196i | 0.985341 | + | 0.170598i | \(0.0545699\pi\) | ||||
−0.985341 | + | 0.170598i | \(0.945430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.0000i | 0.475465i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.3939 | 0.995974 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.89898i | − | 0.165805i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.44949 | + | 1.00000i | 0.0828079 | + | 0.0338062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.8888i | 1.81969i | 0.414943 | + | 0.909847i | \(0.363801\pi\) | ||||
−0.414943 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000i | 0.404750i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5959i | 0.660203i | 0.943945 | + | 0.330102i | \(0.107083\pi\) | ||||
−0.943945 | + | 0.330102i | \(0.892917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.89898 | 0.164864 | 0.0824319 | − | 0.996597i | \(-0.473731\pi\) | ||||
0.0824319 | + | 0.996597i | \(0.473731\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.6969 | 0.493475 | 0.246737 | − | 0.969082i | \(-0.420641\pi\) | ||||
0.246737 | + | 0.969082i | \(0.420641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | + | 24.4949i | −0.335389 | + | 0.821532i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 9.79796i | − | 0.327876i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.79796 | 0.327510 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | 0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 96.0000i | − | 3.20178i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0000 | −0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.79796 | + | 24.0000i | −0.326056 | + | 0.798670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | −0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.89898 | −0.162668 | −0.0813340 | − | 0.996687i | \(-0.525918\pi\) | ||||
−0.0813340 | + | 0.996687i | \(0.525918\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0000i | 0.596367i | 0.954509 | + | 0.298183i | \(0.0963807\pi\) | ||||
−0.954509 | + | 0.298183i | \(0.903619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.0000i | 0.661180i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | + | 14.6969i | −0.198137 | + | 0.485336i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.0000i | − | 0.461817i | −0.972975 | − | 0.230909i | \(-0.925830\pi\) | ||
0.972975 | − | 0.230909i | \(-0.0741699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.0000 | 1.44985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 12.0000i | − | 0.394985i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.89898i | − | 0.161077i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.89898 | −0.160904 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.79796i | − | 0.321461i | −0.986998 | − | 0.160730i | \(-0.948615\pi\) | ||
0.986998 | − | 0.160730i | \(-0.0513849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.79796 | + | 10.0000i | −0.321115 | + | 0.327737i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 58.7878i | 1.92462i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.89898i | 0.160043i | 0.996793 | + | 0.0800213i | \(0.0254988\pi\) | ||||
−0.996793 | + | 0.0800213i | \(0.974501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.3939 | 0.959233 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | − | 9.79796i | 0.130120 | − | 0.318728i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.6969 | 0.477586 | 0.238793 | − | 0.971070i | \(-0.423248\pi\) | ||||
0.238793 | + | 0.971070i | \(0.423248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 9.79796i | − | 0.318055i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.79796 | −0.317721 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.0000 | −1.74923 | −0.874616 | − | 0.484817i | \(-0.838886\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 18.0000i | − | 0.582466i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.6969 | + | 6.00000i | 0.474589 | + | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.0000 | 2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6969 | −0.473602 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000i | 0.707472i | 0.935345 | + | 0.353736i | \(0.115089\pi\) | ||||
−0.935345 | + | 0.353736i | \(0.884911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.5959i | 0.629512i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 30.0000i | − | 0.962746i | −0.876516 | − | 0.481373i | \(-0.840138\pi\) | ||
0.876516 | − | 0.481373i | \(-0.159862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | − | 24.4949i | 0.320585 | − | 0.785270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.00000i | − | 0.128103i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 9.79796i | − | 0.312825i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.89898 | 0.156253 | 0.0781266 | − | 0.996943i | \(-0.475106\pi\) | ||||
0.0781266 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.89898i | 0.156094i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.79796 | − | 24.0000i | 0.311872 | − | 0.763928i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.3939i | 0.934671i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000i | 0.0635321i | 0.999495 | + | 0.0317660i | \(0.0101131\pi\) | ||||
−0.999495 | + | 0.0317660i | \(0.989887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.1918i | 1.24372i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0000 | 0.316703 | 0.158352 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.5959 | −0.619987 |
(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 | 2240.2.h.a.671.1 | ✓ | 4 | |
4.3 | odd | 2 | inner | 2240.2.h.a.671.4 | yes | 4 | |
7.6 | odd | 2 | 2240.2.h.c.671.4 | yes | 4 | ||
8.3 | odd | 2 | 2240.2.h.c.671.2 | yes | 4 | ||
8.5 | even | 2 | 2240.2.h.c.671.3 | yes | 4 | ||
28.27 | even | 2 | 2240.2.h.c.671.1 | yes | 4 | ||
56.13 | odd | 2 | inner | 2240.2.h.a.671.2 | yes | 4 | |
56.27 | even | 2 | inner | 2240.2.h.a.671.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.h.a.671.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2240.2.h.a.671.2 | yes | 4 | 56.13 | odd | 2 | inner | |
2240.2.h.a.671.3 | yes | 4 | 56.27 | even | 2 | inner | |
2240.2.h.a.671.4 | yes | 4 | 4.3 | odd | 2 | inner | |
2240.2.h.c.671.1 | yes | 4 | 28.27 | even | 2 | ||
2240.2.h.c.671.2 | yes | 4 | 8.3 | odd | 2 | ||
2240.2.h.c.671.3 | yes | 4 | 8.5 | even | 2 | ||
2240.2.h.c.671.4 | yes | 4 | 7.6 | odd | 2 |