Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3997,1,Mod(13,3997)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3997, base_ring=CyclotomicField(570))
chi = DirichletCharacter(H, H._module([285, 352]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3997.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3997 = 7 \cdot 571 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3997.cz (of order \(570\), degree \(144\), 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: | \(1.99476285549\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Coefficient field: | \(\Q(\zeta_{570})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{285}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{285} - \cdots)\) |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-0.999757 - 0.0220445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3997.13 |
Dual form | 3997.1.cz.a.615.1 |
$q$-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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).
\(n\) | \(1716\) | \(2285\) |
\(\chi(n)\) | \(e\left(\frac{176}{285}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.341150 | − | 1.74650i | 0.341150 | − | 1.74650i | −0.277403 | − | 0.960754i | \(-0.589474\pi\) |
0.618553 | − | 0.785743i | \(-0.287719\pi\) | |||||||
\(3\) | 0 | 0 | 0.360939 | − | 0.932589i | \(-0.382456\pi\) | ||||
−0.360939 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(4\) | −2.00737 | − | 0.815325i | −2.00737 | − | 0.815325i | ||||
\(5\) | 0 | 0 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
−0.319482 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.461341 | + | 0.887223i | −0.461341 | + | 0.887223i | ||||
\(8\) | −1.13548 | + | 1.73798i | −1.13548 | + | 1.73798i | ||||
\(9\) | −0.739446 | − | 0.673216i | −0.739446 | − | 0.673216i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.000667889 | 0.121178i | −0.000667889 | 0.121178i | 0.997814 | + | 0.0660906i | \(0.0210526\pi\) | ||
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.381410 | − | 0.924406i | \(-0.624561\pi\) | ||||
0.381410 | + | 0.924406i | \(0.375439\pi\) | |||||||
\(14\) | 1.39215 | + | 1.10841i | 1.39215 | + | 1.10841i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.09501 | + | 1.06524i | 1.09501 | + | 1.06524i | ||||
\(17\) | 0 | 0 | −0.989750 | − | 0.142811i | \(-0.954386\pi\) | ||||
0.989750 | + | 0.142811i | \(0.0456140\pi\) | |||||||
\(18\) | −1.42803 | + | 1.06177i | −1.42803 | + | 1.06177i | ||||
\(19\) | 0 | 0 | −0.775409 | − | 0.631460i | \(-0.782456\pi\) | ||||
0.775409 | + | 0.631460i | \(0.217544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.211410 | + | 0.0425064i | 0.211410 | + | 0.0425064i | ||||
\(23\) | −1.65560 | + | 0.448511i | −1.65560 | + | 0.448511i | −0.962268 | − | 0.272103i | \(-0.912281\pi\) |
−0.693336 | + | 0.720615i | \(0.743860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.795863 | − | 0.605477i | −0.795863 | − | 0.605477i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.64946 | − | 1.40485i | 1.64946 | − | 1.40485i | ||||
\(29\) | −0.0415578 | + | 1.50764i | −0.0415578 | + | 1.50764i | 0.635724 | + | 0.771917i | \(0.280702\pi\) |
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(32\) | 0.527965 | − | 0.366083i | 0.527965 | − | 0.366083i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.935454 | + | 1.95429i | 0.935454 | + | 1.95429i | ||||
\(37\) | −0.977928 | − | 0.0756090i | −0.977928 | − | 0.0756090i | −0.421786 | − | 0.906696i | \(-0.638596\pi\) |
−0.556143 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.719909 | + | 1.59325i | 0.719909 | + | 1.59325i | 0.802489 | + | 0.596667i | \(0.203509\pi\) |
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(44\) | 0.100140 | − | 0.242706i | 0.100140 | − | 0.242706i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.218515 | + | 3.04452i | 0.218515 | + | 3.04452i | ||||
\(47\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.574329 | − | 0.818625i | −0.574329 | − | 0.818625i | ||||
\(50\) | −1.32897 | + | 1.18341i | −1.32897 | + | 1.18341i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.39478 | + | 1.29826i | 1.39478 | + | 1.29826i | 0.904357 | + | 0.426776i | \(0.140351\pi\) |
0.490424 | + | 0.871484i | \(0.336842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.01813 | − | 1.80923i | −1.01813 | − | 1.80923i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.61891 | + | 0.586912i | 2.61891 | + | 0.586912i | ||||
\(59\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.857640 | − | 0.514250i | \(-0.171930\pi\) | ||||
−0.857640 | + | 0.514250i | \(0.828070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.938430 | − | 0.345471i | 0.938430 | − | 0.345471i | ||||
\(64\) | 0.154412 | + | 0.352023i | 0.154412 | + | 0.352023i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0859078 | + | 0.373673i | −0.0859078 | + | 0.373673i | −0.999453 | − | 0.0330634i | \(-0.989474\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.46100 | + | 0.310546i | −1.46100 | + | 0.310546i | −0.868768 | − | 0.495219i | \(-0.835088\pi\) |
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(72\) | 2.00967 | − | 0.520720i | 2.00967 | − | 0.520720i | ||||
\(73\) | 0 | 0 | 0.565270 | − | 0.824906i | \(-0.308772\pi\) | ||||
−0.565270 | + | 0.824906i | \(0.691228\pi\) | |||||||
\(74\) | −0.465671 | + | 1.68216i | −0.465671 | + | 1.68216i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.107204 | − | 0.0564971i | −0.107204 | − | 0.0564971i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.77781 | − | 0.863058i | −1.77781 | − | 0.863058i | −0.956036 | − | 0.293250i | \(-0.905263\pi\) |
−0.821778 | − | 0.569808i | \(-0.807018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0935596 | + | 0.995614i | 0.0935596 | + | 0.995614i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.0385714 | − | 0.999256i | \(-0.487719\pi\) | ||||
−0.0385714 | + | 0.999256i | \(0.512281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.02821 | − | 0.713782i | 3.02821 | − | 0.713782i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.209848 | − | 0.138757i | −0.209848 | − | 0.138757i | ||||
\(89\) | 0 | 0 | 0.884667 | − | 0.466224i | \(-0.154386\pi\) | ||||
−0.884667 | + | 0.466224i | \(0.845614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.68910 | + | 0.449525i | 3.68910 | + | 0.449525i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.528360 | − | 0.849020i | \(-0.677193\pi\) | ||||
0.528360 | + | 0.849020i | \(0.322807\pi\) | |||||||
\(98\) | −1.62566 | + | 0.723790i | −1.62566 | + | 0.723790i | ||||
\(99\) | 0.0820731 | − | 0.0891552i | 0.0820731 | − | 0.0891552i | ||||
\(100\) | 1.10393 | + | 1.86431i | 1.10393 | + | 1.86431i | ||||
\(101\) | 0 | 0 | −0.970739 | − | 0.240139i | \(-0.922807\pi\) | ||||
0.970739 | + | 0.240139i | \(0.0771930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.74324 | − | 1.99308i | 2.74324 | − | 1.99308i | ||||
\(107\) | 1.28265 | − | 1.24778i | 1.28265 | − | 1.24778i | 0.329907 | − | 0.944013i | \(-0.392982\pi\) |
0.952745 | − | 0.303771i | \(-0.0982456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0165339 | + | 0.0286376i | 0.0165339 | + | 0.0286376i | 0.874174 | − | 0.485613i | \(-0.161404\pi\) |
−0.857640 | + | 0.514250i | \(0.828070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.45028 | + | 0.480077i | −1.45028 | + | 0.480077i | ||||
\(113\) | 0.464757 | − | 1.92417i | 0.464757 | − | 1.92417i | 0.0935596 | − | 0.995614i | \(-0.470175\pi\) |
0.371197 | − | 0.928554i | \(-0.378947\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.31264 | − | 2.99252i | 1.31264 | − | 2.99252i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.985256 | + | 0.0108610i | 0.985256 | + | 0.0108610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.283218 | − | 1.75682i | −0.283218 | − | 1.75682i | ||||
\(127\) | −1.36397 | + | 1.24180i | −1.36397 | + | 1.24180i | −0.421786 | + | 0.906696i | \(0.638596\pi\) |
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(128\) | 1.29440 | − | 0.290082i | 1.29440 | − | 0.290082i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.623312 | + | 0.277516i | 0.623312 | + | 0.277516i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.24524 | − | 0.947356i | 1.24524 | − | 0.947356i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.952745 | − | 0.303771i | \(-0.901754\pi\) | ||||
0.952745 | + | 0.303771i | \(0.0982456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.0439463 | + | 2.65758i | 0.0439463 | + | 2.65758i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0925618 | − | 1.52486i | −0.0925618 | − | 1.52486i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.90142 | + | 0.949105i | 1.90142 | + | 0.949105i | ||||
\(149\) | −1.85758 | − | 0.503228i | −1.85758 | − | 0.503228i | −0.857640 | − | 0.514250i | \(-0.828070\pi\) |
−0.999939 | + | 0.0110229i | \(0.996491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.82698 | + | 0.0201399i | −1.82698 | + | 0.0201399i | −0.917973 | − | 0.396642i | \(-0.870175\pi\) |
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.135245 | + | 0.167958i | −0.135245 | + | 0.167958i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.618553 | − | 0.785743i | \(-0.287719\pi\) | ||||
−0.618553 | + | 0.785743i | \(0.712281\pi\) | |||||||
\(158\) | −2.11383 | + | 2.81051i | −2.11383 | + | 2.81051i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.365869 | − | 1.67581i | 0.365869 | − | 1.67581i | ||||
\(162\) | 1.77075 | + | 0.176252i | 1.77075 | + | 0.176252i | ||||
\(163\) | 0.918145 | + | 1.76572i | 0.918145 | + | 1.76572i | 0.546948 | + | 0.837166i | \(0.315789\pi\) |
0.371197 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.709053 | + | 0.705155i | −0.709053 | + | 0.705155i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.146110 | − | 3.78521i | −0.146110 | − | 3.78521i | ||||
\(173\) | 0 | 0 | 0.930586 | − | 0.366074i | \(-0.119298\pi\) | ||||
−0.930586 | + | 0.366074i | \(0.880702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.904357 | − | 0.426776i | 0.904357 | − | 0.426776i | ||||
\(176\) | −0.129815 | + | 0.131980i | −0.129815 | + | 0.131980i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.91737 | + | 0.0634294i | −1.91737 | + | 0.0634294i | −0.968033 | − | 0.250825i | \(-0.919298\pi\) |
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.879474 | − | 0.475947i | \(-0.842105\pi\) | ||||
0.879474 | + | 0.475947i | \(0.157895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.10040 | − | 3.38669i | 1.10040 | − | 3.38669i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.248931 | + | 0.0443650i | −0.248931 | + | 0.0443650i | −0.298515 | − | 0.954405i | \(-0.596491\pi\) |
0.0495838 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.73067 | − | 0.367865i | −1.73067 | − | 0.367865i | −0.768401 | − | 0.639969i | \(-0.778947\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.485447 | + | 2.11155i | 0.485447 | + | 2.11155i | ||||
\(197\) | −0.422202 | − | 0.150165i | −0.422202 | − | 0.150165i | 0.115485 | − | 0.993309i | \(-0.463158\pi\) |
−0.537687 | + | 0.843145i | \(0.680702\pi\) | |||||||
\(198\) | −0.127710 | − | 0.173756i | −0.127710 | − | 0.173756i | ||||
\(199\) | 0 | 0 | −0.537687 | − | 0.843145i | \(-0.680702\pi\) | ||||
0.537687 | + | 0.843145i | \(0.319298\pi\) | |||||||
\(200\) | 1.95600 | − | 0.695689i | 1.95600 | − | 0.695689i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.31844 | − | 0.732408i | −1.31844 | − | 0.732408i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.52617 | + | 0.782930i | 1.52617 | + | 0.782930i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0992705 | + | 1.38311i | −0.0992705 | + | 1.38311i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
−0.768401 | + | 0.639969i | \(0.778947\pi\) | |||||||
\(212\) | −1.74134 | − | 3.74329i | −1.74134 | − | 3.74329i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.74167 | − | 2.66583i | −1.74167 | − | 2.66583i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0556561 | − | 0.0191068i | 0.0556561 | − | 0.0191068i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.709053 | − | 0.705155i | \(-0.750877\pi\) | ||||
0.709053 | + | 0.705155i | \(0.249123\pi\) | |||||||
\(224\) | 0.0812250 | + | 0.637311i | 0.0812250 | + | 0.637311i | ||||
\(225\) | 0.180881 | + | 0.983505i | 0.180881 | + | 0.983505i | ||||
\(226\) | −3.20200 | − | 1.46813i | −3.20200 | − | 1.46813i | ||||
\(227\) | 0 | 0 | −0.988116 | − | 0.153712i | \(-0.950877\pi\) | ||||
0.988116 | + | 0.153712i | \(0.0491228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.999028 | − | 0.0440782i | \(-0.985965\pi\) | ||||
0.999028 | + | 0.0440782i | \(0.0140351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.57307 | − | 1.78412i | −2.57307 | − | 1.78412i | ||||
\(233\) | −0.725862 | − | 1.08471i | −0.725862 | − | 1.08471i | −0.992658 | − | 0.120958i | \(-0.961404\pi\) |
0.266796 | − | 0.963753i | \(-0.414035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.701582 | − | 1.55269i | 0.701582 | − | 1.55269i | −0.126427 | − | 0.991976i | \(-0.540351\pi\) |
0.828009 | − | 0.560715i | \(-0.189474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.627176 | − | 0.778877i | \(-0.715789\pi\) | ||||
0.627176 | + | 0.778877i | \(0.284211\pi\) | |||||||
\(242\) | 0.355089 | − | 1.71704i | 0.355089 | − | 1.71704i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.996114 | − | 0.0880708i | \(-0.0280702\pi\) | ||||
−0.996114 | + | 0.0880708i | \(0.971930\pi\) | |||||||
\(252\) | −2.16545 | − | 0.0716362i | −2.16545 | − | 0.0716362i | ||||
\(253\) | −0.0532441 | − | 0.200923i | −0.0532441 | − | 0.200923i | ||||
\(254\) | 1.70348 | + | 2.80580i | 1.70348 | + | 2.80580i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0544509 | − | 1.97538i | −0.0544509 | − | 1.97538i | ||||
\(257\) | 0 | 0 | −0.652586 | − | 0.757715i | \(-0.726316\pi\) | ||||
0.652586 | + | 0.757715i | \(0.273684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.518241 | − | 0.832759i | 0.518241 | − | 0.832759i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.04570 | − | 1.08684i | 1.04570 | − | 1.08684i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.933341 | + | 1.10817i | 0.933341 | + | 1.10817i | 0.993931 | + | 0.110008i | \(0.0350877\pi\) |
−0.0605901 | + | 0.998163i | \(0.519298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.477114 | − | 0.680059i | 0.477114 | − | 0.680059i | ||||
\(269\) | 0 | 0 | 0.180881 | − | 0.983505i | \(-0.442105\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.22974 | − | 2.49800i | −1.22974 | − | 2.49800i | ||||
\(275\) | 0.0739022 | − | 0.0960370i | 0.0739022 | − | 0.0960370i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0621955 | − | 1.25281i | −0.0621955 | − | 1.25281i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.746821 | − | 0.665025i | \(-0.231579\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0743051 | + | 0.122388i | −0.0743051 | + | 0.122388i | −0.889752 | − | 0.456444i | \(-0.849123\pi\) |
0.815447 | + | 0.578832i | \(0.196491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.991264 | − | 0.131892i | \(-0.957895\pi\) | ||||
0.991264 | + | 0.131892i | \(0.0421053\pi\) | |||||||
\(284\) | 3.18598 | + | 0.567811i | 3.18598 | + | 0.567811i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.636854 | − | 0.0847363i | −0.636854 | − | 0.0847363i | ||||
\(289\) | 0.959210 | + | 0.282694i | 0.959210 | + | 0.282694i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.480787 | − | 0.876837i | \(-0.340351\pi\) | ||||
−0.480787 | + | 0.876837i | \(0.659649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.24183 | − | 1.61377i | 1.24183 | − | 1.61377i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.51260 | + | 3.07258i | −1.51260 | + | 3.07258i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.74569 | − | 0.0963126i | −1.74569 | − | 0.0963126i | ||||
\(302\) | −0.588100 | + | 3.19769i | −0.588100 | + | 3.19769i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.815447 | − | 0.578832i | \(-0.196491\pi\) | ||||
−0.815447 | + | 0.578832i | \(0.803509\pi\) | |||||||
\(308\) | 0.169135 | + | 0.200817i | 0.169135 | + | 0.200817i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.949339 | − | 0.314254i | \(-0.898246\pi\) | ||||
0.949339 | + | 0.314254i | \(0.101754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
−0.137354 | + | 0.990522i | \(0.543860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.86506 | + | 3.18198i | 2.86506 | + | 3.18198i | ||||
\(317\) | −0.406433 | − | 0.669434i | −0.406433 | − | 0.669434i | 0.583317 | − | 0.812244i | \(-0.301754\pi\) |
−0.989750 | + | 0.142811i | \(0.954386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.182666 | − | 0.00604285i | −0.182666 | − | 0.00604285i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.80197 | − | 1.21069i | −2.80197 | − | 1.21069i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.623940 | − | 2.07485i | 0.623940 | − | 2.07485i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.39705 | − | 1.00116i | 3.39705 | − | 1.00116i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.195377 | + | 1.85889i | 0.195377 | + | 1.85889i | 0.451533 | + | 0.892254i | \(0.350877\pi\) |
−0.256156 | + | 0.966635i | \(0.582456\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.672224 | + | 0.714266i | 0.672224 | + | 0.714266i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.60967 | − | 0.965176i | −1.60967 | − | 0.965176i | −0.982493 | − | 0.186298i | \(-0.940351\pi\) |
−0.627176 | − | 0.778877i | \(-0.715789\pi\) | |||||||
\(338\) | 0.989659 | + | 1.47892i | 0.989659 | + | 1.47892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.991264 | − | 0.131892i | 0.991264 | − | 0.131892i | ||||
\(344\) | −3.58649 | − | 0.557917i | −3.58649 | − | 0.557917i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.138298 | − | 1.08512i | −0.138298 | − | 1.08512i | −0.899598 | − | 0.436719i | \(-0.856140\pi\) |
0.761300 | − | 0.648400i | \(-0.224561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.802489 | − | 0.596667i | \(-0.796491\pi\) | ||||
0.802489 | + | 0.596667i | \(0.203509\pi\) | |||||||
\(350\) | −0.436842 | − | 1.72505i | −0.436842 | − | 1.72505i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0440087 | + | 0.0642224i | 0.0440087 | + | 0.0642224i | ||||
\(353\) | 0 | 0 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.543332 | + | 3.37032i | −0.543332 | + | 3.37032i | ||||
\(359\) | −0.507055 | − | 1.09000i | −0.507055 | − | 1.09000i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.471093 | − | 0.882084i | \(-0.343860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.202517 | + | 0.979279i | 0.202517 | + | 0.979279i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.782322 | − | 0.622874i | \(-0.214035\pi\) | ||||
−0.782322 | + | 0.622874i | \(0.785965\pi\) | |||||||
\(368\) | −2.29067 | − | 1.27249i | −2.29067 | − | 1.27249i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.79532 | + | 0.638540i | −1.79532 | + | 0.638540i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0587305 | − | 0.0799057i | −0.0587305 | − | 0.0799057i | 0.775409 | − | 0.631460i | \(-0.217544\pi\) |
−0.834139 | + | 0.551554i | \(0.814035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.85936 | − | 0.0820372i | 1.85936 | − | 0.0820372i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.00743951 | + | 0.449892i | −0.00743951 | + | 0.449892i | ||||
\(383\) | 0 | 0 | −0.993931 | − | 0.110008i | \(-0.964912\pi\) | ||||
0.993931 | + | 0.110008i | \(0.0350877\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23289 | + | 2.89711i | −1.23289 | + | 2.89711i | ||||
\(387\) | 0.540269 | − | 1.66278i | 0.540269 | − | 1.66278i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.266744 | − | 0.923837i | 0.266744 | − | 0.923837i | −0.709053 | − | 0.705155i | \(-0.750877\pi\) |
0.975796 | − | 0.218681i | \(-0.0701754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.07490 | − | 0.0686406i | 2.07490 | − | 0.0686406i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.406296 | + | 0.686146i | −0.406296 | + | 0.686146i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.237442 | + | 0.112052i | −0.237442 | + | 0.112052i | ||||
\(397\) | 0 | 0 | 0.556143 | − | 0.831087i | \(-0.312281\pi\) | ||||
−0.556143 | + | 0.831087i | \(0.687719\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.226498 | − | 1.51079i | −0.226498 | − | 1.51079i | ||||
\(401\) | 0.216783 | + | 0.168729i | 0.216783 | + | 0.168729i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.72893 | + | 2.05279i | −1.72893 | + | 2.05279i | ||||
\(407\) | 0.00981532 | − | 0.118453i | 0.00981532 | − | 0.118453i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.995083 | − | 0.0990455i | \(-0.968421\pi\) | ||||
0.995083 | + | 0.0990455i | \(0.0315789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.88804 | − | 2.39836i | 1.88804 | − | 2.39836i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.952745 | − | 0.303771i | \(-0.0982456\pi\) | ||||
−0.952745 | + | 0.303771i | \(0.901754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.660728 | − | 1.76473i | −0.660728 | − | 1.76473i | −0.644194 | − | 0.764862i | \(-0.722807\pi\) |
−0.0165339 | − | 0.999863i | \(-0.505263\pi\) | |||||||
\(422\) | 2.38174 | + | 0.645225i | 2.38174 | + | 0.645225i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.84010 | + | 0.949955i | −3.84010 | + | 0.949955i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.59211 | + | 1.45899i | −3.59211 | + | 1.45899i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.190169 | − | 0.475710i | −0.190169 | − | 0.475710i | 0.802489 | − | 0.596667i | \(-0.203509\pi\) |
−0.992658 | + | 0.120958i | \(0.961404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.956036 | − | 0.293250i | \(-0.905263\pi\) | ||||
0.956036 | + | 0.293250i | \(0.0947368\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.00984084 | − | 0.0709670i | −0.00984084 | − | 0.0709670i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.724425 | − | 0.689353i | \(-0.757895\pi\) | ||||
0.724425 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.126427 | + | 0.991976i | −0.126427 | + | 0.991976i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.24067 | − | 0.278042i | 1.24067 | − | 0.278042i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.383560 | − | 0.0254052i | −0.383560 | − | 0.0254052i | ||||
\(449\) | 0.115719 | + | 0.319762i | 0.115719 | + | 0.319762i | 0.984487 | − | 0.175457i | \(-0.0561404\pi\) |
−0.868768 | + | 0.495219i | \(0.835088\pi\) | |||||||
\(450\) | 1.77940 | + | 0.0196153i | 1.77940 | + | 0.0196153i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.50176 | + | 3.48360i | −2.50176 | + | 3.48360i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.580822 | + | 1.72274i | 0.580822 | + | 1.72274i | 0.685350 | + | 0.728214i | \(0.259649\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.94579 | + | 0.150439i | −1.94579 | + | 0.150439i | −0.989750 | − | 0.142811i | \(-0.954386\pi\) |
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(464\) | −1.65151 | + | 1.60661i | −1.65151 | + | 1.60661i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.14207 | + | 0.897667i | −2.14207 | + | 0.897667i | ||||
\(467\) | 0 | 0 | −0.982493 | − | 0.186298i | \(-0.940351\pi\) | ||||
0.982493 | + | 0.186298i | \(0.0596491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.291899 | − | 0.248610i | −0.291899 | − | 0.248610i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.193548 | + | 0.0861733i | −0.193548 | + | 0.0861733i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.157354 | − | 1.89898i | −0.157354 | − | 1.89898i | ||||
\(478\) | −2.47243 | − | 1.75501i | −2.47243 | − | 1.75501i | ||||
\(479\) | 0 | 0 | −0.992658 | − | 0.120958i | \(-0.961404\pi\) | ||||
0.992658 | + | 0.120958i | \(0.0385965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.96892 | − | 0.825106i | −1.96892 | − | 0.825106i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.636859 | + | 1.82234i | 0.636859 | + | 1.82234i | 0.565270 | + | 0.824906i | \(0.308772\pi\) |
0.0715891 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.205505 | + | 0.105425i | −0.205505 | + | 0.105425i | −0.556143 | − | 0.831087i | \(-0.687719\pi\) |
0.350638 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.398498 | − | 1.43950i | 0.398498 | − | 1.43950i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.516534 | + | 0.133838i | −0.516534 | + | 0.133838i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.0165339 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.863256 | − | 0.504766i | \(-0.831579\pi\) | ||||
0.863256 | + | 0.504766i | \(0.168421\pi\) | |||||||
\(504\) | −0.465147 | + | 2.02325i | −0.465147 | + | 2.02325i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.369075 | + | 0.0244459i | −0.369075 | + | 0.0244459i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.75046 | − | 1.38068i | 3.75046 | − | 1.38068i | ||||
\(509\) | 0 | 0 | −0.904357 | − | 0.426776i | \(-0.859649\pi\) | ||||
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.16015 | − | 0.360465i | −2.16015 | − | 0.360465i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.27761 | − | 1.18920i | −1.27761 | − | 1.18920i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.746821 | − | 0.665025i | \(-0.231579\pi\) | ||||
−0.746821 | + | 0.665025i | \(0.768421\pi\) | |||||||
\(522\) | −1.54142 | − | 2.19708i | −1.54142 | − | 2.19708i | ||||
\(523\) | 0 | 0 | 0.909007 | − | 0.416782i | \(-0.136842\pi\) | ||||
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.25383 | − | 1.25202i | 2.25383 | − | 1.25202i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.67660 | − | 0.980348i | 1.67660 | − | 0.980348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.551891 | − | 0.573605i | −0.551891 | − | 0.573605i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0995832 | − | 0.0690494i | 0.0995832 | − | 0.0690494i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.27443 | + | 1.03784i | −1.27443 | + | 1.03784i | −0.277403 | + | 0.960754i | \(0.589474\pi\) |
−0.997024 | + | 0.0770854i | \(0.975439\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.943827 | − | 1.31424i | −0.943827 | − | 1.31424i | −0.949339 | − | 0.314254i | \(-0.898246\pi\) |
0.00551154 | − | 0.999985i | \(-0.498246\pi\) | |||||||
\(548\) | −3.27207 | + | 0.886420i | −3.27207 | + | 0.886420i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.142517 | − | 0.161833i | −0.142517 | − | 0.161833i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.58590 | − | 1.17915i | 1.58590 | − | 1.17915i | ||||
\(554\) | −2.20925 | − | 0.318772i | −2.20925 | − | 0.318772i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.659944 | + | 0.525439i | 0.659944 | + | 0.525439i | 0.894729 | − | 0.446609i | \(-0.147368\pi\) |
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.188400 | + | 0.171526i | 0.188400 | + | 0.171526i | ||||
\(563\) | 0 | 0 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.926494 | − | 0.376309i | −0.926494 | − | 0.376309i | ||||
\(568\) | 1.11922 | − | 2.89182i | 1.11922 | − | 2.89182i | ||||
\(569\) | −0.383328 | + | 1.96243i | −0.383328 | + | 1.96243i | −0.170028 | + | 0.985439i | \(0.554386\pi\) |
−0.213300 | + | 0.976987i | \(0.568421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.716783 | + | 0.697297i | 0.716783 | + | 0.697297i | ||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.58920 | + | 0.645476i | 1.58920 | + | 0.645476i | ||||
\(576\) | 0.122809 | − | 0.364255i | 0.122809 | − | 0.364255i | ||||
\(577\) | 0 | 0 | −0.846095 | − | 0.533032i | \(-0.821053\pi\) | ||||
0.846095 | + | 0.533032i | \(0.178947\pi\) | |||||||
\(578\) | 0.820958 | − | 1.57882i | 0.820958 | − | 1.57882i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.158253 | + | 0.168150i | −0.158253 | + | 0.168150i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.716783 | − | 0.697297i | \(-0.754386\pi\) | ||||
0.716783 | + | 0.697297i | \(0.245614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.990298 | − | 1.12452i | −0.990298 | − | 1.12452i | ||||
\(593\) | 0 | 0 | −0.980380 | − | 0.197117i | \(-0.936842\pi\) | ||||
0.980380 | + | 0.197117i | \(0.0631579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.31856 | + | 2.52470i | 3.31856 | + | 2.52470i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.32279 | + | 1.12662i | −1.32279 | + | 1.12662i | −0.340293 | + | 0.940319i | \(0.610526\pi\) |
−0.982493 | + | 0.186298i | \(0.940351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.775409 | − | 0.631460i | \(-0.217544\pi\) | ||||
−0.775409 | + | 0.631460i | \(0.782456\pi\) | |||||||
\(602\) | −0.763753 | + | 3.01599i | −0.763753 | + | 3.01599i | ||||
\(603\) | 0.315087 | − | 0.218477i | 0.315087 | − | 0.218477i | ||||
\(604\) | 3.68385 | + | 1.44915i | 3.68385 | + | 1.44915i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.431754 | − | 0.901991i | \(-0.642105\pi\) | ||||
0.431754 | + | 0.901991i | \(0.357895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.478940 | + | 0.280047i | −0.478940 | + | 0.280047i | −0.724425 | − | 0.689353i | \(-0.757895\pi\) |
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.219919 | − | 0.122167i | 0.219919 | − | 0.122167i | ||||
\(617\) | −0.113950 | − | 1.58764i | −0.113950 | − | 1.58764i | −0.660898 | − | 0.750475i | \(-0.729825\pi\) |
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.909007 | − | 0.416782i | \(-0.136842\pi\) | ||||
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.266796 | + | 0.963753i | 0.266796 | + | 0.963753i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.941270 | + | 1.76245i | 0.941270 | + | 1.76245i | 0.509516 | + | 0.860461i | \(0.329825\pi\) |
0.431754 | + | 0.901991i | \(0.357895\pi\) | |||||||
\(632\) | 3.51866 | − | 2.10982i | 3.51866 | − | 2.10982i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.30782 | + | 0.481456i | −1.30782 | + | 0.481456i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0728702 | + | 0.316963i | −0.0728702 | + | 0.316963i | ||||
\(639\) | 1.28940 | + | 0.753939i | 1.28940 | + | 0.753939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.758728 | − | 0.489756i | 0.758728 | − | 0.489756i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.863256 | + | 0.504766i | \(0.168421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.968033 | − | 0.250825i | \(-0.0807018\pi\) | ||||
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(644\) | −2.10076 | + | 3.06567i | −2.10076 | + | 3.06567i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.480787 | − | 0.876837i | \(-0.659649\pi\) | ||||
0.480787 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(648\) | −1.83660 | − | 0.967896i | −1.83660 | − | 0.967896i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.403425 | − | 4.29305i | −0.403425 | − | 4.29305i | ||||
\(653\) | 0.572457 | − | 0.0633595i | 0.572457 | − | 0.0633595i | 0.180881 | − | 0.983505i | \(-0.442105\pi\) |
0.391577 | + | 0.920146i | \(0.371930\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.445090 | − | 0.294304i | −0.445090 | − | 0.294304i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(662\) | 3.31320 | + | 0.292934i | 3.31320 | + | 0.292934i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.47679 | − | 0.930365i | 1.47679 | − | 0.930365i | ||||
\(667\) | −0.607391 | − | 2.51469i | −0.607391 | − | 2.51469i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.901738 | − | 0.768010i | −0.901738 | − | 0.768010i | 0.0715891 | − | 0.997434i | \(-0.477193\pi\) |
−0.973327 | + | 0.229424i | \(0.926316\pi\) | |||||||
\(674\) | −2.23481 | + | 2.48201i | −2.23481 | + | 2.48201i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.99827 | − | 0.837403i | 1.99827 | − | 0.837403i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.89579 | − | 0.627554i | 1.89579 | − | 0.627554i | 0.930586 | − | 0.366074i | \(-0.119298\pi\) |
0.965209 | − | 0.261480i | \(-0.0842105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.107820 | − | 1.77623i | 0.107820 | − | 1.77623i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.908890 | + | 2.51150i | −0.908890 | + | 2.51150i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.956036 | − | 0.293250i | \(-0.0947368\pi\) | ||||
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0412368 | + | 0.113948i | 0.0412368 | + | 0.113948i | ||||
\(694\) | −1.94234 | − | 0.128651i | −1.94234 | − | 0.128651i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.16334 | + | 0.119355i | −2.16334 | + | 0.119355i | ||||
\(701\) | −0.252792 | + | 1.98347i | −0.252792 | + | 1.98347i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.148264 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.0427607 | + | 0.0184762i | −0.0427607 | + | 0.0184762i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.31044 | − | 0.401958i | −1.31044 | − | 0.401958i | −0.441671 | − | 0.897177i | \(-0.645614\pi\) |
−0.868768 | + | 0.495219i | \(0.835088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.733572 | + | 1.83504i | 0.733572 | + | 1.83504i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.90060 | + | 1.43595i | 3.90060 | + | 1.43595i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.07666 | + | 0.513718i | −2.07666 | + | 0.513718i | ||||
\(719\) | 0 | 0 | −0.894729 | − | 0.446609i | \(-0.852632\pi\) | ||||
0.894729 | + | 0.446609i | \(0.147368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.77940 | − | 0.0196153i | 1.77940 | − | 0.0196153i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.945916 | − | 1.17471i | 0.945916 | − | 1.17471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.934564 | − | 0.355794i | \(-0.884211\pi\) | ||||
0.934564 | + | 0.355794i | \(0.115789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.601081 | − | 0.799188i | 0.601081 | − | 0.799188i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.995083 | − | 0.0990455i | \(-0.968421\pi\) | ||||
0.995083 | + | 0.0990455i | \(0.0315789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.709908 | + | 0.842886i | −0.709908 | + | 0.842886i | ||||
\(737\) | −0.0452237 | − | 0.0106597i | −0.0452237 | − | 0.0106597i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.0545438 | + | 0.00787011i | −0.0545438 | + | 0.00787011i | −0.170028 | − | 0.985439i | \(-0.554386\pi\) |
0.115485 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.502737 | + | 3.35335i | 0.502737 | + | 3.35335i | ||||
\(743\) | −0.0638749 | − | 1.65479i | −0.0638749 | − | 1.65479i | −0.592235 | − | 0.805765i | \(-0.701754\pi\) |
0.528360 | − | 0.849020i | \(-0.322807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.159591 | + | 0.0753128i | −0.159591 | + | 0.0753128i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.515322 | + | 1.71365i | 0.515322 | + | 1.71365i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.74603 | − | 0.212758i | 1.74603 | − | 0.212758i | 0.815447 | − | 0.578832i | \(-0.196491\pi\) |
0.930586 | + | 0.366074i | \(0.119298\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.43619 | + | 1.36666i | −1.43619 | + | 1.36666i | −0.627176 | + | 0.778877i | \(0.715789\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(758\) | 0.491044 | − | 3.27536i | 0.491044 | − | 3.27536i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.360939 | − | 0.932589i | \(-0.617544\pi\) | ||||
0.360939 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0330358 | + | 0.00145757i | −0.0330358 | + | 0.00145757i | ||||
\(764\) | 0.535870 | + | 0.113903i | 0.535870 | + | 0.113903i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.592235 | − | 0.805765i | \(-0.701754\pi\) | ||||
0.592235 | + | 0.805765i | \(0.298246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.17417 | + | 2.14950i | 3.17417 | + | 2.14950i | ||||
\(773\) | 0 | 0 | 0.421786 | − | 0.906696i | \(-0.361404\pi\) | ||||
−0.421786 | + | 0.906696i | \(0.638596\pi\) | |||||||
\(774\) | −2.71972 | − | 1.51083i | −2.71972 | − | 1.51083i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.52248 | − | 0.781034i | −1.52248 | − | 0.781034i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0366556 | − | 0.177249i | −0.0366556 | − | 0.177249i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.243138 | − | 1.50820i | 0.243138 | − | 1.50820i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.115485 | − | 0.993309i | \(-0.463158\pi\) | ||||
−0.115485 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(788\) | 0.725085 | + | 0.645669i | 0.725085 | + | 0.645669i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.49275 | + | 1.30004i | 1.49275 | + | 1.30004i | ||||
\(792\) | 0.0617577 | + | 0.243876i | 0.0617577 | + | 0.243876i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.909007 | − | 0.416782i | \(-0.863158\pi\) | ||||
0.909007 | + | 0.416782i | \(0.136842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.641842 | − | 0.0283188i | −0.641842 | − | 0.0283188i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.368639 | − | 0.321048i | 0.368639 | − | 0.321048i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.564407 | + | 0.599706i | 0.564407 | + | 0.599706i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
−0.381410 | + | 0.924406i | \(0.624561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(812\) | 2.04945 | + | 2.54517i | 2.04945 | + | 2.54517i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.203530 | − | 0.0575527i | −0.203530 | − | 0.0575527i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.133158 | − | 0.312902i | −0.133158 | − | 0.312902i | 0.840168 | − | 0.542326i | \(-0.182456\pi\) |
−0.973327 | + | 0.229424i | \(0.926316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.512032 | + | 0.0169388i | 0.512032 | + | 0.0169388i | 0.287976 | − | 0.957638i | \(-0.407018\pi\) |
0.224056 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.0403384 | + | 1.46340i | 0.0403384 | + | 1.46340i | 0.701237 | + | 0.712928i | \(0.252632\pi\) |
−0.660898 | + | 0.750475i | \(0.729825\pi\) | |||||||
\(828\) | −2.42526 | − | 2.81596i | −2.42526 | − | 2.81596i | ||||
\(829\) | 0 | 0 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
−0.137354 | + | 0.990522i | \(0.543860\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.574329 | − | 0.818625i | \(-0.305263\pi\) | ||||
−0.574329 | + | 0.818625i | \(0.694737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.27277 | − | 0.0702208i | −1.27277 | − | 0.0702208i | ||||
\(842\) | −3.30749 | + | 0.551923i | −3.30749 | + | 0.551923i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.32696 | − | 2.69549i | 1.32696 | − | 2.69549i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.464175 | + | 0.869131i | −0.464175 | + | 0.869131i | ||||
\(848\) | 0.144337 | + | 2.90738i | 0.144337 | + | 2.90738i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.65297 | − | 0.313434i | 1.65297 | − | 0.313434i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.959210 | − | 0.282694i | \(-0.908772\pi\) | ||||
0.959210 | + | 0.282694i | \(0.0912281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.712200 | + | 3.64607i | 0.712200 | + | 3.64607i | ||||
\(857\) | 0 | 0 | −0.191711 | − | 0.981451i | \(-0.561404\pi\) | ||||
0.191711 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.991264 | − | 0.131892i | \(-0.957895\pi\) | ||||
0.991264 | + | 0.131892i | \(0.0421053\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.895702 | + | 0.169841i | −0.895702 | + | 0.169841i | ||||
\(863\) | 1.50078 | − | 0.992354i | 1.50078 | − | 0.992354i | 0.509516 | − | 0.860461i | \(-0.329825\pi\) |
0.991264 | − | 0.131892i | \(-0.0421053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.105771 | − | 0.214856i | 0.105771 | − | 0.214856i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.0685457 | − | 0.00378177i | −0.0685457 | − | 0.00378177i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) |
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.693336 | − | 0.720615i | \(-0.256140\pi\) | ||||
−0.693336 | + | 0.720615i | \(0.743860\pi\) | |||||||
\(882\) | 1.68935 | + | 0.559216i | 1.68935 | + | 0.559216i | ||||
\(883\) | −0.110457 | + | 0.177494i | −0.110457 | + | 0.177494i | −0.899598 | − | 0.436719i | \(-0.856140\pi\) |
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0623430 | − | 2.26169i | −0.0623430 | − | 2.26169i | ||||
\(887\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.472500 | − | 1.78304i | −0.472500 | − | 1.78304i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.120709 | + | 0.0106724i | −0.120709 | + | 0.0106724i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.339793 | + | 1.28225i | −0.339793 | + | 1.28225i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.597941 | − | 0.0930162i | 0.597941 | − | 0.0930162i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.438781 | − | 2.12174i | 0.438781 | − | 2.12174i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.81645 | + | 2.99260i | 2.81645 | + | 2.99260i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0296030 | + | 0.596295i | −0.0296030 | + | 0.596295i | 0.938430 | + | 0.345471i | \(0.112281\pi\) |
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.906559 | + | 0.789523i | −0.906559 | + | 0.789523i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.0715891 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.20690 | − | 0.426692i | 3.20690 | − | 0.426692i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.256508 | − | 0.255098i | −0.256508 | − | 0.255098i | 0.565270 | − | 0.824906i | \(-0.308772\pi\) |
−0.821778 | + | 0.569808i | \(0.807018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.732518 | + | 0.652287i | 0.732518 | + | 0.652287i | ||||
\(926\) | −0.401063 | + | 3.44963i | −0.401063 | + | 3.44963i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.529980 | + | 0.811194i | 0.529980 | + | 0.811194i | ||||
\(929\) | 0 | 0 | 0.159156 | − | 0.987253i | \(-0.449123\pi\) | ||||
−0.159156 | + | 0.987253i | \(0.550877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.572685 | + | 2.76923i | 0.572685 | + | 2.76923i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.999757 | − | 0.0220445i | \(-0.992982\pi\) | ||||
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(938\) | −0.533778 | + | 0.424987i | −0.533778 | + | 0.424987i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.828009 | − | 0.560715i | \(-0.810526\pi\) | ||||
0.828009 | + | 0.560715i | \(0.189474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0844724 | + | 0.367430i | 0.0844724 | + | 0.367430i | ||||
\(947\) | 0.394576 | − | 1.26153i | 0.394576 | − | 1.26153i | −0.518970 | − | 0.854793i | \(-0.673684\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.0299052 | + | 1.80847i | −0.0299052 | + | 1.80847i | 0.411766 | + | 0.911290i | \(0.364912\pi\) |
−0.441671 | + | 0.897177i | \(0.645614\pi\) | |||||||
\(954\) | −3.37025 | − | 0.373019i | −3.37025 | − | 0.373019i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.67429 | + | 2.54481i | −2.67429 | + | 2.54481i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.266034 | + | 1.54186i | 0.266034 | + | 1.54186i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.879474 | − | 0.475947i | −0.879474 | − | 0.475947i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.78848 | + | 0.0591655i | −1.78848 | + | 0.0591655i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.21027 | − | 0.571138i | 1.21027 | − | 0.571138i | 0.287976 | − | 0.957638i | \(-0.407018\pi\) |
0.922290 | + | 0.386499i | \(0.126316\pi\) | |||||||
\(968\) | −1.13762 | + | 1.70003i | −1.13762 | + | 1.70003i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.148264 | − | 0.988948i | \(-0.547368\pi\) | ||||
0.148264 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.39998 | − | 0.490582i | 3.39998 | − | 0.490582i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.739958 | − | 0.878565i | 0.739958 | − | 0.878565i | −0.256156 | − | 0.966635i | \(-0.582456\pi\) |
0.996114 | + | 0.0880708i | \(0.0280702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.00705337 | − | 0.0323069i | 0.00705337 | − | 0.0323069i | ||||
\(982\) | 0.114016 | + | 0.394880i | 0.114016 | + | 0.394880i | ||||
\(983\) | 0 | 0 | 0.899598 | − | 0.436719i | \(-0.143860\pi\) | ||||
−0.899598 | + | 0.436719i | \(0.856140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.90648 | − | 2.31491i | −1.90648 | − | 2.31491i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.701233 | + | 0.00773009i | −0.701233 | + | 0.00773009i | −0.360939 | − | 0.932589i | \(-0.617544\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.37814 | − | 1.18706i | −2.37814 | − | 1.18706i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.938430 | − | 0.345471i | \(-0.887719\pi\) | ||||
0.938430 | + | 0.345471i | \(0.112281\pi\) | |||||||
\(998\) | 0.0575320 | + | 0.947784i | 0.0575320 | + | 0.947784i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3997.1.cz.a.13.1 | ✓ | 144 | |
7.6 | odd | 2 | CM | 3997.1.cz.a.13.1 | ✓ | 144 | |
571.44 | even | 285 | inner | 3997.1.cz.a.615.1 | yes | 144 | |
3997.615 | odd | 570 | inner | 3997.1.cz.a.615.1 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3997.1.cz.a.13.1 | ✓ | 144 | 1.1 | even | 1 | trivial | |
3997.1.cz.a.13.1 | ✓ | 144 | 7.6 | odd | 2 | CM | |
3997.1.cz.a.615.1 | yes | 144 | 571.44 | even | 285 | inner | |
3997.1.cz.a.615.1 | yes | 144 | 3997.615 | odd | 570 | inner |