Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(865,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.i (of order \(3\), degree \(2\), not 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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.865 |
Dual form | 2592.2.i.f.1729.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | + | 6.92820i | −0.742781 | + | 1.28654i | 0.208443 | + | 0.978035i | \(0.433160\pi\) |
−0.951224 | + | 0.308500i | \(0.900173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | − | 6.92820i | −0.624695 | − | 1.08200i | −0.988600 | − | 0.150567i | \(-0.951890\pi\) |
0.363905 | − | 0.931436i | \(-0.381443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00000 | − | 8.66025i | 0.729325 | − | 1.26323i | −0.227844 | − | 0.973698i | \(-0.573168\pi\) |
0.957169 | − | 0.289530i | \(-0.0934991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.00000 | − | 12.1244i | −0.911322 | − | 1.57846i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
−0.0991242 | − | 0.995075i | \(-0.531604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.50000 | − | 11.2583i | −0.794101 | − | 1.37542i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) |
0.129307 | − | 0.991605i | \(-0.458725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | − | 1.73205i | −0.113961 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | − | 10.3923i | −0.650791 | − | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00000 | − | 8.66025i | −0.512989 | − | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.50000 | − | 2.59808i | −0.147799 | − | 0.255996i | 0.782614 | − | 0.622507i | \(-0.213886\pi\) |
−0.930414 | + | 0.366511i | \(0.880552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | + | 8.66025i | 0.470360 | + | 0.814688i | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | + | 10.3923i | −0.559503 | + | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 5.19615i | 0.275010 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | − | 13.8564i | −0.698963 | − | 1.21064i | −0.968826 | − | 0.247741i | \(-0.920312\pi\) |
0.269863 | − | 0.962899i | \(-0.413022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50000 | − | 4.33013i | 0.216777 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | + | 7.79423i | −0.366205 | + | 0.634285i | −0.988969 | − | 0.148124i | \(-0.952676\pi\) |
0.622764 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | − | 13.8564i | 0.642575 | − | 1.11297i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.00000 | − | 12.1244i | −0.541676 | − | 0.938211i | −0.998808 | − | 0.0488118i | \(-0.984457\pi\) |
0.457132 | − | 0.889399i | \(-0.348877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0000 | − | 20.7846i | 0.912343 | − | 1.58022i | 0.101598 | − | 0.994826i | \(-0.467605\pi\) |
0.810745 | − | 0.585399i | \(-0.199062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0000 | −1.41226 | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.00000 | + | 8.66025i | 0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5000 | + | 18.1865i | 0.755807 | + | 1.30910i | 0.944972 | + | 0.327150i | \(0.106088\pi\) |
−0.189166 | + | 0.981945i | \(0.560578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0000 | 1.34687 | 0.673437 | − | 0.739244i | \(-0.264817\pi\) | ||||
0.673437 | + | 0.739244i | \(0.264817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | + | 6.92820i | 0.280745 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 13.8564i | −0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.00000 | − | 8.66025i | 0.345857 | − | 0.599042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | + | 0.866025i | 0.0344214 | + | 0.0596196i | 0.882723 | − | 0.469894i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | − | 13.8564i | 0.535720 | − | 0.927894i | −0.463409 | − | 0.886145i | \(-0.653374\pi\) |
0.999128 | − | 0.0417488i | \(-0.0132929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | − | 22.5167i | −0.859064 | − | 1.48794i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) |
0.0137585 | − | 0.999905i | \(-0.495620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0000 | −1.30466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | − | 10.3923i | −0.388108 | − | 0.672222i | 0.604087 | − | 0.796918i | \(-0.293538\pi\) |
−0.992195 | + | 0.124696i | \(0.960204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | + | 11.2583i | −0.418702 | + | 0.725213i | −0.995809 | − | 0.0914555i | \(-0.970848\pi\) |
0.577107 | + | 0.816668i | \(0.304181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.00000 | − | 10.3923i | 0.383326 | − | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | − | 4.33013i | −0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00000 | + | 3.46410i | 0.124757 | + | 0.216085i | 0.921638 | − | 0.388051i | \(-0.126852\pi\) |
−0.796881 | + | 0.604136i | \(0.793518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | + | 4.33013i | −0.155342 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | − | 6.92820i | −0.245718 | − | 0.425596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0000 | 1.27566 | 0.637830 | − | 0.770178i | \(-0.279832\pi\) | ||||
0.637830 | + | 0.770178i | \(0.279832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | − | 1.73205i | −0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | + | 20.7846i | −0.715860 | + | 1.23991i | 0.246767 | + | 0.969075i | \(0.420632\pi\) |
−0.962627 | + | 0.270831i | \(0.912702\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0000 | + | 17.3205i | 0.594438 | + | 1.02960i | 0.993626 | + | 0.112728i | \(0.0359589\pi\) |
−0.399188 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.00000 | + | 15.5885i | 0.525786 | + | 0.910687i | 0.999549 | + | 0.0300351i | \(0.00956192\pi\) |
−0.473763 | + | 0.880652i | \(0.657105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0000 | + | 24.2487i | −0.815112 | + | 1.41181i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 3.46410i | 0.115278 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | + | 25.9808i | 0.850572 | + | 1.47323i | 0.880693 | + | 0.473688i | \(0.157077\pi\) |
−0.0301210 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | − | 14.7224i | 0.480448 | − | 0.832161i | −0.519300 | − | 0.854592i | \(-0.673807\pi\) |
0.999748 | + | 0.0224310i | \(0.00714060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | + | 10.3923i | −0.336994 | + | 0.583690i | −0.983866 | − | 0.178908i | \(-0.942743\pi\) |
0.646872 | + | 0.762598i | \(0.276077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | + | 13.8564i | 0.447914 | + | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.00000 | − | 8.66025i | −0.275659 | − | 0.477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5000 | − | 25.1147i | 0.796992 | − | 1.38043i | −0.124574 | − | 0.992210i | \(-0.539757\pi\) |
0.921567 | − | 0.388221i | \(-0.126910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.0000 | + | 22.5167i | −0.710266 | + | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5000 | + | 26.8468i | 0.844339 | + | 1.46244i | 0.886194 | + | 0.463314i | \(0.153340\pi\) |
−0.0418554 | + | 0.999124i | \(0.513327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00000 | + | 3.46410i | 0.107366 | + | 0.185963i | 0.914702 | − | 0.404128i | \(-0.132425\pi\) |
−0.807337 | + | 0.590091i | \(0.799092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50000 | − | 4.33013i | 0.133822 | − | 0.231786i | −0.791325 | − | 0.611396i | \(-0.790608\pi\) |
0.925147 | + | 0.379610i | \(0.123942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.00000 | + | 3.46410i | −0.106449 | + | 0.184376i | −0.914329 | − | 0.404971i | \(-0.867282\pi\) |
0.807880 | + | 0.589347i | \(0.200615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | + | 6.92820i | 0.212298 | + | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.0000 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | − | 15.5885i | −0.471082 | − | 0.815937i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.50000 | + | 12.9904i | −0.391497 | + | 0.678092i | −0.992647 | − | 0.121044i | \(-0.961376\pi\) |
0.601150 | + | 0.799136i | \(0.294709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | − | 3.46410i | 0.103835 | − | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | + | 3.46410i | −0.101929 | + | 0.176547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 31.1769i | −0.910299 | − | 1.57668i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.0000 | −1.10694 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0000 | − | 24.2487i | −0.699127 | − | 1.21092i | −0.968770 | − | 0.247962i | \(-0.920239\pi\) |
0.269643 | − | 0.962960i | \(-0.413094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.00000 | + | 8.66025i | −0.247841 | + | 0.429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.0000 | −0.688895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0000 | + | 22.5167i | 0.635092 | + | 1.10001i | 0.986496 | + | 0.163787i | \(0.0523710\pi\) |
−0.351404 | + | 0.936224i | \(0.614296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50000 | − | 16.4545i | 0.463002 | − | 0.801942i | −0.536107 | − | 0.844150i | \(-0.680106\pi\) |
0.999109 | + | 0.0422075i | \(0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.50000 | + | 2.59808i | 0.0725901 | + | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000 | 1.44505 | 0.722525 | − | 0.691345i | \(-0.242982\pi\) | ||||
0.722525 | + | 0.691345i | \(0.242982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0000 | − | 25.9808i | −0.717547 | − | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0000 | + | 31.1769i | −0.855206 | + | 1.48126i | 0.0212481 | + | 0.999774i | \(0.493236\pi\) |
−0.876454 | + | 0.481486i | \(0.840097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | + | 1.73205i | 0.0468807 | + | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | + | 25.9808i | −0.698620 | + | 1.21004i | 0.270326 | + | 0.962769i | \(0.412869\pi\) |
−0.968945 | + | 0.247276i | \(0.920465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.50000 | − | 16.4545i | −0.441502 | − | 0.764705i | 0.556299 | − | 0.830982i | \(-0.312221\pi\) |
−0.997801 | + | 0.0662777i | \(0.978888\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.00000 | −0.0925490 | −0.0462745 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462745 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0000 | −0.600284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | + | 6.92820i | 0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0000 | 0.498458 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.00000 | + | 12.1244i | 0.315906 | + | 0.547165i | 0.979630 | − | 0.200813i | \(-0.0643584\pi\) |
−0.663724 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0000 | + | 41.5692i | −1.08091 | + | 1.87218i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.00000 | + | 3.46410i | −0.0897123 | + | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0000 | − | 20.7846i | −0.537194 | − | 0.930447i | −0.999054 | − | 0.0434940i | \(-0.986151\pi\) |
0.461860 | − | 0.886953i | \(-0.347182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.50000 | − | 7.79423i | 0.199068 | − | 0.344796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.00000 | + | 5.19615i | −0.132196 | + | 0.228970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | − | 17.3205i | −0.439799 | − | 0.761755i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | −0.655904 | −0.327952 | − | 0.944694i | \(-0.606358\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.00000 | + | 6.92820i | −0.173259 | + | 0.300094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.00000 | − | 3.46410i | −0.0864675 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0000 | 1.59075 | 0.795377 | − | 0.606115i | \(-0.207273\pi\) | ||||
0.795377 | + | 0.606115i | \(0.207273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | + | 17.3205i | 0.428353 | + | 0.741929i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.50000 | + | 12.9904i | −0.320677 | + | 0.555429i | −0.980628 | − | 0.195880i | \(-0.937244\pi\) |
0.659951 | + | 0.751309i | \(0.270577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.0000 | + | 34.6410i | −0.852029 | + | 1.47576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.50000 | − | 9.52628i | −0.233884 | − | 0.405099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0000 | 0.593199 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | − | 17.3205i | 0.420703 | − | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.00000 | − | 8.66025i | 0.209611 | − | 0.363057i | −0.741981 | − | 0.670421i | \(-0.766114\pi\) |
0.951592 | + | 0.307364i | \(0.0994469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | + | 16.4545i | 0.397563 | + | 0.688599i | 0.993425 | − | 0.114488i | \(-0.0365228\pi\) |
−0.595862 | + | 0.803087i | \(0.703189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | 0.124892 | 0.0624458 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.00000 | − | 5.19615i | 0.123823 | − | 0.214468i | −0.797449 | − | 0.603386i | \(-0.793818\pi\) |
0.921272 | + | 0.388918i | \(0.127151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | + | 34.6410i | 0.824086 | + | 1.42736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.00000 | − | 6.92820i | −0.163436 | − | 0.283079i | 0.772663 | − | 0.634816i | \(-0.218924\pi\) |
−0.936099 | + | 0.351738i | \(0.885591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | − | 22.5167i | 0.530281 | − | 0.918474i | −0.469095 | − | 0.883148i | \(-0.655420\pi\) |
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5000 | + | 35.5070i | 0.832069 | + | 1.44119i | 0.896394 | + | 0.443257i | \(0.146177\pi\) |
−0.0643251 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0000 | −0.404557 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.00000 | −0.363507 | −0.181753 | − | 0.983344i | \(-0.558177\pi\) | ||||
−0.181753 | + | 0.983344i | \(0.558177\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0000 | − | 36.3731i | −0.845428 | − | 1.46432i | −0.885249 | − | 0.465118i | \(-0.846012\pi\) |
0.0398207 | − | 0.999207i | \(-0.487321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.50000 | + | 7.79423i | −0.180870 | + | 0.313276i | −0.942177 | − | 0.335115i | \(-0.891225\pi\) |
0.761307 | + | 0.648392i | \(0.224558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.00000 | + | 1.73205i | −0.0400642 | + | 0.0693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.0000 | −1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00000 | 0.0398094 | 0.0199047 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199047 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0000 | + | 34.6410i | 0.793676 | + | 1.37469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 5.19615i | 0.118864 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | + | 3.46410i | −0.0789953 | + | 0.136824i | −0.902817 | − | 0.430026i | \(-0.858505\pi\) |
0.823821 | + | 0.566849i | \(0.191838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | − | 10.3923i | −0.236617 | − | 0.409832i | 0.723124 | − | 0.690718i | \(-0.242705\pi\) |
−0.959741 | + | 0.280885i | \(0.909372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.0000 | + | 38.1051i | 0.860927 | + | 1.49117i | 0.871036 | + | 0.491220i | \(0.163449\pi\) |
−0.0101092 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | + | 27.7128i | −0.625172 | + | 1.08283i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5000 | − | 19.9186i | −0.447298 | − | 0.774743i | 0.550911 | − | 0.834564i | \(-0.314280\pi\) |
−0.998209 | + | 0.0598209i | \(0.980947\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0000 | −0.387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0000 | 1.85857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | + | 5.19615i | 0.115814 | + | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5000 | + | 19.9186i | −0.443292 | + | 0.767805i | −0.997932 | − | 0.0642860i | \(-0.979523\pi\) |
0.554639 | + | 0.832091i | \(0.312856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.00000 | − | 12.1244i | 0.269032 | − | 0.465977i | −0.699580 | − | 0.714554i | \(-0.746630\pi\) |
0.968612 | + | 0.248577i | \(0.0799630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.500000 | + | 0.866025i | 0.0191882 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0000 | 0.918334 | 0.459167 | − | 0.888350i | \(-0.348148\pi\) | ||||
0.459167 | + | 0.888350i | \(0.348148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | − | 3.46410i | 0.0760836 | − | 0.131781i | −0.825473 | − | 0.564441i | \(-0.809092\pi\) |
0.901557 | + | 0.432660i | \(0.142425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.00000 | − | 8.66025i | 0.189661 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | − | 41.5692i | −0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0000 | −0.942893 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5000 | − | 19.9186i | 0.431892 | − | 0.748058i | −0.565145 | − | 0.824992i | \(-0.691180\pi\) |
0.997036 | + | 0.0769337i | \(0.0245130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | − | 41.5692i | 0.898807 | − | 1.55678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | + | 3.46410i | 0.0747958 | + | 0.129550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −52.0000 | −1.93927 | −0.969636 | − | 0.244551i | \(-0.921359\pi\) | ||||
−0.969636 | + | 0.244551i | \(0.921359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | + | 6.92820i | 0.148556 | + | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0000 | − | 41.5692i | 0.890111 | − | 1.54172i | 0.0503692 | − | 0.998731i | \(-0.483960\pi\) |
0.839742 | − | 0.542986i | \(-0.182706\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0000 | + | 29.4449i | 0.627909 | + | 1.08757i | 0.987971 | + | 0.154642i | \(0.0494225\pi\) |
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.0000 | −0.957722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0000 | + | 36.3731i | 0.770415 | + | 1.33440i | 0.937336 | + | 0.348428i | \(0.113284\pi\) |
−0.166920 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | − | 20.7846i | 0.439646 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.00000 | − | 1.73205i | 0.0365392 | − | 0.0632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5000 | − | 21.6506i | −0.456131 | − | 0.790043i | 0.542621 | − | 0.839978i | \(-0.317432\pi\) |
−0.998752 | + | 0.0499348i | \(0.984099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.0000 | 0.655087 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0000 | 1.19941 | 0.599703 | − | 0.800223i | \(-0.295286\pi\) | ||||
0.599703 | + | 0.800223i | \(0.295286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | + | 36.3731i | 0.761249 | + | 1.31852i | 0.942207 | + | 0.335032i | \(0.108747\pi\) |
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | + | 8.66025i | −0.181012 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.00000 | + | 12.1244i | −0.252755 | + | 0.437785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.50000 | + | 14.7224i | 0.306518 | + | 0.530904i | 0.977598 | − | 0.210480i | \(-0.0675028\pi\) |
−0.671080 | + | 0.741385i | \(0.734169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.0000 | −1.29483 | −0.647415 | − | 0.762138i | \(-0.724150\pi\) | ||||
−0.647415 | + | 0.762138i | \(0.724150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0000 | − | 34.6410i | −0.716574 | − | 1.24114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | + | 6.92820i | −0.143131 | + | 0.247911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | + | 3.46410i | −0.0713831 | + | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | + | 2.59808i | 0.0534692 | + | 0.0926114i | 0.891521 | − | 0.452979i | \(-0.149639\pi\) |
−0.838052 | + | 0.545590i | \(0.816305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.00000 | 0.106533 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | + | 20.7846i | 0.425062 | + | 0.736229i | 0.996426 | − | 0.0844678i | \(-0.0269190\pi\) |
−0.571364 | + | 0.820696i | \(0.693586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0000 | − | 51.9615i | 1.06132 | − | 1.83827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.00000 | − | 15.5885i | 0.317603 | − | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | + | 10.3923i | 0.211472 | + | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.0000 | −0.703163 | −0.351581 | − | 0.936157i | \(-0.614356\pi\) | ||||
−0.351581 | + | 0.936157i | \(0.614356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0000 | − | 19.0526i | −0.385313 | − | 0.667382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0000 | + | 17.3205i | −0.349856 | + | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.00000 | + | 1.73205i | −0.0349002 | + | 0.0604490i | −0.882948 | − | 0.469471i | \(-0.844445\pi\) |
0.848048 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5000 | + | 37.2391i | 0.749443 | + | 1.29807i | 0.948090 | + | 0.318002i | \(0.103012\pi\) |
−0.198647 | + | 0.980071i | \(0.563655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.00000 | −0.0695468 | −0.0347734 | − | 0.999395i | \(-0.511071\pi\) | ||||
−0.0347734 | + | 0.999395i | \(0.511071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.0000 | 1.42399 | 0.711994 | − | 0.702185i | \(-0.247792\pi\) | ||||
0.711994 | + | 0.702185i | \(0.247792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | + | 31.1769i | 0.623663 | + | 1.08022i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | + | 24.2487i | −0.484490 | + | 0.839161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.00000 | − | 3.46410i | 0.0690477 | − | 0.119594i | −0.829435 | − | 0.558604i | \(-0.811337\pi\) |
0.898482 | + | 0.439010i | \(0.144671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | − | 30.3109i | −0.603448 | − | 1.04520i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0000 | −0.825625 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0000 | + | 25.9808i | 0.514193 | + | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.50000 | + | 12.9904i | −0.256795 | + | 0.444782i | −0.965382 | − | 0.260842i | \(-0.916000\pi\) |
0.708586 | + | 0.705624i | \(0.249333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.0000 | + | 24.2487i | −0.478231 | + | 0.828320i | −0.999689 | − | 0.0249570i | \(-0.992055\pi\) |
0.521458 | + | 0.853277i | \(0.325388\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.50000 | − | 16.4545i | −0.324136 | − | 0.561420i | 0.657201 | − | 0.753715i | \(-0.271740\pi\) |
−0.981337 | + | 0.192295i | \(0.938407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.0000 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48.0000 | −1.63205 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0000 | − | 19.0526i | −0.373149 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.50000 | + | 11.2583i | −0.220244 | + | 0.381474i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | + | 10.3923i | −0.202837 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.50000 | + | 14.7224i | 0.287025 | + | 0.497141i | 0.973098 | − | 0.230391i | \(-0.0740005\pi\) |
−0.686074 | + | 0.727532i | \(0.740667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0000 | 1.04323 | 0.521617 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521617 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | + | 17.3205i | −0.335389 | + | 0.580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.0000 | − | 43.3013i | 0.836593 | − | 1.44902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | + | 20.7846i | 0.401116 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −64.0000 | −2.13452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.0000 | + | 32.9090i | 0.631581 | + | 1.09393i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.50000 | + | 14.7224i | −0.282238 | + | 0.488850i | −0.971936 | − | 0.235247i | \(-0.924410\pi\) |
0.689698 | + | 0.724097i | \(0.257743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | − | 41.5692i | 0.795155 | − | 1.37725i | −0.127585 | − | 0.991828i | \(-0.540723\pi\) |
0.922740 | − | 0.385422i | \(-0.125944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 20.7846i | −0.397142 | − | 0.687870i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.0000 | −0.528367 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0000 | −1.58337 | −0.791687 | − | 0.610927i | \(-0.790797\pi\) | ||||
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.00000 | + | 3.46410i | 0.0658308 | + | 0.114022i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.50000 | + | 4.33013i | −0.0821995 | + | 0.142374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | + | 10.3923i | −0.196854 | + | 0.340960i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.750653 | + | 0.660697i | \(0.229739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.0000 | + | 25.9808i | 0.491605 | + | 0.851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.0000 | −0.784884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.0000 | −0.816714 | −0.408357 | − | 0.912822i | \(-0.633898\pi\) | ||||
−0.408357 | + | 0.912822i | \(0.633898\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0000 | − | 19.0526i | −0.358590 | − | 0.621096i | 0.629136 | − | 0.777295i | \(-0.283409\pi\) |
−0.987725 | + | 0.156200i | \(0.950076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | + | 41.5692i | −0.781548 | + | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.00000 | − | 5.19615i | 0.0974869 | − | 0.168852i | −0.813157 | − | 0.582045i | \(-0.802253\pi\) |
0.910644 | + | 0.413192i | \(0.135586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.50000 | − | 7.79423i | −0.146076 | − | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | −0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | − | 5.19615i | −0.0968751 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.0000 | − | 36.3731i | 0.676014 | − | 1.17089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5000 | + | 23.3827i | 0.434131 | + | 0.751936i | 0.997224 | − | 0.0744567i | \(-0.0237223\pi\) |
−0.563094 | + | 0.826393i | \(0.690389\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0000 | 1.09111 | 0.545556 | − | 0.838074i | \(-0.316319\pi\) | ||||
0.545556 | + | 0.838074i | \(0.316319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.00000 | 0.160293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.0000 | − | 38.1051i | −0.703842 | − | 1.21909i | −0.967108 | − | 0.254367i | \(-0.918133\pi\) |
0.263265 | − | 0.964723i | \(-0.415201\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | + | 3.46410i | −0.0639203 | + | 0.110713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.0000 | + | 36.3731i | −0.669796 | + | 1.16012i | 0.308165 | + | 0.951333i | \(0.400285\pi\) |
−0.977961 | + | 0.208788i | \(0.933048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | − | 3.46410i | −0.0637253 | − | 0.110375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.00000 | 0.222362 | 0.111181 | − | 0.993800i | \(-0.464537\pi\) | ||||
0.111181 | + | 0.993800i | \(0.464537\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.0000 | − | 32.9090i | −0.602340 | − | 1.04328i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.0000 | − | 46.7654i | 0.855099 | − | 1.48107i | −0.0214550 | − | 0.999770i | \(-0.506830\pi\) |
0.876554 | − | 0.481304i | \(-0.159837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2592.2.i.f.865.1 | 2 | ||
3.2 | odd | 2 | 2592.2.i.u.865.1 | 2 | |||
4.3 | odd | 2 | 2592.2.i.d.865.1 | 2 | |||
9.2 | odd | 6 | 864.2.a.b.1.1 | ✓ | 1 | ||
9.4 | even | 3 | inner | 2592.2.i.f.1729.1 | 2 | ||
9.5 | odd | 6 | 2592.2.i.u.1729.1 | 2 | |||
9.7 | even | 3 | 864.2.a.j.1.1 | yes | 1 | ||
12.11 | even | 2 | 2592.2.i.s.865.1 | 2 | |||
36.7 | odd | 6 | 864.2.a.k.1.1 | yes | 1 | ||
36.11 | even | 6 | 864.2.a.c.1.1 | yes | 1 | ||
36.23 | even | 6 | 2592.2.i.s.1729.1 | 2 | |||
36.31 | odd | 6 | 2592.2.i.d.1729.1 | 2 | |||
72.11 | even | 6 | 1728.2.a.w.1.1 | 1 | |||
72.29 | odd | 6 | 1728.2.a.v.1.1 | 1 | |||
72.43 | odd | 6 | 1728.2.a.g.1.1 | 1 | |||
72.61 | even | 6 | 1728.2.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.a.b.1.1 | ✓ | 1 | 9.2 | odd | 6 | ||
864.2.a.c.1.1 | yes | 1 | 36.11 | even | 6 | ||
864.2.a.j.1.1 | yes | 1 | 9.7 | even | 3 | ||
864.2.a.k.1.1 | yes | 1 | 36.7 | odd | 6 | ||
1728.2.a.f.1.1 | 1 | 72.61 | even | 6 | |||
1728.2.a.g.1.1 | 1 | 72.43 | odd | 6 | |||
1728.2.a.v.1.1 | 1 | 72.29 | odd | 6 | |||
1728.2.a.w.1.1 | 1 | 72.11 | even | 6 | |||
2592.2.i.d.865.1 | 2 | 4.3 | odd | 2 | |||
2592.2.i.d.1729.1 | 2 | 36.31 | odd | 6 | |||
2592.2.i.f.865.1 | 2 | 1.1 | even | 1 | trivial | ||
2592.2.i.f.1729.1 | 2 | 9.4 | even | 3 | inner | ||
2592.2.i.s.865.1 | 2 | 12.11 | even | 2 | |||
2592.2.i.s.1729.1 | 2 | 36.23 | even | 6 | |||
2592.2.i.u.865.1 | 2 | 3.2 | odd | 2 | |||
2592.2.i.u.1729.1 | 2 | 9.5 | odd | 6 |