Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [639,1,Mod(70,639)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(639, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("639.70");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 639 = 3^{2} \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 639.g (of order \(6\), degree \(2\), 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: | \(0.318902543072\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{21}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{21} - \cdots)\) |
Embedding invariants
Embedding label | 283.6 | ||
Root | \(0.955573 + 0.294755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 639.283 |
Dual form | 639.1.g.b.70.6 |
$q$-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 \(\left(\mathbb{Z}/639\mathbb{Z}\right)^\times\).
\(n\) | \(433\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(3\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(4\) | −1.45557 | + | 2.52113i | −1.45557 | + | 2.52113i | ||||
\(5\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(6\) | 1.78181 | + | 0.858075i | 1.78181 | + | 0.858075i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −3.77960 | −3.77960 | ||||||||
\(9\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(10\) | 0.880142 | 0.880142 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0.217550 | + | 2.90301i | 0.217550 | + | 2.90301i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0332580 | − | 0.443797i | −0.0332580 | − | 0.443797i | ||||
\(16\) | −2.28181 | − | 3.95221i | −2.28181 | − | 3.95221i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.95557 | − | 0.294755i | 1.95557 | − | 0.294755i | ||||
\(19\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(20\) | 0.647791 | + | 1.12201i | 0.647791 | + | 1.12201i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −3.12285 | + | 2.12912i | −3.12285 | + | 2.12912i | ||||
\(25\) | 0.400969 | + | 0.694498i | 0.400969 | + | 0.694498i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(30\) | 0.727208 | − | 0.495802i | 0.727208 | − | 0.495802i | ||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 2.62285 | − | 4.54291i | 2.62285 | − | 4.54291i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.81507 | + | 2.27603i | 1.81507 | + | 2.27603i | ||||
\(37\) | 1.24698 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(38\) | −1.95557 | − | 3.38715i | −1.95557 | − | 3.38715i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.841040 | + | 1.45672i | −0.841040 | + | 1.45672i | ||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −4.11168 | − | 1.98008i | −4.11168 | − | 1.98008i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | −0.792981 | + | 1.37348i | −0.792981 | + | 1.37348i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 1.44973 | − | 1.34515i | 1.44973 | − | 1.34515i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.63402 | + | 1.11406i | −1.63402 | + | 1.11406i | ||||
\(58\) | 1.63402 | − | 2.83021i | 1.63402 | − | 2.83021i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 1.16728 | + | 0.562132i | 1.16728 | + | 0.562132i | ||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.81060 | 5.81060 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | 1.00000 | ||||||||
\(72\) | −1.38084 | + | 3.51833i | −1.38084 | + | 3.51833i | ||||
\(73\) | −0.445042 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(74\) | 1.23305 | + | 2.13571i | 1.23305 | + | 2.13571i | ||||
\(75\) | 0.722521 | + | 0.347948i | 0.722521 | + | 0.347948i | ||||
\(76\) | 2.87863 | − | 4.98593i | 2.87863 | − | 4.98593i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.222521 | + | 0.385418i | 0.222521 | + | 0.385418i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(80\) | −2.03100 | −2.03100 | ||||||||
\(81\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.44973 | + | 2.51100i | −1.44973 | + | 2.51100i | ||||
\(87\) | −1.48883 | − | 0.716983i | −1.48883 | − | 0.716983i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(90\) | 0.321552 | − | 0.819301i | 0.321552 | − | 0.819301i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.440071 | + | 0.762226i | −0.440071 | + | 0.762226i | ||||
\(96\) | −0.392012 | − | 5.23104i | −0.392012 | − | 5.23104i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | −1.97766 | −1.97766 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.33456 | −2.33456 | ||||||||
\(101\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 2.78181 | + | 0.858075i | 2.78181 | + | 0.858075i | ||||
\(109\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.03030 | − | 0.702449i | 1.03030 | − | 0.702449i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | −3.52382 | − | 1.69698i | −3.52382 | − | 1.69698i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.81060 | 4.81060 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.125702 | + | 1.67738i | 0.125702 | + | 1.67738i | ||||
\(121\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.801938 | 0.801938 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 3.12285 | + | 5.40894i | 3.12285 | + | 5.40894i | ||||
\(129\) | 1.32091 | + | 0.636119i | 1.32091 | + | 0.636119i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.425270 | − | 0.131178i | −0.425270 | − | 0.131178i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.51265 | + | 0.680173i | −4.51265 | + | 0.680173i | ||||
\(145\) | −0.735422 | −0.735422 | ||||||||
\(146\) | −0.440071 | − | 0.762226i | −0.440071 | − | 0.762226i | ||||
\(147\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(148\) | −1.81507 | + | 3.14379i | −1.81507 | + | 3.14379i | ||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0.118519 | + | 1.58153i | 0.118519 | + | 1.58153i | ||||
\(151\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(152\) | 7.47477 | 7.47477 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0747301 | + | 0.129436i | −0.0747301 | + | 0.129436i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(158\) | −0.440071 | + | 0.762226i | −0.440071 | + | 0.762226i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.16728 | − | 2.02179i | −1.16728 | − | 2.02179i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.440071 | − | 1.92808i | 0.440071 | − | 1.92808i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.23305 | − | 2.13571i | 1.23305 | − | 2.13571i | ||||
\(167\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.722521 | + | 1.84095i | −0.722521 | + | 1.84095i | ||||
\(172\) | −4.26804 | −4.26804 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | −0.244221 | − | 3.25890i | −0.244221 | − | 3.25890i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.147791 | + | 0.255981i | 0.147791 | + | 0.255981i | ||||
\(179\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(180\) | 1.28111 | − | 0.193096i | 1.28111 | − | 0.193096i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.277479 | − | 0.480608i | 0.277479 | − | 0.480608i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.74062 | −1.74062 | ||||||||
\(191\) | 0.900969 | + | 1.56052i | 0.900969 | + | 1.56052i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(192\) | 4.80095 | − | 3.27323i | 4.80095 | − | 3.27323i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.45557 | − | 2.52113i | −1.45557 | − | 2.52113i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.730682 | 0.730682 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(200\) | −1.51550 | − | 2.62493i | −1.51550 | − | 2.62493i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.722521 | − | 1.25144i | 0.722521 | − | 1.25144i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.26804 | −3.26804 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(214\) | −0.988831 | − | 1.71271i | −0.988831 | − | 1.71271i | ||||
\(215\) | 0.652478 | 0.652478 | ||||||||
\(216\) | 0.841040 | + | 3.68484i | 0.841040 | + | 3.68484i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.63402 | + | 2.83021i | 1.63402 | + | 2.83021i | ||||
\(219\) | −0.367711 | + | 0.250701i | −0.367711 | + | 0.250701i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.22188 | + | 1.07000i | 2.22188 | + | 1.07000i | ||||
\(223\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.792981 | − | 0.119523i | 0.792981 | − | 0.119523i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | −0.430241 | − | 5.74116i | −0.430241 | − | 5.74116i | ||||
\(229\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.12285 | + | 5.40894i | 3.12285 | + | 5.40894i | ||||
\(233\) | 0.730682 | 0.730682 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | −1.67809 | + | 1.14410i | −1.67809 | + | 1.14410i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | −1.97766 | −1.97766 | ||||||||
\(243\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.222521 | + | 0.385418i | 0.222521 | + | 0.385418i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | ||||
\(250\) | 0.792981 | + | 1.37348i | 0.792981 | + | 1.37348i | ||||
\(251\) | 0.730682 | 0.730682 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.27064 | + | 5.66492i | −3.27064 | + | 5.66492i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0.216677 | + | 2.89135i | 0.216677 | + | 2.89135i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.63402 | + | 0.246289i | −1.63402 | + | 0.246289i | ||||
\(262\) | −3.77960 | −3.77960 | ||||||||
\(263\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.123490 | − | 0.0841939i | 0.123490 | − | 0.0841939i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | −0.195850 | − | 0.858075i | −0.195850 | − | 0.858075i | ||||
\(271\) | −1.80194 | −1.80194 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(284\) | −1.45557 | + | 2.52113i | −1.45557 | + | 2.52113i | ||||
\(285\) | 0.0657731 | + | 0.877681i | 0.0657731 | + | 0.877681i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.27064 | − | 4.10126i | −3.27064 | − | 4.10126i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | −0.727208 | − | 1.25956i | −0.727208 | − | 1.25956i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.647791 | − | 1.12201i | 0.647791 | − | 1.12201i | ||||
\(293\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(294\) | −1.63402 | + | 1.11406i | −1.63402 | + | 1.11406i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.71308 | −4.71308 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.92890 | + | 1.31510i | −1.92890 | + | 1.31510i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.147791 | − | 0.255981i | 0.147791 | − | 0.255981i | ||||
\(303\) | −0.658322 | − | 0.317031i | −0.658322 | − | 0.317031i | ||||
\(304\) | 4.51265 | + | 7.81614i | 4.51265 | + | 7.81614i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.123490 | + | 1.64786i | 0.123490 | + | 1.64786i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.623490 | + | 1.07992i | −0.623490 | + | 1.07992i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(314\) | −0.295582 | −0.295582 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.29558 | −1.29558 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.29298 | − | 2.23951i | 1.29298 | − | 2.23951i | ||||
\(321\) | −0.826239 | + | 0.563320i | −0.826239 | + | 0.563320i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.78181 | − | 0.858075i | 2.78181 | − | 0.858075i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.36534 | − | 0.930874i | 1.36534 | − | 0.930874i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 3.63014 | 3.63014 | ||||||||
\(333\) | 0.455573 | − | 1.16078i | 0.455573 | − | 1.16078i | ||||
\(334\) | 2.89946 | 2.89946 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.86746 | + | 0.582926i | −3.86746 | + | 0.582926i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.77064 | − | 4.79889i | −2.77064 | − | 4.79889i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 3.97471 | − | 2.70991i | 3.97471 | − | 2.70991i | ||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | ||||
\(356\) | −0.217550 | + | 0.376808i | −0.217550 | + | 0.376808i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.44973 | − | 2.51100i | −1.44973 | − | 2.51100i | ||||
\(359\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(360\) | 1.04876 | + | 1.31510i | 1.04876 | + | 1.31510i | ||||
\(361\) | 2.91115 | 2.91115 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0990311 | + | 0.171527i | −0.0990311 | + | 0.171527i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.09752 | 1.09752 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.662592 | − | 0.451748i | 0.662592 | − | 0.451748i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(380\) | −1.28111 | − | 2.21895i | −1.28111 | − | 2.21895i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.78181 | + | 3.08619i | −1.78181 | + | 3.08619i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 5.62718 | + | 2.70991i | 5.62718 | + | 2.70991i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44973 | − | 0.218511i | 1.44973 | − | 0.218511i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(393\) | 0.142820 | + | 1.90580i | 0.142820 | + | 1.90580i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.198062 | 0.198062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0.722521 | + | 1.25144i | 0.722521 | + | 1.25144i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.82987 | − | 3.16943i | 1.82987 | − | 3.16943i | ||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.12712 | 2.12712 | ||||||||
\(405\) | −0.425270 | + | 0.131178i | −0.425270 | + | 0.131178i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0747301 | + | 0.129436i | −0.0747301 | + | 0.129436i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.40530 | − | 4.16610i | −2.40530 | − | 4.16610i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.554958 | −0.554958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.78181 | + | 0.858075i | 1.78181 | + | 0.858075i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.45557 | − | 2.52113i | 1.45557 | − | 2.52113i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.645190 | + | 1.11750i | 0.645190 | + | 1.11750i | ||||
\(431\) | 1.24698 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(432\) | −3.34537 | + | 3.10405i | −3.34537 | + | 3.10405i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.607634 | + | 0.414278i | −0.607634 | + | 0.414278i | ||||
\(436\) | −2.40530 | + | 4.16610i | −2.40530 | + | 4.16610i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.792981 | − | 0.381879i | −0.792981 | − | 0.381879i | ||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0.271281 | + | 3.61999i | 0.271281 | + | 3.61999i | ||||
\(445\) | 0.0332580 | − | 0.0576046i | 0.0332580 | − | 0.0576046i | ||||
\(446\) | 1.23305 | − | 2.13571i | 1.23305 | − | 2.13571i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0.988831 | + | 1.23995i | 0.988831 | + | 1.23995i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.134659 | − | 0.0648483i | −0.134659 | − | 0.0648483i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.17594 | − | 4.21069i | 6.17594 | − | 4.21069i | ||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 2.89946 | 2.89946 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(464\) | −3.77064 | + | 6.53094i | −3.77064 | + | 6.53094i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.722521 | + | 1.25144i | 0.722521 | + | 1.25144i | ||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0111692 | + | 0.149042i | 0.0111692 | + | 0.149042i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.0657731 | + | 0.877681i | 0.0657731 | + | 0.877681i | ||||
\(475\) | −0.792981 | − | 1.37348i | −0.792981 | − | 1.37348i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | −2.10336 | − | 1.01293i | −2.10336 | − | 1.01293i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.45557 | − | 2.52113i | −1.45557 | − | 2.52113i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.722521 | − | 1.84095i | −0.722521 | − | 1.84095i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.440071 | + | 0.762226i | −0.440071 | + | 0.762226i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.184292 | − | 2.45921i | −0.184292 | − | 2.45921i | ||||
\(499\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(500\) | −1.16728 | + | 2.02179i | −1.16728 | + | 2.02179i | ||||
\(501\) | −0.109562 | − | 1.46200i | −0.109562 | − | 1.46200i | ||||
\(502\) | 0.722521 | + | 1.25144i | 0.722521 | + | 1.25144i | ||||
\(503\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.325184 | −0.325184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.69074 | −6.69074 | ||||||||
\(513\) | 0.440071 | + | 1.92808i | 0.440071 | + | 1.92808i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.367711 | + | 0.636894i | 0.367711 | + | 0.636894i | ||||
\(516\) | −3.52642 | + | 2.40427i | −3.52642 | + | 2.40427i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(522\) | −2.03759 | − | 2.55506i | −2.03759 | − | 2.55506i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | −2.78181 | − | 4.81824i | −2.78181 | − | 4.81824i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.266310 | + | 0.128248i | 0.266310 | + | 0.128248i | ||||
\(535\) | −0.222521 | + | 0.385418i | −0.222521 | + | 0.385418i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.21135 | + | 0.825886i | −1.21135 | + | 0.825886i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.949729 | − | 0.881219i | 0.949729 | − | 0.881219i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | −1.78181 | − | 3.08619i | −1.78181 | − | 3.08619i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.367711 | − | 0.636894i | 0.367711 | − | 0.636894i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.63402 | + | 2.83021i | 1.63402 | + | 2.83021i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.722521 | − | 1.25144i | 0.722521 | − | 1.25144i | ||||
\(555\) | −0.0414721 | − | 0.553406i | −0.0414721 | − | 0.553406i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.77960 | −3.77960 | ||||||||
\(569\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(570\) | −1.43817 | + | 0.980528i | −1.43817 | + | 0.980528i | ||||
\(571\) | −0.623490 | + | 1.07992i | −0.623490 | + | 1.07992i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.62349 | + | 0.781831i | 1.62349 | + | 0.781831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.12285 | − | 5.40894i | 2.12285 | − | 5.40894i | ||||
\(577\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(578\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.07046 | − | 1.85409i | 1.07046 | − | 1.85409i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.68208 | 1.68208 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.97766 | 1.97766 | ||||||||
\(587\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(588\) | −2.62285 | − | 1.26310i | −2.62285 | − | 1.26310i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.84537 | − | 4.92833i | −2.84537 | − | 4.92833i | ||||
\(593\) | −1.80194 | −1.80194 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | −2.73084 | − | 1.31510i | −2.73084 | − | 1.31510i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.435100 | 0.435100 | ||||||||
\(605\) | 0.222521 | + | 0.385418i | 0.222521 | + | 0.385418i | ||||
\(606\) | −0.107988 | − | 1.44100i | −0.107988 | − | 1.44100i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | −5.18711 | + | 8.98434i | −5.18711 | + | 8.98434i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(618\) | −2.70018 | + | 1.84095i | −2.70018 | + | 1.84095i | ||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.46610 | −2.46610 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.222521 | + | 0.385418i | −0.222521 | + | 0.385418i | ||||
\(626\) | −1.95557 | + | 3.38715i | −1.95557 | + | 3.38715i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.217550 | − | 0.376808i | −0.217550 | − | 0.376808i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | −0.841040 | − | 1.45672i | −0.841040 | − | 1.45672i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(640\) | 2.77960 | 2.77960 | ||||||||
\(641\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(642\) | −1.78181 | − | 0.858075i | −1.78181 | − | 0.858075i | ||||
\(643\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.539102 | − | 0.367554i | 0.539102 | − | 0.367554i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 2.77064 | + | 2.57078i | 2.77064 | + | 2.57078i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 2.94440 | + | 1.41795i | 2.94440 | + | 1.41795i | ||||
\(655\) | 0.425270 | + | 0.736589i | 0.425270 | + | 0.736589i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.162592 | + | 0.414278i | −0.162592 | + | 0.414278i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.35654 | + | 4.08165i | 2.35654 | + | 4.08165i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.43856 | − | 0.367554i | 2.43856 | − | 0.367554i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.13402 | + | 3.69623i | 2.13402 | + | 3.69623i | ||||
\(669\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.587862 | − | 0.545456i | 0.587862 | − | 0.545456i | ||||
\(676\) | 2.91115 | 2.91115 | ||||||||
\(677\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −3.58959 | − | 4.50121i | −3.58959 | − | 4.50121i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.109562 | − | 1.46200i | −0.109562 | − | 1.46200i | ||||
\(688\) | 3.34537 | − | 5.79436i | 3.34537 | − | 5.79436i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.62718 | + | 2.70991i | 5.62718 | + | 2.70991i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46610 | −2.46610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0.880142 | 0.880142 | ||||||||
\(711\) | 0.440071 | − | 0.0663300i | 0.440071 | − | 0.0663300i | ||||
\(712\) | −0.564900 | −0.564900 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.13402 | − | 3.69623i | 2.13402 | − | 3.69623i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.88980 | + | 3.27323i | 1.88980 | + | 3.27323i | ||||
\(719\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(720\) | −0.742009 | + | 1.89061i | −0.742009 | + | 1.89061i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.87863 | + | 4.98593i | 2.87863 | + | 4.98593i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.662592 | − | 1.14764i | 0.662592 | − | 1.14764i | ||||
\(726\) | −1.63402 | + | 1.11406i | −1.63402 | + | 1.11406i | ||||
\(727\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(730\) | −0.391700 | −0.391700 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(735\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0.807782 | + | 1.39912i | 0.807782 | + | 1.39912i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.880142 | 0.880142 | ||||||||
\(747\) | −1.23305 | + | 0.185853i | −1.23305 | + | 0.185853i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.42890 | + | 0.688123i | 1.42890 | + | 0.688123i | ||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0665160 | −0.0665160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0.147791 | + | 0.255981i | 0.147791 | + | 0.255981i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.66329 | − | 2.88091i | 1.66329 | − | 2.88091i | ||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.24570 | −5.24570 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.488831 | + | 6.52299i | 0.488831 | + | 6.52299i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 1.80778 | + | 2.26689i | 1.80778 | + | 2.26689i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.21135 | + | 1.12397i | −1.21135 | + | 1.12397i | ||||
\(784\) | 4.56362 | 4.56362 | ||||||||
\(785\) | 0.0332580 | + | 0.0576046i | 0.0332580 | + | 0.0576046i | ||||
\(786\) | −3.12285 | + | 2.12912i | −3.12285 | + | 2.12912i | ||||
\(787\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.72188 | − | 0.829215i | −1.72188 | − | 0.829215i | ||||
\(790\) | 0.195850 | + | 0.339222i | 0.195850 | + | 0.339222i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.06356 | + | 1.84214i | −1.06356 | + | 1.84214i | ||||
\(797\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.20673 | 4.20673 | ||||||||
\(801\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.38084 | + | 2.39169i | 1.38084 | + | 2.39169i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −0.645190 | − | 0.598649i | −0.645190 | − | 0.598649i | ||||
\(811\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.48883 | + | 1.01507i | −1.48883 | + | 1.01507i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.44973 | − | 2.51100i | −1.44973 | − | 2.51100i | ||||
\(818\) | −0.295582 | −0.295582 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 3.12285 | − | 5.40894i | 3.12285 | − | 5.40894i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(830\) | −0.548760 | − | 0.950480i | −0.548760 | − | 0.950480i | ||||
\(831\) | −0.658322 | − | 0.317031i | −0.658322 | − | 0.317031i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.326239 | − | 0.565062i | −0.326239 | − | 0.565062i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.26804 | −3.26804 | ||||||||
\(839\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.865341 | + | 1.49881i | −0.865341 | + | 1.49881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.445042 | −0.445042 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.217550 | + | 2.90301i | 0.217550 | + | 2.90301i | ||||
\(853\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.548760 | + | 0.688123i | 0.548760 | + | 0.688123i | ||||
\(856\) | 3.77960 | 3.77960 | ||||||||
\(857\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | −0.949729 | + | 1.64498i | −0.949729 | + | 1.64498i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.23305 | + | 2.13571i | 1.23305 | + | 2.13571i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −5.01265 | − | 1.54620i | −5.01265 | − | 1.54620i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.31038 | − | 0.631047i | −1.31038 | − | 0.631047i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.24570 | −6.24570 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0968189 | − | 1.29196i | −0.0968189 | − | 1.29196i | ||||
\(877\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(882\) | −0.722521 | + | 1.84095i | −0.722521 | + | 1.84095i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | −3.89413 | + | 2.65497i | −3.89413 | + | 2.65497i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.131546 | 0.131546 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.63014 | 3.63014 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.326239 | + | 0.565062i | −0.326239 | + | 0.565062i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.852910 | + | 2.17318i | −0.852910 | + | 2.17318i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0220888 | − | 0.294755i | −0.0220888 | − | 0.294755i | ||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.722521 | + | 0.108903i | −0.722521 | + | 0.108903i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 8.13152 | + | 3.91593i | 8.13152 | + | 3.91593i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.13402 | + | 3.69623i | 2.13402 | + | 3.69623i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(926\) | −1.44504 | −1.44504 | ||||||||
\(927\) | 1.03030 | + | 1.29196i | 1.03030 | + | 1.29196i | ||||
\(928\) | −8.66841 | −8.66841 | ||||||||
\(929\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | ||||
\(932\) | −1.06356 | + | 1.84214i | −1.06356 | + | 1.84214i | ||||
\(933\) | 0.0931869 | + | 1.24349i | 0.0931869 | + | 1.24349i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.78181 | + | 0.858075i | 1.78181 | + | 0.858075i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(942\) | −0.244221 | + | 0.166507i | −0.244221 | + | 0.166507i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(948\) | −1.07046 | + | 0.729827i | −1.07046 | + | 0.729827i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.56825 | − | 2.71628i | 1.56825 | − | 2.71628i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.801938 | 0.801938 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.193249 | − | 2.57873i | −0.193249 | − | 2.57873i | ||||
\(961\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 1.81507 | − | 2.27603i | 1.81507 | − | 2.27603i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.29558 | −1.29558 | ||||||||
\(981\) | 0.603718 | − | 1.53825i | 0.603718 | − | 1.53825i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.162592 | − | 0.281618i | 0.162592 | − | 0.281618i | ||||
\(996\) | 2.99936 | − | 2.04493i | 2.99936 | − | 2.04493i | ||||
\(997\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(998\) | 3.56362 | 3.56362 | ||||||||
\(999\) | −0.277479 | − | 1.21572i | −0.277479 | − | 1.21572i |
(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 | 639.1.g.b.283.6 | yes | 12 | |
3.2 | odd | 2 | 1917.1.g.b.496.1 | 12 | |||
9.2 | odd | 6 | 1917.1.g.b.1774.1 | 12 | |||
9.7 | even | 3 | inner | 639.1.g.b.70.6 | ✓ | 12 | |
71.70 | odd | 2 | CM | 639.1.g.b.283.6 | yes | 12 | |
213.212 | even | 2 | 1917.1.g.b.496.1 | 12 | |||
639.70 | odd | 6 | inner | 639.1.g.b.70.6 | ✓ | 12 | |
639.425 | even | 6 | 1917.1.g.b.1774.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
639.1.g.b.70.6 | ✓ | 12 | 9.7 | even | 3 | inner | |
639.1.g.b.70.6 | ✓ | 12 | 639.70 | odd | 6 | inner | |
639.1.g.b.283.6 | yes | 12 | 1.1 | even | 1 | trivial | |
639.1.g.b.283.6 | yes | 12 | 71.70 | odd | 2 | CM | |
1917.1.g.b.496.1 | 12 | 3.2 | odd | 2 | |||
1917.1.g.b.496.1 | 12 | 213.212 | even | 2 | |||
1917.1.g.b.1774.1 | 12 | 9.2 | odd | 6 | |||
1917.1.g.b.1774.1 | 12 | 639.425 | even | 6 |