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 | 70.1 | ||
Root | \(0.826239 + 0.563320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 639.70 |
Dual form | 639.1.g.b.283.1 |
$q$-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 \(\left(\mathbb{Z}/639\mathbb{Z}\right)^\times\).
\(n\) | \(433\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(3\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(4\) | −1.32624 | − | 2.29711i | −1.32624 | − | 2.29711i | ||||
\(5\) | 0.900969 | + | 1.56052i | 0.900969 | + | 1.56052i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(6\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 3.15813 | 3.15813 | ||||||||
\(9\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(10\) | −3.44377 | −3.44377 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −2.62285 | + | 0.395331i | −2.62285 | + | 0.395331i | ||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.78181 | − | 0.268565i | 1.78181 | − | 0.268565i | ||||
\(16\) | −1.69158 | + | 2.92990i | −1.69158 | + | 2.92990i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.82624 | − | 0.563320i | 1.82624 | − | 0.563320i | ||||
\(19\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(20\) | 2.38980 | − | 4.13925i | 2.38980 | − | 4.13925i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 1.15379 | − | 2.93982i | 1.15379 | − | 2.93982i | ||||
\(25\) | −1.12349 | + | 1.94594i | −1.12349 | + | 1.94594i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(30\) | −1.25815 | + | 3.20571i | −1.25815 | + | 3.20571i | ||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −1.65379 | − | 2.86445i | −1.65379 | − | 2.86445i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.590232 | + | 2.58597i | −0.590232 | + | 2.58597i | ||||
\(37\) | −0.445042 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(38\) | −1.82624 | + | 3.16314i | −1.82624 | + | 3.16314i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.84537 | + | 4.92833i | 2.84537 | + | 4.92833i | ||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0747301 | + | 0.129436i | −0.0747301 | + | 0.129436i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 2.10937 | + | 2.64506i | 2.10937 | + | 2.64506i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(50\) | −2.14715 | − | 3.71898i | −2.14715 | − | 3.71898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0.142820 | − | 1.90580i | 0.142820 | − | 1.90580i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.698220 | − | 1.77904i | 0.698220 | − | 1.77904i | ||||
\(58\) | −0.698220 | − | 1.20935i | −0.698220 | − | 1.20935i | ||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | −2.98003 | − | 3.73684i | −2.98003 | − | 3.73684i | ||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.93812 | 2.93812 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | 1.00000 | ||||||||
\(72\) | −2.31507 | − | 2.14807i | −2.31507 | − | 2.14807i | ||||
\(73\) | −1.80194 | −1.80194 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(74\) | 0.425270 | − | 0.736589i | 0.425270 | − | 0.736589i | ||||
\(75\) | 1.40097 | + | 1.75676i | 1.40097 | + | 1.75676i | ||||
\(76\) | −2.53464 | − | 4.39012i | −2.53464 | − | 4.39012i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(80\) | −6.09624 | −6.09624 | ||||||||
\(81\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.142820 | − | 0.247372i | −0.142820 | − | 0.247372i | ||||
\(87\) | 0.455573 | + | 0.571270i | 0.455573 | + | 0.571270i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(90\) | 2.52446 | + | 2.34236i | 2.52446 | + | 2.34236i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.72188 | + | 2.98239i | 1.72188 | + | 2.98239i | ||||
\(96\) | −3.27064 | + | 0.492970i | −3.27064 | + | 0.492970i | ||||
\(97\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(98\) | 1.91115 | 1.91115 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.96006 | 5.96006 | ||||||||
\(101\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 2.19158 | + | 1.49419i | 2.19158 | + | 1.49419i | ||||
\(109\) | 0.730682 | 0.730682 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.162592 | + | 0.414278i | −0.162592 | + | 0.414278i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 2.27728 | + | 2.85562i | 2.27728 | + | 2.85562i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.93812 | 1.93812 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.62718 | − | 0.848162i | 5.62718 | − | 0.848162i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.24698 | −2.24698 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −1.15379 | + | 1.99843i | −1.15379 | + | 1.99843i | ||||
\(129\) | 0.0931869 | + | 0.116853i | 0.0931869 | + | 0.116853i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.48883 | − | 1.01507i | −1.48883 | − | 1.01507i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.23286 | − | 0.997204i | 3.23286 | − | 0.997204i | ||||
\(145\) | −1.31664 | −1.31664 | ||||||||
\(146\) | 1.72188 | − | 2.98239i | 1.72188 | − | 2.98239i | ||||
\(147\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(148\) | 0.590232 | + | 1.02231i | 0.590232 | + | 1.02231i | ||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | −4.24634 | + | 0.640033i | −4.24634 | + | 0.640033i | ||||
\(151\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(152\) | 6.03564 | 6.03564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(158\) | 1.72188 | + | 2.98239i | 1.72188 | + | 2.98239i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.98003 | − | 5.16157i | 2.98003 | − | 5.16157i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.72188 | − | 0.829215i | −1.72188 | − | 0.829215i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.425270 | + | 0.736589i | 0.425270 | + | 0.736589i | ||||
\(167\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.40097 | − | 1.29991i | −1.40097 | − | 1.29991i | ||||
\(172\) | 0.396440 | 0.396440 | ||||||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | −1.38084 | + | 0.208129i | −1.38084 | + | 0.208129i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(179\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(180\) | −4.56726 | + | 1.40881i | −4.56726 | + | 1.40881i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.400969 | − | 0.694498i | −0.400969 | − | 0.694498i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.58154 | −6.58154 | ||||||||
\(191\) | −0.623490 | + | 1.07992i | −0.623490 | + | 1.07992i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(192\) | 1.07341 | − | 2.73502i | 1.07341 | − | 2.73502i | ||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.32624 | + | 2.29711i | −1.32624 | + | 2.29711i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(200\) | −3.54812 | + | 6.14553i | −3.54812 | + | 6.14553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.40097 | + | 2.42655i | 1.40097 | + | 2.42655i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.39644 | 1.39644 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(214\) | 0.955573 | − | 1.65510i | 0.955573 | − | 1.65510i | ||||
\(215\) | −0.269318 | −0.269318 | ||||||||
\(216\) | −2.84537 | + | 1.37026i | −2.84537 | + | 1.37026i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.698220 | + | 1.20935i | −0.698220 | + | 1.20935i | ||||
\(219\) | −0.658322 | + | 1.67738i | −0.658322 | + | 1.67738i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.530303 | − | 0.664979i | −0.530303 | − | 0.664979i | ||||
\(223\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.14715 | − | 0.662309i | 2.14715 | − | 0.662309i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −5.01265 | + | 0.755536i | −5.01265 | + | 0.755536i | ||||
\(229\) | −0.0747301 | − | 0.129436i | −0.0747301 | − | 0.129436i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.15379 | + | 1.99843i | −1.15379 | + | 1.99843i | ||||
\(233\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.12349 | − | 1.40881i | −1.12349 | − | 1.40881i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | −2.22721 | + | 5.67483i | −2.22721 | + | 5.67483i | ||||
\(241\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | 1.91115 | 1.91115 | ||||||||
\(243\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | ||||
\(250\) | 2.14715 | − | 3.71898i | 2.14715 | − | 3.71898i | ||||
\(251\) | −1.46610 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.736007 | − | 1.27480i | −0.736007 | − | 1.27480i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | −0.282450 | + | 0.0425725i | −0.282450 | + | 0.0425725i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.698220 | − | 0.215372i | 0.698220 | − | 0.215372i | ||||
\(262\) | 3.15813 | 3.15813 | ||||||||
\(263\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.722521 | + | 1.84095i | −0.722521 | + | 1.84095i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 3.10273 | − | 1.49419i | 3.10273 | − | 1.49419i | ||||
\(271\) | 1.24698 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | −1.32624 | − | 2.29711i | −1.32624 | − | 2.29711i | ||||
\(285\) | 3.40530 | − | 0.513267i | 3.40530 | − | 0.513267i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.736007 | + | 3.22466i | −0.736007 | + | 3.22466i | ||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 1.25815 | − | 2.17918i | 1.25815 | − | 2.17918i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.38980 | + | 4.13925i | 2.38980 | + | 4.13925i | ||||
\(293\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0.698220 | − | 1.77904i | 0.698220 | − | 1.77904i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.40550 | −1.40550 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.17746 | − | 5.54807i | 2.17746 | − | 5.54807i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.88980 | + | 3.27323i | 1.88980 | + | 3.27323i | ||||
\(303\) | −0.914101 | − | 1.14625i | −0.914101 | − | 1.14625i | ||||
\(304\) | −3.23286 | + | 5.59947i | −3.23286 | + | 5.59947i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.722521 | + | 0.108903i | −0.722521 | + | 0.108903i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.222521 | + | 0.385418i | 0.222521 | + | 0.385418i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(314\) | −3.77960 | −3.77960 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.77960 | −4.77960 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.64715 | + | 4.58500i | 2.64715 | + | 4.58500i | ||||
\(321\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.19158 | − | 1.49419i | 2.19158 | − | 1.49419i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.266948 | − | 0.680173i | 0.266948 | − | 0.680173i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −1.18046 | −1.18046 | ||||||||
\(333\) | 0.326239 | + | 0.302705i | 0.326239 | + | 0.302705i | ||||
\(334\) | 0.285640 | 0.285640 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(338\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.49021 | − | 1.07659i | 3.49021 | − | 1.07659i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.236007 | + | 0.408776i | −0.236007 | + | 0.408776i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0.708074 | − | 1.80414i | 0.708074 | − | 1.80414i | ||||
\(349\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.900969 | + | 1.56052i | 0.900969 | + | 1.56052i | ||||
\(356\) | 2.62285 | + | 4.54291i | 2.62285 | + | 4.54291i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.142820 | + | 0.247372i | −0.142820 | + | 0.247372i | ||||
\(359\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(360\) | 1.26631 | − | 5.54807i | 1.26631 | − | 5.54807i | ||||
\(361\) | 2.65248 | 2.65248 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.62349 | − | 2.81197i | −1.62349 | − | 2.81197i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.53262 | 1.53262 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.900969 | + | 1.56052i | 0.900969 | + | 1.56052i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.820914 | + | 2.09165i | −0.820914 | + | 2.09165i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(380\) | 4.56726 | − | 7.91072i | 4.56726 | − | 7.91072i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.19158 | − | 2.06388i | −1.19158 | − | 2.06388i | ||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 1.43876 | + | 1.80414i | 1.43876 | + | 1.80414i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.142820 | − | 0.0440542i | 0.142820 | − | 0.0440542i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.57906 | − | 2.73502i | −1.57906 | − | 2.73502i | ||||
\(393\) | −1.63402 | + | 0.246289i | −1.63402 | + | 0.246289i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.24698 | 3.24698 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 1.40097 | − | 2.42655i | 1.40097 | − | 2.42655i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.80095 | − | 6.58343i | −3.80095 | − | 6.58343i | ||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.88881 | −3.88881 | ||||||||
\(405\) | −1.48883 | + | 1.01507i | −1.48883 | + | 1.01507i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.988831 | + | 1.71271i | 0.988831 | + | 1.71271i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.969059 | + | 1.67846i | −0.969059 | + | 1.67846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.801938 | 0.801938 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.32624 | + | 2.29711i | 1.32624 | + | 2.29711i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.257353 | − | 0.445748i | 0.257353 | − | 0.445748i | ||||
\(431\) | −0.445042 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(432\) | 0.252824 | − | 3.37370i | 0.252824 | − | 3.37370i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.481024 | + | 1.22563i | −0.481024 | + | 1.22563i | ||||
\(436\) | −0.969059 | − | 1.67846i | −0.969059 | − | 1.67846i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.14715 | − | 2.69244i | −2.14715 | − | 2.69244i | ||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 1.16728 | − | 0.175939i | 1.16728 | − | 0.175939i | ||||
\(445\) | −1.78181 | − | 3.08619i | −1.78181 | − | 3.08619i | ||||
\(446\) | 0.425270 | + | 0.736589i | 0.425270 | + | 0.736589i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −0.955573 | + | 4.18664i | −0.955573 | + | 4.18664i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.23305 | − | 1.54620i | −1.23305 | − | 1.54620i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.20507 | − | 5.61842i | 2.20507 | − | 5.61842i | ||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 0.285640 | 0.285640 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(464\) | −1.23601 | − | 2.14083i | −1.23601 | − | 2.14083i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.40097 | − | 2.42655i | 1.40097 | − | 2.42655i | ||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.95557 | − | 0.294755i | 1.95557 | − | 0.294755i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.40530 | − | 0.513267i | 3.40530 | − | 0.513267i | ||||
\(475\) | −2.14715 | + | 3.71898i | −2.14715 | + | 3.71898i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | −3.71604 | − | 4.65976i | −3.71604 | − | 4.65976i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.32624 | + | 2.29711i | −1.32624 | + | 2.29711i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.72188 | + | 2.98239i | 1.72188 | + | 2.98239i | ||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.841040 | − | 0.126766i | 0.841040 | − | 0.126766i | ||||
\(499\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(500\) | 2.98003 | + | 5.16157i | 2.98003 | + | 5.16157i | ||||
\(501\) | −0.147791 | + | 0.0222759i | −0.147791 | + | 0.0222759i | ||||
\(502\) | 1.40097 | − | 2.42655i | 1.40097 | − | 2.42655i | ||||
\(503\) | 0.730682 | 0.730682 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.64183 | 2.64183 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.505648 | 0.505648 | ||||||||
\(513\) | −1.72188 | + | 0.829215i | −1.72188 | + | 0.829215i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.658322 | − | 1.14025i | 0.658322 | − | 1.14025i | ||||
\(516\) | 0.144836 | − | 0.369035i | 0.144836 | − | 0.369035i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(522\) | −0.310737 | + | 1.36143i | −0.310737 | + | 1.36143i | ||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | −2.19158 | + | 3.79593i | −2.19158 | + | 3.79593i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.57906 | − | 2.73502i | −1.57906 | − | 2.73502i | ||||
\(527\) | 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 | ||||||||
\(534\) | −2.35654 | − | 2.95501i | −2.35654 | − | 2.95501i | ||||
\(535\) | −0.900969 | − | 1.56052i | −0.900969 | − | 1.56052i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.357180 | + | 4.76623i | −0.357180 | + | 4.76623i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | −1.19158 | + | 2.06388i | −1.19158 | + | 2.06388i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.658322 | + | 1.14025i | 0.658322 | + | 1.14025i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.698220 | + | 1.20935i | −0.698220 | + | 1.20935i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.40097 | + | 2.42655i | 1.40097 | + | 2.42655i | ||||
\(555\) | −0.792981 | + | 0.119523i | −0.792981 | + | 0.119523i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.15813 | 3.15813 | ||||||||
\(569\) | −0.0747301 | + | 0.129436i | −0.0747301 | + | 0.129436i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(570\) | −2.40451 | + | 6.12658i | −2.40451 | + | 6.12658i | ||||
\(571\) | 0.222521 | + | 0.385418i | 0.222521 | + | 0.385418i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.777479 | + | 0.974928i | 0.777479 | + | 0.974928i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.15379 | − | 1.99843i | −2.15379 | − | 1.99843i | ||||
\(577\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(578\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.74618 | + | 3.02448i | 1.74618 | + | 3.02448i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.69074 | −5.69074 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.91115 | −1.91115 | ||||||||
\(587\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(588\) | 1.65379 | + | 2.07379i | 1.65379 | + | 2.07379i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.752824 | − | 1.30393i | 0.752824 | − | 1.30393i | ||||
\(593\) | 1.24698 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 4.42444 | + | 5.54807i | 4.42444 | + | 5.54807i | ||||
\(601\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.24570 | −5.24570 | ||||||||
\(605\) | 0.900969 | − | 1.56052i | 0.900969 | − | 1.56052i | ||||
\(606\) | 2.77064 | − | 0.417607i | 2.77064 | − | 0.417607i | ||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | −3.16064 | − | 5.47439i | −3.16064 | − | 5.47439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.97766 | −1.97766 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(618\) | 0.510177 | − | 1.29991i | 0.510177 | − | 1.29991i | ||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.850540 | −0.850540 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.900969 | − | 1.56052i | −0.900969 | − | 1.56052i | ||||
\(626\) | −1.82624 | − | 3.16314i | −1.82624 | − | 3.16314i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.62285 | − | 4.54291i | 2.62285 | − | 4.54291i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 2.84537 | − | 4.92833i | 2.84537 | − | 4.92833i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(640\) | −4.15813 | −4.15813 | ||||||||
\(641\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(642\) | −1.19158 | − | 1.49419i | −1.19158 | − | 1.49419i | ||||
\(643\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0983929 | + | 0.250701i | −0.0983929 | + | 0.250701i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0.236007 | + | 3.14929i | 0.236007 | + | 3.14929i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0.870666 | + | 1.09178i | 0.870666 | + | 1.09178i | ||||
\(655\) | 1.48883 | − | 2.57873i | 1.48883 | − | 2.57873i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.32091 | + | 1.22563i | 1.32091 | + | 1.22563i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.702749 | − | 1.21720i | 0.702749 | − | 1.21720i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.812753 | + | 0.250701i | −0.812753 | + | 0.250701i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.198220 | + | 0.343327i | −0.198220 | + | 0.343327i | ||||
\(669\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.167917 | − | 2.24070i | 0.167917 | − | 2.24070i | ||||
\(676\) | 2.65248 | 2.65248 | ||||||||
\(677\) | 0.988831 | − | 1.71271i | 0.988831 | − | 1.71271i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −1.12802 | + | 4.94217i | −1.12802 | + | 4.94217i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.147791 | + | 0.0222759i | −0.147791 | + | 0.0222759i | ||||
\(688\) | −0.252824 | − | 0.437904i | −0.252824 | − | 0.437904i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.43876 | + | 1.80414i | 1.43876 | + | 1.80414i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.850540 | −0.850540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | −3.44377 | −3.44377 | ||||||||
\(711\) | −1.72188 | + | 0.531130i | −1.72188 | + | 0.531130i | ||||
\(712\) | −6.24570 | −6.24570 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.198220 | − | 0.343327i | −0.198220 | − | 0.343327i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.57906 | + | 2.73502i | −1.57906 | + | 2.73502i | ||||
\(719\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(720\) | 4.46886 | + | 4.14650i | 4.46886 | + | 4.14650i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.53464 | + | 4.39012i | −2.53464 | + | 4.39012i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.820914 | − | 1.42186i | −0.820914 | − | 1.42186i | ||||
\(726\) | 0.698220 | − | 1.77904i | 0.698220 | − | 1.77904i | ||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(730\) | 6.20545 | 6.20545 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(734\) | −1.57906 | − | 2.73502i | −1.57906 | − | 2.73502i | ||||
\(735\) | −1.12349 | − | 1.40881i | −1.12349 | − | 1.40881i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | −1.06356 | + | 1.84214i | −1.06356 | + | 1.84214i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.44377 | −3.44377 | ||||||||
\(747\) | −0.425270 | + | 0.131178i | −0.425270 | + | 0.131178i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.67746 | − | 3.35742i | −2.67746 | − | 3.35742i | ||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.56362 | 3.56362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 1.88980 | − | 3.27323i | 1.88980 | − | 3.27323i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.43792 | + | 9.41876i | 5.43792 | + | 9.41876i | ||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.30759 | 3.30759 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.45557 | + | 0.219392i | −1.45557 | + | 0.219392i | ||||
\(769\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | −0.0635609 | + | 0.278479i | −0.0635609 | + | 0.278479i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0546039 | − | 0.728639i | 0.0546039 | − | 0.728639i | ||||
\(784\) | 3.38316 | 3.38316 | ||||||||
\(785\) | −1.78181 | + | 3.08619i | −1.78181 | + | 3.08619i | ||||
\(786\) | 1.15379 | − | 2.93982i | 1.15379 | − | 2.93982i | ||||
\(787\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.03030 | + | 1.29196i | 1.03030 | + | 1.29196i | ||||
\(790\) | −3.10273 | + | 5.37408i | −3.10273 | + | 5.37408i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.94440 | + | 3.36781i | 1.94440 | + | 3.36781i | ||||
\(797\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.43208 | 7.43208 | ||||||||
\(801\) | 1.44973 | + | 1.34515i | 1.44973 | + | 1.34515i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.31507 | − | 4.00982i | 2.31507 | − | 4.00982i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −0.257353 | − | 3.43414i | −0.257353 | − | 3.43414i | ||||
\(811\) | 1.65248 | 1.65248 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.455573 | − | 1.16078i | 0.455573 | − | 1.16078i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.142820 | + | 0.247372i | −0.142820 | + | 0.247372i | ||||
\(818\) | −3.77960 | −3.77960 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | −1.15379 | − | 1.99843i | −1.15379 | − | 1.99843i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.91115 | 1.91115 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(830\) | −0.766310 | + | 1.32729i | −0.766310 | + | 1.32729i | ||||
\(831\) | −0.914101 | − | 1.14625i | −0.914101 | − | 1.14625i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.134659 | − | 0.233236i | 0.134659 | − | 0.233236i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.39644 | 1.39644 | ||||||||
\(839\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.233052 | + | 0.403658i | 0.233052 | + | 0.403658i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.80194 | −1.80194 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.62285 | + | 0.395331i | −2.62285 | + | 0.395331i | ||||
\(853\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.766310 | − | 3.35742i | 0.766310 | − | 3.35742i | ||||
\(856\) | −3.15813 | −3.15813 | ||||||||
\(857\) | −0.365341 | + | 0.632789i | −0.365341 | + | 0.632789i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(860\) | 0.357180 | + | 0.618654i | 0.357180 | + | 0.618654i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.425270 | − | 0.736589i | 0.425270 | − | 0.736589i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 2.73286 | + | 1.86323i | 2.73286 | + | 1.86323i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.56889 | − | 1.96732i | −1.56889 | − | 1.96732i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.30759 | 2.30759 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.72622 | − | 0.712362i | 4.72622 | − | 0.712362i | ||||
\(877\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(882\) | −1.40097 | − | 1.29991i | −1.40097 | − | 1.29991i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | −0.513486 | + | 1.30834i | −0.513486 | + | 1.30834i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.81060 | 6.81060 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.18046 | −1.18046 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.134659 | + | 0.233236i | 0.134659 | + | 0.233236i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −4.36904 | − | 4.05387i | −4.36904 | − | 4.05387i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.73738 | − | 0.563320i | 3.73738 | − | 0.563320i | ||||
\(907\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.40097 | + | 0.432142i | −1.40097 | + | 0.432142i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(912\) | 4.03130 | + | 5.05510i | 4.03130 | + | 5.05510i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.198220 | + | 0.343327i | −0.198220 | + | 0.343327i | ||||
\(917\) | 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 | ||||
\(926\) | −2.80194 | −2.80194 | ||||||||
\(927\) | −0.162592 | + | 0.712362i | −0.162592 | + | 0.712362i | ||||
\(928\) | 2.41679 | 2.41679 | ||||||||
\(929\) | −0.955573 | + | 1.65510i | −0.955573 | + | 1.65510i | −0.222521 | + | 0.974928i | \(0.571429\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | ||||
\(932\) | 1.94440 | + | 3.36781i | 1.94440 | + | 3.36781i | ||||
\(933\) | 0.440071 | − | 0.0663300i | 0.440071 | − | 0.0663300i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.733052 | + | 1.26968i | 0.733052 | + | 1.26968i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(942\) | −1.38084 | + | 3.51833i | −1.38084 | + | 3.51833i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(948\) | −1.74618 | + | 4.44920i | −1.74618 | + | 4.44920i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.10352 | − | 7.10751i | −4.10352 | − | 7.10751i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.149460 | 0.149460 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.24698 | −2.24698 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.23517 | − | 0.789075i | 5.23517 | − | 0.789075i | ||||
\(961\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | −1.57906 | − | 2.73502i | −1.57906 | − | 2.73502i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | −0.590232 | − | 2.58597i | −0.590232 | − | 2.58597i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.365341 | − | 0.632789i | −0.365341 | − | 0.632789i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.77960 | −4.77960 | ||||||||
\(981\) | −0.535628 | − | 0.496990i | −0.535628 | − | 0.496990i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.733052 | − | 1.26968i | 0.733052 | − | 1.26968i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(984\) | 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 | ||||||||
\(995\) | −1.32091 | − | 2.28789i | −1.32091 | − | 2.28789i | ||||
\(996\) | −0.431272 | + | 1.09886i | −0.431272 | + | 1.09886i | ||||
\(997\) | −0.826239 | + | 1.43109i | −0.826239 | + | 1.43109i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(998\) | 2.38316 | 2.38316 | ||||||||
\(999\) | 0.400969 | − | 0.193096i | 0.400969 | − | 0.193096i |
(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.70.1 | ✓ | 12 | |
3.2 | odd | 2 | 1917.1.g.b.1774.6 | 12 | |||
9.4 | even | 3 | inner | 639.1.g.b.283.1 | yes | 12 | |
9.5 | odd | 6 | 1917.1.g.b.496.6 | 12 | |||
71.70 | odd | 2 | CM | 639.1.g.b.70.1 | ✓ | 12 | |
213.212 | even | 2 | 1917.1.g.b.1774.6 | 12 | |||
639.212 | even | 6 | 1917.1.g.b.496.6 | 12 | |||
639.283 | odd | 6 | inner | 639.1.g.b.283.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
639.1.g.b.70.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
639.1.g.b.70.1 | ✓ | 12 | 71.70 | odd | 2 | CM | |
639.1.g.b.283.1 | yes | 12 | 9.4 | even | 3 | inner | |
639.1.g.b.283.1 | yes | 12 | 639.283 | odd | 6 | inner | |
1917.1.g.b.496.6 | 12 | 9.5 | odd | 6 | |||
1917.1.g.b.496.6 | 12 | 639.212 | even | 6 | |||
1917.1.g.b.1774.6 | 12 | 3.2 | odd | 2 | |||
1917.1.g.b.1774.6 | 12 | 213.212 | even | 2 |