Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(47,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ch (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(-0.173648 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.47 |
Dual form | 912.2.ch.a.815.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.11334 | − | 1.32683i | −0.642788 | − | 0.766044i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.52481 | − | 2.61240i | −1.71022 | − | 0.987396i | −0.934246 | − | 0.356630i | \(-0.883926\pi\) |
−0.775974 | − | 0.630765i | \(-0.782741\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.520945 | + | 2.95442i | −0.173648 | + | 0.984808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.375515 | − | 0.315094i | −0.104149 | − | 0.0873915i | 0.589226 | − | 0.807968i | \(-0.299433\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 4.33013i | −0.114708 | + | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.57145 | + | 8.91215i | 0.342919 | + | 1.94479i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83022 | + | 3.21394i | 0.766044 | + | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.50000 | − | 2.59808i | 0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.97431 | + | 2.87192i | 0.893412 | + | 0.515812i | 0.875057 | − | 0.484020i | \(-0.160824\pi\) |
0.0183550 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.55943 | −1.40716 | −0.703581 | − | 0.710615i | \(-0.748417\pi\) | ||||
−0.703581 | + | 0.710615i | \(0.748417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.849051i | 0.135957i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.07738 | + | 5.70756i | −0.316798 | + | 0.870395i | 0.674443 | + | 0.738327i | \(0.264384\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.1493 | + | 17.5791i | 1.44990 | + | 2.51130i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.30200 | − | 4.15749i | 0.834721 | − | 0.550673i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1356 | − | 3.68907i | 1.29773 | − | 0.472337i | 0.401476 | − | 0.915869i | \(-0.368497\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.0753 | − | 12.0073i | 1.26937 | − | 1.51278i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.7417 | − | 2.24670i | −1.55665 | − | 0.274479i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
−0.884714 | + | 0.466134i | \(0.845646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8289 | + | 9.08651i | −1.26742 | + | 1.06350i | −0.272575 | + | 0.962135i | \(0.587875\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1814 | + | 12.1337i | 1.14550 | + | 1.36515i | 0.920478 | + | 0.390794i | \(0.127800\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.45723 | − | 3.07818i | −0.939693 | − | 0.342020i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.875982 | + | 2.40674i | 0.0918278 | + | 0.252295i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.72756 | − | 9.79747i | −0.179140 | − | 1.01595i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.29932 | + | 18.7113i | 0.334995 | + | 1.89985i | 0.427284 | + | 0.904117i | \(0.359470\pi\) |
−0.0922897 | + | 0.995732i | \(0.529419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.74304 | + | 5.04780i | −0.861477 | + | 0.497374i | −0.864507 | − | 0.502621i | \(-0.832369\pi\) |
0.00302937 | + | 0.999995i | \(0.499036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8542 | − | 6.49838i | −1.71012 | − | 0.622432i | −0.713206 | − | 0.700954i | \(-0.752758\pi\) |
−0.996912 | + | 0.0785223i | \(0.974980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.52956 | + | 11.3569i | 0.904506 | + | 1.07795i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.12654 | − | 0.945283i | 0.104149 | − | 0.0873915i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.79339 | − | 9.28780i | 0.691551 | − | 0.824159i | −0.299991 | − | 0.953942i | \(-0.596984\pi\) |
0.991542 | + | 0.129783i | \(0.0414282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.88578 | − | 3.59813i | 0.870395 | − | 0.316798i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5744 | − | 18.2868i | 1.17705 | − | 1.58567i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9795 | + | 16.6601i | −1.18573 | + | 1.41310i | −0.296866 | + | 0.954919i | \(0.595942\pi\) |
−0.888861 | + | 0.458176i | \(0.848503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0248 | − | 33.0379i | 0.991790 | − | 2.72492i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5885i | 1.26857i | 0.773099 | + | 0.634285i | \(0.218706\pi\) | ||||
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.6322 | − | 8.23746i | −1.80625 | − | 0.657421i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
−0.808640 | − | 0.588304i | \(-0.799796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.3640 | + | 10.0251i | −1.36005 | + | 0.785225i | −0.989630 | − | 0.143639i | \(-0.954120\pi\) |
−0.370420 | + | 0.928864i | \(0.620786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.21570 | − | 12.5659i | −0.170438 | − | 0.966604i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.5326 | − | 3.73297i | −0.958388 | − | 0.285467i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.93494 | − | 24.5486i | −0.675418 | − | 1.85570i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.29932 | − | 18.7113i | 0.245236 | − | 1.39080i | −0.574707 | − | 0.818359i | \(-0.694884\pi\) |
0.819943 | − | 0.572444i | \(-0.194005\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.1792 | − | 9.34105i | −1.19600 | − | 0.690510i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.1489 | −1.97479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1728 | − | 17.7661i | 1.52405 | − | 1.27883i | 0.696261 | − | 0.717788i | \(-0.254845\pi\) |
0.827788 | − | 0.561041i | \(-0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.5633 | − | 4.68383i | −1.88302 | − | 0.332028i | −0.890589 | − | 0.454809i | \(-0.849707\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2049 | + | 19.4074i | 0.790330 | + | 1.36889i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3708 | − | 2.00497i | 0.782796 | − | 0.138028i | 0.232053 | − | 0.972703i | \(-0.425456\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.0052 | − | 25.9898i | −1.01862 | − | 1.76430i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.1125 | + | 4.25168i | 1.62937 | + | 0.287302i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.43289 | − | 9.43178i | 0.229883 | − | 0.631598i | −0.770097 | − | 0.637927i | \(-0.779792\pi\) |
0.999980 | + | 0.00632846i | \(0.00201443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4907 | + | 9.64181i | −0.766044 | + | 0.642788i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.6486 | −1.10017 | −0.550085 | − | 0.835109i | \(-0.685405\pi\) | ||||
−0.550085 | + | 0.835109i | \(0.685405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.76399 | − | 27.0179i | 0.309454 | − | 1.75500i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.43036 | + | 4.55661i | 0.349800 | + | 0.293517i | 0.800710 | − | 0.599052i | \(-0.204456\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.33157 | + | 14.6484i | 0.342020 | + | 0.939693i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.55216 | − | 1.46848i | 0.0987613 | − | 0.0934371i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.7298 | + | 22.3607i | 2.40655 | + | 1.38943i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2555 | + | 30.9243i | −0.683725 | + | 1.87852i | −0.313321 | + | 0.949647i | \(0.601442\pi\) |
−0.370403 | + | 0.928871i | \(0.620781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.21806 | − | 3.84180i | 0.134243 | − | 0.232516i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50000 | + | 4.33013i | 0.150210 | + | 0.260172i | 0.931305 | − | 0.364241i | \(-0.118672\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.0762 | + | 13.2001i | −0.663115 | + | 0.790269i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.4090 | − | 5.71458i | 1.92652 | − | 0.339697i | 0.927130 | − | 0.374741i | \(-0.122268\pi\) |
0.999386 | + | 0.0350443i | \(0.0111572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9748 | + | 5.81434i | −0.939693 | + | 0.342020i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.1535 | − | 25.2097i | 1.24004 | − | 1.47782i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3102 | − | 20.3987i | 1.40122 | − | 1.17576i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9268 | + | 22.5561i | 1.08021 | + | 1.28734i | 0.955449 | + | 0.295156i | \(0.0953717\pi\) |
0.124760 | + | 0.992187i | \(0.460184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.4315 | + | 5.98059i | 0.934758 | + | 0.340224i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.25743 | + | 12.8025i | −0.127597 | + | 0.723640i | 0.852134 | + | 0.523324i | \(0.175308\pi\) |
−0.979731 | + | 0.200316i | \(0.935803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.425612 | − | 2.41376i | −0.0236087 | − | 0.133891i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2555 | + | 30.9243i | 0.622432 | + | 1.71012i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8965 | + | 17.2608i | −1.64326 | + | 0.948737i | −0.663598 | + | 0.748090i | \(0.730971\pi\) |
−0.979663 | + | 0.200648i | \(0.935695\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.45899 | − | 25.2882i | 0.244351 | − | 1.38578i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.4761 | + | 12.5483i | 1.87803 | + | 0.683548i | 0.951985 | + | 0.306145i | \(0.0990393\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 69.4826i | − | 3.75171i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.2729 | + | 31.6496i | −0.978126 | + | 1.69416i | −0.308920 | + | 0.951088i | \(0.599967\pi\) |
−0.669207 | + | 0.743076i | \(0.733366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50846 | − | 0.442308i | −0.133891 | − | 0.0236087i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.7631 | + | 3.30844i | −0.984808 | + | 0.173648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.72116 | − | 2.05120i | 0.0898439 | − | 0.107072i | −0.719249 | − | 0.694752i | \(-0.755514\pi\) |
0.809093 | + | 0.587680i | \(0.199959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | + | 32.9090i | −0.983783 | + | 1.70396i | −0.336557 | + | 0.941663i | \(0.609263\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 33.0709i | − | 1.69874i | −0.527798 | − | 0.849370i | \(-0.676982\pi\) | ||
0.527798 | − | 0.849370i | \(-0.323018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.0000 | −1.07586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.7803 | − | 9.11079i | −0.802160 | − | 0.463127i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.78240 | + | 38.4649i | 0.340399 | + | 1.93050i | 0.365493 | + | 0.930814i | \(0.380900\pi\) |
−0.0250943 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39.3764 | + | 2.34851i | −1.97129 | + | 0.117573i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.963001 | − | 2.64582i | −0.0479705 | − | 0.131798i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.59863 | + | 37.4227i | −0.326281 | + | 1.85043i | 0.174232 | + | 0.984705i | \(0.444256\pi\) |
−0.500514 | + | 0.865729i | \(0.666856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.6691 | 1.84466 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5548 | − | 12.2130i | 0.709360 | − | 0.595223i | −0.215060 | − | 0.976601i | \(-0.568995\pi\) |
0.924419 | + | 0.381377i | \(0.124550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −55.4992 | − | 9.78600i | −2.68579 | − | 0.473578i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.6691 | − | 8.61483i | 1.13746 | − | 0.414003i | 0.296466 | − | 0.955043i | \(-0.404192\pi\) |
0.840996 | + | 0.541041i | \(0.181970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.2827 | − | 6.75027i | 1.82713 | − | 0.322173i | 0.848722 | − | 0.528839i | \(-0.177372\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −57.2233 | + | 20.8276i | −2.72492 | + | 0.991790i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.6832 | − | 17.3553i | 0.971782 | − | 0.815422i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0597 | −0.891577 | −0.445788 | − | 0.895138i | \(-0.647077\pi\) | ||||
−0.445788 | + | 0.895138i | \(0.647077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.9338 | − | 21.3238i | −1.71646 | − | 0.990999i | −0.925166 | − | 0.379563i | \(-0.876074\pi\) |
−0.791294 | − | 0.611435i | \(-0.790592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.7845 | + | 43.4524i | 2.39119 | + | 2.00644i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.2677 | + | 39.2002i | 0.657421 | + | 1.80625i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.8319 | + | 14.9784i | −0.726416 | + | 0.687255i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.21419 | + | 2.69703i | 0.146555 | + | 0.122974i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.5000 | + | 19.9186i | 1.56334 | + | 0.902597i | 0.996915 | + | 0.0784867i | \(0.0250088\pi\) |
0.566429 | + | 0.824110i | \(0.308325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.6336 | + | 11.8776i | 1.47574 | + | 0.537126i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.27678 | − | 17.2453i | 0.280987 | − | 0.772006i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.997246 | − | 0.0741708i | \(-0.0236310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.2059 | + | 16.9299i | −0.630906 | + | 0.751885i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.7363 | − | 12.8254i | 3.21766 | − | 0.567361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | + | 20.7846i | 0.397360 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0576190 | + | 0.0101598i | 0.00251950 | + | 0.000444257i | 0.174908 | − | 0.984585i | \(-0.444037\pi\) |
−0.172388 | + | 0.985029i | \(0.555148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.6241 | + | 39.1860i | −0.987396 | + | 1.71022i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6190 | + | 14.7841i | −0.766044 | + | 0.642788i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.34570 | − | 30.3170i | 0.229830 | − | 1.30343i | −0.623404 | − | 0.781900i | \(-0.714251\pi\) |
0.853233 | − | 0.521529i | \(-0.174638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.5000 | + | 16.4545i | −1.22305 | + | 0.706129i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.44063 | + | 6.70557i | 0.104354 | + | 0.286709i | 0.980870 | − | 0.194662i | \(-0.0623610\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.61897 | + | 31.8667i | 0.239812 | + | 1.36004i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3708 | − | 81.5007i | −0.611107 | − | 3.46576i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.57851 | − | 1.48870i | 0.109059 | − | 0.0629654i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.2260 | + | 36.0219i | 1.26937 | + | 1.51278i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 23.5769i | − | 0.986662i | −0.869842 | − | 0.493331i | \(-0.835779\pi\) | ||
0.869842 | − | 0.493331i | \(-0.164221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5000 | + | 30.3109i | −0.728535 | + | 1.26186i | 0.228968 | + | 0.973434i | \(0.426465\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −47.1450 | − | 8.31294i | −1.95928 | − | 0.345474i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9229 | + | 20.1034i | −0.614888 | + | 0.828347i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.3594 | + | 40.4596i | 0.956036 | + | 1.65590i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3248 | − | 33.4715i | 0.788273 | − | 1.36533i | −0.138751 | − | 0.990327i | \(-0.544309\pi\) |
0.927024 | − | 0.375002i | \(-0.122358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.2754 | − | 36.4740i | 0.540617 | − | 1.48533i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6418i | 0.878412i | 0.898386 | + | 0.439206i | \(0.144740\pi\) | ||||
−0.898386 | + | 0.439206i | \(0.855260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.7686 | + | 12.6547i | 1.40429 | + | 0.511120i | 0.929449 | − | 0.368950i | \(-0.120283\pi\) |
0.474843 | + | 0.880071i | \(0.342505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.46601 | − | 4.31051i | 0.300084 | − | 0.173254i | −0.342396 | − | 0.939556i | \(-0.611239\pi\) |
0.642481 | + | 0.766302i | \(0.277905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3801 | − | 36.7615i | −0.532653 | − | 1.46345i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) |
0.323248 | − | 0.946314i | \(-0.395225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3198 | − | 12.8548i | −0.608907 | − | 0.510934i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.72786 | − | 9.79920i | 0.0684605 | − | 0.388259i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17540 | + | 1.40079i | 0.0463534 | + | 0.0552418i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
−0.742370 | + | 0.669991i | \(0.766298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.7781 | + | 48.8448i | −0.696777 | + | 1.91438i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.2041 | − | 36.7267i | −0.827252 | − | 1.43284i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7083 | + | 12.9968i | −1.38889 | + | 0.505516i | −0.924862 | − | 0.380303i | \(-0.875820\pi\) |
−0.464031 | + | 0.885819i | \(0.653597\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.3363 | + | 5.94593i | −0.631598 | + | 0.229883i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6045 | − | 40.8841i | −0.909886 | − | 1.57597i | −0.814221 | − | 0.580554i | \(-0.802836\pi\) |
−0.0956642 | − | 0.995414i | \(-0.530497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.5861 | + | 4.51151i | 0.984808 | + | 0.173648i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.9528 | − | 93.2845i | 1.30299 | − | 3.57993i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.5355 | + | 22.0898i | 0.707175 | + | 0.842779i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5000 | + | 16.4545i | 1.08419 | + | 0.625958i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.27972 | − | 37.0634i | 0.161413 | − | 1.39787i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.13017 | − | 2.62652i | −0.117556 | − | 0.0986411i | 0.582115 | − | 0.813107i | \(-0.302225\pi\) |
−0.699671 | + | 0.714466i | \(0.746670\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.1520 | + | 23.7591i | −1.54332 | + | 0.891038i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.7475 | 1.96442 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 12.2782i | − | 0.456632i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.1671 | + | 41.6712i | −0.562516 | + | 1.54550i | 0.253419 | + | 0.967357i | \(0.418445\pi\) |
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.5000 | − | 37.2391i | −0.794121 | − | 1.37546i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) |
0.129275 | − | 0.991609i | \(-0.458735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0718 | + | 5.12614i | −1.06942 | + | 0.188568i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
−0.388888 | + | 0.921285i | \(0.627141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.67650 | − | 0.424525i | −0.135060 | − | 0.0155953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.48617 | + | 0.262051i | 0.0542310 | + | 0.00956239i | 0.200698 | − | 0.979653i | \(-0.435679\pi\) |
−0.146467 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.1282 | − | 27.7979i | 1.20406 | − | 1.01033i | 0.204560 | − | 0.978854i | \(-0.434424\pi\) |
0.999505 | − | 0.0314762i | \(-0.0100208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 63.8104 | + | 76.0462i | 2.31009 | + | 2.75306i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.61814 | + | 20.5195i | −0.130474 | + | 0.739953i | 0.847432 | + | 0.530904i | \(0.178148\pi\) |
−0.977905 | + | 0.209048i | \(0.932963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.82254 | + | 26.9872i | 0.352836 | + | 0.969409i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.4507 | − | 76.2829i | −0.482542 | − | 2.73663i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7680 | + | 7.94897i | −0.490777 | + | 0.283350i | −0.724897 | − | 0.688858i | \(-0.758113\pi\) |
0.234120 | + | 0.972208i | \(0.424779\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.96848 | − | 1.80838i | −0.176436 | − | 0.0642175i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5136 | − | 41.1317i | 1.21194 | − | 1.44433i | 0.350423 | − | 0.936592i | \(-0.386038\pi\) |
0.861512 | − | 0.507736i | \(-0.169518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.5625 | − | 19.4951i | 1.87852 | − | 0.683725i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.6758 | − | 11.8491i | −0.828310 | − | 0.414548i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.56687 | + | 1.33424i | −0.264408 | + | 0.0466222i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.1535 | − | 25.2097i | 0.737364 | − | 0.878756i | −0.258830 | − | 0.965923i | \(-0.583337\pi\) |
0.996194 | + | 0.0871670i | \(0.0277814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.48561 | + | 11.2334i | −0.225255 | + | 0.390153i | −0.956396 | − | 0.292074i | \(-0.905655\pi\) |
0.731141 | + | 0.682226i | \(0.238988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.96198 | − | 8.13798i | 0.102750 | − | 0.282303i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.8458 | 1.03162 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2511 | − | 9.91858i | −0.939693 | − | 0.342020i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.7730 | + | 28.7364i | −1.71022 | + | 0.987396i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.6645 | − | 36.6389i | −1.49856 | − | 1.25744i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.564121 | − | 3.19929i | −0.0193152 | − | 0.109542i | 0.973626 | − | 0.228150i | \(-0.0732677\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.77337 | − | 21.3572i | −0.265224 | − | 0.728697i | −0.998795 | − | 0.0490840i | \(-0.984370\pi\) |
0.733571 | − | 0.679613i | \(-0.237852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.5000 | + | 14.7224i | 0.866025 | + | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.07677 | + | 4.85851i | 0.138136 | + | 0.164624i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.0000 | −1.92916 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.92830 | − | 3.29623i | 0.132649 | − | 0.111306i | −0.574049 | − | 0.818821i | \(-0.694628\pi\) |
0.706698 | + | 0.707515i | \(0.250184\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3626 | − | 6.94069i | −1.32466 | − | 0.233573i | −0.533820 | − | 0.845598i | \(-0.679244\pi\) |
−0.790838 | + | 0.612026i | \(0.790355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.5271 | + | 21.6661i | −1.99647 | + | 0.726657i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −54.1311 | − | 9.54477i | −1.80137 | − | 0.317630i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5491 | − | 53.7106i | 0.649116 | − | 1.78343i | 0.0281394 | − | 0.999604i | \(-0.491042\pi\) |
0.620977 | − | 0.783829i | \(-0.286736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.0377 | − | 28.3119i | −1.61760 | − | 0.933924i | −0.987538 | − | 0.157382i | \(-0.949695\pi\) |
−0.630065 | − | 0.776542i | \(-0.716972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.85606 | − | 50.2252i | 0.291817 | − | 1.65498i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.7845 | − | 27.5095i | −1.07795 | − | 0.904506i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.3587 | − | 28.4603i | −0.340224 | − | 0.934758i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −81.1944 | + | 35.1582i | −2.66104 | + | 1.15226i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0344 | − | 10.0980i | −0.393146 | − | 0.329888i | 0.424691 | − | 0.905338i | \(-0.360383\pi\) |
−0.817837 | + | 0.575450i | \(0.804827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.5000 | − | 11.2583i | 0.636358 | − | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.92951 | 0.224941 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.995825 | + | 1.72482i | 0.0321234 | + | 0.0556393i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.32619 | − | 1.64446i | 0.299910 | − | 0.0528822i | −0.0216683 | − | 0.999765i | \(-0.506898\pi\) |
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 106.778 | − | 38.8639i | 3.42314 | − | 1.24592i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.72880 | + | 3.25205i | −0.0873915 | + | 0.104149i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.5000 | − | 49.3634i | 0.909935 | − | 1.57605i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5279 | − | 20.8890i | −0.556793 | − | 0.663559i | 0.412072 | − | 0.911151i | \(-0.364805\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 56.1871 | + | 20.4504i | 1.78304 | + | 0.648974i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.9647 | + | 62.1837i | −0.347255 | + | 1.96938i | −0.158352 | + | 0.987383i | \(0.550618\pi\) |
−0.188903 | + | 0.981996i | \(0.560493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.5174 | + | 22.2381i | −1.21864 | + | 0.703581i |
(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 | 912.2.ch.a.47.1 | ✓ | 6 | |
3.2 | odd | 2 | CM | 912.2.ch.a.47.1 | ✓ | 6 | |
4.3 | odd | 2 | 912.2.ch.b.47.1 | yes | 6 | ||
12.11 | even | 2 | 912.2.ch.b.47.1 | yes | 6 | ||
19.17 | even | 9 | 912.2.ch.b.815.1 | yes | 6 | ||
57.17 | odd | 18 | 912.2.ch.b.815.1 | yes | 6 | ||
76.55 | odd | 18 | inner | 912.2.ch.a.815.1 | yes | 6 | |
228.131 | even | 18 | inner | 912.2.ch.a.815.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ch.a.47.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
912.2.ch.a.47.1 | ✓ | 6 | 3.2 | odd | 2 | CM | |
912.2.ch.a.815.1 | yes | 6 | 76.55 | odd | 18 | inner | |
912.2.ch.a.815.1 | yes | 6 | 228.131 | even | 18 | inner | |
912.2.ch.b.47.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ch.b.47.1 | yes | 6 | 12.11 | even | 2 | ||
912.2.ch.b.815.1 | yes | 6 | 19.17 | even | 9 | ||
912.2.ch.b.815.1 | yes | 6 | 57.17 | odd | 18 |