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 | 719.1 | ||
Root | \(-0.766044 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.719 |
Dual form | 912.2.ch.c.671.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.592396 | + | 1.62760i | 0.342020 | + | 0.939693i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00387 | + | 2.31164i | −1.51332 | + | 0.873716i | −0.513442 | + | 0.858124i | \(0.671630\pi\) |
−0.999878 | + | 0.0155920i | \(0.995037\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.29813 | + | 1.92836i | −0.766044 | + | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.73783 | + | 2.45237i | 1.86874 | + | 0.680165i | 0.970725 | + | 0.240192i | \(0.0772105\pi\) |
0.898011 | + | 0.439972i | \(0.145012\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.13429 | − | 5.14728i | −1.33861 | − | 1.12323i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69846 | − | 1.71010i | −0.939693 | − | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | − | 2.59808i | −0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.12108 | + | 5.26606i | −1.63819 | + | 0.945812i | −0.656740 | + | 0.754117i | \(0.728065\pi\) |
−0.981455 | + | 0.191695i | \(0.938602\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12.1138 | −1.99150 | −0.995749 | − | 0.0921098i | \(-0.970639\pi\) | ||||
−0.995749 | + | 0.0921098i | \(0.970639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.4192i | 1.98867i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.77584 | + | 0.489456i | 0.423312 | + | 0.0746414i | 0.381246 | − | 0.924473i | \(-0.375495\pi\) |
0.0420659 | + | 0.999115i | \(0.486606\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.18732 | − | 12.4488i | 1.02676 | − | 1.77840i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.15523 | − | 7.23567i | 0.285467 | − | 0.958388i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.60694 | + | 9.11343i | 0.205748 | + | 1.16686i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.690510 | + | 0.723323i | \(0.742614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.74376 | − | 13.0334i | 0.597657 | − | 1.64205i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.60994 | + | 6.68566i | 0.685363 | + | 0.816784i | 0.990787 | − | 0.135433i | \(-0.0432425\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1912 | − | 4.07326i | 1.30983 | − | 0.476739i | 0.409644 | − | 0.912245i | \(-0.365653\pi\) |
0.900186 | + | 0.435506i | \(0.143431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.03462 | + | 16.5800i | 0.678947 | + | 1.86539i | 0.453930 | + | 0.891038i | \(0.350022\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.56283 | − | 8.86327i | 0.173648 | − | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −32.6464 | + | 5.75643i | −3.42227 | + | 0.603438i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.9743 | − | 11.7258i | −1.44907 | − | 1.21591i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.83022 | − | 3.21394i | −0.388900 | − | 0.326326i | 0.427284 | − | 0.904117i | \(-0.359470\pi\) |
−0.816185 | + | 0.577791i | \(0.803915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5364 | + | 9.54731i | 1.62938 | + | 0.940724i | 0.984277 | + | 0.176631i | \(0.0565198\pi\) |
0.645105 | + | 0.764094i | \(0.276813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.95202 | + | 16.7417i | −0.282752 | + | 1.60357i | 0.430454 | + | 0.902613i | \(0.358354\pi\) |
−0.713206 | + | 0.700954i | \(0.752758\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.17617 | − | 19.7164i | −0.681132 | − | 1.87140i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.2135 | + | 7.35710i | −1.86874 | + | 0.680165i | ||||
\(118\) | 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 | ||||||||
\(127\) | 7.70115 | − | 21.1587i | 0.683367 | − | 1.87753i | 0.299991 | − | 0.953942i | \(-0.403016\pi\) |
0.383375 | − | 0.923593i | \(-0.374762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.847763 | + | 4.80790i | 0.0746414 | + | 0.423312i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.0194 | + | 2.31164i | 1.73590 | + | 0.200444i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.36050 | − | 11.9804i | 0.369853 | − | 1.01616i | −0.605564 | − | 0.795796i | \(-0.707053\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.5194 | + | 4.32342i | 2.02232 | + | 0.356590i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.66025i | 0.704761i | 0.935857 | + | 0.352381i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.51889 | + | 19.9566i | −0.280838 | + | 1.59271i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.719785 | + | 0.694197i | \(0.755760\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4696 | − | 6.04460i | −0.820039 | − | 0.473450i | 0.0303908 | − | 0.999538i | \(-0.490325\pi\) |
−0.850430 | + | 0.526088i | \(0.823658\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.4256 | + | 24.6910i | 2.26351 | + | 1.89931i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.0535 | − | 0.778544i | 0.998226 | − | 0.0595368i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.7652 | − | 4.01411i | 1.72088 | − | 0.303438i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36231 | − | 4.49951i | 0.398577 | − | 0.334446i | −0.421366 | − | 0.906891i | \(-0.638449\pi\) |
0.819943 | + | 0.572444i | \(0.194005\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8810 | + | 8.01422i | −1.02612 | + | 0.592428i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.0232 | 1.74743 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1789 | + | 6.61656i | −1.30854 | + | 0.476271i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
−0.408773 | + | 0.912636i | \(0.634043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.86319 | − | 11.7545i | −0.699183 | − | 0.833254i | 0.293251 | − | 0.956036i | \(-0.405263\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.55825 | + | 13.0913i | −0.533118 | + | 0.923387i | ||||
\(202\) | 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 | ||||||||
\(211\) | −5.32934 | + | 6.35127i | −0.366887 | + | 0.437239i | −0.917630 | − | 0.397436i | \(-0.869900\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.3464 | − | 42.1692i | 1.65274 | − | 2.86263i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2592 | + | 15.8017i | 0.895976 | + | 1.06778i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.186137 | + | 0.0328209i | 0.0124646 | + | 0.00219785i | 0.179877 | − | 0.983689i | \(-0.442430\pi\) |
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.0954 | − | 5.13030i | 0.939693 | − | 0.342020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.49289 | 0.230817 | 0.115408 | − | 0.993318i | \(-0.463182\pi\) | ||||
0.115408 | + | 0.993318i | \(0.463182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.4106 | + | 19.6438i | −1.52068 | + | 1.27600i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.45558 | − | 1.25773i | −0.222594 | − | 0.0810175i | 0.228316 | − | 0.973587i | \(-0.426678\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3516 | − | 2.70691i | 0.984808 | − | 0.173648i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.2110 | − | 26.0887i | −1.09511 | − | 1.65998i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.5021 | − | 28.0027i | 3.01377 | − | 1.74000i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3516 | + | 2.70691i | 0.932545 | + | 0.164433i | 0.619224 | − | 0.785214i | \(-0.287447\pi\) |
0.313321 | + | 0.949647i | \(0.398558\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.7087 | − | 49.7250i | −1.73753 | − | 3.00949i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | + | 26.8468i | −0.931305 | + | 1.61307i | −0.150210 | + | 0.988654i | \(0.547995\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.8066 | − | 29.6909i | 0.646974 | − | 1.77755i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4734 | + | 17.2488i | −0.860356 | + | 1.02533i | 0.139030 | + | 0.990288i | \(0.455602\pi\) |
−0.999386 | + | 0.0350443i | \(0.988843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.95202 | + | 16.7417i | 0.173648 | + | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.96198 | − | 8.13798i | 0.173634 | − | 0.477057i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2456 | + | 4.45702i | −0.705823 | + | 0.256898i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.592396 | − | 1.62760i | −0.0338098 | − | 0.0928918i | 0.921639 | − | 0.388048i | \(-0.126851\pi\) |
−0.955449 | + | 0.295156i | \(0.904628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.74304 | + | 32.5704i | −0.326710 | + | 1.85287i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8116 | − | 22.4976i | 1.51548 | − | 1.27164i | 0.663345 | − | 0.748314i | \(-0.269136\pi\) |
0.852134 | − | 0.523324i | \(-0.175308\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.4636 | − | 23.0447i | −1.52341 | − | 1.27829i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.9975 | + | 5.11305i | −1.60357 | + | 0.282752i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.3041 | + | 16.9187i | 1.61070 | + | 0.929938i | 0.989208 | + | 0.146518i | \(0.0468065\pi\) |
0.621492 | + | 0.783420i | \(0.286527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.8391 | − | 23.3598i | 1.52558 | − | 1.28011i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.34436 | + | 7.62424i | −0.0732319 | + | 0.415319i | 0.926049 | + | 0.377403i | \(0.123183\pi\) |
−0.999281 | + | 0.0379157i | \(0.987928\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 34.0949i | 1.84095i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4957 | − | 28.5714i | −0.882996 | − | 1.52939i | −0.847994 | − | 0.530006i | \(-0.822190\pi\) |
−0.0350017 | − | 0.999387i | \(-0.511144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.9488 | − | 28.5410i | −1.27829 | − | 1.52341i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.2467 | + | 14.5951i | −0.642788 | + | 0.766044i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.10426 | + | 25.0137i | −0.475238 | + | 1.30571i | 0.438254 | + | 0.898851i | \(0.355597\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | − | 32.9090i | −0.983783 | − | 1.70396i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4953i | 0.744576i | 0.928117 | + | 0.372288i | \(0.121427\pi\) | ||||
−0.928117 | + | 0.372288i | \(0.878573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.0000 | 1.99803 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.32311 | + | 4.22800i | −0.372255 | + | 0.214921i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1573 | + | 9.36208i | 0.559968 | + | 0.469869i | 0.878300 | − | 0.478110i | \(-0.158678\pi\) |
−0.318332 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.09698 | + | 33.9528i | 0.405356 | + | 1.69977i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −74.3706 | + | 13.1135i | −3.70466 | + | 0.653232i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.1097 | + | 24.4259i | −1.43938 | + | 1.20778i | −0.499486 | + | 0.866322i | \(0.666478\pi\) |
−0.939895 | + | 0.341463i | \(0.889078\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.0823 | 1.08138 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5274 | − | 14.0228i | 1.87771 | − | 0.683431i | 0.924419 | − | 0.381377i | \(-0.124550\pi\) |
0.953291 | − | 0.302053i | \(-0.0976721\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.5009 | − | 32.7743i | −1.33086 | − | 1.58606i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.14249 | + | 12.1507i | 0.102962 | + | 0.583924i | 0.992015 | + | 0.126121i | \(0.0402527\pi\) |
−0.889053 | + | 0.457804i | \(0.848636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2447 | − | 16.9762i | 0.679862 | − | 0.810228i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.990090 | + | 0.140434i | \(0.0448499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.48839 | + | 42.4688i | 0.356590 | + | 2.02232i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.0954 | + | 5.13030i | −0.662259 | + | 0.241043i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.82058 | 0.225497 | 0.112749 | − | 0.993624i | \(-0.464034\pi\) | ||||
0.112749 | + | 0.993624i | \(0.464034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3270 | − | 6.53964i | 0.526409 | − | 0.303923i | −0.213144 | − | 0.977021i | \(-0.568370\pi\) |
0.739553 | + | 0.673098i | \(0.235037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.9163 | − | 13.8004i | −1.75081 | − | 0.637243i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.5658 | + | 6.09489i | −1.59271 | + | 0.280838i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0016 | + | 18.1923i | 0.550673 | + | 0.834721i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −81.6207 | − | 29.7075i | −3.72158 | − | 1.35455i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5000 | − | 18.1865i | 1.42740 | − | 0.824110i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.63604 | − | 20.6210i | 0.164427 | − | 0.932514i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.3666 | − | 6.41242i | −1.62799 | − | 0.287059i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
−0.911736 | + | 0.410776i | \(0.865258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.7554 | + | 62.5199i | −1.01060 | + | 2.77660i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.3922 | + | 42.1788i | −1.56566 | + | 1.86588i | ||||
\(512\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.8692 | − | 22.4874i | −0.825091 | − | 0.983306i | 0.174908 | − | 0.984585i | \(-0.444037\pi\) |
−0.999999 | + | 0.00127919i | \(0.999593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.0194 | + | 34.6745i | 0.873716 | + | 1.51332i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 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 | ||||||||
\(541\) | −31.2977 | + | 26.2619i | −1.34559 | + | 1.12909i | −0.365444 | + | 0.930834i | \(0.619083\pi\) |
−0.980151 | + | 0.198254i | \(0.936473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5000 | + | 6.06218i | 0.450598 | + | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.96720 | − | 1.58116i | 0.383410 | − | 0.0676055i | 0.0213785 | − | 0.999771i | \(-0.493195\pi\) |
0.362031 | + | 0.932166i | \(0.382083\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.2670 | − | 17.8451i | −0.907653 | − | 0.761611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −62.4887 | − | 52.4342i | −2.65729 | − | 2.22973i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5028 | + | 10.1053i | 0.740291 | + | 0.427407i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.2313 | + | 39.1001i | 0.597657 | + | 1.64205i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 44.7821i | − | 1.87407i | −0.349231 | − | 0.937037i | \(-0.613557\pi\) | ||
0.349231 | − | 0.937037i | \(-0.386443\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.5382 | − | 25.6682i | −0.895096 | − | 1.06673i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.6054 | + | 5.26606i | 1.87914 | + | 0.216984i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.2886 | − | 23.0166i | 0.543868 | − | 0.942007i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.2114 | + | 31.5431i | 0.742859 | + | 1.28667i | 0.951188 | + | 0.308611i | \(0.0998642\pi\) |
−0.208329 | + | 0.978059i | \(0.566802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.7848 | − | 4.54655i | −1.05004 | − | 0.185150i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.4771i | − | 1.43997i | −0.693990 | − | 0.719985i | \(-0.744149\pi\) | ||
0.693990 | − | 0.719985i | \(-0.255851\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.16146 | − | 46.2860i | 0.329638 | − | 1.86947i | −0.145204 | − | 0.989402i | \(-0.546384\pi\) |
0.474843 | − | 0.880071i | \(-0.342505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.5315 | + | 12.4312i | 0.865425 | + | 0.499653i | 0.865825 | − | 0.500347i | \(-0.166794\pi\) |
−0.000400419 | 1.00000i | \(0.500127\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.55959 | + | 1.68561i | −0.380561 | + | 0.0671032i | −0.360657 | − | 0.932699i | \(-0.617447\pi\) |
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.4944 | − | 4.91155i | −0.536353 | − | 0.195217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 78.9559 | − | 66.2519i | 3.12835 | − | 2.62500i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.34096 | − | 14.6742i | −0.210627 | − | 0.578692i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
−0.999350 | + | 0.0360565i | \(0.988520\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 83.0572 | + | 14.6452i | 3.25527 | + | 0.573991i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.8641 | + | 30.9416i | −0.696946 | + | 1.20715i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.59863 | + | 37.4227i | 0.256657 | + | 1.45557i | 0.791783 | + | 0.610802i | \(0.209153\pi\) |
−0.535126 | + | 0.844772i | \(0.679736\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.0568475 | + | 0.322398i | 0.00219785 | + | 0.0124646i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.8619 | − | 44.7941i | 0.996903 | − | 1.72669i | 0.430346 | − | 0.902664i | \(-0.358391\pi\) |
0.566557 | − | 0.824023i | \(-0.308275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.7001 | + | 19.9024i | 0.642788 | + | 0.766044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.7652 | + | 4.01411i | 0.873647 | + | 0.154048i | ||||
\(680\) | 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 | ||||||||
\(687\) | 2.06917 | + | 5.68501i | 0.0789439 | + | 0.216897i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5000 | + | 9.52628i | −0.627690 | + | 0.362397i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
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 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.3983 | + | 31.4726i | 1.59908 | + | 1.18701i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.4702 | − | 17.6417i | −1.82034 | − | 0.662548i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
−0.825108 | − | 0.564975i | \(-0.808886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45.8405 | − | 26.4661i | −1.71915 | − | 0.992554i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −88.2796 | −3.28770 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6.36937i | − | 0.236879i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.3417 | − | 6.58434i | −1.38493 | − | 0.244200i | −0.568991 | − | 0.822344i | \(-0.692666\pi\) |
−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 | ||||||||
\(733\) | −3.50000 | + | 6.06218i | −0.129275 | + | 0.223912i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) |
0.794121 | + | 0.607760i | \(0.207932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.8684 | − | 33.2123i | 1.02516 | − | 1.22173i | 0.0503375 | − | 0.998732i | \(-0.483970\pi\) |
0.974818 | − | 0.223001i | \(-0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.2661 | − | 43.4673i | 1.18532 | − | 1.59681i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.8505 | + | 41.5332i | 1.27171 | + | 1.51557i | 0.748056 | + | 0.663636i | \(0.230988\pi\) |
0.523655 | + | 0.851930i | \(0.324568\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.5775 | + | 3.84991i | −0.384447 | + | 0.139927i | −0.527011 | − | 0.849858i | \(-0.676688\pi\) |
0.142564 | + | 0.989786i | \(0.454465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.8813 | − | 73.8557i | −0.973168 | − | 2.67376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.5474 | + | 34.8624i | −1.49824 | + | 1.25717i | −0.614745 | + | 0.788726i | \(0.710741\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.8606 | − | 9.14442i | 1.86289 | − | 0.328477i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 74.3096 | + | 62.3531i | 2.66584 | + | 2.23691i | ||||
\(778\) | 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 | ||||||||
\(787\) | 48.2816 | + | 27.8754i | 1.72105 | + | 0.993650i | 0.916783 | + | 0.399385i | \(0.130776\pi\) |
0.804269 | + | 0.594265i | \(0.202557\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5222 | + | 65.3455i | −0.409165 | + | 2.32049i | ||||
\(794\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8099 | − | 40.6899i | 0.520046 | − | 1.42882i | −0.350423 | − | 0.936592i | \(-0.613962\pi\) |
0.870469 | − | 0.492223i | \(-0.163816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.68850 | + | 26.5898i | 0.164433 | + | 0.932545i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.44381 | − | 8.92495i | −0.295412 | − | 0.312245i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 63.9252 | − | 76.1831i | 2.23373 | − | 2.66205i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5491 | − | 53.7106i | 0.681438 | − | 1.87224i | 0.258830 | − | 0.965923i | \(-0.416663\pi\) |
0.422608 | − | 0.906313i | \(-0.361115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6890 | + | 27.1741i | 0.544900 | + | 0.943795i | 0.998613 | + | 0.0526472i | \(0.0167659\pi\) |
−0.453713 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.8778 | − | 9.32379i | −1.83431 | − | 0.323439i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54.7265 | 1.89162 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.03580 | − | 28.5594i | 0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0426 | − | 25.4280i | −1.51332 | − | 0.873716i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.6480 | − | 13.3388i | −1.25776 | − | 0.457786i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.6243 | − | 25.6969i | −1.04856 | − | 0.879844i | −0.0556158 | − | 0.998452i | \(-0.517712\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.83346 | − | 0.499616i | 0.0966765 | − | 0.0170467i | −0.125101 | − | 0.992144i | \(-0.539925\pi\) |
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 21.4031 | + | 58.8045i | 0.725216 | + | 1.99251i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0000 | 0.507673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.4360 | + | 5.25427i | −0.487469 | + | 0.177424i | −0.574049 | − | 0.818821i | \(-0.694628\pi\) |
0.0865807 | + | 0.996245i | \(0.472406\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8120 | + | 40.2955i | 1.13786 | + | 1.35605i | 0.925449 | + | 0.378873i | \(0.123688\pi\) |
0.212415 | + | 0.977180i | \(0.431867\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0769 | + | 102.519i | 0.606279 | + | 3.43838i | ||||
\(890\) | 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 | ||||||||
\(903\) | −14.5085 | − | 17.2905i | −0.482811 | − | 0.575392i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.9402 | − | 2.10537i | −0.396466 | − | 0.0699077i | −0.0281394 | − | 0.999604i | \(-0.508958\pi\) |
−0.368327 | + | 0.929696i | \(0.620069\pi\) | |||||||
\(908\) | 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 | ||||||||
\(919\) | 49.6301 | − | 28.6539i | 1.63714 | − | 0.945206i | 0.655335 | − | 0.755338i | \(-0.272528\pi\) |
0.981810 | − | 0.189867i | \(-0.0608058\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.29813 | − | 1.92836i | 0.0757261 | − | 0.0635417i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56.9163 | + | 20.7158i | 1.87140 | + | 0.681132i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −56.4136 | + | 9.94724i | −1.85287 | + | 0.326710i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.4986 | + | 24.8976i | −1.88444 | + | 0.815986i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.14512 | + | 1.87267i | 0.168084 | + | 0.0611775i | 0.424691 | − | 0.905338i | \(-0.360383\pi\) |
−0.256608 | + | 0.966516i | \(0.582605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.5000 | + | 30.3109i | 1.71327 | + | 0.989158i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.3934 | 2.77199 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.9628 | − | 69.2175i | 1.28912 | − | 2.23282i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7340 | + | 24.7098i | −0.666761 | + | 0.794615i | −0.988339 | − | 0.152268i | \(-0.951342\pi\) |
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.2354 | + | 58.0478i | 0.328131 | + | 1.86093i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.2381 | − | 58.3513i | 0.680165 | − | 1.86874i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | − | 44.1673i | −0.814152 | − | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4948 | − | 48.0667i | −0.555742 | − | 1.52689i | −0.825753 | − | 0.564031i | \(-0.809250\pi\) |
0.270011 | − | 0.962857i | \(-0.412973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.1772 | + | 57.7178i | −0.322964 | + | 1.83162i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5715 | + | 30.6871i | −1.15823 | + | 0.971871i | −0.999880 | − | 0.0155113i | \(-0.995062\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.5121 | + | 31.4726i | 1.72469 | + | 0.995749i |
(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.c.719.1 | yes | 6 | |
3.2 | odd | 2 | CM | 912.2.ch.c.719.1 | yes | 6 | |
4.3 | odd | 2 | 912.2.ch.d.719.1 | yes | 6 | ||
12.11 | even | 2 | 912.2.ch.d.719.1 | yes | 6 | ||
19.6 | even | 9 | 912.2.ch.d.671.1 | yes | 6 | ||
57.44 | odd | 18 | 912.2.ch.d.671.1 | yes | 6 | ||
76.63 | odd | 18 | inner | 912.2.ch.c.671.1 | ✓ | 6 | |
228.215 | even | 18 | inner | 912.2.ch.c.671.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ch.c.671.1 | ✓ | 6 | 76.63 | odd | 18 | inner | |
912.2.ch.c.671.1 | ✓ | 6 | 228.215 | even | 18 | inner | |
912.2.ch.c.719.1 | yes | 6 | 1.1 | even | 1 | trivial | |
912.2.ch.c.719.1 | yes | 6 | 3.2 | odd | 2 | CM | |
912.2.ch.d.671.1 | yes | 6 | 19.6 | even | 9 | ||
912.2.ch.d.671.1 | yes | 6 | 57.44 | odd | 18 | ||
912.2.ch.d.719.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ch.d.719.1 | yes | 6 | 12.11 | even | 2 |