Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.a (trivial) |
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: | yes |
Analytic conductor: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 5 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.79129 | −1.61155 | −0.805775 | − | 0.592221i | \(-0.798251\pi\) | ||||
−0.805775 | + | 0.592221i | \(0.798251\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.79129 | 0.801088 | 0.400544 | − | 0.916277i | \(-0.368821\pi\) | ||||
0.400544 | + | 0.916277i | \(0.368821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.58258 | −1.08019 | −0.540094 | − | 0.841605i | \(-0.681611\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.00000 | −1.29099 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.58258 | 0.329990 | 0.164995 | − | 0.986294i | \(-0.447239\pi\) | ||||
0.164995 | + | 0.986294i | \(0.447239\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79129 | −0.358258 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.208712 | 0.0374858 | 0.0187429 | − | 0.999824i | \(-0.494034\pi\) | ||||
0.0187429 | + | 0.999824i | \(0.494034\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.0000 | 1.74078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.58258 | 0.917770 | 0.458885 | − | 0.888496i | \(-0.348249\pi\) | ||||
0.458885 | + | 0.888496i | \(0.348249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.1652 | −1.78786 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20871 | 0.188769 | 0.0943846 | − | 0.995536i | \(-0.469912\pi\) | ||||
0.0943846 | + | 0.995536i | \(0.469912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.79129 | −0.425667 | −0.212834 | − | 0.977088i | \(-0.568269\pi\) | ||||
−0.212834 | + | 0.977088i | \(0.568269\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.58258 | 1.27941 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.58258 | −0.230842 | −0.115421 | − | 0.993317i | \(-0.536822\pi\) | ||||
−0.115421 | + | 0.993317i | \(0.536822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.79129 | −0.390858 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.79129 | −1.34494 | −0.672468 | − | 0.740126i | \(-0.734766\pi\) | ||||
−0.672468 | + | 0.740126i | \(0.734766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.41742 | −0.865325 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.58258 | −0.739430 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5826 | 1.50792 | 0.753961 | − | 0.656919i | \(-0.228141\pi\) | ||||
0.753961 | + | 0.656919i | \(0.228141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.79129 | 0.869535 | 0.434768 | − | 0.900543i | \(-0.356830\pi\) | ||||
0.434768 | + | 0.900543i | \(0.356830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.16515 | 0.888728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9564 | −1.33854 | −0.669271 | − | 0.743018i | \(-0.733393\pi\) | ||||
−0.669271 | + | 0.743018i | \(0.733393\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.41742 | −0.531795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41742 | 0.524252 | 0.262126 | − | 0.965034i | \(-0.415576\pi\) | ||||
0.262126 | + | 0.965034i | \(0.415576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7913 | 1.73119 | 0.865595 | − | 0.500745i | \(-0.166941\pi\) | ||||
0.865595 | + | 0.500745i | \(0.166941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.58258 | −1.05182 | −0.525912 | − | 0.850539i | \(-0.676276\pi\) | ||||
−0.525912 | + | 0.850539i | \(0.676276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.79129 | 0.194292 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1652 | −1.18350 | −0.591752 | − | 0.806120i | \(-0.701563\pi\) | ||||
−0.591752 | + | 0.806120i | \(0.701563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.582576 | −0.0604103 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.58258 | 0.367565 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.79129 | 0.994155 | 0.497077 | − | 0.867706i | \(-0.334407\pi\) | ||||
0.497077 | + | 0.867706i | \(0.334407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.1652 | −1.72516 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.834849 | −0.0830705 | −0.0415353 | − | 0.999137i | \(-0.513225\pi\) | ||||
−0.0415353 | + | 0.999137i | \(0.513225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.58258 | −0.747133 | −0.373567 | − | 0.927603i | \(-0.621865\pi\) | ||||
−0.373567 | + | 0.927603i | \(0.621865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.41742 | 0.620396 | 0.310198 | − | 0.950672i | \(-0.399605\pi\) | ||||
0.310198 | + | 0.950672i | \(0.399605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.5826 | 1.87567 | 0.937835 | − | 0.347081i | \(-0.112827\pi\) | ||||
0.937835 | + | 0.347081i | \(0.112827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.5826 | −1.47903 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.5826 | −1.84217 | −0.921087 | − | 0.389357i | \(-0.872697\pi\) | ||||
−0.921087 | + | 0.389357i | \(0.872697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.83485 | 0.264351 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.1652 | 1.77182 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83485 | 0.166804 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.37386 | −0.304211 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1652 | −1.08808 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7913 | 1.75619 | 0.878096 | − | 0.478484i | \(-0.158813\pi\) | ||||
0.878096 | + | 0.478484i | \(0.158813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.79129 | 0.685985 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.95644 | −0.770848 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5390 | 1.32759 | 0.663794 | − | 0.747916i | \(-0.268945\pi\) | ||||
0.663794 | + | 0.747916i | \(0.268945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.20871 | 0.696254 | 0.348127 | − | 0.937447i | \(-0.386818\pi\) | ||||
0.348127 | + | 0.937447i | \(0.386818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.41742 | 0.372014 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.3303 | −1.19836 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5390 | 1.27301 | 0.636503 | − | 0.771274i | \(-0.280380\pi\) | ||||
0.636503 | + | 0.771274i | \(0.280380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.95644 | −0.484728 | −0.242364 | − | 0.970185i | \(-0.577923\pi\) | ||||
−0.242364 | + | 0.970185i | \(0.577923\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.79129 | 0.387353 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.373864 | 0.0300294 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.16515 | −0.412224 | −0.206112 | − | 0.978528i | \(-0.566081\pi\) | ||||
−0.206112 | + | 0.978528i | \(0.566081\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.3303 | 2.16743 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.417424 | 0.0326952 | 0.0163476 | − | 0.999866i | \(-0.494796\pi\) | ||||
0.0163476 | + | 0.999866i | \(0.494796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.9129 | 1.39452 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.20871 | 0.403062 | 0.201531 | − | 0.979482i | \(-0.435408\pi\) | ||||
0.201531 | + | 0.979482i | \(0.435408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.58258 | 0.732798 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.6261 | 0.883919 | 0.441959 | − | 0.897035i | \(-0.354284\pi\) | ||||
0.441959 | + | 0.897035i | \(0.354284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.3303 | −2.43009 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.2087 | −0.987265 | −0.493633 | − | 0.869670i | \(-0.664331\pi\) | ||||
−0.493633 | + | 0.869670i | \(0.664331\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.16515 | 0.0866050 | 0.0433025 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433025 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.9564 | −1.40130 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0000 | 0.735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.58258 | −0.261984 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.79129 | −0.563758 | −0.281879 | − | 0.959450i | \(-0.590958\pi\) | ||||
−0.281879 | + | 0.959450i | \(0.590958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7477 | 1.49345 | 0.746727 | − | 0.665131i | \(-0.231624\pi\) | ||||
0.746727 | + | 0.665131i | \(0.231624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.0000 | −1.43223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1652 | 1.65045 | 0.825224 | − | 0.564805i | \(-0.191049\pi\) | ||||
0.825224 | + | 0.564805i | \(0.191049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5390 | 1.10153 | 0.550766 | − | 0.834660i | \(-0.314336\pi\) | ||||
0.550766 | + | 0.834660i | \(0.314336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.5826 | 2.15713 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.16515 | 0.151221 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.58258 | 0.527025 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.16515 | −0.495624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9129 | 1.50854 | 0.754272 | − | 0.656562i | \(-0.227990\pi\) | ||||
0.754272 | + | 0.656562i | \(0.227990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.3303 | −0.844858 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | −0.340997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −41.2867 | −2.78990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1652 | 1.01553 | 0.507767 | − | 0.861495i | \(-0.330471\pi\) | ||||
0.507767 | + | 0.861495i | \(0.330471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.58258 | −0.572172 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.3739 | 1.81687 | 0.908434 | − | 0.418029i | \(-0.137279\pi\) | ||||
0.908434 | + | 0.418029i | \(0.137279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7477 | 1.10672 | 0.553360 | − | 0.832942i | \(-0.313345\pi\) | ||||
0.553360 | + | 0.832942i | \(0.313345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7477 | 0.966156 | 0.483078 | − | 0.875577i | \(-0.339519\pi\) | ||||
0.483078 | + | 0.875577i | \(0.339519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.83485 | −0.184925 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.9129 | 1.81314 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3739 | 0.800399 | 0.400199 | − | 0.916428i | \(-0.368941\pi\) | ||||
0.400199 | + | 0.916428i | \(0.368941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5390 | −0.807709 | −0.403854 | − | 0.914823i | \(-0.632330\pi\) | ||||
−0.403854 | + | 0.914823i | \(0.632330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1652 | 1.03699 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.7477 | 1.69507 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4174 | −0.657542 | −0.328771 | − | 0.944410i | \(-0.606634\pi\) | ||||
−0.328771 | + | 0.944410i | \(0.606634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.66970 | −0.356451 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.00000 | −0.313112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.33030 | −0.519630 | −0.259815 | − | 0.965658i | \(-0.583662\pi\) | ||||
−0.259815 | + | 0.965658i | \(0.583662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.3303 | 1.87025 | 0.935123 | − | 0.354322i | \(-0.115288\pi\) | ||||
0.935123 | + | 0.354322i | \(0.115288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.5390 | −1.07741 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 31.1652 | 1.90728 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.83485 | −0.172844 | −0.0864219 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864219 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.16515 | −0.192269 | −0.0961346 | − | 0.995368i | \(-0.530648\pi\) | ||||
−0.0961346 | + | 0.995368i | \(0.530648\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.41742 | 0.386985 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.7477 | −1.60712 | −0.803558 | − | 0.595227i | \(-0.797062\pi\) | ||||
−0.803558 | + | 0.595227i | \(0.797062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.79129 | 0.584099 | 0.292050 | − | 0.956403i | \(-0.405663\pi\) | ||||
0.292050 | + | 0.956403i | \(0.405663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1216 | 1.55277 | 0.776384 | − | 0.630261i | \(-0.217052\pi\) | ||||
0.776384 | + | 0.630261i | \(0.217052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.0000 | −0.592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.3303 | −1.60213 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7477 | 0.744730 | 0.372365 | − | 0.928086i | \(-0.378547\pi\) | ||||
0.372365 | + | 0.928086i | \(0.378547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7477 | 1.20798 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.9129 | 1.03941 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.33030 | 0.366091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.33030 | 0.133872 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1652 | 0.696575 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.58258 | 0.432760 | 0.216380 | − | 0.976309i | \(-0.430575\pi\) | ||||
0.216380 | + | 0.976309i | \(0.430575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.1652 | 1.20404 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.2087 | −1.14593 | −0.572965 | − | 0.819580i | \(-0.694207\pi\) | ||||
−0.572965 | + | 0.819580i | \(0.694207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.7042 | −1.79203 | −0.896013 | − | 0.444028i | \(-0.853549\pi\) | ||||
−0.896013 | + | 0.444028i | \(0.853549\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3303 | 0.580208 | 0.290104 | − | 0.956995i | \(-0.406310\pi\) | ||||
0.290104 | + | 0.956995i | \(0.406310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.9129 | −0.999799 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.16515 | −0.397451 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −54.6606 | −3.02274 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.37386 | −0.405304 | −0.202652 | − | 0.979251i | \(-0.564956\pi\) | ||||
−0.202652 | + | 0.979251i | \(0.564956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.7477 | 1.46577 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6261 | −1.07229 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1652 | −0.935045 | −0.467523 | − | 0.883981i | \(-0.654853\pi\) | ||||
−0.467523 | + | 0.883981i | \(0.654853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 54.6606 | 2.96876 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.747727 | −0.0404917 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.91288 | −0.426015 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.834849 | 0.0448170 | 0.0224085 | − | 0.999749i | \(-0.492867\pi\) | ||||
0.0224085 | + | 0.999749i | \(0.492867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.417424 | 0.0223442 | 0.0111721 | − | 0.999938i | \(-0.496444\pi\) | ||||
0.0111721 | + | 0.999938i | \(0.496444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0000 | −1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.1652 | −1.44586 | −0.722928 | − | 0.690924i | \(-0.757204\pi\) | ||||
−0.722928 | + | 0.690924i | \(0.757204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.91288 | 0.419972 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.9564 | 1.00048 | 0.500241 | − | 0.865886i | \(-0.333245\pi\) | ||||
0.500241 | + | 0.865886i | \(0.333245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.12159 | −0.268814 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4955 | 1.38684 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.3739 | 1.48110 | 0.740552 | − | 0.671999i | \(-0.234564\pi\) | ||||
0.740552 | + | 0.671999i | \(0.234564\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.79129 | 0.301482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.1216 | 0.886522 | 0.443261 | − | 0.896393i | \(-0.353821\pi\) | ||||
0.443261 | + | 0.896393i | \(0.353821\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.9564 | 1.75350 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3303 | 0.530632 | 0.265316 | − | 0.964162i | \(-0.414524\pi\) | ||||
0.265316 | + | 0.964162i | \(0.414524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −55.2432 | −2.83019 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.41742 | −0.430110 | −0.215055 | − | 0.976602i | \(-0.568993\pi\) | ||||
−0.215055 | + | 0.976602i | \(0.568993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.3739 | −0.679832 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.1216 | −1.02021 | −0.510103 | − | 0.860114i | \(-0.670393\pi\) | ||||
−0.510103 | + | 0.860114i | \(0.670393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.58258 | 0.0800343 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.4955 | −1.68962 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.9129 | −0.901295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2867 | 1.57024 | 0.785118 | − | 0.619346i | \(-0.212602\pi\) | ||||
0.785118 | + | 0.619346i | \(0.212602\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.83485 | −0.141566 | −0.0707828 | − | 0.997492i | \(-0.522550\pi\) | ||||
−0.0707828 | + | 0.997492i | \(0.522550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.834849 | 0.0415868 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.747727 | −0.0371549 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.00000 | −0.197787 | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.3739 | −2.13947 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1652 | −0.842604 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.9129 | −1.12205 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.2087 | −1.18267 | −0.591336 | − | 0.806425i | \(-0.701399\pi\) | ||||
−0.591336 | + | 0.806425i | \(0.701399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.20871 | −0.448805 | −0.224403 | − | 0.974497i | \(-0.572043\pi\) | ||||
−0.224403 | + | 0.974497i | \(0.572043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.58258 | −0.368677 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.79129 | −0.0868902 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 40.0000 | 1.93122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.417424 | −0.0201066 | −0.0100533 | − | 0.999949i | \(-0.503200\pi\) | ||||
−0.0100533 | + | 0.999949i | \(0.503200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.5826 | 1.61388 | 0.806938 | − | 0.590636i | \(-0.201123\pi\) | ||||
0.806938 | + | 0.590636i | \(0.201123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.16515 | 0.151410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.95644 | 0.0933758 | 0.0466879 | − | 0.998910i | \(-0.485133\pi\) | ||||
0.0466879 | + | 0.998910i | \(0.485133\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.66970 | −0.0793297 | −0.0396649 | − | 0.999213i | \(-0.512629\pi\) | ||||
−0.0396649 | + | 0.999213i | \(0.512629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0000 | −0.948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.3739 | −2.05151 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.58258 | −0.0746864 | −0.0373432 | − | 0.999303i | \(-0.511889\pi\) | ||||
−0.0373432 | + | 0.999303i | \(0.511889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.33030 | −0.203906 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.6261 | 0.781164 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.79129 | 0.458017 | 0.229009 | − | 0.973424i | \(-0.426452\pi\) | ||||
0.229009 | + | 0.973424i | \(0.426452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.7477 | 1.43206 | 0.716032 | − | 0.698067i | \(-0.245956\pi\) | ||||
0.716032 | + | 0.698067i | \(0.245956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.3739 | 1.50454 | 0.752271 | − | 0.658854i | \(-0.228959\pi\) | ||||
0.752271 | + | 0.658854i | \(0.228959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04356 | −0.0483940 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1652 | 1.44215 | 0.721076 | − | 0.692856i | \(-0.243648\pi\) | ||||
0.721076 | + | 0.692856i | \(0.243648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4174 | 0.664320 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | 0.459800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.58258 | −0.164380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −46.9129 | −2.14799 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.8693 | −1.54753 | −0.773764 | − | 0.633474i | \(-0.781629\pi\) | ||||
−0.773764 | + | 0.633474i | \(0.781629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3303 | 1.01817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.5390 | 0.796406 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7477 | −1.48394 | −0.741971 | − | 0.670432i | \(-0.766109\pi\) | ||||
−0.741971 | + | 0.670432i | \(0.766109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.16515 | −0.0526900 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04356 | 0.0470952 | 0.0235476 | − | 0.999723i | \(-0.492504\pi\) | ||||
0.0235476 | + | 0.999723i | \(0.492504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.7477 | −1.38201 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.417424 | −0.0186865 | −0.00934324 | − | 0.999956i | \(-0.502974\pi\) | ||||
−0.00934324 | + | 0.999956i | \(0.502974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5390 | −0.649555 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.79129 | −0.169045 | −0.0845226 | − | 0.996422i | \(-0.526937\pi\) | ||||
−0.0845226 | + | 0.996422i | \(0.526937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.49545 | −0.0665468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.37386 | −0.371896 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.33030 | 0.369234 | 0.184617 | − | 0.982811i | \(-0.440896\pi\) | ||||
0.184617 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.0000 | −0.441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.5826 | −0.598520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.66970 | 0.249353 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.4519 | −1.42448 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.04356 | −0.264773 | −0.132387 | − | 0.991198i | \(-0.542264\pi\) | ||||
−0.132387 | + | 0.991198i | \(0.542264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.0780 | −1.44640 | −0.723201 | − | 0.690638i | \(-0.757330\pi\) | ||||
−0.723201 | + | 0.690638i | \(0.757330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.208712 | 0.00909164 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4955 | −0.891107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 55.4955 | 2.40830 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.83485 | 0.209421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4955 | 0.496992 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.8693 | 1.59103 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8348 | 0.551813 | 0.275907 | − | 0.961184i | \(-0.411022\pi\) | ||||
0.275907 | + | 0.961184i | \(0.411022\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.25227 | −0.139568 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.0780 | 1.50258 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.5390 | 1.38873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.9129 | −1.18484 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.3303 | −1.03091 | −0.515454 | − | 0.856917i | \(-0.672377\pi\) | ||||
−0.515454 | + | 0.856917i | \(0.672377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1652 | −0.472236 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.0780 | −1.47574 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.9564 | −1.25584 | −0.627920 | − | 0.778278i | \(-0.716093\pi\) | ||||
−0.627920 | + | 0.778278i | \(0.716093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.5826 | −0.652110 | −0.326055 | − | 0.945351i | \(-0.605720\pi\) | ||||
−0.326055 | + | 0.945351i | \(0.605720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.7477 | 0.908524 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.83485 | −0.118221 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.91288 | 0.412679 | 0.206339 | − | 0.978481i | \(-0.433845\pi\) | ||||
0.206339 | + | 0.978481i | \(0.433845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −57.9129 | −2.40678 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.0780 | 1.45278 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34.3303 | 1.41938 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.4174 | 1.09036 | 0.545182 | − | 0.838318i | \(-0.316461\pi\) | ||||
0.545182 | + | 0.838318i | \(0.316461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.417424 | 0.0171997 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −64.6606 | −2.65978 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0780 | 1.02983 | 0.514916 | − | 0.857241i | \(-0.327823\pi\) | ||||
0.514916 | + | 0.857241i | \(0.327823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.3739 | −1.77517 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.2087 | −0.539693 | −0.269847 | − | 0.962903i | \(-0.586973\pi\) | ||||
−0.269847 | + | 0.962903i | \(0.586973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4955 | −0.958400 | −0.479200 | − | 0.877706i | \(-0.659073\pi\) | ||||
−0.479200 | + | 0.877706i | \(0.659073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −52.4955 | −2.13778 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.28674 | 0.133625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.3739 | −1.59814 | −0.799068 | − | 0.601241i | \(-0.794673\pi\) | ||||
−0.799068 | + | 0.601241i | \(0.794673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.33030 | −0.256097 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2867 | −0.940543 | −0.470271 | − | 0.882522i | \(-0.655844\pi\) | ||||
−0.470271 | + | 0.882522i | \(0.655844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.04356 | −0.243700 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4955 | −0.623823 | −0.311912 | − | 0.950111i | \(-0.600969\pi\) | ||||
−0.311912 | + | 0.950111i | \(0.600969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.6606 | −1.15197 | −0.575983 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575983 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.91288 | −0.317533 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8348 | −0.513394 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | 0.798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.58258 | 0.222592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.9564 | −0.754644 | −0.377322 | − | 0.926082i | \(-0.623155\pi\) | ||||
−0.377322 | + | 0.926082i | \(0.623155\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −61.1652 | −2.43110 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.4519 | 1.40687 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.1652 | 0.837280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.9129 | −1.65546 | −0.827730 | − | 0.561127i | \(-0.810368\pi\) | ||||
−0.827730 | + | 0.561127i | \(0.810368\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.95644 | 0.0771544 | 0.0385772 | − | 0.999256i | \(-0.487717\pi\) | ||||
0.0385772 | + | 0.999256i | \(0.487717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.9564 | 0.549534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.83485 | −0.190078 | −0.0950388 | − | 0.995474i | \(-0.530298\pi\) | ||||
−0.0950388 | + | 0.995474i | \(0.530298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.4955 | −1.62884 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9129 | 0.779251 | 0.389626 | − | 0.920973i | \(-0.372604\pi\) | ||||
0.389626 | + | 0.920973i | \(0.372604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.4955 | 0.839897 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70.8693 | 2.76488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.9564 | −1.05007 | −0.525037 | − | 0.851079i | \(-0.675948\pi\) | ||||
−0.525037 | + | 0.851079i | \(0.675948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4955 | 1.69178 | 0.845889 | − | 0.533360i | \(-0.179071\pi\) | ||||
0.845889 | + | 0.533360i | \(0.179071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.1652 | −0.433619 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.3303 | −1.63658 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.3303 | −0.939261 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0780 | −0.504121 | −0.252061 | − | 0.967711i | \(-0.581108\pi\) | ||||
−0.252061 | + | 0.967711i | \(0.581108\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.95644 | 0.344734 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8348 | −1.03135 | −0.515674 | − | 0.856785i | \(-0.672458\pi\) | ||||
−0.515674 | + | 0.856785i | \(0.672458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −76.4083 | −2.92797 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7477 | 1.25306 | 0.626528 | − | 0.779399i | \(-0.284475\pi\) | ||||
0.626528 | + | 0.779399i | \(0.284475\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.8348 | 1.06351 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.7477 | −1.78354 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.1652 | −1.49207 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.6261 | −0.746613 | −0.373307 | − | 0.927708i | \(-0.621776\pi\) | ||||
−0.373307 | + | 0.927708i | \(0.621776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.7042 | 0.557761 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.20871 | 0.0457832 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.1652 | −1.55701 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1652 | 0.421102 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.91288 | 0.298016 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8348 | 1.15803 | 0.579014 | − | 0.815318i | \(-0.303438\pi\) | ||||
0.579014 | + | 0.815318i | \(0.303438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −47.9129 | −1.79687 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.330303 | 0.0123699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.6697 | −0.959992 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.5390 | −1.28988 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.8693 | 0.666413 | 0.333207 | − | 0.942854i | \(-0.391869\pi\) | ||||
0.333207 | + | 0.942854i | \(0.391869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.0000 | 1.30166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3303 | 1.19906 | 0.599532 | − | 0.800351i | \(-0.295353\pi\) | ||||
0.599532 | + | 0.800351i | \(0.295353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.79129 | −0.103240 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7477 | −0.544720 | −0.272360 | − | 0.962195i | \(-0.587804\pi\) | ||||
−0.272360 | + | 0.962195i | \(0.587804\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.2523 | 1.44588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.9564 | 1.10197 | 0.550983 | − | 0.834517i | \(-0.314253\pi\) | ||||
0.550983 | + | 0.834517i | \(0.314253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.3303 | −0.820324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.1652 | 1.65695 | 0.828474 | − | 0.560027i | \(-0.189209\pi\) | ||||
0.828474 | + | 0.560027i | \(0.189209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.8348 | 1.01979 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.9129 | −1.67986 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.83485 | 0.249407 | 0.124704 | − | 0.992194i | \(-0.460202\pi\) | ||||
0.124704 | + | 0.992194i | \(0.460202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.0780 | 1.05966 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.6697 | −0.388310 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 54.6170 | 1.98509 | 0.992545 | − | 0.121878i | \(-0.0388916\pi\) | ||||
0.992545 | + | 0.121878i | \(0.0388916\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.8258 | 0.574439 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.1652 | −1.12974 | −0.564868 | − | 0.825181i | \(-0.691073\pi\) | ||||
−0.564868 | + | 0.825181i | \(0.691073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.58258 | 0.310304 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.3303 | 1.67289 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4955 | 1.35212 | 0.676060 | − | 0.736846i | \(-0.263686\pi\) | ||||
0.676060 | + | 0.736846i | \(0.263686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.2523 | 0.837410 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.9129 | 1.14783 | 0.573913 | − | 0.818916i | \(-0.305425\pi\) | ||||
0.573913 | + | 0.818916i | \(0.305425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.373864 | −0.0134296 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.41742 | 0.0866132 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8258 | −0.566290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.25227 | −0.330228 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.3303 | 0.795989 | 0.397995 | − | 0.917388i | \(-0.369706\pi\) | ||||
0.397995 | + | 0.917388i | \(0.369706\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −84.6606 | −3.01400 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1652 | 0.964663 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 48.9564 | 1.73631 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0780 | −0.817466 | −0.408733 | − | 0.912654i | \(-0.634029\pi\) | ||||
−0.408733 | + | 0.912654i | \(0.634029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.58258 | −0.0559875 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −53.4955 | −1.89017 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.9909 | −1.87001 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.91288 | 0.278547 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.4955 | −0.966689 | −0.483344 | − | 0.875430i | \(-0.660578\pi\) | ||||
−0.483344 | + | 0.875430i | \(0.660578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.29583 | 0.0455029 | 0.0227514 | − | 0.999741i | \(-0.492757\pi\) | ||||
0.0227514 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.83485 | 0.309852 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.747727 | 0.0261917 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.58258 | −0.195310 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0780 | 0.386156 | 0.193078 | − | 0.981183i | \(-0.438153\pi\) | ||||
0.193078 | + | 0.981183i | \(0.438153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.9129 | −0.623646 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.3303 | 1.40242 | 0.701211 | − | 0.712954i | \(-0.252643\pi\) | ||||
0.701211 | + | 0.712954i | \(0.252643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 74.6606 | 2.58995 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.33030 | 0.322888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.04356 | −0.0360707 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.1652 | −1.76642 | −0.883209 | − | 0.468980i | \(-0.844622\pi\) | ||||
−0.883209 | + | 0.468980i | \(0.844622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.3303 | −0.941306 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.37386 | 0.184867 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −72.9129 | −2.50236 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.83485 | 0.302855 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4955 | −0.393597 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.1652 | 0.587036 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.28674 | −0.112273 | −0.0561365 | − | 0.998423i | \(-0.517878\pi\) | ||||
−0.0561365 | + | 0.998423i | \(0.517878\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.91288 | 0.269984 | 0.134992 | − | 0.990847i | \(-0.456899\pi\) | ||||
0.134992 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.3739 | −0.387171 | −0.193585 | − | 0.981083i | \(-0.562012\pi\) | ||||
−0.193585 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.8258 | 0.708097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.79129 | −0.0947971 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.8258 | 1.21531 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.8258 | −1.48498 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.9129 | 1.58776 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9129 | −0.807481 | −0.403740 | − | 0.914874i | \(-0.632290\pi\) | ||||
−0.403740 | + | 0.914874i | \(0.632290\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −35.5826 | −1.20017 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.1216 | −1.35173 | −0.675865 | − | 0.737025i | \(-0.736230\pi\) | ||||
−0.675865 | + | 0.737025i | \(0.736230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.5390 | −1.16233 | −0.581165 | − | 0.813786i | \(-0.697403\pi\) | ||||
−0.581165 | + | 0.813786i | \(0.697403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.9129 | −1.94672 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.2087 | 0.678542 | 0.339271 | − | 0.940689i | \(-0.389820\pi\) | ||||
0.339271 | + | 0.940689i | \(0.389820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.49545 | 0.0500996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.16515 | −0.105918 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.6606 | −0.790887 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.6697 | −0.589974 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.79129 | −0.326195 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.08712 | 0.0693783 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5826 | −0.451002 | −0.225501 | − | 0.974243i | \(-0.572402\pi\) | ||||
−0.225501 | + | 0.974243i | \(0.572402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.00000 | −0.132672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.66970 | −0.320371 | −0.160186 | − | 0.987087i | \(-0.551209\pi\) | ||||
−0.160186 | + | 0.987087i | \(0.551209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.3303 | 1.13617 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.9564 | −1.12257 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8784 | −0.490793 | −0.245397 | − | 0.969423i | \(-0.578918\pi\) | ||||
−0.245397 | + | 0.969423i | \(0.578918\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.1652 | −0.697415 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.6697 | 0.581605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.3303 | −1.19324 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.37386 | 0.176311 | 0.0881554 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881554 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 56.4083 | 1.84673 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.41742 | −0.209872 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6606 | 0.544278 | 0.272139 | − | 0.962258i | \(-0.412269\pi\) | ||||
0.272139 | + | 0.962258i | \(0.412269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 88.4955 | 2.88794 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.28674 | 0.139744 | 0.0698719 | − | 0.997556i | \(-0.477741\pi\) | ||||
0.0698719 | + | 0.997556i | \(0.477741\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.91288 | 0.0622919 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0871215 | 0.00283107 | 0.00141553 | − | 0.999999i | \(-0.499549\pi\) | ||||
0.00141553 | + | 0.999999i | \(0.499549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1652 | 1.92058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.8348 | −0.935034 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.29583 | −0.268728 | −0.134364 | − | 0.990932i | \(-0.542899\pi\) | ||||
−0.134364 | + | 0.990932i | \(0.542899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9564 | −0.451620 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9564 | −0.998595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.7477 | 0.990832 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1652 | 1.19639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.5390 | 1.27149 | 0.635745 | − | 0.771900i | \(-0.280693\pi\) | ||||
0.635745 | + | 0.771900i | \(0.280693\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.58258 | −0.179338 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.1652 | −1.83452 | −0.917259 | − | 0.398292i | \(-0.869603\pi\) | ||||
−0.917259 | + | 0.398292i | \(0.869603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.0000 | 0.640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.5390 | −1.55290 | −0.776450 | − | 0.630178i | \(-0.782982\pi\) | ||||
−0.776450 | + | 0.630178i | \(0.782982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.0000 | 1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 93.8258 | 2.99563 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.62614 | −0.275131 | −0.137566 | − | 0.990493i | \(-0.543928\pi\) | ||||
−0.137566 | + | 0.990493i | \(0.543928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4955 | 1.32216 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.41742 | −0.140466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0780 | 1.43195 | 0.715975 | − | 0.698126i | \(-0.245982\pi\) | ||||
0.715975 | + | 0.698126i | \(0.245982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.5826 | 0.653168 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.8348 | 0.882424 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29583 | 0.0410395 | 0.0205197 | − | 0.999789i | \(-0.493468\pi\) | ||||
0.0205197 | + | 0.999789i | \(0.493468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.9129 | −0.883124 |
(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 | 3332.2.a.i.1.1 | ✓ | 2 | |
7.6 | odd | 2 | 3332.2.a.m.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.i.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3332.2.a.m.1.2 | yes | 2 | 7.6 | odd | 2 |