Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(17,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.w (of order \(4\), degree \(2\), not 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.3 | ||
Root | \(0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.593 |
Dual form | 720.2.w.e.17.3 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58114 | + | 1.58114i | 0.707107 | + | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23607 | + | 1.23607i | −0.467190 | + | 0.467190i | −0.901003 | − | 0.433813i | \(-0.857168\pi\) |
0.433813 | + | 0.901003i | \(0.357168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.74806i | − | 0.527061i | −0.964651 | − | 0.263531i | \(-0.915113\pi\) | ||
0.964651 | − | 0.263531i | \(-0.0848870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.236068 | + | 0.236068i | 0.0654735 | + | 0.0654735i | 0.739085 | − | 0.673612i | \(-0.235258\pi\) |
−0.673612 | + | 0.739085i | \(0.735258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.57649 | + | 4.57649i | 1.10996 | + | 1.10996i | 0.993155 | + | 0.116808i | \(0.0372661\pi\) |
0.116808 | + | 0.993155i | \(0.462734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.47214i | 1.48481i | 0.669951 | + | 0.742405i | \(0.266315\pi\) | ||||
−0.669951 | + | 0.742405i | \(0.733685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | − | 2.82843i | 0.589768 | − | 0.589768i | −0.347801 | − | 0.937568i | \(-0.613071\pi\) |
0.937568 | + | 0.347801i | \(0.113071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.333851 | 0.0619945 | 0.0309972 | − | 0.999519i | \(-0.490132\pi\) | ||||
0.0309972 | + | 0.999519i | \(0.490132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4721 | −1.88085 | −0.940426 | − | 0.340000i | \(-0.889573\pi\) | ||||
−0.940426 | + | 0.340000i | \(0.889573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.90879 | −0.660706 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.23607 | + | 2.23607i | −0.367607 | + | 0.367607i | −0.866604 | − | 0.498997i | \(-0.833702\pi\) |
0.498997 | + | 0.866604i | \(0.333702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.07107i | − | 1.10432i | −0.833740 | − | 0.552158i | \(-0.813805\pi\) | ||
0.833740 | − | 0.552158i | \(-0.186195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | + | 6.47214i | 0.986991 | + | 0.986991i | 0.999916 | − | 0.0129250i | \(-0.00411427\pi\) |
−0.0129250 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.57649 | + | 4.57649i | 0.667550 | + | 0.667550i | 0.957148 | − | 0.289598i | \(-0.0935217\pi\) |
−0.289598 | + | 0.957148i | \(0.593522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94427i | 0.563467i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.76393 | − | 2.76393i | 0.372689 | − | 0.372689i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.40492 | 0.964038 | 0.482019 | − | 0.876161i | \(-0.339904\pi\) | ||||
0.482019 | + | 0.876161i | \(0.339904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52786 | 0.195623 | 0.0978115 | − | 0.995205i | \(-0.468816\pi\) | ||||
0.0978115 | + | 0.995205i | \(0.468816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.746512i | 0.0925935i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4721 | − | 10.4721i | 1.27938 | − | 1.27938i | 0.338357 | − | 0.941018i | \(-0.390129\pi\) |
0.941018 | − | 0.338357i | \(-0.109871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6491i | 1.50117i | 0.660772 | + | 0.750587i | \(0.270229\pi\) | ||||
−0.660772 | + | 0.750587i | \(0.729771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.47214 | − | 9.47214i | −1.10863 | − | 1.10863i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) |
−0.115299 | − | 0.993331i | \(-0.536783\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16073 | + | 2.16073i | 0.246238 | + | 0.246238i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.52786i | 0.621933i | 0.950421 | + | 0.310967i | \(0.100653\pi\) | ||||
−0.950421 | + | 0.310967i | \(0.899347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.40492 | − | 7.40492i | 0.812795 | − | 0.812795i | −0.172257 | − | 0.985052i | \(-0.555106\pi\) |
0.985052 | + | 0.172257i | \(0.0551059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4721i | 1.56972i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3956 | −1.41993 | −0.709967 | − | 0.704235i | \(-0.751290\pi\) | ||||
−0.709967 | + | 0.704235i | \(0.751290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.583592 | −0.0611771 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2333 | + | 10.2333i | −1.04992 | + | 1.04992i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | − | 1.00000i | 0.101535 | − | 0.101535i | −0.654515 | − | 0.756049i | \(-0.727127\pi\) |
0.756049 | + | 0.654515i | \(0.227127\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 17.3044i | − | 1.72185i | −0.508729 | − | 0.860927i | \(-0.669884\pi\) | ||
0.508729 | − | 0.860927i | \(-0.330116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1803 | − | 10.1803i | −1.00310 | − | 1.00310i | −0.999995 | − | 0.00310351i | \(-0.999012\pi\) |
−0.00310351 | − | 0.999995i | \(-0.500988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.90879 | + | 3.90879i | 0.377877 | + | 0.377877i | 0.870336 | − | 0.492459i | \(-0.163902\pi\) |
−0.492459 | + | 0.870336i | \(0.663902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.4164i | − | 1.09349i | −0.837298 | − | 0.546747i | \(-0.815866\pi\) | ||
0.837298 | − | 0.546747i | \(-0.184134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.16228 | − | 3.16228i | 0.297482 | − | 0.297482i | −0.542545 | − | 0.840027i | \(-0.682539\pi\) |
0.840027 | + | 0.542545i | \(0.182539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427 | 0.834058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.94427 | 0.722207 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | + | 7.90569i | −0.707107 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.76393 | − | 2.76393i | 0.245259 | − | 0.245259i | −0.573762 | − | 0.819022i | \(-0.694517\pi\) |
0.819022 | + | 0.573762i | \(0.194517\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.5579i | − | 1.44667i | −0.690497 | − | 0.723335i | \(-0.742608\pi\) | ||
0.690497 | − | 0.723335i | \(-0.257392\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | − | 8.00000i | −0.693688 | − | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.49458 | + | 2.49458i | 0.213126 | + | 0.213126i | 0.805594 | − | 0.592468i | \(-0.201846\pi\) |
−0.592468 | + | 0.805594i | \(0.701846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.94427i | − | 0.758643i | −0.925265 | − | 0.379322i | \(-0.876157\pi\) | ||
0.925265 | − | 0.379322i | \(-0.123843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.412662 | − | 0.412662i | 0.0345085 | − | 0.0345085i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.527864 | + | 0.527864i | 0.0438367 | + | 0.0438367i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.15143 | −0.667791 | −0.333896 | − | 0.942610i | \(-0.608363\pi\) | ||||
−0.333896 | + | 0.942610i | \(0.608363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9443 | −1.05339 | −0.526695 | − | 0.850054i | \(-0.676569\pi\) | ||||
−0.526695 | + | 0.850054i | \(0.676569\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5579 | − | 16.5579i | −1.32996 | − | 1.32996i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7082 | − | 12.7082i | 1.01423 | − | 1.01423i | 0.0143277 | − | 0.999897i | \(-0.495439\pi\) |
0.999897 | − | 0.0143277i | \(-0.00456082\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.99226i | 0.551067i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.47214 | + | 6.47214i | 0.506937 | + | 0.506937i | 0.913585 | − | 0.406648i | \(-0.133302\pi\) |
−0.406648 | + | 0.913585i | \(0.633302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.32456 | − | 6.32456i | −0.489409 | − | 0.489409i | 0.418711 | − | 0.908120i | \(-0.362482\pi\) |
−0.908120 | + | 0.418711i | \(0.862482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.8885i | − | 0.991426i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.333851 | + | 0.333851i | −0.0253822 | + | 0.0253822i | −0.719684 | − | 0.694302i | \(-0.755713\pi\) |
0.694302 | + | 0.719684i | \(0.255713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.18034 | − | 6.18034i | −0.467190 | − | 0.467190i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.24419 | −0.391969 | −0.195985 | − | 0.980607i | \(-0.562790\pi\) | ||||
−0.195985 | + | 0.980607i | \(0.562790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.52786 | −0.113565 | −0.0567826 | − | 0.998387i | \(-0.518084\pi\) | ||||
−0.0567826 | + | 0.998387i | \(0.518084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.07107 | −0.519875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | − | 8.00000i | 0.585018 | − | 0.585018i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.99226i | − | 0.505942i | −0.967474 | − | 0.252971i | \(-0.918592\pi\) | ||
0.967474 | − | 0.252971i | \(-0.0814077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.47214 | + | 7.47214i | 0.537856 | + | 0.537856i | 0.922899 | − | 0.385043i | \(-0.125813\pi\) |
−0.385043 | + | 0.922899i | \(0.625813\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1437 | + | 15.1437i | 1.07894 | + | 1.07894i | 0.996604 | + | 0.0823386i | \(0.0262389\pi\) |
0.0823386 | + | 0.996604i | \(0.473761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.412662 | + | 0.412662i | −0.0289632 | + | 0.0289632i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1803 | − | 11.1803i | 0.780869 | − | 0.780869i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3137 | 0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4667i | 1.39582i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9443 | − | 12.9443i | 0.878714 | − | 0.878714i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.16073i | 0.145346i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7639 | − | 14.7639i | −0.988666 | − | 0.988666i | 0.0112705 | − | 0.999936i | \(-0.496412\pi\) |
−0.999936 | + | 0.0112705i | \(0.996412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.81758 | + | 7.81758i | 0.518871 | + | 0.518871i | 0.917230 | − | 0.398359i | \(-0.130420\pi\) |
−0.398359 | + | 0.917230i | \(0.630420\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8885i | 1.04994i | 0.851119 | + | 0.524972i | \(0.175924\pi\) | ||||
−0.851119 | + | 0.524972i | \(0.824076\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.41577 | + | 2.41577i | −0.158262 | + | 0.158262i | −0.781796 | − | 0.623534i | \(-0.785696\pi\) |
0.623534 | + | 0.781796i | \(0.285696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.4721i | 0.944058i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.6491 | −0.818203 | −0.409101 | − | 0.912489i | \(-0.634158\pi\) | ||||
−0.409101 | + | 0.912489i | \(0.634158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9443 | −0.962645 | −0.481323 | − | 0.876544i | \(-0.659843\pi\) | ||||
−0.481323 | + | 0.876544i | \(0.659843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.23644 | + | 6.23644i | −0.398432 | + | 0.398432i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.52786 | + | 1.52786i | −0.0972157 | + | 0.0972157i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.7264i | − | 0.740162i | −0.929000 | − | 0.370081i | \(-0.879330\pi\) | ||
0.929000 | − | 0.370081i | \(-0.120670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.94427 | − | 4.94427i | −0.310844 | − | 0.310844i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.16228 | + | 3.16228i | 0.197257 | + | 0.197257i | 0.798823 | − | 0.601566i | \(-0.205456\pi\) |
−0.601566 | + | 0.798823i | \(0.705456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.52786i | − | 0.343485i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.1421 | − | 14.1421i | 0.872041 | − | 0.872041i | −0.120653 | − | 0.992695i | \(-0.538499\pi\) |
0.992695 | + | 0.120653i | \(0.0384989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.65841 | −0.405970 | −0.202985 | − | 0.979182i | \(-0.565064\pi\) | ||||
−0.202985 | + | 0.979182i | \(0.565064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0557 | 0.671588 | 0.335794 | − | 0.941936i | \(-0.390995\pi\) | ||||
0.335794 | + | 0.941936i | \(0.390995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.74032 | 0.527061 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.18034 | + | 7.18034i | −0.431425 | + | 0.431425i | −0.889113 | − | 0.457688i | \(-0.848678\pi\) |
0.457688 | + | 0.889113i | \(0.348678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.3879i | − | 1.21624i | −0.793846 | − | 0.608119i | \(-0.791924\pi\) | ||
0.793846 | − | 0.608119i | \(-0.208076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | + | 8.00000i | 0.475551 | + | 0.475551i | 0.903705 | − | 0.428155i | \(-0.140836\pi\) |
−0.428155 | + | 0.903705i | \(0.640836\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.74032 | + | 8.74032i | 0.515925 | + | 0.515925i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885i | 1.46403i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4760 | − | 14.4760i | 0.845696 | − | 0.845696i | −0.143897 | − | 0.989593i | \(-0.545963\pi\) |
0.989593 | + | 0.143897i | \(0.0459633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7082 | + | 11.7082i | 0.681678 | + | 0.681678i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.33540 | 0.0772283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.41577 | + | 2.41577i | 0.138326 | + | 0.138326i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.52786 | + | 1.52786i | −0.0871998 | + | 0.0871998i | −0.749361 | − | 0.662161i | \(-0.769639\pi\) |
0.662161 | + | 0.749361i | \(0.269639\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.16073i | − | 0.122524i | −0.998122 | − | 0.0612618i | \(-0.980488\pi\) | ||
0.998122 | − | 0.0612618i | \(-0.0195124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.47214 | + | 1.47214i | 0.0832100 | + | 0.0832100i | 0.747487 | − | 0.664277i | \(-0.231260\pi\) |
−0.664277 | + | 0.747487i | \(0.731260\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4667 | − | 20.4667i | −1.14952 | − | 1.14952i | −0.986646 | − | 0.162878i | \(-0.947922\pi\) |
−0.162878 | − | 0.986646i | \(-0.552078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.583592i | − | 0.0326749i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.6197 | + | 29.6197i | −1.64808 | + | 1.64808i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.18034 | + | 1.18034i | −0.0654735 | + | 0.0654735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3137 | −0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4721 | 0.795461 | 0.397730 | − | 0.917502i | \(-0.369798\pi\) | ||||
0.397730 | + | 0.917502i | \(0.369798\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.1158 | 1.80931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4164 | + | 12.4164i | −0.676365 | + | 0.676365i | −0.959176 | − | 0.282811i | \(-0.908733\pi\) |
0.282811 | + | 0.959176i | \(0.408733\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.3060i | 0.991324i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5279 | − | 13.5279i | −0.730436 | − | 0.730436i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3060 | + | 18.3060i | 0.982716 | + | 0.982716i | 0.999853 | − | 0.0171375i | \(-0.00545529\pi\) |
−0.0171375 | + | 0.999853i | \(0.505455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4721i | 0.774676i | 0.921938 | + | 0.387338i | \(0.126605\pi\) | ||||
−0.921938 | + | 0.387338i | \(0.873395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.5687 | − | 11.5687i | 0.615742 | − | 0.615742i | −0.328694 | − | 0.944436i | \(-0.606609\pi\) |
0.944436 | + | 0.328694i | \(0.106609\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.0000 | + | 20.0000i | −1.06149 | + | 1.06149i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.83153 | 0.254998 | 0.127499 | − | 0.991839i | \(-0.459305\pi\) | ||||
0.127499 | + | 0.991839i | \(0.459305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.8885 | −1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 29.9535i | − | 1.56784i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.7082 | + | 15.7082i | −0.819962 | + | 0.819962i | −0.986102 | − | 0.166141i | \(-0.946869\pi\) |
0.166141 | + | 0.986102i | \(0.446869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7082 | + | 24.7082i | 1.27934 | + | 1.27934i | 0.941036 | + | 0.338306i | \(0.109854\pi\) |
0.338306 | + | 0.941036i | \(0.390146\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0788114 | + | 0.0788114i | 0.00405899 | + | 0.00405899i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.944272i | 0.0485040i | 0.999706 | + | 0.0242520i | \(0.00772041\pi\) | ||||
−0.999706 | + | 0.0242520i | \(0.992280\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2333 | − | 10.2333i | 0.522900 | − | 0.522900i | −0.395546 | − | 0.918446i | \(-0.629445\pi\) |
0.918446 | + | 0.395546i | \(0.129445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.83282i | 0.348233i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.7711 | 1.91507 | 0.957536 | − | 0.288315i | \(-0.0930952\pi\) | ||||
0.957536 | + | 0.288315i | \(0.0930952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8885 | 1.30924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.74032 | + | 8.74032i | −0.439773 | + | 0.439773i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.76393 | + | 1.76393i | −0.0885292 | + | 0.0885292i | −0.749985 | − | 0.661455i | \(-0.769939\pi\) |
0.661455 | + | 0.749985i | \(0.269939\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8886i | 0.743504i | 0.928332 | + | 0.371752i | \(0.121243\pi\) | ||||
−0.928332 | + | 0.371752i | \(0.878757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.47214 | − | 2.47214i | −0.123146 | − | 0.123146i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.90879 | + | 3.90879i | 0.193752 | + | 0.193752i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.88854i | − | 0.488957i | −0.969655 | − | 0.244479i | \(-0.921383\pi\) | ||
0.969655 | − | 0.244479i | \(-0.0786168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.15298 | + | 9.15298i | −0.450389 | + | 0.450389i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.4164 | 1.14947 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.0246 | 1.80877 | 0.904385 | − | 0.426718i | \(-0.140330\pi\) | ||||
0.904385 | + | 0.426718i | \(0.140330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.8825 | + | 22.8825i | −1.10996 | + | 1.10996i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.88854 | + | 1.88854i | −0.0913930 | + | 0.0913930i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685i | 0.272481i | 0.990676 | + | 0.136241i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136241i | \(0.956498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.4164 | + | 10.4164i | 0.500581 | + | 0.500581i | 0.911618 | − | 0.411038i | \(-0.134834\pi\) |
−0.411038 | + | 0.911618i | \(0.634834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.3060 | + | 18.3060i | 0.875693 | + | 0.875693i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.05573i | 0.145842i | 0.997338 | + | 0.0729210i | \(0.0232321\pi\) | ||||
−0.997338 | + | 0.0729210i | \(0.976768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.81758 | + | 7.81758i | −0.371424 | + | 0.371424i | −0.867996 | − | 0.496571i | \(-0.834592\pi\) |
0.496571 | + | 0.867996i | \(0.334592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.1803 | − | 21.1803i | −1.00404 | − | 1.00404i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5517 | 1.15867 | 0.579333 | − | 0.815091i | \(-0.303313\pi\) | ||||
0.579333 | + | 0.815091i | \(0.303313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.3607 | −0.582042 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.922740 | − | 0.922740i | −0.0432587 | − | 0.0432587i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | − | 13.0000i | 0.608114 | − | 0.608114i | −0.334339 | − | 0.942453i | \(-0.608513\pi\) |
0.942453 | + | 0.334339i | \(0.108513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.48683i | 0.441846i | 0.975291 | + | 0.220923i | \(0.0709069\pi\) | ||||
−0.975291 | + | 0.220923i | \(0.929093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6525 | + | 20.6525i | 0.959802 | + | 0.959802i | 0.999223 | − | 0.0394208i | \(-0.0125513\pi\) |
−0.0394208 | + | 0.999223i | \(0.512551\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.74806 | + | 1.74806i | 0.0808908 | + | 0.0808908i | 0.746395 | − | 0.665504i | \(-0.231783\pi\) |
−0.665504 | + | 0.746395i | \(0.731783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8885i | 1.19542i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3137 | − | 11.3137i | 0.520205 | − | 0.520205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.3607 | −1.48481 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.5980 | −1.80928 | −0.904639 | − | 0.426179i | \(-0.859859\pi\) | ||||
−0.904639 | + | 0.426179i | \(0.859859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05573 | −0.0481371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.16228 | 0.143592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.2361 | + | 13.2361i | −0.599783 | + | 0.599783i | −0.940255 | − | 0.340471i | \(-0.889413\pi\) |
0.340471 | + | 0.940255i | \(0.389413\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.7264i | − | 0.529204i | −0.964358 | − | 0.264602i | \(-0.914759\pi\) | ||
0.964358 | − | 0.264602i | \(-0.0852405\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.52786 | + | 1.52786i | 0.0688115 | + | 0.0688115i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6352 | − | 15.6352i | −0.701333 | − | 0.701333i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.5279i | − | 0.784655i | −0.919826 | − | 0.392327i | \(-0.871670\pi\) | ||
0.919826 | − | 0.392327i | \(-0.128330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0649 | − | 15.0649i | 0.671710 | − | 0.671710i | −0.286400 | − | 0.958110i | \(-0.592459\pi\) |
0.958110 | + | 0.286400i | \(0.0924588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.3607 | − | 27.3607i | 1.21753 | − | 1.21753i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6398 | −0.826195 | −0.413098 | − | 0.910687i | \(-0.635553\pi\) | ||||
−0.413098 | + | 0.910687i | \(0.635553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4164 | 1.03588 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 32.1931i | − | 1.41860i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | − | 8.00000i | 0.351840 | − | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.7016i | 1.38887i | 0.719555 | + | 0.694436i | \(0.244346\pi\) | ||||
−0.719555 | + | 0.694436i | \(0.755654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.8885 | − | 25.8885i | −1.13203 | − | 1.13203i | −0.989840 | − | 0.142187i | \(-0.954587\pi\) |
−0.142187 | − | 0.989840i | \(-0.545413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.9256 | − | 47.9256i | −2.08767 | − | 2.08767i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000i | 0.304348i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.66925 | − | 1.66925i | 0.0723034 | − | 0.0723034i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3607i | 0.534399i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.89484 | 0.296982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3050 | 1.60387 | 0.801933 | − | 0.597415i | \(-0.203805\pi\) | ||||
0.801933 | + | 0.597415i | \(0.203805\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0509 | − | 18.0509i | 0.773217 | − | 0.773217i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | + | 12.0000i | −0.513083 | + | 0.513083i | −0.915470 | − | 0.402387i | \(-0.868181\pi\) |
0.402387 | + | 0.915470i | \(0.368181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.16073i | 0.0920500i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.83282 | − | 6.83282i | −0.290561 | − | 0.290561i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4744 | − | 13.4744i | −0.570930 | − | 0.570930i | 0.361458 | − | 0.932388i | \(-0.382279\pi\) |
−0.932388 | + | 0.361458i | \(0.882279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.05573i | 0.129244i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.9628 | + | 23.9628i | −1.00991 | + | 1.00991i | −0.00996204 | + | 0.999950i | \(0.503171\pi\) |
−0.999950 | + | 0.00996204i | \(0.996829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.7171 | 0.742738 | 0.371369 | − | 0.928485i | \(-0.378888\pi\) | ||||
0.371369 | + | 0.928485i | \(0.378888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4164 | −0.812551 | −0.406276 | − | 0.913751i | \(-0.633173\pi\) | ||||
−0.406276 | + | 0.913751i | \(0.633173\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.1421 | + | 14.1421i | 0.589768 | + | 0.589768i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.9443 | + | 29.9443i | −1.24660 | + | 1.24660i | −0.289383 | + | 0.957213i | \(0.593450\pi\) |
−0.957213 | + | 0.289383i | \(0.906550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.3060i | 0.759459i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.74032 | − | 8.74032i | −0.360752 | − | 0.360752i | 0.503338 | − | 0.864090i | \(-0.332105\pi\) |
−0.864090 | + | 0.503338i | \(0.832105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 67.7771i | − | 2.79271i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1359 | + | 22.1359i | −0.909014 | + | 0.909014i | −0.996193 | − | 0.0871785i | \(-0.972215\pi\) |
0.0871785 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8885 | − | 17.8885i | −0.733359 | − | 0.733359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.6491 | −0.516829 | −0.258414 | − | 0.966034i | \(-0.583200\pi\) | ||||
−0.258414 | + | 0.966034i | \(0.583200\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8328 | 0.931370 | 0.465685 | − | 0.884951i | \(-0.345808\pi\) | ||||
0.465685 | + | 0.884951i | \(0.345808\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.5610 | + | 12.5610i | 0.510677 | + | 0.510677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.652476 | − | 0.652476i | 0.0264832 | − | 0.0264832i | −0.693741 | − | 0.720224i | \(-0.744039\pi\) |
0.720224 | + | 0.693741i | \(0.244039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.16073i | 0.0874136i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.2918 | − | 13.2918i | −0.536851 | − | 0.536851i | 0.385752 | − | 0.922603i | \(-0.373942\pi\) |
−0.922603 | + | 0.385752i | \(0.873942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.41577 | − | 2.41577i | −0.0972550 | − | 0.0972550i | 0.656805 | − | 0.754060i | \(-0.271907\pi\) |
−0.754060 | + | 0.656805i | \(0.771907\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.8885i | − | 1.20132i | −0.799504 | − | 0.600661i | \(-0.794904\pi\) | ||
0.799504 | − | 0.600661i | \(-0.205096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.5579 | − | 16.5579i | 0.663378 | − | 0.663378i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4667 | −0.816060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3607 | 1.44750 | 0.723748 | − | 0.690064i | \(-0.242418\pi\) | ||||
0.723748 | + | 0.690064i | \(0.242418\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.74032 | 0.346849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.931116 | + | 0.931116i | −0.0368922 | + | 0.0368922i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 19.7202i | − | 0.778900i | −0.921048 | − | 0.389450i | \(-0.872665\pi\) | ||
0.921048 | − | 0.389450i | \(-0.127335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | + | 20.0000i | 0.788723 | + | 0.788723i | 0.981285 | − | 0.192562i | \(-0.0616796\pi\) |
−0.192562 | + | 0.981285i | \(0.561680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0509 | − | 18.0509i | −0.709655 | − | 0.709655i | 0.256807 | − | 0.966463i | \(-0.417329\pi\) |
−0.966463 | + | 0.256807i | \(0.917329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.9443i | − | 0.508107i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3137 | + | 11.3137i | −0.442740 | + | 0.442740i | −0.892932 | − | 0.450192i | \(-0.851356\pi\) |
0.450192 | + | 0.892932i | \(0.351356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.1803 | − | 26.1803i | 1.02295 | − | 1.02295i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.3894 | −0.833214 | −0.416607 | − | 0.909087i | \(-0.636781\pi\) | ||||
−0.416607 | + | 0.909087i | \(0.636781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3050 | −0.828667 | −0.414333 | − | 0.910125i | \(-0.635985\pi\) | ||||
−0.414333 | + | 0.910125i | \(0.635985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 25.2982i | − | 0.981023i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.944272 | − | 0.944272i | 0.0365624 | − | 0.0365624i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.67080i | − | 0.103105i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5279 | + | 10.5279i | 0.405819 | + | 0.405819i | 0.880278 | − | 0.474459i | \(-0.157356\pi\) |
−0.474459 | + | 0.880278i | \(0.657356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.99226 | − | 6.99226i | −0.268734 | − | 0.268734i | 0.559856 | − | 0.828590i | \(-0.310857\pi\) |
−0.828590 | + | 0.559856i | \(0.810857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.47214i | 0.0948719i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.2070 | + | 29.2070i | −1.11758 | + | 1.11758i | −0.125479 | + | 0.992096i | \(0.540047\pi\) |
−0.992096 | + | 0.125479i | \(0.959953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.88854i | 0.301406i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.3607 | −0.926724 | −0.463362 | − | 0.886169i | \(-0.653357\pi\) | ||||
−0.463362 | + | 0.886169i | \(0.653357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421 | − | 14.1421i | 0.536442 | − | 0.536442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.3607 | − | 32.3607i | 1.22575 | − | 1.22575i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.6507i | − | 0.515578i | −0.966201 | − | 0.257789i | \(-0.917006\pi\) | ||
0.966201 | − | 0.257789i | \(-0.0829940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4721 | − | 14.4721i | −0.545827 | − | 0.545827i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.3894 | + | 21.3894i | 0.804432 | + | 0.804432i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8885i | 0.746930i | 0.927644 | + | 0.373465i | \(0.121830\pi\) | ||||
−0.927644 | + | 0.373465i | \(0.878170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.6197 | + | 29.6197i | −1.10927 | + | 1.10927i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.30495 | 0.0488024 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.6197 | 1.10463 | 0.552314 | − | 0.833636i | \(-0.313745\pi\) | ||||
0.552314 | + | 0.833636i | \(0.313745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.1672 | 0.937275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.66925i | 0.0619945i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1246 | − | 31.1246i | 1.15435 | − | 1.15435i | 0.168676 | − | 0.985671i | \(-0.446051\pi\) |
0.985671 | − | 0.168676i | \(-0.0539493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.2393i | 2.19105i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.1803 | − | 11.1803i | −0.412955 | − | 0.412955i | 0.469811 | − | 0.882767i | \(-0.344322\pi\) |
−0.882767 | + | 0.469811i | \(0.844322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.3060 | − | 18.3060i | −0.674309 | − | 0.674309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.3607i | − | 1.19041i | −0.803575 | − | 0.595203i | \(-0.797071\pi\) | ||
0.803575 | − | 0.595203i | \(-0.202929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.0649 | + | 15.0649i | −0.552677 | + | 0.552677i | −0.927212 | − | 0.374536i | \(-0.877802\pi\) |
0.374536 | + | 0.927212i | \(0.377802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8885 | − | 12.8885i | −0.472200 | − | 0.472200i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.66306 | −0.353081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.3607 | 0.451048 | 0.225524 | − | 0.974238i | \(-0.427591\pi\) | ||||
0.225524 | + | 0.974238i | \(0.427591\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.4667 | − | 20.4667i | −0.744859 | − | 0.744859i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.70820 | + | 2.70820i | −0.0984313 | + | 0.0984313i | −0.754608 | − | 0.656176i | \(-0.772173\pi\) |
0.656176 | + | 0.754608i | \(0.272173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 11.9026i | − | 0.431469i | −0.976452 | − | 0.215734i | \(-0.930785\pi\) | ||
0.976452 | − | 0.215734i | \(-0.0692145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.1115 | + | 14.1115i | 0.510869 | + | 0.510869i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.74806 | + | 1.74806i | 0.0631189 | + | 0.0631189i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.0000i | − | 1.15395i | −0.816762 | − | 0.576975i | \(-0.804233\pi\) | ||
0.816762 | − | 0.576975i | \(-0.195767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.4667 | − | 20.4667i | 0.736136 | − | 0.736136i | −0.235692 | − | 0.971828i | \(-0.575736\pi\) |
0.971828 | + | 0.235692i | \(0.0757357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 52.3607i | − | 1.88085i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.7649 | 1.63970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.1115 | 0.791210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.1869 | 1.43433 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5279 | − | 21.5279i | 0.767385 | − | 0.767385i | −0.210260 | − | 0.977645i | \(-0.567431\pi\) |
0.977645 | + | 0.210260i | \(0.0674311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.81758i | 0.277961i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.360680 | + | 0.360680i | 0.0128081 | + | 0.0128081i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.9535 | − | 29.9535i | −1.06101 | − | 1.06101i | −0.998014 | − | 0.0629944i | \(-0.979935\pi\) |
−0.0629944 | − | 0.998014i | \(-0.520065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.8885i | 1.48191i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.5579 | + | 16.5579i | −0.584316 | + | 0.584316i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0557 | + | 11.0557i | −0.389663 | + | 0.389663i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.3693 | −1.13804 | −0.569022 | − | 0.822322i | \(-0.692678\pi\) | ||||
−0.569022 | + | 0.822322i | \(0.692678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.8885 | −0.768611 | −0.384305 | − | 0.923206i | \(-0.625559\pi\) | ||||
−0.384305 | + | 0.923206i | \(0.625559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.4667i | 0.716917i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.8885 | + | 41.8885i | −1.46549 | + | 1.46549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24.2967i | − | 0.847960i | −0.905672 | − | 0.423980i | \(-0.860633\pi\) | ||
0.905672 | − | 0.423980i | \(-0.139367\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.1246 | + | 27.1246i | 0.945505 | + | 0.945505i | 0.998590 | − | 0.0530854i | \(-0.0169056\pi\) |
−0.0530854 | + | 0.998590i | \(0.516906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.4667 | − | 20.4667i | −0.711697 | − | 0.711697i | 0.255193 | − | 0.966890i | \(-0.417861\pi\) |
−0.966890 | + | 0.255193i | \(0.917861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.36068i | − | 0.290378i | −0.989404 | − | 0.145189i | \(-0.953621\pi\) | ||
0.989404 | − | 0.145189i | \(-0.0463791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0509 | + | 18.0509i | −0.625428 | + | 0.625428i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.0000i | − | 0.692129i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1452 | 0.557396 | 0.278698 | − | 0.960379i | \(-0.410097\pi\) | ||||
0.278698 | + | 0.960379i | \(0.410097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8885 | −0.996157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.3786 | − | 20.3786i | 0.701044 | − | 0.701044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.81966 | + | 9.81966i | −0.337408 | + | 0.337408i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6491i | 0.433606i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1246 | + | 12.1246i | 0.415139 | + | 0.415139i | 0.883524 | − | 0.468385i | \(-0.155164\pi\) |
−0.468385 | + | 0.883524i | \(0.655164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0509 | − | 18.0509i | −0.616608 | − | 0.616608i | 0.328052 | − | 0.944660i | \(-0.393608\pi\) |
−0.944660 | + | 0.328052i | \(0.893608\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000i | 0.136478i | 0.997669 | + | 0.0682391i | \(0.0217381\pi\) | ||||
−0.997669 | + | 0.0682391i | \(0.978262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.6088 | − | 34.6088i | 1.17810 | − | 1.17810i | 0.197870 | − | 0.980228i | \(-0.436598\pi\) |
0.980228 | − | 0.197870i | \(-0.0634023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.05573 | −0.0358958 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.66306 | 0.327797 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.94427 | 0.167530 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 19.5440i | − | 0.660706i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7082 | + | 20.7082i | −0.699266 | + | 0.699266i | −0.964252 | − | 0.264986i | \(-0.914633\pi\) |
0.264986 | + | 0.964252i | \(0.414633\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.8886i | 0.501611i | 0.968037 | + | 0.250806i | \(0.0806955\pi\) | ||||
−0.968037 | + | 0.250806i | \(0.919304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4721 | + | 22.4721i | 0.756248 | + | 0.756248i | 0.975637 | − | 0.219390i | \(-0.0704066\pi\) |
−0.219390 | + | 0.975637i | \(0.570407\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.2657 | − | 40.2657i | −1.35199 | − | 1.35199i | −0.883434 | − | 0.468555i | \(-0.844775\pi\) |
−0.468555 | − | 0.883434i | \(-0.655225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.83282i | 0.229165i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.6197 | + | 29.6197i | −0.991185 | + | 0.991185i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.29180 | − | 8.29180i | −0.277164 | − | 0.277164i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.49613 | −0.116602 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.41577 | − | 2.41577i | −0.0803028 | − | 0.0803028i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.4721 | + | 34.4721i | −1.14463 | + | 1.14463i | −0.157036 | + | 0.987593i | \(0.550194\pi\) |
−0.987593 | + | 0.157036i | \(0.949806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.0941i | 1.42777i | 0.700262 | + | 0.713886i | \(0.253066\pi\) | ||||
−0.700262 | + | 0.713886i | \(0.746934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9443 | − | 12.9443i | −0.428393 | − | 0.428393i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.4667 | + | 20.4667i | 0.675870 | + | 0.675870i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5279i | 0.446243i | 0.974791 | + | 0.223122i | \(0.0716247\pi\) | ||||
−0.974791 | + | 0.223122i | \(0.928375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.98605 | + | 2.98605i | −0.0982870 | + | 0.0982870i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1803 | − | 11.1803i | −0.367607 | − | 0.367607i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5672 | 0.346698 | 0.173349 | − | 0.984860i | \(-0.444541\pi\) | ||||
0.173349 | + | 0.984860i | \(0.444541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.5279 | −0.836642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.2982 | 0.827340 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | + | 19.0000i | −0.620703 | + | 0.620703i | −0.945711 | − | 0.325008i | \(-0.894633\pi\) |
0.325008 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.81913i | 0.287495i | 0.989614 | + | 0.143748i | \(0.0459154\pi\) | ||||
−0.989614 | + | 0.143748i | \(0.954085\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0000 | − | 20.0000i | −0.651290 | − | 0.651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8098 | + | 14.8098i | 0.481255 | + | 0.481255i | 0.905532 | − | 0.424277i | \(-0.139472\pi\) |
−0.424277 | + | 0.905532i | \(0.639472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.47214i | − | 0.145172i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.7851 | − | 34.7851i | 1.12680 | − | 1.12680i | 0.136104 | − | 0.990695i | \(-0.456542\pi\) |
0.990695 | − | 0.136104i | \(-0.0434581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0557 | − | 11.0557i | 0.357755 | − | 0.357755i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.16693 | −0.199141 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.6290i | 0.760643i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0689 | + | 24.0689i | −0.774003 | + | 0.774003i | −0.978804 | − | 0.204801i | \(-0.934345\pi\) |
0.204801 | + | 0.978804i | \(0.434345\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.08347i | − | 0.0989531i | −0.998775 | − | 0.0494766i | \(-0.984245\pi\) | ||
0.998775 | − | 0.0494766i | \(-0.0157553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0557 | + | 11.0557i | 0.354430 | + | 0.354430i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.8747 | + | 29.8747i | 0.955777 | + | 0.955777i | 0.999063 | − | 0.0432860i | \(-0.0137827\pi\) |
−0.0432860 | + | 0.999063i | \(0.513783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.4164i | 0.748392i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.7000 | − | 30.7000i | 0.979179 | − | 0.979179i | −0.0206085 | − | 0.999788i | \(-0.506560\pi\) |
0.999788 | + | 0.0206085i | \(0.00656036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.8885i | 1.52586i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.6119 | 1.16419 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.8328 | −0.979437 | −0.489718 | − | 0.871881i | \(-0.662900\pi\) | ||||
−0.489718 | + | 0.871881i | \(0.662900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.6491 | + | 12.6491i | −0.401004 | + | 0.401004i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.65248 | + | 5.65248i | −0.179016 | + | 0.179016i | −0.790927 | − | 0.611911i | \(-0.790401\pi\) |
0.611911 | + | 0.790927i | \(0.290401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 720.2.w.e.593.3 | 8 | ||
3.2 | odd | 2 | inner | 720.2.w.e.593.1 | 8 | ||
4.3 | odd | 2 | 360.2.s.b.233.4 | yes | 8 | ||
5.2 | odd | 4 | inner | 720.2.w.e.17.1 | 8 | ||
5.3 | odd | 4 | 3600.2.w.j.1457.3 | 8 | |||
5.4 | even | 2 | 3600.2.w.j.593.3 | 8 | |||
8.3 | odd | 2 | 2880.2.w.m.2753.2 | 8 | |||
8.5 | even | 2 | 2880.2.w.o.2753.1 | 8 | |||
12.11 | even | 2 | 360.2.s.b.233.2 | yes | 8 | ||
15.2 | even | 4 | inner | 720.2.w.e.17.3 | 8 | ||
15.8 | even | 4 | 3600.2.w.j.1457.4 | 8 | |||
15.14 | odd | 2 | 3600.2.w.j.593.4 | 8 | |||
20.3 | even | 4 | 1800.2.s.e.1457.2 | 8 | |||
20.7 | even | 4 | 360.2.s.b.17.2 | ✓ | 8 | ||
20.19 | odd | 2 | 1800.2.s.e.593.2 | 8 | |||
24.5 | odd | 2 | 2880.2.w.o.2753.3 | 8 | |||
24.11 | even | 2 | 2880.2.w.m.2753.4 | 8 | |||
40.27 | even | 4 | 2880.2.w.m.2177.4 | 8 | |||
40.37 | odd | 4 | 2880.2.w.o.2177.3 | 8 | |||
60.23 | odd | 4 | 1800.2.s.e.1457.1 | 8 | |||
60.47 | odd | 4 | 360.2.s.b.17.4 | yes | 8 | ||
60.59 | even | 2 | 1800.2.s.e.593.1 | 8 | |||
120.77 | even | 4 | 2880.2.w.o.2177.1 | 8 | |||
120.107 | odd | 4 | 2880.2.w.m.2177.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.s.b.17.2 | ✓ | 8 | 20.7 | even | 4 | ||
360.2.s.b.17.4 | yes | 8 | 60.47 | odd | 4 | ||
360.2.s.b.233.2 | yes | 8 | 12.11 | even | 2 | ||
360.2.s.b.233.4 | yes | 8 | 4.3 | odd | 2 | ||
720.2.w.e.17.1 | 8 | 5.2 | odd | 4 | inner | ||
720.2.w.e.17.3 | 8 | 15.2 | even | 4 | inner | ||
720.2.w.e.593.1 | 8 | 3.2 | odd | 2 | inner | ||
720.2.w.e.593.3 | 8 | 1.1 | even | 1 | trivial | ||
1800.2.s.e.593.1 | 8 | 60.59 | even | 2 | |||
1800.2.s.e.593.2 | 8 | 20.19 | odd | 2 | |||
1800.2.s.e.1457.1 | 8 | 60.23 | odd | 4 | |||
1800.2.s.e.1457.2 | 8 | 20.3 | even | 4 | |||
2880.2.w.m.2177.2 | 8 | 120.107 | odd | 4 | |||
2880.2.w.m.2177.4 | 8 | 40.27 | even | 4 | |||
2880.2.w.m.2753.2 | 8 | 8.3 | odd | 2 | |||
2880.2.w.m.2753.4 | 8 | 24.11 | even | 2 | |||
2880.2.w.o.2177.1 | 8 | 120.77 | even | 4 | |||
2880.2.w.o.2177.3 | 8 | 40.37 | odd | 4 | |||
2880.2.w.o.2753.1 | 8 | 8.5 | even | 2 | |||
2880.2.w.o.2753.3 | 8 | 24.5 | odd | 2 | |||
3600.2.w.j.593.3 | 8 | 5.4 | even | 2 | |||
3600.2.w.j.593.4 | 8 | 15.14 | odd | 2 | |||
3600.2.w.j.1457.3 | 8 | 5.3 | odd | 4 | |||
3600.2.w.j.1457.4 | 8 | 15.8 | even | 4 |