Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1848,2,Mod(881,1848)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1848, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1848.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1848.v (of order \(2\), degree \(1\), 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: | \(14.7563542935\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 77x^{12} - 342x^{10} + 1160x^{8} - 3078x^{6} + 6237x^{4} - 8748x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.6 | ||
Root | \(1.63065 - 0.583933i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1848.881 |
Dual form | 1848.2.v.d.881.5 |
$q$-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 \(\left(\mathbb{Z}/1848\mathbb{Z}\right)^\times\).
\(n\) | \(463\) | \(617\) | \(673\) | \(925\) | \(1585\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.583933 | + | 1.63065i | −0.337134 | + | 0.941457i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.70180 | −1.65550 | −0.827748 | − | 0.561100i | \(-0.810378\pi\) | ||||
−0.827748 | + | 0.561100i | \(0.810378\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.42989 | + | 1.04672i | 0.918413 | + | 0.395622i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.31805 | − | 1.90438i | −0.772682 | − | 0.634794i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.623204i | 0.172846i | 0.996259 | + | 0.0864229i | \(0.0275436\pi\) | ||||
−0.996259 | + | 0.0864229i | \(0.972456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.16160 | − | 6.03635i | 0.558124 | − | 1.55858i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.09755 | 0.751267 | 0.375633 | − | 0.926768i | \(-0.377425\pi\) | ||||
0.375633 | + | 0.926768i | \(0.377425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.80596i | − | 0.873148i | −0.899668 | − | 0.436574i | \(-0.856192\pi\) | ||
0.899668 | − | 0.436574i | \(-0.143808\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12573 | + | 3.35109i | −0.682089 | + | 0.731269i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.18299i | − | 1.49776i | −0.662707 | − | 0.748879i | \(-0.730593\pi\) | ||
0.662707 | − | 0.748879i | \(-0.269407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70334 | 1.74067 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.45896 | − | 2.66789i | 0.858128 | − | 0.513436i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.105417i | − | 0.0195754i | −0.999952 | − | 0.00978772i | \(-0.996884\pi\) | ||
0.999952 | − | 0.00978772i | \(-0.00311558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.41844i | 1.15279i | 0.817172 | + | 0.576393i | \(0.195540\pi\) | ||||
−0.817172 | + | 0.576393i | \(0.804460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.63065 | + | 0.583933i | 0.283860 | + | 0.101650i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.99499 | − | 3.87475i | −1.52043 | − | 0.654951i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.28841 | −0.869409 | −0.434705 | − | 0.900573i | \(-0.643147\pi\) | ||||
−0.434705 | + | 0.900573i | \(0.643147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.01623 | − | 0.363909i | −0.162727 | − | 0.0582721i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.33984 | 0.521596 | 0.260798 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260798 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.71703 | 1.17684 | 0.588418 | − | 0.808557i | \(-0.299751\pi\) | ||||
0.588418 | + | 0.808557i | \(0.299751\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.58095 | + | 7.04964i | 1.27917 | + | 1.05090i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.53394 | 0.369613 | 0.184806 | − | 0.982775i | \(-0.440834\pi\) | ||||
0.184806 | + | 0.982775i | \(0.440834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.80876 | + | 5.08683i | 0.686966 | + | 0.726690i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.80876 | + | 5.05103i | −0.253277 | + | 0.707285i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.2639i | 1.40986i | 0.709277 | + | 0.704930i | \(0.249022\pi\) | ||||
−0.709277 | + | 0.704930i | \(0.750978\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.70180i | 0.499151i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.20620 | + | 2.22243i | 0.822031 | + | 0.294368i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.55295 | −0.722932 | −0.361466 | − | 0.932385i | \(-0.617724\pi\) | ||||
−0.361466 | + | 0.932385i | \(0.617724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.33990i | − | 0.811741i | −0.913931 | − | 0.405871i | \(-0.866968\pi\) | ||
0.913931 | − | 0.405871i | \(-0.133032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.63925 | − | 7.05378i | −0.458503 | − | 0.888693i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.30698i | − | 0.286145i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.329112 | −0.0402075 | −0.0201037 | − | 0.999798i | \(-0.506400\pi\) | ||||
−0.0201037 | + | 0.999798i | \(0.506400\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.7130 | + | 4.19438i | 1.41007 | + | 0.504944i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7681i | 1.51529i | 0.652667 | + | 0.757645i | \(0.273650\pi\) | ||||
−0.652667 | + | 0.757645i | \(0.726350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.20128i | − | 0.725805i | −0.931827 | − | 0.362903i | \(-0.881786\pi\) | ||
0.931827 | − | 0.362903i | \(-0.118214\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.08217 | + | 14.1921i | −0.586838 | + | 1.63876i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04672 | − | 2.42989i | 0.119285 | − | 0.276912i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.6093 | 1.86869 | 0.934345 | − | 0.356370i | \(-0.115986\pi\) | ||||
0.934345 | + | 0.356370i | \(0.115986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.74667 | + | 8.82888i | 0.194074 | + | 0.980987i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7814 | −1.51271 | −0.756353 | − | 0.654163i | \(-0.773021\pi\) | ||||
−0.756353 | + | 0.654163i | \(0.773021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.4665 | −1.24372 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.171898 | + | 0.0615564i | 0.0184294 | + | 0.00659954i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.90715 | 0.838156 | 0.419078 | − | 0.907950i | \(-0.362353\pi\) | ||||
0.419078 | + | 0.907950i | \(0.362353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.652319 | + | 1.51432i | −0.0683816 | + | 0.158744i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4662 | − | 3.74794i | −1.08530 | − | 0.388643i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.0889i | 1.44549i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.93386i | − | 0.602492i | −0.953546 | − | 0.301246i | \(-0.902597\pi\) | ||
0.953546 | − | 0.301246i | \(-0.0974025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.90438 | + | 2.31805i | −0.191397 | + | 0.232972i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6746 | 1.36067 | 0.680336 | − | 0.732900i | \(-0.261834\pi\) | ||||
0.680336 | + | 0.732900i | \(0.261834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0833i | 1.38767i | 0.720135 | + | 0.693834i | \(0.244080\pi\) | ||||
−0.720135 | + | 0.693834i | \(0.755920\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.5708 | − | 12.4051i | 1.12920 | − | 1.21061i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.93275i | 0.476867i | 0.971159 | + | 0.238433i | \(0.0766338\pi\) | ||||
−0.971159 | + | 0.238433i | \(0.923366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1237 | 1.64016 | 0.820078 | − | 0.572252i | \(-0.193930\pi\) | ||||
0.820078 | + | 0.572252i | \(0.193930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.08808 | − | 8.62355i | 0.293107 | − | 0.818511i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.50412i | − | 0.235568i | −0.993039 | − | 0.117784i | \(-0.962421\pi\) | ||
0.993039 | − | 0.117784i | \(-0.0375791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.5900i | 2.47953i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.18682 | − | 1.44462i | 0.109721 | − | 0.133555i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.52672 | + | 3.24226i | 0.689973 | + | 0.297218i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.95024 | + | 5.44612i | −0.175848 | + | 0.491060i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.7091 | −1.22617 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.40415 | 0.834483 | 0.417242 | − | 0.908796i | \(-0.362997\pi\) | ||||
0.417242 | + | 0.908796i | \(0.362997\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.50623 | + | 12.5838i | −0.396751 | + | 1.10794i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3226 | 0.989257 | 0.494629 | − | 0.869104i | \(-0.335304\pi\) | ||||
0.494629 | + | 0.869104i | \(0.335304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.98377 | − | 9.24808i | 0.345437 | − | 0.801911i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.5062 | + | 9.87601i | −1.42063 | + | 0.849992i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.53658i | 0.387586i | 0.981042 | + | 0.193793i | \(0.0620790\pi\) | ||||
−0.981042 | + | 0.193793i | \(0.937921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.595413i | − | 0.0505022i | −0.999681 | − | 0.0252511i | \(-0.991961\pi\) | ||
0.999681 | − | 0.0252511i | \(-0.00803854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.47965 | + | 4.13197i | −0.124609 | + | 0.347974i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.623204 | 0.0521149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.390233i | 0.0324071i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1028 | + | 4.87105i | −0.915746 | + | 0.401757i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.22914i | − | 0.264541i | −0.991214 | − | 0.132271i | \(-0.957773\pi\) | ||
0.991214 | − | 0.132271i | \(-0.0422268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1212 | −1.39330 | −0.696651 | − | 0.717410i | \(-0.745327\pi\) | ||||
−0.696651 | + | 0.717410i | \(0.745327\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.18026 | − | 5.89892i | −0.580490 | − | 0.476899i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.7598i | − | 1.90843i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.18021i | 0.333617i | 0.985989 | + | 0.166808i | \(0.0533462\pi\) | ||||
−0.985989 | + | 0.166808i | \(0.946654\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.7369 | − | 5.99345i | −1.32732 | − | 0.475311i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.51857 | − | 17.4539i | 0.592546 | − | 1.37556i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.4606 | −1.68093 | −0.840463 | − | 0.541869i | \(-0.817717\pi\) | ||||
−0.840463 | + | 0.541869i | \(0.817717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.03635 | − | 2.16160i | −0.469929 | − | 0.168281i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.795794 | −0.0615804 | −0.0307902 | − | 0.999526i | \(-0.509802\pi\) | ||||
−0.0307902 | + | 0.999526i | \(0.509802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6116 | 0.970124 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.24800 | + | 8.82240i | −0.554269 | + | 0.674665i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5946 | 1.18564 | 0.592820 | − | 0.805335i | \(-0.298015\pi\) | ||||
0.592820 | + | 0.805335i | \(0.298015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.1482 | + | 9.10995i | 1.59865 | + | 0.688648i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.24255 | − | 9.05492i | 0.243725 | − | 0.680609i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.536579i | − | 0.0401058i | −0.999799 | − | 0.0200529i | \(-0.993617\pi\) | ||
0.999799 | − | 0.0200529i | \(-0.00638347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3077i | 0.914826i | 0.889254 | + | 0.457413i | \(0.151224\pi\) | ||||
−0.889254 | + | 0.457413i | \(0.848776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3382 | + | 3.70207i | 0.764219 | + | 0.273665i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.5767 | 1.43930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.09755i | − | 0.226515i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.6273 | − | 1.81542i | 0.991243 | − | 0.132052i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.35312i | − | 0.314981i | −0.987520 | − | 0.157491i | \(-0.949660\pi\) | ||
0.987520 | − | 0.157491i | \(-0.0503404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.40415 | 0.101073 | 0.0505365 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505365 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.76188 | + | 1.34712i | 0.269394 | + | 0.0964693i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.65105i | 0.258816i | 0.991591 | + | 0.129408i | \(0.0413077\pi\) | ||||
−0.991591 | + | 0.129408i | \(0.958692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.192179 | − | 0.536667i | 0.0135553 | − | 0.0378536i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.110342 | − | 0.256152i | 0.00774448 | − | 0.0179783i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.3634 | −0.863501 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.6792 | + | 16.6505i | −0.950767 | + | 1.15729i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.80596 | −0.263264 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8840 | 1.23119 | 0.615593 | − | 0.788065i | \(-0.288917\pi\) | ||||
0.615593 | + | 0.788065i | \(0.288917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.8202 | − | 7.45569i | −1.42658 | − | 0.510855i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.5669 | −1.94825 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.71830 | + | 15.5961i | −0.456068 | + | 1.05873i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.1121 | + | 3.62113i | 0.683314 | + | 0.244693i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.93041i | 0.129853i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.6125i | − | 1.17942i | −0.807615 | − | 0.589710i | \(-0.799242\pi\) | ||
0.807615 | − | 0.589710i | \(-0.200758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.1747 | − | 16.5745i | −1.34498 | − | 1.10497i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9767 | 1.39227 | 0.696136 | − | 0.717910i | \(-0.254901\pi\) | ||||
0.696136 | + | 0.717910i | \(0.254901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.35904i | 0.486299i | 0.969989 | + | 0.243149i | \(0.0781805\pi\) | ||||
−0.969989 | + | 0.243149i | \(0.921819\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.35109 | + | 3.12573i | 0.220486 | + | 0.205658i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.19688i | 0.274947i | 0.990505 | + | 0.137473i | \(0.0438982\pi\) | ||||
−0.990505 | + | 0.137473i | \(0.956102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.38014 | −0.611893 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.69870 | + | 27.0839i | −0.629998 | + | 1.75929i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.0276i | − | 1.36016i | −0.733137 | − | 0.680080i | \(-0.761945\pi\) | ||
0.733137 | − | 0.680080i | \(-0.238055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.4255i | − | 1.70221i | −0.524992 | − | 0.851107i | \(-0.675932\pi\) | ||
0.524992 | − | 0.851107i | \(-0.324068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4168 | − | 2.30726i | −0.988986 | − | 0.148011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.8011 | − | 18.8304i | −1.13727 | − | 1.20303i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.37189 | 0.150920 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.04742 | − | 22.4727i | 0.509984 | − | 1.42415i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0994 | −1.52114 | −0.760570 | − | 0.649256i | \(-0.775080\pi\) | ||||
−0.760570 | + | 0.649256i | \(0.775080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.18299 | −0.451591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.69568 | − | 18.6979i | 0.419300 | − | 1.17091i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.6041 | 1.78428 | 0.892138 | − | 0.451763i | \(-0.149205\pi\) | ||||
0.892138 | + | 0.451763i | \(0.149205\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8503 | − | 5.53548i | −0.798477 | − | 0.343958i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.200754 | + | 0.244361i | −0.0124264 | + | 0.0151256i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.30698i | 0.512230i | 0.966646 | + | 0.256115i | \(0.0824426\pi\) | ||||
−0.966646 | + | 0.256115i | \(0.917557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 37.9951i | − | 2.33402i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.61724 | + | 12.8938i | −0.282570 | + | 0.789087i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8358 | −0.904554 | −0.452277 | − | 0.891877i | \(-0.649388\pi\) | ||||
−0.452277 | + | 0.891877i | \(0.649388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.3145i | − | 1.71999i | −0.510306 | − | 0.859993i | \(-0.670468\pi\) | ||
0.510306 | − | 0.859993i | \(-0.329532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.08842 | − | 1.94797i | −0.126397 | − | 0.117896i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 8.70334i | − | 0.524831i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.33456 | 0.320522 | 0.160261 | − | 0.987075i | \(-0.448766\pi\) | ||||
0.160261 | + | 0.987075i | \(0.448766\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.2232 | − | 14.8782i | 0.731781 | − | 0.890737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.34514i | 0.199554i | 0.995010 | + | 0.0997772i | \(0.0318130\pi\) | ||||
−0.995010 | + | 0.0997772i | \(0.968187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.6994i | − | 0.814346i | −0.913351 | − | 0.407173i | \(-0.866515\pi\) | ||
0.913351 | − | 0.407173i | \(-0.133485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.9741 | − | 8.22698i | −1.36087 | − | 0.487324i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.11547 | + | 3.49588i | 0.479041 | + | 0.206355i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.40518 | −0.435599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.67605 | + | 3.46497i | 0.567220 | + | 0.203120i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.667290 | −0.0389835 | −0.0194918 | − | 0.999810i | \(-0.506205\pi\) | ||||
−0.0194918 | + | 0.999810i | \(0.506205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.5559 | 1.19681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.66789 | − | 4.45896i | −0.154807 | − | 0.258735i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.47647 | 0.258881 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7516 | + | 8.07756i | 1.08082 | + | 0.465583i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.98504 | + | 22.2985i | −0.458729 | + | 1.28101i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.4691i | 1.34383i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.8143i | − | 1.35915i | −0.733605 | − | 0.679576i | \(-0.762164\pi\) | ||
0.733605 | − | 0.679576i | \(-0.237836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.9649 | − | 8.22370i | −1.30643 | − | 0.467830i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.44151 | −0.421969 | −0.210985 | − | 0.977489i | \(-0.567667\pi\) | ||||
−0.210985 | + | 0.977489i | \(0.567667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.7193i | − | 1.00156i | −0.865576 | − | 0.500778i | \(-0.833047\pi\) | ||
0.865576 | − | 0.500778i | \(-0.166953\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.4718 | + | 26.1117i | 0.759050 | + | 1.47123i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.4062i | 1.93245i | 0.257707 | + | 0.966223i | \(0.417033\pi\) | ||||
−0.257707 | + | 0.966223i | \(0.582967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.105417 | −0.00590222 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.04359 | − | 2.88039i | −0.448949 | − | 0.160768i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.7892i | − | 0.655967i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.42396i | 0.300867i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.99910 | + | 27.9228i | −0.552951 | + | 1.54414i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.15720 | + | 2.65232i | 0.339457 | + | 0.146227i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9242 | 1.53485 | 0.767427 | − | 0.641136i | \(-0.221536\pi\) | ||||
0.767427 | + | 0.641136i | \(0.221536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.2588 | + | 10.0711i | 0.671777 | + | 0.551895i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.21831 | 0.0665633 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.5412 | 1.39132 | 0.695659 | − | 0.718372i | \(-0.255113\pi\) | ||||
0.695659 | + | 0.718372i | \(0.255113\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.08335 | + | 1.46224i | 0.221777 | + | 0.0794179i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.41844 | 0.347578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.36030 | + | 17.3939i | 0.343424 | + | 0.939181i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −43.3590 | − | 15.5268i | −2.33437 | − | 0.835934i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 23.4201i | − | 1.25726i | −0.777705 | − | 0.628629i | \(-0.783616\pi\) | ||
0.777705 | − | 0.628629i | \(-0.216384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.4007i | − | 1.19908i | −0.800345 | − | 0.599540i | \(-0.795350\pi\) | ||
0.800345 | − | 0.599540i | \(-0.204650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.66264 | + | 2.77884i | 0.0887453 | + | 0.148324i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.3038 | 1.61291 | 0.806454 | − | 0.591296i | \(-0.201384\pi\) | ||||
0.806454 | + | 0.591296i | \(0.201384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 47.2648i | − | 2.50856i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.68210 | + | 10.3802i | −0.512431 | + | 0.549378i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7305i | 1.35800i | 0.734137 | + | 0.679001i | \(0.237587\pi\) | ||||
−0.734137 | + | 0.679001i | \(0.762413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.51464 | 0.237613 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.583933 | − | 1.63065i | 0.0306485 | − | 0.0855870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9559i | 1.20157i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6948i | 0.923659i | 0.886969 | + | 0.461829i | \(0.152807\pi\) | ||||
−0.886969 | + | 0.461829i | \(0.847193\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.74191 | − | 6.36034i | −0.403028 | − | 0.331106i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7435 | + | 24.9403i | −0.557772 | + | 1.29483i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8840 | 0.615330 | 0.307665 | − | 0.951495i | \(-0.400452\pi\) | ||||
0.307665 | + | 0.951495i | \(0.400452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00516 | − | 22.3547i | 0.413385 | − | 1.15439i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0656963 | 0.00338353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3091 | 0.991840 | 0.495920 | − | 0.868368i | \(-0.334831\pi\) | ||||
0.495920 | + | 0.868368i | \(0.334831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.49139 | + | 15.3349i | −0.281332 | + | 0.785630i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0701875 | −0.00358641 | −0.00179321 | − | 0.999998i | \(-0.500571\pi\) | ||||
−0.00179321 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.87475 | + | 8.99499i | −0.197475 | + | 0.458427i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.8884 | − | 14.6962i | −0.909320 | − | 0.747048i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 26.2397i | − | 1.33040i | −0.746664 | − | 0.665202i | \(-0.768346\pi\) | ||
0.746664 | − | 0.665202i | \(-0.231654\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 22.2497i | − | 1.12522i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.61162 | + | 18.4632i | −0.333512 | + | 0.931343i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −61.4843 | −3.09361 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4489i | 1.17687i | 0.808546 | + | 0.588433i | \(0.200255\pi\) | ||||
−0.808546 | + | 0.588433i | \(0.799745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.7541 | + | 11.8964i | 0.638506 | + | 0.595565i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 21.5851i | − | 1.07791i | −0.842336 | − | 0.538953i | \(-0.818820\pi\) | ||
0.842336 | − | 0.538953i | \(-0.181180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.46582 | − | 32.6828i | −0.321289 | − | 1.62402i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.28841i | 0.262137i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1513i | 1.24365i | 0.783156 | + | 0.621825i | \(0.213609\pi\) | ||||
−0.783156 | + | 0.621825i | \(0.786391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.39758 | − | 2.64906i | −0.364896 | − | 0.130668i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4931 | − | 5.81237i | −0.663950 | − | 0.286008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 51.0161 | 2.50428 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.970910 | + | 0.347681i | 0.0475457 | + | 0.0170260i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.9050 | 1.80292 | 0.901462 | − | 0.432857i | \(-0.142495\pi\) | ||||
0.901462 | + | 0.432857i | \(0.142495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.76262 | −0.378327 | −0.189163 | − | 0.981946i | \(-0.560578\pi\) | ||||
−0.189163 | + | 0.981946i | \(0.560578\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.87378 | − | 4.82558i | −0.285593 | − | 0.234628i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.9591 | 1.30771 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.63609 | − | 15.4053i | 0.321143 | − | 0.745514i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.363909 | + | 1.01623i | −0.0175697 | + | 0.0490640i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.0972i | − | 1.11255i | −0.830998 | − | 0.556276i | \(-0.812230\pi\) | ||
0.830998 | − | 0.556276i | \(-0.187770\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.7645i | − | 1.47845i | −0.673459 | − | 0.739225i | \(-0.735192\pi\) | ||
0.673459 | − | 0.739225i | \(-0.264808\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.636334 | − | 0.227870i | −0.0305099 | − | 0.0109255i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.3382 | −1.30776 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8236i | 1.47113i | 0.677453 | + | 0.735566i | \(0.263084\pi\) | ||||
−0.677453 | + | 0.735566i | \(0.736916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.45967 | − | 20.9492i | −0.0695081 | − | 0.997581i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.27997i | 0.345882i | 0.984932 | + | 0.172941i | \(0.0553269\pi\) | ||||
−0.984932 | + | 0.172941i | \(0.944673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.2707 | −1.38756 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.26560 | + | 1.88560i | 0.249054 | + | 0.0891858i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9789i | 0.612512i | 0.951949 | + | 0.306256i | \(0.0990763\pi\) | ||||
−0.951949 | + | 0.306256i | \(0.900924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.33984i | − | 0.157267i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.99762 | − | 27.9187i | 0.469729 | − | 1.31173i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.41476 | − | 5.60571i | 0.113206 | − | 0.262800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.98351 | −0.279897 | −0.139948 | − | 0.990159i | \(-0.544694\pi\) | ||||
−0.139948 | + | 0.990159i | \(0.544694\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8119 | − | 8.26394i | 0.644683 | − | 0.385727i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4313 | −0.765283 | −0.382641 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382641 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0678 | −0.700261 | −0.350130 | − | 0.936701i | \(-0.613863\pi\) | ||||
−0.350130 | + | 0.936701i | \(0.613863\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.7440 | + | 13.8741i | 1.79671 | + | 0.643397i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.156602 | 0.00724669 | 0.00362334 | − | 0.999993i | \(-0.498847\pi\) | ||||
0.00362334 | + | 0.999993i | \(0.498847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.799708 | − | 0.344488i | −0.0369271 | − | 0.0159070i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.81646 | − | 2.44096i | −0.314086 | − | 0.112474i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.71703i | − | 0.354830i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 33.1246i | − | 1.51986i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.5464 | − | 23.7923i | 0.894970 | − | 1.08937i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.4027 | 0.840840 | 0.420420 | − | 0.907330i | \(-0.361883\pi\) | ||||
0.420420 | + | 0.907330i | \(0.361883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.29576i | − | 0.150274i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.0709 | + | 22.4521i | 1.09526 | + | 1.02160i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9660i | 0.997423i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.8428 | −1.71482 | −0.857411 | − | 0.514632i | \(-0.827929\pi\) | ||||
−0.857411 | + | 0.514632i | \(0.827929\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5316 | − | 34.9948i | 0.566696 | − | 1.58252i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.99156i | − | 0.180136i | −0.995936 | − | 0.0900682i | \(-0.971291\pi\) | ||
0.995936 | − | 0.0900682i | \(-0.0287085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.326534i | − | 0.0147064i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.04964 | − | 8.58095i | 0.316858 | − | 0.385685i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.3646 | + | 31.0250i | −0.599483 | + | 1.39166i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.7812 | −1.64655 | −0.823277 | − | 0.567640i | \(-0.807857\pi\) | ||||
−0.823277 | + | 0.567640i | \(0.807857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.464690 | − | 1.29766i | 0.0207608 | − | 0.0579753i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7233 | −1.81576 | −0.907881 | − | 0.419229i | \(-0.862301\pi\) | ||||
−0.907881 | + | 0.419229i | \(0.862301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −50.6206 | −2.25259 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.36433 | + | 20.5651i | −0.327062 | + | 0.913330i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.2717 | 0.987175 | 0.493587 | − | 0.869696i | \(-0.335685\pi\) | ||||
0.493587 | + | 0.869696i | \(0.335685\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.49100 | − | 15.0685i | 0.287145 | − | 0.666589i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.1539 | − | 16.9706i | −0.448306 | − | 0.749272i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 52.1336i | − | 2.29728i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.53394i | − | 0.111442i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.10622 | + | 25.4294i | −0.399719 | + | 1.11623i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.66158 | 0.423282 | 0.211641 | − | 0.977348i | \(-0.432119\pi\) | ||||
0.211641 | + | 0.977348i | \(0.432119\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.73427i | − | 0.207015i | −0.994629 | − | 0.103508i | \(-0.966993\pi\) | ||
0.994629 | − | 0.103508i | \(-0.0330066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −27.2043 | + | 29.1657i | −1.18729 | + | 1.27290i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.8815i | 0.866050i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.5954 | −1.24328 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.8720 | + | 10.5749i | 0.558596 | + | 0.458913i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.08140i | 0.0901556i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 18.2601i | − | 0.789451i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.874974 | + | 0.313326i | 0.0377579 | + | 0.0135210i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.08683 | − | 4.80876i | 0.219105 | − | 0.207128i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.8408 | 1.58391 | 0.791954 | − | 0.610581i | \(-0.209064\pi\) | ||||
0.791954 | + | 0.610581i | \(0.209064\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.0696 | − | 7.18688i | −0.861270 | − | 0.308419i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −63.3886 | −2.71527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.0676 | −1.92695 | −0.963475 | − | 0.267799i | \(-0.913704\pi\) | ||||
−0.963475 | + | 0.267799i | \(0.913704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.0736 | + | 14.6962i | −0.515288 | + | 0.627218i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.401213 | −0.0170923 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.3588 | + | 17.3852i | 1.71623 | + | 0.739295i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.4314 | + | 31.9227i | −0.485238 | + | 1.35504i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6492i | 1.00205i | 0.865434 | + | 0.501023i | \(0.167043\pi\) | ||||
−0.865434 | + | 0.501023i | \(0.832957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.80929i | 0.203411i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.05103 | + | 1.80876i | 0.213254 | + | 0.0763660i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.5801 | −0.698769 | −0.349384 | − | 0.936979i | \(-0.613609\pi\) | ||||
−0.349384 | + | 0.936979i | \(0.613609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.26977i | 0.389982i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.99713 | + | 23.2815i | −0.209860 | + | 0.977731i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.2532i | − | 0.471757i | −0.971783 | − | 0.235878i | \(-0.924203\pi\) | ||
0.971783 | − | 0.235878i | \(-0.0757967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.60156 | −0.0670231 | −0.0335115 | − | 0.999438i | \(-0.510669\pi\) | ||||
−0.0335115 | + | 0.999438i | \(0.510669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.09843 | + | 2.54193i | 0.296541 | + | 0.106191i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 62.5161i | − | 2.60710i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.9863i | 1.08182i | 0.841080 | + | 0.540911i | \(0.181920\pi\) | ||||
−0.841080 | + | 0.540911i | \(0.818080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.819929 | + | 2.28968i | −0.0340751 | + | 0.0951558i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.4874 | − | 14.4253i | −1.38929 | − | 0.598460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2639 | 0.425089 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.39337 | + | 5.34768i | −0.181643 | + | 0.221099i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.10779 | 0.0457234 | 0.0228617 | − | 0.999739i | \(-0.492722\pi\) | ||||
0.0228617 | + | 0.999739i | \(0.492722\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.4284 | 1.00655 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.26130 | − | 1.16787i | −0.134152 | − | 0.0480396i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.77927 | 0.0730657 | 0.0365328 | − | 0.999332i | \(-0.488369\pi\) | ||||
0.0365328 | + | 0.999332i | \(0.488369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.8624 | − | 12.0022i | −1.14225 | − | 0.492043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.95359 | − | 2.13197i | −0.243664 | − | 0.0872556i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.0449i | 1.43189i | 0.698155 | + | 0.715947i | \(0.254005\pi\) | ||||
−0.698155 | + | 0.715947i | \(0.745995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.9559i | − | 0.977180i | −0.872514 | − | 0.488590i | \(-0.837511\pi\) | ||
0.872514 | − | 0.488590i | \(-0.162489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.762897 | + | 0.626755i | 0.0310676 | + | 0.0255234i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.70180 | 0.150500 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.4838i | − | 1.11553i | −0.829998 | − | 0.557766i | \(-0.811658\pi\) | ||
0.829998 | − | 0.557766i | \(-0.188342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.353262 | + | 0.329505i | 0.0143149 | + | 0.0133522i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.57916i | 0.0638860i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.6367 | 0.833507 | 0.416753 | − | 0.909020i | \(-0.363168\pi\) | ||||
0.416753 | + | 0.909020i | \(0.363168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.21942 | − | 20.1605i | 0.291115 | − | 0.812949i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.7031i | 1.03477i | 0.855754 | + | 0.517384i | \(0.173094\pi\) | ||||
−0.855754 | + | 0.517384i | \(0.826906\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5912i | 1.22957i | 0.788697 | + | 0.614783i | \(0.210756\pi\) | ||||
−0.788697 | + | 0.614783i | \(0.789244\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.1635 | − | 32.0287i | −0.769003 | − | 1.28527i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.2135 | + | 8.27655i | 0.769773 | + | 0.331593i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.23148 | 0.289259 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.22243 | − | 6.20620i | 0.0887551 | − | 0.247852i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.3811 | −0.653158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.3557 | −1.44730 | −0.723648 | − | 0.690169i | \(-0.757536\pi\) | ||||
−0.723648 | + | 0.690169i | \(0.757536\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4430 | + | 29.1626i | −0.415074 | + | 1.15911i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.8123 | −1.38148 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.17013 | + | 2.99684i | −0.125605 | + | 0.118739i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.3152 | − | 29.5969i | 0.961896 | − | 1.17084i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 10.3582i | − | 0.409124i | −0.978854 | − | 0.204562i | \(-0.934423\pi\) | ||
0.978854 | − | 0.204562i | \(-0.0655771\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0184i | 0.750014i | 0.927022 | + | 0.375007i | \(0.122360\pi\) | ||||
−0.927022 | + | 0.375007i | \(0.877640\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.6812 | − | 46.5827i | 0.656820 | − | 1.83419i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.0602 | 0.985218 | 0.492609 | − | 0.870251i | \(-0.336043\pi\) | ||||
0.492609 | + | 0.870251i | \(0.336043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.55295i | 0.217972i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.5088 | − | 20.0623i | −0.842997 | − | 0.786303i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.0933i | 1.25591i | 0.778250 | + | 0.627955i | \(0.216108\pi\) | ||||
−0.778250 | + | 0.627955i | \(0.783892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.9139 | −1.63771 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.8096 | + | 14.3749i | −0.460737 | + | 0.560817i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.93782i | − | 0.192350i | −0.995364 | − | 0.0961752i | \(-0.969339\pi\) | ||
0.995364 | − | 0.0961752i | \(-0.0306609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.9752i | − | 0.776947i | −0.921460 | − | 0.388473i | \(-0.873003\pi\) | ||
0.921460 | − | 0.388473i | \(-0.126997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.14782 | − | 1.12723i | −0.122251 | − | 0.0437779i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.7471 | + | 34.2346i | −0.571869 | + | 1.32756i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.757209 | −0.0293193 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.7199 | + | 10.2845i | 1.11037 | + | 0.397622i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.33990 | −0.244749 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7737 | −0.492390 | −0.246195 | − | 0.969220i | \(-0.579180\pi\) | ||||
−0.246195 | + | 0.969220i | \(0.579180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38.8079 | − | 23.2196i | 1.49372 | − | 0.893723i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.73533 | −0.374159 | −0.187080 | − | 0.982345i | \(-0.559902\pi\) | ||||
−0.187080 | + | 0.982345i | \(0.559902\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.21108 | − | 14.4186i | 0.238359 | − | 0.553336i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2490 | + | 34.2057i | −0.469382 | + | 1.31076i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 43.7031i | − | 1.67225i | −0.548537 | − | 0.836126i | \(-0.684815\pi\) | ||
0.548537 | − | 0.836126i | \(-0.315185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.7935i | − | 0.641648i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.0000 | − | 4.29718i | −0.457829 | − | 0.163948i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.39653 | −0.243688 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0293i | 0.609782i | 0.952387 | + | 0.304891i | \(0.0986201\pi\) | ||||
−0.952387 | + | 0.304891i | \(0.901380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.05378 | + | 3.63925i | −0.267951 | + | 0.138244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.20410i | 0.0836063i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.3453 | 0.391858 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.84365 | − | 2.45070i | −0.258851 | − | 0.0926938i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.9860i | 1.43471i | 0.696706 | + | 0.717357i | \(0.254648\pi\) | ||||
−0.696706 | + | 0.717357i | \(0.745352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.1275i | 0.759123i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.47737 | − | 15.2957i | 0.206290 | − | 0.576071i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.2278 | + | 14.3134i | 1.24966 | + | 0.538313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.3364 | 1.25198 | 0.625988 | − | 0.779833i | \(-0.284696\pi\) | ||||
0.625988 | + | 0.779833i | \(0.284696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.5011 | − | 31.6304i | −1.44390 | − | 1.18623i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.1036 | 1.72659 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.30698 | −0.0862761 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.2886 | + | 12.2787i | 1.28053 | + | 0.458556i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.7616 | −1.48286 | −0.741428 | − | 0.671032i | \(-0.765851\pi\) | ||||
−0.741428 | + | 0.671032i | \(0.765851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.7412 | + | 34.2209i | −0.548993 | + | 1.27445i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.0907 | + | 15.4307i | 1.60256 | + | 0.573874i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.917480i | − | 0.0340744i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.5278i | 1.05804i | 0.848611 | + | 0.529018i | \(0.177440\pi\) | ||||
−0.848611 | + | 0.529018i | \(0.822560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.7647 | − | 23.7921i | 0.472766 | − | 0.881188i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.9039 | 0.884118 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 33.0504i | − | 1.22074i | −0.792115 | − | 0.610372i | \(-0.791020\pi\) | ||
0.792115 | − | 0.610372i | \(-0.208980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 41.1005 | − | 18.0317i | 1.51601 | − | 0.665108i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.329112i | 0.0121230i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.28867 | −0.268118 | −0.134059 | − | 0.990973i | \(-0.542801\pi\) | ||||
−0.134059 | + | 0.990973i | \(0.542801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.38502 | + | 3.86773i | −0.0508802 | + | 0.142085i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.5060i | 1.26590i | 0.774192 | + | 0.632951i | \(0.218157\pi\) | ||||
−0.774192 | + | 0.632951i | \(0.781843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.9536i | 0.437947i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.9459 | + | 26.2451i | 1.16884 | + | 0.960256i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.16320 | + | 11.9860i | −0.188659 | + | 0.437961i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1699 | −0.699518 | −0.349759 | − | 0.936840i | \(-0.613737\pi\) | ||||
−0.349759 | + | 0.936840i | \(0.613737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.0724 | − | 39.2977i | 0.512827 | − | 1.43209i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.3792 | 2.30661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2158 | 0.371300 | 0.185650 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185650 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.19438 | − | 11.7130i | 0.152246 | − | 0.425153i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.6429 | 1.14705 | 0.573527 | − | 0.819187i | \(-0.305575\pi\) | ||||
0.573527 | + | 0.819187i | \(0.305575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.6088 | + | 17.9237i | 1.50634 | + | 0.648882i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.5799 | + | 21.8366i | 0.960999 | + | 0.789505i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.46062i | − | 0.124956i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.5386i | 1.60610i | 0.595910 | + | 0.803051i | \(0.296791\pi\) | ||||
−0.595910 | + | 0.803051i | \(0.703209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.7029 | + | 46.6433i | −0.601540 | + | 1.67982i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.8133 | 0.532798 | 0.266399 | − | 0.963863i | \(-0.414166\pi\) | ||||
0.266399 | + | 0.963863i | \(0.414166\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.8619i | 2.00662i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.5301 | − | 17.7220i | 0.593015 | − | 0.635772i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 12.7113i | − | 0.455431i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7681 | 0.456877 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.281241 | − | 0.470050i | −0.0100507 | − | 0.0167982i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15.4743i | − | 0.552302i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.9666i | 1.81676i | 0.418141 | + | 0.908382i | \(0.362682\pi\) | ||||
−0.418141 | + | 0.908382i | \(0.637318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.5458 | − | 4.85072i | −0.482243 | − | 0.172690i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.62111 | − | 6.08475i | 0.0931960 | − | 0.216349i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.95105 | 0.140306 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 61.9567 | + | 22.1866i | 2.19738 | + | 0.786876i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51.2155 | −1.81415 | −0.907073 | − | 0.420972i | \(-0.861689\pi\) | ||||
−0.907073 | + | 0.420972i | \(0.861689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.84900 | 0.277678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3291 | − | 15.0582i | −0.647628 | − | 0.532056i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.20128 | −0.218839 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.8323 | + | 64.6109i | −0.980959 | + | 2.27724i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.66310 | − | 24.1920i | 0.304956 | − | 0.851599i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.6266i | 0.584559i | 0.956333 | + | 0.292279i | \(0.0944137\pi\) | ||||
−0.956333 | + | 0.292279i | \(0.905586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.1091i | − | 0.951928i | −0.879465 | − | 0.475964i | \(-0.842099\pi\) | ||
0.879465 | − | 0.475964i | \(-0.157901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.1711 | + | 16.5338i | 1.61929 | + | 0.579865i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 79.4430 | 2.78277 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29.3707i | − | 1.02755i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.39595 | − | 2.26800i | 0.153607 | − | 0.0792502i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.68478i | − | 0.303101i | −0.988450 | − | 0.151550i | \(-0.951573\pi\) | ||
0.988450 | − | 0.151550i | \(-0.0484266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.291975 | −0.0101776 | −0.00508881 | − | 0.999987i | \(-0.501620\pi\) | ||||
−0.00508881 | + | 0.999987i | \(0.501620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.1921 | + | 5.08217i | 0.494106 | + | 0.176938i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.8358i | − | 0.376797i | −0.982093 | − | 0.188398i | \(-0.939670\pi\) | ||
0.982093 | − | 0.188398i | \(-0.0603296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.4578i | − | 1.43989i | −0.694032 | − | 0.719944i | \(-0.744167\pi\) | ||
0.694032 | − | 0.719944i | \(-0.255833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.11502 | + | 8.69880i | −0.108059 | + | 0.301758i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8954 | + | 15.7567i | 0.516094 | + | 0.545938i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.94587 | 0.101946 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.1237 | + | 28.6196i | 0.591882 | + | 0.989238i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.3302 | −0.632830 | −0.316415 | − | 0.948621i | \(-0.602479\pi\) | ||||
−0.316415 | + | 0.948621i | \(0.602479\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9889 | 0.999617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.45476 | − | 1.95334i | −0.187872 | − | 0.0672765i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.6857 | −1.60604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.42989 | − | 1.04672i | −0.0834921 | − | 0.0359657i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.3390 | + | 7.99954i | 0.766672 | + | 0.274543i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9866i | 1.30216i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2649i | 0.762337i | 0.924506 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924506 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.8307 | − | 32.6588i | 0.917590 | − | 1.11691i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.0538 | 0.582547 | 0.291273 | − | 0.956640i | \(-0.405921\pi\) | ||||
0.291273 | + | 0.956640i | \(0.405921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.0827i | − | 0.412256i | −0.978525 | − | 0.206128i | \(-0.933914\pi\) | ||
0.978525 | − | 0.206128i | \(-0.0660864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4394 | + | 11.1921i | −0.355775 | + | 0.381427i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 52.0800i | − | 1.77282i | −0.462899 | − | 0.886411i | \(-0.653191\pi\) | ||
0.462899 | − | 0.886411i | \(-0.346809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.7283 | −1.96282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.32412 | − | 12.0753i | 0.146855 | − | 0.410097i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.6093i | − | 0.563431i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.205104i | − | 0.00694969i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3003 | + | 13.7549i | −0.382458 | + | 0.465534i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.3115 | − | 14.3495i | −1.12614 | − | 0.485102i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.7197 | 1.84775 | 0.923876 | − | 0.382692i | \(-0.125003\pi\) | ||||
0.923876 | + | 0.382692i | \(0.125003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.389653 | − | 1.08812i | 0.0131427 | − | 0.0367013i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.6997 | −0.360481 | −0.180241 | − | 0.983623i | \(-0.557688\pi\) | ||||
−0.180241 | + | 0.983623i | \(0.557688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.6559 | −0.728779 | −0.364389 | − | 0.931247i | \(-0.618722\pi\) | ||||
−0.364389 | + | 0.931247i | \(0.618722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0033 | + | 33.5195i | −0.403485 | + | 1.12675i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.0036 | 1.57823 | 0.789113 | − | 0.614248i | \(-0.210541\pi\) | ||||
0.789113 | + | 0.614248i | \(0.210541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8511 | + | 9.84350i | 0.766401 | + | 0.330140i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.82888 | − | 1.74667i | 0.295779 | − | 0.0585156i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 9.64407i | − | 0.322727i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.98631i | 0.0663951i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.61396 | + | 7.29956i | −0.0872775 | + | 0.243725i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.676613 | 0.0225663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.7931i | 1.05918i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.1213 | + | 25.8605i | −0.802708 | + | 0.860584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 45.5608i | − | 1.51449i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.0300 | 1.49520 | 0.747599 | − | 0.664151i | \(-0.231207\pi\) | ||||
0.747599 | + | 0.664151i | \(0.231207\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.6983 | − | 26.0416i | −1.05137 | − | 0.863746i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.6898i | 1.48064i | 0.672256 | + | 0.740319i | \(0.265325\pi\) | ||||
−0.672256 | + | 0.740319i | \(0.734675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.7814i | 0.456098i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −38.2699 | − | 13.7044i | −1.26516 | − | 0.453052i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.5126 | + | 11.8515i | 0.908547 | + | 0.391372i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3685 | 0.605922 | 0.302961 | − | 0.953003i | \(-0.402025\pi\) | ||||
0.302961 | + | 0.953003i | \(0.402025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.8328 | + | 13.9059i | 1.27958 | + | 0.458216i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.95711 | −0.261911 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.0269 | −1.51335 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.8200 | − | 32.6457i | 0.880883 | − | 1.07223i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.54350 | −0.214685 | −0.107343 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107343 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.3603 | − | 18.3020i | 0.634508 | − | 0.599823i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.34534 | − | 12.1345i | 0.142260 | − | 0.397266i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.4665i | 0.374995i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.3947i | 1.58099i | 0.612471 | + | 0.790493i | \(0.290176\pi\) | ||||
−0.612471 | + | 0.790493i | \(0.709824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.8940 | + | 10.3469i | 0.942921 | + | 0.337658i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0783 | −0.621933 | −0.310967 | − | 0.950421i | \(-0.600653\pi\) | ||||
−0.310967 | + | 0.950421i | \(0.600653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 23.9901i | − | 0.781225i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.4457 | + | 6.72032i | −1.64100 | + | 0.218612i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 42.2511i | − | 1.37298i | −0.727141 | − | 0.686488i | \(-0.759152\pi\) | ||
0.727141 | − | 0.686488i | \(-0.240848\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.86467 | 0.125452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −56.1045 | − | 20.0909i | −1.81931 | − | 0.651493i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.6044i | 0.570262i | 0.958489 | + | 0.285131i | \(0.0920372\pi\) | ||||
−0.958489 | + | 0.285131i | \(0.907963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.1144i | 0.521450i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0615564 | − | 0.171898i | 0.00198984 | − | 0.00555668i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.74852 | + | 11.0234i | −0.153338 | + | 0.355964i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.1964 | −0.328917 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.39383 | − | 11.4343i | 0.302712 | − | 0.368466i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.19789 | −0.167326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3712 | −0.944513 | −0.472257 | − | 0.881461i | \(-0.656560\pi\) | ||||
−0.472257 | + | 0.881461i | \(0.656560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.2240 | + | 6.88408i | 0.617564 | + | 0.221148i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0318 | 0.835400 | 0.417700 | − | 0.908585i | \(-0.362836\pi\) | ||||
0.417700 | + | 0.908585i | \(0.362836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.623229 | − | 1.44679i | 0.0199798 | − | 0.0463819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.84458 | − | 3.16723i | −0.283253 | − | 0.101432i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60.6495i | − | 1.94035i | −0.242406 | − | 0.970175i | \(-0.577936\pi\) | ||
0.242406 | − | 0.970175i | \(-0.422064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.90715i | − | 0.252713i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.6936 | − | 32.6101i | −1.26732 | − | 1.04116i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.9893 | 1.17977 | 0.589887 | − | 0.807486i | \(-0.299172\pi\) | ||||
0.589887 | + | 0.807486i | \(0.299172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.40361i | − | 0.235898i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.92040 | + | 8.49146i | −0.252109 | + | 0.270286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 55.4314i | − | 1.76262i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4447 | 0.554148 | 0.277074 | − | 0.960849i | \(-0.410635\pi\) | ||||
0.277074 | + | 0.960849i | \(0.410635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.3059 | + | 45.5347i | −0.517451 | + | 1.44500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13.5155i | − | 0.428469i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.5937i | 1.60232i | 0.598452 | + | 0.801159i | \(0.295783\pi\) | ||||
−0.598452 | + | 0.801159i | \(0.704217\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.5808 | + | 14.1089i | −0.746064 | + | 0.446386i |
(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 | 1848.2.v.d.881.6 | yes | 16 | |
3.2 | odd | 2 | inner | 1848.2.v.d.881.12 | yes | 16 | |
7.6 | odd | 2 | inner | 1848.2.v.d.881.11 | yes | 16 | |
21.20 | even | 2 | inner | 1848.2.v.d.881.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1848.2.v.d.881.5 | ✓ | 16 | 21.20 | even | 2 | inner | |
1848.2.v.d.881.6 | yes | 16 | 1.1 | even | 1 | trivial | |
1848.2.v.d.881.11 | yes | 16 | 7.6 | odd | 2 | inner | |
1848.2.v.d.881.12 | yes | 16 | 3.2 | odd | 2 | inner |