Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (of order \(2\), degree \(1\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.4 | ||
Root | \(0.866025 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.2.c.c.1727.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.87298i | 1.46385i | 0.681385 | + | 0.731925i | \(0.261378\pi\) | ||||
−0.681385 | + | 0.731925i | \(0.738622\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | −1.44463 | −0.722315 | − | 0.691564i | \(-0.756922\pi\) | ||||
−0.722315 | + | 0.691564i | \(0.756922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.47214i | − 0.830455i | −0.909718 | − | 0.415227i | \(-0.863702\pi\) | ||||
0.909718 | − | 0.415227i | \(-0.136298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 3.87298i | − 0.695608i | −0.937567 | − | 0.347804i | \(-0.886927\pi\) | ||||
0.937567 | − | 0.347804i | \(-0.113073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.66025 | −1.46385 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.94427i | − 1.39686i | −0.715678 | − | 0.698430i | \(-0.753882\pi\) | ||||
0.715678 | − | 0.698430i | \(-0.246118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.74597i | 1.18125i | 0.806947 | + | 0.590624i | \(0.201119\pi\) | ||||
−0.806947 | + | 0.590624i | \(0.798881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.00000 | −1.14286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.23607i | 0.307148i | 0.988137 | + | 0.153574i | \(0.0490783\pi\) | ||||
−0.988137 | + | 0.153574i | \(0.950922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.87298i | − 0.522233i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.46410 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 4.47214i | − 0.554700i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.74597i | − 0.946320i | −0.880976 | − | 0.473160i | \(-0.843113\pi\) | ||||
0.880976 | − | 0.473160i | \(-0.156887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3923 | −1.23334 | −0.616670 | − | 0.787222i | \(-0.711519\pi\) | ||||
−0.616670 | + | 0.787222i | \(0.711519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.70820i | − 0.764471i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7.74597i | − 0.871489i | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
0.900070 | − | 0.435745i | \(-0.143515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1244 | −1.33082 | −0.665410 | − | 0.746478i | \(-0.731743\pi\) | ||||
−0.665410 | + | 0.746478i | \(0.731743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0000 | −1.08465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.47214i | 0.474045i | 0.971504 | + | 0.237023i | \(0.0761716\pi\) | ||||
−0.971504 | + | 0.237023i | \(0.923828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 7.74597i | − 0.811998i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.23607i | 0.222497i | 0.993793 | + | 0.111249i | \(0.0354850\pi\) | ||||
−0.993793 | + | 0.111249i | \(0.964515\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74597i | 0.763233i | 0.924321 | + | 0.381616i | \(0.124632\pi\) | ||||
−0.924321 | + | 0.381616i | \(0.875368\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.19615 | 0.502331 | 0.251166 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251166 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8885i | 1.68281i | 0.540403 | + | 0.841406i | \(0.318272\pi\) | ||||
−0.540403 | + | 0.841406i | \(0.681728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 15.4919i | − 1.44463i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.3205 | −1.58777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6190i | 1.03102i | 0.856885 | + | 0.515508i | \(0.172397\pi\) | ||||
−0.856885 | + | 0.515508i | \(0.827603\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.0526 | −1.66463 | −0.832315 | − | 0.554303i | \(-0.812985\pi\) | ||||
−0.832315 | + | 0.554303i | \(0.812985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.47214i | 0.382080i | 0.981582 | + | 0.191040i | \(0.0611861\pi\) | ||||
−0.981582 | + | 0.191040i | \(0.938814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4919i | 1.31401i | 0.753887 | + | 0.657004i | \(0.228177\pi\) | ||||
−0.753887 | + | 0.657004i | \(0.771823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.23607i | 0.183186i | 0.995797 | + | 0.0915929i | \(0.0291958\pi\) | ||||
−0.995797 | + | 0.0915929i | \(0.970804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.87298i | 0.315179i | 0.987505 | + | 0.157589i | \(0.0503723\pi\) | ||||
−0.987505 | + | 0.157589i | \(0.949628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.66025 | 0.695608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | −1.59617 | −0.798087 | − | 0.602542i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602542i | \(0.794154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 26.8328i | − 2.11472i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2379i | 1.82013i | 0.414462 | + | 0.910066i | \(0.363970\pi\) | ||||
−0.414462 | + | 0.910066i | \(0.636030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.46410 | 0.268060 | 0.134030 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134030 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6525i | 1.19004i | 0.803712 | + | 0.595018i | \(0.202855\pi\) | ||||
−0.803712 | + | 0.595018i | \(0.797145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19615 | −0.388379 | −0.194189 | − | 0.980964i | \(-0.562208\pi\) | ||||
−0.194189 | + | 0.980964i | \(0.562208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.94427i | 0.657596i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 7.74597i | − 0.566441i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3205 | 1.25327 | 0.626634 | − | 0.779314i | \(-0.284432\pi\) | ||||
0.626634 | + | 0.779314i | \(0.284432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.0000 | −1.79954 | −0.899770 | − | 0.436365i | \(-0.856266\pi\) | ||||
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 24.5967i | − 1.75245i | −0.481906 | − | 0.876223i | \(-0.660055\pi\) | ||||
0.481906 | − | 0.876223i | \(-0.339945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.6190i | − 0.823646i | −0.911264 | − | 0.411823i | \(-0.864892\pi\) | ||||
0.911264 | − | 0.411823i | \(-0.135108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.3205 | 1.21566 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | 1.39686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4919i | 1.06651i | 0.845955 | + | 0.533254i | \(0.179031\pi\) | ||||
−0.845955 | + | 0.533254i | \(0.820969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.3205 | −1.18125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 8.94427i | − 0.601657i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.74597i | − 0.518708i | −0.965782 | − | 0.259354i | \(-0.916490\pi\) | ||||
0.965782 | − | 0.259354i | \(-0.0835097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.46410 | 0.229920 | 0.114960 | − | 0.993370i | \(-0.463326\pi\) | ||||
0.114960 | + | 0.993370i | \(0.463326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.47214i | 0.292979i | 0.989212 | + | 0.146490i | \(0.0467975\pi\) | ||||
−0.989212 | + | 0.146490i | \(0.953202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.74597i | − 0.505291i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8564 | 0.896296 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 17.8885i | − 1.14286i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923 | 0.655956 | 0.327978 | − | 0.944685i | \(-0.393633\pi\) | ||||
0.327978 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.3607i | − 1.39482i | −0.716672 | − | 0.697410i | \(-0.754335\pi\) | ||||
0.716672 | − | 0.697410i | \(-0.245665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.4919i | 0.962622i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.92820 | 0.427211 | 0.213606 | − | 0.976920i | \(-0.431479\pi\) | ||||
0.213606 | + | 0.976920i | \(0.431479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.00000 | −0.307148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.47214i | − 0.272671i | −0.990663 | − | 0.136335i | \(-0.956467\pi\) | ||||
0.990663 | − | 0.136335i | \(-0.0435325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6190i | 0.705801i | 0.935661 | + | 0.352900i | \(0.114805\pi\) | ||||
−0.935661 | + | 0.352900i | \(0.885195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0000 | −1.20168 | −0.600842 | − | 0.799368i | \(-0.705168\pi\) | ||||
−0.600842 | + | 0.799368i | \(0.705168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.47214i | 0.266785i | 0.991063 | + | 0.133393i | \(0.0425871\pi\) | ||||
−0.991063 | + | 0.133393i | \(0.957413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 30.9839i | − 1.84180i | −0.389799 | − | 0.920900i | \(-0.627456\pi\) | ||||
0.389799 | − | 0.920900i | \(-0.372544\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.6410 | 2.04479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.3607i | 1.30632i | 0.757218 | + | 0.653162i | \(0.226558\pi\) | ||||
−0.757218 | + | 0.653162i | \(0.773442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 7.74597i | − 0.450988i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8564 | 0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.0000 | −1.72917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.94427i | 0.512148i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 23.2379i | − 1.32626i | −0.748506 | − | 0.663129i | \(-0.769228\pi\) | ||||
0.748506 | − | 0.663129i | \(-0.230772\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.7128 | −1.57145 | −0.785725 | − | 0.618576i | \(-0.787710\pi\) | ||||
−0.785725 | + | 0.618576i | \(0.787710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | 0.282617 | 0.141308 | − | 0.989966i | \(-0.454869\pi\) | ||||
0.141308 | + | 0.989966i | \(0.454869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.6525i | 0.879131i | 0.898211 | + | 0.439565i | \(0.144867\pi\) | ||||
−0.898211 | + | 0.439565i | \(0.855133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.74597i | 0.433691i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 13.4164i | − 0.739671i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.74597i | 0.425757i | 0.977079 | + | 0.212878i | \(0.0682838\pi\) | ||||
−0.977079 | + | 0.212878i | \(0.931716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.3205 | 0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.70820i | 0.363270i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.87298i | − 0.209121i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.9090 | 1.76665 | 0.883323 | − | 0.468765i | \(-0.155301\pi\) | ||||
0.883323 | + | 0.468765i | \(0.155301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.8885i | 0.952111i | 0.879415 | + | 0.476056i | \(0.157934\pi\) | ||||
−0.879415 | + | 0.476056i | \(0.842066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 23.2379i | − 1.23334i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.1769 | 1.64545 | 0.822727 | − | 0.568436i | \(-0.192451\pi\) | ||||
0.822727 | + | 0.568436i | \(0.192451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.1803i | 0.585206i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1109i | 1.41518i | 0.706625 | + | 0.707588i | \(0.250217\pi\) | ||||
−0.706625 | + | 0.707588i | \(0.749783\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.66025 | −0.449618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.94427i | 0.460653i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.2487 | 1.23905 | 0.619526 | − | 0.784976i | \(-0.287325\pi\) | ||||
0.619526 | + | 0.784976i | \(0.287325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | 0.764471 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.23607i | 0.113373i | 0.998392 | + | 0.0566866i | \(0.0180536\pi\) | ||||
−0.998392 | + | 0.0566866i | \(0.981946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 30.9839i | − 1.56692i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.3205 | 0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8885i | 0.893311i | 0.894706 | + | 0.446656i | \(0.147385\pi\) | ||||
−0.894706 | + | 0.446656i | \(0.852615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.74597i | 0.385854i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.92820 | −0.343418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | −0.346128 | −0.173064 | − | 0.984911i | \(-0.555367\pi\) | ||||
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.4164i | − 0.660178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 27.1109i | − 1.33082i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.3205 | 0.846162 | 0.423081 | − | 0.906092i | \(-0.360949\pi\) | ||||
0.423081 | + | 0.906092i | \(0.360949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | 0.194948 | 0.0974740 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974740 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.4919i | 0.749707i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3923 | −0.500580 | −0.250290 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250290 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | −0.624740 | −0.312370 | − | 0.949960i | \(-0.601123\pi\) | ||||
−0.312370 | + | 0.949960i | \(0.601123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.87298i | 0.184847i | 0.995720 | + | 0.0924237i | \(0.0294614\pi\) | ||||
−0.995720 | + | 0.0924237i | \(0.970539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2487 | 1.15209 | 0.576046 | − | 0.817418i | \(-0.304595\pi\) | ||||
0.576046 | + | 0.817418i | \(0.304595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.8885i | 0.844213i | 0.906546 | + | 0.422106i | \(0.138709\pi\) | ||||
−0.906546 | + | 0.422106i | \(0.861291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4919i | 0.729487i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.3205 | 0.811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 38.0132i | − 1.77045i | −0.465164 | − | 0.885225i | \(-0.654005\pi\) | ||||
0.465164 | − | 0.885225i | \(-0.345995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.87298i | − 0.179993i | −0.995942 | − | 0.0899964i | \(-0.971314\pi\) | ||||
0.995942 | − | 0.0899964i | \(-0.0286856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.19615 | −0.240449 | −0.120225 | − | 0.992747i | \(-0.538361\pi\) | ||||
−0.120225 | + | 0.992747i | \(0.538361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.0000 | 1.38527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 13.4164i | − 0.616887i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.3205 | 0.791394 | 0.395697 | − | 0.918381i | \(-0.370503\pi\) | ||||
0.395697 | + | 0.918381i | \(0.370503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.5967i | 1.11688i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2379i | 1.05301i | 0.850172 | + | 0.526505i | \(0.176498\pi\) | ||||
−0.850172 | + | 0.526505i | \(0.823502\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.66025 | −0.390832 | −0.195416 | − | 0.980720i | \(-0.562606\pi\) | ||||
−0.195416 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 40.2492i | − 1.80542i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.7298i | 1.73379i | 0.498495 | + | 0.866893i | \(0.333886\pi\) | ||||
−0.498495 | + | 0.866893i | \(0.666114\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.7846 | −0.926740 | −0.463370 | − | 0.886165i | \(-0.653360\pi\) | ||||
−0.463370 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 11.1803i | − 0.495560i | −0.968816 | − | 0.247780i | \(-0.920299\pi\) | ||||
0.968816 | − | 0.247780i | \(-0.0797010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.3649i | 0.856653i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.3205 | −0.763233 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 22.3607i | − 0.979639i | −0.871824 | − | 0.489820i | \(-0.837063\pi\) | ||||
0.871824 | − | 0.489820i | \(-0.162937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.2379i | 1.01612i | 0.861321 | + | 0.508061i | \(0.169638\pi\) | ||||
−0.861321 | + | 0.508061i | \(0.830362\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3205 | 0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.8885i | 0.774839i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.6190i | 0.502331i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.8564 | 0.596838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.94427i | 0.383131i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.74597i | 0.331194i | 0.986194 | + | 0.165597i | \(0.0529550\pi\) | ||||
−0.986194 | + | 0.165597i | \(0.947045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | 1.27573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6525i | 0.663217i | 0.943417 | + | 0.331608i | \(0.107591\pi\) | ||||
−0.943417 | + | 0.331608i | \(0.892409\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 15.4919i | − 0.655239i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0526 | −0.802970 | −0.401485 | − | 0.915866i | \(-0.631506\pi\) | ||||
−0.401485 | + | 0.915866i | \(0.631506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.0000 | −1.68281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 35.7771i | − 1.49985i | −0.661521 | − | 0.749927i | \(-0.730089\pi\) | ||||
0.661521 | − | 0.749927i | \(-0.269911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 7.74597i | − 0.324159i | −0.986778 | − | 0.162079i | \(-0.948180\pi\) | ||||
0.986778 | − | 0.162079i | \(-0.0518200\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 46.9574i | − 1.94812i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.87298i | − 0.160403i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.0526 | 0.786383 | 0.393192 | − | 0.919457i | \(-0.371371\pi\) | ||||
0.393192 | + | 0.919457i | \(0.371371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.47214i | 0.183649i | 0.995775 | + | 0.0918243i | \(0.0292698\pi\) | ||||
−0.995775 | + | 0.0918243i | \(0.970730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 38.7298i | − 1.58777i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.3205 | −0.707697 | −0.353848 | − | 0.935303i | \(-0.615127\pi\) | ||||
−0.353848 | + | 0.935303i | \(0.615127\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.0000 | −1.26452 | −0.632258 | − | 0.774758i | \(-0.717872\pi\) | ||||
−0.632258 | + | 0.774758i | \(0.717872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.8885i | − 0.727273i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.74597i | 0.314399i | 0.987567 | + | 0.157200i | \(0.0502466\pi\) | ||||
−0.987567 | + | 0.157200i | \(0.949753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.92820 | 0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.0000 | −1.53481 | −0.767403 | − | 0.641165i | \(-0.778451\pi\) | ||||
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8885i | 0.720166i | 0.932920 | + | 0.360083i | \(0.117252\pi\) | ||||
−0.932920 | + | 0.360083i | \(0.882748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 38.7298i | − 1.55668i | −0.627841 | − | 0.778342i | \(-0.716061\pi\) | ||||
0.627841 | − | 0.778342i | \(-0.283939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.3205 | −0.693932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.8885i | 0.713263i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8569i | 1.38763i | 0.720154 | + | 0.693815i | \(0.244071\pi\) | ||||
−0.720154 | + | 0.693815i | \(0.755929\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.9808 | −1.03102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0000 | 0.633943 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.7214i | 1.76639i | 0.469008 | + | 0.883194i | \(0.344611\pi\) | ||||
−0.469008 | + | 0.883194i | \(0.655389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.9839i | − 1.22188i | −0.791675 | − | 0.610942i | \(-0.790791\pi\) | ||||
0.791675 | − | 0.610942i | \(-0.209209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 11.1803i | − 0.437521i | −0.975779 | − | 0.218760i | \(-0.929799\pi\) | ||||
0.975779 | − | 0.218760i | \(-0.0702013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 42.6028i | − 1.66463i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.66025 | 0.337356 | 0.168678 | − | 0.985671i | \(-0.446050\pi\) | ||||
0.168678 | + | 0.985671i | \(0.446050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | 0.622328 | 0.311164 | − | 0.950356i | \(-0.399281\pi\) | ||||
0.311164 | + | 0.950356i | \(0.399281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.9839i | 1.19970i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.92820 | −0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0000 | 0.886585 | 0.443292 | − | 0.896377i | \(-0.353810\pi\) | ||||
0.443292 | + | 0.896377i | \(0.353810\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.3607i | 0.859391i | 0.902974 | + | 0.429695i | \(0.141379\pi\) | ||||
−0.902974 | + | 0.429695i | \(0.858621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.6028i | 1.63495i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3923 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 4.47214i | − 0.170375i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 15.4919i | − 0.589341i | −0.955599 | − | 0.294670i | \(-0.904790\pi\) | ||||
0.955599 | − | 0.294670i | \(-0.0952099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.6410 | −1.31401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.0000 | 1.51511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6525i | 0.591186i | 0.955314 | + | 0.295593i | \(0.0955172\pi\) | ||||
−0.955314 | + | 0.295593i | \(0.904483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.66025 | −0.325702 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0000 | −1.20179 | −0.600893 | − | 0.799330i | \(-0.705188\pi\) | ||||
−0.600893 | + | 0.799330i | \(0.705188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.8328i | 1.00490i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.74597i | 0.289683i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.7846 | −0.775135 | −0.387568 | − | 0.921841i | \(-0.626685\pi\) | ||||
−0.387568 | + | 0.921841i | \(0.626685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 42.6028i | − 1.58005i | −0.613074 | − | 0.790026i | \(-0.710067\pi\) | ||||
0.613074 | − | 0.790026i | \(-0.289933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.6410 | −1.28124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.00000 | −0.295487 | −0.147743 | − | 0.989026i | \(-0.547201\pi\) | ||||
−0.147743 | + | 0.989026i | \(0.547201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.4164i | 0.494200i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 23.2379i | − 0.854820i | −0.904058 | − | 0.427410i | \(-0.859426\pi\) | ||||
0.904058 | − | 0.427410i | \(-0.140574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2487 | 0.889599 | 0.444799 | − | 0.895630i | \(-0.353275\pi\) | ||||
0.444799 | + | 0.895630i | \(0.353275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.00000 | −0.183186 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.1246i | 0.735337i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 3.87298i | − 0.141327i | −0.997500 | − | 0.0706636i | \(-0.977488\pi\) | ||||
0.997500 | − | 0.0706636i | \(-0.0225117\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.66025 | −0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.8885i | 0.648459i | 0.945978 | + | 0.324230i | \(0.105105\pi\) | ||||
−0.945978 | + | 0.324230i | \(0.894895\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4919i | 0.560846i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92820 | 0.250163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0000 | 0.396670 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4.47214i | − 0.160852i | −0.996761 | − | 0.0804258i | \(-0.974372\pi\) | ||||
0.996761 | − | 0.0804258i | \(-0.0256280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 44.7214i | − 1.59617i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4919i | 0.552228i | 0.961125 | + | 0.276114i | \(0.0890467\pi\) | ||||
−0.961125 | + | 0.276114i | \(0.910953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −69.2820 | −2.46339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.4853i | 1.50491i | 0.658646 | + | 0.752453i | \(0.271130\pi\) | ||||
−0.658646 | + | 0.752453i | \(0.728870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 15.4919i | − 0.548065i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.66025 | −0.305614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 60.0000 | 2.11472 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.47214i | 0.157232i | 0.996905 | + | 0.0786160i | \(0.0250501\pi\) | ||||
−0.996905 | + | 0.0786160i | \(0.974950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.9615 | −1.82013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 4.47214i | − 0.156079i | −0.996950 | − | 0.0780393i | \(-0.975134\pi\) | ||||
0.996950 | − | 0.0780393i | \(-0.0248660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 27.1109i | − 0.945026i | −0.881324 | − | 0.472513i | \(-0.843347\pi\) | ||||
0.881324 | − | 0.472513i | \(-0.156653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.1769 | −1.08413 | −0.542064 | − | 0.840337i | \(-0.682357\pi\) | ||||
−0.542064 | + | 0.840337i | \(0.682357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 35.7771i | − 1.23960i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.74597i | 0.268060i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.1051 | 1.31553 | 0.657767 | − | 0.753221i | \(-0.271501\pi\) | ||||
0.657767 | + | 0.753221i | \(0.271501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 20.1246i | − 0.692308i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 30.9839i | − 1.06462i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7128 | −0.949983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.00000 | −0.0684787 | −0.0342393 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342393 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.47214i | 0.152765i | 0.997079 | + | 0.0763826i | \(0.0243370\pi\) | ||||
−0.997079 | + | 0.0763826i | \(0.975663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4919i | 0.528578i | 0.964444 | + | 0.264289i | \(0.0851373\pi\) | ||||
−0.964444 | + | 0.264289i | \(0.914863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.7846 | 0.707516 | 0.353758 | − | 0.935337i | \(-0.384904\pi\) | ||||
0.353758 | + | 0.935337i | \(0.384904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0000 | −1.19004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4164i | 0.455120i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4919i | 0.524924i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.3013 | −1.46385 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0000 | 1.14810 | 0.574049 | − | 0.818821i | \(-0.305372\pi\) | ||||
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 22.3607i | − 0.753350i | −0.926345 | − | 0.376675i | \(-0.877067\pi\) | ||||
0.926345 | − | 0.376675i | \(-0.122933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.1051 | −1.27944 | −0.639722 | − | 0.768606i | \(-0.720951\pi\) | ||||
−0.639722 | + | 0.768606i | \(0.720951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.0000 | −1.50925 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11.6190i | − 0.388379i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3205 | −0.577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0000 | −0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.7771i | 1.18927i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15.4919i | − 0.514401i | −0.966358 | − | 0.257201i | \(-0.917200\pi\) | ||||
0.966358 | − | 0.257201i | \(-0.0828001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.0333 | −1.49202 | −0.746010 | − | 0.665934i | \(-0.768033\pi\) | ||||
−0.746010 | + | 0.665934i | \(0.768033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0000 | 0.694999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 73.7902i | − 2.43677i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 11.6190i | − 0.383274i | −0.981466 | − | 0.191637i | \(-0.938620\pi\) | ||||
0.981466 | − | 0.191637i | \(-0.0613796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.7846 | 0.684134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.7214i | 1.46726i | 0.679549 | + | 0.733630i | \(0.262175\pi\) | ||||
−0.679549 | + | 0.733630i | \(0.737825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.3205 | 0.566441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0000 | −1.01273 | −0.506363 | − | 0.862320i | \(-0.669010\pi\) | ||||
−0.506363 | + | 0.862320i | \(0.669010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.4853i | 1.38498i | 0.721427 | + | 0.692490i | \(0.243487\pi\) | ||||
−0.721427 | + | 0.692490i | \(0.756513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.9677i | 2.01795i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.2295 | 1.63224 | 0.816119 | − | 0.577883i | \(-0.196121\pi\) | ||||
0.816119 | + | 0.577883i | \(0.196121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0000 | −0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 35.7771i | − 1.15893i | −0.814996 | − | 0.579467i | \(-0.803261\pi\) | ||||
0.814996 | − | 0.579467i | \(-0.196739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.7298i | 1.25327i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.3205 | −0.559308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.0000 | 0.516129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 55.9017i | − 1.79954i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 27.1109i | − 0.871827i | −0.899989 | − | 0.435914i | \(-0.856425\pi\) | ||||
0.899989 | − | 0.435914i | \(-0.143575\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.3731 | −1.16727 | −0.583634 | − | 0.812017i | \(-0.698370\pi\) | ||||
−0.583634 | + | 0.812017i | \(0.698370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −60.0000 | −1.92351 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 49.1935i | − 1.57384i | −0.617055 | − | 0.786920i | \(-0.711675\pi\) | ||||
0.617055 | − | 0.786920i | \(-0.288325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.74597i | − 0.247562i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2487 | −0.773414 | −0.386707 | − | 0.922203i | \(-0.626387\pi\) | ||||
−0.386707 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.0000 | 1.75245 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 53.6656i | − 1.70647i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.6190i | 0.369088i | 0.982824 | + | 0.184544i | \(0.0590808\pi\) | ||||
−0.982824 | + | 0.184544i | \(0.940919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.9808 | 0.823646 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 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 | 1728.2.c.c.1727.4 | 4 | ||
3.2 | odd | 2 | inner | 1728.2.c.c.1727.2 | 4 | ||
4.3 | odd | 2 | inner | 1728.2.c.c.1727.3 | 4 | ||
8.3 | odd | 2 | 108.2.b.a.107.1 | ✓ | 4 | ||
8.5 | even | 2 | 108.2.b.a.107.3 | yes | 4 | ||
12.11 | even | 2 | inner | 1728.2.c.c.1727.1 | 4 | ||
24.5 | odd | 2 | 108.2.b.a.107.2 | yes | 4 | ||
24.11 | even | 2 | 108.2.b.a.107.4 | yes | 4 | ||
72.5 | odd | 6 | 324.2.h.d.107.2 | 8 | |||
72.11 | even | 6 | 324.2.h.d.215.3 | 8 | |||
72.13 | even | 6 | 324.2.h.d.107.3 | 8 | |||
72.29 | odd | 6 | 324.2.h.d.215.4 | 8 | |||
72.43 | odd | 6 | 324.2.h.d.215.2 | 8 | |||
72.59 | even | 6 | 324.2.h.d.107.1 | 8 | |||
72.61 | even | 6 | 324.2.h.d.215.1 | 8 | |||
72.67 | odd | 6 | 324.2.h.d.107.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.b.a.107.1 | ✓ | 4 | 8.3 | odd | 2 | ||
108.2.b.a.107.2 | yes | 4 | 24.5 | odd | 2 | ||
108.2.b.a.107.3 | yes | 4 | 8.5 | even | 2 | ||
108.2.b.a.107.4 | yes | 4 | 24.11 | even | 2 | ||
324.2.h.d.107.1 | 8 | 72.59 | even | 6 | |||
324.2.h.d.107.2 | 8 | 72.5 | odd | 6 | |||
324.2.h.d.107.3 | 8 | 72.13 | even | 6 | |||
324.2.h.d.107.4 | 8 | 72.67 | odd | 6 | |||
324.2.h.d.215.1 | 8 | 72.61 | even | 6 | |||
324.2.h.d.215.2 | 8 | 72.43 | odd | 6 | |||
324.2.h.d.215.3 | 8 | 72.11 | even | 6 | |||
324.2.h.d.215.4 | 8 | 72.29 | odd | 6 | |||
1728.2.c.c.1727.1 | 4 | 12.11 | even | 2 | inner | ||
1728.2.c.c.1727.2 | 4 | 3.2 | odd | 2 | inner | ||
1728.2.c.c.1727.3 | 4 | 4.3 | odd | 2 | inner | ||
1728.2.c.c.1727.4 | 4 | 1.1 | even | 1 | trivial |