Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,2,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (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: | \(0.862384341830\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-0.866025 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.2.b.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 1.11803i | −0.612372 | + | 0.790569i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 1.93649i | −0.250000 | − | 0.968246i | ||||
\(5\) | 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 | \(0.738622\pi\) | |||||||
\(8\) | 2.59808 | + | 1.11803i | 0.918559 | + | 0.395285i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.50000 | − | 1.93649i | −0.790569 | − | 0.612372i | ||||
\(11\) | −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 | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −4.33013 | − | 3.35410i | −1.15728 | − | 0.896421i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.50000 | + | 1.93649i | −0.875000 | + | 0.484123i | ||||
\(17\) | − | 4.47214i | − | 1.08465i | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||
0.840168 | − | 0.542326i | \(-0.182456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 4.33013 | − | 1.11803i | 0.968246 | − | 0.250000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 1.93649i | 0.319801 | − | 0.412861i | ||||
\(23\) | 6.92820 | 1.44463 | 0.722315 | − | 0.691564i | \(-0.243078\pi\) | ||||
0.722315 | + | 0.691564i | \(0.243078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.73205 | + | 2.23607i | −0.339683 | + | 0.438529i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.50000 | − | 1.93649i | 1.41737 | − | 0.365963i | ||||
\(29\) | − | 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 | \(-0.113073\pi\) | |||||||
\(32\) | 0.866025 | − | 5.59017i | 0.153093 | − | 0.988212i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00000 | + | 3.87298i | 0.857493 | + | 0.664211i | ||||
\(35\) | −8.66025 | −1.46385 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.50000 | + | 5.80948i | −0.395285 | + | 0.918559i | ||||
\(41\) | 8.94427i | 1.39686i | 0.715678 | + | 0.698430i | \(0.246118\pi\) | ||||
−0.715678 | + | 0.698430i | \(0.753882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.74597i | − | 1.18125i | −0.806947 | − | 0.590624i | \(-0.798881\pi\) | ||
0.806947 | − | 0.590624i | \(-0.201119\pi\) | |||||||
\(44\) | 0.866025 | + | 3.35410i | 0.130558 | + | 0.505650i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | + | 7.74597i | −0.884652 | + | 1.14208i | ||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.00000 | −1.14286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 3.87298i | −0.138675 | − | 0.537086i | ||||
\(53\) | 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 | ||||||
\(56\) | −4.33013 | + | 10.0623i | −0.578638 | + | 1.34463i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.00000 | + | 3.87298i | 0.656532 | + | 0.508548i | ||||
\(59\) | −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 | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | 4.33013 | + | 3.35410i | 0.549927 | + | 0.425971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.50000 | + | 5.80948i | 0.687500 | + | 0.726184i | ||||
\(65\) | 4.47214i | 0.554700i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.74597i | 0.946320i | 0.880976 | + | 0.473160i | \(0.156887\pi\) | ||||
−0.880976 | + | 0.473160i | \(0.843113\pi\) | |||||||
\(68\) | −8.66025 | + | 2.23607i | −1.05021 | + | 0.271163i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.50000 | − | 9.68246i | 0.896421 | − | 1.15728i | ||||
\(71\) | 10.3923 | 1.23334 | 0.616670 | − | 0.787222i | \(-0.288481\pi\) | ||||
0.616670 | + | 0.787222i | \(0.288481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(74\) | 3.46410 | − | 4.47214i | 0.402694 | − | 0.519875i | ||||
\(75\) | 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 | \(-0.143515\pi\) | |||||||
\(80\) | −4.33013 | − | 7.82624i | −0.484123 | − | 0.875000i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.0000 | − | 7.74597i | −1.10432 | − | 0.855399i | ||||
\(83\) | −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 | ||||||||
\(86\) | 8.66025 | + | 6.70820i | 0.933859 | + | 0.723364i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.50000 | − | 1.93649i | −0.479702 | − | 0.206431i | ||||
\(89\) | − | 4.47214i | − | 0.474045i | −0.971504 | − | 0.237023i | \(-0.923828\pi\) | ||
0.971504 | − | 0.237023i | \(-0.0761716\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.74597i | 0.811998i | ||||||||
\(92\) | −3.46410 | − | 13.4164i | −0.361158 | − | 1.39876i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 3.87298i | −0.309426 | + | 0.399468i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | 6.92820 | − | 8.94427i | 0.699854 | − | 0.903508i | ||||
\(99\) | 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 | \(0.875368\pi\) | |||||||
\(104\) | 5.19615 | + | 2.23607i | 0.509525 | + | 0.219265i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.50000 | − | 1.93649i | −0.242821 | − | 0.188089i | ||||
\(107\) | 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 | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 4.33013 | + | 3.35410i | 0.412861 | + | 0.319801i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.50000 | − | 13.5554i | −0.708683 | − | 1.28087i | ||||
\(113\) | − | 17.8885i | − | 1.68281i | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||
0.540403 | − | 0.841406i | \(-0.318272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.4919i | 1.44463i | ||||||||
\(116\) | −8.66025 | + | 2.23607i | −0.804084 | + | 0.207614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | − | 3.87298i | 0.276172 | − | 0.356537i | ||||
\(119\) | 17.3205 | 1.58777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 3.46410 | − | 4.47214i | 0.313625 | − | 0.404888i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.50000 | + | 1.93649i | −0.673520 | + | 0.173902i | ||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6190i | 1.03102i | 0.856885 | + | 0.515508i | \(0.172397\pi\) | ||||
−0.856885 | + | 0.515508i | \(0.827603\pi\) | |||||||
\(128\) | −11.2583 | + | 1.11803i | −0.995105 | + | 0.0988212i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.00000 | − | 3.87298i | −0.438529 | − | 0.339683i | ||||
\(131\) | −19.0526 | −1.66463 | −0.832315 | − | 0.554303i | \(-0.812985\pi\) | ||||
−0.832315 | + | 0.554303i | \(0.812985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.66025 | − | 6.70820i | −0.748132 | − | 0.579501i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.00000 | − | 11.6190i | 0.428746 | − | 0.996317i | ||||
\(137\) | − | 4.47214i | − | 0.382080i | −0.981582 | − | 0.191040i | \(-0.938814\pi\) | ||
0.981582 | − | 0.191040i | \(-0.0611861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.4919i | − | 1.31401i | −0.753887 | − | 0.657004i | \(-0.771823\pi\) | ||
0.753887 | − | 0.657004i | \(-0.228177\pi\) | |||||||
\(140\) | 4.33013 | + | 16.7705i | 0.365963 | + | 1.41737i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.00000 | + | 11.6190i | −0.755263 | + | 0.975041i | ||||
\(143\) | −3.46410 | −0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | −4.33013 | + | 5.59017i | −0.358364 | + | 0.462646i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | + | 7.74597i | 0.164399 | + | 0.636715i | ||||
\(149\) | 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 | ||||||||
\(154\) | 7.50000 | + | 5.80948i | 0.604367 | + | 0.468141i | ||||
\(155\) | 8.66025 | 0.695608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0000 | 1.59617 | 0.798087 | − | 0.602542i | \(-0.205846\pi\) | ||||
0.798087 | + | 0.602542i | \(0.205846\pi\) | |||||||
\(158\) | 8.66025 | + | 6.70820i | 0.688973 | + | 0.533676i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.5000 | + | 1.93649i | 0.988212 | + | 0.153093i | ||||
\(161\) | 26.8328i | 2.11472i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 23.2379i | − | 1.82013i | −0.414462 | − | 0.910066i | \(-0.636030\pi\) | ||
0.414462 | − | 0.910066i | \(-0.363970\pi\) | |||||||
\(164\) | 17.3205 | − | 4.47214i | 1.35250 | − | 0.349215i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5000 | − | 13.5554i | 0.814958 | − | 1.05211i | ||||
\(167\) | −3.46410 | −0.268060 | −0.134030 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134030 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −8.66025 | + | 11.1803i | −0.664211 | + | 0.857493i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.0000 | + | 3.87298i | −1.14374 | + | 0.295312i | ||||
\(173\) | 15.6525i | 1.19004i | 0.803712 | + | 0.595018i | \(0.202855\pi\) | ||||
−0.803712 | + | 0.595018i | \(0.797145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.06218 | − | 3.35410i | 0.456954 | − | 0.252825i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | + | 3.87298i | 0.374766 | + | 0.290292i | ||||
\(179\) | −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 | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | −8.66025 | − | 6.70820i | −0.641941 | − | 0.497245i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.0000 | + | 7.74597i | 1.32698 | + | 0.571040i | ||||
\(185\) | − | 8.94427i | − | 0.657596i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.74597i | 0.566441i | ||||||||
\(188\) | −1.73205 | − | 6.70820i | −0.126323 | − | 0.489246i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3205 | −1.25327 | −0.626634 | − | 0.779314i | \(-0.715568\pi\) | ||||
−0.626634 | + | 0.779314i | \(0.715568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.0000 | −1.79954 | −0.899770 | − | 0.436365i | \(-0.856266\pi\) | ||||
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | −9.52628 | + | 12.2984i | −0.683947 | + | 0.882972i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | + | 15.4919i | 0.285714 | + | 1.10657i | ||||
\(197\) | − | 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 | ||||||||
\(202\) | −2.50000 | − | 1.93649i | −0.175899 | − | 0.136251i | ||||
\(203\) | 17.3205 | 1.21566 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.0000 | −1.39686 | ||||||||
\(206\) | −8.66025 | − | 6.70820i | −0.603388 | − | 0.467383i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.00000 | + | 3.87298i | −0.485363 | + | 0.268543i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.4919i | − | 1.06651i | −0.845955 | − | 0.533254i | \(-0.820969\pi\) | ||
0.845955 | − | 0.533254i | \(-0.179031\pi\) | |||||||
\(212\) | 4.33013 | − | 1.11803i | 0.297394 | − | 0.0767869i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.50000 | + | 5.80948i | −0.307614 | + | 0.397128i | ||||
\(215\) | 17.3205 | 1.18125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | 3.46410 | − | 4.47214i | 0.234619 | − | 0.302891i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.50000 | + | 1.93649i | −0.505650 | + | 0.130558i | ||||
\(221\) | − | 8.94427i | − | 0.601657i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.74597i | − | 0.518708i | −0.965782 | − | 0.259354i | \(-0.916490\pi\) | ||
0.965782 | − | 0.259354i | \(-0.0835097\pi\) | |||||||
\(224\) | 21.6506 | + | 3.35410i | 1.44659 | + | 0.224105i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0000 | + | 15.4919i | 1.33038 | + | 1.03051i | ||||
\(227\) | 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 | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | −17.3205 | − | 13.4164i | −1.14208 | − | 0.884652i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | − | 11.6190i | 0.328266 | − | 0.762821i | ||||
\(233\) | − | 4.47214i | − | 0.292979i | −0.989212 | − | 0.146490i | \(-0.953202\pi\) | ||
0.989212 | − | 0.146490i | \(-0.0467975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.74597i | 0.505291i | ||||||||
\(236\) | 1.73205 | + | 6.70820i | 0.112747 | + | 0.436667i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.0000 | + | 19.3649i | −0.972306 | + | 1.25524i | ||||
\(239\) | −13.8564 | −0.896296 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 6.92820 | − | 8.94427i | 0.445362 | − | 0.574960i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | + | 7.74597i | 0.128037 | + | 0.495885i | ||||
\(245\) | − | 17.8885i | − | 1.14286i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.33013 | − | 10.0623i | 0.274963 | − | 0.638957i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.5000 | − | 9.68246i | −0.790569 | − | 0.612372i | ||||
\(251\) | 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 | ||||||||
\(254\) | −12.9904 | − | 10.0623i | −0.815089 | − | 0.631365i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | − | 13.5554i | 0.531250 | − | 0.847215i | ||||
\(257\) | 22.3607i | 1.39482i | 0.716672 | + | 0.697410i | \(0.245665\pi\) | ||||
−0.716672 | + | 0.697410i | \(0.754335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.4919i | − | 0.962622i | ||||||
\(260\) | 8.66025 | − | 2.23607i | 0.537086 | − | 0.138675i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5000 | − | 21.3014i | 1.01937 | − | 1.31601i | ||||
\(263\) | −6.92820 | −0.427211 | −0.213606 | − | 0.976920i | \(-0.568521\pi\) | ||||
−0.213606 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.00000 | −0.307148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.0000 | − | 3.87298i | 0.916271 | − | 0.236580i | ||||
\(269\) | − | 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 | \(0.885195\pi\) | |||||||
\(272\) | 8.66025 | + | 15.6525i | 0.525105 | + | 0.949071i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.00000 | + | 3.87298i | 0.302061 | + | 0.233975i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000 | 1.20168 | 0.600842 | − | 0.799368i | \(-0.294832\pi\) | ||||
0.600842 | + | 0.799368i | \(0.294832\pi\) | |||||||
\(278\) | 17.3205 | + | 13.4164i | 1.03882 | + | 0.804663i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.5000 | − | 9.68246i | −1.34463 | − | 0.578638i | ||||
\(281\) | − | 4.47214i | − | 0.266785i | −0.991063 | − | 0.133393i | \(-0.957413\pi\) | ||
0.991063 | − | 0.133393i | \(-0.0425871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9839i | 1.84180i | 0.389799 | + | 0.920900i | \(0.372544\pi\) | ||||
−0.389799 | + | 0.920900i | \(0.627456\pi\) | |||||||
\(284\) | −5.19615 | − | 20.1246i | −0.308335 | − | 1.19418i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | − | 3.87298i | 0.177394 | − | 0.229014i | ||||
\(287\) | −34.6410 | −2.04479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | −8.66025 | + | 11.1803i | −0.508548 | + | 0.656532i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.50000 | − | 9.68246i | −0.146301 | − | 0.566623i | ||||
\(293\) | 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 | ||||||
\(296\) | −10.3923 | − | 4.47214i | −0.604040 | − | 0.259938i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.50000 | − | 1.93649i | −0.144821 | − | 0.112178i | ||||
\(299\) | 13.8564 | 0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.0000 | 1.72917 | ||||||||
\(302\) | −4.33013 | − | 3.35410i | −0.249171 | − | 0.193007i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.94427i | − | 0.512148i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2379i | 1.32626i | 0.748506 | + | 0.663129i | \(0.230772\pi\) | ||||
−0.748506 | + | 0.663129i | \(0.769228\pi\) | |||||||
\(308\) | −12.9904 | + | 3.35410i | −0.740196 | + | 0.191118i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.50000 | + | 9.68246i | −0.425971 | + | 0.549927i | ||||
\(311\) | 27.7128 | 1.57145 | 0.785725 | − | 0.618576i | \(-0.212290\pi\) | ||||
0.785725 | + | 0.618576i | \(0.212290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | 0.282617 | 0.141308 | − | 0.989966i | \(-0.454869\pi\) | ||||
0.141308 | + | 0.989966i | \(0.454869\pi\) | |||||||
\(314\) | −17.3205 | + | 22.3607i | −0.977453 | + | 1.26189i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.0000 | + | 3.87298i | −0.843816 | + | 0.217872i | ||||
\(317\) | 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 | ||||||||
\(320\) | −12.9904 | + | 12.2984i | −0.726184 | + | 0.687500i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −30.0000 | − | 23.2379i | −1.67183 | − | 1.29500i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.9808 | + | 20.1246i | 1.43894 | + | 1.11460i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.0000 | + | 23.2379i | −0.552158 | + | 1.28310i | ||||
\(329\) | 13.4164i | 0.739671i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.74597i | − | 0.425757i | −0.977079 | − | 0.212878i | \(-0.931716\pi\) | ||
0.977079 | − | 0.212878i | \(-0.0682838\pi\) | |||||||
\(332\) | 6.06218 | + | 23.4787i | 0.332705 | + | 1.28856i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.00000 | − | 3.87298i | 0.164153 | − | 0.211920i | ||||
\(335\) | −17.3205 | −0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 7.79423 | − | 10.0623i | 0.423950 | − | 0.547317i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.00000 | − | 19.3649i | −0.271163 | − | 1.05021i | ||||
\(341\) | 6.70820i | 0.363270i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.87298i | − | 0.209121i | ||||||
\(344\) | 8.66025 | − | 20.1246i | 0.466930 | − | 1.08505i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.5000 | − | 13.5554i | −0.940806 | − | 0.728745i | ||||
\(347\) | 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 | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | + | 9.68246i | −0.0799503 | + | 0.516077i | ||||
\(353\) | − | 17.8885i | − | 0.952111i | −0.879415 | − | 0.476056i | \(-0.842066\pi\) | ||
0.879415 | − | 0.476056i | \(-0.157934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.2379i | 1.23334i | ||||||||
\(356\) | −8.66025 | + | 2.23607i | −0.458993 | + | 0.118511i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.50000 | − | 5.80948i | 0.237832 | − | 0.307040i | ||||
\(359\) | −31.1769 | −1.64545 | −0.822727 | − | 0.568436i | \(-0.807549\pi\) | ||||
−0.822727 | + | 0.568436i | \(0.807549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 13.8564 | − | 17.8885i | 0.728277 | − | 0.940201i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.0000 | − | 3.87298i | 0.786214 | − | 0.202999i | ||||
\(365\) | 11.1803i | 0.585206i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1109i | 1.41518i | 0.706625 | + | 0.707588i | \(0.250217\pi\) | ||||
−0.706625 | + | 0.707588i | \(0.749783\pi\) | |||||||
\(368\) | −24.2487 | + | 13.4164i | −1.26405 | + | 0.699379i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.0000 | + | 7.74597i | 0.519875 | + | 0.402694i | ||||
\(371\) | −8.66025 | −0.449618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −8.66025 | − | 6.70820i | −0.447811 | − | 0.346873i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.00000 | + | 3.87298i | 0.464140 | + | 0.199734i | ||||
\(377\) | − | 8.94427i | − | 0.460653i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0000 | − | 19.3649i | 0.767467 | − | 0.990795i | ||||
\(383\) | −24.2487 | −1.23905 | −0.619526 | − | 0.784976i | \(-0.712675\pi\) | ||||
−0.619526 | + | 0.784976i | \(0.712675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | 0.764471 | ||||||||
\(386\) | 21.6506 | − | 27.9508i | 1.10199 | − | 1.42266i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.50000 | − | 21.3014i | −0.279220 | − | 1.08142i | ||||
\(389\) | 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 | ||||||
\(392\) | −20.7846 | − | 8.94427i | −1.04978 | − | 0.451754i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.5000 | + | 21.3014i | 1.38543 | + | 1.07315i | ||||
\(395\) | 17.3205 | 0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 12.9904 | + | 10.0623i | 0.651149 | + | 0.504378i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.8885i | − | 0.893311i | −0.894706 | − | 0.446656i | \(-0.852615\pi\) | ||
0.894706 | − | 0.446656i | \(-0.147385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.74597i | − | 0.385854i | ||||||
\(404\) | 4.33013 | − | 1.11803i | 0.215432 | − | 0.0556243i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | + | 19.3649i | −0.744438 | + | 0.961065i | ||||
\(407\) | 6.92820 | 0.343418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | −0.346128 | −0.173064 | − | 0.984911i | \(-0.555367\pi\) | ||||
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 17.3205 | − | 22.3607i | 0.855399 | − | 1.10432i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.0000 | − | 3.87298i | 0.738997 | − | 0.190808i | ||||
\(413\) | − | 13.4164i | − | 0.660178i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.1109i | − | 1.33082i | ||||||
\(416\) | 1.73205 | − | 11.1803i | 0.0849208 | − | 0.548161i | ||||
\(417\) | 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 | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 17.3205 | + | 13.4164i | 0.843149 | + | 0.653101i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.50000 | + | 5.80948i | −0.121411 | + | 0.282133i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 15.4919i | − | 0.749707i | ||||||
\(428\) | −2.59808 | − | 10.0623i | −0.125583 | − | 0.486380i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.0000 | + | 19.3649i | −0.723364 | + | 0.933859i | ||||
\(431\) | 10.3923 | 0.500580 | 0.250290 | − | 0.968171i | \(-0.419474\pi\) | ||||
0.250290 | + | 0.968171i | \(0.419474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | −0.624740 | −0.312370 | − | 0.949960i | \(-0.601123\pi\) | ||||
−0.312370 | + | 0.949960i | \(0.601123\pi\) | |||||||
\(434\) | −12.9904 | + | 16.7705i | −0.623558 | + | 0.805010i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 7.74597i | 0.0957826 | + | 0.370965i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.87298i | 0.184847i | 0.995720 | + | 0.0924237i | \(0.0294614\pi\) | ||||
−0.995720 | + | 0.0924237i | \(0.970539\pi\) | |||||||
\(440\) | 4.33013 | − | 10.0623i | 0.206431 | − | 0.479702i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0000 | + | 7.74597i | 0.475651 | + | 0.368438i | ||||
\(443\) | 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 | ||||||||
\(446\) | 8.66025 | + | 6.70820i | 0.410075 | + | 0.317643i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.5000 | + | 21.3014i | −1.06303 | + | 1.00640i | ||||
\(449\) | − | 17.8885i | − | 0.844213i | −0.906546 | − | 0.422106i | \(-0.861291\pi\) | ||
0.906546 | − | 0.422106i | \(-0.138709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.4919i | − | 0.729487i | ||||||
\(452\) | −34.6410 | + | 8.94427i | −1.62938 | + | 0.420703i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00000 | + | 3.87298i | −0.140797 | + | 0.181768i | ||||
\(455\) | −17.3205 | −0.811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | −1.73205 | + | 2.23607i | −0.0809334 | + | 0.104485i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.0000 | − | 7.74597i | 1.39876 | − | 0.361158i | ||||
\(461\) | − | 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 | \(-0.0286856\pi\) | |||||||
\(464\) | 8.66025 | + | 15.6525i | 0.402042 | + | 0.726648i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.00000 | + | 3.87298i | 0.231621 | + | 0.179412i | ||||
\(467\) | −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 | ||||||||
\(470\) | −8.66025 | − | 6.70820i | −0.399468 | − | 0.309426i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.00000 | − | 3.87298i | −0.414259 | − | 0.178269i | ||||
\(473\) | 13.4164i | 0.616887i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.66025 | − | 33.5410i | −0.396942 | − | 1.53735i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | − | 15.4919i | 0.548867 | − | 0.708585i | ||||
\(479\) | −17.3205 | −0.791394 | −0.395697 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395697 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | −12.1244 | + | 15.6525i | −0.552249 | + | 0.712951i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.00000 | + | 15.4919i | 0.181818 | + | 0.704179i | ||||
\(485\) | 24.5967i | 1.11688i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2379i | 1.05301i | 0.850172 | + | 0.526505i | \(0.176498\pi\) | ||||
−0.850172 | + | 0.526505i | \(0.823502\pi\) | |||||||
\(488\) | −10.3923 | − | 4.47214i | −0.470438 | − | 0.202444i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 20.0000 | + | 15.4919i | 0.903508 | + | 0.699854i | ||||
\(491\) | −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 | ||||||||
\(496\) | 7.50000 | + | 13.5554i | 0.336760 | + | 0.608657i | ||||
\(497\) | 40.2492i | 1.80542i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.7298i | − | 1.73379i | −0.498495 | − | 0.866893i | \(-0.666114\pi\) | ||
0.498495 | − | 0.866893i | \(-0.333886\pi\) | |||||||
\(500\) | 21.6506 | − | 5.59017i | 0.968246 | − | 0.250000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.00000 | + | 11.6190i | −0.401690 | + | 0.518579i | ||||
\(503\) | 20.7846 | 0.926740 | 0.463370 | − | 0.886165i | \(-0.346640\pi\) | ||||
0.463370 | + | 0.886165i | \(0.346640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 10.3923 | − | 13.4164i | 0.461994 | − | 0.596432i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.5000 | − | 5.80948i | 0.998276 | − | 0.257754i | ||||
\(509\) | − | 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 | ||||||||
\(512\) | 7.79423 | + | 21.2426i | 0.344459 | + | 0.938801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.0000 | − | 19.3649i | −1.10270 | − | 0.854150i | ||||
\(515\) | −17.3205 | −0.763233 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 17.3205 | + | 13.4164i | 0.761019 | + | 0.589483i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.00000 | + | 11.6190i | −0.219265 | + | 0.509525i | ||||
\(521\) | 22.3607i | 0.979639i | 0.871824 | + | 0.489820i | \(0.162937\pi\) | ||||
−0.871824 | + | 0.489820i | \(0.837063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.2379i | − | 1.01612i | −0.861321 | − | 0.508061i | \(-0.830362\pi\) | ||
0.861321 | − | 0.508061i | \(-0.169638\pi\) | |||||||
\(524\) | 9.52628 | + | 36.8951i | 0.416157 | + | 1.61177i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | − | 7.74597i | 0.261612 | − | 0.337740i | ||||
\(527\) | −17.3205 | −0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 4.33013 | − | 5.59017i | 0.188089 | − | 0.242821i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.8885i | 0.774839i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.6190i | 0.502331i | ||||||||
\(536\) | −8.66025 | + | 20.1246i | −0.374066 | + | 0.869251i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.00000 | + | 3.87298i | 0.215565 | + | 0.166976i | ||||
\(539\) | 13.8564 | 0.596838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | −12.9904 | − | 10.0623i | −0.557985 | − | 0.432213i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.0000 | − | 3.87298i | −1.07187 | − | 0.166053i | ||||
\(545\) | − | 8.94427i | − | 0.383131i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.74597i | − | 0.331194i | −0.986194 | − | 0.165597i | \(-0.947045\pi\) | ||
0.986194 | − | 0.165597i | \(-0.0529550\pi\) | |||||||
\(548\) | −8.66025 | + | 2.23607i | −0.369948 | + | 0.0955201i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | 1.27573 | ||||||||
\(554\) | −17.3205 | + | 22.3607i | −0.735878 | + | 0.950014i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.0000 | + | 7.74597i | −1.27228 | + | 0.328502i | ||||
\(557\) | 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 | ||||||
\(560\) | 30.3109 | − | 16.7705i | 1.28087 | − | 0.708683i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | + | 3.87298i | 0.210912 | + | 0.163372i | ||||
\(563\) | −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 | ||||||||
\(566\) | −34.6410 | − | 26.8328i | −1.45607 | − | 1.12787i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.0000 | + | 11.6190i | 1.13289 | + | 0.487520i | ||||
\(569\) | 35.7771i | 1.49985i | 0.661521 | + | 0.749927i | \(0.269911\pi\) | ||||
−0.661521 | + | 0.749927i | \(0.730089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.74597i | 0.324159i | 0.986778 | + | 0.162079i | \(0.0518200\pi\) | ||||
−0.986778 | + | 0.162079i | \(0.948180\pi\) | |||||||
\(572\) | 1.73205 | + | 6.70820i | 0.0724207 | + | 0.280484i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30.0000 | − | 38.7298i | 1.25218 | − | 1.61655i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 2.59808 | − | 3.35410i | 0.108066 | − | 0.139512i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.00000 | − | 19.3649i | −0.207614 | − | 0.804084i | ||||
\(581\) | − | 46.9574i | − | 1.94812i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.87298i | − | 0.160403i | ||||||
\(584\) | 12.9904 | + | 5.59017i | 0.537546 | + | 0.231323i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.0000 | − | 19.3649i | −1.03274 | − | 0.799957i | ||||
\(587\) | 19.0526 | 0.786383 | 0.393192 | − | 0.919457i | \(-0.371371\pi\) | ||||
0.393192 | + | 0.919457i | \(0.371371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 8.66025 | + | 6.70820i | 0.356537 | + | 0.276172i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.0000 | − | 7.74597i | 0.575396 | − | 0.318357i | ||||
\(593\) | − | 4.47214i | − | 0.183649i | −0.995775 | − | 0.0918243i | \(-0.970730\pi\) | ||
0.995775 | − | 0.0918243i | \(-0.0292698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.7298i | 1.58777i | ||||||||
\(596\) | 4.33013 | − | 1.11803i | 0.177369 | − | 0.0457965i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0000 | + | 15.4919i | −0.490716 | + | 0.633512i | ||||
\(599\) | 17.3205 | 0.707697 | 0.353848 | − | 0.935303i | \(-0.384873\pi\) | ||||
0.353848 | + | 0.935303i | \(0.384873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.0000 | −1.26452 | −0.632258 | − | 0.774758i | \(-0.717872\pi\) | ||||
−0.632258 | + | 0.774758i | \(0.717872\pi\) | |||||||
\(602\) | −25.9808 | + | 33.5410i | −1.05890 | + | 1.36703i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.50000 | − | 1.93649i | 0.305171 | − | 0.0787947i | ||||
\(605\) | − | 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 | ||||||||
\(610\) | 10.0000 | + | 7.74597i | 0.404888 | + | 0.313625i | ||||
\(611\) | 6.92820 | 0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | −25.9808 | − | 20.1246i | −1.04850 | − | 0.812163i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.50000 | − | 17.4284i | 0.302184 | − | 0.702211i | ||||
\(617\) | − | 17.8885i | − | 0.720166i | −0.932920 | − | 0.360083i | \(-0.882748\pi\) | ||
0.932920 | − | 0.360083i | \(-0.117252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.7298i | 1.55668i | 0.627841 | + | 0.778342i | \(0.283939\pi\) | ||||
−0.627841 | + | 0.778342i | \(0.716061\pi\) | |||||||
\(620\) | −4.33013 | − | 16.7705i | −0.173902 | − | 0.673520i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | + | 30.9839i | −0.962312 | + | 1.24234i | ||||
\(623\) | 17.3205 | 0.693932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | −4.33013 | + | 5.59017i | −0.173067 | + | 0.223428i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | − | 38.7298i | −0.399043 | − | 1.54549i | ||||
\(629\) | 17.8885i | 0.713263i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8569i | 1.38763i | 0.720154 | + | 0.693815i | \(0.244071\pi\) | ||||
−0.720154 | + | 0.693815i | \(0.755929\pi\) | |||||||
\(632\) | 8.66025 | − | 20.1246i | 0.344486 | − | 0.800514i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.5000 | − | 13.5554i | −0.695014 | − | 0.538355i | ||||
\(635\) | −25.9808 | −1.03102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0000 | −0.633943 | ||||||||
\(638\) | −8.66025 | − | 6.70820i | −0.342863 | − | 0.265580i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.50000 | − | 25.1744i | −0.0988212 | − | 0.995105i | ||||
\(641\) | − | 44.7214i | − | 1.76639i | −0.469008 | − | 0.883194i | \(-0.655389\pi\) | ||
0.469008 | − | 0.883194i | \(-0.344611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.9839i | 1.22188i | 0.791675 | + | 0.610942i | \(0.209209\pi\) | ||||
−0.791675 | + | 0.610942i | \(0.790791\pi\) | |||||||
\(644\) | 51.9615 | − | 13.4164i | 2.04757 | − | 0.528681i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.0000 | + | 11.6190i | −1.76234 | + | 0.455033i | ||||
\(653\) | − | 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 | ||||||
\(656\) | −17.3205 | − | 31.3050i | −0.676252 | − | 1.22225i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.0000 | − | 11.6190i | −0.584761 | − | 0.452954i | ||||
\(659\) | 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 | \(-0.600719\pi\) | ||||
−0.311164 | + | 0.950356i | \(0.600719\pi\) | |||||||
\(662\) | 8.66025 | + | 6.70820i | 0.336590 | + | 0.260722i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.5000 | − | 13.5554i | −1.22244 | − | 0.526053i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 30.9839i | − | 1.19970i | ||||||
\(668\) | 1.73205 | + | 6.70820i | 0.0670151 | + | 0.259548i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.0000 | − | 19.3649i | 0.579501 | − | 0.748132i | ||||
\(671\) | 6.92820 | 0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0000 | 0.886585 | 0.443292 | − | 0.896377i | \(-0.353810\pi\) | ||||
0.443292 | + | 0.896377i | \(0.353810\pi\) | |||||||
\(674\) | 8.66025 | − | 11.1803i | 0.333581 | − | 0.430651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 17.4284i | 0.173077 | + | 0.670324i | ||||
\(677\) | 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 | ||||||||
\(680\) | 25.9808 | + | 11.1803i | 0.996317 | + | 0.428746i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.50000 | − | 5.80948i | −0.287190 | − | 0.222456i | ||||
\(683\) | −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 | ||||||||
\(686\) | 4.33013 | + | 3.35410i | 0.165325 | + | 0.128060i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.0000 | + | 27.1109i | 0.571870 | + | 1.03359i | ||||
\(689\) | 4.47214i | 0.170375i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4919i | 0.589341i | 0.955599 | + | 0.294670i | \(0.0952099\pi\) | ||||
−0.955599 | + | 0.294670i | \(0.904790\pi\) | |||||||
\(692\) | 30.3109 | − | 7.82624i | 1.15225 | − | 0.297509i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.5000 | + | 36.7933i | −1.08185 | + | 1.39666i | ||||
\(695\) | 34.6410 | 1.31401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.0000 | 1.51511 | ||||||||
\(698\) | 13.8564 | − | 17.8885i | 0.524473 | − | 0.677091i | ||||
\(699\) | 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 | ||||||||
\(704\) | −9.52628 | − | 10.0623i | −0.359035 | − | 0.379237i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.0000 | + | 15.4919i | 0.752710 | + | 0.583047i | ||||
\(707\) | −8.66025 | −0.325702 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.0000 | 1.20179 | 0.600893 | − | 0.799330i | \(-0.294812\pi\) | ||||
0.600893 | + | 0.799330i | \(0.294812\pi\) | |||||||
\(710\) | −25.9808 | − | 20.1246i | −0.975041 | − | 0.755263i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | − | 11.6190i | 0.187383 | − | 0.435439i | ||||
\(713\) | − | 26.8328i | − | 1.00490i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.74597i | − | 0.289683i | ||||||
\(716\) | 2.59808 | + | 10.0623i | 0.0970947 | + | 0.376046i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.0000 | − | 34.8569i | 1.00763 | − | 1.30085i | ||||
\(719\) | 20.7846 | 0.775135 | 0.387568 | − | 0.921841i | \(-0.373315\pi\) | ||||
0.387568 | + | 0.921841i | \(0.373315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | −16.4545 | + | 21.2426i | −0.612372 | + | 0.790569i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.00000 | + | 30.9839i | 0.297318 | + | 1.15151i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.6028i | − | 1.58005i | −0.613074 | − | 0.790026i | \(-0.710067\pi\) | ||
0.613074 | − | 0.790026i | \(-0.289933\pi\) | |||||||
\(728\) | −8.66025 | + | 20.1246i | −0.320970 | + | 0.745868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.5000 | − | 9.68246i | −0.462646 | − | 0.358364i | ||||
\(731\) | −34.6410 | −1.28124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.00000 | 0.295487 | 0.147743 | − | 0.989026i | \(-0.452799\pi\) | ||||
0.147743 | + | 0.989026i | \(0.452799\pi\) | |||||||
\(734\) | −30.3109 | − | 23.4787i | −1.11880 | − | 0.866615i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | − | 38.7298i | 0.221163 | − | 1.42760i | ||||
\(737\) | − | 13.4164i | − | 0.494200i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.2379i | 0.854820i | 0.904058 | + | 0.427410i | \(0.140574\pi\) | ||||
−0.904058 | + | 0.427410i | \(0.859426\pi\) | |||||||
\(740\) | −17.3205 | + | 4.47214i | −0.636715 | + | 0.164399i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.50000 | − | 9.68246i | 0.275334 | − | 0.355454i | ||||
\(743\) | −24.2487 | −0.889599 | −0.444799 | − | 0.895630i | \(-0.646725\pi\) | ||||
−0.444799 | + | 0.895630i | \(0.646725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.00000 | −0.183186 | ||||||||
\(746\) | 8.66025 | − | 11.1803i | 0.317074 | − | 0.409341i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.0000 | − | 3.87298i | 0.548454 | − | 0.141610i | ||||
\(749\) | 20.1246i | 0.735337i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.87298i | − | 0.141327i | −0.997500 | − | 0.0706636i | \(-0.977488\pi\) | ||
0.997500 | − | 0.0706636i | \(-0.0225117\pi\) | |||||||
\(752\) | −12.1244 | + | 6.70820i | −0.442130 | + | 0.244623i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.0000 | + | 7.74597i | 0.364179 | + | 0.282091i | ||||
\(755\) | −8.66025 | −0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.8885i | − | 0.648459i | −0.945978 | − | 0.324230i | \(-0.894895\pi\) | ||
0.945978 | − | 0.324230i | \(-0.105105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 15.4919i | − | 0.560846i | ||||||
\(764\) | 8.66025 | + | 33.5410i | 0.313317 | + | 1.21347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0000 | − | 27.1109i | 0.758761 | − | 0.979556i | ||||
\(767\) | −6.92820 | −0.250163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0000 | 0.396670 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(770\) | −12.9904 | + | 16.7705i | −0.468141 | + | 0.604367i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.5000 | + | 48.4123i | 0.449885 | + | 1.74240i | ||||
\(773\) | − | 4.47214i | − | 0.160852i | −0.996761 | − | 0.0804258i | \(-0.974372\pi\) | ||
0.996761 | − | 0.0804258i | \(-0.0256280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.5788 | + | 12.2984i | 1.02592 | + | 0.441486i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.50000 | − | 1.93649i | −0.0896293 | − | 0.0694266i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 34.6410 | + | 26.8328i | 1.23876 | + | 0.959540i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | − | 15.4919i | 1.00000 | − | 0.553283i | ||||
\(785\) | 44.7214i | 1.59617i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15.4919i | − | 0.552228i | −0.961125 | − | 0.276114i | \(-0.910953\pi\) | ||
0.961125 | − | 0.276114i | \(-0.0890467\pi\) | |||||||
\(788\) | −47.6314 | + | 12.2984i | −1.69680 | + | 0.438111i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.0000 | + | 19.3649i | −0.533676 | + | 0.688973i | ||||
\(791\) | 69.2820 | 2.46339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | −12.1244 | + | 15.6525i | −0.430277 | + | 0.555486i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.5000 | + | 5.80948i | −0.797491 | + | 0.205911i | ||||
\(797\) | 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 | ||||||||
\(802\) | 20.0000 | + | 15.4919i | 0.706225 | + | 0.547039i | ||||
\(803\) | −8.66025 | −0.305614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60.0000 | −2.11472 | ||||||||
\(806\) | 8.66025 | + | 6.70820i | 0.305044 | + | 0.236286i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.50000 | + | 5.80948i | −0.0879497 | + | 0.204377i | ||||
\(809\) | − | 4.47214i | − | 0.157232i | −0.996905 | − | 0.0786160i | \(-0.974950\pi\) | ||
0.996905 | − | 0.0786160i | \(-0.0250501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −8.66025 | − | 33.5410i | −0.303915 | − | 1.17706i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.00000 | + | 7.74597i | −0.210300 | + | 0.271496i | ||||
\(815\) | 51.9615 | 1.82013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.06218 | − | 7.82624i | 0.211959 | − | 0.273638i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.0000 | + | 38.7298i | 0.349215 | + | 1.35250i | ||||
\(821\) | − | 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 | \(-0.156653\pi\) | |||||||
\(824\) | −8.66025 | + | 20.1246i | −0.301694 | + | 0.701074i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | + | 11.6190i | 0.521917 | + | 0.404275i | ||||
\(827\) | −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 | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 30.3109 | + | 23.4787i | 1.05211 | + | 0.814958i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.0000 | + | 11.6190i | 0.381356 | + | 0.402815i | ||||
\(833\) | 35.7771i | 1.23960i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 7.74597i | − | 0.268060i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.0000 | + | 19.3649i | −0.518166 | + | 0.668950i | ||||
\(839\) | −38.1051 | −1.31553 | −0.657767 | − | 0.753221i | \(-0.728499\pi\) | ||||
−0.657767 | + | 0.753221i | \(0.728499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 3.46410 | − | 4.47214i | 0.119381 | − | 0.154120i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.0000 | + | 7.74597i | −1.03264 | + | 0.266627i | ||||
\(845\) | − | 20.1246i | − | 0.692308i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30.9839i | − | 1.06462i | ||||||
\(848\) | −4.33013 | − | 7.82624i | −0.148697 | − | 0.268754i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7128 | −0.949983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | 0.0684787 | 0.0342393 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342393 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(854\) | 17.3205 | + | 13.4164i | 0.592696 | + | 0.459100i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5000 | + | 5.80948i | 0.461421 | + | 0.198564i | ||||
\(857\) | − | 4.47214i | − | 0.152765i | −0.997079 | − | 0.0763826i | \(-0.975663\pi\) | ||
0.997079 | − | 0.0763826i | \(-0.0243370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.4919i | − | 0.528578i | −0.964444 | − | 0.264289i | \(-0.914863\pi\) | ||
0.964444 | − | 0.264289i | \(-0.0851373\pi\) | |||||||
\(860\) | −8.66025 | − | 33.5410i | −0.295312 | − | 1.14374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.00000 | + | 11.6190i | −0.306541 | + | 0.395743i | ||||
\(863\) | −20.7846 | −0.707516 | −0.353758 | − | 0.935337i | \(-0.615096\pi\) | ||||
−0.353758 | + | 0.935337i | \(0.615096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0000 | −1.19004 | ||||||||
\(866\) | 11.2583 | − | 14.5344i | 0.382574 | − | 0.493900i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.50000 | − | 29.0474i | −0.254567 | − | 0.985932i | ||||
\(869\) | 13.4164i | 0.455120i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4919i | 0.524924i | ||||||||
\(872\) | −10.3923 | − | 4.47214i | −0.351928 | − | 0.151446i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.3013 | −1.46385 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0000 | −1.14810 | −0.574049 | − | 0.818821i | \(-0.694628\pi\) | ||||
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | −4.33013 | − | 3.35410i | −0.146135 | − | 0.113195i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.50000 | + | 13.5554i | 0.252825 | + | 0.456954i | ||||
\(881\) | 22.3607i | 0.753350i | 0.926345 | + | 0.376675i | \(0.122933\pi\) | ||||
−0.926345 | + | 0.376675i | \(0.877067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −17.3205 | + | 4.47214i | −0.582552 | + | 0.150414i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.0000 | + | 27.1109i | −0.705509 | + | 0.910808i | ||||
\(887\) | 38.1051 | 1.27944 | 0.639722 | − | 0.768606i | \(-0.279049\pi\) | ||||
0.639722 | + | 0.768606i | \(0.279049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.0000 | −1.50925 | ||||||||
\(890\) | −8.66025 | + | 11.1803i | −0.290292 | + | 0.374766i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.0000 | + | 3.87298i | −0.502237 | + | 0.129677i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.6190i | − | 0.388379i | ||||||
\(896\) | −4.33013 | − | 43.6033i | −0.144659 | − | 1.45668i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.0000 | + | 15.4919i | 0.667409 | + | 0.516973i | ||||
\(899\) | −17.3205 | −0.577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | 17.3205 | + | 13.4164i | 0.576710 | + | 0.446718i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.0000 | − | 46.4758i | 0.665190 | − | 1.54576i | ||||
\(905\) | − | 35.7771i | − | 1.18927i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4919i | 0.514401i | 0.966358 | + | 0.257201i | \(0.0828001\pi\) | ||||
−0.966358 | + | 0.257201i | \(0.917200\pi\) | |||||||
\(908\) | −1.73205 | − | 6.70820i | −0.0574801 | − | 0.222620i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.0000 | − | 19.3649i | 0.497245 | − | 0.641941i | ||||
\(911\) | 45.0333 | 1.49202 | 0.746010 | − | 0.665934i | \(-0.231967\pi\) | ||||
0.746010 | + | 0.665934i | \(0.231967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0000 | 0.694999 | ||||||||
\(914\) | 26.8468 | − | 34.6591i | 0.888013 | − | 1.14642i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.00000 | − | 3.87298i | −0.0330409 | − | 0.127967i | ||||
\(917\) | − | 73.7902i | − | 2.43677i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 11.6190i | − | 0.383274i | −0.981466 | − | 0.191637i | \(-0.938620\pi\) | ||
0.981466 | − | 0.191637i | \(-0.0613796\pi\) | |||||||
\(920\) | −17.3205 | + | 40.2492i | −0.571040 | + | 1.32698i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.5000 | + | 32.9204i | 1.39966 | + | 1.08417i | ||||
\(923\) | 20.7846 | 0.684134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.33013 | + | 3.35410i | 0.142297 | + | 0.110223i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.0000 | − | 3.87298i | −0.820665 | − | 0.127137i | ||||
\(929\) | − | 44.7214i | − | 1.46726i | −0.679549 | − | 0.733630i | \(-0.737825\pi\) | ||
0.679549 | − | 0.733630i | \(-0.262175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.66025 | + | 2.23607i | −0.283676 | + | 0.0732448i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50000 | − | 5.80948i | 0.147244 | − | 0.190092i | ||||
\(935\) | −17.3205 | −0.566441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0000 | −1.01273 | −0.506363 | − | 0.862320i | \(-0.669010\pi\) | ||||
−0.506363 | + | 0.862320i | \(0.669010\pi\) | |||||||
\(938\) | 25.9808 | − | 33.5410i | 0.848302 | − | 1.09515i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.0000 | − | 3.87298i | 0.489246 | − | 0.126323i | ||||
\(941\) | 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 | ||||||||
\(944\) | 12.1244 | − | 6.70820i | 0.394614 | − | 0.218333i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.0000 | − | 11.6190i | −0.487692 | − | 0.377765i | ||||
\(947\) | 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 | ||||||||
\(952\) | 45.0000 | + | 19.3649i | 1.45846 | + | 0.627621i | ||||
\(953\) | 35.7771i | 1.15893i | 0.814996 | + | 0.579467i | \(0.196739\pi\) | ||||
−0.814996 | + | 0.579467i | \(0.803261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38.7298i | − | 1.25327i | ||||||
\(956\) | 6.92820 | + | 26.8328i | 0.224074 | + | 0.867835i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.0000 | − | 19.3649i | 0.484628 | − | 0.625652i | ||||
\(959\) | 17.3205 | 0.559308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.0000 | 0.516129 | ||||||||
\(962\) | 6.92820 | − | 8.94427i | 0.223374 | − | 0.288375i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.00000 | − | 27.1109i | −0.225455 | − | 0.873183i | ||||
\(965\) | − | 55.9017i | − | 1.79954i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27.1109i | − | 0.871827i | −0.899989 | − | 0.435914i | \(-0.856425\pi\) | ||
0.899989 | − | 0.435914i | \(-0.143575\pi\) | |||||||
\(968\) | −20.7846 | − | 8.94427i | −0.668043 | − | 0.287480i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.5000 | − | 21.3014i | −0.882972 | − | 0.683947i | ||||
\(971\) | −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 | ||||||||
\(974\) | −25.9808 | − | 20.1246i | −0.832477 | − | 0.644834i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0000 | − | 7.74597i | 0.448129 | − | 0.247942i | ||||
\(977\) | 49.1935i | 1.57384i | 0.617055 | + | 0.786920i | \(0.288325\pi\) | ||||
−0.617055 | + | 0.786920i | \(0.711675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.74597i | 0.247562i | ||||||||
\(980\) | −34.6410 | + | 8.94427i | −1.10657 | + | 0.285714i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.50000 | − | 9.68246i | 0.239335 | − | 0.308980i | ||||
\(983\) | 24.2487 | 0.773414 | 0.386707 | − | 0.922203i | \(-0.373613\pi\) | ||||
0.386707 | + | 0.922203i | \(0.373613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.0000 | 1.75245 | ||||||||
\(986\) | 17.3205 | − | 22.3607i | 0.551597 | − | 0.712109i | ||||
\(987\) | 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 | \(0.940919\pi\) | |||||||
\(992\) | −21.6506 | − | 3.35410i | −0.687408 | − | 0.106493i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −45.0000 | − | 34.8569i | −1.42731 | − | 1.10559i | ||||
\(995\) | 25.9808 | 0.823646 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000 | 0.443384 | 0.221692 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221692 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(998\) | 43.3013 | + | 33.5410i | 1.37068 | + | 1.06172i | ||||
\(999\) | 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 | 108.2.b.a.107.2 | yes | 4 | |
3.2 | odd | 2 | inner | 108.2.b.a.107.3 | yes | 4 | |
4.3 | odd | 2 | inner | 108.2.b.a.107.4 | yes | 4 | |
8.3 | odd | 2 | 1728.2.c.c.1727.1 | 4 | |||
8.5 | even | 2 | 1728.2.c.c.1727.2 | 4 | |||
9.2 | odd | 6 | 324.2.h.d.215.1 | 8 | |||
9.4 | even | 3 | 324.2.h.d.107.2 | 8 | |||
9.5 | odd | 6 | 324.2.h.d.107.3 | 8 | |||
9.7 | even | 3 | 324.2.h.d.215.4 | 8 | |||
12.11 | even | 2 | inner | 108.2.b.a.107.1 | ✓ | 4 | |
24.5 | odd | 2 | 1728.2.c.c.1727.4 | 4 | |||
24.11 | even | 2 | 1728.2.c.c.1727.3 | 4 | |||
36.7 | odd | 6 | 324.2.h.d.215.3 | 8 | |||
36.11 | even | 6 | 324.2.h.d.215.2 | 8 | |||
36.23 | even | 6 | 324.2.h.d.107.4 | 8 | |||
36.31 | odd | 6 | 324.2.h.d.107.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.b.a.107.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
108.2.b.a.107.2 | yes | 4 | 1.1 | even | 1 | trivial | |
108.2.b.a.107.3 | yes | 4 | 3.2 | odd | 2 | inner | |
108.2.b.a.107.4 | yes | 4 | 4.3 | odd | 2 | inner | |
324.2.h.d.107.1 | 8 | 36.31 | odd | 6 | |||
324.2.h.d.107.2 | 8 | 9.4 | even | 3 | |||
324.2.h.d.107.3 | 8 | 9.5 | odd | 6 | |||
324.2.h.d.107.4 | 8 | 36.23 | even | 6 | |||
324.2.h.d.215.1 | 8 | 9.2 | odd | 6 | |||
324.2.h.d.215.2 | 8 | 36.11 | even | 6 | |||
324.2.h.d.215.3 | 8 | 36.7 | odd | 6 | |||
324.2.h.d.215.4 | 8 | 9.7 | even | 3 | |||
1728.2.c.c.1727.1 | 4 | 8.3 | odd | 2 | |||
1728.2.c.c.1727.2 | 4 | 8.5 | even | 2 | |||
1728.2.c.c.1727.3 | 4 | 24.11 | even | 2 | |||
1728.2.c.c.1727.4 | 4 | 24.5 | odd | 2 |