Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(737,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bj (of order \(4\), degree \(2\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1313.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1313 |
Dual form | 2880.2.bj.a.737.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 0.224745 | − | 2.22474i | 0.100509 | − | 0.994936i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | + | 1.41421i | −0.534522 | + | 0.534522i | −0.921915 | − | 0.387392i | \(-0.873376\pi\) |
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.14626 | − | 3.14626i | 0.872617 | − | 0.872617i | −0.120140 | − | 0.992757i | \(-0.538334\pi\) |
0.992757 | + | 0.120140i | \(0.0383344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.87832 | + | 4.87832i | 1.18317 | + | 1.18317i | 0.978920 | + | 0.204246i | \(0.0654741\pi\) |
0.204246 | + | 0.978920i | \(0.434526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.89898 | −1.58273 | −0.791367 | − | 0.611341i | \(-0.790630\pi\) | ||||
−0.791367 | + | 0.611341i | \(0.790630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.44949 | + | 4.44949i | −0.927783 | + | 0.927783i | −0.997562 | − | 0.0697797i | \(-0.977770\pi\) |
0.0697797 | + | 0.997562i | \(0.477770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89898 | − | 1.00000i | −0.979796 | − | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.44949i | 1.56903i | 0.620109 | + | 0.784515i | \(0.287088\pi\) | ||||
−0.620109 | + | 0.784515i | \(0.712912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.75663 | 1.75234 | 0.876171 | − | 0.482000i | \(-0.160089\pi\) | ||||
0.876171 | + | 0.482000i | \(0.160089\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | + | 3.46410i | 0.478091 | + | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51059 | + | 2.51059i | 0.412738 | + | 0.412738i | 0.882691 | − | 0.469953i | \(-0.155729\pi\) |
−0.469953 | + | 0.882691i | \(0.655729\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.41421i | − | 0.220863i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) | ||
0.993884 | − | 0.110432i | \(-0.0352233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.89898 | − | 6.89898i | 1.05208 | − | 1.05208i | 0.0535176 | − | 0.998567i | \(-0.482957\pi\) |
0.998567 | − | 0.0535176i | \(-0.0170433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.55051 | − | 1.55051i | −0.226165 | − | 0.226165i | 0.584923 | − | 0.811089i | \(-0.301125\pi\) |
−0.811089 | + | 0.584923i | \(0.801125\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000i | 0.428571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.89898 | + | 6.89898i | 0.947648 | + | 0.947648i | 0.998696 | − | 0.0510485i | \(-0.0162563\pi\) |
−0.0510485 | + | 0.998696i | \(0.516256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.778539 | + | 7.70674i | −0.104978 | + | 1.03918i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.635674i | − | 0.0827578i | −0.999144 | − | 0.0413789i | \(-0.986825\pi\) | ||
0.999144 | − | 0.0413789i | \(-0.0131751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.56388i | − | 0.968455i | −0.874942 | − | 0.484228i | \(-0.839101\pi\) | ||
0.874942 | − | 0.484228i | \(-0.160899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.29253 | − | 7.70674i | −0.780492 | − | 0.955904i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.10102i | − | 0.368023i | −0.982924 | − | 0.184012i | \(-0.941092\pi\) | ||
0.982924 | − | 0.184012i | \(-0.0589084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.89898 | + | 1.89898i | 0.222259 | + | 0.222259i | 0.809449 | − | 0.587190i | \(-0.199766\pi\) |
−0.587190 | + | 0.809449i | \(0.699766\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89898 | − | 4.89898i | 0.558291 | − | 0.558291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1421i | 1.59111i | 0.605878 | + | 0.795557i | \(0.292822\pi\) | ||||
−0.605878 | + | 0.795557i | \(0.707178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.19275 | − | 2.19275i | −0.240686 | − | 0.240686i | 0.576448 | − | 0.817134i | \(-0.304438\pi\) |
−0.817134 | + | 0.576448i | \(0.804438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.9494 | − | 9.75663i | 1.29609 | − | 1.05826i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264 | 0.449719 | 0.224860 | − | 0.974391i | \(-0.427808\pi\) | ||||
0.224860 | + | 0.974391i | \(0.427808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.89898i | 0.932867i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.55051 | + | 15.3485i | −0.159079 | + | 1.57472i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.89898 | − | 1.89898i | 0.192812 | − | 0.192812i | −0.604098 | − | 0.796910i | \(-0.706466\pi\) |
0.796910 | + | 0.604098i | \(0.206466\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.34847 | 0.532193 | 0.266096 | − | 0.963946i | \(-0.414266\pi\) | ||||
0.266096 | + | 0.963946i | \(0.414266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8065 | + | 11.8065i | 1.16333 | + | 1.16333i | 0.983742 | + | 0.179589i | \(0.0574768\pi\) |
0.179589 | + | 0.983742i | \(0.442523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.19275 | + | 2.19275i | −0.211981 | + | 0.211981i | −0.805109 | − | 0.593127i | \(-0.797893\pi\) |
0.593127 | + | 0.805109i | \(0.297893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9494 | 1.14454 | 0.572272 | − | 0.820064i | \(-0.306062\pi\) | ||||
0.572272 | + | 0.820064i | \(0.306062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9494 | + | 11.9494i | −1.12410 | + | 1.12410i | −0.132985 | + | 0.991118i | \(0.542456\pi\) |
−0.991118 | + | 0.132985i | \(0.957544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.89898 | + | 10.8990i | 0.829834 | + | 1.01634i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.7980 | −1.26486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.32577 | + | 10.6742i | −0.297465 | + | 0.954733i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.97809 | − | 8.97809i | 0.796677 | − | 0.796677i | −0.185893 | − | 0.982570i | \(-0.559518\pi\) |
0.982570 | + | 0.185893i | \(0.0595178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0492 | 1.40222 | 0.701111 | − | 0.713052i | \(-0.252688\pi\) | ||||
0.701111 | + | 0.713052i | \(0.252688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.75663 | − | 9.75663i | 0.846007 | − | 0.846007i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.56388 | − | 7.56388i | −0.646226 | − | 0.646226i | 0.305853 | − | 0.952079i | \(-0.401058\pi\) |
−0.952079 | + | 0.305853i | \(0.901058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.79796 | 0.661414 | 0.330707 | − | 0.943733i | \(-0.392713\pi\) | ||||
0.330707 | + | 0.943733i | \(0.392713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.8990 | + | 10.8990i | −0.911418 | + | 0.911418i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7980 | + | 1.89898i | 1.56109 | + | 0.157702i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5505i | 0.946255i | 0.880994 | + | 0.473127i | \(0.156875\pi\) | ||||
−0.880994 | + | 0.473127i | \(0.843125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.38551 | −0.356887 | −0.178444 | − | 0.983950i | \(-0.557106\pi\) | ||||
−0.178444 | + | 0.983950i | \(0.557106\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.19275 | − | 21.7060i | 0.176126 | − | 1.74347i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.87492 | + | 1.87492i | 0.149635 | + | 0.149635i | 0.777955 | − | 0.628320i | \(-0.216257\pi\) |
−0.628320 | + | 0.777955i | \(0.716257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.5851i | − | 0.991841i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.79796 | + | 3.79796i | −0.297479 | + | 0.297479i | −0.840026 | − | 0.542547i | \(-0.817460\pi\) |
0.542547 | + | 0.840026i | \(0.317460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.55051 | − | 3.55051i | −0.274747 | − | 0.274747i | 0.556261 | − | 0.831008i | \(-0.312236\pi\) |
−0.831008 | + | 0.556261i | \(0.812236\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.79796i | − | 0.522920i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55051 | − | 1.55051i | −0.117883 | − | 0.117883i | 0.645704 | − | 0.763587i | \(-0.276564\pi\) |
−0.763587 | + | 0.645704i | \(0.776564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.34242 | − | 5.51399i | 0.630627 | − | 0.416818i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7778i | 1.10455i | 0.833664 | + | 0.552273i | \(0.186239\pi\) | ||||
−0.833664 | + | 0.552273i | \(0.813761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.56388i | − | 0.562219i | −0.959676 | − | 0.281109i | \(-0.909298\pi\) | ||
0.959676 | − | 0.281109i | \(-0.0907023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.14966 | − | 5.02118i | 0.452132 | − | 0.369164i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.8990 | − | 16.8990i | −1.23578 | − | 1.23578i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7980i | 0.998385i | 0.866491 | + | 0.499193i | \(0.166370\pi\) | ||||
−0.866491 | + | 0.499193i | \(0.833630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7980 | − | 18.7980i | −1.35311 | − | 1.35311i | −0.882164 | − | 0.470943i | \(-0.843914\pi\) |
−0.470943 | − | 0.882164i | \(-0.656086\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.44949 | + | 6.44949i | −0.459507 | + | 0.459507i | −0.898494 | − | 0.438987i | \(-0.855338\pi\) |
0.438987 | + | 0.898494i | \(0.355338\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5133i | 1.38326i | 0.722253 | + | 0.691629i | \(0.243107\pi\) | ||||
−0.722253 | + | 0.691629i | \(0.756893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.9494 | − | 11.9494i | −0.838682 | − | 0.838682i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.14626 | − | 0.317837i | −0.219745 | − | 0.0221987i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.8988 | 1.65311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.7980i | − | 0.812205i | −0.913828 | − | 0.406102i | \(-0.866888\pi\) | ||
0.913828 | − | 0.406102i | \(-0.133112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.7980 | − | 16.8990i | −0.941013 | − | 1.15250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.7980 | + | 13.7980i | −0.936666 | + | 0.936666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6969 | 2.06490 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.89949 | + | 9.89949i | 0.662919 | + | 0.662919i | 0.956067 | − | 0.293148i | \(-0.0947028\pi\) |
−0.293148 | + | 0.956067i | \(0.594703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.75663 | + | 9.75663i | −0.647570 | + | 0.647570i | −0.952405 | − | 0.304835i | \(-0.901399\pi\) |
0.304835 | + | 0.952405i | \(0.401399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.26382 | + | 9.26382i | −0.606893 | + | 0.606893i | −0.942133 | − | 0.335240i | \(-0.891183\pi\) |
0.335240 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.79796 | + | 3.10102i | −0.247752 | + | 0.202288i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4949 | 1.58444 | 0.792222 | − | 0.610234i | \(-0.208924\pi\) | ||||
0.792222 | + | 0.610234i | \(0.208924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.79796 | −0.244648 | −0.122324 | − | 0.992490i | \(-0.539035\pi\) | ||||
−0.122324 | + | 0.992490i | \(0.539035\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.67423 | + | 0.674235i | 0.426401 | + | 0.0430753i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.7060 | + | 21.7060i | −1.38112 | + | 1.38112i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6780 | 0.673992 | 0.336996 | − | 0.941506i | \(-0.390589\pi\) | ||||
0.336996 | + | 0.941506i | \(0.390589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4135 | − | 15.4135i | 0.969037 | − | 0.969037i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.9494 | + | 11.9494i | 0.745382 | + | 0.745382i | 0.973608 | − | 0.228226i | \(-0.0732925\pi\) |
−0.228226 | + | 0.973608i | \(0.573293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.10102 | −0.441236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.55051 | − | 7.55051i | 0.465584 | − | 0.465584i | −0.434896 | − | 0.900481i | \(-0.643215\pi\) |
0.900481 | + | 0.434896i | \(0.143215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.8990 | − | 13.7980i | 1.03810 | − | 0.847602i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 11.5505i | − | 0.704247i | −0.935954 | − | 0.352124i | \(-0.885460\pi\) | ||
0.935954 | − | 0.352124i | \(-0.114540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8988 | 1.45175 | 0.725873 | − | 0.687828i | \(-0.241436\pi\) | ||||
0.725873 | + | 0.687828i | \(0.241436\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.9706 | + | 3.46410i | 1.02336 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.317837 | − | 0.317837i | −0.0190970 | − | 0.0190970i | 0.697494 | − | 0.716591i | \(-0.254298\pi\) |
−0.716591 | + | 0.697494i | \(0.754298\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7135i | 0.818081i | 0.912516 | + | 0.409041i | \(0.134137\pi\) | ||||
−0.912516 | + | 0.409041i | \(0.865863\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.10102 | − | 3.10102i | 0.184337 | − | 0.184337i | −0.608906 | − | 0.793242i | \(-0.708391\pi\) |
0.793242 | + | 0.608906i | \(0.208391\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | + | 2.00000i | 0.118056 | + | 0.118056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.5959i | 1.79976i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.651531 | + | 0.651531i | 0.0380628 | + | 0.0380628i | 0.725882 | − | 0.687819i | \(-0.241432\pi\) |
−0.687819 | + | 0.725882i | \(0.741432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.41421 | − | 0.142865i | −0.0823387 | − | 0.00831790i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.9985i | 1.61920i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5133i | 1.12473i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.8277 | − | 1.69994i | −0.963551 | − | 0.0973384i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.89898 | + | 6.89898i | 0.393746 | + | 0.393746i | 0.876020 | − | 0.482275i | \(-0.160189\pi\) |
−0.482275 | + | 0.876020i | \(0.660189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.8990i | 0.958253i | 0.877746 | + | 0.479127i | \(0.159047\pi\) | ||||
−0.877746 | + | 0.479127i | \(0.840953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | − | 5.00000i | −0.282617 | − | 0.282617i | 0.551535 | − | 0.834152i | \(-0.314042\pi\) |
−0.834152 | + | 0.551535i | \(0.814042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.8990 | + | 14.8990i | −0.836810 | + | 0.836810i | −0.988438 | − | 0.151628i | \(-0.951549\pi\) |
0.151628 | + | 0.988438i | \(0.451549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 29.2699i | − | 1.63880i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.6554 | − | 33.6554i | −1.87264 | − | 1.87264i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.5597 | + | 12.2672i | −1.02951 | + | 0.680463i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.38551 | 0.241781 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1010i | 0.720097i | 0.932934 | + | 0.360049i | \(0.117240\pi\) | ||||
−0.932934 | + | 0.360049i | \(0.882760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8990 | + | 11.8990i | −0.648179 | + | 0.648179i | −0.952553 | − | 0.304374i | \(-0.901553\pi\) |
0.304374 | + | 0.952553i | \(0.401553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.7980 | −1.83026 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1421 | − | 14.1421i | −0.763604 | − | 0.763604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.8988 | + | 23.8988i | −1.28295 | + | 1.28295i | −0.343974 | + | 0.938979i | \(0.611773\pi\) |
−0.938979 | + | 0.343974i | \(0.888227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9494 | 0.639636 | 0.319818 | − | 0.947479i | \(-0.396378\pi\) | ||||
0.319818 | + | 0.947479i | \(0.396378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.492810 | − | 0.492810i | 0.0262296 | − | 0.0262296i | −0.693870 | − | 0.720100i | \(-0.744096\pi\) |
0.720100 | + | 0.693870i | \(0.244096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.89898 | − | 0.696938i | −0.366160 | − | 0.0369897i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4949 | −1.29279 | −0.646396 | − | 0.763002i | \(-0.723724\pi\) | ||||
−0.646396 | + | 0.763002i | \(0.723724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.65153 | − | 3.79796i | 0.243472 | − | 0.198794i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.1202 | − | 23.1202i | 1.20687 | − | 1.20687i | 0.234829 | − | 0.972037i | \(-0.424547\pi\) |
0.972037 | − | 0.234829i | \(-0.0754532\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5133 | −1.01308 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0956 | + | 15.0956i | −0.781623 | + | 0.781623i | −0.980105 | − | 0.198482i | \(-0.936399\pi\) |
0.198482 | + | 0.980105i | \(0.436399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.5843 | + | 26.5843i | 1.36916 | + | 1.36916i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7980 | −1.01695 | −0.508476 | − | 0.861076i | \(-0.669791\pi\) | ||||
−0.508476 | + | 0.861076i | \(0.669791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.14643 | − | 9.14643i | 0.467361 | − | 0.467361i | −0.433698 | − | 0.901058i | \(-0.642791\pi\) |
0.901058 | + | 0.433698i | \(0.142791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.79796 | − | 12.0000i | −0.499350 | − | 0.611577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11.5505i | − | 0.585634i | −0.956168 | − | 0.292817i | \(-0.905407\pi\) | ||
0.956168 | − | 0.292817i | \(-0.0945927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.4120 | −2.19544 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.4626 | + | 3.17837i | 1.58306 | + | 0.159921i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0171 | − | 16.0171i | −0.803873 | − | 0.803873i | 0.179826 | − | 0.983698i | \(-0.442447\pi\) |
−0.983698 | + | 0.179826i | \(0.942447\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.4846i | − | 1.12282i | −0.827536 | − | 0.561412i | \(-0.810258\pi\) | ||
0.827536 | − | 0.561412i | \(-0.189742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.6969 | − | 30.6969i | 1.52912 | − | 1.52912i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.69694 | − | 8.69694i | −0.431091 | − | 0.431091i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.7980i | 1.47341i | 0.676212 | + | 0.736707i | \(0.263620\pi\) | ||||
−0.676212 | + | 0.736707i | \(0.736380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.898979 | + | 0.898979i | 0.0442359 | + | 0.0442359i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.37113 | + | 4.38551i | −0.263658 | + | 0.215276i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.40669i | 0.459547i | 0.973244 | + | 0.229773i | \(0.0737985\pi\) | ||||
−0.973244 | + | 0.229773i | \(0.926202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.77101i | − | 0.427473i | −0.976891 | − | 0.213736i | \(-0.931437\pi\) | ||
0.976891 | − | 0.213736i | \(-0.0685634\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.0205 | − | 28.7771i | −0.922627 | − | 1.39589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6969 | + | 10.6969i | 0.517661 | + | 0.517661i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.6969i | − | 0.515253i | −0.966245 | − | 0.257627i | \(-0.917060\pi\) | ||
0.966245 | − | 0.257627i | \(-0.0829405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0000 | − | 15.0000i | −0.720854 | − | 0.720854i | 0.247925 | − | 0.968779i | \(-0.420251\pi\) |
−0.968779 | + | 0.247925i | \(0.920251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.6969 | − | 30.6969i | 1.46843 | − | 1.46843i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.77101i | − | 0.418617i | −0.977850 | − | 0.209309i | \(-0.932879\pi\) | ||
0.977850 | − | 0.209309i | \(-0.0671214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.37113 | + | 5.37113i | 0.255190 | + | 0.255190i | 0.823094 | − | 0.567905i | \(-0.192246\pi\) |
−0.567905 | + | 0.823094i | \(0.692246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.953512 | − | 9.43879i | 0.0452008 | − | 0.447442i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6417 | −0.974144 | −0.487072 | − | 0.873362i | \(-0.661935\pi\) | ||||
−0.487072 | + | 0.873362i | \(0.661935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.89898i | 0.230684i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7980 | + | 2.00000i | 0.928143 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.10102 | + | 8.10102i | −0.378950 | + | 0.378950i | −0.870723 | − | 0.491773i | \(-0.836349\pi\) |
0.491773 | + | 0.870723i | \(0.336349\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.9444 | −1.53437 | −0.767187 | − | 0.641424i | \(-0.778344\pi\) | ||||
−0.767187 | + | 0.641424i | \(0.778344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.42101 | − | 7.42101i | −0.344884 | − | 0.344884i | 0.513316 | − | 0.858200i | \(-0.328417\pi\) |
−0.858200 | + | 0.513316i | \(0.828417\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.3205 | − | 17.3205i | 0.801498 | − | 0.801498i | −0.181832 | − | 0.983330i | \(-0.558203\pi\) |
0.983330 | + | 0.181832i | \(0.0582027\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.8988 | + | 23.8988i | −1.09887 | + | 1.09887i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.7980 | + | 6.89898i | 1.55076 | + | 0.316547i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.10102 | −0.141689 | −0.0708446 | − | 0.997487i | \(-0.522569\pi\) | ||||
−0.0708446 | + | 0.997487i | \(0.522569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7980 | 0.720325 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.79796 | − | 4.65153i | −0.172456 | − | 0.211215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.9063 | + | 15.9063i | −0.720783 | + | 0.720783i | −0.968765 | − | 0.247982i | \(-0.920233\pi\) |
0.247982 | + | 0.968765i | \(0.420233\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.1913 | 1.36251 | 0.681257 | − | 0.732044i | \(-0.261434\pi\) | ||||
0.681257 | + | 0.732044i | \(0.261434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.2193 | + | 41.2193i | −1.85642 | + | 1.85642i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.38551 | + | 4.38551i | 0.196717 | + | 0.196717i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8990 | −1.20416 | −0.602082 | − | 0.798434i | \(-0.705662\pi\) | ||||
−0.602082 | + | 0.798434i | \(0.705662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.5505 | − | 21.5505i | 0.960890 | − | 0.960890i | −0.0383737 | − | 0.999263i | \(-0.512218\pi\) |
0.999263 | + | 0.0383737i | \(0.0122177\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.20204 | − | 11.8990i | 0.0534901 | − | 0.529498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.0454i | − | 1.59768i | −0.601541 | − | 0.798842i | \(-0.705446\pi\) | ||
0.601541 | − | 0.798842i | \(-0.294554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.37113 | −0.237605 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9199 | − | 23.6130i | 1.27437 | − | 1.04051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.37113 | + | 5.37113i | 0.236222 | + | 0.236222i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 37.6123i | − | 1.64783i | −0.566717 | − | 0.823913i | \(-0.691787\pi\) | ||
0.566717 | − | 0.823913i | \(-0.308213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.10102 | − | 3.10102i | 0.135598 | − | 0.135598i | −0.636050 | − | 0.771648i | \(-0.719433\pi\) |
0.771648 | + | 0.636050i | \(0.219433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.5959 | + | 47.5959i | 2.07331 | + | 2.07331i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.5959i | − | 0.721562i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.44949 | − | 4.44949i | −0.192729 | − | 0.192729i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.38551 | + | 5.37113i | 0.189602 | + | 0.232214i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.3923i | − | 0.447628i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9494i | 0.513744i | 0.966445 | + | 0.256872i | \(0.0826919\pi\) | ||||
−0.966445 | + | 0.256872i | \(0.917308\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.68556 | − | 26.5843i | 0.115037 | − | 1.13875i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0000 | − | 10.0000i | −0.427569 | − | 0.427569i | 0.460230 | − | 0.887800i | \(-0.347767\pi\) |
−0.887800 | + | 0.460230i | \(0.847767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 58.2929i | − | 2.48336i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | − | 20.0000i | −0.850487 | − | 0.850487i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5959 | + | 17.5959i | −0.745563 | + | 0.745563i | −0.973643 | − | 0.228080i | \(-0.926755\pi\) |
0.228080 | + | 0.973643i | \(0.426755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 43.4120i | − | 1.83613i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.5276 | − | 18.5276i | −0.780847 | − | 0.780847i | 0.199127 | − | 0.979974i | \(-0.436189\pi\) |
−0.979974 | + | 0.199127i | \(0.936189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.8988 | + | 29.2699i | 1.00543 | + | 1.23139i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.1694 | 1.64207 | 0.821033 | − | 0.570881i | \(-0.193398\pi\) | ||||
0.821033 | + | 0.570881i | \(0.193398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6969i | 0.866140i | 0.901360 | + | 0.433070i | \(0.142570\pi\) | ||||
−0.901360 | + | 0.433070i | \(0.857430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.2474 | − | 17.3485i | 1.09459 | − | 0.723481i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5959 | − | 22.5959i | 0.940680 | − | 0.940680i | −0.0576561 | − | 0.998337i | \(-0.518363\pi\) |
0.998337 | + | 0.0576561i | \(0.0183627\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.20204 | 0.257304 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.8988 | − | 23.8988i | −0.989786 | − | 0.989786i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.3349 | + | 16.3349i | −0.674213 | + | 0.674213i | −0.958684 | − | 0.284472i | \(-0.908182\pi\) |
0.284472 | + | 0.958684i | \(0.408182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.3108 | −2.77349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3349 | + | 16.3349i | −0.670793 | + | 0.670793i | −0.957899 | − | 0.287106i | \(-0.907307\pi\) |
0.287106 | + | 0.957899i | \(0.407307\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.10102 | + | 30.6969i | −0.127129 | + | 1.25845i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.6969 | 0.437065 | 0.218533 | − | 0.975830i | \(-0.429873\pi\) | ||||
0.218533 | + | 0.975830i | \(0.429873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.20204 | 0.252987 | 0.126493 | − | 0.991967i | \(-0.459628\pi\) | ||||
0.126493 | + | 0.991967i | \(0.459628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.224745 | − | 2.22474i | 0.00913718 | − | 0.0904487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7279 | − | 12.7279i | 0.516610 | − | 0.516610i | −0.399934 | − | 0.916544i | \(-0.630967\pi\) |
0.916544 | + | 0.399934i | \(0.130967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.75663 | −0.394711 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1236 | + | 26.1236i | −1.05512 | + | 1.05512i | −0.0567340 | + | 0.998389i | \(0.518069\pi\) |
−0.998389 | + | 0.0567340i | \(0.981931\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.492810 | − | 0.492810i | −0.0198398 | − | 0.0198398i | 0.697117 | − | 0.716957i | \(-0.254466\pi\) |
−0.716957 | + | 0.697117i | \(0.754466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5959 | −0.868013 | −0.434007 | − | 0.900910i | \(-0.642901\pi\) | ||||
−0.434007 | + | 0.900910i | \(0.642901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | + | 6.00000i | −0.240385 | + | 0.240385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.4949i | 0.976676i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.37113 | −0.213821 | −0.106911 | − | 0.994269i | \(-0.534096\pi\) | ||||
−0.106911 | + | 0.994269i | \(0.534096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.9562 | − | 21.9917i | −0.712569 | − | 0.872716i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.43879 | + | 9.43879i | 0.373979 | + | 0.373979i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8557i | 1.10023i | 0.835088 | + | 0.550117i | \(0.185417\pi\) | ||||
−0.835088 | + | 0.550117i | \(0.814583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8990 | − | 26.8990i | 1.06079 | − | 1.06079i | 0.0627638 | − | 0.998028i | \(-0.480009\pi\) |
0.998028 | − | 0.0627638i | \(-0.0199915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.0454 | − | 26.0454i | −1.02395 | − | 1.02395i | −0.999706 | − | 0.0242446i | \(-0.992282\pi\) |
−0.0242446 | − | 0.999706i | \(-0.507718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.20204i | 0.0864377i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.4949 | − | 18.4949i | −0.723761 | − | 0.723761i | 0.245608 | − | 0.969369i | \(-0.421012\pi\) |
−0.969369 | + | 0.245608i | \(0.921012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.60697 | − | 35.7053i | 0.140936 | − | 1.39512i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7922i | 0.537267i | 0.963242 | + | 0.268634i | \(0.0865721\pi\) | ||||
−0.963242 | + | 0.268634i | \(0.913428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16.3349i | − | 0.635354i | −0.948199 | − | 0.317677i | \(-0.897097\pi\) | ||
0.948199 | − | 0.317677i | \(-0.102903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.5133 | − | 23.8988i | −0.756692 | − | 0.926754i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5959 | − | 37.5959i | −1.45572 | − | 1.45572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.2020i | 1.01152i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.5959 | + | 22.5959i | 0.871009 | + | 0.871009i | 0.992582 | − | 0.121574i | \(-0.0387941\pi\) |
−0.121574 | + | 0.992582i | \(0.538794\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6969 | + | 12.6969i | −0.487983 | + | 0.487983i | −0.907669 | − | 0.419686i | \(-0.862140\pi\) |
0.419686 | + | 0.907669i | \(0.362140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.37113i | 0.206125i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.9494 | − | 11.9494i | −0.457230 | − | 0.457230i | 0.440515 | − | 0.897745i | \(-0.354796\pi\) |
−0.897745 | + | 0.440515i | \(0.854796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.5276 | + | 15.1278i | −0.707905 | + | 0.578002i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.4120 | 1.65387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4949i | 1.31225i | 0.754653 | + | 0.656124i | \(0.227805\pi\) | ||||
−0.754653 | + | 0.656124i | \(0.772195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.75255 | − | 17.3485i | 0.0664781 | − | 0.658065i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.89898 | − | 6.89898i | 0.261317 | − | 0.261317i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.44949 | −0.319133 | −0.159566 | − | 0.987187i | \(-0.551010\pi\) | ||||
−0.159566 | + | 0.987187i | \(0.551010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.3205 | − | 17.3205i | −0.653255 | − | 0.653255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.56388 | + | 7.56388i | −0.284469 | + | 0.284469i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2843 | −1.06224 | −0.531119 | − | 0.847297i | \(-0.678228\pi\) | ||||
−0.531119 | + | 0.847297i | \(0.678228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.4120 | + | 43.4120i | −1.62579 | + | 1.62579i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.7980 | + | 26.6969i | 0.815197 | + | 0.998409i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.20204 | 0.231297 | 0.115649 | − | 0.993290i | \(-0.463105\pi\) | ||||
0.115649 | + | 0.993290i | \(0.463105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.3939 | −1.24365 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.44949 | − | 41.3939i | 0.313806 | − | 1.53733i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.7347 | + | 18.7347i | −0.694832 | + | 0.694832i | −0.963291 | − | 0.268459i | \(-0.913486\pi\) |
0.268459 | + | 0.963291i | \(0.413486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 67.3108 | 2.48958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.8523 | − | 24.8523i | 0.917940 | − | 0.917940i | −0.0789396 | − | 0.996879i | \(-0.525153\pi\) |
0.996879 | + | 0.0789396i | \(0.0251534\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.2929 | 1.04077 | 0.520385 | − | 0.853932i | \(-0.325789\pi\) | ||||
0.520385 | + | 0.853932i | \(0.325789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5505 | + | 21.5505i | −0.790612 | + | 0.790612i | −0.981594 | − | 0.190982i | \(-0.938833\pi\) |
0.190982 | + | 0.981594i | \(0.438833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.6969 | + | 2.59592i | 0.941463 | + | 0.0951071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.20204i | − | 0.226618i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.37113 | −0.195995 | −0.0979976 | − | 0.995187i | \(-0.531244\pi\) | ||||
−0.0979976 | + | 0.995187i | \(0.531244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.985620 | + | 9.75663i | −0.0358704 | + | 0.355080i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.2672 | − | 12.2672i | −0.445860 | − | 0.445860i | 0.448116 | − | 0.893976i | \(-0.352095\pi\) |
−0.893976 | + | 0.448116i | \(0.852095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.5563i | − | 0.563917i | −0.959427 | − | 0.281959i | \(-0.909016\pi\) | ||
0.959427 | − | 0.281959i | \(-0.0909841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.8990 | + | 16.8990i | −0.611784 | + | 0.611784i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.00000 | − | 2.00000i | −0.0722158 | − | 0.0722158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.59592i | − | 0.273916i | −0.990577 | − | 0.136958i | \(-0.956267\pi\) | ||
0.990577 | − | 0.136958i | \(-0.0437325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.8990 | − | 22.8990i | −0.823619 | − | 0.823619i | 0.163006 | − | 0.986625i | \(-0.447881\pi\) |
−0.986625 | + | 0.163006i | \(0.947881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.7975 | − | 9.75663i | −1.71694 | − | 0.350469i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.75663i | 0.349568i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7423i | 0.384388i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.59259 | − | 3.74983i | 0.163916 | − | 0.133837i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.3939 | − | 21.3939i | −0.762609 | − | 0.762609i | 0.214184 | − | 0.976793i | \(-0.431291\pi\) |
−0.976793 | + | 0.214184i | \(0.931291\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 33.7980i | − | 1.20172i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.7980 | − | 23.7980i | −0.845090 | − | 0.845090i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.0454 | − | 26.0454i | 0.922576 | − | 0.922576i | −0.0746352 | − | 0.997211i | \(-0.523779\pi\) |
0.997211 | + | 0.0746352i | \(0.0237792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.1278i | − | 0.535182i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.57826 | − | 6.57826i | −0.232142 | − | 0.232142i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.9985 | − | 2.82843i | −0.986819 | − | 0.0996890i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.3115 | 1.87433 | 0.937167 | − | 0.348882i | \(-0.113439\pi\) | ||||
0.937167 | + | 0.348882i | \(0.113439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.1918i | − | 1.16552i | −0.812643 | − | 0.582761i | \(-0.801972\pi\) | ||
0.812643 | − | 0.582761i | \(-0.198028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.59592 | + | 9.30306i | 0.266073 | + | 0.325872i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.5959 | + | 47.5959i | −1.66517 | + | 1.66517i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.44949 | −0.294889 | −0.147445 | − | 0.989070i | \(-0.547105\pi\) | ||||
−0.147445 | + | 0.989070i | \(0.547105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.24264 | − | 4.24264i | −0.147889 | − | 0.147889i | 0.629285 | − | 0.777174i | \(-0.283348\pi\) |
−0.777174 | + | 0.629285i | \(0.783348\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.0409 | + | 38.0409i | −1.32281 | + | 1.32281i | −0.411321 | + | 0.911490i | \(0.634933\pi\) |
−0.911490 | + | 0.411321i | \(0.865067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.8481 | 1.24506 | 0.622529 | − | 0.782597i | \(-0.286105\pi\) | ||||
0.622529 | + | 0.782597i | \(0.286105\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.6349 | + | 14.6349i | −0.507071 | + | 0.507071i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.69694 | + | 7.10102i | −0.300970 | + | 0.245741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.1010 | 1.48801 | 0.744006 | − | 0.668173i | \(-0.232923\pi\) | ||||
0.744006 | + | 0.668173i | \(0.232923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −42.3939 | −1.46186 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.1237 | − | 1.52781i | −0.520272 | − | 0.0525581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41421 | + | 1.41421i | −0.0485930 | + | 0.0485930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.3417 | −0.765863 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.953512 | − | 0.953512i | 0.0326476 | − | 0.0326476i | −0.690595 | − | 0.723242i | \(-0.742651\pi\) |
0.723242 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.6349 | + | 14.6349i | 0.499920 | + | 0.499920i | 0.911413 | − | 0.411493i | \(-0.134992\pi\) |
−0.411493 | + | 0.911413i | \(0.634992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.00000 | −0.204717 | −0.102359 | − | 0.994748i | \(-0.532639\pi\) | ||||
−0.102359 | + | 0.994748i | \(0.532639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.3485 | − | 29.3485i | 0.999034 | − | 0.999034i | −0.000966022 | − | 1.00000i | \(-0.500307\pi\) |
1.00000 | 0.000966022i | \(0.000307495\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.79796 | + | 3.10102i | −0.129134 | + | 0.105438i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 48.9898i | − | 1.66186i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.3923 | − | 19.7990i | −0.351324 | − | 0.669328i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6383 | + | 17.6383i | 0.595605 | + | 0.595605i | 0.939140 | − | 0.343535i | \(-0.111624\pi\) |
−0.343535 | + | 0.939140i | \(0.611624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.35680i | − | 0.247857i | −0.992291 | − | 0.123928i | \(-0.960451\pi\) | ||
0.992291 | − | 0.123928i | \(-0.0395493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.5959 | − | 37.5959i | 1.26520 | − | 1.26520i | 0.316666 | − | 0.948537i | \(-0.397436\pi\) |
0.948537 | − | 0.316666i | \(-0.102564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.2474 | + | 10.2474i | 0.344076 | + | 0.344076i | 0.857897 | − | 0.513821i | \(-0.171771\pi\) |
−0.513821 | + | 0.857897i | \(0.671771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.3939i | 0.851683i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6969 | + | 10.6969i | 0.357959 | + | 0.357959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.8769 | + | 3.32124i | 1.09895 | + | 0.111017i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 82.4385i | 2.74948i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.3108i | 2.24245i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.8277 | − | 1.69994i | −0.559372 | − | 0.0565080i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.1010 | − | 23.1010i | −0.767057 | − | 0.767057i | 0.210530 | − | 0.977587i | \(-0.432481\pi\) |
−0.977587 | + | 0.210530i | \(0.932481\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4949i | 0.811552i | 0.913973 | + | 0.405776i | \(0.132999\pi\) | ||||
−0.913973 | + | 0.405776i | \(0.867001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.59592 | + | 7.59592i | 0.251388 | + | 0.251388i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.6969 | + | 22.6969i | −0.749519 | + | 0.749519i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.37113i | 0.177177i | 0.996068 | + | 0.0885885i | \(0.0282356\pi\) | ||||
−0.996068 | + | 0.0885885i | \(0.971764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.75663 | − | 9.75663i | −0.321143 | − | 0.321143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.78874 | − | 14.8099i | −0.321852 | − | 0.486947i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.89949 | −0.324792 | −0.162396 | − | 0.986726i | \(-0.551922\pi\) | ||||
−0.162396 | + | 0.986726i | \(0.551922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20.6969i | − | 0.678315i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.3939 | + | 33.7980i | −1.35372 | + | 1.10531i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7980 | + | 18.7980i | −0.614103 | + | 0.614103i | −0.944012 | − | 0.329910i | \(-0.892982\pi\) |
0.329910 | + | 0.944012i | \(0.392982\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.7526 | 0.578717 | 0.289358 | − | 0.957221i | \(-0.406558\pi\) | ||||
0.289358 | + | 0.957221i | \(0.406558\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.29253 | + | 6.29253i | 0.204913 | + | 0.204913i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1421 | − | 14.1421i | 0.459558 | − | 0.459558i | −0.438953 | − | 0.898510i | \(-0.644650\pi\) |
0.898510 | + | 0.438953i | \(0.144650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9494 | 0.387893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.56388 | − | 7.56388i | 0.245018 | − | 0.245018i | −0.573904 | − | 0.818922i | \(-0.694572\pi\) |
0.818922 | + | 0.573904i | \(0.194572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.6969 | + | 3.10102i | 0.993330 | + | 0.100347i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.3939 | 0.690844 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.1918 | 2.07070 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.0454 | + | 37.5959i | −1.48225 | + | 1.21026i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.0696 | − | 35.0696i | 1.12776 | − | 1.12776i | 0.137222 | − | 0.990540i | \(-0.456183\pi\) |
0.990540 | − | 0.137222i | \(-0.0438175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0348 | −0.546672 | −0.273336 | − | 0.961919i | \(-0.588127\pi\) | ||||
−0.273336 | + | 0.961919i | \(0.588127\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0280 | + | 11.0280i | −0.353541 | + | 0.353541i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.26382 | + | 9.26382i | 0.296376 | + | 0.296376i | 0.839593 | − | 0.543217i | \(-0.182794\pi\) |
−0.543217 | + | 0.839593i | \(0.682794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6969 | −0.469716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.3485 | − | 15.3485i | 0.489540 | − | 0.489540i | −0.418621 | − | 0.908161i | \(-0.637486\pi\) |
0.908161 | + | 0.418621i | \(0.137486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8990 | + | 15.7980i | 0.410996 | + | 0.503365i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 61.3939i | 1.95221i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.8988 | 0.759169 | 0.379585 | − | 0.925157i | \(-0.376067\pi\) | ||||
0.379585 | + | 0.925157i | \(0.376067\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.4120 | + | 4.38551i | 1.37625 | + | 0.139030i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.1954 | − | 19.1954i | −0.607925 | − | 0.607925i | 0.334478 | − | 0.942403i | \(-0.391440\pi\) |
−0.942403 | + | 0.334478i | \(0.891440\pi\) | |||||||
\(998\) | 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 | 2880.2.bj.a.1313.3 | yes | 8 | |
3.2 | odd | 2 | 2880.2.bj.c.1313.1 | yes | 8 | ||
4.3 | odd | 2 | 2880.2.bj.b.1313.4 | yes | 8 | ||
5.2 | odd | 4 | 2880.2.bj.b.737.3 | yes | 8 | ||
8.3 | odd | 2 | 2880.2.bj.c.1313.2 | yes | 8 | ||
8.5 | even | 2 | 2880.2.bj.d.1313.1 | yes | 8 | ||
12.11 | even | 2 | 2880.2.bj.d.1313.2 | yes | 8 | ||
15.2 | even | 4 | 2880.2.bj.d.737.1 | yes | 8 | ||
20.7 | even | 4 | inner | 2880.2.bj.a.737.4 | yes | 8 | |
24.5 | odd | 2 | 2880.2.bj.b.1313.3 | yes | 8 | ||
24.11 | even | 2 | inner | 2880.2.bj.a.1313.4 | yes | 8 | |
40.27 | even | 4 | 2880.2.bj.d.737.2 | yes | 8 | ||
40.37 | odd | 4 | 2880.2.bj.c.737.1 | yes | 8 | ||
60.47 | odd | 4 | 2880.2.bj.c.737.2 | yes | 8 | ||
120.77 | even | 4 | inner | 2880.2.bj.a.737.3 | ✓ | 8 | |
120.107 | odd | 4 | 2880.2.bj.b.737.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.bj.a.737.3 | ✓ | 8 | 120.77 | even | 4 | inner | |
2880.2.bj.a.737.4 | yes | 8 | 20.7 | even | 4 | inner | |
2880.2.bj.a.1313.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.bj.a.1313.4 | yes | 8 | 24.11 | even | 2 | inner | |
2880.2.bj.b.737.3 | yes | 8 | 5.2 | odd | 4 | ||
2880.2.bj.b.737.4 | yes | 8 | 120.107 | odd | 4 | ||
2880.2.bj.b.1313.3 | yes | 8 | 24.5 | odd | 2 | ||
2880.2.bj.b.1313.4 | yes | 8 | 4.3 | odd | 2 | ||
2880.2.bj.c.737.1 | yes | 8 | 40.37 | odd | 4 | ||
2880.2.bj.c.737.2 | yes | 8 | 60.47 | odd | 4 | ||
2880.2.bj.c.1313.1 | yes | 8 | 3.2 | odd | 2 | ||
2880.2.bj.c.1313.2 | yes | 8 | 8.3 | odd | 2 | ||
2880.2.bj.d.737.1 | yes | 8 | 15.2 | even | 4 | ||
2880.2.bj.d.737.2 | yes | 8 | 40.27 | even | 4 | ||
2880.2.bj.d.1313.1 | yes | 8 | 8.5 | even | 2 | ||
2880.2.bj.d.1313.2 | yes | 8 | 12.11 | even | 2 |