Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(879,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("880.879");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.m (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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 879.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.879 |
Dual form | 880.2.m.f.879.7 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | + | 1.73205i | 0.852803 | + | 0.522233i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89898 | 1.35873 | 0.679366 | − | 0.733799i | \(-0.262255\pi\) | ||||
0.679366 | + | 0.733799i | \(0.262255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898 | 1.18818 | 0.594089 | − | 0.804400i | \(-0.297513\pi\) | ||||
0.594089 | + | 0.804400i | \(0.297513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | −1.44463 | −0.722315 | − | 0.691564i | \(-0.756922\pi\) | ||||
−0.722315 | + | 0.691564i | \(0.756922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.79796i | − | 1.81944i | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||
0.415227 | − | 0.909718i | \(-0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65685 | − | 2.82843i | −0.956183 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.82843i | − | 0.431331i | −0.976467 | − | 0.215666i | \(-0.930808\pi\) | ||
0.976467 | − | 0.215666i | \(-0.0691921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | + | 6.00000i | −0.447214 | + | 0.894427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.29253 | − | 3.92480i | 0.848484 | − | 0.529220i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3923i | 1.35296i | 0.736460 | + | 0.676481i | \(0.236496\pi\) | ||||
−0.736460 | + | 0.676481i | \(0.763504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.79796i | 1.25450i | 0.778818 | + | 0.627250i | \(0.215820\pi\) | ||||
−0.778818 | + | 0.627250i | \(0.784180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.48528i | 1.06904i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.89898 | − | 9.79796i | 0.607644 | − | 1.21529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.8564 | −1.69283 | −0.846415 | − | 0.532524i | \(-0.821244\pi\) | ||||
−0.846415 | + | 0.532524i | \(0.821244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898 | 0.573382 | 0.286691 | − | 0.958023i | \(-0.407445\pi\) | ||||
0.286691 | + | 0.958023i | \(0.407445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89898 | − | 8.00000i | 0.558291 | − | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.1421i | − | 1.55230i | −0.630548 | − | 0.776151i | \(-0.717170\pi\) | ||
0.630548 | − | 0.776151i | \(-0.282830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.89898 | − | 9.79796i | 0.531369 | − | 1.06274i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.8564i | − | 1.45255i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65685 | + | 11.3137i | −0.580381 | + | 1.16076i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.48528 | − | 5.19615i | −0.852803 | − | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.79796i | 0.974933i | 0.873142 | + | 0.487467i | \(0.162079\pi\) | ||||
−0.873142 | + | 0.487467i | \(0.837921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.1421i | − | 1.36717i | −0.729870 | − | 0.683586i | \(-0.760419\pi\) | ||
0.729870 | − | 0.683586i | \(-0.239581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.79796i | 0.938474i | 0.883072 | + | 0.469237i | \(0.155471\pi\) | ||||
−0.883072 | + | 0.469237i | \(0.844529\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.00000i | − | 0.752577i | −0.926503 | − | 0.376288i | \(-0.877200\pi\) | ||
0.926503 | − | 0.376288i | \(-0.122800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.92820 | + | 13.8564i | −0.646058 | + | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.6969 | −1.35873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 13.8564i | − | 1.27021i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 9.79796i | 0.454545 | + | 0.890724i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7990i | 1.75688i | 0.477856 | + | 0.878438i | \(0.341414\pi\) | ||||
−0.477856 | + | 0.878438i | \(0.658586\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000i | 1.38738i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0000i | 1.36697i | 0.729964 | + | 0.683486i | \(0.239537\pi\) | ||||
−0.729964 | + | 0.683486i | \(0.760463\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.65685 | −0.479808 | −0.239904 | − | 0.970797i | \(-0.577116\pi\) | ||||
−0.239904 | + | 0.970797i | \(0.577116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564 | + | 8.48528i | 1.15873 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.5959 | − | 9.79796i | −1.62735 | − | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.79796i | − | 0.802680i | −0.915929 | − | 0.401340i | \(-0.868545\pi\) | ||
0.915929 | − | 0.401340i | \(-0.131455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3137 | 0.920697 | 0.460348 | − | 0.887738i | \(-0.347725\pi\) | ||||
0.460348 | + | 0.887738i | \(0.347725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.6969 | −1.18818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.92820 | − | 3.46410i | −0.556487 | − | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0000i | 0.957704i | 0.877896 | + | 0.478852i | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.5959i | 1.54437i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8564 | 1.08532 | 0.542659 | − | 0.839953i | \(-0.317418\pi\) | ||||
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.48528i | 0.656611i | 0.944572 | + | 0.328305i | \(0.106478\pi\) | ||||
−0.944572 | + | 0.328305i | \(0.893522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | 1.29777 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.6969 | −1.11739 | −0.558694 | − | 0.829374i | \(-0.688697\pi\) | ||||
−0.558694 | + | 0.829374i | \(0.688697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3137 | + | 8.48528i | −0.855236 | + | 0.641427i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3205i | 1.29460i | 0.762237 | + | 0.647298i | \(0.224101\pi\) | ||||
−0.762237 | + | 0.647298i | \(0.775899\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | − | 4.00000i | −0.588172 | − | 0.294086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8564 | + | 8.48528i | 1.01328 | + | 0.620505i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.46410i | − | 0.250654i | −0.992116 | − | 0.125327i | \(-0.960002\pi\) | ||
0.992116 | − | 0.125327i | \(-0.0399979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6969 | −1.05791 | −0.528954 | − | 0.848650i | \(-0.677416\pi\) | ||||
−0.528954 | + | 0.848650i | \(0.677416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.89898 | 0.349038 | 0.174519 | − | 0.984654i | \(-0.444163\pi\) | ||||
0.174519 | + | 0.984654i | \(0.444163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410i | 0.245564i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) | ||||
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.7128 | −1.94506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.7846 | 1.44463 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | − | 9.79796i | −1.10674 | − | 0.677739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.65685 | 0.389434 | 0.194717 | − | 0.980859i | \(-0.437621\pi\) | ||||
0.194717 | + | 0.980859i | \(0.437621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | − | 2.82843i | −0.385794 | − | 0.192897i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.79796 | −0.665129 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.1421i | − | 0.938647i | −0.883026 | − | 0.469323i | \(-0.844498\pi\) | ||
0.883026 | − | 0.469323i | \(-0.155502\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4949 | 1.60471 | 0.802357 | − | 0.596844i | \(-0.203579\pi\) | ||||
0.802357 | + | 0.596844i | \(0.203579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92820 | − | 13.8564i | 0.451946 | − | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5959i | 1.26228i | 0.775667 | + | 0.631142i | \(0.217413\pi\) | ||||
−0.775667 | + | 0.631142i | \(0.782587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 2.00000i | −0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.7128 | −1.76332 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.3205i | − | 1.09326i | −0.837374 | − | 0.546630i | \(-0.815910\pi\) | ||
0.837374 | − | 0.546630i | \(-0.184090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.5959 | − | 12.0000i | −1.23198 | − | 0.754434i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.00000i | 0.499026i | 0.968371 | + | 0.249513i | \(0.0802706\pi\) | ||||
−0.968371 | + | 0.249513i | \(0.919729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3137 | −0.703000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.3939i | 1.81944i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528i | 0.523225i | 0.965173 | + | 0.261612i | \(0.0842542\pi\) | ||||
−0.965173 | + | 0.261612i | \(0.915746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | − | 4.00000i | −0.491436 | − | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.6274 | 1.37452 | 0.687259 | − | 0.726413i | \(-0.258814\pi\) | ||||
0.687259 | + | 0.726413i | \(0.258814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.55708 | − | 16.5099i | −0.0938953 | − | 0.995582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6969 | −0.883053 | −0.441527 | − | 0.897248i | \(-0.645563\pi\) | ||||
−0.441527 | + | 0.897248i | \(0.645563\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3923i | 0.622171i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.7990i | 1.17693i | 0.808523 | + | 0.588464i | \(0.200267\pi\) | ||||
−0.808523 | + | 0.588464i | \(0.799733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.4949 | 1.43101 | 0.715504 | − | 0.698609i | \(-0.246197\pi\) | ||||
0.715504 | + | 0.698609i | \(0.246197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7846 | + | 10.3923i | 1.21013 | + | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.9411 | −1.96287 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5959 | + | 9.79796i | 1.12206 | + | 0.561029i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.82843i | − | 0.161427i | −0.996737 | − | 0.0807134i | \(-0.974280\pi\) | ||
0.996737 | − | 0.0807134i | \(-0.0257199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.2487i | − | 1.37502i | −0.726176 | − | 0.687509i | \(-0.758704\pi\) | ||
0.726176 | − | 0.687509i | \(-0.241296\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.0000i | 1.80875i | 0.426742 | + | 0.904373i | \(0.359661\pi\) | ||||
−0.426742 | + | 0.904373i | \(0.640339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.9706 | + | 8.48528i | 0.956183 | + | 0.478091i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 28.0000i | − | 1.57264i | −0.617822 | − | 0.786318i | \(-0.711985\pi\) | ||
0.617822 | − | 0.786318i | \(-0.288015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9706 | − | 27.7128i | 0.950169 | − | 1.55162i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.7128 | −1.54198 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.6969 | − | 19.5959i | −0.815239 | − | 1.08699i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 19.5959i | − | 1.08036i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1769i | 1.71364i | 0.515617 | + | 0.856819i | \(0.327563\pi\) | ||||
−0.515617 | + | 0.856819i | \(0.672437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000i | 0.657596i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.8564 | + | 27.7128i | −0.757056 | + | 1.51411i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89898 | 0.266864 | 0.133432 | − | 0.991058i | \(-0.457400\pi\) | ||||
0.133432 | + | 0.991058i | \(0.457400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | − | 9.79796i | 0.324918 | − | 0.530589i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.82843i | − | 0.151838i | −0.997114 | − | 0.0759190i | \(-0.975811\pi\) | ||
0.997114 | − | 0.0759190i | \(-0.0241890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.79796i | − | 0.524473i | −0.965004 | − | 0.262236i | \(-0.915540\pi\) | ||
0.965004 | − | 0.262236i | \(-0.0844600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.0000i | − | 0.851594i | −0.904819 | − | 0.425797i | \(-0.859994\pi\) | ||
0.904819 | − | 0.425797i | \(-0.140006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.92820 | + | 3.46410i | 0.367711 | + | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89898 | − | 9.79796i | 0.256424 | − | 0.512849i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.92820 | −0.361649 | −0.180825 | − | 0.983515i | \(-0.557877\pi\) | ||||
−0.180825 | + | 0.983515i | \(0.557877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3137 | −0.587378 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.89898 | 0.253660 | 0.126830 | − | 0.991924i | \(-0.459520\pi\) | ||||
0.126830 | + | 0.991924i | \(0.459520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 48.0000i | − | 2.47213i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.7846 | 1.06204 | 0.531022 | − | 0.847358i | \(-0.321808\pi\) | ||||
0.531022 | + | 0.847358i | \(0.321808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.1010 | − | 17.7980i | −0.565760 | − | 0.907068i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.48528i | 0.431331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.9411 | −1.71648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3137 | − | 22.6274i | 0.569254 | − | 1.13851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.0000i | 1.40528i | 0.711546 | + | 0.702640i | \(0.247995\pi\) | ||||
−0.711546 | + | 0.702640i | \(0.752005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.9706i | − | 0.845364i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | − | 18.0000i | 0.447214 | − | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.92820 | − | 11.3137i | 0.343418 | − | 0.560800i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3939 | 1.44638 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.2843 | − | 14.1421i | −1.38842 | − | 0.694210i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.3205i | 0.846162i | 0.906092 | + | 0.423081i | \(0.139051\pi\) | ||||
−0.906092 | + | 0.423081i | \(0.860949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0000 | −1.46211 | −0.731055 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731055 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.7846 | −1.01058 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.6969 | − | 19.5959i | −0.712906 | − | 0.950542i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.7128 | 1.34112 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00000i | 0.384455i | 0.981350 | + | 0.192228i | \(0.0615712\pi\) | ||||
−0.981350 | + | 0.192228i | \(0.938429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39.1918 | 1.87480 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3137 | 0.539974 | 0.269987 | − | 0.962864i | \(-0.412981\pi\) | ||||
0.269987 | + | 0.962864i | \(0.412981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.7128 | 1.31668 | 0.658338 | − | 0.752723i | \(-0.271260\pi\) | ||||
0.658338 | + | 0.752723i | \(0.271260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | + | 4.00000i | −0.0948091 | + | 0.189618i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.7128 | − | 13.8564i | −1.29920 | − | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.89898 | 0.229165 | 0.114582 | − | 0.993414i | \(-0.463447\pi\) | ||||
0.114582 | + | 0.993414i | \(0.463447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.79796i | − | 0.456336i | −0.973622 | − | 0.228168i | \(-0.926726\pi\) | ||
0.973622 | − | 0.228168i | \(-0.0732736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.6410 | −1.60990 | −0.804952 | − | 0.593340i | \(-0.797809\pi\) | ||||
−0.804952 | + | 0.593340i | \(0.797809\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −41.5692 | −1.92359 | −0.961797 | − | 0.273764i | \(-0.911731\pi\) | ||||
−0.961797 | + | 0.273764i | \(0.911731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.1918i | 1.80971i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89898 | − | 8.00000i | 0.225255 | − | 0.367840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9706 | + | 22.6274i | 0.778663 | + | 1.03822i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 19.5959i | − | 0.893497i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.92820 | 0.313947 | 0.156973 | − | 0.987603i | \(-0.449826\pi\) | ||||
0.156973 | + | 0.987603i | \(0.449826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9706 | −0.765871 | −0.382935 | − | 0.923775i | \(-0.625087\pi\) | ||||
−0.382935 | + | 0.923775i | \(0.625087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 48.0000i | − | 2.16181i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.8776 | + | 11.7744i | −0.848484 | + | 0.529220i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.79796 | 0.439499 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.46410i | − | 0.155074i | −0.996989 | − | 0.0775372i | \(-0.975294\pi\) | ||
0.996989 | − | 0.0775372i | \(-0.0247057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.4558i | − | 1.13502i | −0.823367 | − | 0.567510i | \(-0.807907\pi\) | ||
0.823367 | − | 0.567510i | \(-0.192093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5959 | + | 9.79796i | 0.872007 | + | 0.436003i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 13.8564i | − | 0.612971i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.92820 | − | 13.8564i | 0.305293 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5959 | + | 12.0000i | 0.861827 | + | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1127i | 1.36046i | 0.732997 | + | 0.680232i | \(0.238121\pi\) | ||||
−0.732997 | + | 0.680232i | \(0.761879\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.9706i | − | 0.739249i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.1769i | − | 1.35296i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.2843 | − | 14.1421i | −1.22284 | − | 0.611418i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82843 | − | 1.73205i | −0.121829 | − | 0.0746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 9.79796i | − | 0.421247i | −0.977567 | − | 0.210624i | \(-0.932451\pi\) | ||
0.977567 | − | 0.210624i | \(-0.0675494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5959 | + | 9.79796i | 0.839397 | + | 0.419698i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.82843i | − | 0.120935i | −0.998170 | − | 0.0604674i | \(-0.980741\pi\) | ||
0.998170 | − | 0.0604674i | \(-0.0192591\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 29.3939i | − | 1.25450i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.4256i | 2.36121i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 32.0000i | − | 1.36078i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.89898 | 0.207576 | 0.103788 | − | 0.994599i | \(-0.466904\pi\) | ||||
0.103788 | + | 0.994599i | \(0.466904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.8564i | − | 0.586064i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 25.4558i | − | 1.07284i | −0.843952 | − | 0.536418i | \(-0.819777\pi\) | ||
0.843952 | − | 0.536418i | \(-0.180223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | − | 8.00000i | −0.673125 | − | 0.336563i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 25.4558i | − | 1.06904i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.65685 | 0.236732 | 0.118366 | − | 0.992970i | \(-0.462234\pi\) | ||||
0.118366 | + | 0.992970i | \(0.462234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7846 | + | 27.7128i | 0.866778 | + | 1.15570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.0000 | −1.65948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.92820 | − | 11.3137i | 0.286937 | − | 0.468566i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.6969 | + | 29.3939i | −0.607644 | + | 1.21529i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8564 | −0.571915 | −0.285958 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285958 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.5959i | 0.807436i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.89898 | 0.201177 | 0.100588 | − | 0.994928i | \(-0.467927\pi\) | ||||
0.100588 | + | 0.994928i | \(0.467927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.7128 | − | 13.8564i | −1.13611 | − | 0.568057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3923i | 0.424618i | 0.977203 | + | 0.212309i | \(0.0680983\pi\) | ||||
−0.977203 | + | 0.212309i | \(0.931902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.1918i | − | 1.59867i | −0.600887 | − | 0.799334i | \(-0.705186\pi\) | ||
0.600887 | − | 0.799334i | \(-0.294814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.5692 | 1.69283 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.5959 | − | 0.202041i | 0.999966 | − | 0.00821414i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.1421i | − | 0.574012i | −0.957929 | − | 0.287006i | \(-0.907340\pi\) | ||
0.957929 | − | 0.287006i | \(-0.0926599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.9411 | 1.37311 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2929 | −1.38508 | −0.692538 | − | 0.721382i | \(-0.743507\pi\) | ||||
−0.692538 | + | 0.721382i | \(0.743507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.00000i | 0.322068i | 0.986949 | + | 0.161034i | \(0.0514829\pi\) | ||||
−0.986949 | + | 0.161034i | \(0.948517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.46410i | 0.139234i | 0.997574 | + | 0.0696170i | \(0.0221777\pi\) | ||||
−0.997574 | + | 0.0696170i | \(0.977822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65685i | 0.226637i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 19.5959i | − | 0.781340i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1769i | 1.24113i | 0.784154 | + | 0.620567i | \(0.213097\pi\) | ||||
−0.784154 | + | 0.620567i | \(0.786903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.5980 | + | 19.7990i | 1.57140 | + | 0.785699i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.89898 | −0.194105 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 10.3923i | − | 0.411113i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.92820 | 0.272376 | 0.136188 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136188 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.0000 | + | 29.3939i | −0.706562 | + | 1.15381i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.00000i | 0.156532i | 0.996933 | + | 0.0782660i | \(0.0249384\pi\) | ||||
−0.996933 | + | 0.0782660i | \(0.975062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.65685 | − | 11.3137i | 0.221032 | − | 0.442063i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.6969 | −0.573382 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.5980 | −1.54252 | −0.771259 | − | 0.636521i | \(-0.780373\pi\) | ||||
−0.771259 | + | 0.636521i | \(0.780373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0000 | 1.47803 | 0.739014 | − | 0.673690i | \(-0.235292\pi\) | ||||
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.0000 | + | 16.0000i | 1.24091 | + | 0.620453i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 67.8823i | 2.62841i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.9706 | + | 27.7128i | −0.655141 | + | 1.06984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.89898 | 0.188842 | 0.0944209 | − | 0.995532i | \(-0.469900\pi\) | ||||
0.0944209 | + | 0.995532i | \(0.469900\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.2929 | −1.31798 | −0.658991 | − | 0.752151i | \(-0.729016\pi\) | ||||
−0.658991 | + | 0.752151i | \(0.729016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.0000 | + | 16.0000i | 1.22266 | + | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19.5959i | − | 0.746545i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.46410i | − | 0.131781i | −0.997827 | − | 0.0658903i | \(-0.979011\pi\) | ||
0.997827 | − | 0.0658903i | \(-0.0209887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.6969 | + | 24.0000i | −0.558291 | + | 0.911685i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65685 | + | 11.3137i | −0.214577 | + | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.3939i | − | 1.11019i | −0.831786 | − | 0.555096i | \(-0.812682\pi\) | ||
0.831786 | − | 0.555096i | \(-0.187318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.6274i | 0.853409i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.7128 | 1.04225 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.0000 | 1.27690 | 0.638448 | − | 0.769665i | \(-0.279577\pi\) | ||||
0.638448 | + | 0.769665i | \(0.279577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.9411 | −1.27289 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.8270 | − | 19.2275i | 1.15286 | − | 0.719069i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.1769i | − | 1.16270i | −0.813653 | − | 0.581351i | \(-0.802524\pi\) | ||
0.813653 | − | 0.581351i | \(-0.197476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 19.5959i | − | 0.729790i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.1918 | + | 29.3939i | −1.45555 | + | 1.09166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.6410 | −1.28476 | −0.642382 | − | 0.766385i | \(-0.722054\pi\) | ||||
−0.642382 | + | 0.766385i | \(0.722054\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 13.8564i | − | 0.512498i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6969 | −0.542844 | −0.271422 | − | 0.962460i | \(-0.587494\pi\) | ||||
−0.271422 | + | 0.962460i | \(0.587494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.1918 | − | 24.0000i | −1.44365 | − | 0.884051i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.2843 | 1.04045 | 0.520227 | − | 0.854028i | \(-0.325847\pi\) | ||||
0.520227 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.82843i | − | 0.103765i | −0.998653 | − | 0.0518825i | \(-0.983478\pi\) | ||
0.998653 | − | 0.0518825i | \(-0.0165221\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.5959 | − | 9.79796i | −0.717939 | − | 0.358969i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.4264i | 1.55230i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.0000 | −1.46157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.1051i | − | 1.39048i | −0.718780 | − | 0.695238i | \(-0.755299\pi\) | ||
0.718780 | − | 0.695238i | \(-0.244701\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.3137 | − | 22.6274i | 0.411748 | − | 0.823496i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 20.0000i | − | 0.726912i | −0.931611 | − | 0.363456i | \(-0.881597\pi\) | ||
0.931611 | − | 0.363456i | \(-0.118403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5959i | 0.710351i | 0.934800 | + | 0.355176i | \(0.115579\pi\) | ||||
−0.934800 | + | 0.355176i | \(0.884421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.7128 | 1.00327 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.6969 | + | 29.3939i | −0.531369 | + | 1.06274i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.9117i | 1.83831i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.1918i | 1.41329i | 0.707566 | + | 0.706647i | \(0.249793\pi\) | ||||
−0.707566 | + | 0.706647i | \(0.750207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.0000i | 0.719350i | 0.933078 | + | 0.359675i | \(0.117112\pi\) | ||||
−0.933078 | + | 0.359675i | \(0.882888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.8564 | + | 10.3923i | −0.497737 | + | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 9.79796i | −0.214697 | + | 0.350599i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | + | 12.0000i | 0.856597 | + | 0.428298i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 48.0833i | − | 1.71398i | −0.515330 | − | 0.856992i | \(-0.672331\pi\) | ||
0.515330 | − | 0.856992i | \(-0.327669\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6274 | −0.804538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000i | 1.70453i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.0000i | 0.708436i | 0.935163 | + | 0.354218i | \(0.115253\pi\) | ||||
−0.935163 | + | 0.354218i | \(0.884747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.9411 | 1.20075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8564 | + | 8.48528i | 0.488982 | + | 0.299439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.1918 | + | 19.5959i | 1.38133 | + | 0.690665i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5959i | 0.688956i | 0.938794 | + | 0.344478i | \(0.111944\pi\) | ||||
−0.938794 | + | 0.344478i | \(0.888056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.65685 | 0.198639 | 0.0993195 | − | 0.995056i | \(-0.468333\pi\) | ||||
0.0993195 | + | 0.995056i | \(0.468333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8564 | − | 27.7128i | 0.485369 | − | 0.970737i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000i | 0.559769i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.5692i | 1.45255i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.79796i | − | 0.341951i | −0.985275 | − | 0.170976i | \(-0.945308\pi\) | ||
0.985275 | − | 0.170976i | \(-0.0546919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7846 | −0.724506 | −0.362253 | − | 0.932080i | \(-0.617992\pi\) | ||||
−0.362253 | + | 0.932080i | \(0.617992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.82843i | − | 0.0983540i | −0.998790 | − | 0.0491770i | \(-0.984340\pi\) | ||
0.998790 | − | 0.0491770i | \(-0.0156598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | 0.347314 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.89898 | −0.169740 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.9706 | + | 8.48528i | 0.587291 | + | 0.293645i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.46410i | 0.119594i | 0.998211 | + | 0.0597970i | \(0.0190453\pi\) | ||||
−0.998211 | + | 0.0597970i | \(0.980955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −67.0000 | −2.31034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | − | 22.0000i | 0.378412 | − | 0.756823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7128 | − | 14.1421i | 0.952224 | − | 0.485930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.7128i | 0.949983i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.4949 | 0.838689 | 0.419345 | − | 0.907827i | \(-0.362260\pi\) | ||||
0.419345 | + | 0.907827i | \(0.362260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9706 | − | 33.9411i | 0.580381 | − | 1.16076i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.89898 | 0.167346 | 0.0836730 | − | 0.996493i | \(-0.473335\pi\) | ||||
0.0836730 | + | 0.996493i | \(0.473335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.2487i | − | 0.827355i | −0.910423 | − | 0.413678i | \(-0.864244\pi\) | ||
0.910423 | − | 0.413678i | \(-0.135756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.7846 | −0.707516 | −0.353758 | − | 0.935337i | \(-0.615096\pi\) | ||||
−0.353758 | + | 0.935337i | \(0.615096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6969 | + | 29.3939i | −0.499711 | + | 0.999422i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | + | 19.5959i | 1.08553 | + | 0.664746i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.8823 | −2.30010 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.65685 | + | 31.1127i | 0.191237 | + | 1.05180i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.6969 | −0.496280 | −0.248140 | − | 0.968724i | \(-0.579819\pi\) | ||||
−0.248140 | + | 0.968724i | \(0.579819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.7128 | −0.932610 | −0.466305 | − | 0.884624i | \(-0.654415\pi\) | ||||
−0.466305 | + | 0.884624i | \(0.654415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 14.1421i | − | 0.474846i | −0.971406 | − | 0.237423i | \(-0.923697\pi\) | ||
0.971406 | − | 0.237423i | \(-0.0763028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.0000 | 1.87818 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.4558 | + | 15.5885i | 0.852803 | + | 0.522233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.1918 | −1.31150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.6410 | + | 17.3205i | 1.15792 | + | 0.578961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.9411 | −1.13200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.5959i | − | 0.652835i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | − | 36.0000i | 0.598340 | − | 1.19668i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7128 | 0.920189 | 0.460094 | − | 0.887870i | \(-0.347816\pi\) | ||||
0.460094 | + | 0.887870i | \(0.347816\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 29.3939i | − | 0.974933i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 31.1769i | − | 1.03294i | −0.856306 | − | 0.516469i | \(-0.827246\pi\) | ||
0.856306 | − | 0.516469i | \(-0.172754\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4949 | − | 40.0000i | 0.810663 | − | 1.32381i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.0000i | − | 0.528367i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.5685 | 1.86602 | 0.933012 | − | 0.359845i | \(-0.117171\pi\) | ||||
0.933012 | + | 0.359845i | \(0.117171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9706i | 0.558593i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 12.0000i | −0.526077 | + | 0.394558i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.7846 | −0.682656 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.65685 | 0.185396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.8270 | − | 19.2275i | 1.00815 | − | 0.628808i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.6969 | −0.480128 | −0.240064 | − | 0.970757i | \(-0.577168\pi\) | ||||
−0.240064 | + | 0.970757i | \(0.577168\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.79796i | − | 0.319404i | −0.987165 | − | 0.159702i | \(-0.948947\pi\) | ||
0.987165 | − | 0.159702i | \(-0.0510534\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.2929 | −1.11085 | −0.555427 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555427 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.92820 | − | 3.46410i | −0.224191 | − | 0.112096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.2548 | 1.46135 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.4264i | 1.36717i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.6969 | + | 29.3939i | −0.473111 | + | 0.946222i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48.0833i | − | 1.54625i | −0.634252 | − | 0.773127i | \(-0.718692\pi\) | ||
0.634252 | − | 0.773127i | \(-0.281308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.2487i | − | 0.778178i | −0.921200 | − | 0.389089i | \(-0.872790\pi\) | ||
0.921200 | − | 0.389089i | \(-0.127210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000i | 0.512936i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.0000i | 1.79160i | 0.444459 | + | 0.895799i | \(0.353396\pi\) | ||||
−0.444459 | + | 0.895799i | \(0.646604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.65685 | − | 3.46410i | −0.180794 | − | 0.110713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 29.3939i | − | 0.938474i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.92820 | −0.220975 | −0.110488 | − | 0.993877i | \(-0.535241\pi\) | ||||
−0.110488 | + | 0.993877i | \(0.535241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.89898 | − | 9.79796i | 0.156094 | − | 0.312189i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.5959i | 0.623114i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.9615i | 1.65061i | 0.564686 | + | 0.825306i | \(0.308997\pi\) | ||||
−0.564686 | + | 0.825306i | \(0.691003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92820 | + | 3.46410i | 0.219639 | + | 0.109819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.89898 | 0.155152 | 0.0775761 | − | 0.996986i | \(-0.475282\pi\) | ||||
0.0775761 | + | 0.996986i | \(0.475282\pi\) | |||||||
\(998\) | 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 | 880.2.m.f.879.2 | yes | 8 | |
4.3 | odd | 2 | inner | 880.2.m.f.879.3 | yes | 8 | |
5.4 | even | 2 | inner | 880.2.m.f.879.8 | yes | 8 | |
11.10 | odd | 2 | inner | 880.2.m.f.879.4 | yes | 8 | |
20.19 | odd | 2 | inner | 880.2.m.f.879.5 | yes | 8 | |
44.43 | even | 2 | inner | 880.2.m.f.879.1 | ✓ | 8 | |
55.54 | odd | 2 | inner | 880.2.m.f.879.6 | yes | 8 | |
220.219 | even | 2 | inner | 880.2.m.f.879.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
880.2.m.f.879.1 | ✓ | 8 | 44.43 | even | 2 | inner | |
880.2.m.f.879.2 | yes | 8 | 1.1 | even | 1 | trivial | |
880.2.m.f.879.3 | yes | 8 | 4.3 | odd | 2 | inner | |
880.2.m.f.879.4 | yes | 8 | 11.10 | odd | 2 | inner | |
880.2.m.f.879.5 | yes | 8 | 20.19 | odd | 2 | inner | |
880.2.m.f.879.6 | yes | 8 | 55.54 | odd | 2 | inner | |
880.2.m.f.879.7 | yes | 8 | 220.219 | even | 2 | inner | |
880.2.m.f.879.8 | yes | 8 | 5.4 | even | 2 | inner |