Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(193,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.j (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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.577 |
Dual form | 768.2.j.d.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 2.00000i | 0.894427 | − | 0.894427i | −0.100509 | − | 0.994936i | \(-0.532047\pi\) |
0.994936 | + | 0.100509i | \(0.0320471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.24264i | − | 1.60357i | −0.597614 | − | 0.801784i | \(-0.703885\pi\) | ||
0.597614 | − | 0.801784i | \(-0.296115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | − | 2.82843i | 0.852803 | − | 0.852803i | −0.137675 | − | 0.990478i | \(-0.543963\pi\) |
0.990478 | + | 0.137675i | \(0.0439628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 3.00000i | 0.832050 | + | 0.832050i | 0.987797 | − | 0.155747i | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | −0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41421 | − | 1.41421i | −0.324443 | − | 0.324443i | 0.526026 | − | 0.850469i | \(-0.323682\pi\) |
−0.850469 | + | 0.526026i | \(0.823682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 3.00000i | −0.654654 | + | 0.654654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | + | 4.00000i | 0.742781 | + | 0.742781i | 0.973112 | − | 0.230331i | \(-0.0739809\pi\) |
−0.230331 | + | 0.973112i | \(0.573981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24264 | −0.762001 | −0.381000 | − | 0.924575i | \(-0.624420\pi\) | ||||
−0.381000 | + | 0.924575i | \(0.624420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.48528 | − | 8.48528i | −1.43427 | − | 1.43427i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.24264i | − | 0.679366i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0000i | − | 1.56174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||
0.624695 | − | 0.780869i | \(-0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24264 | + | 4.24264i | −0.646997 | + | 0.646997i | −0.952266 | − | 0.305269i | \(-0.901253\pi\) |
0.305269 | + | 0.952266i | \(0.401253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | + | 2.00000i | 0.298142 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.0000 | −1.57143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.24264 | + | 4.24264i | 0.594089 | + | 0.594089i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | − | 4.00000i | 0.549442 | − | 0.549442i | −0.376837 | − | 0.926279i | \(-0.622988\pi\) |
0.926279 | + | 0.376837i | \(0.122988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 11.3137i | − | 1.52554i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 3.00000i | 0.384111 | + | 0.384111i | 0.872581 | − | 0.488470i | \(-0.162445\pi\) |
−0.488470 | + | 0.872581i | \(0.662445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264 | 0.534522 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | + | 2.82843i | 0.345547 | + | 0.345547i | 0.858448 | − | 0.512901i | \(-0.171429\pi\) |
−0.512901 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | − | 2.00000i | 0.240772 | − | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.82843i | − | 0.335673i | −0.985815 | − | 0.167836i | \(-0.946322\pi\) | ||
0.985815 | − | 0.167836i | \(-0.0536780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0000i | 1.87266i | 0.351123 | + | 0.936329i | \(0.385800\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.12132 | + | 2.12132i | −0.244949 | + | 0.244949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | − | 12.0000i | −1.36753 | − | 1.36753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.24264 | 0.477334 | 0.238667 | − | 0.971101i | \(-0.423290\pi\) | ||||
0.238667 | + | 0.971101i | \(0.423290\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3137 | − | 11.3137i | −1.24184 | − | 1.24184i | −0.959237 | − | 0.282604i | \(-0.908802\pi\) |
−0.282604 | − | 0.959237i | \(-0.591198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | + | 12.0000i | −1.30158 | + | 1.30158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.65685i | − | 0.606478i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.0000i | − | 1.48400i | −0.670402 | − | 0.741999i | \(-0.733878\pi\) | ||
0.670402 | − | 0.741999i | \(-0.266122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.7279 | − | 12.7279i | 1.33425 | − | 1.33425i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.00000 | + | 3.00000i | 0.311086 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65685 | −0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82843 | + | 2.82843i | 0.284268 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | − | 8.00000i | 0.796030 | − | 0.796030i | −0.186437 | − | 0.982467i | \(-0.559694\pi\) |
0.982467 | + | 0.186437i | \(0.0596941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3848i | 1.81151i | 0.423806 | + | 0.905753i | \(0.360694\pi\) | ||||
−0.423806 | + | 0.905753i | \(0.639306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0000i | 1.17108i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 7.00000i | −0.670478 | − | 0.670478i | 0.287348 | − | 0.957826i | \(-0.407226\pi\) |
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.24264 | −0.402694 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | + | 5.65685i | 0.527504 | + | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | + | 3.00000i | −0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.4558i | 2.33353i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.00000i | − | 0.454545i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.07107 | + | 7.07107i | −0.637577 | + | 0.637577i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.24264 | −0.376473 | −0.188237 | − | 0.982124i | \(-0.560277\pi\) | ||||
−0.188237 | + | 0.982124i | \(0.560277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1421 | + | 14.1421i | 1.23560 | + | 1.23560i | 0.961780 | + | 0.273824i | \(0.0882887\pi\) |
0.273824 | + | 0.961780i | \(0.411711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.82843i | − | 0.243432i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.48528 | + | 8.48528i | −0.719712 | + | 0.719712i | −0.968546 | − | 0.248834i | \(-0.919953\pi\) |
0.248834 | + | 0.968546i | \(0.419953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 2.00000i | −0.168430 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.9706 | 1.41915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.77817 | + | 7.77817i | 0.641533 | + | 0.641533i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | − | 6.00000i | 0.491539 | − | 0.491539i | −0.417252 | − | 0.908791i | \(-0.637007\pi\) |
0.908791 | + | 0.417252i | \(0.137007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.41421i | − | 0.115087i | −0.998343 | − | 0.0575435i | \(-0.981673\pi\) | ||
0.998343 | − | 0.0575435i | \(-0.0183268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.48528 | + | 8.48528i | −0.681554 | + | 0.681554i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | + | 5.00000i | 0.399043 | + | 0.399043i | 0.877896 | − | 0.478852i | \(-0.158947\pi\) |
−0.478852 | + | 0.877896i | \(0.658947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.65685 | −0.448618 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07107 | + | 7.07107i | 0.553849 | + | 0.553849i | 0.927549 | − | 0.373701i | \(-0.121911\pi\) |
−0.373701 | + | 0.927549i | \(0.621911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | + | 8.00000i | −0.622799 | + | 0.622799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137i | 0.875481i | 0.899101 | + | 0.437741i | \(0.144221\pi\) | ||||
−0.899101 | + | 0.437741i | \(0.855779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41421 | − | 1.41421i | 0.108148 | − | 0.108148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | − | 2.00000i | −0.152057 | − | 0.152057i | 0.626979 | − | 0.779036i | \(-0.284291\pi\) |
−0.779036 | + | 0.626979i | \(0.784291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7279 | −0.962140 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.00000 | + | 1.00000i | −0.0743294 | + | 0.0743294i | −0.743294 | − | 0.668965i | \(-0.766738\pi\) |
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.24264i | − | 0.313625i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.0000i | − | 0.882258i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.9706 | + | 16.9706i | −1.24101 | + | 1.24101i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.00000 | − | 3.00000i | −0.218218 | − | 0.218218i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274 | 1.63726 | 0.818631 | − | 0.574320i | \(-0.194733\pi\) | ||||
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | 1.29567 | 0.647834 | − | 0.761781i | \(-0.275675\pi\) | ||||
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.48528 | − | 8.48528i | −0.607644 | − | 0.607644i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | − | 4.00000i | 0.284988 | − | 0.284988i | −0.550106 | − | 0.835095i | \(-0.685413\pi\) |
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.07107i | − | 0.501255i | −0.968084 | − | 0.250627i | \(-0.919363\pi\) | ||
0.968084 | − | 0.250627i | \(-0.0806369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.00000i | − | 0.282138i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.9706 | − | 16.9706i | 1.19110 | − | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.0000 | − | 20.0000i | −1.39686 | − | 1.39686i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.48528 | + | 8.48528i | 0.584151 | + | 0.584151i | 0.936041 | − | 0.351890i | \(-0.114461\pi\) |
−0.351890 | + | 0.936041i | \(0.614461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.00000 | + | 2.00000i | −0.137038 | + | 0.137038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.9706i | 1.15738i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000i | 1.22192i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3137 | − | 11.3137i | 0.764510 | − | 0.764510i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | − | 18.0000i | −1.21081 | − | 1.21081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2132 | 1.42054 | 0.710271 | − | 0.703929i | \(-0.248573\pi\) | ||||
0.710271 | + | 0.703929i | \(0.248573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0000 | − | 11.0000i | 0.726900 | − | 0.726900i | −0.243101 | − | 0.970001i | \(-0.578165\pi\) |
0.970001 | + | 0.243101i | \(0.0781645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.9706i | 1.11658i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685 | − | 5.65685i | 0.369012 | − | 0.369012i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00000 | − | 3.00000i | −0.194871 | − | 0.194871i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.0000 | + | 22.0000i | −1.40553 | + | 1.40553i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.48528i | − | 0.539906i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0000i | 1.01396i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.82843 | + | 2.82843i | −0.178529 | + | 0.178529i | −0.790714 | − | 0.612185i | \(-0.790291\pi\) |
0.612185 | + | 0.790714i | \(0.290291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | + | 8.00000i | 0.502956 | + | 0.502956i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.9706 | 1.06274 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.7279 | − | 12.7279i | −0.790875 | − | 0.790875i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00000 | + | 4.00000i | −0.247594 | + | 0.247594i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.6274i | − | 1.39527i | −0.716455 | − | 0.697633i | \(-0.754237\pi\) | ||
0.716455 | − | 0.697633i | \(-0.245763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.0000i | − | 0.982872i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.89949 | + | 9.89949i | −0.605839 | + | 0.605839i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.41421 | 0.0859074 | 0.0429537 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429537 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0000 | −1.08941 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.48528 | − | 8.48528i | −0.511682 | − | 0.511682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.00000i | 0.0600842 | − | 0.0600842i | −0.676426 | − | 0.736510i | \(-0.736472\pi\) |
0.736510 | + | 0.676426i | \(0.236472\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.24264i | − | 0.254000i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.82843 | + | 2.82843i | −0.168133 | + | 0.168133i | −0.786158 | − | 0.618026i | \(-0.787933\pi\) |
0.618026 | + | 0.786158i | \(0.287933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | + | 4.00000i | 0.236940 | + | 0.236940i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.4264 | −2.50435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82843 | + | 2.82843i | 0.165805 | + | 0.165805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | − | 4.00000i | 0.233682 | − | 0.233682i | −0.580545 | − | 0.814228i | \(-0.697161\pi\) |
0.814228 | + | 0.580545i | \(0.197161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.00000i | − | 0.232104i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | + | 8.48528i | −0.490716 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.0000 | + | 18.0000i | 1.03750 | + | 1.03750i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.3137 | −0.649956 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82843 | + | 2.82843i | 0.161427 | + | 0.161427i | 0.783199 | − | 0.621772i | \(-0.213587\pi\) |
−0.621772 | + | 0.783199i | \(0.713587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0000 | − | 13.0000i | 0.739544 | − | 0.739544i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.2843i | − | 1.60385i | −0.597422 | − | 0.801927i | \(-0.703808\pi\) | ||
0.597422 | − | 0.801927i | \(-0.296192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.0000i | − | 1.46961i | −0.678280 | − | 0.734803i | \(-0.737274\pi\) | ||
0.678280 | − | 0.734803i | \(-0.262726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48528 | − | 8.48528i | 0.478091 | − | 0.478091i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0000 | + | 12.0000i | 0.673987 | + | 0.673987i | 0.958633 | − | 0.284646i | \(-0.0918759\pi\) |
−0.284646 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.6274 | 1.26689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.48528 | + | 8.48528i | 0.472134 | + | 0.472134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.00000 | − | 9.00000i | 0.499230 | − | 0.499230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.89949i | 0.547443i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.0000i | − | 0.661581i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82843 | − | 2.82843i | 0.155464 | − | 0.155464i | −0.625089 | − | 0.780553i | \(-0.714937\pi\) |
0.780553 | + | 0.625089i | \(0.214937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | + | 3.00000i | 0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.24264 | − | 4.24264i | −0.230429 | − | 0.230429i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | + | 12.0000i | −0.649836 | + | 0.649836i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 8.00000i | − | 0.430706i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.9706 | + | 16.9706i | −0.911028 | + | 0.911028i | −0.996353 | − | 0.0853256i | \(-0.972807\pi\) |
0.0853256 | + | 0.996353i | \(0.472807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.00000 | − | 3.00000i | −0.160586 | − | 0.160586i | 0.622240 | − | 0.782826i | \(-0.286223\pi\) |
−0.782826 | + | 0.622240i | \(0.786223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.65685 | − | 5.65685i | −0.300235 | − | 0.300235i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.0000 | − | 18.0000i | 0.952661 | − | 0.952661i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.82843i | − | 0.149279i | −0.997211 | − | 0.0746393i | \(-0.976219\pi\) | ||
0.997211 | − | 0.0746393i | \(-0.0237806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 15.0000i | − | 0.789474i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.53553 | + | 3.53553i | −0.185567 | + | 0.185567i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0000 | + | 32.0000i | 1.67496 | + | 1.67496i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3848 | −0.959678 | −0.479839 | − | 0.877357i | \(-0.659305\pi\) | ||||
−0.479839 | + | 0.877357i | \(0.659305\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9706 | − | 16.9706i | −0.881068 | − | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | − | 13.0000i | 0.673114 | − | 0.673114i | −0.285318 | − | 0.958433i | \(-0.592099\pi\) |
0.958433 | + | 0.285318i | \(0.0920993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 5.65685i | − | 0.292119i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000i | 1.23606i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8701 | − | 26.8701i | 1.38022 | − | 1.38022i | 0.536011 | − | 0.844211i | \(-0.319930\pi\) |
0.844211 | − | 0.536011i | \(-0.180070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | + | 3.00000i | 0.153695 | + | 0.153695i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.0000 | −2.44631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.24264 | − | 4.24264i | −0.215666 | − | 0.215666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.00000 | + | 2.00000i | −0.101404 | + | 0.101404i | −0.755989 | − | 0.654585i | \(-0.772844\pi\) |
0.654585 | + | 0.755989i | \(0.272844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.9706i | − | 0.858238i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.0000i | − | 1.00887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.48528 | − | 8.48528i | 0.426941 | − | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.0000 | + | 23.0000i | 1.15434 | + | 1.15434i | 0.985674 | + | 0.168663i | \(0.0539450\pi\) |
0.168663 | + | 0.985674i | \(0.446055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.48528 | 0.424795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7279 | − | 12.7279i | −0.634023 | − | 0.634023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00000 | + | 2.00000i | −0.0993808 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.9706i | − | 0.841200i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.0000i | 1.38451i | 0.721653 | + | 0.692255i | \(0.243383\pi\) | ||||
−0.721653 | + | 0.692255i | \(0.756617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.07107 | − | 7.07107i | 0.348790 | − | 0.348790i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.2548 | −2.22147 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3137 | + | 11.3137i | 0.552711 | + | 0.552711i | 0.927222 | − | 0.374511i | \(-0.122190\pi\) |
−0.374511 | + | 0.927222i | \(0.622190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0000 | + | 25.0000i | −1.21843 | + | 1.21843i | −0.250242 | + | 0.968183i | \(0.580510\pi\) |
−0.968183 | + | 0.250242i | \(0.919490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843i | 0.137523i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0000i | 0.873128i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7279 | − | 12.7279i | 0.615947 | − | 0.615947i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | − | 12.0000i | −0.579365 | − | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.7696 | 1.77113 | 0.885564 | − | 0.464518i | \(-0.153773\pi\) | ||||
0.885564 | + | 0.464518i | \(0.153773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.00000 | −0.384455 | −0.192228 | − | 0.981350i | \(-0.561571\pi\) | ||||
−0.192228 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3137 | − | 11.3137i | −0.542451 | − | 0.542451i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | − | 4.00000i | 0.191346 | − | 0.191346i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.41421i | 0.0674967i | 0.999430 | + | 0.0337484i | \(0.0107445\pi\) | ||||
−0.999430 | + | 0.0337484i | \(0.989256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 11.0000i | − | 0.523810i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9706 | − | 16.9706i | 0.806296 | − | 0.806296i | −0.177775 | − | 0.984071i | \(-0.556890\pi\) |
0.984071 | + | 0.177775i | \(0.0568900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.0000 | − | 28.0000i | −1.32733 | − | 1.32733i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.48528 | −0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.2843 | − | 28.2843i | −1.33185 | − | 1.33185i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.00000 | + | 1.00000i | −0.0469841 | + | 0.0469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 50.9117i | − | 2.38678i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0000i | 0.561336i | 0.959805 | + | 0.280668i | \(0.0905560\pi\) | ||||
−0.959805 | + | 0.280668i | \(0.909444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.24264 | + | 4.24264i | −0.198030 | + | 0.198030i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | + | 6.00000i | 0.279448 | + | 0.279448i | 0.832889 | − | 0.553441i | \(-0.186685\pi\) |
−0.553441 | + | 0.832889i | \(0.686685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7279 | −0.591517 | −0.295758 | − | 0.955263i | \(-0.595572\pi\) | ||||
−0.295758 | + | 0.955263i | \(0.595572\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.0000 | 0.556487 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.9706 | + | 16.9706i | 0.785304 | + | 0.785304i | 0.980720 | − | 0.195416i | \(-0.0626058\pi\) |
−0.195416 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | − | 12.0000i | 0.554109 | − | 0.554109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.07107i | − | 0.325818i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0000i | 1.10352i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.24264 | + | 4.24264i | −0.194666 | + | 0.194666i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.00000 | + | 4.00000i | 0.183147 | + | 0.183147i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4558 | −1.16311 | −0.581554 | − | 0.813508i | \(-0.697555\pi\) | ||||
−0.581554 | + | 0.813508i | \(0.697555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.48528 | − | 8.48528i | −0.386094 | − | 0.386094i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.00000 | + | 8.00000i | −0.363261 | + | 0.363261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.8406i | 1.98661i | 0.115529 | + | 0.993304i | \(0.463144\pi\) | ||||
−0.115529 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10.0000i | − | 0.452216i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.65685 | − | 5.65685i | 0.255290 | − | 0.255290i | −0.567845 | − | 0.823135i | \(-0.692223\pi\) |
0.823135 | + | 0.567845i | \(0.192223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0000 | − | 24.0000i | −1.08091 | − | 1.08091i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3137 | 0.508513 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1421 | − | 14.1421i | −0.633089 | − | 0.633089i | 0.315753 | − | 0.948842i | \(-0.397743\pi\) |
−0.948842 | + | 0.315753i | \(0.897743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | − | 8.00000i | 0.357414 | − | 0.357414i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 14.1421i | − | 0.630567i | −0.948998 | − | 0.315283i | \(-0.897900\pi\) | ||
0.948998 | − | 0.315283i | \(-0.102100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 32.0000i | − | 1.42398i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.53553 | − | 3.53553i | 0.157019 | − | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.0000 | + | 16.0000i | 0.709188 | + | 0.709188i | 0.966364 | − | 0.257177i | \(-0.0827923\pi\) |
−0.257177 | + | 0.966364i | \(0.582792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 67.8823 | 3.00293 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.7696 | + | 36.7696i | 1.62026 | + | 1.62026i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | − | 8.00000i | 0.351840 | − | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82843i | 0.124154i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.0000i | − | 0.963837i | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||
0.876216 | − | 0.481919i | \(-0.160060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5563 | + | 15.5563i | −0.680232 | + | 0.680232i | −0.960052 | − | 0.279821i | \(-0.909725\pi\) |
0.279821 | + | 0.960052i | \(0.409725\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.00000 | + | 9.00000i | 0.392792 | + | 0.392792i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | − | 30.0000i | 1.29944 | − | 1.29944i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.3137i | − | 0.489134i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.1127 | + | 31.1127i | −1.34012 | + | 1.34012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | + | 29.0000i | 1.24681 | + | 1.24681i | 0.957122 | + | 0.289685i | \(0.0935507\pi\) |
0.289685 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41421 | 0.0606897 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.0000 | −1.19939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0416 | − | 24.0416i | −1.02795 | − | 1.02795i | −0.999598 | − | 0.0283478i | \(-0.990975\pi\) |
−0.0283478 | − | 0.999598i | \(-0.509025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | + | 3.00000i | −0.128037 | + | 0.128037i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.3137i | − | 0.481980i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 18.0000i | − | 0.765438i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.48528 | + | 8.48528i | −0.360180 | + | 0.360180i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | − | 14.0000i | −0.593199 | − | 0.593199i | 0.345295 | − | 0.938494i | \(-0.387779\pi\) |
−0.938494 | + | 0.345295i | \(0.887779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.4558 | −1.07667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82843 | + | 2.82843i | 0.119204 | + | 0.119204i | 0.764192 | − | 0.644988i | \(-0.223138\pi\) |
−0.644988 | + | 0.764192i | \(0.723138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0000 | − | 12.0000i | 0.504844 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.24264i | 0.178174i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000i | 0.754599i | 0.926091 | + | 0.377300i | \(0.123147\pi\) | ||||
−0.926091 | + | 0.377300i | \(0.876853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1421 | − | 14.1421i | 0.591830 | − | 0.591830i | −0.346296 | − | 0.938125i | \(-0.612561\pi\) |
0.938125 | + | 0.346296i | \(0.112561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0000 | − | 16.0000i | −0.668410 | − | 0.668410i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.00000 | 0.166522 | 0.0832611 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832611 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.7279 | − | 12.7279i | −0.528954 | − | 0.528954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −48.0000 | + | 48.0000i | −1.99138 | + | 1.99138i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.6274i | − | 0.937132i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0000i | 0.496139i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.9706 | + | 16.9706i | −0.700450 | + | 0.700450i | −0.964507 | − | 0.264057i | \(-0.914939\pi\) |
0.264057 | + | 0.964507i | \(0.414939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | + | 6.00000i | 0.247226 | + | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.65685 | −0.232692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.9117 | + | 50.9117i | 2.08718 | + | 2.08718i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.00000 | + | 5.00000i | −0.204636 | + | 0.204636i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.0833i | 1.96463i | 0.187239 | + | 0.982314i | \(0.440046\pi\) | ||||
−0.187239 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.0000i | − | 1.14214i | −0.820900 | − | 0.571072i | \(-0.806528\pi\) | ||
0.820900 | − | 0.571072i | \(-0.193472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82843 | + | 2.82843i | −0.115182 | + | 0.115182i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.0000 | − | 10.0000i | −0.406558 | − | 0.406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.24264 | −0.172203 | −0.0861017 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861017 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | −0.972529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | + | 8.48528i | 0.343278 | + | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | + | 13.0000i | −0.525065 | + | 0.525065i | −0.919097 | − | 0.394032i | \(-0.871080\pi\) |
0.394032 | + | 0.919097i | \(0.371080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.2843i | 1.14053i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000i | 0.885687i | 0.896599 | + | 0.442843i | \(0.146030\pi\) | ||||
−0.896599 | + | 0.442843i | \(0.853970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.4558 | + | 25.4558i | −1.02316 | + | 1.02316i | −0.0234313 | + | 0.999725i | \(0.507459\pi\) |
−0.999725 | + | 0.0234313i | \(0.992541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | + | 2.00000i | 0.0802572 | + | 0.0802572i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −59.3970 | −2.37969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.65685 | + | 5.65685i | 0.225913 | + | 0.225913i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0000 | + | 18.0000i | −0.717707 | + | 0.717707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.3553i | 1.40747i | 0.710461 | + | 0.703737i | \(0.248487\pi\) | ||||
−0.710461 | + | 0.703737i | \(0.751513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 12.0000i | − | 0.476957i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.48528 | + | 8.48528i | −0.336728 | + | 0.336728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.0000 | − | 33.0000i | −1.30751 | − | 1.30751i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.82843 | 0.111891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.89949 | + | 9.89949i | 0.390398 | + | 0.390398i | 0.874829 | − | 0.484431i | \(-0.160973\pi\) |
−0.484431 | + | 0.874829i | \(0.660973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | − | 12.0000i | 0.472500 | − | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 14.1421i | − | 0.555985i | −0.960583 | − | 0.277992i | \(-0.910331\pi\) | ||
0.960583 | − | 0.277992i | \(-0.0896690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.7279 | − | 12.7279i | 0.498847 | − | 0.498847i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | − | 6.00000i | −0.234798 | − | 0.234798i | 0.579894 | − | 0.814692i | \(-0.303094\pi\) |
−0.814692 | + | 0.579894i | \(0.803094\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.5685 | 2.21032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0000 | −0.624219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | + | 9.00000i | −0.350059 | + | 0.350059i | −0.860132 | − | 0.510072i | \(-0.829619\pi\) |
0.510072 | + | 0.860132i | \(0.329619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.4558i | 0.988623i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000i | 0.930680i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.3137 | + | 11.3137i | −0.438069 | + | 0.438069i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0000 | − | 15.0000i | −0.579934 | − | 0.579934i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9706 | 0.655141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.12132 | − | 2.12132i | −0.0816497 | − | 0.0816497i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.0000 | + | 26.0000i | −0.999261 | + | 0.999261i | −1.00000 | 0.000738553i | \(-0.999765\pi\) | |
0.000738553 | 1.00000i | \(0.499765\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.9706i | 0.651270i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9706 | − | 16.9706i | 0.649361 | − | 0.649361i | −0.303478 | − | 0.952838i | \(-0.598148\pi\) |
0.952838 | + | 0.303478i | \(0.0981479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0000 | + | 20.0000i | 0.764161 | + | 0.764161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.5563 | −0.593512 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5563 | + | 15.5563i | 0.591791 | + | 0.591791i | 0.938115 | − | 0.346324i | \(-0.112570\pi\) |
−0.346324 | + | 0.938115i | \(0.612570\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0000 | − | 12.0000i | 0.455842 | − | 0.455842i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.9411i | 1.28746i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 60.0000i | 2.27266i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.7279 | − | 12.7279i | 0.481414 | − | 0.481414i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.00000 | − | 4.00000i | −0.151078 | − | 0.151078i | 0.627521 | − | 0.778599i | \(-0.284069\pi\) |
−0.778599 | + | 0.627521i | \(0.784069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.48528 | −0.320028 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.9411 | − | 33.9411i | −1.27649 | − | 1.27649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | − | 13.0000i | 0.488225 | − | 0.488225i | −0.419521 | − | 0.907746i | \(-0.637802\pi\) |
0.907746 | + | 0.419521i | \(0.137802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.24264i | 0.159111i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.9411 | − | 33.9411i | 1.26933 | − | 1.26933i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.00000 | + | 8.00000i | 0.298765 | + | 0.298765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.48528 | −0.316448 | −0.158224 | − | 0.987403i | \(-0.550577\pi\) | ||||
−0.158224 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 78.0000 | 2.90487 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.7279 | + | 12.7279i | 0.473357 | + | 0.473357i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0000 | − | 12.0000i | 0.445669 | − | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.8701i | − | 0.996555i | −0.867018 | − | 0.498278i | \(-0.833966\pi\) | ||
0.867018 | − | 0.498278i | \(-0.166034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4558 | − | 25.4558i | 0.941518 | − | 0.941518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0000 | − | 25.0000i | −0.923396 | − | 0.923396i | 0.0738717 | − | 0.997268i | \(-0.476464\pi\) |
−0.997268 | + | 0.0738717i | \(0.976464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.1127 | 1.14761 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4558 | + | 25.4558i | 0.936408 | + | 0.936408i | 0.998096 | − | 0.0616872i | \(-0.0196481\pi\) |
−0.0616872 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | + | 6.00000i | −0.220416 | + | 0.220416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6274i | 0.830119i | 0.909794 | + | 0.415060i | \(0.136239\pi\) | ||||
−0.909794 | + | 0.415060i | \(0.863761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 24.0000i | − | 0.879292i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.3137 | − | 11.3137i | 0.413947 | − | 0.413947i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | − | 12.0000i | −0.438470 | − | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7279 | 0.464448 | 0.232224 | − | 0.972662i | \(-0.425400\pi\) | ||||
0.232224 | + | 0.972662i | \(0.425400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.82843 | − | 2.82843i | −0.102937 | − | 0.102937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0000 | − | 27.0000i | 0.981332 | − | 0.981332i | −0.0184972 | − | 0.999829i | \(-0.505888\pi\) |
0.999829 | + | 0.0184972i | \(0.00588818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 11.3137i | − | 0.410662i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0000i | 1.23250i | 0.787551 | + | 0.616250i | \(0.211349\pi\) | ||||
−0.787551 | + | 0.616250i | \(0.788651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.6985 | + | 29.6985i | −1.07516 | + | 1.07516i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0000 | − | 12.0000i | −0.433861 | − | 0.433861i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.89949 | + | 9.89949i | 0.356522 | + | 0.356522i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.00000 | + | 4.00000i | −0.143870 | + | 0.143870i | −0.775373 | − | 0.631503i | \(-0.782438\pi\) |
0.631503 | + | 0.775373i | \(0.282438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.7279i | 0.457200i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.0000i | 0.645746i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.1421 | + | 14.1421i | −0.506695 | + | 0.506695i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | − | 8.00000i | −0.286263 | − | 0.286263i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.65685 | 0.202159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8701 | − | 26.8701i | −0.957814 | − | 0.957814i | 0.0413314 | − | 0.999145i | \(-0.486840\pi\) |
−0.999145 | + | 0.0413314i | \(0.986840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.0000 | + | 16.0000i | −0.569615 | + | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 25.4558i | − | 0.905106i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000i | 0.639199i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3137 | + | 11.3137i | −0.401256 | + | 0.401256i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.0000 | − | 22.0000i | −0.779280 | − | 0.779280i | 0.200428 | − | 0.979708i | \(-0.435767\pi\) |
−0.979708 | + | 0.200428i | \(0.935767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9706 | −0.600375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0000 | 0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 45.2548 | + | 45.2548i | 1.59701 | + | 1.59701i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | − | 24.0000i | 0.845889 | − | 0.845889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 30.0000i | − | 1.05474i | −0.849635 | − | 0.527372i | \(-0.823177\pi\) | ||
0.849635 | − | 0.527372i | \(-0.176823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41421 | + | 1.41421i | −0.0496598 | + | 0.0496598i | −0.731501 | − | 0.681841i | \(-0.761180\pi\) |
0.681841 | + | 0.731501i | \(0.261180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.00000 | − | 1.00000i | −0.0350715 | − | 0.0350715i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.2843 | 0.990755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.7279 | + | 12.7279i | 0.444750 | + | 0.444750i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.0000 | + | 20.0000i | −0.698005 | + | 0.698005i | −0.963980 | − | 0.265975i | \(-0.914306\pi\) |
0.265975 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.24264i | − | 0.147889i | −0.997262 | − | 0.0739446i | \(-0.976441\pi\) | ||
0.997262 | − | 0.0739446i | \(-0.0235588\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000i | 0.417786i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4558 | + | 25.4558i | −0.885186 | + | 0.885186i | −0.994056 | − | 0.108870i | \(-0.965277\pi\) |
0.108870 | + | 0.994056i | \(0.465277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0000 | + | 15.0000i | 0.520972 | + | 0.520972i | 0.917865 | − | 0.396893i | \(-0.129912\pi\) |
−0.396893 | + | 0.917865i | \(0.629912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | −0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 66.0000 | 2.28676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.6274 | + | 22.6274i | 0.783054 | + | 0.783054i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.00000 | + | 3.00000i | −0.103695 | + | 0.103695i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 31.1127i | − | 1.07413i | −0.843541 | − | 0.537065i | \(-0.819533\pi\) | ||
0.843541 | − | 0.537065i | \(-0.180467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000i | 0.103448i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.24264 | + | 4.24264i | −0.146124 | + | 0.146124i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0000 | + | 10.0000i | 0.344010 | + | 0.344010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.2132 | −0.728894 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.48528 | + | 8.48528i | 0.290872 | + | 0.290872i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | + | 15.0000i | −0.513590 | + | 0.513590i | −0.915625 | − | 0.402034i | \(-0.868303\pi\) |
0.402034 | + | 0.915625i | \(0.368303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.65685i | − | 0.193460i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.0000i | − | 1.02478i | −0.858753 | − | 0.512390i | \(-0.828760\pi\) | ||
0.858753 | − | 0.512390i | \(-0.171240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.07107 | − | 7.07107i | 0.241262 | − | 0.241262i | −0.576110 | − | 0.817372i | \(-0.695430\pi\) |
0.817372 | + | 0.576110i | \(0.195430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.0000 | + | 30.0000i | 1.02240 | + | 1.02240i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2843 | −0.962808 | −0.481404 | − | 0.876499i | \(-0.659873\pi\) | ||||
−0.481404 | + | 0.876499i | \(0.659873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | −0.272008 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4350 | − | 13.4350i | −0.456278 | − | 0.456278i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | − | 12.0000i | 0.407072 | − | 0.407072i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706i | 0.575026i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.00000i | − | 0.135379i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.9706 | − | 16.9706i | 0.573710 | − | 0.573710i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0000 | − | 11.0000i | −0.371444 | − | 0.371444i | 0.496559 | − | 0.868003i | \(-0.334597\pi\) |
−0.868003 | + | 0.496559i | \(0.834597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.65685 | −0.190801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −58.0000 | −1.95407 | −0.977035 | − | 0.213080i | \(-0.931651\pi\) | ||||
−0.977035 | + | 0.213080i | \(0.931651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.0416 | − | 24.0416i | −0.809065 | − | 0.809065i | 0.175427 | − | 0.984492i | \(-0.443869\pi\) |
−0.984492 | + | 0.175427i | \(0.943869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706i | 0.569816i | 0.958555 | + | 0.284908i | \(0.0919630\pi\) | ||||
−0.958555 | + | 0.284908i | \(0.908037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000i | 0.603701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.82843 | + | 2.82843i | −0.0947559 | + | 0.0947559i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.00000 | − | 4.00000i | −0.133855 | − | 0.133855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9706 | − | 16.9706i | −0.566000 | − | 0.566000i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0000 | + | 24.0000i | −0.799556 | + | 0.799556i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 25.4558i | − | 0.847117i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00000i | 0.132964i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.0122 | + | 41.0122i | −1.36179 | + | 1.36179i | −0.490149 | + | 0.871639i | \(0.663058\pi\) |
−0.871639 | + | 0.490149i | \(0.836942\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00000 | + | 8.00000i | 0.265343 | + | 0.265343i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6274 | 0.749680 | 0.374840 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374840 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −64.0000 | −2.11809 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.48528 | − | 8.48528i | −0.280515 | − | 0.280515i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 60.0000 | − | 60.0000i | 1.98137 | − | 1.98137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3848i | 0.606458i | 0.952918 | + | 0.303229i | \(0.0980647\pi\) | ||||
−0.952918 | + | 0.303229i | \(0.901935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 4.00000i | − | 0.131804i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.48528 | − | 8.48528i | 0.279296 | − | 0.279296i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | − | 9.00000i | −0.295918 | − | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.3848 | −0.603835 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.0000 | −1.50921 | −0.754606 | − | 0.656179i | \(-0.772172\pi\) | ||||
−0.754606 | + | 0.656179i | \(0.772172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5563 | + | 15.5563i | 0.509839 | + | 0.509839i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0000 | + | 20.0000i | −0.654771 | + | 0.654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.8823i | 2.21999i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.3848 | + | 18.3848i | −0.599965 | + | 0.599965i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0000 | + | 26.0000i | 0.847576 | + | 0.847576i | 0.989830 | − | 0.142254i | \(-0.0454351\pi\) |
−0.142254 | + | 0.989830i | \(0.545435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2843 | 0.921063 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.0000 | −0.390360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.0000 | + | 48.0000i | −1.55815 | + | 1.55815i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 16.9706i | − | 0.550308i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.2548 | − | 45.2548i | 1.46441 | − | 1.46441i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.0000 | − | 16.0000i | −0.517207 | − | 0.517207i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.4264 | 1.37002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0000 | −0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.82843 | + | 2.82843i | 0.0911448 | + | 0.0911448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.0000 | − | 36.0000i | 1.15888 | − | 1.15888i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.3553i | 1.13695i | 0.822700 | + | 0.568476i | \(0.192467\pi\) | ||||
−0.822700 | + | 0.568476i | \(0.807533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 12.0000i | − | 0.385496i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6274 | − | 22.6274i | 0.726148 | − | 0.726148i | −0.243702 | − | 0.969850i | \(-0.578362\pi\) |
0.969850 | + | 0.243702i | \(0.0783618\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.0000 | + | 36.0000i | 1.15411 | + | 1.15411i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.7279 | −0.407620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.00000 | −0.0639857 | −0.0319928 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319928 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.5980 | − | 39.5980i | −1.26556 | − | 1.26556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00000 | − | 7.00000i | 0.223493 | − | 0.223493i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.6274i | 0.721703i | 0.932623 | + | 0.360851i | \(0.117514\pi\) | ||||
−0.932623 | + | 0.360851i | \(0.882486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 16.0000i | − | 0.509802i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.48528 | + | 8.48528i | −0.270089 | + | 0.270089i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.0000 | − | 12.0000i | −0.381578 | − | 0.381578i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.6690 | −1.48249 | −0.741246 | − | 0.671234i | \(-0.765765\pi\) | ||||
−0.741246 | + | 0.671234i | \(0.765765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.1421 | − | 14.1421i | −0.448336 | − | 0.448336i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0000 | + | 33.0000i | −1.04512 | + | 1.04512i | −0.0461877 | + | 0.998933i | \(0.514707\pi\) |
−0.998933 | + | 0.0461877i | \(0.985293\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.24264i | − | 0.134231i |
(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 | 768.2.j.d.577.1 | yes | 4 | |
3.2 | odd | 2 | 2304.2.k.a.577.1 | 4 | |||
4.3 | odd | 2 | inner | 768.2.j.d.577.2 | yes | 4 | |
8.3 | odd | 2 | 768.2.j.a.577.1 | yes | 4 | ||
8.5 | even | 2 | 768.2.j.a.577.2 | yes | 4 | ||
12.11 | even | 2 | 2304.2.k.a.577.2 | 4 | |||
16.3 | odd | 4 | 768.2.j.a.193.1 | ✓ | 4 | ||
16.5 | even | 4 | inner | 768.2.j.d.193.1 | yes | 4 | |
16.11 | odd | 4 | inner | 768.2.j.d.193.2 | yes | 4 | |
16.13 | even | 4 | 768.2.j.a.193.2 | yes | 4 | ||
24.5 | odd | 2 | 2304.2.k.d.577.1 | 4 | |||
24.11 | even | 2 | 2304.2.k.d.577.2 | 4 | |||
32.3 | odd | 8 | 3072.2.d.d.1537.4 | 4 | |||
32.5 | even | 8 | 3072.2.a.f.1.2 | 2 | |||
32.11 | odd | 8 | 3072.2.a.f.1.1 | 2 | |||
32.13 | even | 8 | 3072.2.d.d.1537.3 | 4 | |||
32.19 | odd | 8 | 3072.2.d.d.1537.1 | 4 | |||
32.21 | even | 8 | 3072.2.a.d.1.1 | 2 | |||
32.27 | odd | 8 | 3072.2.a.d.1.2 | 2 | |||
32.29 | even | 8 | 3072.2.d.d.1537.2 | 4 | |||
48.5 | odd | 4 | 2304.2.k.a.1729.2 | 4 | |||
48.11 | even | 4 | 2304.2.k.a.1729.1 | 4 | |||
48.29 | odd | 4 | 2304.2.k.d.1729.2 | 4 | |||
48.35 | even | 4 | 2304.2.k.d.1729.1 | 4 | |||
96.5 | odd | 8 | 9216.2.a.q.1.1 | 2 | |||
96.11 | even | 8 | 9216.2.a.q.1.2 | 2 | |||
96.53 | odd | 8 | 9216.2.a.e.1.2 | 2 | |||
96.59 | even | 8 | 9216.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.a.193.1 | ✓ | 4 | 16.3 | odd | 4 | ||
768.2.j.a.193.2 | yes | 4 | 16.13 | even | 4 | ||
768.2.j.a.577.1 | yes | 4 | 8.3 | odd | 2 | ||
768.2.j.a.577.2 | yes | 4 | 8.5 | even | 2 | ||
768.2.j.d.193.1 | yes | 4 | 16.5 | even | 4 | inner | |
768.2.j.d.193.2 | yes | 4 | 16.11 | odd | 4 | inner | |
768.2.j.d.577.1 | yes | 4 | 1.1 | even | 1 | trivial | |
768.2.j.d.577.2 | yes | 4 | 4.3 | odd | 2 | inner | |
2304.2.k.a.577.1 | 4 | 3.2 | odd | 2 | |||
2304.2.k.a.577.2 | 4 | 12.11 | even | 2 | |||
2304.2.k.a.1729.1 | 4 | 48.11 | even | 4 | |||
2304.2.k.a.1729.2 | 4 | 48.5 | odd | 4 | |||
2304.2.k.d.577.1 | 4 | 24.5 | odd | 2 | |||
2304.2.k.d.577.2 | 4 | 24.11 | even | 2 | |||
2304.2.k.d.1729.1 | 4 | 48.35 | even | 4 | |||
2304.2.k.d.1729.2 | 4 | 48.29 | odd | 4 | |||
3072.2.a.d.1.1 | 2 | 32.21 | even | 8 | |||
3072.2.a.d.1.2 | 2 | 32.27 | odd | 8 | |||
3072.2.a.f.1.1 | 2 | 32.11 | odd | 8 | |||
3072.2.a.f.1.2 | 2 | 32.5 | even | 8 | |||
3072.2.d.d.1537.1 | 4 | 32.19 | odd | 8 | |||
3072.2.d.d.1537.2 | 4 | 32.29 | even | 8 | |||
3072.2.d.d.1537.3 | 4 | 32.13 | even | 8 | |||
3072.2.d.d.1537.4 | 4 | 32.3 | odd | 8 | |||
9216.2.a.e.1.1 | 2 | 96.59 | even | 8 | |||
9216.2.a.e.1.2 | 2 | 96.53 | odd | 8 | |||
9216.2.a.q.1.1 | 2 | 96.5 | odd | 8 | |||
9216.2.a.q.1.2 | 2 | 96.11 | even | 8 |