Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(257,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.e (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.257 |
Dual form | 1024.2.e.c.769.1 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.00000i | −0.577350 | − | 0.577350i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 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 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.00000i | −0.301511 | + | 0.301511i | −0.841605 | − | 0.540094i | \(-0.818389\pi\) |
0.540094 | + | 0.841605i | \(0.318389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 2.00000i | −0.554700 | − | 0.554700i | 0.373094 | − | 0.927794i | \(-0.378297\pi\) |
−0.927794 | + | 0.373094i | \(0.878297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | − | 5.00000i | −1.14708 | − | 1.14708i | −0.987124 | − | 0.159954i | \(-0.948865\pi\) |
−0.159954 | − | 0.987124i | \(-0.551135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | + | 4.00000i | −0.872872 | + | 0.872872i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | + | 6.00000i | 1.11417 | + | 1.11417i | 0.992580 | + | 0.121592i | \(0.0387999\pi\) |
0.121592 | + | 0.992580i | \(0.461200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.00000 | − | 8.00000i | −1.35225 | − | 1.35225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | + | 2.00000i | −0.328798 | + | 0.328798i | −0.852129 | − | 0.523331i | \(-0.824689\pi\) |
0.523331 | + | 0.852129i | \(0.324689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000i | 0.640513i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | − | 2.00000i | −0.298142 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | − | 4.00000i | −0.560112 | − | 0.560112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | − | 2.00000i | 0.274721 | − | 0.274721i | −0.556276 | − | 0.830997i | \(-0.687770\pi\) |
0.830997 | + | 0.556276i | \(0.187770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000i | 0.539360i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.0000i | 1.32453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 3.00000i | 0.390567 | − | 0.390567i | −0.484323 | − | 0.874889i | \(-0.660934\pi\) |
0.874889 | + | 0.484323i | \(0.160934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 6.00000i | −0.768221 | − | 0.768221i | 0.209572 | − | 0.977793i | \(-0.432793\pi\) |
−0.977793 | + | 0.209572i | \(0.932793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | −0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | − | 3.00000i | −0.366508 | − | 0.366508i | 0.499694 | − | 0.866202i | \(-0.333446\pi\) |
−0.866202 | + | 0.499694i | \(0.833446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | − | 4.00000i | 0.481543 | − | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000i | 0.474713i | 0.971423 | + | 0.237356i | \(0.0762809\pi\) | ||||
−0.971423 | + | 0.237356i | \(0.923719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.00000 | + | 3.00000i | −0.346410 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 4.00000i | 0.455842 | + | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.00000 | − | 7.00000i | −0.768350 | − | 0.768350i | 0.209466 | − | 0.977816i | \(-0.432827\pi\) |
−0.977816 | + | 0.209466i | \(0.932827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | − | 8.00000i | 0.867722 | − | 0.867722i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.0000i | − | 1.27200i | −0.771690 | − | 0.635999i | \(-0.780588\pi\) | ||
0.771690 | − | 0.635999i | \(-0.219412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | + | 8.00000i | −0.838628 | + | 0.838628i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | − | 8.00000i | −0.829561 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.0000 | −2.05196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | + | 1.00000i | 0.100504 | + | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | + | 2.00000i | −0.199007 | + | 0.199007i | −0.799574 | − | 0.600567i | \(-0.794942\pi\) |
0.600567 | + | 0.799574i | \(0.294942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.0000i | − | 1.18240i | −0.806527 | − | 0.591198i | \(-0.798655\pi\) | ||
0.806527 | − | 0.591198i | \(-0.201345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.0000i | 1.56144i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.00000 | − | 7.00000i | 0.676716 | − | 0.676716i | −0.282540 | − | 0.959256i | \(-0.591177\pi\) |
0.959256 | + | 0.282540i | \(0.0911770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | + | 10.0000i | 0.957826 | + | 0.957826i | 0.999146 | − | 0.0413197i | \(-0.0131562\pi\) |
−0.0413197 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | + | 8.00000i | 0.746004 | + | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | + | 2.00000i | −0.184900 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.0000i | − | 1.46672i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000i | 0.818182i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | − | 2.00000i | 0.180334 | − | 0.180334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.00000 | + | 5.00000i | 0.436852 | + | 0.436852i | 0.890951 | − | 0.454099i | \(-0.150039\pi\) |
−0.454099 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.0000 | + | 20.0000i | −1.73422 | + | 1.73422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.0000i | 1.37706i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.0000i | − | 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | + | 3.00000i | −0.254457 | + | 0.254457i | −0.822795 | − | 0.568338i | \(-0.807586\pi\) |
0.568338 | + | 0.822795i | \(0.307586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.0000 | 1.99309 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.00000 | + | 9.00000i | 0.742307 | + | 0.742307i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | + | 2.00000i | −0.163846 | + | 0.163846i | −0.784268 | − | 0.620422i | \(-0.786961\pi\) |
0.620422 | + | 0.784268i | \(0.286961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000i | 0.325515i | 0.986666 | + | 0.162758i | \(0.0520389\pi\) | ||||
−0.986666 | + | 0.162758i | \(0.947961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | − | 16.0000i | 1.28515 | − | 1.28515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | − | 6.00000i | −0.478852 | − | 0.478852i | 0.425912 | − | 0.904764i | \(-0.359953\pi\) |
−0.904764 | + | 0.425912i | \(0.859953\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | + | 7.00000i | 0.548282 | + | 0.548282i | 0.925944 | − | 0.377661i | \(-0.123272\pi\) |
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | − | 4.00000i | 0.311400 | − | 0.311400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.00000 | + | 5.00000i | −0.382360 | + | 0.382360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0000 | − | 10.0000i | −0.760286 | − | 0.760286i | 0.216088 | − | 0.976374i | \(-0.430670\pi\) |
−0.976374 | + | 0.216088i | \(0.930670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0000 | −0.907115 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.00000 | + | 1.00000i | 0.0747435 | + | 0.0747435i | 0.743490 | − | 0.668747i | \(-0.233169\pi\) |
−0.668747 | + | 0.743490i | \(0.733169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | − | 6.00000i | 0.445976 | − | 0.445976i | −0.448038 | − | 0.894015i | \(-0.647877\pi\) |
0.894015 | + | 0.448038i | \(0.147877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000i | 0.588172i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 4.00000i | −0.292509 | + | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.0000 | + | 16.0000i | 1.16383 | + | 1.16383i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000 | + | 8.00000i | 0.572892 | + | 0.572892i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | − | 10.0000i | 0.712470 | − | 0.712470i | −0.254581 | − | 0.967051i | \(-0.581938\pi\) |
0.967051 | + | 0.254581i | \(0.0819375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.00000i | − | 0.283552i | −0.989899 | − | 0.141776i | \(-0.954719\pi\) | ||
0.989899 | − | 0.141776i | \(-0.0452813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000i | 0.423207i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0000 | − | 24.0000i | 1.68447 | − | 1.68447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 4.00000i | 0.279372 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0000 | 0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | + | 17.0000i | 1.17033 | + | 1.17033i | 0.982131 | + | 0.188197i | \(0.0602643\pi\) |
0.188197 | + | 0.982131i | \(0.439736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.00000 | − | 4.00000i | 0.274075 | − | 0.274075i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0000i | 0.818393i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.0000i | − | 2.17230i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | + | 4.00000i | −0.270295 | + | 0.270295i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | − | 8.00000i | −0.538138 | − | 0.538138i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0000 | + | 15.0000i | 0.995585 | + | 0.995585i | 0.999990 | − | 0.00440533i | \(-0.00140226\pi\) |
−0.00440533 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000 | − | 18.0000i | 1.18947 | − | 1.18947i | 0.212260 | − | 0.977213i | \(-0.431918\pi\) |
0.977213 | − | 0.212260i | \(-0.0680825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.00000i | − | 0.526361i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000i | 0.786146i | 0.919507 | + | 0.393073i | \(0.128588\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | − | 8.00000i | −0.519656 | − | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | −0.772988 | −0.386494 | − | 0.922292i | \(-0.626314\pi\) | ||||
−0.386494 | + | 0.922292i | \(0.626314\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0000 | + | 18.0000i | −1.14998 | + | 1.14998i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.0000i | 1.27257i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0000i | 0.887214i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00000 | − | 3.00000i | 0.189358 | − | 0.189358i | −0.606060 | − | 0.795419i | \(-0.707251\pi\) |
0.795419 | + | 0.606060i | \(0.207251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | − | 4.00000i | −0.251478 | − | 0.251478i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.0000 | −1.00196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | + | 8.00000i | 0.497096 | + | 0.497096i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | − | 6.00000i | 0.371391 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.0000i | − | 1.72655i | −0.504730 | − | 0.863277i | \(-0.668408\pi\) | ||
0.504730 | − | 0.863277i | \(-0.331592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.00000i | − | 0.491436i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | + | 12.0000i | −0.734388 | + | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0000 | − | 14.0000i | −0.853595 | − | 0.853595i | 0.136979 | − | 0.990574i | \(-0.456261\pi\) |
−0.990574 | + | 0.136979i | \(0.956261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0000 | −1.94386 | −0.971931 | − | 0.235267i | \(-0.924404\pi\) | ||||
−0.971931 | + | 0.235267i | \(0.924404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 3.00000i | 0.180907 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.00000 | + | 6.00000i | −0.360505 | + | 0.360505i | −0.863999 | − | 0.503494i | \(-0.832048\pi\) |
0.503494 | + | 0.863999i | \(0.332048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.00000i | − | 0.478947i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0000 | − | 17.0000i | 1.01055 | − | 1.01055i | 0.0106013 | − | 0.999944i | \(-0.496625\pi\) |
0.999944 | − | 0.0106013i | \(-0.00337456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.0000 | + | 20.0000i | 1.18470 | + | 1.18470i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | + | 4.00000i | 0.234484 | + | 0.234484i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | + | 6.00000i | −0.350524 | + | 0.350524i | −0.860304 | − | 0.509781i | \(-0.829727\pi\) |
0.509781 | + | 0.860304i | \(0.329727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 12.0000i | − | 0.698667i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 8.00000i | − | 0.464207i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000 | − | 8.00000i | 0.462652 | − | 0.462652i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | + | 12.0000i | 0.691669 | + | 0.691669i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.00000 | 0.229794 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | − | 5.00000i | −0.285365 | − | 0.285365i | 0.549879 | − | 0.835244i | \(-0.314674\pi\) |
−0.835244 | + | 0.549879i | \(0.814674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | + | 12.0000i | −0.682656 | + | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.0000i | − | 1.13410i | −0.823685 | − | 0.567048i | \(-0.808085\pi\) | ||
0.823685 | − | 0.567048i | \(-0.191915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000i | 0.791327i | 0.918396 | + | 0.395663i | \(0.129485\pi\) | ||||
−0.918396 | + | 0.395663i | \(0.870515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.00000 | + | 8.00000i | −0.450749 | + | 0.450749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | − | 2.00000i | −0.112331 | − | 0.112331i | 0.648707 | − | 0.761038i | \(-0.275310\pi\) |
−0.761038 | + | 0.648707i | \(0.775310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | −0.781404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | − | 20.0000i | −1.11283 | − | 1.11283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | + | 6.00000i | −0.332820 | + | 0.332820i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 20.0000i | − | 1.10600i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.00000 | + | 9.00000i | −0.494685 | + | 0.494685i | −0.909779 | − | 0.415094i | \(-0.863749\pi\) |
0.415094 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | + | 2.00000i | 0.109599 | + | 0.109599i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.0000 | −1.63420 | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0000 | + | 14.0000i | 0.760376 | + | 0.760376i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | + | 8.00000i | −0.433224 | + | 0.433224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 16.0000i | − | 0.861411i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0000 | − | 11.0000i | 0.590511 | − | 0.590511i | −0.347259 | − | 0.937769i | \(-0.612887\pi\) |
0.937769 | + | 0.347259i | \(0.112887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | + | 14.0000i | 0.749403 | + | 0.749403i | 0.974367 | − | 0.224964i | \(-0.0722265\pi\) |
−0.224964 | + | 0.974367i | \(0.572227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 8.00000i | 0.424596 | + | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0000 | + | 16.0000i | −0.846810 | + | 0.846810i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.0000i | 1.90001i | 0.312239 | + | 0.950004i | \(0.398921\pi\) | ||||
−0.312239 | + | 0.950004i | \(0.601079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.0000i | 1.63158i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000 | − | 9.00000i | 0.472377 | − | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.00000 | − | 8.00000i | −0.418739 | − | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | −0.835193 | −0.417597 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00000 | − | 8.00000i | −0.415339 | − | 0.415339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0000 | − | 26.0000i | 1.34623 | − | 1.34623i | 0.456511 | − | 0.889718i | \(-0.349099\pi\) |
0.889718 | − | 0.456511i | \(-0.150901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 8.00000i | − | 0.413118i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0000 | + | 21.0000i | −1.07870 | + | 1.07870i | −0.0820711 | + | 0.996626i | \(0.526153\pi\) |
−0.996626 | + | 0.0820711i | \(0.973847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | − | 8.00000i | −0.409852 | − | 0.409852i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0000 | 0.817562 | 0.408781 | − | 0.912633i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912633i | \(0.365954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.00000 | + | 3.00000i | 0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000 | − | 14.0000i | 0.709828 | − | 0.709828i | −0.256671 | − | 0.966499i | \(-0.582626\pi\) |
0.966499 | + | 0.256671i | \(0.0826256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000i | 0.809155i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.0000i | − | 0.504433i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000 | − | 16.0000i | 0.805047 | − | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | + | 2.00000i | 0.100377 | + | 0.100377i | 0.755512 | − | 0.655135i | \(-0.227388\pi\) |
−0.655135 | + | 0.755512i | \(0.727388\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 40.0000 | 2.00250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0000 | 1.79775 | 0.898877 | − | 0.438201i | \(-0.144384\pi\) | ||||
0.898877 | + | 0.438201i | \(0.144384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | − | 16.0000i | −0.797017 | − | 0.797017i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0000 | − | 10.0000i | 0.496904 | − | 0.496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.00000i | − | 0.198273i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000i | 0.692255i | 0.938187 | + | 0.346128i | \(0.112504\pi\) | ||||
−0.938187 | + | 0.346128i | \(0.887496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | + | 18.0000i | −0.887875 | + | 0.887875i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | − | 12.0000i | −0.590481 | − | 0.590481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.0000 | −1.37447 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0000 | − | 19.0000i | −0.928211 | − | 0.928211i | 0.0693796 | − | 0.997590i | \(-0.477898\pi\) |
−0.997590 | + | 0.0693796i | \(0.977898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | + | 6.00000i | −0.292422 | + | 0.292422i | −0.838036 | − | 0.545614i | \(-0.816296\pi\) |
0.545614 | + | 0.838036i | \(0.316296\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 12.0000i | − | 0.582086i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0000 | + | 24.0000i | −1.16144 | + | 1.16144i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | − | 4.00000i | −0.193122 | − | 0.193122i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0000 | 0.961139 | 0.480569 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480569 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.0000 | − | 24.0000i | −1.15071 | − | 1.15071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0000 | − | 20.0000i | 0.956730 | − | 0.956730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.00000i | − | 0.190910i | −0.995434 | − | 0.0954548i | \(-0.969569\pi\) | ||
0.995434 | − | 0.0954548i | \(-0.0304305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000i | 0.428571i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0000 | − | 25.0000i | 1.18779 | − | 1.18779i | 0.210108 | − | 0.977678i | \(-0.432619\pi\) |
0.977678 | − | 0.210108i | \(-0.0673814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | − | 24.0000i | −1.13771 | − | 1.13771i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0000 | −0.943858 | −0.471929 | − | 0.881636i | \(-0.656442\pi\) | ||||
−0.471929 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | − | 2.00000i | −0.0941763 | − | 0.0941763i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | − | 4.00000i | 0.187936 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.0000i | 1.50018i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000i | 0.0935561i | 0.998905 | + | 0.0467780i | \(0.0148953\pi\) | ||||
−0.998905 | + | 0.0467780i | \(0.985105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.0000 | + | 16.0000i | −0.746816 | + | 0.746816i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | + | 10.0000i | 0.465746 | + | 0.465746i | 0.900533 | − | 0.434787i | \(-0.143176\pi\) |
−0.434787 | + | 0.900533i | \(0.643176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32.0000 | −1.48396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.0000 | − | 13.0000i | −0.601568 | − | 0.601568i | 0.339160 | − | 0.940729i | \(-0.389857\pi\) |
−0.940729 | + | 0.339160i | \(0.889857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | + | 12.0000i | −0.554109 | + | 0.554109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0000i | 0.552931i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | + | 15.0000i | −0.688247 | + | 0.688247i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | − | 2.00000i | −0.0915737 | − | 0.0915737i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | − | 16.0000i | −0.728025 | − | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.00000 | + | 8.00000i | −0.363261 | + | 0.363261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 14.0000i | − | 0.633102i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0000 | + | 11.0000i | −0.496423 | + | 0.496423i | −0.910323 | − | 0.413900i | \(-0.864166\pi\) |
0.413900 | + | 0.910323i | \(0.364166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000 | + | 24.0000i | 1.08091 | + | 1.08091i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.00000 | + | 9.00000i | 0.402895 | + | 0.402895i | 0.879252 | − | 0.476357i | \(-0.158043\pi\) |
−0.476357 | + | 0.879252i | \(0.658043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | − | 12.0000i | 0.536120 | − | 0.536120i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000i | 0.891756i | 0.895094 | + | 0.445878i | \(0.147108\pi\) | ||||
−0.895094 | + | 0.445878i | \(0.852892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000i | 0.355995i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | + | 5.00000i | −0.222058 | + | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00000 | + | 2.00000i | 0.0886484 | + | 0.0886484i | 0.750040 | − | 0.661392i | \(-0.230034\pi\) |
−0.661392 | + | 0.750040i | \(0.730034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.0000 | 1.76604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | − | 24.0000i | −1.05757 | − | 1.05757i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.0000i | 0.877903i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000i | 0.613351i | 0.951814 | + | 0.306676i | \(0.0992167\pi\) | ||||
−0.951814 | + | 0.306676i | \(0.900783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.00000 | − | 7.00000i | 0.306089 | − | 0.306089i | −0.537302 | − | 0.843390i | \(-0.680556\pi\) |
0.843390 | + | 0.537302i | \(0.180556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.0000 | + | 12.0000i | 0.523723 | + | 0.523723i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.0000 | 1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | − | 3.00000i | −0.130189 | − | 0.130189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | − | 4.00000i | 0.173259 | − | 0.173259i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 28.0000i | − | 1.21055i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2.00000i | − | 0.0863064i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.00000 | − | 9.00000i | 0.387657 | − | 0.387657i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.00000 | − | 6.00000i | −0.257960 | − | 0.257960i | 0.566264 | − | 0.824224i | \(-0.308388\pi\) |
−0.824224 | + | 0.566264i | \(0.808388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.0000 | 1.71341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0000 | − | 19.0000i | −0.812381 | − | 0.812381i | 0.172609 | − | 0.984990i | \(-0.444780\pi\) |
−0.984990 | + | 0.172609i | \(0.944780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00000 | + | 6.00000i | −0.256074 | + | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 60.0000i | − | 2.55609i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 32.0000i | − | 1.36078i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000 | − | 8.00000i | 0.339581 | − | 0.339581i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.0000 | + | 22.0000i | 0.932170 | + | 0.932170i | 0.997841 | − | 0.0656714i | \(-0.0209189\pi\) |
−0.0656714 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.00000 | − | 5.00000i | −0.210725 | − | 0.210725i | 0.593851 | − | 0.804575i | \(-0.297607\pi\) |
−0.804575 | + | 0.593851i | \(0.797607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.0000 | + | 28.0000i | −1.17797 | + | 1.17797i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 20.0000i | − | 0.839921i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 30.0000i | − | 1.25767i | −0.777541 | − | 0.628833i | \(-0.783533\pi\) | ||
0.777541 | − | 0.628833i | \(-0.216467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.0000 | + | 23.0000i | −0.962520 | + | 0.962520i | −0.999323 | − | 0.0368025i | \(-0.988283\pi\) |
0.0368025 | + | 0.999323i | \(0.488283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | − | 8.00000i | −0.334205 | − | 0.334205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | + | 4.00000i | 0.166234 | + | 0.166234i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.0000 | + | 28.0000i | −1.16164 | + | 1.16164i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.00000i | 0.330759i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.00000 | + | 1.00000i | −0.0412744 | + | 0.0412744i | −0.727443 | − | 0.686168i | \(-0.759291\pi\) |
0.686168 | + | 0.727443i | \(0.259291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.0000 | − | 40.0000i | −1.64817 | − | 1.64817i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.0000 | −0.822690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.0000 | − | 32.0000i | −1.31187 | − | 1.31187i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.00000 | + | 4.00000i | −0.163709 | + | 0.163709i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.0000i | − | 1.47092i | −0.677568 | − | 0.735460i | \(-0.736966\pi\) | ||
0.677568 | − | 0.735460i | \(-0.263034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.00000i | 0.163163i | 0.996667 | + | 0.0815817i | \(0.0259972\pi\) | ||||
−0.996667 | + | 0.0815817i | \(0.974003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.00000 | + | 3.00000i | −0.122169 | + | 0.122169i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.0000 | + | 18.0000i | 0.731804 | + | 0.731804i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.0000 | −1.94506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.00000 | + | 6.00000i | −0.242338 | + | 0.242338i | −0.817817 | − | 0.575479i | \(-0.804816\pi\) |
0.575479 | + | 0.817817i | \(0.304816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 8.00000i | − | 0.322591i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.0000i | 1.12724i | 0.826035 | + | 0.563619i | \(0.190591\pi\) | ||||
−0.826035 | + | 0.563619i | \(0.809409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.00000 | + | 1.00000i | −0.0401934 | + | 0.0401934i | −0.726918 | − | 0.686724i | \(-0.759048\pi\) |
0.686724 | + | 0.726918i | \(0.259048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.0000 | − | 16.0000i | −0.642058 | − | 0.642058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.0000 | −1.92308 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.0000 | − | 10.0000i | −0.399362 | − | 0.399362i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.00000 | + | 8.00000i | −0.318981 | + | 0.318981i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000i | 0.159237i | 0.996825 | + | 0.0796187i | \(0.0253703\pi\) | ||||
−0.996825 | + | 0.0796187i | \(0.974630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 34.0000i | − | 1.35138i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | − | 16.0000i | 0.634941 | − | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000 | + | 18.0000i | 0.713186 | + | 0.713186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.00000 | −0.157991 | −0.0789953 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789953 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | − | 3.00000i | −0.118308 | − | 0.118308i | 0.645474 | − | 0.763782i | \(-0.276660\pi\) |
−0.763782 | + | 0.645474i | \(0.776660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | − | 12.0000i | 0.472500 | − | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000i | 0.235521i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.0000 | + | 32.0000i | −1.25418 | + | 1.25418i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.0000 | + | 34.0000i | 1.33052 | + | 1.33052i | 0.904901 | + | 0.425622i | \(0.139945\pi\) |
0.425622 | + | 0.904901i | \(0.360055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | 0.781465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.0000 | − | 23.0000i | −0.895953 | − | 0.895953i | 0.0991224 | − | 0.995075i | \(-0.468396\pi\) |
−0.995075 | + | 0.0991224i | \(0.968396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | − | 22.0000i | 0.855701 | − | 0.855701i | −0.135127 | − | 0.990828i | \(-0.543144\pi\) |
0.990828 | + | 0.135127i | \(0.0431444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.0000i | 0.621389i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 80.0000i | 3.10227i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | + | 24.0000i | −0.929284 | + | 0.929284i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.0000 | − | 24.0000i | −0.927894 | − | 0.927894i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.0000 | −0.770943 | −0.385472 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0000 | + | 12.0000i | 0.461880 | + | 0.461880i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0000 | − | 30.0000i | 1.15299 | − | 1.15299i | 0.167044 | − | 0.985949i | \(-0.446578\pi\) |
0.985949 | − | 0.167044i | \(-0.0534223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0000i | 0.614024i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 30.0000i | − | 1.14960i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.0000 | − | 21.0000i | 0.803543 | − | 0.803543i | −0.180105 | − | 0.983647i | \(-0.557644\pi\) |
0.983647 | + | 0.180105i | \(0.0576437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | − | 36.0000i | −1.37549 | − | 1.37549i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −36.0000 | −1.37349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.00000 | −0.304776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.0000 | + | 33.0000i | 1.25538 | + | 1.25538i | 0.953275 | + | 0.302104i | \(0.0976891\pi\) |
0.302104 | + | 0.953275i | \(0.402311\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | − | 4.00000i | 0.151947 | − | 0.151947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000i | 0.455186i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000i | 0.303022i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000 | − | 12.0000i | 0.453882 | − | 0.453882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0000 | + | 34.0000i | 1.28416 | + | 1.28416i | 0.938277 | + | 0.345886i | \(0.112421\pi\) |
0.345886 | + | 0.938277i | \(0.387579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.00000 | + | 8.00000i | 0.300871 | + | 0.300871i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | − | 6.00000i | 0.225335 | − | 0.225335i | −0.585406 | − | 0.810740i | \(-0.699065\pi\) |
0.810740 | + | 0.585406i | \(0.199065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.00000i | − | 0.300023i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.0000i | 1.19841i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | − | 8.00000i | 0.299183 | − | 0.299183i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.00000 | − | 8.00000i | −0.298765 | − | 0.298765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0000 | −1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.0000 | + | 12.0000i | 0.446285 | + | 0.446285i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.0000 | − | 18.0000i | 0.668503 | − | 0.668503i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000i | 1.03846i | 0.854634 | + | 0.519231i | \(0.173782\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 12.0000i | −0.443836 | + | 0.443836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | + | 14.0000i | 0.517102 | + | 0.517102i | 0.916693 | − | 0.399592i | \(-0.130848\pi\) |
−0.399592 | + | 0.916693i | \(0.630848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.0000 | 1.32788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0000 | − | 17.0000i | −0.625355 | − | 0.625355i | 0.321541 | − | 0.946896i | \(-0.395799\pi\) |
−0.946896 | + | 0.321541i | \(0.895799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0000 | − | 20.0000i | 0.734718 | − | 0.734718i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.00000i | − | 0.146746i | −0.997305 | − | 0.0733729i | \(-0.976624\pi\) | ||
0.997305 | − | 0.0733729i | \(-0.0233763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000i | 0.293097i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.00000 | + | 7.00000i | −0.256117 | + | 0.256117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.0000 | − | 28.0000i | −1.02310 | − | 1.02310i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | −0.218652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | + | 8.00000i | 0.291150 | + | 0.291150i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | + | 18.0000i | −0.654221 | + | 0.654221i | −0.954007 | − | 0.299786i | \(-0.903085\pi\) |
0.299786 | + | 0.954007i | \(0.403085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000i | 0.290382i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 18.0000i | − | 0.652499i | −0.945284 | − | 0.326250i | \(-0.894215\pi\) | ||
0.945284 | − | 0.326250i | \(-0.105785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0000 | − | 40.0000i | 1.44810 | − | 1.44810i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.00000 | − | 8.00000i | −0.289241 | − | 0.289241i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0000 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | + | 2.00000i | 0.0720282 | + | 0.0720282i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.00000 | − | 6.00000i | 0.215805 | − | 0.215805i | −0.590923 | − | 0.806728i | \(-0.701236\pi\) |
0.806728 | + | 0.590923i | \(0.201236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 24.0000i | − | 0.862105i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 16.0000i | − | 0.573997i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.0000 | − | 10.0000i | 0.358287 | − | 0.358287i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | − | 4.00000i | −0.143131 | − | 0.143131i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.0000 | −1.71538 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.0000 | −0.856597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0000 | + | 33.0000i | 1.17632 | + | 1.17632i | 0.980674 | + | 0.195649i | \(0.0626813\pi\) |
0.195649 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.0000 | + | 28.0000i | −0.996826 | + | 0.996826i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.0000i | 1.99113i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000i | 0.852265i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.00000 | + | 8.00000i | −0.283731 | + | 0.283731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.0000 | − | 14.0000i | −0.495905 | − | 0.495905i | 0.414255 | − | 0.910161i | \(-0.364042\pi\) |
−0.910161 | + | 0.414255i | \(0.864042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00000 | + | 4.00000i | 0.141157 | + | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.0000 | − | 32.0000i | 1.12785 | − | 1.12785i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0000i | 0.985647i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 30.0000i | − | 1.05474i | −0.849635 | − | 0.527372i | \(-0.823177\pi\) | ||
0.849635 | − | 0.527372i | \(-0.176823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0000 | + | 17.0000i | −0.596951 | + | 0.596951i | −0.939500 | − | 0.342549i | \(-0.888710\pi\) |
0.342549 | + | 0.939500i | \(0.388710\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0000 | + | 32.0000i | 1.12229 | + | 1.12229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.0000 | 0.980797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | 1.04957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.00000 | + | 8.00000i | 0.279543 | + | 0.279543i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | + | 6.00000i | −0.209401 | + | 0.209401i | −0.804013 | − | 0.594612i | \(-0.797306\pi\) |
0.594612 | + | 0.804013i | \(0.297306\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.00000i | − | 0.139431i | −0.997567 | − | 0.0697156i | \(-0.977791\pi\) | ||
0.997567 | − | 0.0697156i | \(-0.0222092\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.00000i | − | 0.208893i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.0000 | + | 15.0000i | −0.521601 | + | 0.521601i | −0.918055 | − | 0.396454i | \(-0.870241\pi\) |
0.396454 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | + | 18.0000i | 0.625166 | + | 0.625166i | 0.946848 | − | 0.321682i | \(-0.104248\pi\) |
−0.321682 | + | 0.946848i | \(0.604248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | 0.416275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.0000 | −1.24733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | + | 24.0000i | 0.830554 | + | 0.830554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.0000 | + | 32.0000i | −1.10608 | + | 1.10608i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 20.0000i | − | 0.690477i | −0.938515 | − | 0.345238i | \(-0.887798\pi\) | ||
0.938515 | − | 0.345238i | \(-0.112202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000i | 1.48276i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.0000 | − | 20.0000i | 0.688837 | − | 0.688837i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0000 | − | 10.0000i | −0.344010 | − | 0.344010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.0000 | 1.23697 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.0000 | −1.16688 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | − | 8.00000i | −0.274236 | − | 0.274236i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0000 | + | 30.0000i | −1.02718 | + | 1.02718i | −0.0275603 | + | 0.999620i | \(0.508774\pi\) |
−0.999620 | + | 0.0275603i | \(0.991226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.0000i | 0.683986i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.0000i | 1.16142i | 0.814111 | + | 0.580709i | \(0.197225\pi\) | ||||
−0.814111 | + | 0.580709i | \(0.802775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.0000 | − | 27.0000i | 0.921228 | − | 0.921228i | −0.0758882 | − | 0.997116i | \(-0.524179\pi\) |
0.997116 | + | 0.0758882i | \(0.0241792\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | − | 8.00000i | −0.272639 | − | 0.272639i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | −1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | + | 1.00000i | 0.0339618 | + | 0.0339618i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | + | 8.00000i | −0.271381 | + | 0.271381i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000i | 0.406604i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.00000i | 0.135379i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0000 | − | 16.0000i | 0.540899 | − | 0.540899i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.00000 | − | 6.00000i | −0.202606 | − | 0.202606i | 0.598510 | − | 0.801115i | \(-0.295760\pi\) |
−0.801115 | + | 0.598510i | \(0.795760\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | 0.404750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.0000 | 1.14549 | 0.572745 | − | 0.819734i | \(-0.305879\pi\) | ||||
0.572745 | + | 0.819734i | \(0.305879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.0000 | − | 29.0000i | −0.975928 | − | 0.975928i | 0.0237893 | − | 0.999717i | \(-0.492427\pi\) |
−0.999717 | + | 0.0237893i | \(0.992427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | + | 12.0000i | −0.403376 | + | 0.403376i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.0000i | 0.940148i | 0.882627 | + | 0.470074i | \(0.155773\pi\) | ||||
−0.882627 | + | 0.470074i | \(0.844227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 32.0000i | − | 1.07325i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.00000 | + | 5.00000i | −0.167506 | + | 0.167506i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000 | + | 48.0000i | 1.60089 | + | 1.60089i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | − | 8.00000i | 0.266519 | − | 0.266519i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 24.0000i | − | 0.798670i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 24.0000i | − | 0.797787i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | − | 5.00000i | 0.166022 | − | 0.166022i | −0.619206 | − | 0.785228i | \(-0.712545\pi\) |
0.785228 | + | 0.619206i | \(0.212545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000 | + | 2.00000i | 0.0663358 | + | 0.0663358i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0000 | 0.463332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.0000 | + | 24.0000i | 0.793416 | + | 0.793416i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.0000 | − | 20.0000i | 0.660458 | − | 0.660458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.0000i | − | 1.45143i | −0.687998 | − | 0.725713i | \(-0.741510\pi\) | ||
0.687998 | − | 0.725713i | \(-0.258490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000i | 0.329511i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000 | − | 8.00000i | 0.263323 | − | 0.263323i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | + | 6.00000i | 0.197279 | + | 0.197279i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 60.0000 | 1.96854 | 0.984268 | − | 0.176682i | \(-0.0565363\pi\) | ||||
0.984268 | + | 0.176682i | \(0.0565363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.0000 | + | 45.0000i | 1.47482 | + | 1.47482i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0000 | + | 20.0000i | −0.654771 | + | 0.654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000i | 0.523256i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.0000i | − | 0.653372i | −0.945133 | − | 0.326686i | \(-0.894068\pi\) | ||
0.945133 | − | 0.326686i | \(-0.105932\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | − | 14.0000i | 0.456873 | − | 0.456873i | ||||
\(940\) | 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 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64.0000 | 2.08192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.0000 | + | 43.0000i | 1.39731 | + | 1.39731i | 0.807650 | + | 0.589662i | \(0.200739\pi\) |
0.589662 | + | 0.807650i | \(0.299261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | + | 8.00000i | −0.259691 | + | 0.259691i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000i | 0.129709i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.0000i | − | 0.971795i | −0.874016 | − | 0.485898i | \(-0.838493\pi\) | ||
0.874016 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0000 | − | 16.0000i | 0.517748 | − | 0.517748i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | + | 12.0000i | 0.387905 | + | 0.387905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.0000 | −2.32500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.00000 | − | 7.00000i | −0.225572 | − | 0.225572i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.00000 | + | 8.00000i | −0.257529 | + | 0.257529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20.0000i | − | 0.643157i | −0.946883 | − | 0.321578i | \(-0.895787\pi\) | ||
0.946883 | − | 0.321578i | \(-0.104213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.0000i | 1.28499i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0000 | + | 11.0000i | −0.353007 | + | 0.353007i | −0.861227 | − | 0.508220i | \(-0.830304\pi\) |
0.508220 | + | 0.861227i | \(0.330304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | + | 12.0000i | 0.384702 | + | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | 0.384308 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0000 | −0.383914 | −0.191957 | − | 0.981403i | \(-0.561483\pi\) | ||||
−0.191957 | + | 0.981403i | \(0.561483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | + | 12.0000i | 0.383522 | + | 0.383522i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | − | 10.0000i | 0.319275 | − | 0.319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 36.0000i | − | 1.14822i | −0.818778 | − | 0.574111i | \(-0.805348\pi\) | ||
0.818778 | − | 0.574111i | \(-0.194652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 40.0000i | − | 1.27451i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.0000 | − | 12.0000i | −0.381578 | − | 0.381578i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.0000 | 0.571213 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | − | 8.00000i | −0.253617 | − | 0.253617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0000 | + | 10.0000i | −0.316703 | + | 0.316703i | −0.847499 | − | 0.530796i | \(-0.821893\pi\) |
0.530796 | + | 0.847499i | \(0.321893\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 16.0000i | − | 0.506218i |
(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 | 1024.2.e.c.257.1 | 2 | ||
4.3 | odd | 2 | 1024.2.e.e.257.1 | 2 | |||
8.3 | odd | 2 | 1024.2.e.b.257.1 | 2 | |||
8.5 | even | 2 | 1024.2.e.d.257.1 | 2 | |||
16.3 | odd | 4 | 1024.2.e.b.769.1 | 2 | |||
16.5 | even | 4 | inner | 1024.2.e.c.769.1 | 2 | ||
16.11 | odd | 4 | 1024.2.e.e.769.1 | 2 | |||
16.13 | even | 4 | 1024.2.e.d.769.1 | 2 | |||
32.3 | odd | 8 | 512.2.b.b.257.2 | 2 | |||
32.5 | even | 8 | 512.2.a.d.1.2 | yes | 2 | ||
32.11 | odd | 8 | 512.2.a.c.1.2 | yes | 2 | ||
32.13 | even | 8 | 512.2.b.a.257.2 | 2 | |||
32.19 | odd | 8 | 512.2.b.b.257.1 | 2 | |||
32.21 | even | 8 | 512.2.a.d.1.1 | yes | 2 | ||
32.27 | odd | 8 | 512.2.a.c.1.1 | ✓ | 2 | ||
32.29 | even | 8 | 512.2.b.a.257.1 | 2 | |||
96.5 | odd | 8 | 4608.2.a.m.1.1 | 2 | |||
96.11 | even | 8 | 4608.2.a.f.1.2 | 2 | |||
96.29 | odd | 8 | 4608.2.d.a.2305.1 | 2 | |||
96.35 | even | 8 | 4608.2.d.b.2305.1 | 2 | |||
96.53 | odd | 8 | 4608.2.a.m.1.2 | 2 | |||
96.59 | even | 8 | 4608.2.a.f.1.1 | 2 | |||
96.77 | odd | 8 | 4608.2.d.a.2305.2 | 2 | |||
96.83 | even | 8 | 4608.2.d.b.2305.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.a.c.1.1 | ✓ | 2 | 32.27 | odd | 8 | ||
512.2.a.c.1.2 | yes | 2 | 32.11 | odd | 8 | ||
512.2.a.d.1.1 | yes | 2 | 32.21 | even | 8 | ||
512.2.a.d.1.2 | yes | 2 | 32.5 | even | 8 | ||
512.2.b.a.257.1 | 2 | 32.29 | even | 8 | |||
512.2.b.a.257.2 | 2 | 32.13 | even | 8 | |||
512.2.b.b.257.1 | 2 | 32.19 | odd | 8 | |||
512.2.b.b.257.2 | 2 | 32.3 | odd | 8 | |||
1024.2.e.b.257.1 | 2 | 8.3 | odd | 2 | |||
1024.2.e.b.769.1 | 2 | 16.3 | odd | 4 | |||
1024.2.e.c.257.1 | 2 | 1.1 | even | 1 | trivial | ||
1024.2.e.c.769.1 | 2 | 16.5 | even | 4 | inner | ||
1024.2.e.d.257.1 | 2 | 8.5 | even | 2 | |||
1024.2.e.d.769.1 | 2 | 16.13 | even | 4 | |||
1024.2.e.e.257.1 | 2 | 4.3 | odd | 2 | |||
1024.2.e.e.769.1 | 2 | 16.11 | odd | 4 | |||
4608.2.a.f.1.1 | 2 | 96.59 | even | 8 | |||
4608.2.a.f.1.2 | 2 | 96.11 | even | 8 | |||
4608.2.a.m.1.1 | 2 | 96.5 | odd | 8 | |||
4608.2.a.m.1.2 | 2 | 96.53 | odd | 8 | |||
4608.2.d.a.2305.1 | 2 | 96.29 | odd | 8 | |||
4608.2.d.a.2305.2 | 2 | 96.77 | odd | 8 | |||
4608.2.d.b.2305.1 | 2 | 96.35 | even | 8 | |||
4608.2.d.b.2305.2 | 2 | 96.83 | even | 8 |