Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(575,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.l (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: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1727.1 | ||
Root | \(1.28897 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1727 |
Dual form | 2304.2.l.d.575.1 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.57794 | − | 2.57794i | −1.15289 | − | 1.15289i | −0.985971 | − | 0.166917i | \(-0.946619\pi\) |
−0.166917 | − | 0.985971i | \(-0.553381\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.74166 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.64575 | + | 3.64575i | −1.09924 | + | 1.09924i | −0.104735 | + | 0.994500i | \(0.533400\pi\) |
−0.994500 | + | 0.104735i | \(0.966600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64575 | + | 4.64575i | 1.28850 | + | 1.28850i | 0.935698 | + | 0.352801i | \(0.114771\pi\) |
0.352801 | + | 0.935698i | \(0.385229\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.913230i | 0.221491i | 0.993849 | + | 0.110745i | \(0.0353238\pi\) | ||||
−0.993849 | + | 0.110745i | \(0.964676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41421 | + | 1.41421i | −0.324443 | + | 0.324443i | −0.850469 | − | 0.526026i | \(-0.823682\pi\) |
0.526026 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.29150i | 1.65830i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.66471 | − | 1.66471i | 0.309128 | − | 0.309128i | −0.535443 | − | 0.844571i | \(-0.679855\pi\) |
0.844571 | + | 0.535443i | \(0.179855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.57008i | − | 1.18002i | −0.807395 | − | 0.590011i | \(-0.799123\pi\) | ||
0.807395 | − | 0.590011i | \(-0.200877\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.64575 | + | 9.64575i | 1.63043 | + | 1.63043i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.00000i | 0.164399 | − | 0.164399i | −0.620113 | − | 0.784512i | \(-0.712913\pi\) |
0.784512 | + | 0.620113i | \(0.212913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.913230 | −0.142623 | −0.0713113 | − | 0.997454i | \(-0.522718\pi\) | ||||
−0.0713113 | + | 0.997454i | \(0.522718\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.74166 | + | 3.74166i | 0.570597 | + | 0.570597i | 0.932295 | − | 0.361698i | \(-0.117803\pi\) |
−0.361698 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.49117 | + | 3.49117i | 0.479548 | + | 0.479548i | 0.904987 | − | 0.425439i | \(-0.139880\pi\) |
−0.425439 | + | 0.904987i | \(0.639880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.7970 | 2.53459 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.29150 | − | 1.29150i | 0.168139 | − | 0.168139i | −0.618022 | − | 0.786161i | \(-0.712066\pi\) |
0.786161 | + | 0.618022i | \(0.212066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.291503 | − | 0.291503i | −0.0373231 | − | 0.0373231i | 0.688199 | − | 0.725522i | \(-0.258402\pi\) |
−0.725522 | + | 0.688199i | \(0.758402\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 23.9529i | − | 2.97099i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.32941 | + | 3.32941i | −0.406752 | + | 0.406752i | −0.880604 | − | 0.473852i | \(-0.842863\pi\) |
0.473852 | + | 0.880604i | \(0.342863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.2915i | − | 1.57741i | −0.614771 | − | 0.788706i | \(-0.710752\pi\) | ||
0.614771 | − | 0.788706i | \(-0.289248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.58301i | − | 1.00456i | −0.864704 | − | 0.502282i | \(-0.832494\pi\) | ||
0.864704 | − | 0.502282i | \(-0.167506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6412 | − | 13.6412i | 1.55455 | − | 1.55455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.39655i | 0.944685i | 0.881415 | + | 0.472343i | \(0.156591\pi\) | ||||
−0.881415 | + | 0.472343i | \(0.843409\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.93725 | − | 4.93725i | −0.541934 | − | 0.541934i | 0.382162 | − | 0.924096i | \(-0.375180\pi\) |
−0.924096 | + | 0.382162i | \(0.875180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.35425 | − | 2.35425i | 0.255354 | − | 0.255354i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5544 | 1.54276 | 0.771381 | − | 0.636374i | \(-0.219566\pi\) | ||||
0.771381 | + | 0.636374i | \(0.219566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3828 | − | 17.3828i | −1.82221 | − | 1.82221i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.29150 | 0.748092 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2915 | 1.34955 | 0.674774 | − | 0.738025i | \(-0.264241\pi\) | ||||
0.674774 | + | 0.738025i | \(0.264241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.82058 | − | 6.82058i | −0.678673 | − | 0.678673i | 0.281027 | − | 0.959700i | \(-0.409325\pi\) |
−0.959700 | + | 0.281027i | \(0.909325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.57008 | 0.647370 | 0.323685 | − | 0.946165i | \(-0.395078\pi\) | ||||
0.323685 | + | 0.946165i | \(0.395078\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.29150 | − | 7.29150i | 0.704896 | − | 0.704896i | −0.260561 | − | 0.965457i | \(-0.583908\pi\) |
0.965457 | + | 0.260561i | \(0.0839076\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35425 | + | 1.35425i | 0.129713 | + | 0.129713i | 0.768983 | − | 0.639269i | \(-0.220763\pi\) |
−0.639269 | + | 0.768983i | \(0.720763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.7279i | − | 1.19734i | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||
0.800995 | − | 0.598671i | \(-0.204304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.4676 | + | 15.4676i | −1.44236 | + | 1.44236i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.41699i | − | 0.313235i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 15.5830i | − | 1.41664i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.48528 | − | 8.48528i | 0.758947 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.91520i | 0.169946i | 0.996383 | + | 0.0849731i | \(0.0270804\pi\) | ||||
−0.996383 | + | 0.0849731i | \(0.972920\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | + | 12.0000i | 1.04844 | + | 1.04844i | 0.998765 | + | 0.0496797i | \(0.0158200\pi\) |
0.0496797 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29150 | − | 5.29150i | 0.458831 | − | 0.458831i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.39851 | 0.802969 | 0.401485 | − | 0.915866i | \(-0.368494\pi\) | ||||
0.401485 | + | 0.915866i | \(0.368494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.32941 | + | 3.32941i | 0.282397 | + | 0.282397i | 0.834064 | − | 0.551667i | \(-0.186008\pi\) |
−0.551667 | + | 0.834064i | \(0.686008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.8745 | −2.83273 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.58301 | −0.712780 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.73381 | − | 7.73381i | −0.633578 | − | 0.633578i | 0.315386 | − | 0.948964i | \(-0.397866\pi\) |
−0.948964 | + | 0.315386i | \(0.897866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4005 | 0.846379 | 0.423189 | − | 0.906041i | \(-0.360910\pi\) | ||||
0.423189 | + | 0.906041i | \(0.360910\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.9373 | + | 16.9373i | −1.36043 | + | 1.36043i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.29150 | + | 6.29150i | 0.502117 | + | 0.502117i | 0.912095 | − | 0.409979i | \(-0.134464\pi\) |
−0.409979 | + | 0.912095i | \(0.634464\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.4499i | 1.76930i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.91520 | + | 1.91520i | −0.150010 | + | 0.150010i | −0.778122 | − | 0.628113i | \(-0.783828\pi\) |
0.628113 | + | 0.778122i | \(0.283828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.29150i | 0.564233i | 0.959380 | + | 0.282117i | \(0.0910365\pi\) | ||||
−0.959380 | + | 0.282117i | \(0.908963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.1660i | 2.32046i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.57794 | − | 2.57794i | 0.195997 | − | 0.195997i | −0.602285 | − | 0.798281i | \(-0.705743\pi\) |
0.798281 | + | 0.602285i | \(0.205743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 31.0240i | − | 2.34519i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.8745 | + | 15.8745i | 1.18652 | + | 1.18652i | 0.978024 | + | 0.208492i | \(0.0668557\pi\) |
0.208492 | + | 0.978024i | \(0.433144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.35425 | + | 1.35425i | −0.100661 | + | 0.100661i | −0.755644 | − | 0.654983i | \(-0.772676\pi\) |
0.654983 | + | 0.755644i | \(0.272676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.15587 | −0.379067 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.32941 | − | 3.32941i | −0.243471 | − | 0.243471i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.2915 | 1.39588 | 0.697942 | − | 0.716154i | \(-0.254099\pi\) | ||||
0.697942 | + | 0.716154i | \(0.254099\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.58301 | −0.329892 | −0.164946 | − | 0.986303i | \(-0.552745\pi\) | ||||
−0.164946 | + | 0.986303i | \(0.552745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9764 | + | 11.9764i | 0.853287 | + | 0.853287i | 0.990536 | − | 0.137250i | \(-0.0438263\pi\) |
−0.137250 | + | 0.990536i | \(0.543826\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8818 | −1.19672 | −0.598360 | − | 0.801227i | \(-0.704181\pi\) | ||||
−0.598360 | + | 0.801227i | \(0.704181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.22876 | + | 6.22876i | −0.437173 | + | 0.437173i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.35425 | + | 2.35425i | 0.164428 | + | 0.164428i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.3117i | − | 0.713278i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4676 | − | 15.4676i | 1.06483 | − | 1.06483i | 0.0670873 | − | 0.997747i | \(-0.478629\pi\) |
0.997747 | − | 0.0670873i | \(-0.0213706\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 19.2915i | − | 1.31567i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5830i | 1.66880i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.24264 | + | 4.24264i | −0.285391 | + | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0554i | 1.00818i | 0.863651 | + | 0.504091i | \(0.168172\pi\) | ||||
−0.863651 | + | 0.504091i | \(0.831828\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.35425 | + | 2.35425i | 0.156257 | + | 0.156257i | 0.780906 | − | 0.624649i | \(-0.214758\pi\) |
−0.624649 | + | 0.780906i | \(0.714758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.35425 | − | 9.35425i | 0.618146 | − | 0.618146i | −0.326909 | − | 0.945056i | \(-0.606007\pi\) |
0.945056 | + | 0.326909i | \(0.106007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5544 | −0.953489 | −0.476745 | − | 0.879042i | \(-0.658183\pi\) | ||||
−0.476745 | + | 0.879042i | \(0.658183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4676 | + | 15.4676i | 1.00900 | + | 1.00900i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.87451 | 0.638729 | 0.319364 | − | 0.947632i | \(-0.396531\pi\) | ||||
0.319364 | + | 0.947632i | \(0.396531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8745 | 0.893736 | 0.446868 | − | 0.894600i | \(-0.352539\pi\) | ||||
0.446868 | + | 0.894600i | \(0.352539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0455 | − | 18.0455i | −1.15289 | − | 1.15289i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1402 | −0.836089 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.35425 | + | 8.35425i | −0.527316 | + | 0.527316i | −0.919771 | − | 0.392455i | \(-0.871626\pi\) |
0.392455 | + | 0.919771i | \(0.371626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8745 | + | 21.8745i | 1.37524 | + | 1.37524i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.06910i | − | 0.378580i | −0.981921 | − | 0.189290i | \(-0.939381\pi\) | ||
0.981921 | − | 0.189290i | \(-0.0606186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.74166 | + | 3.74166i | −0.232495 | + | 0.232495i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.41699i | 0.580677i | 0.956924 | + | 0.290338i | \(0.0937679\pi\) | ||||
−0.956924 | + | 0.290338i | \(0.906232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.0000i | − | 1.10573i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9588 | + | 18.9588i | −1.15594 | + | 1.15594i | −0.170596 | + | 0.985341i | \(0.554569\pi\) |
−0.985341 | + | 0.170596i | \(0.945431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.91520i | 0.116340i | 0.998307 | + | 0.0581700i | \(0.0185265\pi\) | ||||
−0.998307 | + | 0.0581700i | \(0.981473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30.2288 | − | 30.2288i | −1.82286 | − | 1.82286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6458 | + | 10.6458i | −0.639641 | + | 0.639641i | −0.950467 | − | 0.310826i | \(-0.899394\pi\) |
0.310826 | + | 0.950467i | \(0.399394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.6926 | −1.59235 | −0.796173 | − | 0.605069i | \(-0.793146\pi\) | ||||
−0.796173 | + | 0.605069i | \(0.793146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7970 | + | 18.7970i | 1.11737 | + | 1.11737i | 0.992126 | + | 0.125241i | \(0.0399703\pi\) |
0.125241 | + | 0.992126i | \(0.460030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.41699 | 0.201699 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1660 | 0.950942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.161755 | + | 0.161755i | 0.00944985 | + | 0.00944985i | 0.711816 | − | 0.702366i | \(-0.247873\pi\) |
−0.702366 | + | 0.711816i | \(0.747873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.65882 | −0.387692 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.8745 | − | 27.8745i | 1.61202 | − | 1.61202i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | − | 14.0000i | −0.806947 | − | 0.806947i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.50295i | 0.0860587i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1264 | − | 22.1264i | 1.26282 | − | 1.26282i | 0.313103 | − | 0.949719i | \(-0.398631\pi\) |
0.949719 | − | 0.313103i | \(-0.101369\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.1660i | − | 1.65385i | −0.562310 | − | 0.826926i | \(-0.690087\pi\) | ||
0.562310 | − | 0.826926i | \(-0.309913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.1660i | − | 1.53551i | −0.640741 | − | 0.767757i | \(-0.721373\pi\) | ||
0.640741 | − | 0.767757i | \(-0.278627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.49117 | − | 3.49117i | 0.196083 | − | 0.196083i | −0.602235 | − | 0.798319i | \(-0.705723\pi\) |
0.798319 | + | 0.602235i | \(0.205723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1382i | 0.679609i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.29150 | − | 1.29150i | −0.0718611 | − | 0.0718611i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −38.5203 | + | 38.5203i | −2.13672 | + | 2.13672i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.4499 | 1.23771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.4676 | − | 15.4676i | −0.850177 | − | 0.850177i | 0.139978 | − | 0.990155i | \(-0.455297\pi\) |
−0.990155 | + | 0.139978i | \(0.955297\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.1660 | 0.937879 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.58301 | 0.467546 | 0.233773 | − | 0.972291i | \(-0.424893\pi\) | ||||
0.233773 | + | 0.972291i | \(0.424893\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.9529 | + | 23.9529i | 1.29712 | + | 1.29712i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.35425 | + | 2.35425i | −0.126383 | + | 0.126383i | −0.767469 | − | 0.641086i | \(-0.778484\pi\) |
0.641086 | + | 0.767469i | \(0.278484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.5830 | − | 21.5830i | −1.15531 | − | 1.15531i | −0.985472 | − | 0.169840i | \(-0.945675\pi\) |
−0.169840 | − | 0.985472i | \(-0.554325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.0397i | 1.22628i | 0.789975 | + | 0.613139i | \(0.210093\pi\) | ||||
−0.789975 | + | 0.613139i | \(0.789907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.2646 | + | 34.2646i | −1.81858 | + | 1.81858i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 37.2915i | 1.96817i | 0.177698 | + | 0.984085i | \(0.443135\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000i | 0.789474i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.1264 | + | 22.1264i | −1.15815 | + | 1.15815i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.74166i | − | 0.195313i | −0.995220 | − | 0.0976565i | \(-0.968865\pi\) | ||
0.995220 | − | 0.0976565i | \(-0.0311346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.0627 | − | 13.0627i | −0.678184 | − | 0.678184i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2915 | − | 24.2915i | 1.25777 | − | 1.25777i | 0.305609 | − | 0.952157i | \(-0.401140\pi\) |
0.952157 | − | 0.305609i | \(-0.0988602\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.4676 | 0.796623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.24461 | − | 5.24461i | −0.269397 | − | 0.269397i | 0.559460 | − | 0.828857i | \(-0.311009\pi\) |
−0.828857 | + | 0.559460i | \(0.811009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.4575 | −1.24972 | −0.624860 | − | 0.780737i | \(-0.714844\pi\) | ||||
−0.624860 | + | 0.780737i | \(0.714844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −70.3320 | −3.58445 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5485 | + | 19.5485i | 0.991148 | + | 0.991148i | 0.999961 | − | 0.00881296i | \(-0.00280529\pi\) |
−0.00881296 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.47938 | 0.277104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.6458 | − | 21.6458i | 1.08912 | − | 1.08912i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.58301 | − | 7.58301i | −0.380580 | − | 0.380580i | 0.490731 | − | 0.871311i | \(-0.336730\pi\) |
−0.871311 | + | 0.490731i | \(0.836730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0573i | 0.801865i | 0.916108 | + | 0.400932i | \(0.131314\pi\) | ||||
−0.916108 | + | 0.400932i | \(0.868686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.5230 | − | 30.5230i | 1.52046 | − | 1.52046i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.29150i | 0.361426i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.7085i | − | 1.12286i | −0.827523 | − | 0.561431i | \(-0.810251\pi\) | ||
0.827523 | − | 0.561431i | \(-0.189749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.83236 | + | 4.83236i | −0.237785 | + | 0.237785i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.4558i | 1.24958i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.93725 | + | 4.93725i | 0.241201 | + | 0.241201i | 0.817347 | − | 0.576146i | \(-0.195444\pi\) |
−0.576146 | + | 0.817347i | \(0.695444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.93725 | − | 5.93725i | 0.289364 | − | 0.289364i | −0.547465 | − | 0.836829i | \(-0.684407\pi\) |
0.836829 | + | 0.547465i | \(0.184407\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.57205 | −0.367298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.09070 | + | 1.09070i | 0.0527828 | + | 0.0527828i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.58301 | −0.413429 | −0.206714 | − | 0.978401i | \(-0.566277\pi\) | ||||
−0.206714 | + | 0.978401i | \(0.566277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.5830 | −1.27750 | −0.638749 | − | 0.769415i | \(-0.720548\pi\) | ||||
−0.638749 | + | 0.769415i | \(0.720548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528 | + | 8.48528i | 0.405906 | + | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0554 | 0.718553 | 0.359277 | − | 0.933231i | \(-0.383023\pi\) | ||||
0.359277 | + | 0.933231i | \(0.383023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.35425 | − | 2.35425i | 0.111854 | − | 0.111854i | −0.648965 | − | 0.760818i | \(-0.724798\pi\) |
0.760818 | + | 0.648965i | \(0.224798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.5203 | − | 37.5203i | −1.77863 | − | 1.77863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.57205i | 0.357347i | 0.983908 | + | 0.178674i | \(0.0571806\pi\) | ||||
−0.983908 | + | 0.178674i | \(0.942819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.32941 | − | 3.32941i | 0.156776 | − | 0.156776i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 89.6235i | 4.20162i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 30.4575i | − | 1.42474i | −0.701803 | − | 0.712371i | \(-0.747621\pi\) | ||
0.701803 | − | 0.712371i | \(-0.252379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.2014 | − | 23.2014i | 1.08060 | − | 1.08060i | 0.0841442 | − | 0.996454i | \(-0.473184\pi\) |
0.996454 | − | 0.0841442i | \(-0.0268157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 37.6828i | − | 1.75127i | −0.482976 | − | 0.875634i | \(-0.660444\pi\) | ||
0.482976 | − | 0.875634i | \(-0.339556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.3542 | − | 14.3542i | −0.664235 | − | 0.664235i | 0.292140 | − | 0.956376i | \(-0.405633\pi\) |
−0.956376 | + | 0.292140i | \(0.905633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4575 | − | 12.4575i | 0.575235 | − | 0.575235i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.2823 | −1.25444 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.7260 | − | 11.7260i | −0.538024 | − | 0.538024i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.2915 | 1.15560 | 0.577799 | − | 0.816179i | \(-0.303912\pi\) | ||||
0.577799 | + | 0.816179i | \(0.303912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.29150 | 0.423656 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.2646 | − | 34.2646i | −1.55588 | − | 1.55588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.74362 | −0.214954 | −0.107477 | − | 0.994208i | \(-0.534277\pi\) | ||||
−0.107477 | + | 0.994208i | \(0.534277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.29150 | + | 1.29150i | −0.0582847 | + | 0.0582847i | −0.735648 | − | 0.677364i | \(-0.763122\pi\) |
0.677364 | + | 0.735648i | \(0.263122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.52026 | + | 1.52026i | 0.0684690 | + | 0.0684690i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 49.7322i | 2.23080i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.65882 | − | 6.65882i | 0.298090 | − | 0.298090i | −0.542176 | − | 0.840265i | \(-0.682399\pi\) |
0.840265 | + | 0.542176i | \(0.182399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.8745i | 1.24286i | 0.783469 | + | 0.621431i | \(0.213449\pi\) | ||||
−0.783469 | + | 0.621431i | \(0.786551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.1660i | 1.56487i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.49117 | + | 3.49117i | −0.154743 | + | 0.154743i | −0.780233 | − | 0.625489i | \(-0.784899\pi\) |
0.625489 | + | 0.780233i | \(0.284899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.1147i | 1.42067i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.9373 | − | 16.9373i | −0.746345 | − | 0.746345i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8745 | − | 21.8745i | 0.962040 | − | 0.962040i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.39851 | 0.411756 | 0.205878 | − | 0.978578i | \(-0.433995\pi\) | ||||
0.205878 | + | 0.978578i | \(0.433995\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5524 | − | 13.5524i | −0.592606 | − | 0.592606i | 0.345729 | − | 0.938335i | \(-0.387632\pi\) |
−0.938335 | + | 0.345729i | \(0.887632\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | 0.261364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24264 | − | 4.24264i | −0.183769 | − | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −37.5940 | −1.62533 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.5203 | + | 25.5203i | −1.09924 | + | 1.09924i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.35425 | − | 3.35425i | −0.144210 | − | 0.144210i | 0.631316 | − | 0.775526i | \(-0.282515\pi\) |
−0.775526 | + | 0.631316i | \(0.782515\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.98233i | − | 0.299090i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5387 | − | 22.5387i | 0.963684 | − | 0.963684i | −0.0356789 | − | 0.999363i | \(-0.511359\pi\) |
0.999363 | + | 0.0356789i | \(0.0113594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.70850i | 0.200589i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 31.4170i | − | 1.33599i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8779 | + | 22.8779i | −0.969368 | + | 0.969368i | −0.999545 | − | 0.0301765i | \(-0.990393\pi\) |
0.0301765 | + | 0.999545i | \(0.490393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.7656i | 1.47043i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6458 | − | 15.6458i | −0.659390 | − | 0.659390i | 0.295846 | − | 0.955236i | \(-0.404399\pi\) |
−0.955236 | + | 0.295846i | \(0.904399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.8118 | + | 32.8118i | −1.38040 | + | 1.38040i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.3632 | 0.979435 | 0.489718 | − | 0.871881i | \(-0.337100\pi\) | ||||
0.489718 | + | 0.871881i | \(0.337100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.7970 | + | 18.7970i | 0.786631 | + | 0.786631i | 0.980940 | − | 0.194309i | \(-0.0622466\pi\) |
−0.194309 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.7490 | 2.07468 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.41699 | −0.392035 | −0.196017 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196017 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.4735 | + | 18.4735i | 0.766410 | + | 0.766410i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.4558 | −1.05427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2915 | − | 13.2915i | 0.548599 | − | 0.548599i | −0.377436 | − | 0.926035i | \(-0.623194\pi\) |
0.926035 | + | 0.377436i | \(0.123194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.29150 | + | 9.29150i | 0.382850 | + | 0.382850i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.24264i | − | 0.174224i | −0.996199 | − | 0.0871122i | \(-0.972236\pi\) | ||
0.996199 | − | 0.0871122i | \(-0.0277639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.80879 | + | 8.80879i | −0.361125 | + | 0.361125i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.1660i | − | 0.946538i | −0.880918 | − | 0.473269i | \(-0.843074\pi\) | ||
0.880918 | − | 0.473269i | \(-0.156926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.41699i | 0.384127i | 0.981382 | + | 0.192064i | \(0.0615180\pi\) | ||||
−0.981382 | + | 0.192064i | \(0.938482\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.1720 | + | 40.1720i | −1.63322 | + | 1.63322i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.09070i | − | 0.0442703i | −0.999755 | − | 0.0221351i | \(-0.992954\pi\) | ||
0.999755 | − | 0.0221351i | \(-0.00704641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.8745 | − | 27.8745i | −1.12768 | − | 1.12768i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58301 | + | 7.58301i | −0.306275 | + | 0.306275i | −0.843463 | − | 0.537188i | \(-0.819487\pi\) |
0.537188 | + | 0.843463i | \(0.319487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5190 | −1.14813 | −0.574067 | − | 0.818808i | \(-0.694635\pi\) | ||||
−0.574067 | + | 0.818808i | \(0.694635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1382 | + | 12.1382i | 0.487876 | + | 0.487876i | 0.907635 | − | 0.419760i | \(-0.137886\pi\) |
−0.419760 | + | 0.907635i | \(0.637886\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −54.4575 | −2.18179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.29150 | −0.0916601 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.913230 | + | 0.913230i | 0.0364129 | + | 0.0364129i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.1916 | −1.04267 | −0.521336 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521336 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.93725 | − | 4.93725i | 0.195929 | − | 0.195929i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5203 | + | 32.5203i | 1.28850 | + | 1.28850i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.5426i | 0.969375i | 0.874687 | + | 0.484687i | \(0.161067\pi\) | ||||
−0.874687 | + | 0.484687i | \(0.838933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.2289 | + | 13.2289i | −0.521697 | + | 0.521697i | −0.918084 | − | 0.396387i | \(-0.870264\pi\) |
0.396387 | + | 0.918084i | \(0.370264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 40.3320i | − | 1.58562i | −0.609472 | − | 0.792808i | \(-0.708618\pi\) | ||
0.609472 | − | 0.792808i | \(-0.291382\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.41699i | 0.369649i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.57794 | + | 2.57794i | −0.100882 | + | 0.100882i | −0.755747 | − | 0.654864i | \(-0.772726\pi\) |
0.654864 | + | 0.755747i | \(0.272726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 61.8705i | − | 2.41748i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.1660 | + | 23.1660i | 0.902420 | + | 0.902420i | 0.995645 | − | 0.0932254i | \(-0.0297177\pi\) |
−0.0932254 | + | 0.995645i | \(0.529718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4575 | + | 23.4575i | −0.912392 | + | 0.912392i | −0.996460 | − | 0.0840685i | \(-0.973209\pi\) |
0.0840685 | + | 0.996460i | \(0.473209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.2823 | −1.05796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.98823 | − | 9.98823i | −0.386746 | − | 0.386746i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12549 | 0.0820537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.7490 | 1.68640 | 0.843200 | − | 0.537600i | \(-0.180669\pi\) | ||||
0.843200 | + | 0.537600i | \(0.180669\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.23086 | + | 6.23086i | 0.239471 | + | 0.239471i | 0.816631 | − | 0.577160i | \(-0.195839\pi\) |
−0.577160 | + | 0.816631i | \(0.695839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.7322 | −1.90855 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6458 | − | 21.6458i | 0.828252 | − | 0.828252i | −0.159023 | − | 0.987275i | \(-0.550834\pi\) |
0.987275 | + | 0.159023i | \(0.0508345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.2288 | − | 24.2288i | −0.925733 | − | 0.925733i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.4382i | 1.23580i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8799 | − | 15.8799i | 0.604098 | − | 0.604098i | −0.337299 | − | 0.941398i | \(-0.609513\pi\) |
0.941398 | + | 0.337299i | \(0.109513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.1660i | − | 0.651144i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.833990i | − | 0.0315896i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.98822 | + | 1.98822i | −0.0750939 | + | 0.0750939i | −0.743656 | − | 0.668562i | \(-0.766910\pi\) |
0.668562 | + | 0.743656i | \(0.266910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.82843i | 0.106676i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.5203 | + | 25.5203i | 0.959788 | + | 0.959788i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6458 | + | 28.6458i | −1.07581 | + | 1.07581i | −0.0789339 | + | 0.996880i | \(0.525152\pi\) |
−0.996880 | + | 0.0789339i | \(0.974848\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.4205 | −1.47631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 87.3263 | + | 87.3263i | 3.26582 | + | 3.26582i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4575 | 0.688349 | 0.344175 | − | 0.938906i | \(-0.388159\pi\) | ||||
0.344175 | + | 0.938906i | \(0.388159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.5830 | −0.915519 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8029 | + | 13.8029i | 0.512627 | + | 0.512627i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.9906 | 1.70570 | 0.852848 | − | 0.522159i | \(-0.174873\pi\) | ||||
0.852848 | + | 0.522159i | \(0.174873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.41699 | + | 3.41699i | −0.126382 | + | 0.126382i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9373 | − | 21.9373i | −0.810271 | − | 0.810271i | 0.174403 | − | 0.984674i | \(-0.444200\pi\) |
−0.984674 | + | 0.174403i | \(0.944200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 24.2764i | − | 0.894233i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7970 | − | 18.7970i | 0.691460 | − | 0.691460i | −0.271093 | − | 0.962553i | \(-0.587385\pi\) |
0.962553 | + | 0.271093i | \(0.0873852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 39.0405i | − | 1.43226i | −0.697968 | − | 0.716129i | \(-0.745912\pi\) | ||
0.697968 | − | 0.716129i | \(-0.254088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.8745i | 1.46089i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.2823 | + | 27.2823i | −0.996874 | + | 0.996874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7063i | 0.646113i | 0.946380 | + | 0.323056i | \(0.104710\pi\) | ||||
−0.946380 | + | 0.323056i | \(0.895290\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.8118 | − | 26.8118i | −0.975780 | − | 0.975780i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6458 | + | 14.6458i | −0.532309 | + | 0.532309i | −0.921259 | − | 0.388950i | \(-0.872838\pi\) |
0.388950 | + | 0.921259i | \(0.372838\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.1661 | 1.63727 | 0.818635 | − | 0.574314i | \(-0.194731\pi\) | ||||
0.818635 | + | 0.574314i | \(0.194731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.06713 | − | 5.06713i | −0.183443 | − | 0.183443i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.1660 | 1.12388 | 0.561938 | − | 0.827180i | \(-0.310056\pi\) | ||||
0.561938 | + | 0.827180i | \(0.310056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.49117 | − | 3.49117i | −0.125569 | − | 0.125569i | 0.641530 | − | 0.767098i | \(-0.278300\pi\) |
−0.767098 | + | 0.641530i | \(0.778300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 54.4759 | 1.95683 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.29150 | − | 1.29150i | 0.0462729 | − | 0.0462729i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.4575 | + | 48.4575i | 1.73395 | + | 1.73395i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 32.4382i | − | 1.15777i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.89753 | + | 8.89753i | −0.317163 | + | 0.317163i | −0.847676 | − | 0.530514i | \(-0.821999\pi\) |
0.530514 | + | 0.847676i | \(0.321999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.6235i | 1.69330i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.70850i | − | 0.0961816i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8897 | + | 12.8897i | −0.456576 | + | 0.456576i | −0.897530 | − | 0.440954i | \(-0.854640\pi\) |
0.440954 | + | 0.897530i | \(0.354640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.47938i | − | 0.193847i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.2915 | + | 31.2915i | 1.10425 | + | 1.10425i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.8745 | − | 57.8745i | 2.03981 | − | 2.03981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.3337 | −1.41806 | −0.709029 | − | 0.705179i | \(-0.750867\pi\) | ||||
−0.709029 | + | 0.705179i | \(0.750867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.0416 | − | 24.0416i | −0.844216 | − | 0.844216i | 0.145188 | − | 0.989404i | \(-0.453621\pi\) |
−0.989404 | + | 0.145188i | \(0.953621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.87451 | 0.345889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5830 | −0.370252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5999 | + | 32.5999i | 1.13775 | + | 1.13775i | 0.988853 | + | 0.148892i | \(0.0475707\pi\) |
0.148892 | + | 0.988853i | \(0.452429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.74756 | −0.235205 | −0.117603 | − | 0.993061i | \(-0.537521\pi\) | ||||
−0.117603 | + | 0.993061i | \(0.537521\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.8745 | + | 33.8745i | −1.17793 | + | 1.17793i | −0.197662 | + | 0.980270i | \(0.563335\pi\) |
−0.980270 | + | 0.197662i | \(0.936665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.06275 | + | 8.06275i | 0.280031 | + | 0.280031i | 0.833121 | − | 0.553090i | \(-0.186552\pi\) |
−0.553090 | + | 0.833121i | \(0.686552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.39261i | 0.221491i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.7970 | − | 18.7970i | 0.650498 | − | 0.650498i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.87451i | 0.133763i | 0.997761 | + | 0.0668814i | \(0.0213049\pi\) | ||||
−0.997761 | + | 0.0668814i | \(0.978695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4575i | 0.808880i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 77.7660 | − | 77.7660i | 2.67523 | − | 2.67523i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.3063i | 2.00343i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | − | 6.00000i | −0.205677 | − | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2915 | − | 18.2915i | 0.626289 | − | 0.626289i | −0.320843 | − | 0.947132i | \(-0.603966\pi\) |
0.947132 | + | 0.320843i | \(0.103966\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.1955 | 0.963141 | 0.481571 | − | 0.876407i | \(-0.340067\pi\) | ||||
0.481571 | + | 0.876407i | \(0.340067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.7083 | − | 18.7083i | −0.638319 | − | 0.638319i | 0.311822 | − | 0.950141i | \(-0.399061\pi\) |
−0.950141 | + | 0.311822i | \(0.899061\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.0405 | 0.920470 | 0.460235 | − | 0.887797i | \(-0.347765\pi\) | ||||
0.460235 | + | 0.887797i | \(0.347765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.2915 | −0.451925 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.6117 | − | 30.6117i | −1.03843 | − | 1.03843i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9352 | −1.04820 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.7490 | + | 31.7490i | −1.07331 | + | 1.07331i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5830 | − | 33.5830i | −1.13402 | − | 1.13402i | −0.989503 | − | 0.144515i | \(-0.953838\pi\) |
−0.144515 | − | 0.989503i | \(-0.546162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 52.1484i | − | 1.75693i | −0.477811 | − | 0.878463i | \(-0.658570\pi\) | ||
0.477811 | − | 0.878463i | \(-0.341430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.74362 | + | 4.74362i | −0.159636 | + | 0.159636i | −0.782405 | − | 0.622770i | \(-0.786007\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.83399i | − | 0.229463i | −0.993397 | − | 0.114731i | \(-0.963399\pi\) | ||
0.993397 | − | 0.114731i | \(-0.0366008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.16601i | − | 0.240340i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.48528 | − | 8.48528i | 0.283949 | − | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 81.8469i | − | 2.73584i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.9373 | − | 10.9373i | −0.364778 | − | 0.364778i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.18824 | + | 3.18824i | −0.106216 | + | 0.106216i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.98233 | 0.232101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.1975 | − | 29.1975i | −0.969487 | − | 0.969487i | 0.0300609 | − | 0.999548i | \(-0.490430\pi\) |
−0.999548 | + | 0.0300609i | \(0.990430\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.6235 | −1.37905 | −0.689524 | − | 0.724262i | \(-0.742180\pi\) | ||||
−0.689524 | + | 0.724262i | \(0.742180\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | 1.19143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.8999 | − | 44.8999i | −1.48272 | − | 1.48272i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.4759 | 1.79699 | 0.898497 | − | 0.438980i | \(-0.144660\pi\) | ||||
0.898497 | + | 0.438980i | \(0.144660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.7490 | − | 61.7490i | 2.03249 | − | 2.03249i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.29150 | + | 8.29150i | 0.272623 | + | 0.272623i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 22.7162i | − | 0.745293i | −0.927973 | − | 0.372646i | \(-0.878450\pi\) | ||
0.927973 | − | 0.372646i | \(-0.121550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.89949 | + | 9.89949i | −0.324443 | + | 0.324443i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.1660i | 0.561389i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.3320i | − | 1.05624i | −0.849169 | − | 0.528121i | \(-0.822897\pi\) | ||
0.849169 | − | 0.528121i | \(-0.177103\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7161 | − | 14.7161i | 0.479732 | − | 0.479732i | −0.425314 | − | 0.905046i | \(-0.639836\pi\) |
0.905046 | + | 0.425314i | \(0.139836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.47938i | 0.178433i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.58301 | − | 8.58301i | −0.278910 | − | 0.278910i | 0.553764 | − | 0.832674i | \(-0.313191\pi\) |
−0.832674 | + | 0.553764i | \(0.813191\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.8745 | − | 39.8745i | 1.29438 | − | 1.29438i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.3691 | −0.854178 | −0.427089 | − | 0.904210i | \(-0.640461\pi\) | ||||
−0.427089 | + | 0.904210i | \(0.640461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.7322 | − | 49.7322i | −1.60930 | − | 1.60930i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.1660 | −1.13557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1660 | −0.392452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.8147 | + | 11.8147i | 0.380328 | + | 0.380328i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0475 | −0.355264 | −0.177632 | − | 0.984097i | \(-0.556844\pi\) | ||||
−0.177632 | + | 0.984097i | \(0.556844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0627 | + | 19.0627i | −0.611753 | + | 0.611753i | −0.943403 | − | 0.331650i | \(-0.892395\pi\) |
0.331650 | + | 0.943403i | \(0.392395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4575 | − | 12.4575i | −0.399370 | − | 0.399370i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.8485i | 1.01892i | 0.860494 | + | 0.509461i | \(0.170155\pi\) | ||||
−0.860494 | + | 0.509461i | \(0.829845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.0617 | + | 53.0617i | −1.69586 | + | 1.69586i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5830i | 0.465126i | 0.972581 | + | 0.232563i | \(0.0747111\pi\) | ||||
−0.972581 | + | 0.232563i | \(0.925289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 61.7490i | − | 1.96749i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.4499 | − | 22.4499i | 0.713867 | − | 0.713867i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5406i | 0.747793i | 0.927470 | + | 0.373897i | \(0.121979\pi\) | ||||
−0.927470 | + | 0.373897i | \(0.878021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.5203 | + | 43.5203i | 1.37968 | + | 1.37968i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.291503 | + | 0.291503i | −0.00923198 | + | 0.00923198i | −0.711708 | − | 0.702476i | \(-0.752078\pi\) |
0.702476 | + | 0.711708i | \(0.252078\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.2.l.d.1727.1 | yes | 8 | |
3.2 | odd | 2 | 2304.2.l.h.1727.4 | yes | 8 | ||
4.3 | odd | 2 | 2304.2.l.h.1727.1 | yes | 8 | ||
8.3 | odd | 2 | 2304.2.l.a.1727.4 | yes | 8 | ||
8.5 | even | 2 | 2304.2.l.e.1727.4 | yes | 8 | ||
12.11 | even | 2 | inner | 2304.2.l.d.1727.4 | yes | 8 | |
16.3 | odd | 4 | 2304.2.l.a.575.1 | ✓ | 8 | ||
16.5 | even | 4 | inner | 2304.2.l.d.575.4 | yes | 8 | |
16.11 | odd | 4 | 2304.2.l.h.575.4 | yes | 8 | ||
16.13 | even | 4 | 2304.2.l.e.575.1 | yes | 8 | ||
24.5 | odd | 2 | 2304.2.l.a.1727.1 | yes | 8 | ||
24.11 | even | 2 | 2304.2.l.e.1727.1 | yes | 8 | ||
48.5 | odd | 4 | 2304.2.l.h.575.1 | yes | 8 | ||
48.11 | even | 4 | inner | 2304.2.l.d.575.1 | yes | 8 | |
48.29 | odd | 4 | 2304.2.l.a.575.4 | yes | 8 | ||
48.35 | even | 4 | 2304.2.l.e.575.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2304.2.l.a.575.1 | ✓ | 8 | 16.3 | odd | 4 | ||
2304.2.l.a.575.4 | yes | 8 | 48.29 | odd | 4 | ||
2304.2.l.a.1727.1 | yes | 8 | 24.5 | odd | 2 | ||
2304.2.l.a.1727.4 | yes | 8 | 8.3 | odd | 2 | ||
2304.2.l.d.575.1 | yes | 8 | 48.11 | even | 4 | inner | |
2304.2.l.d.575.4 | yes | 8 | 16.5 | even | 4 | inner | |
2304.2.l.d.1727.1 | yes | 8 | 1.1 | even | 1 | trivial | |
2304.2.l.d.1727.4 | yes | 8 | 12.11 | even | 2 | inner | |
2304.2.l.e.575.1 | yes | 8 | 16.13 | even | 4 | ||
2304.2.l.e.575.4 | yes | 8 | 48.35 | even | 4 | ||
2304.2.l.e.1727.1 | yes | 8 | 24.11 | even | 2 | ||
2304.2.l.e.1727.4 | yes | 8 | 8.5 | even | 2 | ||
2304.2.l.h.575.1 | yes | 8 | 48.5 | odd | 4 | ||
2304.2.l.h.575.4 | yes | 8 | 16.11 | odd | 4 | ||
2304.2.l.h.1727.1 | yes | 8 | 4.3 | odd | 2 | ||
2304.2.l.h.1727.4 | yes | 8 | 3.2 | odd | 2 |