Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(769,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.d (of order \(2\), degree \(1\), 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: | \(12.2650217505\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.769 |
Dual form | 1536.2.d.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 \(\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(517\) | \(1025\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.24264 | −1.60357 | −0.801784 | − | 0.597614i | \(-0.796115\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.00000i | 1.80907i | 0.426401 | + | 0.904534i | \(0.359781\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.65685i | − 1.56893i | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
0.620174 | − | 0.784465i | \(-0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.00000i | − 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 4.24264i | − 0.925820i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.41421i | − 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41421 | 0.254000 | 0.127000 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127000 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.00000i | − 1.01419i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.48528i | − 1.39497i | −0.716599 | − | 0.697486i | \(-0.754302\pi\) | ||||
0.716599 | − | 0.697486i | \(-0.245698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.65685 | 0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.41421i | − 0.210819i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000 | 1.57143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 6.00000i | − 0.840168i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.89949i | − 1.35980i | −0.733305 | − | 0.679900i | \(-0.762023\pi\) | ||||
0.733305 | − | 0.679900i | \(-0.237977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.48528 | −1.14416 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.48528i | 1.08643i | 0.839594 | + | 0.543214i | \(0.182793\pi\) | ||||
−0.839594 | + | 0.543214i | \(0.817207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264 | 0.534522 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843i | 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.82843 | −0.335673 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000i | 0.346410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 25.4558i | − 2.90096i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7279 | −1.43200 | −0.716002 | − | 0.698099i | \(-0.754030\pi\) | ||||
−0.716002 | + | 0.698099i | \(0.754030\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.00000i | − 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8.48528i | − 0.920358i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41421 | 0.151620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.0000i | 2.51588i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.41421i | 0.146647i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 6.00000i | − 0.603023i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.41421i | − 0.140720i | −0.997522 | − | 0.0703598i | \(-0.977585\pi\) | ||||
0.997522 | − | 0.0703598i | \(-0.0224147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.07107 | 0.696733 | 0.348367 | − | 0.937358i | \(-0.386736\pi\) | ||||
0.348367 | + | 0.937358i | \(0.386736\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | 0.585540 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 16.9706i | − 1.62549i | −0.582623 | − | 0.812743i | \(-0.697974\pi\) | ||||
0.582623 | − | 0.812743i | \(-0.302026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.48528 | 0.805387 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000i | 0.373002i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685i | 0.522976i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.4558 | 2.33353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25.0000 | −2.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7279 | −1.12942 | −0.564710 | − | 0.825289i | \(-0.691012\pi\) | ||||
−0.564710 | + | 0.825289i | \(0.691012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.9706i | 1.47153i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41421 | 0.121716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.82843i | − 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 33.9411 | 2.83830 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0000i | 0.907265i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 4.24264i | − 0.347571i | −0.984784 | − | 0.173785i | \(-0.944400\pi\) | ||||
0.984784 | − | 0.173785i | \(-0.0555999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7279 | −1.03578 | −0.517892 | − | 0.855446i | \(-0.673283\pi\) | ||||
−0.517892 | + | 0.855446i | \(0.673283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000i | 0.160644i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.82843i | − 0.225733i | −0.993610 | − | 0.112867i | \(-0.963997\pi\) | ||||
0.993610 | − | 0.112867i | \(-0.0360032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.89949 | 0.785081 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.00000i | − 0.626608i | −0.949653 | − | 0.313304i | \(-0.898564\pi\) | ||||
0.949653 | − | 0.313304i | \(-0.101436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 8.48528i | − 0.660578i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.6274 | −1.75096 | −0.875481 | − | 0.483252i | \(-0.839455\pi\) | ||||
−0.875481 | + | 0.483252i | \(0.839455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.07107i | 0.537603i | 0.963196 | + | 0.268802i | \(0.0866276\pi\) | ||||
−0.963196 | + | 0.268802i | \(0.913372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7279 | −0.962140 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 20.0000i | − 1.49487i | −0.664335 | − | 0.747435i | \(-0.731285\pi\) | ||||
0.664335 | − | 0.747435i | \(-0.268715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.9706i | − 1.26141i | −0.776022 | − | 0.630706i | \(-0.782765\pi\) | ||||
0.776022 | − | 0.630706i | \(-0.217235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.48528 | −0.627250 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | 0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 36.0000i | − 2.63258i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.24264i | 0.308607i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3137 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0000 | 0.863779 | 0.431889 | − | 0.901927i | \(-0.357847\pi\) | ||||
0.431889 | + | 0.901927i | \(0.357847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000i | 0.572892i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.24264i | − 0.302276i | −0.988513 | − | 0.151138i | \(-0.951706\pi\) | ||||
0.988513 | − | 0.151138i | \(-0.0482937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.24264 | −0.300753 | −0.150376 | − | 0.988629i | \(-0.548049\pi\) | ||||
−0.150376 | + | 0.988629i | \(0.548049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000i | 0.421117i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.82843i | 0.197546i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.82843i | − 0.193801i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 8.00000i | − 0.540590i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.9411i | 2.28313i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.5563 | −1.04173 | −0.520865 | − | 0.853639i | \(-0.674391\pi\) | ||||
−0.520865 | + | 0.853639i | \(0.674391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 14.0000i | − 0.929213i | −0.885517 | − | 0.464606i | \(-0.846196\pi\) | ||||
0.885517 | − | 0.464606i | \(-0.153804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6274i | 1.49526i | 0.664114 | + | 0.747631i | \(0.268809\pi\) | ||||
−0.664114 | + | 0.747631i | \(0.731191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.4558 | 1.67487 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.0000 | −1.44127 | −0.720634 | − | 0.693316i | \(-0.756149\pi\) | ||||
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4.00000i | − 0.260931i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 12.7279i | − 0.826767i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.5563i | 0.993859i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.6274 | −1.43975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.00000 | 0.126745 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 18.0000i | − 1.13615i | −0.822977 | − | 0.568075i | \(-0.807688\pi\) | ||||
0.822977 | − | 0.568075i | \(-0.192312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.9706i | 1.06693i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.48528 | 0.531369 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.0000 | −1.87135 | −0.935674 | − | 0.352865i | \(-0.885208\pi\) | ||||
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.0000i | 2.23693i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41421i | 0.0875376i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.9706 | 1.04645 | 0.523225 | − | 0.852195i | \(-0.324729\pi\) | ||||
0.523225 | + | 0.852195i | \(0.324729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0000 | 0.860013 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.00000i | − 0.122398i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7279i | 0.776035i | 0.921652 | + | 0.388018i | \(0.126840\pi\) | ||||
−0.921652 | + | 0.388018i | \(0.873160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.24264 | −0.257722 | −0.128861 | − | 0.991663i | \(-0.541132\pi\) | ||||
−0.128861 | + | 0.991663i | \(0.541132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.0000 | −1.45255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0000i | 1.08544i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9706i | 1.01966i | 0.860274 | + | 0.509831i | \(0.170292\pi\) | ||||
−0.860274 | + | 0.509831i | \(0.829708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.41421 | −0.0846668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.65685i | 0.335083i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48528 | −0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000i | 0.117242i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0416i | 1.40453i | 0.711917 | + | 0.702264i | \(0.247827\pi\) | ||||
−0.711917 | + | 0.702264i | \(0.752173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.65685 | −0.329355 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.00000 | 0.348155 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 16.0000i | − 0.925304i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.41421 | 0.0812444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000i | 0.913168i | 0.889680 | + | 0.456584i | \(0.150927\pi\) | ||||
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.07107i | 0.402259i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.6274 | 1.28308 | 0.641542 | − | 0.767088i | \(-0.278295\pi\) | ||||
0.641542 | + | 0.767088i | \(0.278295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0000 | 1.13047 | 0.565233 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565233 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.00000i | 0.338062i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.2132i | − 1.19145i | −0.803188 | − | 0.595726i | \(-0.796864\pi\) | ||||
0.803188 | − | 0.595726i | \(-0.203136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.48528 | 0.475085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 16.9706i | − 0.941357i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.9706 | 0.938474 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0000i | 0.879440i | 0.898135 | + | 0.439720i | \(0.144922\pi\) | ||||
−0.898135 | + | 0.439720i | \(0.855078\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.48528i | 0.464991i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 10.0000i | − 0.543125i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.48528i | 0.459504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00000i | 0.107366i | 0.998558 | + | 0.0536828i | \(0.0170960\pi\) | ||||
−0.998558 | + | 0.0536828i | \(0.982904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1421i | 0.757011i | 0.925599 | + | 0.378506i | \(0.123562\pi\) | ||||
−0.925599 | + | 0.378506i | \(0.876438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.00000i | − 0.212298i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.4558i | 1.34727i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.1127 | −1.64207 | −0.821033 | − | 0.570881i | \(-0.806602\pi\) | ||||
−0.821033 | + | 0.570881i | \(0.806602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 25.0000i | − 1.31216i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 11.3137i | − 0.592187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7279 | 0.664392 | 0.332196 | − | 0.943210i | \(-0.392210\pi\) | ||||
0.332196 | + | 0.943210i | \(0.392210\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.0000i | 2.18053i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7990i | 1.02515i | 0.858642 | + | 0.512576i | \(0.171309\pi\) | ||||
−0.858642 | + | 0.512576i | \(0.828691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.3137 | −0.584237 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 12.7279i | − 0.652071i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.65685 | −0.289052 | −0.144526 | − | 0.989501i | \(-0.546166\pi\) | ||||
−0.144526 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.0000 | 1.83473 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.41421i | − 0.0717035i | −0.999357 | − | 0.0358517i | \(-0.988586\pi\) | ||||
0.999357 | − | 0.0358517i | \(-0.0114144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9706 | −0.858238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 18.0000i | − 0.905678i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.1127i | 1.56150i | 0.624843 | + | 0.780751i | \(0.285163\pi\) | ||||
−0.624843 | + | 0.780751i | \(0.714837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9706 | −0.849591 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.00000i | − 0.398508i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.41421i | 0.0702728i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 50.9117 | 2.52360 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000i | 0.887875i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 16.9706i | − 0.835067i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.82843 | 0.138842 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 22.0000i | − 1.07477i | −0.843337 | − | 0.537385i | \(-0.819412\pi\) | ||||
0.843337 | − | 0.537385i | \(-0.180588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 11.3137i | − 0.551396i | −0.961244 | − | 0.275698i | \(-0.911091\pi\) | ||||
0.961244 | − | 0.275698i | \(-0.0889090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0000 | −0.873128 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 36.0000i | − 1.74216i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.9411i | 1.63869i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.7990 | 0.953684 | 0.476842 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476842 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000i | 0.0958927i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 11.3137i | − 0.541208i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.89949 | −0.472477 | −0.236239 | − | 0.971695i | \(-0.575915\pi\) | ||||
−0.236239 | + | 0.971695i | \(0.575915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | −0.523810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 22.0000i | − 1.04525i | −0.852562 | − | 0.522626i | \(-0.824953\pi\) | ||||
0.852562 | − | 0.522626i | \(-0.175047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.82843i | − 0.134080i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.24264 | 0.200670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000i | 0.565058i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 12.7279i | − 0.598010i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.9411 | −1.59118 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −42.0000 | −1.96468 | −0.982339 | − | 0.187112i | \(-0.940087\pi\) | ||||
−0.982339 | + | 0.187112i | \(0.940087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.00000i | 0.280056i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.3553i | 1.64666i | 0.567561 | + | 0.823331i | \(0.307887\pi\) | ||||
−0.567561 | + | 0.823331i | \(0.692113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6985 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000i | 0.832941i | 0.909149 | + | 0.416470i | \(0.136733\pi\) | ||||
−0.909149 | + | 0.416470i | \(0.863267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.9411i | 1.56726i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.82843 | 0.130327 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 12.0000i | − 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.89949i | 0.453267i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.0000 | −2.18861 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 12.0000i | − 0.546019i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.82843i | 0.128432i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3553 | 1.60210 | 0.801052 | − | 0.598595i | \(-0.204274\pi\) | ||||
0.801052 | + | 0.598595i | \(0.204274\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.0000i | − 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528i | 0.382158i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.48528 | 0.381385 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 28.0000i | − 1.25345i | −0.779240 | − | 0.626726i | \(-0.784395\pi\) | ||||
0.779240 | − | 0.626726i | \(-0.215605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 22.6274i | − 1.01092i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1421 | 0.630567 | 0.315283 | − | 0.948998i | \(-0.397900\pi\) | ||||
0.315283 | + | 0.948998i | \(0.397900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 19.0000i | − 0.843820i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.89949i | 0.438787i | 0.975636 | + | 0.219394i | \(0.0704079\pi\) | ||||
−0.975636 | + | 0.219394i | \(0.929592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.9411 | 1.50147 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.0000i | 0.440653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.9706i | − 0.746364i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.07107 | −0.310385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 12.7279i | − 0.555492i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.48528 | −0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 4.00000i | − 0.173585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11.3137i | − 0.490051i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.65685 | 0.244567 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0000 | 0.863064 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 66.0000i | 2.84282i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 22.6274i | − 0.972829i | −0.873728 | − | 0.486414i | \(-0.838305\pi\) | ||||
0.873728 | − | 0.486414i | \(-0.161695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.9706 | 0.728277 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000 | 1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 40.0000i | − 1.71028i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) | ||||
0.518400 | − | 0.855138i | \(-0.326528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.48528i | − 0.362143i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.65685 | −0.240990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.0000 | 2.29631 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.0000i | 0.509372i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.07107i | − 0.299611i | −0.988716 | − | 0.149805i | \(-0.952135\pi\) | ||||
0.988716 | − | 0.149805i | \(-0.0478647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 46.0000i | − 1.93867i | −0.245745 | − | 0.969334i | \(-0.579033\pi\) | ||||
0.245745 | − | 0.969334i | \(-0.420967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 14.1421i | − 0.594964i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.24264 | −0.178174 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 28.0000i | − 1.17176i | −0.810397 | − | 0.585882i | \(-0.800748\pi\) | ||||
0.810397 | − | 0.585882i | \(-0.199252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 11.3137i | − 0.472637i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.0000 | −0.832611 | −0.416305 | − | 0.909225i | \(-0.636675\pi\) | ||||
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000i | 0.498703i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.48528i | 0.352029i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 59.3970 | 2.45997 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.00000 | −0.330759 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.0000i | 1.81607i | 0.418890 | + | 0.908037i | \(0.362419\pi\) | ||||
−0.418890 | + | 0.908037i | \(0.637581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.65685i | − 0.233087i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.24264 | 0.174519 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.0000i | 1.47586i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.24264i | − 0.173640i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1127 | −1.27123 | −0.635615 | − | 0.772006i | \(-0.719253\pi\) | ||||
−0.635615 | + | 0.772006i | \(0.719253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.00000 | 0.163163 | 0.0815817 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815817 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 35.3553i | − 1.43740i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.89949 | 0.401808 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00000 | −0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0000i | 0.647291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.82843i | 0.114239i | 0.998367 | + | 0.0571195i | \(0.0181916\pi\) | ||||
−0.998367 | + | 0.0571195i | \(0.981808\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.82843 | −0.114053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000i | 1.12542i | 0.826656 | + | 0.562708i | \(0.190240\pi\) | ||||
−0.826656 | + | 0.562708i | \(0.809760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.82843i | − 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.48528 | 0.339956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000i | 0.958468i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.9117i | 2.02998i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.41421 | 0.0562990 | 0.0281495 | − | 0.999604i | \(-0.491039\pi\) | ||||
0.0281495 | + | 0.999604i | \(0.491039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 18.0000i | − 0.714308i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 62.2254i | − 2.46546i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.82843 | 0.111891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.0000 | 1.81689 | 0.908445 | − | 0.418004i | \(-0.137270\pi\) | ||||
0.908445 | + | 0.418004i | \(0.137270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0000i | 1.26196i | 0.775800 | + | 0.630978i | \(0.217346\pi\) | ||||
−0.775800 | + | 0.630978i | \(0.782654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.1421 | −0.555985 | −0.277992 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277992 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 6.00000i | − 0.235159i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.6985i | 1.16219i | 0.813835 | + | 0.581096i | \(0.197376\pi\) | ||||
−0.813835 | + | 0.581096i | \(0.802624\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.9706 | −0.663095 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.00000 | 0.312110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 36.0000i | − 1.40236i | −0.712984 | − | 0.701180i | \(-0.752657\pi\) | ||||
0.712984 | − | 0.701180i | \(-0.247343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.48528i | − 0.330039i | −0.986290 | − | 0.165020i | \(-0.947231\pi\) | ||||
0.986290 | − | 0.165020i | \(-0.0527687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.9411 | −1.31816 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.0000 | −0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.00000i | − 0.154881i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 15.5563i | − 0.601443i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.9117 | −1.96542 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.00000i | − 0.115470i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 43.8406i | − 1.68493i | −0.538750 | − | 0.842466i | \(-0.681103\pi\) | ||||
0.538750 | − | 0.842466i | \(-0.318897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.48528 | −0.325635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0000i | 1.14792i | 0.818884 | + | 0.573959i | \(0.194593\pi\) | ||||
−0.818884 | + | 0.573959i | \(0.805407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.4558i | 0.972618i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.6274 | −0.863290 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −56.0000 | −2.13343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 32.0000i | − 1.21734i | −0.793424 | − | 0.608669i | \(-0.791704\pi\) | ||||
0.793424 | − | 0.608669i | \(-0.208296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25.4558i | 0.966988i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 22.0000i | − 0.832116i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 38.1838i | − 1.44218i | −0.692841 | − | 0.721090i | \(-0.743641\pi\) | ||||
0.692841 | − | 0.721090i | \(-0.256359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.9411 | −1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 16.9706i | − 0.637343i | −0.947865 | − | 0.318671i | \(-0.896763\pi\) | ||||
0.947865 | − | 0.318671i | \(-0.103237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.7279 | 0.477334 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.0000i | 1.79510i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11.3137i | − 0.422518i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.1127 | −1.16031 | −0.580154 | − | 0.814507i | \(-0.697008\pi\) | ||||
−0.580154 | + | 0.814507i | \(0.697008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0000 | −1.11726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4.24264i | − 0.157568i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8701 | 0.996555 | 0.498278 | − | 0.867018i | \(-0.333966\pi\) | ||||
0.498278 | + | 0.867018i | \(0.333966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.2843i | − 1.04470i | −0.852730 | − | 0.522352i | \(-0.825055\pi\) | ||||
0.852730 | − | 0.522352i | \(-0.174945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.5563 | −0.573805 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.0000 | 1.76810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20.0000i | − 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 22.6274i | − 0.831239i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.2843 | −1.03765 | −0.518825 | − | 0.854881i | \(-0.673630\pi\) | ||||
−0.518825 | + | 0.854881i | \(0.673630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.00000i | 0.0731762i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706i | 0.620091i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.07107 | −0.258027 | −0.129013 | − | 0.991643i | \(-0.541181\pi\) | ||||
−0.129013 | + | 0.991643i | \(0.541181\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 18.0000i | − 0.655087i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 45.2548i | − 1.64481i | −0.568899 | − | 0.822407i | \(-0.692630\pi\) | ||||
0.568899 | − | 0.822407i | \(-0.307370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.9706 | −0.615992 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.0000 | 1.66750 | 0.833749 | − | 0.552143i | \(-0.186190\pi\) | ||||
0.833749 | + | 0.552143i | \(0.186190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 72.0000i | 2.60658i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.48528i | 0.306786i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6274 | 0.817029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0000 | −1.00971 | −0.504853 | − | 0.863205i | \(-0.668453\pi\) | ||||
−0.504853 | + | 0.863205i | \(0.668453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 30.0000i | − 1.08042i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 18.3848i | − 0.661254i | −0.943761 | − | 0.330627i | \(-0.892740\pi\) | ||||
0.943761 | − | 0.330627i | \(-0.107260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.24264 | 0.152400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.0000 | −1.29149 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 8.00000i | − 0.286630i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.9706i | − 0.607254i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.41421 | −0.0505399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.00000 | 0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000i | 0.998092i | 0.866575 | + | 0.499046i | \(0.166316\pi\) | ||||
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.9706i | 0.604168i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.4264 | 1.50851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.0000i | 0.496529i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 24.0416i | − 0.851598i | −0.904818 | − | 0.425799i | \(-0.859993\pi\) | ||||
0.904818 | − | 0.425799i | \(-0.140007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9706 | 0.600375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 48.0000i | − 1.69388i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 16.9706i | − 0.598134i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.7279 | −0.448044 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20.0000i | − 0.702295i | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||||
0.936320 | − | 0.351147i | \(-0.114208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 4.24264i | − 0.148796i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.3137 | 0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 24.0000i | − 0.838628i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.41421i | − 0.0493564i | −0.999695 | − | 0.0246782i | \(-0.992144\pi\) | ||||
0.999695 | − | 0.0246782i | \(-0.00785611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.0122 | 1.42960 | 0.714798 | − | 0.699331i | \(-0.246519\pi\) | ||||
0.714798 | + | 0.699331i | \(0.246519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.0000 | −0.626680 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 28.0000i | − 0.973655i | −0.873498 | − | 0.486828i | \(-0.838154\pi\) | ||||
0.873498 | − | 0.486828i | \(-0.161846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.2843i | 0.982353i | 0.871060 | + | 0.491177i | \(0.163433\pi\) | ||||
−0.871060 | + | 0.491177i | \(0.836567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9706 | −0.588702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −66.0000 | −2.28676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 32.0000i | − 1.10741i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.41421i | − 0.0488824i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7990 | −0.683537 | −0.341769 | − | 0.939784i | \(-0.611026\pi\) | ||||
−0.341769 | + | 0.939784i | \(0.611026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.0000i | 0.619953i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 26.8701i | − 0.924358i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 106.066 | 3.64447 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 24.0000i | − 0.822709i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 42.4264i | − 1.45265i | −0.687350 | − | 0.726326i | \(-0.741226\pi\) | ||||
0.687350 | − | 0.726326i | \(-0.258774\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.65685 | −0.193460 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.0000 | −1.57133 | −0.785665 | − | 0.618652i | \(-0.787679\pi\) | ||||
−0.785665 | + | 0.618652i | \(0.787679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000i | 1.09183i | 0.837842 | + | 0.545913i | \(0.183817\pi\) | ||||
−0.837842 | + | 0.545913i | \(0.816183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 8.48528i | − 0.289178i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3137 | 0.385123 | 0.192562 | − | 0.981285i | \(-0.438320\pi\) | ||||
0.192562 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | −0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 76.3675i | − 2.59059i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.2548 | −1.53340 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 48.0000i | − 1.62270i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.7696i | 1.24162i | 0.783961 | + | 0.620810i | \(0.213196\pi\) | ||||
−0.783961 | + | 0.620810i | \(0.786804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0416 | −0.810904 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.0000i | − 0.807664i | −0.914833 | − | 0.403832i | \(-0.867678\pi\) | ||||
0.914833 | − | 0.403832i | \(-0.132322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 5.65685i | − 0.190153i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.5980 | −1.32957 | −0.664785 | − | 0.747035i | \(-0.731477\pi\) | ||||
−0.664785 | + | 0.747035i | \(0.731477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.0000 | 1.81110 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.00000i | 0.201008i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.3137i | 0.378599i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.2843 | 0.945439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.00000i | − 0.0667037i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.3970i | 1.97880i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0000 | 0.797787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 32.0000i | − 1.06254i | −0.847202 | − | 0.531271i | \(-0.821714\pi\) | ||||
0.847202 | − | 0.531271i | \(-0.178286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.41421i | 0.0469065i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.2843 | 0.937100 | 0.468550 | − | 0.883437i | \(-0.344777\pi\) | ||||
0.468550 | + | 0.883437i | \(0.344777\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 12.0000i | − 0.396708i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 50.9117i | − 1.68125i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8701 | −0.886361 | −0.443181 | − | 0.896432i | \(-0.646150\pi\) | ||||
−0.443181 | + | 0.896432i | \(0.646150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | −0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000i | 0.526646i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 25.4558i | − 0.836983i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.07107 | −0.232244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 44.0000i | − 1.44204i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.6274i | 0.740788i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.9117 | 1.66499 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.0000i | 0.652675i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.41421i | 0.0461020i | 0.999734 | + | 0.0230510i | \(0.00733802\pi\) | ||||
−0.999734 | + | 0.0230510i | \(0.992662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.65685 | 0.184213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.00000 | −0.195180 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.0000i | 1.68977i | 0.534946 | + | 0.844886i | \(0.320332\pi\) | ||||
−0.534946 | + | 0.844886i | \(0.679668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.2548i | 1.46903i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2132 | 0.687885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 16.0000i | − 0.517748i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.48528i | 0.274290i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −76.3675 | −2.46604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.9706i | 0.546302i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2132 | 0.682171 | 0.341085 | − | 0.940032i | \(-0.389205\pi\) | ||||
0.341085 | + | 0.940032i | \(0.389205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0000i | 0.449281i | 0.974442 | + | 0.224641i | \(0.0721208\pi\) | ||||
−0.974442 | + | 0.224641i | \(0.927879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.9706 | 0.543493 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.0000 | 1.34370 | 0.671850 | − | 0.740688i | \(-0.265500\pi\) | ||||
0.671850 | + | 0.740688i | \(0.265500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 12.0000i | − 0.383522i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9706i | 0.541828i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.2843 | −0.902128 | −0.451064 | − | 0.892492i | \(-0.648955\pi\) | ||||
−0.451064 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.0000i | 0.381964i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.24264 | 0.134772 | 0.0673860 | − | 0.997727i | \(-0.478534\pi\) | ||||
0.0673860 | + | 0.997727i | \(0.478534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.0000 | −0.507745 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.00000i | − 0.190213i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31.1127i | − 0.985349i | −0.870214 | − | 0.492675i | \(-0.836019\pi\) | ||||
0.870214 | − | 0.492675i | \(-0.163981\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.48528 | −0.268462 |
(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 | 1536.2.d.c.769.4 | 4 | ||
3.2 | odd | 2 | 4608.2.d.n.2305.1 | 4 | |||
4.3 | odd | 2 | inner | 1536.2.d.c.769.2 | 4 | ||
8.3 | odd | 2 | inner | 1536.2.d.c.769.3 | 4 | ||
8.5 | even | 2 | inner | 1536.2.d.c.769.1 | 4 | ||
12.11 | even | 2 | 4608.2.d.n.2305.2 | 4 | |||
16.3 | odd | 4 | 1536.2.a.i.1.2 | yes | 2 | ||
16.5 | even | 4 | 1536.2.a.i.1.1 | yes | 2 | ||
16.11 | odd | 4 | 1536.2.a.d.1.1 | ✓ | 2 | ||
16.13 | even | 4 | 1536.2.a.d.1.2 | yes | 2 | ||
24.5 | odd | 2 | 4608.2.d.n.2305.3 | 4 | |||
24.11 | even | 2 | 4608.2.d.n.2305.4 | 4 | |||
48.5 | odd | 4 | 4608.2.a.l.1.2 | 2 | |||
48.11 | even | 4 | 4608.2.a.g.1.2 | 2 | |||
48.29 | odd | 4 | 4608.2.a.g.1.1 | 2 | |||
48.35 | even | 4 | 4608.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.d.1.1 | ✓ | 2 | 16.11 | odd | 4 | ||
1536.2.a.d.1.2 | yes | 2 | 16.13 | even | 4 | ||
1536.2.a.i.1.1 | yes | 2 | 16.5 | even | 4 | ||
1536.2.a.i.1.2 | yes | 2 | 16.3 | odd | 4 | ||
1536.2.d.c.769.1 | 4 | 8.5 | even | 2 | inner | ||
1536.2.d.c.769.2 | 4 | 4.3 | odd | 2 | inner | ||
1536.2.d.c.769.3 | 4 | 8.3 | odd | 2 | inner | ||
1536.2.d.c.769.4 | 4 | 1.1 | even | 1 | trivial | ||
4608.2.a.g.1.1 | 2 | 48.29 | odd | 4 | |||
4608.2.a.g.1.2 | 2 | 48.11 | even | 4 | |||
4608.2.a.l.1.1 | 2 | 48.35 | even | 4 | |||
4608.2.a.l.1.2 | 2 | 48.5 | odd | 4 | |||
4608.2.d.n.2305.1 | 4 | 3.2 | odd | 2 | |||
4608.2.d.n.2305.2 | 4 | 12.11 | even | 2 | |||
4608.2.d.n.2305.3 | 4 | 24.5 | odd | 2 | |||
4608.2.d.n.2305.4 | 4 | 24.11 | even | 2 |