Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.1 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.d.3599.1 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(5\) | −2.98923 | − | 2.98923i | −1.33683 | − | 1.33683i | −0.899116 | − | 0.437710i | \(-0.855790\pi\) |
−0.437710 | − | 0.899116i | \(-0.644210\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32631 | − | 2.32631i | 0.701407 | − | 0.701407i | −0.263305 | − | 0.964713i | \(-0.584813\pi\) |
0.964713 | + | 0.263305i | \(0.0848126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.27678 | + | 1.27678i | 0.354115 | + | 0.354115i | 0.861638 | − | 0.507523i | \(-0.169439\pi\) |
−0.507523 | + | 0.861638i | \(0.669439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56038i | 0.863519i | 0.901989 | + | 0.431759i | \(0.142107\pi\) | ||||
−0.901989 | + | 0.431759i | \(0.857893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.796566 | − | 0.796566i | 0.182745 | − | 0.182745i | −0.609806 | − | 0.792551i | \(-0.708753\pi\) |
0.792551 | + | 0.609806i | \(0.208753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.75549i | 0.366045i | 0.983109 | + | 0.183023i | \(0.0585881\pi\) | ||||
−0.983109 | + | 0.183023i | \(0.941412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.8710i | 2.57421i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.87823 | + | 1.87823i | −0.348779 | + | 0.348779i | −0.859654 | − | 0.510876i | \(-0.829321\pi\) |
0.510876 | + | 0.859654i | \(0.329321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.15500i | 1.28508i | 0.766254 | + | 0.642538i | \(0.222118\pi\) | ||||
−0.766254 | + | 0.642538i | \(0.777882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.98923 | − | 2.98923i | −0.505273 | − | 0.505273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.64081 | − | 4.64081i | 0.762945 | − | 0.762945i | −0.213909 | − | 0.976854i | \(-0.568619\pi\) |
0.976854 | + | 0.213909i | \(0.0686195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.98721 | 1.40357 | 0.701783 | − | 0.712391i | \(-0.252388\pi\) | ||||
0.701783 | + | 0.712391i | \(0.252388\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.04027 | + | 6.04027i | 0.921132 | + | 0.921132i | 0.997110 | − | 0.0759775i | \(-0.0242077\pi\) |
−0.0759775 | + | 0.997110i | \(0.524208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.99236 | −1.01994 | −0.509970 | − | 0.860192i | \(-0.670344\pi\) | ||||
−0.509970 | + | 0.860192i | \(0.670344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.536812 | + | 0.536812i | 0.0737369 | + | 0.0737369i | 0.743013 | − | 0.669277i | \(-0.233396\pi\) |
−0.669277 | + | 0.743013i | \(0.733396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.9077 | −1.87532 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.119264 | − | 0.119264i | 0.0155269 | − | 0.0155269i | −0.699301 | − | 0.714828i | \(-0.746505\pi\) |
0.714828 | + | 0.699301i | \(0.246505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9735 | + | 10.9735i | 1.40501 | + | 1.40501i | 0.783055 | + | 0.621952i | \(0.213660\pi\) |
0.621952 | + | 0.783055i | \(0.286340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.63319i | − | 0.946780i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.83581 | + | 3.83581i | −0.468618 | + | 0.468618i | −0.901467 | − | 0.432848i | \(-0.857509\pi\) |
0.432848 | + | 0.901467i | \(0.357509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.96614i | − | 1.18276i | −0.806392 | − | 0.591382i | \(-0.798583\pi\) | ||
0.806392 | − | 0.591382i | \(-0.201417\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4452i | 1.33956i | 0.742562 | + | 0.669778i | \(0.233611\pi\) | ||||
−0.742562 | + | 0.669778i | \(0.766389\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.32631 | − | 2.32631i | 0.265107 | − | 0.265107i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.4311i | − | 1.73613i | −0.496449 | − | 0.868066i | \(-0.665363\pi\) | ||
0.496449 | − | 0.868066i | \(-0.334637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.23544 | − | 4.23544i | −0.464900 | − | 0.464900i | 0.435358 | − | 0.900258i | \(-0.356622\pi\) |
−0.900258 | + | 0.435358i | \(0.856622\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.6428 | − | 10.6428i | 1.15437 | − | 1.15437i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.38113 | 0.252400 | 0.126200 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126200 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27678 | + | 1.27678i | 0.133843 | + | 0.133843i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.76225 | −0.488596 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00751 | 0.609970 | 0.304985 | − | 0.952357i | \(-0.401348\pi\) | ||||
0.304985 | + | 0.952357i | \(0.401348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.15894 | − | 6.15894i | −0.612837 | − | 0.612837i | 0.330847 | − | 0.943684i | \(-0.392666\pi\) |
−0.943684 | + | 0.330847i | \(0.892666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7016 | −1.74419 | −0.872094 | − | 0.489338i | \(-0.837238\pi\) | ||||
−0.872094 | + | 0.489338i | \(0.837238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.52746 | − | 9.52746i | 0.921055 | − | 0.921055i | −0.0760494 | − | 0.997104i | \(-0.524231\pi\) |
0.997104 | + | 0.0760494i | \(0.0242307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3741 | − | 11.3741i | −1.08945 | − | 1.08945i | −0.995585 | − | 0.0938600i | \(-0.970079\pi\) |
−0.0938600 | − | 0.995585i | \(-0.529921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.65901i | 0.908643i | 0.890838 | + | 0.454321i | \(0.150118\pi\) | ||||
−0.890838 | + | 0.454321i | \(0.849882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.24757 | − | 5.24757i | 0.489339 | − | 0.489339i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.56038i | 0.326379i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.176606i | 0.0160551i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 23.5284 | − | 23.5284i | 2.10444 | − | 2.10444i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3501i | 1.27336i | 0.771127 | + | 0.636682i | \(0.219693\pi\) | ||||
−0.771127 | + | 0.636682i | \(0.780307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3814 | + | 13.3814i | 1.16913 | + | 1.16913i | 0.982413 | + | 0.186721i | \(0.0597861\pi\) |
0.186721 | + | 0.982413i | \(0.440214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.796566 | − | 0.796566i | 0.0690711 | − | 0.0690711i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.59574 | 0.734384 | 0.367192 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367192 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.60098 | − | 2.60098i | −0.220612 | − | 0.220612i | 0.588144 | − | 0.808756i | \(-0.299859\pi\) |
−0.808756 | + | 0.588144i | \(0.799859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.94036 | 0.496758 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2289 | 0.932513 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6833 | + | 13.6833i | 1.12098 | + | 1.12098i | 0.991594 | + | 0.129385i | \(0.0413004\pi\) |
0.129385 | + | 0.991594i | \(0.458700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.21798 | 0.587391 | 0.293696 | − | 0.955899i | \(-0.405115\pi\) | ||||
0.293696 | + | 0.955899i | \(0.405115\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.3880 | − | 21.3880i | 1.71792 | − | 1.71792i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.28205 | + | 2.28205i | 0.182127 | + | 0.182127i | 0.792282 | − | 0.610155i | \(-0.208893\pi\) |
−0.610155 | + | 0.792282i | \(0.708893\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.75549i | 0.138352i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7454 | − | 12.7454i | 0.998293 | − | 0.998293i | −0.00170515 | − | 0.999999i | \(-0.500543\pi\) |
0.999999 | + | 0.00170515i | \(0.000542768\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.86515i | − | 0.608624i | −0.952572 | − | 0.304312i | \(-0.901574\pi\) | ||
0.952572 | − | 0.304312i | \(-0.0984265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.73967i | − | 0.749205i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.37538 | + | 3.37538i | −0.256625 | + | 0.256625i | −0.823680 | − | 0.567055i | \(-0.808083\pi\) |
0.567055 | + | 0.823680i | \(0.308083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.8710i | 0.972959i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.80060 | + | 2.80060i | 0.209327 | + | 0.209327i | 0.803981 | − | 0.594655i | \(-0.202711\pi\) |
−0.594655 | + | 0.803981i | \(0.702711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.63652 | − | 4.63652i | 0.344630 | − | 0.344630i | −0.513475 | − | 0.858105i | \(-0.671642\pi\) |
0.858105 | + | 0.513475i | \(0.171642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.7450 | −2.03985 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.28253 | + | 8.28253i | 0.605679 | + | 0.605679i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.1380 | 1.02299 | 0.511494 | − | 0.859287i | \(-0.329092\pi\) | ||||
0.511494 | + | 0.859287i | \(0.329092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.2621 | 1.60246 | 0.801230 | − | 0.598356i | \(-0.204179\pi\) | ||||
0.801230 | + | 0.598356i | \(0.204179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.84298 | + | 6.84298i | 0.487542 | + | 0.487542i | 0.907530 | − | 0.419988i | \(-0.137966\pi\) |
−0.419988 | + | 0.907530i | \(0.637966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.39131 | 0.0986274 | 0.0493137 | − | 0.998783i | \(-0.484297\pi\) | ||||
0.0493137 | + | 0.998783i | \(0.484297\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.87823 | + | 1.87823i | −0.131826 | + | 0.131826i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.8649 | − | 26.8649i | −1.87632 | − | 1.87632i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.70611i | − | 0.256357i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.57328 | − | 6.57328i | 0.452523 | − | 0.452523i | −0.443668 | − | 0.896191i | \(-0.646323\pi\) |
0.896191 | + | 0.443668i | \(0.146323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 36.1115i | − | 2.46279i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.15500i | 0.485713i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.54582 | + | 4.54582i | −0.305785 | + | 0.305785i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.3598i | − | 1.22946i | −0.788737 | − | 0.614731i | \(-0.789264\pi\) | ||
0.788737 | − | 0.614731i | \(-0.210736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0196 | − | 14.0196i | −0.930514 | − | 0.930514i | 0.0672240 | − | 0.997738i | \(-0.478586\pi\) |
−0.997738 | + | 0.0672240i | \(0.978586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.27105 | − | 2.27105i | 0.150075 | − | 0.150075i | −0.628076 | − | 0.778152i | \(-0.716157\pi\) |
0.778152 | + | 0.628076i | \(0.216157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.95841 | 0.521373 | 0.260687 | − | 0.965424i | \(-0.416051\pi\) | ||||
0.260687 | + | 0.965424i | \(0.416051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.9018 | + | 20.9018i | 1.36348 | + | 1.36348i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.4554 | 1.51720 | 0.758601 | − | 0.651556i | \(-0.225883\pi\) | ||||
0.758601 | + | 0.651556i | \(0.225883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8655 | −1.02199 | −0.510993 | − | 0.859585i | \(-0.670722\pi\) | ||||
−0.510993 | + | 0.859585i | \(0.670722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.98923 | − | 2.98923i | −0.190975 | − | 0.190975i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.03408 | 0.129425 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.26193 | + | 8.26193i | −0.521489 | + | 0.521489i | −0.918021 | − | 0.396532i | \(-0.870214\pi\) |
0.396532 | + | 0.918021i | \(0.370214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.08381 | + | 4.08381i | 0.256747 | + | 0.256747i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1727i | 0.884070i | 0.896998 | + | 0.442035i | \(0.145743\pi\) | ||||
−0.896998 | + | 0.442035i | \(0.854257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.64081 | − | 4.64081i | 0.288366 | − | 0.288366i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 26.0095i | − | 1.60381i | −0.597449 | − | 0.801907i | \(-0.703819\pi\) | ||
0.597449 | − | 0.801907i | \(-0.296181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.20932i | − | 0.197147i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.51572 | − | 6.51572i | 0.397270 | − | 0.397270i | −0.479999 | − | 0.877269i | \(-0.659363\pi\) |
0.877269 | + | 0.479999i | \(0.159363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.92154i | 0.481199i | 0.970624 | + | 0.240600i | \(0.0773441\pi\) | ||||
−0.970624 | + | 0.240600i | \(0.922656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.9420 | + | 29.9420i | 1.80557 | + | 1.80557i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.35852 | + | 5.35852i | −0.321962 | + | 0.321962i | −0.849519 | − | 0.527557i | \(-0.823108\pi\) |
0.527557 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2941 | −1.21065 | −0.605323 | − | 0.795980i | \(-0.706956\pi\) | ||||
−0.605323 | + | 0.795980i | \(0.706956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.32260 | + | 2.32260i | 0.138064 | + | 0.138064i | 0.772761 | − | 0.634697i | \(-0.218875\pi\) |
−0.634697 | + | 0.772761i | \(0.718875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.98721 | 0.530498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.32369 | 0.254335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21418 | − | 4.21418i | −0.246195 | − | 0.246195i | 0.573212 | − | 0.819407i | \(-0.305697\pi\) |
−0.819407 | + | 0.573212i | \(0.805697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.713017 | −0.0415134 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.24137 | + | 2.24137i | −0.129622 | + | 0.129622i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.04027 | + | 6.04027i | 0.348155 | + | 0.348155i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 65.6045i | − | 3.75650i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6414 | − | 18.6414i | 1.06392 | − | 1.06392i | 0.0661106 | − | 0.997812i | \(-0.478941\pi\) |
0.997812 | − | 0.0661106i | \(-0.0210590\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.0781i | 1.08182i | 0.841080 | + | 0.540910i | \(0.181920\pi\) | ||||
−0.841080 | + | 0.540910i | \(0.818080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.3787i | 1.83015i | 0.403282 | + | 0.915076i | \(0.367869\pi\) | ||||
−0.403282 | + | 0.915076i | \(0.632131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.55044 | − | 1.55044i | 0.0870813 | − | 0.0870813i | −0.662224 | − | 0.749306i | \(-0.730387\pi\) |
0.749306 | + | 0.662224i | \(0.230387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.73867i | 0.489272i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.83608 | + | 2.83608i | 0.157804 | + | 0.157804i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.4335 | + | 16.4335i | −0.911565 | + | 0.911565i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.99236 | −0.385501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.20654 | − | 6.20654i | −0.341142 | − | 0.341142i | 0.515654 | − | 0.856797i | \(-0.327549\pi\) |
−0.856797 | + | 0.515654i | \(0.827549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.9322 | 1.25292 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6890 | −0.636739 | −0.318369 | − | 0.947967i | \(-0.603135\pi\) | ||||
−0.318369 | + | 0.947967i | \(0.603135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.6447 | + | 16.6447i | 0.901362 | + | 0.901362i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.2790 | + | 18.2790i | −0.981268 | + | 0.981268i | −0.999828 | − | 0.0185600i | \(-0.994092\pi\) |
0.0185600 | + | 0.999828i | \(0.494092\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5945 | + | 15.5945i | 0.834753 | + | 0.834753i | 0.988163 | − | 0.153409i | \(-0.0490253\pi\) |
−0.153409 | + | 0.988163i | \(0.549025\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5053i | 1.19784i | 0.800810 | + | 0.598918i | \(0.204402\pi\) | ||||
−0.800810 | + | 0.598918i | \(0.795598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.7911 | + | 29.7911i | −1.58115 | + | 1.58115i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.4623i | − | 0.710512i | −0.934769 | − | 0.355256i | \(-0.884394\pi\) | ||
0.934769 | − | 0.355256i | \(-0.115606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7310i | 0.933209i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.2123 | − | 34.2123i | 1.79075 | − | 1.79075i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.96018i | 0.258919i | 0.991585 | + | 0.129460i | \(0.0413242\pi\) | ||||
−0.991585 | + | 0.129460i | \(0.958676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.536812 | + | 0.536812i | 0.0278699 | + | 0.0278699i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.46439 | + | 3.46439i | −0.179379 | + | 0.179379i | −0.791085 | − | 0.611706i | \(-0.790484\pi\) |
0.611706 | + | 0.791085i | \(0.290484\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.79617 | −0.247015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.5198 | − | 12.5198i | −0.643097 | − | 0.643097i | 0.308218 | − | 0.951316i | \(-0.400267\pi\) |
−0.951316 | + | 0.308218i | \(0.900267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.5201 | −1.66170 | −0.830849 | − | 0.556497i | \(-0.812145\pi\) | ||||
−0.830849 | + | 0.556497i | \(0.812145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.9077 | −0.708804 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.73683 | + | 6.73683i | 0.341571 | + | 0.341571i | 0.856958 | − | 0.515387i | \(-0.172352\pi\) |
−0.515387 | + | 0.856958i | \(0.672352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.25021 | −0.316087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.1271 | + | 46.1271i | −2.32091 | + | 2.32091i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6040 | − | 17.6040i | −0.883520 | − | 0.883520i | 0.110370 | − | 0.993891i | \(-0.464796\pi\) |
−0.993891 | + | 0.110370i | \(0.964796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.9384i | − | 0.895803i | −0.894083 | − | 0.447902i | \(-0.852171\pi\) | ||
0.894083 | − | 0.447902i | \(-0.147829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.13536 | + | 9.13536i | −0.455064 | + | 0.455064i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.5919i | − | 1.07027i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5200i | 0.668521i | 0.942481 | + | 0.334261i | \(0.108487\pi\) | ||||
−0.942481 | + | 0.334261i | \(0.891513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.119264 | − | 0.119264i | 0.00586861 | − | 0.00586861i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.3214i | 1.24298i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.57126 | − | 8.57126i | −0.418733 | − | 0.418733i | 0.466034 | − | 0.884767i | \(-0.345683\pi\) |
−0.884767 | + | 0.466034i | \(0.845683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.96735 | − | 6.96735i | 0.339568 | − | 0.339568i | −0.516637 | − | 0.856205i | \(-0.672816\pi\) |
0.856205 | + | 0.516637i | \(0.172816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −45.8258 | −2.22288 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9735 | + | 10.9735i | 0.531043 | + | 0.531043i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.2769 | −1.79557 | −0.897783 | − | 0.440438i | \(-0.854823\pi\) | ||||
−0.897783 | + | 0.440438i | \(0.854823\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5067 | 1.22577 | 0.612886 | − | 0.790171i | \(-0.290008\pi\) | ||||
0.612886 | + | 0.790171i | \(0.290008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.39837 | + | 1.39837i | 0.0668929 | + | 0.0668929i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.7171 | 1.84786 | 0.923932 | − | 0.382556i | \(-0.124956\pi\) | ||||
0.923932 | + | 0.382556i | \(0.124956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8179 | + | 10.8179i | −0.513974 | + | 0.513974i | −0.915742 | − | 0.401767i | \(-0.868396\pi\) |
0.401767 | + | 0.915742i | \(0.368396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.11777 | − | 7.11777i | −0.337415 | − | 0.337415i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.74427i | − | 0.318282i | −0.987256 | − | 0.159141i | \(-0.949128\pi\) | ||
0.987256 | − | 0.159141i | \(-0.0508724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.9070 | − | 20.9070i | 0.984472 | − | 0.984472i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.63319i | − | 0.357849i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 31.1453i | − | 1.45692i | −0.685091 | − | 0.728458i | \(-0.740238\pi\) | ||
0.685091 | − | 0.728458i | \(-0.259762\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.6054 | − | 27.6054i | 1.28571 | − | 1.28571i | 0.348346 | − | 0.937366i | \(-0.386744\pi\) |
0.937366 | − | 0.348346i | \(-0.113256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2024i | 0.938884i | 0.882963 | + | 0.469442i | \(0.155545\pi\) | ||||
−0.882963 | + | 0.469442i | \(0.844455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.5889 | − | 14.5889i | −0.675095 | − | 0.675095i | 0.283791 | − | 0.958886i | \(-0.408408\pi\) |
−0.958886 | + | 0.283791i | \(0.908408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.83581 | + | 3.83581i | −0.177121 | + | 0.177121i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.1030 | 1.29218 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2526 | + | 10.2526i | 0.470423 | + | 0.470423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.50499 | 0.160147 | 0.0800735 | − | 0.996789i | \(-0.474485\pi\) | ||||
0.0800735 | + | 0.996789i | \(0.474485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8506 | 0.540340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.9579 | − | 17.9579i | −0.815424 | − | 0.815424i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8906 | 0.538813 | 0.269407 | − | 0.963027i | \(-0.413172\pi\) | ||||
0.269407 | + | 0.963027i | \(0.413172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.36496 | + | 8.36496i | −0.377505 | + | 0.377505i | −0.870201 | − | 0.492696i | \(-0.836011\pi\) |
0.492696 | + | 0.870201i | \(0.336011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.68721 | − | 6.68721i | −0.301177 | − | 0.301177i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.96614i | − | 0.447043i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.4014 | − | 23.4014i | 1.04759 | − | 1.04759i | 0.0487824 | − | 0.998809i | \(-0.484466\pi\) |
0.998809 | − | 0.0487824i | \(-0.0155341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.4682i | 0.511342i | 0.966764 | + | 0.255671i | \(0.0822963\pi\) | ||||
−0.966764 | + | 0.255671i | \(0.917704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.8210i | 1.63851i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.9963 | + | 27.9963i | −1.24091 | + | 1.24091i | −0.281292 | + | 0.959622i | \(0.590763\pi\) |
−0.959622 | + | 0.281292i | \(0.909237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4452i | 0.506304i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 52.9142 | + | 52.9142i | 2.33168 | + | 2.33168i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2664 | + | 16.2664i | −0.715394 | + | 0.715394i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7733 | −0.515799 | −0.257900 | − | 0.966172i | \(-0.583030\pi\) | ||||
−0.257900 | + | 0.966172i | \(0.583030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3443 | − | 20.3443i | −0.889593 | − | 0.889593i | 0.104891 | − | 0.994484i | \(-0.466551\pi\) |
−0.994484 | + | 0.104891i | \(0.966551\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4745 | −1.10969 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9183 | 0.866011 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4747 | + | 11.4747i | 0.497024 | + | 0.497024i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −56.9596 | −2.46258 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.32631 | − | 2.32631i | 0.100201 | − | 0.100201i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0824 | − | 15.0824i | −0.648445 | − | 0.648445i | 0.304172 | − | 0.952617i | \(-0.401620\pi\) |
−0.952617 | + | 0.304172i | \(0.901620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 68.0000i | 2.91280i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2321 | − | 10.2321i | 0.437492 | − | 0.437492i | −0.453675 | − | 0.891167i | \(-0.649887\pi\) |
0.891167 | + | 0.453675i | \(0.149887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.99227i | 0.127475i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.4311i | − | 0.656196i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.823599 | + | 0.823599i | −0.0348970 | + | 0.0348970i | −0.724340 | − | 0.689443i | \(-0.757855\pi\) |
0.689443 | + | 0.724340i | \(0.257855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4242i | 0.652373i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.9474 | + | 11.9474i | 0.503523 | + | 0.503523i | 0.912531 | − | 0.409008i | \(-0.134125\pi\) |
−0.409008 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.8730 | − | 28.8730i | 1.21470 | − | 1.21470i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9392 | −0.626285 | −0.313142 | − | 0.949706i | \(-0.601382\pi\) | ||||
−0.313142 | + | 0.949706i | \(0.601382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1630 | + | 21.1630i | 0.885642 | + | 0.885642i | 0.994101 | − | 0.108459i | \(-0.0345916\pi\) |
−0.108459 | + | 0.994101i | \(0.534592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.5950 | −0.942276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7022 | −0.570430 | −0.285215 | − | 0.958463i | \(-0.592065\pi\) | ||||
−0.285215 | + | 0.958463i | \(0.592065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.23544 | − | 4.23544i | −0.175716 | − | 0.175716i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.49758 | 0.103439 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9582 | + | 14.9582i | −0.617390 | + | 0.617390i | −0.944861 | − | 0.327471i | \(-0.893804\pi\) |
0.327471 | + | 0.944861i | \(0.393804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.69943 | + | 5.69943i | 0.234841 | + | 0.234841i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.84205i | − | 0.280969i | −0.990083 | − | 0.140485i | \(-0.955134\pi\) | ||
0.990083 | − | 0.140485i | \(-0.0448661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.6428 | − | 10.6428i | 0.436313 | − | 0.436313i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.02266i | 0.286938i | 0.989655 | + | 0.143469i | \(0.0458257\pi\) | ||||
−0.989655 | + | 0.143469i | \(0.954174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.23315i | 0.376628i | 0.982109 | + | 0.188314i | \(0.0603023\pi\) | ||||
−0.982109 | + | 0.188314i | \(0.939698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.527918 | − | 0.527918i | 0.0214629 | − | 0.0214629i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.3413i | − | 0.744450i | −0.928142 | − | 0.372225i | \(-0.878595\pi\) | ||
0.928142 | − | 0.372225i | \(-0.121405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.92770 | − | 8.92770i | −0.361176 | − | 0.361176i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.5942 | + | 30.5942i | −1.23569 | + | 1.23569i | −0.273943 | + | 0.961746i | \(0.588328\pi\) |
−0.961746 | + | 0.273943i | \(0.911672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9418 | 0.480757 | 0.240379 | − | 0.970679i | \(-0.422728\pi\) | ||||
0.240379 | + | 0.970679i | \(0.422728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.31388 | + | 7.31388i | 0.293970 | + | 0.293970i | 0.838646 | − | 0.544676i | \(-0.183348\pi\) |
−0.544676 | + | 0.838646i | \(0.683348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.38113 | 0.0953982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −76.3084 | −3.05234 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.5231 | + | 16.5231i | 0.658817 | + | 0.658817i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9094 | −1.07125 | −0.535623 | − | 0.844457i | \(-0.679923\pi\) | ||||
−0.535623 | + | 0.844457i | \(0.679923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.8957 | − | 42.8957i | 1.70226 | − | 1.70226i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.27678 | + | 1.27678i | 0.0505878 | + | 0.0505878i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.10097i | − | 0.319969i | −0.987120 | − | 0.159984i | \(-0.948856\pi\) | ||
0.987120 | − | 0.159984i | \(-0.0511444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.56333 | + | 8.56333i | −0.337705 | + | 0.337705i | −0.855503 | − | 0.517798i | \(-0.826752\pi\) |
0.517798 | + | 0.855503i | \(0.326752\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.0564i | 1.84998i | 0.379994 | + | 0.924989i | \(0.375926\pi\) | ||||
−0.379994 | + | 0.924989i | \(0.624074\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.554890i | − | 0.0217813i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.5577 | + | 32.5577i | −1.27408 | + | 1.27408i | −0.330153 | + | 0.943927i | \(0.607100\pi\) |
−0.943927 | + | 0.330153i | \(0.892900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 80.0000i | − | 3.12586i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5376 | − | 19.5376i | −0.761077 | − | 0.761077i | 0.215440 | − | 0.976517i | \(-0.430881\pi\) |
−0.976517 | + | 0.215440i | \(0.930881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8137 | − | 20.8137i | 0.809559 | − | 0.809559i | −0.175008 | − | 0.984567i | \(-0.555995\pi\) |
0.984567 | + | 0.175008i | \(0.0559951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.76225 | −0.184672 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.29722 | − | 3.29722i | −0.127669 | − | 0.127669i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.0552 | 1.97097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0918 | 0.466103 | 0.233052 | − | 0.972464i | \(-0.425129\pi\) | ||||
0.233052 | + | 0.972464i | \(0.425129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.11293 | + | 9.11293i | 0.350238 | + | 0.350238i | 0.860198 | − | 0.509960i | \(-0.170340\pi\) |
−0.509960 | + | 0.860198i | \(0.670340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00751 | 0.230547 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.2646 | − | 27.2646i | 1.04325 | − | 1.04325i | 0.0442295 | − | 0.999021i | \(-0.485917\pi\) |
0.999021 | − | 0.0442295i | \(-0.0140833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.6947 | − | 25.6947i | −0.981743 | − | 0.981743i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.37078i | 0.0522226i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.651287 | + | 0.651287i | −0.0247761 | + | 0.0247761i | −0.719386 | − | 0.694610i | \(-0.755577\pi\) |
0.694610 | + | 0.719386i | \(0.255577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.5499i | 0.589840i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.9979i | 1.21201i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.49984 | − | 3.49984i | 0.132187 | − | 0.132187i | −0.637918 | − | 0.770105i | \(-0.720204\pi\) |
0.770105 | + | 0.637918i | \(0.220204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.39343i | − | 0.278849i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.15894 | − | 6.15894i | −0.231631 | − | 0.231631i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.4219 | − | 24.4219i | 0.917184 | − | 0.917184i | −0.0796402 | − | 0.996824i | \(-0.525377\pi\) |
0.996824 | + | 0.0796402i | \(0.0253771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.5605 | −0.470396 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.7571 | − | 17.7571i | −0.664079 | − | 0.664079i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.6847 | 0.547648 | 0.273824 | − | 0.961780i | \(-0.411711\pi\) | ||||
0.273824 | + | 0.961780i | \(0.411711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.7016 | −0.659241 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.1748 | − | 24.1748i | −0.897828 | − | 0.897828i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8567 | −0.699355 | −0.349678 | − | 0.936870i | \(-0.613709\pi\) | ||||
−0.349678 | + | 0.936870i | \(0.613709\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.5056 | + | 21.5056i | −0.795415 | + | 0.795415i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.31258 | − | 7.31258i | −0.270096 | − | 0.270096i | 0.559043 | − | 0.829139i | \(-0.311169\pi\) |
−0.829139 | + | 0.559043i | \(0.811169\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.8465i | 0.657385i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.5266 | − | 32.5266i | 1.19651 | − | 1.19651i | 0.221305 | − | 0.975205i | \(-0.428968\pi\) |
0.975205 | − | 0.221305i | \(-0.0710316\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.8397i | 0.911279i | 0.890164 | + | 0.455640i | \(0.150589\pi\) | ||||
−0.890164 | + | 0.455640i | \(0.849411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 81.8052i | − | 2.99711i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.52746 | − | 9.52746i | 0.348126 | − | 0.348126i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.9769i | − | 0.437042i | −0.975832 | − | 0.218521i | \(-0.929877\pi\) | ||
0.975832 | − | 0.218521i | \(-0.0701233\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5762 | − | 21.5762i | −0.785240 | − | 0.785240i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.1197 | − | 21.1197i | 0.767609 | − | 0.767609i | −0.210076 | − | 0.977685i | \(-0.567371\pi\) |
0.977685 | + | 0.210076i | \(0.0673710\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2727 | 0.807383 | 0.403692 | − | 0.914895i | \(-0.367727\pi\) | ||||
0.403692 | + | 0.914895i | \(0.367727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.3741 | − | 11.3741i | −0.411772 | − | 0.411772i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.304548 | 0.0109966 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.60282 | 0.0577992 | 0.0288996 | − | 0.999582i | \(-0.490800\pi\) | ||||
0.0288996 | + | 0.999582i | \(0.490800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.88678 | + | 1.88678i | 0.0678627 | + | 0.0678627i | 0.740224 | − | 0.672361i | \(-0.234720\pi\) |
−0.672361 | + | 0.740224i | \(0.734720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −92.0923 | −3.30805 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.15891 | − | 7.15891i | 0.256495 | − | 0.256495i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1843 | − | 23.1843i | −0.829599 | − | 0.829599i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 13.6432i | − | 0.486945i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9704 | + | 14.9704i | −0.533636 | + | 0.533636i | −0.921652 | − | 0.388016i | \(-0.873160\pi\) |
0.388016 | + | 0.921652i | \(0.373160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.65901i | 0.343435i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.0214i | 0.995068i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5079 | − | 11.5079i | 0.407631 | − | 0.407631i | −0.473281 | − | 0.880912i | \(-0.656930\pi\) |
0.880912 | + | 0.473281i | \(0.156930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.8955i | − | 0.880738i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.6250 | + | 26.6250i | 0.939574 | + | 0.939574i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.24757 | − | 5.24757i | 0.184953 | − | 0.184953i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4422 | 0.648393 | 0.324197 | − | 0.945990i | \(-0.394906\pi\) | ||||
0.324197 | + | 0.945990i | \(0.394906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.1494 | + | 20.1494i | 0.707541 | + | 0.707541i | 0.966018 | − | 0.258476i | \(-0.0832205\pi\) |
−0.258476 | + | 0.966018i | \(0.583220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −76.1977 | −2.66909 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.62295 | 0.336664 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.2511 | + | 16.2511i | 0.567167 | + | 0.567167i | 0.931334 | − | 0.364167i | \(-0.118646\pi\) |
−0.364167 | + | 0.931334i | \(0.618646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9919 | 1.04545 | 0.522725 | − | 0.852501i | \(-0.324915\pi\) | ||||
0.522725 | + | 0.852501i | \(0.324915\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.98308 | − | 3.98308i | 0.138505 | − | 0.138505i | −0.634455 | − | 0.772960i | \(-0.718775\pi\) |
0.772960 | + | 0.634455i | \(0.218775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.3406 | − | 35.3406i | −1.22743 | − | 1.22743i | −0.964933 | − | 0.262495i | \(-0.915455\pi\) |
−0.262495 | − | 0.964933i | \(-0.584545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.56038i | 0.123360i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.5108 | + | 23.5108i | −0.813624 | + | 0.813624i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.84103i | 0.339750i | 0.985466 | + | 0.169875i | \(0.0543364\pi\) | ||||
−0.985466 | + | 0.169875i | \(0.945664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.9445i | 0.756707i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.1141 | + | 29.1141i | −1.00156 | + | 1.00156i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.176606i | 0.00606827i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.14691 | + | 8.14691i | 0.279272 | + | 0.279272i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4376 | − | 15.4376i | 0.528575 | − | 0.528575i | −0.391573 | − | 0.920147i | \(-0.628069\pi\) |
0.920147 | + | 0.391573i | \(0.128069\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5480 | 0.770225 | 0.385113 | − | 0.922870i | \(-0.374163\pi\) | ||||
0.385113 | + | 0.922870i | \(0.374163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5198 | − | 11.5198i | −0.393051 | − | 0.393051i | 0.482722 | − | 0.875774i | \(-0.339648\pi\) |
−0.875774 | + | 0.482722i | \(0.839648\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.0019 | −1.32764 | −0.663821 | − | 0.747892i | \(-0.731066\pi\) | ||||
−0.663821 | + | 0.747892i | \(0.731066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.1796 | 0.686127 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.8974 | − | 35.8974i | −1.21774 | − | 1.21774i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.79495 | −0.331889 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.5284 | − | 23.5284i | 0.795404 | − | 0.795404i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4024 | + | 10.4024i | 0.351264 | + | 0.351264i | 0.860580 | − | 0.509316i | \(-0.170101\pi\) |
−0.509316 | + | 0.860580i | \(0.670101\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3973i | 0.653511i | 0.945109 | + | 0.326755i | \(0.105955\pi\) | ||||
−0.945109 | + | 0.326755i | \(0.894045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.435961 | − | 0.435961i | 0.0146712 | − | 0.0146712i | −0.699733 | − | 0.714404i | \(-0.746698\pi\) |
0.714404 | + | 0.699733i | \(0.246698\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.2161i | 0.477331i | 0.971102 | + | 0.238665i | \(0.0767099\pi\) | ||||
−0.971102 | + | 0.238665i | \(0.923290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3501i | 0.481286i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.56988 | + | 5.56988i | −0.186389 | + | 0.186389i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 16.7433i | − | 0.559667i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.4387 | − | 13.4387i | −0.448207 | − | 0.448207i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.91126 | + | 1.91126i | −0.0636732 | + | 0.0636732i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.7193 | −0.921420 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.15583 | + | 1.15583i | 0.0383788 | + | 0.0383788i | 0.726036 | − | 0.687657i | \(-0.241361\pi\) |
−0.687657 | + | 0.726036i | \(0.741361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.5370 | 1.14426 | 0.572132 | − | 0.820162i | \(-0.306117\pi\) | ||||
0.572132 | + | 0.820162i | \(0.306117\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.7058 | −0.652168 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.3814 | + | 13.3814i | 0.441891 | + | 0.441891i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.0003 | −0.494816 | −0.247408 | − | 0.968911i | \(-0.579579\pi\) | ||||
−0.247408 | + | 0.968911i | \(0.579579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.7246 | − | 12.7246i | 0.418834 | − | 0.418834i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.7321 | + | 59.7321i | 1.96398 | + | 1.96398i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.94212i | 0.227764i | 0.993494 | + | 0.113882i | \(0.0363285\pi\) | ||||
−0.993494 | + | 0.113882i | \(0.963671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.796566 | − | 0.796566i | 0.0261064 | − | 0.0261064i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 49.5168i | − | 1.61937i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.96161i | − | 0.292763i | −0.989228 | − | 0.146382i | \(-0.953237\pi\) | ||
0.989228 | − | 0.146382i | \(-0.0467627\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6536 | + | 21.6536i | −0.705886 | + | 0.705886i | −0.965667 | − | 0.259782i | \(-0.916349\pi\) |
0.259782 | + | 0.965667i | \(0.416349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.7770i | 0.513769i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.14094 | + | 5.14094i | 0.167058 | + | 0.167058i | 0.785685 | − | 0.618627i | \(-0.212311\pi\) |
−0.618627 | + | 0.785685i | \(0.712311\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.6130 | + | 14.6130i | −0.474357 | + | 0.474357i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.5695 | 0.957851 | 0.478926 | − | 0.877856i | \(-0.341026\pi\) | ||||
0.478926 | + | 0.877856i | \(0.341026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.2617 | − | 42.2617i | −1.36756 | − | 1.36756i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.59574 | 0.277571 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1940 | −0.651420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −66.5466 | − | 66.5466i | −2.14221 | − | 2.14221i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.3751 | 0.623063 | 0.311531 | − | 0.950236i | \(-0.399158\pi\) | ||||
0.311531 | + | 0.950236i | \(0.399158\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.45788 | + | 9.45788i | −0.303518 | + | 0.303518i | −0.842388 | − | 0.538871i | \(-0.818851\pi\) |
0.538871 | + | 0.842388i | \(0.318851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.60098 | − | 2.60098i | −0.0833836 | − | 0.0833836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.4796i | 1.03912i | 0.854435 | + | 0.519558i | \(0.173903\pi\) | ||||
−0.854435 | + | 0.519558i | \(0.826097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.53925 | − | 5.53925i | 0.177035 | − | 0.177035i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.8424i | 0.409609i | 0.978803 | + | 0.204804i | \(0.0656558\pi\) | ||||
−0.978803 | + | 0.204804i | \(0.934344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 40.9106i | − | 1.30352i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.6036 | + | 10.6036i | −0.337176 | + | 0.337176i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 9.67971i | − | 0.307486i | −0.988111 | − | 0.153743i | \(-0.950867\pi\) | ||
0.988111 | − | 0.153743i | \(-0.0491328\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.15895 | − | 4.15895i | −0.131848 | − | 0.131848i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.70473 | − | 1.70473i | 0.0539893 | − | 0.0539893i | −0.679597 | − | 0.733586i | \(-0.737845\pi\) |
0.733586 | + | 0.679597i | \(0.237845\pi\) | |||||||
\(998\) | 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 | 4032.2.v.d.1583.1 | 36 | ||
3.2 | odd | 2 | inner | 4032.2.v.d.1583.18 | 36 | ||
4.3 | odd | 2 | 1008.2.v.d.323.3 | ✓ | 36 | ||
12.11 | even | 2 | 1008.2.v.d.323.16 | yes | 36 | ||
16.5 | even | 4 | 1008.2.v.d.827.16 | yes | 36 | ||
16.11 | odd | 4 | inner | 4032.2.v.d.3599.18 | 36 | ||
48.5 | odd | 4 | 1008.2.v.d.827.3 | yes | 36 | ||
48.11 | even | 4 | inner | 4032.2.v.d.3599.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.d.323.3 | ✓ | 36 | 4.3 | odd | 2 | ||
1008.2.v.d.323.16 | yes | 36 | 12.11 | even | 2 | ||
1008.2.v.d.827.3 | yes | 36 | 48.5 | odd | 4 | ||
1008.2.v.d.827.16 | yes | 36 | 16.5 | even | 4 | ||
4032.2.v.d.1583.1 | 36 | 1.1 | even | 1 | trivial | ||
4032.2.v.d.1583.18 | 36 | 3.2 | odd | 2 | inner | ||
4032.2.v.d.3599.1 | 36 | 48.11 | even | 4 | inner | ||
4032.2.v.d.3599.18 | 36 | 16.11 | odd | 4 | inner |