Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (of order \(3\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(1.71903 - 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.577 |
Dual form | 2736.2.s.z.1873.2 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.675970 | + | 1.17081i | 0.302303 | + | 0.523604i | 0.976657 | − | 0.214804i | \(-0.0689113\pi\) |
−0.674354 | + | 0.738408i | \(0.735578\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.351939 | −0.133021 | −0.0665103 | − | 0.997786i | \(-0.521187\pi\) | ||||
−0.0665103 | + | 0.997786i | \(0.521187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.52420 | 1.66561 | 0.832804 | − | 0.553567i | \(-0.186734\pi\) | ||||
0.832804 | + | 0.553567i | \(0.186734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58613 | − | 4.47931i | 0.717263 | − | 1.24234i | −0.244817 | − | 0.969569i | \(-0.578728\pi\) |
0.962080 | − | 0.272767i | \(-0.0879389\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.43807 | − | 3.61328i | 0.559331 | − | 0.828944i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.41016 | + | 7.63862i | −0.919582 | + | 1.59276i | −0.119531 | + | 0.992830i | \(0.538139\pi\) |
−0.800051 | + | 0.599932i | \(0.795194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.58613 | − | 2.74726i | 0.317226 | − | 0.549452i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.35194 | − | 2.34163i | 0.251049 | − | 0.434829i | −0.712766 | − | 0.701402i | \(-0.752558\pi\) |
0.963815 | + | 0.266573i | \(0.0858912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.524200 | 0.0941490 | 0.0470745 | − | 0.998891i | \(-0.485010\pi\) | ||||
0.0470745 | + | 0.998891i | \(0.485010\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.237900 | − | 0.412055i | −0.0402125 | − | 0.0696500i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.35194 | − | 2.34163i | −0.211137 | − | 0.365701i | 0.740933 | − | 0.671579i | \(-0.234383\pi\) |
−0.952071 | + | 0.305878i | \(0.901050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.26210 | − | 5.65012i | −0.497466 | − | 0.861636i | 0.502530 | − | 0.864560i | \(-0.332403\pi\) |
−0.999996 | + | 0.00292406i | \(0.999069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87614 | −0.982306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.02791 | + | 3.51244i | −0.278555 | + | 0.482471i | −0.971026 | − | 0.238975i | \(-0.923189\pi\) |
0.692471 | + | 0.721446i | \(0.256522\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.73419 | + | 6.46781i | 0.503518 | + | 0.872119i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76210 | + | 4.78410i | 0.359595 | + | 0.622836i | 0.987893 | − | 0.155136i | \(-0.0495816\pi\) |
−0.628298 | + | 0.777972i | \(0.716248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.938069 | − | 1.62478i | 0.120107 | − | 0.208032i | −0.799702 | − | 0.600397i | \(-0.795009\pi\) |
0.919810 | + | 0.392364i | \(0.128343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.99258 | 0.867323 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.99629 | − | 10.3859i | 0.732564 | − | 1.26884i | −0.223221 | − | 0.974768i | \(-0.571657\pi\) |
0.955784 | − | 0.294069i | \(-0.0950096\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.52420 | − | 4.37204i | −0.299567 | − | 0.518866i | 0.676470 | − | 0.736471i | \(-0.263509\pi\) |
−0.976037 | + | 0.217605i | \(0.930176\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.85194 | − | 6.67175i | −0.450835 | − | 0.780870i | 0.547603 | − | 0.836738i | \(-0.315541\pi\) |
−0.998438 | + | 0.0558687i | \(0.982207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.94418 | −0.221560 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.91016 | + | 6.77260i | 0.439927 | + | 0.761977i | 0.997683 | − | 0.0680283i | \(-0.0216708\pi\) |
−0.557756 | + | 0.830005i | \(0.688337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.34452 | 0.915930 | 0.457965 | − | 0.888970i | \(-0.348578\pi\) | ||||
0.457965 | + | 0.888970i | \(0.348578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.32403 | + | 4.02534i | −0.246347 | + | 0.426685i | −0.962509 | − | 0.271248i | \(-0.912564\pi\) |
0.716163 | + | 0.697933i | \(0.245897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.910161 | + | 1.57644i | −0.0954108 | + | 0.165256i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.87854 | + | 0.412055i | 0.603126 | + | 0.0422760i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.90645 | + | 11.9623i | 0.701244 | + | 1.21459i | 0.968030 | + | 0.250834i | \(0.0807049\pi\) |
−0.266786 | + | 0.963756i | \(0.585962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.17226 | + | 2.03041i | −0.116644 | + | 0.202034i | −0.918436 | − | 0.395570i | \(-0.870547\pi\) |
0.801792 | + | 0.597604i | \(0.203880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1042 | 1.58680 | 0.793398 | − | 0.608703i | \(-0.208310\pi\) | ||||
0.793398 | + | 0.608703i | \(0.208310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.592243 | −0.0572543 | −0.0286272 | − | 0.999590i | \(-0.509114\pi\) | ||||
−0.0286272 | + | 0.999590i | \(0.509114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.79001 | + | 11.7606i | 0.650365 | + | 1.12647i | 0.983034 | + | 0.183422i | \(0.0587173\pi\) |
−0.332669 | + | 0.943043i | \(0.607949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9926 | 1.22224 | 0.611120 | − | 0.791538i | \(-0.290719\pi\) | ||||
0.611120 | + | 0.791538i | \(0.290719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.9245 | −1.11197 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5168 | 1.77425 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0484 | 0.988199 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.35194 | − | 9.26983i | 0.474908 | − | 0.822564i | −0.524679 | − | 0.851300i | \(-0.675815\pi\) |
0.999587 | + | 0.0287355i | \(0.00914807\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.64806 | + | 2.85453i | 0.143992 | + | 0.249401i | 0.928996 | − | 0.370089i | \(-0.120673\pi\) |
−0.785005 | + | 0.619490i | \(0.787339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.858052 | + | 1.27166i | −0.0744026 | + | 0.110267i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.52420 | − | 14.7643i | 0.728272 | − | 1.26140i | −0.229342 | − | 0.973346i | \(-0.573657\pi\) |
0.957613 | − | 0.288057i | \(-0.0930094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.96598 | + | 15.5295i | −0.760484 | + | 1.31720i | 0.182117 | + | 0.983277i | \(0.441705\pi\) |
−0.942601 | + | 0.333921i | \(0.891628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.2863 | − | 24.7446i | 1.19468 | − | 2.06925i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.65548 | 0.303571 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.972091 | + | 1.68371i | 0.0796368 | + | 0.137935i | 0.903093 | − | 0.429444i | \(-0.141291\pi\) |
−0.823456 | + | 0.567379i | \(0.807957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6406 | −1.11006 | −0.555030 | − | 0.831830i | \(-0.687293\pi\) | ||||
−0.555030 | + | 0.831830i | \(0.687293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.354343 | + | 0.613740i | 0.0284615 | + | 0.0492968i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.32032 | − | 14.4112i | −0.664034 | − | 1.15014i | −0.979546 | − | 0.201219i | \(-0.935510\pi\) |
0.315512 | − | 0.948921i | \(-0.397824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.55211 | − | 2.68833i | 0.122323 | − | 0.211870i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.99258 | 0.156071 | 0.0780355 | − | 0.996951i | \(-0.475135\pi\) | ||||
0.0780355 | + | 0.996951i | \(0.475135\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.29372 | + | 2.24078i | −0.100111 | + | 0.173397i | −0.911730 | − | 0.410790i | \(-0.865253\pi\) |
0.811619 | + | 0.584187i | \(0.198586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.87614 | − | 11.9098i | −0.528934 | − | 0.916140i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.82032 | + | 15.2772i | 0.670597 | + | 1.16151i | 0.977735 | + | 0.209843i | \(0.0672952\pi\) |
−0.307139 | + | 0.951665i | \(0.599372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.558221 | + | 0.966868i | −0.0421976 | + | 0.0730883i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.22808 | 0.166534 | 0.0832672 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832672 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.73419 | + | 8.19986i | −0.351890 | + | 0.609491i | −0.986581 | − | 0.163275i | \(-0.947794\pi\) |
0.634691 | + | 0.772766i | \(0.281127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.675970 | − | 1.17081i | −0.0496983 | − | 0.0860799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5726 | −1.63330 | −0.816648 | − | 0.577136i | \(-0.804170\pi\) | ||||
−0.816648 | + | 0.577136i | \(0.804170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.93807 | + | 12.0171i | 0.499413 | + | 0.865009i | 1.00000 | 0.000677488i | \(-0.000215651\pi\) | |
−0.500587 | + | 0.865686i | \(0.666882\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.30354 | −0.591603 | −0.295801 | − | 0.955249i | \(-0.595587\pi\) | ||||
−0.295801 | + | 0.955249i | \(0.595587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.44178 | + | 5.96134i | −0.243981 | + | 0.422588i | −0.961845 | − | 0.273596i | \(-0.911787\pi\) |
0.717863 | + | 0.696184i | \(0.245120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.475800 | + | 0.824110i | −0.0333946 | + | 0.0578412i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.82774 | − | 3.16574i | 0.127655 | − | 0.221105i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.4684 | − | 19.9605i | 0.931627 | − | 1.38070i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.31792 | − | 7.47885i | −0.297258 | − | 0.514865i | 0.678250 | − | 0.734831i | \(-0.262739\pi\) |
−0.975508 | + | 0.219966i | \(0.929405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.41016 | − | 7.63862i | 0.300770 | − | 0.520950i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.184486 | −0.0125238 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.13824 | + | 10.6317i | 0.411047 | + | 0.711954i | 0.995004 | − | 0.0998301i | \(-0.0318299\pi\) |
−0.583958 | + | 0.811784i | \(0.698497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.475800 | 0.0315800 | 0.0157900 | − | 0.999875i | \(-0.494974\pi\) | ||||
0.0157900 | + | 0.999875i | \(0.494974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.17226 | −0.341793 | −0.170896 | − | 0.985289i | \(-0.554666\pi\) | ||||
−0.170896 | + | 0.985289i | \(0.554666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.34452 | − | 9.25698i | −0.350131 | − | 0.606445i | 0.636141 | − | 0.771573i | \(-0.280530\pi\) |
−0.986272 | + | 0.165128i | \(0.947196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.11164 | 0.529145 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.475800 | −0.0307770 | −0.0153885 | − | 0.999882i | \(-0.504899\pi\) | ||||
−0.0153885 | + | 0.999882i | \(0.504899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.320321 | − | 0.554813i | 0.0206337 | − | 0.0357386i | −0.855524 | − | 0.517763i | \(-0.826765\pi\) |
0.876158 | + | 0.482024i | \(0.160098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.64806 | − | 8.05068i | −0.296954 | − | 0.514339i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.87985 | − | 20.2653i | −0.628640 | − | 1.28945i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.52420 | − | 4.37204i | 0.159326 | − | 0.275961i | −0.775300 | − | 0.631593i | \(-0.782401\pi\) |
0.934626 | + | 0.355633i | \(0.115735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.3626 | + | 42.1973i | −1.53166 | + | 2.65292i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3724 | − | 17.9656i | 0.647014 | − | 1.12066i | −0.336818 | − | 0.941570i | \(-0.609351\pi\) |
0.983832 | − | 0.179092i | \(-0.0573160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.351939 | 0.0218684 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.52420 | − | 14.7643i | −0.525625 | − | 0.910409i | −0.999555 | − | 0.0298460i | \(-0.990498\pi\) |
0.473930 | − | 0.880563i | \(-0.342835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.48322 | −0.336831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.55211 | + | 7.88448i | 0.277547 | + | 0.480725i | 0.970775 | − | 0.239993i | \(-0.0771453\pi\) |
−0.693228 | + | 0.720719i | \(0.743812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2207 | + | 22.8989i | 0.803098 | + | 1.39101i | 0.917568 | + | 0.397580i | \(0.130150\pi\) |
−0.114470 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.76210 | − | 15.1764i | 0.528374 | − | 0.915171i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.1574 | 1.57165 | 0.785824 | − | 0.618451i | \(-0.212239\pi\) | ||||
0.785824 | + | 0.618451i | \(0.212239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2002 | + | 21.1313i | −0.727801 | + | 1.26059i | 0.230010 | + | 0.973188i | \(0.426124\pi\) |
−0.957811 | + | 0.287400i | \(0.907209\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.172260 | − | 0.298364i | −0.0102398 | − | 0.0177359i | 0.860860 | − | 0.508842i | \(-0.169926\pi\) |
−0.871100 | + | 0.491106i | \(0.836593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.475800 | + | 0.824110i | 0.0280856 | + | 0.0486457i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.2813 | −1.00958 | −0.504792 | − | 0.863241i | \(-0.668431\pi\) | ||||
−0.504792 | + | 0.863241i | \(0.668431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.73419 | + | 6.46781i | −0.217413 | + | 0.376570i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.8105 | + | 39.5089i | 1.31917 | + | 2.28486i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14806 | + | 1.98850i | 0.0661731 | + | 0.114615i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.53643 | 0.145235 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.43807 | + | 7.68696i | 0.253294 | + | 0.438718i | 0.964431 | − | 0.264336i | \(-0.0851527\pi\) |
−0.711137 | + | 0.703054i | \(0.751819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1648 | −0.633100 | −0.316550 | − | 0.948576i | \(-0.602525\pi\) | ||||
−0.316550 | + | 0.948576i | \(0.602525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.25839 | − | 3.91165i | 0.127652 | − | 0.221099i | −0.795115 | − | 0.606459i | \(-0.792589\pi\) |
0.922766 | + | 0.385360i | \(0.125923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.50371 | + | 4.33655i | −0.140622 | + | 0.243565i | −0.927731 | − | 0.373249i | \(-0.878244\pi\) |
0.787109 | + | 0.616814i | \(0.211577\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.46838 | − | 12.9356i | 0.418149 | − | 0.724256i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.20388 | − | 14.2095i | −0.455069 | − | 0.788203i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.05582 | + | 1.82873i | −0.0582091 | + | 0.100821i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1797 | 0.559526 | 0.279763 | − | 0.960069i | \(-0.409744\pi\) | ||||
0.279763 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.2132 | 0.885824 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7584 | − | 20.3661i | −0.640520 | − | 1.10941i | −0.985317 | − | 0.170736i | \(-0.945385\pi\) |
0.344796 | − | 0.938677i | \(-0.387948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.89578 | 0.156815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.88356 | 0.263687 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.23790 | − | 10.8044i | −0.334868 | − | 0.580008i | 0.648591 | − | 0.761137i | \(-0.275358\pi\) |
−0.983459 | + | 0.181128i | \(0.942025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.23550 | 0.333778 | 0.166889 | − | 0.985976i | \(-0.446628\pi\) | ||||
0.166889 | + | 0.985976i | \(0.446628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.8081 | −1.58652 | −0.793262 | − | 0.608880i | \(-0.791619\pi\) | ||||
−0.793262 | + | 0.608880i | \(0.791619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41256 | − | 5.91073i | 0.181120 | − | 0.313709i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.87614 | + | 11.9098i | 0.362909 | + | 0.628576i | 0.988438 | − | 0.151624i | \(-0.0484503\pi\) |
−0.625529 | + | 0.780201i | \(0.715117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.11164 | − | 17.6189i | −0.374297 | − | 0.927309i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.20759 | − | 9.01981i | 0.272578 | − | 0.472118i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.25468 | − | 16.0296i | 0.483090 | − | 0.836737i | −0.516721 | − | 0.856154i | \(-0.672848\pi\) |
0.999811 | + | 0.0194166i | \(0.00618090\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.713701 | − | 1.23617i | 0.0370535 | − | 0.0641785i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.53162 | 0.338194 | 0.169097 | − | 0.985599i | \(-0.445915\pi\) | ||||
0.169097 | + | 0.985599i | \(0.445915\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.99258 | − | 12.1115i | −0.360136 | − | 0.623774i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8687 | −1.27742 | −0.638710 | − | 0.769447i | \(-0.720532\pi\) | ||||
−0.638710 | + | 0.769447i | \(0.720532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.99018 | + | 8.64324i | 0.254986 | + | 0.441649i | 0.964892 | − | 0.262648i | \(-0.0845957\pi\) |
−0.709906 | + | 0.704297i | \(0.751262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.31421 | − | 2.27628i | −0.0669783 | − | 0.116010i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.54469 | + | 14.7998i | −0.433233 | + | 0.750382i | −0.997150 | − | 0.0754502i | \(-0.975961\pi\) |
0.563917 | + | 0.825832i | \(0.309294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.28630 | + | 9.15614i | −0.265983 | + | 0.460695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.821627 | + | 1.42310i | 0.0412363 | + | 0.0714233i | 0.885907 | − | 0.463863i | \(-0.153537\pi\) |
−0.844671 | + | 0.535286i | \(0.820204\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.67597 | − | 6.36697i | −0.183569 | − | 0.317951i | 0.759524 | − | 0.650479i | \(-0.225432\pi\) |
−0.943093 | + | 0.332528i | \(0.892098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.35565 | − | 2.34805i | 0.0675297 | − | 0.116965i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.52420 | −0.273824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.03773 | + | 1.79740i | −0.0513125 | + | 0.0888758i | −0.890541 | − | 0.454903i | \(-0.849674\pi\) |
0.839228 | + | 0.543779i | \(0.183007\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.972091 | − | 1.68371i | −0.0478335 | − | 0.0828500i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.64064 | + | 9.76988i | 0.276888 | + | 0.479585i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.22808 | 0.401968 | 0.200984 | − | 0.979595i | \(-0.435586\pi\) | ||||
0.200984 | + | 0.979595i | \(0.435586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79001 | − | 4.83244i | −0.135977 | − | 0.235519i | 0.789993 | − | 0.613115i | \(-0.210084\pi\) |
−0.925970 | + | 0.377597i | \(0.876751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.330143 | + | 0.571825i | −0.0159768 | + | 0.0276726i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0484 | + | 24.3325i | −0.676688 | + | 1.17206i | 0.299285 | + | 0.954164i | \(0.403252\pi\) |
−0.975973 | + | 0.217893i | \(0.930081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.1661 | + | 24.5365i | −0.680782 | + | 1.17915i | 0.293961 | + | 0.955817i | \(0.405026\pi\) |
−0.974743 | + | 0.223331i | \(0.928307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.8482 | + | 34.5587i | 0.805960 | + | 1.65316i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.16855 | − | 8.95219i | −0.246681 | − | 0.427265i | 0.715922 | − | 0.698181i | \(-0.246007\pi\) |
−0.962603 | + | 0.270916i | \(0.912673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.475800 | − | 0.824110i | 0.0226060 | − | 0.0391547i | −0.854501 | − | 0.519450i | \(-0.826137\pi\) |
0.877107 | + | 0.480295i | \(0.159470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.28390 | −0.297885 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8639 | 1.03182 | 0.515911 | − | 0.856642i | \(-0.327454\pi\) | ||||
0.515911 | + | 0.856642i | \(0.327454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.46838 | − | 12.9356i | −0.351672 | − | 0.609114i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.46096 | −0.115372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.7645 | 1.01810 | 0.509050 | − | 0.860737i | \(-0.329997\pi\) | ||||
0.509050 | + | 0.860737i | \(0.329997\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.5521 | + | 18.2768i | 0.491461 | + | 0.851235i | 0.999952 | − | 0.00983244i | \(-0.00312981\pi\) |
−0.508491 | + | 0.861067i | \(0.669796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.16745 | −0.240152 | −0.120076 | − | 0.992765i | \(-0.538314\pi\) | ||||
−0.120076 | + | 0.992765i | \(0.538314\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.8007 | −1.70293 | −0.851466 | − | 0.524410i | \(-0.824286\pi\) | ||||
−0.851466 | + | 0.524410i | \(0.824286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.11033 | + | 3.65520i | −0.0974460 | + | 0.168781i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0205 | − | 31.2124i | −0.828583 | − | 1.43515i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.05953 | − | 12.4291i | −0.278030 | − | 0.570288i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.28870 | + | 12.6244i | −0.333029 | + | 0.576824i | −0.983104 | − | 0.183046i | \(-0.941404\pi\) |
0.650075 | + | 0.759870i | \(0.274737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.58613 | + | 4.47931i | −0.117917 | + | 0.204239i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.33710 | + | 16.1723i | −0.423976 | + | 0.734348i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.04840 | −0.319393 | −0.159697 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159697 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.22808 | − | 9.05530i | −0.235940 | − | 0.408660i | 0.723606 | − | 0.690214i | \(-0.242484\pi\) |
−0.959545 | + | 0.281554i | \(0.909150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.888365 | + | 1.53869i | 0.0398486 | + | 0.0690198i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.23659 | + | 3.87390i | 0.100124 | + | 0.173419i | 0.911735 | − | 0.410778i | \(-0.134743\pi\) |
−0.811612 | + | 0.584197i | \(0.801409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5242 | + | 19.9605i | −0.513839 | + | 0.889995i | 0.486032 | + | 0.873941i | \(0.338444\pi\) |
−0.999871 | + | 0.0160539i | \(0.994890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.16965 | −0.141048 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1723 | + | 22.8150i | −0.583850 | + | 1.01126i | 0.411168 | + | 0.911560i | \(0.365121\pi\) |
−0.995018 | + | 0.0996984i | \(0.968212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35565 | + | 2.34805i | 0.0599704 | + | 0.103872i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8860 | + | 18.8550i | 0.479693 | + | 0.830852i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.5726 | − | 28.7046i | 0.728862 | − | 1.26243i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.6332 | −1.86780 | −0.933898 | − | 0.357540i | \(-0.883615\pi\) | ||||
−0.933898 | + | 0.357540i | \(0.883615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.94047 | + | 10.2892i | −0.259759 | + | 0.449915i | −0.966177 | − | 0.257879i | \(-0.916976\pi\) |
0.706418 | + | 0.707794i | \(0.250310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.3990 | − | 47.4565i | −1.19126 | − | 2.06333i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.9852 | −0.605765 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.400338 | − | 0.693406i | −0.0173081 | − | 0.0299786i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.9852 | −1.63614 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9610 | + | 29.3773i | −0.729209 | + | 1.26303i | 0.228009 | + | 0.973659i | \(0.426778\pi\) |
−0.957218 | + | 0.289368i | \(0.906555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.17968 | + | 15.8997i | −0.393214 | + | 0.681067i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.49760 | + | 7.79007i | −0.192303 | + | 0.333079i | −0.946013 | − | 0.324128i | \(-0.894929\pi\) |
0.753710 | + | 0.657207i | \(0.228262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.16484 | − | 10.5940i | −0.220030 | − | 0.451319i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.37614 | − | 2.38354i | −0.0585194 | − | 0.101359i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.94418 | − | 8.56358i | 0.209492 | − | 0.362850i | −0.742063 | − | 0.670330i | \(-0.766152\pi\) |
0.951555 | + | 0.307480i | \(0.0994857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7449 | −1.42726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.4413 | −1.53582 | −0.767909 | − | 0.640559i | \(-0.778703\pi\) | ||||
−0.767909 | + | 0.640559i | \(0.778703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.78259 | + | 15.2119i | 0.369486 | + | 0.639969i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.2717 | 1.14329 | 0.571644 | − | 0.820502i | \(-0.306306\pi\) | ||||
0.571644 | + | 0.820502i | \(0.306306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1042 | 0.673940 | 0.336970 | − | 0.941515i | \(-0.390598\pi\) | ||||
0.336970 | + | 0.941515i | \(0.390598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.9902 | + | 24.2317i | 0.583431 | + | 1.01053i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.3323 | −1.13786 | −0.568929 | − | 0.822387i | \(-0.692642\pi\) | ||||
−0.568929 | + | 0.822387i | \(0.692642\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.93676 | −0.121838 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2026 | + | 19.4034i | −0.463963 | + | 0.803608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.0508 | − | 22.6047i | −0.538664 | − | 0.932994i | −0.998976 | − | 0.0452367i | \(-0.985596\pi\) |
0.460312 | − | 0.887757i | \(-0.347738\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.27803 | − | 1.89408i | 0.0526605 | − | 0.0780443i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.55211 | + | 7.88448i | −0.186933 | + | 0.323777i | −0.944226 | − | 0.329298i | \(-0.893188\pi\) |
0.757293 | + | 0.653075i | \(0.226521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.2937 | − | 23.0254i | 0.543167 | − | 0.940792i | −0.455553 | − | 0.890209i | \(-0.650559\pi\) |
0.998720 | − | 0.0505836i | \(-0.0161081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.2691 | 1.27549 | 0.637746 | − | 0.770247i | \(-0.279867\pi\) | ||||
0.637746 | + | 0.770247i | \(0.279867\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.1928 | + | 22.8505i | 0.536362 | + | 0.929006i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.8687 | −0.765858 | −0.382929 | − | 0.923778i | \(-0.625085\pi\) | ||||
−0.382929 | + | 0.923778i | \(0.625085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.5168 | − | 26.8759i | −0.627742 | − | 1.08728i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.61033 | + | 16.6456i | 0.388158 | + | 0.672309i | 0.992202 | − | 0.124642i | \(-0.0397783\pi\) |
−0.604044 | + | 0.796951i | \(0.706445\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.2608 | − | 19.5043i | 0.453343 | − | 0.785212i | −0.545249 | − | 0.838274i | \(-0.683565\pi\) |
0.998591 | + | 0.0530621i | \(0.0168981\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.99258 | −0.240862 | −0.120431 | − | 0.992722i | \(-0.538428\pi\) | ||||
−0.120431 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.817917 | − | 1.41667i | 0.0327692 | − | 0.0567579i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.462269 | − | 0.800673i | −0.0184908 | − | 0.0320269i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.700169 | + | 1.21273i | −0.0278733 | + | 0.0482780i | −0.879626 | − | 0.475667i | \(-0.842207\pi\) |
0.851752 | + | 0.523945i | \(0.175540\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4710 | 0.574264 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.7826 | + | 30.8003i | −0.704572 | + | 1.22035i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.30354 | + | 9.18600i | 0.209477 | + | 0.362825i | 0.951550 | − | 0.307494i | \(-0.0994905\pi\) |
−0.742073 | + | 0.670319i | \(0.766157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.9963 | − | 38.0987i | −0.867449 | − | 1.50247i | −0.864595 | − | 0.502470i | \(-0.832425\pi\) |
−0.00285431 | − | 0.999996i | \(-0.500909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.11164 | −0.318901 | −0.159451 | − | 0.987206i | \(-0.550972\pi\) | ||||
−0.159451 | + | 0.987206i | \(0.550972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2584 | + | 26.4283i | 0.598944 | + | 1.03740i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.6890 | −1.35749 | −0.678744 | − | 0.734375i | \(-0.737475\pi\) | ||||
−0.678744 | + | 0.734375i | \(0.737475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.22808 | + | 3.85914i | −0.0870582 | + | 0.150789i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5218 | + | 26.8845i | −0.604643 | + | 1.04727i | 0.387464 | + | 0.921885i | \(0.373351\pi\) |
−0.992108 | + | 0.125388i | \(0.959982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.34452 | − | 12.7211i | 0.285669 | − | 0.494793i | −0.687102 | − | 0.726561i | \(-0.741118\pi\) |
0.972771 | + | 0.231768i | \(0.0744510\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.06889 | − | 0.145018i | −0.0802281 | − | 0.00562357i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.9245 | + | 20.6539i | 0.461720 | + | 0.799722i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.18208 | − | 8.97563i | 0.200052 | − | 0.346500i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3567 | −0.476318 | −0.238159 | − | 0.971226i | \(-0.576544\pi\) | ||||
−0.238159 | + | 0.971226i | \(0.576544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.7858 | −1.26006 | −0.630031 | − | 0.776570i | \(-0.716958\pi\) | ||||
−0.630031 | + | 0.776570i | \(0.716958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.43065 | − | 4.21001i | −0.0932798 | − | 0.161565i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3977 | 1.58404 | 0.792020 | − | 0.610495i | \(-0.209030\pi\) | ||||
0.792020 | + | 0.610495i | \(0.209030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.0484 | 0.880634 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.4889 | + | 18.1673i | 0.399594 | + | 0.692117i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.9368 | 1.63339 | 0.816696 | − | 0.577069i | \(-0.195803\pi\) | ||||
0.816696 | + | 0.577069i | \(0.195803\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.2429 | −0.919586 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.03533 | − | 1.79324i | −0.0391038 | − | 0.0677297i | 0.845811 | − | 0.533482i | \(-0.179117\pi\) |
−0.884915 | + | 0.465753i | \(0.845784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.43807 | + | 3.61328i | −0.0919535 | + | 0.136278i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.412564 | − | 0.714582i | 0.0155161 | − | 0.0268746i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.28259 | − | 10.8818i | 0.235948 | − | 0.408673i | −0.723600 | − | 0.690220i | \(-0.757514\pi\) |
0.959548 | + | 0.281546i | \(0.0908473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.31180 | + | 4.00416i | −0.0865778 | + | 0.149957i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.6284 | 1.44462 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.1550 | + | 43.5698i | 0.938124 | + | 1.62488i | 0.768966 | + | 0.639289i | \(0.220771\pi\) |
0.169158 | + | 0.985589i | \(0.445895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.66771 | −0.211076 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.28870 | − | 7.42825i | −0.159278 | − | 0.275878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6672 | − | 28.8685i | −0.618154 | − | 1.07067i | −0.989822 | − | 0.142308i | \(-0.954548\pi\) |
0.371668 | − | 0.928366i | \(-0.378786\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8129 | −0.953421 | −0.476711 | − | 0.879060i | \(-0.658171\pi\) | ||||
−0.476711 | + | 0.879060i | \(0.658171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.1247 | − | 57.3737i | 1.22016 | − | 2.11339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.2802 | + | 42.0545i | 0.893161 | + | 1.54700i | 0.836064 | + | 0.548632i | \(0.184851\pi\) |
0.0570970 | + | 0.998369i | \(0.481816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.33470 | − | 12.7041i | −0.269084 | − | 0.466067i | 0.699542 | − | 0.714592i | \(-0.253388\pi\) |
−0.968626 | + | 0.248525i | \(0.920054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.31421 | + | 2.27628i | −0.0481489 | + | 0.0833963i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.208434 | 0.00761600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.87243 | − | 6.70724i | 0.141307 | − | 0.244751i | −0.786682 | − | 0.617358i | \(-0.788203\pi\) |
0.927989 | + | 0.372607i | \(0.121536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.22066 | − | 15.9707i | −0.335574 | − | 0.581231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8626 | + | 27.4748i | 0.576536 | + | 0.998590i | 0.995873 | + | 0.0907593i | \(0.0289294\pi\) |
−0.419337 | + | 0.907831i | \(0.637737\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.2255 | 1.34942 | 0.674711 | − | 0.738082i | \(-0.264268\pi\) | ||||
0.674711 | + | 0.738082i | \(0.264268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.38967 | − | 4.13903i | −0.0865119 | − | 0.149843i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.5726 | 1.03170 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.2645 | − | 19.5107i | 0.406208 | − | 0.703574i | −0.588253 | − | 0.808677i | \(-0.700184\pi\) |
0.994461 | + | 0.105103i | \(0.0335174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.5726 | + | 44.2930i | −0.919782 | + | 1.59311i | −0.120038 | + | 0.992769i | \(0.538302\pi\) |
−0.799744 | + | 0.600341i | \(0.795032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.831449 | − | 1.44011i | 0.0298665 | − | 0.0517303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.7571 | − | 0.824110i | −0.421241 | − | 0.0295268i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.9442 | − | 24.1520i | −0.498962 | − | 0.864228i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.2486 | − | 19.4831i | 0.401479 | − | 0.695381i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.16745 | 0.0416152 | 0.0208076 | − | 0.999783i | \(-0.493376\pi\) | ||||
0.0208076 | + | 0.999783i | \(0.493376\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.57260 | −0.162583 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.85194 | − | 8.40381i | −0.172297 | − | 0.298428i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.1600 | −1.31628 | −0.658138 | − | 0.752897i | \(-0.728656\pi\) | ||||
−0.658138 | + | 0.752897i | \(0.728656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.2789 | − | 36.8561i | −0.750915 | − | 1.30062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.19671 | 0.147915 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.7597 | −1.08145 | −0.540727 | − | 0.841198i | \(-0.681851\pi\) | ||||
−0.540727 | + | 0.841198i | \(0.681851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1042 | + | 29.6254i | −0.600610 | + | 1.04029i | 0.392118 | + | 0.919915i | \(0.371742\pi\) |
−0.992729 | + | 0.120373i | \(0.961591\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.34692 | + | 2.33294i | 0.0471807 | + | 0.0817194i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.3687 | − | 1.98850i | −0.992496 | − | 0.0695688i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4610 | − | 25.0471i | 0.504691 | − | 0.874151i | −0.495294 | − | 0.868725i | \(-0.664940\pi\) |
0.999985 | − | 0.00542532i | \(-0.00172694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.24030 | − | 5.61237i | 0.112950 | − | 0.195635i | −0.804008 | − | 0.594618i | \(-0.797303\pi\) |
0.916958 | + | 0.398983i | \(0.130637\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.2281 | − | 35.0361i | 0.703399 | − | 1.21832i | −0.263867 | − | 0.964559i | \(-0.584998\pi\) |
0.967266 | − | 0.253764i | \(-0.0816687\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5019 | −1.78874 | −0.894368 | − | 0.447331i | \(-0.852374\pi\) | ||||
−0.894368 | + | 0.447331i | \(0.852374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49806 | −0.121055 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8105 | − | 29.1166i | −0.580363 | − | 1.00522i | −0.995436 | − | 0.0954300i | \(-0.969577\pi\) |
0.415073 | − | 0.909788i | \(-0.363756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8445 | + | 18.7833i | 0.373949 | + | 0.647699i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.29612 | − | 16.1014i | 0.319796 | − | 0.553903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.86872 | −0.236012 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.41016 | − | 7.63862i | 0.151178 | − | 0.261849i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.3007 | + | 43.8221i | 0.866279 | + | 1.50044i | 0.865772 | + | 0.500439i | \(0.166828\pi\) |
0.000506763 | 1.00000i | \(0.499839\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.00000 | − | 5.19615i | −0.102478 | − | 0.177497i | 0.810227 | − | 0.586116i | \(-0.199344\pi\) |
−0.912705 | + | 0.408619i | \(0.866010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0447 | − | 19.1300i | 0.376840 | − | 0.652706i | −0.613761 | − | 0.789492i | \(-0.710344\pi\) |
0.990601 | + | 0.136786i | \(0.0436773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.6890 | 0.363859 | 0.181930 | − | 0.983312i | \(-0.441766\pi\) | ||||
0.181930 | + | 0.983312i | \(0.441766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.9245 | + | 20.6539i | −0.405446 | + | 0.702254i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.6005 | + | 37.4132i | 0.732747 | + | 1.26916i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.0144 | − | 53.7185i | −1.05088 | − | 1.82018i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.88836 | −0.131451 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5968 | − | 27.0144i | −0.526666 | − | 0.912213i | −0.999517 | − | 0.0310705i | \(-0.990108\pi\) |
0.472851 | − | 0.881143i | \(-0.343225\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.69646 | 0.326682 | 0.163341 | − | 0.986570i | \(-0.447773\pi\) | ||||
0.163341 | + | 0.986570i | \(0.447773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0750 | + | 33.0389i | −0.641925 | + | 1.11185i | 0.343078 | + | 0.939307i | \(0.388531\pi\) |
−0.985003 | + | 0.172540i | \(0.944803\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.99018 | − | 8.64324i | 0.167554 | − | 0.290212i | −0.770005 | − | 0.638037i | \(-0.779747\pi\) |
0.937559 | + | 0.347826i | \(0.113080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88356 | + | 3.26242i | −0.0631725 | + | 0.109418i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.4610 | − | 23.5084i | −0.383527 | − | 0.786680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.50611 | + | 2.60866i | 0.0503438 | + | 0.0871980i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.708686 | − | 1.22748i | 0.0236360 | − | 0.0409388i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8007 | −0.425509 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2329 | + | 17.7239i | 0.339777 | + | 0.588512i | 0.984391 | − | 0.175997i | \(-0.0563149\pi\) |
−0.644613 | + | 0.764509i | \(0.722982\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.1696 | −0.900171 | −0.450085 | − | 0.892986i | \(-0.648606\pi\) | ||||
−0.450085 | + | 0.892986i | \(0.648606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.0968 | 1.52558 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.580017 | − | 1.00462i | −0.0191539 | − | 0.0331755i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.1378 | −1.09311 | −0.546557 | − | 0.837422i | \(-0.684062\pi\) | ||||
−0.546557 | + | 0.837422i | \(0.684062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.1116 | −0.859475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58613 | + | 2.74726i | −0.0521516 | + | 0.0903293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.3166 | − | 42.1176i | −0.797802 | − | 1.38183i | −0.921045 | − | 0.389457i | \(-0.872663\pi\) |
0.123242 | − | 0.992377i | \(-0.460671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.7645 | + | 24.8454i | −0.549434 | + | 0.814276i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8626 | − | 43.0633i | 0.812226 | − | 1.40682i | −0.0990768 | − | 0.995080i | \(-0.531589\pi\) |
0.911303 | − | 0.411737i | \(-0.135078\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.9245 | − | 41.4385i | 0.779918 | − | 1.35086i | −0.152071 | − | 0.988370i | \(-0.548594\pi\) |
0.931989 | − | 0.362487i | \(-0.118072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.8491 | 0.776633 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.69646 | − | 11.5986i | −0.217606 | − | 0.376904i | 0.736470 | − | 0.676470i | \(-0.236491\pi\) |
−0.954075 | + | 0.299566i | \(0.903158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.8465 | −1.29347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.72437 | − | 4.71875i | −0.0882510 | − | 0.152855i | 0.818521 | − | 0.574477i | \(-0.194794\pi\) |
−0.906772 | + | 0.421622i | \(0.861461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.2584 | − | 26.4283i | −0.493750 | − | 0.855200i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | + | 5.19615i | −0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7252 | −0.991136 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.37985 | + | 16.2464i | −0.301948 | + | 0.522989i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6066 | + | 28.7635i | 0.534033 | + | 0.924972i | 0.999209 | + | 0.0397542i | \(0.0126575\pi\) |
−0.465177 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5652 | + | 46.0122i | 0.852517 | + | 1.47660i | 0.878929 | + | 0.476952i | \(0.158258\pi\) |
−0.0264121 | + | 0.999651i | \(0.508408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.15548 | − | 5.46545i | 0.101160 | − | 0.175214i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9219 | 0.349423 | 0.174712 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174712 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.8384 | + | 22.2368i | −0.410317 | + | 0.710690i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.6941 | + | 34.1111i | 0.628143 | + | 1.08798i | 0.987924 | + | 0.154939i | \(0.0495180\pi\) |
−0.359781 | + | 0.933037i | \(0.617149\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.61294 | − | 9.72190i | −0.178843 | − | 0.309765i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.5455 | 1.82984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.19406 | + | 12.4605i | 0.228527 | + | 0.395820i | 0.957372 | − | 0.288859i | \(-0.0932758\pi\) |
−0.728845 | + | 0.684679i | \(0.759943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.30615 | −0.295025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9758 | + | 31.1350i | −0.569299 | + | 0.986055i | 0.427336 | + | 0.904093i | \(0.359452\pi\) |
−0.996635 | + | 0.0819625i | \(0.973881\pi\) | |||||||
\(998\) | 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 | 2736.2.s.z.577.2 | 6 | ||
3.2 | odd | 2 | 912.2.q.l.577.2 | 6 | |||
4.3 | odd | 2 | 171.2.f.b.64.3 | 6 | |||
12.11 | even | 2 | 57.2.e.b.7.1 | ✓ | 6 | ||
19.11 | even | 3 | inner | 2736.2.s.z.1873.2 | 6 | ||
57.11 | odd | 6 | 912.2.q.l.49.2 | 6 | |||
76.7 | odd | 6 | 3249.2.a.y.1.1 | 3 | |||
76.11 | odd | 6 | 171.2.f.b.163.3 | 6 | |||
76.31 | even | 6 | 3249.2.a.t.1.3 | 3 | |||
228.11 | even | 6 | 57.2.e.b.49.1 | yes | 6 | ||
228.83 | even | 6 | 1083.2.a.l.1.3 | 3 | |||
228.107 | odd | 6 | 1083.2.a.o.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.e.b.7.1 | ✓ | 6 | 12.11 | even | 2 | ||
57.2.e.b.49.1 | yes | 6 | 228.11 | even | 6 | ||
171.2.f.b.64.3 | 6 | 4.3 | odd | 2 | |||
171.2.f.b.163.3 | 6 | 76.11 | odd | 6 | |||
912.2.q.l.49.2 | 6 | 57.11 | odd | 6 | |||
912.2.q.l.577.2 | 6 | 3.2 | odd | 2 | |||
1083.2.a.l.1.3 | 3 | 228.83 | even | 6 | |||
1083.2.a.o.1.1 | 3 | 228.107 | odd | 6 | |||
2736.2.s.z.577.2 | 6 | 1.1 | even | 1 | trivial | ||
2736.2.s.z.1873.2 | 6 | 19.11 | even | 3 | inner | ||
3249.2.a.t.1.3 | 3 | 76.31 | even | 6 | |||
3249.2.a.y.1.1 | 3 | 76.7 | odd | 6 |