Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(269,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.6 | ||
Root | \(-1.56052 - 0.900969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.269 |
Dual form | 756.2.t.e.593.6 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56052 | + | 2.70291i | 0.697887 | + | 1.20878i | 0.969198 | + | 0.246285i | \(0.0792098\pi\) |
−0.271310 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37047 | − | 1.17511i | 0.895953 | − | 0.444148i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23975 | + | 1.87047i | 0.976821 | + | 0.563968i | 0.901309 | − | 0.433177i | \(-0.142608\pi\) |
0.0755120 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.93067i | − | 0.812821i | −0.913691 | − | 0.406410i | \(-0.866780\pi\) | ||
0.913691 | − | 0.406410i | \(-0.133220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.71678 | − | 4.70560i | 0.658915 | − | 1.14127i | −0.321982 | − | 0.946746i | \(-0.604349\pi\) |
0.980897 | − | 0.194529i | \(-0.0623177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.07338 | + | 3.50647i | −1.39333 | + | 0.804438i | −0.993682 | − | 0.112231i | \(-0.964200\pi\) |
−0.399646 | + | 0.916670i | \(0.630867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.44182 | + | 0.832437i | −0.300641 | + | 0.173575i | −0.642731 | − | 0.766092i | \(-0.722199\pi\) |
0.342090 | + | 0.939667i | \(0.388865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.37047 | + | 4.10577i | −0.474094 | + | 0.821155i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07069i | 1.31299i | 0.754329 | + | 0.656497i | \(0.227962\pi\) | ||||
−0.754329 | + | 0.656497i | \(0.772038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.60872 | + | 3.81555i | 1.18696 | + | 0.685292i | 0.957615 | − | 0.288053i | \(-0.0930078\pi\) |
0.229347 | + | 0.973345i | \(0.426341\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.87538 | + | 4.57338i | 1.16215 | + | 0.773042i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.03534 | − | 6.98942i | −0.663406 | − | 1.14905i | −0.979715 | − | 0.200397i | \(-0.935777\pi\) |
0.316308 | − | 0.948656i | \(-0.397557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.60054 | 1.49935 | 0.749677 | − | 0.661804i | \(-0.230209\pi\) | ||||
0.749677 | + | 0.661804i | \(0.230209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.74094 | −0.875485 | −0.437742 | − | 0.899100i | \(-0.644222\pi\) | ||||
−0.437742 | + | 0.899100i | \(0.644222\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.56052 | + | 2.70291i | 0.227626 | + | 0.394259i | 0.957104 | − | 0.289745i | \(-0.0935704\pi\) |
−0.729478 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.23825 | − | 5.57111i | 0.605464 | − | 0.795872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.11266 | − | 1.79709i | −0.427556 | − | 0.246850i | 0.270749 | − | 0.962650i | \(-0.412729\pi\) |
−0.698305 | + | 0.715800i | \(0.746062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.6756i | 1.57434i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.20220 | + | 3.81431i | −0.286701 | + | 0.496581i | −0.973020 | − | 0.230719i | \(-0.925892\pi\) |
0.686319 | + | 0.727301i | \(0.259225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.57069 | + | 1.48419i | −0.329143 | + | 0.190031i | −0.655460 | − | 0.755229i | \(-0.727525\pi\) |
0.326318 | + | 0.945260i | \(0.394192\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.92132 | − | 4.57338i | 0.982519 | − | 0.567257i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.90850 | − | 8.50177i | 0.599669 | − | 1.03866i | −0.393201 | − | 0.919453i | \(-0.628632\pi\) |
0.992870 | − | 0.119204i | \(-0.0380344\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.33513i | 0.870519i | 0.900305 | + | 0.435260i | \(0.143343\pi\) | ||||
−0.900305 | + | 0.435260i | \(0.856657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.46466 | + | 1.42297i | 0.288466 | + | 0.166546i | 0.637250 | − | 0.770657i | \(-0.280072\pi\) |
−0.348784 | + | 0.937203i | \(0.613405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.87772 | + | 0.626842i | 1.12567 | + | 0.0714353i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.57338 | − | 4.45722i | −0.289527 | − | 0.501476i | 0.684170 | − | 0.729323i | \(-0.260165\pi\) |
−0.973697 | + | 0.227847i | \(0.926831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6052 | −1.71290 | −0.856449 | − | 0.516232i | \(-0.827334\pi\) | ||||
−0.856449 | + | 0.516232i | \(0.827334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9584 | 1.83939 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.59808 | + | 4.50000i | 0.275396 | + | 0.476999i | 0.970235 | − | 0.242166i | \(-0.0778579\pi\) |
−0.694839 | + | 0.719165i | \(0.744525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.44385 | − | 6.94706i | −0.361013 | − | 0.728249i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.9553 | − | 10.9438i | −1.94477 | − | 1.12281i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.39723i | 0.243402i | 0.992567 | + | 0.121701i | \(0.0388349\pi\) | ||||
−0.992567 | + | 0.121701i | \(0.961165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.87772 | − | 17.1087i | 0.982870 | − | 1.70238i | 0.331828 | − | 0.943340i | \(-0.392335\pi\) |
0.651043 | − | 0.759041i | \(-0.274332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6468 | − | 6.14691i | 1.04906 | − | 0.605673i | 0.126671 | − | 0.991945i | \(-0.459571\pi\) |
0.922385 | + | 0.386272i | \(0.126237\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.7155 | + | 9.07338i | −1.51928 | + | 0.877156i | −0.519537 | + | 0.854448i | \(0.673896\pi\) |
−0.999742 | + | 0.0227086i | \(0.992771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.74094 | + | 9.94360i | −0.549882 | + | 0.952424i | 0.448400 | + | 0.893833i | \(0.351994\pi\) |
−0.998282 | + | 0.0585909i | \(0.981339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.81163i | − | 0.170423i | −0.996363 | − | 0.0852117i | \(-0.972843\pi\) | ||
0.996363 | − | 0.0852117i | \(-0.0271567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | − | 2.59808i | −0.419627 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.910461 | − | 14.3470i | 0.0834619 | − | 1.31518i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.49731 | + | 2.59342i | 0.136119 | + | 0.235765i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.808542 | 0.0723182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.47650 | −0.663432 | −0.331716 | − | 0.943379i | \(-0.607628\pi\) | ||||
−0.331716 | + | 0.943379i | \(0.607628\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.52532 | − | 6.10603i | −0.308009 | − | 0.533486i | 0.669918 | − | 0.742435i | \(-0.266329\pi\) |
−0.977927 | + | 0.208949i | \(0.932996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2763 | + | 15.4488i | −0.891067 | + | 1.33958i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7048 | − | 7.33513i | −1.08545 | − | 0.626682i | −0.153085 | − | 0.988213i | \(-0.548921\pi\) |
−0.932360 | + | 0.361531i | \(0.882254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.69434i | − | 0.143712i | −0.997415 | − | 0.0718562i | \(-0.977108\pi\) | ||
0.997415 | − | 0.0718562i | \(-0.0228923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.48172 | − | 9.49462i | 0.458405 | − | 0.793980i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.1114 | + | 11.0340i | −1.58712 | + | 0.916322i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8319 | + | 7.40850i | −1.05123 | + | 0.606928i | −0.922994 | − | 0.384815i | \(-0.874265\pi\) |
−0.128237 | + | 0.991744i | \(0.540932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.03534 | − | 5.25737i | 0.247013 | − | 0.427839i | −0.715683 | − | 0.698425i | \(-0.753884\pi\) |
0.962696 | + | 0.270587i | \(0.0872177\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.8170i | 1.91303i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1141 | − | 6.99408i | −0.966810 | − | 0.558188i | −0.0685479 | − | 0.997648i | \(-0.521837\pi\) |
−0.898262 | + | 0.439460i | \(0.855170\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.43960 | + | 3.66756i | −0.192267 | + | 0.289044i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.926624 | − | 1.60496i | −0.0725788 | − | 0.125710i | 0.827452 | − | 0.561536i | \(-0.189790\pi\) |
−0.900031 | + | 0.435826i | \(0.856456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.54991 | −0.197318 | −0.0986588 | − | 0.995121i | \(-0.531455\pi\) | ||||
−0.0986588 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41119 | 0.339322 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.95640 | + | 3.38859i | 0.148743 | + | 0.257630i | 0.930763 | − | 0.365623i | \(-0.119144\pi\) |
−0.782020 | + | 0.623253i | \(0.785811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.794405 | + | 12.5182i | −0.0600514 | + | 0.946284i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.9284 | − | 9.77359i | −1.26529 | − | 0.730513i | −0.291193 | − | 0.956664i | \(-0.594052\pi\) |
−0.974092 | + | 0.226152i | \(0.927386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.1929i | − | 1.35226i | −0.736780 | − | 0.676132i | \(-0.763655\pi\) | ||
0.736780 | − | 0.676132i | \(-0.236345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.5945 | − | 21.8143i | 0.925966 | − | 1.60382i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6033 | − | 10.1633i | 1.28728 | − | 0.743214i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0609 | + | 7.54072i | −0.945054 | + | 0.545627i | −0.891541 | − | 0.452940i | \(-0.850375\pi\) |
−0.0535132 | + | 0.998567i | \(0.517042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.57338 | − | 9.65337i | 0.401180 | − | 0.694865i | −0.592688 | − | 0.805432i | \(-0.701933\pi\) |
0.993869 | + | 0.110567i | \(0.0352667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.3696i | − | 1.45127i | −0.688079 | − | 0.725636i | \(-0.741546\pi\) | ||
0.688079 | − | 0.725636i | \(-0.258454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.42931 | + | 3.71197i | 0.455762 | + | 0.263134i | 0.710261 | − | 0.703939i | \(-0.248577\pi\) |
−0.254499 | + | 0.967073i | \(0.581910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.30881 | + | 16.7608i | 0.583164 | + | 1.17638i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9819 | + | 25.9494i | 1.04638 | + | 1.81238i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.2349 | −1.81471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5526 | −0.932997 | −0.466499 | − | 0.884522i | \(-0.654485\pi\) | ||||
−0.466499 | + | 0.884522i | \(0.654485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.95887 | − | 15.5172i | −0.610990 | − | 1.05827i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.1494 | + | 1.27869i | 1.36783 | + | 0.0868029i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7905 | − | 7.96197i | −0.927652 | − | 0.535580i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.79200i | − | 0.588756i | −0.955689 | − | 0.294378i | \(-0.904888\pi\) | ||
0.955689 | − | 0.294378i | \(-0.0951125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.35241 | − | 11.0027i | 0.421624 | − | 0.730274i | −0.574475 | − | 0.818522i | \(-0.694794\pi\) |
0.996099 | + | 0.0882484i | \(0.0281269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.2201 | − | 13.9835i | 1.60051 | − | 0.924056i | 0.609126 | − | 0.793073i | \(-0.291520\pi\) |
0.991385 | − | 0.130982i | \(-0.0418131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2737 | − | 8.24094i | 0.935103 | − | 0.539882i | 0.0466810 | − | 0.998910i | \(-0.485136\pi\) |
0.888422 | + | 0.459028i | \(0.151802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.87047 | + | 8.43590i | −0.317714 | + | 0.550297i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.52350i | 0.357285i | 0.983914 | + | 0.178643i | \(0.0571706\pi\) | ||||
−0.983914 | + | 0.178643i | \(0.942829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6414 | − | 10.7626i | −1.20080 | − | 0.693280i | −0.240064 | − | 0.970757i | \(-0.577168\pi\) |
−0.960732 | + | 0.277477i | \(0.910502\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.6721 | + | 2.76175i | 1.38458 | + | 0.176442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.2763 | + | 17.7990i | 0.653864 | + | 1.13253i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.808542 | −0.0510347 | −0.0255174 | − | 0.999674i | \(-0.508123\pi\) | ||||
−0.0255174 | + | 0.999674i | \(0.508123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.22819 | −0.391563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.48172 | + | 9.49462i | 0.341941 | + | 0.592258i | 0.984793 | − | 0.173732i | \(-0.0555825\pi\) |
−0.642853 | + | 0.765990i | \(0.722249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.7790 | − | 11.8262i | −1.10473 | − | 0.734847i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.35241 | − | 3.66756i | −0.391706 | − | 0.226152i | 0.291193 | − | 0.956664i | \(-0.405948\pi\) |
−0.682899 | + | 0.730513i | \(0.739281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.2176i | − | 0.689093i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.28569 | + | 7.42303i | −0.261303 | + | 0.452590i | −0.966588 | − | 0.256333i | \(-0.917486\pi\) |
0.705285 | + | 0.708924i | \(0.250819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.79619 | − | 3.92378i | 0.412839 | − | 0.238353i | −0.279170 | − | 0.960242i | \(-0.590059\pi\) |
0.692009 | + | 0.721889i | \(0.256726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.3594 | + | 8.86778i | −0.926210 | + | 0.534747i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.13491 | − | 1.96572i | 0.0681900 | − | 0.118109i | −0.829915 | − | 0.557890i | \(-0.811611\pi\) |
0.898105 | + | 0.439782i | \(0.144944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9584i | 1.72751i | 0.503910 | + | 0.863756i | \(0.331894\pi\) | ||||
−0.503910 | + | 0.863756i | \(0.668106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.11679 | + | 1.22213i | 0.125830 | + | 0.0726479i | 0.561594 | − | 0.827413i | \(-0.310188\pi\) |
−0.435764 | + | 0.900061i | \(0.643522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.7578 | − | 11.2817i | 1.34335 | − | 0.665935i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.26175 | − | 10.8457i | −0.368338 | − | 0.637980i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.55460 | −0.499765 | −0.249883 | − | 0.968276i | \(-0.580392\pi\) | ||||
−0.249883 | + | 0.968276i | \(0.580392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7463 | −0.800341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.43960 | + | 4.22550i | 0.141086 | + | 0.244367i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.6087 | + | 6.74621i | −0.784394 | + | 0.388845i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.02324 | − | 4.63222i | −0.459409 | − | 0.265240i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8000i | 1.35834i | 0.733982 | + | 0.679169i | \(0.237660\pi\) | ||||
−0.733982 | + | 0.679169i | \(0.762340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.55460 | − | 14.8170i | 0.485087 | − | 0.840195i | −0.514766 | − | 0.857331i | \(-0.672121\pi\) |
0.999853 | + | 0.0171354i | \(0.00545463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.35325 | − | 0.781298i | 0.0764901 | − | 0.0441616i | −0.461267 | − | 0.887261i | \(-0.652605\pi\) |
0.537757 | + | 0.843100i | \(0.319272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5511 | − | 13.0199i | 1.26660 | − | 0.731271i | 0.292256 | − | 0.956340i | \(-0.405594\pi\) |
0.974343 | + | 0.225069i | \(0.0722608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.2255 | + | 22.9072i | −0.740486 | + | 1.28256i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.1051i | 2.12023i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0327 | + | 6.94706i | 0.667452 | + | 0.385353i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.87538 | + | 4.57338i | 0.379052 | + | 0.252138i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1087 | + | 26.1691i | 0.830450 | + | 1.43838i | 0.897682 | + | 0.440645i | \(0.145250\pi\) |
−0.0672312 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.6393 | 1.67401 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2228 | −1.21055 | −0.605277 | − | 0.796015i | \(-0.706938\pi\) | ||||
−0.605277 | + | 0.796015i | \(0.706938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2737 | + | 24.7228i | 0.772966 | + | 1.33882i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.50000 | − | 18.1865i | 0.188982 | − | 0.981981i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.6853 | + | 18.2935i | 1.70095 | + | 0.982047i | 0.944796 | + | 0.327658i | \(0.106259\pi\) |
0.756159 | + | 0.654388i | \(0.227074\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.19369i | − | 0.492127i | −0.969254 | − | 0.246063i | \(-0.920863\pi\) | ||
0.969254 | − | 0.246063i | \(-0.0791372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.277180 | − | 0.480090i | 0.0147528 | − | 0.0255526i | −0.858555 | − | 0.512722i | \(-0.828637\pi\) |
0.873308 | + | 0.487169i | \(0.161971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.8262 | + | 11.4466i | −1.05226 | + | 0.607524i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.3487 | + | 7.12953i | −0.651740 | + | 0.376282i | −0.789123 | − | 0.614236i | \(-0.789464\pi\) |
0.137383 | + | 0.990518i | \(0.456131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0906 | − | 26.1377i | 0.794242 | − | 1.37567i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.88231i | 0.464922i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.0814 | − | 6.97522i | −0.630646 | − | 0.364104i | 0.150356 | − | 0.988632i | \(-0.451958\pi\) |
−0.781002 | + | 0.624528i | \(0.785291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.49023 | − | 0.602252i | −0.492708 | − | 0.0312674i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.21744 | − | 14.2330i | −0.425483 | − | 0.736958i | 0.570983 | − | 0.820962i | \(-0.306562\pi\) |
−0.996465 | + | 0.0840042i | \(0.973229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7218 | 1.06723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.5217 | 1.77326 | 0.886630 | − | 0.462479i | \(-0.153040\pi\) | ||||
0.886630 | + | 0.462479i | \(0.153040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.96480 | + | 3.40312i | 0.100396 | + | 0.173892i | 0.911848 | − | 0.410528i | \(-0.134656\pi\) |
−0.811452 | + | 0.584420i | \(0.801322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7201 | + | 27.6768i | 0.699242 | + | 1.41054i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.5992 | − | 10.7383i | −0.943017 | − | 0.544451i | −0.0521120 | − | 0.998641i | \(-0.516595\pi\) |
−0.890905 | + | 0.454190i | \(0.849929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.04618i | 0.457485i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.03163 | − | 13.9112i | 0.404115 | − | 0.699948i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.8913 | + | 9.17483i | −0.797560 | + | 0.460472i | −0.842617 | − | 0.538513i | \(-0.818986\pi\) |
0.0450569 | + | 0.998984i | \(0.485653\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.78349 | − | 2.76175i | 0.238876 | − | 0.137915i | −0.375784 | − | 0.926707i | \(-0.622627\pi\) |
0.614660 | + | 0.788792i | \(0.289293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.1821 | − | 19.3680i | 0.557020 | − | 0.964787i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 30.1919i | − | 1.49656i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.64406 | − | 4.99065i | −0.427421 | − | 0.246772i | 0.270826 | − | 0.962628i | \(-0.412703\pi\) |
−0.698248 | + | 0.715856i | \(0.746037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.738012 | + | 11.6295i | −0.0363152 | + | 0.572252i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.3523 | − | 42.1795i | −1.19541 | − | 2.07051i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.2960 | 0.502991 | 0.251495 | − | 0.967858i | \(-0.419078\pi\) | ||||
0.251495 | + | 0.967858i | \(0.419078\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4873 | 0.511118 | 0.255559 | − | 0.966794i | \(-0.417741\pi\) | ||||
0.255559 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.8801 | + | 22.3089i | 0.624775 | + | 1.08214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.34966 | + | 6.53905i | −0.210495 | + | 0.316447i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.26668 | − | 3.04072i | −0.253687 | − | 0.146466i | 0.367764 | − | 0.929919i | \(-0.380123\pi\) |
−0.621451 | + | 0.783453i | \(0.713457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6452i | 1.23243i | 0.787579 | + | 0.616214i | \(0.211334\pi\) | ||||
−0.787579 | + | 0.616214i | \(0.788666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.83782 | − | 10.1114i | 0.279261 | − | 0.483694i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7228 | − | 14.2737i | 1.17996 | − | 0.681248i | 0.223951 | − | 0.974600i | \(-0.428104\pi\) |
0.956004 | + | 0.293353i | \(0.0947710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.3702 | + | 10.6060i | −0.872794 | + | 0.503908i | −0.868276 | − | 0.496082i | \(-0.834772\pi\) |
−0.00451818 | + | 0.999990i | \(0.501438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.10872 | + | 14.0447i | −0.384390 | + | 0.665783i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5633i | 1.06483i | 0.846484 | + | 0.532414i | \(0.178715\pi\) | ||||
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.1033 | + | 17.9575i | 1.46460 | + | 0.845587i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.4030 | − | 20.1494i | 0.628344 | − | 0.944620i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.72013 | − | 11.6396i | −0.314354 | − | 0.544478i | 0.664946 | − | 0.746892i | \(-0.268455\pi\) |
−0.979300 | + | 0.202414i | \(0.935121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9928 | 0.931160 | 0.465580 | − | 0.885006i | \(-0.345846\pi\) | ||||
0.465580 | + | 0.885006i | \(0.345846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0108 | 0.465239 | 0.232620 | − | 0.972568i | \(-0.425270\pi\) | ||||
0.232620 | + | 0.972568i | \(0.425270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.7699 | + | 29.0463i | 0.776018 | + | 1.34410i | 0.934221 | + | 0.356695i | \(0.116097\pi\) |
−0.158203 | + | 0.987407i | \(0.550570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.64496 | − | 25.9212i | 0.0759574 | − | 1.19693i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.5992 | − | 10.7383i | −0.855192 | − | 0.493745i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 33.2479i | − | 1.52552i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.15860 | + | 7.20291i | −0.190011 | + | 0.329109i | −0.945254 | − | 0.326336i | \(-0.894186\pi\) |
0.755242 | + | 0.655446i | \(0.227519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4837 | + | 11.8262i | −0.933975 | + | 0.539231i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.47950 | + | 3.74094i | −0.294219 | + | 0.169867i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36509 | + | 2.36441i | −0.0618583 | + | 0.107142i | −0.895296 | − | 0.445472i | \(-0.853036\pi\) |
0.833438 | + | 0.552613i | \(0.186369\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4004i | 0.469365i | 0.972072 | + | 0.234683i | \(0.0754051\pi\) | ||||
−0.972072 | + | 0.234683i | \(0.924595\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.2718 | + | 19.2095i | 1.49849 | + | 0.865151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.61955 | + | 17.3877i | 0.386640 | + | 0.779945i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.37585 | + | 9.31124i | 0.240656 | + | 0.416828i | 0.960901 | − | 0.276891i | \(-0.0893041\pi\) |
−0.720245 | + | 0.693719i | \(0.755971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3466 | −0.773447 | −0.386723 | − | 0.922196i | \(-0.626393\pi\) | ||||
−0.386723 | + | 0.922196i | \(0.626393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 61.6577 | 2.74373 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.689842 | − | 1.19484i | −0.0305767 | − | 0.0529604i | 0.850332 | − | 0.526246i | \(-0.176401\pi\) |
−0.880909 | + | 0.473286i | \(0.843068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.51453 | + | 0.476874i | 0.332423 | + | 0.0210956i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.2290 | + | 19.1848i | 1.46425 | + | 0.845383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.6756i | 0.513494i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.19381 | − | 3.79978i | 0.0961123 | − | 0.166471i | −0.813960 | − | 0.580921i | \(-0.802693\pi\) |
0.910072 | + | 0.414450i | \(0.136026\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6494 | + | 17.6955i | −1.34021 | + | 0.773769i | −0.986837 | − | 0.161715i | \(-0.948297\pi\) |
−0.353369 | + | 0.935484i | \(0.614964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.9088 | − | 20.7320i | 1.56421 | − | 0.903099i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1141 | + | 17.5181i | −0.439743 | + | 0.761658i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 28.1360i | − | 1.21871i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.0490 | − | 28.3184i | −2.12057 | − | 1.22431i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.1514 | − | 10.1215i | 1.04028 | − | 0.435962i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1114 | − | 40.0301i | −0.993637 | − | 1.72103i | −0.594359 | − | 0.804200i | \(-0.702594\pi\) |
−0.399278 | − | 0.916830i | \(-0.630739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.8355 | −1.53502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.28813 | 0.183347 | 0.0916735 | − | 0.995789i | \(-0.470778\pi\) | ||||
0.0916735 | + | 0.995789i | \(0.470778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.7931 | − | 42.9429i | −1.05622 | − | 1.82943i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.3378 | − | 7.54171i | −0.482133 | − | 0.320706i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.49023 | + | 5.47919i | 0.402114 | + | 0.232161i | 0.687396 | − | 0.726283i | \(-0.258754\pi\) |
−0.285282 | + | 0.958444i | \(0.592087\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.8248i | 0.711612i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.3572 | + | 28.3315i | −0.689375 | + | 1.19403i | 0.282666 | + | 0.959218i | \(0.408781\pi\) |
−0.972040 | + | 0.234813i | \(0.924552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.89666 | − | 2.82709i | 0.206004 | − | 0.118936i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.8124 | + | 18.3669i | −1.33364 | + | 0.769980i | −0.985856 | − | 0.167594i | \(-0.946400\pi\) |
−0.347788 | + | 0.937573i | \(0.613067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.10603 | + | 12.3080i | −0.297378 | + | 0.515074i | −0.975535 | − | 0.219843i | \(-0.929446\pi\) |
0.678157 | + | 0.734917i | \(0.262779\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.89307i | − | 0.329164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.1848 | + | 12.8084i | 0.923565 | + | 0.533220i | 0.884771 | − | 0.466027i | \(-0.154315\pi\) |
0.0387941 | + | 0.999247i | \(0.487648\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.9917 | + | 18.3378i | −1.53468 | + | 0.760781i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.72282 | − | 11.6443i | −0.278431 | − | 0.482256i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.1013 | 0.582022 | 0.291011 | − | 0.956720i | \(-0.406008\pi\) | ||||
0.291011 | + | 0.956720i | \(0.406008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.5163 | −2.20510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.9721 | − | 32.8606i | −0.779090 | − | 1.34942i | −0.932467 | − | 0.361255i | \(-0.882348\pi\) |
0.153377 | − | 0.988168i | \(-0.450985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.1993 | − | 19.9279i | 1.64801 | − | 0.816964i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9032 | + | 9.75906i | 0.690646 | + | 0.398744i | 0.803854 | − | 0.594827i | \(-0.202779\pi\) |
−0.113208 | + | 0.993571i | \(0.536113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.1555i | 1.55639i | 0.628020 | + | 0.778197i | \(0.283865\pi\) | ||||
−0.628020 | + | 0.778197i | \(0.716135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.67318 | + | 8.09419i | −0.189992 | + | 0.329075i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4756 | + | 17.0177i | −1.19638 | + | 0.690729i | −0.959746 | − | 0.280870i | \(-0.909377\pi\) |
−0.236632 | + | 0.971599i | \(0.576044\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.92132 | − | 4.57338i | 0.320462 | − | 0.185019i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6676 | + | 18.4768i | −0.430859 | + | 0.746269i | −0.996947 | − | 0.0780750i | \(-0.975123\pi\) |
0.566089 | + | 0.824344i | \(0.308456\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6233i | 0.870519i | 0.900305 | + | 0.435260i | \(0.143343\pi\) | ||||
−0.900305 | + | 0.435260i | \(0.856657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1902 | − | 9.92474i | −0.690931 | − | 0.398909i | 0.113030 | − | 0.993592i | \(-0.463944\pi\) |
−0.803961 | + | 0.594682i | \(0.797278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4466 | + | 7.61410i | 0.458600 | + | 0.305052i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.1141 | + | 22.7143i | 0.524564 | + | 0.908571i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.8525 | −1.74851 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.3803 | −1.05018 | −0.525092 | − | 0.851045i | \(-0.675969\pi\) | ||||
−0.525092 | + | 0.851045i | \(0.675969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6673 | − | 20.2083i | −0.463001 | − | 0.801941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3271 | − | 12.4209i | −0.646902 | − | 0.492134i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.7441 | − | 17.7501i | −1.21432 | − | 0.701087i | −0.250621 | − | 0.968085i | \(-0.580635\pi\) |
−0.963697 | + | 0.266999i | \(0.913968\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.48881i | 0.255894i | 0.991781 | + | 0.127947i | \(0.0408387\pi\) | ||||
−0.991781 | + | 0.127947i | \(0.959161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.8076 | − | 37.7718i | 0.857343 | − | 1.48496i | −0.0171104 | − | 0.999854i | \(-0.505447\pi\) |
0.874454 | − | 0.485109i | \(-0.161220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.2691 | + | 8.23828i | −0.560112 | + | 0.323381i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7119 | − | 12.5353i | 0.849650 | − | 0.490546i | −0.0108825 | − | 0.999941i | \(-0.503464\pi\) |
0.860533 | + | 0.509395i | \(0.170131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.0027 | − | 19.0572i | 0.429911 | − | 0.744627i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.4657i | − | 0.524551i | −0.964993 | − | 0.262276i | \(-0.915527\pi\) | ||
0.964993 | − | 0.262276i | \(-0.0844729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.4783 | + | 23.3702i | 1.57442 | + | 0.908994i | 0.995617 | + | 0.0935285i | \(0.0298146\pi\) |
0.578806 | + | 0.815465i | \(0.303519\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −57.7931 | − | 3.66756i | −2.24112 | − | 0.142222i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.88590 | − | 10.1947i | −0.227903 | − | 0.394740i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1045 | −0.428685 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.9275 | −1.46200 | −0.730999 | − | 0.682378i | \(-0.760946\pi\) | ||||
−0.730999 | + | 0.682378i | \(0.760946\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.56891 | − | 2.71744i | −0.0602983 | − | 0.104440i | 0.834300 | − | 0.551310i | \(-0.185872\pi\) |
−0.894599 | + | 0.446870i | \(0.852539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.81700 | + | 5.68257i | 0.108107 | + | 0.218077i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1449 | − | 7.01184i | −0.464711 | − | 0.268301i | 0.249312 | − | 0.968423i | \(-0.419795\pi\) |
−0.714023 | + | 0.700122i | \(0.753129\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 45.7866i | − | 1.74941i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.26668 | + | 9.12216i | −0.200645 | + | 0.347527i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.6141 | − | 16.5204i | 1.08853 | − | 0.628464i | 0.155346 | − | 0.987860i | \(-0.450351\pi\) |
0.933185 | + | 0.359396i | \(0.117017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.57965 | − | 2.64406i | 0.173716 | − | 0.100295i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.0825 | − | 45.1763i | 0.987946 | − | 1.71117i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.4058i | − | 1.22395i | −0.790877 | − | 0.611975i | \(-0.790375\pi\) | ||
0.790877 | − | 0.611975i | \(-0.209625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.0163 | + | 28.2996i | 1.84869 | + | 1.06734i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.31028 | − | 52.1631i | 0.124496 | − | 1.96179i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7528 | + | 41.1410i | 0.892055 | + | 1.54508i | 0.837408 | + | 0.546578i | \(0.184070\pi\) |
0.0546463 | + | 0.998506i | \(0.482597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.7048 | −0.475799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.2174 | 1.27966 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.1139 | − | 40.0344i | −0.862003 | − | 1.49303i | −0.869993 | − | 0.493065i | \(-0.835877\pi\) |
0.00798976 | − | 0.999968i | \(-0.497457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0145 | − | 27.0821i | 0.670896 | − | 1.00859i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.0306 | − | 16.7608i | −1.07817 | − | 0.622482i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.2330i | − | 0.527874i | −0.964540 | − | 0.263937i | \(-0.914979\pi\) | ||
0.964540 | − | 0.263937i | \(-0.0850210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5968 | + | 27.0145i | −0.576870 | + | 0.999169i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.7201 | − | 20.0457i | 1.28242 | − | 0.740404i | 0.305127 | − | 0.952312i | \(-0.401301\pi\) |
0.977290 | + | 0.211908i | \(0.0679676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.8046 | − | 18.3624i | 1.17154 | − | 0.676388i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.99731 | − | 5.19150i | 0.110258 | − | 0.190972i | −0.805616 | − | 0.592438i | \(-0.798166\pi\) |
0.915874 | + | 0.401465i | \(0.131499\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.32437i | − | 0.305392i | −0.988273 | − | 0.152696i | \(-0.951205\pi\) | ||
0.988273 | − | 0.152696i | \(-0.0487955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.0490 | − | 23.1223i | −1.46728 | − | 0.847135i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.5910 | + | 39.9756i | −0.971616 | + | 1.46068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.47650 | − | 9.48558i | −0.199840 | − | 0.346134i | 0.748636 | − | 0.662981i | \(-0.230709\pi\) |
−0.948477 | + | 0.316847i | \(0.897376\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.9469 | 0.689548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.28275 | −0.119314 | −0.0596568 | − | 0.998219i | \(-0.519001\pi\) | ||||
−0.0596568 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.4616 | + | 40.6367i | 0.850483 | + | 1.47308i | 0.880773 | + | 0.473538i | \(0.157023\pi\) |
−0.0302909 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.92394 | + | 30.3172i | −0.0696511 | + | 1.09756i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1785 | + | 6.45390i | 0.403632 | + | 0.233037i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.52166i | 0.163055i | 0.996671 | + | 0.0815276i | \(0.0259799\pi\) | ||||
−0.996671 | + | 0.0815276i | \(0.974020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.8635 | + | 36.1367i | −0.750409 | + | 1.29975i | 0.197216 | + | 0.980360i | \(0.436810\pi\) |
−0.947625 | + | 0.319386i | \(0.896523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.3315 | + | 18.0893i | −1.12546 | + | 0.649786i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.3077 | + | 33.6640i | −2.08909 | + | 1.20614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7201 | + | 23.7640i | −0.490945 | + | 0.850341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 43.6577i | − | 1.55821i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.86957 | + | 3.96615i | 0.244874 | + | 0.141378i | 0.617415 | − | 0.786638i | \(-0.288180\pi\) |
−0.372541 | + | 0.928016i | \(0.621513\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.12885 | − | 4.29440i | −0.0756933 | − | 0.152691i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.34966 | + | 7.53383i | 0.154461 | + | 0.267534i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5840 | 0.622857 | 0.311429 | − | 0.950270i | \(-0.399193\pi\) | ||||
0.311429 | + | 0.950270i | \(0.399193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9584 | 0.599944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.32324 | + | 9.22013i | 0.187853 | + | 0.325371i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7201 | − | 0.870682i | −0.483571 | − | 0.0306875i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.9338 | + | 26.5199i | 1.61495 | + | 0.932390i | 0.988200 | + | 0.153168i | \(0.0489475\pi\) |
0.626747 | + | 0.779223i | \(0.284386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.966384i | − | 0.0339343i | −0.999856 | − | 0.0169672i | \(-0.994599\pi\) | ||
0.999856 | − | 0.0169672i | \(-0.00540108\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.89204 | − | 5.00916i | 0.101304 | − | 0.175463i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.8669 | − | 20.1304i | 1.21984 | − | 0.704274i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.5209 | + | 22.2400i | −1.34439 | + | 0.776183i | −0.987448 | − | 0.157945i | \(-0.949513\pi\) |
−0.356940 | + | 0.934127i | \(0.616180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0327 | + | 22.5732i | −0.454290 | + | 0.786853i | −0.998647 | − | 0.0520005i | \(-0.983440\pi\) |
0.544357 | + | 0.838853i | \(0.316774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.4166i | − | 0.466540i | −0.972412 | − | 0.233270i | \(-0.925057\pi\) | ||
0.972412 | − | 0.233270i | \(-0.0749426\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.407601 | − | 0.235328i | −0.0141566 | − | 0.00817329i | 0.492905 | − | 0.870083i | \(-0.335935\pi\) |
−0.507062 | + | 0.861910i | \(0.669268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.7010 | − | 35.0789i | −0.509359 | − | 1.21541i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.97919 | − | 6.89216i | −0.137706 | − | 0.238513i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.4309 | 0.808923 | 0.404461 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404461 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.9946 | −0.723953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.88377 | + | 11.9230i | 0.236809 | + | 0.410165i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.59688 | + | 4.38812i | 0.226671 | + | 0.150778i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6365 | + | 6.71834i | 0.398894 | + | 0.230302i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 18.9678i | − | 0.649446i | −0.945809 | − | 0.324723i | \(-0.894729\pi\) | ||
0.945809 | − | 0.324723i | \(-0.105271\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.59820 | − | 11.4284i | 0.225390 | − | 0.390387i | −0.731046 | − | 0.682328i | \(-0.760968\pi\) |
0.956436 | + | 0.291941i | \(0.0943010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.78544 | − | 4.49493i | 0.265636 | − | 0.153365i | −0.361267 | − | 0.932462i | \(-0.617656\pi\) |
0.626903 | + | 0.779098i | \(0.284322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0178 | + | 6.93847i | −0.409090 | + | 0.236188i | −0.690399 | − | 0.723429i | \(-0.742565\pi\) |
0.281309 | + | 0.959617i | \(0.409232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.10603 | + | 10.5760i | −0.207611 | + | 0.359593i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.2537i | − | 0.653137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.9159 | − | 14.3852i | −0.844242 | − | 0.487423i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.91662 | − | 0.950123i | 0.0647937 | − | 0.0321200i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.06531 | + | 8.77338i | 0.171043 | + | 0.296256i | 0.938785 | − | 0.344504i | \(-0.111953\pi\) |
−0.767742 | + | 0.640760i | \(0.778620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.7189 | −1.03495 | −0.517473 | − | 0.855700i | \(-0.673127\pi\) | ||||
−0.517473 | + | 0.855700i | \(0.673127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4403 | −1.19266 | −0.596330 | − | 0.802740i | \(-0.703375\pi\) | ||||
−0.596330 | + | 0.802740i | \(0.703375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1384 | − | 31.4166i | −0.609027 | − | 1.05487i | −0.991401 | − | 0.130858i | \(-0.958227\pi\) |
0.382375 | − | 0.924007i | \(-0.375106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.7228 | + | 8.78568i | −0.594404 | + | 0.294662i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.9553 | − | 10.9438i | −0.634315 | − | 0.366222i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 61.0077i | − | 2.03926i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.9785 | + | 46.7282i | −0.899785 | + | 1.55847i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.9128 | + | 9.76460i | −0.563447 | + | 0.325306i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.1736 | − | 28.3904i | 1.63459 | − | 0.943728i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.92931 | + | 6.80577i | −0.130471 | + | 0.225982i | −0.923858 | − | 0.382735i | \(-0.874982\pi\) |
0.793387 | + | 0.608717i | \(0.208316\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.9584i | − | 0.959434i | −0.877423 | − | 0.479717i | \(-0.840739\pi\) | ||
0.877423 | − | 0.479717i | \(-0.159261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.5570 | − | 29.1891i | −1.67319 | − | 0.966019i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.5319 | − | 10.3315i | −0.512908 | − | 0.341177i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1993 | + | 29.7901i | 0.567353 | + | 0.982684i | 0.996826 | + | 0.0796049i | \(0.0253659\pi\) |
−0.429473 | + | 0.903080i | \(0.641301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.4968 | 0.707576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.2626 | 1.25807 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.05052 | − | 5.28365i | −0.100084 | − | 0.173351i | 0.811635 | − | 0.584165i | \(-0.198578\pi\) |
−0.911719 | + | 0.410814i | \(0.865245\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.20560 | + | 48.6967i | −0.203380 | + | 1.59597i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 54.9409 | + | 31.7201i | 1.79676 | + | 1.03736i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.7128i | 1.65671i | 0.560201 | + | 0.828357i | \(0.310724\pi\) | ||||
−0.560201 | + | 0.828357i | \(0.689276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.5616 | + | 30.4177i | −0.572493 | + | 0.991587i | 0.423816 | + | 0.905748i | \(0.360690\pi\) |
−0.996309 | + | 0.0858389i | \(0.972643\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8423 | + | 7.99185i | −0.450767 | + | 0.260250i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2973 | − | 19.8016i | 1.11451 | − | 0.643465i | 0.174519 | − | 0.984654i | \(-0.444163\pi\) |
0.939995 | + | 0.341189i | \(0.110830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.17025 | − | 7.22309i | 0.135372 | − | 0.234471i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.5942i | − | 0.407966i | −0.978974 | − | 0.203983i | \(-0.934611\pi\) | ||
0.978974 | − | 0.203983i | \(-0.0653887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.7637 | − | 23.5349i | −1.31908 | − | 0.761573i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.7359 | − | 2.45819i | −1.25085 | − | 0.0793790i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6168 | + | 23.5850i | 0.439251 | + | 0.760805i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.7895 | 1.11992 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.8407 | 1.66708 | 0.833542 | − | 0.552456i | \(-0.186309\pi\) | ||||
0.833542 | + | 0.552456i | \(0.186309\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.918852 | − | 1.59150i | −0.0294874 | − | 0.0510736i | 0.850905 | − | 0.525319i | \(-0.176054\pi\) |
−0.880392 | + | 0.474246i | \(0.842721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.99103 | − | 4.01639i | −0.0638296 | − | 0.128760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.2808 | + | 13.4412i | 0.744818 | + | 0.430021i | 0.823818 | − | 0.566854i | \(-0.191840\pi\) |
−0.0790007 | + | 0.996875i | \(0.525173\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.4385i | 0.621257i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.19850 | + | 14.2002i | −0.261492 | + | 0.452917i | −0.966638 | − | 0.256145i | \(-0.917548\pi\) |
0.705147 | + | 0.709061i | \(0.250881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.0570 | − | 31.7872i | 1.75426 | − | 1.01282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.27742 | − | 4.77897i | 0.263207 | − | 0.151962i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.17941 | − | 2.04279i | 0.0374651 | − | 0.0648915i | −0.846685 | − | 0.532095i | \(-0.821405\pi\) |
0.884150 | + | 0.467203i | \(0.154738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.1704i | 0.734552i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1114 | − | 7.56988i | −0.415242 | − | 0.239740i | 0.277797 | − | 0.960640i | \(-0.410396\pi\) |
−0.693040 | + | 0.720899i | \(0.743729\pi\) | |||||||
\(998\) | 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 | 756.2.t.e.269.6 | yes | 12 | |
3.2 | odd | 2 | inner | 756.2.t.e.269.1 | ✓ | 12 | |
7.3 | odd | 6 | 5292.2.f.e.2645.11 | 12 | |||
7.4 | even | 3 | 5292.2.f.e.2645.1 | 12 | |||
7.5 | odd | 6 | inner | 756.2.t.e.593.1 | yes | 12 | |
9.2 | odd | 6 | 2268.2.bm.i.1025.6 | 12 | |||
9.4 | even | 3 | 2268.2.w.i.269.6 | 12 | |||
9.5 | odd | 6 | 2268.2.w.i.269.1 | 12 | |||
9.7 | even | 3 | 2268.2.bm.i.1025.1 | 12 | |||
21.5 | even | 6 | inner | 756.2.t.e.593.6 | yes | 12 | |
21.11 | odd | 6 | 5292.2.f.e.2645.12 | 12 | |||
21.17 | even | 6 | 5292.2.f.e.2645.2 | 12 | |||
63.5 | even | 6 | 2268.2.bm.i.593.1 | 12 | |||
63.40 | odd | 6 | 2268.2.bm.i.593.6 | 12 | |||
63.47 | even | 6 | 2268.2.w.i.1349.6 | 12 | |||
63.61 | odd | 6 | 2268.2.w.i.1349.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.t.e.269.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
756.2.t.e.269.6 | yes | 12 | 1.1 | even | 1 | trivial | |
756.2.t.e.593.1 | yes | 12 | 7.5 | odd | 6 | inner | |
756.2.t.e.593.6 | yes | 12 | 21.5 | even | 6 | inner | |
2268.2.w.i.269.1 | 12 | 9.5 | odd | 6 | |||
2268.2.w.i.269.6 | 12 | 9.4 | even | 3 | |||
2268.2.w.i.1349.1 | 12 | 63.61 | odd | 6 | |||
2268.2.w.i.1349.6 | 12 | 63.47 | even | 6 | |||
2268.2.bm.i.593.1 | 12 | 63.5 | even | 6 | |||
2268.2.bm.i.593.6 | 12 | 63.40 | odd | 6 | |||
2268.2.bm.i.1025.1 | 12 | 9.7 | even | 3 | |||
2268.2.bm.i.1025.6 | 12 | 9.2 | odd | 6 | |||
5292.2.f.e.2645.1 | 12 | 7.4 | even | 3 | |||
5292.2.f.e.2645.2 | 12 | 21.17 | even | 6 | |||
5292.2.f.e.2645.11 | 12 | 7.3 | odd | 6 | |||
5292.2.f.e.2645.12 | 12 | 21.11 | odd | 6 |