Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1249,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.6 | ||
Root | \(0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1249 |
Dual form | 1560.2.l.e.1249.2 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.19663 | − | 1.88893i | −0.535151 | − | 0.844756i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.393270 | 0.118575 | 0.0592877 | − | 0.998241i | \(-0.481117\pi\) | ||||
0.0592877 | + | 0.998241i | \(0.481117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.88893 | − | 1.19663i | 0.487720 | − | 0.308970i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.21302i | − | 1.50688i | −0.657517 | − | 0.753440i | \(-0.728393\pi\) | ||
0.657517 | − | 0.753440i | \(-0.271607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.34271 | 1.68453 | 0.842266 | − | 0.539062i | \(-0.181221\pi\) | ||||
0.842266 | + | 0.539062i | \(0.181221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.44383i | 0.301060i | 0.988605 | + | 0.150530i | \(0.0480980\pi\) | ||||
−0.988605 | + | 0.150530i | \(0.951902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.13613 | + | 4.52072i | −0.427226 | + | 0.904145i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.828427 | 0.153835 | 0.0769175 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769175 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65685 | 0.297580 | 0.148790 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148790 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.393270i | 0.0684595i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.34271 | − | 3.38459i | 0.903082 | − | 0.572101i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.78654i | 1.11570i | 0.829942 | + | 0.557850i | \(0.188374\pi\) | ||||
−0.829942 | + | 0.557850i | \(0.811626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77786 | 0.590003 | 0.295002 | − | 0.955497i | \(-0.404680\pi\) | ||||
0.295002 | + | 0.955497i | \(0.404680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.51428i | 0.383424i | 0.981451 | + | 0.191712i | \(0.0614040\pi\) | ||||
−0.981451 | + | 0.191712i | \(0.938596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.19663 | + | 1.88893i | 0.178384 | + | 0.281585i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00868i | 0.438860i | 0.975628 | + | 0.219430i | \(0.0704198\pi\) | ||||
−0.975628 | + | 0.219430i | \(0.929580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.21302 | 0.869997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.55573i | 1.31258i | 0.754509 | + | 0.656290i | \(0.227875\pi\) | ||||
−0.754509 | + | 0.656290i | \(0.772125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.470600 | − | 0.742860i | −0.0634557 | − | 0.100167i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.34271i | 0.972565i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.393270 | −0.0511994 | −0.0255997 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0255997 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0414 | 1.41371 | 0.706856 | − | 0.707357i | \(-0.250113\pi\) | ||||
0.706856 | + | 0.707357i | \(0.250113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.82843i | − | 0.356348i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.88893 | + | 1.19663i | −0.234293 | + | 0.148424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5557i | 1.90043i | 0.311588 | + | 0.950217i | \(0.399139\pi\) | ||||
−0.311588 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.44383 | −0.173817 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.56440 | 0.779051 | 0.389526 | − | 0.921016i | \(-0.372639\pi\) | ||||
0.389526 | + | 0.921016i | \(0.372639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.6150i | − | 1.59351i | −0.604302 | − | 0.796756i | \(-0.706548\pi\) | ||
0.604302 | − | 0.796756i | \(-0.293452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.52072 | − | 2.13613i | −0.522008 | − | 0.246659i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.11233i | 0.126762i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9403 | 1.68092 | 0.840459 | − | 0.541875i | \(-0.182286\pi\) | ||||
0.840459 | + | 0.541875i | \(0.182286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.4633i | − | 1.80708i | −0.428504 | − | 0.903540i | \(-0.640959\pi\) | ||
0.428504 | − | 0.903540i | \(-0.359041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7360 | + | 7.43472i | −1.27295 | + | 0.806408i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.828427i | 0.0888167i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.67674 | 1.02573 | 0.512866 | − | 0.858469i | \(-0.328584\pi\) | ||||
0.512866 | + | 0.858469i | \(0.328584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.65685i | 0.171808i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.78654 | − | 13.8699i | −0.901480 | − | 1.42302i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0418875i | 0.00425303i | 0.999998 | + | 0.00212652i | \(0.000676892\pi\) | ||||
−0.999998 | + | 0.00212652i | \(0.999323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.393270 | −0.0395251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1421 | 1.20819 | 0.604094 | − | 0.796913i | \(-0.293535\pi\) | ||||
0.604094 | + | 0.796913i | \(0.293535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0173504i | 0.00170958i | 1.00000 | 0.000854792i | \(0.000272089\pi\) | |||||
−1.00000 | 0.000854792i | \(0.999728\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.38459 | + | 5.34271i | 0.330303 | + | 0.521395i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.10113i | 0.203123i | 0.994829 | + | 0.101562i | \(0.0323839\pi\) | ||||
−0.994829 | + | 0.101562i | \(0.967616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.21302 | −0.595100 | −0.297550 | − | 0.954706i | \(-0.596169\pi\) | ||||
−0.297550 | + | 0.954706i | \(0.596169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.78654 | −0.644150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.42648i | − | 0.134192i | −0.997747 | − | 0.0670961i | \(-0.978627\pi\) | ||
0.997747 | − | 0.0670961i | \(-0.0213734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.72730 | − | 1.72774i | 0.254322 | − | 0.161113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.5731 | 1.61092 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8453 | −0.985940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.77786i | 0.340639i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0955 | − | 1.37465i | 0.992413 | − | 0.122953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.50307i | 0.133376i | 0.997774 | + | 0.0666880i | \(0.0212432\pi\) | ||||
−0.997774 | + | 0.0666880i | \(0.978757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.51428 | −0.221370 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.85699 | 0.336987 | 0.168493 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168493 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7683i | 1.80084i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.88893 | + | 1.19663i | −0.162573 | + | 0.102990i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.5644i | 1.41519i | 0.706617 | + | 0.707596i | \(0.250220\pi\) | ||||
−0.706617 | + | 0.707596i | \(0.749780\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6854 | −0.906325 | −0.453163 | − | 0.891428i | \(-0.649704\pi\) | ||||
−0.453163 | + | 0.891428i | \(0.649704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00868 | −0.253376 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.393270i | − | 0.0328869i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.991325 | − | 1.56484i | −0.0823250 | − | 0.129953i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.05012 | −0.331799 | −0.165900 | − | 0.986143i | \(-0.553053\pi\) | ||||
−0.165900 | + | 0.986143i | \(0.553053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.02856 | 0.409218 | 0.204609 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204609 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.21302i | 0.502293i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.98265 | − | 3.12969i | −0.159250 | − | 0.251382i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4961i | 1.95500i | 0.210940 | + | 0.977499i | \(0.432347\pi\) | ||||
−0.210940 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.55573 | −0.757819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08378 | −0.321847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.3137i | − | 1.19946i | −0.800202 | − | 0.599731i | \(-0.795274\pi\) | ||
0.800202 | − | 0.599731i | \(-0.204726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.742860 | − | 0.470600i | 0.0578316 | − | 0.0366362i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 15.7770i | − | 1.22086i | −0.792070 | − | 0.610430i | \(-0.790997\pi\) | ||
0.792070 | − | 0.610430i | \(-0.209003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.34271 | −0.561511 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.9706i | 1.13819i | 0.822272 | + | 0.569095i | \(0.192706\pi\) | ||||
−0.822272 | + | 0.569095i | \(0.807294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7865 | − | 6.04189i | −0.966572 | − | 0.456724i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.393270i | − | 0.0295600i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.84578 | 0.362190 | 0.181095 | − | 0.983466i | \(-0.442036\pi\) | ||||
0.181095 | + | 0.983466i | \(0.442036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.99912 | −0.594570 | −0.297285 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297285 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0414i | 0.816207i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8193 | − | 8.12101i | 0.942495 | − | 0.597069i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.44339i | − | 0.178679i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.4260 | −1.47798 | −0.738988 | − | 0.673718i | \(-0.764696\pi\) | ||||
−0.738988 | + | 0.673718i | \(0.764696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.0237i | − | 1.72926i | −0.502408 | − | 0.864630i | \(-0.667553\pi\) | ||
0.502408 | − | 0.864630i | \(-0.332447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.19663 | − | 1.88893i | −0.0856928 | − | 0.135269i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.80642i | − | 0.342444i | −0.985233 | − | 0.171222i | \(-0.945229\pi\) | ||
0.985233 | − | 0.171222i | \(-0.0547715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.9403 | 1.05909 | 0.529546 | − | 0.848281i | \(-0.322362\pi\) | ||||
0.529546 | + | 0.848281i | \(0.322362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5557 | −1.09722 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.34315i | 0.164457i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.52072 | − | 7.13613i | −0.315741 | − | 0.498409i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.44383i | − | 0.100353i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.88767 | 0.199744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.82799 | −0.125844 | −0.0629220 | − | 0.998018i | \(-0.520042\pi\) | ||||
−0.0629220 | + | 0.998018i | \(0.520042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.56440i | 0.449786i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.74930 | − | 3.00868i | 0.323900 | − | 0.205190i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.68629i | 0.318126i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6150 | 0.920014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.21302 | −0.417933 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.07045i | 0.473472i | 0.971574 | + | 0.236736i | \(0.0760777\pi\) | ||||
−0.971574 | + | 0.236736i | \(0.923922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.13613 | − | 4.52072i | 0.142409 | − | 0.301382i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.43560i | 0.360773i | 0.983596 | + | 0.180387i | \(0.0577349\pi\) | ||||
−0.983596 | + | 0.180387i | \(0.942265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.8147 | −1.63980 | −0.819899 | − | 0.572508i | \(-0.805971\pi\) | ||||
−0.819899 | + | 0.572508i | \(0.805971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.11233 | −0.0731863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.4256i | − | 1.53466i | −0.641251 | − | 0.767331i | \(-0.721584\pi\) | ||
0.641251 | − | 0.767331i | \(-0.278416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.68318 | − | 3.60029i | 0.370730 | − | 0.234857i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.9403i | 0.970478i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.7779 | 1.40869 | 0.704346 | − | 0.709856i | \(-0.251240\pi\) | ||||
0.704346 | + | 0.709856i | \(0.251240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2126 | −0.979929 | −0.489964 | − | 0.871742i | \(-0.662990\pi\) | ||||
−0.489964 | + | 0.871742i | \(0.662990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.19663 | + | 1.88893i | 0.0764502 | + | 0.120679i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.34271i | − | 0.467205i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.4633 | 1.04332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9399 | −1.13236 | −0.566178 | − | 0.824283i | \(-0.691578\pi\) | ||||
−0.566178 | + | 0.824283i | \(0.691578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.567816i | 0.0356983i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.43472 | − | 11.7360i | −0.465580 | − | 0.734935i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.88810i | 0.242533i | 0.992620 | + | 0.121267i | \(0.0386956\pi\) | ||||
−0.992620 | + | 0.121267i | \(0.961304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1952 | −1.19273 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.828427 | −0.0512784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.296797i | 0.0183013i | 0.999958 | + | 0.00915064i | \(0.00291278\pi\) | ||||
−0.999958 | + | 0.00915064i | \(0.997087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0501 | − | 11.4347i | 1.10881 | − | 0.702429i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.67674i | 0.592207i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.25447 | 0.0764864 | 0.0382432 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382432 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.81510 | 0.596225 | 0.298112 | − | 0.954531i | \(-0.403643\pi\) | ||||
0.298112 | + | 0.954531i | \(0.403643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843i | 0.171184i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.840075 | + | 1.77786i | −0.0506585 | + | 0.107209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.35603i | − | 0.261729i | −0.991400 | − | 0.130864i | \(-0.958225\pi\) | ||
0.991400 | − | 0.130864i | \(-0.0417752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.45207 | 0.205933 | 0.102967 | − | 0.994685i | \(-0.467167\pi\) | ||||
0.102967 | + | 0.994685i | \(0.467167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.25937i | − | 0.134306i | −0.997743 | − | 0.0671528i | \(-0.978608\pi\) | ||
0.997743 | − | 0.0671528i | \(-0.0213915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.8699 | − | 8.78654i | 0.821581 | − | 0.520470i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6854i | 0.630740i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.6016 | −1.27068 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0418875 | −0.00245549 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.5358i | − | 1.14130i | −0.821195 | − | 0.570648i | \(-0.806692\pi\) | ||
0.821195 | − | 0.570648i | \(-0.193308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.470600 | + | 0.742860i | 0.0273994 | + | 0.0432510i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.393270i | − | 0.0228198i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.44383 | 0.0834990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.11146 | −0.409898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1421i | 0.697547i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.2126 | − | 20.8565i | −0.756550 | − | 1.19424i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.8142i | − | 1.58744i | −0.608282 | − | 0.793721i | \(-0.708141\pi\) | ||
0.608282 | − | 0.793721i | \(-0.291859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0173504 | −0.000987028 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.10113 | 0.119144 | 0.0595719 | − | 0.998224i | \(-0.481026\pi\) | ||||
0.0595719 | + | 0.998224i | \(0.481026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.64397i | − | 0.545109i | −0.962140 | − | 0.272555i | \(-0.912131\pi\) | ||
0.962140 | − | 0.272555i | \(-0.0878685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.34271 | + | 3.38459i | −0.301027 | + | 0.190700i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.1201i | − | 0.905397i | −0.891664 | − | 0.452698i | \(-0.850461\pi\) | ||
0.891664 | − | 0.452698i | \(-0.149539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.325795 | 0.0182410 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.10113 | −0.117273 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 45.6204i | − | 2.53839i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.52072 | + | 2.13613i | 0.250765 | + | 0.118491i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.21302i | − | 0.343581i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.50982 | −0.469161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9537 | 0.766962 | 0.383481 | − | 0.923549i | \(-0.374725\pi\) | ||||
0.383481 | + | 0.923549i | \(0.374725\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.78654i | − | 0.371900i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.3837 | − | 18.6145i | 1.60540 | − | 1.01702i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.66974i | 0.526744i | 0.964694 | + | 0.263372i | \(0.0848347\pi\) | ||||
−0.964694 | + | 0.263372i | \(0.915165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.42648 | 0.0774759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.651591 | 0.0352856 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.72774 | + | 2.72730i | 0.0930184 | + | 0.146833i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2014i | 0.547638i | 0.961781 | + | 0.273819i | \(0.0882870\pi\) | ||||
−0.961781 | + | 0.273819i | \(0.911713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.7402 | −1.53843 | −0.769214 | − | 0.638992i | \(-0.779352\pi\) | ||||
−0.769214 | + | 0.638992i | \(0.779352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 20.9067i | − | 1.11275i | −0.830931 | − | 0.556375i | \(-0.812192\pi\) | ||
0.830931 | − | 0.556375i | \(-0.187808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.85519 | − | 12.3997i | −0.416910 | − | 0.658109i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5731i | 0.930066i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3162 | −1.01947 | −0.509736 | − | 0.860331i | \(-0.670257\pi\) | ||||
−0.509736 | + | 0.860331i | \(0.670257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.9153 | 1.83765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.8453i | − | 0.569233i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.7177 | + | 16.2921i | −1.34613 | + | 0.852770i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.6957i | 1.96770i | 0.178990 | + | 0.983851i | \(0.442717\pi\) | ||||
−0.178990 | + | 0.983851i | \(0.557283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.77786 | −0.196668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.0277 | −1.40321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.4607i | − | 1.16297i | −0.813556 | − | 0.581487i | \(-0.802471\pi\) | ||
0.813556 | − | 0.581487i | \(-0.197529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.37465 | + | 11.0955i | 0.0709867 | + | 0.572970i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.828427i | − | 0.0426662i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3133 | 1.24889 | 0.624444 | − | 0.781069i | \(-0.285325\pi\) | ||||
0.624444 | + | 0.781069i | \(0.285325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50307 | −0.0770046 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 37.2498i | − | 1.90338i | −0.307065 | − | 0.951688i | \(-0.599347\pi\) | ||
0.307065 | − | 0.951688i | \(-0.400653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.10113 | − | 1.33106i | 0.107083 | − | 0.0678370i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.51428i | − | 0.127808i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.467931 | 0.0237250 | 0.0118625 | − | 0.999930i | \(-0.496224\pi\) | ||||
0.0118625 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.97056 | 0.453661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.85699i | 0.194559i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.8781 | − | 28.2213i | −0.899545 | − | 1.41997i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.5263i | 1.73282i | 0.499329 | + | 0.866412i | \(0.333580\pi\) | ||||
−0.499329 | + | 0.866412i | \(0.666420\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.7683 | −1.03972 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.8781 | 1.59192 | 0.795958 | − | 0.605351i | \(-0.206967\pi\) | ||||
0.795958 | + | 0.605351i | \(0.206967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.65685i | − | 0.0825338i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.19663 | − | 1.88893i | −0.0594613 | − | 0.0938618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.66894i | 0.132294i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.01735 | 0.396432 | 0.198216 | − | 0.980158i | \(-0.436485\pi\) | ||||
0.198216 | + | 0.980158i | \(0.436485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5644 | −0.817062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.11233i | − | 0.0547344i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.0980 | + | 19.7005i | −1.52654 | + | 0.967061i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 10.6854i | − | 0.523267i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.40151 | −0.410440 | −0.205220 | − | 0.978716i | \(-0.565791\pi\) | ||||
−0.205220 | + | 0.978716i | \(0.565791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7514 | −0.572728 | −0.286364 | − | 0.958121i | \(-0.592447\pi\) | ||||
−0.286364 | + | 0.958121i | \(0.592447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.00868i | − | 0.146287i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.0874 | + | 13.2718i | 1.36244 | + | 0.643778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.2299i | 1.51132i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.393270 | 0.0189872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5818 | −0.991388 | −0.495694 | − | 0.868497i | \(-0.665086\pi\) | ||||
−0.495694 | + | 0.868497i | \(0.665086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.12522i | 0.246303i | 0.992388 | + | 0.123151i | \(0.0393000\pi\) | ||||
−0.992388 | + | 0.123151i | \(0.960700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.56484 | − | 0.991325i | 0.0750285 | − | 0.0475304i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.6016i | 0.507145i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.8868 | 0.615053 | 0.307526 | − | 0.951540i | \(-0.400499\pi\) | ||||
0.307526 | + | 0.951540i | \(0.400499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.1279i | 1.66898i | 0.551024 | + | 0.834489i | \(0.314237\pi\) | ||||
−0.551024 | + | 0.834489i | \(0.685763\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5795 | − | 18.2787i | −0.548922 | − | 0.866494i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.05012i | − | 0.191564i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.2213 | −0.859914 | −0.429957 | − | 0.902849i | \(-0.641471\pi\) | ||||
−0.429957 | + | 0.902849i | \(0.641471\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.48572 | 0.0699598 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.02856i | 0.236262i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.38459 | − | 5.34271i | −0.158672 | − | 0.250470i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.4118i | − | 1.09516i | −0.836753 | − | 0.547580i | \(-0.815549\pi\) | ||
0.836753 | − | 0.547580i | \(-0.184451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.21302 | −0.289999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.2913 | −0.665611 | −0.332805 | − | 0.942996i | \(-0.607995\pi\) | ||||
−0.332805 | + | 0.942996i | \(0.607995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7152i | 1.10214i | 0.834459 | + | 0.551070i | \(0.185780\pi\) | ||||
−0.834459 | + | 0.551070i | \(0.814220\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.12969 | − | 1.98265i | 0.145136 | − | 0.0919432i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.8989i | 1.01336i | 0.862134 | + | 0.506680i | \(0.169127\pi\) | ||||
−0.862134 | + | 0.506680i | \(0.830873\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.9982 | −2.03165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.4961 | −1.12872 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.988790i | 0.0454646i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.6850 | + | 33.1944i | −0.719676 | + | 1.52306i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.55573i | − | 0.437527i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.0916 | 0.780934 | 0.390467 | − | 0.920617i | \(-0.372314\pi\) | ||||
0.390467 | + | 0.920617i | \(0.372314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.78654 | 0.309440 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.08378i | − | 0.185818i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0791227 | − | 0.0501241i | 0.00359278 | − | 0.00227602i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.87434i | 0.0849343i | 0.999098 | + | 0.0424672i | \(0.0135218\pi\) | ||||
−0.999098 | + | 0.0424672i | \(0.986478\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3137 | 0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7704 | −0.486063 | −0.243031 | − | 0.970018i | \(-0.578142\pi\) | ||||
−0.243031 | + | 0.970018i | \(0.578142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.14704i | − | 0.231811i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.470600 | + | 0.742860i | 0.0211519 | + | 0.0333891i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.5669i | 0.832841i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.5259 | −1.50082 | −0.750412 | − | 0.660971i | \(-0.770145\pi\) | ||||
−0.750412 | + | 0.660971i | \(0.770145\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.7770 | 0.704864 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.58473i | 0.338186i | 0.985600 | + | 0.169093i | \(0.0540839\pi\) | ||||
−0.985600 | + | 0.169093i | \(0.945916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.5297 | − | 22.9357i | −0.646563 | − | 1.02062i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.0145 | −1.68497 | −0.842483 | − | 0.538724i | \(-0.818907\pi\) | ||||
−0.842483 | + | 0.538724i | \(0.818907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.5089 | 1.70354 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.34271i | − | 0.324188i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0327737 | − | 0.0207621i | 0.00144418 | − | 0.000914886i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.18322i | 0.0520380i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9706 | −0.657135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2420 | −0.799197 | −0.399599 | − | 0.916690i | \(-0.630851\pi\) | ||||
−0.399599 | + | 0.916690i | \(0.630851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10.1720i | − | 0.444791i | −0.974957 | − | 0.222396i | \(-0.928612\pi\) | ||
0.974957 | − | 0.222396i | \(-0.0713876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.04189 | − | 12.7865i | 0.263690 | − | 0.558050i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.2941i | − | 0.448417i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9153 | 0.909363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.393270 | 0.0170665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.77786i | − | 0.163637i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.96888 | − | 2.51428i | 0.171590 | − | 0.108702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.84578i | 0.209111i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.393270 | −0.0169393 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.98923 | 0.0855236 | 0.0427618 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427618 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 7.99912i | − | 0.343275i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.43472 | + | 11.7360i | 0.318468 | + | 0.502714i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.31817i | 0.0563609i | 0.999603 | + | 0.0281804i | \(0.00897130\pi\) | ||||
−0.999603 | + | 0.0281804i | \(0.991029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.0414 | −0.471238 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.08290 | 0.259140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2576i | 1.79698i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.12101 | + | 12.8193i | 0.344718 | + | 0.544150i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.0804i | 0.511861i | 0.966695 | + | 0.255931i | \(0.0823819\pi\) | ||||
−0.966695 | + | 0.255931i | \(0.917618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.51428 | 0.106343 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.44339 | 0.103160 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9930i | 0.969039i | 0.874781 | + | 0.484519i | \(0.161005\pi\) | ||||
−0.874781 | + | 0.484519i | \(0.838995\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.69453 | + | 1.70698i | −0.113360 | + | 0.0718131i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.0370 | −1.21729 | −0.608647 | − | 0.793441i | \(-0.708287\pi\) | ||||
−0.608647 | + | 0.793441i | \(0.708287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.56950 | 0.233076 | 0.116538 | − | 0.993186i | \(-0.462820\pi\) | ||||
0.116538 | + | 0.993186i | \(0.462820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 20.4260i | − | 0.853310i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.52717 | − | 3.08421i | −0.272202 | − | 0.128621i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.2822i | − | 0.844357i | −0.906513 | − | 0.422179i | \(-0.861266\pi\) | ||
0.906513 | − | 0.422179i | \(-0.138734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.0237 | 0.998389 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 46.5652 | 1.93185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.75798i | 0.155640i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.88893 | − | 1.19663i | 0.0780977 | − | 0.0494748i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.82377i | 0.364196i | 0.983280 | + | 0.182098i | \(0.0582888\pi\) | ||||
−0.983280 | + | 0.182098i | \(0.941711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.1658 | 0.501283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.80642 | 0.197710 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.2213i | − | 0.419737i | −0.977730 | − | 0.209868i | \(-0.932696\pi\) | ||
0.977730 | − | 0.209868i | \(-0.0673036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.0286 | − | 33.1944i | −0.862087 | − | 1.36084i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9403i | 0.611467i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.4925 | 0.755582 | 0.377791 | − | 0.925891i | \(-0.376684\pi\) | ||||
0.377791 | + | 0.925891i | \(0.376684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0129 | 1.06109 | 0.530544 | − | 0.847657i | \(-0.321988\pi\) | ||||
0.530544 | + | 0.847657i | \(0.321988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 15.5557i | − | 0.633478i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.9779 | + | 20.4861i | 0.527627 | + | 0.832879i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1227i | 0.979109i | 0.871973 | + | 0.489554i | \(0.162841\pi\) | ||||
−0.871973 | + | 0.489554i | \(0.837159\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.34315 | −0.0949491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00868 | 0.121718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.2056i | − | 1.38155i | −0.723070 | − | 0.690775i | \(-0.757270\pi\) | ||
0.723070 | − | 0.690775i | \(-0.242730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.13613 | − | 4.52072i | 0.287757 | − | 0.182293i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.3622i | − | 0.497682i | −0.968544 | − | 0.248841i | \(-0.919950\pi\) | ||
0.968544 | − | 0.248841i | \(-0.0800496\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6685 | 0.468997 | 0.234498 | − | 0.972117i | \(-0.424655\pi\) | ||||
0.234498 | + | 0.972117i | \(0.424655\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.44383 | 0.0579390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.3700i | 1.09655i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.8739 | − | 19.3137i | −0.634956 | − | 0.772548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.88767i | 0.115322i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.1649 | 1.68123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.79775 | 0.151186 | 0.0755930 | − | 0.997139i | \(-0.475915\pi\) | ||||
0.0755930 | + | 0.997139i | \(0.475915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.82799i | − | 0.0726560i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.83920 | − | 1.79863i | 0.112670 | − | 0.0713763i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.56440 | −0.259684 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.91008 | −0.272932 | −0.136466 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136466 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.50139i | 0.0986452i | 0.998783 | + | 0.0493226i | \(0.0157062\pi\) | ||||
−0.998783 | + | 0.0493226i | \(0.984294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00868 | + | 4.74930i | 0.118466 | + | 0.187004i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.3124i | − | 1.19170i | −0.803095 | − | 0.595852i | \(-0.796815\pi\) | ||
0.803095 | − | 0.595852i | \(-0.203185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.154661 | −0.00607098 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.68629 | −0.183670 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.4537i | 1.30915i | 0.755999 | + | 0.654573i | \(0.227151\pi\) | ||||
−0.755999 | + | 0.654573i | \(0.772849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.61541 | − | 7.28559i | −0.180339 | − | 0.284671i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.6150i | 0.531170i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.2942 | 1.21905 | 0.609525 | − | 0.792767i | \(-0.291360\pi\) | ||||
0.609525 | + | 0.792767i | \(0.291360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1119 | 1.56017 | 0.780086 | − | 0.625672i | \(-0.215175\pi\) | ||||
0.780086 | + | 0.625672i | \(0.215175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.21302i | − | 0.241294i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39.2299 | − | 24.8521i | 1.52127 | − | 0.963723i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.19611i | 0.0463136i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.07045 | −0.273359 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.34227 | 0.167631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.99386i | − | 0.192499i | −0.995357 | − | 0.0962496i | \(-0.969315\pi\) | ||
0.995357 | − | 0.0962496i | \(-0.0306847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.52072 | + | 2.13613i | 0.174003 | + | 0.0822197i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.0174i | − | 0.615597i | −0.951452 | − | 0.307798i | \(-0.900408\pi\) | ||
0.951452 | − | 0.307798i | \(-0.0995922\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.118476 | −0.00454668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.43560 | −0.208292 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.5400i | 1.35990i | 0.733258 | + | 0.679951i | \(0.237999\pi\) | ||||
−0.733258 | + | 0.679951i | \(0.762001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.2890 | − | 19.8215i | 1.19549 | − | 0.757342i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.8147i | − | 0.946738i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.55573 | 0.364044 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0393 | 0.496040 | 0.248020 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248020 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.11233i | − | 0.0422541i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.7865 | + | 20.1840i | 0.485021 | + | 0.765624i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 23.4720i | − | 0.889064i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.4256 | 0.886038 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.502632 | −0.0189841 | −0.00949207 | − | 0.999955i | \(-0.503021\pi\) | ||||
−0.00949207 | + | 0.999955i | \(0.503021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.8316i | 1.87943i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.60029 | + | 5.68318i | 0.135595 | + | 0.214041i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.3431i | 1.29161i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0712 | −1.58002 | −0.790009 | − | 0.613095i | \(-0.789924\pi\) | ||||
−0.790009 | + | 0.613095i | \(0.789924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.9403 | −0.560306 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.39222i | 0.0895893i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.742860 | + | 0.470600i | −0.0277814 | + | 0.0175995i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.7779i | 0.813309i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7848 | −1.22267 | −0.611333 | − | 0.791373i | \(-0.709366\pi\) | ||||
−0.611333 | + | 0.791373i | \(0.709366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0490743 | −0.00182762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 15.2126i | − | 0.565762i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.76963 | + | 3.74509i | −0.0657223 | + | 0.139089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 49.5246i | − | 1.83677i | −0.395692 | − | 0.918383i | \(-0.629495\pi\) | ||
0.395692 | − | 0.918383i | \(-0.370505\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6213 | 0.577774 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.11848i | 0.0782477i | 0.999234 | + | 0.0391238i | \(0.0124567\pi\) | ||||
−0.999234 | + | 0.0391238i | \(0.987543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.88893 | + | 1.19663i | −0.0696743 | + | 0.0441385i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.11760i | 0.225345i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.7014 | 1.75473 | 0.877363 | − | 0.479827i | \(-0.159301\pi\) | ||||
0.877363 | + | 0.479827i | \(0.159301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34271 | 0.269741 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.8055i | − | 1.20352i | −0.798677 | − | 0.601759i | \(-0.794467\pi\) | ||
0.798677 | − | 0.601759i | \(-0.205533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.84652 | + | 7.65041i | 0.177563 | + | 0.280289i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.4633i | 0.602360i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.94288 | −0.217148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.852087 | −0.0310931 | −0.0155465 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155465 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 17.9399i | − | 0.653766i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.01735 | − | 9.49861i | −0.218994 | − | 0.345690i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.68454i | − | 0.242954i | −0.992594 | − | 0.121477i | \(-0.961237\pi\) | ||
0.992594 | − | 0.121477i | \(-0.0387630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.567816 | −0.0206104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.92578 | −0.106059 | −0.0530297 | − | 0.998593i | \(-0.516888\pi\) | ||||
−0.0530297 | + | 0.998593i | \(0.516888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.5731i | − | 0.636188i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.7360 | − | 7.43472i | 0.424315 | − | 0.268803i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.393270i | 0.0142001i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.6274 | 0.455356 | 0.227678 | − | 0.973736i | \(-0.426887\pi\) | ||||
0.227678 | + | 0.973736i | \(0.426887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.88810 | −0.140027 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 15.9454i | − | 0.573517i | −0.958003 | − | 0.286758i | \(-0.907422\pi\) | ||
0.958003 | − | 0.286758i | \(-0.0925777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.53926 | + | 7.49018i | −0.127134 | + | 0.269055i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 19.1952i | − | 0.688625i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.7398 | 0.993880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.58158 | 0.0923763 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 0.828427i | − | 0.0296056i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.2714 | − | 29.3128i | 1.65150 | − | 1.04622i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.5825i | 1.73178i | 0.500234 | + | 0.865890i | \(0.333247\pi\) | ||||
−0.500234 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.296797 | −0.0105662 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.03470 | 0.143457 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.0414i | − | 0.392093i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.4347 | + | 18.0501i | 0.405548 | + | 0.640172i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8971i | 0.704792i | 0.935851 | + | 0.352396i | \(0.114633\pi\) | ||||
−0.935851 | + | 0.352396i | \(0.885367\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.6930 | 0.661310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.67674 | −0.341911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5.35436i | − | 0.188951i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.88679 | + | 7.71397i | 0.172237 | + | 0.271882i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.25447i | 0.0441595i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.5487 | 0.441189 | 0.220595 | − | 0.975366i | \(-0.429200\pi\) | ||||
0.220595 | + | 0.975366i | \(0.429200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.9149 | 1.08557 | 0.542785 | − | 0.839872i | \(-0.317370\pi\) | ||||
0.542785 | + | 0.839872i | \(0.317370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.81510i | 0.344231i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.9266 | + | 18.3249i | −1.01325 | + | 0.641894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4616i | 0.645890i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.9308 | −1.04459 | −0.522296 | − | 0.852765i | \(-0.674924\pi\) | ||||
−0.522296 | + | 0.852765i | \(0.674924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1831i | 0.564109i | 0.959398 | + | 0.282055i | \(0.0910159\pi\) | ||||
−0.959398 | + | 0.282055i | \(0.908984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.77786 | − | 0.840075i | −0.0618973 | − | 0.0292477i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.2022i | 1.88479i | 0.334497 | + | 0.942397i | \(0.391434\pi\) | ||||
−0.334497 | + | 0.942397i | \(0.608566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.2929 | 1.46889 | 0.734447 | − | 0.678666i | \(-0.237442\pi\) | ||||
0.734447 | + | 0.678666i | \(0.237442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.35603 | 0.151109 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.21302i | 0.215268i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.8017 | + | 18.8793i | −1.03133 | + | 0.653345i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.65685i | − | 0.0572693i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.7873 | −1.27004 | −0.635020 | − | 0.772496i | \(-0.719008\pi\) | ||||
−0.635020 | + | 0.772496i | \(0.719008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.45207i | 0.118896i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.19663 | + | 1.88893i | 0.0411655 | + | 0.0649812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30.6753i | − | 1.05401i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.25937 | 0.0775414 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79863 | −0.335893 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4148i | 0.527794i | 0.964551 | + | 0.263897i | \(0.0850079\pi\) | ||||
−0.964551 | + | 0.263897i | \(0.914992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.78654 | + | 13.8699i | 0.300493 | + | 0.474340i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0628221i | 0.00214596i | 0.999999 | + | 0.00107298i | \(0.000341540\pi\) | ||||
−0.999999 | + | 0.00107298i | \(0.999658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.6577 | −0.977787 | −0.488893 | − | 0.872344i | \(-0.662599\pi\) | ||||
−0.488893 | + | 0.872344i | \(0.662599\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.6854 | −0.364158 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.96189i | 0.202945i | 0.994838 | + | 0.101473i | \(0.0323554\pi\) | ||||
−0.994838 | + | 0.101473i | \(0.967645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2784 | − | 17.9143i | 0.961494 | − | 0.609104i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 21.6016i | − | 0.733630i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.87558 | 0.199315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5557 | 0.527086 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.0418875i | − | 0.00141768i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.88810 | + | 31.3828i | 0.131442 | + | 1.06093i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.70276i | − | 0.226336i | −0.993576 | − | 0.113168i | \(-0.963900\pi\) | ||
0.993576 | − | 0.113168i | \(-0.0360999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.5358 | 0.658928 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8624 | 1.34300 | 0.671500 | − | 0.741005i | \(-0.265651\pi\) | ||||
0.671500 | + | 0.741005i | \(0.265651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.7131i | − | 0.730704i | −0.930869 | − | 0.365352i | \(-0.880949\pi\) | ||
0.930869 | − | 0.365352i | \(-0.119051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.742860 | + | 0.470600i | −0.0249710 | + | 0.0158191i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3757i | 1.72503i | 0.506035 | + | 0.862513i | \(0.331111\pi\) | ||||
−0.506035 | + | 0.862513i | \(0.668889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.25133 | −0.142585 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.393270 | 0.0131750 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.0918i | 0.739275i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.79863 | − | 9.15335i | −0.193827 | − | 0.305963i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.44383i | 0.0482082i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.37258 | 0.0457782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.3700 | 1.97790 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 7.11146i | − | 0.236654i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.57203 | + | 15.1098i | 0.318185 | + | 0.502267i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21.3966i | − | 0.710463i | −0.934778 | − | 0.355231i | \(-0.884402\pi\) | ||
0.934778 | − | 0.355231i | \(-0.115598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.1421 | −0.402729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.0044 | −1.68985 | −0.844925 | − | 0.534884i | \(-0.820355\pi\) | ||||
−0.844925 | + | 0.534884i | \(0.820355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.47451i | − | 0.214275i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.8565 | − | 13.2126i | 0.689496 | − | 0.436795i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.9092i | 0.360254i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3664 | −0.374942 | −0.187471 | − | 0.982270i | \(-0.560029\pi\) | ||||
−0.187471 | + | 0.982270i | \(0.560029\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.8142 | 0.916510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 6.56440i | − | 0.216070i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.6801 | − | 14.4969i | −1.00875 | − | 0.476656i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.0173504i | − | 0.000569861i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.9344 | −1.57268 | −0.786338 | − | 0.617797i | \(-0.788025\pi\) | ||||
−0.786338 | + | 0.617797i | \(0.788025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.34271 | −0.240648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.10113i | 0.0687878i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.61541 | + | 2.92385i | −0.150940 | + | 0.0956201i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.3266i | − | 0.762047i | −0.924565 | − | 0.381023i | \(-0.875572\pi\) | ||
0.924565 | − | 0.381023i | \(-0.124428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.64397 | 0.314719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.6316 | −1.29195 | −0.645977 | − | 0.763357i | \(-0.723550\pi\) | ||||
−0.645977 | + | 0.763357i | \(0.723550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.45460i | 0.177626i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.38459 | − | 5.34271i | −0.110101 | − | 0.173798i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 19.7770i | − | 0.642666i | −0.946966 | − | 0.321333i | \(-0.895869\pi\) | ||
0.946966 | − | 0.321333i | \(-0.104131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6150 | −0.441961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1201 | 0.522731 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2847i | 1.46692i | 0.679735 | + | 0.733458i | \(0.262095\pi\) | ||||
−0.679735 | + | 0.733458i | \(0.737905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.4425 | + | 38.5834i | 0.790941 | + | 1.24853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.325795i | 0.0105315i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.8512 | −1.51290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.10113i | − | 0.0677078i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.3791 | + | 28.7475i | −1.46080 | + | 0.925416i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3903i | 0.430603i | 0.976548 | + | 0.215301i | \(0.0690734\pi\) | ||||
−0.976548 | + | 0.215301i | \(0.930927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.6204 | 1.46554 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.6150 | −1.27130 | −0.635652 | − | 0.771975i | \(-0.719269\pi\) | ||||
−0.635652 | + | 0.771975i | \(0.719269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 30.2229i | − | 0.968902i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.13613 | + | 4.52072i | −0.0684109 | + | 0.144779i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 19.2100i | − | 0.614584i | −0.951615 | − | 0.307292i | \(-0.900577\pi\) | ||
0.951615 | − | 0.307292i | \(-0.0994228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.80557 | 0.121627 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.21302 | 0.198367 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.3960i | 1.03327i | 0.856205 | + | 0.516636i | \(0.172816\pi\) | ||||
−0.856205 | + | 0.516636i | \(0.827184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.07901 | + | 5.75154i | −0.289281 | + | 0.183259i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 8.50982i | − | 0.270871i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.63020 | −0.115434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5107 | 0.333883 | 0.166942 | − | 0.985967i | \(-0.446611\pi\) | ||||
0.166942 | + | 0.985967i | \(0.446611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9537i | 0.442806i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.8781 | − | 28.2213i | −0.566774 | − | 0.894674i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0753i | 1.30087i | 0.759563 | + | 0.650433i | \(0.225413\pi\) | ||||
−0.759563 | + | 0.650433i | \(0.774587\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.78654 | 0.214717 |
(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 | 1560.2.l.e.1249.6 | yes | 8 | |
3.2 | odd | 2 | 4680.2.l.f.2809.6 | 8 | |||
4.3 | odd | 2 | 3120.2.l.o.1249.2 | 8 | |||
5.2 | odd | 4 | 7800.2.a.bw.1.2 | 4 | |||
5.3 | odd | 4 | 7800.2.a.bv.1.4 | 4 | |||
5.4 | even | 2 | inner | 1560.2.l.e.1249.2 | ✓ | 8 | |
15.14 | odd | 2 | 4680.2.l.f.2809.5 | 8 | |||
20.19 | odd | 2 | 3120.2.l.o.1249.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.e.1249.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
1560.2.l.e.1249.6 | yes | 8 | 1.1 | even | 1 | trivial | |
3120.2.l.o.1249.2 | 8 | 4.3 | odd | 2 | |||
3120.2.l.o.1249.6 | 8 | 20.19 | odd | 2 | |||
4680.2.l.f.2809.5 | 8 | 15.14 | odd | 2 | |||
4680.2.l.f.2809.6 | 8 | 3.2 | odd | 2 | |||
7800.2.a.bv.1.4 | 4 | 5.3 | odd | 4 | |||
7800.2.a.bw.1.2 | 4 | 5.2 | odd | 4 |