Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(239,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.239 |
Dual form | 1344.2.s.a.911.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.41421 | + | 2.41421i | 1.07967 | + | 1.07967i | 0.996539 | + | 0.0831305i | \(0.0264918\pi\) |
0.0831305 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.82843 | − | 1.82843i | 0.551292 | − | 0.551292i | −0.375522 | − | 0.926813i | \(-0.622537\pi\) |
0.926813 | + | 0.375522i | \(0.122537\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58579 | − | 1.58579i | −0.439818 | − | 0.439818i | 0.452133 | − | 0.891951i | \(-0.350663\pi\) |
−0.891951 | + | 0.452133i | \(0.850663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 5.82843i | −0.258199 | − | 1.50489i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.82843i | − | 1.65614i | −0.560627 | − | 0.828068i | \(-0.689440\pi\) | ||
0.560627 | − | 0.828068i | \(-0.310560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41421 | − | 2.41421i | 0.553859 | − | 0.553859i | −0.373694 | − | 0.927552i | \(-0.621909\pi\) |
0.927552 | + | 0.373694i | \(0.121909\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | − | 1.00000i | −0.308607 | − | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.65685i | 0.762507i | 0.924471 | + | 0.381253i | \(0.124507\pi\) | ||||
−0.924471 | + | 0.381253i | \(0.875493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685i | 1.33137i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | − | 3.00000i | 0.557086 | − | 0.557086i | −0.371391 | − | 0.928477i | \(-0.621119\pi\) |
0.928477 | + | 0.371391i | \(0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4853i | 1.88321i | 0.336717 | + | 0.941606i | \(0.390684\pi\) | ||||
−0.336717 | + | 0.941606i | \(0.609316\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.41421 | + | 0.757359i | −0.768416 | + | 0.131839i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.41421 | + | 2.41421i | 0.408077 | + | 0.408077i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.82843 | + | 3.82843i | −0.629390 | + | 0.629390i | −0.947914 | − | 0.318525i | \(-0.896813\pi\) |
0.318525 | + | 0.947914i | \(0.396813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.656854 | + | 3.82843i | 0.105181 | + | 0.613039i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6569 | 1.82049 | 0.910247 | − | 0.414065i | \(-0.135891\pi\) | ||||
0.910247 | + | 0.414065i | \(0.135891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82843 | − | 1.82843i | −0.278833 | − | 0.278833i | 0.553810 | − | 0.832643i | \(-0.313173\pi\) |
−0.832643 | + | 0.553810i | \(0.813173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.41421 | + | 9.24264i | −0.658032 | + | 1.37781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.82843 | + | 9.65685i | −0.956171 | + | 1.35223i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.171573 | + | 0.171573i | 0.0235673 | + | 0.0235673i | 0.718792 | − | 0.695225i | \(-0.244695\pi\) |
−0.695225 | + | 0.718792i | \(0.744695\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.82843 | 1.19042 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.82843 | + | 1.00000i | −0.771994 | + | 0.132453i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.07107 | − | 4.07107i | 0.530008 | − | 0.530008i | −0.390567 | − | 0.920575i | \(-0.627721\pi\) |
0.920575 | + | 0.390567i | \(0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.414214 | − | 0.414214i | −0.0530346 | − | 0.0530346i | 0.680092 | − | 0.733127i | \(-0.261940\pi\) |
−0.733127 | + | 0.680092i | \(0.761940\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | + | 2.82843i | 0.125988 | + | 0.356348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.65685i | − | 0.949716i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | − | 7.00000i | 0.855186 | − | 0.855186i | −0.135580 | − | 0.990766i | \(-0.543290\pi\) |
0.990766 | + | 0.135580i | \(0.0432899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.65685 | − | 5.17157i | 0.440234 | − | 0.622584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8284i | 1.26737i | 0.773591 | + | 0.633686i | \(0.218459\pi\) | ||||
−0.773591 | + | 0.633686i | \(0.781541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65685 | − | 9.41421i | 0.768667 | − | 1.08706i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.82843 | − | 1.82843i | 0.208369 | − | 0.208369i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.00000i | − | 0.225018i | −0.993651 | − | 0.112509i | \(-0.964111\pi\) | ||
0.993651 | − | 0.112509i | \(-0.0358886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8995 | − | 10.8995i | −1.19637 | − | 1.19637i | −0.975244 | − | 0.221131i | \(-0.929025\pi\) |
−0.221131 | − | 0.975244i | \(-0.570975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.4853 | − | 16.4853i | 1.78808 | − | 1.78808i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.24264 | + | 1.24264i | −0.776493 | + | 0.133225i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.34315 | 0.460373 | 0.230186 | − | 0.973147i | \(-0.426066\pi\) | ||||
0.230186 | + | 0.973147i | \(0.426066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.58579 | − | 1.58579i | −0.166236 | − | 0.166236i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.4853 | − | 14.8284i | 1.08727 | − | 1.53764i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.6569 | 1.19597 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.00000 | + | 3.34315i | 0.703526 | + | 0.335999i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.07107 | + | 4.07107i | 0.405086 | + | 0.405086i | 0.880021 | − | 0.474935i | \(-0.157528\pi\) |
−0.474935 | + | 0.880021i | \(0.657528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3137 | 1.11477 | 0.557386 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557386 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 5.82843i | −0.0975900 | − | 0.568796i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.00000 | + | 5.00000i | −0.483368 | + | 0.483368i | −0.906206 | − | 0.422837i | \(-0.861034\pi\) |
0.422837 | + | 0.906206i | \(0.361034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.171573 | + | 0.171573i | 0.0164337 | + | 0.0164337i | 0.715276 | − | 0.698842i | \(-0.246301\pi\) |
−0.698842 | + | 0.715276i | \(0.746301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.24264 | − | 1.58579i | 0.877273 | − | 0.150516i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.65685i | 0.908440i | 0.890889 | + | 0.454220i | \(0.150082\pi\) | ||||
−0.890889 | + | 0.454220i | \(0.849918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.82843 | + | 8.82843i | −0.823255 | + | 0.823255i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.89949 | − | 6.07107i | 0.268058 | − | 0.561270i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.82843i | − | 0.625961i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.31371i | 0.392155i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.4853 | − | 11.6569i | −1.48643 | − | 1.05106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.00000 | + | 4.00000i | −0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315i | 0.385392i | 0.981259 | + | 0.192696i | \(0.0617231\pi\) | ||||
−0.981259 | + | 0.192696i | \(0.938277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.757359 | + | 4.41421i | 0.0666818 | + | 0.388650i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0711 | + | 10.0711i | 0.879913 | + | 0.879913i | 0.993525 | − | 0.113612i | \(-0.0362421\pi\) |
−0.113612 | + | 0.993525i | \(0.536242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.41421 | − | 2.41421i | 0.209339 | − | 0.209339i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.4853 | − | 8.65685i | 1.33276 | − | 0.745063i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.65685 | −0.312426 | −0.156213 | − | 0.987723i | \(-0.549929\pi\) | ||||
−0.156213 | + | 0.987723i | \(0.549929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.58579 | + | 1.58579i | 0.134505 | + | 0.134505i | 0.771154 | − | 0.636649i | \(-0.219680\pi\) |
−0.636649 | + | 0.771154i | \(0.719680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | − | 5.65685i | −0.673722 | − | 0.476393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.79899 | −0.484936 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4853 | 1.20294 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.41421 | − | 1.00000i | −0.116642 | − | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.48528 | + | 7.48528i | 0.613218 | + | 0.613218i | 0.943783 | − | 0.330565i | \(-0.107239\pi\) |
−0.330565 | + | 0.943783i | \(0.607239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.34315 | 0.516198 | 0.258099 | − | 0.966118i | \(-0.416904\pi\) | ||||
0.258099 | + | 0.966118i | \(0.416904\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.3137 | − | 6.82843i | 1.56142 | − | 0.552046i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.3137 | + | 25.3137i | −2.03325 | + | 2.03325i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8995 | − | 16.8995i | −1.34873 | − | 1.34873i | −0.887047 | − | 0.461680i | \(-0.847247\pi\) |
−0.461680 | − | 0.887047i | \(-0.652753\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0710678 | − | 0.414214i | −0.00563604 | − | 0.0328493i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.65685i | 0.288200i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.82843 | + | 3.82843i | −0.299866 | + | 0.299866i | −0.840961 | − | 0.541096i | \(-0.818010\pi\) |
0.541096 | + | 0.840961i | \(0.318010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.4853 | − | 8.82843i | −0.971978 | − | 0.687292i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8284i | 0.992693i | 0.868124 | + | 0.496347i | \(0.165326\pi\) | ||||
−0.868124 | + | 0.496347i | \(0.834674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.97056i | − | 0.613120i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.24264 | + | 4.41421i | 0.706802 | + | 0.337563i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8995 | − | 14.8995i | 1.13279 | − | 1.13279i | 0.143076 | − | 0.989712i | \(-0.454301\pi\) |
0.989712 | − | 0.143076i | \(-0.0456993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.65685i | 0.503211i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.82843 | + | 1.68629i | −0.738750 | + | 0.126749i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | − | 15.0000i | −1.12115 | − | 1.12115i | −0.991568 | − | 0.129584i | \(-0.958636\pi\) |
−0.129584 | − | 0.991568i | \(-0.541364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0711 | − | 12.0711i | 0.897235 | − | 0.897235i | −0.0979554 | − | 0.995191i | \(-0.531230\pi\) |
0.995191 | + | 0.0979554i | \(0.0312303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.171573 | + | 1.00000i | 0.0126830 | + | 0.0739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.4853 | −1.35906 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4853 | − | 12.4853i | −0.913014 | − | 0.913014i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | − | 5.00000i | 0.102869 | − | 0.363696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6569 | −1.27761 | −0.638803 | − | 0.769371i | \(-0.720570\pi\) | ||||
−0.638803 | + | 0.769371i | \(0.720570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34315 | 0.312626 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.65685 | + | 10.8284i | −0.548319 | + | 0.775440i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.171573 | + | 0.171573i | 0.0122241 | + | 0.0122241i | 0.713192 | − | 0.700968i | \(-0.247249\pi\) |
−0.700968 | + | 0.713192i | \(0.747249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.8995 | + | 2.89949i | −1.19200 | + | 0.204515i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | − | 3.00000i | 0.210559 | − | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.1421 | + | 28.1421i | 1.96553 | + | 1.96553i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3431 | + | 3.65685i | −0.718898 | + | 0.254169i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.82843i | − | 0.610675i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | + | 5.00000i | −0.344214 | + | 0.344214i | −0.857949 | − | 0.513735i | \(-0.828262\pi\) |
0.513735 | + | 0.857949i | \(0.328262\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | + | 8.48528i | −0.411113 | + | 0.581402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.82843i | − | 0.602094i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4853i | 0.711787i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.8284 | − | 15.3137i | 0.731717 | − | 1.03480i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8284 | + | 10.8284i | −0.728399 | + | 0.728399i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8284i | 0.859055i | 0.903054 | + | 0.429528i | \(0.141320\pi\) | ||||
−0.903054 | + | 0.429528i | \(0.858680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.8284 | + | 6.65685i | −1.25523 | + | 0.443790i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.07107 | + | 6.07107i | 0.402951 | + | 0.402951i | 0.879272 | − | 0.476321i | \(-0.158030\pi\) |
−0.476321 | + | 0.879272i | \(0.658030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.89949 | + | 8.89949i | −0.588095 | + | 0.588095i | −0.937115 | − | 0.349020i | \(-0.886515\pi\) |
0.349020 | + | 0.937115i | \(0.386515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.41421 | + | 0.757359i | −0.290434 | + | 0.0498306i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.3137 | −1.39631 | −0.698154 | − | 0.715948i | \(-0.745995\pi\) | ||||
−0.698154 | + | 0.715948i | \(0.745995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.6569 | + | 13.6569i | 0.890875 | + | 0.890875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | + | 2.82843i | −0.129914 | + | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6569 | 0.750884 | 0.375442 | − | 0.926846i | \(-0.377491\pi\) | ||||
0.375442 | + | 0.926846i | \(0.377491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.41421 | + | 2.41421i | 0.154238 | + | 0.154238i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.65685 | −0.487194 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.51472 | + | 26.3137i | 0.286109 | + | 1.66756i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.414214 | + | 0.414214i | −0.0261449 | + | 0.0261449i | −0.720058 | − | 0.693913i | \(-0.755885\pi\) |
0.693913 | + | 0.720058i | \(0.255885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.68629 | + | 6.68629i | 0.420364 | + | 0.420364i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −39.7990 | + | 6.82843i | −2.49231 | + | 0.427613i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.1716i | − | 1.32065i | −0.750982 | − | 0.660323i | \(-0.770419\pi\) | ||
0.750982 | − | 0.660323i | \(-0.229581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.82843 | + | 3.82843i | −0.237887 | + | 0.237887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4853 | + | 5.48528i | 0.710921 | + | 0.339530i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.343146i | − | 0.0211593i | −0.999944 | − | 0.0105796i | \(-0.996632\pi\) | ||
0.999944 | − | 0.0105796i | \(-0.00336767\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.828427i | 0.0508899i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.14214 | − | 4.34315i | −0.375893 | − | 0.265796i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.41421 | + | 8.41421i | −0.513024 | + | 0.513024i | −0.915452 | − | 0.402428i | \(-0.868166\pi\) |
0.402428 | + | 0.915452i | \(0.368166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.1716i | − | 0.678625i | −0.940674 | − | 0.339312i | \(-0.889806\pi\) | ||
0.940674 | − | 0.339312i | \(-0.110194\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.656854 | + | 3.82843i | 0.0397546 | + | 0.231707i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.1716 | + | 12.1716i | 0.733973 | + | 0.733973i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3137 | + | 16.3137i | −0.980196 | + | 0.980196i | −0.999808 | − | 0.0196119i | \(-0.993757\pi\) |
0.0196119 | + | 0.999808i | \(0.493757\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.6569 | + | 10.4853i | −1.77551 | + | 0.627737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3137 | −1.74871 | −0.874355 | − | 0.485288i | \(-0.838715\pi\) | ||||
−0.874355 | + | 0.485288i | \(0.838715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.89949 | − | 6.89949i | −0.410132 | − | 0.410132i | 0.471652 | − | 0.881785i | \(-0.343658\pi\) |
−0.881785 | + | 0.471652i | \(0.843658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.4853 | − | 11.6569i | −0.976504 | − | 0.690492i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6569 | 0.688082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82843 | + | 2.00000i | 0.165805 | + | 0.117242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.757359 | + | 0.757359i | 0.0442454 | + | 0.0442454i | 0.728883 | − | 0.684638i | \(-0.240040\pi\) |
−0.684638 | + | 0.728883i | \(0.740040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.6569 | 1.14447 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.55635 | − | 11.7279i | −0.380438 | − | 0.680523i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.79899 | − | 5.79899i | 0.335364 | − | 0.335364i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.82843 | − | 1.82843i | −0.105389 | − | 0.105389i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.68629 | − | 9.82843i | −0.0968749 | − | 0.564628i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.00000i | − | 0.114520i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.89949 | + | 4.89949i | −0.279629 | + | 0.279629i | −0.832961 | − | 0.553332i | \(-0.813356\pi\) |
0.553332 | + | 0.832961i | \(0.313356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | − | 11.3137i | −0.910208 | − | 0.643614i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.4853i | 1.04820i | 0.851655 | + | 0.524102i | \(0.175599\pi\) | ||||
−0.851655 | + | 0.524102i | \(0.824401\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.51472i | 0.198664i | 0.995054 | + | 0.0993318i | \(0.0316705\pi\) | ||||
−0.995054 | + | 0.0993318i | \(0.968329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.41421 | + | 9.24264i | −0.248713 | + | 0.520764i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1421 | + | 15.1421i | −0.850467 | + | 0.850467i | −0.990191 | − | 0.139723i | \(-0.955379\pi\) |
0.139723 | + | 0.990191i | \(0.455379\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.9706i | − | 0.614234i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0711 | − | 2.07107i | 0.673741 | − | 0.115596i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.4853 | − | 16.4853i | −0.917266 | − | 0.917266i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5563 | − | 10.5563i | 0.585561 | − | 0.585561i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0710678 | − | 0.414214i | −0.00393006 | − | 0.0229061i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1421 | + | 11.1421i | 0.612427 | + | 0.612427i | 0.943578 | − | 0.331151i | \(-0.107437\pi\) |
−0.331151 | + | 0.943578i | \(0.607437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6569 | − | 7.00000i | −0.803191 | − | 0.383598i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.7990 | 1.84664 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.68629 | 0.146332 | 0.0731658 | − | 0.997320i | \(-0.476690\pi\) | ||||
0.0731658 | + | 0.997320i | \(0.476690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.65685 | − | 13.6569i | 0.524488 | − | 0.741739i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.1716 | + | 19.1716i | 1.03820 | + | 1.03820i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.3137 | − | 3.65685i | 1.14749 | − | 0.196878i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1421 | + | 15.1421i | −0.812872 | + | 0.812872i | −0.985064 | − | 0.172191i | \(-0.944915\pi\) |
0.172191 | + | 0.985064i | \(0.444915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0711 | + | 12.0711i | 0.646149 | + | 0.646149i | 0.952060 | − | 0.305911i | \(-0.0989609\pi\) |
−0.305911 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.1716 | + | 5.68629i | −0.542918 | + | 0.303512i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.48528i | − | 0.451626i | −0.974171 | − | 0.225813i | \(-0.927496\pi\) | ||
0.974171 | − | 0.225813i | \(-0.0725038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4853 | − | 14.4853i | 0.768799 | − | 0.768799i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.82843 | + | 9.65685i | −0.361399 | + | 0.511095i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 31.6569i | − | 1.67078i | −0.549654 | − | 0.835392i | \(-0.685240\pi\) | ||
0.549654 | − | 0.835392i | \(-0.314760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.34315i | 0.386481i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.31371 | − | 6.10051i | 0.226411 | − | 0.320193i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.1421 | + | 26.1421i | −1.36834 | + | 1.36834i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.1421i | − | 0.633814i | −0.948457 | − | 0.316907i | \(-0.897356\pi\) | ||
0.948457 | − | 0.316907i | \(-0.102644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.6569 | + | 32.9706i | 0.606832 | + | 1.71638i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.171573 | + | 0.171573i | 0.00890762 | + | 0.00890762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3137 | − | 14.3137i | 0.741136 | − | 0.741136i | −0.231661 | − | 0.972797i | \(-0.574416\pi\) |
0.972797 | + | 0.231661i | \(0.0744160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.65685 | − | 1.65685i | 0.498678 | − | 0.0855596i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.51472 | −0.490033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.14214 | − | 1.14214i | −0.0586676 | − | 0.0586676i | 0.677164 | − | 0.735832i | \(-0.263209\pi\) |
−0.735832 | + | 0.677164i | \(0.763209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.34315 | − | 6.14214i | 0.222506 | − | 0.314671i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.31371 | −0.169323 | −0.0846613 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846613 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.82843 | 0.449938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.34315 | − | 7.00000i | 0.169942 | − | 0.355830i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.9706 | − | 13.9706i | −0.708336 | − | 0.708336i | 0.257849 | − | 0.966185i | \(-0.416986\pi\) |
−0.966185 | + | 0.257849i | \(0.916986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.17157 | − | 24.3137i | −0.210428 | − | 1.22646i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.82843 | − | 4.82843i | 0.242945 | − | 0.242945i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.72792 | + | 1.72792i | 0.0867219 | + | 0.0867219i | 0.749137 | − | 0.662415i | \(-0.230468\pi\) |
−0.662415 | + | 0.749137i | \(0.730468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.82843 | + | 1.00000i | −0.291786 | + | 0.0500626i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.31371i | − | 0.165479i | −0.996571 | − | 0.0827394i | \(-0.973633\pi\) | ||
0.996571 | − | 0.0827394i | \(-0.0263669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6274 | − | 16.6274i | 0.828271 | − | 0.828271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.5563 | − | 3.24264i | −1.51836 | − | 0.161128i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.0000i | 0.693954i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.8284i | − | 1.52437i | −0.647361 | − | 0.762184i | \(-0.724127\pi\) | ||
0.647361 | − | 0.762184i | \(-0.275873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.17157 | + | 3.65685i | 0.255095 | + | 0.180379i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.07107 | − | 4.07107i | 0.200324 | − | 0.200324i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 52.6274i | − | 2.58338i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.656854 | − | 3.82843i | −0.0321663 | − | 0.187479i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.75736 | − | 4.75736i | −0.232412 | − | 0.232412i | 0.581287 | − | 0.813699i | \(-0.302550\pi\) |
−0.813699 | + | 0.581287i | \(0.802550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3137 | + | 24.3137i | −1.18498 | + | 1.18498i | −0.206539 | + | 0.978438i | \(0.566220\pi\) |
−0.978438 | + | 0.206539i | \(0.933780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.65685 | + | 16.0000i | 0.275046 | + | 0.777947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 45.4558 | 2.20493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.414214 | − | 0.414214i | −0.0200452 | − | 0.0200452i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.20101 | + | 5.79899i | 0.395949 | + | 0.279978i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3137 | 0.930309 | 0.465154 | − | 0.885230i | \(-0.345999\pi\) | ||||
0.465154 | + | 0.885230i | \(0.345999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.3137 | −1.79318 | −0.896591 | − | 0.442859i | \(-0.853964\pi\) | ||||
−0.896591 | + | 0.442859i | \(0.853964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.4853 | − | 14.4853i | −0.982194 | − | 0.694516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.82843 | + | 8.82843i | 0.422321 | + | 0.422321i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.9706 | −1.57360 | −0.786800 | − | 0.617209i | \(-0.788263\pi\) | ||||
−0.786800 | + | 0.617209i | \(0.788263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.34315 | − | 5.34315i | 0.253861 | − | 0.253861i | −0.568691 | − | 0.822551i | \(-0.692550\pi\) |
0.822551 | + | 0.568691i | \(0.192550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4853 | + | 10.4853i | 0.497050 | + | 0.497050i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.10051 | − | 18.0711i | −0.146649 | − | 0.854732i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.9706i | 0.989662i | 0.868989 | + | 0.494831i | \(0.164770\pi\) | ||||
−0.868989 | + | 0.494831i | \(0.835230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3137 | − | 21.3137i | 1.00362 | − | 1.00362i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.97056 | − | 6.34315i | −0.421474 | − | 0.298027i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.65685i | − | 0.358959i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 37.9411i | − | 1.77481i | −0.460990 | − | 0.887405i | \(-0.652505\pi\) | ||
0.460990 | − | 0.887405i | \(-0.347495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −34.1421 | − | 9.65685i | −1.59362 | − | 0.450743i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5858 | − | 19.5858i | 0.912201 | − | 0.912201i | −0.0842441 | − | 0.996445i | \(-0.526848\pi\) |
0.996445 | + | 0.0842441i | \(0.0268476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.343146i | 0.0159473i | 0.999968 | + | 0.00797367i | \(0.00253812\pi\) | ||||
−0.999968 | + | 0.00797367i | \(0.997462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 61.1127 | − | 10.4853i | 2.83403 | − | 0.486243i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.5858 | − | 11.5858i | −0.536126 | − | 0.536126i | 0.386263 | − | 0.922389i | \(-0.373766\pi\) |
−0.922389 | + | 0.386263i | \(0.873766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | − | 7.00000i | 0.323230 | − | 0.323230i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00000 | + | 40.7990i | 0.322543 | + | 1.87992i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.68629 | −0.307436 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.0711 | + | 16.0711i | 0.737391 | + | 0.737391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.313708 | + | 0.656854i | −0.0143637 | + | 0.0300753i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.68629 | 0.214122 | 0.107061 | − | 0.994252i | \(-0.465856\pi\) | ||||
0.107061 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1421 | 0.553634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.65685 | − | 5.17157i | 0.166393 | − | 0.235315i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.82843 | − | 4.82843i | −0.219248 | − | 0.219248i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.2843 | −1.82545 | −0.912727 | − | 0.408569i | \(-0.866028\pi\) | ||||
−0.912727 | + | 0.408569i | \(0.866028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.24264 | − | 1.58579i | 0.417967 | − | 0.0717117i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3137 | + | 12.3137i | −0.555710 | + | 0.555710i | −0.928083 | − | 0.372373i | \(-0.878544\pi\) |
0.372373 | + | 0.928083i | \(0.378544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.4853 | − | 20.4853i | −0.922611 | − | 0.922611i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.82843 | + | 24.9706i | 0.396808 | + | 1.12234i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.00000i | − | 0.269137i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.3137 | + | 28.3137i | −1.26750 | + | 1.26750i | −0.320118 | + | 0.947378i | \(0.603723\pi\) |
−0.947378 | + | 0.320118i | \(0.896277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8284 | − | 18.1421i | 0.573132 | − | 0.810531i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11.1716i | − | 0.498116i | −0.968489 | − | 0.249058i | \(-0.919879\pi\) | ||
0.968489 | − | 0.249058i | \(-0.0801210\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.6569i | 0.874719i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.97056 | + | 11.2721i | −0.353985 | + | 0.500611i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.24264 | − | 1.24264i | 0.0550791 | − | 0.0550791i | −0.679031 | − | 0.734110i | \(-0.737600\pi\) |
0.734110 | + | 0.679031i | \(0.237600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8284i | 0.479021i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.65685 | − | 15.4853i | −0.382209 | − | 0.683692i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.3137 | + | 27.3137i | 1.20359 | + | 1.20359i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3431 | − | 10.3431i | 0.454891 | − | 0.454891i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.9706 | + | 6.17157i | −1.57893 | + | 0.270902i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.31371 | 0.408041 | 0.204020 | − | 0.978967i | \(-0.434599\pi\) | ||||
0.204020 | + | 0.978967i | \(0.434599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.0416 | + | 27.0416i | 1.18245 | + | 1.18245i | 0.979108 | + | 0.203340i | \(0.0651796\pi\) |
0.203340 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.65685 | − | 9.41421i | 0.290529 | − | 0.410870i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 71.5980 | 3.11886 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.5858 | + | 7.44365i | 0.676366 | + | 0.323027i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.4853 | − | 18.4853i | −0.800686 | − | 0.800686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.1421 | −1.04376 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.21320 | + | 36.2132i | 0.268120 | + | 1.56272i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.82843 | − | 1.82843i | 0.0787559 | − | 0.0787559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0000 | − | 21.0000i | −0.902861 | − | 0.902861i | 0.0928222 | − | 0.995683i | \(-0.470411\pi\) |
−0.995683 | + | 0.0928222i | \(0.970411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.1421 | + | 5.00000i | −1.25061 | + | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.828427i | 0.0354859i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1421 | + | 11.1421i | −0.476403 | + | 0.476403i | −0.903979 | − | 0.427576i | \(-0.859368\pi\) |
0.427576 | + | 0.903979i | \(0.359368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.757359 | − | 1.58579i | 0.0323233 | − | 0.0676797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 14.4853i | − | 0.617094i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.1421 | + | 18.4853i | 1.10967 | + | 0.784656i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1421 | − | 13.1421i | 0.556850 | − | 0.556850i | −0.371559 | − | 0.928409i | \(-0.621177\pi\) |
0.928409 | + | 0.371559i | \(0.121177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.79899i | 0.245271i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.17157 | + | 30.1421i | 0.218344 | + | 1.27260i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.4142 | − | 22.4142i | −0.944646 | − | 0.944646i | 0.0538999 | − | 0.998546i | \(-0.482835\pi\) |
−0.998546 | + | 0.0538999i | \(0.982835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.3137 | + | 23.3137i | −0.980815 | + | 0.980815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | + | 5.65685i | −0.293972 | + | 0.237566i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.6274 | 0.529369 | 0.264684 | − | 0.964335i | \(-0.414732\pi\) | ||||
0.264684 | + | 0.964335i | \(0.414732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8284 | + | 11.8284i | 0.495004 | + | 0.495004i | 0.909879 | − | 0.414874i | \(-0.136174\pi\) |
−0.414874 | + | 0.909879i | \(0.636174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.9706 | + | 17.6569i | 1.04316 | + | 0.737626i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.3431 | −1.01518 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6569 | −0.485281 | −0.242641 | − | 0.970116i | \(-0.578014\pi\) | ||||
−0.242641 | + | 0.970116i | \(0.578014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.14214 | − | 4.34315i | −0.255258 | − | 0.180495i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.8995 | − | 10.8995i | −0.452187 | − | 0.452187i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.627417 | 0.0259850 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.6569 | − | 7.65685i | 0.895401 | − | 0.316572i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.92893 | − | 1.92893i | 0.0796156 | − | 0.0796156i | −0.666178 | − | 0.745793i | \(-0.732071\pi\) |
0.745793 | + | 0.666178i | \(0.232071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.3137 | + | 25.3137i | 1.04303 | + | 1.04303i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0710678 | − | 0.414214i | −0.00292334 | − | 0.0170385i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 30.1421i | − | 1.23779i | −0.785474 | − | 0.618895i | \(-0.787581\pi\) | ||
0.785474 | − | 0.618895i | \(-0.212419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4853 | − | 16.4853i | 0.675831 | − | 0.675831i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.02944i | 0.368933i | 0.982839 | + | 0.184466i | \(0.0590557\pi\) | ||||
−0.982839 | + | 0.184466i | \(0.940944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.485281i | 0.0197950i | 0.999951 | + | 0.00989752i | \(0.00315053\pi\) | ||||
−0.999951 | + | 0.00989752i | \(0.996849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.7990 | + | 12.7990i | 1.09134 | + | 0.521215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.4142 | + | 10.4142i | −0.423398 | + | 0.423398i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.1127i | 1.66871i | 0.551225 | + | 0.834356i | \(0.314160\pi\) | ||||
−0.551225 | + | 0.834356i | \(0.685840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.24264 | + | 1.24264i | −0.293487 | + | 0.0503543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.97056 | − | 8.97056i | −0.362910 | − | 0.362910i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8284 | + | 19.8284i | −0.800863 | + | 0.800863i | −0.983230 | − | 0.182368i | \(-0.941624\pi\) |
0.182368 | + | 0.983230i | \(0.441624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.6569 | − | 67.9411i | −0.470050 | − | 2.73965i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0000 | 1.04672 | 0.523360 | − | 0.852111i | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852111i | \(0.324678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.5858 | − | 23.5858i | −0.947993 | − | 0.947993i | 0.0507201 | − | 0.998713i | \(-0.483848\pi\) |
−0.998713 | + | 0.0507201i | \(0.983848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.2843 | + | 5.17157i | 0.733723 | + | 0.207528i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.34315 | 0.174004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.82843 | + | 12.4853i | −0.352573 | + | 0.498614i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.1421 | + | 26.1421i | 1.04236 | + | 1.04236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.34315 | 0.0932792 | 0.0466396 | − | 0.998912i | \(-0.485149\pi\) | ||||
0.0466396 | + | 0.998912i | \(0.485149\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0711 | − | 2.07107i | 0.479782 | − | 0.0823176i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4853 | + | 10.4853i | −0.416096 | + | 0.416096i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.58579 | − | 1.58579i | −0.0628311 | − | 0.0628311i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.9706 | − | 6.00000i | 0.671345 | − | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.2548i | 1.78746i | 0.448607 | + | 0.893729i | \(0.351920\pi\) | ||||
−0.448607 | + | 0.893729i | \(0.648080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.0416 | + | 27.0416i | −1.06642 | + | 1.06642i | −0.0687864 | + | 0.997631i | \(0.521913\pi\) |
−0.997631 | + | 0.0687864i | \(0.978087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.82843 | + | 12.4853i | −0.347619 | + | 0.491607i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.1421i | − | 0.477357i | −0.971099 | − | 0.238678i | \(-0.923286\pi\) | ||
0.971099 | − | 0.238678i | \(-0.0767141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.8873i | − | 0.584378i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.4853 | − | 14.8284i | 0.410951 | − | 0.581172i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.6569 | + | 22.6569i | −0.886631 | + | 0.886631i | −0.994198 | − | 0.107567i | \(-0.965694\pi\) |
0.107567 | + | 0.994198i | \(0.465694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.6274i | 1.90003i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6274 | + | 10.8284i | −1.19489 | + | 0.422457i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.51472 | + | 8.51472i | 0.331686 | + | 0.331686i | 0.853227 | − | 0.521540i | \(-0.174642\pi\) |
−0.521540 | + | 0.853227i | \(0.674642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.3848 | + | 25.3848i | −0.987353 | + | 0.987353i | −0.999921 | − | 0.0125677i | \(-0.995999\pi\) |
0.0125677 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.1421 | − | 4.48528i | 1.01528 | − | 0.174194i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.6569 | 0.452033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9706 | + | 10.9706i | 0.424782 | + | 0.424782i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.8284 | − | 18.1421i | 0.495976 | − | 0.701415i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.51472 | −0.0584751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.2843 | + | 9.41421i | 1.28111 | + | 0.362353i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.10051 | − | 1.10051i | −0.0422958 | − | 0.0422958i | 0.685643 | − | 0.727938i | \(-0.259521\pi\) |
−0.727938 | + | 0.685643i | \(0.759521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | −0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.51472 | − | 14.6569i | −0.0963642 | − | 0.561652i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3137 | − | 22.3137i | 0.853810 | − | 0.853810i | −0.136790 | − | 0.990600i | \(-0.543678\pi\) |
0.990600 | + | 0.136790i | \(0.0436785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.82843 | − | 8.82843i | −0.337317 | − | 0.337317i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.4853 | − | 3.68629i | 0.819715 | − | 0.140641i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.544156i | − | 0.0207307i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.89949 | + | 4.89949i | −0.186386 | + | 0.186386i | −0.794132 | − | 0.607746i | \(-0.792074\pi\) |
0.607746 | + | 0.794132i | \(0.292074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.00000 | + | 3.34315i | 0.265908 | + | 0.126996i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.65685i | 0.290441i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 79.5980i | − | 3.01499i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.1421 | + | 21.3137i | 1.14008 | + | 0.806158i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.6569 | + | 10.6569i | −0.402504 | + | 0.402504i | −0.879114 | − | 0.476611i | \(-0.841865\pi\) |
0.476611 | + | 0.879114i | \(0.341865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4853i | 0.697186i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.65685 | − | 32.9706i | −0.213049 | − | 1.24174i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.07107 | + | 4.07107i | 0.153108 | + | 0.153108i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.82843 | + | 7.82843i | −0.294003 | + | 0.294003i | −0.838659 | − | 0.544656i | \(-0.816660\pi\) |
0.544656 | + | 0.838659i | \(0.316660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.65685 | − | 2.00000i | 0.212149 | − | 0.0750059i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.3431 | −1.43596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.0000 | − | 14.0000i | −0.523570 | − | 0.523570i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | + | 11.3137i | 0.597531 | + | 0.422518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3137 | 0.421345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.4853 | − | 11.6569i | −0.613094 | − | 0.433523i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.9706 | + | 19.9706i | 0.741688 | + | 0.741688i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.6863 | 0.470509 | 0.235254 | − | 0.971934i | \(-0.424408\pi\) | ||||
0.235254 | + | 0.971934i | \(0.424408\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4853 | + | 12.4853i | −0.461785 | + | 0.461785i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7279 | − | 27.7279i | −1.02415 | − | 1.02415i | −0.999701 | − | 0.0244532i | \(-0.992216\pi\) |
−0.0244532 | − | 0.999701i | \(-0.507784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | − | 5.82843i | −0.0368856 | − | 0.214985i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 25.5980i | − | 0.942914i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1716 | − | 16.1716i | 0.594881 | − | 0.594881i | −0.344065 | − | 0.938946i | \(-0.611804\pi\) |
0.938946 | + | 0.344065i | \(0.111804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.8284 | + | 7.65685i | 0.397792 | + | 0.281282i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.6569i | − | 0.574394i | −0.957871 | − | 0.287197i | \(-0.907277\pi\) | ||
0.957871 | − | 0.287197i | \(-0.0927235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.1421i | 1.32415i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.9289 | − | 41.7279i | 0.729161 | − | 1.52674i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.00000 | + | 5.00000i | −0.182696 | + | 0.182696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41.3137i | − | 1.50756i | −0.657128 | − | 0.753779i | \(-0.728229\pi\) | ||
0.657128 | − | 0.753779i | \(-0.271771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00000 | − | 0.171573i | 0.0364420 | − | 0.00625246i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.3137 | + | 15.3137i | 0.557323 | + | 0.557323i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.4853 | − | 31.4853i | 1.14435 | − | 1.14435i | 0.156707 | − | 0.987645i | \(-0.449912\pi\) |
0.987645 | − | 0.156707i | \(-0.0500878\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.76955 | − | 16.1421i | −0.100528 | − | 0.585922i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.62742 | −0.312744 | −0.156372 | − | 0.987698i | \(-0.549980\pi\) | ||||
−0.156372 | + | 0.987698i | \(0.549980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.171573 | + | 0.171573i | 0.00621136 | + | 0.00621136i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 63.1127 | + | 30.1421i | 2.28184 | + | 1.08979i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9117 | −0.466214 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.6569 | 1.28582 | 0.642910 | − | 0.765942i | \(-0.277727\pi\) | ||||
0.642910 | + | 0.765942i | \(0.277727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.1716 | + | 29.9411i | −0.762476 | + | 1.07830i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.44365 | + | 5.44365i | 0.195795 | + | 0.195795i | 0.798194 | − | 0.602400i | \(-0.205789\pi\) |
−0.602400 | + | 0.798194i | \(0.705789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −69.7990 | −2.50725 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.24264 | − | 1.58579i | 0.331578 | − | 0.0568898i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.1421 | − | 28.1421i | 1.00830 | − | 1.00830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9706 | − | 10.9706i | −0.392558 | − | 0.392558i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.7574 | − | 19.2426i | −0.384437 | − | 0.687676i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 81.5980i | − | 2.91236i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0416 | − | 25.0416i | 0.892638 | − | 0.892638i | −0.102133 | − | 0.994771i | \(-0.532567\pi\) |
0.994771 | + | 0.102133i | \(0.0325667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.343146 | + | 0.485281i | −0.0122163 | + | 0.0172765i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.65685i | 0.343358i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.31371i | 0.0466512i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.828427 | − | 1.17157i | 0.0293813 | − | 0.0415514i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.5858 | − | 31.5858i | 1.11883 | − | 1.11883i | 0.126912 | − | 0.991914i | \(-0.459493\pi\) |
0.991914 | − | 0.126912i | \(-0.0405066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 38.6274i | − | 1.36654i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.34315 | + | 12.2843i | 0.153458 | + | 0.434043i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990 | + | 19.7990i | 0.698691 | + | 0.698691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.82843 | + | 8.82843i | −0.311161 | + | 0.311161i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.3137 | − | 3.48528i | 0.715076 | − | 0.122688i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.3137 | −1.59315 | −0.796573 | − | 0.604543i | \(-0.793356\pi\) | ||||
−0.796573 | + | 0.604543i | \(0.793356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.92893 | − | 1.92893i | −0.0677340 | − | 0.0677340i | 0.672428 | − | 0.740162i | \(-0.265251\pi\) |
−0.740162 | + | 0.672428i | \(0.765251\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.1716 | + | 15.7990i | −0.391804 | + | 0.554095i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.4853 | −0.647511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.82843 | −0.308868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.89949 | − | 6.07107i | 0.101317 | − | 0.212140i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48528 | − | 1.48528i | −0.0518367 | − | 0.0518367i | 0.680713 | − | 0.732550i | \(-0.261670\pi\) |
−0.732550 | + | 0.680713i | \(0.761670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.97056 | 0.312694 | 0.156347 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156347 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.04163 | − | 29.3848i | −0.175527 | − | 1.02305i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.00000 | + | 9.00000i | −0.312961 | + | 0.312961i | −0.846055 | − | 0.533095i | \(-0.821029\pi\) |
0.533095 | + | 0.846055i | \(0.321029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.10051 | − | 5.10051i | −0.177148 | − | 0.177148i | 0.612963 | − | 0.790111i | \(-0.289977\pi\) |
−0.790111 | + | 0.612963i | \(0.789977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.3848 | − | 6.75736i | 1.36624 | − | 0.234410i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.82843i | − | 0.236591i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.9706 | + | 30.9706i | −1.07178 | + | 1.07178i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.4264 | + | 14.8284i | 1.81212 | + | 0.512545i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.544156i | 0.0187863i | 0.999956 | + | 0.00939317i | \(0.00298998\pi\) | ||||
−0.999956 | + | 0.00939317i | \(0.997010\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000i | 0.379310i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.4558 | + | 29.3137i | 1.42782 | + | 1.00962i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.2426 | − | 19.2426i | 0.661967 | − | 0.661967i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.31371i | 0.148221i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.85786 | + | 16.6569i | 0.0980817 | + | 0.571662i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0000 | − | 14.0000i | −0.479914 | − | 0.479914i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.5858 | + | 25.5858i | −0.876041 | + | 0.876041i | −0.993122 | − | 0.117082i | \(-0.962646\pi\) |
0.117082 | + | 0.993122i | \(0.462646\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.6569 | + | 32.9706i | 0.398656 | + | 1.12757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.9411 | −1.22773 | −0.613863 | − | 0.789413i | \(-0.710385\pi\) | ||||
−0.613863 | + | 0.789413i | \(0.710385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.10051 | − | 3.10051i | −0.105788 | − | 0.105788i | 0.652232 | − | 0.758020i | \(-0.273833\pi\) |
−0.758020 | + | 0.652232i | \(0.773833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.4853 | − | 11.6569i | −0.561817 | − | 0.397265i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.6863 | −0.568008 | −0.284004 | − | 0.958823i | \(-0.591663\pi\) | ||||
−0.284004 | + | 0.958823i | \(0.591663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.9411 | 2.44607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.8995 | + | 29.6274i | 1.42298 | + | 1.00620i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.65685 | − | 3.65685i | −0.124050 | − | 0.124050i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.2010 | −0.752253 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00000 | − | 5.65685i | −0.0676897 | − | 0.191456i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.00000 | + | 4.00000i | −0.135225 | + | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4853 | + | 23.4853i | 0.793042 | + | 0.793042i | 0.981987 | − | 0.188946i | \(-0.0605071\pi\) |
−0.188946 | + | 0.981987i | \(0.560507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.313708 | − | 1.82843i | −0.0105811 | − | 0.0616713i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.5147i | 1.06176i | 0.847448 | + | 0.530879i | \(0.178138\pi\) | ||||
−0.847448 | + | 0.530879i | \(0.821862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9411 | − | 28.9411i | 0.973946 | − | 0.973946i | −0.0257227 | − | 0.999669i | \(-0.508189\pi\) |
0.999669 | + | 0.0257227i | \(0.00818869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.7990 | − | 19.6569i | −0.934453 | − | 0.660758i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.8284i | 1.50519i | 0.658483 | + | 0.752596i | \(0.271198\pi\) | ||||
−0.658483 | + | 0.752596i | \(0.728802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.34315i | 0.145664i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.45584 | + | 23.1421i | −0.0822739 | + | 0.775291i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.6569 | − | 13.6569i | 0.457009 | − | 0.457009i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 72.4264i | − | 2.42095i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.0000 | + | 2.40202i | −0.467446 | + | 0.0802011i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.4558 | + | 31.4558i | 1.04911 | + | 1.04911i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.17157 | − | 1.17157i | 0.0390308 | − | 0.0390308i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.757359 | + | 4.41421i | 0.0252033 | + | 0.146896i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 58.2843 | 1.93743 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.31371 | − | 2.31371i | −0.0768254 | − | 0.0768254i | 0.667650 | − | 0.744475i | \(-0.267300\pi\) |
−0.744475 | + | 0.667650i | \(0.767300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.44365 | + | 15.5858i | −0.246890 | + | 0.516948i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2843 | 0.406996 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.8579 | −1.31910 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | + | 2.82843i | −0.0661180 | + | 0.0935049i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0711 | + | 10.0711i | 0.332576 | + | 0.332576i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6569 | 0.450498 | 0.225249 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225249 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8284 | − | 2.02944i | 0.389760 | − | 0.0668722i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.51472 | + | 9.51472i | −0.313181 | + | 0.313181i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.4853 | − | 25.4853i | −0.837951 | − | 0.837951i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3137 | + | 32.0000i | 0.371591 | + | 1.05102i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.1127i | 1.41448i | 0.706973 | + | 0.707241i | \(0.250060\pi\) | ||||
−0.706973 | + | 0.707241i | \(0.749940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.41421 | − | 2.41421i | 0.0791227 | − | 0.0791227i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.4853 | − | 26.1421i | 0.605181 | − | 0.855855i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 60.2843i | − | 1.97151i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.1421i | 0.984701i | 0.870397 | + | 0.492350i | \(0.163862\pi\) | ||||
−0.870397 | + | 0.492350i | \(0.836138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.51472 | − | 4.97056i | 0.114699 | − | 0.162208i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.3553 | − | 28.3553i | 0.924358 | − | 0.924358i | −0.0729761 | − | 0.997334i | \(-0.523250\pi\) |
0.997334 | + | 0.0729761i | \(0.0232497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.6274i | 1.38814i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.4853 | − | 8.65685i | 0.503736 | − | 0.281607i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.14214 | − | 9.14214i | −0.297079 | − | 0.297079i | 0.542789 | − | 0.839869i | \(-0.317368\pi\) |
−0.839869 | + | 0.542789i | \(0.817368\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.1716 | − | 17.1716i | 0.557413 | − | 0.557413i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.5563 | − | 6.27208i | 1.18542 | − | 0.203386i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6569 | 1.02547 | 0.512733 | − | 0.858548i | \(-0.328633\pi\) | ||||
0.512733 | + | 0.858548i | \(0.328633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.6274 | − | 42.6274i | −1.37939 | − | 1.37939i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9706 | + | 15.5147i | −0.354628 | + | 0.501520i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.65685 | −0.118086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.9411 | −2.54649 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1421 | − | 9.14214i | −0.616847 | − | 0.294601i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4853 | + | 10.4853i | 0.337533 | + | 0.337533i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.686292 | 0.0220696 | 0.0110348 | − | 0.999939i | \(-0.496487\pi\) | ||||
0.0110348 | + | 0.999939i | \(0.496487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.82843 | + | 39.7990i | 0.219361 | + | 1.27853i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.8995 | + | 16.8995i | −0.542331 | + | 0.542331i | −0.924212 | − | 0.381881i | \(-0.875276\pi\) |
0.381881 | + | 0.924212i | \(0.375276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.58579 | + | 1.58579i | 0.0508380 | + | 0.0508380i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.4853 | + | 4.37258i | −0.816182 | + | 0.140035i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 31.3137i | − | 1.00181i | −0.865501 | − | 0.500907i | \(-0.833000\pi\) | ||
0.865501 | − | 0.500907i | \(-0.167000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.94113 | − | 7.94113i | 0.253799 | − | 0.253799i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.313708 | + | 0.656854i | −0.0100159 | + | 0.0209717i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 54.4853i | − | 1.73781i | −0.494978 | − | 0.868905i | \(-0.664824\pi\) | ||
0.494978 | − | 0.868905i | \(-0.335176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.828427i | 0.0263959i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | − | 5.65685i | −0.254643 | − | 0.180060i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.68629 | − | 6.68629i | 0.212612 | − | 0.212612i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 45.3137i | − | 1.43944i | −0.694266 | − | 0.719719i | \(-0.744271\pi\) | ||
0.694266 | − | 0.719719i | \(-0.255729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.61522 | − | 26.8995i | −0.146460 | − | 0.853630i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.0711 | + | 34.0711i | −1.07904 | + | 1.07904i | −0.0824460 | + | 0.996596i | \(0.526273\pi\) |
−0.996596 | + | 0.0824460i | \(0.973727\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.7279 | + | 24.5563i | 0.434332 | + | 0.776929i |
(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 | 1344.2.s.a.239.1 | 4 | ||
3.2 | odd | 2 | 1344.2.s.b.239.2 | 4 | |||
4.3 | odd | 2 | 336.2.s.b.323.2 | yes | 4 | ||
12.11 | even | 2 | 336.2.s.a.323.1 | yes | 4 | ||
16.5 | even | 4 | 336.2.s.a.155.2 | ✓ | 4 | ||
16.11 | odd | 4 | 1344.2.s.b.911.1 | 4 | |||
48.5 | odd | 4 | 336.2.s.b.155.2 | yes | 4 | ||
48.11 | even | 4 | inner | 1344.2.s.a.911.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.a.155.2 | ✓ | 4 | 16.5 | even | 4 | ||
336.2.s.a.323.1 | yes | 4 | 12.11 | even | 2 | ||
336.2.s.b.155.2 | yes | 4 | 48.5 | odd | 4 | ||
336.2.s.b.323.2 | yes | 4 | 4.3 | odd | 2 | ||
1344.2.s.a.239.1 | 4 | 1.1 | even | 1 | trivial | ||
1344.2.s.a.911.1 | 4 | 48.11 | even | 4 | inner | ||
1344.2.s.b.239.2 | 4 | 3.2 | odd | 2 | |||
1344.2.s.b.911.1 | 4 | 16.11 | odd | 4 |