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 | 239.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.239 |
Dual form | 1344.2.s.b.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 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.41421 | − | 2.41421i | −1.07967 | − | 1.07967i | −0.996539 | − | 0.0831305i | \(-0.973508\pi\) |
−0.0831305 | − | 0.996539i | \(-0.526492\pi\) | |||||||
\(6\) | 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 | −0.926813 | − | 0.375522i | \(-0.877463\pi\) |
0.375522 | + | 0.926813i | \(0.377463\pi\) | |||||||
\(12\) | 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 | \(0.310560\pi\) | ||||
−0.560627 | + | 0.828068i | \(0.689440\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 1.00000 | + | 1.41421i | 0.218218 | + | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.65685i | − | 0.762507i | −0.924471 | − | 0.381253i | \(-0.875493\pi\) | ||
0.924471 | − | 0.381253i | \(-0.124507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685i | 1.33137i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 3.00000i | −0.557086 | + | 0.557086i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 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 | \(-0.864109\pi\) | ||||
−0.910247 | + | 0.414065i | \(0.864109\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 9.24264 | − | 4.41421i | 1.37781 | − | 0.658032i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.65685 | + | 6.82843i | −1.35223 | + | 0.956171i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.171573 | − | 0.171573i | −0.0235673 | − | 0.0235673i | 0.695225 | − | 0.718792i | \(-0.255305\pi\) |
−0.718792 | + | 0.695225i | \(0.755305\pi\) | |||||||
\(54\) | 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 | −0.920575 | − | 0.390567i | \(-0.872279\pi\) |
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 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 | ||||||||
\(69\) | 5.17157 | − | 3.65685i | 0.622584 | − | 0.440234i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8284i | 1.26737i | 0.773591 | + | 0.633686i | \(0.218459\pi\) | ||||
−0.773591 | + | 0.633686i | \(0.781541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.41421 | + | 6.65685i | −1.08706 | + | 0.768667i | ||||
\(76\) | 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 | \(0.0709748\pi\) |
0.221131 | + | 0.975244i | \(0.429025\pi\) | |||||||
\(84\) | 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 | \(-0.573934\pi\) | ||||
−0.230186 | + | 0.973147i | \(0.573934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.58579 | − | 1.58579i | −0.166236 | − | 0.166236i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.8284 | + | 10.4853i | −1.53764 | + | 1.08727i | ||||
\(94\) | 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 | ||||||||
\(99\) | −3.34315 | − | 7.00000i | −0.335999 | − | 0.703526i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.07107 | − | 4.07107i | −0.405086 | − | 0.405086i | 0.474935 | − | 0.880021i | \(-0.342472\pi\) |
−0.880021 | + | 0.474935i | \(0.842472\pi\) | |||||||
\(102\) | 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 | −0.422837 | − | 0.906206i | \(-0.638966\pi\) |
0.906206 | + | 0.422837i | \(0.138966\pi\) | |||||||
\(108\) | 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 | \(-0.849918\pi\) | ||
0.890889 | − | 0.454220i | \(-0.150082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.82843 | + | 8.82843i | −0.823255 | + | 0.823255i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.07107 | − | 2.89949i | 0.561270 | − | 0.268058i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.82843i | 0.625961i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.31371i | 0.392155i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.6569 | − | 16.4853i | −1.05106 | − | 1.48643i | ||||
\(124\) | 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 | 0.113612 | − | 0.993525i | \(-0.463758\pi\) |
−0.993525 | + | 0.113612i | \(0.963758\pi\) | |||||||
\(132\) | 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 | \(-0.450071\pi\) | ||||
0.156213 | + | 0.987723i | \(0.450071\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −5.65685 | − | 8.00000i | −0.476393 | − | 0.673722i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.79899 | 0.484936 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4853 | 1.20294 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | + | 1.41421i | 0.0824786 | + | 0.116642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.48528 | − | 7.48528i | −0.613218 | − | 0.613218i | 0.330565 | − | 0.943783i | \(-0.392761\pi\) |
−0.943783 | + | 0.330565i | \(0.892761\pi\) | |||||||
\(150\) | 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 | ||||||||
\(165\) | 8.82843 | + | 12.4853i | 0.687292 | + | 0.971978i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.8284i | − | 0.992693i | −0.868124 | − | 0.496347i | \(-0.834674\pi\) | ||
0.868124 | − | 0.496347i | \(-0.165326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.97056i | − | 0.613120i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.41421 | + | 9.24264i | 0.337563 | + | 0.706802i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8995 | + | 14.8995i | −1.13279 | + | 1.13279i | −0.143076 | + | 0.989712i | \(0.545699\pi\) |
−0.989712 | + | 0.143076i | \(0.954301\pi\) | |||||||
\(174\) | 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 | \(0.0413643\pi\) |
0.129584 | + | 0.991568i | \(0.458636\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | −5.00000 | + | 1.41421i | −0.363696 | + | 0.102869i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6569 | 1.27761 | 0.638803 | − | 0.769371i | \(-0.279430\pi\) | ||||
0.638803 | + | 0.769371i | \(0.279430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34315 | 0.312626 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.8284 | + | 7.65685i | −0.775440 | + | 0.548319i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.171573 | − | 0.171573i | −0.0122241 | − | 0.0122241i | 0.700968 | − | 0.713192i | \(-0.252751\pi\) |
−0.713192 | + | 0.700968i | \(0.752751\pi\) | |||||||
\(198\) | 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 | ||||||||
\(213\) | −8.48528 | + | 6.00000i | −0.581402 | + | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.82843i | 0.602094i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4853i | 0.711787i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.3137 | + | 10.8284i | −1.03480 | + | 0.731717i | ||||
\(220\) | 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 | 0.476321 | − | 0.879272i | \(-0.341970\pi\) |
−0.879272 | + | 0.476321i | \(0.841970\pi\) | |||||||
\(228\) | 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 | \(-0.254005\pi\) | ||||
0.698154 | + | 0.715948i | \(0.254005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.6569 | + | 13.6569i | 0.890875 | + | 0.890875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.82843 | − | 2.00000i | 0.183726 | − | 0.129914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6569 | 0.750884 | 0.375442 | − | 0.926846i | \(-0.377491\pi\) | ||||
0.375442 | + | 0.926846i | \(0.377491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 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 | −0.693913 | − | 0.720058i | \(-0.744115\pi\) |
0.720058 | + | 0.693913i | \(0.244115\pi\) | |||||||
\(252\) | 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 | \(0.229581\pi\) | ||||
−0.750982 | + | 0.660323i | \(0.770419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.82843 | + | 3.82843i | −0.237887 | + | 0.237887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.48528 | − | 11.4853i | −0.339530 | − | 0.710921i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.343146i | 0.0211593i | 0.999944 | + | 0.0105796i | \(0.00336767\pi\) | ||||
−0.999944 | + | 0.0105796i | \(0.996632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.828427i | 0.0508899i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.34315 | − | 6.14214i | −0.265796 | − | 0.375893i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.41421 | − | 8.41421i | 0.513024 | − | 0.513024i | −0.402428 | − | 0.915452i | \(-0.631834\pi\) |
0.915452 | + | 0.402428i | \(0.131834\pi\) | |||||||
\(270\) | 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 | \(-0.161285\pi\) | ||||
0.874355 | + | 0.485288i | \(0.161285\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −11.6569 | − | 16.4853i | −0.690492 | − | 0.976504i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.6569 | −0.688082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.00000 | − | 2.82843i | −0.117242 | − | 0.165805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.757359 | − | 0.757359i | −0.0442454 | − | 0.0442454i | 0.684638 | − | 0.728883i | \(-0.259960\pi\) |
−0.728883 | + | 0.684638i | \(0.759960\pi\) | |||||||
\(294\) | 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 | ||||||||
\(309\) | 11.3137 | + | 16.0000i | 0.643614 | + | 0.910208i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.4853i | − | 1.04820i | −0.851655 | − | 0.524102i | \(-0.824401\pi\) | ||
0.851655 | − | 0.524102i | \(-0.175599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.51472i | 0.198664i | 0.995054 | + | 0.0993318i | \(0.0316705\pi\) | ||||
−0.995054 | + | 0.0993318i | \(0.968329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.24264 | − | 4.41421i | 0.520764 | − | 0.248713i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1421 | − | 15.1421i | 0.850467 | − | 0.850467i | −0.139723 | − | 0.990191i | \(-0.544621\pi\) |
0.990191 | + | 0.139723i | \(0.0446214\pi\) | |||||||
\(318\) | 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 | ||||||||
\(333\) | −7.00000 | − | 14.6569i | −0.383598 | − | 0.803191i | ||||
\(334\) | 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 | ||||||||
\(339\) | 13.6569 | − | 9.65685i | 0.741739 | − | 0.524488i | ||||
\(340\) | 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 | −0.172191 | − | 0.985064i | \(-0.555085\pi\) |
0.985064 | + | 0.172191i | \(0.0550847\pi\) | |||||||
\(348\) | 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 | \(0.0725038\pi\) | ||||
−0.974171 | + | 0.225813i | \(0.927496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4853 | − | 14.4853i | 0.768799 | − | 0.768799i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.65685 | + | 6.82843i | −0.511095 | + | 0.361399i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.6569i | 1.67078i | 0.549654 | + | 0.835392i | \(0.314760\pi\) | ||||
−0.549654 | + | 0.835392i | \(0.685240\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.34315i | 0.386481i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.10051 | + | 4.31371i | −0.320193 | + | 0.226411i | ||||
\(364\) | 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 | ||||||||
\(381\) | −6.14214 | + | 4.34315i | −0.314671 | + | 0.222506i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.31371 | 0.169323 | 0.0846613 | − | 0.996410i | \(-0.473019\pi\) | ||||
0.0846613 | + | 0.996410i | \(0.473019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.82843 | 0.449938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.00000 | − | 3.34315i | 0.355830 | − | 0.169942i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.9706 | + | 13.9706i | 0.708336 | + | 0.708336i | 0.966185 | − | 0.257849i | \(-0.0830139\pi\) |
−0.257849 | + | 0.966185i | \(0.583014\pi\) | |||||||
\(390\) | 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 | \(0.0263669\pi\) | ||||
−0.996571 | + | 0.0827394i | \(0.973633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6274 | − | 16.6274i | 0.828271 | − | 0.828271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.24264 | + | 30.5563i | 0.161128 | + | 1.51836i | ||||
\(406\) | 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 | ||||||||
\(411\) | 3.65685 | + | 5.17157i | 0.180379 | + | 0.255095i | ||||
\(412\) | 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 | 0.813699 | − | 0.581287i | \(-0.197450\pi\) |
−0.581287 | + | 0.813699i | \(0.697450\pi\) | |||||||
\(420\) | 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 | ||||||||
\(429\) | 5.79899 | + | 8.20101i | 0.279978 | + | 0.395949i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3137 | −0.930309 | −0.465154 | − | 0.885230i | \(-0.654001\pi\) | ||||
−0.465154 | + | 0.885230i | \(0.654001\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.3137 | −1.79318 | −0.896591 | − | 0.442859i | \(-0.853964\pi\) | ||||
−0.896591 | + | 0.442859i | \(0.853964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4853 | + | 20.4853i | 0.694516 | + | 0.982194i | ||||
\(436\) | 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 | −0.822551 | − | 0.568691i | \(-0.807450\pi\) |
0.568691 | + | 0.822551i | \(0.307450\pi\) | |||||||
\(444\) | 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 | \(-0.835230\pi\) | ||
0.868989 | − | 0.494831i | \(-0.164770\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3137 | − | 21.3137i | 1.00362 | − | 1.00362i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.34315 | + | 8.97056i | 0.298027 | + | 0.421474i | ||||
\(454\) | 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 | ||||||||
\(459\) | −9.65685 | − | 34.1421i | −0.450743 | − | 1.59362i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.5858 | + | 19.5858i | −0.912201 | + | 0.912201i | −0.996445 | − | 0.0842441i | \(-0.973152\pi\) |
0.0842441 | + | 0.996445i | \(0.473152\pi\) | |||||||
\(462\) | 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 | 0.922389 | − | 0.386263i | \(-0.126234\pi\) |
−0.386263 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 0.656854 | − | 0.313708i | 0.0300753 | − | 0.0143637i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.68629 | −0.214122 | −0.107061 | − | 0.994252i | \(-0.534144\pi\) | ||||
−0.107061 | + | 0.994252i | \(0.534144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1421 | 0.553634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.17157 | − | 3.65685i | 0.235315 | − | 0.166393i | ||||
\(484\) | 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 | −0.372373 | − | 0.928083i | \(-0.621456\pi\) |
0.928083 | + | 0.372373i | \(0.121456\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 18.1421 | − | 12.8284i | 0.810531 | − | 0.573132i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.1716i | 0.498116i | 0.968489 | + | 0.249058i | \(0.0801210\pi\) | ||||
−0.968489 | + | 0.249058i | \(0.919879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.6569i | 0.874719i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2721 | − | 7.97056i | 0.500611 | − | 0.353985i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.24264 | + | 1.24264i | −0.0550791 | + | 0.0550791i | −0.734110 | − | 0.679031i | \(-0.762400\pi\) |
0.679031 | + | 0.734110i | \(0.262400\pi\) | |||||||
\(510\) | 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 | \(-0.565401\pi\) | ||||
−0.204020 | + | 0.978967i | \(0.565401\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −9.41421 | + | 6.65685i | −0.410870 | + | 0.290529i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −71.5980 | −3.11886 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.44365 | − | 15.5858i | −0.323027 | − | 0.676366i | ||||
\(532\) | 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 | ||||||||
\(549\) | 1.58579 | − | 0.757359i | 0.0676797 | − | 0.0323233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4853i | 0.617094i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.4853 | + | 26.1421i | 0.784656 | + | 1.10967i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1421 | + | 13.1421i | −0.556850 | + | 0.556850i | −0.928409 | − | 0.371559i | \(-0.878823\pi\) |
0.371559 | + | 0.928409i | \(0.378823\pi\) | |||||||
\(558\) | 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 | 0.998546 | − | 0.0538999i | \(-0.0171652\pi\) |
−0.0538999 | + | 0.998546i | \(0.517165\pi\) | |||||||
\(564\) | 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 | \(-0.585268\pi\) | ||||
−0.264684 | + | 0.964335i | \(0.585268\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 17.6569 | + | 24.9706i | 0.737626 | + | 1.04316i | ||||
\(574\) | 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 | ||||||||
\(579\) | 4.34315 | + | 6.14214i | 0.180495 | + | 0.255258i | ||||
\(580\) | 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 | −0.745793 | − | 0.666178i | \(-0.767929\pi\) |
0.666178 | + | 0.745793i | \(0.267929\pi\) | |||||||
\(588\) | 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 | \(0.212419\pi\) | ||||
−0.785474 | + | 0.618895i | \(0.787581\pi\) | |||||||
\(594\) | 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 | \(-0.940944\pi\) | ||
0.982839 | − | 0.184466i | \(-0.0590557\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.485281i | 0.0197950i | 0.999951 | + | 0.00989752i | \(0.00315053\pi\) | ||||
−0.999951 | + | 0.00989752i | \(0.996849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.7990 | + | 26.7990i | 0.521215 | + | 1.09134i | ||||
\(604\) | 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 | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 5.17157 | + | 18.2843i | 0.207528 | + | 0.733723i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.34315 | −0.174004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.4853 | + | 8.82843i | −0.498614 | + | 0.352573i | ||||
\(628\) | 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 | \(-0.648080\pi\) | ||
0.448607 | − | 0.893729i | \(-0.351920\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −12.4853 | + | 8.82843i | −0.491607 | + | 0.347619i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1421i | 0.477357i | 0.971099 | + | 0.238678i | \(0.0767141\pi\) | ||||
−0.971099 | + | 0.238678i | \(0.923286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.8873i | − | 0.584378i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.8284 | + | 10.4853i | −0.581172 | + | 0.410951i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.6569 | − | 22.6569i | 0.886631 | − | 0.886631i | −0.107567 | − | 0.994198i | \(-0.534306\pi\) |
0.994198 | + | 0.107567i | \(0.0343059\pi\) | |||||||
\(654\) | 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 | 0.521540 | − | 0.853227i | \(-0.325358\pi\) |
−0.853227 | + | 0.521540i | \(0.825358\pi\) | |||||||
\(660\) | 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 | ||||||||
\(669\) | −18.1421 | + | 12.8284i | −0.701415 | + | 0.495976i | ||||
\(670\) | 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 | ||||||||
\(675\) | −9.41421 | − | 33.2843i | −0.362353 | − | 1.28111i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.10051 | + | 1.10051i | 0.0422958 | + | 0.0422958i | 0.727938 | − | 0.685643i | \(-0.240479\pi\) |
−0.685643 | + | 0.727938i | \(0.740479\pi\) | |||||||
\(678\) | 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 | −0.990600 | − | 0.136790i | \(-0.956322\pi\) |
0.136790 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | −3.34315 | − | 7.00000i | −0.126996 | − | 0.265908i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.65685i | − | 0.290441i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 79.5980i | − | 3.01499i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.3137 | + | 30.1421i | 0.806158 | + | 1.14008i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6569 | − | 10.6569i | 0.402504 | − | 0.402504i | −0.476611 | − | 0.879114i | \(-0.658135\pi\) |
0.879114 | + | 0.476611i | \(0.158135\pi\) | |||||||
\(702\) | 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 | ||||||||
\(717\) | 11.3137 | + | 16.0000i | 0.422518 | + | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3137 | 0.421345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6569 | + | 16.4853i | 0.433523 | + | 0.613094i | ||||
\(724\) | 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 | ||||||||
\(741\) | −7.65685 | − | 10.8284i | −0.281282 | − | 0.397792i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6569i | 0.574394i | 0.957871 | + | 0.287197i | \(0.0927235\pi\) | ||||
−0.957871 | + | 0.287197i | \(0.907277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.1421i | 1.32415i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.7279 | + | 19.9289i | −1.52674 | + | 0.729161i | ||||
\(748\) | 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 | \(-0.450020\pi\) | ||||
0.156372 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.171573 | + | 0.171573i | 0.00621136 | + | 0.00621136i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.1421 | + | 63.1127i | 1.08979 | + | 2.28184i | ||||
\(766\) | 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 | ||||||||
\(771\) | −29.9411 | + | 21.1716i | −1.07830 | + | 0.762476i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.44365 | − | 5.44365i | −0.195795 | − | 0.195795i | 0.602400 | − | 0.798194i | \(-0.294211\pi\) |
−0.798194 | + | 0.602400i | \(0.794211\pi\) | |||||||
\(774\) | 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 | ||||||||
\(789\) | −0.485281 | + | 0.343146i | −0.0172765 | + | 0.0122163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 9.65685i | − | 0.343358i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.31371i | 0.0466512i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.17157 | + | 0.828427i | −0.0415514 | + | 0.0293813i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.5858 | + | 31.5858i | −1.11883 | + | 1.11883i | −0.126912 | + | 0.991914i | \(0.540507\pi\) |
−0.991914 | + | 0.126912i | \(0.959493\pi\) | |||||||
\(798\) | 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 | \(-0.206644\pi\) | ||||
0.796573 | + | 0.604543i | \(0.206644\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 15.7990 | − | 11.1716i | 0.554095 | − | 0.391804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.4853 | 0.647511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.82843 | −0.308868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.07107 | − | 2.89949i | 0.212140 | − | 0.101317i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48528 | + | 1.48528i | 0.0518367 | + | 0.0518367i | 0.732550 | − | 0.680713i | \(-0.238330\pi\) |
−0.680713 | + | 0.732550i | \(0.738330\pi\) | |||||||
\(822\) | 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 | −0.533095 | − | 0.846055i | \(-0.678971\pi\) |
0.846055 | + | 0.533095i | \(0.178971\pi\) | |||||||
\(828\) | 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 | ||||||||
\(837\) | −14.8284 | − | 52.4264i | −0.512545 | − | 1.81212i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 0.544156i | − | 0.0187863i | −0.999956 | − | 0.00939317i | \(-0.997010\pi\) | ||
0.999956 | − | 0.00939317i | \(-0.00298998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000i | 0.379310i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.3137 | + | 41.4558i | 1.00962 | + | 1.42782i | ||||
\(844\) | 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 | \(-0.289615\pi\) | ||||
0.613863 | + | 0.789413i | \(0.289615\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −11.6569 | − | 16.4853i | −0.397265 | − | 0.561817i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.6863 | 0.568008 | 0.284004 | − | 0.958823i | \(-0.408337\pi\) | ||||
0.284004 | + | 0.958823i | \(0.408337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.9411 | 2.44607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.6274 | − | 41.8995i | −1.00620 | − | 1.42298i | ||||
\(868\) | 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 | \(-0.821862\pi\) | ||
0.847448 | − | 0.530879i | \(-0.178138\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 19.6569 | + | 27.7990i | 0.660758 | + | 0.934453i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 44.8284i | − | 1.50519i | −0.658483 | − | 0.752596i | \(-0.728802\pi\) | ||
0.658483 | − | 0.752596i | \(-0.271198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.34315i | 0.145664i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.1421 | − | 2.45584i | 0.775291 | − | 0.0822739i | ||||
\(892\) | 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 | ||||||||
\(909\) | 15.5858 | − | 7.44365i | 0.516948 | − | 0.246890i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.2843 | −0.406996 | −0.203498 | − | 0.979075i | \(-0.565231\pi\) | ||||
−0.203498 | + | 0.979075i | \(0.565231\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.8579 | −1.31910 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.82843 | + | 2.00000i | −0.0935049 | + | 0.0661180i | ||||
\(916\) | 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 | \(-0.749940\pi\) | ||
0.706973 | − | 0.707241i | \(-0.250060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.41421 | − | 2.41421i | 0.0791227 | − | 0.0791227i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.1421 | − | 18.4853i | 0.855855 | − | 0.605181i | ||||
\(934\) | 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 | ||||||||
\(939\) | −4.97056 | + | 3.51472i | −0.162208 | + | 0.114699i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.3553 | + | 28.3553i | −0.924358 | + | 0.924358i | −0.997334 | − | 0.0729761i | \(-0.976750\pi\) |
0.0729761 | + | 0.997334i | \(0.476750\pi\) | |||||||
\(942\) | 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 | 0.839869 | − | 0.542789i | \(-0.182632\pi\) |
−0.542789 | + | 0.839869i | \(0.682632\pi\) | |||||||
\(948\) | 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 | \(-0.671367\pi\) | ||||
−0.512733 | + | 0.858548i | \(0.671367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.6274 | − | 42.6274i | −1.37939 | − | 1.37939i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.5147 | − | 10.9706i | 0.501520 | − | 0.354628i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.65685 | 0.118086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.9411 | −2.54649 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.14214 | + | 19.1421i | 0.294601 | + | 0.616847i | ||||
\(964\) | 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 | −0.381881 | − | 0.924212i | \(-0.624724\pi\) |
0.924212 | + | 0.381881i | \(0.124724\pi\) | |||||||
\(972\) | 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 | \(0.167000\pi\) | ||||
−0.865501 | + | 0.500907i | \(0.833000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.94113 | − | 7.94113i | 0.253799 | − | 0.253799i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.656854 | + | 0.313708i | −0.0209717 | + | 0.0100159i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.4853i | 1.73781i | 0.494978 | + | 0.868905i | \(0.335176\pi\) | ||||
−0.494978 | + | 0.868905i | \(0.664824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.828427i | 0.0263959i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.65685 | − | 8.00000i | −0.180060 | − | 0.254643i | ||||
\(988\) | 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.b.239.2 | 4 | ||
3.2 | odd | 2 | 1344.2.s.a.239.1 | 4 | |||
4.3 | odd | 2 | 336.2.s.a.323.1 | yes | 4 | ||
12.11 | even | 2 | 336.2.s.b.323.2 | yes | 4 | ||
16.5 | even | 4 | 336.2.s.b.155.2 | yes | 4 | ||
16.11 | odd | 4 | 1344.2.s.a.911.1 | 4 | |||
48.5 | odd | 4 | 336.2.s.a.155.2 | ✓ | 4 | ||
48.11 | even | 4 | inner | 1344.2.s.b.911.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.a.155.2 | ✓ | 4 | 48.5 | odd | 4 | ||
336.2.s.a.323.1 | yes | 4 | 4.3 | odd | 2 | ||
336.2.s.b.155.2 | yes | 4 | 16.5 | even | 4 | ||
336.2.s.b.323.2 | yes | 4 | 12.11 | even | 2 | ||
1344.2.s.a.239.1 | 4 | 3.2 | odd | 2 | |||
1344.2.s.a.911.1 | 4 | 16.11 | odd | 4 | |||
1344.2.s.b.239.2 | 4 | 1.1 | even | 1 | trivial | ||
1344.2.s.b.911.1 | 4 | 48.11 | even | 4 | inner |