Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(49,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.403374 + 1.68443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.49 |
Dual form | 912.2.q.l.577.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.66044 | + | 2.87597i | −0.742572 | + | 1.28617i | 0.208748 | + | 0.977969i | \(0.433061\pi\) |
−0.951320 | + | 0.308204i | \(0.900272\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.32088 | −0.877212 | −0.438606 | − | 0.898679i | \(-0.644528\pi\) | ||||
−0.438606 | + | 0.898679i | \(0.644528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70739 | 0.514797 | 0.257399 | − | 0.966305i | \(-0.417135\pi\) | ||||
0.257399 | + | 0.966305i | \(0.417135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.01414 | − | 3.48859i | −0.558621 | − | 0.967560i | −0.997612 | − | 0.0690685i | \(-0.977997\pi\) |
0.438991 | − | 0.898492i | \(-0.355336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.66044 | + | 2.87597i | 0.428724 | + | 0.742572i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.193252 | − | 4.35461i | −0.0443351 | − | 0.999017i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.16044 | + | 2.00994i | −0.253229 | + | 0.438606i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17458 | − | 2.03443i | −0.244917 | − | 0.424208i | 0.717191 | − | 0.696876i | \(-0.245427\pi\) |
−0.962108 | + | 0.272668i | \(0.912094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.01414 | − | 5.22064i | −0.602827 | − | 1.04413i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.32088 | − | 5.75194i | −0.616673 | − | 1.06811i | −0.990089 | − | 0.140444i | \(-0.955147\pi\) |
0.373416 | − | 0.927664i | \(-0.378186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.70739 | −1.20468 | −0.602341 | − | 0.798239i | \(-0.705765\pi\) | ||||
−0.602341 | + | 0.798239i | \(0.705765\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.853695 | − | 1.47864i | 0.148609 | − | 0.257399i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.85369 | − | 6.67479i | 0.651393 | − | 1.12825i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.02827 | −0.645040 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.32088 | − | 5.75194i | 0.518635 | − | 0.898302i | −0.481131 | − | 0.876649i | \(-0.659774\pi\) |
0.999766 | − | 0.0216532i | \(-0.00689298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.353695 | − | 0.612617i | 0.0539379 | − | 0.0934232i | −0.837796 | − | 0.545984i | \(-0.816156\pi\) |
0.891734 | + | 0.452561i | \(0.149489\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.32088 | 0.495048 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.61350 | −0.230499 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.98133 | + | 8.62791i | 0.684238 | + | 1.18513i | 0.973676 | + | 0.227938i | \(0.0731983\pi\) |
−0.289438 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.83502 | + | 4.91040i | −0.382274 | + | 0.662118i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.86783 | − | 2.00994i | −0.512307 | − | 0.266224i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.853695 | − | 1.47864i | 0.111142 | − | 0.192503i | −0.805089 | − | 0.593154i | \(-0.797883\pi\) |
0.916231 | + | 0.400651i | \(0.131216\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.69325 | − | 2.93280i | −0.216799 | − | 0.375506i | 0.737029 | − | 0.675861i | \(-0.236228\pi\) |
−0.953828 | + | 0.300355i | \(0.902895\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.16044 | + | 2.00994i | 0.146202 | + | 0.253229i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.3774 | 1.65927 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.18872 | − | 7.25507i | −0.511733 | − | 0.886348i | −0.999907 | − | 0.0136016i | \(-0.995670\pi\) |
0.488174 | − | 0.872746i | \(-0.337663\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.34916 | −0.282805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.70739 | + | 8.15344i | −0.558664 | + | 0.967635i | 0.438944 | + | 0.898514i | \(0.355353\pi\) |
−0.997608 | + | 0.0691206i | \(0.977981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.82088 | + | 10.0821i | −0.681283 | + | 1.18002i | 0.293307 | + | 0.956018i | \(0.405244\pi\) |
−0.974590 | + | 0.223998i | \(0.928089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.02827 | −0.696085 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.96265 | −0.451586 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.67458 | + | 2.90046i | −0.188405 | + | 0.326327i | −0.944719 | − | 0.327882i | \(-0.893665\pi\) |
0.756314 | + | 0.654209i | \(0.226998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0565 | 1.10385 | 0.551925 | − | 0.833894i | \(-0.313894\pi\) | ||||
0.551925 | + | 0.833894i | \(0.313894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.64177 | −0.712072 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.33956 | + | 2.32018i | 0.141993 | + | 0.245939i | 0.928247 | − | 0.371964i | \(-0.121316\pi\) |
−0.786254 | + | 0.617903i | \(0.787982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.67458 | + | 8.09661i | 0.490029 | + | 0.848755i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.35369 | + | 5.80877i | −0.347762 | + | 0.602341i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.8446 | + | 6.67479i | 1.31783 | + | 0.684820i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.86330 | + | 15.3517i | −0.899931 | + | 1.55873i | −0.0723511 | + | 0.997379i | \(0.523050\pi\) |
−0.827580 | + | 0.561347i | \(0.810283\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.853695 | − | 1.47864i | −0.0857995 | − | 0.148609i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.02827 | − | 13.9054i | −0.798843 | − | 1.38364i | −0.920370 | − | 0.391049i | \(-0.872112\pi\) |
0.121527 | − | 0.992588i | \(-0.461221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.54787 | 0.743714 | 0.371857 | − | 0.928290i | \(-0.378721\pi\) | ||||
0.371857 | + | 0.928290i | \(0.378721\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.85369 | − | 6.67479i | −0.376082 | − | 0.651393i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.28354 | −0.704126 | −0.352063 | − | 0.935976i | \(-0.614520\pi\) | ||||
−0.352063 | + | 0.935976i | \(0.614520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.12763 | − | 10.6134i | 0.586921 | − | 1.01658i | −0.407712 | − | 0.913110i | \(-0.633673\pi\) |
0.994633 | − | 0.103466i | \(-0.0329933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.500000 | + | 0.866025i | −0.0474579 | + | 0.0821995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.37743 | 0.694010 | 0.347005 | − | 0.937863i | \(-0.387199\pi\) | ||||
0.347005 | + | 0.937863i | \(0.387199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.80128 | 0.727473 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.01414 | + | 3.48859i | −0.186207 | + | 0.322520i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.08482 | −0.734984 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.32088 | − | 5.75194i | −0.299434 | − | 0.518635i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.41478 | 0.305427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.32088 | + | 12.6801i | 0.649623 | + | 1.12518i | 0.983213 | + | 0.182462i | \(0.0584068\pi\) |
−0.333589 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.353695 | − | 0.612617i | −0.0311411 | − | 0.0539379i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.320884 | − | 0.555788i | 0.0280358 | − | 0.0485594i | −0.851667 | − | 0.524083i | \(-0.824408\pi\) |
0.879703 | + | 0.475524i | \(0.157741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.448517 | + | 10.1066i | 0.0388913 | + | 0.876349i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.66044 | − | 2.87597i | 0.142908 | − | 0.247524i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.29261 | − | 2.23887i | −0.110435 | − | 0.191279i | 0.805511 | − | 0.592581i | \(-0.201891\pi\) |
−0.915946 | + | 0.401302i | \(0.868558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.28807 | − | 16.0874i | −0.787804 | − | 1.36452i | −0.927309 | − | 0.374296i | \(-0.877885\pi\) |
0.139505 | − | 0.990221i | \(-0.455449\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.43892 | − | 5.95638i | −0.287577 | − | 0.498097i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.0565 | 1.83170 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.806748 | + | 1.39733i | −0.0665394 | + | 0.115250i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.98133 | − | 3.43176i | 0.162317 | − | 0.281141i | −0.773382 | − | 0.633940i | \(-0.781437\pi\) |
0.935699 | + | 0.352799i | \(0.114770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.69832 | 0.707859 | 0.353929 | − | 0.935272i | \(-0.384845\pi\) | ||||
0.353929 | + | 0.935272i | \(0.384845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1372 | − | 19.2903i | 0.894564 | − | 1.54943i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.84916 | − | 4.93489i | 0.227388 | − | 0.393847i | −0.729645 | − | 0.683826i | \(-0.760315\pi\) |
0.957033 | + | 0.289979i | \(0.0936482\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.96265 | 0.790090 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.72606 | + | 4.72168i | 0.214844 | + | 0.372120i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.3774 | −1.43943 | −0.719716 | − | 0.694269i | \(-0.755728\pi\) | ||||
−0.719716 | + | 0.694269i | \(0.755728\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.83502 | + | 4.91040i | 0.220706 | + | 0.382274i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.8163 | + | 18.7345i | 0.836994 | + | 1.44972i | 0.892396 | + | 0.451252i | \(0.149023\pi\) |
−0.0554023 | + | 0.998464i | \(0.517644\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.61350 | + | 2.79466i | −0.124115 | + | 0.214974i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67458 | + | 2.34467i | −0.281002 | + | 0.179301i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.34916 | − | 4.06886i | 0.178603 | − | 0.309350i | −0.762799 | − | 0.646636i | \(-0.776175\pi\) |
0.941402 | + | 0.337286i | \(0.109509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.99546 | + | 12.1165i | 0.528807 | + | 0.915921i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.853695 | − | 1.47864i | −0.0641676 | − | 0.111142i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.06562 | 0.0796482 | 0.0398241 | − | 0.999207i | \(-0.487320\pi\) | ||||
0.0398241 | + | 0.999207i | \(0.487320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.83502 | + | 3.17835i | 0.136396 | + | 0.236245i | 0.926130 | − | 0.377205i | \(-0.123115\pi\) |
−0.789734 | + | 0.613450i | \(0.789781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38650 | −0.250338 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66044 | − | 2.87597i | 0.122078 | − | 0.211446i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.32088 | 0.168820 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.877832 | 0.0635177 | 0.0317588 | − | 0.999496i | \(-0.489889\pi\) | ||||
0.0317588 | + | 0.999496i | \(0.489889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.30675 | − | 7.45951i | 0.310006 | − | 0.536947i | −0.668357 | − | 0.743841i | \(-0.733002\pi\) |
0.978363 | + | 0.206894i | \(0.0663354\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.68872 | − | 11.5852i | 0.478989 | − | 0.829633i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7357 | 1.76234 | 0.881172 | − | 0.472797i | \(-0.156756\pi\) | ||||
0.881172 | + | 0.472797i | \(0.156756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9955 | − | 19.0447i | −0.779448 | − | 1.35004i | −0.932260 | − | 0.361788i | \(-0.882166\pi\) |
0.152813 | − | 0.988255i | \(-0.451167\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.37743 | −0.590899 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.70739 | + | 13.3496i | 0.540953 | + | 0.936958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0283 | + | 19.1015i | 0.770248 | + | 1.33411i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.17458 | + | 2.03443i | −0.0816389 | + | 0.141403i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.329957 | − | 7.43502i | −0.0228236 | − | 0.514291i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.60896 | + | 11.4471i | −0.454979 | + | 0.788048i | −0.998687 | − | 0.0512272i | \(-0.983687\pi\) |
0.543708 | + | 0.839275i | \(0.317020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.70739 | + | 8.15344i | 0.322545 | + | 0.558664i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.17458 | + | 2.03443i | 0.0801056 | + | 0.138747i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5671 | 1.05676 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.82088 | + | 10.0821i | 0.393339 | + | 0.681283i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.74020 | + | 4.74616i | −0.183497 | + | 0.317827i | −0.943069 | − | 0.332597i | \(-0.892075\pi\) |
0.759572 | + | 0.650423i | \(0.225409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.01414 | + | 5.22064i | −0.200942 | + | 0.348043i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.70739 | −0.511557 | −0.255779 | − | 0.966735i | \(-0.582332\pi\) | ||||
−0.255779 | + | 0.966735i | \(0.582332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.02827 | 0.266196 | 0.133098 | − | 0.991103i | \(-0.457508\pi\) | ||||
0.133098 | + | 0.991103i | \(0.457508\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.98133 | + | 3.43176i | −0.130362 | + | 0.225793i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0565 | + | 22.6146i | −0.855363 | + | 1.48153i | 0.0209451 | + | 0.999781i | \(0.493332\pi\) |
−0.876308 | + | 0.481751i | \(0.840001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.9253 | 1.29978 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.67458 | + | 2.90046i | 0.108776 | + | 0.188405i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.70739 | 0.498550 | 0.249275 | − | 0.968433i | \(-0.419808\pi\) | ||||
0.249275 | + | 0.968433i | \(0.419808\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8492 | − | 18.7913i | −0.698856 | − | 1.21045i | −0.968863 | − | 0.247595i | \(-0.920360\pi\) |
0.270008 | − | 0.962858i | \(-0.412974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.67912 | − | 4.64036i | 0.171162 | − | 0.296462i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.8022 | + | 9.44496i | −0.941842 | + | 0.600969i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.02827 | − | 8.70923i | 0.318654 | − | 0.551925i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.70739 | + | 8.15344i | 0.297128 | + | 0.514640i | 0.975478 | − | 0.220099i | \(-0.0706379\pi\) |
−0.678350 | + | 0.734739i | \(0.737305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00546 | − | 3.47357i | −0.126082 | − | 0.218381i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.07522 | + | 8.79054i | 0.316584 | + | 0.548339i | 0.979773 | − | 0.200113i | \(-0.0641309\pi\) |
−0.663189 | + | 0.748452i | \(0.730798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.32088 | 0.144213 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.32088 | + | 5.75194i | −0.205558 | + | 0.356036i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.29261 | − | 2.23887i | 0.0797058 | − | 0.138054i | −0.823417 | − | 0.567436i | \(-0.807935\pi\) |
0.903123 | + | 0.429382i | \(0.141269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.0848 | −2.03238 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.67912 | 0.163959 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.273937 | + | 0.474473i | −0.0167023 | + | 0.0289292i | −0.874256 | − | 0.485466i | \(-0.838650\pi\) |
0.857553 | + | 0.514395i | \(0.171983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4431 | + | 18.0879i | −0.634370 | + | 1.09876i | 0.352278 | + | 0.935895i | \(0.385407\pi\) |
−0.986648 | + | 0.162866i | \(0.947926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.34916 | 0.565837 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.14631 | − | 8.91366i | −0.310334 | − | 0.537514i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.7831 | −1.42899 | −0.714495 | − | 0.699640i | \(-0.753344\pi\) | ||||
−0.714495 | + | 0.699640i | \(0.753344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.35369 | + | 5.80877i | 0.200780 | + | 0.347762i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.95305 | + | 10.3110i | 0.355129 | + | 0.615102i | 0.987140 | − | 0.159858i | \(-0.0511035\pi\) |
−0.632011 | + | 0.774960i | \(0.717770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.02827 | − | 15.6374i | 0.536675 | − | 0.929549i | −0.462405 | − | 0.886669i | \(-0.653013\pi\) |
0.999080 | − | 0.0428799i | \(-0.0136533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.2029 | − | 7.78637i | 0.722835 | − | 0.461225i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.70739 | + | 13.3496i | −0.454953 | + | 0.788001i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.86330 | + | 15.3517i | 0.519576 | + | 0.899931i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.3966 | −1.60053 | −0.800264 | − | 0.599648i | \(-0.795307\pi\) | ||||
−0.800264 | + | 0.599648i | \(0.795307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.83502 | + | 4.91040i | 0.165061 | + | 0.285895i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.70739 | −0.0990728 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.73153 | + | 8.19524i | −0.273631 | + | 0.473943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.820884 | + | 1.42181i | −0.0473150 | + | 0.0819520i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.0565 | −0.922425 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.2462 | 0.643955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80675 | − | 3.12938i | 0.103117 | − | 0.178603i | −0.809851 | − | 0.586636i | \(-0.800452\pi\) |
0.912967 | + | 0.408033i | \(0.133785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.77394 | − | 6.53665i | 0.214692 | − | 0.371857i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.4057 | −1.04369 | −0.521846 | − | 0.853040i | \(-0.674756\pi\) | ||||
−0.521846 | + | 0.853040i | \(0.674756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5424 | − | 19.9920i | −0.652416 | − | 1.13002i | −0.982535 | − | 0.186078i | \(-0.940422\pi\) |
0.330119 | − | 0.943939i | \(-0.392911\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.70739 | −0.434262 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6887 | + | 21.9775i | 0.712669 | + | 1.23438i | 0.963852 | + | 0.266440i | \(0.0858473\pi\) |
−0.251182 | + | 0.967940i | \(0.580819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.67004 | − | 9.82080i | −0.317461 | − | 0.549859i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.64177 | + | 6.30773i | −0.203264 | + | 0.352063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1418 | + | 21.0302i | −0.673504 | + | 1.16654i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.12763 | − | 10.6134i | −0.338859 | − | 0.586921i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.96265 | + | 12.0597i | 0.383864 | + | 0.664871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3492 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.500000 | + | 0.866025i | 0.0273998 | + | 0.0474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.8205 | 1.52000 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.04241 | − | 3.53756i | 0.111257 | − | 0.192703i | −0.805020 | − | 0.593247i | \(-0.797846\pi\) |
0.916277 | + | 0.400544i | \(0.131179\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.68872 | − | 6.38904i | 0.200344 | − | 0.347005i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4521 | −0.620167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9909 | 1.07941 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.90064 | − | 6.75611i | 0.210003 | − | 0.363737i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.85369 | − | 17.0671i | 0.528974 | − | 0.916210i | −0.470455 | − | 0.882424i | \(-0.655910\pi\) |
0.999429 | − | 0.0337860i | \(-0.0107565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.3118 | 1.24785 | 0.623926 | − | 0.781483i | \(-0.285537\pi\) | ||||
0.623926 | + | 0.781483i | \(0.285537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.01414 | + | 3.48859i | 0.107507 | + | 0.186207i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.1896 | 1.34071 | 0.670355 | − | 0.742041i | \(-0.266142\pi\) | ||||
0.670355 | + | 0.742041i | \(0.266142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.6327 | − | 27.0766i | −0.829697 | − | 1.43708i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.61350 | + | 2.79466i | −0.0851570 | + | 0.147496i | −0.905458 | − | 0.424436i | \(-0.860473\pi\) |
0.820301 | + | 0.571932i | \(0.193806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9253 | + | 1.68308i | −0.996069 | + | 0.0885831i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.04241 | + | 7.00166i | −0.212172 | + | 0.367492i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.3305 | − | 33.4814i | −1.01180 | − | 1.75250i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7311 | − | 25.5151i | −0.768959 | − | 1.33188i | −0.938128 | − | 0.346288i | \(-0.887442\pi\) |
0.169170 | − | 0.985587i | \(-0.445891\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.64177 | −0.345757 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5611 | − | 20.0244i | −0.600222 | − | 1.03961i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6700 | 1.01848 | 0.509238 | − | 0.860626i | \(-0.329927\pi\) | ||||
0.509238 | + | 0.860626i | \(0.329927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.70739 | − | 2.95729i | 0.0881692 | − | 0.152714i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.3774 | + | 23.1704i | −0.688973 | + | 1.19334i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.763937 | 0.0392408 | 0.0196204 | − | 0.999808i | \(-0.493754\pi\) | ||||
0.0196204 | + | 0.999808i | \(0.493754\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.6418 | 0.750121 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.91932 | − | 3.32435i | 0.0980724 | − | 0.169866i | −0.812814 | − | 0.582523i | \(-0.802066\pi\) |
0.910887 | + | 0.412656i | \(0.135399\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.57976 | − | 11.3965i | 0.335335 | − | 0.580818i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.707389 | −0.0359586 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1035 | − | 27.8921i | −0.816480 | − | 1.41418i | −0.908261 | − | 0.418405i | \(-0.862589\pi\) |
0.0917810 | − | 0.995779i | \(-0.470744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.320884 | − | 0.555788i | −0.0161865 | − | 0.0280358i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.56108 | − | 9.63208i | −0.279809 | − | 0.484643i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2977 | − | 23.0322i | 0.667391 | − | 1.15596i | −0.311240 | − | 0.950331i | \(-0.600744\pi\) |
0.978631 | − | 0.205624i | \(-0.0659224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.97679 | + | 4.66485i | 0.449402 | + | 0.233535i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.66044 | − | 8.07212i | 0.232731 | − | 0.403103i | −0.725880 | − | 0.687822i | \(-0.758567\pi\) |
0.958611 | + | 0.284719i | \(0.0919004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5096 | + | 23.3993i | 0.672961 | + | 1.16560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.66044 | − | 2.87597i | −0.0825080 | − | 0.142908i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.70739 | −0.0846321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9006 | − | 18.8805i | −0.539002 | − | 0.933579i | −0.998958 | − | 0.0456372i | \(-0.985468\pi\) |
0.459956 | − | 0.887942i | \(-0.347865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.58522 | −0.127520 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98133 | + | 3.43176i | −0.0974947 | + | 0.168866i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.6983 | + | 28.9223i | −0.819688 | + | 1.41974i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.5761 | −0.909678 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.93438 | −0.241060 | −0.120530 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.12763 | + | 3.68517i | −0.103694 | + | 0.179604i | −0.913204 | − | 0.407503i | \(-0.866400\pi\) |
0.809510 | + | 0.587107i | \(0.199733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.92984 | + | 6.80669i | 0.190178 | + | 0.329399i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.87783 | −0.332065 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.414779 | − | 0.718418i | −0.0199792 | − | 0.0346050i | 0.855863 | − | 0.517203i | \(-0.173027\pi\) |
−0.875842 | + | 0.482598i | \(0.839693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.24113 | − | 14.2741i | −0.396043 | − | 0.685967i | 0.597190 | − | 0.802099i | \(-0.296284\pi\) |
−0.993234 | + | 0.116132i | \(0.962950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0283 | − | 19.1015i | 0.528765 | − | 0.915848i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.63217 | + | 5.50800i | −0.412933 | + | 0.263483i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2170 | − | 24.6245i | 0.678540 | − | 1.17527i | −0.296881 | − | 0.954915i | \(-0.595946\pi\) |
0.975421 | − | 0.220351i | \(-0.0707203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.806748 | + | 1.39733i | 0.0384166 | + | 0.0665394i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.70739 | − | 13.3496i | −0.366189 | − | 0.634258i | 0.622777 | − | 0.782399i | \(-0.286004\pi\) |
−0.988966 | + | 0.148141i | \(0.952671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.89703 | −0.421760 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.98133 | − | 3.43176i | −0.0937135 | − | 0.162317i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1523 | −1.09262 | −0.546312 | − | 0.837582i | \(-0.683969\pi\) | ||||
−0.546312 | + | 0.837582i | \(0.683969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.67004 | − | 9.82080i | 0.266992 | − | 0.462444i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.34916 | − | 7.53296i | 0.204341 | − | 0.353929i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.0475 | −1.45553 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.68819 | 0.219304 | 0.109652 | − | 0.993970i | \(-0.465026\pi\) | ||||
0.109652 | + | 0.993970i | \(0.465026\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.27394 | + | 10.8668i | −0.292206 | + | 0.506116i | −0.974331 | − | 0.225119i | \(-0.927723\pi\) |
0.682125 | + | 0.731236i | \(0.261056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8880 | −1.06369 | −0.531847 | − | 0.846841i | \(-0.678502\pi\) | ||||
−0.531847 | + | 0.846841i | \(0.678502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.1372 | − | 19.2903i | −0.516477 | − | 0.894564i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.8122 | 0.546604 | 0.273302 | − | 0.961928i | \(-0.411884\pi\) | ||||
0.273302 | + | 0.961928i | \(0.411884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.72153 | + | 16.8382i | 0.448898 | + | 0.777515i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.84916 | − | 4.93489i | −0.131282 | − | 0.227388i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.603895 | − | 1.04598i | 0.0277671 | − | 0.0480940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.1514 | + | 14.1343i | −1.01637 | + | 0.648526i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.98133 | − | 8.62791i | 0.228079 | − | 0.395045i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0192 | − | 29.4781i | −0.777627 | − | 1.34689i | −0.933306 | − | 0.359082i | \(-0.883090\pi\) |
0.155679 | − | 0.987808i | \(-0.450244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.01414 | + | 3.48859i | 0.0918367 | + | 0.159066i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.45213 | 0.248080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.4340 | − | 50.9811i | −1.33653 | − | 2.31493i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.41478 | 0.335996 | 0.167998 | − | 0.985787i | \(-0.446270\pi\) | ||||
0.167998 | + | 0.985787i | \(0.446270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.18872 | + | 15.9153i | −0.415528 | + | 0.719716i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.93438 | − | 3.35044i | 0.0872973 | − | 0.151203i | −0.819071 | − | 0.573693i | \(-0.805510\pi\) |
0.906368 | + | 0.422489i | \(0.138844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.67004 | 0.254849 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9253 | − | 18.9232i | 0.490067 | − | 0.848821i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7931 | + | 30.8186i | −0.796530 | + | 1.37963i | 0.125333 | + | 0.992115i | \(0.460000\pi\) |
−0.921863 | + | 0.387516i | \(0.873333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6327 | 0.966478 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.29261 | + | 7.43502i | 0.191398 | + | 0.331511i | 0.945714 | − | 0.325001i | \(-0.105365\pi\) |
−0.754316 | + | 0.656512i | \(0.772031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.3219 | 2.37280 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.61350 | + | 2.79466i | 0.0716578 | + | 0.124115i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.97173 | + | 6.87923i | 0.176044 | + | 0.304917i | 0.940522 | − | 0.339733i | \(-0.110337\pi\) |
−0.764478 | + | 0.644649i | \(0.777003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5096 | − | 23.3993i | 0.597630 | − | 1.03512i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.193252 | + | 4.35461i | 0.00853230 | + | 0.192261i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.5328 | + | 21.7075i | −0.552262 | + | 0.956545i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.12217 | − | 8.87186i | −0.225273 | − | 0.390184i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.34916 | − | 4.06886i | −0.103117 | − | 0.178603i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0757489 | −0.00331862 | −0.00165931 | − | 0.999999i | \(-0.500528\pi\) | ||||
−0.00165931 | + | 0.999999i | \(0.500528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1514 | + | 17.5827i | 0.443888 | + | 0.768837i | 0.997974 | − | 0.0636224i | \(-0.0202653\pi\) |
−0.554086 | + | 0.832460i | \(0.686932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.9909 | 0.610614 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.74073 | − | 15.1394i | 0.380032 | − | 0.658234i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.70739 | −0.0740944 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.7549 | −1.15888 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0939 | − | 20.9472i | 0.522865 | − | 0.905628i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.532810 | − | 0.922854i | 0.0229925 | − | 0.0398241i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.75486 | −0.118660 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5475 | + | 28.6611i | 0.711432 | + | 1.23224i | 0.964320 | + | 0.264740i | \(0.0852862\pi\) |
−0.252888 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.67004 | 0.157497 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.3492 | + | 35.2458i | 0.871662 | + | 1.50976i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.9581 | − | 31.1044i | −0.767834 | − | 1.32993i | −0.938735 | − | 0.344639i | \(-0.888001\pi\) |
0.170902 | − | 0.985288i | \(-0.445332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.69325 | + | 2.93280i | −0.0722663 | + | 0.125169i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4057 | + | 15.5727i | −1.03972 | + | 0.663421i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.88650 | − | 6.73162i | 0.165271 | − | 0.286258i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.66044 | − | 2.87597i | −0.0704818 | − | 0.122078i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.962653 | + | 1.66736i | 0.0407889 | + | 0.0706485i | 0.885699 | − | 0.464260i | \(-0.153680\pi\) |
−0.844910 | + | 0.534908i | \(0.820346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.84956 | −0.120523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.8861 | −0.458795 | −0.229397 | − | 0.973333i | \(-0.573676\pi\) | ||||
−0.229397 | + | 0.973333i | \(0.573676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2498 | + | 21.2173i | −0.515353 | + | 0.892618i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.16044 | − | 2.00994i | 0.0487340 | − | 0.0844098i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.4358 | −1.52747 | −0.763735 | − | 0.645530i | \(-0.776636\pi\) | ||||
−0.763735 | + | 0.645530i | \(0.776636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.54787 | 0.315869 | 0.157934 | − | 0.987450i | \(-0.449517\pi\) | ||||
0.157934 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.438916 | − | 0.760225i | 0.0183360 | − | 0.0317588i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.08068 | + | 12.2641i | −0.295285 | + | 0.511449i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.4823 | −0.644535 | −0.322267 | − | 0.946649i | \(-0.604445\pi\) | ||||
−0.322267 | + | 0.946649i | \(0.604445\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.30675 | − | 7.45951i | −0.178982 | − | 0.310006i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.3401 | −0.968310 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.50506 | + | 14.7312i | 0.352244 | + | 0.610104i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.68872 | − | 11.5852i | −0.276544 | − | 0.478989i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.8729 | + | 25.7606i | −0.613870 | + | 1.06325i | 0.376712 | + | 0.926331i | \(0.377055\pi\) |
−0.990582 | + | 0.136924i | \(0.956279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29622 | + | 29.2081i | 0.0534098 | + | 1.20350i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.3678 | − | 21.4217i | 0.508745 | − | 0.881172i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.273937 | + | 0.474473i | 0.0112493 | + | 0.0194843i | 0.871595 | − | 0.490226i | \(-0.163086\pi\) |
−0.860346 | + | 0.509711i | \(0.829753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.9909 | −0.900029 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.8163 | − | 39.5191i | −0.932251 | − | 1.61471i | −0.779465 | − | 0.626446i | \(-0.784509\pi\) |
−0.152786 | − | 0.988259i | \(-0.548825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.85783 | −0.279737 | −0.139868 | − | 0.990170i | \(-0.544668\pi\) | ||||
−0.139868 | + | 0.990170i | \(0.544668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.18872 | + | 7.25507i | −0.170578 | + | 0.295449i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4244 | − | 23.2517i | 0.545779 | − | 0.945316i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.76394 | 0.274540 | 0.137270 | − | 0.990534i | \(-0.456167\pi\) | ||||
0.137270 | + | 0.990534i | \(0.456167\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.4148 | 0.624638 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0848 | + | 20.9315i | −0.488900 | + | 0.846799i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.22153 | + | 3.84780i | −0.0897266 | + | 0.155411i | −0.907396 | − | 0.420278i | \(-0.861933\pi\) |
0.817669 | + | 0.575689i | \(0.195266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.0565 | 0.889406 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0005 | + | 27.7137i | 0.644157 | + | 1.11571i | 0.984496 | + | 0.175410i | \(0.0561250\pi\) |
−0.340339 | + | 0.940303i | \(0.610542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.3774 | 0.577878 | 0.288939 | − | 0.957348i | \(-0.406698\pi\) | ||||
0.288939 | + | 0.957348i | \(0.406698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.17458 | + | 2.03443i | 0.0471342 | + | 0.0816389i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.10896 | − | 5.38487i | −0.124558 | − | 0.215740i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.40064 | − | 16.2824i | 0.376026 | − | 0.651296i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.60389 | − | 3.43176i | −0.263734 | − | 0.137051i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.54695 | + | 9.60759i | 0.220820 | + | 0.382472i | 0.955057 | − | 0.296421i | \(-0.0957932\pi\) |
−0.734237 | + | 0.678893i | \(0.762460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.60896 | + | 11.4471i | 0.262683 | + | 0.454979i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48.6236 | −1.92957 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.24980 | + | 5.62882i | 0.128762 | + | 0.223022i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.41478 | 0.372443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.7357 | + | 37.6473i | −0.858507 | + | 1.48698i | 0.0148458 | + | 0.999890i | \(0.495274\pi\) |
−0.873353 | + | 0.487088i | \(0.838059\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8113 | + | 20.4577i | −0.465792 | + | 0.806775i | −0.999237 | − | 0.0390599i | \(-0.987564\pi\) |
0.533445 | + | 0.845835i | \(0.320897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.34916 | 0.0924980 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9253 | 0.783345 | 0.391672 | − | 0.920105i | \(-0.371897\pi\) | ||||
0.391672 | + | 0.920105i | \(0.371897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.45759 | − | 2.52462i | 0.0572154 | − | 0.0990999i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.78354 | − | 13.4815i | 0.305061 | − | 0.528381i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.11310 | −0.0826918 | −0.0413459 | − | 0.999145i | \(-0.513165\pi\) | ||||
−0.0413459 | + | 0.999145i | \(0.513165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.06562 | + | 1.84571i | 0.0416372 | + | 0.0721178i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6418 | 0.454189 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.7507 | + | 37.6734i | 0.847288 | + | 1.46755i | 0.883619 | + | 0.468206i | \(0.155100\pi\) |
−0.0363312 | + | 0.999340i | \(0.511567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0565 | − | 19.1505i | −0.430050 | − | 0.744868i | 0.566827 | − | 0.823837i | \(-0.308171\pi\) |
−0.996877 | + | 0.0789685i | \(0.974837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.8109 | − | 15.4914i | −1.15602 | − | 0.600732i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.80128 | + | 13.5122i | −0.302067 | + | 0.523195i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.74020 | + | 4.74616i | 0.105942 | + | 0.183497i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.89104 | − | 5.00743i | −0.111607 | − | 0.193310i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5953 | 0.485515 | 0.242758 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242758 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.01414 | + | 5.22064i | 0.116014 | + | 0.200942i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.9427 | −1.26609 | −0.633045 | − | 0.774115i | \(-0.718195\pi\) | ||||
−0.633045 | + | 0.774115i | \(0.718195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.5707 | − | 35.6295i | 0.789430 | − | 1.36733i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.85369 | + | 6.67479i | −0.147674 | + | 0.255779i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.3876 | 0.703580 | 0.351790 | − | 0.936079i | \(-0.385573\pi\) | ||||
0.351790 | + | 0.936079i | \(0.385573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.58522 | 0.328024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.01414 | − | 3.48859i | 0.0768441 | − | 0.133098i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.0661 | − | 34.7556i | 0.764459 | − | 1.32408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6599 | 0.633773 | 0.316887 | − | 0.948463i | \(-0.397363\pi\) | ||||
0.316887 | + | 0.948463i | \(0.397363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.98133 | + | 3.43176i | 0.0752644 | + | 0.130362i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 61.6892 | 2.34001 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0565 | + | 22.6146i | 0.493844 | + | 0.855363i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.3588 | − | 42.1906i | 0.920018 | − | 1.59352i | 0.120633 | − | 0.992697i | \(-0.461507\pi\) |
0.799384 | − | 0.600820i | \(-0.205159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.193252 | + | 4.35461i | 0.00728865 | + | 0.164237i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.96265 | − | 17.2558i | 0.375215 | − | 0.649892i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.6327 | + | 32.2728i | 0.700755 | + | 1.21374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.7498 | − | 25.5474i | −0.553940 | − | 0.959453i | −0.997985 | − | 0.0634483i | \(-0.979790\pi\) |
0.444045 | − | 0.896005i | \(-0.353543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.34916 | 0.125603 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.87836 | + | 13.6457i | 0.295047 | + | 0.511036i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8405 | 0.854186 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.85369 | − | 6.67479i | 0.143919 | − | 0.249275i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3250 | − | 19.6155i | 0.422352 | − | 0.731535i | −0.573817 | − | 0.818984i | \(-0.694538\pi\) |
0.996169 | + | 0.0874484i | \(0.0278713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5177 | −0.652395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.6983 | −0.806969 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0192 | + | 34.6743i | −0.743494 | + | 1.28777i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.3638 | − | 45.6635i | 0.977780 | − | 1.69356i | 0.307342 | − | 0.951599i | \(-0.400560\pi\) |
0.670438 | − | 0.741966i | \(-0.266106\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.72659 | 0.211516 | 0.105758 | − | 0.994392i | \(-0.466273\pi\) | ||||
0.105758 | + | 0.994392i | \(0.466273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.67912 | − | 4.64036i | −0.0988207 | − | 0.171162i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.15177 | − | 12.3872i | −0.263439 | − | 0.456289i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.7083 | − | 28.9397i | 0.614625 | − | 1.06456i | −0.375825 | − | 0.926691i | \(-0.622641\pi\) |
0.990450 | − | 0.137872i | \(-0.0440261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.778474 | + | 17.5416i | 0.0285979 | + | 0.644406i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.9759 | + | 31.1351i | −0.659470 | + | 1.14224i | 0.321282 | + | 0.946983i | \(0.395886\pi\) |
−0.980753 | + | 0.195253i | \(0.937447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.57976 | + | 11.3965i | 0.241064 | + | 0.417534i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.02827 | − | 8.70923i | −0.183975 | − | 0.318654i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9043 | 0.617668 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5752 | − | 20.0489i | −0.422386 | − | 0.731594i | 0.573787 | − | 0.819005i | \(-0.305474\pi\) |
−0.996172 | + | 0.0874112i | \(0.972141\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.41478 | 0.343094 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.4431 | + | 25.0161i | −0.525637 | + | 0.910429i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49454 | + | 11.2489i | −0.236048 | + | 0.408847i | −0.959577 | − | 0.281447i | \(-0.909186\pi\) |
0.723529 | + | 0.690294i | \(0.242519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.01093 | −0.145587 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3593 | 0.484274 | 0.242137 | − | 0.970242i | \(-0.422152\pi\) | ||||
0.242137 | + | 0.970242i | \(0.422152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2215 | + | 24.6324i | −0.514854 | + | 0.891753i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.87783 | −0.248344 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.81181 | − | 10.0664i | −0.209579 | − | 0.363002i | 0.742003 | − | 0.670397i | \(-0.233876\pi\) |
−0.951582 | + | 0.307395i | \(0.900543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1504 | 0.365559 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.87783 | + | 6.71660i | 0.139476 | + | 0.241579i | 0.927298 | − | 0.374323i | \(-0.122125\pi\) |
−0.787822 | + | 0.615902i | \(0.788792\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.2170 | + | 35.0169i | 0.726216 | + | 1.25784i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.16044 | − | 2.00994i | 0.0416306 | − | 0.0721064i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.6892 | − | 13.3496i | −0.920413 | − | 0.478299i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.03735 | + | 13.9211i | −0.287599 | + | 0.498136i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.32088 | + | 5.75194i | 0.118679 | + | 0.205558i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.46173 | + | 16.3882i | 0.337703 | + | 0.584920i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8880 | 0.673283 | 0.336642 | − | 0.941633i | \(-0.390709\pi\) | ||||
0.336642 | + | 0.941633i | \(0.390709\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.29261 | − | 2.23887i | −0.0460182 | − | 0.0797058i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1222 | −0.608794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.82088 | + | 11.8141i | −0.242217 | + | 0.419532i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.5424 | + | 28.6523i | −0.586699 | + | 1.01619i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.5105 | 1.22243 | 0.611213 | − | 0.791466i | \(-0.290682\pi\) | ||||
0.611213 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.33956 | − | 2.32018i | 0.0473309 | − | 0.0819796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.93852 | + | 17.2140i | −0.350723 | + | 0.607469i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.1059 | −0.638148 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.273937 | + | 0.474473i | 0.00964305 | + | 0.0167023i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.6044 | 1.42758 | 0.713788 | − | 0.700362i | \(-0.246978\pi\) | ||||
0.713788 | + | 0.700362i | \(0.246978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.54787 | − | 14.8054i | −0.300156 | − | 0.519886i | 0.676015 | − | 0.736888i | \(-0.263706\pi\) |
−0.976171 | + | 0.217002i | \(0.930372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.4431 | + | 18.0879i | 0.366254 | + | 0.634370i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.5147 | − | 52.8529i | 1.06888 | − | 1.85136i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73606 | − | 1.42181i | −0.0957227 | − | 0.0497430i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.67458 | − | 8.09661i | 0.163343 | − | 0.282918i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.0475 | + | 32.9912i | 0.664761 | + | 1.15140i | 0.979350 | + | 0.202172i | \(0.0648002\pi\) |
−0.314588 | + | 0.949228i | \(0.601867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.60442 | − | 11.4392i | −0.230216 | − | 0.398745i | 0.727656 | − | 0.685942i | \(-0.240610\pi\) |
−0.957871 | + | 0.287197i | \(0.907277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.2926 | −0.358343 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9344 | − | 29.3312i | −0.588866 | − | 1.01995i | −0.994381 | − | 0.105858i | \(-0.966241\pi\) |
0.405515 | − | 0.914088i | \(-0.367092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8397 | 0.584866 | 0.292433 | − | 0.956286i | \(-0.405535\pi\) | ||||
0.292433 | + | 0.956286i | \(0.405535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.8916 | + | 20.5968i | −0.412514 | + | 0.714495i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −71.8397 | −2.48611 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.70739 | 0.231841 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.26847 | + | 2.19706i | −0.0437926 | + | 0.0758509i | −0.887091 | − | 0.461595i | \(-0.847277\pi\) |
0.843298 | + | 0.537446i | \(0.180611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.55655 | + | 13.0883i | −0.260571 | + | 0.451322i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.9061 | 0.410068 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.35823 | − | 9.28073i | −0.184329 | − | 0.319267i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.7639 | 0.644737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.02827 | − | 15.6374i | −0.309850 | − | 0.536675i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17458 | + | 2.03443i | 0.0402641 | + | 0.0697394i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.312212 | − | 0.540766i | 0.0106899 | − | 0.0185155i | −0.860631 | − | 0.509229i | \(-0.829931\pi\) |
0.871321 | + | 0.490714i | \(0.163264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.641769 | − | 14.4612i | −0.0219480 | − | 0.494561i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | − | 5.19615i | 0.102478 | − | 0.177497i | −0.810227 | − | 0.586116i | \(-0.800656\pi\) |
0.912705 | + | 0.408619i | \(0.133990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6035 | − | 23.5619i | −0.464145 | − | 0.803923i | 0.535017 | − | 0.844841i | \(-0.320305\pi\) |
−0.999163 | + | 0.0409180i | \(0.986972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.70739 | + | 13.3496i | 0.262667 | + | 0.454953i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.1131 | 0.888900 | 0.444450 | − | 0.895804i | \(-0.353399\pi\) | ||||
0.444450 | + | 0.895804i | \(0.353399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.80128 | + | 13.5122i | 0.265252 | + | 0.459429i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.85916 | + | 4.95221i | −0.0969903 | + | 0.167992i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8733 | + | 29.2254i | −0.571730 | + | 0.990265i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.7266 | 0.599954 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.92531 | −0.267924 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.3296 | − | 23.0875i | 0.450107 | − | 0.779608i | −0.548285 | − | 0.836292i | \(-0.684719\pi\) |
0.998392 | + | 0.0566830i | \(0.0180524\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.6983 | + | 23.7262i | −0.462033 | + | 0.800264i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.73566 | 0.226930 | 0.113465 | − | 0.993542i | \(-0.463805\pi\) | ||||
0.113465 | + | 0.993542i | \(0.463805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0803 | + | 27.8519i | 0.541145 | + | 0.937290i | 0.998839 | + | 0.0481803i | \(0.0153422\pi\) |
−0.457694 | + | 0.889110i | \(0.651324\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.67004 | 0.190596 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.91932 | + | 3.32435i | 0.0644443 | + | 0.111621i | 0.896447 | − | 0.443150i | \(-0.146139\pi\) |
−0.832003 | + | 0.554771i | \(0.812806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9909 | − | 29.4291i | −0.569857 | − | 0.987022i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.853695 | + | 1.47864i | −0.0285998 | + | 0.0495364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.0475 | + | 14.0680i | −0.737791 | + | 0.470768i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76940 | + | 3.06469i | −0.0591446 | + | 0.102441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.73153 | + | 8.19524i | 0.157981 | + | 0.273631i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.2745 | + | 38.5805i | 0.742895 | + | 1.28673i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.820884 | + | 1.42181i | 0.0273173 | + | 0.0473150i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1878 | −0.405136 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9819 | + | 34.6096i | −0.663487 | + | 1.14919i | 0.316207 | + | 0.948690i | \(0.397591\pi\) |
−0.979693 | + | 0.200502i | \(0.935743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.02827 | + | 13.9054i | −0.266281 | + | 0.461212i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3219 | −0.971479 | −0.485740 | − | 0.874104i | \(-0.661450\pi\) | ||||
−0.485740 | + | 0.874104i | \(0.661450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1704 | 0.568259 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.62310 | − | 9.73949i | 0.185894 | − | 0.321978i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.744736 | + | 1.28992i | −0.0245933 | + | 0.0425969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.6218 | 1.01012 | 0.505059 | − | 0.863085i | \(-0.331471\pi\) | ||||
0.505059 | + | 0.863085i | \(0.331471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.80675 | − | 3.12938i | −0.0595344 | − | 0.103117i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.9253 | 1.24833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.01414 | + | 5.22064i | 0.0991042 | + | 0.171654i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.77394 | − | 6.53665i | −0.123952 | − | 0.214692i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.96213 | − | 5.13055i | 0.0971842 | − | 0.168328i | −0.813334 | − | 0.581797i | \(-0.802350\pi\) |
0.910518 | + | 0.413469i | \(0.135683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.311812 | + | 7.02615i | 0.0102192 | + | 0.230273i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.20285 | + | 15.9398i | −0.301288 | + | 0.521846i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.50546 | + | 4.33959i | 0.0818499 | + | 0.141768i | 0.904045 | − | 0.427438i | \(-0.140584\pi\) |
−0.822195 | + | 0.569206i | \(0.807251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.0848 | −0.753345 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.19872 | − | 7.27239i | −0.136874 | − | 0.237073i | 0.789438 | − | 0.613831i | \(-0.210372\pi\) |
−0.926312 | + | 0.376758i | \(0.877039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.6026 | −0.508089 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.85369 | + | 6.67479i | −0.125361 | + | 0.217131i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.73566 | + | 16.8627i | −0.316367 | + | 0.547963i | −0.979727 | − | 0.200337i | \(-0.935796\pi\) |
0.663360 | + | 0.748300i | \(0.269130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.8962 | 1.52232 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.3774 | 0.822920 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.7543 | + | 18.6271i | −0.348367 | + | 0.603390i | −0.985960 | − | 0.166984i | \(-0.946597\pi\) |
0.637592 | + | 0.770374i | \(0.279930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.45759 | + | 2.52462i | −0.0471665 | + | 0.0816947i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.3401 | −0.366573 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | + | 5.19615i | 0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.9891 | 0.451260 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.64177 | + | 6.30773i | 0.117354 | + | 0.203264i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3022 | + | 24.7722i | 0.460404 | + | 0.797444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.41024 | + | 9.37081i | −0.173982 | + | 0.301345i | −0.939808 | − | 0.341702i | \(-0.888997\pi\) |
0.765827 | + | 0.643047i | \(0.222330\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.4996 | − | 26.8461i | 0.497406 | − | 0.861532i | −0.502590 | − | 0.864525i | \(-0.667619\pi\) |
0.999996 | + | 0.00299289i | \(0.000952667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.5565 | + | 37.3370i | 0.691071 | + | 1.19697i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.1418 | + | 21.0302i | 0.388848 | + | 0.673504i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.0950 | 1.79464 | 0.897318 | − | 0.441384i | \(-0.145512\pi\) | ||||
0.897318 | + | 0.441384i | \(0.145512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.28715 | + | 3.96145i | 0.0730975 | + | 0.126609i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2553 | −0.391280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.7225 | + | 28.9641i | −0.533363 | + | 0.923813i | 0.465877 | + | 0.884849i | \(0.345739\pi\) |
−0.999241 | + | 0.0389632i | \(0.987594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.0721 | + | 71.1390i | −1.30867 | + | 2.26668i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.9253 | 0.443247 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66177 | −0.0528412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.22245 | − | 7.31350i | 0.134131 | − | 0.232321i | −0.791134 | − | 0.611642i | \(-0.790509\pi\) |
0.925265 | + | 0.379321i | \(0.123842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.6746 | − | 18.4889i | 0.338748 | − | 0.586728i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73.0293 | 2.31519 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.2074 | − | 43.6605i | −0.798326 | − | 1.38274i | −0.920706 | − | 0.390258i | \(-0.872386\pi\) |
0.122380 | − | 0.992483i | \(-0.460947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.00000 | 0.0316386 |
(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 | 912.2.q.l.49.1 | 6 | ||
3.2 | odd | 2 | 2736.2.s.z.1873.3 | 6 | |||
4.3 | odd | 2 | 57.2.e.b.49.3 | yes | 6 | ||
12.11 | even | 2 | 171.2.f.b.163.1 | 6 | |||
19.7 | even | 3 | inner | 912.2.q.l.577.1 | 6 | ||
57.26 | odd | 6 | 2736.2.s.z.577.3 | 6 | |||
76.7 | odd | 6 | 57.2.e.b.7.3 | ✓ | 6 | ||
76.11 | odd | 6 | 1083.2.a.l.1.1 | 3 | |||
76.27 | even | 6 | 1083.2.a.o.1.3 | 3 | |||
228.11 | even | 6 | 3249.2.a.y.1.3 | 3 | |||
228.83 | even | 6 | 171.2.f.b.64.1 | 6 | |||
228.179 | odd | 6 | 3249.2.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.e.b.7.3 | ✓ | 6 | 76.7 | odd | 6 | ||
57.2.e.b.49.3 | yes | 6 | 4.3 | odd | 2 | ||
171.2.f.b.64.1 | 6 | 228.83 | even | 6 | |||
171.2.f.b.163.1 | 6 | 12.11 | even | 2 | |||
912.2.q.l.49.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.q.l.577.1 | 6 | 19.7 | even | 3 | inner | ||
1083.2.a.l.1.1 | 3 | 76.11 | odd | 6 | |||
1083.2.a.o.1.3 | 3 | 76.27 | even | 6 | |||
2736.2.s.z.577.3 | 6 | 57.26 | odd | 6 | |||
2736.2.s.z.1873.3 | 6 | 3.2 | odd | 2 | |||
3249.2.a.t.1.1 | 3 | 228.179 | odd | 6 | |||
3249.2.a.y.1.3 | 3 | 228.11 | even | 6 |