Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(145,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.bc (of order \(12\), degree \(4\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1009.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1009 |
Dual form | 1728.2.bc.a.721.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 0.267949i | −0.447214 | + | 0.119831i | −0.475395 | − | 0.879772i | \(-0.657695\pi\) |
0.0281817 | + | 0.999603i | \(0.491028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.36603 | + | 1.36603i | −0.894274 | + | 0.516309i | −0.875338 | − | 0.483512i | \(-0.839361\pi\) |
−0.0189356 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.13397 | − | 4.23205i | 0.341906 | − | 1.27601i | −0.554279 | − | 0.832331i | \(-0.687006\pi\) |
0.896185 | − | 0.443680i | \(-0.146327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.901924 | + | 3.36603i | 0.250149 | + | 0.933567i | 0.970725 | + | 0.240192i | \(0.0772105\pi\) |
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.73205 | 1.39023 | 0.695113 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.36603 | − | 2.36603i | 0.542803 | − | 0.542803i | −0.381546 | − | 0.924350i | \(-0.624608\pi\) |
0.924350 | + | 0.381546i | \(0.124608\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.09808 | − | 2.36603i | −0.854508 | − | 0.493350i | 0.00766135 | − | 0.999971i | \(-0.497561\pi\) |
−0.862169 | + | 0.506620i | \(0.830895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40192 | + | 1.96410i | −0.680385 | + | 0.392820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.36603 | − | 0.633975i | −0.439360 | − | 0.117726i | 0.0323566 | − | 0.999476i | \(-0.489699\pi\) |
−0.471717 | + | 0.881750i | \(0.656365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.267949 | − | 0.464102i | 0.0481251 | − | 0.0833551i | −0.840959 | − | 0.541098i | \(-0.818009\pi\) |
0.889085 | + | 0.457743i | \(0.151342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 2.00000i | 0.338062 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.73205 | + | 4.73205i | 0.777944 | + | 0.777944i | 0.979481 | − | 0.201537i | \(-0.0645935\pi\) |
−0.201537 | + | 0.979481i | \(0.564594\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.59808 | + | 1.50000i | 0.405751 | + | 0.234261i | 0.688963 | − | 0.724797i | \(-0.258066\pi\) |
−0.283211 | + | 0.959058i | \(0.591400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23205 | + | 8.33013i | −0.340385 | + | 1.27033i | 0.557528 | + | 0.830158i | \(0.311750\pi\) |
−0.897912 | + | 0.440174i | \(0.854917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.83013 | + | 6.63397i | 0.558681 | + | 0.967665i | 0.997607 | + | 0.0691412i | \(0.0220259\pi\) |
−0.438925 | + | 0.898523i | \(0.644641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.232051 | − | 0.401924i | 0.0331501 | − | 0.0574177i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.46410 | + | 7.46410i | 1.02527 | + | 1.02527i | 0.999672 | + | 0.0256010i | \(0.00814993\pi\) |
0.0256010 | + | 0.999672i | \(0.491850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.53590i | 0.611620i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.33013 | − | 1.96410i | 0.954301 | − | 0.255704i | 0.252115 | − | 0.967697i | \(-0.418874\pi\) |
0.702186 | + | 0.711993i | \(0.252207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1962 | + | 3.00000i | 1.43352 | + | 0.384111i | 0.890260 | − | 0.455453i | \(-0.150523\pi\) |
0.543261 | + | 0.839564i | \(0.317189\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.80385 | − | 3.12436i | −0.223740 | − | 0.387529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.76795 | + | 6.59808i | 0.215989 | + | 0.806083i | 0.985816 | + | 0.167830i | \(0.0536760\pi\) |
−0.769827 | + | 0.638253i | \(0.779657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.92820i | − | 0.347514i | −0.984789 | − | 0.173757i | \(-0.944409\pi\) | ||
0.984789 | − | 0.173757i | \(-0.0555907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.26795i | 0.733608i | 0.930298 | + | 0.366804i | \(0.119548\pi\) | ||||
−0.930298 | + | 0.366804i | \(0.880452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.09808 | + | 11.5622i | 0.353059 | + | 1.31763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.36603 | − | 0.366025i | −0.149941 | − | 0.0401765i | 0.183068 | − | 0.983100i | \(-0.441397\pi\) |
−0.333009 | + | 0.942924i | \(0.608064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.73205 | + | 1.53590i | −0.621728 | + | 0.166592i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.00000i | − | 0.212000i | −0.994366 | − | 0.106000i | \(-0.966196\pi\) | ||
0.994366 | − | 0.106000i | \(-0.0338043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.73205 | − | 6.73205i | −0.705711 | − | 0.705711i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.73205 | + | 3.00000i | −0.177705 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86603 | − | 10.1603i | −0.595605 | − | 1.03162i | −0.993461 | − | 0.114170i | \(-0.963579\pi\) |
0.397857 | − | 0.917448i | \(-0.369754\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.535898 | + | 2.00000i | −0.0533239 | + | 0.199007i | −0.987449 | − | 0.157938i | \(-0.949515\pi\) |
0.934125 | + | 0.356946i | \(0.116182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0981 | − | 7.56218i | −1.29059 | − | 0.745124i | −0.311833 | − | 0.950137i | \(-0.600943\pi\) |
−0.978759 | + | 0.205014i | \(0.934276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4904 | + | 12.4904i | 1.20749 | + | 1.20749i | 0.971837 | + | 0.235654i | \(0.0757231\pi\) |
0.235654 | + | 0.971837i | \(0.424277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7321 | − | 10.7321i | 1.02794 | − | 1.02794i | 0.0283459 | − | 0.999598i | \(-0.490976\pi\) |
0.999598 | − | 0.0283459i | \(-0.00902398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.92820 | − | 12.0000i | 0.651751 | − | 1.12887i | −0.330947 | − | 0.943649i | \(-0.607368\pi\) |
0.982698 | − | 0.185216i | \(-0.0592984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.73205 | + | 1.26795i | 0.441266 | + | 0.118237i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.5622 | + | 7.83013i | −1.24324 | + | 0.717787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.09808 | − | 4.09808i | −0.645280 | − | 0.372552i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.53590 | − | 6.53590i | 0.584589 | − | 0.584589i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.19615 | −0.372348 | −0.186174 | − | 0.982517i | \(-0.559609\pi\) | ||||
−0.186174 | + | 0.982517i | \(0.559609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.09808 | + | 7.83013i | 0.183310 | + | 0.684121i | 0.994986 | + | 0.100014i | \(0.0318887\pi\) |
−0.811676 | + | 0.584108i | \(0.801445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.36603 | + | 8.83013i | −0.205160 | + | 0.765669i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.25833 | + | 4.76795i | −0.705557 | + | 0.407353i | −0.809414 | − | 0.587239i | \(-0.800215\pi\) |
0.103857 | + | 0.994592i | \(0.466882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.4282 | − | 3.06218i | 0.969328 | − | 0.259731i | 0.260784 | − | 0.965397i | \(-0.416019\pi\) |
0.708544 | + | 0.705667i | \(0.249352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.2679 | 1.27677 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.53590 | 0.210595 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.83013 | + | 2.09808i | −0.641469 | + | 0.171881i | −0.564869 | − | 0.825181i | \(-0.691073\pi\) |
−0.0766003 | + | 0.997062i | \(0.524407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.633975 | + | 0.366025i | −0.0515921 | + | 0.0297867i | −0.525574 | − | 0.850748i | \(-0.676149\pi\) |
0.473982 | + | 0.880534i | \(0.342816\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.143594 | + | 0.535898i | −0.0115337 | + | 0.0430444i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.26795 | + | 4.73205i | 0.101193 | + | 0.377659i | 0.997886 | − | 0.0649959i | \(-0.0207034\pi\) |
−0.896692 | + | 0.442655i | \(0.854037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9282 | 1.01889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | − | 7.00000i | 0.548282 | − | 0.548282i | −0.377661 | − | 0.925944i | \(-0.623272\pi\) |
0.925944 | + | 0.377661i | \(0.123272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.46410 | + | 3.73205i | 0.500207 | + | 0.288795i | 0.728799 | − | 0.684728i | \(-0.240079\pi\) |
−0.228592 | + | 0.973522i | \(0.573412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.741670 | − | 0.428203i | 0.0570515 | − | 0.0329387i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.63397 | − | 0.437822i | −0.124229 | − | 0.0332870i | 0.196169 | − | 0.980570i | \(-0.437150\pi\) |
−0.320398 | + | 0.947283i | \(0.603817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.36603 | − | 9.29423i | 0.405633 | − | 0.702578i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.92820 | + | 1.92820i | −0.144121 | + | 0.144121i | −0.775486 | − | 0.631365i | \(-0.782495\pi\) |
0.631365 | + | 0.775486i | \(0.282495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.39230 | − | 7.39230i | −0.549466 | − | 0.549466i | 0.376821 | − | 0.926286i | \(-0.377017\pi\) |
−0.926286 | + | 0.376821i | \(0.877017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 3.46410i | −0.441129 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.50000 | − | 24.2583i | 0.475327 | − | 1.77394i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0263 | − | 20.8301i | −0.870191 | − | 1.50722i | −0.861799 | − | 0.507250i | \(-0.830662\pi\) |
−0.00839227 | − | 0.999965i | \(-0.502671\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8660 | + | 18.8205i | −0.782154 | + | 1.35473i | 0.148531 | + | 0.988908i | \(0.452545\pi\) |
−0.930685 | + | 0.365822i | \(0.880788\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.6603 | − | 13.6603i | −0.973253 | − | 0.973253i | 0.0263987 | − | 0.999651i | \(-0.491596\pi\) |
−0.999651 | + | 0.0263987i | \(0.991596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.1244i | 1.78102i | 0.454965 | + | 0.890509i | \(0.349652\pi\) | ||||
−0.454965 | + | 0.890509i | \(0.650348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.46410 | − | 1.73205i | 0.453691 | − | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 0.803848i | −0.209529 | − | 0.0561432i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.33013 | − | 12.6962i | −0.507035 | − | 0.878211i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.09808 | + | 4.09808i | 0.0755947 | + | 0.282123i | 0.993367 | − | 0.114983i | \(-0.0366812\pi\) |
−0.917773 | + | 0.397106i | \(0.870015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.92820i | − | 0.608898i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.46410i | 0.0993897i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.16987 | + | 19.2942i | 0.347763 | + | 1.29787i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.02628 | + | 13.9019i | 0.537479 | + | 0.930942i | 0.999039 | + | 0.0438324i | \(0.0139568\pi\) |
−0.461559 | + | 0.887109i | \(0.652710\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.13397 | + | 0.571797i | 0.141637 | + | 0.0379515i | 0.328941 | − | 0.944351i | \(-0.393308\pi\) |
−0.187304 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.83013 | − | 1.83013i | 0.451347 | − | 0.120938i | −0.0259823 | − | 0.999662i | \(-0.508271\pi\) |
0.477330 | + | 0.878724i | \(0.341605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.19615i | − | 0.209387i | −0.994505 | − | 0.104693i | \(-0.966614\pi\) | ||
0.994505 | − | 0.104693i | \(-0.0333861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.60770 | − | 5.60770i | −0.365806 | − | 0.365806i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.90192 | + | 13.6865i | −0.511133 | + | 0.885308i | 0.488784 | + | 0.872405i | \(0.337441\pi\) |
−0.999917 | + | 0.0129033i | \(0.995893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5981 | − | 20.0885i | −0.747098 | − | 1.29401i | −0.949208 | − | 0.314649i | \(-0.898113\pi\) |
0.202110 | − | 0.979363i | \(-0.435220\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.124356 | + | 0.464102i | −0.00794479 | + | 0.0296504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0981 | + | 5.83013i | 0.642525 | + | 0.370962i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.83013 | − | 5.83013i | −0.367994 | − | 0.367994i | 0.498751 | − | 0.866745i | \(-0.333792\pi\) |
−0.866745 | + | 0.498751i | \(0.833792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6603 | + | 14.6603i | −0.921682 | + | 0.921682i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.42820 | + | 16.3301i | −0.588115 | + | 1.01865i | 0.406364 | + | 0.913711i | \(0.366796\pi\) |
−0.994479 | + | 0.104934i | \(0.966537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.6603 | − | 4.73205i | −1.09735 | − | 0.294035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.49038 | + | 1.43782i | −0.153563 | + | 0.0886599i | −0.574813 | − | 0.818285i | \(-0.694925\pi\) |
0.421249 | + | 0.906945i | \(0.361592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.46410 | − | 5.46410i | −0.581375 | − | 0.335657i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.26795 | + | 1.26795i | −0.0773082 | + | 0.0773082i | −0.744704 | − | 0.667395i | \(-0.767409\pi\) |
0.667395 | + | 0.744704i | \(0.267409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.392305 | 0.0238308 | 0.0119154 | − | 0.999929i | \(-0.496207\pi\) | ||||
0.0119154 | + | 0.999929i | \(0.496207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.45448 | + | 16.6244i | 0.268615 | + | 1.00249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.75833 | + | 25.2224i | −0.406069 | + | 1.51547i | 0.396007 | + | 0.918247i | \(0.370395\pi\) |
−0.802076 | + | 0.597222i | \(0.796271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.66025 | − | 5.00000i | 0.516627 | − | 0.298275i | −0.218926 | − | 0.975741i | \(-0.570255\pi\) |
0.735554 | + | 0.677466i | \(0.236922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.5622 | − | 5.24167i | 1.16285 | − | 0.311585i | 0.374747 | − | 0.927127i | \(-0.377730\pi\) |
0.788104 | + | 0.615542i | \(0.211063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.19615 | −0.483804 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8564 | 0.932730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.36603 | − | 1.43782i | 0.313487 | − | 0.0839985i | −0.0986454 | − | 0.995123i | \(-0.531451\pi\) |
0.412132 | + | 0.911124i | \(0.364784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.80385 | + | 3.92820i | −0.396135 | + | 0.228709i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.26795 | − | 15.9282i | 0.246822 | − | 0.921152i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.09808 | − | 22.7583i | −0.351487 | − | 1.31177i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.02628 | + | 3.02628i | −0.172719 | + | 0.172719i | −0.788173 | − | 0.615454i | \(-0.788973\pi\) |
0.615454 | + | 0.788173i | \(0.288973\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.0981 | − | 11.0263i | −1.08295 | − | 0.625243i | −0.151261 | − | 0.988494i | \(-0.548333\pi\) |
−0.931691 | + | 0.363251i | \(0.881667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6506 | − | 10.7679i | 1.05420 | − | 0.608640i | 0.130375 | − | 0.991465i | \(-0.458382\pi\) |
0.923821 | + | 0.382824i | \(0.125049\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.5622 | + | 5.50962i | 1.15489 | + | 0.309451i | 0.784922 | − | 0.619595i | \(-0.212703\pi\) |
0.369965 | + | 0.929046i | \(0.379370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.36603 | + | 9.29423i | −0.300440 | + | 0.520377i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5622 | − | 13.5622i | 0.754620 | − | 0.754620i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67949 | − | 9.67949i | −0.536922 | − | 0.536922i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.1244 | − | 10.4641i | −0.999228 | − | 0.576905i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0262794 | + | 0.0980762i | −0.00144445 | + | 0.00539076i | −0.966644 | − | 0.256123i | \(-0.917555\pi\) |
0.965200 | + | 0.261513i | \(0.0842216\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.53590 | − | 6.12436i | −0.193187 | − | 0.334609i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.89230 | − | 15.4019i | 0.484395 | − | 0.838996i | −0.515445 | − | 0.856923i | \(-0.672373\pi\) |
0.999839 | + | 0.0179267i | \(0.00570654\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.66025 | − | 1.66025i | −0.0899078 | − | 0.0899078i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.8564i | − | 0.964155i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.6244 | + | 4.72243i | −0.946125 | + | 0.253513i | −0.698717 | − | 0.715398i | \(-0.746245\pi\) |
−0.247408 | + | 0.968911i | \(0.579579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9282 | + | 4.26795i | 0.852617 | + | 0.228458i | 0.658556 | − | 0.752531i | \(-0.271167\pi\) |
0.194061 | + | 0.980989i | \(0.437834\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.16025 | − | 12.4019i | −0.381102 | − | 0.660088i | 0.610118 | − | 0.792310i | \(-0.291122\pi\) |
−0.991220 | + | 0.132223i | \(0.957789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.784610 | + | 2.92820i | 0.0416428 | + | 0.155413i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.2679i | − | 0.594700i | −0.954769 | − | 0.297350i | \(-0.903897\pi\) | ||
0.954769 | − | 0.297350i | \(-0.0961028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.80385i | 0.410729i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.67949 | − | 6.26795i | −0.0879086 | − | 0.328079i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1244 | − | 24.4641i | −0.737285 | − | 1.27702i | −0.953713 | − | 0.300717i | \(-0.902774\pi\) |
0.216428 | − | 0.976299i | \(-0.430559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.8564 | − | 7.46410i | −1.44623 | − | 0.387517i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.4904 | − | 7.36603i | 1.42340 | − | 0.381398i | 0.536710 | − | 0.843767i | \(-0.319667\pi\) |
0.886688 | + | 0.462368i | \(0.153000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.53590i | − | 0.439621i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.75833 | − | 3.75833i | −0.193052 | − | 0.193052i | 0.603961 | − | 0.797014i | \(-0.293588\pi\) |
−0.797014 | + | 0.603961i | \(0.793588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.73205 | + | 11.6603i | −0.343992 | + | 0.595811i | −0.985170 | − | 0.171581i | \(-0.945113\pi\) |
0.641178 | + | 0.767392i | \(0.278446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.19615 | − | 10.7321i | −0.315785 | − | 0.546956i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.29423 | − | 19.7583i | 0.268428 | − | 1.00179i | −0.691691 | − | 0.722194i | \(-0.743134\pi\) |
0.960119 | − | 0.279593i | \(-0.0901996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.4904 | − | 13.5622i | −1.18796 | − | 0.685869i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.78461 | − | 8.78461i | −0.442002 | − | 0.442002i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.26795 | + | 9.26795i | −0.465145 | + | 0.465145i | −0.900337 | − | 0.435192i | \(-0.856680\pi\) |
0.435192 | + | 0.900337i | \(0.356680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.79423 | − | 3.10770i | 0.0895995 | − | 0.155191i | −0.817742 | − | 0.575584i | \(-0.804775\pi\) |
0.907342 | + | 0.420393i | \(0.138108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.80385 | + | 0.483340i | 0.0898560 | + | 0.0240769i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.3923 | − | 14.6603i | 1.25865 | − | 0.726682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.8660 | + | 16.0885i | 1.37789 | + | 0.795523i | 0.991905 | − | 0.126984i | \(-0.0405295\pi\) |
0.385981 | + | 0.922507i | \(0.373863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.6603 | + | 14.6603i | −0.721384 | + | 0.721384i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.46410 | 0.0718699 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.77757 | + | 6.63397i | 0.0868399 | + | 0.324091i | 0.995656 | − | 0.0931055i | \(-0.0296794\pi\) |
−0.908816 | + | 0.417196i | \(0.863013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.19615 | − | 30.5885i | 0.399456 | − | 1.49079i | −0.414600 | − | 0.910004i | \(-0.636078\pi\) |
0.814056 | − | 0.580786i | \(-0.197255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5000 | + | 11.2583i | −0.945889 | + | 0.546109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.5885 | + | 8.19615i | −1.48028 | + | 0.396640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1962 | −0.780141 | −0.390071 | − | 0.920785i | \(-0.627549\pi\) | ||||
−0.390071 | + | 0.920785i | \(0.627549\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.73205 | −0.275465 | −0.137732 | − | 0.990469i | \(-0.543981\pi\) | ||||
−0.137732 | + | 0.990469i | \(0.543981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.2942 | + | 4.09808i | −0.731622 | + | 0.196038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.8564 | − | 13.1962i | 1.09088 | − | 0.629818i | 0.157067 | − | 0.987588i | \(-0.449796\pi\) |
0.933810 | + | 0.357770i | \(0.116463\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.62436 | + | 17.2583i | −0.219710 | + | 0.819968i | 0.764745 | + | 0.644332i | \(0.222865\pi\) |
−0.984455 | + | 0.175636i | \(0.943802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.535898 | + | 2.00000i | 0.0254040 | + | 0.0948091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.33975 | 0.157612 | 0.0788062 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788062 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.29423 | − | 9.29423i | 0.437648 | − | 0.437648i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.53590 | + | 4.92820i | 0.400169 | + | 0.231038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.25833 | − | 1.30385i | 0.105640 | − | 0.0609914i | −0.446249 | − | 0.894909i | \(-0.647240\pi\) |
0.551889 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.6865 | − | 9.56218i | −1.66209 | − | 0.445355i | −0.699127 | − | 0.714997i | \(-0.746428\pi\) |
−0.962961 | + | 0.269642i | \(0.913094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.19615 | + | 2.07180i | −0.0555899 | + | 0.0962846i | −0.892481 | − | 0.451085i | \(-0.851037\pi\) |
0.836891 | + | 0.547369i | \(0.184371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.63397 | − | 2.63397i | 0.121886 | − | 0.121886i | −0.643533 | − | 0.765419i | \(-0.722532\pi\) |
0.765419 | + | 0.643533i | \(0.222532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1962 | − | 13.1962i | −0.609342 | − | 0.609342i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.7224 | + | 18.8923i | 1.50458 | + | 0.868669i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.40192 | + | 12.6962i | −0.156091 | + | 0.582539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.16987 | + | 7.22243i | 0.190526 | + | 0.330001i | 0.945425 | − | 0.325840i | \(-0.105647\pi\) |
−0.754898 | + | 0.655842i | \(0.772314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6603 | + | 20.1962i | −0.531662 | + | 0.920865i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.58846 | + | 8.58846i | 0.389982 | + | 0.389982i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.80385i | 0.262997i | 0.991316 | + | 0.131499i | \(0.0419789\pi\) | ||||
−0.991316 | + | 0.131499i | \(0.958021\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8923 | + | 3.72243i | −0.626951 | + | 0.167991i | −0.558286 | − | 0.829649i | \(-0.688541\pi\) |
−0.0686652 | + | 0.997640i | \(0.521874\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5622 | − | 3.63397i | −0.610810 | − | 0.163666i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.33013 | + | 8.69615i | 0.104311 | + | 0.389293i | 0.998266 | − | 0.0588630i | \(-0.0187475\pi\) |
−0.893955 | + | 0.448156i | \(0.852081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7128i | 1.23565i | 0.786314 | + | 0.617827i | \(0.211987\pi\) | ||||
−0.786314 | + | 0.617827i | \(0.788013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.14359i | − | 0.0953887i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.07180 | − | 11.4641i | −0.136155 | − | 0.508137i | −0.999990 | − | 0.00436335i | \(-0.998611\pi\) |
0.863835 | − | 0.503774i | \(-0.168056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.56218 | − | 14.8301i | −0.378768 | − | 0.656046i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.1244 | + | 4.05256i | 0.666459 | + | 0.178577i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.4186 | − | 8.68653i | 1.42577 | − | 0.382033i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000i | 0.569540i | 0.958596 | + | 0.284770i | \(0.0919173\pi\) | ||||
−0.958596 | + | 0.284770i | \(0.908083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.53590 | + | 7.53590i | 0.329522 | + | 0.329522i | 0.852405 | − | 0.522883i | \(-0.175143\pi\) |
−0.522883 | + | 0.852405i | \(0.675143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.53590 | − | 2.66025i | 0.0669048 | − | 0.115882i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.303848 | − | 0.526279i | −0.0132108 | − | 0.0228817i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.70577 | + | 10.0981i | −0.117200 | + | 0.437396i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8372 | − | 9.14359i | −0.684701 | − | 0.395312i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.43782 | − | 1.43782i | −0.0619314 | − | 0.0619314i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.19615 | − | 2.19615i | 0.0944200 | − | 0.0944200i | −0.658319 | − | 0.752739i | \(-0.728732\pi\) |
0.752739 | + | 0.658319i | \(0.228732\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.85641 | + | 13.6077i | −0.336531 | + | 0.582890i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.6244 | − | 8.74167i | −1.39492 | − | 0.373767i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.09808 | + | 4.09808i | −0.302388 | + | 0.174584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.3923 | − | 16.3923i | −1.20736 | − | 0.697072i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8038 | − | 14.8038i | 0.627259 | − | 0.627259i | −0.320118 | − | 0.947378i | \(-0.603723\pi\) |
0.947378 | + | 0.320118i | \(0.103723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.0526 | −1.27109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.23205 | − | 26.9904i | −0.304795 | − | 1.13751i | −0.933122 | − | 0.359560i | \(-0.882927\pi\) |
0.628327 | − | 0.777949i | \(-0.283740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.71281 | + | 13.8564i | −0.156199 | + | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4019 | − | 10.6244i | 0.771449 | − | 0.445396i | −0.0619424 | − | 0.998080i | \(-0.519730\pi\) |
0.833391 | + | 0.552684i | \(0.186396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.33013 | − | 0.892305i | 0.139361 | − | 0.0373418i | −0.188464 | − | 0.982080i | \(-0.560351\pi\) |
0.327825 | + | 0.944738i | \(0.393684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.5885 | 0.775192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.78461 | −0.240816 | −0.120408 | − | 0.992724i | \(-0.538420\pi\) | ||||
−0.120408 | + | 0.992724i | \(0.538420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.73205 | − | 1.00000i | 0.154832 | − | 0.0414870i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.0526 | − | 23.1244i | 1.65881 | − | 0.957713i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.23205 | − | 26.9904i | 0.298499 | − | 1.11401i | −0.639900 | − | 0.768458i | \(-0.721024\pi\) |
0.938399 | − | 0.345554i | \(-0.112309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.464102 | − | 1.73205i | −0.0191230 | − | 0.0713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.4641 | −0.717165 | −0.358582 | − | 0.933498i | \(-0.616740\pi\) | ||||
−0.358582 | + | 0.933498i | \(0.616740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4641 | − | 11.4641i | 0.469982 | − | 0.469982i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3205 | + | 6.53590i | 0.462543 | + | 0.267050i | 0.713113 | − | 0.701049i | \(-0.247285\pi\) |
−0.250570 | + | 0.968099i | \(0.580618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.5526 | + | 11.8660i | −0.838356 | + | 0.484025i | −0.856705 | − | 0.515806i | \(-0.827492\pi\) |
0.0183488 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.19615 | + | 2.19615i | 0.333221 | + | 0.0892863i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.58846 | − | 14.8756i | 0.348595 | − | 0.603784i | −0.637405 | − | 0.770529i | \(-0.719992\pi\) |
0.986000 | + | 0.166745i | \(0.0533256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8756 | + | 18.8756i | −0.763627 | + | 0.763627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6603 | − | 15.6603i | −0.632512 | − | 0.632512i | 0.316186 | − | 0.948697i | \(-0.397598\pi\) |
−0.948697 | + | 0.316186i | \(0.897598\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.0885 | + | 20.2583i | 1.41261 | + | 0.815570i | 0.995633 | − | 0.0933485i | \(-0.0297571\pi\) |
0.416975 | + | 0.908918i | \(0.363090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.17949 | + | 15.5981i | −0.167988 | + | 0.626940i | 0.829652 | + | 0.558281i | \(0.188539\pi\) |
−0.997640 | + | 0.0686590i | \(0.978128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.73205 | + | 4.73205i | 0.109457 | + | 0.189586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.03590 | − | 8.72243i | 0.201436 | − | 0.348897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.1244 | + | 27.1244i | 1.08152 | + | 1.08152i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6077i | 0.700951i | 0.936572 | + | 0.350476i | \(0.113980\pi\) | ||||
−0.936572 | + | 0.350476i | \(0.886020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.19615 | − | 1.12436i | 0.166519 | − | 0.0446187i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.56218 | + | 0.418584i | 0.0618957 | + | 0.0165849i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7942 | + | 34.2846i | 0.781825 | + | 1.35416i | 0.930878 | + | 0.365331i | \(0.119044\pi\) |
−0.149053 | + | 0.988829i | \(0.547622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.34936 | + | 8.76795i | 0.0926499 | + | 0.345774i | 0.996653 | − | 0.0817525i | \(-0.0260517\pi\) |
−0.904003 | + | 0.427527i | \(0.859385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.7321i | − | 0.657805i | −0.944364 | − | 0.328902i | \(-0.893321\pi\) | ||
0.944364 | − | 0.328902i | \(-0.106679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 33.2487i | − | 1.30513i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.36603 | − | 27.4904i | −0.288255 | − | 1.07578i | −0.946428 | − | 0.322915i | \(-0.895337\pi\) |
0.658173 | − | 0.752867i | \(-0.271329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.19615 | − | 7.26795i | −0.163957 | − | 0.283982i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0263 | − | 4.02628i | −0.585341 | − | 0.156842i | −0.0460178 | − | 0.998941i | \(-0.514653\pi\) |
−0.539323 | + | 0.842099i | \(0.681320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.19615 | + | 2.19615i | −0.318793 | + | 0.0854204i | −0.414667 | − | 0.909973i | \(-0.636102\pi\) |
0.0958740 | + | 0.995393i | \(0.469435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.46410i | − | 0.367002i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.19615 | + | 8.19615i | 0.317356 | + | 0.317356i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.3923 | − | 43.9808i | 0.980259 | − | 1.69786i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1962 | + | 33.2487i | 0.739957 | + | 1.28164i | 0.952514 | + | 0.304495i | \(0.0984877\pi\) |
−0.212557 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.26795 | + | 4.73205i | −0.0487312 | + | 0.181867i | −0.986002 | − | 0.166736i | \(-0.946677\pi\) |
0.937270 | + | 0.348603i | \(0.113344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7583 | + | 16.0263i | 1.06527 | + | 0.615032i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.2942 | − | 20.2942i | −0.776537 | − | 0.776537i | 0.202703 | − | 0.979240i | \(-0.435027\pi\) |
−0.979240 | + | 0.202703i | \(0.935027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.98076 | − | 6.98076i | 0.266721 | − | 0.266721i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.3923 | + | 31.8564i | −0.700691 | + | 1.21363i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.29423 | − | 2.49038i | −0.353569 | − | 0.0947386i | 0.0776628 | − | 0.996980i | \(-0.475254\pi\) |
−0.431232 | + | 0.902241i | \(0.641921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.6077 | + | 6.12436i | −0.402373 | + | 0.232310i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8923 | + | 8.59808i | 0.564086 | + | 0.325675i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.66025 | − | 6.66025i | 0.251554 | − | 0.251554i | −0.570053 | − | 0.821608i | \(-0.693077\pi\) |
0.821608 | + | 0.570053i | \(0.193077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.3923 | 0.844542 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.46410 | − | 5.46410i | −0.0550632 | − | 0.205499i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.80385 | + | 36.5885i | −0.368191 | + | 1.37411i | 0.494852 | + | 0.868978i | \(0.335222\pi\) |
−0.863043 | + | 0.505131i | \(0.831444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.19615 | + | 1.26795i | −0.0822466 | + | 0.0474851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.2679 | + | 4.09103i | −0.570989 | + | 0.152996i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.39230 | 0.163805 | 0.0819027 | − | 0.996640i | \(-0.473900\pi\) | ||||
0.0819027 | + | 0.996640i | \(0.473900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.3205 | 1.53886 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.29423 | − | 2.49038i | 0.345179 | − | 0.0924904i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8109 | − | 16.6340i | 1.06854 | − | 0.616920i | 0.140755 | − | 0.990044i | \(-0.455047\pi\) |
0.927781 | + | 0.373124i | \(0.121714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.7942 | + | 47.7487i | −0.473212 | + | 1.76605i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.95448 | + | 11.0263i | 0.109126 | + | 0.407265i | 0.998781 | − | 0.0493698i | \(-0.0157213\pi\) |
−0.889654 | + | 0.456635i | \(0.849055\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.9282 | 1.10242 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.22243 | − | 8.22243i | 0.302467 | − | 0.302467i | −0.539511 | − | 0.841978i | \(-0.681391\pi\) |
0.841978 | + | 0.539511i | \(0.181391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.7583 | + | 14.2942i | 0.908295 | + | 0.524404i | 0.879882 | − | 0.475192i | \(-0.157621\pi\) |
0.0284129 | + | 0.999596i | \(0.490955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.26795 | − | 4.19615i | 0.266277 | − | 0.153735i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.6147 | − | 12.4904i | −1.70327 | − | 0.456389i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.85641 | − | 15.3397i | 0.323175 | − | 0.559755i | −0.657966 | − | 0.753047i | \(-0.728583\pi\) |
0.981141 | + | 0.193292i | \(0.0619165\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.535898 | − | 0.535898i | 0.0195033 | − | 0.0195033i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9282 | − | 19.9282i | −0.724303 | − | 0.724303i | 0.245176 | − | 0.969479i | \(-0.421154\pi\) |
−0.969479 | + | 0.245176i | \(0.921154\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.3731 | − | 26.1962i | −1.64477 | − | 0.949610i | −0.979104 | − | 0.203363i | \(-0.934813\pi\) |
−0.665669 | − | 0.746247i | \(-0.731854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7321 | + | 40.0526i | −0.388526 | + | 1.45000i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2224 | + | 22.9019i | 0.477434 | + | 0.826941i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.1244 | + | 24.4641i | −0.509337 | + | 0.882198i | 0.490604 | + | 0.871383i | \(0.336776\pi\) |
−0.999942 | + | 0.0108155i | \(0.996557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.5885 | − | 35.5885i | −1.28003 | − | 1.28003i | −0.940650 | − | 0.339378i | \(-0.889784\pi\) |
−0.339378 | − | 0.940650i | \(-0.610216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.10512i | 0.0756181i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.69615 | − | 2.59808i | 0.347401 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3923 | − | 3.32051i | −0.443432 | − | 0.118817i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.53590 | − | 4.39230i | −0.0905101 | − | 0.156768i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.8109 | + | 40.3468i | 0.385367 | + | 1.43821i | 0.837588 | + | 0.546302i | \(0.183965\pi\) |
−0.452222 | + | 0.891906i | \(0.649368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.8564i | 1.34602i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.3923i | 1.43437i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.17691 | − | 30.5167i | −0.289641 | − | 1.08096i | −0.945381 | − | 0.325968i | \(-0.894310\pi\) |
0.655740 | − | 0.754987i | \(-0.272357\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9545 | + | 38.0263i | 0.776694 | + | 1.34527i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.5263 | + | 7.10770i | 0.936092 | + | 0.250825i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.9282 | + | 3.46410i | −0.455659 | + | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.32051i | − | 0.222217i | −0.993808 | − | 0.111109i | \(-0.964560\pi\) | ||
0.993808 | − | 0.111109i | \(-0.0354401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0263 | + | 14.0263i | 0.492529 | + | 0.492529i | 0.909102 | − | 0.416573i | \(-0.136769\pi\) |
−0.416573 | + | 0.909102i | \(0.636769\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.12436 | + | 8.87564i | −0.179498 | + | 0.310900i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.4282 | + | 24.9904i | 0.504779 | + | 0.874303i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.77757 | + | 10.3660i | −0.0969378 | + | 0.361777i | −0.997306 | − | 0.0733518i | \(-0.976630\pi\) |
0.900368 | + | 0.435129i | \(0.143297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.26795 | − | 4.19615i | −0.253345 | − | 0.146269i | 0.367950 | − | 0.929846i | \(-0.380060\pi\) |
−0.621295 | + | 0.783577i | \(0.713393\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5359 | + | 17.5359i | 0.609783 | + | 0.609783i | 0.942889 | − | 0.333106i | \(-0.108097\pi\) |
−0.333106 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5167 | + | 20.5167i | −0.712573 | + | 0.712573i | −0.967073 | − | 0.254500i | \(-0.918089\pi\) |
0.254500 | + | 0.967073i | \(0.418089\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.33013 | − | 2.30385i | 0.0460862 | − | 0.0798236i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.46410 | − | 2.00000i | −0.258306 | − | 0.0692129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.4449 | − | 13.5359i | 0.809407 | − | 0.467311i | −0.0373432 | − | 0.999303i | \(-0.511889\pi\) |
0.846750 | + | 0.531991i | \(0.178556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.9186 | − | 11.5000i | −0.686848 | − | 0.396552i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.626933 | + | 0.626933i | −0.0215672 | + | 0.0215672i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3923 | 0.769409 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.19615 | − | 30.5885i | −0.280960 | − | 1.04856i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.437822 | + | 1.63397i | −0.0149907 | + | 0.0559462i | −0.973016 | − | 0.230737i | \(-0.925886\pi\) |
0.958025 | + | 0.286684i | \(0.0925528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.9090 | − | 25.9282i | 1.53406 | − | 0.885691i | 0.534892 | − | 0.844920i | \(-0.320352\pi\) |
0.999169 | − | 0.0407704i | \(-0.0129812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2583 | + | 3.82051i | −0.486488 | + | 0.130354i | −0.493722 | − | 0.869620i | \(-0.664364\pi\) |
0.00723407 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.4641 | −0.526404 | −0.263202 | − | 0.964741i | \(-0.584779\pi\) | ||||
−0.263202 | + | 0.964741i | \(0.584779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.75129 | 0.0595456 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.7846 | − | 13.6077i | 1.72275 | − | 0.461609i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6147 | + | 11.9019i | −0.698504 | + | 0.403281i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.53590 | + | 24.3923i | −0.220954 | + | 0.824610i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.46410 | − | 31.5885i | −0.285812 | − | 1.06667i | −0.948244 | − | 0.317544i | \(-0.897142\pi\) |
0.662431 | − | 0.749123i | \(-0.269525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.3205 | −0.920451 | −0.460226 | − | 0.887802i | \(-0.652231\pi\) | ||||
−0.460226 | + | 0.887802i | \(0.652231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.6340 | − | 12.6340i | 0.425167 | − | 0.425167i | −0.461811 | − | 0.886978i | \(-0.652800\pi\) |
0.886978 | + | 0.461811i | \(0.152800\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.87564 | + | 5.12436i | 0.298015 | + | 0.172059i | 0.641551 | − | 0.767081i | \(-0.278291\pi\) |
−0.343536 | + | 0.939140i | \(0.611625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.92820 | − | 5.73205i | 0.332981 | − | 0.192247i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.7583 | + | 6.63397i | 0.828506 | + | 0.221997i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.41154 | − | 2.44486i | 0.0471827 | − | 0.0817228i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.928203 | + | 0.928203i | −0.0309573 | + | 0.0309573i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7846 | + | 42.7846i | 1.42536 | + | 1.42536i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.37307 | + | 5.41154i | 0.311571 | + | 0.179886i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.20577 | − | 4.50000i | 0.0400370 | − | 0.149420i | −0.943014 | − | 0.332754i | \(-0.892022\pi\) |
0.983051 | + | 0.183334i | \(0.0586889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.46410 | + | 4.26795i | 0.0816393 | + | 0.141403i | 0.903954 | − | 0.427629i | \(-0.140651\pi\) |
−0.822315 | + | 0.569033i | \(0.807318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.09808 | + | 5.36603i | −0.102531 | + | 0.177590i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6603 | − | 15.6603i | −0.517147 | − | 0.517147i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9808i | 0.626118i | 0.949734 | + | 0.313059i | \(0.101354\pi\) | ||||
−0.949734 | + | 0.313059i | \(0.898646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.85641 | − | 2.64102i | 0.324428 | − | 0.0869301i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.3923 | − | 6.80385i | −0.834894 | − | 0.223709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.5359 | + | 19.9808i | 0.378481 | + | 0.655548i | 0.990841 | − | 0.135031i | \(-0.0431134\pi\) |
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.401924 | − | 1.50000i | −0.0131725 | − | 0.0491605i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.0000i | 0.850291i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1769i | 0.365134i | 0.983193 | + | 0.182567i | \(0.0584406\pi\) | ||||
−0.983193 | + | 0.182567i | \(0.941559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.80385 | + | 6.73205i | 0.0588038 | + | 0.219459i | 0.989075 | − | 0.147414i | \(-0.0470951\pi\) |
−0.930271 | + | 0.366873i | \(0.880428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.09808 | − | 12.2942i | −0.231145 | − | 0.400355i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.0167 | + | 10.9904i | 1.33286 | + | 0.357139i | 0.853782 | − | 0.520631i | \(-0.174303\pi\) |
0.479081 | + | 0.877771i | \(0.340970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0981 | + | 5.65321i | −0.684873 | + | 0.183511i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1051i | 0.554089i | 0.960857 | + | 0.277045i | \(0.0893550\pi\) | ||||
−0.960857 | + | 0.277045i | \(0.910645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6077 | + | 17.6077i | 0.569772 | + | 0.569772i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0263 | − | 22.5622i | 0.420641 | − | 0.728571i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3564 | + | 26.5981i | 0.495368 | + | 0.858002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.82309 | − | 21.7321i | 0.187452 | − | 0.699579i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8301 | − | 10.2942i | −0.573378 | − | 0.331040i | 0.185119 | − | 0.982716i | \(-0.440733\pi\) |
−0.758497 | + | 0.651676i | \(0.774066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5359 | + | 15.5359i | 0.498571 | + | 0.498571i | 0.910993 | − | 0.412422i | \(-0.135317\pi\) |
−0.412422 | + | 0.910993i | \(0.635317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8564 | + | 22.8564i | −0.732743 | + | 0.732743i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.0622 | − | 38.2128i | 0.705832 | − | 1.22254i | −0.260559 | − | 0.965458i | \(-0.583907\pi\) |
0.966391 | − | 0.257078i | \(-0.0827598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.46410 | − | 2.26795i | −0.270514 | − | 0.0724840i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.3205 | + | 10.0000i | 0.551877 | + | 0.318626i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.8564 | − | 28.8564i | 0.917580 | − | 0.917580i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.6410 | −1.16394 | −0.581970 | − | 0.813210i | \(-0.697718\pi\) | ||||
−0.581970 | + | 0.813210i | \(0.697718\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.73205 | − | 25.1244i | −0.213420 | − | 0.796496i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.87564 | − | 29.3923i | 0.249424 | − | 0.930864i | −0.721684 | − | 0.692223i | \(-0.756632\pi\) |
0.971108 | − | 0.238641i | \(-0.0767018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.bc.a.1009.1 | 4 | ||
3.2 | odd | 2 | 576.2.bb.c.49.1 | 4 | |||
4.3 | odd | 2 | 432.2.y.b.37.1 | 4 | |||
9.2 | odd | 6 | 576.2.bb.d.241.1 | 4 | |||
9.7 | even | 3 | 1728.2.bc.d.1585.1 | 4 | |||
12.11 | even | 2 | 144.2.x.c.85.1 | yes | 4 | ||
16.3 | odd | 4 | 432.2.y.c.253.1 | 4 | |||
16.13 | even | 4 | 1728.2.bc.d.145.1 | 4 | |||
36.7 | odd | 6 | 432.2.y.c.181.1 | 4 | |||
36.11 | even | 6 | 144.2.x.b.133.1 | yes | 4 | ||
48.29 | odd | 4 | 576.2.bb.d.337.1 | 4 | |||
48.35 | even | 4 | 144.2.x.b.13.1 | ✓ | 4 | ||
144.29 | odd | 12 | 576.2.bb.c.529.1 | 4 | |||
144.61 | even | 12 | inner | 1728.2.bc.a.721.1 | 4 | ||
144.83 | even | 12 | 144.2.x.c.61.1 | yes | 4 | ||
144.115 | odd | 12 | 432.2.y.b.397.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.b.13.1 | ✓ | 4 | 48.35 | even | 4 | ||
144.2.x.b.133.1 | yes | 4 | 36.11 | even | 6 | ||
144.2.x.c.61.1 | yes | 4 | 144.83 | even | 12 | ||
144.2.x.c.85.1 | yes | 4 | 12.11 | even | 2 | ||
432.2.y.b.37.1 | 4 | 4.3 | odd | 2 | |||
432.2.y.b.397.1 | 4 | 144.115 | odd | 12 | |||
432.2.y.c.181.1 | 4 | 36.7 | odd | 6 | |||
432.2.y.c.253.1 | 4 | 16.3 | odd | 4 | |||
576.2.bb.c.49.1 | 4 | 3.2 | odd | 2 | |||
576.2.bb.c.529.1 | 4 | 144.29 | odd | 12 | |||
576.2.bb.d.241.1 | 4 | 9.2 | odd | 6 | |||
576.2.bb.d.337.1 | 4 | 48.29 | odd | 4 | |||
1728.2.bc.a.721.1 | 4 | 144.61 | even | 12 | inner | ||
1728.2.bc.a.1009.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.bc.d.145.1 | 4 | 16.13 | even | 4 | |||
1728.2.bc.d.1585.1 | 4 | 9.7 | even | 3 |