Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(433,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.r (of order \(6\), 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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 648) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.2161 |
Dual form | 2592.2.r.b.433.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23205 | + | 1.86603i | −1.44542 | + | 0.834512i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.366025 | + | 0.633975i | −0.138345 | + | 0.239620i | −0.926870 | − | 0.375382i | \(-0.877511\pi\) |
0.788526 | + | 0.615002i | \(0.210845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.09808 | − | 2.36603i | −1.23562 | − | 0.713384i | −0.267421 | − | 0.963580i | \(-0.586172\pi\) |
−0.968195 | + | 0.250196i | \(0.919505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.13397 | − | 1.23205i | 0.591858 | − | 0.341709i | −0.173974 | − | 0.984750i | \(-0.555661\pi\) |
0.765832 | + | 0.643041i | \(0.222327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.73205 | 0.905155 | 0.452578 | − | 0.891725i | \(-0.350505\pi\) | ||||
0.452578 | + | 0.891725i | \(0.350505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26795i | 0.749719i | 0.927082 | + | 0.374859i | \(0.122309\pi\) | ||||
−0.927082 | + | 0.374859i | \(0.877691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.36603 | − | 7.56218i | −0.910379 | − | 1.57682i | −0.813529 | − | 0.581524i | \(-0.802457\pi\) |
−0.0968500 | − | 0.995299i | \(-0.530877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | − | 7.73205i | 0.892820 | − | 1.54641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50000 | − | 2.59808i | −0.835629 | − | 0.482451i | 0.0201471 | − | 0.999797i | \(-0.493587\pi\) |
−0.855776 | + | 0.517346i | \(0.826920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.73205i | − | 0.461801i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000i | 0.821995i | 0.911636 | + | 0.410997i | \(0.134819\pi\) | ||||
−0.911636 | + | 0.410997i | \(0.865181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.26795 | + | 3.92820i | 0.354194 | + | 0.613482i | 0.986980 | − | 0.160845i | \(-0.0514219\pi\) |
−0.632786 | + | 0.774327i | \(0.718089\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.36603 | − | 4.83013i | −1.27581 | − | 0.736587i | −0.299732 | − | 0.954023i | \(-0.596897\pi\) |
−0.976075 | + | 0.217436i | \(0.930231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.73205 | + | 3.00000i | −0.252646 | + | 0.437595i | −0.964253 | − | 0.264982i | \(-0.914634\pi\) |
0.711608 | + | 0.702577i | \(0.247967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.23205 | + | 5.59808i | 0.461722 | + | 0.799725i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.928203i | 0.127499i | 0.997966 | + | 0.0637493i | \(0.0203058\pi\) | ||||
−0.997966 | + | 0.0637493i | \(0.979694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.6603 | 2.38131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.26795 | − | 4.19615i | 0.946206 | − | 0.546293i | 0.0543060 | − | 0.998524i | \(-0.482705\pi\) |
0.891900 | + | 0.452232i | \(0.149372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.79423 | + | 4.50000i | 0.997949 | + | 0.576166i | 0.907641 | − | 0.419748i | \(-0.137882\pi\) |
0.0903080 | + | 0.995914i | \(0.471215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.59808 | + | 7.96410i | −0.570321 | + | 0.987825i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.09808 | − | 2.36603i | 0.500660 | − | 0.289056i | −0.228326 | − | 0.973585i | \(-0.573325\pi\) |
0.728986 | + | 0.684529i | \(0.239992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.66025 | 0.671749 | 0.335874 | − | 0.941907i | \(-0.390968\pi\) | ||||
0.335874 | + | 0.941907i | \(0.390968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | − | 1.73205i | 0.341882 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.63397 | − | 4.56218i | 0.296345 | − | 0.513285i | −0.678952 | − | 0.734183i | \(-0.737565\pi\) |
0.975297 | + | 0.220898i | \(0.0708988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1244 | + | 7.00000i | 1.33082 | + | 0.768350i | 0.985426 | − | 0.170107i | \(-0.0544115\pi\) |
0.345395 | + | 0.938457i | \(0.387745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0622 | + | 6.96410i | −1.30833 | + | 0.755363i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.7321 | 1.24359 | 0.621797 | − | 0.783178i | \(-0.286403\pi\) | ||||
0.621797 | + | 0.783178i | \(0.286403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80385i | 0.189095i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.09808 | − | 10.5622i | −0.625649 | − | 1.08366i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | − | 6.92820i | 0.406138 | − | 0.703452i | −0.588315 | − | 0.808632i | \(-0.700208\pi\) |
0.994453 | + | 0.105180i | \(0.0335417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.92820 | + | 4.00000i | 0.689382 | + | 0.398015i | 0.803380 | − | 0.595466i | \(-0.203033\pi\) |
−0.113998 | + | 0.993481i | \(0.536366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | − | 3.00000i | −0.170664 | − | 0.295599i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.8564i | − | 1.23142i | −0.787973 | − | 0.615710i | \(-0.788869\pi\) | ||
0.787973 | − | 0.615710i | \(-0.211131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.86603 | − | 6.69615i | −0.363685 | − | 0.629921i | 0.624879 | − | 0.780721i | \(-0.285148\pi\) |
−0.988564 | + | 0.150800i | \(0.951815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.2224 | + | 16.2942i | 2.63176 | + | 1.51944i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.36603 | + | 2.36603i | −0.125223 | + | 0.216893i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.69615 | + | 9.86603i | 0.517832 | + | 0.896911i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.6603i | 1.31125i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6603 | 1.21215 | 0.606076 | − | 0.795407i | \(-0.292743\pi\) | ||||
0.606076 | + | 0.795407i | \(0.292743\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.169873 | − | 0.0980762i | 0.0148419 | − | 0.00856896i | −0.492561 | − | 0.870278i | \(-0.663939\pi\) |
0.507403 | + | 0.861709i | \(0.330606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.07180 | − | 1.19615i | −0.179648 | − | 0.103720i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.59808 | + | 14.8923i | −0.734583 | + | 1.27234i | 0.220323 | + | 0.975427i | \(0.429289\pi\) |
−0.954906 | + | 0.296908i | \(0.904044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8564 | + | 9.73205i | −1.42974 | + | 0.825462i | −0.997100 | − | 0.0761041i | \(-0.975752\pi\) |
−0.432642 | + | 0.901566i | \(0.642419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.6603 | −0.975079 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.3923 | 1.61044 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | − | 2.59808i | 0.368654 | − | 0.212843i | −0.304216 | − | 0.952603i | \(-0.598394\pi\) |
0.672870 | + | 0.739760i | \(0.265061\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820 | − | 12.0000i | 0.563809 | − | 0.976546i | −0.433350 | − | 0.901226i | \(-0.642669\pi\) |
0.997159 | − | 0.0753205i | \(-0.0239980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.46410 | − | 3.73205i | −0.519209 | − | 0.299766i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13397 | − | 1.23205i | 0.170310 | − | 0.0983284i | −0.412422 | − | 0.910993i | \(-0.635317\pi\) |
0.582732 | + | 0.812664i | \(0.301984\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.39230 | 0.503784 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53590i | 0.511931i | 0.966686 | + | 0.255966i | \(0.0823934\pi\) | ||||
−0.966686 | + | 0.255966i | \(0.917607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.36603 | + | 12.7583i | 0.570000 | + | 0.987269i | 0.996565 | + | 0.0828123i | \(0.0263902\pi\) |
−0.426565 | + | 0.904457i | \(0.640276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.46410 | + | 6.00000i | −0.266469 | + | 0.461538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | + | 0.866025i | 0.114043 | + | 0.0658427i | 0.555936 | − | 0.831225i | \(-0.312360\pi\) |
−0.441894 | + | 0.897067i | \(0.645693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.26795 | + | 5.66025i | 0.247034 | + | 0.427875i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.0000i | − | 1.04641i | −0.852207 | − | 0.523205i | \(-0.824736\pi\) | ||
0.852207 | − | 0.523205i | \(-0.175264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.53590i | 0.485810i | 0.970050 | + | 0.242905i | \(0.0781002\pi\) | ||||
−0.970050 | + | 0.242905i | \(0.921900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.33013 | − | 16.1603i | −0.685965 | − | 1.18813i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2942 | − | 8.83013i | −1.11842 | − | 0.645723i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.29423 | + | 14.3660i | −0.600149 | + | 1.03949i | 0.392649 | + | 0.919689i | \(0.371559\pi\) |
−0.992798 | + | 0.119801i | \(0.961774\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.42820 | − | 9.40192i | −0.390731 | − | 0.676765i | 0.601815 | − | 0.798635i | \(-0.294444\pi\) |
−0.992546 | + | 0.121870i | \(0.961111\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.12436i | − | 0.293848i | −0.989148 | − | 0.146924i | \(-0.953063\pi\) | ||
0.989148 | − | 0.146924i | \(-0.0469373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.39230 | −0.169586 | −0.0847930 | − | 0.996399i | \(-0.527023\pi\) | ||||
−0.0847930 | + | 0.996399i | \(0.527023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.29423 | − | 1.90192i | 0.231210 | − | 0.133489i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.6603 | − | 8.46410i | −1.02392 | − | 0.591158i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.73205 | − | 13.3923i | 0.534837 | − | 0.926365i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5622 | − | 13.0263i | 1.55324 | − | 0.896766i | 0.555370 | − | 0.831604i | \(-0.312577\pi\) |
0.997875 | − | 0.0651625i | \(-0.0207566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.0526 | 2.45876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.46410 | −0.0993897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.96410 | − | 4.59808i | 0.535723 | − | 0.309300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5622 | − | 20.0263i | 0.774261 | − | 1.34106i | −0.160948 | − | 0.986963i | \(-0.551455\pi\) |
0.935209 | − | 0.354096i | \(-0.115211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.83013 | − | 3.36603i | −0.386959 | − | 0.223411i | 0.293883 | − | 0.955842i | \(-0.405053\pi\) |
−0.680842 | + | 0.732431i | \(0.738386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.86603 | − | 5.69615i | 0.651965 | − | 0.376412i | −0.137243 | − | 0.990537i | \(-0.543824\pi\) |
0.789209 | + | 0.614125i | \(0.210491\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.73205 | −0.244495 | −0.122247 | − | 0.992500i | \(-0.539010\pi\) | ||||
−0.122247 | + | 0.992500i | \(0.539010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.9282i | − | 0.843343i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.92820 | − | 6.80385i | −0.254094 | − | 0.440104i | 0.710555 | − | 0.703642i | \(-0.248444\pi\) |
−0.964649 | + | 0.263538i | \(0.915111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.23205 | − | 3.86603i | 0.143779 | − | 0.249033i | −0.785138 | − | 0.619321i | \(-0.787408\pi\) |
0.928917 | + | 0.370289i | \(0.120741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.8923 | − | 12.0622i | −1.33476 | − | 0.770624i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.02628 | + | 6.97372i | 0.256186 | + | 0.443727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.26795i | 0.458749i | 0.973338 | + | 0.229374i | \(0.0736680\pi\) | ||||
−0.973338 | + | 0.229374i | \(0.926332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.3205i | 2.59780i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.66987 | − | 2.89230i | −0.104164 | − | 0.180417i | 0.809232 | − | 0.587489i | \(-0.199883\pi\) |
−0.913396 | + | 0.407072i | \(0.866550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.16987 | − | 1.83013i | −0.196966 | − | 0.113719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.12436 | − | 14.0718i | 0.500969 | − | 0.867704i | −0.499030 | − | 0.866585i | \(-0.666310\pi\) |
0.999999 | − | 0.00111953i | \(-0.000356359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.73205 | − | 3.00000i | −0.106399 | − | 0.184289i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 25.7321i | − | 1.56891i | −0.620185 | − | 0.784455i | \(-0.712943\pi\) | ||
0.620185 | − | 0.784455i | \(-0.287057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7321 | −0.651926 | −0.325963 | − | 0.945383i | \(-0.605688\pi\) | ||||
−0.325963 | + | 0.945383i | \(0.605688\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.5885 | + | 21.1244i | −2.20637 | + | 1.27385i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.53590 | + | 4.92820i | 0.512872 | + | 0.296107i | 0.734014 | − | 0.679135i | \(-0.237645\pi\) |
−0.221141 | + | 0.975242i | \(0.570978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.86603 | − | 11.8923i | 0.409593 | − | 0.709435i | −0.585251 | − | 0.810852i | \(-0.699004\pi\) |
0.994844 | + | 0.101417i | \(0.0323375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.53590 | + | 3.19615i | −0.329075 | + | 0.189992i | −0.655430 | − | 0.755256i | \(-0.727513\pi\) |
0.326355 | + | 0.945247i | \(0.394179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.32051 | −0.196003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.07180 | −0.180694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.89230 | + | 1.66987i | −0.168970 | + | 0.0975550i | −0.582100 | − | 0.813117i | \(-0.697769\pi\) |
0.413130 | + | 0.910672i | \(0.364436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.6603 | + | 27.1244i | −0.911775 | + | 1.57924i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.6340 | − | 10.7583i | −1.07763 | − | 0.622170i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.12436 | − | 3.53590i | 0.353002 | − | 0.203806i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.5885 | −1.92327 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7846i | 0.843802i | 0.906642 | + | 0.421901i | \(0.138637\pi\) | ||||
−0.906642 | + | 0.421901i | \(0.861363\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.66025 | + | 16.7321i | 0.547783 | + | 0.948788i | 0.998426 | + | 0.0560835i | \(0.0178613\pi\) |
−0.450643 | + | 0.892704i | \(0.648805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23205 | + | 2.13397i | −0.0696396 | + | 0.120619i | −0.898743 | − | 0.438476i | \(-0.855518\pi\) |
0.829103 | + | 0.559096i | \(0.188852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.03590 | + | 0.598076i | 0.0581818 | + | 0.0335913i | 0.528809 | − | 0.848741i | \(-0.322639\pi\) |
−0.470627 | + | 0.882332i | \(0.655972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.2942 | + | 21.2942i | 0.688345 | + | 1.19225i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1962i | 0.678612i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 22.0000i | − | 1.22034i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.26795 | − | 2.19615i | −0.0699043 | − | 0.121078i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3660 | − | 6.56218i | −0.624733 | − | 0.360690i | 0.153976 | − | 0.988075i | \(-0.450792\pi\) |
−0.778710 | + | 0.627385i | \(0.784125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.83013 | + | 15.2942i | −0.482441 | + | 0.835613i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | − | 3.46410i | −0.108947 | − | 0.188702i | 0.806397 | − | 0.591375i | \(-0.201415\pi\) |
−0.915344 | + | 0.402673i | \(0.868081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.46410i | − | 0.512510i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.85641 | −0.532196 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.83013 | − | 3.36603i | 0.312978 | − | 0.180698i | −0.335281 | − | 0.942118i | \(-0.608831\pi\) |
0.648258 | + | 0.761421i | \(0.275498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.2679 | + | 5.92820i | 0.549631 | + | 0.317329i | 0.748973 | − | 0.662600i | \(-0.230547\pi\) |
−0.199342 | + | 0.979930i | \(0.563881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.46410 | + | 6.00000i | −0.184376 | + | 0.319348i | −0.943366 | − | 0.331754i | \(-0.892360\pi\) |
0.758990 | + | 0.651102i | \(0.225693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.2942 | + | 10.5622i | −0.970957 | + | 0.560582i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.12436 | 0.0593412 | 0.0296706 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296706 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.32051 | 0.437921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.0885 | + | 16.7942i | −1.52256 | + | 0.879050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.26795 | − | 2.19615i | 0.0661864 | − | 0.114638i | −0.831033 | − | 0.556223i | \(-0.812250\pi\) |
0.897220 | + | 0.441585i | \(0.145583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.588457 | − | 0.339746i | −0.0305512 | − | 0.0176387i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.8564 | − | 11.4641i | 1.02813 | − | 0.593589i | 0.111679 | − | 0.993744i | \(-0.464377\pi\) |
0.916447 | + | 0.400156i | \(0.131044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.8038 | −0.659432 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.0000i | − | 0.513665i | −0.966456 | − | 0.256833i | \(-0.917321\pi\) | ||
0.966456 | − | 0.256833i | \(-0.0826790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0981 | + | 17.4904i | 0.515988 | + | 0.893717i | 0.999828 | + | 0.0185603i | \(0.00590828\pi\) |
−0.483840 | + | 0.875156i | \(0.660758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.46410 | + | 11.1962i | −0.329441 | + | 0.570609i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6603 | + | 8.46410i | 0.743304 | + | 0.429147i | 0.823270 | − | 0.567651i | \(-0.192148\pi\) |
−0.0799651 | + | 0.996798i | \(0.525481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2942 | − | 28.2224i | −0.824035 | − | 1.42727i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.6603i | 0.989215i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.4641i | − | 1.62933i | −0.579934 | − | 0.814663i | \(-0.696922\pi\) | ||
0.579934 | − | 0.814663i | \(-0.303078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.79423 | − | 8.30385i | −0.239412 | − | 0.414674i | 0.721133 | − | 0.692796i | \(-0.243621\pi\) |
−0.960546 | + | 0.278122i | \(0.910288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.26795 | + | 2.46410i | 0.212602 | + | 0.122746i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.8301 | − | 20.4904i | 0.586398 | − | 1.01567i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.3564 | − | 24.8660i | −0.709879 | − | 1.22955i | −0.964902 | − | 0.262611i | \(-0.915416\pi\) |
0.255023 | − | 0.966935i | \(-0.417917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.14359i | 0.302306i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.2487 | −2.56479 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5885 | − | 10.7321i | 0.908106 | − | 0.524295i | 0.0282844 | − | 0.999600i | \(-0.490996\pi\) |
0.879821 | + | 0.475305i | \(0.157662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2583 | − | 6.50000i | −0.548697 | − | 0.316791i | 0.199899 | − | 0.979817i | \(-0.435939\pi\) |
−0.748596 | + | 0.663026i | \(0.769272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.6603 | − | 28.8564i | 0.808141 | − | 1.39974i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.70577 | + | 3.29423i | −0.276122 | + | 0.159419i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.7128 | −1.04587 | −0.522935 | − | 0.852373i | \(-0.675163\pi\) | ||||
−0.522935 | + | 0.852373i | \(0.675163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7846 | −1.04690 | −0.523451 | − | 0.852056i | \(-0.675356\pi\) | ||||
−0.523451 | + | 0.852056i | \(0.675356\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.7128 | − | 14.2679i | 1.18217 | − | 0.682529i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0000 | + | 25.9808i | −0.715911 | + | 1.23999i | 0.246696 | + | 0.969093i | \(0.420655\pi\) |
−0.962607 | + | 0.270901i | \(0.912678\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3923 | + | 14.6603i | 1.20642 | + | 0.696530i | 0.961976 | − | 0.273133i | \(-0.0880598\pi\) |
0.244448 | + | 0.969662i | \(0.421393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.9186 | + | 21.8923i | −1.79751 | + | 1.03779i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.9282 | 1.17643 | 0.588217 | − | 0.808703i | \(-0.299830\pi\) | ||||
0.588217 | + | 0.808703i | \(0.299830\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 21.4641i | − | 1.01071i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.36603 | − | 5.83013i | −0.157802 | − | 0.273321i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.16025 | − | 5.47372i | 0.147830 | − | 0.256050i | −0.782595 | − | 0.622531i | \(-0.786104\pi\) |
0.930425 | + | 0.366481i | \(0.119438\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.7846 | + | 20.6603i | 1.66666 | + | 0.962244i | 0.969422 | + | 0.245400i | \(0.0789193\pi\) |
0.697233 | + | 0.716844i | \(0.254414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.73205 | + | 11.6603i | 0.312865 | + | 0.541898i | 0.978981 | − | 0.203950i | \(-0.0653779\pi\) |
−0.666116 | + | 0.745848i | \(0.732045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 24.7846i | − | 1.14689i | −0.819242 | − | 0.573447i | \(-0.805606\pi\) | ||
0.819242 | − | 0.573447i | \(-0.194394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.46410i | 0.159957i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.8564 | + | 39.5885i | 1.05094 | + | 1.82028i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.2679 | + | 14.5885i | 1.15937 | + | 0.669364i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.830127 | + | 1.43782i | −0.0379295 | + | 0.0656958i | −0.884367 | − | 0.466792i | \(-0.845410\pi\) |
0.846437 | + | 0.532488i | \(0.178743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.16025 | + | 10.6699i | 0.280883 | + | 0.486504i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.8564i | 1.35571i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7128 | 1.16516 | 0.582579 | − | 0.812774i | \(-0.302044\pi\) | ||||
0.582579 | + | 0.812774i | \(0.302044\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9545 | − | 6.90192i | 0.539498 | − | 0.311479i | −0.205377 | − | 0.978683i | \(-0.565842\pi\) |
0.744876 | + | 0.667203i | \(0.232509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.7942 | − | 9.69615i | −0.756374 | − | 0.436693i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.07180 | + | 3.58846i | −0.0929328 | + | 0.160964i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.09808 | − | 4.09808i | 0.317754 | − | 0.183455i | −0.332637 | − | 0.943055i | \(-0.607938\pi\) |
0.650391 | + | 0.759600i | \(0.274605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.679492 | −0.0302970 | −0.0151485 | − | 0.999885i | \(-0.504822\pi\) | ||||
−0.0151485 | + | 0.999885i | \(0.504822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.8564 | −1.32859 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.3923 | − | 14.6603i | 1.12549 | − | 0.649804i | 0.182696 | − | 0.983169i | \(-0.441517\pi\) |
0.942798 | + | 0.333365i | \(0.108184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.29423 | + | 5.70577i | −0.145728 | + | 0.252408i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.1962 | + | 6.46410i | 0.493361 | + | 0.284842i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1962 | − | 8.19615i | 0.624346 | − | 0.360466i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7846 | −1.17346 | −0.586728 | − | 0.809784i | \(-0.699584\pi\) | ||||
−0.586728 | + | 0.809784i | \(0.699584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.2679i | − | 0.580167i | −0.957001 | − | 0.290083i | \(-0.906317\pi\) | ||
0.957001 | − | 0.290083i | \(-0.0936831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.73205 | + | 6.46410i | 0.162571 | + | 0.281581i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.6244 | + | 46.1147i | −1.15758 | + | 2.00499i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.67949 | + | 5.58846i | 0.419265 | + | 0.242063i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3923 | − | 33.5885i | −0.838402 | − | 1.45216i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 30.5885i | − | 1.31754i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.1769i | 1.03945i | 0.854335 | + | 0.519723i | \(0.173965\pi\) | ||||
−0.854335 | + | 0.519723i | \(0.826035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.9904 | + | 41.5526i | 1.02764 | + | 1.77992i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5167 | − | 13.0000i | −0.962743 | − | 0.555840i | −0.0657267 | − | 0.997838i | \(-0.520937\pi\) |
−0.897016 | + | 0.441998i | \(0.854270\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.49038 | − | 14.7058i | 0.361702 | − | 0.626487i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.92820 | + | 3.33975i | 0.0819955 | + | 0.142020i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13.0526i | − | 0.553055i | −0.961006 | − | 0.276527i | \(-0.910816\pi\) | ||
0.961006 | − | 0.276527i | \(-0.0891836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.8038 | −1.00680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.0000 | − | 12.1244i | 0.885044 | − | 0.510981i | 0.0127261 | − | 0.999919i | \(-0.495949\pi\) |
0.872318 | + | 0.488938i | \(0.162616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.9904 | + | 14.4282i | 1.05135 | + | 0.606999i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.7942 | + | 29.0885i | −0.704051 | + | 1.21945i | 0.262982 | + | 0.964801i | \(0.415294\pi\) |
−0.967033 | + | 0.254651i | \(0.918039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.7321 | − | 13.1244i | 0.951307 | − | 0.549237i | 0.0578201 | − | 0.998327i | \(-0.481585\pi\) |
0.893487 | + | 0.449090i | \(0.148252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −77.9615 | −3.25122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.2487 | −1.88373 | −0.941864 | − | 0.335994i | \(-0.890928\pi\) | ||||
−0.941864 | + | 0.335994i | \(0.890928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.87564 | + | 5.12436i | −0.368224 | + | 0.212594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19615 | − | 3.80385i | 0.0909553 | − | 0.157539i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.6340 | + | 21.1506i | 1.51205 | + | 0.872980i | 0.999901 | + | 0.0140812i | \(0.00448233\pi\) |
0.512145 | + | 0.858899i | \(0.328851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.66025 | + | 3.26795i | −0.233227 | + | 0.134654i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.4115 | 0.591811 | 0.295906 | − | 0.955217i | \(-0.404379\pi\) | ||||
0.295906 | + | 0.955217i | \(0.404379\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 10.1962i | − | 0.418001i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.12436 | + | 7.14359i | 0.168517 | + | 0.291879i | 0.937899 | − | 0.346910i | \(-0.112769\pi\) |
−0.769382 | + | 0.638789i | \(0.779436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.62436 | + | 14.9378i | −0.351795 | + | 0.609326i | −0.986564 | − | 0.163375i | \(-0.947762\pi\) |
0.634769 | + | 0.772702i | \(0.281095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.8205 | − | 21.2583i | −1.49697 | − | 0.864274i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9545 | − | 22.4378i | −0.525806 | − | 0.910723i | −0.999548 | − | 0.0300594i | \(-0.990430\pi\) |
0.473742 | − | 0.880664i | \(-0.342903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.53590i | 0.345325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.3923i | − | 0.985196i | −0.870257 | − | 0.492598i | \(-0.836047\pi\) | ||
0.870257 | − | 0.492598i | \(-0.163953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0622 | − | 22.6244i | −0.525863 | − | 0.910822i | −0.999546 | − | 0.0301266i | \(-0.990409\pi\) |
0.473683 | − | 0.880696i | \(-0.342924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.41154 | + | 3.12436i | 0.217508 | + | 0.125578i | 0.604796 | − | 0.796380i | \(-0.293255\pi\) |
−0.387288 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.29423 | + | 7.43782i | −0.172045 | + | 0.297990i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.03590 | − | 8.72243i | −0.201436 | − | 0.348897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6603i | 0.744033i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.784610 | −0.0312348 | −0.0156174 | − | 0.999878i | \(-0.504971\pi\) | ||||
−0.0156174 | + | 0.999878i | \(0.504971\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.1506 | + | 25.4904i | −1.75206 | + | 1.01155i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.7942 | + | 7.96410i | 0.546547 | + | 0.315549i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5263 | − | 19.9641i | 0.455261 | − | 0.788535i | −0.543442 | − | 0.839446i | \(-0.682879\pi\) |
0.998703 | + | 0.0509118i | \(0.0162127\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.53590 | + | 3.19615i | −0.218315 | + | 0.126044i | −0.605170 | − | 0.796097i | \(-0.706895\pi\) |
0.386855 | + | 0.922141i | \(0.373561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.7654 | 1.95648 | 0.978239 | − | 0.207480i | \(-0.0665261\pi\) | ||||
0.978239 | + | 0.207480i | \(0.0665261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.7128 | −1.55886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.8038 | + | 17.7846i | −1.20545 | + | 0.695966i | −0.961761 | − | 0.273889i | \(-0.911690\pi\) |
−0.243686 | + | 0.969854i | \(0.578357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.366025 | + | 0.633975i | −0.0143018 | + | 0.0247714i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.70577 | − | 5.02628i | −0.339129 | − | 0.195796i | 0.320758 | − | 0.947161i | \(-0.396062\pi\) |
−0.659887 | + | 0.751365i | \(0.729396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.8660 | + | 16.0885i | −1.08386 | + | 0.625768i | −0.931936 | − | 0.362623i | \(-0.881881\pi\) |
−0.151927 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.92820 | 0.346221 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.3731i | 1.75685i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.2942 | − | 36.8827i | −0.822055 | − | 1.42384i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6244 | − | 32.2583i | 0.717916 | − | 1.24347i | −0.243908 | − | 0.969798i | \(-0.578429\pi\) |
0.961824 | − | 0.273669i | \(-0.0882372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.3923 | − | 14.6603i | −0.975906 | − | 0.563439i | −0.0748741 | − | 0.997193i | \(-0.523855\pi\) |
−0.901031 | + | 0.433754i | \(0.857189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.92820 | + | 5.07180i | 0.112374 | + | 0.194638i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 34.1051i | − | 1.30500i | −0.757790 | − | 0.652498i | \(-0.773721\pi\) | ||
0.757790 | − | 0.652498i | \(-0.226279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 64.1769i | − | 2.45207i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.14359 | + | 1.98076i | 0.0435674 | + | 0.0754610i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0263 | − | 6.36603i | −0.419459 | − | 0.242175i | 0.275387 | − | 0.961334i | \(-0.411194\pi\) |
−0.694846 | + | 0.719159i | \(0.744527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.3205 | − | 62.9090i | 1.37772 | − | 2.38627i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.46410 | + | 14.6603i | 0.320601 | + | 0.555297i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.1244i | 0.382392i | 0.981552 | + | 0.191196i | \(0.0612365\pi\) | ||||
−0.981552 | + | 0.191196i | \(0.938763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3397 | −0.616265 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.07180 | + | 2.92820i | −0.190745 | + | 0.110126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.0429 | − | 23.6962i | −1.54140 | − | 0.889928i | −0.998751 | − | 0.0499682i | \(-0.984088\pi\) |
−0.542649 | − | 0.839959i | \(-0.682579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.73205 | − | 15.1244i | 0.327018 | − | 0.566412i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.6865 | − | 21.7583i | 1.40940 | − | 0.813715i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.0526 | −1.79206 | −0.896029 | − | 0.443995i | \(-0.853561\pi\) | ||||
−0.896029 | + | 0.443995i | \(0.853561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53590 | 0.0944418 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.1769 | + | 23.1962i | −1.49213 | + | 0.861483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.7583 | + | 42.8827i | −0.918236 | + | 1.59043i | −0.116142 | + | 0.993233i | \(0.537053\pi\) |
−0.802094 | + | 0.597198i | \(0.796281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.2224 | − | 18.0263i | −1.15480 | − | 0.666726i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.5167 | − | 14.7321i | 0.942479 | − | 0.544141i | 0.0517427 | − | 0.998660i | \(-0.483522\pi\) |
0.890737 | + | 0.454520i | \(0.150189\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.3923 | −0.824831 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.60770i | − | 0.353425i | −0.984263 | − | 0.176712i | \(-0.943454\pi\) | ||
0.984263 | − | 0.176712i | \(-0.0565462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3923 | + | 26.6603i | 0.564689 | + | 0.978070i | 0.997079 | + | 0.0763830i | \(0.0243372\pi\) |
−0.432390 | + | 0.901687i | \(0.642329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.69615 | + | 16.7942i | −0.355240 | + | 0.615293i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.58846 | − | 3.80385i | −0.240737 | − | 0.138990i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.75833 | − | 15.1699i | −0.319596 | − | 0.553557i | 0.660808 | − | 0.750555i | \(-0.270214\pi\) |
−0.980404 | + | 0.196999i | \(0.936881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.7128i | 1.88202i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2487i | 0.663261i | 0.943409 | + | 0.331630i | \(0.107599\pi\) | ||||
−0.943409 | + | 0.331630i | \(0.892401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.9904 | + | 31.1603i | 0.652151 | + | 1.12956i | 0.982600 | + | 0.185735i | \(0.0594664\pi\) |
−0.330449 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.15064 | + | 4.70577i | 0.295073 | + | 0.170360i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3397 | − | 17.9090i | 0.373347 | − | 0.646655i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.6962 | + | 34.1147i | 0.710261 | + | 1.23021i | 0.964759 | + | 0.263135i | \(0.0847566\pi\) |
−0.254497 | + | 0.967073i | \(0.581910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40.6603i | − | 1.46245i | −0.682138 | − | 0.731224i | \(-0.738949\pi\) | ||
0.682138 | − | 0.731224i | \(-0.261051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.8564 | 0.641421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.8372 | + | 7.41154i | −0.459939 | + | 0.265546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1962 | − | 13.3923i | −0.830024 | − | 0.479214i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.59808 | + | 7.96410i | −0.164112 | + | 0.284251i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5096 | + | 7.22243i | −0.445920 | + | 0.257452i | −0.706105 | − | 0.708107i | \(-0.749550\pi\) |
0.260186 | + | 0.965559i | \(0.416216\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.66025 | 0.201255 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.1769 | 0.787525 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.6244 | − | 6.13397i | 0.376334 | − | 0.217277i | −0.299888 | − | 0.953974i | \(-0.596949\pi\) |
0.676222 | + | 0.736698i | \(0.263616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.46410 | + | 11.1962i | −0.228683 | + | 0.396091i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.8827 | − | 21.2942i | −1.30156 | − | 0.751457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.6603 | + | 11.9282i | −0.728178 | + | 0.420414i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.0526 | 1.72460 | 0.862298 | − | 0.506401i | \(-0.169024\pi\) | ||||
0.862298 | + | 0.506401i | \(0.169024\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.7846i | 1.71306i | 0.516098 | + | 0.856530i | \(0.327384\pi\) | ||||
−0.516098 | + | 0.856530i | \(0.672616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1962 | − | 21.1244i | −0.427213 | − | 0.739954i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.7846 | − | 27.3397i | 0.552234 | − | 0.956497i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.37564 | − | 0.794229i | −0.0480103 | − | 0.0277188i | 0.475803 | − | 0.879552i | \(-0.342158\pi\) |
−0.523813 | + | 0.851833i | \(0.675491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.80385 | − | 15.2487i | −0.306883 | − | 0.531537i | 0.670796 | − | 0.741642i | \(-0.265953\pi\) |
−0.977679 | + | 0.210105i | \(0.932619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.3397i | − | 0.429095i | −0.976714 | − | 0.214548i | \(-0.931172\pi\) | ||
0.976714 | − | 0.214548i | \(-0.0688277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.1769i | 1.84691i | 0.383706 | + | 0.923455i | \(0.374648\pi\) | ||||
−0.383706 | + | 0.923455i | \(0.625352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0622 | + | 20.8923i | 0.417930 | + | 0.723875i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.6147 | − | 27.4904i | −1.64778 | − | 0.951344i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.9019 | + | 36.2032i | −0.721615 | + | 1.24987i | 0.238738 | + | 0.971084i | \(0.423266\pi\) |
−0.960352 | + | 0.278789i | \(0.910067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | − | 1.73205i | −0.0344828 | − | 0.0597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 25.8564i | − | 0.889487i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.33975 | −0.286557 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.8109 | − | 21.8301i | 1.29614 | − | 0.748327i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.39230 | + | 2.53590i | 0.150390 | + | 0.0868275i | 0.573307 | − | 0.819341i | \(-0.305660\pi\) |
−0.422917 | + | 0.906168i | \(0.638994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0621778 | − | 0.107695i | 0.00212395 | − | 0.00367880i | −0.864961 | − | 0.501838i | \(-0.832657\pi\) |
0.867085 | + | 0.498159i | \(0.165991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.73205 | + | 1.00000i | −0.0590968 | + | 0.0341196i | −0.529257 | − | 0.848461i | \(-0.677529\pi\) |
0.470160 | + | 0.882581i | \(0.344196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5167 | −0.868597 | −0.434299 | − | 0.900769i | \(-0.643004\pi\) | ||||
−0.434299 | + | 0.900769i | \(0.643004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.46410 | −0.219786 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.5885 | + | 12.4641i | −0.732338 | + | 0.422816i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.83013 | − | 10.0981i | 0.197546 | − | 0.342160i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.29423 | − | 5.36603i | −0.314202 | − | 0.181405i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.4545 | − | 28.5526i | 1.66996 | − | 0.964151i | 0.702303 | − | 0.711878i | \(-0.252155\pi\) |
0.967656 | − | 0.252274i | \(-0.0811783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.8564 | −0.938506 | −0.469253 | − | 0.883064i | \(-0.655477\pi\) | ||||
−0.469253 | + | 0.883064i | \(0.655477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.32051i | − | 0.0444386i | −0.999753 | − | 0.0222193i | \(-0.992927\pi\) | ||
0.999753 | − | 0.0222193i | \(-0.00707321\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.09808 | − | 1.90192i | −0.0368698 | − | 0.0638604i | 0.847002 | − | 0.531590i | \(-0.178405\pi\) |
−0.883871 | + | 0.467730i | \(0.845072\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.00000 | + | 8.66025i | −0.167695 | + | 0.290456i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.80385 | − | 5.66025i | −0.328073 | − | 0.189413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.1244 | + | 45.2487i | 0.873241 | + | 1.51250i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10.3923i | − | 0.346603i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.46410i | 0.115406i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1962 | − | 21.1244i | −0.405414 | − | 0.702197i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0526 | + | 16.1962i | 0.931470 | + | 0.537784i | 0.887276 | − | 0.461239i | \(-0.152595\pi\) |
0.0441938 | + | 0.999023i | \(0.485928\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.36603 | + | 14.4904i | −0.277179 | + | 0.480088i | −0.970683 | − | 0.240365i | \(-0.922733\pi\) |
0.693504 | + | 0.720453i | \(0.256066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.1244 | − | 57.3731i | −1.09626 | − | 1.89877i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.143594i | 0.00474188i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9808 | −0.560144 | −0.280072 | − | 0.959979i | \(-0.590358\pi\) | ||||
−0.280072 | + | 0.959979i | \(0.590358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0788 | − | 6.97372i | 0.397580 | − | 0.229543i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.6603 | + | 22.3205i | 1.27114 | + | 0.733894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.258330 | + | 0.447441i | −0.00847554 | + | 0.0146801i | −0.870232 | − | 0.492642i | \(-0.836031\pi\) |
0.861757 | + | 0.507322i | \(0.169365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.2942 | + | 10.5622i | −0.599569 | + | 0.346161i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 65.9090 | 2.15545 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.24871 | −0.236805 | −0.118403 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118403 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9115 | − | 9.18653i | 0.518701 | − | 0.299472i | −0.217702 | − | 0.976015i | \(-0.569856\pi\) |
0.736403 | + | 0.676543i | \(0.236523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.8038 | − | 34.3013i | 0.644902 | − | 1.11700i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.4904 | + | 10.0981i | 0.568361 | + | 0.328143i | 0.756494 | − | 0.654000i | \(-0.226910\pi\) |
−0.188133 | + | 0.982143i | \(0.560244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.2058 | − | 11.0885i | 0.623446 | − | 0.359947i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.6603 | −0.863610 | −0.431805 | − | 0.901967i | \(-0.642123\pi\) | ||||
−0.431805 | + | 0.901967i | \(0.642123\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 61.9090i | − | 2.00333i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.29423 | − | 10.9019i | −0.203251 | − | 0.352041i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.0885 | + | 20.2583i | 1.12954 | + | 0.652139i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.09808 | + | 8.83013i | 0.163943 | + | 0.283958i | 0.936279 | − | 0.351256i | \(-0.114245\pi\) |
−0.772336 | + | 0.635214i | \(0.780912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 51.1244i | − | 1.64066i | −0.571891 | − | 0.820329i | \(-0.693790\pi\) | ||
0.571891 | − | 0.820329i | \(-0.306210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.2487i | − | 0.456793i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.3923 | − | 19.7321i | −0.364472 | − | 0.631284i | 0.624219 | − | 0.781249i | \(-0.285417\pi\) |
−0.988691 | + | 0.149965i | \(0.952084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.0788 | − | 27.7583i | −1.53661 | − | 0.887160i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.732051 | − | 1.26795i | 0.0233488 | − | 0.0404413i | −0.854115 | − | 0.520084i | \(-0.825901\pi\) |
0.877464 | + | 0.479643i | \(0.159234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.69615 | + | 13.3301i | 0.245220 | + | 0.424733i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 84.3538i | 2.68230i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.58846 | −0.0822251 | −0.0411125 | − | 0.999155i | \(-0.513090\pi\) | ||||
−0.0411125 | + | 0.999155i | \(0.513090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.73205 | − | 4.46410i | 0.245122 | − | 0.141522i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1865 | + | 13.9641i | 0.765995 | + | 0.442248i | 0.831444 | − | 0.555608i | \(-0.187515\pi\) |
−0.0654489 | + | 0.997856i | \(0.520848\pi\) | |||||||
\(998\) | 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 | 2592.2.r.b.2161.1 | 4 | ||
3.2 | odd | 2 | 2592.2.r.k.2161.2 | 4 | |||
4.3 | odd | 2 | 648.2.n.b.541.2 | 4 | |||
8.3 | odd | 2 | 648.2.n.m.541.1 | 4 | |||
8.5 | even | 2 | 2592.2.r.j.2161.2 | 4 | |||
9.2 | odd | 6 | 2592.2.d.g.1297.4 | 4 | |||
9.4 | even | 3 | 2592.2.r.j.433.2 | 4 | |||
9.5 | odd | 6 | 2592.2.r.a.433.1 | 4 | |||
9.7 | even | 3 | 2592.2.d.h.1297.1 | 4 | |||
12.11 | even | 2 | 648.2.n.l.541.1 | 4 | |||
24.5 | odd | 2 | 2592.2.r.a.2161.1 | 4 | |||
24.11 | even | 2 | 648.2.n.a.541.2 | 4 | |||
36.7 | odd | 6 | 648.2.d.e.325.2 | yes | 4 | ||
36.11 | even | 6 | 648.2.d.i.325.3 | yes | 4 | ||
36.23 | even | 6 | 648.2.n.a.109.1 | 4 | |||
36.31 | odd | 6 | 648.2.n.m.109.2 | 4 | |||
72.5 | odd | 6 | 2592.2.r.k.433.2 | 4 | |||
72.11 | even | 6 | 648.2.d.i.325.4 | yes | 4 | ||
72.13 | even | 6 | inner | 2592.2.r.b.433.1 | 4 | ||
72.29 | odd | 6 | 2592.2.d.g.1297.1 | 4 | |||
72.43 | odd | 6 | 648.2.d.e.325.1 | ✓ | 4 | ||
72.59 | even | 6 | 648.2.n.l.109.1 | 4 | |||
72.61 | even | 6 | 2592.2.d.h.1297.4 | 4 | |||
72.67 | odd | 6 | 648.2.n.b.109.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.d.e.325.1 | ✓ | 4 | 72.43 | odd | 6 | ||
648.2.d.e.325.2 | yes | 4 | 36.7 | odd | 6 | ||
648.2.d.i.325.3 | yes | 4 | 36.11 | even | 6 | ||
648.2.d.i.325.4 | yes | 4 | 72.11 | even | 6 | ||
648.2.n.a.109.1 | 4 | 36.23 | even | 6 | |||
648.2.n.a.541.2 | 4 | 24.11 | even | 2 | |||
648.2.n.b.109.2 | 4 | 72.67 | odd | 6 | |||
648.2.n.b.541.2 | 4 | 4.3 | odd | 2 | |||
648.2.n.l.109.1 | 4 | 72.59 | even | 6 | |||
648.2.n.l.541.1 | 4 | 12.11 | even | 2 | |||
648.2.n.m.109.2 | 4 | 36.31 | odd | 6 | |||
648.2.n.m.541.1 | 4 | 8.3 | odd | 2 | |||
2592.2.d.g.1297.1 | 4 | 72.29 | odd | 6 | |||
2592.2.d.g.1297.4 | 4 | 9.2 | odd | 6 | |||
2592.2.d.h.1297.1 | 4 | 9.7 | even | 3 | |||
2592.2.d.h.1297.4 | 4 | 72.61 | even | 6 | |||
2592.2.r.a.433.1 | 4 | 9.5 | odd | 6 | |||
2592.2.r.a.2161.1 | 4 | 24.5 | odd | 2 | |||
2592.2.r.b.433.1 | 4 | 72.13 | even | 6 | inner | ||
2592.2.r.b.2161.1 | 4 | 1.1 | even | 1 | trivial | ||
2592.2.r.j.433.2 | 4 | 9.4 | even | 3 | |||
2592.2.r.j.2161.2 | 4 | 8.5 | even | 2 | |||
2592.2.r.k.433.2 | 4 | 72.5 | odd | 6 | |||
2592.2.r.k.2161.2 | 4 | 3.2 | odd | 2 |