Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.5 | ||
Root | \(-0.453990 + 0.891007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.d.3025.12 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.60758i | − 0.718930i | −0.933158 | − | 0.359465i | \(-0.882959\pi\) | ||||
0.933158 | − | 0.359465i | \(-0.117041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.0549306i | − 0.0165622i | −0.999966 | − | 0.00828109i | \(-0.997364\pi\) | ||||
0.999966 | − | 0.00828109i | \(-0.00263598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.75621i | − 1.04179i | −0.853622 | − | 0.520893i | \(-0.825599\pi\) | ||||
0.853622 | − | 0.520893i | \(-0.174401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.726543i | 0.166680i | 0.996521 | + | 0.0833401i | \(0.0265588\pi\) | ||||
−0.996521 | + | 0.0833401i | \(0.973441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.77604 | 1.62142 | 0.810708 | − | 0.585450i | \(-0.199082\pi\) | ||||
0.810708 | + | 0.585450i | \(0.199082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.41570 | 0.483139 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.75789i | 0.512128i | 0.966660 | + | 0.256064i | \(0.0824257\pi\) | ||||
−0.966660 | + | 0.256064i | \(0.917574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.14475 | 0.385208 | 0.192604 | − | 0.981277i | \(-0.438307\pi\) | ||||
0.192604 | + | 0.981277i | \(0.438307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.60758i | − 0.271730i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.600848i | − 0.0987788i | −0.998780 | − | 0.0493894i | \(-0.984272\pi\) | ||||
0.998780 | − | 0.0493894i | \(-0.0157275\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.53658 | −0.708495 | −0.354248 | − | 0.935152i | \(-0.615263\pi\) | ||||
−0.354248 | + | 0.935152i | \(0.615263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.85004i | 1.04462i | 0.852755 | + | 0.522311i | \(0.174930\pi\) | ||||
−0.852755 | + | 0.522311i | \(0.825070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.744883 | 0.108652 | 0.0543261 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543261 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.5822i | − 1.45358i | −0.686860 | − | 0.726790i | \(-0.741011\pi\) | ||||
0.686860 | − | 0.726790i | \(-0.258989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0883051 | −0.0119071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.58013i | − 0.335905i | −0.985795 | − | 0.167952i | \(-0.946285\pi\) | ||||
0.985795 | − | 0.167952i | \(-0.0537155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.80423i | 1.25530i | 0.778495 | + | 0.627651i | \(0.215984\pi\) | ||||
−0.778495 | + | 0.627651i | \(0.784016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.03841 | −0.748972 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2627i | 1.49813i | 0.662496 | + | 0.749065i | \(0.269497\pi\) | ||||
−0.662496 | + | 0.749065i | \(0.730503\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.19025 | 1.09068 | 0.545341 | − | 0.838214i | \(-0.316400\pi\) | ||||
0.545341 | + | 0.838214i | \(0.316400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.85224 | 0.450870 | 0.225435 | − | 0.974258i | \(-0.427620\pi\) | ||||
0.225435 | + | 0.974258i | \(0.427620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.0549306i | − 0.00625992i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9057 | −1.22698 | −0.613491 | − | 0.789701i | \(-0.710235\pi\) | ||||
−0.613491 | + | 0.789701i | \(0.710235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 13.1624i | − 1.44476i | −0.691499 | − | 0.722378i | \(-0.743049\pi\) | ||||
0.691499 | − | 0.722378i | \(-0.256951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.08361i | − 0.551394i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.90356 | 0.837776 | 0.418888 | − | 0.908038i | \(-0.362420\pi\) | ||||
0.418888 | + | 0.908038i | \(0.362420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.75621i | − 0.393758i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.16797 | 0.119832 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1803 | 1.23673 | 0.618363 | − | 0.785893i | \(-0.287796\pi\) | ||||
0.618363 | + | 0.785893i | \(0.287796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.35250i | − 0.433090i | −0.976273 | − | 0.216545i | \(-0.930521\pi\) | ||||
0.976273 | − | 0.216545i | \(-0.0694788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5574 | −1.72998 | −0.864992 | − | 0.501785i | \(-0.832677\pi\) | ||||
−0.864992 | + | 0.501785i | \(0.832677\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.44944i | 0.623491i | 0.950166 | + | 0.311745i | \(0.100914\pi\) | ||||
−0.950166 | + | 0.311745i | \(0.899086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.03559i | − 0.194975i | −0.995237 | − | 0.0974873i | \(-0.968919\pi\) | ||||
0.995237 | − | 0.0974873i | \(-0.0310805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.61946 | −0.246418 | −0.123209 | − | 0.992381i | \(-0.539319\pi\) | ||||
−0.123209 | + | 0.992381i | \(0.539319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 12.5006i | − 1.16569i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.16228 | 0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9970 | 0.999726 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.9213i | − 1.06627i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6733 | 1.21331 | 0.606656 | − | 0.794965i | \(-0.292511\pi\) | ||||
0.606656 | + | 0.794965i | \(0.292511\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 11.2592i | − 0.983721i | −0.870674 | − | 0.491861i | \(-0.836317\pi\) | ||||
0.870674 | − | 0.491861i | \(-0.163683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.726543i | 0.0629992i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00318 | −0.0857076 | −0.0428538 | − | 0.999081i | \(-0.513645\pi\) | ||||
−0.0428538 | + | 0.999081i | \(0.513645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.60253i | 0.220744i | 0.993890 | + | 0.110372i | \(0.0352042\pi\) | ||||
−0.993890 | + | 0.110372i | \(0.964796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.206331 | −0.0172543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.43352 | 0.368184 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 19.1514i | − 1.56895i | −0.620163 | − | 0.784473i | \(-0.712934\pi\) | ||||
0.620163 | − | 0.784473i | \(-0.287066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8848 | −1.29269 | −0.646344 | − | 0.763046i | \(-0.723703\pi\) | ||||
−0.646344 | + | 0.763046i | \(0.723703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.44784i | − 0.276937i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.7099i | − 1.17398i | −0.809595 | − | 0.586988i | \(-0.800313\pi\) | ||||
0.809595 | − | 0.586988i | \(-0.199687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.77604 | 0.612838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.69687i | − 0.759517i | −0.925086 | − | 0.379759i | \(-0.876007\pi\) | ||||
0.925086 | − | 0.379759i | \(-0.123993\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57013 | 0.198882 | 0.0994412 | − | 0.995043i | \(-0.468294\pi\) | ||||
0.0994412 | + | 0.995043i | \(0.468294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10915 | −0.0853193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.69460i | 0.128838i | 0.997923 | + | 0.0644192i | \(0.0205195\pi\) | ||||
−0.997923 | + | 0.0644192i | \(0.979481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.41570 | 0.182609 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.1383i | 0.832518i | 0.909246 | + | 0.416259i | \(0.136659\pi\) | ||||
−0.909246 | + | 0.416259i | \(0.863341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.80203i | 0.505591i | 0.967520 | + | 0.252796i | \(0.0813500\pi\) | ||||
−0.967520 | + | 0.252796i | \(0.918650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.965909 | −0.0710151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.173706i | − 0.0127026i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.6397 | 1.13165 | 0.565824 | − | 0.824526i | \(-0.308558\pi\) | ||||
0.565824 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5893 | 1.41007 | 0.705034 | − | 0.709174i | \(-0.250932\pi\) | ||||
0.705034 | + | 0.709174i | \(0.250932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.29916i | 0.520044i | 0.965603 | + | 0.260022i | \(0.0837298\pi\) | ||||
−0.965603 | + | 0.260022i | \(0.916270\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8002 | −0.978273 | −0.489136 | − | 0.872207i | \(-0.662688\pi\) | ||||
−0.489136 | + | 0.872207i | \(0.662688\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.75789i | 0.193566i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.29291i | 0.509359i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0399094 | 0.00276059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.25731i | 0.361928i | 0.983490 | + | 0.180964i | \(0.0579218\pi\) | ||||
−0.983490 | + | 0.180964i | \(0.942078\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0120 | 0.751011 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.14475 | 0.145595 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 11.8782i | − 0.799014i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.96512 | −0.332489 | −0.166244 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166244 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 15.1773i | − 1.00735i | −0.863893 | − | 0.503676i | \(-0.831981\pi\) | ||||
0.863893 | − | 0.503676i | \(-0.168019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.69636i | − 0.376426i | −0.982128 | − | 0.188213i | \(-0.939730\pi\) | ||||
0.982128 | − | 0.188213i | \(-0.0602695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5086 | 1.08151 | 0.540756 | − | 0.841179i | \(-0.318138\pi\) | ||||
0.540756 | + | 0.841179i | \(0.318138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.19746i | − 0.0781134i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1437 | −0.979564 | −0.489782 | − | 0.871845i | \(-0.662924\pi\) | ||||
−0.489782 | + | 0.871845i | \(0.662924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.5047 | −1.83615 | −0.918075 | − | 0.396407i | \(-0.870257\pi\) | ||||
−0.918075 | + | 0.396407i | \(0.870257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.60758i | − 0.102704i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.72905 | 0.173645 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 7.18930i | − 0.453785i | −0.973920 | − | 0.226892i | \(-0.927143\pi\) | ||||
0.973920 | − | 0.226892i | \(-0.0728566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.427142i | − 0.0268542i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.4469 | 1.89922 | 0.949612 | − | 0.313427i | \(-0.101477\pi\) | ||||
0.949612 | + | 0.313427i | \(0.101477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.600848i | − 0.0373349i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.28410 | −0.510820 | −0.255410 | − | 0.966833i | \(-0.582210\pi\) | ||||
−0.255410 | + | 0.966833i | \(0.582210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0117 | −1.04502 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.16222i | 0.436689i | 0.975872 | + | 0.218344i | \(0.0700656\pi\) | ||||
−0.975872 | + | 0.218344i | \(0.929934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.4721 | −0.757628 | −0.378814 | − | 0.925473i | \(-0.623668\pi\) | ||||
−0.378814 | + | 0.925473i | \(0.623668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 0.132696i | − 0.00800184i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.91531i | − 0.535669i | −0.963465 | − | 0.267835i | \(-0.913692\pi\) | ||||
0.963465 | − | 0.267835i | \(-0.0863081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3577 | 0.737198 | 0.368599 | − | 0.929589i | \(-0.379838\pi\) | ||||
0.368599 | + | 0.929589i | \(0.379838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4245i | 1.27356i | 0.771047 | + | 0.636778i | \(0.219733\pi\) | ||||
−0.771047 | + | 0.636778i | \(0.780267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.53658 | −0.267786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 0.0647976i | − 0.00378552i | −0.999998 | − | 0.00189276i | \(-0.999398\pi\) | ||||
0.999998 | − | 0.00189276i | \(-0.000602484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.14776 | −0.241492 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 29.2085i | − 1.68917i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.85004i | 0.394830i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.7611 | 0.902475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.8474i | − 0.904460i | −0.891901 | − | 0.452230i | \(-0.850629\pi\) | ||||
0.891901 | − | 0.452230i | \(-0.149371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0254 | −0.738602 | −0.369301 | − | 0.929310i | \(-0.620403\pi\) | ||||
−0.369301 | + | 0.929310i | \(0.620403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0265 | 1.35806 | 0.679030 | − | 0.734110i | \(-0.262401\pi\) | ||||
0.679030 | + | 0.734110i | \(0.262401\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.71438i | − 0.208620i | −0.994545 | − | 0.104310i | \(-0.966737\pi\) | ||||
0.994545 | − | 0.104310i | \(-0.0332635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.151493 | 0.00848195 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.29753i | 0.127838i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9.07387i | − 0.503328i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.744883 | 0.0410667 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.50059i | − 0.192410i | −0.995362 | − | 0.0962048i | \(-0.969330\pi\) | ||||
0.995362 | − | 0.0962048i | \(-0.0306704\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.7133 | 1.07705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.9917 | −0.925595 | −0.462797 | − | 0.886464i | \(-0.653154\pi\) | ||||
−0.462797 | + | 0.886464i | \(0.653154\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 0.117812i | − 0.00637988i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 36.6651i | − 1.96829i | −0.177373 | − | 0.984144i | \(-0.556760\pi\) | ||||
0.177373 | − | 0.984144i | \(-0.443240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.7887i | 1.86220i | 0.364770 | + | 0.931098i | \(0.381148\pi\) | ||||
−0.364770 | + | 0.931098i | \(0.618852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1913 | 0.648876 | 0.324438 | − | 0.945907i | \(-0.394825\pi\) | ||||
0.324438 | + | 0.945907i | \(0.394825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 14.7740i | − 0.784125i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4411 | 1.76495 | 0.882477 | − | 0.470355i | \(-0.155874\pi\) | ||||
0.882477 | + | 0.470355i | \(0.155874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4721 | 0.972218 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.19277i | − 0.324144i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4869 | 0.756212 | 0.378106 | − | 0.925762i | \(-0.376575\pi\) | ||||
0.378106 | + | 0.925762i | \(0.376575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 10.5822i | − 0.549401i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 28.7612i | − 1.48920i | −0.667512 | − | 0.744599i | \(-0.732641\pi\) | ||||
0.667512 | − | 0.744599i | \(-0.267359\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3592 | 0.533528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1036i | 0.827188i | 0.910461 | + | 0.413594i | \(0.135727\pi\) | ||||
−0.910461 | + | 0.413594i | \(0.864273\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.7602 | −1.31629 | −0.658143 | − | 0.752893i | \(-0.728658\pi\) | ||||
−0.658143 | + | 0.752893i | \(0.728658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0883051 | −0.00450045 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.82322i | 0.498057i | 0.968496 | + | 0.249029i | \(0.0801113\pi\) | ||||
−0.968496 | + | 0.249029i | \(0.919889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.5900 | 1.24357 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.5317i | 0.882115i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 24.1824i | − 1.21368i | −0.794824 | − | 0.606840i | \(-0.792437\pi\) | ||||
0.794824 | − | 0.606840i | \(-0.207563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.4216 | −1.16962 | −0.584810 | − | 0.811170i | \(-0.698831\pi\) | ||||
−0.584810 | + | 0.811170i | \(0.698831\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.05613i | − 0.401304i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0330049 | −0.00163599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6813 | −1.61599 | −0.807994 | − | 0.589191i | \(-0.799447\pi\) | ||||
−0.807994 | + | 0.589191i | \(0.799447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.58013i | − 0.126960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1595 | −1.03868 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 29.3981i | − 1.43619i | −0.695945 | − | 0.718095i | \(-0.745014\pi\) | ||||
0.695945 | − | 0.718095i | \(-0.254986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59493i | 0.0777319i | 0.999244 | + | 0.0388660i | \(0.0123745\pi\) | ||||
−0.999244 | + | 0.0388660i | \(0.987625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.63910 | 0.370551 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.80423i | 0.474460i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7336 | −0.517020 | −0.258510 | − | 0.966009i | \(-0.583232\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.43352 | −0.405289 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.64962i | 0.270258i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3452 | 0.827842 | 0.413921 | − | 0.910313i | \(-0.364159\pi\) | ||||
0.413921 | + | 0.910313i | \(0.364159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 29.8824i | − 1.41976i | −0.704325 | − | 0.709878i | \(-0.748750\pi\) | ||||
0.704325 | − | 0.709878i | \(-0.251250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.7056i | − 0.602302i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.6303 | −0.879217 | −0.439608 | − | 0.898190i | \(-0.644883\pi\) | ||||
−0.439608 | + | 0.898190i | \(0.644883\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.249197i | 0.0117342i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.03841 | −0.283085 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.63702 | −0.310466 | −0.155233 | − | 0.987878i | \(-0.549613\pi\) | ||||
−0.155233 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 42.1500i | − 1.96312i | −0.191155 | − | 0.981560i | \(-0.561223\pi\) | ||||
0.191155 | − | 0.981560i | \(-0.438777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.1209 | 1.26041 | 0.630207 | − | 0.776427i | \(-0.282970\pi\) | ||||
0.630207 | + | 0.776427i | \(0.282970\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.06443i | − 0.0492561i | −0.999697 | − | 0.0246280i | \(-0.992160\pi\) | ||||
0.999697 | − | 0.0246280i | \(-0.00784014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.2627i | 0.566240i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.376277 | 0.0173012 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.75511i | 0.0805298i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.7777 | −1.49765 | −0.748825 | − | 0.662767i | \(-0.769382\pi\) | ||||
−0.748825 | + | 0.662767i | \(0.769382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.25691 | −0.102906 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 19.5808i | − 0.889120i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.44329 | 0.110716 | 0.0553580 | − | 0.998467i | \(-0.482370\pi\) | ||||
0.0553580 | + | 0.998467i | \(0.482370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5978i | 1.15521i | 0.816315 | + | 0.577606i | \(0.196013\pi\) | ||||
−0.816315 | + | 0.577606i | \(0.803987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.72122i | 0.392784i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.19025 | 0.412239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.96720i | 0.356661i | 0.983971 | + | 0.178330i | \(0.0570696\pi\) | ||||
−0.983971 | + | 0.178330i | \(0.942930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.3158 | 1.39630 | 0.698151 | − | 0.715951i | \(-0.254007\pi\) | ||||
0.698151 | + | 0.715951i | \(0.254007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.99698 | −0.311362 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 40.7362i | − 1.80560i | −0.430061 | − | 0.902800i | \(-0.641508\pi\) | ||||
0.430061 | − | 0.902800i | \(-0.358492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.85224 | 0.170413 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.2249i | 1.24374i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.0409168i | − 0.00179952i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.3880 | 1.90086 | 0.950432 | − | 0.310931i | \(-0.100641\pi\) | ||||
0.950432 | + | 0.310931i | \(0.100641\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.9726i | 0.785887i | 0.919563 | + | 0.392944i | \(0.128543\pi\) | ||||
−0.919563 | + | 0.392944i | \(0.871457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.78228 | 0.295441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.4668 | 1.62899 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0404i | 0.738101i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.3680 | 0.448246 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.0549306i | − 0.00236603i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5151i | 0.495074i | 0.968878 | + | 0.247537i | \(0.0796212\pi\) | ||||
−0.968878 | + | 0.247537i | \(0.920379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.27238 | −0.140173 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 14.5265i | − 0.621107i | −0.950556 | − | 0.310553i | \(-0.899486\pi\) | ||||
0.950556 | − | 0.310553i | \(-0.100514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.00373 | −0.0853616 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9057 | −0.463756 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 44.6492i | 1.89185i | 0.324387 | + | 0.945924i | \(0.394842\pi\) | ||||
−0.324387 | + | 0.945924i | \(0.605158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.7302 | 1.08827 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.26356i | 0.179688i | 0.995956 | + | 0.0898438i | \(0.0286368\pi\) | ||||
−0.995956 | + | 0.0898438i | \(0.971363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.21098i | 0.177157i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.6045 | −1.61838 | −0.809192 | − | 0.587544i | \(-0.800095\pi\) | ||||
−0.809192 | + | 0.587544i | \(0.800095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0556i | 1.17409i | 0.809554 | + | 0.587045i | \(0.199709\pi\) | ||||
−0.809554 | + | 0.587045i | \(0.800291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7845 | 0.783370 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.46468 | −0.102606 | −0.0513029 | − | 0.998683i | \(-0.516337\pi\) | ||||
−0.0513029 | + | 0.998683i | \(0.516337\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 13.1624i | − 0.546066i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.581287 | −0.0240745 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.7523i | 1.76458i | 0.470710 | + | 0.882288i | \(0.343998\pi\) | ||||
−0.470710 | + | 0.882288i | \(0.656002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55825i | 0.0642065i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7945 | 0.730733 | 0.365367 | − | 0.930864i | \(-0.380944\pi\) | ||||
0.365367 | + | 0.930864i | \(0.380944\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 5.08361i | − 0.208408i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.5626 | 0.595011 | 0.297506 | − | 0.954720i | \(-0.403845\pi\) | ||||
0.297506 | + | 0.954720i | \(0.403845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1497 | −1.10746 | −0.553730 | − | 0.832696i | \(-0.686796\pi\) | ||||
−0.553730 | + | 0.832696i | \(0.686796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.6785i | − 0.718733i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8708 | −0.441231 | −0.220616 | − | 0.975361i | \(-0.570807\pi\) | ||||
−0.220616 | + | 0.975361i | \(0.570807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.79794i | − 0.113192i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1387i | 1.05573i | 0.849327 | + | 0.527866i | \(0.177008\pi\) | ||||
−0.849327 | + | 0.527866i | \(0.822992\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.5464 | −1.71285 | −0.856427 | − | 0.516269i | \(-0.827321\pi\) | ||||
−0.856427 | + | 0.516269i | \(0.827321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 41.0012i | − 1.64798i | −0.566606 | − | 0.823989i | \(-0.691744\pi\) | ||||
0.566606 | − | 0.823989i | \(-0.308256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.90356 | 0.316649 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.08594 | −0.283437 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.90005i | − 0.0757599i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8045 | 1.18650 | 0.593249 | − | 0.805019i | \(-0.297845\pi\) | ||||
0.593249 | + | 0.805019i | \(0.297845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 21.9809i | − 0.872286i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.75621i | − 0.148827i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.1768 | 0.717941 | 0.358971 | − | 0.933349i | \(-0.383128\pi\) | ||||
0.358971 | + | 0.933349i | \(0.383128\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.8490i | − 0.822203i | −0.911590 | − | 0.411101i | \(-0.865144\pi\) | ||||
0.911590 | − | 0.411101i | \(-0.134856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7706 | 0.737948 | 0.368974 | − | 0.929440i | \(-0.379709\pi\) | ||||
0.368974 | + | 0.929440i | \(0.379709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.141728 | −0.00556332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 25.5220i | − 0.998751i | −0.866386 | − | 0.499376i | \(-0.833563\pi\) | ||||
0.866386 | − | 0.499376i | \(-0.166437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1000 | −0.707227 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8249i | 0.733314i | 0.930356 | + | 0.366657i | \(0.119498\pi\) | ||||
−0.930356 | + | 0.366657i | \(0.880502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1764i | 0.979247i | 0.871934 | + | 0.489623i | \(0.162866\pi\) | ||||
−0.871934 | + | 0.489623i | \(0.837134\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.16797 | 0.0452921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.4455i | 0.830372i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.538552 | 0.0207906 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.29322 | 0.319680 | 0.159840 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159840 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6825i | 0.448993i | 0.974475 | + | 0.224497i | \(0.0720738\pi\) | ||||
−0.974475 | + | 0.224497i | \(0.927926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1803 | 0.467439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22.9388i | − 0.877727i | −0.898554 | − | 0.438864i | \(-0.855381\pi\) | ||||
0.898554 | − | 0.438864i | \(-0.144619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.61269i | 0.0616178i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.7491 | −1.51432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 41.2800i | − 1.57036i | −0.619265 | − | 0.785182i | \(-0.712569\pi\) | ||||
0.619265 | − | 0.785182i | \(-0.287431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.18377 | 0.158699 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3459 | −0.543391 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9596i | 0.867174i | 0.901112 | + | 0.433587i | \(0.142752\pi\) | ||||
−0.901112 | + | 0.433587i | \(0.857248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.436542 | 0.0164645 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.35250i | − 0.163693i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0831i | 0.829348i | 0.909970 | + | 0.414674i | \(0.136104\pi\) | ||||
−0.909970 | + | 0.414674i | \(0.863896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.6776 | 0.624582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.331693i | 0.0124046i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.4594 | 1.09865 | 0.549325 | − | 0.835609i | \(-0.314885\pi\) | ||||
0.549325 | + | 0.835609i | \(0.314885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5574 | −0.653873 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.66223i | 0.247429i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5893 | 0.949054 | 0.474527 | − | 0.880241i | \(-0.342619\pi\) | ||||
0.474527 | + | 0.880241i | \(0.342619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.6617i | 0.801189i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.3587i | 0.899711i | 0.893101 | + | 0.449855i | \(0.148524\pi\) | ||||
−0.893101 | + | 0.449855i | \(0.851476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.673598 | 0.0248123 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 18.8064i | − 0.691805i | −0.938270 | − | 0.345903i | \(-0.887573\pi\) | ||||
0.938270 | − | 0.345903i | \(-0.112427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4039 | −1.07873 | −0.539363 | − | 0.842074i | \(-0.681335\pi\) | ||||
−0.539363 | + | 0.842074i | \(0.681335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.7874 | −1.12796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.44944i | 0.235657i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9057 | 0.616896 | 0.308448 | − | 0.951241i | \(-0.400190\pi\) | ||||
0.308448 | + | 0.951241i | \(0.400190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.5361i | 0.929353i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.3657i | 1.10366i | 0.833957 | + | 0.551830i | \(0.186070\pi\) | ||||
−0.833957 | + | 0.551830i | \(0.813930\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0960 | −0.655979 | −0.327990 | − | 0.944681i | \(-0.606371\pi\) | ||||
−0.327990 | + | 0.944681i | \(0.606371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.03559i | − 0.0736935i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.69153 | −0.349941 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4944 | 0.558743 | 0.279371 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279371 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.1186i | 1.19119i | 0.803284 | + | 0.595597i | \(0.203084\pi\) | ||||
−0.803284 | + | 0.595597i | \(0.796916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.18105 | 0.186109 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3.29602i | − 0.118092i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 0.504826i | − 0.0180641i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.6473 | −0.844008 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.8484i | − 0.493641i | −0.969061 | − | 0.246820i | \(-0.920614\pi\) | ||||
0.969061 | − | 0.246820i | \(-0.0793858\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.61946 | −0.0931372 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8268 | 1.30776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.5510i | 0.975908i | 0.872869 | + | 0.487954i | \(0.162257\pi\) | ||||
−0.872869 | + | 0.487954i | \(0.837743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.35553 | 0.0833325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 0.211606i | − 0.00746740i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 12.5006i | − 0.440588i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.181117 | 0.00636775 | 0.00318388 | − | 0.999995i | \(-0.498987\pi\) | ||||
0.00318388 | + | 0.999995i | \(0.498987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7508i | 0.834003i | 0.908906 | + | 0.417002i | \(0.136919\pi\) | ||||
−0.908906 | + | 0.417002i | \(0.863081\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.5885 | −0.546040 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.97685 | −0.174118 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.16381i | 0.284919i | 0.989801 | + | 0.142460i | \(0.0455011\pi\) | ||||
−0.989801 | + | 0.142460i | \(0.954499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.6984 | −1.38380 | −0.691900 | − | 0.721993i | \(-0.743226\pi\) | ||||
−0.691900 | + | 0.721993i | \(0.743226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0390i | 1.60093i | 0.599377 | + | 0.800467i | \(0.295415\pi\) | ||||
−0.599377 | + | 0.800467i | \(0.704585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1434i | 0.491220i | 0.969369 | + | 0.245610i | \(0.0789882\pi\) | ||||
−0.969369 | + | 0.245610i | \(0.921012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4.13168i | − 0.142983i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.0217 | 1.07099 | 0.535494 | − | 0.844539i | \(-0.320125\pi\) | ||||
0.535494 | + | 0.844539i | \(0.320125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3940 | 0.737725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.78305i | 0.0613386i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9970 | 0.377861 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.67222i | − 0.160162i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 36.2812i | − 1.24224i | −0.783714 | − | 0.621121i | \(-0.786677\pi\) | ||||
0.783714 | − | 0.621121i | \(-0.213323\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.6532 | −0.944616 | −0.472308 | − | 0.881434i | \(-0.656579\pi\) | ||||
−0.472308 | + | 0.881434i | \(0.656579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.0733i | 0.923729i | 0.886950 | + | 0.461865i | \(0.152819\pi\) | ||||
−0.886950 | + | 0.461865i | \(0.847181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.98203 | 0.305752 | 0.152876 | − | 0.988245i | \(-0.451147\pi\) | ||||
0.152876 | + | 0.988245i | \(0.451147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.72421 | 0.0926258 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.599054i | 0.0203215i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.0614 | 1.56073 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.9213i | − 0.403014i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 27.9552i | − 0.943980i | −0.881604 | − | 0.471990i | \(-0.843536\pi\) | ||||
0.881604 | − | 0.471990i | \(-0.156464\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0213 | 1.11252 | 0.556258 | − | 0.831010i | \(-0.312237\pi\) | ||||
0.556258 | + | 0.831010i | \(0.312237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 19.1451i | − 0.644283i | −0.946692 | − | 0.322141i | \(-0.895597\pi\) | ||||
0.946692 | − | 0.322141i | \(-0.104403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.99598 | 0.302056 | 0.151028 | − | 0.988530i | \(-0.451742\pi\) | ||||
0.151028 | + | 0.988530i | \(0.451742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6733 | 0.458588 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.541189i | 0.0181102i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.9057 | 0.598522 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.91498i | 0.197276i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 33.4639i | − 1.11484i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9348 | 0.363485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.5978i | 1.77969i | 0.456267 | + | 0.889843i | \(0.349186\pi\) | ||||
−0.456267 | + | 0.889843i | \(0.650814\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.1958 | −1.56367 | −0.781833 | − | 0.623487i | \(-0.785715\pi\) | ||||
−0.781833 | + | 0.623487i | \(0.785715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.723015 | −0.0239283 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 11.2592i | − 0.371812i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.6942 | −0.748612 | −0.374306 | − | 0.927305i | \(-0.622119\pi\) | ||||
−0.374306 | + | 0.927305i | \(0.622119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 34.5206i | − 1.13626i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.45147i | − 0.0477239i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0001 | −1.01708 | −0.508541 | − | 0.861038i | \(-0.669815\pi\) | ||||
−0.508541 | + | 0.861038i | \(0.669815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.726543i | 0.0238115i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.279245 | −0.00913230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.0011 | −1.60080 | −0.800398 | − | 0.599469i | \(-0.795378\pi\) | ||||
−0.800398 | + | 0.599469i | \(0.795378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.2485i | 1.60546i | 0.596345 | + | 0.802728i | \(0.296619\pi\) | ||||
−0.596345 | + | 0.802728i | \(0.703381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.2766 | −1.14877 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.28008i | 0.301562i | 0.988567 | + | 0.150781i | \(0.0481788\pi\) | ||||
−0.988567 | + | 0.150781i | \(0.951821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 14.4698i | − 0.469711i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.1855 | −1.62567 | −0.812834 | − | 0.582496i | \(-0.802076\pi\) | ||||
−0.812834 | + | 0.582496i | \(0.802076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 25.1420i | − 0.813576i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00318 | −0.0323944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4001 | −0.851615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 31.4913i | − 1.01374i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.81736 | 0.251389 | 0.125695 | − | 0.992069i | \(-0.459884\pi\) | ||||
0.125695 | + | 0.992069i | \(0.459884\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 7.60460i | − 0.244043i | −0.992527 | − | 0.122022i | \(-0.961062\pi\) | ||||
0.992527 | − | 0.122022i | \(-0.0389377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.60253i | 0.0834333i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.9179 | −1.21310 | −0.606551 | − | 0.795044i | \(-0.707447\pi\) | ||||
−0.606551 | + | 0.795044i | \(0.707447\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 0.434147i | − 0.0138754i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7230 | −1.07560 | −0.537798 | − | 0.843074i | \(-0.680744\pi\) | ||||
−0.537798 | + | 0.843074i | \(0.680744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7340 | 0.373875 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.2662i | 1.69377i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.3137 | −1.47120 | −0.735602 | − | 0.677414i | \(-0.763101\pi\) | ||||
−0.735602 | + | 0.677414i | \(0.763101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.1849i | 0.703310i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.20068i | 0.164707i | 0.996603 | + | 0.0823535i | \(0.0262437\pi\) | ||||
−0.996603 | + | 0.0823535i | \(0.973756\pi\) | |||||||
\(998\) | 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 | 6048.2.c.d.3025.5 | 16 | ||
3.2 | odd | 2 | inner | 6048.2.c.d.3025.11 | 16 | ||
4.3 | odd | 2 | 1512.2.c.d.757.13 | yes | 16 | ||
8.3 | odd | 2 | 1512.2.c.d.757.16 | yes | 16 | ||
8.5 | even | 2 | inner | 6048.2.c.d.3025.12 | 16 | ||
12.11 | even | 2 | 1512.2.c.d.757.4 | yes | 16 | ||
24.5 | odd | 2 | inner | 6048.2.c.d.3025.6 | 16 | ||
24.11 | even | 2 | 1512.2.c.d.757.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.1 | ✓ | 16 | 24.11 | even | 2 | ||
1512.2.c.d.757.4 | yes | 16 | 12.11 | even | 2 | ||
1512.2.c.d.757.13 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.c.d.757.16 | yes | 16 | 8.3 | odd | 2 | ||
6048.2.c.d.3025.5 | 16 | 1.1 | even | 1 | trivial | ||
6048.2.c.d.3025.6 | 16 | 24.5 | odd | 2 | inner | ||
6048.2.c.d.3025.11 | 16 | 3.2 | odd | 2 | inner | ||
6048.2.c.d.3025.12 | 16 | 8.5 | even | 2 | inner |