Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(577,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.k (of order \(4\), degree \(2\), 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: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.577 |
Dual form | 2304.2.k.e.1729.1 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.73205 | + | 2.73205i | −1.22181 | + | 1.22181i | −0.254822 | + | 0.966988i | \(0.582017\pi\) |
−0.966988 | + | 0.254822i | \(0.917983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.03528 | + | 1.03528i | −0.312148 | + | 0.312148i | −0.845741 | − | 0.533594i | \(-0.820841\pi\) |
0.533594 | + | 0.845741i | \(0.320841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 3.00000i | 0.832050 | + | 0.832050i | 0.987797 | − | 0.155747i | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.27792 | + | 5.27792i | 1.21084 | + | 1.21084i | 0.970752 | + | 0.240085i | \(0.0771754\pi\) |
0.240085 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 9.92820i | − | 1.98564i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.19615 | + | 6.19615i | 1.15060 | + | 1.15060i | 0.986433 | + | 0.164163i | \(0.0524925\pi\) |
0.164163 | + | 0.986433i | \(0.447508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.34847 | −1.31982 | −0.659912 | − | 0.751343i | \(-0.729406\pi\) | ||||
−0.659912 | + | 0.751343i | \(0.729406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.69213 | − | 6.69213i | −1.13118 | − | 1.13118i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.464102 | − | 0.464102i | 0.0762978 | − | 0.0762978i | −0.667928 | − | 0.744226i | \(-0.732819\pi\) |
0.744226 | + | 0.667928i | \(0.232819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.53590i | − | 0.708388i | −0.935172 | − | 0.354194i | \(-0.884755\pi\) | ||
0.935172 | − | 0.354194i | \(-0.115245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44949 | − | 2.44949i | 0.373544 | − | 0.373544i | −0.495222 | − | 0.868766i | \(-0.664913\pi\) |
0.868766 | + | 0.495222i | \(0.164913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.26795 | + | 3.26795i | −0.448887 | + | 0.448887i | −0.894985 | − | 0.446097i | \(-0.852814\pi\) |
0.446097 | + | 0.894985i | \(0.352814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.65685i | − | 0.762770i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.79796 | + | 9.79796i | −1.27559 | + | 1.27559i | −0.332473 | + | 0.943113i | \(0.607883\pi\) |
−0.943113 | + | 0.332473i | \(0.892117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.464102 | + | 0.464102i | 0.0594221 | + | 0.0594221i | 0.736193 | − | 0.676771i | \(-0.236621\pi\) |
−0.676771 | + | 0.736193i | \(0.736621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.3923 | −2.03322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5558 | − | 10.5558i | −1.28960 | − | 1.28960i | −0.935029 | − | 0.354571i | \(-0.884627\pi\) |
−0.354571 | − | 0.935029i | \(-0.615373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.41473i | − | 0.761288i | −0.924722 | − | 0.380644i | \(-0.875702\pi\) | ||
0.924722 | − | 0.380644i | \(-0.124298\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.53590 | − | 2.53590i | −0.288992 | − | 0.288992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.44949 | −0.275589 | −0.137795 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137795 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.86370 | − | 3.86370i | −0.424097 | − | 0.424097i | 0.462515 | − | 0.886611i | \(-0.346947\pi\) |
−0.886611 | + | 0.462515i | \(0.846947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.46410 | − | 9.46410i | 1.02653 | − | 1.02653i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.92820i | − | 0.522388i | −0.965286 | − | 0.261194i | \(-0.915884\pi\) | ||
0.965286 | − | 0.261194i | \(-0.0841163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.34847 | + | 7.34847i | −0.770329 | + | 0.770329i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −28.8391 | −2.95883 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1962 | − | 10.1962i | 1.01456 | − | 1.01456i | 0.0146626 | − | 0.999892i | \(-0.495333\pi\) |
0.999892 | − | 0.0146626i | \(-0.00466741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.20736i | − | 0.316031i | −0.987437 | − | 0.158016i | \(-0.949490\pi\) | ||
0.987437 | − | 0.158016i | \(-0.0505096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | + | 2.82843i | −0.273434 | + | 0.273434i | −0.830481 | − | 0.557047i | \(-0.811934\pi\) |
0.557047 | + | 0.830481i | \(0.311934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.00000i | 0.0957826 | + | 0.0957826i | 0.753374 | − | 0.657592i | \(-0.228425\pi\) |
−0.657592 | + | 0.753374i | \(0.728425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.72741 | − | 7.72741i | −0.720584 | − | 0.720584i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.48528i | − | 0.777844i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641i | 0.805128i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.4641 | + | 13.4641i | 1.20427 | + | 1.20427i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5211 | −1.28854 | −0.644268 | − | 0.764799i | \(-0.722838\pi\) | ||||
−0.644268 | + | 0.764799i | \(0.722838\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5558 | − | 10.5558i | −0.922267 | − | 0.922267i | 0.0749219 | − | 0.997189i | \(-0.476129\pi\) |
−0.997189 | + | 0.0749219i | \(0.976129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9282 | + | 12.9282i | −1.12102 | + | 1.12102i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.3923i | − | 1.22962i | −0.788676 | − | 0.614809i | \(-0.789233\pi\) | ||
0.788676 | − | 0.614809i | \(-0.210767\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.89898 | + | 4.89898i | −0.415526 | + | 0.415526i | −0.883658 | − | 0.468132i | \(-0.844927\pi\) |
0.468132 | + | 0.883658i | \(0.344927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.21166 | −0.519445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8564 | −2.81162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.80385 | + | 3.80385i | −0.311623 | + | 0.311623i | −0.845538 | − | 0.533915i | \(-0.820720\pi\) |
0.533915 | + | 0.845538i | \(0.320720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.59059i | − | 0.536335i | −0.963372 | − | 0.268167i | \(-0.913582\pi\) | ||
0.963372 | − | 0.268167i | \(-0.0864181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0764 | − | 20.0764i | 1.61257 | − | 1.61257i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.53590 | − | 1.53590i | −0.122578 | − | 0.122578i | 0.643157 | − | 0.765735i | \(-0.277624\pi\) |
−0.765735 | + | 0.643157i | \(0.777624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.92820 | −0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.20736 | − | 3.20736i | −0.251220 | − | 0.251220i | 0.570251 | − | 0.821471i | \(-0.306846\pi\) |
−0.821471 | + | 0.570251i | \(0.806846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.72741i | 0.597965i | 0.954259 | + | 0.298982i | \(0.0966472\pi\) | ||||
−0.954259 | + | 0.298982i | \(0.903353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1962 | + | 12.1962i | 0.927256 | + | 0.927256i | 0.997528 | − | 0.0702716i | \(-0.0223866\pi\) |
−0.0702716 | + | 0.997528i | \(0.522387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.3190 | 1.83835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3843 | + | 13.3843i | 1.00039 | + | 1.00039i | 1.00000 | 0.000386700i | \(0.000123091\pi\) | |
0.000386700 | 1.00000i | \(0.499877\pi\) | ||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.00000 | + | 5.00000i | −0.371647 | + | 0.371647i | −0.868077 | − | 0.496430i | \(-0.834644\pi\) |
0.496430 | + | 0.868077i | \(0.334644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.53590i | 0.186443i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.58630 | − | 3.58630i | 0.262256 | − | 0.262256i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.72741 | −0.559136 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.19615 | − | 6.19615i | 0.441458 | − | 0.441458i | −0.451044 | − | 0.892502i | \(-0.648948\pi\) |
0.892502 | + | 0.451044i | \(0.148948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6622i | 1.32293i | 0.749977 | + | 0.661463i | \(0.230064\pi\) | ||||
−0.749977 | + | 0.661463i | \(0.769936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.1774 | + | 15.1774i | −1.06525 | + | 1.06525i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3923 | + | 12.3923i | 0.865516 | + | 0.865516i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9282 | −0.755920 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89898 | + | 4.89898i | 0.337260 | + | 0.337260i | 0.855335 | − | 0.518075i | \(-0.173351\pi\) |
−0.518075 | + | 0.855335i | \(0.673351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.3843i | 0.912799i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 18.0000i | − | 1.22192i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.3923 | − | 10.3923i | −0.699062 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5211 | 0.972403 | 0.486201 | − | 0.873847i | \(-0.338382\pi\) | ||||
0.486201 | + | 0.873847i | \(0.338382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.00481 | + | 8.00481i | 0.531298 | + | 0.531298i | 0.920958 | − | 0.389661i | \(-0.127408\pi\) |
−0.389661 | + | 0.920958i | \(0.627408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9282 | + | 11.9282i | −0.788238 | + | 0.788238i | −0.981205 | − | 0.192967i | \(-0.938189\pi\) |
0.192967 | + | 0.981205i | \(0.438189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 12.9282i | − | 0.846955i | −0.905907 | − | 0.423477i | \(-0.860809\pi\) | ||
0.905907 | − | 0.423477i | \(-0.139191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.72741 | + | 7.72741i | −0.504080 | + | 0.504080i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.72741 | −0.499844 | −0.249922 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249922 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7846 | 1.72535 | 0.862674 | − | 0.505760i | \(-0.168788\pi\) | ||||
0.862674 | + | 0.505760i | \(0.168788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.73205 | + | 2.73205i | −0.174544 | + | 0.174544i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.6675i | 2.01495i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.62158 | − | 4.62158i | 0.291711 | − | 0.291711i | −0.546045 | − | 0.837756i | \(-0.683867\pi\) |
0.837756 | + | 0.546045i | \(0.183867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.92820 | − | 2.92820i | −0.184095 | − | 0.184095i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7846 | 1.42126 | 0.710632 | − | 0.703563i | \(-0.248409\pi\) | ||||
0.710632 | + | 0.703563i | \(0.248409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13681 | + | 1.13681i | 0.0706381 | + | 0.0706381i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.6274i | − | 1.39527i | −0.716455 | − | 0.697633i | \(-0.754237\pi\) | ||
0.716455 | − | 0.697633i | \(-0.245763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.8564i | − | 1.09691i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.26795 | − | 7.26795i | −0.443135 | − | 0.443135i | 0.449929 | − | 0.893064i | \(-0.351449\pi\) |
−0.893064 | + | 0.449929i | \(0.851449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.20736 | −0.194834 | −0.0974168 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974168 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.2784 | + | 10.2784i | 0.619813 | + | 0.619813i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.85641 | + | 8.85641i | −0.532130 | + | 0.532130i | −0.921206 | − | 0.389076i | \(-0.872794\pi\) |
0.389076 | + | 0.921206i | \(0.372794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.928203i | 0.0553720i | 0.999617 | + | 0.0276860i | \(0.00881385\pi\) | ||||
−0.999617 | + | 0.0276860i | \(0.991186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.96953 | − | 6.96953i | 0.414296 | − | 0.414296i | −0.468936 | − | 0.883232i | \(-0.655363\pi\) |
0.883232 | + | 0.468936i | \(0.155363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1106 | 0.655840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.66025 | + | 7.66025i | −0.447517 | + | 0.447517i | −0.894528 | − | 0.447011i | \(-0.852488\pi\) |
0.447011 | + | 0.894528i | \(0.352488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 53.5370i | − | 3.11705i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | + | 8.48528i | −0.490716 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 6.00000i | 0.345834 | + | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.53590 | −0.145205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2127 | + | 16.2127i | 0.925307 | + | 0.925307i | 0.997398 | − | 0.0720911i | \(-0.0229672\pi\) |
−0.0720911 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.4254i | 1.83867i | 0.393471 | + | 0.919337i | \(0.371274\pi\) | ||||
−0.393471 | + | 0.919337i | \(0.628726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.85641i | − | 0.217977i | −0.994043 | − | 0.108988i | \(-0.965239\pi\) | ||
0.994043 | − | 0.108988i | \(-0.0347612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.73205 | + | 4.73205i | 0.265778 | + | 0.265778i | 0.827397 | − | 0.561618i | \(-0.189821\pi\) |
−0.561618 | + | 0.827397i | \(0.689821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8295 | −0.718312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.2832 | − | 18.2832i | −1.01731 | − | 1.01731i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.7846 | − | 29.7846i | 1.65215 | − | 1.65215i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.92820i | 0.381964i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.757875 | + | 0.757875i | −0.0416566 | + | 0.0416566i | −0.727628 | − | 0.685972i | \(-0.759377\pi\) |
0.685972 | + | 0.727628i | \(0.259377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 57.6781 | 3.15129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.85641 | −0.536913 | −0.268456 | − | 0.963292i | \(-0.586514\pi\) | ||||
−0.268456 | + | 0.963292i | \(0.586514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.60770 | − | 7.60770i | 0.411980 | − | 0.411980i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.79315 | + | 1.79315i | −0.0962614 | + | 0.0962614i | −0.753598 | − | 0.657336i | \(-0.771683\pi\) |
0.657336 | + | 0.753598i | \(0.271683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3923 | − | 19.3923i | −1.03805 | − | 1.03805i | −0.999247 | − | 0.0387993i | \(-0.987647\pi\) |
−0.0387993 | − | 0.999247i | \(-0.512353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.928203 | 0.0494033 | 0.0247016 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247016 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5254 | + | 17.5254i | 0.930150 | + | 0.930150i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.8380i | − | 0.994234i | −0.867684 | − | 0.497117i | \(-0.834392\pi\) | ||
0.867684 | − | 0.497117i | \(-0.165608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128i | 1.93225i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.9282 | − | 10.9282i | −0.572008 | − | 0.572008i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3886 | −0.855476 | −0.427738 | − | 0.903903i | \(-0.640689\pi\) | ||||
−0.427738 | + | 0.903903i | \(0.640689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00481 | − | 8.00481i | −0.415589 | − | 0.415589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.39230 | − | 9.39230i | 0.486315 | − | 0.486315i | −0.420826 | − | 0.907141i | \(-0.638260\pi\) |
0.907141 | + | 0.420826i | \(0.138260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.1769i | 1.91471i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.41902 | − | 9.41902i | 0.483823 | − | 0.483823i | −0.422527 | − | 0.906350i | \(-0.638857\pi\) |
0.906350 | + | 0.422527i | \(0.138857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.8391 | 1.47361 | 0.736804 | − | 0.676106i | \(-0.236334\pi\) | ||||
0.736804 | + | 0.676106i | \(0.236334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8564 | 0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.73205 | + | 6.73205i | −0.341329 | + | 0.341329i | −0.856867 | − | 0.515538i | \(-0.827592\pi\) |
0.515538 | + | 0.856867i | \(0.327592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.79796i | − | 0.495504i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.69213 | − | 6.69213i | 0.336718 | − | 0.336718i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3205 | − | 16.3205i | −0.819103 | − | 0.819103i | 0.166875 | − | 0.985978i | \(-0.446632\pi\) |
−0.985978 | + | 0.166875i | \(0.946632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3923 | −0.918468 | −0.459234 | − | 0.888315i | \(-0.651876\pi\) | ||||
−0.459234 | + | 0.888315i | \(0.651876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0454 | − | 22.0454i | −1.09816 | − | 1.09816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.960947i | 0.0476324i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07180i | 0.448571i | 0.974523 | + | 0.224286i | \(0.0720049\pi\) | ||||
−0.974523 | + | 0.224286i | \(0.927995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | − | 24.0000i | −1.18096 | − | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.1117 | 1.03633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.277401 | + | 0.277401i | 0.0135519 | + | 0.0135519i | 0.713850 | − | 0.700298i | \(-0.246950\pi\) |
−0.700298 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9282 | − | 13.9282i | 0.678819 | − | 0.678819i | −0.280914 | − | 0.959733i | \(-0.590638\pi\) |
0.959733 | + | 0.280914i | \(0.0906375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.3923i | 1.66827i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13681 | + | 1.13681i | −0.0550142 | + | 0.0550142i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.34418 | −0.209252 | −0.104626 | − | 0.994512i | \(-0.533364\pi\) | ||||
−0.104626 | + | 0.994512i | \(0.533364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8564 | 1.43481 | 0.717404 | − | 0.696658i | \(-0.245330\pi\) | ||||
0.717404 | + | 0.696658i | \(0.245330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.9282 | + | 14.9282i | −0.714113 | + | 0.714113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.83272i | − | 0.278381i | −0.990266 | − | 0.139190i | \(-0.955550\pi\) | ||
0.990266 | − | 0.139190i | \(-0.0444500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.9754 | − | 24.9754i | 1.18662 | − | 1.18662i | 0.208619 | − | 0.977997i | \(-0.433103\pi\) |
0.977997 | − | 0.208619i | \(-0.0668967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4641 | + | 13.4641i | 0.638260 | + | 0.638260i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.39230 | 0.301672 | 0.150836 | − | 0.988559i | \(-0.451804\pi\) | ||||
0.150836 | + | 0.988559i | \(0.451804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.69591 | + | 4.69591i | 0.221122 | + | 0.221122i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 40.1528i | − | 1.88239i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.7846i | − | 0.972263i | −0.873886 | − | 0.486132i | \(-0.838408\pi\) | ||
0.873886 | − | 0.486132i | \(-0.161592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0526 | − | 22.0526i | −1.02709 | − | 1.02709i | −0.999623 | − | 0.0274674i | \(-0.991256\pi\) |
−0.0274674 | − | 0.999623i | \(-0.508744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2180 | −1.35788 | −0.678938 | − | 0.734196i | \(-0.737560\pi\) | ||||
−0.678938 | + | 0.734196i | \(0.737560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.3891 | + | 21.3891i | 0.989768 | + | 0.989768i | 0.999948 | − | 0.0101801i | \(-0.00324049\pi\) |
−0.0101801 | + | 0.999948i | \(0.503240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8564 | − | 25.8564i | 1.19394 | − | 1.19394i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.07180i | 0.233201i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 52.4002 | − | 52.4002i | 2.40429 | − | 2.40429i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0421 | −1.32697 | −0.663485 | − | 0.748190i | \(-0.730923\pi\) | ||||
−0.663485 | + | 0.748190i | \(0.730923\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78461 | 0.126967 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.92820 | + | 2.92820i | −0.132963 | + | 0.132963i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4896i | 0.520642i | 0.965522 | + | 0.260321i | \(0.0838284\pi\) | ||||
−0.965522 | + | 0.260321i | \(0.916172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.14110 | − | 4.14110i | 0.186885 | − | 0.186885i | −0.607463 | − | 0.794348i | \(-0.707813\pi\) |
0.794348 | + | 0.607463i | \(0.207813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.4641 | − | 21.4641i | −0.966695 | − | 0.966695i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.7128 | 0.704816 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.82843 | + | 2.82843i | 0.126618 | + | 0.126618i | 0.767576 | − | 0.640958i | \(-0.221463\pi\) |
−0.640958 | + | 0.767576i | \(0.721463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.3853i | 1.04270i | 0.853343 | + | 0.521349i | \(0.174571\pi\) | ||||
−0.853343 | + | 0.521349i | \(0.825429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.7128i | 2.47919i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.12436 | − | 5.12436i | −0.227133 | − | 0.227133i | 0.584361 | − | 0.811494i | \(-0.301345\pi\) |
−0.811494 | + | 0.584361i | \(0.801345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.76268 | + | 8.76268i | 0.386130 | + | 0.386130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.92820 | + | 2.92820i | −0.128782 | + | 0.128782i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3205i | 0.934068i | 0.884239 | + | 0.467034i | \(0.154678\pi\) | ||||
−0.884239 | + | 0.467034i | \(0.845322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2485 | + | 22.2485i | −0.972858 | + | 0.972858i | −0.999641 | − | 0.0267832i | \(-0.991474\pi\) |
0.0267832 | + | 0.999641i | \(0.491474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6077 | − | 13.6077i | 0.589415 | − | 0.589415i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.4548i | − | 0.668170i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.03528 | + | 1.03528i | −0.0445925 | + | 0.0445925i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9282 | + | 19.9282i | 0.856780 | + | 0.856780i | 0.990957 | − | 0.134177i | \(-0.0428391\pi\) |
−0.134177 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46410 | −0.234056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.3886 | − | 16.3886i | −0.700724 | − | 0.700724i | 0.263842 | − | 0.964566i | \(-0.415010\pi\) |
−0.964566 | + | 0.263842i | \(0.915010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.4056i | 2.78637i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.00000i | − | 0.255146i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.8038 | + | 19.8038i | 0.839116 | + | 0.839116i | 0.988743 | − | 0.149627i | \(-0.0478072\pi\) |
−0.149627 | + | 0.988743i | \(0.547807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6969 | 0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.03528 | − | 1.03528i | −0.0436317 | − | 0.0436317i | 0.684954 | − | 0.728586i | \(-0.259822\pi\) |
−0.728586 | + | 0.684954i | \(0.759822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −49.1769 | + | 49.1769i | −2.06889 | + | 2.06889i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.46410i | − | 0.145223i | −0.997360 | − | 0.0726113i | \(-0.976867\pi\) | ||
0.997360 | − | 0.0726113i | \(-0.0231333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.4243 | + | 22.4243i | −0.938430 | + | 0.938430i | −0.998211 | − | 0.0597818i | \(-0.980959\pi\) |
0.0597818 | + | 0.998211i | \(0.480959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0812 | 1.17107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8564 | −0.909894 | −0.454947 | − | 0.890518i | \(-0.650342\pi\) | ||||
−0.454947 | + | 0.890518i | \(0.650342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.46410 | − | 9.46410i | 0.392637 | − | 0.392637i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.76646i | − | 0.280238i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.3548 | + | 30.3548i | −1.25288 | + | 1.25288i | −0.298453 | + | 0.954424i | \(0.596471\pi\) |
−0.954424 | + | 0.298453i | \(0.903529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.7846 | − | 38.7846i | −1.59809 | − | 1.59809i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.7128 | 1.54868 | 0.774340 | − | 0.632770i | \(-0.218082\pi\) | ||||
0.774340 | + | 0.632770i | \(0.218082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.1822 | + | 23.1822i | 0.950378 | + | 0.950378i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.96953i | 0.284767i | 0.989812 | + | 0.142384i | \(0.0454767\pi\) | ||||
−0.989812 | + | 0.142384i | \(0.954523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.7128i | − | 0.804102i | −0.915617 | − | 0.402051i | \(-0.868297\pi\) | ||
0.915617 | − | 0.402051i | \(-0.131703\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.1962 | − | 24.1962i | −0.983713 | − | 0.983713i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8434 | 1.29248 | 0.646241 | − | 0.763133i | \(-0.276340\pi\) | ||||
0.646241 | + | 0.763133i | \(0.276340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | + | 8.48528i | 0.343278 | + | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.32051 | + | 4.32051i | −0.174504 | + | 0.174504i | −0.788955 | − | 0.614451i | \(-0.789377\pi\) |
0.614451 | + | 0.788955i | \(0.289377\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.8564i | 1.60456i | 0.596949 | + | 0.802279i | \(0.296379\pi\) | ||||
−0.596949 | + | 0.802279i | \(0.703621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.48528 | − | 8.48528i | 0.341052 | − | 0.341052i | −0.515711 | − | 0.856763i | \(-0.672472\pi\) |
0.856763 | + | 0.515711i | \(0.172472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0716 | 0.483638 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9282 | −0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60770 | + | 1.60770i | −0.0641030 | + | 0.0641030i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5612i | 0.937955i | 0.883210 | + | 0.468977i | \(0.155377\pi\) | ||||
−0.883210 | + | 0.468977i | \(0.844623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.6723 | − | 39.6723i | 1.57435 | − | 1.57435i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 3.00000i | 0.118864 | + | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.6077 | 1.01144 | 0.505722 | − | 0.862697i | \(-0.331226\pi\) | ||||
0.505722 | + | 0.862697i | \(0.331226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1779 | + | 20.1779i | 0.795740 | + | 0.795740i | 0.982421 | − | 0.186681i | \(-0.0597730\pi\) |
−0.186681 | + | 0.982421i | \(0.559773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 40.9107i | − | 1.60836i | −0.594383 | − | 0.804182i | \(-0.702604\pi\) | ||
0.594383 | − | 0.804182i | \(-0.297396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.2872i | − | 0.796342i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.6603 | + | 17.6603i | 0.691099 | + | 0.691099i | 0.962474 | − | 0.271375i | \(-0.0874782\pi\) |
−0.271375 | + | 0.962474i | \(0.587478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.6781 | 2.25367 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706 | + | 16.9706i | 0.661079 | + | 0.661079i | 0.955634 | − | 0.294555i | \(-0.0951715\pi\) |
−0.294555 | + | 0.955634i | \(0.595171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.60770 | + | 4.60770i | −0.179219 | + | 0.179219i | −0.791015 | − | 0.611797i | \(-0.790447\pi\) |
0.611797 | + | 0.791015i | \(0.290447\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 70.6410i | − | 2.73934i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5254 | + | 17.5254i | −0.678585 | + | 0.678585i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.960947 | −0.0370969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.33975 | + | 2.33975i | −0.0899237 | + | 0.0899237i | −0.750638 | − | 0.660714i | \(-0.770254\pi\) |
0.660714 | + | 0.750638i | \(0.270254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.62536i | 0.100752i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8028 | − | 17.8028i | 0.681204 | − | 0.681204i | −0.279068 | − | 0.960271i | \(-0.590025\pi\) |
0.960271 | + | 0.279068i | \(0.0900253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.3205 | + | 39.3205i | 1.50236 | + | 1.50236i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6077 | −0.746994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.6622 | + | 18.6622i | 0.709943 | + | 0.709943i | 0.966523 | − | 0.256580i | \(-0.0825958\pi\) |
−0.256580 | + | 0.966523i | \(0.582596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 26.7685i | − | 1.01539i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128i | 0.595165i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.5885 | − | 10.5885i | −0.399921 | − | 0.399921i | 0.478284 | − | 0.878205i | \(-0.341259\pi\) |
−0.878205 | + | 0.478284i | \(0.841259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | 0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9754 | + | 24.9754i | 0.939295 | + | 0.939295i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7128 | + | 34.7128i | −1.30367 | + | 1.30367i | −0.377766 | + | 0.925901i | \(0.623308\pi\) |
−0.925901 | + | 0.377766i | \(0.876692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.7846i | − | 0.778390i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9706 | − | 16.9706i | 0.634663 | − | 0.634663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.27362 | 0.0847919 | 0.0423959 | − | 0.999101i | \(-0.486501\pi\) | ||||
0.0423959 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.85641 | 0.292588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 61.5167 | − | 61.5167i | 2.28467 | − | 2.28467i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.10634i | 0.300648i | 0.988637 | + | 0.150324i | \(0.0480316\pi\) | ||||
−0.988637 | + | 0.150324i | \(0.951968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.48528 | + | 8.48528i | −0.313839 | + | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.00000 | − | 5.00000i | −0.184679 | − | 0.184679i | 0.608712 | − | 0.793391i | \(-0.291686\pi\) |
−0.793391 | + | 0.608712i | \(0.791686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.8564 | 0.805091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4558 | − | 25.4558i | −0.936408 | − | 0.936408i | 0.0616872 | − | 0.998096i | \(-0.480352\pi\) |
−0.998096 | + | 0.0616872i | \(0.980352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.3233i | − | 1.00240i | −0.865333 | − | 0.501198i | \(-0.832893\pi\) | ||
0.865333 | − | 0.501198i | \(-0.167107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 20.7846i | − | 0.761489i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.92820 | − | 6.92820i | −0.253151 | − | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.1886 | 1.68545 | 0.842723 | − | 0.538348i | \(-0.180951\pi\) | ||||
0.842723 | + | 0.538348i | \(0.180951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.0058 | + | 18.0058i | 0.655300 | + | 0.655300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7846 | − | 23.7846i | 0.864466 | − | 0.864466i | −0.127387 | − | 0.991853i | \(-0.540659\pi\) |
0.991853 | + | 0.127387i | \(0.0406589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 52.2487i | − | 1.89401i | −0.321212 | − | 0.947007i | \(-0.604090\pi\) | ||
0.321212 | − | 0.947007i | \(-0.395910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44949 | + | 2.44949i | −0.0886775 | + | 0.0886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.7878 | −2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.5885 | + | 34.5885i | −1.24406 | + | 1.24406i | −0.285759 | + | 0.958302i | \(0.592246\pi\) |
−0.958302 | + | 0.285759i | \(0.907754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 72.9571i | 2.62070i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.9401 | − | 23.9401i | 0.857743 | − | 0.857743i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.64102 | + | 6.64102i | 0.237634 | + | 0.237634i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.39230 | 0.299534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5916 | − | 16.5916i | −0.591428 | − | 0.591428i | 0.346589 | − | 0.938017i | \(-0.387340\pi\) |
−0.938017 | + | 0.346589i | \(0.887340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.0908i | 1.56769i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.78461i | 0.0988844i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5167 | + | 15.5167i | 0.549628 | + | 0.549628i | 0.926333 | − | 0.376705i | \(-0.122943\pi\) |
−0.376705 | + | 0.926333i | \(0.622943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | −0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.14110 | − | 4.14110i | −0.146136 | − | 0.146136i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.9282 | − | 18.9282i | 0.667132 | − | 0.667132i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.67949i | 0.234838i | 0.993082 | + | 0.117419i | \(0.0374621\pi\) | ||||
−0.993082 | + | 0.117419i | \(0.962538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.4612 | + | 38.4612i | −1.35055 | + | 1.35055i | −0.465513 | + | 0.885041i | \(0.654130\pi\) |
−0.885041 | + | 0.465513i | \(0.845870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5254 | 0.613887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8564 | 0.904601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8038 | + | 17.8038i | −0.621359 | + | 0.621359i | −0.945879 | − | 0.324520i | \(-0.894797\pi\) |
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.97382i | − | 0.347666i | −0.984775 | − | 0.173833i | \(-0.944385\pi\) | ||
0.984775 | − | 0.173833i | \(-0.0556152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.6675 | + | 31.6675i | −1.10119 | + | 1.10119i | −0.106919 | + | 0.994268i | \(0.534099\pi\) |
−0.994268 | + | 0.106919i | \(0.965901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.14359 | + | 1.14359i | 0.0397186 | + | 0.0397186i | 0.726687 | − | 0.686969i | \(-0.241059\pi\) |
−0.686969 | + | 0.726687i | \(0.741059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1117 | − | 21.1117i | −0.730599 | − | 0.730599i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.0106i | 0.897987i | 0.893535 | + | 0.448994i | \(0.148217\pi\) | ||||
−0.893535 | + | 0.448994i | \(0.851783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.7846i | 1.64775i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.6603 | − | 13.6603i | −0.469927 | − | 0.469927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.6937 | −0.745404 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31268 | + | 1.31268i | 0.0449980 | + | 0.0449980i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.2487 | + | 33.2487i | −1.13841 | + | 1.13841i | −0.149680 | + | 0.988735i | \(0.547824\pi\) |
−0.988735 | + | 0.149680i | \(0.952176\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.1769i | 1.47490i | 0.675404 | + | 0.737448i | \(0.263969\pi\) | ||||
−0.675404 | + | 0.737448i | \(0.736031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.8033 | + | 22.8033i | −0.778038 | + | 0.778038i | −0.979497 | − | 0.201459i | \(-0.935432\pi\) |
0.201459 | + | 0.979497i | \(0.435432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.1213 | −1.26362 | −0.631812 | − | 0.775122i | \(-0.717688\pi\) | ||||
−0.631812 | + | 0.775122i | \(0.717688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.6410 | −2.26586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.53590 | − | 2.53590i | 0.0860245 | − | 0.0860245i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.3350i | − | 2.14602i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.9802 | + | 32.9802i | −1.11493 | + | 1.11493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2487 | − | 25.2487i | −0.852588 | − | 0.852588i | 0.137863 | − | 0.990451i | \(-0.455977\pi\) |
−0.990451 | + | 0.137863i | \(0.955977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6410 | −1.23447 | −0.617234 | − | 0.786780i | \(-0.711747\pi\) | ||||
−0.617234 | + | 0.786780i | \(0.711747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.96524 | − | 3.96524i | −0.133441 | − | 0.133441i | 0.637232 | − | 0.770672i | \(-0.280080\pi\) |
−0.770672 | + | 0.637232i | \(0.780080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 36.5665i | − | 1.22778i | −0.789391 | − | 0.613891i | \(-0.789603\pi\) | ||
0.789391 | − | 0.613891i | \(-0.210397\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 35.5692i | − | 1.19295i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.9282 | + | 14.9282i | 0.499553 | + | 0.499553i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −73.1330 | −2.44457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.5322 | − | 45.5322i | −1.51859 | − | 1.51859i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3205 | − | 11.3205i | 0.377141 | − | 0.377141i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 27.3205i | − | 0.908164i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.9759 | − | 29.9759i | 0.995333 | − | 0.995333i | −0.00465619 | − | 0.999989i | \(-0.501482\pi\) |
0.999989 | + | 0.00465619i | \(0.00148212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0726 | −0.731298 | −0.365649 | − | 0.930753i | \(-0.619153\pi\) | ||||
−0.365649 | + | 0.930753i | \(0.619153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | 0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.8564 | − | 25.8564i | 0.853854 | − | 0.853854i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 0.582009i | − | 0.0191987i | −0.999954 | − | 0.00959936i | \(-0.996944\pi\) | ||
0.999954 | − | 0.00959936i | \(-0.00305562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.2442 | − | 19.2442i | 0.633430 | − | 0.633430i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.60770 | − | 4.60770i | −0.151500 | − | 0.151500i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.3205 | 1.48692 | 0.743459 | − | 0.668782i | \(-0.233184\pi\) | ||||
0.743459 | + | 0.668782i | \(0.233184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.27792 | + | 5.27792i | 0.172977 | + | 0.172977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959i | 0.640855i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.6603 | + | 25.6603i | 0.836500 | + | 0.836500i | 0.988396 | − | 0.151896i | \(-0.0485379\pi\) |
−0.151896 | + | 0.988396i | \(0.548538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8295 | 0.417785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.5569 | − | 20.5569i | −0.668008 | − | 0.668008i | 0.289246 | − | 0.957255i | \(-0.406595\pi\) |
−0.957255 | + | 0.289246i | \(0.906595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 12.0000i | −0.389536 | + | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.3923i | 1.50279i | 0.659850 | + | 0.751397i | \(0.270620\pi\) | ||||
−0.659850 | + | 0.751397i | \(0.729380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1117 | − | 21.1117i | 0.683158 | − | 0.683158i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.2538 | 1.13840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.3923 | + | 16.3923i | −0.527687 | + | 0.527687i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.3800i | − | 0.333797i | −0.985974 | − | 0.166899i | \(-0.946625\pi\) | ||
0.985974 | − | 0.166899i | \(-0.0533753\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7322 | − | 15.7322i | 0.504871 | − | 0.504871i | −0.408077 | − | 0.912948i | \(-0.633800\pi\) |
0.912948 | + | 0.408077i | \(0.133800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | − | 12.0000i | −0.384702 | − | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1769 | −1.12541 | −0.562705 | − | 0.826658i | \(-0.690239\pi\) | ||||
−0.562705 | + | 0.826658i | \(0.690239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.10205 | + | 5.10205i | 0.163062 | + | 0.163062i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 23.7370i | − | 0.757093i | −0.925582 | − | 0.378547i | \(-0.876424\pi\) | ||
0.925582 | − | 0.378547i | \(-0.123576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.8564i | 1.07875i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.92820 | + | 6.92820i | 0.220304 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2474 | −0.389053 | −0.194527 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194527 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.9860 | − | 50.9860i | −1.61637 | − | 1.61637i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.4641 | − | 12.4641i | 0.394742 | − | 0.394742i | −0.481632 | − | 0.876374i | \(-0.659956\pi\) |
0.876374 | + | 0.481632i | \(0.159956\pi\) | |||||||
\(998\) | 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 | 2304.2.k.e.577.2 | 8 | ||
3.2 | odd | 2 | 768.2.j.f.577.2 | yes | 8 | ||
4.3 | odd | 2 | inner | 2304.2.k.e.577.1 | 8 | ||
8.3 | odd | 2 | 2304.2.k.l.577.3 | 8 | |||
8.5 | even | 2 | 2304.2.k.l.577.4 | 8 | |||
12.11 | even | 2 | 768.2.j.f.577.4 | yes | 8 | ||
16.3 | odd | 4 | 2304.2.k.l.1729.4 | 8 | |||
16.5 | even | 4 | inner | 2304.2.k.e.1729.1 | 8 | ||
16.11 | odd | 4 | inner | 2304.2.k.e.1729.2 | 8 | ||
16.13 | even | 4 | 2304.2.k.l.1729.3 | 8 | |||
24.5 | odd | 2 | 768.2.j.e.577.3 | yes | 8 | ||
24.11 | even | 2 | 768.2.j.e.577.1 | yes | 8 | ||
32.5 | even | 8 | 9216.2.a.bc.1.1 | 4 | |||
32.11 | odd | 8 | 9216.2.a.bc.1.4 | 4 | |||
32.21 | even | 8 | 9216.2.a.bi.1.4 | 4 | |||
32.27 | odd | 8 | 9216.2.a.bi.1.1 | 4 | |||
48.5 | odd | 4 | 768.2.j.f.193.2 | yes | 8 | ||
48.11 | even | 4 | 768.2.j.f.193.4 | yes | 8 | ||
48.29 | odd | 4 | 768.2.j.e.193.3 | yes | 8 | ||
48.35 | even | 4 | 768.2.j.e.193.1 | ✓ | 8 | ||
96.5 | odd | 8 | 3072.2.a.r.1.4 | 4 | |||
96.11 | even | 8 | 3072.2.a.r.1.1 | 4 | |||
96.29 | odd | 8 | 3072.2.d.h.1537.4 | 8 | |||
96.35 | even | 8 | 3072.2.d.h.1537.8 | 8 | |||
96.53 | odd | 8 | 3072.2.a.l.1.1 | 4 | |||
96.59 | even | 8 | 3072.2.a.l.1.4 | 4 | |||
96.77 | odd | 8 | 3072.2.d.h.1537.5 | 8 | |||
96.83 | even | 8 | 3072.2.d.h.1537.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.1 | ✓ | 8 | 48.35 | even | 4 | ||
768.2.j.e.193.3 | yes | 8 | 48.29 | odd | 4 | ||
768.2.j.e.577.1 | yes | 8 | 24.11 | even | 2 | ||
768.2.j.e.577.3 | yes | 8 | 24.5 | odd | 2 | ||
768.2.j.f.193.2 | yes | 8 | 48.5 | odd | 4 | ||
768.2.j.f.193.4 | yes | 8 | 48.11 | even | 4 | ||
768.2.j.f.577.2 | yes | 8 | 3.2 | odd | 2 | ||
768.2.j.f.577.4 | yes | 8 | 12.11 | even | 2 | ||
2304.2.k.e.577.1 | 8 | 4.3 | odd | 2 | inner | ||
2304.2.k.e.577.2 | 8 | 1.1 | even | 1 | trivial | ||
2304.2.k.e.1729.1 | 8 | 16.5 | even | 4 | inner | ||
2304.2.k.e.1729.2 | 8 | 16.11 | odd | 4 | inner | ||
2304.2.k.l.577.3 | 8 | 8.3 | odd | 2 | |||
2304.2.k.l.577.4 | 8 | 8.5 | even | 2 | |||
2304.2.k.l.1729.3 | 8 | 16.13 | even | 4 | |||
2304.2.k.l.1729.4 | 8 | 16.3 | odd | 4 | |||
3072.2.a.l.1.1 | 4 | 96.53 | odd | 8 | |||
3072.2.a.l.1.4 | 4 | 96.59 | even | 8 | |||
3072.2.a.r.1.1 | 4 | 96.11 | even | 8 | |||
3072.2.a.r.1.4 | 4 | 96.5 | odd | 8 | |||
3072.2.d.h.1537.1 | 8 | 96.83 | even | 8 | |||
3072.2.d.h.1537.4 | 8 | 96.29 | odd | 8 | |||
3072.2.d.h.1537.5 | 8 | 96.77 | odd | 8 | |||
3072.2.d.h.1537.8 | 8 | 96.35 | even | 8 | |||
9216.2.a.bc.1.1 | 4 | 32.5 | even | 8 | |||
9216.2.a.bc.1.4 | 4 | 32.11 | odd | 8 | |||
9216.2.a.bi.1.1 | 4 | 32.27 | odd | 8 | |||
9216.2.a.bi.1.4 | 4 | 32.21 | even | 8 |