Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(193,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.j (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: | \(6.13251087523\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.577 |
Dual form | 768.2.j.f.193.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73205 | − | 2.73205i | 1.22181 | − | 1.22181i | 0.254822 | − | 0.966988i | \(-0.417983\pi\) |
0.966988 | − | 0.254822i | \(-0.0820170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03528 | − | 1.03528i | 0.312148 | − | 0.312148i | −0.533594 | − | 0.845741i | \(-0.679159\pi\) |
0.845741 | + | 0.533594i | \(0.179159\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −3.86370 | −0.997604 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 1.73205 | − | 1.73205i | 0.377964 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 9.92820i | − | 1.98564i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.19615 | − | 6.19615i | −1.15060 | − | 1.15060i | −0.986433 | − | 0.164163i | \(-0.947508\pi\) |
−0.164163 | − | 0.986433i | \(-0.552492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.34847 | −1.31982 | −0.659912 | − | 0.751343i | \(-0.729406\pi\) | ||||
−0.659912 | + | 0.751343i | \(0.729406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46410 | −0.254867 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | − | 4.24264i | − | 0.679366i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.53590i | 0.708388i | 0.935172 | + | 0.354194i | \(0.115245\pi\) | ||||
−0.935172 | + | 0.354194i | \(0.884755\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 2.73205 | + | 2.73205i | 0.407270 | + | 0.407270i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.44949 | − | 2.44949i | −0.342997 | − | 0.342997i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.26795 | − | 3.26795i | 0.448887 | − | 0.448887i | −0.446097 | − | 0.894985i | \(-0.647186\pi\) |
0.894985 | + | 0.446097i | \(0.147186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.65685i | − | 0.762770i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.46410i | − | 0.988644i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796 | − | 9.79796i | 1.27559 | − | 1.27559i | 0.332473 | − | 0.943113i | \(-0.392117\pi\) |
0.943113 | − | 0.332473i | \(-0.107883\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −2.44949 | −0.308607 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | −2.00000 | + | 2.00000i | −0.240772 | + | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.41473i | 0.761288i | 0.924722 | + | 0.380644i | \(0.124298\pi\) | ||||
−0.924722 | + | 0.380644i | \(0.875702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.02030 | + | 7.02030i | −0.810634 | + | 0.810634i | ||||
\(76\) | 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 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86370 | + | 3.86370i | 0.424097 | + | 0.424097i | 0.886611 | − | 0.462515i | \(-0.153053\pi\) |
−0.462515 | + | 0.886611i | \(0.653053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.46410 | − | 9.46410i | 1.02653 | − | 1.02653i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.76268i | 0.939458i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.92820i | 0.522388i | 0.965286 | + | 0.261194i | \(0.0841163\pi\) | ||||
−0.965286 | + | 0.261194i | \(0.915884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.34847 | + | 7.34847i | −0.770329 | + | 0.770329i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19615 | + | 5.19615i | 0.538816 | + | 0.538816i | ||||
\(94\) | 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 | ||||||||
\(99\) | 1.03528 | + | 1.03528i | 0.104049 | + | 0.104049i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1962 | + | 10.1962i | −1.01456 | + | 1.01456i | −0.0146626 | + | 0.999892i | \(0.504667\pi\) |
−0.999892 | + | 0.0146626i | \(0.995333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.20736i | − | 0.316031i | −0.987437 | − | 0.158016i | \(-0.949490\pi\) | ||
0.987437 | − | 0.158016i | \(-0.0505096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 9.46410i | − | 0.923602i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −0.656339 | −0.0622969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.72741 | − | 7.72741i | −0.720584 | − | 0.720584i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | + | 3.00000i | −0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528i | 0.777844i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641i | 0.805128i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.20736 | − | 3.20736i | 0.289198 | − | 0.289198i | ||||
\(124\) | 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 | ||||||||
\(129\) | −3.46410 | −0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5558 | + | 10.5558i | 0.922267 | + | 0.922267i | 0.997189 | − | 0.0749219i | \(-0.0238708\pi\) |
−0.0749219 | + | 0.997189i | \(0.523871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9282 | + | 12.9282i | −1.12102 | + | 1.12102i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.86370i | − | 0.332535i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3923i | 1.22962i | 0.788676 | + | 0.614809i | \(0.210767\pi\) | ||||
−0.788676 | + | 0.614809i | \(0.789233\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 2.00000 | + | 2.00000i | 0.168430 | + | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.21166 | 0.519445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8564 | −2.81162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.707107 | − | 0.707107i | −0.0583212 | − | 0.0583212i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.80385 | − | 3.80385i | 0.311623 | − | 0.311623i | −0.533915 | − | 0.845538i | \(-0.679280\pi\) |
0.845538 | + | 0.533915i | \(0.179280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.59059i | − | 0.536335i | −0.963372 | − | 0.268167i | \(-0.913582\pi\) | ||
0.963372 | − | 0.268167i | \(-0.0864181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410i | 0.280056i | ||||||||
\(154\) | 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 | ||||||||
\(159\) | −4.62158 | −0.366515 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | −4.00000 | + | 4.00000i | −0.311400 | + | 0.311400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.72741i | − | 0.597965i | −0.954259 | − | 0.298982i | \(-0.903353\pi\) | ||
0.954259 | − | 0.298982i | \(-0.0966472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.27792 | + | 5.27792i | −0.403612 | + | 0.403612i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1962 | − | 12.1962i | −0.927256 | − | 0.927256i | 0.0702716 | − | 0.997528i | \(-0.477613\pi\) |
−0.997528 | + | 0.0702716i | \(0.977613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.3190 | 1.83835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.8564 | −1.04151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.3843 | − | 13.3843i | −1.00039 | − | 1.00039i | −1.00000 | 0.000386700i | \(-0.999877\pi\) | |
−0.000386700 | − | 1.00000i | \(-0.500123\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | − | 0.656339i | − | 0.0485180i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.53590i | − | 0.186443i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.58630 | − | 3.58630i | 0.262256 | − | 0.262256i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.73205 | + | 1.73205i | 0.125988 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.72741 | 0.559136 | 0.279568 | − | 0.960126i | \(-0.409809\pi\) | ||||
0.279568 | + | 0.960126i | \(0.409809\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.5911 | − | 11.5911i | −0.830057 | − | 0.830057i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.19615 | + | 6.19615i | −0.441458 | + | 0.441458i | −0.892502 | − | 0.451044i | \(-0.851052\pi\) |
0.451044 | + | 0.892502i | \(0.351052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6622i | 1.32293i | 0.749977 | + | 0.661463i | \(0.230064\pi\) | ||||
−0.749977 | + | 0.661463i | \(0.769936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.9282i | 1.05295i | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 4.53590 | − | 4.53590i | 0.310795 | − | 0.310795i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 13.3843i | − | 0.912799i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 18.0000i | − | 1.22192i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.82843 | − | 2.82843i | 0.191127 | − | 0.191127i | ||||
\(220\) | 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 | ||||||||
\(225\) | 9.92820 | 0.661880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.00481 | − | 8.00481i | −0.531298 | − | 0.531298i | 0.389661 | − | 0.920958i | \(-0.372592\pi\) |
−0.920958 | + | 0.389661i | \(0.872592\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | − | 3.58630i | − | 0.235961i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9282i | 0.846955i | 0.905907 | + | 0.423477i | \(0.139191\pi\) | ||||
−0.905907 | + | 0.423477i | \(0.860809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.72741 | + | 7.72741i | −0.504080 | + | 0.504080i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73205 | + | 1.73205i | 0.112509 | + | 0.112509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.72741 | 0.499844 | 0.249922 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249922 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7846 | 1.72535 | 0.862674 | − | 0.505760i | \(-0.168788\pi\) | ||||
0.862674 | + | 0.505760i | \(0.168788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.73205 | − | 2.73205i | 0.174544 | − | 0.174544i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.6675i | 2.01495i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.46410i | − | 0.346273i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.62158 | + | 4.62158i | −0.291711 | + | 0.291711i | −0.837756 | − | 0.546045i | \(-0.816133\pi\) |
0.546045 | + | 0.837756i | \(0.316133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.92820 | − | 2.92820i | −0.184095 | − | 0.184095i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.3843 | −0.838155 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.7846 | −1.42126 | −0.710632 | − | 0.703563i | \(-0.751591\pi\) | ||||
−0.710632 | + | 0.703563i | \(0.751591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.13681 | + | 1.13681i | 0.0706381 | + | 0.0706381i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.19615 | − | 6.19615i | 0.383532 | − | 0.383532i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6274i | 1.39527i | 0.716455 | + | 0.697633i | \(0.245763\pi\) | ||||
−0.716455 | + | 0.697633i | \(0.754237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.8564i | − | 1.09691i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.48477 | − | 3.48477i | 0.213264 | − | 0.213264i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.26795 | + | 7.26795i | 0.443135 | + | 0.443135i | 0.893064 | − | 0.449929i | \(-0.148551\pi\) |
−0.449929 | + | 0.893064i | \(0.648551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.20736 | −0.194834 | −0.0974168 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974168 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3923 | 0.628971 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | − | 7.34847i | − | 0.439941i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.928203i | − | 0.0553720i | −0.999617 | − | 0.0276860i | \(-0.991186\pi\) | ||
0.999617 | − | 0.0276860i | \(-0.00881385\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −20.3923 | − | 20.3923i | −1.20794 | − | 1.20794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1106 | −0.655840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.757875 | − | 0.757875i | −0.0444274 | − | 0.0444274i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.66025 | − | 7.66025i | 0.447517 | − | 0.447517i | −0.447011 | − | 0.894528i | \(-0.647512\pi\) |
0.894528 | + | 0.447011i | \(0.147512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 53.5370i | − | 3.11705i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.46410i | − | 0.0849558i | ||||||
\(298\) | 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 | ||||||||
\(303\) | 14.4195 | 0.828381 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | −2.26795 | + | 2.26795i | −0.129019 | + | 0.129019i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.4254i | − | 1.83867i | −0.393471 | − | 0.919337i | \(-0.628726\pi\) | ||
0.393471 | − | 0.919337i | \(-0.371274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.85641i | − | 0.217977i | −0.994043 | − | 0.108988i | \(-0.965239\pi\) | ||
0.994043 | − | 0.108988i | \(-0.0347612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.69213 | + | 6.69213i | −0.377059 | + | 0.377059i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.73205 | − | 4.73205i | −0.265778 | − | 0.265778i | 0.561618 | − | 0.827397i | \(-0.310179\pi\) |
−0.827397 | + | 0.561618i | \(0.810179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8295 | −0.718312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | − | 1.41421i | − | 0.0782062i | ||||||
\(328\) | 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 | ||||||||
\(333\) | 0.464102 | + | 0.464102i | 0.0254326 | + | 0.0254326i | ||||
\(334\) | 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 | ||||||||
\(339\) | 12.7279 | + | 12.7279i | 0.691286 | + | 0.691286i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.60770 | + | 7.60770i | −0.411980 | + | 0.411980i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.9282i | 0.588355i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.79315 | − | 1.79315i | 0.0962614 | − | 0.0962614i | −0.657336 | − | 0.753598i | \(-0.728317\pi\) |
0.753598 | + | 0.657336i | \(0.228317\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5254 | + | 17.5254i | 0.930150 | + | 0.930150i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.00000 | − | 6.00000i | 0.317554 | − | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8380i | 0.994234i | 0.867684 | + | 0.497117i | \(0.165608\pi\) | ||||
−0.867684 | + | 0.497117i | \(0.834392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128i | 1.93225i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.26243 | − | 6.26243i | 0.328692 | − | 0.328692i | ||||
\(364\) | 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 | ||||||||
\(369\) | −4.53590 | −0.236129 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 19.0411i | 0.983279i | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 10.2679 | + | 10.2679i | 0.526043 | + | 0.526043i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.8391 | −1.47361 | −0.736804 | − | 0.676106i | \(-0.763666\pi\) | ||||
−0.736804 | + | 0.676106i | \(0.763666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8564 | 0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.44949 | + | 2.44949i | 0.124515 | + | 0.124515i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.73205 | − | 6.73205i | 0.341329 | − | 0.341329i | −0.515538 | − | 0.856867i | \(-0.672408\pi\) |
0.856867 | + | 0.515538i | \(0.172408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.79796i | − | 0.495504i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.9282i | − | 0.753028i | ||||||
\(394\) | 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 | ||||||||
\(399\) | 18.2832 | 0.915307 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3923 | 0.918468 | 0.459234 | − | 0.888315i | \(-0.348124\pi\) | ||||
0.459234 | + | 0.888315i | \(0.348124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0454 | − | 22.0454i | −1.09816 | − | 1.09816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.73205 | + | 2.73205i | −0.135757 | + | 0.135757i | ||||
\(406\) | 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 | ||||||||
\(411\) | 10.1769 | − | 10.1769i | 0.501989 | − | 0.501989i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | + | 24.0000i | 1.18096 | + | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.1117 | 1.03633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.92820 | 0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.277401 | − | 0.277401i | −0.0135519 | − | 0.0135519i | 0.700298 | − | 0.713850i | \(-0.253050\pi\) |
−0.713850 | + | 0.700298i | \(0.753050\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | − | 2.82843i | − | 0.137523i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 34.3923i | − | 1.66827i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13681 | + | 1.13681i | −0.0550142 | + | 0.0550142i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.39230 | − | 4.39230i | −0.212062 | − | 0.212062i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.34418 | 0.209252 | 0.104626 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104626 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8564 | 1.43481 | 0.717404 | − | 0.696658i | \(-0.245330\pi\) | ||||
0.717404 | + | 0.696658i | \(0.245330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.9401 | + | 23.9401i | 1.14784 | + | 1.14784i | ||||
\(436\) | 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 | ||||||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.9754 | + | 24.9754i | −1.18662 | + | 1.18662i | −0.208619 | + | 0.977997i | \(0.566897\pi\) |
−0.977997 | + | 0.208619i | \(0.933103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4641 | + | 13.4641i | 0.638260 | + | 0.638260i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.37945 | −0.254439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.39230 | −0.301672 | −0.150836 | − | 0.988559i | \(-0.548196\pi\) | ||||
−0.150836 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.69591 | + | 4.69591i | 0.221122 | + | 0.221122i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.66025 | + | 4.66025i | −0.218958 | + | 0.218958i | ||||
\(454\) | 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 | ||||||||
\(459\) | 2.44949 | − | 2.44949i | 0.114332 | − | 0.114332i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0526 | + | 22.0526i | 1.02709 | + | 1.02709i | 0.999623 | + | 0.0274674i | \(0.00874423\pi\) |
0.0274674 | + | 0.999623i | \(0.491256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2180 | −1.35788 | −0.678938 | − | 0.734196i | \(-0.737560\pi\) | ||||
−0.678938 | + | 0.734196i | \(0.737560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.3923 | 1.31666 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.3891 | − | 21.3891i | −0.989768 | − | 0.989768i | 0.0101801 | − | 0.999948i | \(-0.496760\pi\) |
−0.999948 | + | 0.0101801i | \(0.996760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8564 | − | 25.8564i | 1.19394 | − | 1.19394i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17209i | 0.100085i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.07180i | − | 0.233201i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 52.4002 | − | 52.4002i | 2.40429 | − | 2.40429i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.26795 | + | 3.26795i | 0.149629 | + | 0.149629i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0421 | 1.32697 | 0.663485 | − | 0.748190i | \(-0.269077\pi\) | ||||
0.663485 | + | 0.748190i | \(0.269077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78461 | 0.126967 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.89898 | − | 4.89898i | −0.222911 | − | 0.222911i | ||||
\(484\) | 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 | ||||||||
\(489\) | 4.53590i | 0.205120i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.14110 | + | 4.14110i | −0.186885 | + | 0.186885i | −0.794348 | − | 0.607463i | \(-0.792187\pi\) |
0.607463 | + | 0.794348i | \(0.292187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.4641 | − | 21.4641i | −0.966695 | − | 0.966695i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | −5.46410 | + | 5.46410i | −0.244118 | + | 0.244118i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.3853i | − | 1.04270i | −0.853343 | − | 0.521349i | \(-0.825429\pi\) | ||
0.853343 | − | 0.521349i | \(-0.174571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.7128i | 2.47919i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.53553 | − | 3.53553i | 0.157019 | − | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.12436 | + | 5.12436i | 0.227133 | + | 0.227133i | 0.811494 | − | 0.584361i | \(-0.198655\pi\) |
−0.584361 | + | 0.811494i | \(0.698655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.46410 | 0.329548 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 17.2480i | 0.757102i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.3205i | − | 0.934068i | −0.884239 | − | 0.467034i | \(-0.845322\pi\) | ||
0.884239 | − | 0.467034i | \(-0.154678\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −17.1962 | − | 17.1962i | −0.750502 | − | 0.750502i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4558 | −1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.79796 | + | 9.79796i | 0.425195 | + | 0.425195i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6077 | + | 13.6077i | −0.589415 | + | 0.589415i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.4548i | − | 0.668170i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.9282i | 0.816812i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 7.07107 | 0.303449 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | −0.464102 | + | 0.464102i | −0.0198074 | + | 0.0198074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 65.4056i | − | 2.78637i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.00000i | − | 0.255146i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.79315 | + | 1.79315i | −0.0761150 | + | 0.0761150i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8038 | − | 19.8038i | −0.839116 | − | 0.839116i | 0.149627 | − | 0.988743i | \(-0.452193\pi\) |
−0.988743 | + | 0.149627i | \(0.952193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6969 | 0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.07180 | −0.214131 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03528 | + | 1.03528i | 0.0436317 | + | 0.0436317i | 0.728586 | − | 0.684954i | \(-0.240178\pi\) |
−0.684954 | + | 0.728586i | \(0.740178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −49.1769 | + | 49.1769i | −2.06889 | + | 2.06889i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.44949i | − | 0.102869i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.46410i | 0.145223i | 0.997360 | + | 0.0726113i | \(0.0231333\pi\) | ||||
−0.997360 | + | 0.0726113i | \(0.976867\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −5.46410 | − | 5.46410i | −0.228266 | − | 0.228266i | ||||
\(574\) | 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 | ||||||||
\(579\) | −4.24264 | − | 4.24264i | −0.176318 | − | 0.176318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.46410 | + | 9.46410i | −0.392637 | + | 0.392637i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.76646i | − | 0.280238i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.3923i | 0.677738i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.3548 | − | 30.3548i | 1.25288 | − | 1.25288i | 0.298453 | − | 0.954424i | \(-0.403529\pi\) |
0.954424 | − | 0.298453i | \(-0.0964708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.7846 | − | 38.7846i | −1.59809 | − | 1.59809i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.76268 | 0.360449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.7128 | −1.54868 | −0.774340 | − | 0.632770i | \(-0.781918\pi\) | ||||
−0.774340 | + | 0.632770i | \(0.781918\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.1822 | + | 23.1822i | 0.950378 | + | 0.950378i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.1962 | − | 13.1962i | 0.540083 | − | 0.540083i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.96953i | − | 0.284767i | −0.989812 | − | 0.142384i | \(-0.954523\pi\) | ||
0.989812 | − | 0.142384i | \(-0.0454767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.7128i | − | 0.804102i | −0.915617 | − | 0.402051i | \(-0.868297\pi\) | ||
0.915617 | − | 0.402051i | \(-0.131703\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5558 | − | 10.5558i | 0.429867 | − | 0.429867i | ||||
\(604\) | 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 | ||||||||
\(609\) | −21.4641 | −0.869769 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | − | 17.5254i | − | 0.706691i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.8564i | − | 1.60456i | −0.596949 | − | 0.802279i | \(-0.703621\pi\) | ||
0.596949 | − | 0.802279i | \(-0.296379\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −2.00000 | − | 2.00000i | −0.0802572 | − | 0.0802572i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0716 | −0.483638 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9282 | −0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.72741 | − | 7.72741i | −0.308603 | − | 0.308603i | ||||
\(628\) | 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 | ||||||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | 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 | ||||||||
\(639\) | −6.41473 | −0.253763 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.6077 | −1.01144 | −0.505722 | − | 0.862697i | \(-0.668774\pi\) | ||||
−0.505722 | + | 0.862697i | \(0.668774\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −9.46410 | + | 9.46410i | −0.372649 | + | 0.372649i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9107i | 1.60836i | 0.594383 | + | 0.804182i | \(0.297396\pi\) | ||||
−0.594383 | + | 0.804182i | \(0.702604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.2872i | − | 0.796342i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7279 | + | 12.7279i | −0.498847 | + | 0.498847i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.6603 | − | 17.6603i | −0.691099 | − | 0.691099i | 0.271375 | − | 0.962474i | \(-0.412522\pi\) |
−0.962474 | + | 0.271375i | \(0.912522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.6781 | 2.25367 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9706 | − | 16.9706i | −0.661079 | − | 0.661079i | 0.294555 | − | 0.955634i | \(-0.404829\pi\) |
−0.955634 | + | 0.294555i | \(0.904829\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | − | 14.6969i | − | 0.570782i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 70.6410i | 2.73934i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5254 | + | 17.5254i | −0.678585 | + | 0.678585i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2679 | − | 10.2679i | −0.396982 | − | 0.396982i | ||||
\(670\) | 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 | ||||||||
\(675\) | −7.02030 | − | 7.02030i | −0.270211 | − | 0.270211i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.33975 | − | 2.33975i | 0.0899237 | − | 0.0899237i | −0.660714 | − | 0.750638i | \(-0.729746\pi\) |
0.750638 | + | 0.660714i | \(0.229746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.62536i | 0.100752i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3205i | 0.433803i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.8028 | + | 17.8028i | −0.681204 | + | 0.681204i | −0.960271 | − | 0.279068i | \(-0.909975\pi\) |
0.279068 | + | 0.960271i | \(0.409975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.3205 | + | 39.3205i | 1.50236 | + | 1.50236i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8690 | 0.643594 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −2.53590 | + | 2.53590i | −0.0963308 | + | 0.0963308i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.7685i | 1.01539i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128i | 0.595165i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.14162 | − | 9.14162i | 0.345768 | − | 0.345768i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.5885 | + | 10.5885i | 0.399921 | + | 0.399921i | 0.878205 | − | 0.478284i | \(-0.158741\pi\) |
−0.478284 | + | 0.878205i | \(0.658741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | 0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9282 | 0.411580 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | − | 2.44949i | − | 0.0918630i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846i | 0.778390i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9706 | − | 16.9706i | 0.634663 | − | 0.634663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.46410 | − | 5.46410i | −0.204061 | − | 0.204061i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.27362 | −0.0847919 | −0.0423959 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423959 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.85641 | 0.292588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.9396 | − | 18.9396i | −0.704371 | − | 0.704371i | ||||
\(724\) | 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 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 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 | ||||||||
\(735\) | −3.86370 | −0.142515 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 22.3923 | − | 22.3923i | 0.822602 | − | 0.822602i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.3233i | 1.00240i | 0.865333 | + | 0.501198i | \(0.167107\pi\) | ||||
−0.865333 | + | 0.501198i | \(0.832893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 20.7846i | − | 0.761489i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.86370 | + | 3.86370i | −0.141366 | + | 0.141366i | ||||
\(748\) | 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 | ||||||||
\(753\) | 6.53590 | 0.238181 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 4.14110i | 0.150313i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.2487i | 1.89401i | 0.321212 | + | 0.947007i | \(0.395910\pi\) | ||||
−0.321212 | + | 0.947007i | \(0.604090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44949 | + | 2.44949i | −0.0886775 | + | 0.0886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.46410 | + | 9.46410i | 0.342175 | + | 0.342175i | ||||
\(766\) | 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 | ||||||||
\(771\) | 16.1112 | + | 16.1112i | 0.580229 | + | 0.580229i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.5885 | − | 34.5885i | 1.24406 | − | 1.24406i | 0.285759 | − | 0.958302i | \(-0.407754\pi\) |
0.958302 | − | 0.285759i | \(-0.0922456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 72.9571i | 2.62070i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.60770i | − | 0.0576757i | ||||||
\(778\) | 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 | ||||||||
\(783\) | −8.76268 | −0.313153 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 16.0000 | − | 16.0000i | 0.569615 | − | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 44.0908i | − | 1.56769i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.78461i | 0.0988844i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.6264 | + | 12.6264i | −0.447812 | + | 0.447812i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.5167 | − | 15.5167i | −0.549628 | − | 0.549628i | 0.376705 | − | 0.926333i | \(-0.377057\pi\) |
−0.926333 | + | 0.376705i | \(0.877057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | −0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.92820 | −0.174129 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | − | 10.2784i | − | 0.361818i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.67949i | − | 0.234838i | −0.993082 | − | 0.117419i | \(-0.962538\pi\) | ||
0.993082 | − | 0.117419i | \(-0.0374621\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 2.26795 | + | 2.26795i | 0.0795405 | + | 0.0795405i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5254 | −0.613887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8564 | 0.904601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.34847 | − | 7.34847i | −0.256776 | − | 0.256776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.8038 | − | 17.8038i | 0.621359 | − | 0.621359i | −0.324520 | − | 0.945879i | \(-0.605203\pi\) |
0.945879 | + | 0.324520i | \(0.105203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.97382i | − | 0.347666i | −0.984775 | − | 0.173833i | \(-0.944385\pi\) | ||
0.984775 | − | 0.173833i | \(-0.0556152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.5359i | 0.506075i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.6675 | − | 31.6675i | 1.10119 | − | 1.10119i | 0.106919 | − | 0.994268i | \(-0.465901\pi\) |
0.994268 | − | 0.106919i | \(-0.0340986\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 12.5249 | 0.434482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1117 | − | 21.1117i | −0.730599 | − | 0.730599i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.19615 | + | 5.19615i | −0.179605 | + | 0.179605i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.0106i | − | 0.897987i | −0.893535 | − | 0.448994i | \(-0.851783\pi\) | ||
0.893535 | − | 0.448994i | \(-0.148217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.7846i | 1.64775i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.656339 | + | 0.656339i | −0.0226055 | + | 0.0226055i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.6603 | + | 13.6603i | 0.469927 | + | 0.469927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.6937 | −0.745404 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.85641 | −0.338271 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 28.8391i | 0.986276i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 43.1769i | − | 1.47490i | −0.675404 | − | 0.737448i | \(-0.736031\pi\) | ||
0.675404 | − | 0.737448i | \(-0.263969\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 7.85641 | + | 7.85641i | 0.267746 | + | 0.267746i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1213 | 1.26362 | 0.631812 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631812 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.6410 | −2.26586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.53553 | + | 3.53553i | 0.120073 | + | 0.120073i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.53590 | + | 2.53590i | −0.0860245 | + | 0.0860245i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.3350i | − | 2.14602i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.07180i | 0.0362748i | ||||||||
\(874\) | 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 | ||||||||
\(879\) | −10.8332 | −0.365396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.6410 | 1.23447 | 0.617234 | − | 0.786780i | \(-0.288253\pi\) | ||||
0.617234 | + | 0.786780i | \(0.288253\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | −37.8564 | + | 37.8564i | −1.27253 | + | 1.27253i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5665i | 1.22778i | 0.789391 | + | 0.613891i | \(0.210397\pi\) | ||||
−0.789391 | + | 0.613891i | \(0.789603\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 35.5692i | − | 1.19295i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.03528 | + | 1.03528i | −0.0346831 | + | 0.0346831i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.9282 | − | 14.9282i | −0.499553 | − | 0.499553i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −73.1330 | −2.44457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | − | 8.48528i | − | 0.282372i | ||||||
\(904\) | 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 | ||||||||
\(909\) | −10.1962 | − | 10.1962i | −0.338185 | − | 0.338185i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0726 | 0.731298 | 0.365649 | − | 0.930753i | \(-0.380847\pi\) | ||||
0.365649 | + | 0.930753i | \(0.380847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | 0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.79315 | − | 1.79315i | −0.0592797 | − | 0.0592797i | ||||
\(916\) | 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 | ||||||||
\(921\) | − | 22.9282i | − | 0.755510i | ||||||
\(922\) | 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 | ||||||||
\(927\) | 3.20736 | 0.105344 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.3205 | −1.48692 | −0.743459 | − | 0.668782i | \(-0.766816\pi\) | ||||
−0.743459 | + | 0.668782i | \(0.766816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.27792 | + | 5.27792i | 0.172977 | + | 0.172977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.9282 | + | 22.9282i | −0.750636 | + | 0.750636i | ||||
\(934\) | 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 | ||||||||
\(939\) | −2.72689 | + | 2.72689i | −0.0889887 | + | 0.0889887i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6603 | − | 25.6603i | −0.836500 | − | 0.836500i | 0.151896 | − | 0.988396i | \(-0.451462\pi\) |
−0.988396 | + | 0.151896i | \(0.951462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8295 | 0.417785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.46410 | 0.307867 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.5569 | + | 20.5569i | 0.668008 | + | 0.668008i | 0.957255 | − | 0.289246i | \(-0.0934047\pi\) |
−0.289246 | + | 0.957255i | \(0.593405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 12.0000i | −0.389536 | + | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.69213i | 0.217007i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46.3923i | − | 1.50279i | −0.659850 | − | 0.751397i | \(-0.729380\pi\) | ||
0.659850 | − | 0.751397i | \(-0.270620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1117 | − | 21.1117i | 0.683158 | − | 0.683158i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.07180 | + | 9.07180i | 0.293250 | + | 0.293250i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.2538 | −1.13840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.82843 | + | 2.82843i | 0.0911448 | + | 0.0911448i | ||||
\(964\) | 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 | ||||||||
\(969\) | − | 25.8564i | − | 0.830627i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7322 | + | 15.7322i | −0.504871 | + | 0.504871i | −0.912948 | − | 0.408077i | \(-0.866200\pi\) |
0.408077 | + | 0.912948i | \(0.366200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | − | 12.0000i | −0.384702 | − | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.1218 | −1.34898 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.1769 | 1.12541 | 0.562705 | − | 0.826658i | \(-0.309761\pi\) | ||||
0.562705 | + | 0.826658i | \(0.309761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.10205 | + | 5.10205i | 0.163062 | + | 0.163062i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | + | 1.00000i | −0.0319275 | + | 0.0319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.7370i | 0.757093i | 0.925582 | + | 0.378547i | \(0.123576\pi\) | ||||
−0.925582 | + | 0.378547i | \(0.876424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.8564i | 1.07875i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.89898 | + | 4.89898i | −0.155936 | + | 0.155936i | ||||
\(988\) | 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 | ||||||||
\(993\) | 1.07180 | 0.0340124 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | − | 0.656339i | − | 0.0207656i |
(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 | 768.2.j.f.577.2 | yes | 8 | |
3.2 | odd | 2 | 2304.2.k.e.577.2 | 8 | |||
4.3 | odd | 2 | inner | 768.2.j.f.577.4 | yes | 8 | |
8.3 | odd | 2 | 768.2.j.e.577.1 | yes | 8 | ||
8.5 | even | 2 | 768.2.j.e.577.3 | yes | 8 | ||
12.11 | even | 2 | 2304.2.k.e.577.1 | 8 | |||
16.3 | odd | 4 | 768.2.j.e.193.1 | ✓ | 8 | ||
16.5 | even | 4 | inner | 768.2.j.f.193.2 | yes | 8 | |
16.11 | odd | 4 | inner | 768.2.j.f.193.4 | yes | 8 | |
16.13 | even | 4 | 768.2.j.e.193.3 | yes | 8 | ||
24.5 | odd | 2 | 2304.2.k.l.577.4 | 8 | |||
24.11 | even | 2 | 2304.2.k.l.577.3 | 8 | |||
32.3 | odd | 8 | 3072.2.d.h.1537.8 | 8 | |||
32.5 | even | 8 | 3072.2.a.r.1.4 | 4 | |||
32.11 | odd | 8 | 3072.2.a.r.1.1 | 4 | |||
32.13 | even | 8 | 3072.2.d.h.1537.5 | 8 | |||
32.19 | odd | 8 | 3072.2.d.h.1537.1 | 8 | |||
32.21 | even | 8 | 3072.2.a.l.1.1 | 4 | |||
32.27 | odd | 8 | 3072.2.a.l.1.4 | 4 | |||
32.29 | even | 8 | 3072.2.d.h.1537.4 | 8 | |||
48.5 | odd | 4 | 2304.2.k.e.1729.1 | 8 | |||
48.11 | even | 4 | 2304.2.k.e.1729.2 | 8 | |||
48.29 | odd | 4 | 2304.2.k.l.1729.3 | 8 | |||
48.35 | even | 4 | 2304.2.k.l.1729.4 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bc.1.1 | 4 | |||
96.11 | even | 8 | 9216.2.a.bc.1.4 | 4 | |||
96.53 | odd | 8 | 9216.2.a.bi.1.4 | 4 | |||
96.59 | even | 8 | 9216.2.a.bi.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.1 | ✓ | 8 | 16.3 | odd | 4 | ||
768.2.j.e.193.3 | yes | 8 | 16.13 | even | 4 | ||
768.2.j.e.577.1 | yes | 8 | 8.3 | odd | 2 | ||
768.2.j.e.577.3 | yes | 8 | 8.5 | even | 2 | ||
768.2.j.f.193.2 | yes | 8 | 16.5 | even | 4 | inner | |
768.2.j.f.193.4 | yes | 8 | 16.11 | odd | 4 | inner | |
768.2.j.f.577.2 | yes | 8 | 1.1 | even | 1 | trivial | |
768.2.j.f.577.4 | yes | 8 | 4.3 | odd | 2 | inner | |
2304.2.k.e.577.1 | 8 | 12.11 | even | 2 | |||
2304.2.k.e.577.2 | 8 | 3.2 | odd | 2 | |||
2304.2.k.e.1729.1 | 8 | 48.5 | odd | 4 | |||
2304.2.k.e.1729.2 | 8 | 48.11 | even | 4 | |||
2304.2.k.l.577.3 | 8 | 24.11 | even | 2 | |||
2304.2.k.l.577.4 | 8 | 24.5 | odd | 2 | |||
2304.2.k.l.1729.3 | 8 | 48.29 | odd | 4 | |||
2304.2.k.l.1729.4 | 8 | 48.35 | even | 4 | |||
3072.2.a.l.1.1 | 4 | 32.21 | even | 8 | |||
3072.2.a.l.1.4 | 4 | 32.27 | odd | 8 | |||
3072.2.a.r.1.1 | 4 | 32.11 | odd | 8 | |||
3072.2.a.r.1.4 | 4 | 32.5 | even | 8 | |||
3072.2.d.h.1537.1 | 8 | 32.19 | odd | 8 | |||
3072.2.d.h.1537.4 | 8 | 32.29 | even | 8 | |||
3072.2.d.h.1537.5 | 8 | 32.13 | even | 8 | |||
3072.2.d.h.1537.8 | 8 | 32.3 | odd | 8 | |||
9216.2.a.bc.1.1 | 4 | 96.5 | odd | 8 | |||
9216.2.a.bc.1.4 | 4 | 96.11 | even | 8 | |||
9216.2.a.bi.1.1 | 4 | 96.59 | even | 8 | |||
9216.2.a.bi.1.4 | 4 | 96.53 | odd | 8 |