Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(81,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.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: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.81 |
Dual form | 136.2.k.b.89.1 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.00000i | −0.577350 | − | 0.577350i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 2.00000i | 0.894427 | + | 0.894427i | 0.994936 | − | 0.100509i | \(-0.0320471\pi\) |
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 2.00000i | 0.755929 | − | 0.755929i | −0.219650 | − | 0.975579i | \(-0.570491\pi\) |
0.975579 | + | 0.219650i | \(0.0704915\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.00000i | 0.301511 | − | 0.301511i | −0.540094 | − | 0.841605i | \(-0.681611\pi\) |
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.00000i | − | 1.03280i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | + | 1.00000i | −0.970143 | + | 0.242536i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | + | 4.00000i | −0.834058 | + | 0.834058i | −0.988069 | − | 0.154011i | \(-0.950781\pi\) |
0.154011 | + | 0.988069i | \(0.450781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | + | 6.00000i | 1.11417 | + | 1.11417i | 0.992580 | + | 0.121592i | \(0.0387999\pi\) |
0.121592 | + | 0.992580i | \(0.461200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | − | 6.00000i | −1.07763 | − | 1.07763i | −0.996721 | − | 0.0809104i | \(-0.974217\pi\) |
−0.0809104 | − | 0.996721i | \(-0.525783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.00000 | 1.35225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00000 | − | 8.00000i | −1.31519 | − | 1.31519i | −0.917534 | − | 0.397658i | \(-0.869823\pi\) |
−0.397658 | − | 0.917534i | \(-0.630177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | − | 2.00000i | −0.320256 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | − | 1.00000i | 0.156174 | − | 0.156174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) |
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | − | 2.00000i | 0.298142 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.00000 | + | 3.00000i | 0.700140 | + | 0.420084i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | − | 4.00000i | 0.529813 | − | 0.529813i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.0000i | 1.82264i | 0.411693 | + | 0.911322i | \(0.364937\pi\) | ||||
−0.411693 | + | 0.911322i | \(0.635063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 4.00000i | −0.512148 | + | 0.512148i | −0.915184 | − | 0.403036i | \(-0.867955\pi\) |
0.403036 | + | 0.915184i | \(0.367955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | − | 2.00000i | −0.251976 | − | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | + | 4.00000i | 0.496139 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.00000 | − | 9.00000i | −1.05337 | − | 1.05337i | −0.998493 | − | 0.0548772i | \(-0.982523\pi\) |
−0.0548772 | − | 0.998493i | \(-0.517477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | − | 3.00000i | 0.346410 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | − | 4.00000i | 0.450035 | − | 0.450035i | −0.445331 | − | 0.895366i | \(-0.646914\pi\) |
0.895366 | + | 0.445331i | \(0.146914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0000 | − | 6.00000i | −1.08465 | − | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.0000 | 1.69600 | 0.847998 | − | 0.529999i | \(-0.177808\pi\) | ||||
0.847998 | + | 0.529999i | \(0.177808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 4.00000i | 0.419314 | − | 0.419314i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.0000i | 1.24434i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | + | 8.00000i | −0.820783 | + | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | − | 1.00000i | −0.100504 | − | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.0000 | 1.97066 | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) | ||||
0.985329 | + | 0.170664i | \(0.0545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | − | 8.00000i | −0.780720 | − | 0.780720i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0000 | − | 13.0000i | −1.25676 | − | 1.25676i | −0.952632 | − | 0.304125i | \(-0.901636\pi\) |
−0.304125 | − | 0.952632i | \(-0.598364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | + | 6.00000i | −0.574696 | + | 0.574696i | −0.933437 | − | 0.358741i | \(-0.883206\pi\) |
0.358741 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.0000i | 1.51865i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.00000 | + | 5.00000i | −0.470360 | + | 0.470360i | −0.902031 | − | 0.431671i | \(-0.857924\pi\) |
0.431671 | + | 0.902031i | \(0.357924\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0000 | −1.49201 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | + | 10.0000i | −0.550019 | + | 0.916698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000i | 0.818182i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0000i | − | 1.41977i | −0.704317 | − | 0.709885i | \(-0.748747\pi\) | ||
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | − | 2.00000i | 0.176090 | − | 0.176090i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | + | 1.00000i | 0.0873704 | + | 0.0873704i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 8.00000i | 0.693688 | + | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.0000 | −1.37706 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0000 | −1.19610 | −0.598050 | − | 0.801459i | \(-0.704058\pi\) | ||||
−0.598050 | + | 0.801459i | \(0.704058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.00000 | + | 1.00000i | 0.0848189 | + | 0.0848189i | 0.748243 | − | 0.663424i | \(-0.230898\pi\) |
−0.663424 | + | 0.748243i | \(0.730898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | − | 2.00000i | 0.167248 | − | 0.167248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.0000i | 1.99309i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | + | 1.00000i | −0.0824786 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.00000 | + | 4.00000i | 0.0808452 | + | 0.323381i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 24.0000i | − | 1.92773i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 6.00000i | −0.475831 | + | 0.475831i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000i | 1.26098i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.00000 | + | 9.00000i | −0.704934 | + | 0.704934i | −0.965465 | − | 0.260531i | \(-0.916102\pi\) |
0.260531 | + | 0.965465i | \(0.416102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | − | 4.00000i | −0.311400 | − | 0.311400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | + | 2.00000i | 0.154765 | + | 0.154765i | 0.780242 | − | 0.625478i | \(-0.215096\pi\) |
−0.625478 | + | 0.780242i | \(0.715096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | − | 2.00000i | −0.152057 | − | 0.152057i | 0.626979 | − | 0.779036i | \(-0.284291\pi\) |
−0.779036 | + | 0.626979i | \(0.784291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | + | 6.00000i | 0.453557 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0000 | − | 14.0000i | 1.05230 | − | 1.05230i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00000 | − | 4.00000i | 0.297318 | − | 0.297318i | −0.542645 | − | 0.839962i | \(-0.682577\pi\) |
0.839962 | + | 0.542645i | \(0.182577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 32.0000i | − | 2.35269i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | + | 5.00000i | −0.219382 | + | 0.365636i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.0000i | 1.16383i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | − | 9.00000i | 0.647834 | − | 0.647834i | −0.304635 | − | 0.952469i | \(-0.598534\pi\) |
0.952469 | + | 0.304635i | \(0.0985345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 8.00000i | − | 0.572892i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | − | 4.00000i | 0.284988 | − | 0.284988i | −0.550106 | − | 0.835095i | \(-0.685413\pi\) |
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000 | + | 12.0000i | 0.850657 | + | 0.850657i | 0.990214 | − | 0.139557i | \(-0.0445677\pi\) |
−0.139557 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | − | 6.00000i | −0.423207 | − | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0000 | 1.68447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | + | 4.00000i | 0.278019 | + | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | + | 4.00000i | 0.276686 | + | 0.276686i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0000 | − | 15.0000i | 1.03264 | − | 1.03264i | 0.0331936 | − | 0.999449i | \(-0.489432\pi\) |
0.999449 | − | 0.0331936i | \(-0.0105678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | + | 4.00000i | −0.272798 | + | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | −1.62923 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.0000i | 1.21633i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | + | 2.00000i | −0.538138 | + | 0.134535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.00000 | − | 5.00000i | 0.331862 | − | 0.331862i | −0.521431 | − | 0.853293i | \(-0.674602\pi\) |
0.853293 | + | 0.521431i | \(0.174602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | + | 4.00000i | −0.263181 | + | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.00000 | + | 1.00000i | 0.0655122 | + | 0.0655122i | 0.739104 | − | 0.673592i | \(-0.235249\pi\) |
−0.673592 | + | 0.739104i | \(0.735249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.00000i | −0.0644157 | − | 0.0644157i | 0.674165 | − | 0.738581i | \(-0.264504\pi\) |
−0.738581 | + | 0.674165i | \(0.764504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | − | 2.00000i | 0.127775 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000i | 0.509028i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 6.00000i | 0.380235 | − | 0.380235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | + | 16.0000i | 0.250490 | + | 1.00196i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.0000i | 1.24757i | 0.781598 | + | 0.623783i | \(0.214405\pi\) | ||||
−0.781598 | + | 0.623783i | \(0.785595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.0000 | −1.98838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | − | 6.00000i | 0.371391 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.00000i | − | 0.493301i | −0.969104 | − | 0.246651i | \(-0.920670\pi\) | ||
0.969104 | − | 0.246651i | \(-0.0793300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | − | 12.0000i | 0.737154 | − | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.0000 | − | 16.0000i | −0.979184 | − | 0.979184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | − | 2.00000i | −0.121942 | − | 0.121942i | 0.643502 | − | 0.765444i | \(-0.277481\pi\) |
−0.765444 | + | 0.643502i | \(0.777481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0000 | 1.70088 | 0.850439 | − | 0.526073i | \(-0.176336\pi\) | ||||
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | −0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 3.00000i | 0.180907 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.00000 | − | 6.00000i | −0.360505 | − | 0.360505i | 0.503494 | − | 0.863999i | \(-0.332048\pi\) |
−0.863999 | + | 0.503494i | \(0.832048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | + | 6.00000i | −0.359211 | + | 0.359211i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0000i | − | 1.31241i | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||
0.754583 | − | 0.656205i | \(-0.227839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | − | 5.00000i | 0.297219 | − | 0.297219i | −0.542705 | − | 0.839924i | \(-0.682600\pi\) |
0.839924 | + | 0.542705i | \(0.182600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.0000 | 0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.00000i | − | 0.236113i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | − | 8.00000i | 0.882353 | − | 0.470588i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.00000i | − | 0.351726i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.0000 | −1.28525 | −0.642627 | − | 0.766179i | \(-0.722155\pi\) | ||||
−0.642627 | + | 0.766179i | \(0.722155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.0000 | + | 28.0000i | −1.63022 | + | 1.63022i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000i | 0.464207i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | + | 8.00000i | −0.462652 | + | 0.462652i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 4.00000i | 0.230556 | + | 0.230556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000 | + | 6.00000i | 0.344691 | + | 0.344691i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.0000 | −0.916157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.0000 | − | 20.0000i | −1.13776 | − | 1.13776i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | − | 6.00000i | −0.340229 | − | 0.340229i | 0.516225 | − | 0.856453i | \(-0.327337\pi\) |
−0.856453 | + | 0.516225i | \(0.827337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.0000 | + | 21.0000i | −1.18699 | + | 1.18699i | −0.209095 | + | 0.977895i | \(0.567052\pi\) |
−0.977895 | + | 0.209095i | \(0.932948\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 8.00000i | − | 0.450749i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.0000i | 1.45118i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | − | 16.0000i | −0.222566 | − | 0.890264i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000i | 0.332820i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000 | 0.663602 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0000i | 1.20923i | 0.796518 | + | 0.604615i | \(0.206673\pi\) | ||||
−0.796518 | + | 0.604615i | \(0.793327\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | + | 8.00000i | −0.438397 | + | 0.438397i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | + | 12.0000i | 0.655630 | + | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | − | 5.00000i | −0.272367 | − | 0.272367i | 0.557685 | − | 0.830053i | \(-0.311690\pi\) |
−0.830053 | + | 0.557685i | \(0.811690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0000 | + | 16.0000i | 0.861411 | + | 0.861411i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.00000 | + | 3.00000i | −0.161048 | + | 0.161048i | −0.783031 | − | 0.621983i | \(-0.786327\pi\) |
0.621983 | + | 0.783031i | \(0.286327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000i | 0.107058i | 0.998566 | + | 0.0535288i | \(0.0170469\pi\) | ||||
−0.998566 | + | 0.0535288i | \(0.982953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | + | 8.00000i | −0.427008 | + | 0.427008i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000 | 0.212899 | 0.106449 | − | 0.994318i | \(-0.466052\pi\) | ||||
0.106449 | + | 0.994318i | \(0.466052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0000 | − | 4.00000i | 0.846810 | − | 0.211702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.0000i | − | 0.844448i | −0.906492 | − | 0.422224i | \(-0.861250\pi\) | ||
0.906492 | − | 0.422224i | \(-0.138750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000 | − | 9.00000i | 0.472377 | − | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 36.0000i | − | 1.88433i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | − | 16.0000i | 0.835193 | − | 0.835193i | −0.153029 | − | 0.988222i | \(-0.548903\pi\) |
0.988222 | + | 0.153029i | \(0.0489027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | − | 1.00000i | −0.0520579 | − | 0.0520579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 12.0000i | −0.623009 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.00000 | −0.413118 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | + | 12.0000i | 0.618031 | + | 0.618031i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | − | 5.00000i | −0.256833 | − | 0.256833i | 0.566932 | − | 0.823765i | \(-0.308130\pi\) |
−0.823765 | + | 0.566932i | \(0.808130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0000 | + | 16.0000i | −0.819705 | + | 0.819705i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 36.0000i | − | 1.83951i | −0.392488 | − | 0.919757i | \(-0.628386\pi\) | ||
0.392488 | − | 0.919757i | \(-0.371614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | − | 8.00000i | 0.407718 | − | 0.407718i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000i | 0.709828i | 0.934899 | + | 0.354914i | \(0.115490\pi\) | ||||
−0.934899 | + | 0.354914i | \(0.884510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | − | 20.0000i | 0.606866 | − | 1.01144i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.00000i | − | 0.100887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0000 | − | 12.0000i | 0.602263 | − | 0.602263i | −0.338650 | − | 0.940913i | \(-0.609970\pi\) |
0.940913 | + | 0.338650i | \(0.109970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 16.0000i | − | 0.801002i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0000 | − | 19.0000i | 0.948815 | − | 0.948815i | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) |
0.998752 | + | 0.0499376i | \(0.0159023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 12.0000i | −0.597763 | − | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0000 | + | 10.0000i | 0.496904 | + | 0.496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.0000 | −0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0000 | 1.58230 | 0.791149 | − | 0.611623i | \(-0.209483\pi\) | ||||
0.791149 | + | 0.611623i | \(0.209483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.0000 | + | 14.0000i | 0.690569 | + | 0.690569i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.0000 | + | 28.0000i | 1.37779 | + | 1.37779i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 12.0000i | −0.589057 | + | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.00000i | − | 0.0979404i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0000 | + | 15.0000i | −0.732798 | + | 0.732798i | −0.971173 | − | 0.238375i | \(-0.923385\pi\) |
0.238375 | + | 0.971173i | \(0.423385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 12.0000i | −0.145521 | − | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0000i | 0.774294i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | + | 12.0000i | −0.578020 | + | 0.578020i | −0.934357 | − | 0.356338i | \(-0.884025\pi\) |
0.356338 | + | 0.934357i | \(0.384025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0000 | − | 24.0000i | 1.15071 | − | 1.15071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | − | 16.0000i | −0.765384 | − | 0.765384i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 12.0000i | −0.572729 | − | 0.572729i | 0.360161 | − | 0.932890i | \(-0.382722\pi\) |
−0.932890 | + | 0.360161i | \(0.882722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0000 | 0.855206 | 0.427603 | − | 0.903967i | \(-0.359358\pi\) | ||||
0.427603 | + | 0.903967i | \(0.359358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.0000 | + | 32.0000i | 1.51695 | + | 1.51695i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.0000 | − | 10.0000i | −0.472984 | − | 0.472984i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.0000 | + | 13.0000i | −0.613508 | + | 0.613508i | −0.943858 | − | 0.330350i | \(-0.892833\pi\) |
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.00000i | − | 0.0941763i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0000 | + | 12.0000i | −0.563809 | + | 0.563809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0000 | 0.750092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000i | 0.467780i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) | ||||
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.0000 | − | 20.0000i | 0.560112 | − | 0.933520i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.00000i | − | 0.0931493i | −0.998915 | − | 0.0465746i | \(-0.985169\pi\) | ||
0.998915 | − | 0.0465746i | \(-0.0148305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.0000 | + | 24.0000i | −1.11297 | + | 1.11297i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0000i | 1.29569i | 0.761774 | + | 0.647843i | \(0.224329\pi\) | ||||
−0.761774 | + | 0.647843i | \(0.775671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | − | 12.0000i | 0.554109 | − | 0.554109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | − | 10.0000i | −0.460776 | − | 0.460776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | + | 2.00000i | 0.0919601 | + | 0.0919601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | −0.550598 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.00000 | − | 4.00000i | −0.182765 | − | 0.182765i | 0.609795 | − | 0.792559i | \(-0.291252\pi\) |
−0.792559 | + | 0.609795i | \(0.791252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | − | 16.0000i | −0.729537 | − | 0.729537i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.0000 | − | 16.0000i | 0.728025 | − | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000i | 0.544892i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | − | 8.00000i | 0.362515 | − | 0.362515i | −0.502223 | − | 0.864738i | \(-0.667484\pi\) |
0.864738 | + | 0.502223i | \(0.167484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0000 | 0.813988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000i | 0.541552i | 0.962642 | + | 0.270776i | \(0.0872803\pi\) | ||||
−0.962642 | + | 0.270776i | \(0.912720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.0000 | − | 18.0000i | −1.35113 | − | 0.810679i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.00000i | − | 0.179787i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0000 | + | 27.0000i | −1.20869 | + | 1.20869i | −0.237233 | + | 0.971453i | \(0.576241\pi\) |
−0.971453 | + | 0.237233i | \(0.923759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 4.00000i | − | 0.178707i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.00000 | + | 4.00000i | −0.178351 | + | 0.178351i | −0.790637 | − | 0.612286i | \(-0.790250\pi\) |
0.612286 | + | 0.790637i | \(0.290250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | − | 12.0000i | −0.533993 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | + | 9.00000i | 0.399704 | + | 0.399704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.0000 | −1.59255 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.0000 | − | 16.0000i | −0.706417 | − | 0.706417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.0000 | + | 40.0000i | 1.76261 | + | 1.76261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.00000i | 0.175581i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0000 | + | 13.0000i | −0.569540 | + | 0.569540i | −0.932000 | − | 0.362459i | \(-0.881937\pi\) |
0.362459 | + | 0.932000i | \(0.381937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.0000 | −1.31181 | −0.655904 | − | 0.754844i | \(-0.727712\pi\) | ||||
−0.655904 | + | 0.754844i | \(0.727712\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 12.0000i | − | 0.523723i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0000 | + | 18.0000i | 1.30682 | + | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.00000i | − | 0.391304i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0000 | 0.607548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | − | 2.00000i | 0.0866296 | − | 0.0866296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 52.0000i | − | 2.24816i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | + | 12.0000i | −0.517838 | + | 0.517838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | − | 1.00000i | −0.0430730 | − | 0.0430730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0000 | + | 16.0000i | 0.687894 | + | 0.687894i | 0.961766 | − | 0.273872i | \(-0.0883046\pi\) |
−0.273872 | + | 0.961766i | \(0.588305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.00000 | −0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.0000 | + | 25.0000i | 1.06892 | + | 1.06892i | 0.997442 | + | 0.0714808i | \(0.0227725\pi\) |
0.0714808 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | + | 4.00000i | 0.170716 | + | 0.170716i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0000 | + | 24.0000i | −1.02243 | + | 1.02243i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.0000i | − | 0.680389i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.0000 | + | 32.0000i | −1.35832 | + | 1.35832i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.0000 | −0.932170 | −0.466085 | − | 0.884740i | \(-0.654336\pi\) | ||||
−0.466085 | + | 0.884740i | \(0.654336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000i | 0.169182i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | − | 2.00000i | 0.337760 | − | 0.0844401i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000i | 0.758610i | 0.925272 | + | 0.379305i | \(0.123837\pi\) | ||||
−0.925272 | + | 0.379305i | \(0.876163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.0000 | − | 10.0000i | 0.419961 | − | 0.419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 36.0000i | − | 1.50920i | −0.656186 | − | 0.754599i | \(-0.727831\pi\) | ||
0.656186 | − | 0.754599i | \(-0.272169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0000 | − | 33.0000i | 1.38101 | − | 1.38101i | 0.538172 | − | 0.842835i | \(-0.319115\pi\) |
0.842835 | − | 0.538172i | \(-0.180885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00000 | − | 4.00000i | −0.167102 | − | 0.167102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | − | 12.0000i | −0.500435 | − | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.0000 | −0.748054 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | + | 12.0000i | 0.497844 | + | 0.497844i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 6.00000i | −0.248495 | − | 0.248495i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000 | − | 4.00000i | 0.165380 | − | 0.165380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | − | 24.0000i | 0.988903 | − | 0.988903i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.00000 | −0.329076 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0000i | 0.985562i | 0.870153 | + | 0.492781i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492781i | \(0.835980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.0000 | + | 8.00000i | −1.31187 | + | 0.327968i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 24.0000i | − | 0.982255i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | + | 9.00000i | −0.367118 | + | 0.367118i | −0.866425 | − | 0.499307i | \(-0.833588\pi\) |
0.499307 | + | 0.866425i | \(0.333588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.00000i | − | 0.244339i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.0000 | + | 18.0000i | −0.731804 | + | 0.731804i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0000 | + | 26.0000i | 1.05531 | + | 1.05531i | 0.998378 | + | 0.0569292i | \(0.0181309\pi\) |
0.0569292 | + | 0.998378i | \(0.481869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | − | 24.0000i | −0.972529 | − | 0.972529i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0000 | −0.888572 | −0.444286 | − | 0.895885i | \(-0.646543\pi\) | ||||
−0.444286 | + | 0.895885i | \(0.646543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00000 | − | 4.00000i | −0.161296 | − | 0.161296i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | + | 15.0000i | 0.603877 | + | 0.603877i | 0.941339 | − | 0.337462i | \(-0.109568\pi\) |
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.00000 | + | 5.00000i | −0.200967 | + | 0.200967i | −0.800414 | − | 0.599447i | \(-0.795387\pi\) |
0.599447 | + | 0.800414i | \(0.295387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 32.0000i | − | 1.28412i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.0000 | − | 32.0000i | 1.28205 | − | 1.28205i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 8.00000i | − | 0.319489i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.0000 | + | 24.0000i | 1.59490 | + | 0.956943i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000i | 1.27390i | 0.770905 | + | 0.636950i | \(0.219804\pi\) | ||||
−0.770905 | + | 0.636950i | \(0.780196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.0000 | −1.19239 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.0000 | − | 32.0000i | 1.26988 | − | 1.26988i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.00000i | − | 0.0792429i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0000 | − | 11.0000i | −0.434474 | − | 0.434474i | 0.455673 | − | 0.890147i | \(-0.349399\pi\) |
−0.890147 | + | 0.455673i | \(0.849399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0000 | + | 21.0000i | 0.828159 | + | 0.828159i | 0.987262 | − | 0.159103i | \(-0.0508601\pi\) |
−0.159103 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.00000 | −0.157256 | −0.0786281 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786281 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.0000 | + | 14.0000i | 0.549548 | + | 0.549548i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0000 | + | 24.0000i | 0.940634 | + | 0.940634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.0000 | − | 14.0000i | 0.547862 | − | 0.547862i | −0.377960 | − | 0.925822i | \(-0.623374\pi\) |
0.925822 | + | 0.377960i | \(0.123374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000i | 0.156293i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.00000 | + | 9.00000i | −0.351123 | + | 0.351123i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 26.0000i | − | 1.01128i | −0.862744 | − | 0.505641i | \(-0.831256\pi\) | ||
0.862744 | − | 0.505641i | \(-0.168744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.0000 | + | 6.00000i | 0.388368 | + | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.0000i | 1.24091i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.0000 | −1.85857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 4.00000i | 0.154649 | − | 0.154649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.00000i | 0.308837i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.00000 | − | 9.00000i | 0.346925 | − | 0.346925i | −0.512038 | − | 0.858963i | \(-0.671109\pi\) |
0.858963 | + | 0.512038i | \(0.171109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0000 | − | 12.0000i | −0.461880 | − | 0.461880i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0000 | + | 16.0000i | 0.614930 | + | 0.614930i | 0.944227 | − | 0.329297i | \(-0.106812\pi\) |
−0.329297 | + | 0.944227i | \(0.606812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | −0.383201 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0000 | − | 11.0000i | −0.420903 | − | 0.420903i | 0.464611 | − | 0.885515i | \(-0.346194\pi\) |
−0.885515 | + | 0.464611i | \(0.846194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.0000 | − | 28.0000i | −1.06983 | − | 1.06983i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.00000 | + | 6.00000i | −0.228914 | + | 0.228914i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.0000i | − | 0.457164i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | − | 9.00000i | 0.342376 | − | 0.342376i | −0.514884 | − | 0.857260i | \(-0.672165\pi\) |
0.857260 | + | 0.514884i | \(0.172165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000i | 0.151729i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00000 | + | 5.00000i | −0.113633 | + | 0.189389i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 2.00000i | − | 0.0756469i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.0000 | − | 32.0000i | 1.20690 | − | 1.20690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.0000 | + | 12.0000i | −0.451306 | + | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0000 | + | 18.0000i | 0.676004 | + | 0.676004i | 0.959094 | − | 0.283089i | \(-0.0913593\pi\) |
−0.283089 | + | 0.959094i | \(0.591359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 4.00000i | −0.150012 | − | 0.150012i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0000 | 1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | + | 12.0000i | 0.448148 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0000 | − | 28.0000i | −1.04422 | − | 1.04422i | −0.998976 | − | 0.0452480i | \(-0.985592\pi\) |
−0.0452480 | − | 0.998976i | \(-0.514408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.0000 | − | 40.0000i | 1.48968 | − | 1.48968i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000i | 0.0743808i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 18.0000i | −0.668503 | + | 0.668503i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.00000 | − | 8.00000i | −0.0739727 | − | 0.295891i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.0000i | − | 0.664845i | −0.943131 | − | 0.332423i | \(-0.892134\pi\) | ||
0.943131 | − | 0.332423i | \(-0.107866\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.00000 | −0.147542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | − | 6.00000i | 0.221013 | − | 0.221013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.00000i | − | 0.147142i | −0.997290 | − | 0.0735712i | \(-0.976560\pi\) | ||
0.997290 | − | 0.0735712i | \(-0.0234396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.00000 | − | 8.00000i | 0.293887 | − | 0.293887i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0000 | − | 10.0000i | −0.366864 | − | 0.366864i | 0.499468 | − | 0.866332i | \(-0.333529\pi\) |
−0.866332 | + | 0.499468i | \(0.833529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0000 | + | 20.0000i | 0.732743 | + | 0.732743i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.0000 | −1.90004 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0000 | − | 36.0000i | −1.31366 | − | 1.31366i | −0.918698 | − | 0.394961i | \(-0.870758\pi\) |
−0.394961 | − | 0.918698i | \(-0.629242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.0000 | + | 10.0000i | 0.364420 | + | 0.364420i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | − | 24.0000i | 0.873449 | − | 0.873449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.0000i | 1.67190i | 0.548807 | + | 0.835949i | \(0.315082\pi\) | ||||
−0.548807 | + | 0.835949i | \(0.684918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | − | 8.00000i | 0.290382 | − | 0.290382i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0000i | 0.868858i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | + | 10.0000i | −0.216930 | + | 0.361551i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.0000i | 1.01102i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | − | 20.0000i | 0.720282 | − | 0.720282i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0000 | − | 18.0000i | 0.646579 | − | 0.646579i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.0000 | + | 32.0000i | 1.14799 | + | 1.14799i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00000 | + | 4.00000i | 0.143315 | + | 0.143315i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.0000 | −1.71538 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | + | 20.0000i | 0.713831 | + | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | + | 15.0000i | 0.534692 | + | 0.534692i | 0.921965 | − | 0.387273i | \(-0.126583\pi\) |
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.00000 | + | 8.00000i | −0.284808 | + | 0.284808i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0000i | 0.711118i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | + | 8.00000i | −0.284088 | + | 0.284088i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.0000 | −0.851192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.0000i | 1.06265i | 0.847167 | + | 0.531327i | \(0.178307\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 16.0000i | − | 0.565332i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0000 | −0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.0000 | + | 32.0000i | −1.12785 | + | 1.12785i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.00000i | 0.140807i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.0000 | + | 13.0000i | −0.457056 | + | 0.457056i | −0.897688 | − | 0.440632i | \(-0.854754\pi\) |
0.440632 | + | 0.897688i | \(0.354754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0000 | − | 27.0000i | −0.948098 | − | 0.948098i | 0.0506198 | − | 0.998718i | \(-0.483880\pi\) |
−0.998718 | + | 0.0506198i | \(0.983880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.0000 | − | 28.0000i | −0.982003 | − | 0.982003i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.0000 | −1.26102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | − | 4.00000i | −0.139771 | − | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.00000 | − | 4.00000i | −0.139601 | − | 0.139601i | 0.633853 | − | 0.773454i | \(-0.281473\pi\) |
−0.773454 | + | 0.633853i | \(0.781473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | + | 20.0000i | −0.697156 | + | 0.697156i | −0.963796 | − | 0.266640i | \(-0.914087\pi\) |
0.266640 | + | 0.963796i | \(0.414087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.00000i | − | 0.208893i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.00000 | + | 5.00000i | −0.173867 | + | 0.173867i | −0.788676 | − | 0.614809i | \(-0.789233\pi\) |
0.614809 | + | 0.788676i | \(0.289233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.0000 | −1.45872 | −0.729360 | − | 0.684130i | \(-0.760182\pi\) | ||||
−0.729360 | + | 0.684130i | \(0.760182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000i | 0.416275i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | + | 4.00000i | 0.0346479 | + | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000i | 0.276851i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.0000 | 1.65912 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.00000 | + | 2.00000i | −0.0690477 | + | 0.0690477i | −0.740787 | − | 0.671740i | \(-0.765547\pi\) |
0.671740 | + | 0.740787i | \(0.265547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000i | 1.48276i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.0000 | + | 22.0000i | −0.757720 | + | 0.757720i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.0000 | − | 18.0000i | −0.619219 | − | 0.619219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0000 | + | 18.0000i | 0.618487 | + | 0.618487i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.0000 | −0.343199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.0000 | 2.19389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | − | 10.0000i | −0.342393 | − | 0.342393i | 0.514873 | − | 0.857266i | \(-0.327839\pi\) |
−0.857266 | + | 0.514873i | \(0.827839\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | + | 8.00000i | 0.273594 | + | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.0000 | + | 27.0000i | −0.922302 | + | 0.922302i | −0.997192 | − | 0.0748894i | \(-0.976140\pi\) |
0.0748894 | + | 0.997192i | \(0.476140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 18.0000i | − | 0.614152i | −0.951685 | − | 0.307076i | \(-0.900649\pi\) | ||
0.951685 | − | 0.307076i | \(-0.0993506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | + | 4.00000i | −0.136320 | + | 0.136320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0000 | 1.08929 | 0.544646 | − | 0.838666i | \(-0.316664\pi\) | ||||
0.544646 | + | 0.838666i | \(0.316664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 8.00000i | − | 0.272008i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.0000 | − | 7.00000i | −0.781121 | − | 0.237732i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.00000i | − | 0.271381i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | − | 3.00000i | 0.101535 | − | 0.101535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 16.0000i | − | 0.540899i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0000 | − | 22.0000i | 0.742887 | − | 0.742887i | −0.230245 | − | 0.973133i | \(-0.573953\pi\) |
0.973133 | + | 0.230245i | \(0.0739529\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.0000 | + | 22.0000i | 0.742042 | + | 0.742042i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0000 | − | 23.0000i | −0.774890 | − | 0.774890i | 0.204067 | − | 0.978957i | \(-0.434584\pi\) |
−0.978957 | + | 0.204067i | \(0.934584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.0000 | −1.54802 | −0.774012 | − | 0.633171i | \(-0.781753\pi\) | ||||
−0.774012 | + | 0.633171i | \(0.781753\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.0000 | 1.88242 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0000 | − | 16.0000i | −0.537227 | − | 0.537227i | 0.385486 | − | 0.922714i | \(-0.374034\pi\) |
−0.922714 | + | 0.385486i | \(0.874034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | − | 32.0000i | −1.07325 | − | 1.07325i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | − | 5.00000i | 0.167506 | − | 0.167506i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | − | 24.0000i | 0.802232 | − | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | 0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 72.0000i | − | 2.40133i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | + | 24.0000i | 0.199889 | + | 0.799556i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 8.00000i | − | 0.266223i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.0000 | 0.531858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.00000 | + | 7.00000i | −0.232431 | + | 0.232431i | −0.813707 | − | 0.581276i | \(-0.802554\pi\) |
0.581276 | + | 0.813707i | \(0.302554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000i | 0.199007i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.0000 | + | 34.0000i | −1.12647 | + | 1.12647i | −0.135724 | + | 0.990747i | \(0.543336\pi\) |
−0.990747 | + | 0.135724i | \(0.956664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | + | 6.00000i | 0.198571 | + | 0.198571i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.0000 | + | 16.0000i | 0.528944 | + | 0.528944i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | + | 12.0000i | 0.395413 | + | 0.395413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0000 | − | 24.0000i | 0.789115 | − | 0.789115i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 20.0000i | − | 0.656886i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0000 | − | 13.0000i | 0.426516 | − | 0.426516i | −0.460924 | − | 0.887440i | \(-0.652482\pi\) |
0.887440 | + | 0.460924i | \(0.152482\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000i | 0.392862i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.0000 | + | 4.00000i | −0.523256 | + | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.0000i | − | 1.24141i | −0.784046 | − | 0.620703i | \(-0.786847\pi\) | ||
0.784046 | − | 0.620703i | \(-0.213153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0000 | 1.37062 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 12.0000i | −0.391189 | + | 0.391189i | −0.875111 | − | 0.483922i | \(-0.839212\pi\) |
0.483922 | + | 0.875111i | \(0.339212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000i | 0.260516i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.0000 | + | 32.0000i | −1.04096 | + | 1.04096i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.0000 | − | 33.0000i | −1.07236 | − | 1.07236i | −0.997169 | − | 0.0751864i | \(-0.976045\pi\) |
−0.0751864 | − | 0.997169i | \(-0.523955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | − | 18.0000i | −0.584305 | − | 0.584305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0000 | 1.94359 | 0.971795 | − | 0.235826i | \(-0.0757795\pi\) | ||||
0.971795 | + | 0.235826i | \(0.0757795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | + | 8.00000i | 0.258874 | + | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0000 | − | 12.0000i | −0.387905 | − | 0.387905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.0000 | + | 28.0000i | −0.904167 | + | 0.904167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000i | 1.32258i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.0000 | + | 13.0000i | −0.418919 | + | 0.418919i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.0000 | 1.15888 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | + | 20.0000i | −0.385496 | + | 0.642493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000i | 0.192549i | 0.995355 | + | 0.0962746i | \(0.0306927\pi\) | ||||
−0.995355 | + | 0.0962746i | \(0.969307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | 0.128234 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.00000 | − | 6.00000i | 0.192154 | − | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 28.0000i | − | 0.895799i | −0.894084 | − | 0.447900i | \(-0.852172\pi\) | ||
0.894084 | − | 0.447900i | \(-0.147828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0000 | − | 16.0000i | 0.511362 | − | 0.511362i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | + | 6.00000i | 0.191565 | + | 0.191565i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.0000 | + | 28.0000i | 0.893061 | + | 0.893061i | 0.994810 | − | 0.101749i | \(-0.0324438\pi\) |
−0.101749 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | − | 8.00000i | −0.254385 | − | 0.254385i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | − | 24.0000i | −0.762385 | − | 0.762385i | 0.214368 | − | 0.976753i | \(-0.431231\pi\) |
−0.976753 | + | 0.214368i | \(0.931231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.0000 | − | 22.0000i | 0.698149 | − | 0.698149i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000i | 1.52170i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.0000 | + | 28.0000i | −0.886769 | + | 0.886769i | −0.994211 | − | 0.107442i | \(-0.965734\pi\) |
0.107442 | + | 0.994211i | \(0.465734\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64.0000 | 2.02487 |
(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 | 136.2.k.b.81.1 | ✓ | 2 | |
3.2 | odd | 2 | 1224.2.w.a.217.1 | 2 | |||
4.3 | odd | 2 | 272.2.o.e.81.1 | 2 | |||
8.3 | odd | 2 | 1088.2.o.c.897.1 | 2 | |||
8.5 | even | 2 | 1088.2.o.m.897.1 | 2 | |||
12.11 | even | 2 | 2448.2.be.a.1441.1 | 2 | |||
17.2 | even | 8 | 2312.2.a.j.1.1 | 2 | |||
17.4 | even | 4 | inner | 136.2.k.b.89.1 | yes | 2 | |
17.8 | even | 8 | 2312.2.b.d.577.2 | 2 | |||
17.9 | even | 8 | 2312.2.b.d.577.1 | 2 | |||
17.15 | even | 8 | 2312.2.a.j.1.2 | 2 | |||
51.38 | odd | 4 | 1224.2.w.a.361.1 | 2 | |||
68.15 | odd | 8 | 4624.2.a.o.1.1 | 2 | |||
68.19 | odd | 8 | 4624.2.a.o.1.2 | 2 | |||
68.55 | odd | 4 | 272.2.o.e.225.1 | 2 | |||
136.21 | even | 4 | 1088.2.o.m.769.1 | 2 | |||
136.123 | odd | 4 | 1088.2.o.c.769.1 | 2 | |||
204.191 | even | 4 | 2448.2.be.a.1585.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.k.b.81.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
136.2.k.b.89.1 | yes | 2 | 17.4 | even | 4 | inner | |
272.2.o.e.81.1 | 2 | 4.3 | odd | 2 | |||
272.2.o.e.225.1 | 2 | 68.55 | odd | 4 | |||
1088.2.o.c.769.1 | 2 | 136.123 | odd | 4 | |||
1088.2.o.c.897.1 | 2 | 8.3 | odd | 2 | |||
1088.2.o.m.769.1 | 2 | 136.21 | even | 4 | |||
1088.2.o.m.897.1 | 2 | 8.5 | even | 2 | |||
1224.2.w.a.217.1 | 2 | 3.2 | odd | 2 | |||
1224.2.w.a.361.1 | 2 | 51.38 | odd | 4 | |||
2312.2.a.j.1.1 | 2 | 17.2 | even | 8 | |||
2312.2.a.j.1.2 | 2 | 17.15 | even | 8 | |||
2312.2.b.d.577.1 | 2 | 17.9 | even | 8 | |||
2312.2.b.d.577.2 | 2 | 17.8 | even | 8 | |||
2448.2.be.a.1441.1 | 2 | 12.11 | even | 2 | |||
2448.2.be.a.1585.1 | 2 | 204.191 | even | 4 | |||
4624.2.a.o.1.1 | 2 | 68.15 | odd | 8 | |||
4624.2.a.o.1.2 | 2 | 68.19 | odd | 8 |