Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1053,2,Mod(352,1053)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1053, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1053.352");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1053 = 3^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1053.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.40824733284\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 352.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1053.352 |
Dual form | 1053.2.e.i.703.2 |
$q$-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 \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(730\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 1.50000i | 0.612372 | + | 1.06066i | 0.990839 | + | 0.135045i | \(0.0431180\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | − | 3.00000i | −0.522233 | − | 0.904534i | −0.999665 | − | 0.0258656i | \(-0.991766\pi\) |
0.477432 | − | 0.878668i | \(-0.341568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | ||||
\(14\) | 1.73205 | − | 3.00000i | 0.462910 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | 6.92820 | 1.68034 | 0.840168 | − | 0.542326i | \(-0.182456\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | − | 5.19615i | 0.639602 | − | 1.10782i | ||||
\(23\) | 3.46410 | − | 6.00000i | 0.722315 | − | 1.25109i | −0.237754 | − | 0.971325i | \(-0.576411\pi\) |
0.960070 | − | 0.279761i | \(-0.0902553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | 3.46410 | + | 6.00000i | 0.643268 | + | 1.11417i | 0.984699 | + | 0.174265i | \(0.0557550\pi\) |
−0.341431 | + | 0.939907i | \(0.610912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | −2.59808 | + | 4.50000i | −0.459279 | + | 0.795495i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | + | 10.3923i | 1.02899 | + | 1.78227i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 1.73205 | + | 3.00000i | 0.280976 | + | 0.486664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | − | 6.00000i | 0.541002 | − | 0.937043i | −0.457845 | − | 0.889032i | \(-0.651379\pi\) |
0.998847 | − | 0.0480106i | \(-0.0152881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | −5.19615 | − | 9.00000i | −0.757937 | − | 1.31278i | −0.943901 | − | 0.330228i | \(-0.892874\pi\) |
0.185964 | − | 0.982556i | \(-0.440459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −4.33013 | + | 7.50000i | −0.612372 | + | 1.06066i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | − | 0.866025i | −0.0693375 | − | 0.120096i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73205 | − | 3.00000i | −0.231455 | − | 0.400892i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | + | 10.3923i | −0.787839 | + | 1.36458i | ||||
\(59\) | 1.73205 | − | 3.00000i | 0.225494 | − | 0.390567i | −0.730974 | − | 0.682406i | \(-0.760934\pi\) |
0.956467 | + | 0.291839i | \(0.0942671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | −3.46410 | −0.439941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | + | 12.1244i | −0.855186 | + | 1.48123i | 0.0212861 | + | 0.999773i | \(0.493224\pi\) |
−0.876472 | + | 0.481452i | \(0.840109\pi\) | |||||||
\(68\) | −3.46410 | + | 6.00000i | −0.420084 | + | 0.727607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.46410 | −0.411113 | −0.205557 | − | 0.978645i | \(-0.565900\pi\) | ||||
−0.205557 | + | 0.978645i | \(0.565900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 1.73205 | + | 3.00000i | 0.201347 | + | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −3.46410 | + | 6.00000i | −0.394771 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0000 | 1.32518 | ||||||||
\(83\) | 5.19615 | + | 9.00000i | 0.570352 | + | 0.987878i | 0.996530 | + | 0.0832389i | \(0.0265265\pi\) |
−0.426178 | + | 0.904639i | \(0.640140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.92820 | − | 12.0000i | 0.747087 | − | 1.29399i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | − | 5.19615i | −0.319801 | − | 0.553912i | ||||
\(89\) | −6.92820 | −0.734388 | −0.367194 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367194 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 3.46410 | + | 6.00000i | 0.361158 | + | 0.625543i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000 | − | 15.5885i | 0.928279 | − | 1.60783i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 5.19615 | 0.524891 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −6.92820 | − | 12.0000i | −0.689382 | − | 1.19404i | −0.972038 | − | 0.234823i | \(-0.924549\pi\) |
0.282656 | − | 0.959221i | \(-0.408784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | −0.866025 | + | 1.50000i | −0.0849208 | + | 0.147087i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92820 | −0.669775 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.00000 | − | 8.66025i | 0.472456 | − | 0.818317i | ||||
\(113\) | −3.46410 | + | 6.00000i | −0.325875 | + | 0.564433i | −0.981689 | − | 0.190490i | \(-0.938992\pi\) |
0.655814 | + | 0.754923i | \(0.272326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.92820 | −0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | −6.92820 | − | 12.0000i | −0.635107 | − | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −8.66025 | + | 15.0000i | −0.784063 | + | 1.35804i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 6.06218 | + | 10.5000i | 0.535826 | + | 0.928078i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3923 | + | 18.0000i | −0.907980 | + | 1.57267i | −0.0911134 | + | 0.995841i | \(0.529043\pi\) |
−0.816866 | + | 0.576827i | \(0.804291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | −24.2487 | −2.09477 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | 1.02899 | ||||||||
\(137\) | −3.46410 | − | 6.00000i | −0.295958 | − | 0.512615i | 0.679249 | − | 0.733908i | \(-0.262306\pi\) |
−0.975207 | + | 0.221293i | \(0.928972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.66025 | − | 15.0000i | −0.716728 | − | 1.24141i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 6.92820 | − | 12.0000i | 0.567581 | − | 0.983078i | −0.429224 | − | 0.903198i | \(-0.641213\pi\) |
0.996804 | − | 0.0798802i | \(-0.0254538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.00000 | − | 12.1244i | −0.569652 | − | 0.986666i | −0.996600 | − | 0.0823900i | \(-0.973745\pi\) |
0.426948 | − | 0.904276i | \(-0.359589\pi\) | |||||||
\(152\) | 3.46410 | 0.280976 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | −3.46410 | + | 6.00000i | −0.275589 | + | 0.477334i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.8564 | −1.09204 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | 3.46410 | + | 6.00000i | 0.270501 | + | 0.468521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | + | 15.5885i | −0.698535 | + | 1.20990i | ||||
\(167\) | 8.66025 | − | 15.0000i | 0.670151 | − | 1.16073i | −0.307711 | − | 0.951480i | \(-0.599563\pi\) |
0.977861 | − | 0.209255i | \(-0.0671038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 6.92820 | + | 12.0000i | 0.526742 | + | 0.912343i | 0.999514 | + | 0.0311588i | \(0.00991976\pi\) |
−0.472773 | + | 0.881184i | \(0.656747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | − | 8.66025i | 0.377964 | − | 0.654654i | ||||
\(176\) | 8.66025 | − | 15.0000i | 0.652791 | − | 1.13067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.00000 | − | 10.3923i | −0.449719 | − | 0.778936i | ||||
\(179\) | 13.8564 | 1.03568 | 0.517838 | − | 0.855479i | \(-0.326737\pi\) | ||||
0.517838 | + | 0.855479i | \(0.326737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 1.73205 | + | 3.00000i | 0.128388 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | − | 10.3923i | 0.442326 | − | 0.766131i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 20.7846i | −0.877527 | − | 1.51992i | ||||
\(188\) | 10.3923 | 0.757937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.92820 | + | 12.0000i | 0.501307 | + | 0.868290i | 0.999999 | + | 0.00151007i | \(0.000480671\pi\) |
−0.498692 | + | 0.866779i | \(0.666186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0000 | + | 22.5167i | −0.935760 | + | 1.62078i | −0.162488 | + | 0.986710i | \(0.551952\pi\) |
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(194\) | −8.66025 | + | 15.0000i | −0.621770 | + | 1.07694i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | 13.8564 | 0.987228 | 0.493614 | − | 0.869681i | \(-0.335676\pi\) | ||||
0.493614 | + | 0.869681i | \(0.335676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 4.33013 | + | 7.50000i | 0.306186 | + | 0.530330i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | − | 20.7846i | 0.844317 | − | 1.46240i | ||||
\(203\) | 6.92820 | − | 12.0000i | 0.486265 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.92820 | 0.482711 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.00000 | −0.346688 | ||||||||
\(209\) | −3.46410 | − | 6.00000i | −0.239617 | − | 0.415029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | −8.66025 | − | 15.0000i | −0.586546 | − | 1.01593i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | + | 6.00000i | −0.233021 | + | 0.403604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | − | 1.73205i | −0.0669650 | − | 0.115987i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(224\) | 10.3923 | 0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | 1.73205 | + | 3.00000i | 0.114960 | + | 0.199117i | 0.917764 | − | 0.397127i | \(-0.129993\pi\) |
−0.802804 | + | 0.596244i | \(0.796659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | + | 10.3923i | 0.393919 | + | 0.682288i | ||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.73205 | + | 3.00000i | 0.112747 | + | 0.195283i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0000 | − | 20.7846i | 0.777844 | − | 1.34727i | ||||
\(239\) | −5.19615 | + | 9.00000i | −0.336111 | + | 0.582162i | −0.983698 | − | 0.179830i | \(-0.942445\pi\) |
0.647586 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | −1.73205 | −0.111340 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | + | 1.73205i | −0.0636285 | + | 0.110208i | ||||
\(248\) | −1.73205 | + | 3.00000i | −0.109985 | + | 0.190500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.92820 | 0.437304 | 0.218652 | − | 0.975803i | \(-0.429834\pi\) | ||||
0.218652 | + | 0.975803i | \(0.429834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0000 | −1.50887 | ||||||||
\(254\) | −13.8564 | − | 24.0000i | −0.869428 | − | 1.50589i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 13.8564 | − | 24.0000i | 0.864339 | − | 1.49708i | −0.00336324 | − | 0.999994i | \(-0.501071\pi\) |
0.867702 | − | 0.497085i | \(-0.165596\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | − | 3.46410i | −0.124274 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −36.0000 | −2.22409 | ||||||||
\(263\) | 3.46410 | + | 6.00000i | 0.213606 | + | 0.369976i | 0.952840 | − | 0.303472i | \(-0.0981459\pi\) |
−0.739235 | + | 0.673448i | \(0.764813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.46410 | − | 6.00000i | 0.212398 | − | 0.367884i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.00000 | − | 12.1244i | −0.427593 | − | 0.740613i | ||||
\(269\) | 6.92820 | 0.422420 | 0.211210 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211210 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0000 | −1.33640 | −0.668202 | − | 0.743980i | \(-0.732936\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | 17.3205 | + | 30.0000i | 1.05021 | + | 1.81902i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 8.66025 | − | 15.0000i | 0.522233 | − | 0.904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 6.92820 | 0.415526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3923 | − | 18.0000i | −0.619953 | − | 1.07379i | −0.989494 | − | 0.144575i | \(-0.953818\pi\) |
0.369541 | − | 0.929214i | \(-0.379515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 1.73205 | − | 3.00000i | 0.102778 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | + | 5.19615i | 0.177394 | + | 0.307255i | ||||
\(287\) | −13.8564 | −0.817918 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.00000 | − | 8.66025i | 0.292603 | − | 0.506803i | ||||
\(293\) | 6.92820 | − | 12.0000i | 0.404750 | − | 0.701047i | −0.589542 | − | 0.807737i | \(-0.700692\pi\) |
0.994292 | + | 0.106690i | \(0.0340252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.0000 | 1.39028 | ||||||||
\(299\) | 3.46410 | + | 6.00000i | 0.200334 | + | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | + | 13.8564i | −0.461112 | + | 0.798670i | ||||
\(302\) | 12.1244 | − | 21.0000i | 0.697678 | − | 1.20841i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.00000 | + | 8.66025i | 0.286770 | + | 0.496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | −3.46410 | − | 6.00000i | −0.197386 | − | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3923 | + | 18.0000i | −0.589294 | + | 1.02069i | 0.405032 | + | 0.914303i | \(0.367261\pi\) |
−0.994325 | + | 0.106384i | \(0.966073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | −3.46410 | −0.195491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | − | 20.7846i | 0.671871 | − | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | − | 20.7846i | −0.668734 | − | 1.15828i | ||||
\(323\) | 13.8564 | 0.770991 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | −0.277350 | ||||||||
\(326\) | 12.1244 | + | 21.0000i | 0.671506 | + | 1.16308i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.00000 | − | 10.3923i | 0.331295 | − | 0.573819i | ||||
\(329\) | −10.3923 | + | 18.0000i | −0.572946 | + | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | + | 8.66025i | 0.274825 | + | 0.476011i | 0.970091 | − | 0.242742i | \(-0.0780468\pi\) |
−0.695266 | + | 0.718752i | \(0.744713\pi\) | |||||||
\(332\) | −10.3923 | −0.570352 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 30.0000 | 1.64153 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.73205i | −0.0544735 | + | 0.0943508i | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | 0.866025 | − | 1.50000i | 0.0471056 | − | 0.0815892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820 | 0.375183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −6.92820 | − | 12.0000i | −0.373544 | − | 0.646997i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | + | 20.7846i | −0.645124 | + | 1.11739i | ||||
\(347\) | −13.8564 | + | 24.0000i | −0.743851 | + | 1.28839i | 0.206879 | + | 0.978367i | \(0.433669\pi\) |
−0.950730 | + | 0.310021i | \(0.899664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | − | 22.5167i | −0.695874 | − | 1.20529i | −0.969885 | − | 0.243563i | \(-0.921684\pi\) |
0.274011 | − | 0.961727i | \(-0.411649\pi\) | |||||||
\(350\) | 17.3205 | 0.925820 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.0000 | 0.959403 | ||||||||
\(353\) | 3.46410 | + | 6.00000i | 0.184376 | + | 0.319348i | 0.943366 | − | 0.331754i | \(-0.107640\pi\) |
−0.758990 | + | 0.651102i | \(0.774307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.46410 | − | 6.00000i | 0.183597 | − | 0.317999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | + | 20.7846i | 0.634220 | + | 1.09850i | ||||
\(359\) | 10.3923 | 0.548485 | 0.274242 | − | 0.961661i | \(-0.411573\pi\) | ||||
0.274242 | + | 0.961661i | \(0.411573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −8.66025 | − | 15.0000i | −0.455173 | − | 0.788382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | + | 1.73205i | −0.0524142 | + | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 34.6410 | 1.80579 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | + | 22.5167i | −0.673114 | + | 1.16587i | 0.303902 | + | 0.952703i | \(0.401711\pi\) |
−0.977016 | + | 0.213165i | \(0.931623\pi\) | |||||||
\(374\) | 20.7846 | − | 36.0000i | 1.07475 | − | 1.86152i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | − | 15.5885i | −0.464140 | − | 0.803913i | ||||
\(377\) | −6.92820 | −0.356821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | + | 20.7846i | −0.613973 | + | 1.06343i | ||||
\(383\) | −8.66025 | + | 15.0000i | −0.442518 | + | 0.766464i | −0.997876 | − | 0.0651476i | \(-0.979248\pi\) |
0.555357 | + | 0.831612i | \(0.312581\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −45.0333 | −2.29214 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 10.3923 | + | 18.0000i | 0.526911 | + | 0.912636i | 0.999508 | + | 0.0313578i | \(0.00998314\pi\) |
−0.472597 | + | 0.881278i | \(0.656684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | − | 41.5692i | 1.21373 | − | 2.10225i | ||||
\(392\) | 2.59808 | − | 4.50000i | 0.131223 | − | 0.227284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | −13.8564 | − | 24.0000i | −0.694559 | − | 1.20301i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.5000 | + | 21.6506i | −0.625000 | + | 1.08253i | ||||
\(401\) | −17.3205 | + | 30.0000i | −0.864945 | + | 1.49813i | 0.00215698 | + | 0.999998i | \(0.499313\pi\) |
−0.867102 | + | 0.498131i | \(0.834020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.00000 | − | 1.73205i | −0.0498135 | − | 0.0862796i | ||||
\(404\) | 13.8564 | 0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | −3.46410 | − | 6.00000i | −0.171709 | − | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | − | 8.66025i | 0.247234 | − | 0.428222i | −0.715523 | − | 0.698589i | \(-0.753812\pi\) |
0.962757 | + | 0.270367i | \(0.0871450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00000 | + | 3.46410i | 0.0985329 | + | 0.170664i | ||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.59808 | − | 4.50000i | −0.127381 | − | 0.220631i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | − | 10.3923i | 0.293470 | − | 0.508304i | ||||
\(419\) | 3.46410 | − | 6.00000i | 0.169232 | − | 0.293119i | −0.768918 | − | 0.639348i | \(-0.779204\pi\) |
0.938150 | + | 0.346228i | \(0.112538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | −13.8564 | −0.674519 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.3205 | + | 30.0000i | 0.840168 | + | 1.45521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | − | 17.3205i | 0.483934 | − | 0.838198i | ||||
\(428\) | 3.46410 | − | 6.00000i | 0.167444 | − | 0.290021i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.1051 | −1.83546 | −0.917729 | − | 0.397206i | \(-0.869980\pi\) | ||||
−0.917729 | + | 0.397206i | \(0.869980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 3.46410 | + | 6.00000i | 0.166282 | + | 0.288009i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | 6.92820 | − | 12.0000i | 0.331421 | − | 0.574038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 10.3923 | + | 18.0000i | 0.493753 | + | 0.855206i | 0.999974 | − | 0.00719811i | \(-0.00229125\pi\) |
−0.506221 | + | 0.862404i | \(0.668958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.73205 | − | 3.00000i | 0.0820150 | − | 0.142054i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | − | 1.73205i | −0.0472456 | − | 0.0818317i | ||||
\(449\) | 6.92820 | 0.326962 | 0.163481 | − | 0.986546i | \(-0.447728\pi\) | ||||
0.163481 | + | 0.986546i | \(0.447728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | −3.46410 | − | 6.00000i | −0.162938 | − | 0.282216i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00000 | + | 5.19615i | −0.140797 | + | 0.243868i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | + | 8.66025i | 0.233890 | + | 0.405110i | 0.958950 | − | 0.283577i | \(-0.0915211\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | −24.2487 | −1.13307 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.8564 | − | 24.0000i | −0.645357 | − | 1.11779i | −0.984219 | − | 0.176955i | \(-0.943375\pi\) |
0.338862 | − | 0.940836i | \(-0.389958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | + | 1.73205i | −0.0464739 | + | 0.0804952i | −0.888327 | − | 0.459212i | \(-0.848132\pi\) |
0.841853 | + | 0.539707i | \(0.181465\pi\) | |||||||
\(464\) | −17.3205 | + | 30.0000i | −0.804084 | + | 1.39272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7846 | −0.961797 | −0.480899 | − | 0.876776i | \(-0.659689\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | 1.29292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | −13.8564 | + | 24.0000i | −0.637118 | + | 1.10352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | + | 8.66025i | 0.229416 | + | 0.397360i | ||||
\(476\) | 13.8564 | 0.635107 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.0000 | −0.823301 | ||||||||
\(479\) | −1.73205 | − | 3.00000i | −0.0791394 | − | 0.137073i | 0.823739 | − | 0.566969i | \(-0.191884\pi\) |
−0.902879 | + | 0.429895i | \(0.858551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00000 | + | 1.73205i | −0.0455961 | + | 0.0789747i | ||||
\(482\) | −8.66025 | + | 15.0000i | −0.394464 | + | 0.683231i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | − | 0.866025i | −0.0227273 | − | 0.0393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 8.66025 | + | 15.0000i | 0.392031 | + | 0.679018i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.46410 | − | 6.00000i | 0.156333 | − | 0.270776i | −0.777211 | − | 0.629240i | \(-0.783366\pi\) |
0.933544 | + | 0.358464i | \(0.116699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000 | + | 41.5692i | 1.08091 | + | 1.87218i | ||||
\(494\) | −3.46410 | −0.155857 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 3.46410 | + | 6.00000i | 0.155386 | + | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00000 | + | 12.1244i | −0.313363 | + | 0.542761i | −0.979088 | − | 0.203436i | \(-0.934789\pi\) |
0.665725 | + | 0.746197i | \(0.268122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | 6.92820 | 0.308913 | 0.154457 | − | 0.988000i | \(-0.450637\pi\) | ||||
0.154457 | + | 0.988000i | \(0.450637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.7846 | − | 36.0000i | −0.923989 | − | 1.60040i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | − | 13.8564i | 0.354943 | − | 0.614779i | ||||
\(509\) | −6.92820 | + | 12.0000i | −0.307087 | + | 0.531891i | −0.977724 | − | 0.209895i | \(-0.932688\pi\) |
0.670637 | + | 0.741786i | \(0.266021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | + | 17.3205i | 0.442374 | + | 0.766214i | ||||
\(512\) | −8.66025 | −0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 48.0000 | 2.11719 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0000 | + | 31.1769i | −0.791639 | + | 1.37116i | ||||
\(518\) | 3.46410 | − | 6.00000i | 0.152204 | − | 0.263625i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7846 | −0.910590 | −0.455295 | − | 0.890341i | \(-0.650466\pi\) | ||||
−0.455295 | + | 0.890341i | \(0.650466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −10.3923 | − | 18.0000i | −0.453990 | − | 0.786334i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | + | 10.3923i | −0.261612 | + | 0.453126i | ||||
\(527\) | −6.92820 | + | 12.0000i | −0.301797 | + | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5000 | − | 21.6506i | −0.543478 | − | 0.941332i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | 0.173422 | ||||||||
\(533\) | 3.46410 | + | 6.00000i | 0.150047 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.1244 | + | 21.0000i | −0.523692 | + | 0.907062i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | + | 10.3923i | 0.258678 | + | 0.448044i | ||||
\(539\) | −10.3923 | −0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −19.0526 | − | 33.0000i | −0.818377 | − | 1.41747i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.0000 | + | 31.1769i | −0.771744 | + | 1.33670i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00000 | + | 3.46410i | 0.0855138 | + | 0.148114i | 0.905610 | − | 0.424111i | \(-0.139413\pi\) |
−0.820096 | + | 0.572226i | \(0.806080\pi\) | |||||||
\(548\) | 6.92820 | 0.295958 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.0000 | 1.27920 | ||||||||
\(551\) | 6.92820 | + | 12.0000i | 0.295151 | + | 0.511217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 6.92820i | 0.170097 | − | 0.294617i | ||||
\(554\) | 1.73205 | − | 3.00000i | 0.0735878 | − | 0.127458i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −27.7128 | −1.17423 | −0.587115 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587115 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | − | 31.1769i | 0.759284 | − | 1.31512i | ||||
\(563\) | 6.92820 | − | 12.0000i | 0.291989 | − | 0.505740i | −0.682291 | − | 0.731081i | \(-0.739016\pi\) |
0.974280 | + | 0.225341i | \(0.0723496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.92820 | 0.291214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −6.92820 | − | 12.0000i | −0.290445 | − | 0.503066i | 0.683470 | − | 0.729979i | \(-0.260470\pi\) |
−0.973915 | + | 0.226913i | \(0.927137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −1.73205 | + | 3.00000i | −0.0724207 | + | 0.125436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 20.7846i | −0.500870 | − | 0.867533i | ||||
\(575\) | 34.6410 | 1.44463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0000 | 1.08239 | 0.541197 | − | 0.840896i | \(-0.317971\pi\) | ||||
0.541197 | + | 0.840896i | \(0.317971\pi\) | |||||||
\(578\) | 26.8468 | + | 46.5000i | 1.11668 | + | 1.93415i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923 | − | 18.0000i | 0.431145 | − | 0.746766i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −17.3205 | −0.716728 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | −22.5167 | − | 39.0000i | −0.929362 | − | 1.60970i | −0.784391 | − | 0.620266i | \(-0.787025\pi\) |
−0.144971 | − | 0.989436i | \(-0.546309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.00000 | + | 8.66025i | 0.205499 | + | 0.355934i | ||||
\(593\) | −20.7846 | −0.853522 | −0.426761 | − | 0.904365i | \(-0.640345\pi\) | ||||
−0.426761 | + | 0.904365i | \(0.640345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.92820 | + | 12.0000i | 0.283790 | + | 0.491539i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | + | 10.3923i | −0.245358 | + | 0.424973i | ||||
\(599\) | 10.3923 | − | 18.0000i | 0.424618 | − | 0.735460i | −0.571767 | − | 0.820416i | \(-0.693742\pi\) |
0.996385 | + | 0.0849563i | \(0.0270751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | + | 29.4449i | 0.693444 | + | 1.20108i | 0.970702 | + | 0.240285i | \(0.0772411\pi\) |
−0.277258 | + | 0.960796i | \(0.589426\pi\) | |||||||
\(602\) | −27.7128 | −1.12949 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | − | 34.6410i | 0.811775 | − | 1.40604i | −0.0998457 | − | 0.995003i | \(-0.531835\pi\) |
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(608\) | −5.19615 | + | 9.00000i | −0.210732 | + | 0.364998i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3923 | 0.420428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 22.5167 | + | 39.0000i | 0.908698 | + | 1.57391i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | + | 10.3923i | −0.241747 | + | 0.418718i | ||||
\(617\) | −3.46410 | + | 6.00000i | −0.139459 | + | 0.241551i | −0.927292 | − | 0.374338i | \(-0.877870\pi\) |
0.787833 | + | 0.615889i | \(0.211203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | − | 22.5167i | −0.522514 | − | 0.905021i | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
0.477143 | − | 0.878826i | \(-0.341672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −36.0000 | −1.44347 | ||||||||
\(623\) | 6.92820 | + | 12.0000i | 0.277573 | + | 0.480770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 12.1244 | − | 21.0000i | 0.484587 | − | 0.839329i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | − | 1.73205i | −0.0399043 | − | 0.0691164i | ||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 3.46410 | + | 6.00000i | 0.137795 | + | 0.238667i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50000 | + | 2.59808i | 0.0594322 | + | 0.102940i | ||||
\(638\) | 41.5692 | 1.64574 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3205 | + | 30.0000i | 0.684119 | + | 1.18493i | 0.973713 | + | 0.227779i | \(0.0731464\pi\) |
−0.289594 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | + | 12.1244i | −0.276053 | + | 0.478138i | −0.970400 | − | 0.241502i | \(-0.922360\pi\) |
0.694347 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(644\) | 6.92820 | − | 12.0000i | 0.273009 | − | 0.472866i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | 13.8564 | 0.544752 | 0.272376 | − | 0.962191i | \(-0.412191\pi\) | ||||
0.272376 | + | 0.962191i | \(0.412191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | −4.33013 | − | 7.50000i | −0.169842 | − | 0.294174i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.00000 | + | 12.1244i | −0.274141 | + | 0.474826i | ||||
\(653\) | −17.3205 | + | 30.0000i | −0.677804 | + | 1.17399i | 0.297837 | + | 0.954617i | \(0.403735\pi\) |
−0.975641 | + | 0.219374i | \(0.929599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.6410 | 1.35250 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.0000 | −1.40343 | ||||||||
\(659\) | 6.92820 | + | 12.0000i | 0.269884 | + | 0.467454i | 0.968832 | − | 0.247720i | \(-0.0796812\pi\) |
−0.698947 | + | 0.715173i | \(0.746348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | + | 22.5167i | −0.505641 | + | 0.875797i | 0.494337 | + | 0.869270i | \(0.335411\pi\) |
−0.999979 | + | 0.00652642i | \(0.997923\pi\) | |||||||
\(662\) | −8.66025 | + | 15.0000i | −0.336590 | + | 0.582992i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | + | 15.5885i | 0.349268 | + | 0.604949i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0000 | 1.85857 | ||||||||
\(668\) | 8.66025 | + | 15.0000i | 0.335075 | + | 0.580367i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.3205 | − | 30.0000i | 0.668651 | − | 1.15814i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | + | 8.66025i | 0.192736 | + | 0.333828i | 0.946156 | − | 0.323711i | \(-0.104931\pi\) |
−0.753420 | + | 0.657539i | \(0.771597\pi\) | |||||||
\(674\) | −3.46410 | −0.133432 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −20.7846 | − | 36.0000i | −0.798817 | − | 1.38359i | −0.920387 | − | 0.391009i | \(-0.872126\pi\) |
0.121569 | − | 0.992583i | \(-0.461207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | − | 17.3205i | 0.383765 | − | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | + | 10.3923i | 0.229752 | + | 0.397942i | ||||
\(683\) | 17.3205 | 0.662751 | 0.331375 | − | 0.943499i | \(-0.392487\pi\) | ||||
0.331375 | + | 0.943499i | \(0.392487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.3205 | − | 30.0000i | −0.661300 | − | 1.14541i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.0000 | − | 34.6410i | 0.762493 | − | 1.32068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | + | 8.66025i | 0.190209 | + | 0.329452i | 0.945319 | − | 0.326146i | \(-0.105750\pi\) |
−0.755110 | + | 0.655598i | \(0.772417\pi\) | |||||||
\(692\) | −13.8564 | −0.526742 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.0000 | −1.82206 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | − | 41.5692i | 0.909065 | − | 1.57455i | ||||
\(698\) | 22.5167 | − | 39.0000i | 0.852268 | − | 1.47617i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.00000 | + | 8.66025i | 0.188982 | + | 0.327327i | ||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | −1.73205 | − | 3.00000i | −0.0652791 | − | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | + | 10.3923i | −0.225813 | + | 0.391120i | ||||
\(707\) | −13.8564 | + | 24.0000i | −0.521124 | + | 0.902613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.0000 | −0.449719 | ||||||||
\(713\) | 6.92820 | + | 12.0000i | 0.259463 | + | 0.449404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.92820 | + | 12.0000i | −0.258919 | + | 0.448461i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | + | 15.5885i | 0.335877 | + | 0.581756i | ||||
\(719\) | −34.6410 | −1.29189 | −0.645946 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645946 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | −12.9904 | − | 22.5000i | −0.483452 | − | 0.837363i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | −17.3205 | + | 30.0000i | −0.643268 | + | 1.11417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | − | 27.7128i | −0.593407 | − | 1.02781i | −0.993770 | − | 0.111454i | \(-0.964449\pi\) |
0.400362 | − | 0.916357i | \(-0.368884\pi\) | |||||||
\(728\) | 3.46410 | 0.128388 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.7128 | − | 48.0000i | −1.02500 | − | 1.77534i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0000 | − | 29.4449i | 0.627909 | − | 1.08757i | −0.360061 | − | 0.932929i | \(-0.617244\pi\) |
0.987971 | − | 0.154642i | \(-0.0494225\pi\) | |||||||
\(734\) | 6.92820 | − | 12.0000i | 0.255725 | − | 0.442928i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0000 | + | 31.1769i | 0.663489 | + | 1.14920i | ||||
\(737\) | 48.4974 | 1.78643 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0000 | −0.809283 | −0.404642 | − | 0.914475i | \(-0.632604\pi\) | ||||
−0.404642 | + | 0.914475i | \(0.632604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1244 | + | 21.0000i | −0.444799 | + | 0.770415i | −0.998038 | − | 0.0626075i | \(-0.980058\pi\) |
0.553239 | + | 0.833023i | \(0.313392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.0333 | −1.64879 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.0000 | 0.877527 | ||||||||
\(749\) | 6.92820 | + | 12.0000i | 0.253151 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | 25.9808 | − | 45.0000i | 0.947421 | − | 1.64098i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | − | 10.3923i | −0.218507 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 1.73205 | + | 3.00000i | 0.0629109 | + | 0.108965i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.3205 | − | 30.0000i | 0.627868 | − | 1.08750i | −0.360111 | − | 0.932910i | \(-0.617261\pi\) |
0.987979 | − | 0.154590i | \(-0.0494055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | + | 17.3205i | 0.362024 | + | 0.627044i | ||||
\(764\) | −13.8564 | −0.501307 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.0000 | −1.08394 | ||||||||
\(767\) | 1.73205 | + | 3.00000i | 0.0625407 | + | 0.108324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0000 | + | 43.3013i | −0.901523 | + | 1.56148i | −0.0760054 | + | 0.997107i | \(0.524217\pi\) |
−0.825518 | + | 0.564376i | \(0.809117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0000 | − | 22.5167i | −0.467880 | − | 0.810392i | ||||
\(773\) | −13.8564 | −0.498380 | −0.249190 | − | 0.968455i | \(-0.580164\pi\) | ||||
−0.249190 | + | 0.968455i | \(0.580164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | −0.359211 | ||||||||
\(776\) | 8.66025 | + | 15.0000i | 0.310885 | + | 0.538469i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.0000 | + | 31.1769i | −0.645331 | + | 1.11775i | ||||
\(779\) | 6.92820 | − | 12.0000i | 0.248229 | − | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | + | 10.3923i | 0.214697 | + | 0.371866i | ||||
\(782\) | 83.1384 | 2.97302 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.0000 | 0.535714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0000 | − | 19.0526i | 0.392108 | − | 0.679150i | −0.600620 | − | 0.799535i | \(-0.705079\pi\) |
0.992727 | + | 0.120384i | \(0.0384127\pi\) | |||||||
\(788\) | −6.92820 | + | 12.0000i | −0.246807 | + | 0.427482i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8564 | 0.492677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | −0.355110 | ||||||||
\(794\) | 1.73205 | + | 3.00000i | 0.0614682 | + | 0.106466i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | 17.3205 | − | 30.0000i | 0.613524 | − | 1.06265i | −0.377118 | − | 0.926165i | \(-0.623085\pi\) |
0.990642 | − | 0.136489i | \(-0.0435819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.0000 | − | 62.3538i | −1.27359 | − | 2.20592i | ||||
\(800\) | −25.9808 | −0.918559 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −60.0000 | −2.11867 | ||||||||
\(803\) | 17.3205 | + | 30.0000i | 0.611227 | + | 1.05868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.73205 | − | 3.00000i | 0.0610089 | − | 0.105670i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.0000 | − | 20.7846i | −0.422159 | − | 0.731200i | ||||
\(809\) | −6.92820 | −0.243583 | −0.121791 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121791 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.0000 | 0.912983 | 0.456492 | − | 0.889728i | \(-0.349106\pi\) | ||||
0.456492 | + | 0.889728i | \(0.349106\pi\) | |||||||
\(812\) | 6.92820 | + | 12.0000i | 0.243132 | + | 0.421117i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 10.3923i | 0.210300 | − | 0.364250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 17.3205 | 0.605597 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.8564 | + | 24.0000i | 0.483592 | + | 0.837606i | 0.999822 | − | 0.0188439i | \(-0.00599856\pi\) |
−0.516231 | + | 0.856450i | \(0.672665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | 3.46410 | − | 6.00000i | 0.120678 | − | 0.209020i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | − | 10.3923i | −0.208767 | − | 0.361595i | ||||
\(827\) | −10.3923 | −0.361376 | −0.180688 | − | 0.983540i | \(-0.557832\pi\) | ||||
−0.180688 | + | 0.983540i | \(0.557832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.500000 | + | 0.866025i | −0.0173344 | + | 0.0300240i | ||||
\(833\) | 10.3923 | − | 18.0000i | 0.360072 | − | 0.623663i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820 | 0.239617 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | 12.1244 | + | 21.0000i | 0.418579 | + | 0.725001i | 0.995797 | − | 0.0915899i | \(-0.0291949\pi\) |
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | + | 16.4545i | −0.327586 | + | 0.567396i | ||||
\(842\) | −8.66025 | + | 15.0000i | −0.298452 | + | 0.516934i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.0000 | + | 51.9615i | −1.02899 | + | 1.78227i | ||||
\(851\) | 6.92820 | − | 12.0000i | 0.237496 | − | 0.411355i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | + | 39.8372i | 0.787505 | + | 1.36400i | 0.927491 | + | 0.373845i | \(0.121961\pi\) |
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(854\) | 34.6410 | 1.18539 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.0000 | − | 57.1577i | −1.12398 | − | 1.94680i | ||||
\(863\) | 31.1769 | 1.06127 | 0.530637 | − | 0.847599i | \(-0.321953\pi\) | ||||
0.530637 | + | 0.847599i | \(0.321953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.73205 | + | 3.00000i | 0.0588575 | + | 0.101944i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.00000 | + | 3.46410i | −0.0678844 | + | 0.117579i | ||||
\(869\) | 6.92820 | − | 12.0000i | 0.235023 | − | 0.407072i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | − | 12.1244i | −0.237186 | − | 0.410818i | ||||
\(872\) | −17.3205 | −0.586546 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | − | 19.0526i | 0.371444 | − | 0.643359i | −0.618344 | − | 0.785907i | \(-0.712196\pi\) |
0.989788 | + | 0.142548i | \(0.0455296\pi\) | |||||||
\(878\) | −24.2487 | + | 42.0000i | −0.818354 | + | 1.41743i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564 | 0.466834 | 0.233417 | − | 0.972377i | \(-0.425009\pi\) | ||||
0.233417 | + | 0.972377i | \(0.425009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | −3.46410 | − | 6.00000i | −0.116510 | − | 0.201802i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | + | 31.1769i | −0.604722 | + | 1.04741i | ||||
\(887\) | 13.8564 | − | 24.0000i | 0.465253 | − | 0.805841i | −0.533960 | − | 0.845510i | \(-0.679297\pi\) |
0.999213 | + | 0.0396684i | \(0.0126302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 27.7128i | 0.536623 | + | 0.929458i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | −10.3923 | − | 18.0000i | −0.347765 | − | 0.602347i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.1244 | − | 21.0000i | 0.405046 | − | 0.701561i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | + | 10.3923i | 0.200223 | + | 0.346796i | ||||
\(899\) | −13.8564 | −0.462137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −20.7846 | − | 36.0000i | −0.692052 | − | 1.19867i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | + | 10.3923i | −0.199557 | + | 0.345643i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | −3.46410 | −0.114960 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7846 | − | 36.0000i | −0.688625 | − | 1.19273i | −0.972283 | − | 0.233808i | \(-0.924881\pi\) |
0.283658 | − | 0.958926i | \(-0.408452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | −8.66025 | + | 15.0000i | −0.286456 | + | 0.496156i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | − | 12.1244i | −0.231287 | − | 0.400600i | ||||
\(917\) | 41.5692 | 1.37274 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.0000 | − | 41.5692i | 0.790398 | − | 1.36901i | ||||
\(923\) | 1.73205 | − | 3.00000i | 0.0570111 | − | 0.0987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | + | 8.66025i | 0.164399 | + | 0.284747i | ||||
\(926\) | −3.46410 | −0.113837 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36.0000 | −1.18176 | ||||||||
\(929\) | −24.2487 | − | 42.0000i | −0.795574 | − | 1.37798i | −0.922474 | − | 0.386060i | \(-0.873836\pi\) |
0.126899 | − | 0.991916i | \(-0.459497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00000 | − | 5.19615i | 0.0983210 | − | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.0000 | − | 31.1769i | −0.588978 | − | 1.02014i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 24.2487 | + | 42.0000i | 0.791748 | + | 1.37135i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7846 | − | 36.0000i | 0.677559 | − | 1.17357i | −0.298155 | − | 0.954517i | \(-0.596371\pi\) |
0.975714 | − | 0.219049i | \(-0.0702955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | − | 41.5692i | −0.781548 | − | 1.35368i | ||||
\(944\) | 17.3205 | 0.563735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.0000 | −1.56061 | ||||||||
\(947\) | 8.66025 | + | 15.0000i | 0.281420 | + | 0.487435i | 0.971735 | − | 0.236075i | \(-0.0758611\pi\) |
−0.690314 | + | 0.723510i | \(0.742528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.00000 | − | 8.66025i | 0.162307 | − | 0.281124i | ||||
\(950\) | −8.66025 | + | 15.0000i | −0.280976 | + | 0.486664i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | − | 20.7846i | −0.388922 | − | 0.673633i | ||||
\(953\) | 27.7128 | 0.897706 | 0.448853 | − | 0.893606i | \(-0.351833\pi\) | ||||
0.448853 | + | 0.893606i | \(0.351833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.19615 | − | 9.00000i | −0.168056 | − | 0.291081i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.00000 | − | 5.19615i | 0.0969256 | − | 0.167880i | ||||
\(959\) | −6.92820 | + | 12.0000i | −0.223723 | + | 0.387500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −3.46410 | −0.111687 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | + | 1.73205i | −0.0321578 | + | 0.0556990i | −0.881656 | − | 0.471892i | \(-0.843571\pi\) |
0.849499 | + | 0.527591i | \(0.176905\pi\) | |||||||
\(968\) | −0.866025 | + | 1.50000i | −0.0278351 | + | 0.0482118i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.4256 | −1.77869 | −0.889346 | − | 0.457234i | \(-0.848840\pi\) | ||||
−0.889346 | + | 0.457234i | \(0.848840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 1.73205 | + | 3.00000i | 0.0554985 | + | 0.0961262i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.0000 | + | 43.3013i | −0.800230 | + | 1.38604i | ||||
\(977\) | 3.46410 | − | 6.00000i | 0.110826 | − | 0.191957i | −0.805277 | − | 0.592898i | \(-0.797984\pi\) |
0.916104 | + | 0.400941i | \(0.131317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | + | 20.7846i | 0.383522 | + | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.0000 | 0.382935 | ||||||||
\(983\) | 5.19615 | + | 9.00000i | 0.165732 | + | 0.287055i | 0.936915 | − | 0.349558i | \(-0.113668\pi\) |
−0.771183 | + | 0.636613i | \(0.780335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.5692 | + | 72.0000i | −1.32383 | + | 2.29295i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00000 | − | 1.73205i | −0.0318142 | − | 0.0551039i | ||||
\(989\) | −55.4256 | −1.76243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | −5.19615 | − | 9.00000i | −0.164978 | − | 0.285750i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | + | 10.3923i | −0.190308 | + | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | −24.2487 | −0.767580 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1053.2.e.i.352.2 | 4 | ||
3.2 | odd | 2 | inner | 1053.2.e.i.352.1 | 4 | ||
9.2 | odd | 6 | inner | 1053.2.e.i.703.1 | 4 | ||
9.4 | even | 3 | 117.2.a.b.1.1 | ✓ | 2 | ||
9.5 | odd | 6 | 117.2.a.b.1.2 | yes | 2 | ||
9.7 | even | 3 | inner | 1053.2.e.i.703.2 | 4 | ||
36.23 | even | 6 | 1872.2.a.v.1.2 | 2 | |||
36.31 | odd | 6 | 1872.2.a.v.1.1 | 2 | |||
45.4 | even | 6 | 2925.2.a.y.1.2 | 2 | |||
45.13 | odd | 12 | 2925.2.c.s.2224.3 | 4 | |||
45.14 | odd | 6 | 2925.2.a.y.1.1 | 2 | |||
45.22 | odd | 12 | 2925.2.c.s.2224.2 | 4 | |||
45.23 | even | 12 | 2925.2.c.s.2224.1 | 4 | |||
45.32 | even | 12 | 2925.2.c.s.2224.4 | 4 | |||
63.13 | odd | 6 | 5733.2.a.t.1.1 | 2 | |||
63.41 | even | 6 | 5733.2.a.t.1.2 | 2 | |||
72.5 | odd | 6 | 7488.2.a.cq.1.2 | 2 | |||
72.13 | even | 6 | 7488.2.a.cq.1.1 | 2 | |||
72.59 | even | 6 | 7488.2.a.cj.1.1 | 2 | |||
72.67 | odd | 6 | 7488.2.a.cj.1.2 | 2 | |||
117.5 | even | 12 | 1521.2.b.i.1351.2 | 4 | |||
117.31 | odd | 12 | 1521.2.b.i.1351.4 | 4 | |||
117.77 | odd | 6 | 1521.2.a.j.1.1 | 2 | |||
117.86 | even | 12 | 1521.2.b.i.1351.3 | 4 | |||
117.103 | even | 6 | 1521.2.a.j.1.2 | 2 | |||
117.112 | odd | 12 | 1521.2.b.i.1351.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.a.b.1.1 | ✓ | 2 | 9.4 | even | 3 | ||
117.2.a.b.1.2 | yes | 2 | 9.5 | odd | 6 | ||
1053.2.e.i.352.1 | 4 | 3.2 | odd | 2 | inner | ||
1053.2.e.i.352.2 | 4 | 1.1 | even | 1 | trivial | ||
1053.2.e.i.703.1 | 4 | 9.2 | odd | 6 | inner | ||
1053.2.e.i.703.2 | 4 | 9.7 | even | 3 | inner | ||
1521.2.a.j.1.1 | 2 | 117.77 | odd | 6 | |||
1521.2.a.j.1.2 | 2 | 117.103 | even | 6 | |||
1521.2.b.i.1351.1 | 4 | 117.112 | odd | 12 | |||
1521.2.b.i.1351.2 | 4 | 117.5 | even | 12 | |||
1521.2.b.i.1351.3 | 4 | 117.86 | even | 12 | |||
1521.2.b.i.1351.4 | 4 | 117.31 | odd | 12 | |||
1872.2.a.v.1.1 | 2 | 36.31 | odd | 6 | |||
1872.2.a.v.1.2 | 2 | 36.23 | even | 6 | |||
2925.2.a.y.1.1 | 2 | 45.14 | odd | 6 | |||
2925.2.a.y.1.2 | 2 | 45.4 | even | 6 | |||
2925.2.c.s.2224.1 | 4 | 45.23 | even | 12 | |||
2925.2.c.s.2224.2 | 4 | 45.22 | odd | 12 | |||
2925.2.c.s.2224.3 | 4 | 45.13 | odd | 12 | |||
2925.2.c.s.2224.4 | 4 | 45.32 | even | 12 | |||
5733.2.a.t.1.1 | 2 | 63.13 | odd | 6 | |||
5733.2.a.t.1.2 | 2 | 63.41 | even | 6 | |||
7488.2.a.cj.1.1 | 2 | 72.59 | even | 6 | |||
7488.2.a.cj.1.2 | 2 | 72.67 | odd | 6 | |||
7488.2.a.cq.1.1 | 2 | 72.13 | even | 6 | |||
7488.2.a.cq.1.2 | 2 | 72.5 | odd | 6 |