Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.361 |
Dual form | 2646.2.h.t.667.2 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.03528 | −0.462990 | −0.231495 | − | 0.972836i | \(-0.574362\pi\) | ||||
−0.231495 | + | 0.972836i | \(0.574362\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.517638 | + | 0.896575i | −0.163692 | + | 0.283522i | ||||
\(11\) | 0.267949 | 0.0807897 | 0.0403949 | − | 0.999184i | \(-0.487138\pi\) | ||||
0.0403949 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.896575 | − | 1.55291i | 0.248665 | − | 0.430701i | −0.714490 | − | 0.699645i | \(-0.753341\pi\) |
0.963156 | + | 0.268944i | \(0.0866747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.41542 | − | 5.91567i | 0.828360 | − | 1.43476i | −0.0709642 | − | 0.997479i | \(-0.522608\pi\) |
0.899324 | − | 0.437283i | \(-0.144059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19067 | + | 3.79435i | 0.502574 | + | 0.870484i | 0.999996 | + | 0.00297513i | \(0.000947015\pi\) |
−0.497421 | + | 0.867509i | \(0.665720\pi\) | |||||||
\(20\) | 0.517638 | + | 0.896575i | 0.115747 | + | 0.200480i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.133975 | − | 0.232051i | 0.0285635 | − | 0.0494734i | ||||
\(23\) | −5.46410 | −1.13934 | −0.569672 | − | 0.821872i | \(-0.692930\pi\) | ||||
−0.569672 | + | 0.821872i | \(0.692930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.92820 | −0.785641 | ||||||||
\(26\) | −0.896575 | − | 1.55291i | −0.175833 | − | 0.304552i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | − | 3.46410i | −0.371391 | − | 0.643268i | 0.618389 | − | 0.785872i | \(-0.287786\pi\) |
−0.989780 | + | 0.142605i | \(0.954452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.34607 | + | 5.79555i | 0.600971 | + | 1.04091i | 0.992674 | + | 0.120821i | \(0.0385526\pi\) |
−0.391703 | + | 0.920092i | \(0.628114\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.41542 | − | 5.91567i | −0.585739 | − | 1.01453i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.73205 | − | 6.46410i | −0.613545 | − | 1.06269i | −0.990638 | − | 0.136516i | \(-0.956409\pi\) |
0.377092 | − | 0.926176i | \(-0.376924\pi\) | |||||||
\(38\) | 4.38134 | 0.710747 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.03528 | 0.163692 | ||||||||
\(41\) | 4.31199 | − | 7.46859i | 0.673420 | − | 1.16640i | −0.303508 | − | 0.952829i | \(-0.598158\pi\) |
0.976928 | − | 0.213569i | \(-0.0685087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.133975 | − | 0.232051i | −0.0204309 | − | 0.0353874i | 0.855629 | − | 0.517589i | \(-0.173170\pi\) |
−0.876060 | + | 0.482202i | \(0.839837\pi\) | |||||||
\(44\) | −0.133975 | − | 0.232051i | −0.0201974 | − | 0.0349830i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.73205 | + | 4.73205i | −0.402819 | + | 0.697703i | ||||
\(47\) | −0.378937 | + | 0.656339i | −0.0552737 | + | 0.0957369i | −0.892338 | − | 0.451367i | \(-0.850936\pi\) |
0.837065 | + | 0.547104i | \(0.184270\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.96410 | + | 3.40192i | −0.277766 | + | 0.481105i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.79315 | −0.248665 | ||||||||
\(53\) | 5.46410 | − | 9.46410i | 0.750552 | − | 1.29999i | −0.197003 | − | 0.980403i | \(-0.563121\pi\) |
0.947555 | − | 0.319592i | \(-0.103546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.277401 | −0.0374048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | −0.525226 | ||||||||
\(59\) | 0.637756 | + | 1.10463i | 0.0830288 | + | 0.143810i | 0.904550 | − | 0.426369i | \(-0.140207\pi\) |
−0.821521 | + | 0.570179i | \(0.806874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.31319 | + | 10.9348i | −0.808322 | + | 1.40005i | 0.105704 | + | 0.994398i | \(0.466290\pi\) |
−0.914026 | + | 0.405656i | \(0.867043\pi\) | |||||||
\(62\) | 6.69213 | 0.849901 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.928203 | + | 1.60770i | −0.115129 | + | 0.199410i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.23205 | − | 10.7942i | −0.761366 | − | 1.31872i | −0.942146 | − | 0.335201i | \(-0.891196\pi\) |
0.180780 | − | 0.983524i | \(-0.442138\pi\) | |||||||
\(68\) | −6.83083 | −0.828360 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.70831 | − | 4.69093i | 0.316984 | − | 0.549032i | −0.662874 | − | 0.748731i | \(-0.730663\pi\) |
0.979857 | + | 0.199700i | \(0.0639967\pi\) | |||||||
\(74\) | −7.46410 | −0.867684 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.19067 | − | 3.79435i | 0.251287 | − | 0.435242i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.46410 | + | 7.73205i | −0.502251 | + | 0.869924i | 0.497746 | + | 0.867323i | \(0.334161\pi\) |
−0.999997 | + | 0.00260080i | \(0.999172\pi\) | |||||||
\(80\) | 0.517638 | − | 0.896575i | 0.0578737 | − | 0.100240i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.31199 | − | 7.46859i | −0.476180 | − | 0.824768i | ||||
\(83\) | −3.29530 | − | 5.70762i | −0.361706 | − | 0.626493i | 0.626536 | − | 0.779393i | \(-0.284472\pi\) |
−0.988242 | + | 0.152900i | \(0.951139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.53590 | + | 6.12436i | −0.383522 | + | 0.664280i | ||||
\(86\) | −0.267949 | −0.0288937 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.267949 | −0.0285635 | ||||||||
\(89\) | −3.53553 | − | 6.12372i | −0.374766 | − | 0.649113i | 0.615526 | − | 0.788116i | \(-0.288944\pi\) |
−0.990292 | + | 0.139003i | \(0.955610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.73205 | + | 4.73205i | 0.284836 | + | 0.493350i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.378937 | + | 0.656339i | 0.0390844 | + | 0.0676962i | ||||
\(95\) | −2.26795 | − | 3.92820i | −0.232687 | − | 0.403025i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.07227 | − | 15.7136i | −0.921149 | − | 1.59548i | −0.797640 | − | 0.603134i | \(-0.793918\pi\) |
−0.123510 | − | 0.992343i | \(-0.539415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.96410 | + | 3.40192i | 0.196410 | + | 0.340192i | ||||
\(101\) | −4.89898 | −0.487467 | −0.243733 | − | 0.969842i | \(-0.578372\pi\) | ||||
−0.243733 | + | 0.969842i | \(0.578372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3490 | −1.21678 | −0.608391 | − | 0.793638i | \(-0.708185\pi\) | ||||
−0.608391 | + | 0.793638i | \(0.708185\pi\) | |||||||
\(104\) | −0.896575 | + | 1.55291i | −0.0879165 | + | 0.152276i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.46410 | − | 9.46410i | −0.530720 | − | 0.919235i | ||||
\(107\) | −8.69615 | − | 15.0622i | −0.840689 | − | 1.45612i | −0.889313 | − | 0.457299i | \(-0.848817\pi\) |
0.0486244 | − | 0.998817i | \(-0.484516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.46410 | + | 4.26795i | −0.236018 | + | 0.408795i | −0.959568 | − | 0.281477i | \(-0.909176\pi\) |
0.723550 | + | 0.690272i | \(0.242509\pi\) | |||||||
\(110\) | −0.138701 | + | 0.240237i | −0.0132246 | + | 0.0229057i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −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 | ||||||||
\(115\) | 5.65685 | 0.527504 | ||||||||
\(116\) | −2.00000 | + | 3.46410i | −0.185695 | + | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.27551 | 0.117420 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9282 | −0.993473 | ||||||||
\(122\) | 6.31319 | + | 10.9348i | 0.571570 | + | 0.989988i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.34607 | − | 5.79555i | 0.300486 | − | 0.520456i | ||||
\(125\) | 9.24316 | 0.826733 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4641 | 1.19475 | 0.597373 | − | 0.801964i | \(-0.296211\pi\) | ||||
0.597373 | + | 0.801964i | \(0.296211\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.928203 | + | 1.60770i | 0.0814088 | + | 0.141004i | ||||
\(131\) | 10.9348 | 0.955375 | 0.477688 | − | 0.878530i | \(-0.341475\pi\) | ||||
0.477688 | + | 0.878530i | \(0.341475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.4641 | −1.07673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.41542 | + | 5.91567i | −0.292869 | + | 0.507265i | ||||
\(137\) | −8.66025 | −0.739895 | −0.369948 | − | 0.929053i | \(-0.620624\pi\) | ||||
−0.369948 | + | 0.929053i | \(0.620624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.397520 | − | 0.688524i | 0.0337172 | − | 0.0583999i | −0.848674 | − | 0.528916i | \(-0.822599\pi\) |
0.882392 | + | 0.470516i | \(0.155932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.73205 | + | 8.19615i | −0.397105 | + | 0.687806i | ||||
\(143\) | 0.240237 | − | 0.416102i | 0.0200896 | − | 0.0347962i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.07055 | + | 3.58630i | 0.171950 | + | 0.297826i | ||||
\(146\) | −2.70831 | − | 4.69093i | −0.224141 | − | 0.388224i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.73205 | + | 6.46410i | −0.306773 | + | 0.531346i | ||||
\(149\) | −22.9282 | −1.87835 | −0.939176 | − | 0.343437i | \(-0.888409\pi\) | ||||
−0.939176 | + | 0.343437i | \(0.888409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3923 | 1.49674 | 0.748372 | − | 0.663279i | \(-0.230836\pi\) | ||||
0.748372 | + | 0.663279i | \(0.230836\pi\) | |||||||
\(152\) | −2.19067 | − | 3.79435i | −0.177687 | − | 0.307763i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.46410 | − | 6.00000i | −0.278243 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.76028 | + | 8.24504i | 0.379912 | + | 0.658026i | 0.991049 | − | 0.133498i | \(-0.0426211\pi\) |
−0.611137 | + | 0.791524i | \(0.709288\pi\) | |||||||
\(158\) | 4.46410 | + | 7.73205i | 0.355145 | + | 0.615129i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.517638 | − | 0.896575i | −0.0409229 | − | 0.0708805i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.66025 | + | 11.5359i | 0.521671 | + | 0.903561i | 0.999682 | + | 0.0252074i | \(0.00802461\pi\) |
−0.478011 | + | 0.878354i | \(0.658642\pi\) | |||||||
\(164\) | −8.62398 | −0.673420 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.59059 | −0.511529 | ||||||||
\(167\) | −0.757875 | + | 1.31268i | −0.0586461 | + | 0.101578i | −0.893858 | − | 0.448350i | \(-0.852012\pi\) |
0.835212 | + | 0.549928i | \(0.185345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.89230 | + | 8.47372i | 0.376331 | + | 0.651825i | ||||
\(170\) | 3.53590 | + | 6.12436i | 0.271191 | + | 0.469717i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.133975 | + | 0.232051i | −0.0102155 | + | 0.0176937i | ||||
\(173\) | −3.34607 | + | 5.79555i | −0.254397 | + | 0.440628i | −0.964731 | − | 0.263236i | \(-0.915210\pi\) |
0.710335 | + | 0.703864i | \(0.248544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.133975 | + | 0.232051i | −0.0100987 | + | 0.0174915i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.07107 | −0.529999 | ||||||||
\(179\) | 2.53590 | − | 4.39230i | 0.189542 | − | 0.328296i | −0.755556 | − | 0.655084i | \(-0.772633\pi\) |
0.945098 | + | 0.326788i | \(0.105966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9706 | 1.26141 | 0.630706 | − | 0.776022i | \(-0.282765\pi\) | ||||
0.630706 | + | 0.776022i | \(0.282765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.46410 | 0.402819 | ||||||||
\(185\) | 3.86370 | + | 6.69213i | 0.284065 | + | 0.492015i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.915158 | − | 1.58510i | 0.0669230 | − | 0.115914i | ||||
\(188\) | 0.757875 | 0.0552737 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.53590 | −0.329069 | ||||||||
\(191\) | 7.46410 | − | 12.9282i | 0.540083 | − | 0.935452i | −0.458815 | − | 0.888532i | \(-0.651726\pi\) |
0.998899 | − | 0.0469202i | \(-0.0149407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.52628 | − | 13.0359i | −0.541753 | − | 0.938344i | −0.998804 | − | 0.0489035i | \(-0.984427\pi\) |
0.457050 | − | 0.889441i | \(-0.348906\pi\) | |||||||
\(194\) | −18.1445 | −1.30270 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9282 | 1.20608 | 0.603042 | − | 0.797709i | \(-0.293955\pi\) | ||||
0.603042 | + | 0.797709i | \(0.293955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1440 | − | 22.7661i | 0.931755 | − | 1.61385i | 0.151435 | − | 0.988467i | \(-0.451611\pi\) |
0.780320 | − | 0.625380i | \(-0.215056\pi\) | |||||||
\(200\) | 3.92820 | 0.277766 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.44949 | + | 4.24264i | −0.172345 | + | 0.298511i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.46410 | + | 7.73205i | −0.311786 | + | 0.540030i | ||||
\(206\) | −6.17449 | + | 10.6945i | −0.430197 | + | 0.745124i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.896575 | + | 1.55291i | 0.0621663 | + | 0.107675i | ||||
\(209\) | 0.586988 | + | 1.01669i | 0.0406028 | + | 0.0703262i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.46410 | + | 16.3923i | −0.651536 | + | 1.12849i | 0.331215 | + | 0.943555i | \(0.392542\pi\) |
−0.982750 | + | 0.184937i | \(0.940792\pi\) | |||||||
\(212\) | −10.9282 | −0.750552 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.3923 | −1.18891 | ||||||||
\(215\) | 0.138701 | + | 0.240237i | 0.00945931 | + | 0.0163840i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.46410 | + | 4.26795i | 0.166890 | + | 0.289062i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.138701 | + | 0.240237i | 0.00935120 | + | 0.0161968i | ||||
\(221\) | −6.12436 | − | 10.6077i | −0.411969 | − | 0.713551i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.58630 | − | 6.21166i | −0.240157 | − | 0.415963i | 0.720602 | − | 0.693349i | \(-0.243865\pi\) |
−0.960759 | + | 0.277385i | \(0.910532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.46410 | + | 6.00000i | 0.230429 | + | 0.399114i | ||||
\(227\) | −27.6651 | −1.83620 | −0.918098 | − | 0.396352i | \(-0.870276\pi\) | ||||
−0.918098 | + | 0.396352i | \(0.870276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.480473 | −0.0317506 | −0.0158753 | − | 0.999874i | \(-0.505053\pi\) | ||||
−0.0158753 | + | 0.999874i | \(0.505053\pi\) | |||||||
\(230\) | 2.82843 | − | 4.89898i | 0.186501 | − | 0.323029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | + | 3.46410i | 0.131306 | + | 0.227429i | ||||
\(233\) | 0.0621778 | + | 0.107695i | 0.00407340 | + | 0.00705534i | 0.868055 | − | 0.496468i | \(-0.165370\pi\) |
−0.863982 | + | 0.503524i | \(0.832037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.392305 | − | 0.679492i | 0.0255911 | − | 0.0443252i | ||||
\(236\) | 0.637756 | − | 1.10463i | 0.0415144 | − | 0.0719051i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.464102 | − | 0.803848i | 0.0300202 | − | 0.0519966i | −0.850625 | − | 0.525773i | \(-0.823776\pi\) |
0.880645 | + | 0.473776i | \(0.157109\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.27603 | −0.404275 | −0.202137 | − | 0.979357i | \(-0.564789\pi\) | ||||
−0.202137 | + | 0.979357i | \(0.564789\pi\) | |||||||
\(242\) | −5.46410 | + | 9.46410i | −0.351246 | + | 0.608375i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6264 | 0.808322 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.85641 | 0.499891 | ||||||||
\(248\) | −3.34607 | − | 5.79555i | −0.212475 | − | 0.368018i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.62158 | − | 8.00481i | 0.292294 | − | 0.506269i | ||||
\(251\) | 0.795040 | 0.0501824 | 0.0250912 | − | 0.999685i | \(-0.492012\pi\) | ||||
0.0250912 | + | 0.999685i | \(0.492012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.46410 | −0.0920473 | ||||||||
\(254\) | 6.73205 | − | 11.6603i | 0.422406 | − | 0.731629i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 10.0382 | 0.626165 | 0.313083 | − | 0.949726i | \(-0.398638\pi\) | ||||
0.313083 | + | 0.949726i | \(0.398638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.85641 | 0.115129 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.46739 | − | 9.46979i | 0.337776 | − | 0.585046i | ||||
\(263\) | 8.53590 | 0.526346 | 0.263173 | − | 0.964749i | \(-0.415231\pi\) | ||||
0.263173 | + | 0.964749i | \(0.415231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | + | 9.79796i | −0.347498 | + | 0.601884i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.23205 | + | 10.7942i | −0.380683 | + | 0.659362i | ||||
\(269\) | 2.82843 | − | 4.89898i | 0.172452 | − | 0.298696i | −0.766824 | − | 0.641857i | \(-0.778164\pi\) |
0.939277 | + | 0.343161i | \(0.111498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.55343 | + | 11.3509i | 0.398093 | + | 0.689516i | 0.993491 | − | 0.113914i | \(-0.0363390\pi\) |
−0.595398 | + | 0.803431i | \(0.703006\pi\) | |||||||
\(272\) | 3.41542 | + | 5.91567i | 0.207090 | + | 0.358690i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.33013 | + | 7.50000i | −0.261593 | + | 0.453092i | ||||
\(275\) | −1.05256 | −0.0634717 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.4641 | 1.89049 | 0.945247 | − | 0.326355i | \(-0.105820\pi\) | ||||
0.945247 | + | 0.326355i | \(0.105820\pi\) | |||||||
\(278\) | −0.397520 | − | 0.688524i | −0.0238417 | − | 0.0412949i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.92820 | + | 15.4641i | 0.532612 | + | 0.922511i | 0.999275 | + | 0.0380757i | \(0.0121228\pi\) |
−0.466663 | + | 0.884435i | \(0.654544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.53794 | − | 13.0561i | −0.448084 | − | 0.776104i | 0.550177 | − | 0.835048i | \(-0.314560\pi\) |
−0.998261 | + | 0.0589437i | \(0.981227\pi\) | |||||||
\(284\) | 4.73205 | + | 8.19615i | 0.280796 | + | 0.486352i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.240237 | − | 0.416102i | −0.0142055 | − | 0.0246046i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8301 | − | 25.6865i | −0.872360 | − | 1.51097i | ||||
\(290\) | 4.14110 | 0.243174 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.41662 | −0.316984 | ||||||||
\(293\) | 4.62158 | − | 8.00481i | 0.269995 | − | 0.467646i | −0.698865 | − | 0.715254i | \(-0.746311\pi\) |
0.968860 | + | 0.247608i | \(0.0796445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.660254 | − | 1.14359i | −0.0384415 | − | 0.0665826i | ||||
\(296\) | 3.73205 | + | 6.46410i | 0.216921 | + | 0.375718i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.4641 | + | 19.8564i | −0.664098 | + | 1.15025i | ||||
\(299\) | −4.89898 | + | 8.48528i | −0.283315 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.19615 | − | 15.9282i | 0.529179 | − | 0.916565i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.38134 | −0.251287 | ||||||||
\(305\) | 6.53590 | − | 11.3205i | 0.374244 | − | 0.648210i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.17398 | −0.0670024 | −0.0335012 | − | 0.999439i | \(-0.510666\pi\) | ||||
−0.0335012 | + | 0.999439i | \(0.510666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.92820 | −0.393496 | ||||||||
\(311\) | 3.72500 | + | 6.45189i | 0.211226 | + | 0.365853i | 0.952098 | − | 0.305792i | \(-0.0989212\pi\) |
−0.740873 | + | 0.671645i | \(0.765588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.13801 | − | 5.43520i | 0.177371 | − | 0.307216i | −0.763608 | − | 0.645680i | \(-0.776574\pi\) |
0.940979 | + | 0.338464i | \(0.109907\pi\) | |||||||
\(314\) | 9.52056 | 0.537276 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.92820 | 0.502251 | ||||||||
\(317\) | −13.0000 | + | 22.5167i | −0.730153 | + | 1.26466i | 0.226665 | + | 0.973973i | \(0.427218\pi\) |
−0.956818 | + | 0.290689i | \(0.906116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.535898 | − | 0.928203i | −0.0300045 | − | 0.0519694i | ||||
\(320\) | −1.03528 | −0.0578737 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.9282 | 1.66525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.52193 | + | 6.10016i | −0.195362 | + | 0.338376i | ||||
\(326\) | 13.3205 | 0.737755 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.31199 | + | 7.46859i | −0.238090 | + | 0.412384i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.73205 | − | 9.92820i | 0.315062 | − | 0.545703i | −0.664389 | − | 0.747387i | \(-0.731308\pi\) |
0.979451 | + | 0.201684i | \(0.0646413\pi\) | |||||||
\(332\) | −3.29530 | + | 5.70762i | −0.180853 | + | 0.313246i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.757875 | + | 1.31268i | 0.0414691 | + | 0.0718265i | ||||
\(335\) | 6.45189 | + | 11.1750i | 0.352505 | + | 0.610556i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50000 | − | 6.06218i | 0.190657 | − | 0.330228i | −0.754811 | − | 0.655942i | \(-0.772271\pi\) |
0.945468 | + | 0.325714i | \(0.105605\pi\) | |||||||
\(338\) | 9.78461 | 0.532213 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.07180 | 0.383522 | ||||||||
\(341\) | 0.896575 | + | 1.55291i | 0.0485523 | + | 0.0840950i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.133975 | + | 0.232051i | 0.00722343 | + | 0.0125113i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.34607 | + | 5.79555i | 0.179886 | + | 0.311571i | ||||
\(347\) | −4.79423 | − | 8.30385i | −0.257368 | − | 0.445774i | 0.708168 | − | 0.706044i | \(-0.249522\pi\) |
−0.965536 | + | 0.260270i | \(0.916188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00240 | − | 6.93237i | −0.214244 | − | 0.371081i | 0.738795 | − | 0.673931i | \(-0.235395\pi\) |
−0.953038 | + | 0.302850i | \(0.902062\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.133975 | + | 0.232051i | 0.00714087 | + | 0.0123683i | ||||
\(353\) | 25.0125 | 1.33128 | 0.665641 | − | 0.746272i | \(-0.268158\pi\) | ||||
0.665641 | + | 0.746272i | \(0.268158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.79796 | 0.520022 | ||||||||
\(356\) | −3.53553 | + | 6.12372i | −0.187383 | + | 0.324557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.53590 | − | 4.39230i | −0.134026 | − | 0.232141i | ||||
\(359\) | 3.73205 | + | 6.46410i | 0.196970 | + | 0.341162i | 0.947545 | − | 0.319624i | \(-0.103556\pi\) |
−0.750574 | + | 0.660786i | \(0.770223\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0980762 | + | 0.169873i | −0.00516191 | + | 0.00894068i | ||||
\(362\) | 8.48528 | − | 14.6969i | 0.445976 | − | 0.772454i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.80385 | + | 4.85641i | −0.146760 | + | 0.254196i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5606 | −0.968858 | −0.484429 | − | 0.874831i | \(-0.660973\pi\) | ||||
−0.484429 | + | 0.874831i | \(0.660973\pi\) | |||||||
\(368\) | 2.73205 | − | 4.73205i | 0.142418 | − | 0.246675i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.72741 | 0.401729 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7846 | −0.558406 | −0.279203 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279203 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(374\) | −0.915158 | − | 1.58510i | −0.0473217 | − | 0.0819636i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.378937 | − | 0.656339i | 0.0195422 | − | 0.0338481i | ||||
\(377\) | −7.17260 | −0.369408 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5885 | 0.697992 | 0.348996 | − | 0.937124i | \(-0.386523\pi\) | ||||
0.348996 | + | 0.937124i | \(0.386523\pi\) | |||||||
\(380\) | −2.26795 | + | 3.92820i | −0.116343 | + | 0.201513i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.46410 | − | 12.9282i | −0.381897 | − | 0.661464i | ||||
\(383\) | 27.3233 | 1.39616 | 0.698078 | − | 0.716021i | \(-0.254039\pi\) | ||||
0.698078 | + | 0.716021i | \(0.254039\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.0526 | −0.766155 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.07227 | + | 15.7136i | −0.460575 | + | 0.797739i | ||||
\(389\) | −8.00000 | −0.405616 | −0.202808 | − | 0.979219i | \(-0.565007\pi\) | ||||
−0.202808 | + | 0.979219i | \(0.565007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.6622 | + | 32.3238i | −0.943787 | + | 1.63469i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.46410 | − | 14.6603i | 0.426415 | − | 0.738573i | ||||
\(395\) | 4.62158 | − | 8.00481i | 0.232537 | − | 0.402766i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.55343 | + | 11.3509i | 0.328907 | + | 0.569684i | 0.982295 | − | 0.187339i | \(-0.0599863\pi\) |
−0.653388 | + | 0.757023i | \(0.726653\pi\) | |||||||
\(398\) | −13.1440 | − | 22.7661i | −0.658850 | − | 1.14116i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.96410 | − | 3.40192i | 0.0982051 | − | 0.170096i | ||||
\(401\) | 23.7846 | 1.18775 | 0.593873 | − | 0.804559i | \(-0.297598\pi\) | ||||
0.593873 | + | 0.804559i | \(0.297598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | 0.597763 | ||||||||
\(404\) | 2.44949 | + | 4.24264i | 0.121867 | + | 0.211079i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00000 | − | 1.73205i | −0.0495682 | − | 0.0858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.24144 | + | 3.88229i | 0.110832 | + | 0.191967i | 0.916106 | − | 0.400936i | \(-0.131315\pi\) |
−0.805274 | + | 0.592903i | \(0.797982\pi\) | |||||||
\(410\) | 4.46410 | + | 7.73205i | 0.220466 | + | 0.381859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.17449 | + | 10.6945i | 0.304195 | + | 0.526882i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.41154 | + | 5.90897i | 0.167466 | + | 0.290060i | ||||
\(416\) | 1.79315 | 0.0879165 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.17398 | 0.0574211 | ||||||||
\(419\) | −18.0938 | + | 31.3393i | −0.883939 | + | 1.53103i | −0.0370132 | + | 0.999315i | \(0.511784\pi\) |
−0.846925 | + | 0.531712i | \(0.821549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.80385 | − | 6.58846i | −0.185388 | − | 0.321102i | 0.758319 | − | 0.651884i | \(-0.226021\pi\) |
−0.943707 | + | 0.330782i | \(0.892688\pi\) | |||||||
\(422\) | 9.46410 | + | 16.3923i | 0.460705 | + | 0.797965i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.46410 | + | 9.46410i | −0.265360 | + | 0.459617i | ||||
\(425\) | −13.4164 | + | 23.2380i | −0.650793 | + | 1.12721i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.69615 | + | 15.0622i | −0.420344 | + | 0.728058i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.277401 | 0.0133775 | ||||||||
\(431\) | −5.07180 | + | 8.78461i | −0.244300 | + | 0.423140i | −0.961935 | − | 0.273280i | \(-0.911891\pi\) |
0.717635 | + | 0.696420i | \(0.245225\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8362 | 0.953265 | 0.476632 | − | 0.879103i | \(-0.341857\pi\) | ||||
0.476632 | + | 0.879103i | \(0.341857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.92820 | 0.236018 | ||||||||
\(437\) | −11.9700 | − | 20.7327i | −0.572605 | − | 0.991781i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.79796 | − | 16.9706i | 0.467631 | − | 0.809961i | −0.531685 | − | 0.846942i | \(-0.678441\pi\) |
0.999316 | + | 0.0369815i | \(0.0117743\pi\) | |||||||
\(440\) | 0.277401 | 0.0132246 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.2487 | −0.582612 | ||||||||
\(443\) | 8.16025 | − | 14.1340i | 0.387705 | − | 0.671525i | −0.604435 | − | 0.796654i | \(-0.706601\pi\) |
0.992140 | + | 0.125129i | \(0.0399345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.66025 | + | 6.33975i | 0.173513 | + | 0.300533i | ||||
\(446\) | −7.17260 | −0.339633 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.7846 | −1.12247 | −0.561233 | − | 0.827658i | \(-0.689673\pi\) | ||||
−0.561233 | + | 0.827658i | \(0.689673\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15539 | − | 2.00120i | 0.0544054 | − | 0.0942329i | ||||
\(452\) | 6.92820 | 0.325875 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.8325 | + | 23.9587i | −0.649194 | + | 1.12444i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5263 | − | 26.8923i | 0.726289 | − | 1.25797i | −0.232153 | − | 0.972679i | \(-0.574577\pi\) |
0.958441 | − | 0.285290i | \(-0.0920898\pi\) | |||||||
\(458\) | −0.240237 | + | 0.416102i | −0.0112255 | + | 0.0194432i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.82843 | − | 4.89898i | −0.131876 | − | 0.228416i | ||||
\(461\) | 5.51815 | + | 9.55772i | 0.257006 | + | 0.445148i | 0.965438 | − | 0.260631i | \(-0.0839306\pi\) |
−0.708432 | + | 0.705779i | \(0.750597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3205 | − | 26.5359i | 0.712004 | − | 1.23323i | −0.252099 | − | 0.967701i | \(-0.581121\pi\) |
0.964104 | − | 0.265526i | \(-0.0855457\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.124356 | 0.00576066 | ||||||||
\(467\) | −4.58939 | − | 7.94906i | −0.212372 | − | 0.367839i | 0.740085 | − | 0.672514i | \(-0.234785\pi\) |
−0.952456 | + | 0.304675i | \(0.901452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.392305 | − | 0.679492i | −0.0180957 | − | 0.0313426i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.637756 | − | 1.10463i | −0.0293551 | − | 0.0508446i | ||||
\(473\) | −0.0358984 | − | 0.0621778i | −0.00165061 | − | 0.00285894i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.60540 | − | 14.9050i | −0.394843 | − | 0.683888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.464102 | − | 0.803848i | −0.0212275 | − | 0.0367671i | ||||
\(479\) | −4.14110 | −0.189212 | −0.0946060 | − | 0.995515i | \(-0.530159\pi\) | ||||
−0.0946060 | + | 0.995515i | \(0.530159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3843 | −0.610270 | ||||||||
\(482\) | −3.13801 | + | 5.43520i | −0.142933 | + | 0.247567i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.46410 | + | 9.46410i | 0.248368 | + | 0.430186i | ||||
\(485\) | 9.39230 | + | 16.2679i | 0.426483 | + | 0.738690i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.39230 | − | 2.41154i | 0.0630914 | − | 0.109277i | −0.832754 | − | 0.553643i | \(-0.813237\pi\) |
0.895846 | + | 0.444365i | \(0.146571\pi\) | |||||||
\(488\) | 6.31319 | − | 10.9348i | 0.285785 | − | 0.494994i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.69615 | − | 16.7942i | 0.437581 | − | 0.757913i | −0.559921 | − | 0.828546i | \(-0.689169\pi\) |
0.997502 | + | 0.0706330i | \(0.0225019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.3233 | −1.23058 | ||||||||
\(494\) | 3.92820 | − | 6.80385i | 0.176738 | − | 0.306120i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.69213 | −0.300486 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3923 | 1.49484 | 0.747422 | − | 0.664349i | \(-0.231291\pi\) | ||||
0.747422 | + | 0.664349i | \(0.231291\pi\) | |||||||
\(500\) | −4.62158 | − | 8.00481i | −0.206683 | − | 0.357986i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.397520 | − | 0.688524i | 0.0177422 | − | 0.0307303i | ||||
\(503\) | −12.3490 | −0.550614 | −0.275307 | − | 0.961356i | \(-0.588780\pi\) | ||||
−0.275307 | + | 0.961356i | \(0.588780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.07180 | 0.225692 | ||||||||
\(506\) | −0.732051 | + | 1.26795i | −0.0325436 | + | 0.0563672i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.73205 | − | 11.6603i | −0.298686 | − | 0.517340i | ||||
\(509\) | 21.5921 | 0.957055 | 0.478527 | − | 0.878073i | \(-0.341171\pi\) | ||||
0.478527 | + | 0.878073i | \(0.341171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.01910 | − | 8.69333i | 0.221383 | − | 0.383446i | ||||
\(515\) | 12.7846 | 0.563357 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.101536 | + | 0.175865i | −0.00446555 | + | 0.00773455i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.928203 | − | 1.60770i | 0.0407044 | − | 0.0705021i | ||||
\(521\) | 16.8876 | − | 29.2502i | 0.739860 | − | 1.28147i | −0.212699 | − | 0.977118i | \(-0.568225\pi\) |
0.952558 | − | 0.304357i | \(-0.0984414\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3664 | + | 17.9551i | 0.453289 | + | 0.785120i | 0.998588 | − | 0.0531215i | \(-0.0169170\pi\) |
−0.545299 | + | 0.838242i | \(0.683584\pi\) | |||||||
\(524\) | −5.46739 | − | 9.46979i | −0.238844 | − | 0.413690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.26795 | − | 7.39230i | 0.186091 | − | 0.322320i | ||||
\(527\) | 45.7128 | 1.99128 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | 5.65685 | + | 9.79796i | 0.245718 | + | 0.425596i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.73205 | − | 13.3923i | −0.334912 | − | 0.580085i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00292 | + | 15.5935i | 0.389230 | + | 0.674166i | ||||
\(536\) | 6.23205 | + | 10.7942i | 0.269184 | + | 0.466240i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.82843 | − | 4.89898i | −0.121942 | − | 0.211210i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.66025 | − | 13.2679i | −0.329340 | − | 0.570434i | 0.653041 | − | 0.757323i | \(-0.273493\pi\) |
−0.982381 | + | 0.186889i | \(0.940160\pi\) | |||||||
\(542\) | 13.1069 | 0.562988 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.83083 | 0.292869 | ||||||||
\(545\) | 2.55103 | − | 4.41851i | 0.109274 | − | 0.189268i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1865 | − | 29.7679i | −0.734843 | − | 1.27279i | −0.954792 | − | 0.297274i | \(-0.903922\pi\) |
0.219949 | − | 0.975511i | \(-0.429411\pi\) | |||||||
\(548\) | 4.33013 | + | 7.50000i | 0.184974 | + | 0.320384i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.526279 | + | 0.911543i | −0.0224406 | + | 0.0388683i | ||||
\(551\) | 8.76268 | − | 15.1774i | 0.373303 | − | 0.646579i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.7321 | − | 27.2487i | 0.668391 | − | 1.15769i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.795040 | −0.0337172 | ||||||||
\(557\) | −3.46410 | + | 6.00000i | −0.146779 | + | 0.254228i | −0.930035 | − | 0.367471i | \(-0.880224\pi\) |
0.783256 | + | 0.621699i | \(0.213557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.480473 | −0.0203219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.8564 | 0.753227 | ||||||||
\(563\) | 9.12304 | + | 15.8016i | 0.384490 | + | 0.665957i | 0.991698 | − | 0.128586i | \(-0.0410439\pi\) |
−0.607208 | + | 0.794543i | \(0.707711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.58630 | − | 6.21166i | 0.150877 | − | 0.261326i | ||||
\(566\) | −15.0759 | −0.633686 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46410 | 0.397105 | ||||||||
\(569\) | −12.8923 | + | 22.3301i | −0.540474 | + | 0.936128i | 0.458403 | + | 0.888744i | \(0.348422\pi\) |
−0.998877 | + | 0.0473833i | \(0.984912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5263 | + | 28.6244i | 0.691603 | + | 1.19789i | 0.971312 | + | 0.237807i | \(0.0764286\pi\) |
−0.279709 | + | 0.960085i | \(0.590238\pi\) | |||||||
\(572\) | −0.480473 | −0.0200896 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.4641 | 0.895115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7446 | + | 23.8064i | −0.572196 | + | 0.991072i | 0.424144 | + | 0.905595i | \(0.360575\pi\) |
−0.996340 | + | 0.0854776i | \(0.972758\pi\) | |||||||
\(578\) | −29.6603 | −1.23370 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.07055 | − | 3.58630i | 0.0859750 | − | 0.148913i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.46410 | − | 2.53590i | 0.0606369 | − | 0.105026i | ||||
\(584\) | −2.70831 | + | 4.69093i | −0.112071 | + | 0.194112i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.62158 | − | 8.00481i | −0.190916 | − | 0.330676i | ||||
\(587\) | 20.9408 | + | 36.2705i | 0.864319 | + | 1.49704i | 0.867722 | + | 0.497049i | \(0.165583\pi\) |
−0.00340370 | + | 0.999994i | \(0.501083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.6603 | + | 25.3923i | −0.604065 | + | 1.04627i | ||||
\(590\) | −1.32051 | −0.0543645 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.46410 | 0.306773 | ||||||||
\(593\) | −8.43451 | − | 14.6090i | −0.346364 | − | 0.599920i | 0.639237 | − | 0.769010i | \(-0.279250\pi\) |
−0.985601 | + | 0.169090i | \(0.945917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.4641 | + | 19.8564i | 0.469588 | + | 0.813350i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.89898 | + | 8.48528i | 0.200334 | + | 0.346989i | ||||
\(599\) | 2.39230 | + | 4.14359i | 0.0977469 | + | 0.169303i | 0.910752 | − | 0.412954i | \(-0.135503\pi\) |
−0.813005 | + | 0.582257i | \(0.802170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.67303 | − | 2.89778i | −0.0682444 | − | 0.118203i | 0.829884 | − | 0.557936i | \(-0.188406\pi\) |
−0.898129 | + | 0.439733i | \(0.855073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.19615 | − | 15.9282i | −0.374186 | − | 0.648109i | ||||
\(605\) | 11.3137 | 0.459968 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.27362 | 0.0922836 | 0.0461418 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461418 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(608\) | −2.19067 | + | 3.79435i | −0.0888434 | + | 0.153881i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.53590 | − | 11.3205i | −0.264631 | − | 0.458354i | ||||
\(611\) | 0.679492 | + | 1.17691i | 0.0274893 | + | 0.0476129i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4641 | + | 21.5885i | −0.503420 | + | 0.871950i | 0.496572 | + | 0.867996i | \(0.334592\pi\) |
−0.999992 | + | 0.00395396i | \(0.998741\pi\) | |||||||
\(614\) | −0.586988 | + | 1.01669i | −0.0236889 | + | 0.0410304i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.57180 | + | 2.72243i | −0.0632782 | + | 0.109601i | −0.895929 | − | 0.444197i | \(-0.853489\pi\) |
0.832651 | + | 0.553798i | \(0.186822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7047 | 1.27432 | 0.637159 | − | 0.770732i | \(-0.280109\pi\) | ||||
0.637159 | + | 0.770732i | \(0.280109\pi\) | |||||||
\(620\) | −3.46410 | + | 6.00000i | −0.139122 | + | 0.240966i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.45001 | 0.298718 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | −3.13801 | − | 5.43520i | −0.125420 | − | 0.217234i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.76028 | − | 8.24504i | 0.189956 | − | 0.329013i | ||||
\(629\) | −50.9860 | −2.03295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7128 | −0.784755 | −0.392377 | − | 0.919804i | \(-0.628347\pi\) | ||||
−0.392377 | + | 0.919804i | \(0.628347\pi\) | |||||||
\(632\) | 4.46410 | − | 7.73205i | 0.177572 | − | 0.307564i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.0000 | + | 22.5167i | 0.516296 | + | 0.894251i | ||||
\(635\) | −13.9391 | −0.553155 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.07180 | −0.0424328 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.517638 | + | 0.896575i | −0.0204614 | + | 0.0354403i | ||||
\(641\) | −4.07180 | −0.160826 | −0.0804132 | − | 0.996762i | \(-0.525624\pi\) | ||||
−0.0804132 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.4565 | + | 38.8959i | −0.885599 | + | 1.53390i | −0.0405737 | + | 0.999177i | \(0.512919\pi\) |
−0.845025 | + | 0.534726i | \(0.820415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.9641 | − | 25.9186i | 0.588755 | − | 1.01975i | ||||
\(647\) | −10.9348 | + | 18.9396i | −0.429890 | + | 0.744592i | −0.996863 | − | 0.0791447i | \(-0.974781\pi\) |
0.566973 | + | 0.823736i | \(0.308114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.170886 | + | 0.295984i | 0.00670787 | + | 0.0116184i | ||||
\(650\) | 3.52193 | + | 6.10016i | 0.138141 | + | 0.239268i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.66025 | − | 11.5359i | 0.260836 | − | 0.451781i | ||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.3205 | −0.442329 | ||||||||
\(656\) | 4.31199 | + | 7.46859i | 0.168355 | + | 0.291599i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.1244 | − | 41.7846i | −0.939751 | − | 1.62770i | −0.765934 | − | 0.642919i | \(-0.777723\pi\) |
−0.173818 | − | 0.984778i | \(-0.555610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | −5.73205 | − | 9.92820i | −0.222782 | − | 0.385871i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.29530 | + | 5.70762i | 0.127882 | + | 0.221499i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9282 | + | 18.9282i | 0.423142 | + | 0.732903i | ||||
\(668\) | 1.51575 | 0.0586461 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.9038 | 0.498517 | ||||||||
\(671\) | −1.69161 | + | 2.92996i | −0.0653041 | + | 0.113110i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.7846 | − | 36.0000i | −0.801188 | − | 1.38770i | −0.918835 | − | 0.394643i | \(-0.870868\pi\) |
0.117647 | − | 0.993055i | \(-0.462465\pi\) | |||||||
\(674\) | −3.50000 | − | 6.06218i | −0.134815 | − | 0.233506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.89230 | − | 8.47372i | 0.188166 | − | 0.325912i | ||||
\(677\) | 2.68973 | − | 4.65874i | 0.103375 | − | 0.179050i | −0.809698 | − | 0.586846i | \(-0.800369\pi\) |
0.913073 | + | 0.407796i | \(0.133703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.53590 | − | 6.12436i | 0.135596 | − | 0.234858i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.79315 | 0.0686633 | ||||||||
\(683\) | −19.1603 | + | 33.1865i | −0.733147 | + | 1.26985i | 0.222385 | + | 0.974959i | \(0.428616\pi\) |
−0.955532 | + | 0.294888i | \(0.904718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.96575 | 0.342564 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.267949 | 0.0102155 | ||||||||
\(689\) | −9.79796 | − | 16.9706i | −0.373273 | − | 0.646527i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1595 | − | 21.0609i | 0.462570 | − | 0.801194i | −0.536518 | − | 0.843889i | \(-0.680261\pi\) |
0.999088 | + | 0.0426942i | \(0.0135941\pi\) | |||||||
\(692\) | 6.69213 | 0.254397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.58846 | −0.363973 | ||||||||
\(695\) | −0.411543 | + | 0.712813i | −0.0156107 | + | 0.0270385i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.4545 | − | 51.0167i | −1.11567 | − | 1.93239i | ||||
\(698\) | −8.00481 | −0.302986 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3514 | − | 28.3214i | 0.616704 | − | 1.06816i | ||||
\(704\) | 0.267949 | 0.0100987 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5063 | − | 21.6615i | 0.470680 | − | 0.815241i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.19615 | − | 10.7321i | 0.232701 | − | 0.403051i | −0.725901 | − | 0.687799i | \(-0.758577\pi\) |
0.958602 | + | 0.284749i | \(0.0919102\pi\) | |||||||
\(710\) | 4.89898 | − | 8.48528i | 0.183855 | − | 0.318447i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.53553 | + | 6.12372i | 0.132500 | + | 0.229496i | ||||
\(713\) | −18.2832 | − | 31.6675i | −0.684713 | − | 1.18596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.248711 | + | 0.430781i | −0.00930128 | + | 0.0161103i | ||||
\(716\) | −5.07180 | −0.189542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.46410 | 0.278558 | ||||||||
\(719\) | 24.8367 | + | 43.0184i | 0.926251 | + | 1.60431i | 0.789536 | + | 0.613704i | \(0.210321\pi\) |
0.136716 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.0980762 | + | 0.169873i | 0.00365002 | + | 0.00632202i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.48528 | − | 14.6969i | −0.315353 | − | 0.546207i | ||||
\(725\) | 7.85641 | + | 13.6077i | 0.291780 | + | 0.505377i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3514 | + | 28.3214i | 0.606439 | + | 1.05038i | 0.991822 | + | 0.127627i | \(0.0407361\pi\) |
−0.385383 | + | 0.922757i | \(0.625931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.80385 | + | 4.85641i | 0.103775 | + | 0.179744i | ||||
\(731\) | −1.83032 | −0.0676967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.00481 | −0.295664 | −0.147832 | − | 0.989012i | \(-0.547230\pi\) | ||||
−0.147832 | + | 0.989012i | \(0.547230\pi\) | |||||||
\(734\) | −9.28032 | + | 16.0740i | −0.342543 | + | 0.593302i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.73205 | − | 4.73205i | −0.100705 | − | 0.174426i | ||||
\(737\) | −1.66987 | − | 2.89230i | −0.0615106 | − | 0.106539i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.06218 | + | 5.30385i | −0.112644 | + | 0.195105i | −0.916836 | − | 0.399265i | \(-0.869265\pi\) |
0.804191 | + | 0.594370i | \(0.202599\pi\) | |||||||
\(740\) | 3.86370 | − | 6.69213i | 0.142033 | − | 0.246008i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7846 | + | 27.3397i | −0.579081 | + | 1.00300i | 0.416504 | + | 0.909134i | \(0.363255\pi\) |
−0.995585 | + | 0.0938641i | \(0.970078\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.7370 | 0.869657 | ||||||||
\(746\) | −5.39230 | + | 9.33975i | −0.197426 | + | 0.341952i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.83032 | −0.0669230 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.7846 | 1.26931 | 0.634654 | − | 0.772796i | \(-0.281143\pi\) | ||||
0.634654 | + | 0.772796i | \(0.281143\pi\) | |||||||
\(752\) | −0.378937 | − | 0.656339i | −0.0138184 | − | 0.0239342i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.58630 | + | 6.21166i | −0.130605 | + | 0.226215i | ||||
\(755\) | −19.0411 | −0.692977 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3205 | 0.702216 | 0.351108 | − | 0.936335i | \(-0.385805\pi\) | ||||
0.351108 | + | 0.936335i | \(0.385805\pi\) | |||||||
\(758\) | 6.79423 | − | 11.7679i | 0.246777 | − | 0.427431i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.26795 | + | 3.92820i | 0.0822672 | + | 0.142491i | ||||
\(761\) | −40.2543 | −1.45922 | −0.729609 | − | 0.683865i | \(-0.760298\pi\) | ||||
−0.729609 | + | 0.683865i | \(0.760298\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.9282 | −0.540083 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6617 | − | 23.6627i | 0.493616 | − | 0.854968i | ||||
\(767\) | 2.28719 | 0.0825855 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0919 | − | 33.0681i | 0.688471 | − | 1.19247i | −0.283862 | − | 0.958865i | \(-0.591616\pi\) |
0.972332 | − | 0.233601i | \(-0.0750511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.52628 | + | 13.0359i | −0.270877 | + | 0.469172i | ||||
\(773\) | −19.6975 | + | 34.1170i | −0.708468 | + | 1.22710i | 0.256957 | + | 0.966423i | \(0.417280\pi\) |
−0.965425 | + | 0.260680i | \(0.916053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.1440 | − | 22.7661i | −0.472147 | − | 0.817783i | ||||
\(776\) | 9.07227 | + | 15.7136i | 0.325676 | + | 0.564087i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.00000 | + | 6.92820i | −0.143407 | + | 0.248388i | ||||
\(779\) | 37.7846 | 1.35377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.53590 | −0.0907416 | ||||||||
\(782\) | 18.6622 | + | 32.3238i | 0.667358 | + | 1.15590i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.92820 | − | 8.53590i | −0.175895 | − | 0.304659i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.57270 | + | 6.18810i | 0.127353 | + | 0.220582i | 0.922650 | − | 0.385638i | \(-0.126019\pi\) |
−0.795297 | + | 0.606220i | \(0.792685\pi\) | |||||||
\(788\) | −8.46410 | − | 14.6603i | −0.301521 | − | 0.522250i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.62158 | − | 8.00481i | −0.164428 | − | 0.284798i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3205 | + | 19.6077i | 0.402003 | + | 0.696290i | ||||
\(794\) | 13.1069 | 0.465145 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.2880 | −0.931755 | ||||||||
\(797\) | 18.9396 | − | 32.8043i | 0.670874 | − | 1.16199i | −0.306782 | − | 0.951780i | \(-0.599252\pi\) |
0.977657 | − | 0.210209i | \(-0.0674143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.58846 | + | 4.48334i | 0.0915730 | + | 0.158609i | ||||
\(800\) | −1.96410 | − | 3.40192i | −0.0694415 | − | 0.120276i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.8923 | − | 20.5981i | 0.419932 | − | 0.727343i | ||||
\(803\) | 0.725689 | − | 1.25693i | 0.0256090 | − | 0.0443561i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00000 | − | 10.3923i | 0.211341 | − | 0.366053i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.89898 | 0.172345 | ||||||||
\(809\) | −14.8660 | + | 25.7487i | −0.522662 | + | 0.905276i | 0.476991 | + | 0.878908i | \(0.341728\pi\) |
−0.999652 | + | 0.0263681i | \(0.991606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9110 | 0.874744 | 0.437372 | − | 0.899281i | \(-0.355909\pi\) | ||||
0.437372 | + | 0.899281i | \(0.355909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | −6.89520 | − | 11.9428i | −0.241528 | − | 0.418339i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.586988 | − | 1.01669i | 0.0205361 | − | 0.0355696i | ||||
\(818\) | 4.48288 | 0.156740 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.92820 | 0.311786 | ||||||||
\(821\) | 5.19615 | − | 9.00000i | 0.181347 | − | 0.314102i | −0.760993 | − | 0.648761i | \(-0.775288\pi\) |
0.942339 | + | 0.334659i | \(0.108621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.39230 | + | 9.33975i | 0.187964 | + | 0.325563i | 0.944571 | − | 0.328306i | \(-0.106478\pi\) |
−0.756607 | + | 0.653870i | \(0.773145\pi\) | |||||||
\(824\) | 12.3490 | 0.430197 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.96524 | − | 6.86800i | 0.137718 | − | 0.238535i | −0.788914 | − | 0.614503i | \(-0.789356\pi\) |
0.926633 | + | 0.375968i | \(0.122690\pi\) | |||||||
\(830\) | 6.82309 | 0.236833 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.896575 | − | 1.55291i | 0.0310832 | − | 0.0538376i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.784610 | − | 1.35898i | 0.0271525 | − | 0.0470296i | ||||
\(836\) | 0.586988 | − | 1.01669i | 0.0203014 | − | 0.0351631i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.0938 | + | 31.3393i | 0.625039 | + | 1.08260i | ||||
\(839\) | −11.3137 | − | 19.5959i | −0.390593 | − | 0.676526i | 0.601935 | − | 0.798545i | \(-0.294397\pi\) |
−0.992528 | + | 0.122019i | \(0.961063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | −7.60770 | −0.262178 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.9282 | 0.651536 | ||||||||
\(845\) | −5.06489 | − | 8.77264i | −0.174237 | − | 0.301788i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.46410 | + | 9.46410i | 0.187638 | + | 0.324999i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.4164 | + | 23.2380i | 0.460180 | + | 0.797056i | ||||
\(851\) | 20.3923 | + | 35.3205i | 0.699039 | + | 1.21077i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4901 | + | 28.5617i | 0.564610 | + | 0.977933i | 0.997086 | + | 0.0762876i | \(0.0243067\pi\) |
−0.432476 | + | 0.901645i | \(0.642360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.69615 | + | 15.0622i | 0.297228 | + | 0.514815i | ||||
\(857\) | −11.2122 | −0.383001 | −0.191500 | − | 0.981493i | \(-0.561335\pi\) | ||||
−0.191500 | + | 0.981493i | \(0.561335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.6042 | 1.41952 | 0.709758 | − | 0.704446i | \(-0.248804\pi\) | ||||
0.709758 | + | 0.704446i | \(0.248804\pi\) | |||||||
\(860\) | 0.138701 | − | 0.240237i | 0.00472965 | − | 0.00819200i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.07180 | + | 8.78461i | 0.172746 | + | 0.299205i | ||||
\(863\) | −27.0526 | − | 46.8564i | −0.920880 | − | 1.59501i | −0.798057 | − | 0.602582i | \(-0.794139\pi\) |
−0.122823 | − | 0.992429i | \(-0.539195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.46410 | − | 6.00000i | 0.117783 | − | 0.204006i | ||||
\(866\) | 9.91808 | − | 17.1786i | 0.337030 | − | 0.583753i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.19615 | + | 2.07180i | −0.0405767 | + | 0.0702809i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.3500 | −0.757301 | ||||||||
\(872\) | 2.46410 | − | 4.26795i | 0.0834450 | − | 0.144531i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −23.9401 | −0.809786 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.1769 | −0.985234 | −0.492617 | − | 0.870246i | \(-0.663960\pi\) | ||||
−0.492617 | + | 0.870246i | \(0.663960\pi\) | |||||||
\(878\) | −9.79796 | − | 16.9706i | −0.330665 | − | 0.572729i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.138701 | − | 0.240237i | 0.00467560 | − | 0.00809838i | ||||
\(881\) | −12.7279 | −0.428815 | −0.214407 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214407 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4641 | 0.486756 | 0.243378 | − | 0.969932i | \(-0.421744\pi\) | ||||
0.243378 | + | 0.969932i | \(0.421744\pi\) | |||||||
\(884\) | −6.12436 | + | 10.6077i | −0.205984 | + | 0.356775i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.16025 | − | 14.1340i | −0.274149 | − | 0.474840i | ||||
\(887\) | 53.2596 | 1.78828 | 0.894142 | − | 0.447784i | \(-0.147787\pi\) | ||||
0.894142 | + | 0.447784i | \(0.147787\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.32051 | 0.245384 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.58630 | + | 6.21166i | −0.120078 | + | 0.207982i | ||||
\(893\) | −3.32051 | −0.111117 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.62536 | + | 4.54725i | −0.0877559 | + | 0.151998i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.8923 | + | 20.5981i | −0.396851 | + | 0.687367i | ||||
\(899\) | 13.3843 | − | 23.1822i | 0.446390 | − | 0.773170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3244 | − | 64.6477i | −1.24345 | − | 2.15373i | ||||
\(902\) | −1.15539 | − | 2.00120i | −0.0384704 | − | 0.0666327i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.46410 | − | 6.00000i | 0.115214 | − | 0.199557i | ||||
\(905\) | −17.5692 | −0.584021 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.24871 | −0.174281 | −0.0871403 | − | 0.996196i | \(-0.527773\pi\) | ||||
−0.0871403 | + | 0.996196i | \(0.527773\pi\) | |||||||
\(908\) | 13.8325 | + | 23.9587i | 0.459049 | + | 0.795097i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.5359 | − | 28.6410i | −0.547859 | − | 0.948919i | −0.998421 | − | 0.0561742i | \(-0.982110\pi\) |
0.450562 | − | 0.892745i | \(-0.351224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.882972 | − | 1.52935i | −0.0292221 | − | 0.0506142i | ||||
\(914\) | −15.5263 | − | 26.8923i | −0.513564 | − | 0.889518i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.240237 | + | 0.416102i | 0.00793764 | + | 0.0137484i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.53590 | − | 7.85641i | −0.149625 | − | 0.259159i | 0.781464 | − | 0.623951i | \(-0.214473\pi\) |
−0.931089 | + | 0.364792i | \(0.881140\pi\) | |||||||
\(920\) | −5.65685 | −0.186501 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.0363 | 0.363461 | ||||||||
\(923\) | −8.48528 | + | 14.6969i | −0.279296 | + | 0.483756i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6603 | + | 25.3923i | 0.482026 | + | 0.834894i | ||||
\(926\) | −15.3205 | − | 26.5359i | −0.503463 | − | 0.872024i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.00000 | − | 3.46410i | 0.0656532 | − | 0.113715i | ||||
\(929\) | −15.4040 | + | 26.6806i | −0.505390 | + | 0.875362i | 0.494590 | + | 0.869126i | \(0.335318\pi\) |
−0.999981 | + | 0.00623544i | \(0.998015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0621778 | − | 0.107695i | 0.00203670 | − | 0.00352767i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.17878 | −0.300339 | ||||||||
\(935\) | −0.947441 | + | 1.64102i | −0.0309846 | + | 0.0536670i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.89949 | 0.323402 | 0.161701 | − | 0.986840i | \(-0.448302\pi\) | ||||
0.161701 | + | 0.986840i | \(0.448302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.784610 | −0.0255911 | ||||||||
\(941\) | 23.9401 | + | 41.4655i | 0.780425 | + | 1.35174i | 0.931694 | + | 0.363243i | \(0.118330\pi\) |
−0.151270 | + | 0.988493i | \(0.548336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.5612 | + | 40.8091i | −0.767257 | + | 1.32893i | ||||
\(944\) | −1.27551 | −0.0415144 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0717968 | −0.00233431 | ||||||||
\(947\) | −9.06218 | + | 15.6962i | −0.294481 | + | 0.510056i | −0.974864 | − | 0.222800i | \(-0.928480\pi\) |
0.680383 | + | 0.732857i | \(0.261814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.85641 | − | 8.41154i | −0.157646 | − | 0.273050i | ||||
\(950\) | −17.2108 | −0.558392 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.0000 | −0.615470 | −0.307735 | − | 0.951472i | \(-0.599571\pi\) | ||||
−0.307735 | + | 0.951472i | \(0.599571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.72741 | + | 13.3843i | −0.250053 | + | 0.433105i | ||||
\(956\) | −0.928203 | −0.0300202 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.07055 | + | 3.58630i | −0.0668965 | + | 0.115868i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.89230 | + | 11.9378i | −0.222332 | + | 0.385091i | ||||
\(962\) | −6.69213 | + | 11.5911i | −0.215763 | + | 0.373712i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.13801 | + | 5.43520i | 0.101069 | + | 0.175056i | ||||
\(965\) | 7.79178 | + | 13.4958i | 0.250826 | + | 0.434444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7846 | − | 41.1962i | 0.764861 | − | 1.32478i | −0.175458 | − | 0.984487i | \(-0.556141\pi\) |
0.940320 | − | 0.340292i | \(-0.110526\pi\) | |||||||
\(968\) | 10.9282 | 0.351246 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.7846 | 0.603137 | ||||||||
\(971\) | −15.6443 | − | 27.0967i | −0.502049 | − | 0.869574i | −0.999997 | − | 0.00236748i | \(-0.999246\pi\) |
0.497948 | − | 0.867207i | \(-0.334087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.39230 | − | 2.41154i | −0.0446123 | − | 0.0772708i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.31319 | − | 10.9348i | −0.202080 | − | 0.350013i | ||||
\(977\) | 0.990381 | + | 1.71539i | 0.0316851 | + | 0.0548802i | 0.881433 | − | 0.472309i | \(-0.156579\pi\) |
−0.849748 | + | 0.527189i | \(0.823246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.947343 | − | 1.64085i | −0.0302772 | − | 0.0524417i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.69615 | − | 16.7942i | −0.309417 | − | 0.535925i | ||||
\(983\) | 12.6264 | 0.402719 | 0.201360 | − | 0.979517i | \(-0.435464\pi\) | ||||
0.201360 | + | 0.979517i | \(0.435464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.5254 | −0.558405 | ||||||||
\(986\) | −13.6617 | + | 23.6627i | −0.435076 | + | 0.753574i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.92820 | − | 6.80385i | −0.124973 | − | 0.216459i | ||||
\(989\) | 0.732051 | + | 1.26795i | 0.0232779 | + | 0.0403184i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1244 | + | 43.5167i | −0.798101 | + | 1.38235i | 0.122750 | + | 0.992438i | \(0.460829\pi\) |
−0.920851 | + | 0.389915i | \(0.872505\pi\) | |||||||
\(992\) | −3.34607 | + | 5.79555i | −0.106238 | + | 0.184009i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.6077 | + | 23.5692i | −0.431393 | + | 0.747194i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.6018 | 1.19086 | 0.595430 | − | 0.803407i | \(-0.296982\pi\) | ||||
0.595430 | + | 0.803407i | \(0.296982\pi\) | |||||||
\(998\) | 16.6962 | − | 28.9186i | 0.528507 | − | 0.915402i | ||||
\(999\) | 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 | 2646.2.h.t.361.2 | 8 | ||
3.2 | odd | 2 | 882.2.h.q.67.2 | 8 | |||
7.2 | even | 3 | 2646.2.e.q.1549.3 | 8 | |||
7.3 | odd | 6 | 2646.2.f.r.1765.2 | 8 | |||
7.4 | even | 3 | 2646.2.f.r.1765.3 | 8 | |||
7.5 | odd | 6 | 2646.2.e.q.1549.2 | 8 | |||
7.6 | odd | 2 | inner | 2646.2.h.t.361.3 | 8 | ||
9.2 | odd | 6 | 882.2.e.s.655.2 | 8 | |||
9.7 | even | 3 | 2646.2.e.q.2125.3 | 8 | |||
21.2 | odd | 6 | 882.2.e.s.373.2 | 8 | |||
21.5 | even | 6 | 882.2.e.s.373.3 | 8 | |||
21.11 | odd | 6 | 882.2.f.q.589.4 | yes | 8 | ||
21.17 | even | 6 | 882.2.f.q.589.1 | yes | 8 | ||
21.20 | even | 2 | 882.2.h.q.67.3 | 8 | |||
63.2 | odd | 6 | 882.2.h.q.79.1 | 8 | |||
63.4 | even | 3 | 7938.2.a.ci.1.2 | 4 | |||
63.11 | odd | 6 | 882.2.f.q.295.4 | yes | 8 | ||
63.16 | even | 3 | inner | 2646.2.h.t.667.2 | 8 | ||
63.20 | even | 6 | 882.2.e.s.655.3 | 8 | |||
63.25 | even | 3 | 2646.2.f.r.883.3 | 8 | |||
63.31 | odd | 6 | 7938.2.a.ci.1.3 | 4 | |||
63.32 | odd | 6 | 7938.2.a.cp.1.3 | 4 | |||
63.34 | odd | 6 | 2646.2.e.q.2125.2 | 8 | |||
63.38 | even | 6 | 882.2.f.q.295.1 | ✓ | 8 | ||
63.47 | even | 6 | 882.2.h.q.79.4 | 8 | |||
63.52 | odd | 6 | 2646.2.f.r.883.2 | 8 | |||
63.59 | even | 6 | 7938.2.a.cp.1.2 | 4 | |||
63.61 | odd | 6 | inner | 2646.2.h.t.667.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.s.373.2 | 8 | 21.2 | odd | 6 | |||
882.2.e.s.373.3 | 8 | 21.5 | even | 6 | |||
882.2.e.s.655.2 | 8 | 9.2 | odd | 6 | |||
882.2.e.s.655.3 | 8 | 63.20 | even | 6 | |||
882.2.f.q.295.1 | ✓ | 8 | 63.38 | even | 6 | ||
882.2.f.q.295.4 | yes | 8 | 63.11 | odd | 6 | ||
882.2.f.q.589.1 | yes | 8 | 21.17 | even | 6 | ||
882.2.f.q.589.4 | yes | 8 | 21.11 | odd | 6 | ||
882.2.h.q.67.2 | 8 | 3.2 | odd | 2 | |||
882.2.h.q.67.3 | 8 | 21.20 | even | 2 | |||
882.2.h.q.79.1 | 8 | 63.2 | odd | 6 | |||
882.2.h.q.79.4 | 8 | 63.47 | even | 6 | |||
2646.2.e.q.1549.2 | 8 | 7.5 | odd | 6 | |||
2646.2.e.q.1549.3 | 8 | 7.2 | even | 3 | |||
2646.2.e.q.2125.2 | 8 | 63.34 | odd | 6 | |||
2646.2.e.q.2125.3 | 8 | 9.7 | even | 3 | |||
2646.2.f.r.883.2 | 8 | 63.52 | odd | 6 | |||
2646.2.f.r.883.3 | 8 | 63.25 | even | 3 | |||
2646.2.f.r.1765.2 | 8 | 7.3 | odd | 6 | |||
2646.2.f.r.1765.3 | 8 | 7.4 | even | 3 | |||
2646.2.h.t.361.2 | 8 | 1.1 | even | 1 | trivial | ||
2646.2.h.t.361.3 | 8 | 7.6 | odd | 2 | inner | ||
2646.2.h.t.667.2 | 8 | 63.16 | even | 3 | inner | ||
2646.2.h.t.667.3 | 8 | 63.61 | odd | 6 | inner | ||
7938.2.a.ci.1.2 | 4 | 63.4 | even | 3 | |||
7938.2.a.ci.1.3 | 4 | 63.31 | odd | 6 | |||
7938.2.a.cp.1.2 | 4 | 63.59 | even | 6 | |||
7938.2.a.cp.1.3 | 4 | 63.32 | odd | 6 |