Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(95,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 479.7 | ||
Root | \(-0.192865 + 0.334053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.479 |
Dual form | 576.2.p.c.95.7 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 1.46399 | − | 0.925606i | 0.845232 | − | 0.534399i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.06470 | + | 3.57617i | 0.923364 | + | 1.59931i | 0.794172 | + | 0.607693i | \(0.207905\pi\) |
0.129192 | + | 0.991620i | \(0.458762\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.287429 | − | 0.165947i | −0.108638 | − | 0.0627222i | 0.444696 | − | 0.895681i | \(-0.353312\pi\) |
−0.553335 | + | 0.832959i | \(0.686645\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.28651 | − | 2.71015i | 0.428836 | − | 0.903382i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.62268 | − | 2.09155i | −1.09228 | − | 0.630627i | −0.158096 | − | 0.987424i | \(-0.550536\pi\) |
−0.934182 | + | 0.356797i | \(0.883869\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.27682 | − | 2.46922i | 1.18618 | − | 0.684839i | 0.228741 | − | 0.973487i | \(-0.426539\pi\) |
0.957435 | + | 0.288648i | \(0.0932059\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.33282 | + | 3.32436i | 1.63513 | + | 0.858347i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.20639i | 0.777664i | 0.921309 | + | 0.388832i | \(0.127121\pi\) | ||||
−0.921309 | + | 0.388832i | \(0.872879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.42029 | 1.24350 | 0.621750 | − | 0.783215i | \(-0.286422\pi\) | ||||
0.621750 | + | 0.783215i | \(0.286422\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.574394 | + | 0.0231017i | −0.125343 | + | 0.00504120i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39438 | + | 2.41514i | 0.290748 | + | 0.503591i | 0.973987 | − | 0.226604i | \(-0.0727624\pi\) |
−0.683239 | + | 0.730195i | \(0.739429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.02601 | + | 10.4374i | −1.20520 | + | 2.08747i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.625100 | − | 5.15842i | −0.120301 | − | 0.992738i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.03570 | + | 1.79388i | −0.192324 | + | 0.333115i | −0.946020 | − | 0.324108i | \(-0.894936\pi\) |
0.753696 | + | 0.657223i | \(0.228269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.60828 | + | 2.08324i | −0.648067 | + | 0.374161i | −0.787715 | − | 0.616040i | \(-0.788736\pi\) |
0.139649 | + | 0.990201i | \(0.455403\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.23950 | + | 0.291167i | −1.26024 | + | 0.0506857i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.37053i | − | 0.231662i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.21390i | 0.363963i | 0.983302 | + | 0.181982i | \(0.0582511\pi\) | ||||
−0.983302 | + | 0.181982i | \(0.941749\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.97567 | − | 7.57355i | 0.636617 | − | 1.21274i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41298 | − | 0.815784i | 0.220670 | − | 0.127404i | −0.385590 | − | 0.922670i | \(-0.626002\pi\) |
0.606261 | + | 0.795266i | \(0.292669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.99758 | − | 5.19195i | 0.457126 | − | 0.791766i | −0.541682 | − | 0.840584i | \(-0.682212\pi\) |
0.998808 | + | 0.0488181i | \(0.0155455\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.3482 | − | 0.994880i | 1.84076 | − | 0.148308i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.97567 | + | 6.88607i | −0.579912 | + | 1.00444i | 0.415577 | + | 0.909558i | \(0.363580\pi\) |
−0.995489 | + | 0.0948784i | \(0.969754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.44492 | − | 5.96678i | −0.492132 | − | 0.852397i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.96786 | + | 4.69411i | 0.415583 | + | 0.657307i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.05801 | −0.282690 | −0.141345 | − | 0.989960i | \(-0.545143\pi\) | ||||
−0.141345 | + | 0.989960i | \(0.545143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 17.2738i | − | 2.32919i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.93523 | − | 5.01706i | 1.05105 | − | 0.664525i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.40497 | − | 3.12056i | 0.703667 | − | 0.406262i | −0.105045 | − | 0.994467i | \(-0.533499\pi\) |
0.808712 | + | 0.588205i | \(0.200165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.10709 | − | 5.25798i | −1.16604 | − | 0.673216i | −0.213299 | − | 0.976987i | \(-0.568421\pi\) |
−0.952745 | + | 0.303771i | \(0.901754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.819522 | + | 0.565483i | −0.103250 | + | 0.0712442i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.6607 | + | 10.1964i | 2.19054 | + | 1.26471i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.83658 | − | 10.1093i | −0.713052 | − | 1.23504i | −0.963706 | − | 0.266965i | \(-0.913979\pi\) |
0.250655 | − | 0.968077i | \(-0.419354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.27682 | + | 2.24508i | 0.514868 | + | 0.270276i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.66299 | −0.909429 | −0.454715 | − | 0.890637i | \(-0.650259\pi\) | ||||
−0.454715 | + | 0.890637i | \(0.650259\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.21742 | −0.727695 | −0.363847 | − | 0.931459i | \(-0.618537\pi\) | ||||
−0.363847 | + | 0.931459i | \(0.618537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.838886 | + | 20.8578i | 0.0968662 | + | 2.40846i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.694175 | + | 1.20235i | 0.0791086 | + | 0.137020i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.719039 | − | 0.415137i | −0.0808982 | − | 0.0467066i | 0.459005 | − | 0.888434i | \(-0.348206\pi\) |
−0.539903 | + | 0.841727i | \(0.681539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.68980 | − | 6.97325i | −0.632200 | − | 0.774806i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.96543 | − | 3.44414i | −0.654791 | − | 0.378044i | 0.135498 | − | 0.990778i | \(-0.456737\pi\) |
−0.790289 | + | 0.612734i | \(0.790070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.4666 | + | 6.62025i | −1.24373 | + | 0.718067i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.144180 | + | 3.58486i | 0.0154578 | + | 0.384338i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.14211i | − | 0.969061i | −0.874774 | − | 0.484531i | \(-0.838990\pi\) | ||
0.874774 | − | 0.484531i | \(-0.161010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.63904 | −0.171818 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.35421 | + | 6.38968i | −0.347815 | + | 0.662579i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.1913 | + | 19.3839i | 1.14820 | + | 1.98875i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.749190 | + | 1.29763i | −0.0760687 | + | 0.131755i | −0.901551 | − | 0.432674i | \(-0.857570\pi\) |
0.825482 | + | 0.564429i | \(0.190904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3290 | + | 7.12719i | −1.03811 | + | 0.716309i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82358 | − | 8.35469i | 0.479965 | − | 0.831323i | −0.519771 | − | 0.854305i | \(-0.673983\pi\) |
0.999736 | + | 0.0229825i | \(0.00731619\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.32639 | + | 2.49784i | −0.426292 | + | 0.246120i | −0.697766 | − | 0.716326i | \(-0.745822\pi\) |
0.271474 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.26857 | − | 2.00643i | −0.123800 | − | 0.195808i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1294i | 1.26927i | 0.772813 | + | 0.634634i | \(0.218849\pi\) | ||||
−0.772813 | + | 0.634634i | \(0.781151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.7401i | − | 1.02872i | −0.857576 | − | 0.514358i | \(-0.828030\pi\) | ||
0.857576 | − | 0.514358i | \(-0.171970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.04920 | + | 3.24112i | 0.194502 | + | 0.307634i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.02870 | − | 2.32597i | 0.378989 | − | 0.218809i | −0.298390 | − | 0.954444i | \(-0.596449\pi\) |
0.677378 | + | 0.735635i | \(0.263116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.75797 | + | 9.97309i | −0.536933 | + | 0.929995i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.18980 | − | 14.7675i | −0.109997 | − | 1.36525i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.532092 | − | 0.921611i | 0.0487768 | − | 0.0844839i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.24919 | + | 5.62776i | 0.295381 | + | 0.511615i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.31349 | − | 2.50216i | 0.118433 | − | 0.225612i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.1207 | −2.60463 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.663789i | − | 0.0589018i | −0.999566 | − | 0.0294509i | \(-0.990624\pi\) | ||
0.999566 | − | 0.0294509i | \(-0.00937587\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.417295 | − | 10.3755i | −0.0367408 | − | 0.913514i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.77467 | + | 2.75666i | −0.417165 | + | 0.240850i | −0.693864 | − | 0.720106i | \(-0.744093\pi\) |
0.276699 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.55795 | − | 0.899484i | −0.135092 | − | 0.0779951i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.1567 | − | 12.8861i | 1.47662 | − | 1.10906i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.41730 | + | 1.97298i | 0.291959 | + | 0.168563i | 0.638825 | − | 0.769352i | \(-0.279421\pi\) |
−0.346866 | + | 0.937915i | \(0.612754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.09321 | + | 15.7499i | 0.771276 | + | 1.33589i | 0.936864 | + | 0.349695i | \(0.113715\pi\) |
−0.165588 | + | 0.986195i | \(0.552952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.553457 | + | 13.7610i | 0.0466095 | + | 1.15889i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.6580 | −1.72751 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.55364 | −0.710341 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.5662 | − | 5.54664i | −0.871486 | − | 0.457479i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.33052 | + | 12.6968i | 0.600539 | + | 1.04016i | 0.992739 | + | 0.120285i | \(0.0383807\pi\) |
−0.392200 | + | 0.919880i | \(0.628286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4236 | − | 10.6369i | −1.49929 | − | 0.865617i | −0.499293 | − | 0.866433i | \(-0.666407\pi\) |
−1.00000 | 0.000816542i | \(0.999740\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.68980 | + | 4.12505i | 0.702528 | + | 0.333490i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.9001 | − | 8.60256i | −1.19680 | − | 0.690974i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.74343 | − | 5.62537i | 0.777611 | − | 0.448954i | −0.0579722 | − | 0.998318i | \(-0.518463\pi\) |
0.835583 | + | 0.549365i | \(0.185130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.01290 | + | 1.90491i | −0.238939 | + | 0.151069i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.925575i | − | 0.0729455i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3410 | 1.04495 | 0.522473 | − | 0.852656i | \(-0.325009\pi\) | ||||
0.522473 | + | 0.852656i | \(0.325009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.9887 | − | 25.2885i | −1.24472 | − | 1.96871i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.3782 | − | 21.4397i | −0.957855 | − | 1.65905i | −0.727694 | − | 0.685901i | \(-0.759408\pi\) |
−0.230161 | − | 0.973153i | \(-0.573925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.69411 | − | 9.86249i | 0.438009 | − | 0.758653i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.97325 | − | 14.6898i | 0.533258 | − | 1.12336i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.13610 | + | 7.16393i | −0.314462 | + | 0.544664i | −0.979323 | − | 0.202303i | \(-0.935157\pi\) |
0.664861 | + | 0.746967i | \(0.268491\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | − | 2.00000i | 0.261861 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.02439 | − | 9.57133i | 0.377656 | − | 0.719425i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3748i | 0.924939i | 0.886635 | + | 0.462470i | \(0.153037\pi\) | ||||
−0.886635 | + | 0.462470i | \(0.846963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.41487i | − | 0.179496i | −0.995965 | − | 0.0897478i | \(-0.971394\pi\) | ||
0.995965 | − | 0.0897478i | \(-0.0286061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.1995 | + | 0.731968i | −1.34534 | + | 0.0541086i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.91730 | + | 4.57105i | −0.582091 | + | 0.336070i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70634 | − | 11.6157i | 0.490416 | − | 0.849426i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.676353 | + | 1.58641i | −0.0491975 | + | 0.115395i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.21563 | − | 12.4978i | 0.522105 | − | 0.904312i | −0.477564 | − | 0.878597i | \(-0.658480\pi\) |
0.999669 | − | 0.0257154i | \(-0.00818637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.63904 | + | 14.9632i | 0.621851 | + | 1.07708i | 0.989141 | + | 0.146971i | \(0.0469526\pi\) |
−0.367289 | + | 0.930107i | \(0.619714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 35.2929 | − | 1.41945i | 2.52738 | − | 0.101649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1427 | 1.07887 | 0.539435 | − | 0.842027i | \(-0.318638\pi\) | ||||
0.539435 | + | 0.842027i | \(0.318638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6057i | 1.53158i | 0.643088 | + | 0.765792i | \(0.277653\pi\) | ||||
−0.643088 | + | 0.765792i | \(0.722347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.9018 | − | 9.39743i | −1.26270 | − | 0.662843i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.595379 | − | 0.343742i | 0.0417874 | − | 0.0241260i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83477 | + | 3.36871i | 0.407518 | + | 0.235281i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.33926 | − | 0.671883i | 0.579619 | − | 0.0466991i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.6360 | − | 11.3368i | −1.35825 | − | 0.784185i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.70129 | + | 6.41082i | 0.254807 | + | 0.441339i | 0.964843 | − | 0.262826i | \(-0.0846546\pi\) |
−0.710036 | + | 0.704166i | \(0.751321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.2185 | + | 7.09290i | −0.768679 | + | 0.485998i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.7564 | 1.68837 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.38283 | 0.0938729 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.10222 | + | 5.75488i | −0.615071 | + | 0.388879i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.91730 | + | 13.7132i | 0.532575 | + | 0.922447i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.60181 | − | 1.50216i | −0.174230 | − | 0.100592i | 0.410349 | − | 0.911929i | \(-0.365407\pi\) |
−0.584579 | + | 0.811337i | \(0.698740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.5343 | + | 29.7591i | 1.36895 | + | 1.98394i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.28027 | − | 4.20326i | −0.483208 | − | 0.278980i | 0.238544 | − | 0.971132i | \(-0.423330\pi\) |
−0.721753 | + | 0.692151i | \(0.756663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.74775 | + | 1.58641i | −0.181576 | + | 0.104833i | −0.588033 | − | 0.808837i | \(-0.700098\pi\) |
0.406457 | + | 0.913670i | \(0.366764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.12916 | + | 1.11769i | 0.140089 | + | 0.0735383i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0341i | 0.657357i | 0.944442 | + | 0.328678i | \(0.106603\pi\) | ||||
−0.944442 | + | 0.328678i | \(0.893397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.8344 | −2.14188 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.43692 | + | 0.0577916i | −0.0933377 | + | 0.00375397i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.95896 | + | 8.58918i | 0.320769 | + | 0.555588i | 0.980647 | − | 0.195785i | \(-0.0627254\pi\) |
−0.659878 | + | 0.751373i | \(0.729392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.334590 | − | 0.579528i | 0.0215529 | − | 0.0373307i | −0.855048 | − | 0.518549i | \(-0.826472\pi\) |
0.876601 | + | 0.481219i | \(0.159806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7843 | − | 4.94223i | −0.948411 | − | 0.317044i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.2255 | − | 24.6393i | 0.908833 | − | 1.57415i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.1816 | − | 13.3839i | 1.47501 | − | 0.851598i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.9212 | + | 0.479462i | −0.755477 | + | 0.0303847i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.38823i | − | 0.213863i | −0.994266 | − | 0.106931i | \(-0.965897\pi\) | ||
0.994266 | − | 0.106931i | \(-0.0341025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.6657i | − | 0.733415i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6592 | + | 20.3055i | −0.667506 | + | 1.27158i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.5531 | + | 11.2890i | −1.21969 | + | 0.704187i | −0.964851 | − | 0.262797i | \(-0.915355\pi\) |
−0.254837 | + | 0.966984i | \(0.582022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.367391 | − | 0.636340i | 0.0228286 | − | 0.0395403i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.52925 | + | 5.11473i | 0.218455 | + | 0.316594i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.70876 | + | 6.42377i | −0.228692 | + | 0.396107i | −0.957421 | − | 0.288696i | \(-0.906778\pi\) |
0.728729 | + | 0.684803i | \(0.240112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.24919 | − | 7.35981i | −0.261026 | − | 0.452110i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.46199 | − | 13.3839i | −0.517865 | − | 0.819082i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.9774 | −1.21804 | −0.609021 | − | 0.793154i | \(-0.708438\pi\) | ||||
−0.609021 | + | 0.793154i | \(0.708438\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.1040i | 1.58571i | 0.609412 | + | 0.792853i | \(0.291405\pi\) | ||||
−0.609412 | + | 0.792853i | \(0.708595\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.39954 | + | 1.51711i | −0.145227 | + | 0.0918196i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 43.6606 | − | 25.2074i | 2.63283 | − | 1.52007i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2472 | + | 12.2671i | 1.27662 | + | 0.737057i | 0.976225 | − | 0.216757i | \(-0.0695481\pi\) |
0.300395 | + | 0.953815i | \(0.402881\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00381 | + | 12.4591i | 0.0600967 | + | 0.745906i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8348 | + | 13.7610i | 1.42186 | + | 0.820913i | 0.996458 | − | 0.0840901i | \(-0.0267983\pi\) |
0.425405 | + | 0.905003i | \(0.360132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.480920 | − | 0.832977i | −0.0285877 | − | 0.0495154i | 0.851378 | − | 0.524553i | \(-0.175768\pi\) |
−0.879965 | + | 0.475038i | \(0.842434\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 34.3258 | + | 18.0190i | 2.03328 | + | 1.06735i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.541509 | −0.0319643 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.71904 | 0.395238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.104295 | + | 2.59317i | 0.00611390 | + | 0.152015i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.36384 | + | 2.36224i | 0.0796763 | + | 0.138003i | 0.903110 | − | 0.429409i | \(-0.141278\pi\) |
−0.823434 | + | 0.567412i | \(0.807945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.3193 | + | 12.8861i | 1.29948 | + | 0.750256i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.52457 | + | 19.9947i | −0.494645 | + | 1.16021i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.9270 | + | 6.88607i | 0.689757 | + | 0.398232i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.72318 | + | 0.994880i | −0.0993226 | + | 0.0573439i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.671495 | − | 16.6959i | −0.0385764 | − | 0.959154i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 43.4247i | − | 2.48649i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.29186 | −0.302022 | −0.151011 | − | 0.988532i | \(-0.548253\pi\) | ||||
−0.151011 | + | 0.988532i | \(0.548253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.02175 | + | 7.66134i | −0.228790 | + | 0.435838i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1708 | + | 21.0804i | 0.690140 | + | 1.19536i | 0.971792 | + | 0.235841i | \(0.0757844\pi\) |
−0.281652 | + | 0.959517i | \(0.590882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2158 | − | 26.3545i | 0.860048 | − | 1.48965i | −0.0118333 | − | 0.999930i | \(-0.503767\pi\) |
0.871881 | − | 0.489717i | \(-0.162900\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.71434 | − | 1.76320i | −0.209279 | − | 0.0993448i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8885 | − | 25.7876i | 0.836220 | − | 1.44837i | −0.0568140 | − | 0.998385i | \(-0.518094\pi\) |
0.893034 | − | 0.449990i | \(-0.148572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50399 | − | 4.33243i | 0.420143 | − | 0.242570i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1527 | + | 19.2213i | 0.678295 | + | 1.07283i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.3796i | 0.967026i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 59.5182i | 3.30148i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.94111 | − | 15.7234i | −0.549744 | − | 0.869504i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.28545 | − | 1.31950i | 0.126001 | − | 0.0727467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.53922 | − | 16.5224i | 0.524323 | − | 0.908154i | −0.475276 | − | 0.879837i | \(-0.657652\pi\) |
0.999599 | − | 0.0283170i | \(-0.00901480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | + | 2.84820i | 0.328798 | + | 0.156080i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.1016 | − | 41.7452i | 1.31681 | − | 2.28079i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.33027 | − | 2.30410i | −0.0724647 | − | 0.125512i | 0.827516 | − | 0.561442i | \(-0.189753\pi\) |
−0.899981 | + | 0.435929i | \(0.856420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.74503 | − | 7.13418i | 0.203402 | − | 0.387476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4289 | 0.943825 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.60997i | 0.248915i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.801571 | + | 19.9301i | 0.0431551 | + | 1.07300i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.1413 | − | 11.0512i | 1.02756 | − | 0.593261i | 0.111275 | − | 0.993790i | \(-0.464507\pi\) |
0.916284 | + | 0.400528i | \(0.131173\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.9088 | + | 10.3397i | 0.958638 | + | 0.553470i | 0.895754 | − | 0.444551i | \(-0.146637\pi\) |
0.0628846 | + | 0.998021i | \(0.479970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4107 | − | 20.5181i | −0.822563 | − | 1.09517i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7969 | − | 6.81094i | −0.627885 | − | 0.362510i | 0.152047 | − | 0.988373i | \(-0.451413\pi\) |
−0.779933 | + | 0.625864i | \(0.784747\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.8218 | − | 27.4042i | −0.839734 | − | 1.45446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0740730 | − | 1.84173i | −0.00392036 | − | 0.0974749i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3818 | −0.917377 | −0.458688 | − | 0.888597i | \(-0.651681\pi\) | ||||
−0.458688 | + | 0.888597i | \(0.651681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3796 | 0.546294 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.96586 | + | 5.23149i | 0.523072 | + | 0.274582i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.8371 | − | 22.2346i | −0.671927 | − | 1.16381i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3976 | + | 9.46715i | 0.855947 | + | 0.494181i | 0.862653 | − | 0.505796i | \(-0.168801\pi\) |
−0.00670584 | + | 0.999978i | \(0.502135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.393086 | − | 4.87889i | −0.0204633 | − | 0.253985i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.591533 | + | 0.341522i | 0.0307109 | + | 0.0177309i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2230 | + | 13.9852i | −1.25422 | + | 0.724124i | −0.971945 | − | 0.235210i | \(-0.924422\pi\) |
−0.282275 | + | 0.959334i | \(0.591089\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −42.6322 | + | 26.9542i | −2.20152 | + | 1.39191i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2295i | 0.526844i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7997 | 0.606111 | 0.303056 | − | 0.952973i | \(-0.401993\pi\) | ||||
0.303056 | + | 0.952973i | \(0.401993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.614407 | − | 0.971778i | −0.0314770 | − | 0.0497857i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.87782 | − | 17.1089i | −0.504733 | − | 0.874223i | −0.999985 | − | 0.00547380i | \(-0.998258\pi\) |
0.495252 | − | 0.868749i | \(-0.335076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.86653 | + | 4.96498i | −0.146092 | + | 0.253039i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2146 | − | 14.8034i | −0.519235 | − | 0.752497i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.76557 | − | 4.79011i | 0.140220 | − | 0.242868i | −0.787359 | − | 0.616494i | \(-0.788552\pi\) |
0.927579 | + | 0.373626i | \(0.121886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.74388 | + | 4.47093i | −0.391625 | + | 0.226105i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.43847 | + | 8.45518i | −0.223891 | + | 0.426507i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.42854i | − | 0.172509i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.5247i | − | 1.58218i | −0.611700 | − | 0.791090i | \(-0.709514\pi\) | ||
0.611700 | − | 0.791090i | \(-0.290486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.11339 | + | 0.125218i | −0.155864 | + | 0.00626873i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.9709 | + | 10.3755i | −0.897425 | + | 0.518129i | −0.876364 | − | 0.481649i | \(-0.840038\pi\) |
−0.0210614 | + | 0.999778i | \(0.506705\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2880 | + | 17.8193i | −0.512481 | + | 0.887642i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.1898 | − | 34.7454i | 0.655406 | − | 1.72651i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.63049 | − | 8.02025i | 0.229525 | − | 0.397549i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.99838 | − | 10.3895i | −0.296601 | − | 0.513728i | 0.678755 | − | 0.734365i | \(-0.262520\pi\) |
−0.975356 | + | 0.220637i | \(0.929186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.82907 | − | 0.274660i | 0.336853 | − | 0.0135480i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.07139 | −0.101927 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 28.4446i | − | 1.39629i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.8905 | + | 14.6409i | 1.36581 | + | 0.716968i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.8617 | + | 12.0445i | −1.01916 | + | 0.588412i | −0.913860 | − | 0.406029i | \(-0.866913\pi\) |
−0.105299 | + | 0.994441i | \(0.533580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3884 | − | 15.2354i | −1.28609 | − | 0.742526i | −0.308137 | − | 0.951342i | \(-0.599706\pi\) |
−0.977955 | + | 0.208816i | \(0.933039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.5475 | + | 19.6336i | 0.658703 | + | 0.954620i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.4662 | − | 19.3217i | −1.62335 | − | 0.937242i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.74510 | + | 3.02260i | 0.0844511 | + | 0.146274i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −30.2431 | + | 19.1212i | −1.46015 | + | 0.923180i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.902398 | −0.0434670 | −0.0217335 | − | 0.999764i | \(-0.506919\pi\) | ||||
−0.0217335 | + | 0.999764i | \(0.506919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.559027 | 0.0268651 | 0.0134326 | − | 0.999910i | \(-0.495724\pi\) | ||||
0.0134326 | + | 0.999910i | \(0.495724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.5224 | + | 7.91730i | −0.600403 | + | 0.379605i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.55795 | + | 13.0908i | 0.361546 | + | 0.626216i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1482 | + | 11.6326i | 0.961621 | + | 0.555192i | 0.896671 | − | 0.442697i | \(-0.145978\pi\) |
0.0649491 | + | 0.997889i | \(0.479311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.6028 | + | 1.65994i | −0.981085 | + | 0.0790447i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0835 | + | 12.7499i | 1.04922 | + | 0.605766i | 0.922430 | − | 0.386164i | \(-0.126200\pi\) |
0.126788 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.6937 | − | 18.8757i | 1.54983 | − | 0.894796i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.4840 | + | 11.8028i | 1.06346 | + | 0.558253i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6758i | 0.786981i | 0.919329 | + | 0.393490i | \(0.128732\pi\) | ||||
−0.919329 | + | 0.393490i | \(0.871268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.82502 | −0.321378 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36.8175 | + | 1.48077i | −1.72984 | + | 0.0695726i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.38414 | − | 5.86150i | −0.158651 | − | 0.274791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.30283 | − | 5.72066i | 0.154500 | − | 0.267601i | −0.778377 | − | 0.627797i | \(-0.783957\pi\) |
0.932877 | + | 0.360196i | \(0.117290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.5399 | − | 2.00432i | 0.772017 | − | 0.0935535i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.40191 | + | 16.2846i | −0.437891 | + | 0.758449i | −0.997527 | − | 0.0702897i | \(-0.977608\pi\) |
0.559636 | + | 0.828739i | \(0.310941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5994 | + | 12.4704i | −1.00381 | + | 0.579548i | −0.909372 | − | 0.415983i | \(-0.863438\pi\) |
−0.0944346 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −29.7761 | + | 1.19757i | −1.38083 | + | 0.0555360i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.2003i | − | 0.472015i | −0.971751 | − | 0.236007i | \(-0.924161\pi\) | ||
0.971751 | − | 0.236007i | \(-0.0758389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.87426i | 0.178897i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.05737 | − | 17.2540i | 0.417341 | − | 0.795024i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.7185 | + | 12.5392i | −0.998618 | + | 0.576552i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.6627 | + | 56.5735i | −1.49867 | + | 2.59577i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.64765 | + | 5.57752i | −0.121228 | + | 0.255377i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.43334 | − | 9.41082i | 0.248256 | − | 0.429991i | −0.714786 | − | 0.699343i | \(-0.753476\pi\) |
0.963042 | + | 0.269352i | \(0.0868094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.46661 | + | 9.46845i | 0.249256 | + | 0.431724i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.856717 | − | 1.35503i | −0.0389820 | − | 0.0616559i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.18742 | −0.280956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1073i | 0.956462i | 0.878234 | + | 0.478231i | \(0.158722\pi\) | ||||
−0.878234 | + | 0.478231i | \(0.841278\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5310 | − | 12.3485i | 0.883223 | − | 0.558418i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5189 | + | 10.6919i | −0.835746 | + | 0.482518i | −0.855816 | − | 0.517280i | \(-0.826944\pi\) |
0.0200698 | + | 0.999799i | \(0.493611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.75189 | − | 3.32085i | −0.259052 | − | 0.149564i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −46.8144 | − | 22.2228i | −2.10415 | − | 0.998841i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.20257 | + | 1.27165i | 0.0987986 | + | 0.0570414i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9981 | + | 22.5134i | 0.581876 | + | 1.00784i | 0.995257 | + | 0.0972805i | \(0.0310144\pi\) |
−0.413381 | + | 0.910558i | \(0.635652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.9662 | − | 19.9301i | −1.69621 | − | 0.890410i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.4476 | 1.26842 | 0.634208 | − | 0.773163i | \(-0.281326\pi\) | ||||
0.634208 | + | 0.773163i | \(0.281326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.8371 | 1.77273 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.792682 | − | 19.7091i | −0.0352043 | − | 0.875310i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.928302 | − | 1.60787i | −0.0411462 | − | 0.0712674i | 0.844719 | − | 0.535210i | \(-0.179768\pi\) |
−0.885865 | + | 0.463943i | \(0.846434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.78707 | + | 1.03177i | 0.0790553 | + | 0.0456426i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.38823 | − | 27.9601i | −0.149594 | − | 1.23447i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8654 | − | 10.3146i | −0.787245 | − | 0.454516i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.8052 | − | 16.6307i | 1.26685 | − | 0.731416i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.575790 | + | 14.3163i | 0.0252744 | + | 0.628416i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.2415i | − | 1.76301i | −0.472173 | − | 0.881506i | \(-0.656530\pi\) | ||
0.472173 | − | 0.881506i | \(-0.343470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.0040 | 0.918440 | 0.459220 | − | 0.888323i | \(-0.348129\pi\) | ||||
0.459220 | + | 0.888323i | \(0.348129\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.22018 | − | 6.13436i | 0.140540 | − | 0.267726i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.67969 | − | 11.5696i | −0.290972 | − | 0.503978i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.61141 | − | 13.1833i | 0.330931 | − | 0.573189i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.50364 | − | 18.6629i | −0.0652526 | − | 0.809900i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.02870 | − | 6.97792i | 0.174503 | − | 0.302247i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.9530 | + | 27.1083i | −2.02996 | + | 1.17200i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.4542 | + | 18.1166i | 0.494286 | + | 0.781789i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.8210i | 1.24141i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.33020i | 0.229163i | 0.993414 | + | 0.114582i | \(0.0365528\pi\) | ||||
−0.993414 | + | 0.114582i | \(0.963447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.23522 | − | 3.53533i | −0.0959223 | − | 0.151716i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.4085 | − | 22.1751i | 1.64524 | − | 0.949879i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.09162 | + | 1.89075i | −0.0466745 | + | 0.0808426i | −0.888419 | − | 0.459034i | \(-0.848196\pi\) |
0.841744 | + | 0.539876i | \(0.181529\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.9662 | + | 17.9171i | −1.10821 | + | 0.764684i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.61378 | + | 9.72336i | −0.239155 | + | 0.414229i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.137782 | + | 0.238645i | 0.00585908 | + | 0.0101482i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.35981 | + | 14.0202i | −0.312407 | + | 0.595126i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.6744 | −0.621775 | −0.310887 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310887 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 29.6067i | − | 1.25223i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.933596 | − | 23.2127i | −0.0394164 | − | 0.980040i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.62742 | + | 2.67164i | −0.195023 | + | 0.112596i | −0.594332 | − | 0.804220i | \(-0.702583\pi\) |
0.399309 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.6362 | + | 9.60489i | 0.699889 | + | 0.404081i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.478222 | + | 2.94852i | 0.0200834 | + | 0.123826i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.77232 | + | 1.02325i | 0.0742997 | + | 0.0428969i | 0.536690 | − | 0.843780i | \(-0.319675\pi\) |
−0.462390 | + | 0.886677i | \(0.653008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.29802 | + | 7.44439i | 0.179866 | + | 0.311538i | 0.941835 | − | 0.336077i | \(-0.109100\pi\) |
−0.761968 | + | 0.647614i | \(0.775767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.00449 | − | 24.9755i | −0.0419634 | − | 1.04337i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.6102 | −1.40164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.6609 | 1.10991 | 0.554954 | − | 0.831881i | \(-0.312736\pi\) | ||||
0.554954 | + | 0.831881i | \(0.312736\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.4975 | + | 13.9096i | 1.10120 | + | 0.578065i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.14309 | + | 1.97990i | 0.0474235 | + | 0.0821399i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.45552 | + | 4.30445i | 0.308776 | + | 0.178272i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 50.3545 | − | 34.7454i | 2.08190 | − | 1.43655i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.9759 | − | 23.0801i | −1.64998 | − | 0.952618i | −0.977076 | − | 0.212892i | \(-0.931712\pi\) |
−0.672908 | − | 0.739726i | \(-0.734955\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.5580 | + | 11.2918i | −0.805871 | + | 0.465270i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.1686 | − | 14.0161i | 0.911896 | − | 0.576547i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.7409i | 0.646402i | 0.946330 | + | 0.323201i | \(0.104759\pi\) | ||||
−0.946330 | + | 0.323201i | \(0.895241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.39445 | 0.180155 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.9983 | + | 31.6304i | 0.818477 | + | 1.29454i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5203 | − | 37.2743i | −0.879297 | − | 1.52299i | −0.852114 | − | 0.523356i | \(-0.824680\pi\) |
−0.0271823 | − | 0.999630i | \(-0.508653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6867 | + | 34.0984i | −0.803039 | + | 1.39090i | 0.114569 | + | 0.993415i | \(0.463451\pi\) |
−0.917607 | + | 0.397488i | \(0.869882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.9064 | + | 2.81236i | −1.42150 | + | 0.114528i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.4172 | + | 23.2393i | −0.545488 | + | 0.944813i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.7834 | − | 14.8861i | 1.04652 | − | 0.604207i | 0.124845 | − | 0.992176i | \(-0.460157\pi\) |
0.921672 | + | 0.387969i | \(0.126823\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.553457 | − | 1.05432i | 0.0224272 | − | 0.0427232i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.2673i | 1.58858i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.615900i | − | 0.0248760i | −0.999923 | − | 0.0124380i | \(-0.996041\pi\) | ||
0.999923 | − | 0.0124380i | \(-0.00395924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.6601 | − | 0.468960i | 0.470181 | − | 0.0189103i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.03339 | − | 1.17398i | 0.0818610 | − | 0.0472625i | −0.458511 | − | 0.888689i | \(-0.651617\pi\) |
0.540372 | + | 0.841426i | \(0.318284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.58718 | − | 16.6055i | 0.385341 | − | 0.667431i | −0.606475 | − | 0.795102i | \(-0.707417\pi\) |
0.991816 | + | 0.127672i | \(0.0407504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5867 | − | 8.70249i | 0.464956 | − | 0.349219i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.51711 | + | 2.62771i | −0.0607817 | + | 0.105277i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9955 | − | 51.9537i | −1.19982 | − | 2.07815i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.2402 | + | 1.57821i | −1.56710 | + | 0.0630277i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.09864 | −0.283041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.77969i | − | 0.150467i | −0.997166 | − | 0.0752336i | \(-0.976030\pi\) | ||
0.997166 | − | 0.0752336i | \(-0.0239702\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3525 | + | 5.95941i | 0.451222 | + | 0.236865i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.37383 | − | 1.37053i | 0.0942024 | − | 0.0543878i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.4666 | − | 17.0126i | −1.16751 | − | 0.674062i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.85849 | + | 20.7678i | −0.389996 | + | 0.821562i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.1609 | + | 7.02110i | 0.480327 | + | 0.277317i | 0.720553 | − | 0.693400i | \(-0.243888\pi\) |
−0.240226 | + | 0.970717i | \(0.577221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.39850 | + | 7.61843i | 0.173460 | + | 0.300441i | 0.939627 | − | 0.342200i | \(-0.111172\pi\) |
−0.766167 | + | 0.642641i | \(0.777839\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.2431 | − | 22.9147i | 1.42707 | − | 0.902266i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.5118 | 1.16023 | 0.580114 | − | 0.814535i | \(-0.303008\pi\) | ||||
0.580114 | + | 0.814535i | \(0.303008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.1073 | −1.02480 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.02445 | − | 1.27996i | 0.0793444 | − | 0.0501656i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.00669049 | + | 0.0115883i | 0.000261819 | + | 0.000453484i | 0.866156 | − | 0.499773i | \(-0.166583\pi\) |
−0.865894 | + | 0.500227i | \(0.833250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.7166 | − | 11.3834i | −0.770390 | − | 0.444785i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.99876 | + | 16.8501i | −0.312061 | + | 0.657386i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.3244 | + | 19.8172i | 1.33709 | + | 0.771970i | 0.986375 | − | 0.164513i | \(-0.0526051\pi\) |
0.350715 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.8008 | + | 6.81322i | −0.458999 | + | 0.265003i | −0.711623 | − | 0.702561i | \(-0.752040\pi\) |
0.252624 | + | 0.967565i | \(0.418706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.2838 | + | 12.7476i | 0.943104 | + | 0.495075i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.42867i | − | 0.288071i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.77662 | −0.223672 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.19942 | + | 0.209117i | −0.201021 | + | 0.00808492i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.9947 | + | 38.0959i | 0.849096 | + | 1.47068i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.22156 | + | 5.57991i | −0.124182 | + | 0.215090i | −0.921413 | − | 0.388585i | \(-0.872964\pi\) |
0.797231 | + | 0.603675i | \(0.206297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 57.6071 | + | 24.5603i | 2.21730 | + | 0.945325i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.67204 | − | 13.2884i | 0.294860 | − | 0.510713i | −0.680092 | − | 0.733127i | \(-0.738060\pi\) |
0.974952 | + | 0.222414i | \(0.0713935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.430678 | − | 0.248652i | 0.0165279 | − | 0.00954239i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5488 | + | 0.585140i | −0.557510 | + | 0.0224226i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.2454i | − | 0.659878i | −0.944002 | − | 0.329939i | \(-0.892972\pi\) | ||
0.944002 | − | 0.329939i | \(-0.107028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2945i | 0.622579i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.55427 | + | 4.86582i | −0.0974515 | + | 0.185643i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.80175 | + | 5.08169i | −0.335320 | + | 0.193597i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.97083 | − | 17.2700i | 0.379308 | − | 0.656981i | −0.611654 | − | 0.791126i | \(-0.709495\pi\) |
0.990962 | + | 0.134145i | \(0.0428287\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.15160 | − | 0.334489i | 0.157706 | − | 0.0127062i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.5496 | + | 65.0378i | −1.42434 | + | 2.46702i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.61572 | + | 4.53057i | 0.0990776 | + | 0.171607i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.28763 | + | 14.6898i | 0.351291 | + | 0.555619i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.45975 | 0.130673 | 0.0653364 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653364 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000i | 0.452589i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −48.0690 | + | 30.3917i | −1.81038 | + | 1.14462i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.77288 | + | 1.60092i | −0.104285 | + | 0.0602089i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.2429 | − | 19.7701i | −1.28602 | − | 0.742483i | −0.308077 | − | 0.951361i | \(-0.599685\pi\) |
−0.977942 | + | 0.208878i | \(0.933019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.05013 | + | 1.41462i | −0.0768860 | + | 0.0530525i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.0626 | − | 5.80966i | −0.376849 | − | 0.217574i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.6527 | − | 73.8767i | −1.59512 | − | 2.76283i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2100 | + | 7.98439i | 0.568030 | + | 0.298182i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.62877 | −0.172624 | −0.0863120 | − | 0.996268i | \(-0.527508\pi\) | ||||
−0.0863120 | + | 0.996268i | \(0.527508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.65804 | 0.0617487 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0465786 | − | 1.15812i | −0.00173228 | − | 0.0430709i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.4822 | − | 21.6199i | −0.463579 | − | 0.802942i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.33286 | − | 3.07893i | −0.197785 | − | 0.114191i | 0.397837 | − | 0.917456i | \(-0.369761\pi\) |
−0.595622 | + | 0.803265i | \(0.703094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.2185 | + | 6.44905i | −0.971056 | + | 0.238854i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.6474 | + | 9.61141i | 0.615728 | + | 0.355491i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9417 | + | 10.9360i | −0.699627 | + | 0.403930i | −0.807208 | − | 0.590266i | \(-0.799023\pi\) |
0.107581 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.98034 | − | 49.2388i | −0.0730461 | − | 1.81620i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.8301i | 1.79868i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5677 | −0.903738 | −0.451869 | − | 0.892084i | \(-0.649243\pi\) | ||||
−0.451869 | + | 0.892084i | \(0.649243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.5493 | − | 41.0509i | 0.791634 | − | 1.50804i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.52447 | + | 6.10457i | 0.129300 | + | 0.223955i | 0.923406 | − | 0.383825i | \(-0.125394\pi\) |
−0.794105 | + | 0.607780i | \(0.792060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.2707 | + | 52.4304i | −1.10903 | + | 1.92090i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.0087 | + | 11.7363i | −0.622316 | + | 0.429408i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.17879 | − | 3.77378i | 0.0796113 | − | 0.137891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9770 | − | 12.1110i | 0.765460 | − | 0.441938i | −0.0657928 | − | 0.997833i | \(-0.520958\pi\) |
0.831253 | + | 0.555895i | \(0.187624\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.13616 | − | 4.96031i | −0.114288 | − | 0.180764i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 87.8480i | − | 3.19712i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.8780i | − | 1.08593i | −0.839754 | − | 0.542967i | \(-0.817301\pi\) | ||
0.839754 | − | 0.542967i | \(-0.182699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.7978 | − | 17.0784i | −0.391936 | − | 0.619906i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.2631 | − | 20.9365i | 1.31454 | − | 0.758949i | 0.331694 | − | 0.943387i | \(-0.392380\pi\) |
0.982844 | + | 0.184438i | \(0.0590466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.78229 | + | 3.08702i | −0.0645233 | + | 0.111758i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.18998 | + | 39.5932i | 0.115334 | + | 1.43150i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.4107 | − | 26.6921i | 0.556449 | − | 0.963797i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.30858 | + | 10.9268i | 0.227493 | + | 0.394030i | 0.957065 | − | 0.289875i | \(-0.0936137\pi\) |
−0.729571 | + | 0.683905i | \(0.760280\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1763 | + | 34.6254i | −0.654603 | + | 1.24700i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6390 | 1.03007 | 0.515037 | − | 0.857168i | \(-0.327778\pi\) | ||||
0.515037 | + | 0.857168i | \(0.327778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 50.2145i | − | 1.80376i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0511448 | − | 1.27165i | −0.00183481 | − | 0.0456203i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.65876 | − | 4.42179i | 0.274404 | − | 0.158427i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7605 | + | 16.0275i | 0.993349 | + | 0.573511i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.90100 | + | 4.22120i | 0.353833 | + | 0.150853i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.2346 | + | 23.2295i | 1.43603 | + | 0.829095i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7520 | + | 34.2115i | 0.704083 | + | 1.21951i | 0.967021 | + | 0.254695i | \(0.0819751\pi\) |
−0.262938 | + | 0.964813i | \(0.584692\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.516300 | + | 12.8372i | 0.0183808 | + | 0.457015i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.54396 | −0.0548968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.9325 | −1.84418 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.0330 | − | 6.84158i | −0.462234 | − | 0.242646i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.6253 | − | 23.5998i | −0.482634 | − | 0.835947i | 0.517167 | − | 0.855884i | \(-0.326987\pi\) |
−0.999801 | + | 0.0199377i | \(0.993653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.0794 | − | 12.7476i | −0.781114 | − | 0.450977i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.7765 | − | 11.7614i | −0.875433 | − | 0.415568i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.5237 | + | 13.0041i | 0.794845 | + | 0.458904i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.31002 | − | 1.91104i | 0.116663 | − | 0.0673552i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.2466 | + | 18.4912i | −1.02953 | + | 0.650920i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.7182i | 1.15031i | 0.818045 | + | 0.575155i | \(0.195058\pi\) | ||||
−0.818045 | + | 0.575155i | \(0.804942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3901 | 0.821336 | 0.410668 | − | 0.911785i | \(-0.365296\pi\) | ||||
0.410668 | + | 0.911785i | \(0.365296\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.1620 | + | 38.2159i | 0.847400 | + | 1.34029i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.5452 | + | 47.7097i | 0.964866 | + | 1.67120i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2477 | − | 28.1419i | 0.568437 | − | 0.984561i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.10864 | + | 4.44205i | −0.0736819 | + | 0.155218i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4953 | + | 26.8387i | −0.540790 | + | 0.936676i | 0.458069 | + | 0.888917i | \(0.348541\pi\) |
−0.998859 | + | 0.0477594i | \(0.984792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.9067 | − | 24.1948i | 1.46077 | − | 0.843379i | 0.461728 | − | 0.887022i | \(-0.347230\pi\) |
0.999047 | + | 0.0436430i | \(0.0138964\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 40.5863 | − | 77.3158i | 1.41303 | − | 2.69179i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 53.6957i | − | 1.86718i | −0.358340 | − | 0.933591i | \(-0.616657\pi\) | ||
0.358340 | − | 0.933591i | \(-0.383343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1371i | 0.491001i | 0.969396 | + | 0.245500i | \(0.0789523\pi\) | ||||
−0.969396 | + | 0.245500i | \(0.921048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.4601 | − | 1.70771i | 1.47292 | − | 0.0592398i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1318 | − | 11.0458i | 0.662879 | − | 0.382713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.1147 | − | 88.5333i | 1.76890 | − | 3.06382i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.0018 | + | 17.3108i | 0.449407 | + | 0.598348i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.1957 | + | 36.7120i | −0.731757 | + | 1.26744i | 0.224375 | + | 0.974503i | \(0.427966\pi\) |
−0.956132 | + | 0.292937i | \(0.905367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3547 | + | 21.3989i | 0.426023 | + | 0.737893i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.6310 | − | 1.91568i | 1.64050 | − | 0.0659796i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.0266 | 1.61777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.15678i | − | 0.0741078i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.47507 | − | 0.774325i | −0.0506242 | − | 0.0265747i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.34688 | + | 3.08702i | −0.183289 | + | 0.105822i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.7766 | + | 11.9954i | 0.711378 | + | 0.410714i | 0.811571 | − | 0.584254i | \(-0.198613\pi\) |
−0.100193 | + | 0.994968i | \(0.531946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 66.9309 | − | 5.39254i | 2.28899 | − | 0.184421i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.4336 | + | 8.33324i | 0.493042 | + | 0.284658i | 0.725836 | − | 0.687868i | \(-0.241453\pi\) |
−0.232793 | + | 0.972526i | \(0.574787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.78253 | + | 16.9438i | 0.333776 | + | 0.578116i | 0.983249 | − | 0.182268i | \(-0.0583439\pi\) |
−0.649473 | + | 0.760384i | \(0.725011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.792761 | + | 0.501224i | −0.0270172 | + | 0.0170817i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5794 | −1.04094 | −0.520468 | − | 0.853881i | \(-0.674242\pi\) | ||||
−0.520468 | + | 0.853881i | \(0.674242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.1593 | −1.16145 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.83658 | − | 6.21919i | 0.334068 | − | 0.211215i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.73656 | + | 3.00782i | 0.0589089 | + | 0.102033i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.9240 | − | 28.8236i | −1.69161 | − | 0.976651i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.55294 | + | 3.69983i | 0.0864040 | + | 0.125220i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.37013 | + | 4.83250i | 0.282962 | + | 0.163368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.9915 | − | 19.6250i | 1.14781 | − | 0.662690i | 0.199460 | − | 0.979906i | \(-0.436081\pi\) |
0.948353 | + | 0.317216i | \(0.102748\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.18314 | + | 2.19590i | 0.141094 | + | 0.0740660i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.2971i | − | 0.683828i | −0.939731 | − | 0.341914i | \(-0.888925\pi\) | ||
0.939731 | − | 0.341914i | \(-0.111075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.2658 | −0.446431 | −0.223216 | − | 0.974769i | \(-0.571655\pi\) | ||||
−0.223216 | + | 0.974769i | \(0.571655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 44.6026 | − | 1.79388i | 1.49930 | − | 0.0603006i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2973 | − | 21.2996i | −0.412904 | − | 0.715170i | 0.582302 | − | 0.812972i | \(-0.302152\pi\) |
−0.995206 | + | 0.0978022i | \(0.968819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.110154 | + | 0.190792i | −0.00369445 | + | 0.00639897i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.02737 | + | 37.1623i | 0.201925 | + | 1.24499i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.5493 | + | 37.3245i | −0.721120 | + | 1.24902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.2546 | + | 25.5504i | −1.47927 | + | 0.854056i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.8348 | − | 0.958615i | 0.795820 | − | 0.0320072i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 8.63044i | − | 0.287841i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.59880i | − | 0.219838i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.60185 | + | 3.05148i | −0.0533061 | + | 0.101547i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.63598 | − | 4.98599i | 0.287070 | − | 0.165740i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.21712 | + | 7.30427i | −0.140027 | + | 0.242534i | −0.927507 | − | 0.373807i | \(-0.878052\pi\) |
0.787479 | + | 0.616341i | \(0.211386\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.4369 | − | 23.8210i | −0.545177 | − | 0.790093i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.35597 | + | 12.7409i | −0.243714 | + | 0.422125i | −0.961769 | − | 0.273861i | \(-0.911699\pi\) |
0.718055 | + | 0.695986i | \(0.245033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4072 | + | 24.9540i | 0.476809 | + | 0.825858i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −40.1942 | − | 63.5732i | −1.32878 | − | 2.10166i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.82984 | 0.0604267 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4521i | 1.26842i | 0.773162 | + | 0.634209i | \(0.218674\pi\) | ||||
−0.773162 | + | 0.634209i | \(0.781326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.74720 | + | 4.89817i | −0.255279 | + | 0.161400i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.7732 | + | 18.9216i | −1.07874 | + | 0.622812i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.1073 | − | 13.3410i | −0.759762 | − | 0.438649i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20359 | + | 14.9386i | 0.0395310 | + | 0.490649i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.88859 | − | 2.24508i | −0.127581 | − | 0.0736587i | 0.434851 | − | 0.900502i | \(-0.356801\pi\) |
−0.562432 | + | 0.826844i | \(0.690134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.6725 | − | 32.3417i | −0.611966 | − | 1.05996i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.3299 | + | 19.5960i | 1.22213 | + | 0.641545i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 55.3864 | 1.81133 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9267 | −0.748984 | −0.374492 | − | 0.927230i | \(-0.622183\pi\) | ||||
−0.374492 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.11821 | − | 52.6665i | −0.0691250 | − | 1.71871i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.6316 | + | 47.8593i | 0.900764 | + | 1.56017i | 0.826504 | + | 0.562931i | \(0.190326\pi\) |
0.0742601 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.94046 | + | 2.27503i | 0.128319 | + | 0.0740850i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.06976 | + | 0.856717i | −0.229979 | + | 0.0278690i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.4482 | − | 11.8058i | −0.664479 | − | 0.383637i | 0.129503 | − | 0.991579i | \(-0.458662\pi\) |
−0.793981 | + | 0.607942i | \(0.791995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.5908 | + | 15.3522i | −0.863174 | + | 0.498354i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.07264 | − | 51.5335i | −0.0672098 | − | 1.67109i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.892008i | 0.0288950i | 0.999896 | + | 0.0144475i | \(0.00459894\pi\) | ||||
−0.999896 | + | 0.0144475i | \(0.995401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.5926 | 1.92837 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.97561 | − | 13.2884i | 0.225490 | − | 0.429552i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.654820 | − | 1.13418i | −0.0211453 | − | 0.0366247i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.82020 | + | 11.8129i | −0.220006 | + | 0.381062i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.5826 | + | 16.8911i | 1.14663 | + | 0.544308i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.6741 | + | 61.7894i | −1.14839 | + | 1.98907i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3105 | − | 18.0771i | 1.00688 | − | 0.581321i | 0.0966015 | − | 0.995323i | \(-0.469203\pi\) |
0.910276 | + | 0.414002i | \(0.135869\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0867 | + | 25.4435i | 0.516778 | + | 0.817362i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0395i | 1.34911i | 0.738223 | + | 0.674556i | \(0.235665\pi\) | ||||
−0.738223 | + | 0.674556i | \(0.764335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.03598i | − | 0.193505i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 55.0904 | + | 87.1338i | 1.76430 | + | 2.79051i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2808 | + | 7.66765i | −0.424889 | + | 0.245310i | −0.697167 | − | 0.716909i | \(-0.745556\pi\) |
0.272278 | + | 0.962219i | \(0.412223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1212 | + | 33.1189i | −0.611116 | + | 1.05848i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.1073 | − | 13.8172i | −0.929324 | − | 0.441150i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.90976 | + | 5.03986i | −0.0928071 | + | 0.160747i | −0.908691 | − | 0.417469i | \(-0.862917\pi\) |
0.815884 | + | 0.578215i | \(0.196251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.2651 | + | 54.1528i | 0.996190 | + | 1.72545i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.12452 | − | 4.04716i | 0.0676243 | − | 0.128823i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7190 | 0.531635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.7700i | 1.35863i | 0.733845 | + | 0.679316i | \(0.237724\pi\) | ||||
−0.733845 | + | 0.679316i | \(0.762276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32796 | − | 33.0181i | −0.0421416 | − | 1.04780i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.2655 | + | 44.6093i | −2.44948 | + | 1.41421i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.0247 | + | 25.9950i | 1.42595 | + | 0.823271i | 0.996798 | − | 0.0799618i | \(-0.0254798\pi\) |
0.429150 | + | 0.903233i | \(0.358813\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4202 | − | 1.38391i | 0.361320 | − | 0.0437850i |
(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 | 576.2.p.c.479.7 | yes | 16 | |
3.2 | odd | 2 | 1728.2.p.a.1439.1 | 16 | |||
4.3 | odd | 2 | inner | 576.2.p.c.479.2 | yes | 16 | |
8.3 | odd | 2 | 576.2.p.a.479.7 | yes | 16 | ||
8.5 | even | 2 | 576.2.p.a.479.2 | yes | 16 | ||
9.2 | odd | 6 | 5184.2.f.f.2591.16 | 16 | |||
9.4 | even | 3 | 1728.2.p.c.287.8 | 16 | |||
9.5 | odd | 6 | 576.2.p.a.95.7 | yes | 16 | ||
9.7 | even | 3 | 5184.2.f.a.2591.4 | 16 | |||
12.11 | even | 2 | 1728.2.p.a.1439.2 | 16 | |||
24.5 | odd | 2 | 1728.2.p.c.1439.7 | 16 | |||
24.11 | even | 2 | 1728.2.p.c.1439.8 | 16 | |||
36.7 | odd | 6 | 5184.2.f.a.2591.2 | 16 | |||
36.11 | even | 6 | 5184.2.f.f.2591.14 | 16 | |||
36.23 | even | 6 | 576.2.p.a.95.2 | ✓ | 16 | ||
36.31 | odd | 6 | 1728.2.p.c.287.7 | 16 | |||
72.5 | odd | 6 | inner | 576.2.p.c.95.2 | yes | 16 | |
72.11 | even | 6 | 5184.2.f.a.2591.1 | 16 | |||
72.13 | even | 6 | 1728.2.p.a.287.2 | 16 | |||
72.29 | odd | 6 | 5184.2.f.a.2591.3 | 16 | |||
72.43 | odd | 6 | 5184.2.f.f.2591.13 | 16 | |||
72.59 | even | 6 | inner | 576.2.p.c.95.7 | yes | 16 | |
72.61 | even | 6 | 5184.2.f.f.2591.15 | 16 | |||
72.67 | odd | 6 | 1728.2.p.a.287.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.p.a.95.2 | ✓ | 16 | 36.23 | even | 6 | ||
576.2.p.a.95.7 | yes | 16 | 9.5 | odd | 6 | ||
576.2.p.a.479.2 | yes | 16 | 8.5 | even | 2 | ||
576.2.p.a.479.7 | yes | 16 | 8.3 | odd | 2 | ||
576.2.p.c.95.2 | yes | 16 | 72.5 | odd | 6 | inner | |
576.2.p.c.95.7 | yes | 16 | 72.59 | even | 6 | inner | |
576.2.p.c.479.2 | yes | 16 | 4.3 | odd | 2 | inner | |
576.2.p.c.479.7 | yes | 16 | 1.1 | even | 1 | trivial | |
1728.2.p.a.287.1 | 16 | 72.67 | odd | 6 | |||
1728.2.p.a.287.2 | 16 | 72.13 | even | 6 | |||
1728.2.p.a.1439.1 | 16 | 3.2 | odd | 2 | |||
1728.2.p.a.1439.2 | 16 | 12.11 | even | 2 | |||
1728.2.p.c.287.7 | 16 | 36.31 | odd | 6 | |||
1728.2.p.c.287.8 | 16 | 9.4 | even | 3 | |||
1728.2.p.c.1439.7 | 16 | 24.5 | odd | 2 | |||
1728.2.p.c.1439.8 | 16 | 24.11 | even | 2 | |||
5184.2.f.a.2591.1 | 16 | 72.11 | even | 6 | |||
5184.2.f.a.2591.2 | 16 | 36.7 | odd | 6 | |||
5184.2.f.a.2591.3 | 16 | 72.29 | odd | 6 | |||
5184.2.f.a.2591.4 | 16 | 9.7 | even | 3 | |||
5184.2.f.f.2591.13 | 16 | 72.43 | odd | 6 | |||
5184.2.f.f.2591.14 | 16 | 36.11 | even | 6 | |||
5184.2.f.f.2591.15 | 16 | 72.61 | even | 6 | |||
5184.2.f.f.2591.16 | 16 | 9.2 | odd | 6 |