Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(911,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.911");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.cc (of order \(6\), 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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 911.6 | ||
Character | \(\chi\) | \(=\) | 1440.911 |
Dual form | 1440.2.cc.a.1391.6 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.36390 | − | 1.06761i | −0.787446 | − | 0.616384i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02179 | − | 0.589933i | −0.386202 | − | 0.222974i | 0.294311 | − | 0.955710i | \(-0.404910\pi\) |
−0.680513 | + | 0.732736i | \(0.738243\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.720424 | + | 2.91221i | 0.240141 | + | 0.970738i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46604 | − | 0.846417i | −0.442027 | − | 0.255204i | 0.262430 | − | 0.964951i | \(-0.415476\pi\) |
−0.704457 | + | 0.709747i | \(0.748809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.622400 | − | 0.359343i | 0.172623 | − | 0.0996638i | −0.411199 | − | 0.911546i | \(-0.634890\pi\) |
0.583822 | + | 0.811882i | \(0.301557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.242628 | + | 1.71497i | −0.0626463 | + | 0.442804i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.05527i | 0.983547i | 0.870723 | + | 0.491773i | \(0.163651\pi\) | ||||
−0.870723 | + | 0.491773i | \(0.836349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.64306 | −1.29461 | −0.647303 | − | 0.762232i | \(-0.724103\pi\) | ||||
−0.647303 | + | 0.762232i | \(0.724103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.763803 | + | 1.89548i | 0.166675 | + | 0.413628i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.06520 | + | 3.57703i | 0.430624 | + | 0.745863i | 0.996927 | − | 0.0783339i | \(-0.0249600\pi\) |
−0.566303 | + | 0.824197i | \(0.691627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.12652 | − | 4.74109i | 0.409249 | − | 0.912423i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.77305 | − | 3.07101i | 0.329247 | − | 0.570273i | −0.653115 | − | 0.757258i | \(-0.726538\pi\) |
0.982363 | + | 0.186985i | \(0.0598717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.580112 | − | 0.334928i | 0.104191 | − | 0.0601548i | −0.446999 | − | 0.894534i | \(-0.647507\pi\) |
0.551190 | + | 0.834380i | \(0.314174\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.09588 | + | 2.71958i | 0.190768 | + | 0.473418i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.17987i | 0.199434i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3000i | 1.85772i | 0.370437 | + | 0.928858i | \(0.379208\pi\) | ||||
−0.370437 | + | 0.928858i | \(0.620792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.23253 | − | 0.174373i | −0.197362 | − | 0.0279221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.943354 | − | 0.544646i | 0.147327 | − | 0.0850593i | −0.424524 | − | 0.905416i | \(-0.639559\pi\) |
0.571851 | + | 0.820357i | \(0.306225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.39038 | + | 2.40820i | −0.212030 | + | 0.367247i | −0.952350 | − | 0.305008i | \(-0.901341\pi\) |
0.740320 | + | 0.672255i | \(0.234674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.16184 | − | 2.08001i | 0.322268 | − | 0.310070i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.66393 | − | 4.61407i | 0.388575 | − | 0.673031i | −0.603683 | − | 0.797224i | \(-0.706301\pi\) |
0.992258 | + | 0.124193i | \(0.0396342\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.80396 | − | 4.85660i | −0.400565 | − | 0.693800i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.32944 | − | 5.53096i | 0.606242 | − | 0.774490i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.15371 | 1.25736 | 0.628680 | − | 0.777664i | \(-0.283596\pi\) | ||||
0.628680 | + | 0.777664i | \(0.283596\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.69283i | 0.228262i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.69655 | + | 6.02458i | 1.01943 | + | 0.797975i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.11816 | + | 3.53232i | −0.796516 | + | 0.459869i | −0.842251 | − | 0.539085i | \(-0.818770\pi\) |
0.0457354 | + | 0.998954i | \(0.485437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.33213 | + | 1.34646i | 0.298599 | + | 0.172396i | 0.641813 | − | 0.766861i | \(-0.278182\pi\) |
−0.343214 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.981886 | − | 3.40068i | 0.123706 | − | 0.428446i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.622400 | − | 0.359343i | −0.0771993 | − | 0.0445710i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.74884 | + | 13.4214i | 0.946672 | + | 1.63968i | 0.752369 | + | 0.658742i | \(0.228911\pi\) |
0.194303 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00215 | − | 7.08353i | 0.120645 | − | 0.852757i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1211 | 1.20115 | 0.600576 | − | 0.799568i | \(-0.294938\pi\) | ||||
0.600576 | + | 0.799568i | \(0.294938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.59376 | −0.888782 | −0.444391 | − | 0.895833i | \(-0.646580\pi\) | ||||
−0.444391 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.60652 | − | 0.647364i | 0.185505 | − | 0.0747512i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.998659 | + | 1.72973i | 0.113808 | + | 0.197121i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3263 | + | 6.53925i | 1.27431 | + | 0.735723i | 0.975796 | − | 0.218682i | \(-0.0701757\pi\) |
0.298514 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.96198 | + | 4.19606i | −0.884664 | + | 0.466229i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0184 | + | 6.93884i | 1.31919 | + | 0.761637i | 0.983599 | − | 0.180369i | \(-0.0577293\pi\) |
0.335595 | + | 0.942006i | \(0.391063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.51196 | − | 2.02763i | 0.380926 | − | 0.219928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.69690 | + | 2.29562i | −0.610772 | + | 0.246116i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.96883i | 0.526695i | 0.964701 | + | 0.263347i | \(0.0848265\pi\) | ||||
−0.964701 | + | 0.263347i | \(0.915173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.847953 | −0.0888896 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.14878 | − | 0.162526i | −0.119123 | − | 0.0168531i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.82153 | + | 4.88703i | 0.289483 | + | 0.501399i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.862865 | + | 1.49453i | −0.0876107 | + | 0.151746i | −0.906501 | − | 0.422204i | \(-0.861256\pi\) |
0.818890 | + | 0.573950i | \(0.194590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.40878 | − | 4.87919i | 0.141588 | − | 0.490377i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.41428 | − | 11.1099i | 0.638244 | − | 1.10547i | −0.347573 | − | 0.937653i | \(-0.612994\pi\) |
0.985818 | − | 0.167819i | \(-0.0536724\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.07102 | + | 2.35040i | −0.401129 | + | 0.231592i | −0.686971 | − | 0.726685i | \(-0.741060\pi\) |
0.285842 | + | 0.958277i | \(0.407727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.25963 | − | 1.60921i | 0.122928 | − | 0.157043i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3904i | 1.00448i | 0.864728 | + | 0.502240i | \(0.167491\pi\) | ||||
−0.864728 | + | 0.502240i | \(0.832509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.0084i | − | 1.15020i | −0.818085 | − | 0.575098i | \(-0.804964\pi\) | ||
0.818085 | − | 0.575098i | \(-0.195036\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0640 | − | 15.4121i | 1.14507 | − | 1.46285i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.20551 | − | 3.00540i | 0.489693 | − | 0.282725i | −0.234754 | − | 0.972055i | \(-0.575428\pi\) |
0.724447 | + | 0.689330i | \(0.242095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.06520 | − | 3.57703i | 0.192581 | − | 0.333560i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.49488 | + | 1.55368i | 0.138201 | + | 0.143638i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.39234 | − | 4.14365i | 0.219305 | − | 0.379847i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.06716 | − | 7.04452i | −0.369741 | − | 0.640411i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.86810 | − | 0.264293i | −0.168441 | − | 0.0238305i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.294527i | − | 0.0261350i | −0.999915 | − | 0.0130675i | \(-0.995840\pi\) | ||
0.999915 | − | 0.0130675i | \(-0.00415964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.46734 | − | 1.80016i | 0.393328 | − | 0.158495i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7549 | + | 8.51875i | −1.28914 | + | 0.744287i | −0.978501 | − | 0.206241i | \(-0.933877\pi\) |
−0.310641 | + | 0.950527i | \(0.600544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.76604 | + | 3.32903i | 0.499979 | + | 0.288663i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.16916 | + | 0.528923i | −0.444891 | + | 0.0455224i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4836 | + | 6.63009i | 0.981114 | + | 0.566447i | 0.902606 | − | 0.430467i | \(-0.141651\pi\) |
0.0785079 | + | 0.996913i | \(0.474984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.95041 | + | 10.3064i | 0.504707 | + | 0.874179i | 0.999985 | + | 0.00544412i | \(0.00173293\pi\) |
−0.495278 | + | 0.868735i | \(0.664934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.55935 | + | 3.44907i | −0.720827 | + | 0.290464i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.21662 | −0.101739 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.54610 | −0.294488 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.36064 | + | 9.61742i | −0.112224 | + | 0.793232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.19823 | + | 15.9318i | 0.753548 | + | 1.30518i | 0.946093 | + | 0.323896i | \(0.104993\pi\) |
−0.192545 | + | 0.981288i | \(0.561674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.302444 | + | 0.174616i | 0.0246126 | + | 0.0142101i | 0.512256 | − | 0.858833i | \(-0.328810\pi\) |
−0.487643 | + | 0.873043i | \(0.662143\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.8098 | + | 2.92151i | −0.954766 | + | 0.236190i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.580112 | − | 0.334928i | −0.0465957 | − | 0.0269020i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6531 | + | 10.7693i | −1.48868 | + | 0.859488i | −0.999916 | − | 0.0129307i | \(-0.995884\pi\) |
−0.488760 | + | 0.872418i | \(0.662551\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4847 | − | 9.77258i | −0.990102 | − | 0.775016i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.87332i | − | 0.384072i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.31335 | −0.572826 | −0.286413 | − | 0.958106i | \(-0.592463\pi\) | ||||
−0.286413 | + | 0.958106i | \(0.592463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.80728 | − | 2.30885i | 0.140697 | − | 0.179744i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.04946 | + | 12.2100i | 0.545504 | + | 0.944840i | 0.998575 | + | 0.0533657i | \(0.0169949\pi\) |
−0.453071 | + | 0.891474i | \(0.649672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24175 | + | 10.8110i | −0.480134 | + | 0.831617i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.06540 | − | 16.4338i | −0.310889 | − | 1.25672i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.65925 | − | 14.9983i | 0.658351 | − | 1.14030i | −0.322692 | − | 0.946504i | \(-0.604588\pi\) |
0.981043 | − | 0.193793i | \(-0.0620789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.02179 | − | 0.589933i | 0.0772404 | − | 0.0445947i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.1157 | + | 1.71408i | 0.910669 | + | 0.128838i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.99037i | − | 0.372998i | −0.982455 | − | 0.186499i | \(-0.940286\pi\) | ||
0.982455 | − | 0.186499i | \(-0.0597141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6992i | 1.53856i | 0.638911 | + | 0.769281i | \(0.279385\pi\) | ||||
−0.638911 | + | 0.769281i | \(0.720615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.74330 | − | 4.32623i | −0.128868 | − | 0.319804i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.78612 | − | 5.65002i | 0.719490 | − | 0.415398i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.43245 | − | 5.94517i | 0.251005 | − | 0.434754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.96979 | + | 3.58991i | −0.361499 | + | 0.261127i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.61931 | − | 16.6611i | 0.696029 | − | 1.20556i | −0.273803 | − | 0.961786i | \(-0.588282\pi\) |
0.969833 | − | 0.243772i | \(-0.0783849\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.6944 | − | 18.5233i | −0.769801 | − | 1.33333i | −0.937671 | − | 0.347525i | \(-0.887022\pi\) |
0.167870 | − | 0.985809i | \(-0.446311\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.465252 | + | 1.15459i | 0.0333174 | + | 0.0826816i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.9347 | −1.34904 | −0.674522 | − | 0.738255i | \(-0.735650\pi\) | ||||
−0.674522 | + | 0.738255i | \(0.735650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2052i | 1.71586i | 0.513765 | + | 0.857931i | \(0.328250\pi\) | ||||
−0.513765 | + | 0.857931i | \(0.671750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.76017 | − | 26.5781i | 0.265222 | − | 1.87467i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.62339 | + | 2.09196i | −0.254312 | + | 0.146827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.943354 | − | 0.544646i | −0.0658867 | − | 0.0380397i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.92927 | + | 8.59129i | −0.620627 | + | 0.597136i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.27294 | + | 4.77638i | 0.572251 | + | 0.330389i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.25728 | − | 16.0341i | −0.637297 | − | 1.10383i | −0.986023 | − | 0.166606i | \(-0.946719\pi\) |
0.348726 | − | 0.937225i | \(-0.386614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8041 | − | 10.8054i | −0.945842 | − | 0.740371i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.78075 | 0.189646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.790340 | −0.0536517 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3571 | + | 8.10716i | 0.699868 | + | 0.547831i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.45723 | + | 2.52400i | 0.0980240 | + | 0.169783i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3230 | − | 5.95998i | −0.691278 | − | 0.399110i | 0.112813 | − | 0.993616i | \(-0.464014\pi\) |
−0.804091 | + | 0.594507i | \(0.797347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.88226 | − | 0.832201i | −0.192151 | − | 0.0554801i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.34236 | + | 5.39382i | 0.620074 | + | 0.358000i | 0.776898 | − | 0.629627i | \(-0.216792\pi\) |
−0.156824 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.7576 | + | 13.1391i | −1.50386 | + | 0.868257i | −0.503875 | + | 0.863777i | \(0.668093\pi\) |
−0.999990 | + | 0.00448002i | \(0.998574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.484605 | − | 3.42535i | 0.0318847 | − | 0.225371i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.55605i | 0.626037i | 0.949747 | + | 0.313019i | \(0.101340\pi\) | ||||
−0.949747 | + | 0.313019i | \(0.898660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.32787 | −0.347552 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.46656 | − | 21.0109i | −0.549962 | − | 1.36481i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.6389 | − | 20.1591i | −0.752856 | − | 1.30398i | −0.946433 | − | 0.322899i | \(-0.895342\pi\) |
0.193578 | − | 0.981085i | \(-0.437991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.37713 | + | 5.84936i | −0.217540 | + | 0.376791i | −0.954055 | − | 0.299630i | \(-0.903137\pi\) |
0.736515 | + | 0.676421i | \(0.236470\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3391 | + | 2.77729i | 0.984001 | + | 0.178163i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.80396 | + | 4.85660i | −0.179138 | + | 0.310277i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.51224 | + | 2.02779i | −0.223479 | + | 0.129025i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.98392 | − | 22.2948i | −0.569333 | − | 1.41288i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.53803i | − | 0.538916i | −0.963012 | − | 0.269458i | \(-0.913155\pi\) | ||
0.963012 | − | 0.269458i | \(-0.0868445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.99209i | − | 0.439589i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.95467 | − | 0.983922i | −0.435518 | − | 0.0616156i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.26049 | + | 4.19184i | −0.452897 | + | 0.261480i | −0.709053 | − | 0.705155i | \(-0.750877\pi\) |
0.256156 | + | 0.966635i | \(0.417544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.66627 | − | 11.5463i | 0.414222 | − | 0.717453i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2208 | + | 2.95107i | 0.632652 | + | 0.182667i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.9363 | + | 20.6742i | −0.736022 | + | 1.27483i | 0.218252 | + | 0.975892i | \(0.429965\pi\) |
−0.954274 | + | 0.298935i | \(0.903369\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.57686 | − | 7.92735i | −0.281154 | − | 0.486973i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.30476 | − | 6.77696i | 0.324646 | − | 0.414743i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.11822 | −0.129150 | −0.0645752 | − | 0.997913i | \(-0.520569\pi\) | ||||
−0.0645752 | + | 0.997913i | \(0.520569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.47151i | − | 0.210879i | −0.994426 | − | 0.105440i | \(-0.966375\pi\) | ||
0.994426 | − | 0.105440i | \(-0.0336250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15652 | + | 0.905282i | 0.0699958 | + | 0.0547902i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.46604 | − | 0.846417i | 0.0884054 | − | 0.0510409i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4700 | + | 8.93161i | 0.929502 | + | 0.536648i | 0.886654 | − | 0.462433i | \(-0.153024\pi\) |
0.0428481 | + | 0.999082i | \(0.486357\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.39331 | + | 1.44812i | 0.0834151 | + | 0.0866966i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.19927 | − | 3.57915i | −0.369817 | − | 0.213514i | 0.303561 | − | 0.952812i | \(-0.401824\pi\) |
−0.673379 | + | 0.739298i | \(0.735158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.40809 | − | 12.8312i | −0.440365 | − | 0.762735i | 0.557351 | − | 0.830277i | \(-0.311818\pi\) |
−0.997716 | + | 0.0675418i | \(0.978484\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.36917 | − | 9.67769i | 0.0811023 | − | 0.573257i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.28522 | −0.0758640 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.554813 | 0.0326361 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.77243 | − | 1.11718i | 0.162523 | − | 0.0654900i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.14191 | − | 3.70990i | −0.125132 | − | 0.216735i | 0.796653 | − | 0.604437i | \(-0.206602\pi\) |
−0.921784 | + | 0.387703i | \(0.873269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.11816 | + | 3.53232i | 0.356213 | + | 0.205660i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.13050 | + | 5.15069i | −0.413753 | + | 0.298873i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.57076 | + | 1.48423i | 0.148671 | + | 0.0858353i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.84135 | − | 1.64046i | 0.163773 | − | 0.0945543i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.6094 | + | 8.30475i | −1.18398 | + | 0.477095i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.69292i | − | 0.154196i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.72522 | −0.383828 | −0.191914 | − | 0.981412i | \(-0.561470\pi\) | ||||
−0.191914 | + | 0.981412i | \(0.561470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.06175 | + | 1.14055i | 0.458617 | + | 0.0648835i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.29216 | − | 2.23808i | −0.0732715 | − | 0.126910i | 0.827062 | − | 0.562111i | \(-0.190011\pi\) |
−0.900333 | + | 0.435201i | \(0.856677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.48570 | − | 6.03740i | 0.197023 | − | 0.341254i | −0.750539 | − | 0.660826i | \(-0.770206\pi\) |
0.947562 | + | 0.319572i | \(0.103539\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.43602 | + | 0.850004i | −0.193598 | + | 0.0478923i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.840946 | − | 1.45656i | 0.0472322 | − | 0.0818086i | −0.841443 | − | 0.540346i | \(-0.818293\pi\) |
0.888675 | + | 0.458538i | \(0.151627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.19872 | + | 3.00148i | −0.291072 | + | 0.168051i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0929 | − | 14.1714i | 0.619145 | − | 0.790973i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.8841i | − | 1.27331i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.718686i | 0.0398655i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.8203 | + | 16.3782i | −0.708962 | + | 0.905716i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.44398 | + | 3.14309i | −0.300137 | + | 0.173284i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.29513 | − | 2.24323i | 0.0711868 | − | 0.123299i | −0.828235 | − | 0.560381i | \(-0.810655\pi\) |
0.899422 | + | 0.437082i | \(0.143988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.9081 | + | 8.14082i | −1.80335 | + | 0.446114i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.74884 | − | 13.4214i | 0.423364 | − | 0.733289i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.84149 | + | 10.1178i | 0.318206 | + | 0.551150i | 0.980114 | − | 0.198436i | \(-0.0635862\pi\) |
−0.661907 | + | 0.749586i | \(0.730253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3084 | − | 1.45839i | −0.559874 | − | 0.0792089i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.13395 | −0.0614071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.8757i | 0.803210i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.63559 | + | 2.67388i | −0.357248 | + | 0.143957i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.55078 | + | 3.20475i | −0.297982 | + | 0.172040i | −0.641536 | − | 0.767093i | \(-0.721702\pi\) |
0.343554 | + | 0.939133i | \(0.388369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.5635 | − | 10.1403i | −0.940153 | − | 0.542797i | −0.0501445 | − | 0.998742i | \(-0.515968\pi\) |
−0.890008 | + | 0.455945i | \(0.849302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.380129 | − | 3.71500i | −0.0202898 | − | 0.198292i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1091 | + | 5.83648i | 0.538052 | + | 0.310645i | 0.744289 | − | 0.667858i | \(-0.232788\pi\) |
−0.206237 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.06054 | − | 8.76512i | −0.268586 | − | 0.465204i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.68669 | + | 3.09742i | −0.406823 | + | 0.163933i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.88907 | −0.363591 | −0.181796 | − | 0.983336i | \(-0.558191\pi\) | ||||
−0.181796 | + | 0.983336i | \(0.558191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8441 | 0.676007 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.97361 | + | 13.9501i | −0.103588 | + | 0.732192i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.79688 | + | 6.57639i | 0.198738 | + | 0.344224i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.5870 | − | 17.6594i | −1.59663 | − | 0.921812i | −0.992131 | − | 0.125203i | \(-0.960042\pi\) |
−0.604495 | − | 0.796609i | \(-0.706625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.26574 | + | 2.35487i | 0.117950 | + | 0.122590i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.35321 | − | 5.40008i | −0.485594 | − | 0.280358i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8589 | − | 10.3108i | 0.924699 | − | 0.533875i | 0.0395680 | − | 0.999217i | \(-0.487402\pi\) |
0.885131 | + | 0.465342i | \(0.154068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.36390 | − | 1.06761i | −0.0704313 | − | 0.0551311i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.54853i | − | 0.131256i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.47680 | −0.486791 | −0.243395 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243395 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.314439 | + | 0.401704i | −0.0161092 | + | 0.0205799i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6393 | + | 23.6240i | 0.696938 | + | 1.20713i | 0.969523 | + | 0.245000i | \(0.0787879\pi\) |
−0.272585 | + | 0.962132i | \(0.587879\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.998659 | − | 1.72973i | 0.0508964 | − | 0.0881551i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.01485 | − | 2.31414i | −0.407418 | − | 0.117635i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.12156 | + | 10.6029i | −0.310375 | + | 0.537586i | −0.978444 | − | 0.206514i | \(-0.933788\pi\) |
0.668068 | + | 0.744100i | \(0.267121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.5058 | + | 8.37494i | −0.733591 | + | 0.423539i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.2188 | + | 4.13378i | 1.47390 | + | 0.208521i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13.0785i | − | 0.658051i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.50428i | − | 0.175875i | −0.996126 | − | 0.0879373i | \(-0.971972\pi\) | ||
0.996126 | − | 0.0879373i | \(-0.0280275\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.31019 | − | 10.6963i | −0.215779 | − | 0.535486i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.5002 | + | 19.9187i | −1.72286 | + | 0.994691i | −0.809975 | + | 0.586465i | \(0.800519\pi\) |
−0.912881 | + | 0.408226i | \(0.866148\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.240708 | − | 0.416918i | 0.0119905 | − | 0.0207682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.61488 | + | 4.79725i | 0.378387 | + | 0.238377i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.56455 | − | 16.5663i | 0.474097 | − | 0.821160i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4218 | + | 21.5152i | 0.614219 | + | 1.06386i | 0.990521 | + | 0.137362i | \(0.0438624\pi\) |
−0.376301 | + | 0.926497i | \(0.622804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.58416 | − | 21.3028i | −0.423426 | − | 1.05079i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.33533 | 0.410155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.8777i | − | 0.681229i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.88747 | − | 20.4096i | 0.141400 | − | 0.999462i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.15450 | − | 0.666549i | 0.0564009 | − | 0.0325631i | −0.471534 | − | 0.881848i | \(-0.656300\pi\) |
0.527935 | + | 0.849285i | \(0.322966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.60932 | − | 3.23854i | −0.273381 | − | 0.157837i | 0.357042 | − | 0.934088i | \(-0.383785\pi\) |
−0.630423 | + | 0.776252i | \(0.717119\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.3563 | + | 4.43386i | 0.746650 | + | 0.215582i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.51196 | − | 2.02763i | −0.170355 | − | 0.0983547i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.58864 | − | 2.75160i | −0.0768797 | − | 0.133159i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.65934 | + | 1.29887i | 0.0801136 | + | 0.0627100i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0064 | −0.771000 | −0.385500 | − | 0.922708i | \(-0.625971\pi\) | ||||
−0.385500 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.9579 | 0.863003 | 0.431501 | − | 0.902112i | \(-0.357984\pi\) | ||||
0.431501 | + | 0.902112i | \(0.357984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.83651 | + | 3.78585i | 0.231893 | + | 0.181518i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6541 | − | 20.1854i | −0.557489 | − | 0.965600i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.75341 | + | 4.47643i | 0.370050 | + | 0.213648i | 0.673480 | − | 0.739205i | \(-0.264799\pi\) |
−0.303430 | + | 0.952854i | \(0.598132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1234 | − | 11.6645i | 0.577305 | − | 0.555454i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8234 | + | 17.7959i | 1.46447 | + | 0.845509i | 0.999213 | − | 0.0396689i | \(-0.0126303\pi\) |
0.465252 | + | 0.885178i | \(0.345964\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.30313 | − | 2.48441i | 0.203988 | − | 0.117772i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.46350 | − | 31.5494i | 0.211116 | − | 1.49224i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.62925i | 0.360047i | 0.983662 | + | 0.180023i | \(0.0576173\pi\) | ||||
−0.983662 | + | 0.180023i | \(0.942383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.84399 | −0.0868301 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.226081 | − | 0.561051i | −0.0106222 | − | 0.0263605i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.423977 | + | 0.734349i | 0.0198763 | + | 0.0344268i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0212 | + | 26.0174i | −0.702660 | + | 1.21704i | 0.264869 | + | 0.964284i | \(0.414671\pi\) |
−0.967529 | + | 0.252759i | \(0.918662\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.2264 | + | 8.62361i | 0.897410 | + | 0.402516i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1809 | − | 28.0261i | 0.753618 | − | 1.30531i | −0.192440 | − | 0.981309i | \(-0.561640\pi\) |
0.946058 | − | 0.323997i | \(-0.105027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9061 | − | 8.02871i | 0.646273 | − | 0.373126i | −0.140754 | − | 0.990045i | \(-0.544953\pi\) |
0.787027 | + | 0.616919i | \(0.211619\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.433640 | + | 1.07614i | 0.0201096 | + | 0.0499047i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7880i | 0.684308i | 0.939644 | + | 0.342154i | \(0.111156\pi\) | ||||
−0.939644 | + | 0.342154i | \(0.888844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 18.2852i | − | 0.844332i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.9383 | + | 5.22589i | 1.70203 | + | 0.240797i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.07668 | − | 2.35367i | 0.187446 | − | 0.108222i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82153 | − | 4.88703i | 0.129461 | − | 0.224232i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.59456 | + | 26.6576i | 0.301944 | + | 1.22057i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.3061 | − | 23.0468i | 0.607969 | − | 1.05303i | −0.383606 | − | 0.923497i | \(-0.625318\pi\) |
0.991575 | − | 0.129536i | \(-0.0413489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.06059 | + | 7.03315i | 0.185147 | + | 0.320684i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.20280 | + | 6.64671i | −0.236736 | + | 0.302436i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.72573 | 0.0783614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0627i | 1.22633i | 0.789956 | + | 0.613164i | \(0.210104\pi\) | ||||
−0.789956 | + | 0.613164i | \(0.789896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.97465 | + | 7.80779i | 0.451069 | + | 0.353081i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.3680 | − | 11.7595i | 0.919194 | − | 0.530697i | 0.0358165 | − | 0.999358i | \(-0.488597\pi\) |
0.883378 | + | 0.468661i | \(0.155263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4538 | + | 7.19019i | 0.560890 | + | 0.323830i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.92990 | + | 1.21956i | −0.221582 | + | 0.0548151i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3417 | − | 5.97076i | −0.463887 | − | 0.267825i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.21984 | + | 5.57692i | 0.144140 | + | 0.249657i | 0.929052 | − | 0.369950i | \(-0.120625\pi\) |
−0.784912 | + | 0.619607i | \(0.787292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.42079 | − | 24.1793i | 0.152830 | − | 1.08025i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9851 | −0.712738 | −0.356369 | − | 0.934345i | \(-0.615985\pi\) | ||||
−0.356369 | + | 0.934345i | \(0.615985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8286 | −0.570863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0550 | − | 8.08137i | 0.890675 | − | 0.358906i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0256 | + | 36.4174i | 0.931944 | + | 1.61417i | 0.779994 | + | 0.625787i | \(0.215222\pi\) |
0.151950 | + | 0.988388i | \(0.451445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.75925 | + | 4.47981i | 0.343249 | + | 0.198175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0001 | + | 26.7542i | −0.529817 | + | 1.18123i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.07102 | + | 2.35040i | 0.179390 | + | 0.103571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.81086 | + | 4.50960i | −0.343521 | + | 0.198332i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.8226 | + | 11.2114i | −1.22128 | + | 0.492125i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.0924i | − | 1.14313i | −0.820558 | − | 0.571563i | \(-0.806337\pi\) | ||
0.820558 | − | 0.571563i | \(-0.193663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.9530 | −1.30975 | −0.654876 | − | 0.755737i | \(-0.727279\pi\) | ||||
−0.654876 | + | 0.755737i | \(0.727279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.02344 | − | 0.286269i | −0.0883101 | − | 0.0124938i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.35822 | + | 2.35251i | 0.0591650 | + | 0.102477i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.96988 | − | 5.14398i | 0.129125 | − | 0.223651i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.6945 | − | 15.2726i | −0.637688 | − | 0.662775i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.391429 | − | 0.677975i | 0.0169547 | − | 0.0293664i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.99837 | − | 5.19521i | 0.389033 | − | 0.224608i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.32776 | + | 6.80634i | −0.229910 | + | 0.293715i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.49327i | 0.408904i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.81980i | − | 0.0782393i | −0.999235 | − | 0.0391196i | \(-0.987545\pi\) | ||
0.999235 | − | 0.0391196i | \(-0.0124553\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.0987 | − | 28.2316i | 0.948345 | − | 1.21153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3996 | + | 6.00420i | −0.445469 | + | 0.257191i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.93203 | + | 12.0066i | −0.296392 | + | 0.513367i | −0.975308 | − | 0.220850i | \(-0.929117\pi\) |
0.678915 | + | 0.734216i | \(0.262450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.24105 | + | 7.76169i | −0.0956456 | + | 0.331261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0054 | + | 17.3299i | −0.426246 | + | 0.738279i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.71544 | − | 13.3635i | −0.328094 | − | 0.568275i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.3793 | − | 2.74171i | −0.822604 | − | 0.116379i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1558 | 0.557428 | 0.278714 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278714 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.99849i | 0.0845270i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0286 | + | 4.44409i | −0.465629 | + | 0.187630i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.3026 | − | 16.3405i | 1.19281 | − | 0.688671i | 0.233869 | − | 0.972268i | \(-0.424861\pi\) |
0.958943 | + | 0.283598i | \(0.0915280\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.20551 | − | 3.00540i | −0.218998 | − | 0.126438i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6109 | + | 0.409527i | 0.445616 | + | 0.0171985i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.9164 | + | 8.03462i | 0.583404 | + | 0.336829i | 0.762485 | − | 0.647006i | \(-0.223979\pi\) |
−0.179081 | + | 0.983834i | \(0.557312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1991 | + | 34.9859i | 0.845308 | + | 1.46412i | 0.885354 | + | 0.464918i | \(0.153916\pi\) |
−0.0400464 | + | 0.999198i | \(0.512751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.9073 | + | 12.4544i | −1.29117 | + | 0.520290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.13040 | −0.172250 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.7400 | 1.61277 | 0.806384 | − | 0.591392i | \(-0.201421\pi\) | ||||
0.806384 | + | 0.591392i | \(0.201421\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.18953 | + | 36.6812i | −0.215670 | + | 1.52442i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.18691 | − | 14.1801i | −0.339650 | − | 0.588291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4197 | − | 7.74786i | −0.555787 | − | 0.320884i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.598091 | − | 2.07144i | 0.0247280 | − | 0.0856436i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.1211 | − | 6.42078i | −0.459018 | − | 0.265014i | 0.252613 | − | 0.967567i | \(-0.418710\pi\) |
−0.711631 | + | 0.702553i | \(0.752043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.27361 | + | 1.89002i | −0.134887 | + | 0.0778768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.8250 | + | 20.2149i | 1.06230 | + | 0.831529i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.8596i | − | 1.47258i | −0.676668 | − | 0.736288i | \(-0.736577\pi\) | ||
0.676668 | − | 0.736288i | \(-0.263423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.78467 | −0.196152 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.8417 | − | 33.0134i | 1.05763 | − | 1.35115i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.760967 | + | 1.31803i | 0.0310923 | + | 0.0538534i | 0.881153 | − | 0.472832i | \(-0.156768\pi\) |
−0.850061 | + | 0.526685i | \(0.823435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4622 | − | 23.3172i | 0.549135 | − | 0.951130i | −0.449199 | − | 0.893432i | \(-0.648291\pi\) |
0.998334 | − | 0.0576983i | \(-0.0183761\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.5035 | + | 32.2354i | −1.36437 | + | 1.31273i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.06716 | + | 7.04452i | −0.165353 | + | 0.286400i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.9753 | − | 6.33658i | 0.445473 | − | 0.257194i | −0.260444 | − | 0.965489i | \(-0.583869\pi\) |
0.705916 | + | 0.708295i | \(0.250535\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.17532 | + | 1.01514i | 0.290759 | + | 0.0411355i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.82906i | − | 0.154907i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4783i | 0.907890i | 0.891030 | + | 0.453945i | \(0.149984\pi\) | ||||
−0.891030 | + | 0.453945i | \(0.850016\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.705168 | + | 1.74997i | 0.0284351 | + | 0.0705657i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8335 | + | 20.6885i | −1.44260 | + | 0.832886i | −0.998023 | − | 0.0628537i | \(-0.979980\pi\) |
−0.444578 | + | 0.895740i | \(0.646647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.75193 | − | 9.96263i | 0.231190 | − | 0.400432i | −0.726969 | − | 0.686670i | \(-0.759072\pi\) |
0.958158 | + | 0.286238i | \(0.0924049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.3507 | − | 2.18466i | 0.856775 | − | 0.0876676i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.93127 | − | 5.07712i | 0.117439 | − | 0.203410i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.18412 | − | 15.3467i | −0.246970 | − | 0.612890i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.8247 | −1.82715 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.70901i | − | 0.147654i | −0.997271 | − | 0.0738268i | \(-0.976479\pi\) | ||
0.997271 | − | 0.0738268i | \(-0.0235212\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.49215 | + | 31.7520i | −0.178547 | + | 1.26203i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.255068 | + | 0.147263i | −0.0101221 | + | 0.00584397i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.49037 | − | 2.01517i | −0.138293 | − | 0.0798438i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.29147 | + | 29.4748i | 0.288446 | + | 1.16600i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.6920 | − | 8.48244i | −0.580300 | − | 0.335036i | 0.180953 | − | 0.983492i | \(-0.442082\pi\) |
−0.761252 | + | 0.648456i | \(0.775415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0107 | − | 20.8032i | −0.473657 | − | 0.820398i | 0.525888 | − | 0.850554i | \(-0.323733\pi\) |
−0.999545 | + | 0.0301558i | \(0.990400\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.79265 | − | 2.96875i | −0.149336 | − | 0.116895i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.1081 | −1.22299 | −0.611493 | − | 0.791250i | \(-0.709431\pi\) | ||||
−0.611493 | + | 0.791250i | \(0.709431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.9593 | 0.469442 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.07794 | + | 0.843773i | 0.0422478 | + | 0.0330701i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.2158 | + | 41.9430i | 0.947638 | + | 1.64136i | 0.750381 | + | 0.661005i | \(0.229870\pi\) |
0.197257 | + | 0.980352i | \(0.436797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7549 | + | 8.51875i | 0.576522 | + | 0.332855i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.47073 | − | 22.1146i | −0.213433 | − | 0.862774i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.3198 | + | 8.26752i | 0.557819 | + | 0.322057i | 0.752270 | − | 0.658855i | \(-0.228959\pi\) |
−0.194451 | + | 0.980912i | \(0.562292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9686 | − | 11.5289i | 0.776687 | − | 0.448420i | −0.0585680 | − | 0.998283i | \(-0.518653\pi\) |
0.835255 | + | 0.549863i | \(0.185320\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.707131 | − | 4.99822i | 0.0274627 | − | 0.194115i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.65805i | − | 0.258188i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6468 | 0.567128 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.71655 | + | 19.1497i | 0.298339 | + | 0.740370i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.27933 | − | 3.94791i | −0.0879926 | − | 0.152408i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6629 | + | 25.3969i | −0.565213 | + | 0.978977i | 0.431817 | + | 0.901961i | \(0.357873\pi\) |
−0.997030 | + | 0.0770158i | \(0.975461\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.04264 | + | 4.21216i | 0.117111 | + | 0.162126i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.94679 | + | 6.83604i | −0.151687 | + | 0.262730i | −0.931848 | − | 0.362849i | \(-0.881804\pi\) |
0.780161 | + | 0.625579i | \(0.215137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76334 | − | 1.01806i | 0.0676708 | − | 0.0390697i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.98353 | − | 17.3306i | −0.267609 | − | 0.664110i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.634665i | − | 0.0242848i | −0.999926 | − | 0.0121424i | \(-0.996135\pi\) | ||
0.999926 | − | 0.0121424i | \(-0.00386514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13.2602i | − | 0.506645i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.0664 | + | 6.37584i | 1.71939 | + | 0.243253i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.69727 | − | 3.28932i | 0.217049 | − | 0.125313i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0251 | + | 27.7562i | −0.609622 | + | 1.05590i | 0.381681 | + | 0.924294i | \(0.375345\pi\) |
−0.991303 | + | 0.131602i | \(0.957988\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.31788 | + | 4.15445i | −0.164023 | + | 0.157814i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.95041 | − | 10.3064i | 0.225712 | − | 0.390945i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.20868 | + | 3.82555i | 0.0836598 | + | 0.144903i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.2021 | − | 13.0335i | 0.385879 | − | 0.492970i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.21948 | 0.0838288 | 0.0419144 | − | 0.999121i | \(-0.486654\pi\) | ||||
0.0419144 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 63.7668i | − | 2.40501i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.26666 | + | 5.68808i | 0.273678 | + | 0.214225i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.1081 | + | 7.56799i | −0.492982 | + | 0.284623i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5688 | + | 10.7207i | 0.697364 | + | 0.402624i | 0.806365 | − | 0.591418i | \(-0.201432\pi\) |
−0.109001 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.8839 | + | 37.6957i | −0.408180 | + | 1.41370i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.39610 | + | 1.38339i | 0.0897345 | + | 0.0518082i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.608308 | + | 1.05362i | 0.0227494 | + | 0.0394032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.64783 | + | 39.9207i | −0.210922 | + | 1.49087i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0608 | 0.412498 | 0.206249 | − | 0.978499i | \(-0.433874\pi\) | ||||
0.206249 | + | 0.978499i | \(0.433874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.54632 | 0.206556 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.8509 | − | 4.37247i | 0.403549 | − | 0.162614i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.77305 | + | 3.07101i | 0.0658495 | + | 0.114055i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.9631 | − | 9.21629i | −0.592038 | − | 0.341813i | 0.173865 | − | 0.984769i | \(-0.444374\pi\) |
−0.765903 | + | 0.642956i | \(0.777708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.9558 | − | 20.1640i | −0.665030 | − | 0.746816i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.76589 | − | 5.63834i | −0.361205 | − | 0.208542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9150 | − | 10.9206i | 0.698641 | − | 0.403360i | −0.108200 | − | 0.994129i | \(-0.534509\pi\) |
0.806841 | + | 0.590769i | \(0.201175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00925 | − | 3.63036i | 0.332311 | − | 0.133908i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 26.2350i | − | 0.966379i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2982 | 0.636326 | 0.318163 | − | 0.948036i | \(-0.396934\pi\) | ||||
0.318163 | + | 0.948036i | \(0.396934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.95522 | + | 0.984000i | 0.255506 | + | 0.0361481i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.2134 | + | 43.6709i | 0.924990 | + | 1.60213i | 0.791577 | + | 0.611069i | \(0.209260\pi\) |
0.133413 | + | 0.991061i | \(0.457406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.19823 | − | 15.9318i | 0.336997 | − | 0.583696i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.5490 | + | 39.9991i | −0.422557 | + | 1.46349i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.12965 | − | 10.6169i | 0.223973 | − | 0.387932i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9397 | + | 10.9349i | −0.691120 | + | 0.399019i | −0.804032 | − | 0.594587i | \(-0.797316\pi\) |
0.112911 | + | 0.993605i | \(0.463982\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.11528 | + | 11.6450i | −0.332179 | + | 0.424367i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 0.349233i | − | 0.0127099i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.81492i | − | 0.247693i | −0.992301 | − | 0.123846i | \(-0.960477\pi\) | ||
0.992301 | − | 0.123846i | \(-0.0395230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.46481 | + | 9.53648i | −0.270956 | + | 0.346152i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.8048 | + | 19.5172i | −1.22542 | + | 0.707498i | −0.966069 | − | 0.258284i | \(-0.916843\pi\) |
−0.259354 | + | 0.965782i | \(0.583510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.08415 | + | 12.2701i | −0.256463 | + | 0.444207i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.43500 | + | 8.76683i | 0.304968 | + | 0.316966i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.53863 | + | 4.39703i | −0.0916645 | + | 0.158768i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.96893 | − | 6.87439i | −0.143123 | − | 0.247897i | 0.785548 | − | 0.618801i | \(-0.212381\pi\) |
−0.928671 | + | 0.370904i | \(0.879048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3778 | + | 2.03412i | 0.517804 | + | 0.0732570i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −54.8377 | −1.97238 | −0.986188 | − | 0.165632i | \(-0.947034\pi\) | ||||
−0.986188 | + | 0.165632i | \(0.947034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.669855i | 0.0240619i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.4190 | + | 8.63101i | −0.768404 | + | 0.309636i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.32340 | + | 3.07347i | −0.190731 | + | 0.110118i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.8379 | − | 8.56666i | −0.530941 | − | 0.306539i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.7895 | − | 14.9368i | −0.385586 | − | 0.533796i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.6531 | + | 10.7693i | 0.665756 | + | 0.384375i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.6878 | + | 20.2439i | 0.416625 | + | 0.721616i | 0.995598 | − | 0.0937309i | \(-0.0298793\pi\) |
−0.578972 | + | 0.815347i | \(0.696546\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.3518 | − | 15.4542i | 1.36536 | − | 0.550185i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.09195 | −0.252161 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.93536 | 0.0687267 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.22095 | + | 15.6984i | −0.0787689 | + | 0.556764i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.2474 | − | 19.4810i | −0.398403 | − | 0.690054i | 0.595126 | − | 0.803632i | \(-0.297102\pi\) |
−0.993529 | + | 0.113578i | \(0.963769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.7113 | + | 10.8030i | 0.661958 | + | 0.382181i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.4703 | + | 3.57966i | −0.511282 | + | 0.126481i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.1327 | + | 6.42749i | 0.392866 | + | 0.226821i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.22042 | + | 2.43666i | −0.148750 | + | 0.0858810i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.88904 | + | 2.26143i | 0.101699 | + | 0.0796062i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.6019i | − | 0.372744i | −0.982479 | − | 0.186372i | \(-0.940327\pi\) | ||
0.982479 | − | 0.186372i | \(-0.0596730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.4705 | 1.59668 | 0.798342 | − | 0.602204i | \(-0.205711\pi\) | ||||
0.798342 | + | 0.602204i | \(0.205711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.70621 | + | 4.73478i | −0.129983 | + | 0.166056i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.65667 | + | 6.33355i | 0.128088 | + | 0.221854i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.84597 | − | 13.5896i | 0.274496 | − | 0.475441i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.610886 | − | 2.46942i | −0.0213461 | − | 0.0862885i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.79733 | − | 11.7733i | 0.237229 | − | 0.410892i | −0.722689 | − | 0.691173i | \(-0.757094\pi\) |
0.959918 | + | 0.280281i | \(0.0904276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.8629 | − | 26.4790i | 1.59868 | − | 0.922998i | 0.606938 | − | 0.794749i | \(-0.292397\pi\) |
0.991742 | − | 0.128250i | \(-0.0409358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.90316 | − | 0.410729i | −0.101075 | − | 0.0142998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.1858i | − | 0.458517i | −0.973366 | − | 0.229258i | \(-0.926370\pi\) | ||
0.973366 | − | 0.229258i | \(-0.0736301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.6691i | − | 0.960987i | −0.876998 | − | 0.480494i | \(-0.840458\pi\) | ||
0.876998 | − | 0.480494i | \(-0.159542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5640 | − | 28.6977i | −0.401151 | − | 0.995512i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.6948 | − | 11.3708i | 0.682384 | − | 0.393975i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.04946 | − | 12.2100i | 0.243957 | − | 0.422545i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.354302 | − | 3.46259i | −0.0122465 | − | 0.119685i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.30540 | + | 12.6533i | −0.252210 | + | 0.436841i | −0.964134 | − | 0.265416i | \(-0.914491\pi\) |
0.711924 | + | 0.702257i | \(0.247824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.21258 | + | 14.2246i | 0.283192 | + | 0.490504i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.63403 | + | 11.5000i | 0.159604 | + | 0.396080i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4835 | 0.429445 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.59740i | 0.329770i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.59482 | + | 25.4093i | −0.123374 | + | 0.872047i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.4206 | + | 23.3369i | −1.38560 | + | 0.799978i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9267 | + | 6.88590i | 0.408364 | + | 0.235769i | 0.690086 | − | 0.723727i | \(-0.257573\pi\) |
−0.281723 | + | 0.959496i | \(0.590906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.1994 | + | 11.7376i | −0.417210 | + | 0.401419i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7045 | + | 13.6858i | 0.809729 | + | 0.467497i | 0.846862 | − | 0.531813i | \(-0.178489\pi\) |
−0.0371325 | + | 0.999310i | \(0.511822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.49539 | − | 6.05420i | −0.119261 | − | 0.206567i | 0.800214 | − | 0.599715i | \(-0.204719\pi\) |
−0.919475 | + | 0.393148i | \(0.871386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75290 | + | 1.37211i | 0.0597388 | + | 0.0467614i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.01460 | 0.170699 | 0.0853495 | − | 0.996351i | \(-0.472799\pi\) | ||||
0.0853495 | + | 0.996351i | \(0.472799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.3185 | −0.588847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.756708 | − | 0.592324i | −0.0256991 | − | 0.0201164i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0699 | − | 19.1736i | −0.375520 | − | 0.650419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.64576 | + | 5.56898i | 0.326834 | + | 0.188698i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.97401 | − | 1.43615i | −0.168345 | − | 0.0486065i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.02179 | − | 0.589933i | −0.0345429 | − | 0.0199434i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.3620 | − | 25.6124i | 1.49800 | − | 0.864870i | 0.498002 | − | 0.867176i | \(-0.334067\pi\) |
0.999997 | + | 0.00230558i | \(0.000733889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.03938 | + | 7.34664i | −0.0350573 | + | 0.247796i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.2669i | 1.25555i | 0.778394 | + | 0.627777i | \(0.216035\pi\) | ||||
−0.778394 | + | 0.627777i | \(0.783965\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8819 | 0.938301 | 0.469151 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469151 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.57339 | − | 11.3495i | −0.153733 | − | 0.381510i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.74805 | + | 13.4200i | 0.260154 | + | 0.450600i | 0.966283 | − | 0.257483i | \(-0.0828933\pi\) |
−0.706129 | + | 0.708084i | \(0.749560\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.173751 | + | 0.300946i | −0.00582742 | + | 0.0100934i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.2242 | + | 0.587577i | 0.510029 | + | 0.0196846i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.0327 | + | 26.0375i | −0.503052 | + | 0.871311i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.32179 | + | 2.49518i | −0.144461 | + | 0.0834048i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.92168 | − | 4.76891i | −0.0641629 | − | 0.159229i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.37538i | − | 0.0792232i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1207i | 1.23667i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.62668 | − | 0.796042i | −0.187244 | − | 0.0264906i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.9261 | − | 10.3496i | 0.595882 | − | 0.344033i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.14332 | − | 3.71233i | 0.0711676 | − | 0.123266i | −0.828246 | − | 0.560365i | \(-0.810661\pi\) |
0.899413 | + | 0.437099i | \(0.143994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.9753 | + | 10.6759i | 1.22639 | + | 0.354099i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.66147 | − | 6.34185i | 0.121310 | − | 0.210115i | −0.798975 | − | 0.601365i | \(-0.794624\pi\) |
0.920284 | + | 0.391250i | \(0.127957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.7463 | − | 20.3452i | −0.388746 | − | 0.673328i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.87498 | + | 3.67286i | −0.0950439 | + | 0.121421i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.1020 | 0.663825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.3957i | − | 0.606818i | −0.952860 | − | 0.303409i | \(-0.901875\pi\) | ||
0.952860 | − | 0.303409i | \(-0.0981249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.17250 | + | 7.17990i | 0.302244 | + | 0.236586i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.29937 | − | 3.63694i | 0.207346 | − | 0.119711i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.78612 | − | 5.65002i | −0.321766 | − | 0.185772i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.77773 | − | 10.1624i | −0.321143 | − | 0.333776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.9190 | − | 10.3455i | −0.587903 | − | 0.339426i | 0.176365 | − | 0.984325i | \(-0.443566\pi\) |
−0.764268 | + | 0.644899i | \(0.776899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8229 | + | 27.4061i | 0.518575 | + | 0.898198i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.627027 | + | 4.43203i | −0.0205280 | + | 0.145098i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.86489 | −0.224506 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.59458 | −0.280773 | −0.140386 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140386 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1997 | + | 4.51303i | −0.365489 | + | 0.147277i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.07610 | + | 12.2562i | 0.230674 | + | 0.399540i | 0.958007 | − | 0.286746i | \(-0.0925735\pi\) |
−0.727332 | + | 0.686285i | \(0.759240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.89643 | + | 2.24961i | 0.126885 | + | 0.0732573i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.59385 | + | 2.50901i | 0.181968 | + | 0.0816181i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.0703 | − | 19.0932i | −1.07464 | − | 0.620445i | −0.145196 | − | 0.989403i | \(-0.546381\pi\) |
−0.929446 | + | 0.368958i | \(0.879715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.72636 | + | 2.72876i | −0.153424 | + | 0.0885794i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.70200 | + | 1.08880i | −0.0876183 | + | 0.0353067i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.88922i | 0.0611978i | 0.999532 | + | 0.0305989i | \(0.00974145\pi\) | ||||
−0.999532 | + | 0.0305989i | \(0.990259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.2386 | −0.622547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.2949 | + | 1.45649i | 0.332787 | + | 0.0470816i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.82261 | − | 13.5492i | −0.252605 | − | 0.437525i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2756 | + | 26.4582i | −0.492763 | + | 0.853490i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.2591 | + | 7.48551i | −0.975086 | + | 0.241217i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6944 | + | 18.5233i | −0.344265 | + | 0.596285i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5058 | − | 12.4164i | 0.691579 | − | 0.399283i | −0.112624 | − | 0.993638i | \(-0.535926\pi\) |
0.804203 | + | 0.594354i | \(0.202592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.4313 | + | 31.2115i | −0.784846 | + | 1.00266i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4099i | 0.687075i | 0.939139 | + | 0.343538i | \(0.111625\pi\) | ||||
−0.939139 | + | 0.343538i | \(0.888375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.0414i | − | 0.450146i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.767275 | − | 0.980213i | 0.0245725 | − | 0.0313919i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.0044 | − | 6.35337i | 0.352061 | − | 0.203262i | −0.313532 | − | 0.949578i | \(-0.601512\pi\) |
0.665593 | + | 0.746315i | \(0.268179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.20570 | − | 7.28449i | 0.134415 | − | 0.232813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.9710 | − | 8.65113i | 1.11654 | − | 0.276209i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.35255 | + | 2.34269i | −0.0431397 | + | 0.0747202i | −0.886789 | − | 0.462174i | \(-0.847069\pi\) |
0.843649 | + | 0.536895i | \(0.180403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.46736 | + | 16.3980i | 0.301655 | + | 0.522482i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7806 | + | 1.52520i | 0.343151 | + | 0.0485477i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.4856 | −0.365222 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.6055i | − | 0.591024i | −0.955339 | − | 0.295512i | \(-0.904510\pi\) | ||
0.955339 | − | 0.295512i | \(-0.0954903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.16132 | + | 1.67684i | −0.132055 | + | 0.0532130i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.9623 | − | 12.1026i | 0.664550 | − | 0.383678i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.4956 | − | 8.36903i | −0.459080 | − | 0.265050i | 0.252578 | − | 0.967577i | \(-0.418722\pi\) |
−0.711657 | + | 0.702527i | \(0.752055\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 53.5745 | + | 24.0298i | 1.69502 | + | 0.760268i |
(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 | 1440.2.cc.a.911.6 | 48 | ||
3.2 | odd | 2 | 4320.2.cc.b.1871.10 | 48 | |||
4.3 | odd | 2 | 360.2.bm.a.11.1 | ✓ | 48 | ||
8.3 | odd | 2 | 1440.2.cc.b.911.6 | 48 | |||
8.5 | even | 2 | 360.2.bm.b.11.10 | yes | 48 | ||
9.4 | even | 3 | 4320.2.cc.a.3311.15 | 48 | |||
9.5 | odd | 6 | 1440.2.cc.b.1391.6 | 48 | |||
12.11 | even | 2 | 1080.2.bm.b.251.24 | 48 | |||
24.5 | odd | 2 | 1080.2.bm.a.251.15 | 48 | |||
24.11 | even | 2 | 4320.2.cc.a.1871.15 | 48 | |||
36.23 | even | 6 | 360.2.bm.b.131.10 | yes | 48 | ||
36.31 | odd | 6 | 1080.2.bm.a.611.15 | 48 | |||
72.5 | odd | 6 | 360.2.bm.a.131.1 | yes | 48 | ||
72.13 | even | 6 | 1080.2.bm.b.611.24 | 48 | |||
72.59 | even | 6 | inner | 1440.2.cc.a.1391.6 | 48 | ||
72.67 | odd | 6 | 4320.2.cc.b.3311.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bm.a.11.1 | ✓ | 48 | 4.3 | odd | 2 | ||
360.2.bm.a.131.1 | yes | 48 | 72.5 | odd | 6 | ||
360.2.bm.b.11.10 | yes | 48 | 8.5 | even | 2 | ||
360.2.bm.b.131.10 | yes | 48 | 36.23 | even | 6 | ||
1080.2.bm.a.251.15 | 48 | 24.5 | odd | 2 | |||
1080.2.bm.a.611.15 | 48 | 36.31 | odd | 6 | |||
1080.2.bm.b.251.24 | 48 | 12.11 | even | 2 | |||
1080.2.bm.b.611.24 | 48 | 72.13 | even | 6 | |||
1440.2.cc.a.911.6 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.cc.a.1391.6 | 48 | 72.59 | even | 6 | inner | ||
1440.2.cc.b.911.6 | 48 | 8.3 | odd | 2 | |||
1440.2.cc.b.1391.6 | 48 | 9.5 | odd | 6 | |||
4320.2.cc.a.1871.15 | 48 | 24.11 | even | 2 | |||
4320.2.cc.a.3311.15 | 48 | 9.4 | even | 3 | |||
4320.2.cc.b.1871.10 | 48 | 3.2 | odd | 2 | |||
4320.2.cc.b.3311.10 | 48 | 72.67 | odd | 6 |