Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.11 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.11 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.498607 | − | 1.65873i | −0.287871 | − | 0.957669i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.623597 | −0.278881 | −0.139440 | − | 0.990230i | \(-0.544530\pi\) | ||||
−0.139440 | + | 0.990230i | \(0.544530\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.996837 | + | 2.45078i | −0.376769 | + | 0.926307i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50278 | + | 1.65411i | −0.834261 | + | 0.551370i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19907i | 1.56758i | 0.621026 | + | 0.783790i | \(0.286716\pi\) | ||||
−0.621026 | + | 0.783790i | \(0.713284\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.74023 | − | 1.58207i | −0.760004 | − | 0.438788i | 0.0692932 | − | 0.997596i | \(-0.477926\pi\) |
−0.829297 | + | 0.558808i | \(0.811259\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.310929 | + | 1.03438i | 0.0802816 | + | 0.267076i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.437594 | − | 0.757935i | 0.106132 | − | 0.183826i | −0.808068 | − | 0.589089i | \(-0.799487\pi\) |
0.914200 | + | 0.405263i | \(0.132820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41874 | + | 0.819107i | −0.325480 | + | 0.187916i | −0.653833 | − | 0.756639i | \(-0.726840\pi\) |
0.328352 | + | 0.944555i | \(0.393507\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56221 | + | 0.431510i | 0.995557 | + | 0.0941633i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.25480i | 1.72124i | 0.509245 | + | 0.860622i | \(0.329925\pi\) | ||||
−0.509245 | + | 0.860622i | \(0.670075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61113 | −0.922225 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.99163 | + | 3.32670i | 0.768189 | + | 0.640223i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.96435 | − | 2.86617i | 0.921856 | − | 0.532234i | 0.0376295 | − | 0.999292i | \(-0.488019\pi\) |
0.884227 | + | 0.467058i | \(0.154686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02256 | − | 2.32243i | 0.722474 | − | 0.417120i | −0.0931888 | − | 0.995648i | \(-0.529706\pi\) |
0.815662 | + | 0.578528i | \(0.196373\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.62387 | − | 2.59229i | 1.50122 | − | 0.451260i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.621624 | − | 1.52830i | 0.105074 | − | 0.258329i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.24291 | + | 2.15278i | 0.204333 | + | 0.353916i | 0.949920 | − | 0.312493i | \(-0.101164\pi\) |
−0.745587 | + | 0.666408i | \(0.767831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.25794 | + | 5.33415i | −0.201431 | + | 0.854147i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.52382 | + | 6.10344i | −0.550329 | + | 0.953198i | 0.447922 | + | 0.894073i | \(0.352164\pi\) |
−0.998251 | + | 0.0591249i | \(0.981169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.56398 | − | 2.70890i | −0.238505 | − | 0.413103i | 0.721780 | − | 0.692122i | \(-0.243324\pi\) |
−0.960286 | + | 0.279019i | \(0.909991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.56073 | − | 1.03150i | 0.232659 | − | 0.153766i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.73384 | + | 8.19925i | −0.690502 | + | 1.19598i | 0.281172 | + | 0.959657i | \(0.409277\pi\) |
−0.971674 | + | 0.236327i | \(0.924056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.01263 | − | 4.88605i | −0.716090 | − | 0.698007i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.47540 | − | 0.347940i | −0.206597 | − | 0.0487213i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.15189 | − | 0.665044i | −0.158224 | − | 0.0913508i | 0.418797 | − | 0.908080i | \(-0.362452\pi\) |
−0.577021 | + | 0.816729i | \(0.695785\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.24212i | − | 0.437168i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06607 | + | 1.94489i | 0.273658 | + | 0.257607i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.18334 | − | 5.51370i | −0.414435 | − | 0.717823i | 0.580934 | − | 0.813951i | \(-0.302687\pi\) |
−0.995369 | + | 0.0961281i | \(0.969354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.65975 | + | 5.57706i | 1.23680 | + | 0.714069i | 0.968440 | − | 0.249248i | \(-0.0801835\pi\) |
0.268365 | + | 0.963317i | \(0.413517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.55899 | − | 7.78264i | −0.196414 | − | 0.980521i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.70880 | + | 0.986576i | 0.211951 | + | 0.122370i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.04951 | − | 10.4781i | −0.739065 | − | 1.28010i | −0.952917 | − | 0.303232i | \(-0.901934\pi\) |
0.213851 | − | 0.976866i | \(-0.431399\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.6925 | − | 4.11590i | 1.64838 | − | 0.495496i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5861i | 1.25634i | 0.778076 | + | 0.628171i | \(0.216196\pi\) | ||||
−0.778076 | + | 0.628171i | \(0.783804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6719 | − | 6.73878i | −1.36609 | − | 0.788714i | −0.375666 | − | 0.926755i | \(-0.622586\pi\) |
−0.990427 | + | 0.138041i | \(0.955920\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.29914 | + | 7.64862i | 0.265482 | + | 0.883187i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.7418 | − | 5.18263i | −1.45206 | − | 0.590615i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.84840 | + | 8.39767i | −0.545487 | + | 0.944811i | 0.453089 | + | 0.891465i | \(0.350322\pi\) |
−0.998576 | + | 0.0533461i | \(0.983011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.52785 | − | 8.27975i | 0.391983 | − | 0.919973i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.192030 | − | 0.332606i | −0.0210781 | − | 0.0365083i | 0.855294 | − | 0.518143i | \(-0.173377\pi\) |
−0.876372 | + | 0.481635i | \(0.840043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.272882 | + | 0.472646i | −0.0295982 | + | 0.0512656i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.22946 | − | 6.80543i | −0.775079 | − | 0.729619i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0198983 | + | 0.0344648i | 0.00210921 | + | 0.00365326i | 0.867078 | − | 0.498172i | \(-0.165995\pi\) |
−0.864969 | + | 0.501826i | \(0.832662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.60888 | − | 5.13864i | 0.692799 | − | 0.538675i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.85796 | − | 5.51438i | −0.607442 | − | 0.571814i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.884719 | − | 0.510793i | 0.0907702 | − | 0.0524062i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.94681 | − | 3.43339i | 0.603807 | − | 0.348608i | −0.166731 | − | 0.986002i | \(-0.553321\pi\) |
0.770538 | + | 0.637394i | \(0.219988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.59984 | − | 13.0122i | −0.864316 | − | 1.30777i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.92598 | 0.888168 | 0.444084 | − | 0.895985i | \(-0.353529\pi\) | ||||
0.444084 | + | 0.895985i | \(0.353529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.86879i | − | 0.873868i | −0.899494 | − | 0.436934i | \(-0.856064\pi\) | ||
0.899494 | − | 0.436934i | \(-0.143936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.84498 | − | 0.269088i | −0.277642 | − | 0.0262603i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.64326 | + | 1.52609i | −0.255534 | + | 0.147532i | −0.622295 | − | 0.782782i | \(-0.713800\pi\) |
0.366762 | + | 0.930315i | \(0.380466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55069 | + | 9.61408i | −0.531660 | + | 0.920862i | 0.467657 | + | 0.883910i | \(0.345098\pi\) |
−0.999317 | + | 0.0369519i | \(0.988235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.95117 | − | 3.13505i | 0.280113 | − | 0.297566i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.13836 | − | 1.81193i | −0.295232 | − | 0.170452i | 0.345067 | − | 0.938578i | \(-0.387856\pi\) |
−0.640299 | + | 0.768126i | \(0.721190\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.14766i | − | 0.480022i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.47513 | − | 0.573056i | 0.875976 | − | 0.0529791i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.42132 | + | 1.82798i | 0.130292 | + | 0.167571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0304 | −1.45731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.8810 | + | 2.80186i | 1.07127 | + | 0.252636i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.99347 | 0.536072 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1408 | −0.899852 | −0.449926 | − | 0.893066i | \(-0.648550\pi\) | ||||
−0.449926 | + | 0.893066i | \(0.648550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.71352 | + | 3.94490i | −0.326957 | + | 0.347329i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.7576 | 1.90097 | 0.950484 | − | 0.310774i | \(-0.100588\pi\) | ||||
0.950484 | + | 0.310774i | \(0.100588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.593203 | − | 4.29352i | −0.0514372 | − | 0.372296i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.48917 | − | 2.07452i | −0.214233 | − | 0.178546i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.393118i | 0.0335863i | 0.999859 | + | 0.0167932i | \(0.00534568\pi\) | ||||
−0.999859 | + | 0.0167932i | \(0.994654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6647 | − | 9.04400i | −1.32866 | − | 0.767102i | −0.343568 | − | 0.939128i | \(-0.611635\pi\) |
−0.985092 | + | 0.172026i | \(0.944969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.9607 | + | 3.76397i | 1.34413 | + | 0.316984i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.22532 | − | 14.2467i | 0.687836 | − | 1.19137i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.09575 | + | 1.78733i | −0.257088 | + | 0.148430i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.60532 | + | 10.7508i | −0.462319 | + | 0.886714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.2508i | − | 0.839781i | −0.907575 | − | 0.419891i | \(-0.862068\pi\) | ||
0.907575 | − | 0.419891i | \(-0.137932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.8012 | 1.93691 | 0.968457 | − | 0.249181i | \(-0.0801614\pi\) | ||||
0.968457 | + | 0.249181i | \(0.0801614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.158505 | + | 2.62078i | 0.0128143 | + | 0.211877i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.50846 | + | 1.44826i | −0.201484 | + | 0.116327i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.96626 | − | 5.75402i | 0.795394 | − | 0.459221i | −0.0464641 | − | 0.998920i | \(-0.514795\pi\) |
0.841858 | + | 0.539699i | \(0.181462\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.528789 | + | 2.24227i | −0.0419357 | + | 0.177824i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.2307 | − | 8.22868i | −1.59440 | − | 0.648511i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4614 | + | 18.1197i | 0.819399 | + | 1.41924i | 0.906125 | + | 0.423009i | \(0.139026\pi\) |
−0.0867261 | + | 0.996232i | \(0.527640\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.37782 | + | 1.61654i | −0.418662 | + | 0.125848i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.69358 | + | 11.5936i | −0.517965 | + | 0.897141i | 0.481817 | + | 0.876272i | \(0.339977\pi\) |
−0.999782 | + | 0.0208697i | \(0.993357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.49408 | − | 2.58782i | −0.114929 | − | 0.199063i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.19589 | − | 4.39679i | 0.167924 | − | 0.336231i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.94433 | + | 5.09972i | −0.223853 | + | 0.387725i | −0.955975 | − | 0.293449i | \(-0.905197\pi\) |
0.732122 | + | 0.681174i | \(0.238530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.59654 | − | 11.3009i | 0.347466 | − | 0.854264i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.55852 | + | 8.02947i | −0.568133 | + | 0.603532i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.4333 | + | 8.33310i | 1.07880 | + | 0.622845i | 0.930572 | − | 0.366109i | \(-0.119310\pi\) |
0.148227 | + | 0.988953i | \(0.452643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.462705i | 0.0343926i | 0.999852 | + | 0.0171963i | \(0.00547402\pi\) | ||||
−0.999852 | + | 0.0171963i | \(0.994526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.43443 | − | 18.8037i | 0.327803 | − | 1.39001i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.775075 | − | 1.34247i | −0.0569846 | − | 0.0987003i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.94056 | + | 2.27508i | 0.288162 | + | 0.166371i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.1320 | + | 6.46642i | −0.882473 | + | 0.470363i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8113 | − | 6.81927i | −0.854637 | − | 0.493425i | 0.00757544 | − | 0.999971i | \(-0.497589\pi\) |
−0.862213 | + | 0.506546i | \(0.830922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.73933 | + | 9.94080i | 0.413126 | + | 0.715555i | 0.995230 | − | 0.0975597i | \(-0.0311037\pi\) |
−0.582104 | + | 0.813114i | \(0.697770\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.784447 | − | 3.32636i | 0.0561754 | − | 0.238205i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.78184i | 0.340692i | 0.985384 | + | 0.170346i | \(0.0544885\pi\) | ||||
−0.985384 | + | 0.170346i | \(0.945511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.87833 | + | 4.54856i | 0.558480 | + | 0.322439i | 0.752535 | − | 0.658552i | \(-0.228831\pi\) |
−0.194055 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.3640 | + | 15.2589i | −1.01316 | + | 1.07628i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.07570 | + | 15.0236i | 0.145685 | + | 1.05445i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.19745 | − | 3.80609i | 0.153476 | − | 0.265829i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.6543 | − | 20.6600i | −0.949042 | − | 1.43597i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.25860 | − | 7.37611i | −0.294573 | − | 0.510216i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.47477 | − | 2.55437i | 0.101527 | − | 0.175850i | −0.810787 | − | 0.585341i | \(-0.800960\pi\) |
0.912314 | + | 0.409491i | \(0.134294\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.5595 | − | 5.27831i | 1.20316 | − | 0.361664i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.975294 | + | 1.68926i | 0.0665145 | + | 0.115207i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.68192 | + | 12.1735i | 0.114176 | + | 0.826391i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.35814 | + | 22.7206i | −0.362069 | + | 1.53531i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.39822 | + | 1.38461i | −0.161322 | + | 0.0931391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.4564 | − | 11.8105i | 1.36986 | − | 0.790891i | 0.378954 | − | 0.925416i | \(-0.376284\pi\) |
0.990910 | + | 0.134524i | \(0.0429506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.5407 | − | 7.62731i | 0.769377 | − | 0.508487i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0507 | −1.19807 | −0.599033 | − | 0.800725i | \(-0.704448\pi\) | ||||
−0.599033 | + | 0.800725i | \(0.704448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1488i | 0.802815i | 0.915900 | + | 0.401407i | \(0.131479\pi\) | ||||
−0.915900 | + | 0.401407i | \(0.868521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.24345 | + | 23.7193i | −0.147608 | + | 1.56061i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.39111 | − | 1.95786i | 0.222159 | − | 0.128264i | −0.384791 | − | 0.923004i | \(-0.625726\pi\) |
0.606950 | + | 0.794740i | \(0.292393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.95201 | − | 5.11303i | 0.192568 | − | 0.333537i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.3469 | + | 3.85506i | 1.06185 | + | 0.250413i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3996 | + | 6.00423i | 0.672696 | + | 0.388381i | 0.797097 | − | 0.603851i | \(-0.206368\pi\) |
−0.124401 | + | 0.992232i | \(0.539701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2853i | 1.82202i | 0.412385 | + | 0.911010i | \(0.364696\pi\) | ||||
−0.412385 | + | 0.911010i | \(0.635304\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4929 | − | 1.72341i | −0.993870 | − | 0.110557i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.12586 | + | 3.04693i | 0.199704 | + | 0.194661i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.18355 | 0.329822 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.455957 | + | 0.484367i | −0.0288951 | + | 0.0306955i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0425 | −0.760117 | −0.380059 | − | 0.924962i | \(-0.624096\pi\) | ||||
−0.380059 | + | 0.924962i | \(0.624096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.9173 | −2.69819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.920054 | + | 0.216974i | 0.0576160 | + | 0.0135874i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6504 | 0.913868 | 0.456934 | − | 0.889501i | \(-0.348948\pi\) | ||||
0.456934 | + | 0.889501i | \(0.348948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.51498 | + | 0.900125i | −0.404821 | + | 0.0559310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.68373 | + | 15.3850i | −0.475611 | + | 0.952306i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.73134i | − | 0.353410i | −0.984264 | − | 0.176705i | \(-0.943456\pi\) | ||
0.984264 | − | 0.176705i | \(-0.0565438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.718314 | + | 0.414719i | 0.0441257 | + | 0.0254760i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0472464 | − | 0.0501902i | 0.00289144 | − | 0.00307159i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.61724 | − | 2.80114i | 0.0986047 | − | 0.170788i | −0.812503 | − | 0.582957i | \(-0.801895\pi\) |
0.911107 | + | 0.412169i | \(0.135229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6677 | + | 11.9325i | −1.25548 | + | 0.724849i | −0.972192 | − | 0.234187i | \(-0.924757\pi\) |
−0.283284 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.8188 | − | 8.40020i | −0.715309 | − | 0.508403i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 23.9736i | − | 1.44566i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.66845 | −0.460753 | −0.230376 | − | 0.973102i | \(-0.573996\pi\) | ||||
−0.230376 | + | 0.973102i | \(0.573996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.22605 | + | 12.4663i | −0.372744 | + | 0.746337i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.78880 | − | 5.07422i | 0.524296 | − | 0.302702i | −0.214395 | − | 0.976747i | \(-0.568778\pi\) |
0.738690 | + | 0.674045i | \(0.235445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8373 | − | 6.83427i | 0.703654 | − | 0.406255i | −0.105053 | − | 0.994467i | \(-0.533501\pi\) |
0.808707 | + | 0.588212i | \(0.200168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.28839 | − | 1.21283i | −0.0763179 | − | 0.0718417i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4455 | − | 14.7203i | −0.675607 | − | 0.868909i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.11702 | + | 14.0591i | 0.477472 | + | 0.827006i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.66019 | − | 8.15225i | −0.507669 | − | 0.477893i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.70903 | + | 4.69218i | −0.158263 | + | 0.274120i | −0.934242 | − | 0.356639i | \(-0.883923\pi\) |
0.775979 | + | 0.630758i | \(0.217256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98512 | + | 3.43833i | 0.115578 | + | 0.200187i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.2957 | + | 20.7528i | −1.00360 | + | 1.20420i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.0597 | − | 22.6201i | 0.755262 | − | 1.30815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19794 | − | 1.13265i | 0.472522 | − | 0.0652847i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.45055 | − | 14.8058i | −0.255677 | − | 0.850571i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.02379 | − | 3.47784i | −0.344921 | − | 0.199140i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.56336i | 0.203372i | 0.994817 | + | 0.101686i | \(0.0324236\pi\) | ||||
−0.994817 | + | 0.101686i | \(0.967576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7109 | + | 4.42204i | −0.836876 | + | 0.251561i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.63234 | + | 9.75550i | 0.319381 | + | 0.553184i | 0.980359 | − | 0.197221i | \(-0.0631918\pi\) |
−0.660978 | + | 0.750405i | \(0.729858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.89696 | + | 5.71401i | 0.559409 | + | 0.322975i | 0.752908 | − | 0.658125i | \(-0.228650\pi\) |
−0.193499 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.972181 | + | 4.85323i | 0.0547762 | + | 0.273449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.8604 | + | 9.73436i | 0.946975 | + | 0.546736i | 0.892140 | − | 0.451759i | \(-0.149203\pi\) |
0.0548352 | + | 0.998495i | \(0.482537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.9014 | + | 25.8100i | 0.834319 | + | 1.44508i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.84932 | + | 3.62354i | 0.214848 | + | 0.202247i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43375i | 0.0797758i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6356 | + | 7.29515i | 0.700895 | + | 0.404662i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.7148 | + | 4.41347i | 1.03493 | + | 0.244065i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3757 | − | 19.7749i | −0.847689 | − | 1.09023i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4838 | + | 23.3546i | −0.741135 | + | 1.28368i | 0.210844 | + | 0.977520i | \(0.432379\pi\) |
−0.951979 | + | 0.306164i | \(0.900955\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.67168 | − | 3.33204i | −0.365606 | − | 0.182595i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.77245 | + | 6.53408i | 0.206111 | + | 0.356995i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.993296 | − | 1.72044i | 0.0541083 | − | 0.0937183i | −0.837703 | − | 0.546127i | \(-0.816102\pi\) |
0.891811 | + | 0.452408i | \(0.149435\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.44070 | + | 6.10914i | −0.0782483 | + | 0.331803i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0745 | + | 20.9136i | 0.653869 | + | 1.13254i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9714 | − | 7.41426i | 0.916370 | − | 0.400332i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.53859 | + | 2.56666i | −0.459702 | + | 0.138184i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.7673 | − | 17.1862i | 1.59799 | − | 0.922603i | 0.606122 | − | 0.795372i | \(-0.292724\pi\) |
0.991873 | − | 0.127231i | \(-0.0406089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.3935 | − | 14.6609i | 1.35928 | − | 0.784781i | 0.369754 | − | 0.929130i | \(-0.379442\pi\) |
0.989527 | + | 0.144348i | \(0.0461085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.67491 | − | 15.4310i | −0.302904 | − | 0.823645i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.17305 | 0.0624353 | 0.0312177 | − | 0.999513i | \(-0.490061\pi\) | ||||
0.0312177 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.60147i | − | 0.350370i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.32345 | − | 3.26904i | 0.122970 | − | 0.173016i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.69591 | − | 3.28854i | 0.300619 | − | 0.173562i | −0.342102 | − | 0.939663i | \(-0.611139\pi\) |
0.642721 | + | 0.766101i | \(0.277806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.15813 | + | 14.1303i | −0.429375 | + | 0.743699i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.99285 | + | 26.5901i | 0.419516 | + | 1.39562i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.27856 | + | 4.20228i | 0.380977 | + | 0.219957i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.51617i | − | 0.496740i | −0.968665 | − | 0.248370i | \(-0.920105\pi\) | ||
0.968665 | − | 0.248370i | \(-0.0798948\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.27639 | − | 21.1044i | −0.0664464 | − | 1.09865i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.77812 | − | 2.16009i | 0.144233 | − | 0.112146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6303 | 1.06820 | 0.534098 | − | 0.845422i | \(-0.320651\pi\) | ||||
0.534098 | + | 0.845422i | \(0.320651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.98838 | − | 9.94155i | −0.154319 | − | 0.513380i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.1380 | −0.934153 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.98265 | −0.410041 | −0.205020 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205020 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.05628 | + | 16.8209i | 0.259041 | + | 0.861761i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.0968 | −1.43568 | −0.717840 | − | 0.696208i | \(-0.754869\pi\) | ||||
−0.717840 | + | 0.696208i | \(0.754869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.94573 | + | 3.23187i | 0.404952 | + | 0.164711i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.39512 | + | 4.19278i | 0.426748 | + | 0.213131i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 32.8397i | − | 1.66504i | −0.553997 | − | 0.832519i | \(-0.686898\pi\) | ||
0.553997 | − | 0.832519i | \(-0.313102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.25660 | + | 3.61225i | 0.316410 | + | 0.182679i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8485 | − | 36.0900i | −0.547233 | − | 1.82050i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.02344 | − | 5.23676i | 0.152126 | − | 0.263490i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.24672 | − | 5.33859i | 0.464079 | − | 0.267936i | −0.249679 | − | 0.968329i | \(-0.580325\pi\) |
0.713758 | + | 0.700392i | \(0.246992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.82603 | + | 3.12474i | −0.341729 | + | 0.156433i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.2789i | − | 0.713052i | −0.934285 | − | 0.356526i | \(-0.883961\pi\) | ||
0.934285 | − | 0.356526i | \(-0.116039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6970 | −0.732111 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.19995 | + | 5.16323i | −0.109317 | + | 0.256563i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.1925 | + | 6.46198i | −0.554791 | + | 0.320309i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.04206 | − | 4.06574i | 0.348208 | − | 0.201038i | −0.315688 | − | 0.948863i | \(-0.602235\pi\) |
0.663896 | + | 0.747825i | \(0.268902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.652077 | − | 0.196011i | 0.0321646 | − | 0.00966852i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.6861 | − | 2.30539i | 0.821071 | − | 0.113441i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.119750 | + | 0.207412i | 0.00587827 | + | 0.0101815i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.19107 | + | 30.4929i | −0.352148 | + | 1.49324i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.53415 | − | 2.65723i | 0.0749481 | − | 0.129814i | −0.826116 | − | 0.563501i | \(-0.809454\pi\) |
0.901064 | + | 0.433687i | \(0.142788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.25752 | + | 7.37424i | 0.207499 | + | 0.359398i | 0.950926 | − | 0.309418i | \(-0.100134\pi\) |
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.71468 | − | 28.3512i | −0.0833708 | − | 1.37848i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.01780 | + | 3.49494i | −0.0978778 | + | 0.169529i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.2973 | + | 18.1145i | −1.12744 | + | 0.876622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.7326 | − | 6.54012i | −1.33894 | − | 0.315760i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8414 | + | 11.4554i | 0.955727 | + | 0.551789i | 0.894855 | − | 0.446356i | \(-0.147279\pi\) |
0.0608716 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.7273i | − | 1.57278i | −0.617733 | − | 0.786388i | \(-0.711949\pi\) | ||
0.617733 | − | 0.786388i | \(-0.288051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.50827 | + | 4.24384i | 0.216155 | + | 0.203477i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.76156 | − | 11.7114i | −0.323449 | − | 0.560231i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.57285 | + | 3.21749i | 0.265978 | + | 0.153562i | 0.627058 | − | 0.778972i | \(-0.284259\pi\) |
−0.361081 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.6276 | + | 3.93729i | 0.982267 | + | 0.187490i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.1159 | − | 12.7686i | −1.05076 | − | 0.606656i | −0.127898 | − | 0.991787i | \(-0.540823\pi\) |
−0.922862 | + | 0.385131i | \(0.874156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0124085 | − | 0.0214921i | −0.000588219 | − | 0.00101882i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.0034 | + | 5.11113i | −0.804233 | + | 0.241748i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.1008i | 1.89247i | 0.323474 | + | 0.946237i | \(0.395149\pi\) | ||||
−0.323474 | + | 0.946237i | \(0.604851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.7322 | − | 18.3206i | −1.49421 | − | 0.862684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8674 | − | 39.4798i | −0.557581 | − | 1.85492i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.12128 | + | 3.20444i | −0.193208 | + | 0.150226i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.2357 | − | 33.3173i | 0.899810 | − | 1.55852i | 0.0720726 | − | 0.997399i | \(-0.477039\pi\) |
0.827737 | − | 0.561116i | \(-0.189628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.26813 | − | 1.56965i | 0.199219 | − | 0.0732651i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0830 | − | 20.9283i | −0.562759 | − | 0.974728i | −0.997254 | − | 0.0740533i | \(-0.976407\pi\) |
0.434495 | − | 0.900674i | \(-0.356927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.65455 | + | 14.9901i | −0.402211 | + | 0.696650i | −0.993992 | − | 0.109449i | \(-0.965091\pi\) |
0.591781 | + | 0.806098i | \(0.298425\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.65301 | + | 3.43875i | 0.169404 | + | 0.159468i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.46858 | − | 9.47185i | −0.253056 | − | 0.438305i | 0.711310 | − | 0.702878i | \(-0.248102\pi\) |
−0.964366 | + | 0.264573i | \(0.914769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.7098 | − | 4.38110i | 1.46422 | − | 0.202300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5136 | − | 13.6624i | −0.668752 | − | 0.629528i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.0838 | − | 8.13126i | 0.647572 | − | 0.373876i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.54197 | − | 3.77701i | 0.300166 | − | 0.173301i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.98298 | − | 0.240891i | 0.182368 | − | 0.0110296i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.51349 | 0.0691531 | 0.0345765 | − | 0.999402i | \(-0.488992\pi\) | ||||
0.0345765 | + | 0.999402i | \(0.488992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.86551i | − | 0.358636i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.56203 | + | 37.6601i | −0.162078 | + | 1.71360i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.70841 | + | 2.14105i | −0.168390 | + | 0.0972201i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0853077 | + | 0.147757i | −0.00386566 | + | 0.00669552i | −0.867952 | − | 0.496649i | \(-0.834564\pi\) |
0.864086 | + | 0.503344i | \(0.167897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.8395 | − | 26.3872i | 1.12328 | − | 1.19327i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5139 | + | 13.5757i | 1.06117 | + | 0.612665i | 0.925755 | − | 0.378125i | \(-0.123431\pi\) |
0.135412 | + | 0.990789i | \(0.456764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.01687i | − | 0.225949i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.36283 | + | 8.11434i | 0.241041 | + | 0.364712i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9442 | − | 10.5526i | −1.16376 | − | 0.473350i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.2654 | 0.996738 | 0.498369 | − | 0.866965i | \(-0.333933\pi\) | ||||
0.498369 | + | 0.866965i | \(0.333933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.5682 | + | 5.32220i | 1.00827 | + | 0.237778i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.2005 | −1.43575 | −0.717876 | − | 0.696171i | \(-0.754885\pi\) | ||||
−0.717876 | + | 0.696171i | \(0.754885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.56621 | −0.247693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.54755 | + | 3.76859i | −0.157552 | + | 0.167369i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.21817 | −0.408588 | −0.204294 | − | 0.978910i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978910i | \(0.565490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1502 | − | 21.8878i | 1.24529 | − | 0.968259i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.38799 | − | 1.45013i | −0.370339 | − | 0.0640248i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.53055i | 0.243705i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.6285 | − | 24.6116i | −1.87480 | − | 1.08242i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.92714 | + | 2.34109i | 0.435753 | + | 0.102763i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.44581 | + | 12.8965i | −0.326207 | + | 0.565007i | −0.981756 | − | 0.190146i | \(-0.939104\pi\) |
0.655549 | + | 0.755153i | \(0.272437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.3725 | + | 16.9582i | −1.28437 | + | 0.741532i | −0.977644 | − | 0.210266i | \(-0.932567\pi\) |
−0.306727 | + | 0.951798i | \(0.599234\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.0370 | − | 1.98975i | −0.918128 | − | 0.0868398i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.06512i | − | 0.177080i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −45.1416 | −1.96268 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.0875 | + | 8.53401i | 0.741533 | + | 0.370344i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3122 | − | 11.1499i | 0.836504 | − | 0.482956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.64833 | − | 0.951663i | 0.0712635 | − | 0.0411440i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.62581 | − | 28.0960i | 0.285925 | − | 1.21243i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.4029 | − | 26.0610i | 1.09418 | − | 1.12253i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.65164 | − | 4.59278i | −0.114003 | − | 0.197459i | 0.803378 | − | 0.595470i | \(-0.203034\pi\) |
−0.917381 | + | 0.398011i | \(0.869701\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.767504 | − | 0.230708i | 0.0329368 | − | 0.00990062i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.46139 | − | 5.99531i | 0.148270 | − | 0.256811i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.13892 | − | 7.16882i | −0.176967 | − | 0.306517i | 0.763873 | − | 0.645367i | \(-0.223295\pi\) |
−0.940840 | + | 0.338850i | \(0.889962\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.4013 | + | 2.02011i | −1.42553 | + | 0.0862163i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.69540 | + | 8.13267i | −0.200031 | + | 0.346463i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.7478 | − | 20.2534i | −0.669663 | − | 0.861264i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.84034 | + | 1.95501i | −0.0781180 | + | 0.0829854i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.96801 | − | 4.02299i | −0.295244 | − | 0.170459i | 0.345060 | − | 0.938581i | \(-0.387858\pi\) |
−0.640304 | + | 0.768121i | \(0.721192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.89735i | 0.418613i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.80896 | − | 7.67070i | 0.0763745 | − | 0.323857i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.9578 | − | 25.9077i | −0.630396 | − | 1.09188i | −0.987471 | − | 0.157802i | \(-0.949559\pi\) |
0.357074 | − | 0.934076i | \(-0.383774\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.95707 | + | 1.12992i | 0.0823346 | + | 0.0475359i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.7752 | + | 16.8995i | 0.704490 | + | 0.709714i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.6942 | + | 15.4119i | 1.11908 | + | 0.646101i | 0.941166 | − | 0.337946i | \(-0.109732\pi\) |
0.177913 | + | 0.984046i | \(0.443065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.67347 | + | 4.63058i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.42214 | + | 22.9920i | −0.226513 | + | 0.960503i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 38.0639i | − | 1.58737i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3235 | + | 9.42437i | 0.679556 | + | 0.392342i | 0.799688 | − | 0.600416i | \(-0.204998\pi\) |
−0.120132 | + | 0.992758i | \(0.538332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.6275 | − | 14.4766i | 0.566338 | − | 0.601625i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00657 | − | 0.139070i | 0.0417595 | − | 0.00576959i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.45761 | − | 5.98876i | 0.143200 | − | 0.248029i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.90866 | + | 0.357356i | −0.244293 | + | 0.0147749i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.3955 | + | 21.4697i | 0.511619 | + | 0.886150i | 0.999909 | + | 0.0134687i | \(0.00428734\pi\) |
−0.488290 | + | 0.872681i | \(0.662379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.80464 | + | 6.58982i | −0.156767 | + | 0.271529i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.93179 | − | 2.38426i | 0.326270 | − | 0.0980752i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.87451 | + | 3.24675i | 0.0769770 | + | 0.133328i | 0.901944 | − | 0.431852i | \(-0.142140\pi\) |
−0.824967 | + | 0.565180i | \(0.808807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.886331 | − | 1.13992i | −0.0363360 | − | 0.0467323i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.61665 | − | 15.3360i | 0.148020 | − | 0.627660i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7711 | + | 16.0337i | −1.13470 | + | 0.655118i | −0.945112 | − | 0.326746i | \(-0.894048\pi\) |
−0.189586 | + | 0.981864i | \(0.560714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.98069 | + | 3.45296i | −0.243958 | + | 0.140849i | −0.616994 | − | 0.786968i | \(-0.711650\pi\) |
0.373037 | + | 0.927817i | \(0.378317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.4725 | + | 16.2178i | 1.32238 | + | 0.660438i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.99648 | 0.406415 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6959i | 0.880608i | 0.897849 | + | 0.440304i | \(0.145129\pi\) | ||||
−0.897849 | + | 0.440304i | \(0.854871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.8852 | − | 10.9339i | 0.967877 | − | 0.443064i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.9437 | − | 14.9786i | 1.04957 | − | 0.605968i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.96928 | − | 15.5352i | 0.362266 | − | 0.627463i | −0.626068 | − | 0.779769i | \(-0.715337\pi\) |
0.988333 | + | 0.152306i | \(0.0486699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.40894 | − | 1.74723i | −0.298757 | − | 0.0704552i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.9146 | + | 19.0033i | 1.32509 | + | 0.765043i | 0.984536 | − | 0.175181i | \(-0.0560509\pi\) |
0.340557 | + | 0.940224i | \(0.389384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.3774i | 1.74349i | 0.489964 | + | 0.871743i | \(0.337010\pi\) | ||||
−0.489964 | + | 0.871743i | \(0.662990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.4612 | + | 32.9501i | −1.10198 | + | 1.32224i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.104301 | + | 0.0144105i | −0.00417873 | + | 0.000577343i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3181 | 0.772725 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.1116 | + | 10.7417i | −0.403819 | + | 0.428980i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.17556 | 0.0867453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2735 | 0.448793 | 0.224396 | − | 0.974498i | \(-0.427959\pi\) | ||||
0.224396 | + | 0.974498i | \(0.427959\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.97234 | − | 1.17262i | −0.197633 | − | 0.0466073i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.32378 | 0.250952 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00569 | + | 21.3193i | 0.237954 | + | 0.844701i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.5106 | − | 26.4948i | −0.692709 | − | 1.04812i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.7553i | 1.17526i | 0.809129 | + | 0.587631i | \(0.199939\pi\) | ||||
−0.809129 | + | 0.587631i | \(0.800061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.4271 | − | 21.6085i | −1.47598 | − | 0.852158i | −0.476348 | − | 0.879257i | \(-0.658040\pi\) |
−0.999633 | + | 0.0270991i | \(0.991373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.31574 | − | 2.46003i | 0.0911822 | − | 0.0968635i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.42940 | + | 16.3322i | −0.370708 | + | 0.642085i | −0.989675 | − | 0.143332i | \(-0.954218\pi\) |
0.618967 | + | 0.785417i | \(0.287552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.6661 | − | 16.5504i | 1.12524 | − | 0.649660i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.3539 | − | 8.85964i | 0.758541 | − | 0.347237i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.71777i | 0.380286i | 0.981756 | + | 0.190143i | \(0.0608951\pi\) | ||||
−0.981756 | + | 0.190143i | \(0.939105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5679 | −0.530144 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.3589 | − | 2.44091i | 1.57455 | − | 0.0952289i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.5327 | + | 16.4734i | −1.11148 | + | 0.641712i | −0.939212 | − | 0.343338i | \(-0.888442\pi\) |
−0.172266 | + | 0.985050i | \(0.555109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.08957 | + | 0.629061i | −0.0423792 | + | 0.0244677i | −0.521040 | − | 0.853532i | \(-0.674456\pi\) |
0.478661 | + | 0.878000i | \(0.341122\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49247 | + | 3.28763i | 0.135636 | + | 0.127681i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.369920 | + | 2.67743i | 0.0143449 | + | 0.103826i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6596 | + | 40.9797i | 0.916104 | + | 1.58674i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.7902 | − | 28.0429i | −1.15176 | − | 1.08420i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.9955 | + | 50.2217i | −1.11936 | + | 1.93879i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2655 | − | 21.2445i | −0.472800 | − | 0.818914i | 0.526715 | − | 0.850042i | \(-0.323423\pi\) |
−0.999515 | + | 0.0311279i | \(0.990090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.4059 | − | 15.3398i | −0.708444 | − | 0.590430i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5616 | + | 20.0253i | −0.444350 | + | 0.769636i | −0.998007 | − | 0.0631088i | \(-0.979899\pi\) |
0.553657 | + | 0.832745i | \(0.313232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.48649 | + | 17.9968i | 0.0954226 | + | 0.690655i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00018 | + | 29.9412i | 0.344888 | + | 1.14735i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.4945 | − | 7.21370i | −0.478089 | − | 0.276025i | 0.241531 | − | 0.970393i | \(-0.422350\pi\) |
−0.719620 | + | 0.694368i | \(0.755684\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.245147i | − | 0.00936659i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1516 | − | 6.05747i | 0.768831 | − | 0.231107i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.10430 | + | 3.64475i | 0.0801673 | + | 0.138854i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.3993 | − | 18.7057i | −1.23253 | − | 0.711599i | −0.264970 | − | 0.964257i | \(-0.585362\pi\) |
−0.967556 | + | 0.252657i | \(0.918695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.4625 | − | 8.10530i | 1.53704 | − | 0.307895i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.76844 | + | 5.63981i | 0.370538 | + | 0.213930i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.08401 | + | 5.34166i | 0.116815 | + | 0.202330i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.93839 | − | 4.64874i | −0.186787 | − | 0.175832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0429i | 1.55017i | 0.631859 | + | 0.775084i | \(0.282292\pi\) | ||||
−0.631859 | + | 0.775084i | \(0.717708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.52672 | − | 2.03615i | −0.133013 | − | 0.0767950i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.95303 | − | 2.34720i | −0.374853 | − | 0.0884007i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.89774 | + | 21.8756i | −0.334634 | + | 0.822716i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6623 | + | 20.1997i | −0.437987 | + | 0.758616i | −0.997534 | − | 0.0701829i | \(-0.977642\pi\) |
0.559547 | + | 0.828798i | \(0.310975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75618 | − | 29.0373i | −0.0658618 | − | 1.08898i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.1712 | + | 33.2054i | 0.717966 | + | 1.24355i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.12928 | + | 8.88418i | −0.191824 | + | 0.332249i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.77408 | − | 20.2439i | 0.178291 | − | 0.756024i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7489 | − | 37.6701i | −0.811096 | − | 1.40486i | −0.912098 | − | 0.409973i | \(-0.865538\pi\) |
0.101002 | − | 0.994886i | \(-0.467795\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.7354 | + | 8.84073i | 0.809470 | + | 0.329246i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.9178 | − | 14.1033i | 1.74489 | − | 0.524506i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.8912 | + | 13.2163i | −0.850159 | + | 0.490840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3715 | + | 6.56536i | −0.421747 | + | 0.243496i | −0.695824 | − | 0.718212i | \(-0.744961\pi\) |
0.274078 | + | 0.961708i | \(0.411627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.86618 | + | 26.5579i | 0.180229 | + | 0.983625i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.73756 | −0.101252 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.1795i | − | 1.48406i | −0.670364 | − | 0.742032i | \(-0.733862\pi\) | ||
0.670364 | − | 0.742032i | \(-0.266138\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.49546 | − | 6.70418i | 0.128932 | − | 0.247288i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.4762 | − | 31.4518i | 2.00666 | − | 1.15854i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7073 | − | 32.4020i | 0.688158 | − | 1.19193i | −0.284275 | − | 0.958743i | \(-0.591753\pi\) |
0.972433 | − | 0.233182i | \(-0.0749139\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.58455 | − | 8.59813i | −0.0949460 | − | 0.315860i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0501 | + | 17.3494i | 1.10243 | + | 0.636488i | 0.936858 | − | 0.349709i | \(-0.113720\pi\) |
0.165572 | + | 0.986198i | \(0.447053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.39239i | 0.234199i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.03078 | + | 0.514802i | 0.0377142 | + | 0.0188356i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.10520 | − | 7.99931i | −0.0403833 | − | 0.292288i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.0140 | −1.05873 | −0.529367 | − | 0.848393i | \(-0.677571\pi\) | ||||
−0.529367 | + | 0.848393i | \(0.677571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00448 | + | 19.9753i | 0.218815 | + | 0.727941i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.8423 | −0.540168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.62406 | −0.313447 | −0.156723 | − | 0.987643i | \(-0.550093\pi\) | ||||
−0.156723 | + | 0.987643i | \(0.550093\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.3988 | + | 71.1883i | 0.776729 | + | 2.58397i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.8213 | −0.827272 | −0.413636 | − | 0.910442i | \(-0.635741\pi\) | ||||
−0.413636 | + | 0.910442i | \(0.635741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0288 | − | 23.1872i | −0.652688 | − | 0.839432i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0988429 | − | 1.63431i | −0.00357367 | − | 0.0590885i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.1451i | 0.727397i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6397 | + | 15.9578i | 0.996714 | + | 0.575453i | 0.907275 | − | 0.420539i | \(-0.138159\pi\) |
0.0894399 | + | 0.995992i | \(0.471492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.30479 | − | 24.3011i | −0.263076 | − | 0.875183i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.8503 | + | 30.9176i | −0.642030 | + | 1.11203i | 0.342949 | + | 0.939354i | \(0.388574\pi\) |
−0.984979 | + | 0.172675i | \(0.944759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.5486 | + | 10.7090i | −0.666284 | + | 0.384679i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.74148 | + | 10.3578i | 0.170099 | + | 0.371584i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 11.5456i | − | 0.413663i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.0380 | −1.96942 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.3507 | + | 5.07420i | 1.04891 | + | 0.181337i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.21492 | + | 3.58819i | −0.221820 | + | 0.128068i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0233 | + | 6.94168i | −0.428586 | + | 0.247444i | −0.698744 | − | 0.715372i | \(-0.746257\pi\) |
0.270158 | + | 0.962816i | \(0.412924\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.50676 | + | 2.85768i | −0.338449 | + | 0.101736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.56908 | − | 5.88522i | 0.269125 | − | 0.209254i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.6466 | − | 30.5649i | −0.626651 | − | 1.08539i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.329751 | − | 1.39827i | 0.0116951 | − | 0.0495916i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.2145 | + | 24.6203i | −0.503504 | + | 0.872094i | 0.496488 | + | 0.868044i | \(0.334623\pi\) |
−0.999992 | + | 0.00405063i | \(0.998711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.14300 | + | 7.17589i | 0.146569 | + | 0.253865i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.106810 | − | 0.0533440i | −0.00377393 | − | 0.00188482i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.0354 | − | 60.6831i | 1.23637 | − | 2.14146i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6158 | + | 5.13138i | 0.444648 | + | 0.180857i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.45270 | − | 1.28590i | −0.191944 | − | 0.0452657i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1074 | + | 12.1864i | 0.742096 | + | 0.428449i | 0.822831 | − | 0.568286i | \(-0.192393\pi\) |
−0.0807348 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.2739i | − | 1.23863i | −0.785141 | − | 0.619317i | \(-0.787409\pi\) | ||
0.785141 | − | 0.619317i | \(-0.212591\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.0979 | + | 28.3326i | 1.05558 | + | 0.993668i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.52369 | − | 11.2994i | −0.228515 | − | 0.395799i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.43776 | + | 2.56214i | 0.155257 | + | 0.0896379i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.04073 | + | 23.7927i | −0.280966 | + | 0.831384i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8999 | − | 9.75719i | −0.589812 | − | 0.340528i | 0.175211 | − | 0.984531i | \(-0.443939\pi\) |
−0.765023 | + | 0.644003i | \(0.777273\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8285 | + | 27.4158i | 0.551747 | + | 0.955653i | 0.998149 | + | 0.0608208i | \(0.0193718\pi\) |
−0.446402 | + | 0.894833i | \(0.647295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.7658 | + | 11.9534i | −1.38447 | + | 0.416164i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4749i | 0.851075i | 0.904941 | + | 0.425537i | \(0.139915\pi\) | ||||
−0.904941 | + | 0.425537i | \(0.860085\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.846010 | + | 0.488444i | 0.0293831 | + | 0.0169644i | 0.514620 | − | 0.857419i | \(-0.327933\pi\) |
−0.485236 | + | 0.874383i | \(0.661266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.82354 | + | 12.7199i | 0.132637 | + | 0.441249i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.89681 | + | 1.66114i | −0.204312 | + | 0.0575552i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17409 | − | 7.22974i | 0.144450 | − | 0.250196i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.7826 | + | 4.11158i | 0.822047 | + | 0.142117i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.6920 | + | 34.1075i | 0.679843 | + | 1.17752i | 0.975028 | + | 0.222083i | \(0.0712856\pi\) |
−0.295184 | + | 0.955440i | \(0.595381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.92983 | − | 3.34257i | 0.0665459 | − | 0.115261i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.7989 | − | 12.0482i | −0.440818 | − | 0.414963i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.931704 | + | 1.61376i | 0.0320516 | + | 0.0555150i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9797 | − | 39.2869i | 0.549067 | − | 1.34991i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.2384 | − | 16.2273i | −0.591620 | − | 0.556919i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.7708 | + | 10.2600i | −0.609175 | + | 0.351707i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3507 | + | 12.3268i | −0.731033 | + | 0.422062i | −0.818800 | − | 0.574079i | \(-0.805360\pi\) |
0.0877672 | + | 0.996141i | \(0.472027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.36935 | + | 2.74182i | −0.0468309 | + | 0.0937684i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.8290 | 0.779823 | 0.389911 | − | 0.920852i | \(-0.372506\pi\) | ||||
0.389911 | + | 0.920852i | \(0.372506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 47.7150i | − | 1.62801i | −0.580855 | − | 0.814007i | \(-0.697282\pi\) | ||
0.580855 | − | 0.814007i | \(-0.302718\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.7101 | + | 26.3246i | −0.637640 | + | 0.897142i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0645 | + | 10.4296i | −0.614923 | + | 0.355026i | −0.774890 | − | 0.632096i | \(-0.782195\pi\) |
0.159967 | + | 0.987122i | \(0.448861\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.83607 | − | 3.18017i | 0.0624283 | − | 0.108129i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.2731 | − | 20.4739i | 0.654548 | − | 0.695331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.6601 | − | 25.2072i | −1.48107 | − | 0.855094i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.2831i | 1.29717i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.20437 | + | 18.4297i | −0.311521 | + | 0.623751i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.97451 | + | 14.6887i | −0.201975 | + | 0.496567i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5436 | −0.795011 | −0.397506 | − | 0.917600i | \(-0.630124\pi\) | ||||
−0.397506 | + | 0.917600i | \(0.630124\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.13380 | + | 2.15400i | 0.308075 | + | 0.0726527i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.5975 | −1.77205 | −0.886027 | − | 0.463633i | \(-0.846546\pi\) | ||||
−0.886027 | + | 0.463633i | \(0.846546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6815 | −1.13347 | −0.566737 | − | 0.823899i | \(-0.691794\pi\) | ||||
−0.566737 | + | 0.823899i | \(0.691794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.71347 | − | 5.00715i | 0.158441 | − | 0.168314i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0228 | 0.504415 | 0.252208 | − | 0.967673i | \(-0.418843\pi\) | ||||
0.252208 | + | 0.967673i | \(0.418843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1087 | − | 24.8529i | 0.339036 | − | 0.833540i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.0470 | + | 18.3415i | 1.44213 | + | 0.614464i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 15.5101i | − | 0.519026i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00059 | − | 5.19649i | −0.300856 | − | 0.173700i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.0323 | − | 10.3840i | −1.47019 | − | 0.346713i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.3129 | − | 23.0587i | 0.444011 | − | 0.769050i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.00812 | + | 0.582038i | −0.0335853 | + | 0.0193905i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.96631 | − | 13.0334i | −0.198546 | − | 0.433726i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.288542i | − | 0.00959144i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.6949 | −0.388324 | −0.194162 | − | 0.980969i | \(-0.562199\pi\) | ||||
−0.194162 | + | 0.980969i | \(0.562199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.3398 | + | 14.7645i | −0.740964 | + | 0.489709i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.9026 | + | 8.02666i | −0.460613 | + | 0.265935i | −0.712302 | − | 0.701873i | \(-0.752347\pi\) |
0.251689 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.72925 | − | 0.998380i | 0.0572297 | − | 0.0330416i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.76530 | + | 11.7259i | −0.0914179 | + | 0.387647i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.6887 | + | 53.3230i | −0.716225 | + | 1.76088i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.26860 | + | 16.0537i | 0.305743 | + | 0.529562i | 0.977426 | − | 0.211276i | \(-0.0677618\pi\) |
−0.671683 | + | 0.740838i | \(0.734428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.91066 | − | 1.77671i | 0.194763 | − | 0.0585447i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.7480 | − | 29.0084i | 0.551268 | − | 0.954824i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.73122 | − | 9.92676i | −0.188441 | − | 0.326390i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6699 | + | 22.1967i | 0.481824 | + | 0.729034i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.8357 | + | 46.4808i | −0.880451 | + | 1.52499i | −0.0296102 | + | 0.999562i | \(0.509427\pi\) |
−0.850841 | + | 0.525424i | \(0.823907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1138 | + | 2.82613i | 0.364240 | + | 0.0926227i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.3734 | − | 14.2067i | 0.437827 | − | 0.465107i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.45732 | − | 1.41873i | −0.0803630 | − | 0.0463976i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.7752i | 0.548023i | 0.961726 | + | 0.274012i | \(0.0883506\pi\) | ||||
−0.961726 | + | 0.274012i | \(0.911649\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.54333 | − | 19.2655i | 0.148266 | − | 0.628704i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.5343 | + | 32.1023i | 0.604200 | + | 1.04651i | 0.992177 | + | 0.124837i | \(0.0398406\pi\) |
−0.387977 | + | 0.921669i | \(0.626826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.3827 | − | 29.0885i | −1.64069 | − | 0.947250i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.56547 | − | 4.03244i | 0.246105 | − | 0.131175i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.73735 | + | 1.58041i | 0.0889520 | + | 0.0513565i | 0.543816 | − | 0.839204i | \(-0.316979\pi\) |
−0.454864 | + | 0.890561i | \(0.650312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.3225 | + | 36.9316i | 0.692157 | + | 1.19885i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.73999 | − | 32.8205i | 0.250986 | − | 1.06428i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38.9680i | − | 1.26230i | −0.775662 | − | 0.631149i | \(-0.782584\pi\) | ||
0.775662 | − | 0.631149i | \(-0.217416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.36550 | + | 4.25247i | 0.238342 | + | 0.137607i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.3819 | − | 37.5865i | 1.14374 | − | 1.21500i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.963445 | − | 0.391874i | −0.0311113 | − | 0.0126543i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.71266 | + | 8.16256i | −0.152021 | + | 0.263308i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.09119 | − | 8.19171i | 0.131837 | − | 0.263974i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.57902 | − | 6.19905i | −0.115213 | − | 0.199555i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.29560 | + | 12.6363i | −0.234611 | + | 0.406357i | −0.959159 | − | 0.282866i | \(-0.908715\pi\) |
0.724549 | + | 0.689223i | \(0.242048\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.37820 | − | 0.714875i | 0.0763988 | − | 0.0229651i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3537 | + | 19.6652i | 0.364358 | + | 0.631086i | 0.988673 | − | 0.150087i | \(-0.0479553\pi\) |
−0.624315 | + | 0.781172i | \(0.714622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.7800 | − | 29.3752i | 1.21117 | − | 0.941727i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.80052 | − | 24.5964i | 0.185765 | − | 0.787716i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.5426 | − | 20.5206i | 1.13711 | − | 0.656511i | 0.191397 | − | 0.981513i | \(-0.438698\pi\) |
0.945713 | + | 0.325002i | \(0.105365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.179185 | + | 0.103453i | −0.00572678 | + | 0.00330636i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.01056 | − | 33.2434i | −0.0641923 | − | 1.06138i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.9305 | 0.667579 | 0.333790 | − | 0.942648i | \(-0.391672\pi\) | ||||
0.333790 | + | 0.942648i | \(0.391672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.98194i | − | 0.0950125i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.1349 | + | 35.3640i | −0.800051 | + | 1.12565i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3614 | − | 12.9104i | 0.711051 | − | 0.410525i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9709 | − | 46.7149i | 0.856758 | − | 1.48395i | −0.0182456 | − | 0.999834i | \(-0.505808\pi\) |
0.875004 | − | 0.484116i | \(-0.160859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.4621 | + | 10.7212i | 1.44269 | + | 0.340227i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.91290 | − | 2.83647i | −0.155749 | − | 0.0899220i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.21654i | 0.101869i | 0.998702 | + | 0.0509345i | \(0.0162200\pi\) | ||||
−0.998702 | + | 0.0509345i | \(0.983780\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.20042 | + | 12.7279i | −0.0696183 | + | 0.402693i |
(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 | 504.2.cx.a.185.11 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.14 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.14 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.3 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.3 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.14 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.14 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.14 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.22 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.14 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.22 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.11 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.14 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.14 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.14 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.14 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.3 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.3 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.11 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.11 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.22 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.22 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.14 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.14 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.14 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.14 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.14 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.14 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.14 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.14 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.14 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.14 | 48 | 252.187 | even | 6 |