Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (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 | 257.3 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.3 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.68581 | − | 0.397560i | −0.973301 | − | 0.229531i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.311798 | − | 0.540051i | −0.139440 | − | 0.241518i | 0.787845 | − | 0.615874i | \(-0.211197\pi\) |
−0.927285 | + | 0.374356i | \(0.877864\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62086 | + | 0.362103i | 0.990590 | + | 0.136862i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68389 | + | 1.34042i | 0.894631 | + | 0.446806i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.50253 | − | 2.59954i | −1.35756 | − | 0.783790i | −0.368269 | − | 0.929719i | \(-0.620049\pi\) |
−0.989295 | + | 0.145930i | \(0.953383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74023 | + | 1.58207i | 0.760004 | + | 0.438788i | 0.829297 | − | 0.558808i | \(-0.188741\pi\) |
−0.0692932 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(14\) | 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 | \(-0.200513\pi\) |
−0.914200 | + | 0.405263i | \(0.867180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41874 | − | 0.819107i | −0.325480 | − | 0.187916i | 0.328352 | − | 0.944555i | \(-0.393507\pi\) |
−0.653833 | + | 0.756639i | \(0.726840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.27430 | − | 1.65238i | −0.932728 | − | 0.360580i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.14886 | − | 4.12740i | 1.49064 | − | 0.860622i | 0.490698 | − | 0.871330i | \(-0.336742\pi\) |
0.999943 | + | 0.0107077i | \(0.00340844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.30556 | − | 3.99335i | 0.461113 | − | 0.798671i | ||||
\(26\) | 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 | ||||||||
\(31\) | − | 4.64486i | − | 0.834241i | −0.908851 | − | 0.417120i | \(-0.863039\pi\) | ||
0.908851 | − | 0.417120i | \(-0.136961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.55693 | + | 6.17234i | 1.14141 | + | 1.07447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.621624 | − | 1.52830i | −0.105074 | − | 0.258329i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.24291 | − | 2.15278i | 0.204333 | − | 0.353916i | −0.745587 | − | 0.666408i | \(-0.767831\pi\) |
0.949920 | + | 0.312493i | \(0.101164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.99054 | − | 3.75648i | −0.638997 | − | 0.601518i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.52382 | − | 6.10344i | 0.550329 | − | 0.953198i | −0.447922 | − | 0.894073i | \(-0.647836\pi\) |
0.998251 | − | 0.0591249i | \(-0.0188310\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −0.112939 | − | 1.86738i | −0.0168360 | − | 0.278372i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.46768 | −1.38100 | −0.690502 | − | 0.723331i | \(-0.742610\pi\) | ||||
−0.690502 | + | 0.723331i | \(0.742610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.73776 | + | 1.89804i | 0.962537 | + | 0.271149i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.436375 | + | 1.45170i | 0.0611047 | + | 0.203279i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.15189 | − | 0.665044i | 0.158224 | − | 0.0913508i | −0.418797 | − | 0.908080i | \(-0.637548\pi\) |
0.577021 | + | 0.816729i | \(0.304215\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24212i | 0.437168i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06607 | + | 1.94489i | 0.273658 | + | 0.257607i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.36667 | −0.828870 | −0.414435 | − | 0.910079i | \(-0.636021\pi\) | ||||
−0.414435 | + | 0.910079i | \(0.636021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1541i | 1.42814i | 0.700075 | + | 0.714069i | \(0.253150\pi\) | ||||
−0.700075 | + | 0.714069i | \(0.746850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.54872 | + | 4.48489i | 0.825061 | + | 0.565043i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.97315i | − | 0.244739i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0990 | 1.47813 | 0.739065 | − | 0.673634i | \(-0.235267\pi\) | ||||
0.739065 | + | 0.673634i | \(0.235267\pi\) | |||||||
\(68\) | 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 | −0.990427 | − | 0.138041i | \(-0.955920\pi\) |
−0.375666 | + | 0.926755i | \(0.622586\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.47433 | + | 5.81542i | −0.632122 | + | 0.671507i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.8592 | − | 8.44339i | −1.23752 | − | 0.962214i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.69679 | 1.09097 | 0.545487 | − | 0.838119i | \(-0.316345\pi\) | ||||
0.545487 | + | 0.838119i | \(0.316345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.40655 | + | 7.19508i | 0.600728 | + | 0.799453i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.192030 | + | 0.332606i | 0.0210781 | + | 0.0365083i | 0.876372 | − | 0.481635i | \(-0.159957\pi\) |
−0.855294 | + | 0.518143i | \(0.826623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.272882 | + | 0.472646i | −0.0295982 | + | 0.0512656i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.50841 | + | 2.85818i | −1.01941 | + | 0.306429i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.0198983 | + | 0.0344648i | −0.00210921 | + | 0.00365326i | −0.867078 | − | 0.498172i | \(-0.834005\pi\) |
0.864969 | + | 0.501826i | \(0.167338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.60888 | + | 5.13864i | 0.692799 | + | 0.538675i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.84661 | + | 7.83033i | −0.191484 | + | 0.811968i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.02159i | 0.104812i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.94681 | + | 3.43339i | −0.603807 | + | 0.348608i | −0.770538 | − | 0.637394i | \(-0.780012\pi\) |
0.166731 | + | 0.986002i | \(0.446679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.59984 | − | 13.0122i | −0.864316 | − | 1.30777i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.46299 | − | 7.73012i | 0.444084 | − | 0.769176i | −0.553904 | − | 0.832581i | \(-0.686863\pi\) |
0.997988 | + | 0.0634046i | \(0.0201959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68060 | − | 4.43439i | 0.756792 | − | 0.436934i | −0.0713510 | − | 0.997451i | \(-0.522731\pi\) |
0.828143 | + | 0.560517i | \(0.189398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.440348 | + | 2.82355i | 0.0429736 | + | 0.275550i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.64326 | + | 1.52609i | 0.255534 | + | 0.147532i | 0.622295 | − | 0.782782i | \(-0.286200\pi\) |
−0.366762 | + | 0.930315i | \(0.619534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55069 | − | 9.61408i | −0.531660 | − | 0.920862i | −0.999317 | − | 0.0369519i | \(-0.988235\pi\) |
0.467657 | − | 0.883910i | \(-0.345098\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −4.45801 | − | 2.57383i | −0.415711 | − | 0.240011i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.23385 | + | 7.91918i | 0.483869 | + | 0.732128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.872420 | − | 2.14489i | −0.0799746 | − | 0.196622i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.01518 | + | 13.8827i | 0.728653 | + | 1.26206i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.36697 | + | 8.88830i | −0.754425 | + | 0.801431i | ||||
\(124\) | 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 | ||||||||
\(129\) | 1.55962 | + | 5.18846i | 0.137317 | + | 0.456818i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8788 | + | 18.8426i | 0.950484 | + | 1.64629i | 0.744380 | + | 0.667756i | \(0.232745\pi\) |
0.206103 | + | 0.978530i | \(0.433922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.42170 | − | 2.66049i | −0.296699 | − | 0.230694i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.552001 | + | 3.19294i | −0.0475087 | + | 0.274804i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.340450 | − | 0.196559i | −0.0290866 | − | 0.0167932i | 0.485386 | − | 0.874300i | \(-0.338679\pi\) |
−0.514473 | + | 0.857507i | \(0.672012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6647 | + | 9.04400i | 1.32866 | + | 0.767102i | 0.985092 | − | 0.172026i | \(-0.0550312\pi\) |
0.343568 | + | 0.939128i | \(0.388365\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −10.6040 | − | 5.87840i | −0.874602 | − | 0.484842i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.87748 | + | 5.12542i | −0.727272 | + | 0.419891i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.0901515 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9006 | + | 20.6124i | −0.968457 | + | 1.67742i | −0.268432 | + | 0.963299i | \(0.586505\pi\) |
−0.700025 | + | 0.714118i | \(0.746828\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | − | 11.5080i | − | 0.918442i | −0.888322 | − | 0.459221i | \(-0.848129\pi\) | ||
0.888322 | − | 0.459221i | \(-0.151871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.20626 | + | 0.663190i | −0.174968 | + | 0.0525944i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2307 | − | 8.22868i | 1.59440 | − | 0.648511i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4614 | − | 18.1197i | 0.819399 | − | 1.41924i | −0.0867261 | − | 0.996232i | \(-0.527640\pi\) |
0.906125 | − | 0.423009i | \(-0.139026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.28894 | − | 5.46560i | 0.100344 | − | 0.425496i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.69358 | − | 11.5936i | 0.517965 | − | 0.897141i | −0.481817 | − | 0.876272i | \(-0.660023\pi\) |
0.999782 | − | 0.0208697i | \(-0.00664350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.49408 | − | 2.58782i | −0.114929 | − | 0.199063i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.70979 | − | 4.10010i | −0.207223 | − | 0.313542i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.88865 | −0.447706 | −0.223853 | − | 0.974623i | \(-0.571864\pi\) | ||||
−0.223853 | + | 0.974623i | \(0.571864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.48856 | − | 9.63115i | 0.566082 | − | 0.728046i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7330 | + | 2.53113i | 0.806740 | + | 0.190252i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.4333 | + | 8.33310i | −1.07880 | + | 0.622845i | −0.930572 | − | 0.366109i | \(-0.880690\pi\) |
−0.148227 | + | 0.988953i | \(0.547357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.462705i | − | 0.0343926i | −0.999852 | − | 0.0171963i | \(-0.994526\pi\) | ||
0.999852 | − | 0.0171963i | \(-0.00547402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.43443 | − | 18.8037i | 0.327803 | − | 1.39001i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.55015 | −0.113969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.55017i | 0.332741i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.25687 | − | 10.1642i | −0.673338 | − | 0.739335i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6385i | 0.986850i | 0.869788 | + | 0.493425i | \(0.164255\pi\) | ||||
−0.869788 | + | 0.493425i | \(0.835745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4787 | −0.826251 | −0.413126 | − | 0.910674i | \(-0.635563\pi\) | ||||
−0.413126 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(194\) | 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 | −0.194055 | − | 0.980991i | \(-0.562164\pi\) |
0.752535 | + | 0.658552i | \(0.228831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.3966 | − | 4.81009i | −1.43867 | − | 0.339277i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0487 | − | 5.71420i | 0.986024 | − | 0.401058i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.39489 | −0.306952 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.7192 | − | 1.49502i | 1.71810 | − | 0.103911i | ||||
\(208\) | 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 | ||||||||
\(213\) | 4.20862 | − | 17.8462i | 0.288370 | − | 1.22280i | ||||
\(214\) | 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 | ||||||||
\(219\) | 22.3556 | − | 6.72000i | 1.51065 | − | 0.454095i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.76923i | − | 0.186278i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.4564 | + | 11.8105i | −1.36986 | + | 0.790891i | −0.990910 | − | 0.134524i | \(-0.957049\pi\) |
−0.378954 | + | 0.925416i | \(0.623716\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.5407 | − | 7.62731i | 0.769377 | − | 0.508487i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.02534 | + | 15.6323i | −0.599033 | + | 1.03755i | 0.393932 | + | 0.919140i | \(0.371115\pi\) |
−0.992964 | + | 0.118415i | \(0.962219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5212 | + | 6.07439i | −0.695258 | + | 0.401407i | −0.805579 | − | 0.592489i | \(-0.798145\pi\) |
0.110321 | + | 0.993896i | \(0.464812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9497 | + | 18.5511i | 0.983620 | + | 1.22057i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.39111 | − | 1.95786i | −0.222159 | − | 0.128264i | 0.384791 | − | 0.923004i | \(-0.374274\pi\) |
−0.606950 | + | 0.794740i | \(0.707607\pi\) | |||||||
\(234\) | 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 | ||||||||
\(241\) | 24.4958 | + | 14.1427i | 1.57792 | + | 0.911010i | 0.995150 | + | 0.0983690i | \(0.0313626\pi\) |
0.582765 | + | 0.812641i | \(0.301971\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.25393 | − | 14.2789i | −0.401190 | − | 0.915995i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.07578 | − | 4.23054i | −0.0687294 | − | 0.270279i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.59178 | − | 4.48909i | −0.164911 | − | 0.285634i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.191495 | − | 0.637054i | −0.0121355 | − | 0.0403716i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0425 | 0.760117 | 0.380059 | − | 0.924962i | \(-0.375904\pi\) | ||||
0.380059 | + | 0.924962i | \(0.375904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.9173 | −2.69819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.647932 | − | 0.688303i | 0.0405751 | − | 0.0431032i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.32521 | + | 12.6876i | 0.456934 | + | 0.791433i | 0.998797 | − | 0.0490340i | \(-0.0156143\pi\) |
−0.541863 | + | 0.840467i | \(0.682281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.03702 | − | 5.19207i | 0.250848 | − | 0.322620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1656 | − | 1.03818i | 1.06253 | − | 0.0642616i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.96349 | + | 2.86567i | 0.306062 | + | 0.176705i | 0.645163 | − | 0.764045i | \(-0.276790\pi\) |
−0.339101 | + | 0.940750i | \(0.610123\pi\) | |||||||
\(264\) | 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 | \(-0.198105\pi\) |
−0.911107 | + | 0.412169i | \(0.864771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6677 | − | 11.9325i | −1.25548 | − | 0.724849i | −0.283284 | − | 0.959036i | \(-0.591424\pi\) |
−0.972192 | + | 0.234187i | \(0.924757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.09838 | − | 11.2902i | −0.550659 | − | 0.683312i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.7617 | + | 11.9868i | −1.25198 | + | 0.722831i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.83423 | − | 6.64107i | 0.230376 | − | 0.399023i | −0.727543 | − | 0.686063i | \(-0.759338\pi\) |
0.957919 | + | 0.287039i | \(0.0926710\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | − | 13.6685i | − | 0.812510i | −0.913760 | − | 0.406255i | \(-0.866834\pi\) | ||
0.913760 | − | 0.406255i | \(-0.133166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.406141 | − | 1.72220i | 0.0240577 | − | 0.102014i | ||||
\(286\) | 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 | ||||||||
\(291\) | 11.3902 | − | 3.42382i | 0.667702 | − | 0.200708i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.70903 | − | 4.69218i | 0.158263 | − | 0.274120i | −0.775979 | − | 0.630758i | \(-0.782744\pi\) |
0.934242 | + | 0.356639i | \(0.116077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98512 | + | 3.43833i | 0.115578 | + | 0.200187i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.32455 | + | 25.3549i | 0.541065 | + | 1.47124i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.1194 | 1.51052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.11807 | − | 7.66595i | −0.179723 | − | 0.441858i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.5969 | + | 11.2572i | −0.608777 | + | 0.646709i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.02379 | − | 3.47784i | 0.344921 | − | 0.199140i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.56336i | − | 0.203372i | −0.994817 | − | 0.101686i | \(-0.967576\pi\) | ||
0.994817 | − | 0.101686i | \(-0.0324236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7109 | + | 4.42204i | −0.836876 | + | 0.251561i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2647 | 0.638762 | 0.319381 | − | 0.947626i | \(-0.396525\pi\) | ||||
0.319381 | + | 0.947626i | \(0.396525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4280i | 0.645950i | 0.946407 | + | 0.322975i | \(0.104683\pi\) | ||||
−0.946407 | + | 0.322975i | \(0.895317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.380187 | − | 4.93502i | 0.0214211 | − | 0.278057i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.4687i | − | 1.09347i | −0.837305 | − | 0.546736i | \(-0.815870\pi\) | ||
0.837305 | − | 0.546736i | \(-0.184130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.8028 | −1.66864 | ||||||||
\(320\) | 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 | ||||||||
\(327\) | 5.53522 | + | 18.4142i | 0.306098 | + | 1.01831i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.8134 | − | 3.42828i | −1.36801 | − | 0.189007i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.9675 | 1.48227 | 0.741135 | − | 0.671356i | \(-0.234288\pi\) | ||||
0.741135 | + | 0.671356i | \(0.234288\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.22147 | − | 4.11182i | 0.340935 | − | 0.225326i | ||||
\(334\) | 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 | ||||||||
\(339\) | 4.57032 | + | 4.30226i | 0.248226 | + | 0.233666i | ||||
\(340\) | 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 | ||||||||
\(345\) | 6.49209 | + | 6.11131i | 0.349522 | + | 0.329022i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.3724i | 1.84521i | 0.385752 | + | 0.922603i | \(0.373942\pi\) | ||||
−0.385752 | + | 0.922603i | \(0.626058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3935 | + | 14.6609i | −1.35928 | + | 0.784781i | −0.989527 | − | 0.144348i | \(-0.953891\pi\) |
−0.369754 | + | 0.929130i | \(0.620558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.67491 | − | 15.4310i | −0.302904 | − | 0.823645i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.586526 | − | 1.01589i | 0.0312177 | − | 0.0540706i | −0.849994 | − | 0.526792i | \(-0.823395\pi\) |
0.881212 | + | 0.472721i | \(0.156728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.71704 | − | 3.30074i | 0.303429 | − | 0.175185i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.618008 | + | 3.96271i | 0.0327084 | + | 0.209729i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.69591 | − | 3.28854i | −0.300619 | − | 0.173562i | 0.342102 | − | 0.939663i | \(-0.388861\pi\) |
−0.642721 | + | 0.766101i | \(0.722194\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −8.24124 | − | 4.75808i | −0.430189 | − | 0.248370i | 0.269238 | − | 0.963074i | \(-0.413228\pi\) |
−0.699427 | + | 0.714704i | \(0.746562\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.6387 | − | 11.6576i | 0.918236 | − | 0.606869i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.25975 | − | 1.32588i | 0.169238 | − | 0.0688362i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3152 | − | 17.8664i | −0.534098 | − | 0.925085i | −0.999206 | − | 0.0398315i | \(-0.987318\pi\) |
0.465108 | − | 0.885254i | \(-0.346015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.1038 | + | 2.38276i | 0.521760 | + | 0.123045i | ||||
\(376\) | 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 | ||||||||
\(381\) | 17.0955 | + | 4.03158i | 0.875827 | + | 0.206544i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0484 | − | 24.3326i | −0.717840 | − | 1.24334i | −0.961854 | − | 0.273564i | \(-0.911797\pi\) |
0.244013 | − | 0.969772i | \(-0.421536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.17398 | + | 8.49714i | −0.0598318 | + | 0.433054i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.566503 | − | 9.36678i | −0.0287970 | − | 0.476140i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.4400 | + | 16.4198i | 1.44196 | + | 0.832519i | 0.997981 | − | 0.0635162i | \(-0.0202314\pi\) |
0.443984 | + | 0.896035i | \(0.353565\pi\) | |||||||
\(390\) | 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 | 0.713758 | − | 0.700392i | \(-0.246992\pi\) |
−0.249679 | + | 0.968329i | \(0.580325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.71062 | + | 5.84540i | 0.235826 | + | 0.292636i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.3658 | + | 7.13943i | −0.617521 | + | 0.356526i | −0.775903 | − | 0.630852i | \(-0.782706\pi\) |
0.158382 | + | 0.987378i | \(0.449372\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.34851 | − | 12.7280i | 0.366055 | − | 0.634026i | ||||
\(404\) | 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 | ||||||||
\(409\) | − | 8.13148i | − | 0.402076i | −0.979583 | − | 0.201038i | \(-0.935569\pi\) | ||
0.979583 | − | 0.201038i | \(-0.0644314\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.495789 | + | 0.466710i | 0.0244555 | + | 0.0230211i | ||||
\(412\) | 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 | ||||||||
\(417\) | −22.8121 | − | 21.4741i | −1.11711 | − | 1.05159i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.53415 | + | 2.65723i | −0.0749481 | + | 0.129814i | −0.901064 | − | 0.433687i | \(-0.857212\pi\) |
0.826116 | + | 0.563501i | \(0.190546\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −25.4102 | − | 12.6907i | −1.23549 | − | 0.617041i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.03560 | −0.195756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.03894 | + | 29.2333i | −0.195458 | + | 1.41470i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.20240 | + | 27.2872i | 0.396016 | + | 1.31744i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.8414 | + | 11.4554i | −0.955727 | + | 0.551789i | −0.894855 | − | 0.446356i | \(-0.852721\pi\) |
−0.0608716 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7273i | 1.57278i | 0.617733 | + | 0.786388i | \(0.288051\pi\) | ||||
−0.617733 | + | 0.786388i | \(0.711949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.50827 | + | 4.24384i | 0.216155 | + | 0.203477i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.5231 | −0.646899 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.43498i | 0.307125i | 0.988139 | + | 0.153562i | \(0.0490746\pi\) | ||||
−0.988139 | + | 0.153562i | \(0.950925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.5393 | + | 14.1256i | 0.739965 | + | 0.672646i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.5373i | 1.21331i | 0.794964 | + | 0.606656i | \(0.207490\pi\) | ||||
−0.794964 | + | 0.606656i | \(0.792510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0248170 | 0.00117644 | ||||||||
\(446\) | 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 | ||||||||
\(453\) | 28.2568 | − | 30.0174i | 1.32762 | − | 1.41034i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.714485 | − | 5.17135i | 0.0334956 | − | 0.242436i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.4715 | −1.79962 | −0.899810 | − | 0.436283i | \(-0.856295\pi\) | ||||
−0.899810 | + | 0.436283i | \(0.856295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.774707 | + | 4.48114i | −0.0361602 | + | 0.209162i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0830 | + | 20.9283i | 0.562759 | + | 0.974728i | 0.997254 | + | 0.0740533i | \(0.0235935\pi\) |
−0.434495 | + | 0.900674i | \(0.643073\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 4.80454 | − | 1.44422i | 0.222805 | − | 0.0669742i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.46858 | − | 9.47185i | 0.253056 | − | 0.438305i | −0.711310 | − | 0.702878i | \(-0.751898\pi\) |
0.964366 | + | 0.264573i | \(0.0852311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.7098 | + | 4.38110i | 1.46422 | + | 0.202300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.57514 | + | 19.4003i | −0.210811 | + | 0.893920i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.2625i | 0.747751i | ||||||||
\(474\) | 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 | ||||||||
\(479\) | 0.756744 | − | 1.31072i | 0.0345765 | − | 0.0598883i | −0.848219 | − | 0.529645i | \(-0.822325\pi\) |
0.882796 | + | 0.469757i | \(0.155658\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.81173 | − | 3.93275i | 0.310588 | − | 0.179318i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.3764 | + | 5.82907i | −1.70069 | + | 0.265232i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.70841 | + | 2.14105i | 0.168390 | + | 0.0972201i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0853077 | − | 0.147757i | −0.00386566 | − | 0.00669552i | 0.864086 | − | 0.503344i | \(-0.167897\pi\) |
−0.867952 | + | 0.496649i | \(0.834564\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −4.34474 | − | 2.50844i | −0.195677 | − | 0.112974i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.34581 | + | 8.70151i | −0.195329 | + | 0.391104i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.83327 | + | 27.7447i | −0.171946 | + | 1.24452i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1327 | − | 19.2824i | −0.498369 | − | 0.863200i | 0.501629 | − | 0.865083i | \(-0.332734\pi\) |
−0.999998 | + | 0.00188245i | \(0.999401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.8932 | + | 16.8835i | −0.710058 | + | 0.754300i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2005 | 1.43575 | 0.717876 | − | 0.696171i | \(-0.245115\pi\) | ||||
0.717876 | + | 0.696171i | \(0.245115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.56621 | −0.247693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.48992 | + | 4.95656i | 0.0661696 | + | 0.220129i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.60909 | − | 7.98317i | −0.204294 | − | 0.353848i | 0.745613 | − | 0.666379i | \(-0.232157\pi\) |
−0.949908 | + | 0.312531i | \(0.898823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.0305 | + | 13.4349i | −1.46118 | + | 0.594326i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.93814 | + | 7.98927i | 0.129722 | + | 0.352735i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.78959 | − | 2.76527i | −0.211055 | − | 0.121853i | ||||
\(516\) | 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 | \(-0.0608961\pi\) |
−0.655549 | + | 0.755153i | \(0.727563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.3725 | − | 16.9582i | −1.28437 | − | 0.741532i | −0.306727 | − | 0.951798i | \(-0.599234\pi\) |
−0.977644 | + | 0.210266i | \(0.932567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.4532 | + | 13.2591i | −0.718077 | + | 0.578675i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.52050 | + | 2.03256i | −0.153355 | + | 0.0885398i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5708 | − | 39.0938i | 0.981340 | − | 1.69973i | ||||
\(530\) | 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 | ||||||||
\(535\) | − | 1.90333i | − | 0.0822880i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.6447 | − | 8.30987i | 1.19296 | − | 0.358597i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.4029 | − | 26.0610i | −1.09418 | − | 1.12253i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.65164 | + | 4.59278i | −0.114003 | + | 0.197459i | −0.917381 | − | 0.398011i | \(-0.869701\pi\) |
0.803378 | + | 0.595470i | \(0.203034\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.183953 | + | 0.780032i | −0.00789418 | + | 0.0334744i | ||||
\(544\) | 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 | ||||||||
\(549\) | −14.9512 | + | 29.9364i | −0.638101 | + | 1.27766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.39080 | −0.400061 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.4139 | + | 3.51124i | 1.08071 | + | 0.149313i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.61325 | + | 0.616278i | 0.110926 | + | 0.0261595i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.96801 | − | 4.02299i | 0.295244 | − | 0.170459i | −0.345060 | − | 0.938581i | \(-0.612142\pi\) |
0.640304 | + | 0.768121i | \(0.278808\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.89735i | − | 0.418613i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.80896 | − | 7.67070i | 0.0763745 | − | 0.323857i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.9156 | −1.26079 | −0.630396 | − | 0.776274i | \(-0.717108\pi\) | ||||
−0.630396 | + | 0.776274i | \(0.717108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.25983i | 0.0950718i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.5644 | + | 20.8150i | 0.485660 | + | 0.874148i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 30.8238i | − | 1.29220i | −0.763252 | − | 0.646101i | \(-0.776399\pi\) | ||
0.763252 | − | 0.646101i | \(-0.223601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.34693 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(572\) | 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 | −0.120132 | − | 0.992758i | \(-0.538332\pi\) |
0.799688 | + | 0.600416i | \(0.204998\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.3508 | + | 4.56345i | 0.804192 | + | 0.189651i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.382846 | + | 0.941248i | 0.0158831 | + | 0.0390495i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.91522 | −0.286399 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.64485 | − | 5.29573i | 0.109351 | − | 0.218951i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.3955 | − | 21.4697i | −0.511619 | − | 0.886150i | −0.999909 | − | 0.0134687i | \(-0.995713\pi\) |
0.488290 | − | 0.872681i | \(-0.337621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.80464 | + | 6.58982i | −0.156767 | + | 0.271529i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.90107 | − | 8.06126i | 0.0781995 | − | 0.331596i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.87451 | + | 3.24675i | −0.0769770 | + | 0.133328i | −0.901944 | − | 0.431852i | \(-0.857860\pi\) |
0.824967 | + | 0.565180i | \(0.191193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.886331 | + | 1.13992i | −0.0363360 | + | 0.0467323i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.0897 | + | 4.53588i | −0.617579 | + | 0.185641i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 32.0673i | − | 1.31024i | −0.755527 | − | 0.655118i | \(-0.772619\pi\) | ||
0.755527 | − | 0.655118i | \(-0.227381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.98069 | − | 3.45296i | 0.243958 | − | 0.140849i | −0.373037 | − | 0.927817i | \(-0.621683\pi\) |
0.616994 | + | 0.786968i | \(0.288350\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.4725 | + | 16.2178i | 1.32238 | + | 0.660438i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.99824 | − | 8.65721i | 0.203207 | − | 0.351966i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7892 | + | 10.8479i | −0.762629 | + | 0.440304i | −0.830239 | − | 0.557408i | \(-0.811796\pi\) |
0.0676102 | + | 0.997712i | \(0.478463\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.9551 | + | 4.04785i | −1.05175 | + | 0.164027i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.9437 | − | 14.9786i | −1.04957 | − | 0.605968i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.96928 | + | 15.5352i | 0.362266 | + | 0.627463i | 0.988333 | − | 0.152306i | \(-0.0486699\pi\) |
−0.626068 | + | 0.779769i | \(0.715337\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 37.5659 | + | 21.6887i | 1.50990 | + | 0.871743i | 0.999933 | + | 0.0115498i | \(0.00367650\pi\) |
0.509969 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −42.2662 | − | 7.30706i | −1.69608 | − | 0.293222i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0646303 | + | 0.0831220i | −0.00258936 | + | 0.00333021i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.65906 | − | 16.7300i | −0.386363 | − | 0.669200i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.24673 | − | 14.1277i | −0.169598 | − | 0.564208i | ||||
\(628\) | 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 | ||||||||
\(633\) | −3.50169 | + | 3.71987i | −0.139179 | + | 0.147851i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.16189 | + | 5.47655i | 0.125476 | + | 0.217330i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.4602 | + | 15.8607i | 0.612555 | + | 0.628425i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1898 | + | 28.4120i | −0.561341 | + | 1.12396i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.7688 | − | 14.8776i | −1.01781 | − | 0.587631i | −0.104339 | − | 0.994542i | \(-0.533273\pi\) |
−0.913468 | + | 0.406911i | \(0.866606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.4271 | + | 21.6085i | 1.47598 | + | 0.852158i | 0.999633 | − | 0.0270991i | \(-0.00862696\pi\) |
0.476348 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(644\) | 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 | \(-0.0457817\pi\) |
−0.618967 | + | 0.785417i | \(0.712448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.6661 | + | 16.5504i | 1.12524 | + | 0.649660i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.67508 | + | 19.8535i | −0.300810 | + | 0.778120i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.41584 | − | 4.85889i | 0.329337 | − | 0.190143i | −0.326210 | − | 0.945297i | \(-0.605772\pi\) |
0.655547 | + | 0.755155i | \(0.272438\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.78397 | − | 11.7502i | 0.265072 | − | 0.459118i | ||||
\(656\) | 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 | ||||||||
\(661\) | 1.25812i | 0.0489353i | 0.999701 | + | 0.0244677i | \(0.00778907\pi\) | ||||
−0.999701 | + | 0.0244677i | \(0.992211\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.10093 | + | 4.66838i | −0.0427567 | + | 0.181305i | ||||
\(664\) | 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 | ||||||||
\(669\) | 39.1810 | − | 11.7776i | 1.51482 | − | 0.455349i | ||||
\(670\) | 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 | ||||||||
\(675\) | −22.4876 | + | 8.27007i | −0.865549 | + | 0.318315i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.1233 | −0.888699 | −0.444350 | − | 0.895853i | \(-0.646565\pi\) | ||||
−0.444350 | + | 0.895853i | \(0.646565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.8290 | + | 6.84506i | −0.645836 | + | 0.262689i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.4298 | − | 22.7650i | 0.821191 | − | 0.872357i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.4945 | − | 7.21370i | 0.478089 | − | 0.276025i | −0.241531 | − | 0.970393i | \(-0.577650\pi\) |
0.719620 | + | 0.694368i | \(0.244316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.245147i | 0.00936659i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1516 | − | 6.05747i | 0.768831 | − | 0.231107i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.20859 | 0.160335 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.4114i | − | 1.42320i | −0.702586 | − | 0.711599i | \(-0.747971\pi\) | ||
0.702586 | − | 0.711599i | \(-0.252029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.8272 | − | 37.2170i | −0.677198 | − | 1.41376i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11.2796i | − | 0.427860i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.16802 | −0.233630 | ||||||||
\(698\) | 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 | ||||||||
\(705\) | −2.94378 | − | 9.79318i | −0.110869 | − | 0.368832i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.4959 | − | 18.6435i | 0.545176 | − | 0.701160i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3246 | 0.875974 | 0.437987 | − | 0.898981i | \(-0.355692\pi\) | ||||
0.437987 | + | 0.898981i | \(0.355692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.0251 | + | 12.9978i | 0.976019 | + | 0.487454i | ||||
\(712\) | 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 | ||||||||
\(717\) | −15.1447 | − | 14.2565i | −0.565590 | − | 0.532417i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.7489 | − | 37.6701i | 0.811096 | − | 1.40486i | −0.101002 | − | 0.994886i | \(-0.532205\pi\) |
0.912098 | − | 0.409973i | \(-0.134462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.7354 | − | 8.84073i | 0.809470 | − | 0.329246i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.6727 | − | 33.5804i | −1.32668 | − | 1.24887i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 26.4325i | − | 0.981679i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.3715 | − | 6.56536i | 0.421747 | − | 0.243496i | −0.274078 | − | 0.961708i | \(-0.588373\pi\) |
0.695824 | + | 0.718212i | \(0.255039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.86618 | + | 26.5579i | 0.180229 | + | 0.983625i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.36878 | + | 2.37079i | −0.0506261 | + | 0.0876870i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.7965 | − | 20.0898i | 1.28524 | − | 0.742032i | 0.307436 | − | 0.951569i | \(-0.400529\pi\) |
0.977801 | + | 0.209537i | \(0.0671955\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.131673 | + | 7.55956i | 0.00485683 | + | 0.278839i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.4762 | − | 31.4518i | −2.00666 | − | 1.15854i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7073 | + | 32.4020i | 0.688158 | + | 1.19193i | 0.972433 | + | 0.233182i | \(0.0749139\pi\) |
−0.284275 | + | 0.958743i | \(0.591753\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | 5.53597 | + | 3.19619i | 0.202822 | + | 0.117099i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0695569 | + | 1.15008i | 0.00254495 | + | 0.0420793i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.37500 | + | 4.95679i | 0.232938 | + | 0.181117i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5070 | + | 25.1268i | 0.529367 | + | 0.916891i | 0.999413 | + | 0.0342492i | \(0.0109040\pi\) |
−0.470046 | + | 0.882642i | \(0.655763\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.3014 | − | 4.78762i | −0.739823 | − | 0.174471i | ||||
\(754\) | 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 | ||||||||
\(759\) | 72.3503 | + | 17.0622i | 2.62615 | + | 0.619318i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4107 | − | 19.7638i | −0.413636 | − | 0.716439i | 0.581648 | − | 0.813440i | \(-0.302408\pi\) |
−0.995284 | + | 0.0970019i | \(0.969075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0663 | − | 27.2070i | −0.400626 | − | 0.984961i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.36593 | + | 0.902754i | −0.0493853 | + | 0.0326391i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.4462 | − | 10.0725i | −0.629945 | − | 0.363699i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6397 | − | 15.9578i | −0.996714 | − | 0.575453i | −0.0894399 | − | 0.995992i | \(-0.528508\pi\) |
−0.907275 | + | 0.420539i | \(0.861841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.30479 | − | 24.3011i | −0.263076 | − | 0.875183i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.8503 | + | 30.9176i | 0.642030 | + | 1.11203i | 0.984979 | + | 0.172675i | \(0.0552410\pi\) |
−0.342949 | + | 0.939354i | \(0.611426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.5486 | − | 10.7090i | −0.666284 | − | 0.384679i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.86980 | + | 7.14788i | −0.318202 | + | 0.256429i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.99875 | + | 5.77278i | −0.358242 | + | 0.206831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.5190 | − | 47.6643i | 0.984708 | − | 1.70556i | ||||
\(782\) | 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 | ||||||||
\(787\) | 13.8834i | 0.494888i | 0.968902 | + | 0.247444i | \(0.0795907\pi\) | ||||
−0.968902 | + | 0.247444i | \(0.920409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.22820 | − | 6.80425i | −0.257331 | − | 0.242238i | ||||
\(790\) | 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 | ||||||||
\(795\) | 1.04606 | + | 0.984709i | 0.0371001 | + | 0.0349240i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2145 | − | 24.6203i | 0.503504 | − | 0.872094i | −0.496488 | − | 0.868044i | \(-0.665377\pi\) |
0.999992 | − | 0.00405063i | \(-0.00128936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.14300 | + | 7.17589i | 0.146569 | + | 0.253865i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0996020 | + | 0.0658278i | −0.00351927 | + | 0.00232591i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 70.0708 | 2.47274 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7518 | − | 8.35990i | −0.378951 | − | 0.294648i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.61273 | + | 5.36512i | 0.0567708 | + | 0.188861i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.1074 | + | 12.1864i | −0.742096 | + | 0.428449i | −0.822831 | − | 0.568286i | \(-0.807607\pi\) |
0.0807348 | + | 0.996736i | \(0.474273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2739i | 1.23863i | 0.785141 | + | 0.619317i | \(0.212591\pi\) | ||||
−0.785141 | + | 0.619317i | \(0.787409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.0979 | + | 28.3326i | 1.05558 | + | 0.993668i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.0474 | −0.457030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.12428i | 0.179276i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.8496 | + | 22.6502i | 0.379116 | + | 0.791462i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5144i | 0.681056i | 0.940234 | + | 0.340528i | \(0.110606\pi\) | ||||
−0.940234 | + | 0.340528i | \(0.889394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.6570 | −1.10349 | −0.551747 | − | 0.834012i | \(-0.686038\pi\) | ||||
−0.551747 | + | 0.834012i | \(0.686038\pi\) | |||||||
\(824\) | 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 | −0.485236 | − | 0.874383i | \(-0.661266\pi\) |
0.514620 | + | 0.857419i | \(0.327933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.10399 | + | 9.67123i | −0.315814 | + | 0.335491i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.50981 | − | 5.93736i | −0.0523119 | − | 0.205717i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.34819 | −0.288901 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.4520 | + | 18.5405i | −0.534100 | + | 0.640855i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.6920 | − | 34.1075i | −0.679843 | − | 1.17752i | −0.975028 | − | 0.222083i | \(-0.928714\pi\) |
0.295184 | − | 0.955440i | \(-0.404619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.92983 | − | 3.34257i | 0.0665459 | − | 0.115261i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.8335 | + | 5.06007i | −0.579777 | + | 0.174278i | ||||
\(844\) | 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 | ||||||||
\(849\) | −5.43406 | + | 23.0425i | −0.186497 | + | 0.790817i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 20.5199i | − | 0.703415i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3507 | − | 12.3268i | 0.731033 | − | 0.422062i | −0.0877672 | − | 0.996141i | \(-0.527973\pi\) |
0.818800 | + | 0.574079i | \(0.194640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.36935 | + | 2.74182i | −0.0468309 | + | 0.0937684i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4145 | − | 19.7705i | 0.389911 | − | 0.675346i | −0.602526 | − | 0.798099i | \(-0.705839\pi\) |
0.992437 | + | 0.122753i | \(0.0391723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3224 | − | 23.8575i | 1.40990 | − | 0.814007i | 0.414523 | − | 0.910039i | \(-0.363948\pi\) |
0.995378 | + | 0.0960315i | \(0.0306150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.1471 | + | 20.2652i | −0.857011 | + | 0.690637i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0645 | + | 10.4296i | 0.614923 | + | 0.355026i | 0.774890 | − | 0.632096i | \(-0.217805\pi\) |
−0.159967 | + | 0.987122i | \(0.551139\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 33.1541 | + | 19.1416i | 1.12339 | + | 0.648587i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.5628 | + | 1.24364i | −0.695944 | + | 0.0420907i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.7080 | − | 2.17026i | −0.531028 | − | 0.0733680i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7718 | + | 20.3894i | 0.397506 | + | 0.688500i | 0.993417 | − | 0.114550i | \(-0.0365426\pi\) |
−0.595912 | + | 0.803050i | \(0.703209\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.43232 | + | 6.83310i | −0.216957 | + | 0.230475i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.5975 | 1.77205 | 0.886027 | − | 0.463633i | \(-0.153454\pi\) | ||||
0.886027 | + | 0.463633i | \(0.153454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6815 | −1.13347 | −0.566737 | − | 0.823899i | \(-0.691794\pi\) | ||||
−0.566737 | + | 0.823899i | \(0.691794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.97959 | − | 6.58556i | −0.0665430 | − | 0.221371i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.51139 | + | 13.0101i | 0.252208 | + | 0.436837i | 0.964133 | − | 0.265418i | \(-0.0855100\pi\) |
−0.711926 | + | 0.702255i | \(0.752177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.5776 | − | 3.67203i | −0.891385 | − | 0.123156i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.63929 | − | 46.4506i | −0.188923 | − | 1.55615i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4321 | + | 7.75505i | 0.449489 | + | 0.259513i | ||||
\(894\) | 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 | ||||||||
\(903\) | 2.20879 | + | 14.1629i | 0.0735039 | + | 0.471313i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.249884 | + | 0.144271i | −0.00830643 | + | 0.00479572i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.84747 | − | 10.1281i | 0.194162 | − | 0.336299i | −0.752463 | − | 0.658634i | \(-0.771135\pi\) |
0.946626 | + | 0.322335i | \(0.104468\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 1.99676i | − | 0.0660831i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.5376 | + | 3.46814i | −0.381421 | + | 0.114653i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.6887 | + | 53.3230i | 0.716225 | + | 1.76088i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.26860 | − | 16.0537i | 0.305743 | − | 0.529562i | −0.671683 | − | 0.740838i | \(-0.734428\pi\) |
0.977426 | + | 0.211276i | \(0.0677618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.41665 | + | 6.00714i | −0.0466802 | + | 0.197942i | ||||
\(922\) | 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 | ||||||||
\(927\) | 26.5578 | − | 1.60622i | 0.872274 | − | 0.0527551i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.6714 | −1.76090 | −0.880451 | − | 0.474138i | \(-0.842760\pi\) | ||||
−0.880451 | + | 0.474138i | \(0.842760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.00440 | − | 8.21177i | −0.262334 | − | 0.269130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.9901 | − | 4.47839i | −0.621707 | − | 0.146616i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.45732 | − | 1.41873i | 0.0803630 | − | 0.0463976i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.7752i | − | 0.548023i | −0.961726 | − | 0.274012i | \(-0.911649\pi\) | ||
0.961726 | − | 0.274012i | \(-0.0883506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.54333 | − | 19.2655i | 0.148266 | − | 0.628704i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.0686 | 1.20840 | 0.604200 | − | 0.796833i | \(-0.293493\pi\) | ||||
0.604200 | + | 0.796833i | \(0.293493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 58.1769i | − | 1.89450i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.60289 | + | 8.16835i | −0.0846720 | + | 0.265716i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.16082i | − | 0.102713i | −0.998680 | − | 0.0513565i | \(-0.983646\pi\) | ||
0.998680 | − | 0.0513565i | \(-0.0163545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.6450 | −1.38431 | ||||||||
\(950\) | 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 | ||||||||
\(957\) | 50.2418 | + | 11.8484i | 1.62409 | + | 0.383005i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.821096 | − | 0.638431i | −0.0265146 | − | 0.0206160i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.42531 | 0.304042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.04863 | + | 7.63893i | 0.162690 | + | 0.246161i | ||||
\(964\) | 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 | ||||||||
\(969\) | 0.570000 | − | 2.41702i | 0.0183110 | − | 0.0776458i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3537 | + | 19.6652i | −0.364358 | + | 0.631086i | −0.988673 | − | 0.150087i | \(-0.952045\pi\) |
0.624315 | + | 0.781172i | \(0.285378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.7800 | + | 29.3752i | 1.21117 | + | 0.941727i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.2014 | + | 7.27482i | −0.775065 | + | 0.232981i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.0411i | 1.31302i | 0.754317 | + | 0.656511i | \(0.227968\pi\) | ||||
−0.754317 | + | 0.656511i | \(0.772032\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 10.4653 | − | 18.1263i | 0.333790 | − | 0.578141i | −0.649462 | − | 0.760394i | \(-0.725006\pi\) |
0.983252 | + | 0.182253i | \(0.0583391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.58243 | − | 1.49097i | 0.0822832 | − | 0.0475062i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 40.4677 | + | 15.6442i | 1.28810 | + | 0.497962i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.3614 | − | 12.9104i | −0.711051 | − | 0.410525i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9709 | + | 46.7149i | 0.856758 | + | 1.48395i | 0.875004 | + | 0.484116i | \(0.160859\pi\) |
−0.0182456 | + | 0.999834i | \(0.505808\pi\) | |||||||
\(992\) | 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 | ||||||||
\(997\) | 2.78561 | + | 1.60827i | 0.0882211 | + | 0.0509345i | 0.543462 | − | 0.839434i | \(-0.317113\pi\) |
−0.455240 | + | 0.890369i | \(0.650447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.1229 | + | 4.45833i | −0.383551 | + | 0.141055i |
(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.bs.a.257.3 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.14 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.22 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.11 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.11 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.14 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.14 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.14 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.14 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.14 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.14 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.3 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.14 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.14 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.14 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.22 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.3 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.11 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.11 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.22 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.22 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.14 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.14 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.14 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.14 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.14 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.14 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.14 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.14 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.14 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.14 | 48 | 36.7 | odd | 6 |