Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
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, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\), 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: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.6095158642368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.4 | ||
Root | \(1.34147 + 1.09565i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.169 |
Dual form | 504.2.r.f.337.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.742385 | + | 1.56488i | 0.428616 | + | 0.903487i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.76217 | − | 3.05216i | −0.788065 | − | 1.36497i | −0.927151 | − | 0.374688i | \(-0.877750\pi\) |
0.139086 | − | 0.990280i | \(-0.455583\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.89773 | + | 2.32349i | −0.632576 | + | 0.774498i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.08386 | − | 3.60934i | 0.628306 | − | 1.08826i | −0.359585 | − | 0.933112i | \(-0.617082\pi\) |
0.987892 | − | 0.155146i | \(-0.0495848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52051 | − | 2.63361i | −0.421715 | − | 0.730431i | 0.574393 | − | 0.818580i | \(-0.305238\pi\) |
−0.996107 | + | 0.0881486i | \(0.971905\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46807 | − | 5.02347i | 0.895453 | − | 1.29705i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79546 | 0.920533 | 0.460267 | − | 0.887781i | \(-0.347754\pi\) | ||||
0.460267 | + | 0.887781i | \(0.347754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.40544 | 1.24009 | 0.620047 | − | 0.784565i | \(-0.287114\pi\) | ||||
0.620047 | + | 0.784565i | \(0.287114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.72642 | + | 0.139518i | 0.376736 | + | 0.0304453i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.48540 | − | 7.76894i | −0.935271 | − | 1.61994i | −0.774150 | − | 0.633002i | \(-0.781822\pi\) |
−0.161121 | − | 0.986935i | \(-0.551511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.71046 | + | 6.42670i | −0.742092 | + | 1.28534i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.04485 | − | 1.24480i | −0.970881 | − | 0.239561i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.46107 | − | 2.53065i | 0.271314 | − | 0.469929i | −0.697885 | − | 0.716210i | \(-0.745875\pi\) |
0.969199 | + | 0.246281i | \(0.0792086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.08767 | + | 5.34801i | 0.554563 | + | 0.960531i | 0.997937 | + | 0.0641943i | \(0.0204477\pi\) |
−0.443375 | + | 0.896336i | \(0.646219\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.19523 | + | 0.581470i | 1.25253 | + | 0.101221i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.52433 | −0.595721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.66649 | −0.767166 | −0.383583 | − | 0.923506i | \(-0.625310\pi\) | ||||
−0.383583 | + | 0.923506i | \(0.625310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.99249 | − | 4.33458i | 0.479181 | − | 0.694088i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.83828 | + | 3.18400i | 0.287092 | + | 0.497257i | 0.973114 | − | 0.230323i | \(-0.0739782\pi\) |
−0.686023 | + | 0.727580i | \(0.740645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31777 | − | 2.28244i | 0.200958 | − | 0.348069i | −0.747879 | − | 0.663835i | \(-0.768928\pi\) |
0.948837 | + | 0.315765i | \(0.102261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4358 | + | 1.69779i | 1.55568 | + | 0.253091i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.860518 | + | 1.49046i | −0.125519 | + | 0.217406i | −0.921936 | − | 0.387343i | \(-0.873393\pi\) |
0.796416 | + | 0.604749i | \(0.206726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.81769 | + | 5.93945i | 0.394556 | + | 0.831690i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4209 | 1.56878 | 0.784392 | − | 0.620265i | \(-0.212975\pi\) | ||||
0.784392 | + | 0.620265i | \(0.212975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.6884 | −1.98058 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.01292 | + | 8.45890i | 0.531524 | + | 1.12041i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.564482 | + | 0.977712i | 0.0734894 | + | 0.127287i | 0.900428 | − | 0.435004i | \(-0.143253\pi\) |
−0.826939 | + | 0.562292i | \(0.809920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.03597 | + | 10.4546i | −0.772826 | + | 1.33857i | 0.163182 | + | 0.986596i | \(0.447824\pi\) |
−0.936008 | + | 0.351979i | \(0.885509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.06334 | + | 2.80523i | 0.133968 | + | 0.353426i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.35880 | + | 9.28171i | −0.664677 | + | 1.15125i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.12782 | − | 1.95345i | −0.137786 | − | 0.238652i | 0.788873 | − | 0.614557i | \(-0.210665\pi\) |
−0.926658 | + | 0.375905i | \(0.877332\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.82761 | − | 12.7867i | 1.06272 | − | 1.53934i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.92978 | −1.17845 | −0.589224 | − | 0.807970i | \(-0.700566\pi\) | ||||
−0.589224 | + | 0.807970i | \(0.700566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50106 | 0.292727 | 0.146364 | − | 0.989231i | \(-0.453243\pi\) | ||||
0.146364 | + | 0.989231i | \(0.453243\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.8116 | − | 1.03535i | −1.47936 | − | 0.119552i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.08386 | − | 3.60934i | −0.237477 | − | 0.411323i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.16763 | − | 5.48650i | 0.356387 | − | 0.617280i | −0.630968 | − | 0.775809i | \(-0.717342\pi\) |
0.987354 | + | 0.158530i | \(0.0506753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79726 | − | 8.81872i | −0.199695 | − | 0.979858i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.52319 | − | 9.56645i | 0.606249 | − | 1.05005i | −0.385604 | − | 0.922664i | \(-0.626007\pi\) |
0.991853 | − | 0.127390i | \(-0.0406599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.68823 | − | 11.5843i | −0.725440 | − | 1.25650i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.04485 | + | 0.407691i | 0.540864 | + | 0.0437090i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.4697 | −1.42779 | −0.713895 | − | 0.700253i | \(-0.753071\pi\) | ||||
−0.713895 | + | 0.700253i | \(0.753071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.04103 | −0.318786 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.07677 | + | 8.80214i | −0.630132 | + | 0.912739i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.52529 | − | 16.4983i | −0.977274 | − | 1.69269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.46871 | + | 16.4003i | −0.961401 | + | 1.66520i | −0.242414 | + | 0.970173i | \(0.577939\pi\) |
−0.718987 | + | 0.695023i | \(0.755394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.43170 | + | 11.6914i | 0.445403 | + | 1.17503i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.82940 | + | 8.36477i | −0.480544 | + | 0.832326i | −0.999751 | − | 0.0223224i | \(-0.992894\pi\) |
0.519207 | + | 0.854648i | \(0.326227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.981584 | + | 1.70015i | 0.0967183 | + | 0.167521i | 0.910324 | − | 0.413895i | \(-0.135832\pi\) |
−0.813606 | + | 0.581416i | \(0.802499\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.61641 | − | 5.51517i | −0.255336 | − | 0.538226i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5072 | 1.78916 | 0.894578 | − | 0.446912i | \(-0.147476\pi\) | ||||
0.894578 | + | 0.446912i | \(0.147476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.67237 | 0.255967 | 0.127983 | − | 0.991776i | \(-0.459150\pi\) | ||||
0.127983 | + | 0.991776i | \(0.459150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46433 | − | 7.30252i | −0.328820 | − | 0.693125i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.65605 | − | 8.06452i | −0.438005 | − | 0.758646i | 0.559531 | − | 0.828809i | \(-0.310981\pi\) |
−0.997536 | + | 0.0701632i | \(0.977648\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8080 | + | 27.3803i | −1.47411 | + | 2.55323i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00470 | + | 1.46497i | 0.832485 | + | 0.135436i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.89773 | − | 3.28696i | 0.173964 | − | 0.301315i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.18491 | − | 5.51642i | −0.289537 | − | 0.501493i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.61788 | + | 5.24046i | −0.326213 | + | 0.472516i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.53213 | 0.763137 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7663 | 1.48777 | 0.743883 | − | 0.668310i | \(-0.232982\pi\) | ||||
0.743883 | + | 0.668310i | \(0.232982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.55005 | + | 0.367705i | 0.400610 | + | 0.0323746i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.36566 | + | 2.36539i | 0.119318 | + | 0.206665i | 0.919498 | − | 0.393096i | \(-0.128596\pi\) |
−0.800180 | + | 0.599761i | \(0.795263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.70272 | − | 4.68125i | 0.234356 | − | 0.405916i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.09054 | + | 17.5912i | 0.438124 | + | 1.51401i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.12870 | + | 14.0793i | −0.694482 | + | 1.20288i | 0.275873 | + | 0.961194i | \(0.411033\pi\) |
−0.970355 | + | 0.241684i | \(0.922300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.654057 | − | 1.13286i | −0.0554764 | − | 0.0960879i | 0.836954 | − | 0.547274i | \(-0.184334\pi\) |
−0.892430 | + | 0.451186i | \(0.851001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.97124 | − | 0.240115i | −0.250223 | − | 0.0202214i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6741 | −1.05986 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2986 | −0.855251 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.984037 | − | 1.42537i | 0.0811620 | − | 0.117562i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.54580 | + | 11.3377i | 0.536253 | + | 0.928818i | 0.999102 | + | 0.0423802i | \(0.0134941\pi\) |
−0.462848 | + | 0.886437i | \(0.653173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.10933 | + | 12.3137i | −0.578549 | + | 1.00208i | 0.417097 | + | 0.908862i | \(0.363048\pi\) |
−0.995646 | + | 0.0932143i | \(0.970286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.20274 | + | 8.81872i | −0.582307 | + | 0.712951i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8820 | − | 18.8482i | 0.874062 | − | 1.51392i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.87043 | + | 8.43584i | 0.388703 | + | 0.673253i | 0.992275 | − | 0.124055i | \(-0.0395899\pi\) |
−0.603572 | + | 0.797308i | \(0.706257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.47872 | + | 17.8724i | 0.672406 | + | 1.41738i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.97080 | −0.706998 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2129 | 1.42655 | 0.713274 | − | 0.700886i | \(-0.247212\pi\) | ||||
0.713274 | + | 0.700886i | \(0.247212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.9045 | − | 22.9857i | −0.848910 | − | 1.78943i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.81475 | + | 13.5355i | 0.604724 | + | 1.04741i | 0.992095 | + | 0.125488i | \(0.0400498\pi\) |
−0.387371 | + | 0.921924i | \(0.626617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.87607 | − | 3.24945i | 0.144313 | − | 0.249958i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.2581 | + | 12.5595i | −0.784454 | + | 0.960450i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.23991 | − | 9.07579i | 0.398383 | − | 0.690019i | −0.595144 | − | 0.803619i | \(-0.702905\pi\) |
0.993527 | + | 0.113600i | \(0.0362382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.71046 | + | 6.42670i | 0.280484 | + | 0.485813i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.11094 | + | 1.60919i | −0.0835036 | + | 0.120954i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0874 | −1.35192 | −0.675958 | − | 0.736940i | \(-0.736270\pi\) | ||||
−0.675958 | + | 0.736940i | \(0.736270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.4020 | 1.66513 | 0.832564 | − | 0.553929i | \(-0.186872\pi\) | ||||
0.832564 | + | 0.553929i | \(0.186872\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.8413 | − | 1.68425i | −1.54063 | − | 0.124503i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.22313 | + | 14.2429i | 0.604577 | + | 1.04716i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.90918 | − | 13.6991i | 0.578377 | − | 1.00178i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.60045 | + | 3.74657i | −0.261894 | + | 0.272523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.69490 | − | 2.93566i | 0.122639 | − | 0.212417i | −0.798169 | − | 0.602434i | \(-0.794198\pi\) |
0.920808 | + | 0.390017i | \(0.127531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.99828 | − | 13.8534i | −0.575729 | − | 0.997191i | −0.995962 | − | 0.0897754i | \(-0.971385\pi\) |
0.420233 | − | 0.907416i | \(-0.361948\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.5031 | − | 1.49530i | −1.32503 | − | 0.107080i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.75083 | −0.480977 | −0.240488 | − | 0.970652i | \(-0.577308\pi\) | ||||
−0.240488 | + | 0.970652i | \(0.577308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4209 | 0.809608 | 0.404804 | − | 0.914404i | \(-0.367340\pi\) | ||||
0.404804 | + | 0.914404i | \(0.367340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.21964 | − | 3.21513i | 0.156561 | − | 0.226777i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.46107 | − | 2.53065i | −0.102547 | − | 0.177617i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47872 | − | 11.2215i | 0.452494 | − | 0.783742i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.5632 | + | 4.32154i | 1.84627 | + | 0.300368i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2642 | − | 19.5101i | 0.779158 | − | 1.34954i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.40147 | − | 11.0877i | −0.440695 | − | 0.763307i | 0.557046 | − | 0.830482i | \(-0.311935\pi\) |
−0.997741 | + | 0.0671751i | \(0.978601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.37172 | − | 15.5390i | −0.505102 | − | 1.06471i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.28851 | −0.633471 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.17535 | 0.419210 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85675 | + | 3.91387i | 0.125468 | + | 0.264475i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.77105 | − | 9.99574i | −0.388203 | − | 0.672387i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.86357 | − | 10.1560i | 0.392654 | − | 0.680096i | −0.600145 | − | 0.799891i | \(-0.704890\pi\) |
0.992799 | + | 0.119795i | \(0.0382237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.89097 | − | 20.8174i | −0.526065 | − | 1.38782i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.30312 | − | 10.9173i | 0.418353 | − | 0.724608i | −0.577421 | − | 0.816446i | \(-0.695941\pi\) |
0.995774 | + | 0.0918384i | \(0.0292743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.34480 | + | 7.52542i | 0.287113 | + | 0.497294i | 0.973119 | − | 0.230302i | \(-0.0739713\pi\) |
−0.686007 | + | 0.727595i | \(0.740638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.10118 | − | 5.94052i | 0.269838 | − | 0.390857i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9251 | 0.846748 | 0.423374 | − | 0.905955i | \(-0.360846\pi\) | ||||
0.423374 | + | 0.905955i | \(0.360846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.06550 | 0.395670 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9373 | + | 0.883883i | 0.710457 | + | 0.0574143i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8020 | + | 18.7097i | 0.698725 | + | 1.21023i | 0.968909 | + | 0.247419i | \(0.0795823\pi\) |
−0.270183 | + | 0.962809i | \(0.587084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.66179 | + | 2.87831i | −0.107046 | + | 0.185408i | −0.914572 | − | 0.404423i | \(-0.867472\pi\) |
0.807527 | + | 0.589831i | \(0.200806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.4660 | − | 9.35939i | 0.799696 | − | 0.600405i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.76217 | + | 3.05216i | −0.112581 | + | 0.194995i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.21905 | − | 14.2358i | −0.522966 | − | 0.905803i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.0707 | + | 1.54117i | 1.20856 | + | 0.0976675i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.67969 | 0.169140 | 0.0845701 | − | 0.996418i | \(-0.473048\pi\) | ||||
0.0845701 | + | 0.996418i | \(0.473048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.3877 | −2.35055 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.1629 | − | 19.0663i | 0.824294 | − | 1.19398i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.75443 | − | 6.50286i | −0.234195 | − | 0.405637i | 0.724844 | − | 0.688913i | \(-0.241912\pi\) |
−0.959038 | + | 0.283276i | \(0.908579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.33325 | + | 4.04130i | −0.144981 | + | 0.251114i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.10723 | + | 8.19727i | 0.192333 | + | 0.507398i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.35062 | + | 16.1957i | −0.576584 | + | 0.998672i | 0.419284 | + | 0.907855i | \(0.362281\pi\) |
−0.995868 | + | 0.0908171i | \(0.971052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.1256 | − | 34.8585i | −1.23630 | − | 2.14134i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.99974 | − | 21.0786i | −0.611974 | − | 1.28999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.0035 | −1.03672 | −0.518360 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518360 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1427 | 1.40582 | 0.702910 | − | 0.711279i | \(-0.251884\pi\) | ||||
0.702910 | + | 0.711279i | \(0.251884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.25761 | − | 4.75886i | −0.136637 | − | 0.288019i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4641 | + | 26.7846i | 0.932522 | + | 1.61518i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.93092 | − | 12.0047i | 0.416438 | − | 0.721293i | −0.579140 | − | 0.815228i | \(-0.696611\pi\) |
0.995578 | + | 0.0939357i | \(0.0299448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.2856 | − | 2.97487i | −1.09473 | − | 0.178101i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.56926 | + | 7.91419i | −0.272579 | + | 0.472121i | −0.969521 | − | 0.245006i | \(-0.921210\pi\) |
0.696942 | + | 0.717127i | \(0.254543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.45421 | + | 5.98287i | 0.205331 | + | 0.355645i | 0.950238 | − | 0.311524i | \(-0.100839\pi\) |
−0.744907 | + | 0.667169i | \(0.767506\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.7465 | − | 27.1541i | 1.11045 | − | 1.60847i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.67657 | 0.217021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.59451 | −0.152618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.6940 | − | 2.64211i | −1.91655 | − | 0.154883i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.30083 | + | 16.1095i | 0.543361 | + | 0.941128i | 0.998708 | + | 0.0508143i | \(0.0161817\pi\) |
−0.455348 | + | 0.890314i | \(0.650485\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98942 | − | 3.44578i | 0.115829 | − | 0.200621i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.0056 | + | 15.6146i | −0.870715 | + | 0.906051i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.6402 | + | 23.6256i | −0.788835 | + | 1.36630i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31777 | − | 2.28244i | −0.0759550 | − | 0.131558i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.6752 | − | 1.34758i | −0.957964 | − | 0.0774162i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.5455 | 2.43615 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9553 | 0.796473 | 0.398236 | − | 0.917283i | \(-0.369622\pi\) | ||||
0.398236 | + | 0.917283i | \(0.369622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.93183 | + | 2.79823i | −0.109898 | + | 0.159186i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.86140 | + | 15.3484i | 0.502484 | + | 0.870327i | 0.999996 | + | 0.00287031i | \(0.000913649\pi\) |
−0.497512 | + | 0.867457i | \(0.665753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.38305 | + | 12.7878i | −0.417315 | + | 0.722810i | −0.995668 | − | 0.0929758i | \(-0.970362\pi\) |
0.578354 | + | 0.815786i | \(0.303695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.68823 | − | 8.18877i | 0.376839 | − | 0.461385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.28820 | − | 2.23122i | 0.0723523 | − | 0.125318i | −0.827580 | − | 0.561348i | \(-0.810283\pi\) |
0.899932 | + | 0.436031i | \(0.143616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.08932 | − | 10.5470i | −0.340936 | − | 0.590519i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7395 | + | 28.9616i | 0.766861 | + | 1.61648i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.5161 | 1.14155 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.5672 | 1.25180 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.98393 | + | 4.18195i | 0.109712 | + | 0.231263i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.860518 | + | 1.49046i | 0.0474419 | + | 0.0821718i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.158777 | − | 0.275009i | 0.00872716 | − | 0.0151159i | −0.861629 | − | 0.507539i | \(-0.830555\pi\) |
0.870356 | + | 0.492423i | \(0.163889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.85573 | − | 10.8426i | 0.485291 | − | 0.594169i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.97483 | + | 6.88460i | −0.217168 | + | 0.376146i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.97761 | + | 12.0856i | 0.380095 | + | 0.658343i | 0.991075 | − | 0.133302i | \(-0.0425581\pi\) |
−0.610981 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.16346 | − | 13.2732i | 0.497691 | − | 0.720899i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.7371 | 1.39374 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −54.5827 | − | 4.41101i | −2.93864 | − | 0.237481i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0401 | − | 20.8540i | −0.646344 | − | 1.11950i | −0.983989 | − | 0.178228i | \(-0.942964\pi\) |
0.337645 | − | 0.941274i | \(-0.390370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1616 | − | 22.7966i | 0.704526 | − | 1.22027i | −0.262337 | − | 0.964976i | \(-0.584493\pi\) |
0.966862 | − | 0.255298i | \(-0.0821736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.39245 | + | 15.1789i | 0.234452 | + | 0.810189i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.30502 | + | 2.26036i | −0.0694590 | + | 0.120307i | −0.898663 | − | 0.438639i | \(-0.855461\pi\) |
0.829204 | + | 0.558946i | \(0.188794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.4979 | + | 30.3073i | 0.928693 | + | 1.60854i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.55256 | + | 0.529534i | 0.346798 | + | 0.0280259i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.48082 | 0.183711 | 0.0918553 | − | 0.995772i | \(-0.470720\pi\) | ||||
0.0918553 | + | 0.995772i | \(0.470720\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2188 | 0.537832 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.26814 | − | 9.07932i | 0.328992 | − | 0.476541i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.40729 | − | 7.63365i | −0.230688 | − | 0.399563i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.960991 | + | 1.66449i | −0.0501633 | + | 0.0868854i | −0.890017 | − | 0.455928i | \(-0.849308\pi\) |
0.839853 | + | 0.542813i | \(0.182641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.8866 | − | 1.77113i | −0.566732 | − | 0.0922011i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.71046 | − | 9.89081i | 0.296472 | − | 0.513505i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1228 | − | 27.9255i | −0.834806 | − | 1.44593i | −0.894189 | − | 0.447691i | \(-0.852247\pi\) |
0.0593828 | − | 0.998235i | \(-0.481087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.33412 | + | 13.3518i | 0.327093 | + | 0.689484i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.88631 | −0.457668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.98892 | −0.256264 | −0.128132 | − | 0.991757i | \(-0.540898\pi\) | ||||
−0.128132 | + | 0.991757i | \(0.540898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4470 | + | 26.2373i | 0.637680 | + | 1.34418i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.284377 | + | 0.492556i | 0.0145310 | + | 0.0251684i | 0.873199 | − | 0.487363i | \(-0.162041\pi\) |
−0.858668 | + | 0.512531i | \(0.828708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.34420 | + | 12.7205i | −0.374295 | + | 0.648298i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.80248 | + | 7.39329i | 0.142458 | + | 0.375822i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.4259 | + | 21.5223i | −0.630017 | + | 1.09122i | 0.357531 | + | 0.933901i | \(0.383619\pi\) |
−0.987548 | + | 0.157320i | \(0.949715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.0241 | − | 29.4867i | −0.860948 | − | 1.49121i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.68772 | + | 3.89313i | −0.135577 | + | 0.196382i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.3276 | −1.12342 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.87576 | −0.194519 | −0.0972593 | − | 0.995259i | \(-0.531008\pi\) | ||||
−0.0972593 | + | 0.995259i | \(0.531008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.33208 | + | 0.754156i | 0.467188 | + | 0.0377550i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.43200 | + | 12.8726i | 0.371136 | + | 0.642827i | 0.989741 | − | 0.142876i | \(-0.0456349\pi\) |
−0.618604 | + | 0.785703i | \(0.712302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.38970 | − | 16.2634i | 0.467734 | − | 0.810140i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.7491 | + | 21.0256i | −1.18010 | + | 1.04477i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.72429 | + | 16.8430i | −0.482015 | + | 0.834875i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6707 | + | 20.2142i | 0.577078 | + | 0.999529i | 0.995812 | + | 0.0914201i | \(0.0291406\pi\) |
−0.418734 | + | 0.908109i | \(0.637526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.0671 | − | 2.26820i | −1.38445 | − | 0.111882i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.12896 | 0.0555527 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.9311 | −1.91105 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.28723 | − | 1.86454i | 0.0630360 | − | 0.0913070i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7749 | − | 18.6627i | −0.526389 | − | 0.911733i | −0.999527 | − | 0.0307446i | \(-0.990212\pi\) |
0.473138 | − | 0.880988i | \(-0.343121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.83901 | − | 17.0417i | 0.479524 | − | 0.830560i | −0.520200 | − | 0.854044i | \(-0.674143\pi\) |
0.999724 | + | 0.0234847i | \(0.00747609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.83005 | − | 4.82790i | −0.0889800 | − | 0.234740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0829 | + | 24.3923i | −0.683120 | + | 1.18320i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.03597 | + | 10.4546i | 0.292101 | + | 0.505934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.40909 | − | 19.8335i | −0.454275 | − | 0.957573i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3862 | −0.933798 | −0.466899 | − | 0.884311i | \(-0.654629\pi\) | ||||
−0.466899 | + | 0.884311i | \(0.654629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.9983 | 1.68191 | 0.840956 | − | 0.541104i | \(-0.181993\pi\) | ||||
0.840956 | + | 0.541104i | \(0.181993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.64552 | − | 16.1161i | −0.366575 | − | 0.772708i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.2456 | − | 41.9946i | −1.15982 | − | 2.00887i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.94437 | − | 3.36775i | 0.0927999 | − | 0.160734i | −0.815888 | − | 0.578209i | \(-0.803752\pi\) |
0.908688 | + | 0.417475i | \(0.137085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.96107 | + | 0.481734i | 0.141003 | + | 0.0229397i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.8632 | − | 18.8156i | 0.516126 | − | 0.893956i | −0.483699 | − | 0.875235i | \(-0.660707\pi\) |
0.999825 | − | 0.0187219i | \(-0.00595970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.7359 | + | 41.1118i | 1.12519 | + | 1.94889i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.8826 | + | 18.6603i | −0.609327 | + | 0.882604i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.3098 | −0.911287 | −0.455643 | − | 0.890162i | \(-0.650591\pi\) | ||||
−0.455643 | + | 0.890162i | \(0.650591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3229 | 0.721526 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.5474 | − | 1.98376i | −1.15334 | − | 0.0932050i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.35880 | + | 9.28171i | 0.251224 | + | 0.435133i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.03867 | − | 13.9234i | 0.376033 | − | 0.651308i | −0.614448 | − | 0.788957i | \(-0.710621\pi\) |
0.990481 | + | 0.137649i | \(0.0439546\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.1475 | − | 4.72458i | −0.893729 | − | 0.220524i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6888 | + | 28.9058i | −0.777274 | + | 1.34628i | 0.156233 | + | 0.987720i | \(0.450065\pi\) |
−0.933507 | + | 0.358558i | \(0.883269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.67623 | − | 11.5636i | −0.310271 | − | 0.537404i | 0.668150 | − | 0.744026i | \(-0.267086\pi\) |
−0.978421 | + | 0.206622i | \(0.933753\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.5738 | + | 3.03646i | 1.74244 | + | 0.140813i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4976 | 0.532047 | 0.266023 | − | 0.963967i | \(-0.414290\pi\) | ||||
0.266023 | + | 0.963967i | \(0.414290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.25565 | −0.104156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.58537 | + | 13.8843i | −0.441671 | + | 0.639755i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.49208 | − | 9.51256i | −0.252526 | − | 0.437388i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.0567 | + | 34.7392i | −0.920264 | + | 1.59394i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6738 | + | 26.5364i | −0.992375 | + | 1.21502i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.48078 | − | 4.29684i | 0.113350 | − | 0.196328i | −0.803769 | − | 0.594941i | \(-0.797175\pi\) |
0.917119 | + | 0.398614i | \(0.130509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.09547 | + | 12.2897i | 0.323525 | + | 0.560363i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.65979 | − | 14.0383i | −0.303031 | − | 0.638764i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 66.7417 | 3.03059 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.4801 | 1.19993 | 0.599964 | − | 0.800027i | \(-0.295182\pi\) | ||||
0.599964 | + | 0.800027i | \(0.295182\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.5210 | + | 28.5011i | 0.611441 | + | 1.28887i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7019 | + | 18.5362i | 0.482970 | + | 0.836529i | 0.999809 | − | 0.0195540i | \(-0.00622463\pi\) |
−0.516839 | + | 0.856083i | \(0.672891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.54543 | − | 9.60496i | 0.249753 | − | 0.432586i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.8746 | − | 34.1284i | 1.25287 | − | 1.53396i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.96489 | + | 8.59944i | −0.222706 | + | 0.385738i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.63554 | + | 11.4931i | 0.297048 | + | 0.514501i | 0.975459 | − | 0.220181i | \(-0.0706647\pi\) |
−0.678412 | + | 0.734682i | \(0.737331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3800 | + | 22.2778i | −0.687128 | + | 0.995298i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.3009 | −1.44022 | −0.720112 | − | 0.693857i | \(-0.755910\pi\) | ||||
−0.720112 | + | 0.693857i | \(0.755910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.0409 | 1.51480 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.47779 | + | 0.523491i | 0.287689 | + | 0.0232491i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3401 | − | 19.6417i | −0.502642 | − | 0.870601i | −0.999995 | − | 0.00305334i | \(-0.999028\pi\) |
0.497353 | − | 0.867548i | \(-0.334305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.25053 | − | 2.16598i | 0.0553203 | − | 0.0958175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.2696 | − | 6.72868i | −1.20398 | − | 0.297079i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.45943 | − | 5.99190i | 0.152441 | − | 0.264035i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.58639 | + | 6.21181i | 0.157729 | + | 0.273195i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0926 | + | 1.46212i | 0.794177 | + | 0.0641800i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2159 | −1.01710 | −0.508552 | − | 0.861031i | \(-0.669819\pi\) | ||||
−0.508552 | + | 0.861031i | \(0.669819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.4196 | −0.892885 | −0.446442 | − | 0.894812i | \(-0.647309\pi\) | ||||
−0.446442 | + | 0.894812i | \(0.647309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.30246 | + | 10.5775i | −0.318706 | + | 0.461641i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.7191 | + | 20.2981i | 0.510493 | + | 0.884200i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.7377 | + | 49.7751i | −1.24946 | + | 2.16413i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.34294 | − | 0.543860i | −0.145071 | − | 0.0236015i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.59027 | − | 9.68264i | 0.242142 | − | 0.419402i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.6127 | − | 56.4869i | −1.40997 | − | 2.44214i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.4278 | − | 28.3047i | −0.579454 | − | 1.22144i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.16771 | −0.179516 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.4226 | −1.69491 | −0.847455 | − | 0.530868i | \(-0.821866\pi\) | ||||
−0.847455 | + | 0.530868i | \(0.821866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.6309 | + | 35.0566i | 0.713701 | + | 1.50442i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.70916 | − | 8.15651i | −0.201718 | − | 0.349386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2911 | + | 21.2888i | −0.525529 | + | 0.910243i | 0.474029 | + | 0.880509i | \(0.342799\pi\) |
−0.999558 | + | 0.0297339i | \(0.990534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.8366 | − | 33.8645i | −0.547852 | − | 1.44530i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.89773 | − | 13.6793i | 0.336455 | − | 0.582756i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.16763 | − | 5.48650i | −0.134701 | − | 0.233310i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.1837 | + | 23.4420i | −0.686962 | + | 0.995056i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.4619 | −0.528026 | −0.264013 | − | 0.964519i | \(-0.585046\pi\) | ||||
−0.264013 | + | 0.964519i | \(0.585046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.01475 | −0.338988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.3092 | + | 2.20694i | 1.15299 | + | 0.0931773i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.24949 | + | 9.09239i | 0.221240 | + | 0.383198i | 0.955185 | − | 0.296011i | \(-0.0956563\pi\) |
−0.733945 | + | 0.679209i | \(0.762323\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.4095 | + | 28.4221i | −0.690352 | + | 1.19572i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.53587 | − | 2.85289i | −0.358473 | − | 0.119810i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.11698 | − | 8.86288i | 0.214515 | − | 0.371551i | −0.738607 | − | 0.674136i | \(-0.764516\pi\) |
0.953122 | + | 0.302585i | \(0.0978495\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.34986 | + | 4.07008i | 0.0983387 | + | 0.170328i | 0.910997 | − | 0.412413i | \(-0.135314\pi\) |
−0.812658 | + | 0.582740i | \(0.801980\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.85224 | + | 0.472939i | 0.244481 | + | 0.0197573i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 66.5716 | 2.77623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.3980 | −1.14060 | −0.570298 | − | 0.821438i | \(-0.693172\pi\) | ||||
−0.570298 | + | 0.821438i | \(0.693172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.7412 | − | 22.8010i | 0.654182 | − | 0.947576i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.52319 | − | 9.56645i | −0.229141 | − | 0.396883i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7995 | − | 41.2220i | 0.985677 | − | 1.70724i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.3965 | − | 30.0653i | −0.471186 | − | 1.24305i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.334943 | − | 0.580138i | 0.0138246 | − | 0.0239448i | −0.859030 | − | 0.511925i | \(-0.828933\pi\) |
0.872855 | + | 0.487980i | \(0.162266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.6902 | + | 28.9084i | 0.687710 | + | 1.19115i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.01172 | − | 10.5643i | −0.206155 | − | 0.434556i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.83861 | −0.404023 | −0.202012 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202012 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.3765 | −0.548381 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.47872 | + | 17.8724i | 0.347011 | + | 0.731470i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.0135159 | + | 0.0234103i | 0.000552245 | + | 0.000956517i | 0.866301 | − | 0.499522i | \(-0.166491\pi\) |
−0.865749 | + | 0.500478i | \(0.833158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1676 | − | 31.4672i | 0.741073 | − | 1.28358i | −0.210934 | − | 0.977500i | \(-0.567651\pi\) |
0.952007 | − | 0.306076i | \(-0.0990160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.67913 | + | 1.08662i | 0.271995 | + | 0.0442506i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.2247 | + | 19.4417i | −0.456348 | + | 0.790418i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.6590 | − | 18.4620i | −0.432637 | − | 0.749349i | 0.564463 | − | 0.825459i | \(-0.309083\pi\) |
−0.997099 | + | 0.0761098i | \(0.975750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.87549 | − | 4.16512i | 0.116521 | − | 0.168779i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.23372 | 0.211734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5229 | −0.505793 | −0.252897 | − | 0.967493i | \(-0.581383\pi\) | ||||
−0.252897 | + | 0.967493i | \(0.581383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.3700 | + | 1.80779i | 0.902046 | + | 0.0728973i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.2691 | + | 38.5713i | 0.896521 | + | 1.55282i | 0.831911 | + | 0.554910i | \(0.187247\pi\) |
0.0646104 | + | 0.997911i | \(0.479420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4100 | + | 24.9588i | −0.579186 | + | 1.00318i | 0.416387 | + | 0.909187i | \(0.363296\pi\) |
−0.995573 | + | 0.0939920i | \(0.970037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9574 | + | 44.7766i | 0.519963 | + | 1.79682i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.73487 | + | 11.6651i | −0.269827 | + | 0.467354i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.51728 | + | 6.09210i | 0.140691 | + | 0.243684i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 38.8934 | + | 3.14310i | 1.55325 | + | 0.125523i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7115 | −0.706202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3192 | −1.40604 | −0.703018 | − | 0.711172i | \(-0.748165\pi\) | ||||
−0.703018 | + | 0.711172i | \(0.748165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5986 | − | 18.2489i | 0.500748 | − | 0.725328i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.5449 | − | 51.1733i | −1.17246 | − | 2.03075i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52051 | + | 2.63361i | −0.0602450 | + | 0.104347i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.8440 | − | 23.0718i | 0.745458 | − | 0.912706i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.2261 | − | 31.5685i | 0.719888 | − | 1.24688i | −0.241156 | − | 0.970486i | \(-0.577526\pi\) |
0.961044 | − | 0.276396i | \(-0.0891402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8629 | − | 34.4036i | −0.783317 | − | 1.35674i | −0.929999 | − | 0.367561i | \(-0.880193\pi\) |
0.146682 | − | 0.989184i | \(-0.453140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.89566 | − | 14.5355i | −0.271516 | − | 0.572333i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.649904 | −0.0255504 | −0.0127752 | − | 0.999918i | \(-0.504067\pi\) | ||||
−0.0127752 | + | 0.999918i | \(0.504067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.70520 | 0.184695 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.58449 | + | 9.66371i | 0.179680 | + | 0.378751i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.40239 | − | 12.8213i | −0.289678 | − | 0.501737i | 0.684055 | − | 0.729430i | \(-0.260215\pi\) |
−0.973733 | + | 0.227694i | \(0.926881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.81303 | − | 8.33641i | 0.188061 | − | 0.325731i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.74634 | + | 5.81121i | −0.185172 | + | 0.226717i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.53713 | − | 6.12649i | 0.137787 | − | 0.238654i | −0.788872 | − | 0.614558i | \(-0.789334\pi\) |
0.926659 | + | 0.375904i | \(0.122668\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3419 | + | 21.3767i | 0.480043 | + | 0.831459i | 0.999738 | − | 0.0228933i | \(-0.00728778\pi\) |
−0.519695 | + | 0.854352i | \(0.673954\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3578 | − | 16.4517i | 0.441102 | − | 0.638932i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.0506 | −0.738750 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.2139 | −1.01501 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.2460 | + | 1.63615i | 0.782756 | + | 0.0632571i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.1562 | + | 43.5718i | 0.971143 | + | 1.68207i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.5508 | − | 28.6669i | 0.637988 | − | 1.10503i | −0.347886 | − | 0.937537i | \(-0.613100\pi\) |
0.985874 | − | 0.167491i | \(-0.0535664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.7186 | − | 27.8030i | 1.02840 | − | 1.07014i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.59003 | + | 9.68222i | −0.214842 | + | 0.372118i | −0.953224 | − | 0.302265i | \(-0.902257\pi\) |
0.738381 | + | 0.674383i | \(0.235590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.46871 | + | 16.4003i | 0.363376 | + | 0.629385i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7637 | + | 1.75879i | 0.833986 | + | 0.0673972i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.1925 | −1.27008 | −0.635039 | − | 0.772480i | \(-0.719016\pi\) | ||||
−0.635039 | + | 0.772480i | \(0.719016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.2965 | 2.18919 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.55089 | + | 12.3859i | −0.326237 | + | 0.472551i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3657 | − | 30.0782i | −0.661579 | − | 1.14589i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.96460 | + | 15.5271i | −0.341030 | + | 0.590680i | −0.984624 | − | 0.174686i | \(-0.944109\pi\) |
0.643595 | + | 0.765367i | \(0.277442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3409 | + | 2.00773i | 0.468791 | + | 0.0762672i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.30511 | + | 3.99257i | −0.0874379 | + | 0.151447i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.97713 | + | 12.0847i | 0.264277 | + | 0.457742i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.59537 | + | 20.2262i | 0.362930 | + | 0.765026i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6754 | 0.856438 | 0.428219 | − | 0.903675i | \(-0.359141\pi\) | ||||
0.428219 | + | 0.903675i | \(0.359141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.2245 | −0.951358 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.50294 | + | 9.49181i | 0.169591 | + | 0.357482i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.82940 | + | 8.36477i | 0.181628 | + | 0.314590i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.47722 | + | 7.75477i | −0.168146 | + | 0.291237i | −0.937768 | − | 0.347263i | \(-0.887111\pi\) |
0.769622 | + | 0.638499i | \(0.220445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.73655 | + | 17.7719i | 0.252640 | + | 0.666497i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.6989 | − | 47.9759i | 1.03733 | − | 1.79671i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.3339 | + | 38.6835i | 0.835241 | + | 1.44668i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.2592 | + | 30.7937i | −0.793939 | + | 1.15001i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.9896 | −1.26760 | −0.633799 | − | 0.773498i | \(-0.718505\pi\) | ||||
−0.633799 | + | 0.773498i | \(0.718505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.96317 | 0.0731122 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.73792 | − | 0.463700i | −0.213396 | − | 0.0172452i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.8425 | + | 18.7797i | 0.402680 | + | 0.697461i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.95103 | + | 12.0395i | −0.257799 | + | 0.446521i | −0.965652 | − | 0.259839i | \(-0.916331\pi\) |
0.707853 | + | 0.706360i | \(0.249664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.9010 | + | 12.5596i | 0.885221 | + | 0.465171i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.00154 | − | 8.66291i | 0.184988 | − | 0.320409i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3180 | − | 24.7996i | −0.528849 | − | 0.915993i | −0.999434 | − | 0.0336388i | \(-0.989290\pi\) |
0.470585 | − | 0.882355i | \(-0.344043\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.08449 | − | 0.491707i | −0.224430 | − | 0.0181369i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.40089 | −0.346286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.2398 | 0.597389 | 0.298695 | − | 0.954349i | \(-0.403449\pi\) | ||||
0.298695 | + | 0.954349i | \(0.403449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.1757 | − | 23.4303i | 0.594230 | − | 0.860735i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.10227 | − | 8.83739i | −0.187184 | − | 0.324213i | 0.757126 | − | 0.653269i | \(-0.226603\pi\) |
−0.944310 | + | 0.329056i | \(0.893269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.0696 | − | 39.9577i | 0.845204 | − | 1.46394i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.7461 | + | 30.9876i | 0.429766 | + | 1.13378i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.25359 | − | 16.0277i | 0.338119 | − | 0.585639i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.09533 | − | 8.82537i | −0.185931 | − | 0.322042i | 0.757959 | − | 0.652303i | \(-0.226197\pi\) |
−0.943890 | + | 0.330260i | \(0.892863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.98936 | + | 4.19340i | 0.0724963 | + | 0.152816i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 50.1113 | 1.82374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.9880 | −1.85319 | −0.926595 | − | 0.376061i | \(-0.877278\pi\) | ||||
−0.926595 | + | 0.376061i | \(0.877278\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.7561 | − | 58.5075i | −1.00748 | − | 2.12369i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.54569 | + | 7.87336i | 0.164781 | + | 0.285409i | 0.936578 | − | 0.350460i | \(-0.113975\pi\) |
−0.771796 | + | 0.635870i | \(0.780642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.33619 | − | 2.31434i | 0.0483732 | − | 0.0837848i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 39.6086 | + | 6.44388i | 1.43205 | + | 0.232979i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.71661 | − | 2.97325i | 0.0619831 | − | 0.107358i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4748 | − | 18.1429i | −0.377731 | − | 0.654250i | 0.613001 | − | 0.790082i | \(-0.289962\pi\) |
−0.990732 | + | 0.135833i | \(0.956629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.38899 | − | 10.7029i | 0.266108 | − | 0.385455i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.323229 | −0.0116258 | −0.00581288 | − | 0.999983i | \(-0.501850\pi\) | ||||
−0.00581288 | + | 0.999983i | \(0.501850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45.8268 | −1.64615 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.05634 | − | 0.651059i | −0.289019 | − | 0.0233566i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.93674 | + | 17.2109i | 0.356021 | + | 0.616646i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6922 | + | 35.8400i | −0.740426 | + | 1.28246i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.5210 | + | 10.9480i | −0.375990 | + | 0.391249i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.1650 | − | 29.7307i | 0.612646 | − | 1.06113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3607 | + | 47.3901i | 0.975302 | + | 1.68927i | 0.678934 | + | 0.734200i | \(0.262442\pi\) |
0.296369 | + | 0.955074i | \(0.404224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.2862 | − | 2.60916i | −1.14942 | − | 0.0928884i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.31211 | −0.331100 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.7111 | 1.30365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 39.6086 | − | 57.3726i | 1.40477 | − | 2.03480i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0498 | − | 26.0670i | −0.533091 | − | 0.923341i | −0.999253 | − | 0.0386418i | \(-0.987697\pi\) |
0.466162 | − | 0.884699i | \(-0.345636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.26606 | + | 5.65698i | −0.115545 | + | 0.200130i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.5619 | − | 31.2969i | 0.903186 | − | 1.10582i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.21185 | − | 9.02720i | 0.183922 | − | 0.318563i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.8080 | + | 27.3803i | 0.557160 | + | 0.965030i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.6231 | − | 26.6085i | −0.444355 | − | 0.936662i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.81348 | 0.309866 | 0.154933 | − | 0.987925i | \(-0.450484\pi\) | ||||
0.154933 | + | 0.987925i | \(0.450484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3997 | −1.48886 | −0.744428 | − | 0.667702i | \(-0.767278\pi\) | ||||
−0.744428 | + | 0.667702i | \(0.767278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.1808 | + | 36.2157i | 0.602557 | + | 1.27014i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.0942 | − | 55.5888i | −1.12421 | − | 1.94719i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.12313 | − | 12.3376i | 0.249207 | − | 0.431639i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.77105 | − | 7.06581i | 0.201657 | − | 0.246900i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.67904 | − | 16.7646i | 0.337801 | − | 0.585088i | −0.646218 | − | 0.763153i | \(-0.723650\pi\) |
0.984019 | + | 0.178065i | \(0.0569836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2996 | − | 21.3035i | −0.428737 | − | 0.742594i | 0.568024 | − | 0.823012i | \(-0.307708\pi\) |
−0.996761 | + | 0.0804178i | \(0.974375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.4345 | + | 44.0841i | −1.05960 | + | 1.53481i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.3747 | −1.36919 | −0.684597 | − | 0.728922i | \(-0.740022\pi\) | ||||
−0.684597 | + | 0.728922i | \(0.740022\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.25597 | 0.252010 | 0.126005 | − | 0.992030i | \(-0.459784\pi\) | ||||
0.126005 | + | 0.992030i | \(0.459784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.9314 | + | 1.93397i | 0.830170 | + | 0.0670888i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.89773 | − | 3.28696i | −0.0657524 | − | 0.113886i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.5418 | − | 47.7038i | 0.953123 | − | 1.65086i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.91965 | − | 30.8234i | −0.308308 | − | 1.06541i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.72910 | − | 9.92309i | 0.197790 | − | 0.342583i | −0.750021 | − | 0.661414i | \(-0.769957\pi\) |
0.947812 | + | 0.318831i | \(0.103290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2306 | + | 17.7198i | 0.352778 | + | 0.611029i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.7769 | − | 1.27499i | −0.543387 | − | 0.0439129i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.2238 | −0.454913 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.36982 | −0.218869 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.79814 | + | 9.84703i | −0.233312 | + | 0.337949i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9311 | + | 36.2537i | 0.717509 | + | 1.24276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1979 | + | 43.6440i | −0.862758 | + | 1.49434i | 0.00649778 | + | 0.999979i | \(0.497932\pi\) |
−0.869256 | + | 0.494362i | \(0.835402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.4101 | + | 9.17730i | 1.92918 | + | 0.313857i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0113 | − | 41.5888i | 0.820211 | − | 1.42065i | −0.0853131 | − | 0.996354i | \(-0.527189\pi\) |
0.905525 | − | 0.424294i | \(-0.139478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1422 | + | 33.1552i | 0.653123 | + | 1.13124i | 0.982361 | + | 0.186995i | \(0.0598747\pi\) |
−0.329238 | + | 0.944247i | \(0.606792\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.72943 | + | 5.75340i | 0.0930187 | + | 0.196075i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.2049 | −0.449500 | −0.224750 | − | 0.974416i | \(-0.572157\pi\) | ||||
−0.224750 | + | 0.974416i | \(0.572157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.9344 | −1.25581 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.92613 | − | 4.06011i | −0.0654147 | − | 0.137889i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.2018 | − | 22.8662i | −0.447840 | − | 0.775681i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.42974 | + | 5.94049i | −0.116212 | + | 0.201286i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.1369 | − | 53.1238i | −0.681532 | − | 1.79797i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.26606 | − | 7.38904i | 0.144219 | − | 0.249795i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.9815 | − | 20.7526i | −0.404586 | − | 0.700764i | 0.589687 | − | 0.807632i | \(-0.299251\pi\) |
−0.994273 | + | 0.106868i | \(0.965918\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3047 | + | 26.5142i | −0.617403 | + | 0.894302i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3964 | 1.32730 | 0.663650 | − | 0.748044i | \(-0.269007\pi\) | ||||
0.663650 | + | 0.748044i | \(0.269007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3593 | 0.617840 | 0.308920 | − | 0.951088i | \(-0.400033\pi\) | ||||
0.308920 | + | 0.951088i | \(0.400033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.86917 | + | 0.555120i | 0.230905 | + | 0.0186602i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.3324 | − | 26.5566i | −0.514813 | − | 0.891682i | −0.999852 | − | 0.0171897i | \(-0.994528\pi\) |
0.485039 | − | 0.874492i | \(-0.338805\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.38313 | − | 14.5200i | 0.281161 | − | 0.486985i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.5750 | − | 11.8900i | −1.19181 | − | 0.398331i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.65148 | + | 8.05660i | −0.155656 | + | 0.269604i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.8730 | + | 55.2057i | 1.06540 | + | 1.84532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.0976 | − | 3.80611i | −1.57254 | − | 0.127082i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.0452 | 0.601842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.3476 | 1.44412 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.59347 | − | 3.75661i | 0.0863052 | − | 0.125012i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.4761 | − | 68.3745i | −1.31223 | − | 2.27285i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.9899 | − | 36.3556i | 0.696960 | − | 1.20717i | −0.272556 | − | 0.962140i | \(-0.587869\pi\) |
0.969516 | − | 0.245030i | \(-0.0787977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.2706 | − | 27.0952i | −0.340655 | − | 0.898690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5714 | + | 32.1667i | −0.615299 | + | 1.06573i | 0.375033 | + | 0.927012i | \(0.377631\pi\) |
−0.990332 | + | 0.138718i | \(0.955702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.0191 | − | 39.8702i | −0.761820 | − | 1.31951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.5852 | + | 66.5788i | 1.04417 | + | 2.20103i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.73131 | 0.0901960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.5903 | 0.547263 | 0.273632 | − | 0.961835i | \(-0.411775\pi\) | ||||
0.273632 | + | 0.961835i | \(0.411775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3602 | + | 21.8385i | 0.341381 | + | 0.719602i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.0984 | + | 26.1511i | 0.496969 | + | 0.860775i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.3148 | − | 29.9902i | 0.569308 | − | 0.986071i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.81308 | − | 0.945724i | −0.190926 | − | 0.0310616i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.5800 | − | 32.1814i | 0.609589 | − | 1.05584i | −0.381719 | − | 0.924278i | \(-0.624668\pi\) |
0.991308 | − | 0.131560i | \(-0.0419987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.70272 | − | 4.68125i | −0.0885781 | − | 0.153422i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.4399 | + | 25.2615i | −0.570956 | + | 0.827024i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55.7492 | −1.82319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.5323 | −1.78149 | −0.890746 | − | 0.454502i | \(-0.849817\pi\) | ||||
−0.890746 | + | 0.454502i | \(0.849817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.4925 | − | 2.06014i | −0.831917 | − | 0.0672300i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.9394 | − | 36.2682i | −0.682606 | − | 1.18231i | −0.974183 | − | 0.225761i | \(-0.927513\pi\) |
0.291577 | − | 0.956547i | \(-0.405820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.4909 | − | 28.5630i | 0.537017 | − | 0.930141i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.7797 | + | 4.38708i | 0.578374 | + | 0.142712i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.71450 | − | 11.6299i | 0.218192 | − | 0.377919i | −0.736063 | − | 0.676913i | \(-0.763317\pi\) |
0.954255 | + | 0.298993i | \(0.0966508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.80290 | − | 6.58682i | −0.123447 | − | 0.213817i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.44794 | + | 0.359453i | 0.144234 | + | 0.0116560i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.1328 | −0.716950 | −0.358475 | − | 0.933539i | \(-0.616703\pi\) | ||||
−0.358475 | + | 0.933539i | \(0.616703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9468 | −0.386590 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.9842 | − | 17.3590i | 0.387395 | − | 0.561137i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.12870 | + | 14.0793i | 0.262489 | + | 0.454645i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.56746 | + | 6.17902i | −0.115079 | + | 0.199323i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.1216 | + | 43.0013i | −1.13178 | + | 1.38570i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.1886 | + | 48.8241i | −0.907423 | + | 1.57170i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9516 | + | 25.8969i | 0.480811 | + | 0.832788i | 0.999758 | − | 0.0220180i | \(-0.00700911\pi\) |
−0.518947 | + | 0.854806i | \(0.673676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.2309 | + | 32.1054i | 0.489286 | + | 1.03137i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.0708 | 0.547827 | 0.273914 | − | 0.961754i | \(-0.411682\pi\) | ||||
0.273914 | + | 0.961754i | \(0.411682\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.30811 | −0.0419362 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.7536 | + | 35.3151i | 0.536544 | + | 1.13099i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6299 | + | 28.8038i | 0.532037 | + | 0.921515i | 0.999300 | + | 0.0373970i | \(0.0119066\pi\) |
−0.467263 | + | 0.884118i | \(0.654760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.0690 | + | 48.6169i | −0.897089 | + | 1.55380i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.07143 | + | 6.20924i | −0.161918 | + | 0.198246i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.2794 | − | 23.0006i | 0.423548 | − | 0.733606i | −0.572736 | − | 0.819740i | \(-0.694118\pi\) |
0.996284 | + | 0.0861339i | \(0.0274513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.8961 | + | 20.6046i | 0.379041 | + | 0.656518i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.69356 | + | 2.45311i | −0.0539067 | + | 0.0780833i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.6429 | −0.751800 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.1268 | 1.52880 | 0.764398 | − | 0.644744i | \(-0.223036\pi\) | ||||
0.764398 | + | 0.644744i | \(0.223036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.548232 | + | 0.0443044i | 0.0173976 | + | 0.00140596i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.1256 | − | 34.8585i | −0.638023 | − | 1.10509i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.67869 | + | 16.7640i | −0.306527 | + | 0.530921i | −0.977600 | − | 0.210471i | \(-0.932500\pi\) |
0.671073 | + | 0.741391i | \(0.265834\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.5417 | + | 5.80884i | 0.744828 | + | 0.183783i |
(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.r.f.169.4 | ✓ | 10 | |
3.2 | odd | 2 | 1512.2.r.f.505.5 | 10 | |||
4.3 | odd | 2 | 1008.2.r.n.673.2 | 10 | |||
9.2 | odd | 6 | 4536.2.a.bc.1.1 | 5 | |||
9.4 | even | 3 | inner | 504.2.r.f.337.4 | yes | 10 | |
9.5 | odd | 6 | 1512.2.r.f.1009.5 | 10 | |||
9.7 | even | 3 | 4536.2.a.bd.1.5 | 5 | |||
12.11 | even | 2 | 3024.2.r.n.2017.5 | 10 | |||
36.7 | odd | 6 | 9072.2.a.cn.1.5 | 5 | |||
36.11 | even | 6 | 9072.2.a.cm.1.1 | 5 | |||
36.23 | even | 6 | 3024.2.r.n.1009.5 | 10 | |||
36.31 | odd | 6 | 1008.2.r.n.337.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.f.169.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
504.2.r.f.337.4 | yes | 10 | 9.4 | even | 3 | inner | |
1008.2.r.n.337.2 | 10 | 36.31 | odd | 6 | |||
1008.2.r.n.673.2 | 10 | 4.3 | odd | 2 | |||
1512.2.r.f.505.5 | 10 | 3.2 | odd | 2 | |||
1512.2.r.f.1009.5 | 10 | 9.5 | odd | 6 | |||
3024.2.r.n.1009.5 | 10 | 36.23 | even | 6 | |||
3024.2.r.n.2017.5 | 10 | 12.11 | even | 2 | |||
4536.2.a.bc.1.1 | 5 | 9.2 | odd | 6 | |||
4536.2.a.bd.1.5 | 5 | 9.7 | even | 3 | |||
9072.2.a.cm.1.1 | 5 | 36.11 | even | 6 | |||
9072.2.a.cn.1.5 | 5 | 36.7 | odd | 6 |