Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
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: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.34147 - 1.09565i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.n.673.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.139086 | + | 0.990280i | \(0.455583\pi\) |
−0.927151 | + | 0.374688i | \(0.877750\pi\) | |||||||
\(6\) | 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 | −0.987892 | − | 0.155146i | \(-0.950415\pi\) |
0.359585 | − | 0.933112i | \(-0.382918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52051 | + | 2.63361i | −0.421715 | + | 0.730431i | −0.996107 | − | 0.0881486i | \(-0.971905\pi\) |
0.574393 | + | 0.818580i | \(0.305238\pi\) | |||||||
\(14\) | 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 | \(-0.712886\pi\) | ||||
−0.620047 | + | 0.784565i | \(0.712886\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.72642 | − | 0.139518i | 0.376736 | − | 0.0304453i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.48540 | − | 7.76894i | 0.935271 | − | 1.61994i | 0.161121 | − | 0.986935i | \(-0.448489\pi\) |
0.774150 | − | 0.633002i | \(-0.218178\pi\) | |||||||
\(24\) | 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 | 0.969199 | − | 0.246281i | \(-0.0792086\pi\) |
−0.697885 | + | 0.716210i | \(0.745875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.08767 | + | 5.34801i | −0.554563 | + | 0.960531i | 0.443375 | + | 0.896336i | \(0.353781\pi\) |
−0.997937 | + | 0.0641943i | \(0.979552\pi\) | |||||||
\(32\) | 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 | −0.686023 | − | 0.727580i | \(-0.740645\pi\) |
0.973114 | + | 0.230323i | \(0.0739782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.31777 | − | 2.28244i | −0.200958 | − | 0.348069i | 0.747879 | − | 0.663835i | \(-0.231072\pi\) |
−0.948837 | + | 0.315765i | \(0.897739\pi\) | |||||||
\(44\) | 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 | \(-0.126607\pi\) |
−0.796416 | + | 0.604749i | \(0.793274\pi\) | |||||||
\(48\) | 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 | \(-0.856747\pi\) |
0.826939 | + | 0.562292i | \(0.190080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.03597 | − | 10.4546i | −0.772826 | − | 1.33857i | −0.936008 | − | 0.351979i | \(-0.885509\pi\) |
0.163182 | − | 0.986596i | \(-0.447824\pi\) | |||||||
\(62\) | 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 | \(-0.789335\pi\) |
0.926658 | + | 0.375905i | \(0.122668\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.82761 | + | 12.7867i | 1.06272 | + | 1.53934i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.92978 | 1.17845 | 0.589224 | − | 0.807970i | \(-0.299434\pi\) | ||||
0.589224 | + | 0.807970i | \(0.299434\pi\) | |||||||
\(72\) | 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 | \(-0.282658\pi\) |
−0.987354 | + | 0.158530i | \(0.949325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79726 | + | 8.81872i | −0.199695 | + | 0.979858i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.52319 | − | 9.56645i | −0.606249 | − | 1.05005i | −0.991853 | − | 0.127390i | \(-0.959340\pi\) |
0.385604 | − | 0.922664i | \(-0.373993\pi\) | |||||||
\(84\) | 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 | −0.718987 | − | 0.695023i | \(-0.755394\pi\) |
−0.242414 | − | 0.970173i | \(-0.577939\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.43170 | + | 11.6914i | −0.445403 | + | 1.17503i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.82940 | − | 8.36477i | −0.480544 | − | 0.832326i | 0.519207 | − | 0.854648i | \(-0.326227\pi\) |
−0.999751 | + | 0.0223224i | \(0.992894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.981584 | + | 1.70015i | −0.0967183 | + | 0.167521i | −0.910324 | − | 0.413895i | \(-0.864168\pi\) |
0.813606 | + | 0.581416i | \(0.197501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.61641 | + | 5.51517i | −0.255336 | + | 0.538226i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.5072 | −1.78916 | −0.894578 | − | 0.446912i | \(-0.852524\pi\) | ||||
−0.894578 | + | 0.446912i | \(0.852524\pi\) | |||||||
\(108\) | 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 | −0.997536 | − | 0.0701632i | \(-0.977648\pi\) |
0.559531 | + | 0.828809i | \(0.310981\pi\) | |||||||
\(114\) | 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 | \(-0.767018\pi\) | ||||
−0.743883 | + | 0.668310i | \(0.767018\pi\) | |||||||
\(128\) | 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 | \(-0.871404\pi\) |
0.800180 | + | 0.599761i | \(0.204737\pi\) | |||||||
\(132\) | 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 | −0.970355 | − | 0.241684i | \(-0.922300\pi\) |
0.275873 | − | 0.961194i | \(-0.411033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.654057 | − | 1.13286i | 0.0554764 | − | 0.0960879i | −0.836954 | − | 0.547274i | \(-0.815666\pi\) |
0.892430 | + | 0.451186i | \(0.148999\pi\) | |||||||
\(140\) | 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 | −0.462848 | − | 0.886437i | \(-0.653173\pi\) |
0.999102 | − | 0.0423802i | \(-0.0134941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.10933 | + | 12.3137i | 0.578549 | + | 1.00208i | 0.995646 | + | 0.0932143i | \(0.0297142\pi\) |
−0.417097 | + | 0.908862i | \(0.636952\pi\) | |||||||
\(152\) | 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 | −0.603572 | − | 0.797308i | \(-0.706257\pi\) |
0.992275 | + | 0.124055i | \(0.0395899\pi\) | |||||||
\(158\) | 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 | \(-0.752788\pi\) | ||||
−0.713274 | + | 0.700886i | \(0.752788\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.9045 | + | 22.9857i | −0.848910 | + | 1.78943i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.81475 | + | 13.5355i | −0.604724 | + | 1.04741i | 0.387371 | + | 0.921924i | \(0.373383\pi\) |
−0.992095 | + | 0.125488i | \(0.959950\pi\) | |||||||
\(168\) | 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 | 0.993527 | − | 0.113600i | \(-0.0362382\pi\) |
−0.595144 | + | 0.803619i | \(0.702905\pi\) | |||||||
\(174\) | 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 | \(-0.263730\pi\) | ||||
0.675958 | + | 0.736940i | \(0.263730\pi\) | |||||||
\(180\) | 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 | \(-0.205802\pi\) |
−0.920808 | + | 0.390017i | \(0.872469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.99828 | + | 13.8534i | −0.575729 | + | 0.997191i | 0.420233 | + | 0.907416i | \(0.361948\pi\) |
−0.995962 | + | 0.0897754i | \(0.971385\pi\) | |||||||
\(194\) | 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 | \(-0.632660\pi\) | ||||
−0.404804 | + | 0.914404i | \(0.632660\pi\) | |||||||
\(200\) | 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 | \(-0.688065\pi\) |
0.997741 | + | 0.0671751i | \(0.0213986\pi\) | |||||||
\(212\) | 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 | \(-0.295110\pi\) |
−0.992799 | + | 0.119795i | \(0.961776\pi\) | |||||||
\(224\) | 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 | \(-0.304059\pi\) |
−0.995774 | + | 0.0918384i | \(0.970726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.34480 | − | 7.52542i | 0.287113 | − | 0.497294i | −0.686007 | − | 0.727595i | \(-0.740638\pi\) |
0.973119 | + | 0.230302i | \(0.0739713\pi\) | |||||||
\(230\) | 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 | 0.270183 | + | 0.962809i | \(0.412916\pi\) |
−0.968909 | + | 0.247419i | \(0.920418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.66179 | − | 2.87831i | −0.107046 | − | 0.185408i | 0.807527 | − | 0.589831i | \(-0.200806\pi\) |
−0.914572 | + | 0.404423i | \(0.867472\pi\) | |||||||
\(242\) | 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 | \(-0.526952\pi\) | ||||
−0.0845701 | + | 0.996418i | \(0.526952\pi\) | |||||||
\(252\) | 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 | −0.959038 | − | 0.283276i | \(-0.908579\pi\) |
0.724844 | + | 0.688913i | \(0.241912\pi\) | |||||||
\(258\) | 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 | 0.995868 | + | 0.0908171i | \(0.0289479\pi\) |
−0.419284 | + | 0.907855i | \(0.637719\pi\) | |||||||
\(264\) | 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 | \(-0.748116\pi\) | ||||
−0.702910 | + | 0.711279i | \(0.748116\pi\) | |||||||
\(272\) | 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 | 0.995578 | − | 0.0939357i | \(-0.0299448\pi\) |
−0.579140 | + | 0.815228i | \(0.696611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.2856 | − | 2.97487i | 1.09473 | − | 0.178101i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.56926 | − | 7.91419i | −0.272579 | − | 0.472121i | 0.696942 | − | 0.717127i | \(-0.254543\pi\) |
−0.969521 | + | 0.245006i | \(0.921210\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.45421 | + | 5.98287i | −0.205331 | + | 0.355645i | −0.950238 | − | 0.311524i | \(-0.899161\pi\) |
0.744907 | + | 0.667169i | \(0.232494\pi\) | |||||||
\(284\) | 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 | −0.455348 | − | 0.890314i | \(-0.650485\pi\) |
0.998708 | − | 0.0508143i | \(-0.0161817\pi\) | |||||||
\(294\) | 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 | \(-0.630378\pi\) | ||||
−0.398236 | + | 0.917283i | \(0.630378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.93183 | − | 2.79823i | −0.109898 | − | 0.159186i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.86140 | + | 15.3484i | −0.502484 | + | 0.870327i | 0.497512 | + | 0.867457i | \(0.334247\pi\) |
−0.999996 | + | 0.00287031i | \(0.999086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.38305 | − | 12.7878i | −0.417315 | − | 0.722810i | 0.578354 | − | 0.815786i | \(-0.303695\pi\) |
−0.995668 | + | 0.0929758i | \(0.970362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.68823 | − | 8.18877i | −0.376839 | − | 0.461385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.28820 | + | 2.23122i | 0.0723523 | + | 0.125318i | 0.899932 | − | 0.436031i | \(-0.143616\pi\) |
−0.827580 | + | 0.561348i | \(0.810283\pi\) | |||||||
\(318\) | 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 | \(-0.169445\pi\) |
−0.870356 | + | 0.492423i | \(0.836111\pi\) | |||||||
\(332\) | 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 | −0.610981 | − | 0.791645i | \(-0.709225\pi\) |
0.991075 | + | 0.133302i | \(0.0425581\pi\) | |||||||
\(338\) | 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 | −0.337645 | − | 0.941274i | \(-0.609630\pi\) |
0.983989 | − | 0.178228i | \(-0.0570364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1616 | + | 22.7966i | 0.704526 | + | 1.22027i | 0.966862 | + | 0.255298i | \(0.0821736\pi\) |
−0.262337 | + | 0.964976i | \(0.584493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.39245 | + | 15.1789i | −0.234452 | + | 0.810189i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.30502 | − | 2.26036i | −0.0694590 | − | 0.120307i | 0.829204 | − | 0.558946i | \(-0.188794\pi\) |
−0.898663 | + | 0.438639i | \(0.855461\pi\) | |||||||
\(354\) | 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 | \(-0.529280\pi\) | ||||
−0.0918553 | + | 0.995772i | \(0.529280\pi\) | |||||||
\(360\) | 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 | \(-0.150692\pi\) |
−0.839853 | + | 0.542813i | \(0.817359\pi\) | |||||||
\(368\) | 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 | 0.0593828 | + | 0.998235i | \(0.481087\pi\) |
−0.894189 | + | 0.447691i | \(0.852247\pi\) | |||||||
\(374\) | 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 | \(-0.459102\pi\) | ||||
0.128132 | + | 0.991757i | \(0.459102\pi\) | |||||||
\(380\) | 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 | \(-0.837959\pi\) |
0.858668 | + | 0.512531i | \(0.171292\pi\) | |||||||
\(384\) | 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 | −0.987548 | − | 0.157320i | \(-0.949715\pi\) |
0.357531 | − | 0.933901i | \(-0.383619\pi\) | |||||||
\(390\) | 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 | −0.618604 | − | 0.785703i | \(-0.712302\pi\) |
0.989741 | + | 0.142876i | \(0.0456349\pi\) | |||||||
\(402\) | 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 | −0.418734 | − | 0.908109i | \(-0.637526\pi\) |
0.995812 | − | 0.0914201i | \(-0.0291406\pi\) | |||||||
\(410\) | 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 | −0.473138 | − | 0.880988i | \(-0.656879\pi\) |
0.999527 | − | 0.0307446i | \(-0.00978785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.83901 | + | 17.0417i | 0.479524 | + | 0.830560i | 0.999724 | − | 0.0234847i | \(-0.00747609\pi\) |
−0.520200 | + | 0.854044i | \(0.674143\pi\) | |||||||
\(422\) | 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 | \(-0.345371\pi\) | ||||
0.466899 | + | 0.884311i | \(0.345371\pi\) | |||||||
\(432\) | 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 | \(-0.196248\pi\) |
−0.908688 | + | 0.417475i | \(0.862915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.96107 | − | 0.481734i | 0.141003 | − | 0.0229397i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8632 | − | 18.8156i | −0.516126 | − | 0.893956i | −0.999825 | − | 0.0187219i | \(-0.994040\pi\) |
0.483699 | − | 0.875235i | \(-0.339293\pi\) | |||||||
\(444\) | 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 | 0.990481 | − | 0.137649i | \(-0.0439546\pi\) |
−0.614448 | + | 0.788957i | \(0.710621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1475 | − | 4.72458i | 0.893729 | − | 0.220524i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6888 | − | 28.9058i | −0.777274 | − | 1.34628i | −0.933507 | − | 0.358558i | \(-0.883269\pi\) |
0.156233 | − | 0.987720i | \(-0.450065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.67623 | − | 11.5636i | 0.310271 | − | 0.537404i | −0.668150 | − | 0.744026i | \(-0.732914\pi\) |
0.978421 | + | 0.206622i | \(0.0662470\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.5738 | − | 3.03646i | 1.74244 | − | 0.140813i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4976 | −0.532047 | −0.266023 | − | 0.963967i | \(-0.585710\pi\) | ||||
−0.266023 | + | 0.963967i | \(0.585710\pi\) | |||||||
\(468\) | 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 | \(-0.202825\pi\) |
−0.917119 | + | 0.398614i | \(0.869491\pi\) | |||||||
\(480\) | 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 | \(-0.704818\pi\) | ||||
−0.599964 | + | 0.800027i | \(0.704818\pi\) | |||||||
\(488\) | 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 | \(-0.993775\pi\) |
0.516839 | + | 0.856083i | \(0.327109\pi\) | |||||||
\(492\) | 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 | \(-0.929335\pi\) |
0.678412 | + | 0.734682i | \(0.262669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3800 | − | 22.2778i | −0.687128 | − | 0.995298i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.3009 | 1.44022 | 0.720112 | − | 0.693857i | \(-0.244090\pi\) | ||||
0.720112 | + | 0.693857i | \(0.244090\pi\) | |||||||
\(504\) | 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 | 0.497353 | + | 0.867548i | \(0.334305\pi\) |
−0.999995 | + | 0.00305334i | \(0.999028\pi\) | |||||||
\(510\) | 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 | \(-0.352691\pi\) | ||||
0.446442 | + | 0.894812i | \(0.352691\pi\) | |||||||
\(524\) | 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 | 0.999558 | + | 0.0297339i | \(0.00946598\pi\) |
−0.474029 | + | 0.880509i | \(0.657201\pi\) | |||||||
\(548\) | 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 | \(-0.904344\pi\) |
0.733945 | + | 0.679209i | \(0.237677\pi\) | |||||||
\(564\) | 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 | 0.953122 | − | 0.302585i | \(-0.0978495\pi\) |
−0.738607 | + | 0.674136i | \(0.764516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.34986 | + | 4.07008i | −0.0983387 | + | 0.170328i | −0.910997 | − | 0.412413i | \(-0.864686\pi\) |
0.812658 | + | 0.582740i | \(0.198020\pi\) | |||||||
\(572\) | 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 | \(-0.171067\pi\) |
−0.872855 | + | 0.487980i | \(0.837734\pi\) | |||||||
\(588\) | 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 | \(-0.833509\pi\) |
0.865749 | + | 0.500478i | \(0.166842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1676 | + | 31.4672i | 0.741073 | + | 1.28358i | 0.952007 | + | 0.306076i | \(0.0990160\pi\) |
−0.210934 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(602\) | 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 | \(-0.690917\pi\) |
0.997099 | + | 0.0761098i | \(0.0242500\pi\) | |||||||
\(608\) | 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 | 0.0646104 | − | 0.997911i | \(-0.479420\pi\) |
0.831911 | − | 0.554910i | \(-0.187247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.4100 | + | 24.9588i | 0.579186 | + | 1.00318i | 0.995573 | + | 0.0939920i | \(0.0299628\pi\) |
−0.416387 | + | 0.909187i | \(0.636704\pi\) | |||||||
\(620\) | 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 | \(-0.251835\pi\) | ||||
0.703018 | + | 0.711172i | \(0.251835\pi\) | |||||||
\(632\) | 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 | 0.961044 | + | 0.276396i | \(0.0891402\pi\) |
−0.241156 | + | 0.970486i | \(0.577526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8629 | − | 34.4036i | 0.783317 | − | 1.35674i | −0.146682 | − | 0.989184i | \(-0.546860\pi\) |
0.929999 | − | 0.367561i | \(-0.119807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.89566 | + | 14.5355i | −0.271516 | + | 0.572333i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.649904 | 0.0255504 | 0.0127752 | − | 0.999918i | \(-0.495933\pi\) | ||||
0.0127752 | + | 0.999918i | \(0.495933\pi\) | |||||||
\(648\) | 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 | −0.973733 | − | 0.227694i | \(-0.926881\pi\) |
0.684055 | + | 0.729430i | \(0.260215\pi\) | |||||||
\(654\) | 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 | \(-0.210666\pi\) |
−0.926659 | + | 0.375904i | \(0.877332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3419 | − | 21.3767i | 0.480043 | − | 0.831459i | −0.519695 | − | 0.854352i | \(-0.673954\pi\) |
0.999738 | + | 0.0228933i | \(0.00728778\pi\) | |||||||
\(662\) | 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 | 0.985874 | + | 0.167491i | \(0.0535664\pi\) |
−0.347886 | + | 0.937537i | \(0.613100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.7186 | − | 27.8030i | −1.02840 | − | 1.07014i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.59003 | − | 9.68222i | −0.214842 | − | 0.372118i | 0.738381 | − | 0.674383i | \(-0.235590\pi\) |
−0.953224 | + | 0.302265i | \(0.902257\pi\) | |||||||
\(678\) | 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 | \(-0.280984\pi\) | ||||
0.635039 | + | 0.772480i | \(0.280984\pi\) | |||||||
\(684\) | 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 | \(-0.0558911\pi\) |
−0.643595 | + | 0.765367i | \(0.722558\pi\) | |||||||
\(692\) | 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 | 0.769622 | − | 0.638499i | \(-0.220445\pi\) |
−0.937768 | + | 0.347263i | \(0.887111\pi\) | |||||||
\(710\) | 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 | \(-0.281495\pi\) | ||||
0.633799 | + | 0.773498i | \(0.281495\pi\) | |||||||
\(720\) | 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 | \(-0.0836693\pi\) |
−0.707853 | + | 0.706360i | \(0.750336\pi\) | |||||||
\(728\) | 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 | 0.470585 | + | 0.882355i | \(0.344043\pi\) |
−0.999434 | + | 0.0336388i | \(0.989290\pi\) | |||||||
\(734\) | 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 | \(-0.596551\pi\) | ||||
−0.298695 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(740\) | 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 | \(-0.773397\pi\) |
0.944310 | + | 0.329056i | \(0.106731\pi\) | |||||||
\(744\) | 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 | \(-0.773803\pi\) |
0.943890 | + | 0.330260i | \(0.107137\pi\) | |||||||
\(752\) | 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 | −0.771796 | − | 0.635870i | \(-0.780642\pi\) |
0.936578 | + | 0.350460i | \(0.113975\pi\) | |||||||
\(762\) | 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 | −0.990732 | − | 0.135833i | \(-0.956629\pi\) |
0.613001 | + | 0.790082i | \(0.289962\pi\) | |||||||
\(770\) | 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 | −0.296369 | + | 0.955074i | \(0.595776\pi\) |
−0.678934 | + | 0.734200i | \(0.737558\pi\) | |||||||
\(788\) | 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 | 0.466162 | + | 0.884699i | \(0.345636\pi\) |
−0.999253 | + | 0.0386418i | \(0.987697\pi\) | |||||||
\(798\) | 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 | \(-0.232722\pi\) | ||||
0.744428 | + | 0.667702i | \(0.232722\pi\) | |||||||
\(812\) | 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 | 0.984019 | − | 0.178065i | \(-0.0569836\pi\) |
−0.646218 | + | 0.763153i | \(0.723650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.2996 | − | 21.3035i | 0.428737 | − | 0.742594i | −0.568024 | − | 0.823012i | \(-0.692292\pi\) |
0.996761 | + | 0.0804178i | \(0.0256254\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.4345 | − | 44.0841i | −1.05960 | − | 1.53481i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.3747 | 1.36919 | 0.684597 | − | 0.728922i | \(-0.259978\pi\) | ||||
0.684597 | + | 0.728922i | \(0.259978\pi\) | |||||||
\(828\) | 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 | \(-0.230043\pi\) |
−0.947812 | + | 0.318831i | \(0.896710\pi\) | |||||||
\(840\) | 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 | −0.869256 | − | 0.494362i | \(-0.835402\pi\) |
0.00649778 | − | 0.999979i | \(-0.497932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56.4101 | + | 9.17730i | −1.92918 | + | 0.313857i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0113 | + | 41.5888i | 0.820211 | + | 1.42065i | 0.905525 | + | 0.424294i | \(0.139478\pi\) |
−0.0853131 | + | 0.996354i | \(0.527189\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.1422 | + | 33.1552i | −0.653123 | + | 1.13124i | 0.329238 | + | 0.944247i | \(0.393208\pi\) |
−0.982361 | + | 0.186995i | \(0.940125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.72943 | − | 5.75340i | 0.0930187 | − | 0.196075i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.2049 | 0.449500 | 0.224750 | − | 0.974416i | \(-0.427843\pi\) | ||||
0.224750 | + | 0.974416i | \(0.427843\pi\) | |||||||
\(864\) | 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 | −0.994273 | − | 0.106868i | \(-0.965918\pi\) |
0.589687 | + | 0.807632i | \(0.299251\pi\) | |||||||
\(878\) | 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 | \(-0.599967\pi\) | ||||
−0.308920 | + | 0.951088i | \(0.599967\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.86917 | − | 0.555120i | 0.230905 | − | 0.0186602i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.3324 | − | 26.5566i | 0.514813 | − | 0.891682i | −0.485039 | − | 0.874492i | \(-0.661195\pi\) |
0.999852 | − | 0.0171897i | \(-0.00547191\pi\) | |||||||
\(888\) | 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 | −0.969516 | − | 0.245030i | \(-0.921202\pi\) |
0.272556 | − | 0.962140i | \(-0.412131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.2706 | + | 27.0952i | −0.340655 | + | 0.898690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.5714 | + | 32.1667i | 0.615299 | + | 1.06573i | 0.990332 | + | 0.138718i | \(0.0442981\pi\) |
−0.375033 | + | 0.927012i | \(0.622369\pi\) | |||||||
\(912\) | 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 | \(-0.588225\pi\) | ||||
−0.273632 | + | 0.961835i | \(0.588225\pi\) | |||||||
\(920\) | 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 | 0.991308 | + | 0.131560i | \(0.0419987\pi\) |
−0.381719 | + | 0.924278i | \(0.624668\pi\) | |||||||
\(930\) | 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 | 0.291577 | + | 0.956547i | \(0.405820\pi\) |
−0.974183 | + | 0.225761i | \(0.927513\pi\) | |||||||
\(942\) | 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 | \(-0.236683\pi\) |
−0.954255 | + | 0.298993i | \(0.903349\pi\) | |||||||
\(948\) | 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 | \(-0.992991\pi\) |
0.518947 | + | 0.854806i | \(0.326324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.2309 | − | 32.1054i | 0.489286 | − | 1.03137i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0708 | −0.547827 | −0.273914 | − | 0.961754i | \(-0.588318\pi\) | ||||
−0.273914 | + | 0.961754i | \(0.588318\pi\) | |||||||
\(972\) | 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 | −0.467263 | − | 0.884118i | \(-0.654760\pi\) |
0.999300 | − | 0.0373970i | \(-0.0119066\pi\) | |||||||
\(978\) | 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 | \(-0.305882\pi\) |
−0.996284 | + | 0.0861339i | \(0.972549\pi\) | |||||||
\(984\) | 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 | \(-0.776964\pi\) | ||||
−0.764398 | + | 0.644744i | \(0.776964\pi\) | |||||||
\(992\) | 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 | 0.671073 | − | 0.741391i | \(-0.265834\pi\) |
−0.977600 | + | 0.210471i | \(0.932500\pi\) | |||||||
\(998\) | 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 | 1008.2.r.n.337.2 | 10 | ||
3.2 | odd | 2 | 3024.2.r.n.1009.5 | 10 | |||
4.3 | odd | 2 | 504.2.r.f.337.4 | yes | 10 | ||
9.2 | odd | 6 | 3024.2.r.n.2017.5 | 10 | |||
9.4 | even | 3 | 9072.2.a.cn.1.5 | 5 | |||
9.5 | odd | 6 | 9072.2.a.cm.1.1 | 5 | |||
9.7 | even | 3 | inner | 1008.2.r.n.673.2 | 10 | ||
12.11 | even | 2 | 1512.2.r.f.1009.5 | 10 | |||
36.7 | odd | 6 | 504.2.r.f.169.4 | ✓ | 10 | ||
36.11 | even | 6 | 1512.2.r.f.505.5 | 10 | |||
36.23 | even | 6 | 4536.2.a.bc.1.1 | 5 | |||
36.31 | odd | 6 | 4536.2.a.bd.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.f.169.4 | ✓ | 10 | 36.7 | odd | 6 | ||
504.2.r.f.337.4 | yes | 10 | 4.3 | odd | 2 | ||
1008.2.r.n.337.2 | 10 | 1.1 | even | 1 | trivial | ||
1008.2.r.n.673.2 | 10 | 9.7 | even | 3 | inner | ||
1512.2.r.f.505.5 | 10 | 36.11 | even | 6 | |||
1512.2.r.f.1009.5 | 10 | 12.11 | even | 2 | |||
3024.2.r.n.1009.5 | 10 | 3.2 | odd | 2 | |||
3024.2.r.n.2017.5 | 10 | 9.2 | odd | 6 | |||
4536.2.a.bc.1.1 | 5 | 36.23 | even | 6 | |||
4536.2.a.bd.1.5 | 5 | 36.31 | odd | 6 | |||
9072.2.a.cm.1.1 | 5 | 9.5 | odd | 6 | |||
9072.2.a.cn.1.5 | 5 | 9.4 | even | 3 |