Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.d.323.2 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41047 | − | 0.102782i | −0.997355 | − | 0.0726779i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.97887 | + | 0.289943i | 0.989436 | + | 0.144971i | ||||
\(5\) | −2.90802 | −1.30051 | −0.650253 | − | 0.759718i | \(-0.725337\pi\) | ||||
−0.650253 | + | 0.759718i | \(0.725337\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.76135 | − | 0.612349i | −0.976283 | − | 0.216498i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.10168 | + | 0.298892i | 1.29707 | + | 0.0945180i | ||||
\(11\) | 1.28828i | 0.388432i | 0.980959 | + | 0.194216i | \(0.0622163\pi\) | ||||
−0.980959 | + | 0.194216i | \(0.937784\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.86999i | − | 0.518642i | −0.965791 | − | 0.259321i | \(-0.916501\pi\) | ||
0.965791 | − | 0.259321i | \(-0.0834988\pi\) | |||||||
\(14\) | −0.102782 | + | 1.41047i | −0.0274697 | + | 0.376965i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.83187 | + | 1.14752i | 0.957967 | + | 0.286880i | ||||
\(17\) | 3.87222i | 0.939151i | 0.882892 | + | 0.469576i | \(0.155593\pi\) | ||||
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.04228 | −0.468532 | −0.234266 | − | 0.972173i | \(-0.575269\pi\) | ||||
−0.234266 | + | 0.972173i | \(0.575269\pi\) | |||||||
\(20\) | −5.75460 | − | 0.843159i | −1.28677 | − | 0.188536i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.132412 | − | 1.81709i | 0.0282304 | − | 0.387405i | ||||
\(23\) | 0.934839 | 0.194927 | 0.0974637 | − | 0.995239i | \(-0.468927\pi\) | ||||
0.0974637 | + | 0.995239i | \(0.468927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.45657 | 0.691315 | ||||||||
\(26\) | −0.192202 | + | 2.63757i | −0.0376938 | + | 0.517271i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.289943 | − | 1.97887i | 0.0547940 | − | 0.373972i | ||||
\(29\) | −2.98295 | −0.553920 | −0.276960 | − | 0.960881i | \(-0.589327\pi\) | ||||
−0.276960 | + | 0.960881i | \(0.589327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.85691i | 0.333511i | 0.985998 | + | 0.166756i | \(0.0533291\pi\) | ||||
−0.985998 | + | 0.166756i | \(0.946671\pi\) | |||||||
\(32\) | −5.28680 | − | 2.01239i | −0.934583 | − | 0.355744i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.397995 | − | 5.46166i | 0.0682555 | − | 0.936668i | ||||
\(35\) | 2.90802i | 0.491545i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.85846i | 0.634327i | 0.948371 | + | 0.317163i | \(0.102730\pi\) | ||||
−0.948371 | + | 0.317163i | \(0.897270\pi\) | |||||||
\(38\) | 2.88059 | + | 0.209910i | 0.467293 | + | 0.0340519i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.03004 | + | 1.78072i | 1.26966 | + | 0.281557i | ||||
\(41\) | − | 8.72247i | − | 1.36222i | −0.732181 | − | 0.681110i | \(-0.761497\pi\) | ||
0.732181 | − | 0.681110i | \(-0.238503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.19319 | −0.181959 | −0.0909796 | − | 0.995853i | \(-0.529000\pi\) | ||||
−0.0909796 | + | 0.995853i | \(0.529000\pi\) | |||||||
\(44\) | −0.373528 | + | 2.54935i | −0.0563115 | + | 0.384329i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.31857 | − | 0.0960846i | −0.194412 | − | 0.0141669i | ||||
\(47\) | 11.1537 | 1.62694 | 0.813468 | − | 0.581609i | \(-0.197577\pi\) | ||||
0.813468 | + | 0.581609i | \(0.197577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.87541 | − | 0.355274i | −0.689487 | − | 0.0502433i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.542190 | − | 3.70047i | 0.0751883 | − | 0.513163i | ||||
\(53\) | 4.43885 | 0.609723 | 0.304862 | − | 0.952397i | \(-0.401390\pi\) | ||||
0.304862 | + | 0.952397i | \(0.401390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.74635i | − | 0.505158i | ||||||
\(56\) | −0.612349 | + | 2.76135i | −0.0818286 | + | 0.369000i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.20737 | + | 0.306594i | 0.552455 | + | 0.0402577i | ||||
\(59\) | − | 10.9714i | − | 1.42836i | −0.699964 | − | 0.714178i | \(-0.746801\pi\) | ||
0.699964 | − | 0.714178i | \(-0.253199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.70930i | − | 0.602964i | −0.953472 | − | 0.301482i | \(-0.902519\pi\) | ||
0.953472 | − | 0.301482i | \(-0.0974813\pi\) | |||||||
\(62\) | 0.190857 | − | 2.61913i | 0.0242389 | − | 0.332629i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.25006 | + | 3.38181i | 0.906257 | + | 0.422727i | ||||
\(65\) | 5.43797i | 0.674497i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.41800 | 0.539745 | 0.269872 | − | 0.962896i | \(-0.413019\pi\) | ||||
0.269872 | + | 0.962896i | \(0.413019\pi\) | |||||||
\(68\) | −1.12272 | + | 7.66263i | −0.136150 | + | 0.929230i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.298892 | − | 4.10168i | 0.0357244 | − | 0.490245i | ||||
\(71\) | 9.72888 | 1.15461 | 0.577303 | − | 0.816530i | \(-0.304105\pi\) | ||||
0.577303 | + | 0.816530i | \(0.304105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.40756 | 1.10107 | 0.550536 | − | 0.834812i | \(-0.314423\pi\) | ||||
0.550536 | + | 0.834812i | \(0.314423\pi\) | |||||||
\(74\) | 0.396580 | − | 5.44225i | 0.0461015 | − | 0.632649i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.04142 | − | 0.592145i | −0.463582 | − | 0.0679237i | ||||
\(77\) | 1.28828 | 0.146813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.4660i | 1.85257i | 0.376822 | + | 0.926286i | \(0.377017\pi\) | ||||
−0.376822 | + | 0.926286i | \(0.622983\pi\) | |||||||
\(80\) | −11.1431 | − | 3.33701i | −1.24584 | − | 0.373089i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.896513 | + | 12.3028i | −0.0990033 | + | 1.35862i | ||||
\(83\) | − | 3.72150i | − | 0.408488i | −0.978920 | − | 0.204244i | \(-0.934526\pi\) | ||
0.978920 | − | 0.204244i | \(-0.0654736\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.2605i | − | 1.22137i | ||||||
\(86\) | 1.68296 | + | 0.122638i | 0.181478 | + | 0.0132244i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.788879 | − | 3.55739i | 0.0840948 | − | 0.379220i | ||||
\(89\) | 12.2297i | 1.29635i | 0.761492 | + | 0.648174i | \(0.224467\pi\) | ||||
−0.761492 | + | 0.648174i | \(0.775533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.86999 | −0.196028 | ||||||||
\(92\) | 1.84993 | + | 0.271050i | 0.192868 | + | 0.0282589i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.7320 | − | 1.14640i | −1.62263 | − | 0.118242i | ||||
\(95\) | 5.93900 | 0.609329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8302 | 1.60731 | 0.803657 | − | 0.595093i | \(-0.202885\pi\) | ||||
0.803657 | + | 0.595093i | \(0.202885\pi\) | |||||||
\(98\) | 1.41047 | + | 0.102782i | 0.142479 | + | 0.0103826i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.84012 | + | 1.00221i | 0.684012 | + | 0.100221i | ||||
\(101\) | 0.737825 | 0.0734163 | 0.0367081 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367081 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.2518i | − | 1.60134i | −0.599109 | − | 0.800668i | \(-0.704478\pi\) | ||
0.599109 | − | 0.800668i | \(-0.295522\pi\) | |||||||
\(104\) | −1.14509 | + | 5.16369i | −0.112285 | + | 0.506342i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.26088 | − | 0.456234i | −0.608111 | − | 0.0443134i | ||||
\(107\) | 1.49407i | 0.144438i | 0.997389 | + | 0.0722188i | \(0.0230080\pi\) | ||||
−0.997389 | + | 0.0722188i | \(0.976992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8362i | 1.13370i | 0.823821 | + | 0.566850i | \(0.191838\pi\) | ||||
−0.823821 | + | 0.566850i | \(0.808162\pi\) | |||||||
\(110\) | −0.385058 | + | 5.28413i | −0.0367138 | + | 0.503822i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.14752 | − | 3.83187i | 0.108430 | − | 0.362077i | ||||
\(113\) | − | 15.3287i | − | 1.44200i | −0.692934 | − | 0.721001i | \(-0.743682\pi\) | ||
0.692934 | − | 0.721001i | \(-0.256318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.71853 | −0.253504 | ||||||||
\(116\) | −5.90288 | − | 0.864885i | −0.548068 | − | 0.0803026i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.12766 | + | 15.4749i | −0.103810 | + | 1.42458i | ||||
\(119\) | 3.87222 | 0.354966 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.34033 | 0.849121 | ||||||||
\(122\) | −0.484032 | + | 6.64234i | −0.0438222 | + | 0.601370i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.538398 | + | 3.67459i | −0.0483496 | + | 0.329988i | ||||
\(125\) | 4.48831 | 0.401447 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.55275i | − | 0.581462i | −0.956805 | − | 0.290731i | \(-0.906101\pi\) | ||
0.956805 | − | 0.290731i | \(-0.0938985\pi\) | |||||||
\(128\) | −9.87842 | − | 5.51514i | −0.873138 | − | 0.487474i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.558926 | − | 7.67011i | 0.0490210 | − | 0.672713i | ||||
\(131\) | 11.6893i | 1.02130i | 0.859790 | + | 0.510648i | \(0.170595\pi\) | ||||
−0.859790 | + | 0.510648i | \(0.829405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.04228i | 0.177088i | ||||||||
\(134\) | −6.23147 | − | 0.454091i | −0.538317 | − | 0.0392275i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.37115 | − | 10.6925i | 0.203324 | − | 0.916877i | ||||
\(137\) | − | 7.35868i | − | 0.628694i | −0.949308 | − | 0.314347i | \(-0.898214\pi\) | ||
0.949308 | − | 0.314347i | \(-0.101786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2683 | −1.29504 | −0.647520 | − | 0.762048i | \(-0.724194\pi\) | ||||
−0.647520 | + | 0.762048i | \(0.724194\pi\) | |||||||
\(140\) | −0.843159 | + | 5.75460i | −0.0712599 | + | 0.486352i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.7223 | − | 0.999955i | −1.15155 | − | 0.0839143i | ||||
\(143\) | 2.40908 | 0.201457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.67448 | 0.720376 | ||||||||
\(146\) | −13.2691 | − | 0.966928i | −1.09816 | − | 0.0800235i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.11873 | + | 7.63540i | −0.0919592 | + | 0.627626i | ||||
\(149\) | 16.6778 | 1.36630 | 0.683148 | − | 0.730280i | \(-0.260611\pi\) | ||||
0.683148 | + | 0.730280i | \(0.260611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4838i | 1.34143i | 0.741714 | + | 0.670716i | \(0.234013\pi\) | ||||
−0.741714 | + | 0.670716i | \(0.765987\pi\) | |||||||
\(152\) | 5.63945 | + | 1.25059i | 0.457420 | + | 0.101436i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.81709 | − | 0.132412i | −0.146425 | − | 0.0106701i | ||||
\(155\) | − | 5.39994i | − | 0.433733i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.0196i | − | 1.27851i | −0.768997 | − | 0.639253i | \(-0.779244\pi\) | ||
0.768997 | − | 0.639253i | \(-0.220756\pi\) | |||||||
\(158\) | 1.69241 | − | 23.2249i | 0.134641 | − | 1.84767i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.3741 | + | 5.85208i | 1.21543 | + | 0.462647i | ||||
\(161\) | − | 0.934839i | − | 0.0736756i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.18368 | 0.484343 | 0.242172 | − | 0.970233i | \(-0.422140\pi\) | ||||
0.242172 | + | 0.970233i | \(0.422140\pi\) | |||||||
\(164\) | 2.52902 | − | 17.2606i | 0.197483 | − | 1.34783i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.382504 | + | 5.24908i | −0.0296881 | + | 0.407408i | ||||
\(167\) | 12.7232 | 0.984549 | 0.492275 | − | 0.870440i | \(-0.336166\pi\) | ||||
0.492275 | + | 0.870440i | \(0.336166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.50313 | 0.731010 | ||||||||
\(170\) | −1.15738 | + | 15.8826i | −0.0887667 | + | 1.21814i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.36116 | − | 0.345956i | −0.180037 | − | 0.0263789i | ||||
\(173\) | 11.2579 | 0.855925 | 0.427963 | − | 0.903796i | \(-0.359231\pi\) | ||||
0.427963 | + | 0.903796i | \(0.359231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.45657i | − | 0.261292i | ||||||
\(176\) | −1.47833 | + | 4.93653i | −0.111433 | + | 0.372105i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.25700 | − | 17.2497i | 0.0942159 | − | 1.29292i | ||||
\(179\) | 8.68048i | 0.648809i | 0.945918 | + | 0.324405i | \(0.105164\pi\) | ||||
−0.945918 | + | 0.324405i | \(0.894836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.48587i | 0.184773i | 0.995723 | + | 0.0923866i | \(0.0294496\pi\) | ||||
−0.995723 | + | 0.0923866i | \(0.970550\pi\) | |||||||
\(182\) | 2.63757 | + | 0.192202i | 0.195510 | + | 0.0142469i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.58141 | − | 0.572448i | −0.190304 | − | 0.0422014i | ||||
\(185\) | − | 11.2205i | − | 0.824945i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.98851 | −0.364796 | ||||||||
\(188\) | 22.0718 | + | 3.23394i | 1.60975 | + | 0.235859i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.37680 | − | 0.610423i | −0.607717 | − | 0.0442847i | ||||
\(191\) | −3.40263 | −0.246206 | −0.123103 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123103 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7031 | 1.49024 | 0.745121 | − | 0.666929i | \(-0.232392\pi\) | ||||
0.745121 | + | 0.666929i | \(0.232392\pi\) | |||||||
\(194\) | −22.3281 | − | 1.62706i | −1.60306 | − | 0.116816i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.97887 | − | 0.289943i | −0.141348 | − | 0.0207102i | ||||
\(197\) | 16.3546 | 1.16521 | 0.582607 | − | 0.812754i | \(-0.302033\pi\) | ||||
0.582607 | + | 0.812754i | \(0.302033\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.3717i | − | 0.806121i | −0.915173 | − | 0.403061i | \(-0.867946\pi\) | ||
0.915173 | − | 0.403061i | \(-0.132054\pi\) | |||||||
\(200\) | −9.54480 | − | 2.11663i | −0.674919 | − | 0.149668i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.04068 | − | 0.0758351i | −0.0732221 | − | 0.00533574i | ||||
\(203\) | 2.98295i | 0.209362i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.3651i | 1.77158i | ||||||||
\(206\) | −1.67039 | + | 22.9227i | −0.116382 | + | 1.59710i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.14585 | − | 7.16556i | 0.148788 | − | 0.496842i | ||||
\(209\) | − | 2.63104i | − | 0.181993i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.56405 | −0.176517 | −0.0882583 | − | 0.996098i | \(-0.528130\pi\) | ||||
−0.0882583 | + | 0.996098i | \(0.528130\pi\) | |||||||
\(212\) | 8.78392 | + | 1.28701i | 0.603282 | + | 0.0883924i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.153564 | − | 2.10735i | 0.0104974 | − | 0.144056i | ||||
\(215\) | 3.46981 | 0.236639 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85691 | 0.126055 | ||||||||
\(218\) | 1.21655 | − | 16.6946i | 0.0823950 | − | 1.13070i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.08623 | − | 7.41355i | 0.0732334 | − | 0.499821i | ||||
\(221\) | 7.24102 | 0.487083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.37584i | − | 0.0921329i | −0.998938 | − | 0.0460665i | \(-0.985331\pi\) | ||
0.998938 | − | 0.0460665i | \(-0.0146686\pi\) | |||||||
\(224\) | −2.01239 | + | 5.28680i | −0.134459 | + | 0.353239i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.57551 | + | 21.6207i | −0.104802 | + | 1.43819i | ||||
\(227\) | − | 27.3740i | − | 1.81688i | −0.418020 | − | 0.908438i | \(-0.637276\pi\) | ||
0.418020 | − | 0.908438i | \(-0.362724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.3066i | − | 0.813243i | −0.913597 | − | 0.406621i | \(-0.866707\pi\) | ||
0.913597 | − | 0.406621i | \(-0.133293\pi\) | |||||||
\(230\) | 3.83441 | + | 0.279416i | 0.252834 | + | 0.0184241i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.23696 | + | 1.82661i | 0.540783 | + | 0.119923i | ||||
\(233\) | 24.0829i | 1.57772i | 0.614571 | + | 0.788862i | \(0.289329\pi\) | ||||
−0.614571 | + | 0.788862i | \(0.710671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.4352 | −2.11584 | ||||||||
\(236\) | 3.18108 | − | 21.7110i | 0.207071 | − | 1.41327i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.46166 | − | 0.397995i | −0.354027 | − | 0.0257982i | ||||
\(239\) | −18.0426 | −1.16708 | −0.583540 | − | 0.812085i | \(-0.698333\pi\) | ||||
−0.583540 | + | 0.812085i | \(0.698333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8541 | −0.699174 | −0.349587 | − | 0.936904i | \(-0.613678\pi\) | ||||
−0.349587 | + | 0.936904i | \(0.613678\pi\) | |||||||
\(242\) | −13.1743 | − | 0.960018i | −0.846875 | − | 0.0617123i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.36543 | − | 9.31910i | 0.0874125 | − | 0.596594i | ||||
\(245\) | 2.90802 | 0.185787 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.81905i | 0.243001i | ||||||||
\(248\) | 1.13708 | − | 5.12758i | 0.0722046 | − | 0.325601i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.33065 | − | 0.461318i | −0.400385 | − | 0.0291763i | ||||
\(251\) | 6.63032i | 0.418502i | 0.977862 | + | 0.209251i | \(0.0671025\pi\) | ||||
−0.977862 | + | 0.209251i | \(0.932897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.20434i | 0.0757160i | ||||||||
\(254\) | −0.673505 | + | 9.24248i | −0.0422595 | + | 0.579925i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.3664 | + | 8.79428i | 0.835400 | + | 0.549642i | ||||
\(257\) | 12.2398i | 0.763497i | 0.924266 | + | 0.381748i | \(0.124678\pi\) | ||||
−0.924266 | + | 0.381748i | \(0.875322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.85846 | 0.239753 | ||||||||
\(260\) | −1.57670 | + | 10.7610i | −0.0977828 | + | 0.667372i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.20145 | − | 16.4874i | 0.0742257 | − | 1.01860i | ||||
\(263\) | −2.87474 | −0.177264 | −0.0886320 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886320 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9083 | −0.792948 | ||||||||
\(266\) | 0.209910 | − | 2.88059i | 0.0128704 | − | 0.176620i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.74265 | + | 1.28097i | 0.534043 | + | 0.0782475i | ||||
\(269\) | 6.17565 | 0.376536 | 0.188268 | − | 0.982118i | \(-0.439713\pi\) | ||||
0.188268 | + | 0.982118i | \(0.439713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.5103i | − | 1.18517i | −0.805510 | − | 0.592583i | \(-0.798108\pi\) | ||
0.805510 | − | 0.592583i | \(-0.201892\pi\) | |||||||
\(272\) | −4.44345 | + | 14.8378i | −0.269423 | + | 0.899675i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.756340 | + | 10.3792i | −0.0456922 | + | 0.627031i | ||||
\(275\) | 4.45305i | 0.268529i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.82757i | − | 0.169892i | −0.996386 | − | 0.0849460i | \(-0.972928\pi\) | ||
0.996386 | − | 0.0849460i | \(-0.0270718\pi\) | |||||||
\(278\) | 21.5355 | + | 1.56931i | 1.29162 | + | 0.0941208i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.78072 | − | 8.03004i | 0.106419 | − | 0.479887i | ||||
\(281\) | − | 29.7569i | − | 1.77515i | −0.460663 | − | 0.887575i | \(-0.652388\pi\) | ||
0.460663 | − | 0.887575i | \(-0.347612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.7427 | −1.82746 | −0.913731 | − | 0.406319i | \(-0.866812\pi\) | ||||
−0.913731 | + | 0.406319i | \(0.866812\pi\) | |||||||
\(284\) | 19.2522 | + | 2.82082i | 1.14241 | + | 0.167385i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.39794 | − | 0.247610i | −0.200924 | − | 0.0146415i | ||||
\(287\) | −8.72247 | −0.514871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.00592 | 0.117995 | ||||||||
\(290\) | −12.2351 | − | 0.891581i | −0.718471 | − | 0.0523554i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.6164 | + | 2.72765i | 1.08944 | + | 0.159624i | ||||
\(293\) | 5.70430 | 0.333249 | 0.166624 | − | 0.986020i | \(-0.446713\pi\) | ||||
0.166624 | + | 0.986020i | \(0.446713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.9051i | 1.85758i | ||||||||
\(296\) | 2.36272 | − | 10.6545i | 0.137331 | − | 0.619282i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.5235 | − | 1.71417i | −1.36268 | − | 0.0992995i | ||||
\(299\) | − | 1.74814i | − | 0.101098i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.19319i | 0.0687741i | ||||||||
\(302\) | 1.69424 | − | 23.2499i | 0.0974924 | − | 1.33788i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.82576 | − | 2.34356i | −0.448838 | − | 0.134412i | ||||
\(305\) | 13.6947i | 0.784158i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.47411 | −0.369497 | −0.184748 | − | 0.982786i | \(-0.559147\pi\) | ||||
−0.184748 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(308\) | 2.54935 | + | 0.373528i | 0.145263 | + | 0.0212838i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.555016 | + | 7.61647i | −0.0315228 | + | 0.432586i | ||||
\(311\) | 2.44723 | 0.138770 | 0.0693848 | − | 0.997590i | \(-0.477896\pi\) | ||||
0.0693848 | + | 0.997590i | \(0.477896\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.03434 | −0.454128 | −0.227064 | − | 0.973880i | \(-0.572913\pi\) | ||||
−0.227064 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(314\) | −1.64653 | + | 22.5953i | −0.0929191 | + | 1.27512i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.77420 | + | 32.5841i | −0.268570 | + | 1.83300i | ||||
\(317\) | 19.0098 | 1.06770 | 0.533850 | − | 0.845579i | \(-0.320745\pi\) | ||||
0.533850 | + | 0.845579i | \(0.320745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.84289i | − | 0.215160i | ||||||
\(320\) | −21.0833 | − | 9.83438i | −1.17859 | − | 0.549759i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0960846 | + | 1.31857i | −0.00535459 | + | 0.0734808i | ||||
\(323\) | − | 7.90817i | − | 0.440022i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.46376i | − | 0.358545i | ||||||
\(326\) | −8.72192 | − | 0.635571i | −0.483062 | − | 0.0352010i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.34119 | + | 24.0857i | −0.294918 | + | 1.32991i | ||||
\(329\) | − | 11.1537i | − | 0.614924i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.8597 | −1.97103 | −0.985515 | − | 0.169588i | \(-0.945756\pi\) | ||||
−0.985515 | + | 0.169588i | \(0.945756\pi\) | |||||||
\(332\) | 1.07902 | − | 7.36438i | 0.0592191 | − | 0.404173i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.9457 | − | 1.30771i | −0.981946 | − | 0.0715550i | ||||
\(335\) | −12.8476 | −0.701941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.90274 | −0.376016 | −0.188008 | − | 0.982168i | \(-0.560203\pi\) | ||||
−0.188008 | + | 0.982168i | \(0.560203\pi\) | |||||||
\(338\) | −13.4039 | − | 0.976751i | −0.729077 | − | 0.0531283i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.26490 | − | 22.2831i | 0.177064 | − | 1.20847i | ||||
\(341\) | −2.39223 | −0.129546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 3.29480 | + | 0.730646i | 0.177644 | + | 0.0393938i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.8790 | − | 1.15711i | −0.853662 | − | 0.0622068i | ||||
\(347\) | 36.6932i | 1.96980i | 0.173135 | + | 0.984898i | \(0.444610\pi\) | ||||
−0.173135 | + | 0.984898i | \(0.555390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.2560i | 1.51251i | 0.654278 | + | 0.756254i | \(0.272973\pi\) | ||||
−0.654278 | + | 0.756254i | \(0.727027\pi\) | |||||||
\(350\) | −0.355274 | + | 4.87541i | −0.0189902 | + | 0.260601i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59253 | − | 6.81090i | 0.138182 | − | 0.363022i | ||||
\(353\) | 24.3138i | 1.29410i | 0.762450 | + | 0.647048i | \(0.223997\pi\) | ||||
−0.762450 | + | 0.647048i | \(0.776003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.2918 | −1.50157 | ||||||||
\(356\) | −3.54592 | + | 24.2011i | −0.187933 | + | 1.28265i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.892197 | − | 12.2436i | 0.0471541 | − | 0.647094i | ||||
\(359\) | 1.95382 | 0.103119 | 0.0515594 | − | 0.998670i | \(-0.483581\pi\) | ||||
0.0515594 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8291 | −0.780478 | ||||||||
\(362\) | 0.255503 | − | 3.50625i | 0.0134289 | − | 0.184284i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.70047 | − | 0.542190i | −0.193957 | − | 0.0284185i | ||||
\(365\) | −27.3574 | −1.43195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3819i | 1.11613i | 0.829798 | + | 0.558064i | \(0.188456\pi\) | ||||
−0.829798 | + | 0.558064i | \(0.811544\pi\) | |||||||
\(368\) | 3.58218 | + | 1.07275i | 0.186734 | + | 0.0559207i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.15326 | + | 15.8262i | −0.0599553 | + | 0.822764i | ||||
\(371\) | − | 4.43885i | − | 0.230454i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.0682i | 1.71221i | 0.516804 | + | 0.856104i | \(0.327122\pi\) | ||||
−0.516804 | + | 0.856104i | \(0.672878\pi\) | |||||||
\(374\) | 7.03617 | + | 0.512730i | 0.363832 | + | 0.0265126i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.7993 | − | 6.82997i | −1.58835 | − | 0.352229i | ||||
\(377\) | 5.57809i | 0.287286i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0331 | −0.874934 | −0.437467 | − | 0.899235i | \(-0.644124\pi\) | ||||
−0.437467 | + | 0.899235i | \(0.644124\pi\) | |||||||
\(380\) | 11.7525 | + | 1.72197i | 0.602892 | + | 0.0883352i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.79932 | + | 0.349729i | 0.245555 | + | 0.0178937i | ||||
\(383\) | −15.7372 | −0.804132 | −0.402066 | − | 0.915611i | \(-0.631708\pi\) | ||||
−0.402066 | + | 0.915611i | \(0.631708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.74635 | −0.190932 | ||||||||
\(386\) | −29.2012 | − | 2.12791i | −1.48630 | − | 0.108308i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31.3259 | + | 4.58985i | 1.59033 | + | 0.233015i | ||||
\(389\) | −22.7854 | −1.15527 | −0.577634 | − | 0.816296i | \(-0.696024\pi\) | ||||
−0.577634 | + | 0.816296i | \(0.696024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.61990i | 0.183066i | ||||||||
\(392\) | 2.76135 | + | 0.612349i | 0.139469 | + | 0.0309283i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.0677 | − | 1.68096i | −1.16213 | − | 0.0846853i | ||||
\(395\) | − | 47.8835i | − | 2.40928i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.6829i | − | 1.18861i | −0.804239 | − | 0.594306i | \(-0.797427\pi\) | ||
0.804239 | − | 0.594306i | \(-0.202573\pi\) | |||||||
\(398\) | −1.16881 | + | 16.0395i | −0.0585872 | + | 0.803990i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2451 | + | 3.96648i | 0.662257 | + | 0.198324i | ||||
\(401\) | − | 1.51029i | − | 0.0754204i | −0.999289 | − | 0.0377102i | \(-0.987994\pi\) | ||
0.999289 | − | 0.0377102i | \(-0.0120064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.47241 | 0.172973 | ||||||||
\(404\) | 1.46006 | + | 0.213927i | 0.0726407 | + | 0.0106433i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.306594 | − | 4.20737i | 0.0152160 | − | 0.208808i | ||||
\(407\) | −4.97079 | −0.246393 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.86160 | 0.487625 | 0.243812 | − | 0.969822i | \(-0.421602\pi\) | ||||
0.243812 | + | 0.969822i | \(0.421602\pi\) | |||||||
\(410\) | 2.60708 | − | 35.7768i | 0.128754 | − | 1.76689i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.71209 | − | 32.1602i | 0.232148 | − | 1.58442i | ||||
\(413\) | −10.9714 | −0.539868 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8222i | 0.531241i | ||||||||
\(416\) | −3.76316 | + | 9.88627i | −0.184504 | + | 0.484714i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.270424 | + | 3.71101i | −0.0132269 | + | 0.181512i | ||||
\(419\) | 20.8183i | 1.01704i | 0.861050 | + | 0.508520i | \(0.169807\pi\) | ||||
−0.861050 | + | 0.508520i | \(0.830193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.5459i | − | 1.39124i | −0.718409 | − | 0.695621i | \(-0.755129\pi\) | ||
0.718409 | − | 0.695621i | \(-0.244871\pi\) | |||||||
\(422\) | 3.61653 | + | 0.263538i | 0.176050 | + | 0.0128288i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.2572 | − | 2.71813i | −0.595262 | − | 0.132004i | ||||
\(425\) | 13.3846i | 0.649249i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.70930 | −0.227899 | ||||||||
\(428\) | −0.433196 | + | 2.95658i | −0.0209393 | + | 0.142912i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.89407 | − | 0.356634i | −0.236013 | − | 0.0171984i | ||||
\(431\) | −6.53111 | −0.314593 | −0.157296 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157296 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.2151 | 0.683136 | 0.341568 | − | 0.939857i | \(-0.389042\pi\) | ||||
0.341568 | + | 0.939857i | \(0.389042\pi\) | |||||||
\(434\) | −2.61913 | − | 0.190857i | −0.125722 | − | 0.00916144i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.43182 | + | 23.4223i | −0.164354 | + | 1.12172i | ||||
\(437\) | −1.90921 | −0.0913297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.5811i | − | 1.07773i | −0.842391 | − | 0.538867i | \(-0.818852\pi\) | ||
0.842391 | − | 0.538867i | \(-0.181148\pi\) | |||||||
\(440\) | −2.29408 | + | 10.3450i | −0.109366 | + | 0.493177i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.2133 | − | 0.744247i | −0.485795 | − | 0.0354002i | ||||
\(443\) | − | 15.7932i | − | 0.750359i | −0.926952 | − | 0.375179i | \(-0.877581\pi\) | ||
0.926952 | − | 0.375179i | \(-0.122419\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 35.5643i | − | 1.68591i | ||||||
\(446\) | −0.141411 | + | 1.94058i | −0.00669603 | + | 0.0918893i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.38181 | − | 7.25006i | 0.159776 | − | 0.342533i | ||||
\(449\) | − | 26.9861i | − | 1.27355i | −0.771049 | − | 0.636776i | \(-0.780267\pi\) | ||
0.771049 | − | 0.636776i | \(-0.219733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2370 | 0.529130 | ||||||||
\(452\) | 4.44444 | − | 30.3335i | 0.209049 | − | 1.42677i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.81356 | + | 38.6103i | −0.132047 | + | 1.81207i | ||||
\(455\) | 5.43797 | 0.254936 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9588 | 1.77564 | 0.887818 | − | 0.460195i | \(-0.152220\pi\) | ||||
0.887818 | + | 0.460195i | \(0.152220\pi\) | |||||||
\(458\) | −1.26490 | + | 17.3581i | −0.0591048 | + | 0.811092i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.37962 | − | 0.788218i | −0.250826 | − | 0.0367508i | ||||
\(461\) | −8.35921 | −0.389327 | −0.194664 | − | 0.980870i | \(-0.562362\pi\) | ||||
−0.194664 | + | 0.980870i | \(0.562362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4723i | 0.858483i | 0.903190 | + | 0.429241i | \(0.141219\pi\) | ||||
−0.903190 | + | 0.429241i | \(0.858781\pi\) | |||||||
\(464\) | −11.4303 | − | 3.42299i | −0.530637 | − | 0.158908i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.47529 | − | 33.9683i | 0.114666 | − | 1.57355i | ||||
\(467\) | − | 4.34051i | − | 0.200855i | −0.994944 | − | 0.100427i | \(-0.967979\pi\) | ||
0.994944 | − | 0.100427i | \(-0.0320210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.41800i | − | 0.204004i | ||||||
\(470\) | 45.7490 | + | 3.33376i | 2.11024 | + | 0.153775i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.71833 | + | 30.2958i | −0.309236 | + | 1.39448i | ||||
\(473\) | − | 1.53716i | − | 0.0706788i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.05931 | −0.323903 | ||||||||
\(476\) | 7.66263 | + | 1.12272i | 0.351216 | + | 0.0514599i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.4486 | + | 1.85446i | 1.16399 | + | 0.0848209i | ||||
\(479\) | −33.7292 | −1.54113 | −0.770564 | − | 0.637363i | \(-0.780025\pi\) | ||||
−0.770564 | + | 0.637363i | \(0.780025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.21528 | 0.328989 | ||||||||
\(482\) | 15.3094 | + | 1.11561i | 0.697325 | + | 0.0508145i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.4833 | + | 2.70816i | 0.840150 | + | 0.123098i | ||||
\(485\) | −46.0345 | −2.09032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.00662i | − | 0.272186i | −0.990696 | − | 0.136093i | \(-0.956545\pi\) | ||
0.990696 | − | 0.136093i | \(-0.0434546\pi\) | |||||||
\(488\) | −2.88374 | + | 13.0040i | −0.130541 | + | 0.588664i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.10168 | − | 0.298892i | −0.185295 | − | 0.0135026i | ||||
\(491\) | 26.2731i | 1.18569i | 0.805318 | + | 0.592844i | \(0.201995\pi\) | ||||
−0.805318 | + | 0.592844i | \(0.798005\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.5506i | − | 0.520215i | ||||||
\(494\) | 0.392530 | − | 5.38667i | 0.0176608 | − | 0.242358i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13084 | + | 7.11544i | −0.0956776 | + | 0.319493i | ||||
\(497\) | − | 9.72888i | − | 0.436400i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.9974 | 1.61147 | 0.805733 | − | 0.592279i | \(-0.201772\pi\) | ||||
0.805733 | + | 0.592279i | \(0.201772\pi\) | |||||||
\(500\) | 8.88179 | + | 1.30135i | 0.397206 | + | 0.0581983i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.681478 | − | 9.35189i | 0.0304158 | − | 0.417395i | ||||
\(503\) | −15.7775 | −0.703485 | −0.351743 | − | 0.936097i | \(-0.614411\pi\) | ||||
−0.351743 | + | 0.936097i | \(0.614411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.14561 | −0.0954783 | ||||||||
\(506\) | 0.123784 | − | 1.69869i | 0.00550288 | − | 0.0755158i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.89992 | − | 12.9670i | 0.0842954 | − | 0.575320i | ||||
\(509\) | −6.09029 | −0.269947 | −0.134974 | − | 0.990849i | \(-0.543095\pi\) | ||||
−0.134974 | + | 0.990849i | \(0.543095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.40756i | − | 0.416166i | ||||||
\(512\) | −17.9491 | − | 13.7779i | −0.793244 | − | 0.608904i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.25803 | − | 17.2639i | 0.0554893 | − | 0.761478i | ||||
\(515\) | 47.2605i | 2.08255i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3691i | 0.631954i | ||||||||
\(518\) | −5.44225 | − | 0.396580i | −0.239119 | − | 0.0174247i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.32994 | − | 15.0161i | 0.146027 | − | 0.658500i | ||||
\(521\) | 18.1215i | 0.793916i | 0.917837 | + | 0.396958i | \(0.129934\pi\) | ||||
−0.917837 | + | 0.396958i | \(0.870066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00317 | 0.175046 | 0.0875232 | − | 0.996162i | \(-0.472105\pi\) | ||||
0.0875232 | + | 0.996162i | \(0.472105\pi\) | |||||||
\(524\) | −3.38922 | + | 23.1316i | −0.148059 | + | 1.01051i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.05474 | + | 0.295472i | 0.176795 | + | 0.0128832i | ||||
\(527\) | −7.19037 | −0.313217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1261 | −0.962003 | ||||||||
\(530\) | 18.2068 | + | 1.32674i | 0.790851 | + | 0.0576298i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.592145 | + | 4.04142i | −0.0256728 | + | 0.175218i | ||||
\(533\) | −16.3109 | −0.706505 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.34480i | − | 0.187842i | ||||||
\(536\) | −12.1996 | − | 2.70536i | −0.526943 | − | 0.116854i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.71059 | − | 0.634746i | −0.375540 | − | 0.0273658i | ||||
\(539\) | − | 1.28828i | − | 0.0554903i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.52777i | 0.194664i | 0.995252 | + | 0.0973320i | \(0.0310309\pi\) | ||||
−0.995252 | + | 0.0973320i | \(0.968969\pi\) | |||||||
\(542\) | −2.00531 | + | 27.5187i | −0.0861353 | + | 1.18203i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.79243 | − | 20.4717i | 0.334097 | − | 0.877715i | ||||
\(545\) | − | 34.4198i | − | 1.47438i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.99785 | 0.0854218 | 0.0427109 | − | 0.999087i | \(-0.486401\pi\) | ||||
0.0427109 | + | 0.999087i | \(0.486401\pi\) | |||||||
\(548\) | 2.13359 | − | 14.5619i | 0.0911426 | − | 0.622052i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.457693 | − | 6.28090i | 0.0195161 | − | 0.267819i | ||||
\(551\) | 6.09203 | 0.259529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.4660 | 0.700206 | ||||||||
\(554\) | −0.290623 | + | 3.98821i | −0.0123474 | + | 0.169443i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.2140 | − | 4.42693i | −1.28136 | − | 0.187744i | ||||
\(557\) | 14.9242 | 0.632360 | 0.316180 | − | 0.948699i | \(-0.397600\pi\) | ||||
0.316180 | + | 0.948699i | \(0.397600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.23125i | 0.0943717i | ||||||||
\(560\) | −3.33701 | + | 11.1431i | −0.141014 | + | 0.470884i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.05848 | + | 41.9714i | −0.129014 | + | 1.77046i | ||||
\(563\) | 0.157861i | 0.00665305i | 0.999994 | + | 0.00332653i | \(0.00105887\pi\) | ||||
−0.999994 | + | 0.00332653i | \(0.998941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.5761i | 1.87533i | ||||||||
\(566\) | 43.3617 | + | 3.15980i | 1.82263 | + | 0.132816i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.8648 | − | 5.95747i | −1.12722 | − | 0.249970i | ||||
\(569\) | 11.8914i | 0.498514i | 0.968437 | + | 0.249257i | \(0.0801864\pi\) | ||||
−0.968437 | + | 0.249257i | \(0.919814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0748 | 0.589013 | 0.294507 | − | 0.955649i | \(-0.404845\pi\) | ||||
0.294507 | + | 0.955649i | \(0.404845\pi\) | |||||||
\(572\) | 4.76726 | + | 0.698495i | 0.199329 | + | 0.0292055i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.3028 | + | 0.896513i | 0.513509 | + | 0.0374197i | ||||
\(575\) | 3.23134 | 0.134756 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5261 | 1.06267 | 0.531333 | − | 0.847163i | \(-0.321691\pi\) | ||||
0.531333 | + | 0.847163i | \(0.321691\pi\) | |||||||
\(578\) | −2.82929 | − | 0.206172i | −0.117683 | − | 0.00857564i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.1657 | + | 2.51510i | 0.712766 | + | 0.104434i | ||||
\(581\) | −3.72150 | −0.154394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.71850i | 0.236836i | ||||||||
\(584\) | −25.9775 | − | 5.76071i | −1.07496 | − | 0.238380i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.04576 | − | 0.586299i | −0.332367 | − | 0.0242198i | ||||
\(587\) | − | 9.47422i | − | 0.391043i | −0.980699 | − | 0.195521i | \(-0.937360\pi\) | ||
0.980699 | − | 0.195521i | \(-0.0626399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.79234i | − | 0.156261i | ||||||
\(590\) | 3.27927 | − | 45.0012i | 0.135005 | − | 1.85267i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.42766 | + | 14.7851i | −0.181976 | + | 0.607664i | ||||
\(593\) | 18.9405i | 0.777792i | 0.921282 | + | 0.388896i | \(0.127143\pi\) | ||||
−0.921282 | + | 0.388896i | \(0.872857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2605 | −0.461635 | ||||||||
\(596\) | 33.0031 | + | 4.83560i | 1.35186 | + | 0.198074i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.179677 | + | 2.46571i | −0.00734756 | + | 0.100830i | ||||
\(599\) | 34.9184 | 1.42673 | 0.713364 | − | 0.700794i | \(-0.247171\pi\) | ||||
0.713364 | + | 0.700794i | \(0.247171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8342 | 1.05380 | 0.526899 | − | 0.849928i | \(-0.323355\pi\) | ||||
0.526899 | + | 0.849928i | \(0.323355\pi\) | |||||||
\(602\) | 0.122638 | − | 1.68296i | 0.00499836 | − | 0.0685922i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.77935 | + | 32.6193i | −0.194469 | + | 1.32726i | ||||
\(605\) | −27.1618 | −1.10429 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.4361i | − | 0.585943i | −0.956121 | − | 0.292972i | \(-0.905356\pi\) | ||
0.956121 | − | 0.292972i | \(-0.0946442\pi\) | |||||||
\(608\) | 10.7972 | + | 4.10988i | 0.437882 | + | 0.166678i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.40757 | − | 19.3161i | 0.0569910 | − | 0.782085i | ||||
\(611\) | − | 20.8574i | − | 0.843798i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 46.3647i | − | 1.87265i | −0.351133 | − | 0.936325i | \(-0.614204\pi\) | ||
0.351133 | − | 0.936325i | \(-0.385796\pi\) | |||||||
\(614\) | 9.13156 | + | 0.665422i | 0.368520 | + | 0.0268543i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.55739 | − | 0.788879i | −0.143332 | − | 0.0317848i | ||||
\(617\) | − | 29.3648i | − | 1.18218i | −0.806605 | − | 0.591091i | \(-0.798697\pi\) | ||
0.806605 | − | 0.591091i | \(-0.201303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.7590 | 0.553021 | 0.276510 | − | 0.961011i | \(-0.410822\pi\) | ||||
0.276510 | + | 0.961011i | \(0.410822\pi\) | |||||||
\(620\) | 1.56567 | − | 10.6858i | 0.0628789 | − | 0.429151i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.45175 | − | 0.251531i | −0.138403 | − | 0.0100855i | ||||
\(623\) | 12.2297 | 0.489974 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3350 | −1.21340 | ||||||||
\(626\) | 11.3322 | + | 0.825786i | 0.452927 | + | 0.0330050i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.64478 | − | 31.7008i | 0.185347 | − | 1.26500i | ||||
\(629\) | −14.9408 | −0.595729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9228i | 1.31064i | 0.755352 | + | 0.655319i | \(0.227466\pi\) | ||||
−0.755352 | + | 0.655319i | \(0.772534\pi\) | |||||||
\(632\) | 10.0830 | − | 45.4684i | 0.401078 | − | 1.80863i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.8129 | − | 1.95387i | −1.06488 | − | 0.0775981i | ||||
\(635\) | 19.0555i | 0.756195i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.86999i | 0.0740918i | ||||||||
\(638\) | −0.394980 | + | 5.42029i | −0.0156374 | + | 0.214591i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 28.7266 | + | 16.0381i | 1.13552 | + | 0.633962i | ||||
\(641\) | 39.5844i | 1.56349i | 0.623597 | + | 0.781746i | \(0.285670\pi\) | ||||
−0.623597 | + | 0.781746i | \(0.714330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0571 | 1.73744 | 0.868720 | − | 0.495303i | \(-0.164943\pi\) | ||||
0.868720 | + | 0.495303i | \(0.164943\pi\) | |||||||
\(644\) | 0.271050 | − | 1.84993i | 0.0106809 | − | 0.0728973i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.812818 | + | 11.1543i | −0.0319799 | + | 0.438859i | ||||
\(647\) | 39.4430 | 1.55066 | 0.775331 | − | 0.631555i | \(-0.217583\pi\) | ||||
0.775331 | + | 0.631555i | \(0.217583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1343 | 0.554819 | ||||||||
\(650\) | −0.664359 | + | 9.11697i | −0.0260583 | + | 0.357597i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.2367 | + | 1.79291i | 0.479227 | + | 0.0702159i | ||||
\(653\) | −43.4794 | −1.70148 | −0.850741 | − | 0.525585i | \(-0.823846\pi\) | ||||
−0.850741 | + | 0.525585i | \(0.823846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 33.9926i | − | 1.32820i | ||||||
\(656\) | 10.0092 | − | 33.4233i | 0.390793 | − | 1.30496i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.14640 | + | 15.7320i | −0.0446914 | + | 0.613298i | ||||
\(659\) | − | 26.8653i | − | 1.04652i | −0.852172 | − | 0.523262i | \(-0.824715\pi\) | ||
0.852172 | − | 0.523262i | \(-0.175285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.365746i | − | 0.0142259i | −0.999975 | − | 0.00711293i | \(-0.997736\pi\) | ||
0.999975 | − | 0.00711293i | \(-0.00226414\pi\) | |||||||
\(662\) | 50.5792 | + | 3.68574i | 1.96582 | + | 0.143250i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.27886 | + | 10.2764i | −0.0884369 | + | 0.398800i | ||||
\(665\) | − | 5.93900i | − | 0.230305i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.78858 | −0.107974 | ||||||||
\(668\) | 25.1775 | + | 3.68899i | 0.974148 | + | 0.142731i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.1212 | + | 1.32051i | 0.700085 | + | 0.0510156i | ||||
\(671\) | 6.06691 | 0.234211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2522 | 1.35887 | 0.679435 | − | 0.733735i | \(-0.262225\pi\) | ||||
0.679435 | + | 0.733735i | \(0.262225\pi\) | |||||||
\(674\) | 9.73613 | + | 0.709477i | 0.375022 | + | 0.0273280i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.8055 | + | 2.75536i | 0.723288 | + | 0.105976i | ||||
\(677\) | 28.6841 | 1.10242 | 0.551211 | − | 0.834366i | \(-0.314166\pi\) | ||||
0.551211 | + | 0.834366i | \(0.314166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15.8302i | − | 0.607508i | ||||||
\(680\) | −6.89535 | + | 31.0941i | −0.264425 | + | 1.19240i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.37418 | + | 0.245878i | 0.129204 | + | 0.00941516i | ||||
\(683\) | 22.7609i | 0.870921i | 0.900208 | + | 0.435460i | \(0.143414\pi\) | ||||
−0.900208 | + | 0.435460i | \(0.856586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.3992i | 0.817620i | ||||||||
\(686\) | 0.102782 | − | 1.41047i | 0.00392424 | − | 0.0538521i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.57213 | − | 1.36920i | −0.174311 | − | 0.0522004i | ||||
\(689\) | − | 8.30061i | − | 0.316228i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1270 | 1.37434 | 0.687168 | − | 0.726499i | \(-0.258854\pi\) | ||||
0.687168 | + | 0.726499i | \(0.258854\pi\) | |||||||
\(692\) | 22.2780 | + | 3.26416i | 0.846883 | + | 0.124085i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.77141 | − | 51.7548i | 0.143161 | − | 1.96459i | ||||
\(695\) | 44.4005 | 1.68421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.7753 | 1.27933 | ||||||||
\(698\) | 2.90421 | − | 39.8543i | 0.109926 | − | 1.50851i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00221 | − | 6.84012i | 0.0378799 | − | 0.258532i | ||||
\(701\) | 24.7739 | 0.935699 | 0.467849 | − | 0.883808i | \(-0.345029\pi\) | ||||
0.467849 | + | 0.883808i | \(0.345029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.88007i | − | 0.297202i | ||||||
\(704\) | −4.35673 | + | 9.34013i | −0.164201 | + | 0.352019i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.49903 | − | 34.2940i | 0.0940521 | − | 1.29067i | ||||
\(707\) | − | 0.737825i | − | 0.0277487i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.4819i | 0.881881i | 0.897536 | + | 0.440941i | \(0.145355\pi\) | ||||
−0.897536 | + | 0.440941i | \(0.854645\pi\) | |||||||
\(710\) | 39.9048 | + | 2.90789i | 1.49760 | + | 0.109131i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.48886 | − | 33.7705i | 0.280657 | − | 1.26560i | ||||
\(713\) | 1.73591i | 0.0650105i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.00564 | −0.261996 | ||||||||
\(716\) | −2.51684 | + | 17.1776i | −0.0940588 | + | 0.641955i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.75581 | − | 0.200818i | −0.102846 | − | 0.00749446i | ||||
\(719\) | −38.0908 | −1.42055 | −0.710274 | − | 0.703926i | \(-0.751429\pi\) | ||||
−0.710274 | + | 0.703926i | \(0.751429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2518 | −0.605248 | ||||||||
\(722\) | 20.9160 | + | 1.52416i | 0.778414 | + | 0.0567235i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.720759 | + | 4.91921i | −0.0267868 | + | 0.182821i | ||||
\(725\) | −10.3108 | −0.382933 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.53603i | 0.242408i | 0.992628 | + | 0.121204i | \(0.0386755\pi\) | ||||
−0.992628 | + | 0.121204i | \(0.961324\pi\) | |||||||
\(728\) | 5.16369 | + | 1.14509i | 0.191379 | + | 0.0424398i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.5868 | + | 2.81185i | 1.42816 | + | 0.104071i | ||||
\(731\) | − | 4.62028i | − | 0.170887i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.5549i | 1.20244i | 0.799082 | + | 0.601222i | \(0.205319\pi\) | ||||
−0.799082 | + | 0.601222i | \(0.794681\pi\) | |||||||
\(734\) | 2.19768 | − | 30.1587i | 0.0811178 | − | 1.11318i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.94231 | − | 1.88126i | −0.182176 | − | 0.0693442i | ||||
\(737\) | 5.69163i | 0.209654i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.47095 | −0.201252 | −0.100626 | − | 0.994924i | \(-0.532085\pi\) | ||||
−0.100626 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(740\) | 3.25329 | − | 22.2039i | 0.119593 | − | 0.816231i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.456234 | + | 6.26088i | −0.0167489 | + | 0.229844i | ||||
\(743\) | −7.23548 | −0.265444 | −0.132722 | − | 0.991153i | \(-0.542372\pi\) | ||||
−0.132722 | + | 0.991153i | \(0.542372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.4992 | −1.77687 | ||||||||
\(746\) | 3.39882 | − | 46.6419i | 0.124440 | − | 1.70768i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.87163 | − | 1.44638i | −0.360943 | − | 0.0528850i | ||||
\(749\) | 1.49407 | 0.0545923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 24.5924i | − | 0.897391i | −0.893685 | − | 0.448695i | \(-0.851889\pi\) | ||
0.893685 | − | 0.448695i | \(-0.148111\pi\) | |||||||
\(752\) | 42.7396 | + | 12.7991i | 1.55855 | + | 0.466735i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.573328 | − | 7.86775i | 0.0208794 | − | 0.286527i | ||||
\(755\) | − | 47.9352i | − | 1.74454i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.5168i | − | 1.18184i | −0.806728 | − | 0.590922i | \(-0.798764\pi\) | ||
0.806728 | − | 0.590922i | \(-0.201236\pi\) | |||||||
\(758\) | 24.0248 | + | 1.75070i | 0.872620 | + | 0.0635883i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.3996 | − | 3.63674i | −0.594877 | − | 0.131918i | ||||
\(761\) | − | 21.5639i | − | 0.781689i | −0.920457 | − | 0.390845i | \(-0.872183\pi\) | ||
0.920457 | − | 0.390845i | \(-0.127817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8362 | 0.428499 | ||||||||
\(764\) | −6.73337 | − | 0.986568i | −0.243605 | − | 0.0356928i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.1969 | + | 1.61750i | 0.802005 | + | 0.0584426i | ||||
\(767\) | −20.5164 | −0.740806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.56057 | −0.0562756 | −0.0281378 | − | 0.999604i | \(-0.508958\pi\) | ||||
−0.0281378 | + | 0.999604i | \(0.508958\pi\) | |||||||
\(770\) | 5.28413 | + | 0.385058i | 0.190427 | + | 0.0138765i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40.9688 | + | 6.00271i | 1.47450 | + | 0.216042i | ||||
\(773\) | −24.0539 | −0.865160 | −0.432580 | − | 0.901596i | \(-0.642397\pi\) | ||||
−0.432580 | + | 0.901596i | \(0.642397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.41855i | 0.230561i | ||||||||
\(776\) | −43.7127 | − | 9.69361i | −1.56919 | − | 0.347980i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.1383 | + | 2.34193i | 1.15221 | + | 0.0839624i | ||||
\(779\) | 17.8138i | 0.638244i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5336i | 0.448486i | ||||||||
\(782\) | 0.372061 | − | 5.10577i | 0.0133049 | − | 0.182582i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.83187 | − | 1.14752i | −0.136852 | − | 0.0409828i | ||||
\(785\) | 46.5854i | 1.66270i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.99996 | 0.142583 | 0.0712916 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712916 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(788\) | 32.3636 | + | 4.74189i | 1.15290 | + | 0.168923i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.92156 | + | 67.5384i | −0.175101 | + | 2.40291i | ||||
\(791\) | −15.3287 | −0.545025 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.80635 | −0.312723 | ||||||||
\(794\) | −2.43418 | + | 33.4041i | −0.0863858 | + | 1.18547i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.29715 | − | 22.5032i | 0.116865 | − | 0.797605i | ||||
\(797\) | 7.18205 | 0.254401 | 0.127201 | − | 0.991877i | \(-0.459401\pi\) | ||||
0.127201 | + | 0.991877i | \(0.459401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.1896i | 1.52794i | ||||||||
\(800\) | −18.2742 | − | 6.95598i | −0.646091 | − | 0.245931i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.155231 | + | 2.13023i | −0.00548139 | + | 0.0752209i | ||||
\(803\) | 12.1196i | 0.427691i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.71853i | 0.0958155i | ||||||||
\(806\) | −4.89774 | − | 0.356901i | −0.172516 | − | 0.0125713i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.03739 | − | 0.451806i | −0.0716751 | − | 0.0158945i | ||||
\(809\) | 48.2698i | 1.69707i | 0.529136 | + | 0.848537i | \(0.322516\pi\) | ||||
−0.529136 | + | 0.848537i | \(0.677484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.3182 | 0.713469 | 0.356735 | − | 0.934206i | \(-0.383890\pi\) | ||||
0.356735 | + | 0.934206i | \(0.383890\pi\) | |||||||
\(812\) | −0.864885 | + | 5.90288i | −0.0303515 | + | 0.207150i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.01116 | + | 0.510908i | 0.245741 | + | 0.0179073i | ||||
\(815\) | −17.9823 | −0.629891 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.43682 | 0.0852537 | ||||||||
\(818\) | −13.9095 | − | 1.01360i | −0.486335 | − | 0.0354395i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.35443 | + | 50.1943i | −0.256828 | + | 1.75286i | ||||
\(821\) | 35.0745 | 1.22411 | 0.612055 | − | 0.790815i | \(-0.290343\pi\) | ||||
0.612055 | + | 0.790815i | \(0.290343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.4211i | − | 0.537544i | −0.963204 | − | 0.268772i | \(-0.913382\pi\) | ||
0.963204 | − | 0.268772i | \(-0.0866179\pi\) | |||||||
\(824\) | −9.95176 | + | 44.8768i | −0.346686 | + | 1.56336i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.4749 | + | 1.12766i | 0.538440 | + | 0.0392364i | ||||
\(827\) | − | 27.5561i | − | 0.958218i | −0.877755 | − | 0.479109i | \(-0.840960\pi\) | ||
0.877755 | − | 0.479109i | \(-0.159040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 56.9495i | − | 1.97794i | −0.148124 | − | 0.988969i | \(-0.547323\pi\) | ||
0.148124 | − | 0.988969i | \(-0.452677\pi\) | |||||||
\(830\) | 1.11233 | − | 15.2644i | 0.0386095 | − | 0.529836i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.32396 | − | 13.5575i | 0.219244 | − | 0.470023i | ||||
\(833\) | − | 3.87222i | − | 0.134164i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.9992 | −1.28041 | ||||||||
\(836\) | 0.762851 | − | 5.20649i | 0.0263838 | − | 0.180070i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.13975 | − | 29.3636i | 0.0739163 | − | 1.01435i | ||||
\(839\) | −2.54853 | −0.0879849 | −0.0439925 | − | 0.999032i | \(-0.514008\pi\) | ||||
−0.0439925 | + | 0.999032i | \(0.514008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1020 | −0.693173 | ||||||||
\(842\) | −2.93401 | + | 40.2632i | −0.101113 | + | 1.38756i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.07393 | − | 0.743428i | −0.174652 | − | 0.0255898i | ||||
\(845\) | −27.6353 | −0.950683 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.34033i | − | 0.320937i | ||||||
\(848\) | 17.0091 | + | 5.09367i | 0.584094 | + | 0.174917i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.37570 | − | 18.8786i | 0.0471861 | − | 0.647532i | ||||
\(851\) | 3.60704i | 0.123648i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.1990i | 0.794319i | 0.917750 | + | 0.397159i | \(0.130004\pi\) | ||||
−0.917750 | + | 0.397159i | \(0.869996\pi\) | |||||||
\(854\) | 6.64234 | + | 0.484032i | 0.227296 | + | 0.0165632i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.914895 | − | 4.12566i | 0.0312705 | − | 0.141012i | ||||
\(857\) | − | 19.5713i | − | 0.668544i | −0.942477 | − | 0.334272i | \(-0.891510\pi\) | ||
0.942477 | − | 0.334272i | \(-0.108490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.8322 | −1.73437 | −0.867186 | − | 0.497985i | \(-0.834073\pi\) | ||||
−0.867186 | + | 0.497985i | \(0.834073\pi\) | |||||||
\(860\) | 6.86630 | + | 1.00605i | 0.234139 | + | 0.0343059i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.21196 | + | 0.671281i | 0.313761 | + | 0.0228639i | ||||
\(863\) | −39.1106 | −1.33134 | −0.665671 | − | 0.746246i | \(-0.731854\pi\) | ||||
−0.665671 | + | 0.746246i | \(0.731854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.7383 | −1.11314 | ||||||||
\(866\) | −20.0501 | − | 1.46106i | −0.681330 | − | 0.0496489i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.67459 | + | 0.538398i | 0.124724 | + | 0.0182744i | ||||
\(869\) | −21.2129 | −0.719598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.26162i | − | 0.279934i | ||||||
\(872\) | 7.24788 | − | 32.6838i | 0.245444 | − | 1.10681i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.69288 | + | 0.196232i | 0.0910882 | + | 0.00663765i | ||||
\(875\) | − | 4.48831i | − | 0.151733i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.1514i | − | 0.883070i | −0.897244 | − | 0.441535i | \(-0.854434\pi\) | ||
0.897244 | − | 0.441535i | \(-0.145566\pi\) | |||||||
\(878\) | −2.32093 | + | 31.8500i | −0.0783275 | + | 1.07488i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.29901 | − | 14.3555i | 0.144920 | − | 0.483924i | ||||
\(881\) | − | 49.2277i | − | 1.65852i | −0.558860 | − | 0.829262i | \(-0.688761\pi\) | ||
0.558860 | − | 0.829262i | \(-0.311239\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3014 | 1.49086 | 0.745430 | − | 0.666584i | \(-0.232244\pi\) | ||||
0.745430 | + | 0.666584i | \(0.232244\pi\) | |||||||
\(884\) | 14.3290 | + | 2.09948i | 0.481938 | + | 0.0706132i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.62326 | + | 22.2759i | −0.0545345 | + | 0.748374i | ||||
\(887\) | 6.83633 | 0.229542 | 0.114771 | − | 0.993392i | \(-0.463387\pi\) | ||||
0.114771 | + | 0.993392i | \(0.463387\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.55275 | −0.219772 | ||||||||
\(890\) | −3.65537 | + | 50.1625i | −0.122528 | + | 1.68145i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.398914 | − | 2.72261i | 0.0133566 | − | 0.0911596i | ||||
\(893\) | −22.7791 | −0.762272 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 25.2430i | − | 0.843780i | ||||||
\(896\) | −5.51514 | + | 9.87842i | −0.184248 | + | 0.330015i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.77369 | + | 38.0632i | −0.0925591 | + | 1.27018i | ||||
\(899\) | − | 5.53908i | − | 0.184739i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.1882i | 0.572622i | ||||||||
\(902\) | −15.8495 | − | 1.15496i | −0.527731 | − | 0.0384560i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.38651 | + | 42.3278i | −0.312191 | + | 1.40780i | ||||
\(905\) | − | 7.22895i | − | 0.240298i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.2295 | 0.804528 | 0.402264 | − | 0.915524i | \(-0.368223\pi\) | ||||
0.402264 | + | 0.915524i | \(0.368223\pi\) | |||||||
\(908\) | 7.93689 | − | 54.1696i | 0.263395 | − | 1.79768i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.67011 | − | 0.558926i | −0.254262 | − | 0.0185282i | ||||
\(911\) | 6.75748 | 0.223885 | 0.111943 | − | 0.993715i | \(-0.464293\pi\) | ||||
0.111943 | + | 0.993715i | \(0.464293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.79435 | 0.158670 | ||||||||
\(914\) | −53.5398 | − | 3.90148i | −1.77094 | − | 0.129049i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.56821 | − | 24.3532i | 0.117897 | − | 0.804652i | ||||
\(917\) | 11.6893 | 0.386014 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.77205i | 0.0584546i | 0.999573 | + | 0.0292273i | \(0.00930466\pi\) | ||||
−0.999573 | + | 0.0292273i | \(0.990695\pi\) | |||||||
\(920\) | 7.50680 | + | 1.66469i | 0.247492 | + | 0.0548832i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.7904 | + | 0.859177i | 0.388298 | + | 0.0282955i | ||||
\(923\) | − | 18.1929i | − | 0.598827i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.3370i | 0.438519i | ||||||||
\(926\) | 1.89863 | − | 26.0548i | 0.0623927 | − | 0.856212i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.7703 | + | 6.00287i | 0.517685 | + | 0.197054i | ||||
\(929\) | 15.3376i | 0.503212i | 0.967830 | + | 0.251606i | \(0.0809587\pi\) | ||||
−0.967830 | + | 0.251606i | \(0.919041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.04228 | 0.0669332 | ||||||||
\(932\) | −6.98266 | + | 47.6570i | −0.228725 | + | 1.56106i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.446126 | + | 6.12217i | −0.0145977 | + | 0.200324i | ||||
\(935\) | 14.5067 | 0.474420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.6373 | −1.58891 | −0.794456 | − | 0.607322i | \(-0.792244\pi\) | ||||
−0.794456 | + | 0.607322i | \(0.792244\pi\) | |||||||
\(938\) | −0.454091 | + | 6.23147i | −0.0148266 | + | 0.203465i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −64.1851 | − | 9.40436i | −2.09349 | − | 0.306736i | ||||
\(941\) | 34.4202 | 1.12207 | 0.561034 | − | 0.827793i | \(-0.310404\pi\) | ||||
0.561034 | + | 0.827793i | \(0.310404\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.15410i | − | 0.265534i | ||||||
\(944\) | 12.5899 | − | 42.0410i | 0.409766 | − | 1.36832i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.157993 | + | 2.16813i | −0.00513678 | + | 0.0704918i | ||||
\(947\) | 27.8402i | 0.904684i | 0.891844 | + | 0.452342i | \(0.149411\pi\) | ||||
−0.891844 | + | 0.452342i | \(0.850589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 17.5921i | − | 0.571062i | ||||||
\(950\) | 9.95697 | + | 0.725570i | 0.323047 | + | 0.0235406i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.6925 | − | 2.37115i | −0.346547 | − | 0.0768494i | ||||
\(953\) | 22.7401i | 0.736624i | 0.929702 | + | 0.368312i | \(0.120064\pi\) | ||||
−0.929702 | + | 0.368312i | \(0.879936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.89491 | 0.320192 | ||||||||
\(956\) | −35.7040 | − | 5.23132i | −1.15475 | − | 0.169193i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47.5742 | + | 3.46676i | 1.53705 | + | 0.112006i | ||||
\(959\) | −7.35868 | −0.237624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.5519 | 0.888770 | ||||||||
\(962\) | −10.1770 | − | 0.741602i | −0.328119 | − | 0.0239102i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.4789 | − | 3.14707i | −0.691787 | − | 0.101360i | ||||
\(965\) | −60.2050 | −1.93807 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0470i | 0.901931i | 0.892541 | + | 0.450965i | \(0.148920\pi\) | ||||
−0.892541 | + | 0.450965i | \(0.851080\pi\) | |||||||
\(968\) | −25.7919 | − | 5.71954i | −0.828982 | − | 0.183833i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 64.9305 | + | 4.73152i | 2.08479 | + | 0.151920i | ||||
\(971\) | 10.0931i | 0.323904i | 0.986799 | + | 0.161952i | \(0.0517790\pi\) | ||||
−0.986799 | + | 0.161952i | \(0.948221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.2683i | 0.489479i | ||||||||
\(974\) | −0.617373 | + | 8.47218i | −0.0197819 | + | 0.271466i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.40401 | − | 18.0454i | 0.172978 | − | 0.577620i | ||||
\(977\) | − | 1.93536i | − | 0.0619176i | −0.999521 | − | 0.0309588i | \(-0.990144\pi\) | ||
0.999521 | − | 0.0309588i | \(-0.00985607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7553 | −0.503543 | ||||||||
\(980\) | 5.75460 | + | 0.843159i | 0.183824 | + | 0.0269337i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.70040 | − | 37.0575i | 0.0861733 | − | 1.18255i | ||||
\(983\) | −45.8652 | −1.46287 | −0.731436 | − | 0.681910i | \(-0.761150\pi\) | ||||
−0.731436 | + | 0.681910i | \(0.761150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.5594 | −1.51537 | ||||||||
\(986\) | −1.18720 | + | 16.2919i | −0.0378081 | + | 0.518839i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.10731 | + | 7.55742i | −0.0352281 | + | 0.240433i | ||||
\(989\) | −1.11544 | −0.0354688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5946i | 0.654209i | 0.944988 | + | 0.327105i | \(0.106073\pi\) | ||||
−0.944988 | + | 0.327105i | \(0.893927\pi\) | |||||||
\(992\) | 3.73684 | − | 9.81713i | 0.118645 | − | 0.311694i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.999955 | + | 13.7223i | −0.0317166 | + | 0.435246i | ||||
\(995\) | 33.0692i | 1.04837i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0478i | 0.349889i | 0.984578 | + | 0.174944i | \(0.0559745\pi\) | ||||
−0.984578 | + | 0.174944i | \(0.944025\pi\) | |||||||
\(998\) | −50.7734 | − | 3.69989i | −1.60720 | − | 0.117118i | ||||
\(999\) | 0 | 0 |
(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 | 1512.2.j.d.323.1 | ✓ | 48 | |
3.2 | odd | 2 | inner | 1512.2.j.d.323.48 | yes | 48 | |
4.3 | odd | 2 | 6048.2.j.d.5615.7 | 48 | |||
8.3 | odd | 2 | inner | 1512.2.j.d.323.47 | yes | 48 | |
8.5 | even | 2 | 6048.2.j.d.5615.41 | 48 | |||
12.11 | even | 2 | 6048.2.j.d.5615.42 | 48 | |||
24.5 | odd | 2 | 6048.2.j.d.5615.8 | 48 | |||
24.11 | even | 2 | inner | 1512.2.j.d.323.2 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1512.2.j.d.323.2 | yes | 48 | 24.11 | even | 2 | inner | |
1512.2.j.d.323.47 | yes | 48 | 8.3 | odd | 2 | inner | |
1512.2.j.d.323.48 | yes | 48 | 3.2 | odd | 2 | inner | |
6048.2.j.d.5615.7 | 48 | 4.3 | odd | 2 | |||
6048.2.j.d.5615.8 | 48 | 24.5 | odd | 2 | |||
6048.2.j.d.5615.41 | 48 | 8.5 | even | 2 | |||
6048.2.j.d.5615.42 | 48 | 12.11 | even | 2 |