Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{14} + 178x^{12} - 1024x^{10} + 4267x^{8} - 7936x^{6} + 10594x^{4} - 2800x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 959.1 | ||
Root | \(1.21704 - 0.702656i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.959 |
Dual form | 1152.2.p.d.191.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.65068 | + | 0.524648i | −0.953021 | + | 0.302905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.01255 | + | 1.75379i | −0.452826 | + | 0.784317i | −0.998560 | − | 0.0536411i | \(-0.982917\pi\) |
0.545735 | + | 0.837958i | \(0.316251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.09406 | + | 2.36371i | −1.54741 | + | 0.893398i | −0.549072 | + | 0.835775i | \(0.685019\pi\) |
−0.998338 | + | 0.0576227i | \(0.981648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.44949 | − | 1.73205i | 0.816497 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93038 | + | 1.69185i | −0.883542 | + | 0.510113i | −0.871825 | − | 0.489818i | \(-0.837063\pi\) |
−0.0117176 | + | 0.999931i | \(0.503730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.51787 | − | 3.18575i | −1.53038 | − | 0.883567i | −0.999344 | − | 0.0362198i | \(-0.988468\pi\) |
−0.531039 | − | 0.847347i | \(-0.678198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.751275 | − | 3.42617i | 0.193978 | − | 0.884634i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.87832i | − | 1.18317i | −0.806244 | − | 0.591583i | \(-0.798503\pi\) | ||
0.806244 | − | 0.591583i | \(-0.201497\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48393 | 0.340436 | 0.170218 | − | 0.985406i | \(-0.445553\pi\) | ||||
0.170218 | + | 0.985406i | \(0.445553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.51787 | − | 6.04967i | 1.20410 | − | 1.32015i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.751275 | − | 1.30125i | 0.156652 | − | 0.271328i | −0.777008 | − | 0.629491i | \(-0.783263\pi\) |
0.933659 | + | 0.358163i | \(0.116597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.449490 | + | 0.778539i | 0.0898979 | + | 0.155708i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.13461 | + | 4.14418i | −0.603256 | + | 0.797548i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.49278 | + | 6.04967i | 0.648592 | + | 1.12339i | 0.983459 | + | 0.181129i | \(0.0579753\pi\) |
−0.334867 | + | 0.942265i | \(0.608691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.93430 | + | 3.42617i | 1.06583 | + | 0.615358i | 0.927040 | − | 0.374963i | \(-0.122345\pi\) |
0.138792 | + | 0.990321i | \(0.455678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.94949 | − | 4.33013i | 0.687518 | − | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 9.57348i | − | 1.61821i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.86392i | 0.470826i | 0.971895 | + | 0.235413i | \(0.0756442\pi\) | ||||
−0.971895 | + | 0.235413i | \(0.924356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.7796 | + | 2.36371i | 1.72612 | + | 0.378496i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62372 | + | 2.66951i | 0.722104 | + | 0.416907i | 0.815527 | − | 0.578719i | \(-0.196447\pi\) |
−0.0934223 | + | 0.995627i | \(0.529781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.76363 | + | 4.78674i | 0.421449 | + | 0.729971i | 0.996081 | − | 0.0884405i | \(-0.0281883\pi\) |
−0.574632 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.557419 | + | 6.04967i | 0.0830950 | + | 0.901831i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.09406 | − | 7.09113i | −0.597180 | − | 1.03435i | −0.993235 | − | 0.116120i | \(-0.962954\pi\) |
0.396055 | − | 0.918227i | \(-0.370379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.67423 | − | 13.2922i | 1.09632 | − | 1.89888i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.55940 | + | 8.05254i | 0.358387 | + | 1.12758i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.96046 | −0.681371 | −0.340686 | − | 0.940177i | \(-0.610659\pi\) | ||||
−0.340686 | + | 0.940177i | \(0.610659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.85234i | − | 0.923970i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.44949 | + | 0.778539i | −0.324443 | + | 0.103120i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.88242 | − | 4.55092i | −1.02620 | − | 0.592479i | −0.110309 | − | 0.993897i | \(-0.535184\pi\) |
−0.915895 | + | 0.401418i | \(0.868517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.51787 | − | 3.18575i | 0.706491 | − | 0.407893i | −0.103269 | − | 0.994653i | \(-0.532930\pi\) |
0.809761 | + | 0.586760i | \(0.199597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.93430 | + | 12.8810i | −0.747652 | + | 1.62285i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.1742 | − | 6.45145i | 1.38599 | − | 0.800204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.48977 | − | 9.50857i | 0.670683 | − | 1.16166i | −0.307028 | − | 0.951700i | \(-0.599335\pi\) |
0.977711 | − | 0.209956i | \(-0.0673321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.557419 | + | 2.54209i | −0.0671053 | + | 0.306032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.68558 | −0.793432 | −0.396716 | − | 0.917941i | \(-0.629850\pi\) | ||||
−0.396716 | + | 0.917941i | \(0.629850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.449490 | 0.0526088 | 0.0263044 | − | 0.999654i | \(-0.491626\pi\) | ||||
0.0263044 | + | 0.999654i | \(0.491626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.15042 | − | 1.04930i | −0.132839 | − | 0.121162i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.99810 | − | 13.8531i | 0.911468 | − | 1.57871i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.93430 | + | 3.42617i | −0.667661 | + | 0.385474i | −0.795190 | − | 0.606361i | \(-0.792629\pi\) |
0.127529 | + | 0.991835i | \(0.459296\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.00000 | − | 8.48528i | 0.333333 | − | 0.942809i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.06499 | − | 3.50162i | 0.665719 | − | 0.384353i | −0.128734 | − | 0.991679i | \(-0.541091\pi\) |
0.794452 | + | 0.607326i | \(0.207758\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.55552 | + | 4.93953i | 0.927977 | + | 0.535768i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.93940 | − | 8.15359i | −0.958404 | − | 0.874156i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.142865i | 0.0151436i | 0.999971 | + | 0.00757181i | \(0.00241020\pi\) | ||||
−0.999971 | + | 0.00757181i | \(0.997590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.1207 | 3.15751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.5932 | − | 2.54209i | −1.20216 | − | 0.263603i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50255 | + | 2.60249i | −0.154158 | + | 0.267010i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.724745 | + | 1.25529i | 0.0735867 | + | 0.127456i | 0.900471 | − | 0.434916i | \(-0.143222\pi\) |
−0.826884 | + | 0.562372i | \(0.809889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24755 | + | 9.21975i | −0.426895 | + | 0.926619i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.03765 | − | 5.26136i | −0.302257 | − | 0.523525i | 0.674390 | − | 0.738376i | \(-0.264407\pi\) |
−0.976647 | + | 0.214851i | \(0.931073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.09406 | + | 2.36371i | 0.403400 | + | 0.232903i | 0.687950 | − | 0.725758i | \(-0.258511\pi\) |
−0.284550 | + | 0.958661i | \(0.591844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.02270 | + | 15.8028i | 0.490166 | + | 1.54219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.9079i | − | 1.15118i | −0.817739 | − | 0.575590i | \(-0.804773\pi\) | ||
0.817739 | − | 0.575590i | \(-0.195227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.15122i | 0.397615i | 0.980039 | + | 0.198808i | \(0.0637069\pi\) | ||||
−0.980039 | + | 0.198808i | \(0.936293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.50255 | − | 4.72742i | −0.142616 | − | 0.448707i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.39898 | − | 3.69445i | −0.601965 | − | 0.347545i | 0.167849 | − | 0.985813i | \(-0.446318\pi\) |
−0.769814 | + | 0.638268i | \(0.779651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.52140 | + | 2.63515i | 0.141872 | + | 0.245729i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.0339 | + | 1.75379i | −1.75968 | + | 0.162138i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5309 | + | 19.9721i | 1.05704 | + | 1.83084i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.224745 | − | 0.389270i | 0.0204314 | − | 0.0353881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.03284 | − | 1.98068i | −0.814464 | − | 0.178592i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9460 | −1.06848 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.45483i | − | 0.838981i | −0.907760 | − | 0.419490i | \(-0.862209\pi\) | ||
0.907760 | − | 0.419490i | \(-0.137791\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.07321 | − | 6.45145i | −0.622762 | − | 0.568018i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5168 | − | 6.07186i | −0.918854 | − | 0.530501i | −0.0355850 | − | 0.999367i | \(-0.511329\pi\) |
−0.883269 | + | 0.468866i | \(0.844663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.07529 | + | 3.50757i | −0.526795 | + | 0.304145i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.09406 | − | 9.69362i | −0.352361 | − | 0.834294i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.27526 | + | 5.35507i | −0.792439 | + | 0.457515i | −0.840820 | − | 0.541314i | \(-0.817927\pi\) |
0.0483818 | + | 0.998829i | \(0.484594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50559 | − | 6.07186i | 0.297340 | − | 0.515008i | −0.678186 | − | 0.734890i | \(-0.737234\pi\) |
0.975527 | + | 0.219882i | \(0.0705671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4783 | + | 9.55724i | 0.882435 | + | 0.804865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.5593 | 1.80288 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.1464 | −1.17480 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.69400 | + | 25.9674i | −0.469634 | + | 2.14175i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.49278 | − | 6.04967i | 0.286139 | − | 0.495608i | −0.686745 | − | 0.726898i | \(-0.740961\pi\) |
0.972885 | + | 0.231290i | \(0.0742946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.25382 | − | 1.30125i | 0.183414 | − | 0.105894i | −0.405482 | − | 0.914103i | \(-0.632896\pi\) |
0.588896 | + | 0.808209i | \(0.299563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.44949 | − | 11.9494i | −0.683101 | − | 0.966050i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0175 | + | 6.93833i | −0.965272 | + | 0.557300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9586 | + | 7.48163i | 1.03421 | + | 0.597099i | 0.918187 | − | 0.396148i | \(-0.129653\pi\) |
0.116019 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.18813 | − | 2.60249i | 0.649361 | − | 0.206391i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.10318i | 0.559809i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.63487 | −0.284705 | −0.142352 | − | 0.989816i | \(-0.545467\pi\) | ||||
−0.142352 | + | 0.989816i | \(0.545467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.59506 | + | 11.3110i | 0.279875 | + | 0.880562i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59151 | − | 4.48863i | 0.200537 | − | 0.347341i | −0.748164 | − | 0.663513i | \(-0.769065\pi\) |
0.948702 | + | 0.316173i | \(0.102398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7980 | + | 23.8988i | 1.06138 | + | 1.83837i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.63487 | − | 2.57024i | 0.277965 | − | 0.196551i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.01255 | − | 1.75379i | −0.0769827 | − | 0.133338i | 0.824964 | − | 0.565185i | \(-0.191195\pi\) |
−0.901947 | + | 0.431847i | \(0.857862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.68048 | − | 2.12493i | −0.278218 | − | 0.160629i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.3990 | + | 3.37662i | 1.15746 | + | 0.253802i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16.5767i | − | 1.23900i | −0.784996 | − | 0.619501i | \(-0.787335\pi\) | ||
0.784996 | − | 0.619501i | \(-0.212665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.6220i | − | 1.68148i | −0.541436 | − | 0.840742i | \(-0.682119\pi\) | ||
0.541436 | − | 0.840742i | \(-0.317881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.43685 | + | 8.15359i | −0.549748 | + | 0.602731i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.02270 | − | 2.89986i | −0.369277 | − | 0.213202i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.25340 | + | 14.2953i | 0.603548 | + | 1.04538i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.03765 | − | 24.3758i | 0.220956 | − | 1.77308i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.59151 | − | 4.48863i | −0.187515 | − | 0.324786i | 0.756906 | − | 0.653524i | \(-0.226710\pi\) |
−0.944421 | + | 0.328738i | \(0.893377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.376276 | + | 0.651729i | −0.0270849 | + | 0.0469124i | −0.879250 | − | 0.476360i | \(-0.841956\pi\) |
0.852165 | + | 0.523273i | \(0.175289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.0604 | + | 16.5118i | −1.07849 | + | 1.18244i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0213 | 1.28396 | 0.641982 | − | 0.766719i | \(-0.278112\pi\) | ||||
0.641982 | + | 0.766719i | \(0.278112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.12493i | 0.150632i | 0.997160 | + | 0.0753160i | \(0.0239965\pi\) | ||||
−0.997160 | + | 0.0753160i | \(0.976003\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.07321 | + | 18.5758i | −0.287302 | + | 1.31024i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.5993 | − | 16.5118i | −2.00728 | − | 1.15890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.36349 | + | 5.40602i | −0.653975 | + | 0.377572i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.413584 | − | 4.48863i | −0.0287461 | − | 0.311982i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.34847 | + | 2.51059i | −0.300790 | + | 0.173661i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.33884 | + | 5.78304i | −0.229855 | + | 0.398121i | −0.957765 | − | 0.287552i | \(-0.907159\pi\) |
0.727910 | + | 0.685673i | \(0.240492\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0357 | − | 3.50757i | 0.756157 | − | 0.240335i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1932 | −0.763372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.3939 | −2.19904 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.741964 | + | 0.235824i | −0.0501373 | + | 0.0159355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5411 | + | 26.9179i | −1.04541 | + | 1.81070i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9627 | − | 9.21605i | 1.06894 | − | 0.617152i | 0.141048 | − | 0.990003i | \(-0.454953\pi\) |
0.927891 | + | 0.372850i | \(0.121620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.44949 | + | 1.12848i | 0.163299 | + | 0.0752323i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2862 | − | 9.98022i | 1.14733 | − | 0.662410i | 0.199093 | − | 0.979981i | \(-0.436200\pi\) |
0.948235 | + | 0.317570i | \(0.102867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9586 | − | 7.48163i | −0.856326 | − | 0.494400i | 0.00645448 | − | 0.999979i | \(-0.497945\pi\) |
−0.862780 | + | 0.505579i | \(0.831279\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.93430 | + | 27.0633i | −0.390448 | + | 1.78063i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.75663i | 0.639178i | 0.947556 | + | 0.319589i | \(0.103545\pi\) | ||||
−0.947556 | + | 0.319589i | \(0.896455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.5818 | 1.08167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.99810 | − | 8.76893i | 0.519533 | − | 0.569603i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.6199 | + | 21.8583i | −0.816312 | + | 1.41389i | 0.0920698 | + | 0.995753i | \(0.470652\pi\) |
−0.908382 | + | 0.418142i | \(0.862682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.94949 | + | 8.57277i | 0.318825 | + | 0.552221i | 0.980243 | − | 0.197797i | \(-0.0633786\pi\) |
−0.661418 | + | 0.750017i | \(0.730045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500258 | + | 15.5804i | −0.0320915 | + | 0.999485i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.5411 | + | 26.9179i | 0.992883 | + | 1.71972i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.18813 | − | 4.72742i | −0.520998 | − | 0.300798i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.17423 | + | 8.96204i | −0.518021 | + | 0.567946i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2037i | 1.14901i | 0.818503 | + | 0.574503i | \(0.194804\pi\) | ||||
−0.818503 | + | 0.574503i | \(0.805196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.08419i | 0.319640i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.7139 | − | 3.66495i | −1.04667 | − | 0.229508i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.05051 | − | 2.91591i | −0.315042 | − | 0.181890i | 0.334138 | − | 0.942524i | \(-0.391555\pi\) |
−0.649181 | + | 0.760634i | \(0.724888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.76947 | − | 11.7251i | −0.420635 | − | 0.728560i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.0339 | + | 8.76893i | 1.17817 | + | 0.542783i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1224 | − | 24.4608i | −0.870826 | − | 1.50832i | −0.861143 | − | 0.508362i | \(-0.830251\pi\) |
−0.00968287 | − | 0.999953i | \(-0.503082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.02270 | − | 8.69958i | 0.308542 | − | 0.534411i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0749536 | − | 0.235824i | −0.00458708 | − | 0.0144322i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.910261 | 0.0554996 | 0.0277498 | − | 0.999615i | \(-0.491166\pi\) | ||||
0.0277498 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.9097i | 1.14868i | 0.818617 | + | 0.574340i | \(0.194741\pi\) | ||||
−0.818617 | + | 0.574340i | \(0.805259\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −49.7196 | + | 15.8028i | −3.00917 | + | 0.956426i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.63435 | − | 1.52094i | −0.158857 | − | 0.0917163i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.11294 | + | 5.26136i | −0.547543 | + | 0.316124i | −0.748131 | − | 0.663551i | \(-0.769048\pi\) |
0.200587 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.4703 | − | 1.88614i | 1.22553 | − | 0.112920i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0732 | + | 11.0119i | −1.13781 | + | 0.656916i | −0.945888 | − | 0.324493i | \(-0.894806\pi\) |
−0.191925 | + | 0.981410i | \(0.561473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1083 | − | 17.5081i | 0.600877 | − | 1.04075i | −0.391812 | − | 0.920045i | \(-0.628152\pi\) |
0.992689 | − | 0.120704i | \(-0.0385151\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.11484 | − | 5.08419i | 0.0660372 | − | 0.301161i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.2398 | −1.48986 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.79796 | −0.399880 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.85491 | − | 1.69185i | −0.108737 | − | 0.0991783i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.01255 | − | 1.75379i | 0.0591537 | − | 0.102457i | −0.834932 | − | 0.550353i | \(-0.814493\pi\) |
0.894086 | + | 0.447896i | \(0.147826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.9627 | − | 9.21605i | 0.929382 | − | 0.536579i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.17423 | − | 17.4473i | 0.126162 | − | 1.01240i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.29088 | + | 4.78674i | −0.479474 | + | 0.276824i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.6289 | − | 13.0648i | −1.30431 | − | 0.753043i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.77454 | + | 7.09113i | 0.446636 | + | 0.407374i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9029i | 0.738818i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.96786 | 0.169384 | 0.0846922 | − | 0.996407i | \(-0.473009\pi\) | ||||
0.0846922 | + | 0.996407i | \(0.473009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.99810 | − | 1.75379i | −0.454996 | − | 0.0997694i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6250 | − | 27.0633i | 0.886011 | − | 1.53462i | 0.0414609 | − | 0.999140i | \(-0.486799\pi\) |
0.844550 | − | 0.535476i | \(-0.179868\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.94949 | − | 3.37662i | −0.110192 | − | 0.190858i | 0.805656 | − | 0.592384i | \(-0.201813\pi\) |
−0.915847 | + | 0.401526i | \(0.868480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.5818 | − | 23.4501i | −0.934276 | − | 1.32127i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.45323 | − | 14.6414i | −0.474781 | − | 0.822345i | 0.524802 | − | 0.851224i | \(-0.324139\pi\) |
−0.999583 | + | 0.0288797i | \(0.990806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4703 | − | 11.8185i | −1.14612 | − | 0.661711i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.24745 | + | 19.6561i | 0.348699 | + | 1.09710i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.23907i | − | 0.402792i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.72784i | − | 0.317723i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.17793 | − | 6.85234i | −0.120440 | − | 0.378935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.5227 | + | 19.3543i | 1.84817 | + | 1.06704i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8778 | + | 29.2332i | 0.927687 | + | 1.60680i | 0.787182 | + | 0.616721i | \(0.211539\pi\) |
0.140505 | + | 0.990080i | \(0.455127\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.96046 | + | 7.01514i | 0.271831 | + | 0.384428i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1173 | + | 19.2558i | 0.607405 | + | 1.05206i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0505103 | + | 0.0874863i | −0.00275147 | + | 0.00476568i | −0.867398 | − | 0.497615i | \(-0.834209\pi\) |
0.864646 | + | 0.502381i | \(0.167542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5010 | + | 2.74115i | 0.678959 | + | 0.148879i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.1863 | −1.25561 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.4667i | 2.13100i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.89388 | − | 3.55159i | −0.209639 | − | 0.191211i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.60805 | + | 5.54721i | 0.515787 | + | 0.297790i | 0.735209 | − | 0.677840i | \(-0.237084\pi\) |
−0.219422 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.9190 | − | 10.3455i | 0.959183 | − | 0.553784i | 0.0632614 | − | 0.997997i | \(-0.479850\pi\) |
0.895921 | + | 0.444213i | \(0.146516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.4987 | − | 12.8810i | 1.62790 | − | 0.687537i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.62372 | + | 2.66951i | −0.246096 | + | 0.142084i | −0.617975 | − | 0.786197i | \(-0.712047\pi\) |
0.371879 | + | 0.928281i | \(0.378714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.76947 | − | 11.7251i | 0.359286 | − | 0.622302i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.5122 | − | 26.9179i | −1.56195 | − | 1.42465i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.7474 | 1.57001 | 0.785004 | − | 0.619491i | \(-0.212661\pi\) | ||||
0.785004 | + | 0.619491i | \(0.212661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7980 | −0.884103 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.166753 | + | 0.760471i | −0.00875224 | + | 0.0399144i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.455130 | + | 0.788309i | −0.0238226 | + | 0.0412620i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4419 | + | 6.02866i | −0.545065 | + | 0.314694i | −0.747129 | − | 0.664679i | \(-0.768568\pi\) |
0.202064 | + | 0.979372i | \(0.435235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.9495 | − | 1.46959i | 0.830297 | − | 0.0765039i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3084 | − | 11.7251i | 1.05436 | − | 0.608735i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4783 | + | 6.04967i | 0.542547 | + | 0.313240i | 0.746111 | − | 0.665822i | \(-0.231919\pi\) |
−0.203563 | + | 0.979062i | \(0.565252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.7190 | − | 6.26745i | 1.01829 | − | 0.323649i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 44.5084i | − | 2.29230i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.60324 | 0.390552 | 0.195276 | − | 0.980748i | \(-0.437440\pi\) | ||||
0.195276 | + | 0.980748i | \(0.437440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.96046 | + | 15.6069i | 0.254132 | + | 0.799566i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2822 | − | 21.2734i | 0.627591 | − | 1.08702i | −0.360443 | − | 0.932781i | \(-0.617375\pi\) |
0.988034 | − | 0.154238i | \(-0.0492921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.1969 | + | 28.0539i | 0.825472 | + | 1.42976i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.0604 | + | 6.93833i | 0.765561 | + | 0.352695i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.9586 | − | 22.4449i | −0.657025 | − | 1.13800i | −0.981382 | − | 0.192066i | \(-0.938481\pi\) |
0.324357 | − | 0.945935i | \(-0.394852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.34789 | − | 3.66495i | −0.321026 | − | 0.185345i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.5454 | + | 4.50510i | 1.03638 | + | 0.227252i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13.8767i | − | 0.698211i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9094i | 1.19998i | 0.800009 | + | 0.599988i | \(0.204828\pi\) | ||||
−0.800009 | + | 0.599988i | \(0.795172\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.18813 | − | 8.97727i | 0.409919 | − | 0.449426i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6237 | − | 9.59771i | −0.830149 | − | 0.479287i | 0.0237546 | − | 0.999718i | \(-0.492438\pi\) |
−0.853904 | + | 0.520431i | \(0.825771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8298 | − | 37.8104i | −1.08742 | − | 1.88347i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.8437 | + | 13.8531i | 0.588519 | + | 0.688367i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.84534 | − | 8.39237i | −0.240174 | − | 0.415994i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3990 | − | 30.1359i | 0.860324 | − | 1.49013i | −0.0112920 | − | 0.999936i | \(-0.503594\pi\) |
0.871616 | − | 0.490189i | \(-0.163072\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5010 | − | 13.7057i | 0.616627 | − | 0.676055i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 43.0282 | 2.11728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.1823i | 0.696179i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.60102 | + | 11.8619i | −0.127373 | + | 0.580880i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.8252 | + | 17.7969i | 1.50591 | + | 0.869437i | 0.999976 | + | 0.00686390i | \(0.00218486\pi\) |
0.505933 | + | 0.862573i | \(0.331148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7080 | − | 7.33697i | 0.619350 | − | 0.357582i | −0.157266 | − | 0.987556i | \(-0.550268\pi\) |
0.776616 | + | 0.629974i | \(0.216935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.3106 | − | 10.2785i | −1.08478 | − | 0.499758i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.79796 | − | 2.19275i | 0.184228 | − | 0.106364i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0604 | + | 26.0853i | −0.728821 | + | 1.26236i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −35.5875 | + | 11.3110i | −1.71818 | + | 0.546101i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00510 | 0.144750 | 0.0723752 | − | 0.997377i | \(-0.476942\pi\) | ||||
0.0723752 | + | 0.997377i | \(0.476942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.2474 | −1.26137 | −0.630686 | − | 0.776038i | \(-0.717226\pi\) | ||||
−0.630686 | + | 0.776038i | \(0.717226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.3512 | − | 7.42189i | 1.11961 | − | 0.355852i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.11484 | − | 1.93095i | 0.0533299 | − | 0.0923701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4419 | + | 6.02866i | −0.498367 | + | 0.287732i | −0.728039 | − | 0.685536i | \(-0.759568\pi\) |
0.229672 | + | 0.973268i | \(0.426235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.22474 | − | 45.8512i | −0.201178 | − | 2.18339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7339 | + | 18.3216i | −1.50772 | + | 0.870484i | −0.507764 | + | 0.861496i | \(0.669528\pi\) |
−0.999960 | + | 0.00898805i | \(0.997139\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.250554 | − | 0.144657i | −0.0118774 | − | 0.00685742i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.59151 | + | 11.8185i | −0.122574 | + | 0.558998i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.8980i | 1.78852i | 0.447549 | + | 0.894259i | \(0.352297\pi\) | ||||
−0.447549 | + | 0.894259i | \(0.647703\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0657 | −0.850680 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.03765 | + | 3.33040i | −0.142721 | + | 0.156476i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.4987 | + | 52.8253i | −1.42980 | + | 2.47649i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0732 | + | 20.9114i | 0.564761 | + | 0.978195i | 0.997072 | + | 0.0764703i | \(0.0243650\pi\) |
−0.432311 | + | 0.901725i | \(0.642302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.2166 | + | 15.2916i | 0.943631 | + | 0.713751i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.51787 | − | 9.55724i | −0.256993 | − | 0.445125i | 0.708442 | − | 0.705769i | \(-0.249398\pi\) |
−0.965435 | + | 0.260644i | \(0.916065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.93430 | − | 3.42617i | −0.275790 | − | 0.159228i | 0.355726 | − | 0.934590i | \(-0.384234\pi\) |
−0.631516 | + | 0.775363i | \(0.717567\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.1969 | − | 17.7579i | 0.751115 | − | 0.823505i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 20.7739i | − | 0.961302i | −0.876912 | − | 0.480651i | \(-0.840400\pi\) | ||
0.876912 | − | 0.480651i | \(-0.159600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.9049i | 2.39675i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.3157 | − | 5.55110i | −1.16648 | − | 0.255781i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.1969 | − | 9.35131i | −0.744736 | − | 0.429974i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.667010 | + | 1.15530i | 0.0306045 | + | 0.0530086i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.1506 | + | 8.59176i | −0.556337 | + | 0.393390i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.43175 | − | 7.67602i | −0.202492 | − | 0.350726i | 0.746839 | − | 0.665005i | \(-0.231571\pi\) |
−0.949331 | + | 0.314279i | \(0.898237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.12372 | − | 15.8028i | 0.416006 | − | 0.720544i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.72666 | − | 11.7251i | −0.169569 | − | 0.533509i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.93536 | −0.133288 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.9097i | − | 0.856879i | −0.903571 | − | 0.428439i | \(-0.859064\pi\) | ||
0.903571 | − | 0.428439i | \(-0.140936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | − | 1.90702i | 0.271329 | − | 0.0862386i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1083 | + | 5.83604i | 0.456182 | + | 0.263377i | 0.710437 | − | 0.703760i | \(-0.248497\pi\) |
−0.254256 | + | 0.967137i | \(0.581830\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.5122 | − | 17.0389i | 1.32916 | − | 0.767392i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.8686 | − | 16.7847i | −0.533454 | − | 0.754418i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.3712 | − | 15.8028i | 1.22776 | − | 0.708850i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0767 | + | 24.3815i | −0.630159 | + | 1.09147i | 0.357360 | + | 0.933967i | \(0.383677\pi\) |
−0.987519 | + | 0.157500i | \(0.949656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.92281 | + | 8.76893i | −0.0859048 | + | 0.391767i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.4279 | −1.49048 | −0.745238 | − | 0.666799i | \(-0.767664\pi\) | ||||
−0.745238 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.3031 | 0.547479 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.3144 | − | 32.2102i | −1.56837 | − | 1.43050i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.5932 | − | 20.0800i | 0.513858 | − | 0.890028i | −0.486013 | − | 0.873952i | \(-0.661549\pi\) |
0.999871 | − | 0.0160766i | \(-0.00511756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.84024 | + | 1.06246i | −0.0814074 | + | 0.0470006i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.65153 | + | 6.14966i | −0.205370 | + | 0.271514i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.29088 | + | 4.78674i | −0.365340 | + | 0.210929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9943 | + | 13.8531i | 1.05527 | + | 0.609260i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.59151 | + | 2.36371i | 0.113755 | + | 0.103755i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.0771i | − | 1.18627i | −0.805103 | − | 0.593135i | \(-0.797890\pi\) | ||
0.805103 | − | 0.593135i | \(-0.202110\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.9820 | −1.61711 | −0.808554 | − | 0.588421i | \(-0.799750\pi\) | ||||
−0.808554 | + | 0.588421i | \(0.799750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.19013 | + | 1.57662i | 0.313803 | + | 0.0688092i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.7139 | − | 28.9494i | 0.728071 | − | 1.26106i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.3712 | + | 17.9634i | 0.450921 | + | 0.781017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.1903 | + | 2.50533i | −1.17996 | + | 0.108722i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.0088 | − | 29.4600i | −0.736731 | − | 1.27606i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.8839 | + | 12.0573i | 0.902890 | + | 0.521284i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.69694 | + | 27.3629i | 0.375301 | + | 1.18079i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 51.9348i | 2.23699i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 43.9568i | − | 1.88985i | −0.327287 | − | 0.944925i | \(-0.606134\pi\) | ||
0.327287 | − | 0.944925i | \(-0.393866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.8686 | + | 37.3418i | 0.509331 | + | 1.60249i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.28036 | − | 4.20332i | −0.311856 | − | 0.180050i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.23174 | + | 10.7937i | 0.266450 | + | 0.461505i | 0.967942 | − | 0.251172i | \(-0.0808160\pi\) |
−0.701493 | + | 0.712677i | \(0.747483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.99810 | − | 17.3607i | 0.341351 | − | 0.740936i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.18303 | + | 8.97727i | 0.220804 | + | 0.382444i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.1969 | − | 28.0539i | 0.688764 | − | 1.19297i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.81228 | + | 2.15159i | 0.416508 | + | 0.0913299i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0608 | 0.553406 | 0.276703 | − | 0.960956i | \(-0.410758\pi\) | ||||
0.276703 | + | 0.960956i | \(0.410758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 35.2168i | − | 1.48951i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.1237 | − | 19.2669i | −0.891844 | − | 0.813447i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.19959 | + | 5.31139i | 0.387717 | + | 0.223848i | 0.681170 | − | 0.732125i | \(-0.261471\pi\) |
−0.293454 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9586 | − | 7.48163i | 0.545171 | − | 0.314754i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.77454 | + | 41.8304i | 0.326500 | + | 1.75671i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.7020 | − | 9.06558i | 0.658264 | − | 0.380049i | −0.133351 | − | 0.991069i | \(-0.542574\pi\) |
0.791615 | + | 0.611020i | \(0.209241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.12412 | − | 14.0714i | 0.339984 | − | 0.588870i | −0.644445 | − | 0.764650i | \(-0.722912\pi\) |
0.984429 | + | 0.175781i | \(0.0562450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.63271 | + | 6.04967i | 0.277085 | + | 0.252728i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.35076 | 0.0563306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.44949 | −0.268496 | −0.134248 | − | 0.990948i | \(-0.542862\pi\) | ||||
−0.134248 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.279183 | − | 1.27321i | 0.0116024 | − | 0.0529127i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.5536 | + | 28.6717i | −0.686760 | + | 1.18950i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5360 | − | 8.39237i | 0.602020 | − | 0.347576i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.1969 | − | 35.1571i | 0.669661 | − | 1.45357i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.20474 | − | 0.695560i | 0.0497251 | − | 0.0287088i | −0.474931 | − | 0.880023i | \(-0.657527\pi\) |
0.524656 | + | 0.851314i | \(0.324194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.80607 | + | 5.08419i | 0.362848 | + | 0.209490i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.7474 | + | 9.45483i | −1.22364 | + | 0.388920i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.04989i | − | 0.0841788i | −0.999114 | − | 0.0420894i | \(-0.986599\pi\) | ||
0.999114 | − | 0.0420894i | \(-0.0134014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46.7025 | −1.91461 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.11484 | − | 3.50757i | −0.0456272 | − | 0.143555i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.59151 | − | 4.48863i | 0.105886 | − | 0.183401i | −0.808214 | − | 0.588889i | \(-0.799565\pi\) |
0.914100 | + | 0.405489i | \(0.132899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.7247 | − | 28.9681i | −0.682217 | − | 1.18163i | −0.974303 | − | 0.225242i | \(-0.927683\pi\) |
0.292086 | − | 0.956392i | \(-0.405651\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.02218 | − | 32.7997i | −0.123073 | − | 1.33571i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.455130 | + | 0.788309i | 0.0185037 | + | 0.0320493i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.3389 | + | 18.6709i | 1.31260 | + | 0.757828i | 0.982525 | − | 0.186128i | \(-0.0595940\pi\) |
0.330071 | + | 0.943956i | \(0.392927\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 55.8712 | + | 12.2512i | 2.26401 | + | 0.496442i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.1706i | 2.11060i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.57662i | − | 0.0636790i | −0.999493 | − | 0.0318395i | \(-0.989863\pi\) | ||
0.999493 | − | 0.0318395i | \(-0.0101365\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.6199 | − | 13.8361i | 0.508883 | − | 0.557927i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3763 | + | 5.99075i | 0.417733 | + | 0.241178i | 0.694107 | − | 0.719872i | \(-0.255799\pi\) |
−0.276374 | + | 0.961050i | \(0.589133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5443 | − | 28.6555i | −0.664971 | − | 1.15176i | −0.979293 | − | 0.202447i | \(-0.935111\pi\) |
0.314323 | − | 0.949316i | \(-0.398223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.03765 | + | 7.19231i | 0.121897 | + | 0.288618i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.337690 | − | 0.584897i | −0.0135293 | − | 0.0234334i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.84847 | − | 17.0580i | 0.393939 | − | 0.682322i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.86076 | − | 6.42559i | 0.234056 | − | 0.256614i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.9711 | 0.557065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 46.3190i | − | 1.84393i | −0.387271 | − | 0.921966i | \(-0.626582\pi\) | ||
0.387271 | − | 0.921966i | \(-0.373418\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.47730 | − | 11.2977i | 0.0984637 | − | 0.449041i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5818 | + | 9.57348i | 0.658027 | + | 0.379912i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −84.6909 | + | 48.8963i | −3.35558 | + | 1.93734i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.3763 | + | 11.5798i | −0.647835 | + | 0.458088i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2980 | − | 16.9152i | 1.15720 | − | 0.668110i | 0.206568 | − | 0.978432i | \(-0.433770\pi\) |
0.950631 | + | 0.310323i | \(0.100437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.71567 | + | 13.3639i | −0.304276 | + | 0.527022i | −0.977100 | − | 0.212781i | \(-0.931748\pi\) |
0.672824 | + | 0.739803i | \(0.265081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.4764 | − | 5.87250i | 0.727509 | − | 0.231229i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.1288 | 1.93145 | 0.965725 | − | 0.259566i | \(-0.0835795\pi\) | ||||
0.965725 | + | 0.259566i | \(0.0835795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.7980 | 1.20893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 53.4719 | − | 16.9954i | 2.09573 | − | 0.666101i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0734 | + | 24.3758i | −0.550735 | + | 0.953900i | 0.447487 | + | 0.894290i | \(0.352319\pi\) |
−0.998222 | + | 0.0596098i | \(0.981014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.2975 | − | 12.2961i | 0.832162 | − | 0.480449i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.10102 | − | 0.778539i | 0.0429549 | − | 0.0303737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.33832 | + | 1.35003i | −0.0910881 | + | 0.0525897i | −0.544852 | − | 0.838532i | \(-0.683414\pi\) |
0.453764 | + | 0.891122i | \(0.350081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.9152 | − | 19.5810i | −1.31915 | − | 0.761611i | −0.335557 | − | 0.942020i | \(-0.608925\pi\) |
−0.983592 | + | 0.180409i | \(0.942258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.5309 | − | 52.5865i | 0.447824 | − | 2.04229i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 14.2064i | − | 0.550899i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4961 | 0.406412 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.5141 | + | 23.5875i | −0.831782 | + | 0.911946i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7796 | + | 18.6709i | −0.416143 | + | 0.720781i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.07321 | + | 3.59091i | 0.0799165 | + | 0.138419i | 0.903214 | − | 0.429191i | \(-0.141201\pi\) |
−0.823297 | + | 0.567611i | \(0.807868\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.63538 | − | 0.577648i | −0.178416 | − | 0.0222337i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0734 | + | 24.3758i | 0.540885 | + | 0.936839i | 0.998854 | + | 0.0478713i | \(0.0152437\pi\) |
−0.457969 | + | 0.888968i | \(0.651423\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.93430 | − | 3.42617i | −0.227738 | − | 0.131484i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2980 | + | 25.5433i | −0.892780 | + | 0.978823i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.51353i | 0.134442i | 0.997738 | + | 0.0672208i | \(0.0214132\pi\) | ||||
−0.997738 | + | 0.0672208i | \(0.978587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.6891i | − | 0.828697i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.3157 | + | 5.55110i | 0.965852 | + | 0.211788i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.3712 | + | 15.8028i | 1.04276 | + | 0.602037i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.47344 | − | 11.2123i | −0.246261 | − | 0.426537i | 0.716224 | − | 0.697870i | \(-0.245869\pi\) |
−0.962486 | + | 0.271333i | \(0.912536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.40304 | − | 47.7862i | −0.167258 | − | 1.81525i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.09916 | + | 12.2961i | 0.269287 | + | 0.466418i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0227 | − | 22.5560i | 0.493270 | − | 0.854369i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.11879 | − | 16.1051i | −0.193611 | − | 0.609150i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.3118 | −1.25817 | −0.629085 | − | 0.777336i | \(-0.716570\pi\) | ||||
−0.629085 | + | 0.777336i | \(0.716570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.24985i | 0.160286i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.3712 | + | 8.69958i | −1.03086 | + | 0.327645i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.8726 | + | 14.3602i | 0.935432 | + | 0.540072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.99810 | + | 4.61771i | −0.300375 | + | 0.173422i | −0.642611 | − | 0.766192i | \(-0.722149\pi\) |
0.342236 | + | 0.939614i | \(0.388816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.60171 | + | 18.6709i | −0.322589 | + | 0.700213i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.91658 | − | 5.14799i | 0.333929 | − | 0.192794i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.8298 | + | 37.8104i | −0.816389 | + | 1.41403i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.36349 | − | 42.7020i | 0.349686 | − | 1.59474i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7525 | −1.22146 | −0.610731 | − | 0.791838i | \(-0.709124\pi\) | ||||
−0.610731 | + | 0.791838i | \(0.709124\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3485 | −0.832300 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.6677 | − | 11.5542i | −0.471117 | − | 0.429704i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.13993 | + | 5.43853i | −0.116614 | + | 0.201982i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9910 | + | 15.0059i | −0.963954 | + | 0.556539i | −0.897388 | − | 0.441243i | \(-0.854538\pi\) |
−0.0665663 | + | 0.997782i | \(0.521204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.34847 | − | 25.9808i | −0.272166 | − | 0.962250i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.3512 | − | 13.4818i | 0.863676 | − | 0.498644i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.40304 | − | 2.54209i | −0.162630 | − | 0.0938944i | 0.416476 | − | 0.909147i | \(-0.363265\pi\) |
−0.579106 | + | 0.815252i | \(0.696598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −39.7758 | − | 36.2793i | −1.46715 | − | 1.33818i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.1516i | 1.36850i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8719 | −0.473502 | −0.236751 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236751 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.9962 | + | 3.50757i | 0.587635 | + | 0.128854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.09406 | + | 7.09113i | −0.150197 | + | 0.260148i | −0.931300 | − | 0.364254i | \(-0.881324\pi\) |
0.781103 | + | 0.624402i | \(0.214657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.07321 | + | 12.2512i | 0.259143 | + | 0.448848i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.79114 | − | 19.0820i | 0.321651 | − | 0.698176i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.1468 | + | 48.7517i | 1.02846 | + | 1.78135i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4550 | + | 6.61356i | 0.418000 | + | 0.241332i | 0.694221 | − | 0.719762i | \(-0.255749\pi\) |
−0.276221 | + | 0.961094i | \(0.589082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.55051 | − | 30.0484i | −0.348040 | − | 1.09503i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.27030i | 0.191806i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.3973i | − | 1.75903i | −0.475870 | − | 0.879516i | \(-0.657867\pi\) | ||
0.475870 | − | 0.879516i | \(-0.342133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.66741 | − | 8.39237i | −0.0968208 | − | 0.304624i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9722 | + | 12.1083i | 0.760241 | + | 0.438926i | 0.829382 | − | 0.558681i | \(-0.188693\pi\) |
−0.0691410 | + | 0.997607i | \(0.522026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.81228 | − | 16.9954i | −0.355228 | − | 0.615274i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.5122 | − | 2.71926i | 1.06702 | − | 0.0983152i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9961 | + | 50.2228i | 1.04699 | + | 1.81344i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.3990 | − | 23.2077i | 0.483180 | − | 0.836892i | −0.516634 | − | 0.856206i | \(-0.672815\pi\) |
0.999813 | + | 0.0193149i | \(0.00614850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.86660 | + | 2.16350i | 0.355337 | + | 0.0779166i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.910261 | 0.0327398 | 0.0163699 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163699 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.16011i | 0.221278i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.3258 | + | 15.8028i | 0.621558 | + | 0.566921i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.86127 | + | 3.96136i | 0.245831 | + | 0.141930i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5913 | − | 11.3110i | 0.701031 | − | 0.404740i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.0194 | − | 4.48863i | −1.28723 | − | 0.160411i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.2423 | + | 15.1510i | −0.936629 | + | 0.540763i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.47344 | + | 11.2123i | −0.230753 | + | 0.399677i | −0.958030 | − | 0.286668i | \(-0.907452\pi\) |
0.727277 | + | 0.686344i | \(0.240786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.1449 | + | 32.9676i | 1.28679 | + | 1.17368i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.9304 | 1.24198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.5959 | −1.44160 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.72666 | + | 16.9954i | −0.132171 | + | 0.602764i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5034 | − | 21.6566i | 0.442894 | − | 0.767115i | −0.555009 | − | 0.831845i | \(-0.687285\pi\) |
0.997903 | + | 0.0647294i | \(0.0206184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.5927 | + | 19.9721i | −1.22380 | + | 0.706563i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.247449 | + | 0.349945i | 0.00874317 | + | 0.0123647i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.31718 | + | 0.760471i | −0.0464821 | + | 0.0268365i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.4575 | − | 7.19231i | −0.439067 | − | 0.253496i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.50255 | + | 0.477566i | −0.0528922 | + | 0.0168111i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 34.7839i | − | 1.22294i | −0.791269 | − | 0.611468i | \(-0.790579\pi\) | ||
0.791269 | − | 0.611468i | \(-0.209421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.6708 | −1.77929 | −0.889647 | − | 0.456650i | \(-0.849049\pi\) | ||||
−0.889647 | + | 0.456650i | \(0.849049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.92091 | − | 31.2138i | −0.347942 | − | 1.09472i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.68048 | − | 6.37478i | 0.128922 | − | 0.223299i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.10102 | + | 7.10318i | 0.143477 | + | 0.248509i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 73.7803 | − | 52.1706i | 2.57809 | − | 1.82299i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.45323 | + | 14.6414i | 0.295020 | + | 0.510989i | 0.974990 | − | 0.222251i | \(-0.0713404\pi\) |
−0.679970 | + | 0.733240i | \(0.738007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.8182 | − | 15.4835i | −0.934824 | − | 0.539721i | −0.0464898 | − | 0.998919i | \(-0.514804\pi\) |
−0.888334 | + | 0.459198i | \(0.848137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.14643 | + | 1.12848i | 0.179176 | + | 0.0392888i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.4362i | 0.397677i | 0.980032 | + | 0.198839i | \(0.0637170\pi\) | ||||
−0.980032 | + | 0.198839i | \(0.936283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.57662i | 0.0547582i | 0.999625 | + | 0.0273791i | \(0.00871613\pi\) | ||||
−0.999625 | + | 0.0273791i | \(0.991284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.2822 | − | 13.4659i | 0.426064 | − | 0.467127i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −64.8434 | − | 37.4373i | −2.24669 | − | 1.29713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.24807 | + | 9.08992i | 0.181617 | + | 0.314570i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.8004 | + | 13.8531i | −1.13375 | + | 0.478834i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.4703 | − | 35.4556i | −0.706714 | − | 1.22406i | −0.966069 | − | 0.258282i | \(-0.916844\pi\) |
0.259356 | − | 0.965782i | \(-0.416490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.89898 | + | 17.1455i | −0.341344 | + | 0.591225i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.7064 | − | 28.1839i | 0.885375 | − | 0.970704i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −55.8844 | −1.92248 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12493i | 0.0730133i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50000 | + | 34.2036i | −0.257399 | + | 1.17386i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.72666 | + | 2.15159i | 0.127748 | + | 0.0737556i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2844 | + | 11.1339i | −0.660285 | + | 0.381216i | −0.792386 | − | 0.610020i | \(-0.791161\pi\) |
0.132100 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.827169 | + | 8.97727i | 0.0282886 | + | 0.307016i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.3207 | + | 26.7432i | −1.58228 | + | 0.913532i | −0.587758 | + | 0.809037i | \(0.699989\pi\) |
−0.994525 | + | 0.104495i | \(0.966677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6197 | − | 30.5183i | 0.601178 | − | 1.04127i | −0.391465 | − | 0.920193i | \(-0.628032\pi\) |
0.992643 | − | 0.121078i | \(-0.0386351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41.6628 | − | 13.2420i | 1.41986 | − | 0.451285i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.00510 | 0.102295 | 0.0511474 | − | 0.998691i | \(-0.483712\pi\) | ||||
0.0511474 | + | 0.998691i | \(0.483712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.10102 | 0.139439 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.2213 | − | 3.56653i | 0.381094 | − | 0.121126i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5932 | − | 20.0800i | 0.393271 | − | 0.681166i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.5838 | + | 34.9781i | −2.05280 | + | 1.18519i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.94949 | + | 1.81954i | 0.133670 | + | 0.0615820i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 48.9077 | − | 28.2369i | 1.65338 | − | 0.954581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.7400 | + | 22.9439i | 1.34192 | + | 0.774760i | 0.987089 | − | 0.160170i | \(-0.0512042\pi\) |
0.354834 | + | 0.934929i | \(0.384538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.751275 | + | 3.42617i | −0.0253399 | + | 0.115562i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.0416i | − | 0.809983i | −0.914320 | − | 0.404992i | \(-0.867274\pi\) | ||
0.914320 | − | 0.404992i | \(-0.132726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.9270 | −0.838859 | −0.419429 | − | 0.907788i | \(-0.637770\pi\) | ||||
−0.419429 | + | 0.907788i | \(0.637770\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.5141 | + | 23.5875i | −0.723188 | + | 0.792886i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.1173 | + | 19.2558i | −0.373283 | + | 0.646546i | −0.990069 | − | 0.140586i | \(-0.955101\pi\) |
0.616785 | + | 0.787132i | \(0.288435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.3485 | + | 38.7087i | 0.749544 | + | 1.29825i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.56473 | + | 29.9406i | 0.186425 | + | 1.00305i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.07529 | − | 10.5227i | −0.203302 | − | 0.352129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.0720 | + | 16.7847i | 0.971771 | + | 0.561052i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.1742 | − | 12.2512i | 0.373097 | − | 0.409055i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47.8674i | 1.59647i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.1987i | 0.806174i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 44.2075 | + | 9.69362i | 1.47113 | + | 0.322583i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.6742 | + | 22.9059i | 1.31882 | + | 0.761419i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.09662 | + | 3.63144i | 0.0696170 | + | 0.120580i | 0.898733 | − | 0.438497i | \(-0.144489\pi\) |
−0.829116 | + | 0.559077i | \(0.811156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.5536 | − | 7.62628i | −0.549049 | − | 0.252948i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.3106 | − | 38.6430i | −0.739182 | − | 1.28030i | −0.952864 | − | 0.303397i | \(-0.901879\pi\) |
0.213683 | − | 0.976903i | \(-0.431454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.8485 | + | 20.5222i | −0.392127 | + | 0.679184i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.76947 | − | 21.2986i | −0.223792 | − | 0.704108i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 57.4084 | 1.89579 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.6598i | − | 0.483583i | −0.970328 | − | 0.241791i | \(-0.922265\pi\) | ||
0.970328 | − | 0.241791i | \(-0.0777350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.89898 | + | 1.55708i | −0.161427 | + | 0.0513075i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.8902 | + | 21.2986i | 1.21425 | + | 0.701050i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.22967 | + | 1.28730i | −0.0733112 | + | 0.0423263i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1224 | − | 1.30125i | 0.463841 | − | 0.0427385i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.9722 | − | 27.6968i | 1.57392 | − | 0.908701i | 0.578235 | − | 0.815870i | \(-0.303742\pi\) |
0.995682 | − | 0.0928307i | \(-0.0295915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.3880 | − | 19.7246i | 0.373227 | − | 0.646448i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.5932 | + | 52.8704i | −0.379543 | + | 1.73090i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33.4279 | −1.09321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.1464 | −1.21352 | −0.606760 | − | 0.794885i | \(-0.707531\pi\) | ||||
−0.606760 | + | 0.794885i | \(0.707531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.98952 | + | 4.55092i | 0.162827 | + | 0.148514i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.97300 | + | 10.3455i | −0.194714 | + | 0.337255i | −0.946807 | − | 0.321802i | \(-0.895711\pi\) |
0.752092 | + | 0.659058i | \(0.229045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.94737 | − | 4.01107i | 0.226238 | − | 0.130618i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.6742 | + | 30.0091i | 1.29060 | + | 0.976196i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.15679 | + | 3.55462i | −0.200069 | + | 0.115510i | −0.596687 | − | 0.802474i | \(-0.703517\pi\) |
0.396619 | + | 0.917983i | \(0.370183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.48023 | − | 1.43196i | −0.0805116 | − | 0.0464834i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.6352 | + | 19.7333i | 0.701569 | + | 0.639898i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5699i | 0.893078i | 0.894764 | + | 0.446539i | \(0.147344\pi\) | ||||
−0.894764 | + | 0.446539i | \(0.852656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4961 | 0.339647 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39.9905 | + | 8.76893i | 1.29271 | + | 0.283459i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.3157 | − | 43.8480i | 0.817485 | − | 1.41593i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.97730 | + | 13.8171i | 0.257332 | + | 0.445712i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.6251 | − | 29.1683i | −0.664634 | − | 0.939934i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.761995 | − | 1.31981i | −0.0245295 | − | 0.0424863i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.1792 | + | 19.7333i | 1.09913 | + | 0.634582i | 0.935992 | − | 0.352022i | \(-0.114506\pi\) |
0.163136 | + | 0.986604i | \(0.447839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.79796 | + | 11.9494i | 0.122008 | + | 0.383869i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.7394i | − | 0.505102i | −0.967584 | − | 0.252551i | \(-0.918730\pi\) | ||
0.967584 | − | 0.252551i | \(-0.0812696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.1448i | 1.06257i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00510 | + | 9.45483i | 0.0962402 | + | 0.302797i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.94949 | − | 5.74434i | −0.318312 | − | 0.183778i | 0.332328 | − | 0.943164i | \(-0.392166\pi\) |
−0.650640 | + | 0.759386i | \(0.725499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.241706 | − | 0.418647i | −0.00772496 | − | 0.0133800i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.19013 | + | 10.1684i | 0.229563 | + | 0.324651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.43175 | + | 7.67602i | 0.141351 | + | 0.244827i | 0.928006 | − | 0.372566i | \(-0.121522\pi\) |
−0.786655 | + | 0.617393i | \(0.788189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2474 | + | 31.6055i | −0.581412 | + | 1.00704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −65.4895 | − | 14.3602i | −2.08455 | − | 0.457091i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.30497 | 0.264083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.0692i | − | 1.33637i | −0.743994 | − | 0.668186i | \(-0.767071\pi\) | ||
0.743994 | − | 0.668186i | \(-0.232929\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.1969 | − | 39.3997i | −1.37081 | − | 1.25031i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.72666 | − | 2.15159i | −0.118143 | − | 0.0682100i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.0301 | − | 20.2246i | 1.10941 | − | 0.640520i | 0.170736 | − | 0.985317i | \(-0.445386\pi\) |
0.938677 | + | 0.344797i | \(0.112052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8686 | − | 8.97727i | −0.375506 | − | 0.284028i |
(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 | 1152.2.p.d.959.1 | yes | 16 | |
3.2 | odd | 2 | 3456.2.p.d.2879.5 | 16 | |||
4.3 | odd | 2 | inner | 1152.2.p.d.959.7 | yes | 16 | |
8.3 | odd | 2 | inner | 1152.2.p.d.959.2 | yes | 16 | |
8.5 | even | 2 | inner | 1152.2.p.d.959.8 | yes | 16 | |
9.2 | odd | 6 | inner | 1152.2.p.d.191.2 | yes | 16 | |
9.7 | even | 3 | 3456.2.p.d.575.4 | 16 | |||
12.11 | even | 2 | 3456.2.p.d.2879.6 | 16 | |||
24.5 | odd | 2 | 3456.2.p.d.2879.3 | 16 | |||
24.11 | even | 2 | 3456.2.p.d.2879.4 | 16 | |||
36.7 | odd | 6 | 3456.2.p.d.575.3 | 16 | |||
36.11 | even | 6 | inner | 1152.2.p.d.191.8 | yes | 16 | |
72.11 | even | 6 | inner | 1152.2.p.d.191.1 | ✓ | 16 | |
72.29 | odd | 6 | inner | 1152.2.p.d.191.7 | yes | 16 | |
72.43 | odd | 6 | 3456.2.p.d.575.5 | 16 | |||
72.61 | even | 6 | 3456.2.p.d.575.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.d.191.1 | ✓ | 16 | 72.11 | even | 6 | inner | |
1152.2.p.d.191.2 | yes | 16 | 9.2 | odd | 6 | inner | |
1152.2.p.d.191.7 | yes | 16 | 72.29 | odd | 6 | inner | |
1152.2.p.d.191.8 | yes | 16 | 36.11 | even | 6 | inner | |
1152.2.p.d.959.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1152.2.p.d.959.2 | yes | 16 | 8.3 | odd | 2 | inner | |
1152.2.p.d.959.7 | yes | 16 | 4.3 | odd | 2 | inner | |
1152.2.p.d.959.8 | yes | 16 | 8.5 | even | 2 | inner | |
3456.2.p.d.575.3 | 16 | 36.7 | odd | 6 | |||
3456.2.p.d.575.4 | 16 | 9.7 | even | 3 | |||
3456.2.p.d.575.5 | 16 | 72.43 | odd | 6 | |||
3456.2.p.d.575.6 | 16 | 72.61 | even | 6 | |||
3456.2.p.d.2879.3 | 16 | 24.5 | odd | 2 | |||
3456.2.p.d.2879.4 | 16 | 24.11 | even | 2 | |||
3456.2.p.d.2879.5 | 16 | 3.2 | odd | 2 | |||
3456.2.p.d.2879.6 | 16 | 12.11 | even | 2 |