Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.4 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.e.1537.5 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.49661i | 1.11652i | 0.829667 | + | 0.558258i | \(0.188530\pi\) | ||||
−0.829667 | + | 0.558258i | \(0.811470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.917608 | −0.346823 | −0.173412 | − | 0.984849i | \(-0.555479\pi\) | ||||
−0.173412 | + | 0.984849i | \(0.555479\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.69552i | 1.11424i | 0.830432 | + | 0.557120i | \(0.188094\pi\) | ||||
−0.830432 | + | 0.557120i | \(0.811906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.81204i | − 1.61197i | −0.591936 | − | 0.805985i | \(-0.701636\pi\) | ||||
0.591936 | − | 0.805985i | \(-0.298364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.49661 | 0.644621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.867091 | −0.210300 | −0.105150 | − | 0.994456i | \(-0.533532\pi\) | ||||
−0.105150 | + | 0.994456i | \(0.533532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.52395i | − 1.49670i | −0.663306 | − | 0.748348i | \(-0.730847\pi\) | ||||
0.663306 | − | 0.748348i | \(-0.269153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.917608i | 0.200238i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.23304 | −0.246608 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.72286i | 1.43410i | 0.697022 | + | 0.717049i | \(0.254508\pi\) | ||||
−0.697022 | + | 0.717049i | \(0.745492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14386 | −0.385049 | −0.192524 | − | 0.981292i | \(-0.561667\pi\) | ||||
−0.192524 | + | 0.981292i | \(0.561667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.69552 | 0.643307 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.29090i | − 0.387234i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.47568i | − 0.406999i | −0.979075 | − | 0.203500i | \(-0.934768\pi\) | ||||
0.979075 | − | 0.203500i | \(-0.0652316\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.81204 | −0.930671 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.58541 | 1.49699 | 0.748495 | − | 0.663140i | \(-0.230777\pi\) | ||||
0.748495 | + | 0.663140i | \(0.230777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.58541i | − 1.46176i | −0.682505 | − | 0.730881i | \(-0.739109\pi\) | ||||
0.682505 | − | 0.730881i | \(-0.260891\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.49661i | − 0.372172i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65685 | −0.241677 | −0.120839 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120839 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.15800 | −0.879714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.867091i | 0.121417i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.39329i | 0.466104i | 0.972464 | + | 0.233052i | \(0.0748712\pi\) | ||||
−0.972464 | + | 0.233052i | \(0.925129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.22625 | −1.24407 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.52395 | −0.864118 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.7183i | − 1.65578i | −0.560887 | − | 0.827892i | \(-0.689540\pi\) | ||||
0.560887 | − | 0.827892i | \(-0.310460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.0231773i | − 0.00296755i | −0.999999 | − | 0.00148377i | \(-0.999528\pi\) | ||||
0.999999 | − | 0.00148377i | \(-0.000472300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.917608 | 0.115608 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.5104 | 1.79979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.32729i | − 0.650832i | −0.945571 | − | 0.325416i | \(-0.894496\pi\) | ||||
0.945571 | − | 0.325416i | \(-0.105504\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000i | 0.481543i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8216 | −1.40297 | −0.701485 | − | 0.712684i | \(-0.747479\pi\) | ||||
−0.701485 | + | 0.712684i | \(0.747479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2809 | 1.78850 | 0.894249 | − | 0.447570i | \(-0.147711\pi\) | ||||
0.894249 | + | 0.447570i | \(0.147711\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.23304i | 0.142379i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.39104i | − 0.386444i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.40968 | 0.946163 | 0.473081 | − | 0.881019i | \(-0.343142\pi\) | ||||
0.473081 | + | 0.881019i | \(0.343142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.96134i | − 0.215285i | −0.994190 | − | 0.107642i | \(-0.965670\pi\) | ||||
0.994190 | − | 0.107642i | \(-0.0343301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.16478i | − 0.234804i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.72286 | 0.827977 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.79565 | −0.296338 | −0.148169 | − | 0.988962i | \(-0.547338\pi\) | ||||
−0.148169 | + | 0.988962i | \(0.547338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.33317i | 0.559068i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.14386i | 0.222308i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.2877 | 1.67108 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.26582 | −0.230059 | −0.115029 | − | 0.993362i | \(-0.536696\pi\) | ||||
−0.115029 | + | 0.993362i | \(0.536696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.69552i | − 0.371414i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 9.98868i | − 0.993910i | −0.867776 | − | 0.496955i | \(-0.834451\pi\) | ||||
0.867776 | − | 0.496955i | \(-0.165549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4180 | 1.61771 | 0.808857 | − | 0.588006i | \(-0.200087\pi\) | ||||
0.808857 | + | 0.588006i | \(0.200087\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.29090 | −0.223569 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.2522i | − 1.18447i | −0.805766 | − | 0.592234i | \(-0.798246\pi\) | ||||
0.805766 | − | 0.592234i | \(-0.201754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 18.2973i | − 1.75257i | −0.481797 | − | 0.876283i | \(-0.660016\pi\) | ||||
0.481797 | − | 0.876283i | \(-0.339984\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47568 | −0.234981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.65685 | 0.344008 | 0.172004 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172004 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 9.98642i | − 0.931239i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.81204i | 0.537323i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.795649 | 0.0729371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65685 | −0.241532 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 9.58541i | − 0.864288i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.40461i | 0.841174i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6382 | 1.83135 | 0.915673 | − | 0.401925i | \(-0.131659\pi\) | ||||
0.915673 | + | 0.401925i | \(0.131659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.58541 | −0.843949 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 17.5140i | − 1.53020i | −0.643910 | − | 0.765101i | \(-0.722689\pi\) | ||||
0.643910 | − | 0.765101i | \(-0.277311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.98642i | 0.519089i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.49661 | −0.214874 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.25813 | −0.705539 | −0.352770 | − | 0.935710i | \(-0.614760\pi\) | ||||
−0.352770 | + | 0.935710i | \(0.614760\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 14.7047i | − 1.24724i | −0.781728 | − | 0.623620i | \(-0.785661\pi\) | ||||
0.781728 | − | 0.623620i | \(-0.214339\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.65685i | 0.139532i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.4785 | 1.79612 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.2809 | −1.60119 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.15800i | 0.507903i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 16.1535i | − 1.32334i | −0.749794 | − | 0.661672i | \(-0.769847\pi\) | ||||
0.749794 | − | 0.661672i | \(-0.230153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2691 | −1.56810 | −0.784048 | − | 0.620701i | \(-0.786848\pi\) | ||||
−0.784048 | + | 0.620701i | \(0.786848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.867091 | 0.0701002 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.35237i | − 0.429913i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.818827i | − 0.0653495i | −0.999466 | − | 0.0326747i | \(-0.989597\pi\) | ||||
0.999466 | − | 0.0326747i | \(-0.0104025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.39329 | 0.269105 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.67043 | 0.289271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6492i | 1.85235i | 0.377100 | + | 0.926173i | \(0.376921\pi\) | ||||
−0.377100 | + | 0.926173i | \(0.623079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.22625i | 0.718263i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.30358 | −0.719933 | −0.359966 | − | 0.932965i | \(-0.617212\pi\) | ||||
−0.359966 | + | 0.932965i | \(0.617212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.7798 | −1.59845 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.52395i | 0.498899i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.10557i | 0.540226i | 0.962829 | + | 0.270113i | \(0.0870611\pi\) | ||||
−0.962829 | + | 0.270113i | \(0.912939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.13145 | 0.0855294 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.7183 | −0.955968 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.67271i | 0.199768i | 0.994999 | + | 0.0998840i | \(0.0318472\pi\) | ||||
−0.994999 | + | 0.0998840i | \(0.968153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 0.640465i | − 0.0476054i | −0.999717 | − | 0.0238027i | \(-0.992423\pi\) | ||||
0.999717 | − | 0.0238027i | \(-0.00757735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0231773 | −0.00171332 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.18080 | 0.454421 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.20435i | − 0.234325i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 0.917608i | − 0.0667461i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6037 | −1.05669 | −0.528344 | − | 0.849031i | \(-0.677187\pi\) | ||||
−0.528344 | + | 0.849031i | \(0.677187\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.81485 | −0.634507 | −0.317253 | − | 0.948341i | \(-0.602761\pi\) | ||||
−0.317253 | + | 0.948341i | \(0.602761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 14.5104i | − 1.03911i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.74551i | − 0.266856i | −0.991058 | − | 0.133428i | \(-0.957401\pi\) | ||||
0.991058 | − | 0.133428i | \(-0.0425985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8267 | −1.05104 | −0.525519 | − | 0.850782i | \(-0.676129\pi\) | ||||
−0.525519 | + | 0.850782i | \(0.676129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.32729 | −0.375758 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.08655i | − 0.497379i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.9310i | 1.67141i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.1094 | 1.66768 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 11.3910i | − 0.784191i | −0.919924 | − | 0.392096i | \(-0.871750\pi\) | ||||
0.919924 | − | 0.392096i | \(-0.128250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8216i | 0.810005i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.9310 | 1.63208 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.96722 | 0.133544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 15.2809i | − 1.03259i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.03957i | 0.338998i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.78110 | 0.320166 | 0.160083 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160083 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.23304 | 0.0822027 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.83840i | − 0.254764i | −0.991854 | − | 0.127382i | \(-0.959343\pi\) | ||||
0.991854 | − | 0.127382i | \(-0.0406574\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.34596i | − 0.0889434i | −0.999011 | − | 0.0444717i | \(-0.985840\pi\) | ||||
0.999011 | − | 0.0444717i | \(-0.0141604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.39104 | −0.223114 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.6433 | 1.15585 | 0.577925 | − | 0.816090i | \(-0.303863\pi\) | ||||
0.577925 | + | 0.816090i | \(0.303863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4.13651i | − 0.269836i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.40968i | − 0.546267i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.61500 | −0.621943 | −0.310971 | − | 0.950419i | \(-0.600654\pi\) | ||||
−0.310971 | + | 0.950419i | \(0.600654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3583 | 1.37581 | 0.687903 | − | 0.725802i | \(-0.258531\pi\) | ||||
0.687903 | + | 0.725802i | \(0.258531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 15.3741i | − 0.982214i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37.9174 | −2.41263 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.96134 | −0.124295 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.30448i | 0.271696i | 0.990730 | + | 0.135848i | \(0.0433760\pi\) | ||||
−0.990730 | + | 0.135848i | \(0.956624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 14.7821i | − 0.929341i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.16478 | −0.135564 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.67271 | −0.291476 | −0.145738 | − | 0.989323i | \(-0.546556\pi\) | ||||
−0.145738 | + | 0.989323i | \(0.546556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.27170i | 0.141157i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 7.72286i | − 0.478033i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.4502 | −0.952701 | −0.476351 | − | 0.879255i | \(-0.658041\pi\) | ||||
−0.476351 | + | 0.879255i | \(0.658041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47170 | −0.520413 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.79565i | 0.171091i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.2459i | 1.90510i | 0.304388 | + | 0.952548i | \(0.401548\pi\) | ||||
−0.304388 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.88817 | 0.600664 | 0.300332 | − | 0.953835i | \(-0.402903\pi\) | ||||
0.300332 | + | 0.953835i | \(0.402903\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.33317 | 0.322778 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.55672i | − 0.274781i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9565i | 1.37932i | 0.724133 | + | 0.689660i | \(0.242240\pi\) | ||||
−0.724133 | + | 0.689660i | \(0.757760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.14386 | 0.128350 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5754 | 0.869498 | 0.434749 | − | 0.900552i | \(-0.356837\pi\) | ||||
0.434749 | + | 0.900552i | \(0.356837\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.71832i | 0.280475i | 0.990118 | + | 0.140238i | \(0.0447866\pi\) | ||||
−0.990118 | + | 0.140238i | \(0.955213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 16.2877i | − 0.964801i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.79565 | −0.519191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2482 | −0.955774 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.26582i | 0.132825i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 23.9204i | − 1.39745i | −0.715392 | − | 0.698723i | \(-0.753752\pi\) | ||||
0.715392 | − | 0.698723i | \(-0.246248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.7526 | 1.84871 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.69552 | −0.214436 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.2482i | 1.34448i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79565i | 0.506973i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.98868 | −0.573834 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0578646 | 0.00331332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 20.7685i | − 1.18532i | −0.805453 | − | 0.592660i | \(-0.798078\pi\) | ||||
0.805453 | − | 0.592660i | \(-0.201922\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 16.4180i | − 0.933988i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7798 | −0.667971 | −0.333985 | − | 0.942578i | \(-0.608394\pi\) | ||||
−0.333985 | + | 0.942578i | \(0.608394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1580 | −0.630687 | −0.315344 | − | 0.948978i | \(-0.602120\pi\) | ||||
−0.315344 | + | 0.948978i | \(0.602120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.29090i | 0.129078i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 15.9140i | − 0.893822i | −0.894578 | − | 0.446911i | \(-0.852524\pi\) | ||||
0.894578 | − | 0.446911i | \(-0.147476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.5400 | −1.59793 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2522 | −0.683853 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685i | 0.314756i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.16648i | 0.397525i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.2973 | −1.01184 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.52034 | 0.0838192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.73190i | − 0.150159i | −0.997178 | − | 0.0750794i | \(-0.976079\pi\) | ||||
0.997178 | − | 0.0750794i | \(-0.0239210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.47568i | 0.135666i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.3001 | 0.726664 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.49657 | −0.0815236 | −0.0407618 | − | 0.999169i | \(-0.512978\pi\) | ||||
−0.0407618 | + | 0.999169i | \(0.512978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 3.65685i | − 0.198613i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.92267i | − 0.429037i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0739 | 0.651928 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.98642 | −0.537651 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.22944i | 0.173365i | 0.996236 | + | 0.0866826i | \(0.0276266\pi\) | ||||
−0.996236 | + | 0.0866826i | \(0.972373\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.51074i | − 0.402041i | −0.979587 | − | 0.201020i | \(-0.935574\pi\) | ||||
0.979587 | − | 0.201020i | \(-0.0644258\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.81204 | 0.310224 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.17491 | 0.115759 | 0.0578795 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578795 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 29.5140i | − 1.56644i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.795649i | − 0.0421102i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.6828 | 0.669375 | 0.334687 | − | 0.942329i | \(-0.391369\pi\) | ||||
0.334687 | + | 0.942329i | \(0.391369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.5619 | −1.24010 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.65685i | 0.139449i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.1505i | 1.99689i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.4576 | −1.12008 | −0.560038 | − | 0.828467i | \(-0.689213\pi\) | ||||
−0.560038 | + | 0.828467i | \(0.689213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.58541 | −0.498997 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.11371i | − 0.161656i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 0.508459i | − 0.0263270i | −0.999913 | − | 0.0131635i | \(-0.995810\pi\) | ||||
0.999913 | − | 0.0131635i | \(-0.00419019\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.40461 | 0.485652 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.8855 | 2.31172 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9286i | 1.02366i | 0.859086 | + | 0.511831i | \(0.171032\pi\) | ||||
−0.859086 | + | 0.511831i | \(0.828968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 20.6382i | − 1.05733i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.3858 | 1.50154 | 0.750772 | − | 0.660562i | \(-0.229682\pi\) | ||||
0.750772 | + | 0.660562i | \(0.229682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.46608 | 0.431471 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.58541i | 0.487254i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00379i | 0.0508941i | 0.999676 | + | 0.0254470i | \(0.00810092\pi\) | ||||
−0.999676 | + | 0.0254470i | \(0.991899\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.46836 | 0.175403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5140 | −0.883463 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.9956i | 1.05641i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.02546i | − 0.352598i | −0.984337 | − | 0.176299i | \(-0.943587\pi\) | ||||
0.984337 | − | 0.176299i | \(-0.0564125\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.98642 | 0.299696 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.18080 | 0.208779 | 0.104390 | − | 0.994536i | \(-0.466711\pi\) | ||||
0.104390 | + | 0.994536i | \(0.466711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4602i | 0.620686i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.49661i | 0.124057i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.14892 | 0.453495 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5818 | −0.819918 | −0.409959 | − | 0.912104i | \(-0.634457\pi\) | ||||
−0.409959 | + | 0.912104i | \(0.634457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.25813i | 0.407343i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6704i | 0.574264i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.89668 | 0.240369 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.7047 | −0.720094 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 22.2574i | − 1.08734i | −0.839298 | − | 0.543672i | \(-0.817034\pi\) | ||||
0.839298 | − | 0.543672i | \(-0.182966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.4203i | 1.38512i | 0.721361 | + | 0.692559i | \(0.243517\pi\) | ||||
−0.721361 | + | 0.692559i | \(0.756483\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.65685 | 0.0805590 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.06916 | 0.0518618 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0212677i | 0.00102921i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 21.4785i | − 1.03699i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.6138 | −1.76363 | −0.881813 | − | 0.471599i | \(-0.843677\pi\) | ||||
−0.881813 | + | 0.471599i | \(0.843677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7526 | 1.33371 | 0.666853 | − | 0.745189i | \(-0.267641\pi\) | ||||
0.666853 | + | 0.745189i | \(0.267641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.2809i | 0.924450i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.0958i | 1.24833i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1461 | 1.00925 | 0.504625 | − | 0.863339i | \(-0.331631\pi\) | ||||
0.504625 | + | 0.863339i | \(0.331631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.15800 | 0.293238 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 7.30677i | − 0.347155i | −0.984820 | − | 0.173577i | \(-0.944467\pi\) | ||||
0.984820 | − | 0.173577i | \(-0.0555327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.97963i | − 0.330866i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.1535 | −0.764032 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.6356 | −0.832275 | −0.416137 | − | 0.909302i | \(-0.636616\pi\) | ||||
−0.416137 | + | 0.909302i | \(0.636616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.4231i | 1.66801i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.2691i | 0.905340i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.3148 | −0.624209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7070 | −0.828300 | −0.414150 | − | 0.910209i | \(-0.635921\pi\) | ||||
−0.414150 | + | 0.910209i | \(0.635921\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 0.867091i | − 0.0404723i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 36.9811i | − 1.72238i | −0.508280 | − | 0.861192i | \(-0.669719\pi\) | ||||
0.508280 | − | 0.861192i | \(-0.330281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9632 | 0.509504 | 0.254752 | − | 0.967006i | \(-0.418006\pi\) | ||||
0.254752 | + | 0.967006i | \(0.418006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.35237 | −0.248210 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6661i | 0.586116i | 0.956095 | + | 0.293058i | \(0.0946730\pi\) | ||||
−0.956095 | + | 0.293058i | \(0.905327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.88836i | 0.225723i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.818827 | −0.0377295 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.4231 | 1.62875 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.04429i | 0.369097i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.39329i | − 0.155368i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.3036 | −0.607856 | −0.303928 | − | 0.952695i | \(-0.598298\pi\) | ||||
−0.303928 | + | 0.952695i | \(0.598298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3888 | −0.656071 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.67043i | − 0.167010i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5.65685i | − 0.256865i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.44924 | 0.246929 | 0.123464 | − | 0.992349i | \(-0.460600\pi\) | ||||
0.123464 | + | 0.992349i | \(0.460600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.6492 | 1.06945 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 21.7844i | − 0.983114i | −0.870845 | − | 0.491557i | \(-0.836428\pi\) | ||||
0.870845 | − | 0.491557i | \(-0.163572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.69642i | − 0.301592i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.22625 | 0.414689 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8476 | 0.486583 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1595i | 0.902465i | 0.892407 | + | 0.451232i | \(0.149015\pi\) | ||||
−0.892407 | + | 0.451232i | \(0.850985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.30358i | 0.415653i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.5879 | −1.49761 | −0.748804 | − | 0.662791i | \(-0.769372\pi\) | ||||
−0.748804 | + | 0.662791i | \(0.769372\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.9378 | 1.10972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.7798i | 0.922863i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1957i | 0.496242i | 0.968729 | + | 0.248121i | \(0.0798130\pi\) | ||||
−0.968729 | + | 0.248121i | \(0.920187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0219 | −0.620292 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.52395 | 0.288039 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.9893i | 1.80620i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.12293i | − 0.269286i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.10557 | 0.311900 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.2151 | 1.54280 | 0.771401 | − | 0.636349i | \(-0.219556\pi\) | ||||
0.771401 | + | 0.636349i | \(0.219556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 12.9444i | − 0.566020i | −0.959117 | − | 0.283010i | \(-0.908667\pi\) | ||||
0.959117 | − | 0.283010i | \(-0.0913329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.13145i | − 0.0493804i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.85892 | 0.0809759 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7183i | 0.551928i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 55.7108i | − 2.41310i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.5890 | 1.32248 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.67271 | 0.115336 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 22.7570i | − 0.980213i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 17.8584i | − 0.767792i | −0.923376 | − | 0.383896i | \(-0.874582\pi\) | ||||
0.923376 | − | 0.383896i | \(-0.125418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.640465 | −0.0274850 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45.6812 | 1.95677 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9191i | 0.637893i | 0.947773 | + | 0.318947i | \(0.103329\pi\) | ||||
−0.947773 | + | 0.318947i | \(0.896671\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0231773i | 0 0.000989183i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.3835 | 2.14641 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.71679 | −0.328151 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 6.18080i | − 0.262360i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4649i | 1.03661i | 0.855196 | + | 0.518305i | \(0.173437\pi\) | ||||
−0.855196 | + | 0.518305i | \(0.826563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.7108 | −2.35632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.20435 | −0.135288 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.4459i | 1.70459i | 0.523061 | + | 0.852295i | \(0.324790\pi\) | ||||
−0.523061 | + | 0.852295i | \(0.675210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.12972i | 0.384090i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.917608 | −0.0385359 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.1017 | −1.76499 | −0.882497 | − | 0.470318i | \(-0.844139\pi\) | ||||
−0.882497 | + | 0.470318i | \(0.844139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24996i | 0.0523091i | 0.999658 | + | 0.0261546i | \(0.00832620\pi\) | ||||
−0.999658 | + | 0.0261546i | \(0.991674\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6037i | 0.610079i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.93216 | 0.205685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3767 | 1.22297 | 0.611484 | − | 0.791257i | \(-0.290573\pi\) | ||||
0.611484 | + | 0.791257i | \(0.290573\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.81485i | 0.366333i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.79974i | 0.0746657i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5400 | −0.519352 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.5104 | −0.599930 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.7070i | 0.730847i | 0.930841 | + | 0.365424i | \(0.119076\pi\) | ||||
−0.930841 | + | 0.365424i | \(0.880924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.9864i | 0.576301i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.74551 | −0.154070 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.1207 | 0.703061 | 0.351530 | − | 0.936176i | \(-0.385661\pi\) | ||||
0.351530 | + | 0.936176i | \(0.385661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.98642i | 0.0814354i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.8267i | 0.606817i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.1908 | 1.02927 | 0.514634 | − | 0.857410i | \(-0.327928\pi\) | ||||
0.514634 | + | 0.857410i | \(0.327928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.5946 | −0.921655 | −0.460827 | − | 0.887490i | \(-0.652447\pi\) | ||||
−0.460827 | + | 0.887490i | \(0.652447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.32729i | 0.216944i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6.63312i | − 0.269675i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.88408 | 0.360594 | 0.180297 | − | 0.983612i | \(-0.442294\pi\) | ||||
0.180297 | + | 0.983612i | \(0.442294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.08655 | −0.287162 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.62970i | 0.389576i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.9960i | 0.646073i | 0.946386 | + | 0.323037i | \(0.104704\pi\) | ||||
−0.946386 | + | 0.323037i | \(0.895296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.9310 | 0.964991 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.99772 | 0.120684 | 0.0603418 | − | 0.998178i | \(-0.480781\pi\) | ||||
0.0603418 | + | 0.998178i | \(0.480781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0279i | 0.604024i | 0.953304 | + | 0.302012i | \(0.0976583\pi\) | ||||
−0.953304 | + | 0.302012i | \(0.902342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 4.00000i | − 0.160514i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.56531 | 0.102777 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6448 | −1.18579 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 24.1094i | − 0.962835i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.14664i | 0.0855922i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.3701 | 0.771112 | 0.385556 | − | 0.922684i | \(-0.374010\pi\) | ||||
0.385556 | + | 0.922684i | \(0.374010\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.3910 | −0.452753 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.5255i | 2.04473i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.7905i | 1.41807i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8216 | 0.467657 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4489 | 0.531200 | 0.265600 | − | 0.964083i | \(-0.414430\pi\) | ||||
0.265600 | + | 0.964083i | \(0.414430\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.44662i | 0.0964852i | 0.998836 | + | 0.0482426i | \(0.0153621\pi\) | ||||
−0.998836 | + | 0.0482426i | \(0.984638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 23.9310i | − 0.942282i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1275 | 0.634038 | 0.317019 | − | 0.948419i | \(-0.397318\pi\) | ||||
0.317019 | + | 0.948419i | \(0.397318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.0008 | 1.84494 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.96722i | − 0.0771015i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 28.6244i | − 1.12016i | −0.828439 | − | 0.560080i | \(-0.810770\pi\) | ||||
0.828439 | − | 0.560080i | \(-0.189230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.7255 | 1.70850 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2809 | −0.596166 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.75185i | 0.185106i | 0.995708 | + | 0.0925528i | \(0.0295027\pi\) | ||||
−0.995708 | + | 0.0925528i | \(0.970497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.8086i | 0.848256i | 0.905602 | + | 0.424128i | \(0.139419\pi\) | ||||
−0.905602 | + | 0.424128i | \(0.860581\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.03957 | 0.195721 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.9457 | −0.579571 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 30.8914i | − 1.19612i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 4.78110i | − 0.184848i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0856521 | 0.00330656 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.34315 | 0.244510 | 0.122255 | − | 0.992499i | \(-0.460987\pi\) | ||||
0.122255 | + | 0.992499i | \(0.460987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.23304i | − 0.0474597i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 45.6339i | − 1.75385i | −0.480624 | − | 0.876927i | \(-0.659590\pi\) | ||||
0.480624 | − | 0.876927i | \(-0.340410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.07913 | 0.0797898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.83840 | −0.147088 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.9342i | 1.45151i | 0.687953 | + | 0.725756i | \(0.258510\pi\) | ||||
−0.687953 | + | 0.725756i | \(0.741490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20.6173i | − 0.787746i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.34596 | −0.0513515 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.7219 | 0.751345 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3716i | 1.26951i | 0.772712 | + | 0.634757i | \(0.218900\pi\) | ||||
−0.772712 | + | 0.634757i | \(0.781100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.39104i | 0.128815i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.7120 | 1.39256 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.31143 | −0.314818 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 17.6433i | − 0.667330i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.4480i | 0.885618i | 0.896616 | + | 0.442809i | \(0.146018\pi\) | ||||
−0.896616 | + | 0.442809i | \(0.853982\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1512 | −0.609154 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.13651 | −0.155790 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.16569i | 0.344711i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 12.1562i | − 0.456537i | −0.973598 | − | 0.228269i | \(-0.926694\pi\) | ||||
0.973598 | − | 0.228269i | \(-0.0733064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.40968 | −0.315388 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.57544 | 0.321153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.6233i | 2.00540i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.61500i | 0.359079i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.06900 | −0.151748 | −0.0758741 | − | 0.997117i | \(-0.524175\pi\) | ||||
−0.0758741 | + | 0.997117i | \(0.524175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0653 | −0.561061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 21.3583i | − 0.794322i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 9.52259i | − 0.353660i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3211 | 0.642402 | 0.321201 | − | 0.947011i | \(-0.395913\pi\) | ||||
0.321201 | + | 0.947011i | \(0.395913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.31143i | 0.307409i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4361i | 0.791761i | 0.918302 | + | 0.395880i | \(0.129561\pi\) | ||||
−0.918302 | + | 0.395880i | \(0.870439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.3741 | −0.567082 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.6871 | 0.725183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 31.2545i | − 1.14972i | −0.818253 | − | 0.574858i | \(-0.805057\pi\) | ||||
0.818253 | − | 0.574858i | \(-0.194943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 37.9174i | 1.39293i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.7244 | 0.650244 | 0.325122 | − | 0.945672i | \(-0.394595\pi\) | ||||
0.325122 | + | 0.945672i | \(0.394595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.3288 | 1.47753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.96134i | 0.0717615i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2428i | 0.410801i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.38826 | 0.269601 | 0.134801 | − | 0.990873i | \(-0.456961\pi\) | ||||
0.134801 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.30448 | 0.156864 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 48.1073i | − 1.75080i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2804i | 0.482684i | 0.970440 | + | 0.241342i | \(0.0775876\pi\) | ||||
−0.970440 | + | 0.241342i | \(0.922412\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.7821 | −0.536555 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.1473 | −1.02034 | −0.510169 | − | 0.860074i | \(-0.670417\pi\) | ||||
−0.510169 | + | 0.860074i | \(0.670417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.7898i | 0.607830i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.16478i | 0.0782679i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −73.9194 | −2.66907 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9355 | −0.430405 | −0.215203 | − | 0.976569i | \(-0.569041\pi\) | ||||
−0.215203 | + | 0.976569i | \(0.569041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.67271i | 0.168284i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5868i | 0.524649i | 0.964980 | + | 0.262325i | \(0.0844891\pi\) | ||||
−0.964980 | + | 0.262325i | \(0.915511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.64347 | 0.0949561 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.27170 | 0.0814969 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 62.5347i | − 2.24054i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 43.6871i | − 1.56325i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.72286 | −0.275992 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.04429 | 0.0729638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.6835i | 1.37892i | 0.724325 | + | 0.689459i | \(0.242151\pi\) | ||||
−0.724325 | + | 0.689459i | \(0.757849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.4502i | 0.550042i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.35556 | −0.119310 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.134707 | −0.00478360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.47170i | 0.300460i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.4107i | 1.04178i | 0.853624 | + | 0.520890i | \(0.174400\pi\) | ||||
−0.853624 | + | 0.520890i | \(0.825600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.43664 | 0.0508248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.79565 | 0.0987794 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.4710i | 1.99282i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.16362i | 0.322975i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.2459 | 1.09991 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.80334 | −0.0985602 | −0.0492801 | − | 0.998785i | \(-0.515693\pi\) | ||||
−0.0492801 | + | 0.998785i | \(0.515693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.0722i | 1.79339i | 0.442650 | + | 0.896694i | \(0.354038\pi\) | ||||
−0.442650 | + | 0.896694i | \(0.645962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9.88817i | − 0.346793i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −59.0426 | −2.06817 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.5347 | −2.18781 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 5.33317i | − 0.186356i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4389i | 0.608622i | 0.952573 | + | 0.304311i | \(0.0984261\pi\) | ||||
−0.952573 | + | 0.304311i | \(0.901574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0665 | −0.769191 | −0.384595 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.55672 | −0.158645 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.76621i | 0.0614172i | 0.999528 | + | 0.0307086i | \(0.00977639\pi\) | ||||
−0.999528 | + | 0.0307086i | \(0.990224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 22.0514i | − 0.765879i | −0.923774 | − | 0.382939i | \(-0.874912\pi\) | ||||
0.923774 | − | 0.382939i | \(-0.125088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.9565 | 0.796351 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.33954 | 0.185004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 23.2274i | − 0.803816i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.14386i | − 0.0741026i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1904 | −0.766099 | −0.383050 | − | 0.923728i | \(-0.625126\pi\) | ||||
−0.383050 | + | 0.923728i | \(0.625126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.6425 | −1.05664 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 14.5754i | − 0.502005i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 51.8789i | − 1.78469i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.43795 | 0.0837690 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.71832 | 0.161932 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.90272i | 0.339461i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 37.4972i | − 1.28388i | −0.766756 | − | 0.641939i | \(-0.778130\pi\) | ||||
0.766756 | − | 0.641939i | \(-0.221870\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.2877 | −0.557028 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.4761 | 0.596971 | 0.298485 | − | 0.954414i | \(-0.403519\pi\) | ||||
0.298485 | + | 0.954414i | \(0.403519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7442i | 0.366586i | 0.983058 | + | 0.183293i | \(0.0586757\pi\) | ||||
−0.983058 | + | 0.183293i | \(0.941324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.79565i | 0.299755i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1791 | −0.789027 | −0.394514 | − | 0.918890i | \(-0.629087\pi\) | ||||
−0.394514 | + | 0.918890i | \(0.629087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7398 | −0.603171 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.2482i | 0.551816i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.0781i | 1.05425i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9624 | −1.04912 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.26582 | 0.0766863 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.62975i | − 0.291739i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 28.3694i | − 0.957966i | −0.877824 | − | 0.478983i | \(-0.841005\pi\) | ||||
0.877824 | − | 0.478983i | \(-0.158995\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.9204 | −0.806816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −58.0822 | −1.95684 | −0.978420 | − | 0.206628i | \(-0.933751\pi\) | ||||
−0.978420 | + | 0.206628i | \(0.933751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.55826i | 0.187050i | 0.995617 | + | 0.0935252i | \(0.0298136\pi\) | ||||
−0.995617 | + | 0.0935252i | \(0.970186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 31.7526i | − 1.06735i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.24359 | −0.310369 | −0.155185 | − | 0.987885i | \(-0.549597\pi\) | ||||
−0.155185 | + | 0.987885i | \(0.549597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9378 | −0.635153 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.69552i | 0.123805i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.8092i | 0.361717i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.67271 | −0.223044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.2482 | 0.776233 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 16.5567i | − 0.552198i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.94229i | − 0.0980219i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.79565 | 0.292701 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.59899 | 0.0531522 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4945i | 0.514487i | 0.966347 | + | 0.257243i | \(0.0828142\pi\) | ||||
−0.966347 | + | 0.257243i | \(0.917186\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.98868i | 0.331303i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.7108 | 1.44820 | 0.724101 | − | 0.689693i | \(-0.242255\pi\) | ||||
0.724101 | + | 0.689693i | \(0.242255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.24815 | 0.239879 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 0.0578646i | − 0.00191294i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0710i | 0.530710i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.7955 | 1.37871 | 0.689353 | − | 0.724426i | \(-0.257895\pi\) | ||||
0.689353 | + | 0.724426i | \(0.257895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.7685 | −0.684345 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.7078i | 2.26155i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.05261i | 0.100369i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.4180 | −0.539238 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.1989 | 0.793942 | 0.396971 | − | 0.917831i | \(-0.370061\pi\) | ||||
0.396971 | + | 0.917831i | \(0.370061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1744i | 1.31666i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7798i | 0.385653i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3183 | −0.500426 | −0.250213 | − | 0.968191i | \(-0.580501\pi\) | ||||
−0.250213 | + | 0.968191i | \(0.580501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1580i | 0.364127i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3016i | 1.15080i | 0.817872 | + | 0.575400i | \(0.195154\pi\) | ||||
−0.817872 | + | 0.575400i | \(0.804846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.3417 | −1.24858 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.29090 | 0.0745231 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 14.2051i | − 0.461605i | −0.973001 | − | 0.230802i | \(-0.925865\pi\) | ||||
0.973001 | − | 0.230802i | \(-0.0741351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 88.8134i | − 2.88300i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.9140 | −0.516048 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6428 | 0.636292 | 0.318146 | − | 0.948042i | \(-0.396940\pi\) | ||||
0.318146 | + | 0.948042i | \(0.396940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 36.4597i | − 1.17981i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.5400i | 0.922566i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.57772 | 0.244697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4039 | −0.851738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.2522i | 0.394823i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 22.0072i | − 0.708437i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.5337 | −1.43211 | −0.716054 | − | 0.698045i | \(-0.754054\pi\) | ||||
−0.716054 | + | 0.698045i | \(0.754054\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.65685 | 0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.40255i | − 0.0450099i | −0.999747 | − | 0.0225049i | \(-0.992836\pi\) | ||||
0.999747 | − | 0.0225049i | \(-0.00716415\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.4932i | 0.432572i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.16648 | 0.229511 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.0794 | −1.18628 | −0.593138 | − | 0.805101i | \(-0.702111\pi\) | ||||
−0.593138 | + | 0.805101i | \(0.702111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 10.3314i | − 0.330192i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2973i | 0.584188i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.6894 | −1.48916 | −0.744580 | − | 0.667534i | \(-0.767350\pi\) | ||||
−0.744580 | + | 0.667534i | \(0.767350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.35105 | 0.297949 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.52034i | − 0.0483930i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.3417i | 1.21919i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8780 | −0.377318 | −0.188659 | − | 0.982043i | \(-0.560414\pi\) | ||||
−0.188659 | + | 0.982043i | \(0.560414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.73190 | −0.0866942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 37.0164i | − 1.17350i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 51.1515i | − 1.61998i | −0.586441 | − | 0.809992i | \(-0.699472\pi\) | ||||
0.586441 | − | 0.809992i | \(-0.300528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.47568 | 0.0783271 |
(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 | 3072.2.d.e.1537.4 | 8 | ||
4.3 | odd | 2 | 3072.2.d.j.1537.8 | 8 | |||
8.3 | odd | 2 | 3072.2.d.j.1537.1 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.e.1537.5 | 8 | ||
16.3 | odd | 4 | 3072.2.a.j.1.4 | 4 | |||
16.5 | even | 4 | 3072.2.a.m.1.1 | 4 | |||
16.11 | odd | 4 | 3072.2.a.p.1.1 | 4 | |||
16.13 | even | 4 | 3072.2.a.s.1.4 | 4 | |||
32.3 | odd | 8 | 1536.2.j.f.385.1 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.e.1153.3 | yes | 8 | ||
32.11 | odd | 8 | 1536.2.j.i.1153.4 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.j.385.2 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.i.385.4 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.j.1153.2 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.f.1153.1 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.e.385.3 | ✓ | 8 | ||
48.5 | odd | 4 | 9216.2.a.bl.1.4 | 4 | |||
48.11 | even | 4 | 9216.2.a.z.1.4 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bm.1.1 | 4 | |||
48.35 | even | 4 | 9216.2.a.ba.1.1 | 4 | |||
96.5 | odd | 8 | 4608.2.k.bh.1153.3 | 8 | |||
96.11 | even | 8 | 4608.2.k.bc.1153.2 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bh.3457.3 | 8 | |||
96.35 | even | 8 | 4608.2.k.bj.3457.3 | 8 | |||
96.53 | odd | 8 | 4608.2.k.be.1153.2 | 8 | |||
96.59 | even | 8 | 4608.2.k.bj.1153.3 | 8 | |||
96.77 | odd | 8 | 4608.2.k.be.3457.2 | 8 | |||
96.83 | even | 8 | 4608.2.k.bc.3457.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.e.385.3 | ✓ | 8 | 32.29 | even | 8 | ||
1536.2.j.e.1153.3 | yes | 8 | 32.5 | even | 8 | ||
1536.2.j.f.385.1 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.f.1153.1 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.i.385.4 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.i.1153.4 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.j.385.2 | yes | 8 | 32.13 | even | 8 | ||
1536.2.j.j.1153.2 | yes | 8 | 32.21 | even | 8 | ||
3072.2.a.j.1.4 | 4 | 16.3 | odd | 4 | |||
3072.2.a.m.1.1 | 4 | 16.5 | even | 4 | |||
3072.2.a.p.1.1 | 4 | 16.11 | odd | 4 | |||
3072.2.a.s.1.4 | 4 | 16.13 | even | 4 | |||
3072.2.d.e.1537.4 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.e.1537.5 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.j.1537.1 | 8 | 8.3 | odd | 2 | |||
3072.2.d.j.1537.8 | 8 | 4.3 | odd | 2 | |||
4608.2.k.bc.1153.2 | 8 | 96.11 | even | 8 | |||
4608.2.k.bc.3457.2 | 8 | 96.83 | even | 8 | |||
4608.2.k.be.1153.2 | 8 | 96.53 | odd | 8 | |||
4608.2.k.be.3457.2 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bh.1153.3 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bh.3457.3 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bj.1153.3 | 8 | 96.59 | even | 8 | |||
4608.2.k.bj.3457.3 | 8 | 96.35 | even | 8 | |||
9216.2.a.z.1.4 | 4 | 48.11 | even | 4 | |||
9216.2.a.ba.1.1 | 4 | 48.35 | even | 4 | |||
9216.2.a.bl.1.4 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bm.1.1 | 4 | 48.29 | odd | 4 |