Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.a (trivial) |
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: | yes |
Analytic conductor: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1100) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.79129 | −1.61155 | −0.805775 | − | 0.592221i | \(-0.798251\pi\) | ||||
−0.805775 | + | 0.592221i | \(0.798251\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.208712 | −0.0788858 | −0.0394429 | − | 0.999222i | \(-0.512558\pi\) | ||||
−0.0394429 | + | 0.999222i | \(0.512558\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.791288 | −0.191915 | −0.0959577 | − | 0.995385i | \(-0.530591\pi\) | ||||
−0.0959577 | + | 0.995385i | \(0.530591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.58258 | −1.51015 | −0.755073 | − | 0.655640i | \(-0.772399\pi\) | ||||
−0.755073 | + | 0.655640i | \(0.772399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.582576 | 0.127128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.79129 | −0.790538 | −0.395269 | − | 0.918565i | \(-0.629349\pi\) | ||||
−0.395269 | + | 0.918565i | \(0.629349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.79129 | 1.26111 | 0.630555 | − | 0.776144i | \(-0.282827\pi\) | ||||
0.630555 | + | 0.776144i | \(0.282827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.58258 | 1.54148 | 0.770738 | − | 0.637152i | \(-0.219888\pi\) | ||||
0.770738 | + | 0.637152i | \(0.219888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.79129 | −0.485901 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.58258 | 0.424573 | 0.212286 | − | 0.977207i | \(-0.431909\pi\) | ||||
0.212286 | + | 0.977207i | \(0.431909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.79129 | −0.446964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41742 | −0.221364 | −0.110682 | − | 0.993856i | \(-0.535304\pi\) | ||||
−0.110682 | + | 0.993856i | \(0.535304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.41742 | −0.206753 | −0.103376 | − | 0.994642i | \(-0.532965\pi\) | ||||
−0.103376 | + | 0.994642i | \(0.532965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95644 | −0.993777 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.20871 | 0.309282 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.3739 | −1.56232 | −0.781160 | − | 0.624331i | \(-0.785372\pi\) | ||||
−0.781160 | + | 0.624331i | \(0.785372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.3739 | 2.43368 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.5826 | 1.37773 | 0.688867 | − | 0.724888i | \(-0.258108\pi\) | ||||
0.688867 | + | 0.724888i | \(0.258108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.20871 | 0.538870 | 0.269435 | − | 0.963019i | \(-0.413163\pi\) | ||||
0.269435 | + | 0.963019i | \(0.413163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5826 | 1.27399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7477 | 1.27552 | 0.637760 | − | 0.770235i | \(-0.279861\pi\) | ||||
0.637760 | + | 0.770235i | \(0.279861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79129 | 0.911901 | 0.455951 | − | 0.890005i | \(-0.349299\pi\) | ||||
0.455951 | + | 0.890005i | \(0.349299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.208712 | −0.0237850 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5390 | 1.74828 | 0.874138 | − | 0.485678i | \(-0.161427\pi\) | ||||
0.874138 | + | 0.485678i | \(0.161427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.95644 | −1.09286 | −0.546431 | − | 0.837504i | \(-0.684014\pi\) | ||||
−0.546431 | + | 0.837504i | \(0.684014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.9564 | −2.03234 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.791288 | −0.0838763 | −0.0419382 | − | 0.999120i | \(-0.513353\pi\) | ||||
−0.0419382 | + | 0.999120i | \(0.513353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.208712 | −0.0218790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.9564 | −2.48417 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.20871 | 0.630399 | 0.315200 | − | 0.949025i | \(-0.397929\pi\) | ||||
0.315200 | + | 0.949025i | \(0.397929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.79129 | 0.481543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3739 | −1.72876 | −0.864382 | − | 0.502836i | \(-0.832290\pi\) | ||||
−0.864382 | + | 0.502836i | \(0.832290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.95644 | 0.586905 | 0.293453 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293453 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.7477 | 1.90908 | 0.954542 | − | 0.298075i | \(-0.0963446\pi\) | ||||
0.954542 | + | 0.298075i | \(0.0963446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.79129 | −0.458922 | −0.229461 | − | 0.973318i | \(-0.573696\pi\) | ||||
−0.229461 | + | 0.973318i | \(0.573696\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.20871 | −0.684221 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.41742 | −0.133340 | −0.0666700 | − | 0.997775i | \(-0.521237\pi\) | ||||
−0.0666700 | + | 0.997775i | \(0.521237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.79129 | 0.442955 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.165151 | 0.0151394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.95644 | 0.356740 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3739 | 1.45295 | 0.726473 | − | 0.687195i | \(-0.241158\pi\) | ||||
0.726473 | + | 0.687195i | \(0.241158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.9129 | 2.45759 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.626136 | 0.0547058 | 0.0273529 | − | 0.999626i | \(-0.491292\pi\) | ||||
0.0273529 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37386 | 0.119129 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5390 | 0.985845 | 0.492922 | − | 0.870073i | \(-0.335929\pi\) | ||||
0.492922 | + | 0.870073i | \(0.335929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.74773 | −0.826791 | −0.413396 | − | 0.910551i | \(-0.635657\pi\) | ||||
−0.413396 | + | 0.910551i | \(0.635657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.95644 | 0.333192 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.4174 | 1.60152 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.16515 | 0.259299 | 0.129650 | − | 0.991560i | \(-0.458615\pi\) | ||||
0.129650 | + | 0.991560i | \(0.458615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.79129 | −0.306507 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1652 | −1.36993 | −0.684964 | − | 0.728577i | \(-0.740182\pi\) | ||||
−0.684964 | + | 0.728577i | \(0.740182\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.7477 | 2.51776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.791288 | 0.0623622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.3739 | −1.67413 | −0.837065 | − | 0.547103i | \(-0.815730\pi\) | ||||
−0.837065 | + | 0.547103i | \(0.815730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5826 | −1.28320 | −0.641599 | − | 0.767040i | \(-0.721729\pi\) | ||||
−0.641599 | + | 0.767040i | \(0.721729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.5390 | −2.41185 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7477 | 1.04522 | 0.522610 | − | 0.852572i | \(-0.324958\pi\) | ||||
0.522610 | + | 0.852572i | \(0.324958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −29.5390 | −2.22029 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1216 | −1.65345 | −0.826723 | − | 0.562610i | \(-0.809797\pi\) | ||||
−0.826723 | + | 0.562610i | \(0.809797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.37386 | −0.250777 | −0.125389 | − | 0.992108i | \(-0.540018\pi\) | ||||
−0.125389 | + | 0.992108i | \(0.540018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.7477 | −0.868417 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.791288 | −0.0578647 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.04356 | 0.0759079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2087 | −1.24518 | −0.622589 | − | 0.782549i | \(-0.713919\pi\) | ||||
−0.622589 | + | 0.782549i | \(0.713919\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.16515 | 0.515759 | 0.257879 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257879 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.5390 | −1.89083 | −0.945413 | − | 0.325874i | \(-0.894342\pi\) | ||||
−0.945413 | + | 0.325874i | \(0.894342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.62614 | 0.115274 | 0.0576369 | − | 0.998338i | \(-0.481643\pi\) | ||||
0.0576369 | + | 0.998338i | \(0.481643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1652 | 0.787529 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.41742 | −0.0994837 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.1652 | −1.26257 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.58258 | −0.455326 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −30.0000 | −2.05557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.79129 | −0.121601 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.7477 | −1.46958 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.791288 | −0.0532278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5826 | −1.37831 | −0.689156 | − | 0.724613i | \(-0.742018\pi\) | ||||
−0.689156 | + | 0.724613i | \(0.742018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5390 | 0.765871 | 0.382936 | − | 0.923775i | \(-0.374913\pi\) | ||||
0.382936 | + | 0.923775i | \(0.374913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.62614 | −0.503949 | −0.251975 | − | 0.967734i | \(-0.581080\pi\) | ||||
−0.251975 | + | 0.967734i | \(0.581080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.582576 | 0.0383307 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.7913 | −1.03452 | −0.517261 | − | 0.855828i | \(-0.673048\pi\) | ||||
−0.517261 | + | 0.855828i | \(0.673048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −43.3739 | −2.81744 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.20871 | 0.142870 | 0.0714349 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714349 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1216 | −1.48939 | −0.744696 | − | 0.667404i | \(-0.767406\pi\) | ||||
−0.744696 | + | 0.667404i | \(0.767406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1652 | 1.03699 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.58258 | −0.418839 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.7913 | 1.76120 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5390 | 0.728336 | 0.364168 | − | 0.931333i | \(-0.381353\pi\) | ||||
0.364168 | + | 0.931333i | \(0.381353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.79129 | −0.238356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.539015 | −0.0334928 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.5390 | 2.01411 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1652 | 1.49009 | 0.745044 | − | 0.667016i | \(-0.232429\pi\) | ||||
0.745044 | + | 0.667016i | \(0.232429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.20871 | 0.135171 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7042 | −1.26236 | −0.631178 | − | 0.775638i | \(-0.717428\pi\) | ||||
−0.631178 | + | 0.775638i | \(0.717428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.7477 | −0.956606 | −0.478303 | − | 0.878195i | \(-0.658748\pi\) | ||||
−0.478303 | + | 0.878195i | \(0.658748\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.582576 | 0.0352591 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.58258 | 0.515677 | 0.257838 | − | 0.966188i | \(-0.416990\pi\) | ||||
0.257838 | + | 0.966188i | \(0.416990\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 41.1216 | 2.46189 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.7477 | −0.820121 | −0.410060 | − | 0.912058i | \(-0.634492\pi\) | ||||
−0.410060 | + | 0.912058i | \(0.634492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.7042 | −1.82517 | −0.912587 | − | 0.408883i | \(-0.865918\pi\) | ||||
−0.912587 | + | 0.408883i | \(0.865918\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.295834 | 0.0174625 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3739 | −0.963168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.3303 | −1.01592 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.83485 | 0.165614 | 0.0828068 | − | 0.996566i | \(-0.473612\pi\) | ||||
0.0828068 | + | 0.996566i | \(0.473612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00000 | −0.290129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.79129 | −0.219256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08712 | 0.120300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 48.4955 | 2.78599 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.2087 | −1.55288 | −0.776442 | − | 0.630189i | \(-0.782977\pi\) | ||||
−0.776442 | + | 0.630189i | \(0.782977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.6261 | −0.945828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.83485 | 0.330864 | 0.165432 | − | 0.986221i | \(-0.447098\pi\) | ||||
0.165432 | + | 0.986221i | \(0.447098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.74773 | −0.381404 | −0.190702 | − | 0.981648i | \(-0.561076\pi\) | ||||
−0.190702 | + | 0.981648i | \(0.561076\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.37386 | 0.470323 | 0.235162 | − | 0.971956i | \(-0.424438\pi\) | ||||
0.235162 | + | 0.971956i | \(0.424438\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.79129 | 0.380239 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.1216 | −3.07659 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.20871 | 0.289820 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.3739 | 0.739576 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.295834 | 0.0163098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3303 | −0.952560 | −0.476280 | − | 0.879294i | \(-0.658015\pi\) | ||||
−0.476280 | + | 0.879294i | \(0.658015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.3739 | 0.678084 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.95644 | 0.214884 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.58258 | 0.464773 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.91288 | 0.157281 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6261 | 0.677807 | 0.338903 | − | 0.940821i | \(-0.389944\pi\) | ||||
0.338903 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5826 | −0.780587 | −0.390294 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390294 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.1652 | −0.966833 | −0.483417 | − | 0.875390i | \(-0.660604\pi\) | ||||
−0.483417 | + | 0.875390i | \(0.660604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.460985 | −0.0243979 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.3303 | 1.28054 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.79129 | −0.146505 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.62614 | 0.450281 | 0.225140 | − | 0.974326i | \(-0.427716\pi\) | ||||
0.225140 | + | 0.974326i | \(0.427716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.79129 | −0.353540 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.37386 | 0.123245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.3303 | 1.00089 | 0.500443 | − | 0.865770i | \(-0.333171\pi\) | ||||
0.500443 | + | 0.865770i | \(0.333171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.79129 | 0.349769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.0000 | 1.59236 | 0.796182 | − | 0.605058i | \(-0.206850\pi\) | ||||
0.796182 | + | 0.605058i | \(0.206850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.7042 | −2.34150 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | −0.919757 | −0.459879 | − | 0.887982i | \(-0.652107\pi\) | ||||
−0.459879 | + | 0.887982i | \(0.652107\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −47.9129 | −2.43555 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | 0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.74773 | −0.0881612 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.20871 | −0.361795 | −0.180897 | − | 0.983502i | \(-0.557900\pi\) | ||||
−0.180897 | + | 0.983502i | \(0.557900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.83485 | −0.191983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8348 | −0.740817 | −0.370408 | − | 0.928869i | \(-0.620782\pi\) | ||||
−0.370408 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.58258 | 0.427529 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58258 | 0.128014 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0000 | 0.840596 | 0.420298 | − | 0.907386i | \(-0.361926\pi\) | ||||
0.420298 | + | 0.907386i | \(0.361926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.2087 | −1.58874 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20871 | −0.108684 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.2087 | 1.33242 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.0000 | −1.31904 | −0.659518 | − | 0.751689i | \(-0.729240\pi\) | ||||
−0.659518 | + | 0.751689i | \(0.729240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3739 | 1.23665 | 0.618323 | − | 0.785924i | \(-0.287812\pi\) | ||||
0.618323 | + | 0.785924i | \(0.287812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.79129 | −0.330204 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.878409 | −0.0425092 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.79129 | −0.134765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.9129 | −0.525655 | −0.262827 | − | 0.964843i | \(-0.584655\pi\) | ||||
−0.262827 | + | 0.964843i | \(0.584655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3303 | 0.640613 | 0.320307 | − | 0.947314i | \(-0.396214\pi\) | ||||
0.320307 | + | 0.947314i | \(0.396214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.9564 | 1.19383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9564 | −0.570650 | −0.285325 | − | 0.958431i | \(-0.592101\pi\) | ||||
−0.285325 | + | 0.958431i | \(0.592101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.3303 | −1.58716 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.4174 | 1.06508 | 0.532542 | − | 0.846404i | \(-0.321237\pi\) | ||||
0.532542 | + | 0.846404i | \(0.321237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.83485 | −0.417874 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.2087 | 1.23687 | 0.618433 | − | 0.785838i | \(-0.287768\pi\) | ||||
0.618433 | + | 0.785838i | \(0.287768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.41742 | −0.0667439 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.9564 | 0.655731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.3739 | −0.625603 | −0.312801 | − | 0.949819i | \(-0.601267\pi\) | ||||
−0.312801 | + | 0.949819i | \(0.601267\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.95644 | 0.184671 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4955 | −1.14087 | −0.570434 | − | 0.821344i | \(-0.693225\pi\) | ||||
−0.570434 | + | 0.821344i | \(0.693225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.25227 | −0.104672 | −0.0523360 | − | 0.998630i | \(-0.516667\pi\) | ||||
−0.0523360 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5826 | 0.489703 | 0.244852 | − | 0.969561i | \(-0.421261\pi\) | ||||
0.244852 | + | 0.969561i | \(0.421261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.834849 | 0.0385497 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 47.9129 | 2.20771 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0000 | −0.459800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −54.4955 | −2.49518 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.165151 | −0.00754596 | −0.00377298 | − | 0.999993i | \(-0.501201\pi\) | ||||
−0.00377298 | + | 0.999993i | \(0.501201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.58258 | 0.117755 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.20871 | −0.100500 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7477 | −1.34800 | −0.673999 | − | 0.738732i | \(-0.735425\pi\) | ||||
−0.673999 | + | 0.738732i | \(0.735425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 59.6606 | 2.69795 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.41742 | 0.334744 | 0.167372 | − | 0.985894i | \(-0.446472\pi\) | ||||
0.167372 | + | 0.985894i | \(0.446472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.37386 | −0.242027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.24318 | −0.100620 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9564 | −0.669542 | −0.334771 | − | 0.942299i | \(-0.608659\pi\) | ||||
−0.334771 | + | 0.942299i | \(0.608659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.2867 | 2.06794 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.4174 | 0.732017 | 0.366008 | − | 0.930612i | \(-0.380724\pi\) | ||||
0.366008 | + | 0.930612i | \(0.380724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.4955 | 1.48759 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1216 | 0.448632 | 0.224316 | − | 0.974517i | \(-0.427985\pi\) | ||||
0.224316 | + | 0.974517i | \(0.427985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.62614 | −0.0719360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9129 | 1.45314 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41742 | −0.0623382 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.3739 | −1.68443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.58258 | 0.0693339 | 0.0346670 | − | 0.999399i | \(-0.488963\pi\) | ||||
0.0346670 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.1652 | −1.10040 | −0.550198 | − | 0.835034i | \(-0.685448\pi\) | ||||
−0.550198 | + | 0.835034i | \(0.685448\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.79129 | −0.295833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.62614 | −0.375049 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 50.7042 | 2.20037 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.41742 | −0.0613955 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 61.7477 | 2.66461 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.95644 | −0.299635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6261 | −0.456853 | −0.228427 | − | 0.973561i | \(-0.573358\pi\) | ||||
−0.228427 | + | 0.973561i | \(0.573358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.41742 | 0.404140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.37386 | 0.315284 | 0.157642 | − | 0.987496i | \(-0.449611\pi\) | ||||
0.157642 | + | 0.987496i | \(0.449611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.1652 | 0.860628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44.7042 | −1.90446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.24318 | −0.137914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.6606 | 1.93470 | 0.967351 | − | 0.253441i | \(-0.0815622\pi\) | ||||
0.967351 | + | 0.253441i | \(0.0815622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.20871 | 0.0932519 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.1216 | −1.69092 | −0.845462 | − | 0.534036i | \(-0.820675\pi\) | ||||
−0.845462 | + | 0.534036i | \(0.820675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0871215 | 0.00365876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9564 | 0.794695 | 0.397348 | − | 0.917668i | \(-0.369931\pi\) | ||||
0.397348 | + | 0.917668i | \(0.369931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.2867 | −1.14191 | −0.570957 | − | 0.820980i | \(-0.693428\pi\) | ||||
−0.570957 | + | 0.820980i | \(0.693428\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.0345 | 2.00667 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.9564 | −0.497753 | −0.248877 | − | 0.968535i | \(-0.580061\pi\) | ||||
−0.248877 | + | 0.968535i | \(0.580061\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.07803 | 0.0862112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3739 | −0.471057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.9564 | 0.658593 | 0.329296 | − | 0.944227i | \(-0.393188\pi\) | ||||
0.329296 | + | 0.944227i | \(0.393188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.4955 | −2.32785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 74.0780 | 3.04716 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5826 | 0.927355 | 0.463678 | − | 0.886004i | \(-0.346530\pi\) | ||||
0.463678 | + | 0.886004i | \(0.346530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.53901 | −0.185770 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.7042 | −1.82656 | −0.913281 | − | 0.407329i | \(-0.866460\pi\) | ||||
−0.913281 | + | 0.407329i | \(0.866460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.5390 | 1.16413 | 0.582065 | − | 0.813142i | \(-0.302245\pi\) | ||||
0.582065 | + | 0.813142i | \(0.302245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.1652 | −0.780465 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0000 | −1.38002 | −0.690009 | − | 0.723801i | \(-0.742393\pi\) | ||||
−0.690009 | + | 0.723801i | \(0.742393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.95644 | 0.160323 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.41742 | −0.0573428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.4519 | −1.35111 | −0.675555 | − | 0.737310i | \(-0.736096\pi\) | ||||
−0.675555 | + | 0.737310i | \(0.736096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.7477 | 1.15734 | 0.578670 | − | 0.815562i | \(-0.303572\pi\) | ||||
0.578670 | + | 0.815562i | \(0.303572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.25227 | −0.251300 | −0.125650 | − | 0.992075i | \(-0.540102\pi\) | ||||
−0.125650 | + | 0.992075i | \(0.540102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9564 | 0.760696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.165151 | 0.00661665 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.3739 | 0.733781 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.04356 | −0.0814821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1216 | −0.721409 | −0.360705 | − | 0.932680i | \(-0.617464\pi\) | ||||
−0.360705 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9564 | 0.554719 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.95644 | −0.275624 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 51.4955 | 2.03713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8348 | −0.941420 | −0.470710 | − | 0.882288i | \(-0.656002\pi\) | ||||
−0.470710 | + | 0.882288i | \(0.656002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.4955 | −1.71529 | −0.857647 | − | 0.514239i | \(-0.828074\pi\) | ||||
−0.857647 | + | 0.514239i | \(0.828074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.3303 | 0.838581 | 0.419290 | − | 0.907852i | \(-0.362279\pi\) | ||||
0.419290 | + | 0.907852i | \(0.362279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.5826 | 0.415402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.00000 | 0.195965 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.7042 | −1.04501 | −0.522507 | − | 0.852635i | \(-0.675003\pi\) | ||||
−0.522507 | + | 0.852635i | \(0.675003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.3303 | 1.45639 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.460985 | −0.0179574 | −0.00897871 | − | 0.999960i | \(-0.502858\pi\) | ||||
−0.00897871 | + | 0.999960i | \(0.502858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5826 | 1.18952 | 0.594762 | − | 0.803902i | \(-0.297246\pi\) | ||||
0.594762 | + | 0.803902i | \(0.297246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.20871 | 0.0857793 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.7477 | −0.996956 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 57.4519 | 2.22122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.20871 | 0.162476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.9129 | 1.49998 | 0.749991 | − | 0.661448i | \(-0.230058\pi\) | ||||
0.749991 | + | 0.661448i | \(0.230058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.58258 | 0.0608233 | 0.0304117 | − | 0.999537i | \(-0.490318\pi\) | ||||
0.0304117 | + | 0.999537i | \(0.490318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.29583 | −0.0497295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.2087 | −1.23424 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9129 | 1.33590 | 0.667952 | − | 0.744204i | \(-0.267171\pi\) | ||||
0.667952 | + | 0.744204i | \(0.267171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2867 | 0.812140 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3739 | −0.433310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.1216 | 1.22196 | 0.610981 | − | 0.791645i | \(-0.290775\pi\) | ||||
0.610981 | + | 0.791645i | \(0.290775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.12159 | 0.0424833 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.0780 | 1.66718 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8348 | 0.786921 | 0.393461 | − | 0.919341i | \(-0.371278\pi\) | ||||
0.393461 | + | 0.919341i | \(0.371278\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.0000 | −0.641167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.62614 | 0.136375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.4955 | 1.10773 | 0.553863 | − | 0.832608i | \(-0.313153\pi\) | ||||
0.553863 | + | 0.832608i | \(0.313153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 74.4519 | 2.79216 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.5390 | −1.21860 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.16515 | −0.230242 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.49545 | −0.242240 | −0.121120 | − | 0.992638i | \(-0.538649\pi\) | ||||
−0.121120 | + | 0.992638i | \(0.538649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.24318 | −0.0462985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 64.5390 | 2.40023 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1216 | −0.857532 | −0.428766 | − | 0.903416i | \(-0.641052\pi\) | ||||
−0.428766 | + | 0.903416i | \(0.641052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.91288 | 0.292668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.2432 | −1.15399 | −0.576997 | − | 0.816747i | \(-0.695775\pi\) | ||||
−0.576997 | + | 0.816747i | \(0.695775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1216 | −1.54947 | −0.774734 | − | 0.632287i | \(-0.782116\pi\) | ||||
−0.774734 | + | 0.632287i | \(0.782116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.3739 | 0.674981 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7913 | 1.45980 | 0.729900 | − | 0.683554i | \(-0.239566\pi\) | ||||
0.729900 | + | 0.683554i | \(0.239566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −47.7042 | −1.74540 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.12159 | −0.150600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2087 | −0.481993 | −0.240996 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240996 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32.2087 | −1.17375 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.33030 | 0.266424 | 0.133212 | − | 0.991088i | \(-0.457471\pi\) | ||||
0.133212 | + | 0.991088i | \(0.457471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.5826 | 0.384123 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.3303 | 1.09947 | 0.549736 | − | 0.835338i | \(-0.314728\pi\) | ||||
0.549736 | + | 0.835338i | \(0.314728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | 0.0362024 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5826 | 0.382115 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.7477 | −1.50546 | −0.752731 | − | 0.658328i | \(-0.771264\pi\) | ||||
−0.752731 | + | 0.658328i | \(0.771264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.2432 | 1.80946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.2087 | −0.942662 | −0.471331 | − | 0.881956i | \(-0.656226\pi\) | ||||
−0.471331 | + | 0.881956i | \(0.656226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.50455 | 0.0539753 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.33030 | 0.334293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7477 | 0.384584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −33.9564 | −1.21350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7477 | −0.632638 | −0.316319 | − | 0.948653i | \(-0.602447\pi\) | ||||
−0.316319 | + | 0.948653i | \(0.602447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −67.4519 | −2.40135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.295834 | 0.0105186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.20871 | 0.149456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.2867 | −1.21450 | −0.607249 | − | 0.794511i | \(-0.707727\pi\) | ||||
−0.607249 | + | 0.794511i | \(0.707727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.12159 | 0.0396790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.79129 | −0.133959 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.79129 | 0.274949 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 57.7913 | 2.03435 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.4955 | −1.59953 | −0.799767 | − | 0.600310i | \(-0.795044\pi\) | ||||
−0.799767 | + | 0.600310i | \(0.795044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.6606 | 1.95451 | 0.977254 | − | 0.212072i | \(-0.0680210\pi\) | ||||
0.977254 | + | 0.212072i | \(0.0680210\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.9564 | 1.54162 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.8258 | 2.30295 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.6606 | 1.69827 | 0.849133 | − | 0.528178i | \(-0.177125\pi\) | ||||
0.849133 | + | 0.528178i | \(0.177125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.4174 | −0.362249 | −0.181125 | − | 0.983460i | \(-0.557974\pi\) | ||||
−0.181125 | + | 0.983460i | \(0.557974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.9564 | −1.31828 | −0.659141 | − | 0.752020i | \(-0.729080\pi\) | ||||
−0.659141 | + | 0.752020i | \(0.729080\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.9564 | −0.831040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.50455 | 0.190721 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.9129 | −1.48329 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.7042 | 0.818359 | 0.409179 | − | 0.912454i | \(-0.365815\pi\) | ||||
0.409179 | + | 0.912454i | \(0.365815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.1216 | 0.590400 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.3739 | 1.32167 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.208712 | −0.00717143 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 85.7042 | 2.94136 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79129 | −0.335641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.12159 | −0.106881 | −0.0534406 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534406 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.4955 | 1.04170 | 0.520852 | − | 0.853647i | \(-0.325614\pi\) | ||||
0.520852 | + | 0.853647i | \(0.325614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.08712 | 0.0712117 | 0.0356058 | − | 0.999366i | \(-0.488664\pi\) | ||||
0.0356058 | + | 0.999366i | \(0.488664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.825757 | −0.0281417 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.3303 | −0.930334 | −0.465167 | − | 0.885223i | \(-0.654006\pi\) | ||||
−0.465167 | + | 0.885223i | \(0.654006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.7042 | 1.55219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.5390 | 0.527125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | −0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.7477 | 1.00681 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6606 | 0.562589 | 0.281294 | − | 0.959622i | \(-0.409236\pi\) | ||||
0.281294 | + | 0.959622i | \(0.409236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.91288 | −0.266895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.87841 | 0.0632852 | 0.0316426 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316426 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.1652 | 0.880527 | 0.440264 | − | 0.897869i | \(-0.354885\pi\) | ||||
0.440264 | + | 0.897869i | \(0.354885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.3303 | −1.32058 | −0.660291 | − | 0.751010i | \(-0.729567\pi\) | ||||
−0.660291 | + | 0.751010i | \(0.729567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.41742 | −0.114617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.417424 | −0.0139842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.33030 | 0.312227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5826 | 0.353342 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.2867 | 1.94397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.82576 | −0.193869 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.6606 | 1.08448 | 0.542239 | − | 0.840224i | \(-0.317577\pi\) | ||||
0.542239 | + | 0.840224i | \(0.317577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −83.2432 | −2.76100 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3303 | 0.408521 | 0.204261 | − | 0.978917i | \(-0.434521\pi\) | ||||
0.204261 | + | 0.978917i | \(0.434521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.95644 | −0.329510 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.130682 | −0.00431551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.8348 | −0.951174 | −0.475587 | − | 0.879669i | \(-0.657764\pi\) | ||||
−0.475587 | + | 0.879669i | \(0.657764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.9473 | 2.50255 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.7477 | 0.353766 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.5390 | 0.937344 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7477 | 0.451048 | 0.225524 | − | 0.974238i | \(-0.427591\pi\) | ||||
0.225524 | + | 0.974238i | \(0.427591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.7913 | 1.50075 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.2867 | −0.533204 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1652 | −1.14880 | −0.574398 | − | 0.818576i | \(-0.694764\pi\) | ||||
−0.574398 | + | 0.818576i | \(0.694764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.8348 | 0.614652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0780 | −1.63250 | −0.816249 | − | 0.577701i | \(-0.803950\pi\) | ||||
−0.816249 | + | 0.577701i | \(0.803950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.37386 | 0.174997 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.91288 | −0.159647 | −0.0798235 | − | 0.996809i | \(-0.525436\pi\) | ||||
−0.0798235 | + | 0.996809i | \(0.525436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.79129 | 0.252916 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3739 | −0.757949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000 | 1.36051 | 0.680257 | − | 0.732974i | \(-0.261868\pi\) | ||||
0.680257 | + | 0.732974i | \(0.261868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.9564 | −0.612775 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.40833 | −0.0777691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.6606 | 1.37615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 94.6170 | 3.04899 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5390 | 1.40012 | 0.700060 | − | 0.714084i | \(-0.253156\pi\) | ||||
0.700060 | + | 0.714084i | \(0.253156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.5390 | −0.467060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.9564 | −0.608341 | −0.304171 | − | 0.952618i | \(-0.598379\pi\) | ||||
−0.304171 | + | 0.952618i | \(0.598379\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.03447 | 0.0652221 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7477 | 0.823743 | 0.411871 | − | 0.911242i | \(-0.364875\pi\) | ||||
0.411871 | + | 0.911242i | \(0.364875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.791288 | −0.0252897 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.9564 | −0.732943 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.6606 | −1.55203 | −0.776016 | − | 0.630713i | \(-0.782763\pi\) | ||||
−0.776016 | + | 0.630713i | \(0.782763\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.825757 | −0.0262841 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.9129 | 1.20556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.8693 | −1.77475 | −0.887374 | − | 0.461051i | \(-0.847473\pi\) | ||||
−0.887374 | + | 0.461051i | \(0.847473\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.3739 | 1.53510 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.3739 | −1.27865 | −0.639327 | − | 0.768935i | \(-0.720787\pi\) | ||||
−0.639327 | + | 0.768935i | \(0.720787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.9129 | −0.408545 |
(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 | 4400.2.a.bi.1.1 | 2 | ||
4.3 | odd | 2 | 1100.2.a.h.1.2 | yes | 2 | ||
5.2 | odd | 4 | 4400.2.b.s.4049.4 | 4 | |||
5.3 | odd | 4 | 4400.2.b.s.4049.1 | 4 | |||
5.4 | even | 2 | 4400.2.a.bu.1.2 | 2 | |||
12.11 | even | 2 | 9900.2.a.bz.1.1 | 2 | |||
20.3 | even | 4 | 1100.2.b.d.749.4 | 4 | |||
20.7 | even | 4 | 1100.2.b.d.749.1 | 4 | |||
20.19 | odd | 2 | 1100.2.a.g.1.1 | ✓ | 2 | ||
60.23 | odd | 4 | 9900.2.c.x.5149.2 | 4 | |||
60.47 | odd | 4 | 9900.2.c.x.5149.3 | 4 | |||
60.59 | even | 2 | 9900.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1100.2.a.g.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
1100.2.a.h.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1100.2.b.d.749.1 | 4 | 20.7 | even | 4 | |||
1100.2.b.d.749.4 | 4 | 20.3 | even | 4 | |||
4400.2.a.bi.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.a.bu.1.2 | 2 | 5.4 | even | 2 | |||
4400.2.b.s.4049.1 | 4 | 5.3 | odd | 4 | |||
4400.2.b.s.4049.4 | 4 | 5.2 | odd | 4 | |||
9900.2.a.bh.1.2 | 2 | 60.59 | even | 2 | |||
9900.2.a.bz.1.1 | 2 | 12.11 | even | 2 | |||
9900.2.c.x.5149.2 | 4 | 60.23 | odd | 4 | |||
9900.2.c.x.5149.3 | 4 | 60.47 | odd | 4 |