Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.339877\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −0.339877 | −0.196228 | −0.0981140 | − | 0.995175i | \(-0.531281\pi\) | ||||
−0.0981140 | + | 0.995175i | \(0.531281\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.88448 | 1.46820 | 0.734098 | − | 0.679043i | \(-0.237605\pi\) | ||||
0.734098 | + | 0.679043i | \(0.237605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.88448 | −0.961495 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.54461 | 0.465716 | 0.232858 | − | 0.972511i | \(-0.425192\pi\) | ||||
0.232858 | + | 0.972511i | \(0.425192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.339877 | 0.0877558 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.86485 | −0.657242 | −0.328621 | − | 0.944462i | \(-0.606584\pi\) | ||||
−0.328621 | + | 0.944462i | \(0.606584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.32025 | −0.288101 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.42909 | −1.13204 | −0.566022 | − | 0.824390i | \(-0.691518\pi\) | ||||
−0.566022 | + | 0.824390i | \(0.691518\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.20473 | −0.966494 | −0.483247 | − | 0.875484i | \(-0.660543\pi\) | ||||
−0.483247 | + | 0.875484i | \(0.660543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.22436 | −1.11793 | −0.558964 | − | 0.829192i | \(-0.688801\pi\) | ||||
−0.558964 | + | 0.829192i | \(0.688801\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.524976 | −0.0913866 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.88448 | −0.656598 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.56424 | −1.40795 | −0.703976 | − | 0.710224i | \(-0.748594\pi\) | ||||
−0.703976 | + | 0.710224i | \(0.748594\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.08921 | 1.41950 | 0.709748 | − | 0.704455i | \(-0.248809\pi\) | ||||
0.709748 | + | 0.704455i | \(0.248809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.980369 | −0.149505 | −0.0747525 | − | 0.997202i | \(-0.523817\pi\) | ||||
−0.0747525 | + | 0.997202i | \(0.523817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.88448 | 0.429993 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.52498 | −0.951766 | −0.475883 | − | 0.879509i | \(-0.657871\pi\) | ||||
−0.475883 | + | 0.879509i | \(0.657871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.08921 | 1.15560 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.44872 | 0.885800 | 0.442900 | − | 0.896571i | \(-0.353950\pi\) | ||||
0.442900 | + | 0.896571i | \(0.353950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.54461 | −0.208275 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.973697 | 0.128969 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.45539 | 0.580043 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.65345 | 1.23600 | 0.617999 | − | 0.786179i | \(-0.287944\pi\) | ||||
0.617999 | + | 0.786179i | \(0.287944\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.2047 | −1.41166 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.97370 | −0.851973 | −0.425986 | − | 0.904730i | \(-0.640073\pi\) | ||||
−0.425986 | + | 0.904730i | \(0.640073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.84522 | 0.222139 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6731 | 1.50402 | 0.752009 | − | 0.659153i | \(-0.229085\pi\) | ||||
0.752009 | + | 0.659153i | \(0.229085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.43576 | −0.402126 | −0.201063 | − | 0.979578i | \(-0.564440\pi\) | ||||
−0.201063 | + | 0.979578i | \(0.564440\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.339877 | −0.0392456 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1285 | −1.47707 | −0.738534 | − | 0.674216i | \(-0.764482\pi\) | ||||
−0.738534 | + | 0.674216i | \(0.764482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.97370 | 0.885966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.56424 | −0.940047 | −0.470024 | − | 0.882654i | \(-0.655755\pi\) | ||||
−0.470024 | + | 0.882654i | \(0.655755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.76897 | 0.189653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.1285 | −1.81561 | −0.907807 | − | 0.419387i | \(-0.862245\pi\) | ||||
−0.907807 | + | 0.419387i | \(0.862245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.11552 | 0.219369 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.86485 | 0.293928 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7690 | −1.39803 | −0.699013 | − | 0.715109i | \(-0.746377\pi\) | ||||
−0.699013 | + | 0.715109i | \(0.746377\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.45539 | −0.447784 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.44872 | 0.641672 | 0.320836 | − | 0.947135i | \(-0.396036\pi\) | ||||
0.320836 | + | 0.947135i | \(0.396036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1088 | −1.19312 | −0.596560 | − | 0.802569i | \(-0.703466\pi\) | ||||
−0.596560 | + | 0.802569i | \(0.703466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.32025 | 0.128843 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.4291 | 1.68493 | 0.842467 | − | 0.538748i | \(-0.181103\pi\) | ||||
0.842467 | + | 0.538748i | \(0.181103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4095 | −1.57174 | −0.785871 | − | 0.618391i | \(-0.787785\pi\) | ||||
−0.785871 | + | 0.618391i | \(0.787785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.91079 | 0.276280 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.59054 | 0.149625 | 0.0748127 | − | 0.997198i | \(-0.476164\pi\) | ||||
0.0748127 | + | 0.997198i | \(0.476164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.42909 | 0.506265 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.61419 | −0.783108 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.08921 | −0.278545 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.108844 | 0.00965837 | 0.00482918 | − | 0.999988i | \(-0.498463\pi\) | ||||
0.00482918 | + | 0.999988i | \(0.498463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.333205 | 0.0293371 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4095 | −0.909479 | −0.454739 | − | 0.890625i | \(-0.650268\pi\) | ||||
−0.454739 | + | 0.890625i | \(0.650268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.1285 | −0.964961 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.08921 | 0.776544 | 0.388272 | − | 0.921545i | \(-0.373072\pi\) | ||||
0.388272 | + | 0.921545i | \(0.373072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.04995 | 0.767607 | 0.383803 | − | 0.923415i | \(-0.374614\pi\) | ||||
0.383803 | + | 0.923415i | \(0.374614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.21769 | 0.186763 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.20473 | 0.432229 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.74934 | −0.226761 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1285 | −0.911680 | −0.455840 | − | 0.890062i | \(-0.650661\pi\) | ||||
−0.455840 | + | 0.890062i | \(0.650661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.13515 | −0.743408 | −0.371704 | − | 0.928351i | \(-0.621226\pi\) | ||||
−0.371704 | + | 0.928351i | \(0.621226\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.22436 | 0.499953 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.91079 | 0.391923 | 0.195962 | − | 0.980612i | \(-0.437217\pi\) | ||||
0.195962 | + | 0.980612i | \(0.437217\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.19177 | −0.173819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.0892 | −1.66206 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9344 | 1.32641 | 0.663204 | − | 0.748439i | \(-0.269196\pi\) | ||||
0.663204 | + | 0.748439i | \(0.269196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.524976 | 0.0408693 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.6142 | −1.67256 | −0.836278 | − | 0.548306i | \(-0.815273\pi\) | ||||
−0.836278 | + | 0.548306i | \(0.815273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.26362 | 0.631935 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.03926 | 0.611214 | 0.305607 | − | 0.952158i | \(-0.401141\pi\) | ||||
0.305607 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.88448 | 0.293639 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.51429 | −0.113821 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8582 | −0.811579 | −0.405789 | − | 0.913967i | \(-0.633003\pi\) | ||||
−0.405789 | + | 0.913967i | \(0.633003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5642 | −0.785234 | −0.392617 | − | 0.919702i | \(-0.628430\pi\) | ||||
−0.392617 | + | 0.919702i | \(0.628430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.28098 | −0.242537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.56424 | 0.629655 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.76897 | 0.565109 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.81892 | −0.638115 | −0.319057 | − | 0.947735i | \(-0.603366\pi\) | ||||
−0.319057 | + | 0.947735i | \(0.603366\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.270294 | −0.0194562 | −0.00972809 | − | 0.999953i | \(-0.503097\pi\) | ||||
−0.00972809 | + | 0.999953i | \(0.503097\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.96074 | 0.282191 | 0.141095 | − | 0.989996i | \(-0.454938\pi\) | ||||
0.141095 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.03926 | −0.428112 | −0.214056 | − | 0.976821i | \(-0.568667\pi\) | ||||
−0.214056 | + | 0.976821i | \(0.568667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.37020 | 0.167181 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.2177 | −1.41900 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.08921 | −0.634818 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.6601 | 1.08845 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.42507 | −0.306089 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2177 | −1.11647 | −0.558236 | − | 0.829682i | \(-0.688522\pi\) | ||||
−0.558236 | + | 0.829682i | \(0.688522\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.30729 | −0.295130 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.980369 | 0.0668606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.1784 | −1.64134 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.16774 | 0.0789083 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0629 | 0.673862 | 0.336931 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336931 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.88448 | −0.192299 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.43576 | 0.228040 | 0.114020 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114020 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.8582 | −1.51051 | −0.755256 | − | 0.655430i | \(-0.772487\pi\) | ||||
−0.755256 | + | 0.655430i | \(0.772487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.03926 | −0.134174 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.40946 | 0.288873 | 0.144437 | − | 0.989514i | \(-0.453863\pi\) | ||||
0.144437 | + | 0.989514i | \(0.453863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.52498 | 0.425643 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.46207 | 0.289842 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.8122 | 1.47560 | 0.737801 | − | 0.675018i | \(-0.235864\pi\) | ||||
0.737801 | + | 0.675018i | \(0.235864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6798 | −0.687943 | −0.343972 | − | 0.938980i | \(-0.611772\pi\) | ||||
−0.343972 | + | 0.938980i | \(0.611772\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.71008 | −0.558752 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.08921 | −0.516801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.91079 | 0.184464 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.2676 | 1.34240 | 0.671201 | − | 0.741276i | \(-0.265779\pi\) | ||||
0.671201 | + | 0.741276i | \(0.265779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.38581 | −0.527211 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.8974 | −1.17879 | −0.589395 | − | 0.807845i | \(-0.700634\pi\) | ||||
−0.589395 | + | 0.807845i | \(0.700634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.2676 | −2.06715 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0130 | 0.929279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0196 | −0.802825 | −0.401412 | − | 0.915897i | \(-0.631481\pi\) | ||||
−0.401412 | + | 0.915897i | \(0.631481\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.44872 | −0.396142 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.82157 | 0.356274 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3702 | 0.876166 | 0.438083 | − | 0.898934i | \(-0.355658\pi\) | ||||
0.438083 | + | 0.898934i | \(0.355658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7230 | −0.833615 | −0.416807 | − | 0.908995i | \(-0.636851\pi\) | ||||
−0.416807 | + | 0.908995i | \(0.636851\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.54461 | 0.0931433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2676 | 1.15768 | 0.578840 | − | 0.815441i | \(-0.303506\pi\) | ||||
0.578840 | + | 0.815441i | \(0.303506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.9541 | 1.07488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.96074 | 0.236278 | 0.118139 | − | 0.992997i | \(-0.462307\pi\) | ||||
0.118139 | + | 0.992997i | \(0.462307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1981 | 1.26009 | 0.630047 | − | 0.776557i | \(-0.283036\pi\) | ||||
0.630047 | + | 0.776557i | \(0.283036\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.973697 | −0.0576769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.3069 | 2.08410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.67975 | 0.274332 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6927 | −0.799937 | −0.399968 | − | 0.916529i | \(-0.630979\pi\) | ||||
−0.399968 | + | 0.916529i | \(0.630979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.45539 | −0.259403 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.08921 | 0.179254 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.80823 | −0.219503 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.19177 | −0.125914 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.65345 | −0.552755 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7953 | −0.730265 | −0.365132 | − | 0.930956i | \(-0.618976\pi\) | ||||
−0.365132 | + | 0.930956i | \(0.618976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.11552 | 0.234124 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8582 | 1.29617 | 0.648084 | − | 0.761569i | \(-0.275570\pi\) | ||||
0.648084 | + | 0.761569i | \(0.275570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.2284 | −1.53904 | −0.769520 | − | 0.638623i | \(-0.779504\pi\) | ||||
−0.769520 | + | 0.638623i | \(0.779504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.2047 | 0.631315 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.7926 | −1.56099 | −0.780494 | − | 0.625163i | \(-0.785033\pi\) | ||||
−0.780494 | + | 0.625163i | \(0.785033\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.03926 | −0.450112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.92375 | −0.330631 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.57720 | 0.308420 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.3462 | −1.39738 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7230 | −1.08408 | −0.542038 | − | 0.840354i | \(-0.682347\pi\) | ||||
−0.542038 | + | 0.840354i | \(0.682347\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.7034 | 1.35374 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.97370 | 0.381014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.540588 | −0.0293607 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.61419 | −0.520638 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.23103 | 0.228454 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.84522 | −0.0993434 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.61017 | −0.140121 | −0.0700607 | − | 0.997543i | \(-0.522319\pi\) | ||||
−0.0700607 | + | 0.997543i | \(0.522319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.08921 | −0.165362 | −0.0826809 | − | 0.996576i | \(-0.526348\pi\) | ||||
−0.0826809 | + | 0.996576i | \(0.526348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9211 | −1.11352 | −0.556759 | − | 0.830674i | \(-0.687955\pi\) | ||||
−0.556759 | + | 0.830674i | \(0.687955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6731 | −0.672617 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8515 | 1.62828 | 0.814140 | − | 0.580668i | \(-0.197209\pi\) | ||||
0.814140 | + | 0.580668i | \(0.197209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7926 | −0.568032 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.92776 | 0.153668 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.43576 | 0.179836 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0196 | 1.09722 | 0.548608 | − | 0.836080i | \(-0.315158\pi\) | ||||
0.548608 | + | 0.836080i | \(0.315158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.2177 | −1.36484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.0500 | 1.30053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3462 | 1.51949 | 0.759743 | − | 0.650223i | \(-0.225325\pi\) | ||||
0.759743 | + | 0.650223i | \(0.225325\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.339877 | 0.0175512 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3528 | −0.583156 | −0.291578 | − | 0.956547i | \(-0.594180\pi\) | ||||
−0.291578 | + | 0.956547i | \(0.594180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0369937 | −0.00189524 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.5642 | 1.05078 | 0.525392 | − | 0.850860i | \(-0.323919\pi\) | ||||
0.525392 | + | 0.850860i | \(0.323919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | −0.305788 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.82786 | 0.143748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.8189 | −1.35977 | −0.679887 | − | 0.733317i | \(-0.737971\pi\) | ||||
−0.679887 | + | 0.733317i | \(0.737971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.53793 | 0.178465 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.1285 | 0.660565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.1022 | −1.81192 | −0.905958 | − | 0.423367i | \(-0.860848\pi\) | ||||
−0.905958 | + | 0.423367i | \(0.860848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.78231 | 0.189352 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.07852 | −0.203672 | −0.101836 | − | 0.994801i | \(-0.532472\pi\) | ||||
−0.101836 | + | 0.994801i | \(0.532472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.97370 | −0.396216 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.2284 | −0.655706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.627148 | 0.0310105 | 0.0155052 | − | 0.999880i | \(-0.495064\pi\) | ||||
0.0155052 | + | 0.999880i | \(0.495064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.08921 | −0.152380 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.3069 | 0.851617 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.56424 | 0.420402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.07587 | −0.150626 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.5513 | −0.564317 | −0.282158 | − | 0.959368i | \(-0.591050\pi\) | ||||
−0.282158 | + | 0.959368i | \(0.591050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.4853 | 1.72945 | 0.864725 | − | 0.502246i | \(-0.167493\pi\) | ||||
0.864725 | + | 0.502246i | \(0.167493\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.8212 | 0.915117 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.4987 | 1.81469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7623 | −1.62627 | −0.813136 | − | 0.582073i | \(-0.802242\pi\) | ||||
−0.813136 | + | 0.582073i | \(0.802242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.76897 | −0.0848155 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.5535 | 0.744027 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0892 | 0.911078 | 0.455539 | − | 0.890216i | \(-0.349446\pi\) | ||||
0.455539 | + | 0.890216i | \(0.349446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.3332 | −1.11110 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.2873 | −0.488763 | −0.244382 | − | 0.969679i | \(-0.578585\pi\) | ||||
−0.244382 | + | 0.969679i | \(0.578585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.1285 | 0.811968 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.78231 | 0.178897 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.21769 | 0.104659 | 0.0523296 | − | 0.998630i | \(-0.483335\pi\) | ||||
0.0523296 | + | 0.998630i | \(0.483335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0393 | 0.661083 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.10483 | 0.145877 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3069 | 0.809583 | 0.404791 | − | 0.914409i | \(-0.367344\pi\) | ||||
0.404791 | + | 0.914409i | \(0.367344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.1392 | −0.751676 | −0.375838 | − | 0.926685i | \(-0.622645\pi\) | ||||
−0.375838 | + | 0.926685i | \(0.622645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.52498 | −0.303241 | −0.151621 | − | 0.988439i | \(-0.548449\pi\) | ||||
−0.151621 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.11552 | −0.0981047 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.4291 | 1.63946 | 0.819731 | − | 0.572748i | \(-0.194123\pi\) | ||||
0.819731 | + | 0.572748i | \(0.194123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.0892 | −1.25086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.66906 | −0.0769064 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.51429 | −0.0696269 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.86485 | −0.131448 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.6012 | −0.851692 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.7730 | 1.22329 | 0.611644 | − | 0.791133i | \(-0.290508\pi\) | ||||
0.611644 | + | 0.791133i | \(0.290508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.16774 | 0.326143 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.7690 | 0.625217 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3725 | 0.832536 | 0.416268 | − | 0.909242i | \(-0.363338\pi\) | ||||
0.416268 | + | 0.909242i | \(0.363338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.75562 | −0.260278 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.81892 | 0.397992 | 0.198996 | − | 0.980000i | \(-0.436232\pi\) | ||||
0.198996 | + | 0.980000i | \(0.436232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.45539 | 0.200255 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 49.2284 | 2.20819 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7756 | 1.06434 | 0.532172 | − | 0.846636i | \(-0.321376\pi\) | ||||
0.532172 | + | 0.846636i | \(0.321376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.34616 | 0.328202 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.1455 | 1.74541 | 0.872705 | − | 0.488248i | \(-0.162364\pi\) | ||||
0.872705 | + | 0.488248i | \(0.162364\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.44872 | −0.286964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 44.5745 | 1.97573 | 0.987866 | − | 0.155309i | \(-0.0496373\pi\) | ||||
0.987866 | + | 0.155309i | \(0.0496373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.3462 | −0.590400 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.72971 | −0.252973 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.1088 | 0.533579 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0785 | −0.443253 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.73236 | −0.119937 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2047 | −0.753753 | −0.376876 | − | 0.926264i | \(-0.623002\pi\) | ||||
−0.376876 | + | 0.926264i | \(0.623002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.19806 | 0.139841 | 0.0699207 | − | 0.997553i | \(-0.477725\pi\) | ||||
0.0699207 | + | 0.997553i | \(0.477725\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.32025 | −0.0576203 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.47502 | 0.281523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8515 | −0.557708 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.4291 | −0.753525 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.69044 | 0.159254 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.4947 | 0.538183 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.65118 | −0.0709899 | −0.0354950 | − | 0.999370i | \(-0.511301\pi\) | ||||
−0.0354950 | + | 0.999370i | \(0.511301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.59054 | 0.154085 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.4095 | 0.702904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.3265 | 1.63872 | 0.819362 | − | 0.573276i | \(-0.194328\pi\) | ||||
0.819362 | + | 0.573276i | \(0.194328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.8452 | −1.18841 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9108 | 0.635221 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.9973 | −2.16863 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.91079 | −0.123556 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8711 | 1.35042 | 0.675212 | − | 0.737624i | \(-0.264052\pi\) | ||||
0.675212 | + | 0.737624i | \(0.264052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.87781 | −0.247720 | −0.123860 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123860 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.59054 | −0.0669145 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.9737 | 1.30077 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0629 | 0.673392 | 0.336696 | − | 0.941613i | \(-0.390690\pi\) | ||||
0.336696 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.04995 | −0.211334 | −0.105667 | − | 0.994402i | \(-0.533698\pi\) | ||||
−0.105667 | + | 0.994402i | \(0.533698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.99735 | 0.125216 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.42909 | −0.226409 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3832 | 0.723670 | 0.361835 | − | 0.932242i | \(-0.382150\pi\) | ||||
0.361835 | + | 0.932242i | \(0.382150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0918667 | 0.00381785 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.2676 | −1.38017 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.96074 | 0.412532 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.57493 | 0.312651 | 0.156325 | − | 0.987706i | \(-0.450035\pi\) | ||||
0.156325 | + | 0.987706i | \(0.450035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8319 | 0.734750 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.34616 | −0.0553738 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9500 | 0.696055 | 0.348028 | − | 0.937484i | \(-0.386852\pi\) | ||||
0.348028 | + | 0.937484i | \(0.386852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.05261 | 0.0840075 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.6771 | −1.78460 | −0.892299 | − | 0.451445i | \(-0.850909\pi\) | ||||
−0.892299 | + | 0.451445i | \(0.850909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.07852 | 0.0847847 | 0.0423924 | − | 0.999101i | \(-0.486502\pi\) | ||||
0.0423924 | + | 0.999101i | \(0.486502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.1155 | 0.819167 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.61419 | 0.350217 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.3265 | −1.39327 | −0.696635 | − | 0.717425i | \(-0.745320\pi\) | ||||
−0.696635 | + | 0.717425i | \(0.745320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.87153 | 0.278448 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.3569 | 0.741426 | 0.370713 | − | 0.928747i | \(-0.379113\pi\) | ||||
0.370713 | + | 0.928747i | \(0.379113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.08921 | 0.124569 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.5246 | 1.51068 | 0.755342 | − | 0.655331i | \(-0.227471\pi\) | ||||
0.755342 | + | 0.655331i | \(0.227471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8256 | −0.515504 | −0.257752 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257752 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.8582 | −0.435724 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −66.5353 | −2.66568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.50398 | 0.0600632 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6472 | −0.503476 | −0.251738 | − | 0.967795i | \(-0.581002\pi\) | ||||
−0.251738 | + | 0.967795i | \(0.581002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.51202 | 0.219083 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.108844 | −0.00431935 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.5553 | −1.44611 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.10256 | −0.201539 | −0.100769 | − | 0.994910i | \(-0.532130\pi\) | ||||
−0.100769 | + | 0.994910i | \(0.532130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.346549 | −0.0136666 | −0.00683328 | − | 0.999977i | \(-0.502175\pi\) | ||||
−0.00683328 | + | 0.999977i | \(0.502175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.333205 | −0.0131199 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.2480 | −1.73957 | −0.869784 | − | 0.493432i | \(-0.835742\pi\) | ||||
−0.869784 | + | 0.493432i | \(0.835742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.88183 | 0.270135 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.21769 | 0.322077 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0393 | −0.549399 | −0.274699 | − | 0.961530i | \(-0.588578\pi\) | ||||
−0.274699 | + | 0.961530i | \(0.588578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4095 | 0.406731 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.91040 | 0.386642 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.4487 | 0.484933 | 0.242467 | − | 0.970160i | \(-0.422043\pi\) | ||||
0.242467 | + | 0.970160i | \(0.422043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8216 | 0.459806 | 0.229903 | − | 0.973214i | \(-0.426159\pi\) | ||||
0.229903 | + | 0.973214i | \(0.426159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.1285 | 0.431544 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.2569 | 1.09411 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.42015 | −0.132231 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.9108 | 0.575625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.3069 | −1.20679 | −0.603396 | − | 0.797442i | \(-0.706186\pi\) | ||||
−0.603396 | + | 0.797442i | \(0.706186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | 0.0769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8582 | 1.10911 | 0.554555 | − | 0.832147i | \(-0.312889\pi\) | ||||
0.554555 | + | 0.832147i | \(0.312889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53.4853 | −2.05258 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.16774 | −0.0447478 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.5642 | 0.786869 | 0.393434 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393434 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.08921 | −0.347281 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.76897 | 0.296405 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.67308 | −0.253856 | −0.126928 | − | 0.991912i | \(-0.540512\pi\) | ||||
−0.126928 | + | 0.991912i | \(0.540512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.3069 | −0.657435 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.04995 | −0.343284 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.49867 | −0.0566850 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.62980 | −0.363713 | −0.181856 | − | 0.983325i | \(-0.558211\pi\) | ||||
−0.181856 | + | 0.983325i | \(0.558211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.5353 | 0.925366 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.21769 | −0.0835230 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.0500 | 0.942100 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.8082 | −1.26969 | −0.634847 | − | 0.772638i | \(-0.718937\pi\) | ||||
−0.634847 | + | 0.772638i | \(0.718937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.8689 | 1.42019 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.7926 | 1.26554 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.75336 | −0.289554 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.2043 | 1.35019 | 0.675097 | − | 0.737729i | \(-0.264102\pi\) | ||||
0.675097 | + | 0.737729i | \(0.264102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.0366 | −1.75173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.62980 | 0.134994 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.20473 | −0.193299 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.2480 | 1.71524 | 0.857622 | − | 0.514281i | \(-0.171941\pi\) | ||||
0.857622 | + | 0.514281i | \(0.171941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.9607 | −0.776324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0393 | 0.740167 | 0.370084 | − | 0.928998i | \(-0.379329\pi\) | ||||
0.370084 | + | 0.928998i | \(0.379329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.74934 | 0.101411 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.7716 | −0.396778 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.6338 | 1.93617 | 0.968083 | − | 0.250629i | \(-0.0806374\pi\) | ||||
0.968083 | + | 0.250629i | \(0.0806374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.9497 | −1.75910 | −0.879551 | − | 0.475804i | \(-0.842157\pi\) | ||||
−0.879551 | + | 0.475804i | \(0.842157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1285 | 0.407716 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.7034 | 0.903850 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 67.7030 | 2.47381 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0892 | −0.842537 | −0.421269 | − | 0.906936i | \(-0.638415\pi\) | ||||
−0.421269 | + | 0.906936i | \(0.638415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.22838 | −0.263417 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.13515 | 0.332462 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.3176 | 1.61075 | 0.805375 | − | 0.592765i | \(-0.201964\pi\) | ||||
0.805375 | + | 0.592765i | \(0.201964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.85014 | 0.103454 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.4853 | −1.50384 | −0.751921 | − | 0.659253i | \(-0.770873\pi\) | ||||
−0.751921 | + | 0.659253i | \(0.770873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.7423 | −2.30763 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.5879 | −1.03091 | −0.515453 | − | 0.856918i | \(-0.672376\pi\) | ||||
−0.515453 | + | 0.856918i | \(0.672376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.42280 | 0.231312 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.4358 | 0.555186 | 0.277593 | − | 0.960699i | \(-0.410463\pi\) | ||||
0.277593 | + | 0.960699i | \(0.410463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.22436 | −0.223586 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.3069 | 0.405633 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.0393 | −0.932953 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5749 | 0.700446 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.4095 | −0.372004 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.91079 | −0.175273 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.38316 | 0.191889 | 0.0959444 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959444 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.42507 | 0.157537 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.17843 | 0.219680 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.19177 | 0.0777341 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.7556 | −1.26653 | −0.633265 | − | 0.773935i | \(-0.718286\pi\) | ||||
−0.633265 | + | 0.773935i | \(0.718286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.4068 | 1.74570 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.30690 | −0.187277 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0892 | 0.743297 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.88410 | −0.171928 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.7712 | −1.25765 | −0.628825 | − | 0.777547i | \(-0.716464\pi\) | ||||
−0.628825 | + | 0.777547i | \(0.716464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2244 | 1.06132 | 0.530660 | − | 0.847585i | \(-0.321944\pi\) | ||||
0.530660 | + | 0.847585i | \(0.321944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.66414 | 0.163579 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9344 | −0.593187 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.80861 | 0.0982610 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2284 | −0.880477 | −0.440238 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440238 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.9804 | −1.07991 | −0.539954 | − | 0.841695i | \(-0.681558\pi\) | ||||
−0.539954 | + | 0.841695i | \(0.681558\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.524976 | −0.0182773 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.82119 | −0.237196 | −0.118598 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118598 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.39650 | 0.117965 | 0.0589827 | − | 0.998259i | \(-0.481214\pi\) | ||||
0.0589827 | + | 0.998259i | \(0.481214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.54863 | −0.227169 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.6142 | 0.747990 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.4487 | −0.430291 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.76230 | −0.337032 | −0.168516 | − | 0.985699i | \(-0.553897\pi\) | ||||
−0.168516 | + | 0.985699i | \(0.553897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.91079 | −0.0658892 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.34616 | −0.0463643 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.4617 | −1.14976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.20473 | −0.247266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.4960 | 1.59386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2806 | 0.625916 | 0.312958 | − | 0.949767i | \(-0.398680\pi\) | ||||
0.312958 | + | 0.949767i | \(0.398680\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.26362 | −0.282610 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6691 | 0.398608 | 0.199304 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199304 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.92148 | −0.133799 | −0.0668995 | − | 0.997760i | \(-0.521311\pi\) | ||||
−0.0668995 | + | 0.997760i | \(0.521311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.83188 | −0.198519 | −0.0992597 | − | 0.995062i | \(-0.531647\pi\) | ||||
−0.0992597 | + | 0.995062i | \(0.531647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.03926 | −0.273343 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.77791 | 0.196228 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.2783 | −0.687895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.7164 | 1.34420 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.88448 | −0.131320 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.5379 | −1.94292 | −0.971459 | − | 0.237208i | \(-0.923768\pi\) | ||||
−0.971459 | + | 0.237208i | \(0.923768\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.65384 | 0.156970 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 55.4483 | 1.86810 | 0.934051 | − | 0.357140i | \(-0.116248\pi\) | ||||
0.934051 | + | 0.357140i | \(0.116248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75199 | −0.0589591 | −0.0294796 | − | 0.999565i | \(-0.509385\pi\) | ||||
−0.0294796 | + | 0.999565i | \(0.509385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.51429 | 0.0509021 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.3265 | 1.21973 | 0.609863 | − | 0.792507i | \(-0.291225\pi\) | ||||
0.609863 | + | 0.792507i | \(0.291225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.422804 | 0.0141804 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.3162 | 0.412609 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.6931 | 0.625541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.8582 | 0.362949 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.3961 | 1.08047 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.29433 | 0.0430726 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.5642 | 0.351167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0696 | 0.334355 | 0.167178 | − | 0.985927i | \(-0.446535\pi\) | ||||
0.167178 | + | 0.985927i | \(0.446535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.6012 | −0.616964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.8341 | −1.31976 | −0.659882 | − | 0.751369i | \(-0.729394\pi\) | ||||
−0.659882 | + | 0.751369i | \(0.729394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2284 | −0.437795 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.28098 | 0.108466 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.4354 | −1.33529 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8608 | 0.391253 | 0.195626 | − | 0.980678i | \(-0.437326\pi\) | ||||
0.195626 | + | 0.980678i | \(0.437326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.34882 | 0.143298 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.56424 | −0.281590 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.9278 | 1.14718 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.34616 | −0.241020 | −0.120510 | − | 0.992712i | \(-0.538453\pi\) | ||||
−0.120510 | + | 0.992712i | \(0.538453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.1744 | −0.759511 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.76897 | −0.254345 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.3069 | 1.48011 | 0.740056 | − | 0.672545i | \(-0.234799\pi\) | ||||
0.740056 | + | 0.672545i | \(0.234799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.25430 | 0.302003 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.88222 | −0.191755 | −0.0958774 | − | 0.995393i | \(-0.530566\pi\) | ||||
−0.0958774 | + | 0.995393i | \(0.530566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.3462 | −1.60693 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.76897 | −0.252725 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.7427 | −0.479072 | −0.239536 | − | 0.970887i | \(-0.576995\pi\) | ||||
−0.239536 | + | 0.970887i | \(0.576995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.44607 | 0.306310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.2284 | 1.20595 | 0.602973 | − | 0.797762i | \(-0.293983\pi\) | ||||
0.602973 | + | 0.797762i | \(0.293983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.81892 | 0.285374 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.73236 | 0.0883246 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.3069 | 1.14012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.74266 | 0.249763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.2739 | −1.62005 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.270294 | 0.00870107 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.8711 | 1.02491 | 0.512453 | − | 0.858715i | \(-0.328737\pi\) | ||||
0.512453 | + | 0.858715i | \(0.328737\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.6531 | 1.17625 | 0.588126 | − | 0.808769i | \(-0.299866\pi\) | ||||
0.588126 | + | 0.808769i | \(0.299866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.1544 | 1.12700 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.61419 | −0.307585 | −0.153793 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153793 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.4568 | −0.845562 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.3328 | 1.51122 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.78193 | −0.152520 | −0.0762599 | − | 0.997088i | \(-0.524298\pi\) | ||||
−0.0762599 | + | 0.997088i | \(0.524298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.96074 | −0.126200 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.61458 | 0.274205 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.32251 | 0.169246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.8814 | 1.64807 | 0.824034 | − | 0.566540i | \(-0.191718\pi\) | ||||
0.824034 | + | 0.566540i | \(0.191718\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.70340 | 0.212726 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.03926 | 0.191457 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3176 | 0.390102 | 0.195051 | − | 0.980793i | \(-0.437513\pi\) | ||||
0.195051 | + | 0.980793i | \(0.437513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.1285 | −0.541921 |
(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 | 3380.2.a.m.1.2 | 3 | ||
13.5 | odd | 4 | 260.2.f.a.181.4 | yes | 6 | ||
13.8 | odd | 4 | 260.2.f.a.181.3 | ✓ | 6 | ||
13.12 | even | 2 | 3380.2.a.n.1.2 | 3 | |||
39.5 | even | 4 | 2340.2.c.d.181.3 | 6 | |||
39.8 | even | 4 | 2340.2.c.d.181.4 | 6 | |||
52.31 | even | 4 | 1040.2.k.c.961.4 | 6 | |||
52.47 | even | 4 | 1040.2.k.c.961.3 | 6 | |||
65.8 | even | 4 | 1300.2.d.d.649.3 | 6 | |||
65.18 | even | 4 | 1300.2.d.c.649.3 | 6 | |||
65.34 | odd | 4 | 1300.2.f.e.701.4 | 6 | |||
65.44 | odd | 4 | 1300.2.f.e.701.3 | 6 | |||
65.47 | even | 4 | 1300.2.d.c.649.4 | 6 | |||
65.57 | even | 4 | 1300.2.d.d.649.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.f.a.181.3 | ✓ | 6 | 13.8 | odd | 4 | ||
260.2.f.a.181.4 | yes | 6 | 13.5 | odd | 4 | ||
1040.2.k.c.961.3 | 6 | 52.47 | even | 4 | |||
1040.2.k.c.961.4 | 6 | 52.31 | even | 4 | |||
1300.2.d.c.649.3 | 6 | 65.18 | even | 4 | |||
1300.2.d.c.649.4 | 6 | 65.47 | even | 4 | |||
1300.2.d.d.649.3 | 6 | 65.8 | even | 4 | |||
1300.2.d.d.649.4 | 6 | 65.57 | even | 4 | |||
1300.2.f.e.701.3 | 6 | 65.44 | odd | 4 | |||
1300.2.f.e.701.4 | 6 | 65.34 | odd | 4 | |||
2340.2.c.d.181.3 | 6 | 39.5 | even | 4 | |||
2340.2.c.d.181.4 | 6 | 39.8 | even | 4 | |||
3380.2.a.m.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3380.2.a.n.1.2 | 3 | 13.12 | even | 2 |