Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 27 x^{13} + 106 x^{12} + 266 x^{11} - 1004 x^{10} - 1105 x^{9} + 4076 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.04745\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.04745 | −0.915649 | −0.457824 | − | 0.889043i | \(-0.651371\pi\) | ||||
−0.457824 | + | 0.889043i | \(0.651371\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.89716 | 1.47299 | 0.736495 | − | 0.676443i | \(-0.236480\pi\) | ||||
0.736495 | + | 0.676443i | \(0.236480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.70738 | −1.41933 | −0.709664 | − | 0.704541i | \(-0.751153\pi\) | ||||
−0.709664 | + | 0.704541i | \(0.751153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.326886 | −0.0906618 | −0.0453309 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453309 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.04745 | −0.528650 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.01396 | −1.21606 | −0.608032 | − | 0.793912i | \(-0.708041\pi\) | ||||
−0.608032 | + | 0.793912i | \(0.708041\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82435 | 0.418535 | 0.209267 | − | 0.977858i | \(-0.432892\pi\) | ||||
0.209267 | + | 0.977858i | \(0.432892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.89716 | 0.850431 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.20909 | −0.252112 | −0.126056 | − | 0.992023i | \(-0.540232\pi\) | ||||
−0.126056 | + | 0.992023i | \(0.540232\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.807938 | −0.161588 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.55087 | 0.473685 | 0.236843 | − | 0.971548i | \(-0.423887\pi\) | ||||
0.236843 | + | 0.971548i | \(0.423887\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.52387 | 1.35133 | 0.675663 | − | 0.737210i | \(-0.263857\pi\) | ||||
0.675663 | + | 0.737210i | \(0.263857\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.70738 | −0.819449 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.97926 | −1.34874 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.54315 | 1.56888 | 0.784442 | − | 0.620202i | \(-0.212949\pi\) | ||||
0.784442 | + | 0.620202i | \(0.212949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.326886 | −0.0523436 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.47431 | −1.32346 | −0.661732 | − | 0.749740i | \(-0.730178\pi\) | ||||
−0.661732 | + | 0.749740i | \(0.730178\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.76687 | −0.726941 | −0.363470 | − | 0.931606i | \(-0.618408\pi\) | ||||
−0.363470 | + | 0.931606i | \(0.618408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.04745 | −0.305216 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.57901 | −0.667917 | −0.333959 | − | 0.942588i | \(-0.608385\pi\) | ||||
−0.333959 | + | 0.942588i | \(0.608385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.18789 | 1.16970 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.01396 | −0.702095 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.27828 | −0.175586 | −0.0877928 | − | 0.996139i | \(-0.527981\pi\) | ||||
−0.0877928 | + | 0.996139i | \(0.527981\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.63813 | 1.29960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82435 | 0.241641 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.43663 | −0.968167 | −0.484083 | − | 0.875022i | \(-0.660847\pi\) | ||||
−0.484083 | + | 0.875022i | \(0.660847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.825352 | −0.105675 | −0.0528377 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528377 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.89716 | 0.490997 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.669283 | 0.0830144 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.57998 | −0.559533 | −0.279767 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279767 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.20909 | −0.145557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.48910 | 0.651437 | 0.325718 | − | 0.945467i | \(-0.394394\pi\) | ||||
0.325718 | + | 0.945467i | \(0.394394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0048 | −1.52209 | −0.761046 | − | 0.648698i | \(-0.775314\pi\) | ||||
−0.761046 | + | 0.648698i | \(0.775314\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.807938 | −0.0932927 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.3454 | −2.09065 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.2651 | −1.49244 | −0.746222 | − | 0.665697i | \(-0.768134\pi\) | ||||
−0.746222 | + | 0.665697i | \(0.768134\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86744 | 0.424507 | 0.212254 | − | 0.977215i | \(-0.431920\pi\) | ||||
0.212254 | + | 0.977215i | \(0.431920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2659 | 1.11349 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.55087 | 0.273482 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.91231 | −0.520704 | −0.260352 | − | 0.965514i | \(-0.583839\pi\) | ||||
−0.260352 | + | 0.965514i | \(0.583839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.27393 | −0.133544 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.52387 | 0.780189 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.73527 | −0.383231 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32029 | −0.946332 | −0.473166 | − | 0.880973i | \(-0.656889\pi\) | ||||
−0.473166 | + | 0.880973i | \(0.656889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.70738 | −0.473109 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.59179 | 0.257893 | 0.128946 | − | 0.991652i | \(-0.458841\pi\) | ||||
0.128946 | + | 0.991652i | \(0.458841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1898 | −1.00403 | −0.502015 | − | 0.864859i | \(-0.667408\pi\) | ||||
−0.502015 | + | 0.864859i | \(0.667408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.97926 | −0.778696 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.11685 | 0.204644 | 0.102322 | − | 0.994751i | \(-0.467373\pi\) | ||||
0.102322 | + | 0.994751i | \(0.467373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.58991 | −0.631198 | −0.315599 | − | 0.948893i | \(-0.602206\pi\) | ||||
−0.315599 | + | 0.948893i | \(0.602206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.54315 | 0.905796 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.987955 | 0.0929390 | 0.0464695 | − | 0.998920i | \(-0.485203\pi\) | ||||
0.0464695 | + | 0.998920i | \(0.485203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.47554 | 0.230846 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.326886 | −0.0302206 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.5402 | −1.79125 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1594 | 1.01449 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.47431 | −0.764102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8915 | 1.06361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.523002 | −0.0464089 | −0.0232045 | − | 0.999731i | \(-0.507387\pi\) | ||||
−0.0232045 | + | 0.999731i | \(0.507387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.76687 | −0.419699 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8830 | −1.03823 | −0.519113 | − | 0.854706i | \(-0.673737\pi\) | ||||
−0.519113 | + | 0.854706i | \(0.673737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.10980 | 0.616498 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.04745 | −0.176217 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.31909 | −0.539876 | −0.269938 | − | 0.962878i | \(-0.587003\pi\) | ||||
−0.269938 | + | 0.962878i | \(0.587003\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.794226 | 0.0673654 | 0.0336827 | − | 0.999433i | \(-0.489276\pi\) | ||||
0.0336827 | + | 0.999433i | \(0.489276\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.57901 | −0.385622 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.53877 | 0.128679 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.22279 | −0.433729 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.18789 | 0.675326 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.51557 | −0.697623 | −0.348811 | − | 0.937193i | \(-0.613415\pi\) | ||||
−0.348811 | + | 0.937193i | \(0.613415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.19256 | −0.422565 | −0.211282 | − | 0.977425i | \(-0.567764\pi\) | ||||
−0.211282 | + | 0.977425i | \(0.567764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.01396 | −0.405355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.4048 | −1.23734 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7694 | 1.81720 | 0.908598 | − | 0.417672i | \(-0.137154\pi\) | ||||
0.908598 | + | 0.417672i | \(0.137154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.27828 | −0.101374 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.71200 | −0.371358 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9768 | −1.56471 | −0.782353 | − | 0.622835i | \(-0.785981\pi\) | ||||
−0.782353 | + | 0.622835i | \(0.785981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.63813 | 0.750327 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.06406 | −0.314486 | −0.157243 | − | 0.987560i | \(-0.550261\pi\) | ||||
−0.157243 | + | 0.987560i | \(0.550261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8931 | −0.991780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.82435 | 0.139512 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4948 | 1.10202 | 0.551009 | − | 0.834499i | \(-0.314243\pi\) | ||||
0.551009 | + | 0.834499i | \(0.314243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.14867 | −0.238017 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.43663 | −0.558971 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8963 | 1.11340 | 0.556700 | − | 0.830714i | \(-0.312067\pi\) | ||||
0.556700 | + | 0.830714i | \(0.312067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0958839 | 0.00712699 | 0.00356350 | − | 0.999994i | \(-0.498866\pi\) | ||||
0.00356350 | + | 0.999994i | \(0.498866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.825352 | −0.0610118 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.5391 | −1.43655 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.6026 | 1.72599 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.89716 | 0.283477 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2133 | −0.883721 | −0.441860 | − | 0.897084i | \(-0.645681\pi\) | ||||
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.3900 | 1.89960 | 0.949798 | − | 0.312863i | \(-0.101288\pi\) | ||||
0.949798 | + | 0.312863i | \(0.101288\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.669283 | 0.0479284 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.655343 | 0.0466913 | 0.0233456 | − | 0.999727i | \(-0.492568\pi\) | ||||
0.0233456 | + | 0.999727i | \(0.492568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.47514 | −0.529899 | −0.264949 | − | 0.964262i | \(-0.585355\pi\) | ||||
−0.264949 | + | 0.964262i | \(0.585355\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.57998 | −0.323047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.94118 | 0.697734 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3507 | 1.21183 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.20909 | −0.0840372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.58791 | −0.594038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.77812 | −0.397782 | −0.198891 | − | 0.980022i | \(-0.563734\pi\) | ||||
−0.198891 | + | 0.980022i | \(0.563734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.48910 | 0.376107 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.75994 | 0.665622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.3218 | 1.99049 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.0048 | −0.878780 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.63899 | 0.110251 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7158 | 1.58813 | 0.794064 | − | 0.607835i | \(-0.207962\pi\) | ||||
0.794064 | + | 0.607835i | \(0.207962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.807938 | −0.0538626 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.1401 | −1.27038 | −0.635188 | − | 0.772358i | \(-0.719077\pi\) | ||||
−0.635188 | + | 0.772358i | \(0.719077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0306 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.3454 | −1.20704 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.00287566 | 0.000188391 0 | 9.41955e−5 | − | 1.00000i | \(-0.499970\pi\) | ||||
9.41955e−5 | 1.00000i | \(0.499970\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.37530 | 0.611577 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.2651 | −0.861663 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.7797 | 1.08539 | 0.542693 | − | 0.839931i | \(-0.317405\pi\) | ||||
0.542693 | + | 0.839931i | \(0.317405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.01472 | 0.129780 | 0.0648898 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648898 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.7643 | −1.07103 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.596355 | −0.0379451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.86744 | 0.245089 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.46557 | −0.218745 | −0.109372 | − | 0.994001i | \(-0.534884\pi\) | ||||
−0.109372 | + | 0.994001i | \(0.534884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.69162 | 0.357829 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.2659 | 0.642873 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.64966 | −0.102903 | −0.0514514 | − | 0.998676i | \(-0.516385\pi\) | ||||
−0.0514514 | + | 0.998676i | \(0.516385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.1912 | 2.31095 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.55087 | 0.157895 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1195 | 0.685660 | 0.342830 | − | 0.939397i | \(-0.388614\pi\) | ||||
0.342830 | + | 0.939397i | \(0.388614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.61722 | 0.160775 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.91231 | −0.300629 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.751890 | −0.0458435 | −0.0229218 | − | 0.999737i | \(-0.507297\pi\) | ||||
−0.0229218 | + | 0.999737i | \(0.507297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.2087 | −1.10610 | −0.553051 | − | 0.833148i | \(-0.686536\pi\) | ||||
−0.553051 | + | 0.833148i | \(0.686536\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.27393 | −0.0771016 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.80327 | 0.229346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.2198 | −1.51531 | −0.757654 | − | 0.652656i | \(-0.773655\pi\) | ||||
−0.757654 | + | 0.652656i | \(0.773655\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.52387 | 0.450442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.79663 | 0.166833 | 0.0834166 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834166 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4378 | −0.798792 | −0.399396 | − | 0.916779i | \(-0.630780\pi\) | ||||
−0.399396 | + | 0.916779i | \(0.630780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.73527 | −0.221258 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.0258 | −1.94945 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.13983 | 0.478814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.32029 | −0.546365 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.3446 | 1.36381 | 0.681903 | − | 0.731443i | \(-0.261153\pi\) | ||||
0.681903 | + | 0.731443i | \(0.261153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2261 | 0.886501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.70738 | −0.273150 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.395233 | 0.0228569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5773 | −1.07078 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.59179 | 0.148894 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.68987 | 0.0967616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.2791 | −1.89934 | −0.949670 | − | 0.313253i | \(-0.898581\pi\) | ||||
−0.949670 | + | 0.313253i | \(0.898581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1898 | −0.579677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4700 | 0.820519 | 0.410260 | − | 0.911969i | \(-0.365438\pi\) | ||||
0.410260 | + | 0.911969i | \(0.365438\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.2012 | −1.25488 | −0.627442 | − | 0.778663i | \(-0.715898\pi\) | ||||
−0.627442 | + | 0.778663i | \(0.715898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.97926 | −0.449580 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.95963 | −0.390892 | −0.195446 | − | 0.980714i | \(-0.562615\pi\) | ||||
−0.195446 | + | 0.980714i | \(0.562615\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0079 | −0.672315 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.11685 | 0.118151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.14723 | −0.508966 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.264104 | 0.0146498 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.58991 | −0.364423 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.8452 | −0.983835 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9114 | −0.764640 | −0.382320 | − | 0.924030i | \(-0.624875\pi\) | ||||
−0.382320 | + | 0.924030i | \(0.624875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.54315 | 0.522961 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.37729 | 0.512336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.97814 | 0.107756 | 0.0538782 | − | 0.998548i | \(-0.482842\pi\) | ||||
0.0538782 | + | 0.998548i | \(0.482842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.987955 | 0.0536584 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.4177 | −1.91797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.62940 | 0.249964 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.47554 | 0.133279 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00457 | −0.483391 | −0.241695 | − | 0.970352i | \(-0.577703\pi\) | ||||
−0.241695 | + | 0.970352i | \(0.577703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.401688 | 0.0215019 | 0.0107509 | − | 0.999942i | \(-0.496578\pi\) | ||||
0.0107509 | + | 0.999942i | \(0.496578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.326886 | −0.0174479 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.46991 | −0.504032 | −0.252016 | − | 0.967723i | \(-0.581094\pi\) | ||||
−0.252016 | + | 0.967723i | \(0.581094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.2387 | −0.596487 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.5402 | −1.03418 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.7941 | 1.25581 | 0.627903 | − | 0.778292i | \(-0.283914\pi\) | ||||
0.627903 | + | 0.778292i | \(0.283914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6717 | −0.824828 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.1594 | 0.585716 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.6266 | 1.39370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3921 | −0.699061 | −0.349531 | − | 0.936925i | \(-0.613659\pi\) | ||||
−0.349531 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.47431 | −0.441155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.98167 | −0.258636 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.99893 | −0.103501 | −0.0517503 | − | 0.998660i | \(-0.516480\pi\) | ||||
−0.0517503 | + | 0.998660i | \(0.516480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8915 | 0.614073 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.833845 | −0.0429452 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9518 | −0.716654 | −0.358327 | − | 0.933596i | \(-0.616653\pi\) | ||||
−0.358327 | + | 0.933596i | \(0.616653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.523002 | −0.0267942 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3853 | −1.39932 | −0.699661 | − | 0.714475i | \(-0.746666\pi\) | ||||
−0.699661 | + | 0.714475i | \(0.746666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.5614 | 1.91430 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.76687 | −0.242314 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.95165 | 0.251059 | 0.125529 | − | 0.992090i | \(-0.459937\pi\) | ||||
0.125529 | + | 0.992090i | \(0.459937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.06231 | 0.306584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8830 | −0.599420 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.1597 | 1.36656 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.20465 | 0.261214 | 0.130607 | − | 0.991434i | \(-0.458307\pi\) | ||||
0.130607 | + | 0.991434i | \(0.458307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.10980 | 0.355935 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.0630 | 1.25158 | 0.625792 | − | 0.779990i | \(-0.284776\pi\) | ||||
0.625792 | + | 0.779990i | \(0.284776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.45945 | −0.122514 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.04745 | −0.101739 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.9232 | −2.22676 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9726 | −1.08648 | −0.543239 | − | 0.839578i | \(-0.682802\pi\) | ||||
−0.543239 | + | 0.839578i | \(0.682802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.31909 | −0.311698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.9818 | −1.42610 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.91841 | −0.388699 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.794226 | 0.0388934 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.1619 | 1.32694 | 0.663472 | − | 0.748201i | \(-0.269082\pi\) | ||||
0.663472 | + | 0.748201i | \(0.269082\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0600 | 1.12388 | 0.561938 | − | 0.827179i | \(-0.310056\pi\) | ||||
0.561938 | + | 0.827179i | \(0.310056\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.57901 | −0.222639 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.05097 | 0.196501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.21653 | −0.155659 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.53877 | 0.0742927 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0875 | 0.774906 | 0.387453 | − | 0.921890i | \(-0.373355\pi\) | ||||
0.387453 | + | 0.921890i | \(0.373355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.424933 | −0.0204210 | −0.0102105 | − | 0.999948i | \(-0.503250\pi\) | ||||
−0.0102105 | + | 0.999948i | \(0.503250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.22279 | −0.250414 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.20580 | −0.105518 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.7546 | −0.895110 | −0.447555 | − | 0.894257i | \(-0.647705\pi\) | ||||
−0.447555 | + | 0.894257i | \(0.647705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.18789 | 0.389900 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.60334 | −0.123689 | −0.0618443 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618443 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0577 | 0.476782 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.51557 | −0.402773 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.69027 | −0.126962 | −0.0634808 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634808 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.8917 | 1.87843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.19256 | −0.243968 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.60831 | 0.122279 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.37173 | 0.157723 | 0.0788613 | − | 0.996886i | \(-0.474872\pi\) | ||||
0.0788613 | + | 0.996886i | \(0.474872\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.01396 | −0.234032 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8684 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6764 | −1.37918 | −0.689589 | − | 0.724201i | \(-0.742209\pi\) | ||||
−0.689589 | + | 0.724201i | \(0.742209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.4048 | −0.714379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.8093 | −1.14804 | −0.574018 | − | 0.818843i | \(-0.694616\pi\) | ||||
−0.574018 | + | 0.818843i | \(0.694616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.8489 | −0.824187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7694 | 1.04916 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.4394 | 1.03177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.47396 | −0.0676301 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.27828 | −0.0585285 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.2970 | −0.927394 | −0.463697 | − | 0.885994i | \(-0.653477\pi\) | ||||
−0.463697 | + | 0.885994i | \(0.653477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.11952 | −0.142238 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.71200 | −0.214404 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.0828 | 0.866507 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.05720 | −0.0479061 | −0.0239530 | − | 0.999713i | \(-0.507625\pi\) | ||||
−0.0239530 | + | 0.999713i | \(0.507625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.9768 | −0.903383 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2245 | −0.506556 | −0.253278 | − | 0.967393i | \(-0.581509\pi\) | ||||
−0.253278 | + | 0.967393i | \(0.581509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7900 | −0.576032 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.63813 | 0.433202 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.3919 | 0.959559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.38326 | 0.285754 | 0.142877 | − | 0.989740i | \(-0.454365\pi\) | ||||
0.142877 | + | 0.989740i | \(0.454365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.06406 | −0.181569 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30656 | −0.236139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8931 | −0.572605 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.9545 | −0.928794 | −0.464397 | − | 0.885627i | \(-0.653729\pi\) | ||||
−0.464397 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −50.6817 | −2.24202 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.82435 | 0.0805471 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.8631 | 0.919338 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.5551 | 0.947993 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.4948 | 0.636250 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.5474 | −0.637331 | −0.318666 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318666 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.6429 | 1.64601 | 0.823004 | − | 0.568036i | \(-0.192297\pi\) | ||||
0.823004 | + | 0.568036i | \(0.192297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.14867 | −0.137419 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.7244 | −1.64330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5381 | −0.936440 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.43663 | −0.322722 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.77013 | 0.119988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.33415 | −0.187382 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.8963 | 0.642822 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.5435 | −1.66018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.131363 | 0.00564775 | 0.00282387 | − | 0.999996i | \(-0.499101\pi\) | ||||
0.00282387 | + | 0.999996i | \(0.499101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0958839 | 0.00411477 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.4925 | 0.577956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9179 | 0.637843 | 0.318922 | − | 0.947781i | \(-0.396679\pi\) | ||||
0.318922 | + | 0.947781i | \(0.396679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.825352 | −0.0352252 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.65369 | 0.198254 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.6964 | −2.19836 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.5391 | −0.829390 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.52271 | −0.234005 | −0.117002 | − | 0.993132i | \(-0.537329\pi\) | ||||
−0.117002 | + | 0.993132i | \(0.537329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.55822 | 0.0659057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.6026 | 0.996503 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3716 | 0.774271 | 0.387135 | − | 0.922023i | \(-0.373465\pi\) | ||||
0.387135 | + | 0.922023i | \(0.373465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.02279 | −0.0850995 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.89716 | 0.163666 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.1494 | 0.886627 | 0.443313 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443313 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.9516 | 1.88117 | 0.940583 | − | 0.339564i | \(-0.110279\pi\) | ||||
0.940583 | + | 0.339564i | \(0.110279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2133 | −0.510216 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.976866 | 0.0407381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.14898 | 0.339247 | 0.169623 | − | 0.985509i | \(-0.445745\pi\) | ||||
0.169623 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.3900 | 1.09673 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0721 | 0.625295 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.01735 | 0.249213 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.669283 | 0.0276715 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.6714 | 1.43104 | 0.715521 | − | 0.698592i | \(-0.246190\pi\) | ||||
0.715521 | + | 0.698592i | \(0.246190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.7262 | 0.565578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.655343 | 0.0269572 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.4584 | 0.716930 | 0.358465 | − | 0.933543i | \(-0.383300\pi\) | ||||
0.358465 | + | 0.933543i | \(0.383300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.0077 | 1.64016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.47514 | −0.305937 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.2755 | −1.35960 | −0.679801 | − | 0.733397i | \(-0.737934\pi\) | ||||
−0.679801 | + | 0.733397i | \(0.737934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3864 | −0.872368 | −0.436184 | − | 0.899857i | \(-0.643670\pi\) | ||||
−0.436184 | + | 0.899857i | \(0.643670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.57998 | −0.186511 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.8483 | −0.928916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.03385 | 0.163729 | 0.0818645 | − | 0.996643i | \(-0.473913\pi\) | ||||
0.0818645 | + | 0.996643i | \(0.473913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.94118 | 0.402837 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.49681 | 0.0605546 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.8434 | 0.761079 | 0.380539 | − | 0.924765i | \(-0.375738\pi\) | ||||
0.380539 | + | 0.924765i | \(0.375738\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.3507 | 0.699649 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9673 | 0.884372 | 0.442186 | − | 0.896923i | \(-0.354203\pi\) | ||||
0.442186 | + | 0.896923i | \(0.354203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.2152 | 1.77716 | 0.888579 | − | 0.458723i | \(-0.151693\pi\) | ||||
0.888579 | + | 0.458723i | \(0.151693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20909 | −0.0485189 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.1441 | −0.766992 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.3075 | −0.812302 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.58791 | −0.342968 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47.8490 | −1.90786 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3264 | −0.411087 | −0.205543 | − | 0.978648i | \(-0.565896\pi\) | ||||
−0.205543 | + | 0.978648i | \(0.565896\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.77812 | −0.229660 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.07082 | 0.0424942 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.67651 | −0.106047 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.48910 | 0.217146 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.9443 | −0.708759 | −0.354379 | − | 0.935102i | \(-0.615308\pi\) | ||||
−0.354379 | + | 0.935102i | \(0.615308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.52846 | −0.336330 | −0.168165 | − | 0.985759i | \(-0.553784\pi\) | ||||
−0.168165 | + | 0.985759i | \(0.553784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.75994 | 0.384297 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.9515 | 0.548490 | 0.274245 | − | 0.961660i | \(-0.411572\pi\) | ||||
0.274245 | + | 0.961660i | \(0.411572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0070 | 1.37415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.3218 | 1.14921 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.8740 | 1.44299 | 0.721496 | − | 0.692418i | \(-0.243455\pi\) | ||||
0.721496 | + | 0.692418i | \(0.243455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3299 | 0.950650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.0048 | −0.507364 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.4745 | 1.84935 | 0.924673 | − | 0.380763i | \(-0.124339\pi\) | ||||
0.924673 | + | 0.380763i | \(0.124339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.2703 | 0.866213 | 0.433107 | − | 0.901343i | \(-0.357417\pi\) | ||||
0.433107 | + | 0.901343i | \(0.357417\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.63899 | 0.0636532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.5570 | −0.564495 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.08422 | −0.119422 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.7158 | 0.916906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.88524 | 0.149988 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.63814 | −0.140240 | −0.0701201 | − | 0.997539i | \(-0.522338\pi\) | ||||
−0.0701201 | + | 0.997539i | \(0.522338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.807938 | −0.0310976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.8147 | −0.454075 | −0.227037 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227037 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.3227 | −1.39394 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.1401 | −0.733451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.99351 | 0.344127 | 0.172064 | − | 0.985086i | \(-0.444957\pi\) | ||||
0.172064 | + | 0.985086i | \(0.444957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9380 | 0.494337 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.0306 | −0.649759 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.417852 | 0.0159189 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2929 | 1.26652 | 0.633260 | − | 0.773939i | \(-0.281716\pi\) | ||||
0.633260 | + | 0.773939i | \(0.281716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.3454 | −0.696885 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.62614 | −0.0616830 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.4899 | 1.60942 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.00287566 | 0.000108768 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6421 | −0.704103 | −0.352051 | − | 0.935981i | \(-0.614516\pi\) | ||||
−0.352051 | + | 0.935981i | \(0.614516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4101 | 0.656633 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.37530 | 0.353094 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1006 | 0.379873 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0309 | −0.526943 | −0.263471 | − | 0.964667i | \(-0.584867\pi\) | ||||
−0.263471 | + | 0.964667i | \(0.584867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2651 | −0.497482 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.09700 | −0.340685 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.15057 | −0.117825 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.7797 | 0.626648 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.6576 | −1.55357 | −0.776784 | − | 0.629767i | \(-0.783150\pi\) | ||||
−0.776784 | + | 0.629767i | \(0.783150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.7113 | −1.47892 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.01472 | 0.0749283 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.06095 | −0.0765417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.2156 | 1.26898 | 0.634492 | − | 0.772929i | \(-0.281209\pi\) | ||||
0.634492 | + | 0.772929i | \(0.281209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.9009 | 0.884007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.0439 | 0.592595 | 0.296297 | − | 0.955096i | \(-0.404248\pi\) | ||||
0.296297 | + | 0.955096i | \(0.404248\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.7643 | −0.618361 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.5597 | 0.794161 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.2862 | 1.11410 | 0.557048 | − | 0.830480i | \(-0.311934\pi\) | ||||
0.557048 | + | 0.830480i | \(0.311934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.596355 | −0.0219076 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.4411 | 0.859971 | 0.429985 | − | 0.902836i | \(-0.358519\pi\) | ||||
0.429985 | + | 0.902836i | \(0.358519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.4352 | 0.638777 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.86744 | 0.141502 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.24971 | 0.301438 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.5229 | 0.894854 | 0.447427 | − | 0.894321i | \(-0.352340\pi\) | ||||
0.447427 | + | 0.894321i | \(0.352340\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.46557 | −0.126292 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.6315 | 0.386921 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1214 | −0.658634 | −0.329317 | − | 0.944219i | \(-0.606819\pi\) | ||||
−0.329317 | + | 0.944219i | \(0.606819\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.69162 | 0.206593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.7164 | 0.497217 | 0.248609 | − | 0.968604i | \(-0.420027\pi\) | ||||
0.248609 | + | 0.968604i | \(0.420027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.6819 | −0.929749 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.2659 | 0.371163 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.43093 | 0.0877758 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.23898 | −0.297105 | −0.148553 | − | 0.988905i | \(-0.547461\pi\) | ||||
−0.148553 | + | 0.988905i | \(0.547461\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.64966 | −0.0594109 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.1354 | −1.69534 | −0.847671 | − | 0.530523i | \(-0.821996\pi\) | ||||
−0.847671 | + | 0.530523i | \(0.821996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.07882 | −0.218358 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.1912 | 1.33423 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4601 | −0.553916 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.8393 | −0.924602 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.55087 | 0.0911608 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.6193 | −1.66391 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.4429 | −0.942589 | −0.471295 | − | 0.881976i | \(-0.656213\pi\) | ||||
−0.471295 | + | 0.881976i | \(0.656213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.1195 | 0.395866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.85022 | 0.136898 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.269796 | 0.00958073 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.61722 | 0.0928233 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0538 | −0.533231 | −0.266616 | − | 0.963803i | \(-0.585905\pi\) | ||||
−0.266616 | + | 0.963803i | \(0.585905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.9590 | 0.812231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.91231 | −0.173568 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 61.2183 | 2.16035 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.64760 | 0.340033 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.751890 | −0.0264678 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.4681 | 1.52826 | 0.764129 | − | 0.645064i | \(-0.223169\pi\) | ||||
0.764129 | + | 0.645064i | \(0.223169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.5643 | 0.827453 | 0.413727 | − | 0.910401i | \(-0.364227\pi\) | ||||
0.413727 | + | 0.910401i | \(0.364227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2087 | −0.638608 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.9016 | 1.43272 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.69644 | −0.304250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.27393 | −0.0445146 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1403 | 1.12170 | 0.560852 | − | 0.827916i | \(-0.310474\pi\) | ||||
0.560852 | + | 0.827916i | \(0.310474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4882 | 0.923320 | 0.461660 | − | 0.887057i | \(-0.347254\pi\) | ||||
0.461660 | + | 0.887057i | \(0.347254\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.80327 | 0.132413 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.0849 | 1.63730 | 0.818651 | − | 0.574292i | \(-0.194722\pi\) | ||||
0.818651 | + | 0.574292i | \(0.194722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.1417 | 0.560626 | 0.280313 | − | 0.959909i | \(-0.409562\pi\) | ||||
0.280313 | + | 0.959909i | \(0.409562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.2198 | −0.874863 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.0538 | −1.42243 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.32096 | 0.287959 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.52387 | 0.260063 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.36319 | 0.288729 | 0.144365 | − | 0.989525i | \(-0.453886\pi\) | ||||
0.144365 | + | 0.989525i | \(0.453886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4930 | −0.775622 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.79663 | 0.0963211 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.3981 | 0.908122 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.4899 | 1.49433 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.4378 | −0.461183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.5385 | −0.395534 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.87310 | 0.303809 | 0.151905 | − | 0.988395i | \(-0.451459\pi\) | ||||
0.151905 | + | 0.988395i | \(0.451459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.73527 | −0.127744 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.7147 | −1.83486 | −0.917429 | − | 0.397899i | \(-0.869739\pi\) | ||||
−0.917429 | + | 0.397899i | \(0.869739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.4400 | 1.65275 | 0.826376 | − | 0.563119i | \(-0.190399\pi\) | ||||
0.826376 | + | 0.563119i | \(0.190399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.0258 | −1.12551 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.7291 | −0.807747 | −0.403874 | − | 0.914815i | \(-0.632336\pi\) | ||||
−0.403874 | + | 0.914815i | \(0.632336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.6774 | −1.00906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.13983 | 0.276443 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.4440 | 2.11827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.49713 | 0.0507283 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.32029 | −0.315444 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.3430 | 1.56668 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.5283 | −0.355514 | −0.177757 | − | 0.984074i | \(-0.556884\pi\) | ||||
−0.177757 | + | 0.984074i | \(0.556884\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.3446 | 0.787394 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.9326 | −1.07584 | −0.537918 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537918 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.5893 | −1.29863 | −0.649316 | − | 0.760519i | \(-0.724945\pi\) | ||||
−0.649316 | + | 0.760519i | \(0.724945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.2261 | 0.511821 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.1741 | 1.58395 | 0.791976 | − | 0.610552i | \(-0.209053\pi\) | ||||
0.791976 | + | 0.610552i | \(0.209053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.03822 | −0.0683598 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.70738 | −0.157703 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.35372 | −0.279547 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.4994 | −1.01948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.395233 | 0.0131964 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.1924 | 0.640104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.40926 | 0.213523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.5773 | −0.618213 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.196318 | −0.00652582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.31330 | 0.0768120 | 0.0384060 | − | 0.999262i | \(-0.487772\pi\) | ||||
0.0384060 | + | 0.999262i | \(0.487772\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.59179 | 0.0859642 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.4575 | −1.40668 | −0.703340 | − | 0.710854i | \(-0.748309\pi\) | ||||
−0.703340 | + | 0.710854i | \(0.748309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.2055 | −0.602514 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.68987 | 0.0558653 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.3101 | −1.52930 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.19226 | −0.204264 | −0.102132 | − | 0.994771i | \(-0.532566\pi\) | ||||
−0.102132 | + | 0.994771i | \(0.532566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.2791 | −1.09658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.79431 | −0.0590604 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.71028 | −0.253512 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1898 | −0.334676 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.0820 | −1.18381 | −0.591906 | − | 0.806007i | \(-0.701624\pi\) | ||||
−0.591906 | + | 0.806007i | \(0.701624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.9376 | 0.489560 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.4700 | 0.473727 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48.3252 | −1.58040 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.8658 | 0.877668 | 0.438834 | − | 0.898568i | \(-0.355392\pi\) | ||||
0.438834 | + | 0.898568i | \(0.355392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.2012 | −0.724508 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.4271 | 0.861500 | 0.430750 | − | 0.902471i | \(-0.358249\pi\) | ||||
0.430750 | + | 0.902471i | \(0.358249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2462 | 0.333661 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.97926 | −0.259565 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.4368 | −1.15154 | −0.575770 | − | 0.817612i | \(-0.695298\pi\) | ||||
−0.575770 | + | 0.817612i | \(0.695298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.25107 | 0.137996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.95963 | −0.225682 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.3955 | 0.433922 | 0.216961 | − | 0.976180i | \(-0.430386\pi\) | ||||
0.216961 | + | 0.976180i | \(0.430386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.0061 | 0.809177 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0079 | −0.388161 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.6265 | −0.795232 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.6086 | 0.826084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.11685 | 0.0682145 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.0323 | −1.73936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6998 | 0.440557 | 0.220278 | − | 0.975437i | \(-0.429303\pi\) | ||||
0.220278 | + | 0.975437i | \(0.429303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.14723 | −0.293851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.8360 | 0.668658 | 0.334329 | − | 0.942457i | \(-0.391490\pi\) | ||||
0.334329 | + | 0.942457i | \(0.391490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.09523 | 0.0992285 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.264104 | 0.00845809 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2444 | 0.679668 | 0.339834 | − | 0.940485i | \(-0.389629\pi\) | ||||
0.339834 | + | 0.940485i | \(0.389629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.1241 | 0.739049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.58991 | −0.210399 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.2204 | 0.708720 | 0.354360 | − | 0.935109i | \(-0.384699\pi\) | ||||
0.354360 | + | 0.935109i | \(0.384699\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.34178 | −0.0427528 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.8452 | −0.568017 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.76355 | 0.183270 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.9681 | 0.411944 | 0.205972 | − | 0.978558i | \(-0.433964\pi\) | ||||
0.205972 | + | 0.978558i | \(0.433964\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.9114 | −0.441465 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.3050 | 0.485201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.7803 | 1.22818 | 0.614092 | − | 0.789235i | \(-0.289522\pi\) | ||||
0.614092 | + | 0.789235i | \(0.289522\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.54315 | 0.301932 |
(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 | 6036.2.a.g.1.4 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.g.1.4 | ✓ | 15 | 1.1 | even | 1 | trivial |