Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.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: | \(27.3088374913\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1140) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67282 | 1.76616 | 0.883081 | − | 0.469221i | \(-0.155465\pi\) | ||||
0.883081 | + | 0.469221i | \(0.155465\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.81681 | −1.75383 | −0.876917 | − | 0.480642i | \(-0.840404\pi\) | ||||
−0.876917 | + | 0.480642i | \(0.840404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.67282 | −0.741308 | −0.370654 | − | 0.928771i | \(-0.620866\pi\) | ||||
−0.370654 | + | 0.928771i | \(0.620866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.48963 | 1.57397 | 0.786984 | − | 0.616974i | \(-0.211642\pi\) | ||||
0.786984 | + | 0.616974i | \(0.211642\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.20166 | −1.71016 | −0.855082 | − | 0.518492i | \(-0.826493\pi\) | ||||
−0.855082 | + | 0.518492i | \(0.826493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.81681 | 0.708764 | 0.354382 | − | 0.935101i | \(-0.384691\pi\) | ||||
0.354382 | + | 0.935101i | \(0.384691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.20166 | −1.11385 | −0.556926 | − | 0.830562i | \(-0.688019\pi\) | ||||
−0.556926 | + | 0.830562i | \(0.688019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.67282 | −0.789851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12.0185 | −1.97582 | −0.987912 | − | 0.155014i | \(-0.950458\pi\) | ||||
−0.987912 | + | 0.155014i | \(0.950458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.183190 | −0.0286094 | −0.0143047 | − | 0.999898i | \(-0.504553\pi\) | ||||
−0.0143047 | + | 0.999898i | \(0.504553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.96080 | −1.06151 | −0.530756 | − | 0.847525i | \(-0.678092\pi\) | ||||
−0.530756 | + | 0.847525i | \(0.678092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.20166 | 0.612875 | 0.306438 | − | 0.951891i | \(-0.400863\pi\) | ||||
0.306438 | + | 0.951891i | \(0.400863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8353 | 2.11933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7776 | −1.48042 | −0.740209 | − | 0.672377i | \(-0.765273\pi\) | ||||
−0.740209 | + | 0.672377i | \(0.765273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.81681 | 0.784339 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.05767 | 0.918831 | 0.459415 | − | 0.888221i | \(-0.348059\pi\) | ||||
0.459415 | + | 0.888221i | \(0.348059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.14399 | 0.658620 | 0.329310 | − | 0.944222i | \(-0.393184\pi\) | ||||
0.329310 | + | 0.944222i | \(0.393184\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.67282 | 0.331523 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6913 | 1.30615 | 0.653075 | − | 0.757293i | \(-0.273479\pi\) | ||||
0.653075 | + | 0.757293i | \(0.273479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0577 | −1.31230 | −0.656152 | − | 0.754629i | \(-0.727817\pi\) | ||||
−0.656152 | + | 0.754629i | \(0.727817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.28797 | −0.501869 | −0.250935 | − | 0.968004i | \(-0.580738\pi\) | ||||
−0.250935 | + | 0.968004i | \(0.580738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.1809 | −3.09755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.28797 | −0.707452 | −0.353726 | − | 0.935349i | \(-0.615086\pi\) | ||||
−0.353726 | + | 0.935349i | \(0.615086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.14399 | −0.125569 | −0.0627844 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627844 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.48963 | −0.703900 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.81681 | 0.404581 | 0.202291 | − | 0.979326i | \(-0.435161\pi\) | ||||
0.202291 | + | 0.979326i | \(0.435161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4896 | −1.30927 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.67282 | −0.677523 | −0.338761 | − | 0.940872i | \(-0.610008\pi\) | ||||
−0.338761 | + | 0.940872i | \(0.610008\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.654353 | −0.0651105 | −0.0325553 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325553 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.71203 | −0.168691 | −0.0843455 | − | 0.996437i | \(-0.526880\pi\) | ||||
−0.0843455 | + | 0.996437i | \(0.526880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.05767 | −0.867568 | −0.433784 | − | 0.901017i | \(-0.642822\pi\) | ||||
−0.433784 | + | 0.901017i | \(0.642822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5473 | −1.08628 | −0.543140 | − | 0.839642i | \(-0.682765\pi\) | ||||
−0.543140 | + | 0.839642i | \(0.682765\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.20166 | 0.764809 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.3249 | 2.77988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.8353 | 2.07593 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.18319 | −0.190746 | −0.0953731 | − | 0.995442i | \(-0.530404\pi\) | ||||
−0.0953731 | + | 0.995442i | \(0.530404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.67282 | −0.405185 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.36638 | −0.370351 | −0.185176 | − | 0.982705i | \(-0.559285\pi\) | ||||
−0.185176 | + | 0.982705i | \(0.559285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5473 | 1.30013 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.81681 | −0.316969 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.28797 | −0.351284 | −0.175642 | − | 0.984454i | \(-0.556200\pi\) | ||||
−0.175642 | + | 0.984454i | \(0.556200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8930 | 1.37473 | 0.687365 | − | 0.726313i | \(-0.258767\pi\) | ||||
0.687365 | + | 0.726313i | \(0.258767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.20166 | 0.498129 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3249 | 1.30287 | 0.651435 | − | 0.758704i | \(-0.274167\pi\) | ||||
0.651435 | + | 0.758704i | \(0.274167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −38.3249 | −3.02043 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0185 | −1.41132 | −0.705658 | − | 0.708553i | \(-0.749348\pi\) | ||||
−0.705658 | + | 0.708553i | \(0.749348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.14399 | 0.552818 | 0.276409 | − | 0.961040i | \(-0.410856\pi\) | ||||
0.276409 | + | 0.961040i | \(0.410856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.85601 | −0.450463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4112 | 1.70389 | 0.851947 | − | 0.523628i | \(-0.175422\pi\) | ||||
0.851947 | + | 0.523628i | \(0.175422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.67282 | 0.353232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0369 | −1.19866 | −0.599329 | − | 0.800503i | \(-0.704566\pi\) | ||||
−0.599329 | + | 0.800503i | \(0.704566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9216 | −0.886125 | −0.443063 | − | 0.896491i | \(-0.646108\pi\) | ||||
−0.443063 | + | 0.896491i | \(0.646108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0185 | 0.883616 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.7490 | −2.76048 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.47116 | −0.612952 | −0.306476 | − | 0.951878i | \(-0.599150\pi\) | ||||
−0.306476 | + | 0.951878i | \(0.599150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.7305 | −0.988343 | −0.494171 | − | 0.869364i | \(-0.664528\pi\) | ||||
−0.494171 | + | 0.869364i | \(0.664528\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4689 | 1.38710 | 0.693551 | − | 0.720408i | \(-0.256045\pi\) | ||||
0.693551 | + | 0.720408i | \(0.256045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.942326 | −0.0667997 | −0.0333998 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333998 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.8353 | 1.25179 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.183190 | 0.0127945 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.81681 | 0.402357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.71203 | −0.393232 | −0.196616 | − | 0.980481i | \(-0.562995\pi\) | ||||
−0.196616 | + | 0.980481i | \(0.562995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.96080 | 0.474722 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.9793 | −1.96724 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.3456 | −1.16679 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.71203 | −0.114646 | −0.0573229 | − | 0.998356i | \(-0.518256\pi\) | ||||
−0.0573229 | + | 0.998356i | \(0.518256\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.452692 | 0.0300462 | 0.0150231 | − | 0.999887i | \(-0.495218\pi\) | ||||
0.0150231 | + | 0.999887i | \(0.495218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1233 | −0.933291 | −0.466645 | − | 0.884444i | \(-0.654538\pi\) | ||||
−0.466645 | + | 0.884444i | \(0.654538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7120 | 0.767280 | 0.383640 | − | 0.923483i | \(-0.374670\pi\) | ||||
0.383640 | + | 0.923483i | \(0.374670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.20166 | −0.274086 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4874 | −1.64864 | −0.824321 | − | 0.566123i | \(-0.808443\pi\) | ||||
−0.824321 | + | 0.566123i | \(0.808443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.8353 | −0.947791 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.67282 | 0.170068 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.12552 | −0.197281 | −0.0986404 | − | 0.995123i | \(-0.531449\pi\) | ||||
−0.0986404 | + | 0.995123i | \(0.531449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 47.7075 | 2.99935 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5680 | 0.908729 | 0.454365 | − | 0.890816i | \(-0.349866\pi\) | ||||
0.454365 | + | 0.890816i | \(0.349866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −56.1602 | −3.48962 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.54731 | −0.342062 | −0.171031 | − | 0.985266i | \(-0.554710\pi\) | ||||
−0.171031 | + | 0.985266i | \(0.554710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7776 | 0.662063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.1625 | −1.77807 | −0.889033 | − | 0.457843i | \(-0.848622\pi\) | ||||
−0.889033 | + | 0.457843i | \(0.848622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.92159 | 0.116728 | 0.0583642 | − | 0.998295i | \(-0.481412\pi\) | ||||
0.0583642 | + | 0.998295i | \(0.481412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.81681 | −0.350767 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.9793 | −1.62103 | −0.810514 | − | 0.585720i | \(-0.800812\pi\) | ||||
−0.810514 | + | 0.585720i | \(0.800812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.39276 | −0.262050 | −0.131025 | − | 0.991379i | \(-0.541827\pi\) | ||||
−0.131025 | + | 0.991379i | \(0.541827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.8824 | −1.47910 | −0.739552 | − | 0.673099i | \(-0.764963\pi\) | ||||
−0.739552 | + | 0.673099i | \(0.764963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.856013 | −0.0505289 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.1153 | 1.47737 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.83528 | −0.107218 | −0.0536091 | − | 0.998562i | \(-0.517073\pi\) | ||||
−0.0536091 | + | 0.998562i | \(0.517073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.05767 | −0.410914 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.9216 | 1.26776 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.5266 | −1.87480 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.14399 | −0.294544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3664 | −0.705787 | −0.352893 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352893 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.79608 | 0.385370 | 0.192685 | − | 0.981261i | \(-0.438280\pi\) | ||||
0.192685 | + | 0.981261i | \(0.438280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.23030 | 0.295634 | 0.147817 | − | 0.989015i | \(-0.452775\pi\) | ||||
0.147817 | + | 0.989015i | \(0.452775\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.7569 | −1.78364 | −0.891822 | − | 0.452387i | \(-0.850573\pi\) | ||||
−0.891822 | + | 0.452387i | \(0.850573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.2017 | −1.24305 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.48963 | −0.361093 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.67282 | −0.148262 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.6336 | 1.08244 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8930 | 0.708661 | 0.354330 | − | 0.935120i | \(-0.384709\pi\) | ||||
0.354330 | + | 0.935120i | \(0.384709\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6913 | −0.584128 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2280 | −1.31979 | −0.659893 | − | 0.751360i | \(-0.729398\pi\) | ||||
−0.659893 | + | 0.751360i | \(0.729398\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.0739 | 1.95351 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.6129 | 1.97691 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.45269 | 0.346399 | 0.173199 | − | 0.984887i | \(-0.444590\pi\) | ||||
0.173199 | + | 0.984887i | \(0.444590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.3087 | 0.605341 | 0.302671 | − | 0.953095i | \(-0.402122\pi\) | ||||
0.302671 | + | 0.953095i | \(0.402122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.6913 | 1.73998 | 0.869991 | − | 0.493068i | \(-0.164124\pi\) | ||||
0.869991 | + | 0.493068i | \(0.164124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0577 | 0.586880 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.04711 | −0.266376 | −0.133188 | − | 0.991091i | \(-0.542521\pi\) | ||||
−0.133188 | + | 0.991091i | \(0.542521\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.28797 | 0.224443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.2280 | −1.78669 | −0.893345 | − | 0.449372i | \(-0.851648\pi\) | ||||
−0.893345 | + | 0.449372i | \(0.851648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.3619 | −2.61466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.3064 | 1.36210 | 0.681048 | − | 0.732239i | \(-0.261524\pi\) | ||||
0.681048 | + | 0.732239i | \(0.261524\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.2017 | −0.525412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38.6050 | −1.98300 | −0.991502 | − | 0.130089i | \(-0.958474\pi\) | ||||
−0.991502 | + | 0.130089i | \(0.958474\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.40332 | −0.429390 | −0.214695 | − | 0.976681i | \(-0.568876\pi\) | ||||
−0.214695 | + | 0.976681i | \(0.568876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.1809 | 1.38527 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2880 | −0.623025 | −0.311512 | − | 0.950242i | \(-0.600836\pi\) | ||||
−0.311512 | + | 0.950242i | \(0.600836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.2258 | −2.69174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.28797 | 0.316382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.6498 | 1.73903 | 0.869513 | − | 0.493911i | \(-0.164433\pi\) | ||||
0.869513 | + | 0.493911i | \(0.164433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.73840 | 0.286562 | 0.143281 | − | 0.989682i | \(-0.454235\pi\) | ||||
0.143281 | + | 0.989682i | \(0.454235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5759 | 0.825707 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 69.9092 | 3.46527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.9009 | 1.42906 | 0.714528 | − | 0.699607i | \(-0.246642\pi\) | ||||
0.714528 | + | 0.699607i | \(0.246642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.9793 | 1.62280 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.14399 | 0.0561561 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.87448 | 0.238134 | 0.119067 | − | 0.992886i | \(-0.462010\pi\) | ||||
0.119067 | + | 0.992886i | \(0.462010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.48963 | 0.314793 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0369 | 1.16323 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6544 | −0.513202 | −0.256601 | − | 0.966517i | \(-0.582603\pi\) | ||||
−0.256601 | + | 0.966517i | \(0.582603\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.88239 | −0.330747 | −0.165373 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165373 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.20166 | 0.392339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.0739 | 1.91262 | 0.956311 | − | 0.292351i | \(-0.0944376\pi\) | ||||
0.956311 | + | 0.292351i | \(0.0944376\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8930 | 1.46777 | 0.733884 | − | 0.679274i | \(-0.237705\pi\) | ||||
0.733884 | + | 0.679274i | \(0.237705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.81681 | −0.180934 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7961 | 0.603884 | 0.301942 | − | 0.953326i | \(-0.402365\pi\) | ||||
0.301942 | + | 0.953326i | \(0.402365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06558 | 0.0501762 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.4896 | 0.585523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.3249 | 1.32498 | 0.662492 | − | 0.749069i | \(-0.269499\pi\) | ||||
0.662492 | + | 0.749069i | \(0.269499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.42405 | −0.0663248 | −0.0331624 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331624 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.7305 | 1.47464 | 0.737321 | − | 0.675543i | \(-0.236091\pi\) | ||||
0.737321 | + | 0.675543i | \(0.236091\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4896 | 0.670500 | 0.335250 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335250 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 49.9585 | 2.30687 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.4896 | 1.86172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.1994 | 1.42554 | 0.712768 | − | 0.701399i | \(-0.247441\pi\) | ||||
0.712768 | + | 0.701399i | \(0.247441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.1233 | 1.46469 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.67282 | 0.302997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.3249 | 1.73667 | 0.868334 | − | 0.495980i | \(-0.165191\pi\) | ||||
0.868334 | + | 0.495980i | \(0.165191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1625 | −0.684272 | −0.342136 | − | 0.939650i | \(-0.611150\pi\) | ||||
−0.342136 | + | 0.939650i | \(0.611150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.7697 | 1.11557 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −51.6706 | −2.31774 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.9009 | −1.20425 | −0.602124 | − | 0.798403i | \(-0.705679\pi\) | ||||
−0.602124 | + | 0.798403i | \(0.705679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.8560 | −1.55415 | −0.777076 | − | 0.629406i | \(-0.783298\pi\) | ||||
−0.777076 | + | 0.629406i | \(0.783298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.654353 | 0.0291183 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7591 | 0.565539 | 0.282769 | − | 0.959188i | \(-0.408747\pi\) | ||||
0.282769 | + | 0.959188i | \(0.408747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0369 | −0.886382 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.71203 | 0.0754409 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.4403 | −1.07488 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.52884 | −0.242223 | −0.121111 | − | 0.992639i | \(-0.538646\pi\) | ||||
−0.121111 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0577 | 0.483518 | 0.241759 | − | 0.970336i | \(-0.422276\pi\) | ||||
0.241759 | + | 0.970336i | \(0.422276\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −40.2465 | −1.75317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.2672 | 1.92466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.489634 | 0.0212084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −86.2940 | −3.71695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9585 | −1.03006 | −0.515029 | − | 0.857173i | \(-0.672219\pi\) | ||||
−0.515029 | + | 0.857173i | \(0.672219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.05767 | 0.387988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.209567 | 0.00896042 | 0.00448021 | − | 0.999990i | \(-0.498574\pi\) | ||||
0.00448021 | + | 0.999990i | \(0.498574\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.81681 | −0.162602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.3826 | −1.24947 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9793 | 0.634692 | 0.317346 | − | 0.948310i | \(-0.397208\pi\) | ||||
0.317346 | + | 0.948310i | \(0.397208\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.6050 | 0.786907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.6992 | −0.703787 | −0.351894 | − | 0.936040i | \(-0.614462\pi\) | ||||
−0.351894 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.5473 | 0.485799 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.5450 | −1.44820 | −0.724102 | − | 0.689693i | \(-0.757745\pi\) | ||||
−0.724102 | + | 0.689693i | \(0.757745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.92159 | −0.247811 | −0.123905 | − | 0.992294i | \(-0.539542\pi\) | ||||
−0.123905 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.20166 | −0.342033 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.6544 | 1.02637 | 0.513187 | − | 0.858277i | \(-0.328465\pi\) | ||||
0.513187 | + | 0.858277i | \(0.328465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.34565 | −0.221775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 62.6913 | 2.59641 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2017 | −0.503616 | −0.251808 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251808 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.20166 | 0.255535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.02073 | 0.0419164 | 0.0209582 | − | 0.999780i | \(-0.493328\pi\) | ||||
0.0209582 | + | 0.999780i | \(0.493328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.3249 | −1.24320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.42405 | −0.303339 | −0.151669 | − | 0.988431i | \(-0.548465\pi\) | ||||
−0.151669 | + | 0.988431i | \(0.548465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3456 | 0.789125 | 0.394563 | − | 0.918869i | \(-0.370896\pi\) | ||||
0.394563 | + | 0.918869i | \(0.370896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.8353 | −0.928386 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0369 | −0.650919 | −0.325460 | − | 0.945556i | \(-0.605519\pi\) | ||||
−0.325460 | + | 0.945556i | \(0.605519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.2303 | −0.454329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.1523 | −1.46018 | −0.730089 | − | 0.683352i | \(-0.760521\pi\) | ||||
−0.730089 | + | 0.683352i | \(0.760521\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.4482 | 1.62838 | 0.814191 | − | 0.580597i | \(-0.197181\pi\) | ||||
0.814191 | + | 0.580597i | \(0.197181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.19376 | −0.168561 | −0.0842806 | − | 0.996442i | \(-0.526859\pi\) | ||||
−0.0842806 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.8353 | 0.714555 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −77.9955 | −3.10988 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.30871 | 0.211336 | 0.105668 | − | 0.994401i | \(-0.466302\pi\) | ||||
0.105668 | + | 0.994401i | \(0.466302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.6521 | −1.57107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.24086 | 0.285997 | 0.142998 | − | 0.989723i | \(-0.454326\pi\) | ||||
0.142998 | + | 0.989723i | \(0.454326\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.38485 | 0.0940493 | 0.0470247 | − | 0.998894i | \(-0.485026\pi\) | ||||
0.0470247 | + | 0.998894i | \(0.485026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.47342 | −0.0579263 | −0.0289631 | − | 0.999580i | \(-0.509221\pi\) | ||||
−0.0289631 | + | 0.999580i | \(0.509221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.0532 | −1.61148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9137 | 1.01408 | 0.507040 | − | 0.861922i | \(-0.330739\pi\) | ||||
0.507040 | + | 0.861922i | \(0.330739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.18319 | 0.0853043 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.9793 | 0.973054 | 0.486527 | − | 0.873666i | \(-0.338264\pi\) | ||||
0.486527 | + | 0.873666i | \(0.338264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.4195 | 1.53324 | 0.766621 | − | 0.642100i | \(-0.221937\pi\) | ||||
0.766621 | + | 0.642100i | \(0.221937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.67282 | 0.181204 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3042 | −1.21210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.9216 | −1.15511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0185 | 0.463278 | 0.231639 | − | 0.972802i | \(-0.425591\pi\) | ||||
0.231639 | + | 0.972802i | \(0.425591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.2017 | −0.853279 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.1809 | −1.19661 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0739 | 1.22727 | 0.613637 | − | 0.789589i | \(-0.289706\pi\) | ||||
0.613637 | + | 0.789589i | \(0.289706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.8066 | 1.09745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0369 | 1.67524 | 0.837622 | − | 0.546250i | \(-0.183945\pi\) | ||||
0.837622 | + | 0.546250i | \(0.183945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.36638 | 0.165626 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.18883 | −0.0450303 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.9793 | 0.716837 | 0.358419 | − | 0.933561i | \(-0.383316\pi\) | ||||
0.358419 | + | 0.933561i | \(0.383316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0185 | 0.453285 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.05767 | −0.114996 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12325 | −0.0797405 | −0.0398702 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398702 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.8639 | 1.90487 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.5473 | −0.581436 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5658 | 0.431331 | 0.215665 | − | 0.976467i | \(-0.430808\pi\) | ||||
0.215665 | + | 0.976467i | \(0.430808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.81681 | 0.141753 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3064 | 1.19818 | 0.599090 | − | 0.800682i | \(-0.295529\pi\) | ||||
0.599090 | + | 0.800682i | \(0.295529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.1730 | −1.67078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.4033 | 0.679742 | 0.339871 | − | 0.940472i | \(-0.389617\pi\) | ||||
0.339871 | + | 0.940472i | \(0.389617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −62.1892 | −2.29077 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.5552 | −1.23102 | −0.615511 | − | 0.788129i | \(-0.711050\pi\) | ||||
−0.615511 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.28797 | 0.157099 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.06558 | 0.330808 | 0.165404 | − | 0.986226i | \(-0.447107\pi\) | ||||
0.165404 | + | 0.986226i | \(0.447107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.8930 | −0.614798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.1316 | 1.78572 | 0.892858 | − | 0.450337i | \(-0.148696\pi\) | ||||
0.892858 | + | 0.450337i | \(0.148696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.4033 | 0.957120 | 0.478560 | − | 0.878055i | \(-0.341159\pi\) | ||||
0.478560 | + | 0.878055i | \(0.341159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.3249 | −1.53226 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.8639 | −0.681137 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6913 | 0.601903 | 0.300952 | − | 0.953639i | \(-0.402696\pi\) | ||||
0.300952 | + | 0.953639i | \(0.402696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.8722 | −1.36217 | −0.681085 | − | 0.732205i | \(-0.738491\pi\) | ||||
−0.681085 | + | 0.732205i | \(0.738491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.20166 | −0.222770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.183190 | 0.00656345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.3204 | 2.30156 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.3249 | −0.582661 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4817 | −0.516218 | −0.258109 | − | 0.966116i | \(-0.583099\pi\) | ||||
−0.258109 | + | 0.966116i | \(0.583099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53.9585 | −1.91854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.7490 | −0.488240 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6419 | 1.51045 | 0.755227 | − | 0.655463i | \(-0.227527\pi\) | ||||
0.755227 | + | 0.655463i | \(0.227527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.2672 | 0.964646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.9423 | 0.880196 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.3249 | 1.35078 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.6706 | 1.46506 | 0.732529 | − | 0.680735i | \(-0.238340\pi\) | ||||
0.732529 | + | 0.680735i | \(0.238340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.9585 | 1.89474 | 0.947370 | − | 0.320140i | \(-0.103730\pi\) | ||||
0.947370 | + | 0.320140i | \(0.103730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.0185 | 0.631160 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.96080 | 0.243527 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.74897 | −0.270441 | −0.135220 | − | 0.990816i | \(-0.543174\pi\) | ||||
−0.135220 | + | 0.990816i | \(0.543174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.0554 | −1.32653 | −0.663264 | − | 0.748385i | \(-0.730829\pi\) | ||||
−0.663264 | + | 0.748385i | \(0.730829\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.9299 | 1.70146 | 0.850730 | − | 0.525604i | \(-0.176160\pi\) | ||||
0.850730 | + | 0.525604i | \(0.176160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0369 | −0.626449 | −0.313224 | − | 0.949679i | \(-0.601409\pi\) | ||||
−0.313224 | + | 0.949679i | \(0.601409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 96.2755 | 3.33575 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.14399 | −0.247228 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0577 | −0.934135 | −0.467067 | − | 0.884222i | \(-0.654689\pi\) | ||||
−0.467067 | + | 0.884222i | \(0.654689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4320 | −0.497654 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.85601 | 0.201453 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 106.705 | 3.66644 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 98.5714 | 3.37898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.6336 | −1.42551 | −0.712754 | − | 0.701414i | \(-0.752552\pi\) | ||||
−0.712754 | + | 0.701414i | \(0.752552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.8722 | −1.56697 | −0.783483 | − | 0.621414i | \(-0.786559\pi\) | ||||
−0.783483 | + | 0.621414i | \(0.786559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5187 | 1.04128 | 0.520642 | − | 0.853775i | \(-0.325693\pi\) | ||||
0.520642 | + | 0.853775i | \(0.325693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.42405 | −0.252718 | −0.126359 | − | 0.991985i | \(-0.540329\pi\) | ||||
−0.126359 | + | 0.991985i | \(0.540329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.4112 | −0.762005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.5759 | 1.24075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.5759 | −0.968259 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.67282 | −0.157970 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.0554 | −0.812294 | −0.406147 | − | 0.913808i | \(-0.633128\pi\) | ||||
−0.406147 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.481728 | 0.0162298 | 0.00811492 | − | 0.999967i | \(-0.497417\pi\) | ||||
0.00811492 | + | 0.999967i | \(0.497417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.4056 | 0.854966 | 0.427483 | − | 0.904023i | \(-0.359400\pi\) | ||||
0.427483 | + | 0.904023i | \(0.359400\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.2307 | −0.947894 | −0.473947 | − | 0.880553i | \(-0.657171\pi\) | ||||
−0.473947 | + | 0.880553i | \(0.657171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.6913 | −0.626886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.20166 | −0.140603 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0369 | 0.536056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.6706 | −0.789457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.9427 | −2.33013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.9216 | 0.396287 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.1888 | −1.23483 | −0.617417 | − | 0.786636i | \(-0.711821\pi\) | ||||
−0.617417 | + | 0.786636i | \(0.711821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5187 | −0.613551 | −0.306775 | − | 0.951782i | \(-0.599250\pi\) | ||||
−0.306775 | + | 0.951782i | \(0.599250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.65435 | 0.220227 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2017 | −0.336889 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.3294 | 0.406711 | 0.203355 | − | 0.979105i | \(-0.434815\pi\) | ||||
0.203355 | + | 0.979105i | \(0.434815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5552 | 0.972822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0185 | −0.395165 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.67508 | 0.251811 | 0.125906 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125906 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.8353 | −0.486207 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.7490 | 1.23452 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.05767 | −0.295901 | −0.147951 | − | 0.988995i | \(-0.547268\pi\) | ||||
−0.147951 | + | 0.988995i | \(0.547268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.2201 | 1.83272 | 0.916362 | − | 0.400351i | \(-0.131112\pi\) | ||||
0.916362 | + | 0.400351i | \(0.131112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.50246 | 0.0489268 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.2179 | 1.07944 | 0.539718 | − | 0.841846i | \(-0.318531\pi\) | ||||
0.539718 | + | 0.841846i | \(0.318531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.4610 | 0.372040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.81455 | −0.220745 | −0.110372 | − | 0.993890i | \(-0.535204\pi\) | ||||
−0.110372 | + | 0.993890i | \(0.535204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.47116 | 0.274120 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.34565 | −0.301787 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.46060 | 0.240664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.7305 | 0.442000 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2857 | 1.45629 | 0.728145 | − | 0.685423i | \(-0.240383\pi\) | ||||
0.728145 | + | 0.685423i | \(0.240383\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0207 | −0.482038 | −0.241019 | − | 0.970520i | \(-0.577482\pi\) | ||||
−0.241019 | + | 0.970520i | \(0.577482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.4033 | −0.654100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.77761 | −0.216835 | −0.108417 | − | 0.994105i | \(-0.534578\pi\) | ||||
−0.108417 | + | 0.994105i | \(0.534578\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.2017 | −0.709568 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.1025 | −1.05581 | −0.527903 | − | 0.849305i | \(-0.677022\pi\) | ||||
−0.527903 | + | 0.849305i | \(0.677022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.4689 | −0.620331 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.0901 | 1.81536 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2672 | −1.50149 | −0.750747 | − | 0.660590i | \(-0.770306\pi\) | ||||
−0.750747 | + | 0.660590i | \(0.770306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.942326 | 0.0298737 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.09422 | 0.129665 | 0.0648326 | − | 0.997896i | \(-0.479349\pi\) | ||||
0.0648326 | + | 0.997896i | \(0.479349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3420.2.a.m.1.3 | 3 | ||
3.2 | odd | 2 | 1140.2.a.g.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.br.1.1 | 3 | |||
15.2 | even | 4 | 5700.2.f.q.3649.3 | 6 | |||
15.8 | even | 4 | 5700.2.f.q.3649.4 | 6 | |||
15.14 | odd | 2 | 5700.2.a.w.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.g.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
3420.2.a.m.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4560.2.a.br.1.1 | 3 | 12.11 | even | 2 | |||
5700.2.a.w.1.1 | 3 | 15.14 | odd | 2 | |||
5700.2.f.q.3649.3 | 6 | 15.2 | even | 4 | |||
5700.2.f.q.3649.4 | 6 | 15.8 | even | 4 |