Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9016,2,Mod(1,9016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9016, 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("9016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9016.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: | \(71.9931224624\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4 x^{10} - 14 x^{9} + 61 x^{8} + 71 x^{7} - 343 x^{6} - 152 x^{5} + 867 x^{4} + 102 x^{3} + \cdots + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1288) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.59106\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9016.1 |
$q$-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 | ||||||||
\(3\) | −1.59106 | −0.918602 | −0.459301 | − | 0.888281i | \(-0.651900\pi\) | ||||
−0.459301 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.83508 | 1.26788 | 0.633942 | − | 0.773380i | \(-0.281436\pi\) | ||||
0.633942 | + | 0.773380i | \(0.281436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.468513 | −0.156171 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.68688 | 1.71466 | 0.857329 | − | 0.514769i | \(-0.172122\pi\) | ||||
0.857329 | + | 0.514769i | \(0.172122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.47160 | 1.51755 | 0.758775 | − | 0.651353i | \(-0.225798\pi\) | ||||
0.758775 | + | 0.651353i | \(0.225798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.51079 | −1.16468 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.927480 | −0.224947 | −0.112473 | − | 0.993655i | \(-0.535877\pi\) | ||||
−0.112473 | + | 0.993655i | \(0.535877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.70110 | −1.76675 | −0.883377 | − | 0.468663i | \(-0.844736\pi\) | ||||
−0.883377 | + | 0.468663i | \(0.844736\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.03766 | 0.607532 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.51863 | 1.06206 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.155642 | −0.0289021 | −0.0144510 | − | 0.999896i | \(-0.504600\pi\) | ||||
−0.0144510 | + | 0.999896i | \(0.504600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.19318 | −1.11233 | −0.556164 | − | 0.831072i | \(-0.687727\pi\) | ||||
−0.556164 | + | 0.831072i | \(0.687727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.04819 | −1.57509 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.13469 | −0.679739 | −0.339870 | − | 0.940473i | \(-0.610383\pi\) | ||||
−0.339870 | + | 0.940473i | \(0.610383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.70567 | −1.39402 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.77277 | −0.901556 | −0.450778 | − | 0.892636i | \(-0.648853\pi\) | ||||
−0.450778 | + | 0.892636i | \(0.648853\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.58237 | −1.30880 | −0.654399 | − | 0.756149i | \(-0.727078\pi\) | ||||
−0.654399 | + | 0.756149i | \(0.727078\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32827 | −0.198007 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.52968 | −0.223127 | −0.111563 | − | 0.993757i | \(-0.535586\pi\) | ||||
−0.111563 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.47568 | 0.206637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.51278 | −0.482517 | −0.241258 | − | 0.970461i | \(-0.577560\pi\) | ||||
−0.241258 | + | 0.970461i | \(0.577560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.1227 | 2.17399 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.2530 | 1.62294 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0446442 | 0.00581218 | 0.00290609 | − | 0.999996i | \(-0.499075\pi\) | ||||
0.00290609 | + | 0.999996i | \(0.499075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.01884 | −1.15474 | −0.577372 | − | 0.816481i | \(-0.695922\pi\) | ||||
−0.577372 | + | 0.816481i | \(0.695922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.5124 | 1.92408 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6206 | −1.66402 | −0.832012 | − | 0.554757i | \(-0.812811\pi\) | ||||
−0.832012 | + | 0.554757i | \(0.812811\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.59106 | 0.191542 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.38742 | −0.164656 | −0.0823280 | − | 0.996605i | \(-0.526236\pi\) | ||||
−0.0823280 | + | 0.996605i | \(0.526236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9422 | −1.63182 | −0.815908 | − | 0.578182i | \(-0.803763\pi\) | ||||
−0.815908 | + | 0.578182i | \(0.803763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.83312 | −0.558080 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.51114 | −1.07009 | −0.535043 | − | 0.844825i | \(-0.679705\pi\) | ||||
−0.535043 | + | 0.844825i | \(0.679705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.37496 | −0.819440 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.29488 | −0.910481 | −0.455241 | − | 0.890368i | \(-0.650447\pi\) | ||||
−0.455241 | + | 0.890368i | \(0.650447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.62948 | −0.285207 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.247637 | 0.0265495 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.13979 | 0.968816 | 0.484408 | − | 0.874842i | \(-0.339035\pi\) | ||||
0.484408 | + | 0.874842i | \(0.339035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.85375 | 1.02179 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.8332 | −2.24004 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.16127 | −0.320979 | −0.160489 | − | 0.987038i | \(-0.551307\pi\) | ||||
−0.160489 | + | 0.987038i | \(0.551307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.66437 | −0.267780 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.04967 | 0.900476 | 0.450238 | − | 0.892909i | \(-0.351339\pi\) | ||||
0.450238 | + | 0.892909i | \(0.351339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.0747 | −1.68242 | −0.841210 | − | 0.540708i | \(-0.818156\pi\) | ||||
−0.841210 | + | 0.540708i | \(0.818156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6947 | −1.22725 | −0.613623 | − | 0.789599i | \(-0.710288\pi\) | ||||
−0.613623 | + | 0.789599i | \(0.710288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.99507 | 0.478441 | 0.239221 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239221 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.57856 | 0.624410 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9019 | 1.21371 | 0.606856 | − | 0.794812i | \(-0.292431\pi\) | ||||
0.606856 | + | 0.794812i | \(0.292431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.83508 | −0.264372 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.56351 | −0.236997 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.3406 | 1.94005 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.18486 | 0.828171 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.56338 | −0.497604 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8162 | 1.22599 | 0.612993 | − | 0.790088i | \(-0.289965\pi\) | ||||
0.612993 | + | 0.790088i | \(0.289965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.6551 | 1.20226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0502 | −0.965459 | −0.482730 | − | 0.875769i | \(-0.660355\pi\) | ||||
−0.482730 | + | 0.875769i | \(0.660355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.6457 | 1.34657 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.69956 | 0.145203 | 0.0726017 | − | 0.997361i | \(-0.476870\pi\) | ||||
0.0726017 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0798 | −1.02460 | −0.512298 | − | 0.858808i | \(-0.671206\pi\) | ||||
−0.512298 | + | 0.858808i | \(0.671206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.43382 | 0.204965 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.1163 | 2.60208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.441258 | −0.0366445 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.12978 | −0.502171 | −0.251085 | − | 0.967965i | \(-0.580788\pi\) | ||||
−0.251085 | + | 0.967965i | \(0.580788\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.190212 | 0.0154792 | 0.00773960 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00773960 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.434536 | 0.0351301 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.5581 | −1.41030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.02361 | −0.400927 | −0.200464 | − | 0.979701i | \(-0.564245\pi\) | ||||
−0.200464 | + | 0.979701i | \(0.564245\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.58906 | 0.443241 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7623 | 0.921292 | 0.460646 | − | 0.887584i | \(-0.347618\pi\) | ||||
0.460646 | + | 0.887584i | \(0.347618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.6523 | −1.99703 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.7283 | 1.75877 | 0.879386 | − | 0.476109i | \(-0.157953\pi\) | ||||
0.879386 | + | 0.476109i | \(0.157953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9384 | 1.30296 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.60806 | 0.275915 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.64265 | −0.124888 | −0.0624442 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624442 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0710319 | −0.00533908 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.0732 | 1.64983 | 0.824913 | − | 0.565259i | \(-0.191224\pi\) | ||||
0.824913 | + | 0.565259i | \(0.191224\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.85689 | 0.286680 | 0.143340 | − | 0.989673i | \(-0.454216\pi\) | ||||
0.143340 | + | 0.989673i | \(0.454216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3496 | 1.06075 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.7222 | −0.861831 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.27446 | −0.385707 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.86103 | 0.496447 | 0.248223 | − | 0.968703i | \(-0.420153\pi\) | ||||
0.248223 | + | 0.968703i | \(0.420153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81022 | 0.490210 | 0.245105 | − | 0.969496i | \(-0.421177\pi\) | ||||
0.245105 | + | 0.969496i | \(0.421177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.6813 | −1.76746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.2767 | 0.803435 | 0.401717 | − | 0.915764i | \(-0.368413\pi\) | ||||
0.401717 | + | 0.915764i | \(0.368413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.4941 | −1.66545 | −0.832725 | − | 0.553687i | \(-0.813220\pi\) | ||||
−0.832725 | + | 0.553687i | \(0.813220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.6713 | 1.52858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.3663 | −1.14307 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.468513 | 0.0325639 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −43.7952 | −3.02938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.71973 | −0.187234 | −0.0936170 | − | 0.995608i | \(-0.529843\pi\) | ||||
−0.0936170 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.20747 | 0.151253 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.3317 | −1.65941 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.1830 | 1.49899 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.07480 | −0.341368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8482 | −1.19520 | −0.597602 | − | 0.801793i | \(-0.703880\pi\) | ||||
−0.597602 | + | 0.801793i | \(0.703880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.42318 | −0.0948788 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6572 | −0.906457 | −0.453229 | − | 0.891394i | \(-0.649728\pi\) | ||||
−0.453229 | + | 0.891394i | \(0.649728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.75676 | −0.116090 | −0.0580451 | − | 0.998314i | \(-0.518487\pi\) | ||||
−0.0580451 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9297 | 1.69871 | 0.849354 | − | 0.527823i | \(-0.176992\pi\) | ||||
0.849354 | + | 0.527823i | \(0.176992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.33676 | −0.282899 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1328 | 0.982983 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.01201 | −0.518254 | −0.259127 | − | 0.965843i | \(-0.583435\pi\) | ||||
−0.259127 | + | 0.965843i | \(0.583435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.83084 | −0.246766 | −0.123383 | − | 0.992359i | \(-0.539374\pi\) | ||||
−0.123383 | + | 0.992359i | \(0.539374\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.82185 | −0.309322 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.1374 | −2.68114 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1977 | 0.836369 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.15527 | 0.136040 | 0.0680198 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680198 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.68688 | −0.357531 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.18367 | 0.261991 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.70356 | 0.231022 | 0.115511 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115511 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0729204 | 0.00451366 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.35262 | −0.453382 | −0.226691 | − | 0.973967i | \(-0.572791\pi\) | ||||
−0.226691 | + | 0.973967i | \(0.572791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.95899 | −0.611776 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.5420 | −0.889956 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4244 | −0.879473 | −0.439737 | − | 0.898127i | \(-0.644928\pi\) | ||||
−0.439737 | + | 0.898127i | \(0.644928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1101 | 1.28235 | 0.641175 | − | 0.767395i | \(-0.278447\pi\) | ||||
0.641175 | + | 0.767395i | \(0.278447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.2748 | 1.04171 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.23187 | 0.554689 | 0.277345 | − | 0.960771i | \(-0.410546\pi\) | ||||
0.277345 | + | 0.960771i | \(0.410546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.90158 | 0.173713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.53493 | 0.330186 | 0.165093 | − | 0.986278i | \(-0.447208\pi\) | ||||
0.165093 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.89184 | −0.528565 | −0.264283 | − | 0.964445i | \(-0.585135\pi\) | ||||
−0.264283 | + | 0.964445i | \(0.585135\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 34.7381 | 2.05771 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1398 | −0.949399 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.02979 | 0.294852 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.3380 | −1.30500 | −0.652499 | − | 0.757790i | \(-0.726279\pi\) | ||||
−0.652499 | + | 0.757790i | \(0.726279\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.126570 | 0.00736918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.3838 | 1.82107 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.47160 | −0.316431 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3986 | −0.827179 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.5691 | −1.46408 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4507 | 1.39547 | 0.697737 | − | 0.716354i | \(-0.254190\pi\) | ||||
0.697737 | + | 0.716354i | \(0.254190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.1670 | 1.54547 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8294 | 1.01101 | 0.505507 | − | 0.862822i | \(-0.331305\pi\) | ||||
0.505507 | + | 0.862822i | \(0.331305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0265 | 1.07544 | 0.537722 | − | 0.843122i | \(-0.319285\pi\) | ||||
0.537722 | + | 0.843122i | \(0.319285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.9421 | 1.40089 | 0.700443 | − | 0.713708i | \(-0.252986\pi\) | ||||
0.700443 | + | 0.713708i | \(0.252986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.885119 | −0.0495571 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.1981 | 1.12735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.14262 | 0.397426 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.6209 | 0.921960 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.94749 | −0.439497 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.4302 | 1.17791 | 0.588954 | − | 0.808166i | \(-0.299540\pi\) | ||||
0.588954 | + | 0.808166i | \(0.299540\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.93715 | 0.106155 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.6155 | −2.10979 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.1959 | −1.37251 | −0.686255 | − | 0.727361i | \(-0.740746\pi\) | ||||
−0.686255 | + | 0.727361i | \(0.740746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.5278 | −1.11492 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.2199 | −1.90726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.51079 | 0.242853 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1561 | 1.08203 | 0.541017 | − | 0.841012i | \(-0.318040\pi\) | ||||
0.541017 | + | 0.841012i | \(0.318040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12556 | −0.220836 | −0.110418 | − | 0.993885i | \(-0.535219\pi\) | ||||
−0.110418 | + | 0.993885i | \(0.535219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.1957 | 1.61173 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.77923 | 0.147923 | 0.0739617 | − | 0.997261i | \(-0.476436\pi\) | ||||
0.0739617 | + | 0.997261i | \(0.476436\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.93343 | −0.208765 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.2275 | 1.27868 | 0.639340 | − | 0.768925i | \(-0.279208\pi\) | ||||
0.639340 | + | 0.768925i | \(0.279208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.3070 | 2.12142 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −33.9542 | −1.78213 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.5273 | −2.06896 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.14581 | −0.373008 | −0.186504 | − | 0.982454i | \(-0.559716\pi\) | ||||
−0.186504 | + | 0.982454i | \(0.559716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.70462 | 0.140797 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6183 | 0.653353 | 0.326676 | − | 0.945136i | \(-0.394071\pi\) | ||||
0.326676 | + | 0.945136i | \(0.394071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.85170 | 0.457100 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.851613 | −0.0438603 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.4112 | −1.56212 | −0.781060 | − | 0.624456i | \(-0.785321\pi\) | ||||
−0.781060 | + | 0.624456i | \(0.785321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.9824 | −1.12619 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7852 | 1.47086 | 0.735428 | − | 0.677603i | \(-0.236981\pi\) | ||||
0.735428 | + | 0.677603i | \(0.236981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.02095 | 0.204396 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.54256 | −0.433125 | −0.216562 | − | 0.976269i | \(-0.569484\pi\) | ||||
−0.216562 | + | 0.976269i | \(0.569484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.927480 | 0.0469047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.5816 | 0.886873 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.9648 | −1.35675 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8368 | 0.744640 | 0.372320 | − | 0.928104i | \(-0.378562\pi\) | ||||
0.372320 | + | 0.928104i | \(0.378562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.67987 | 0.0838888 | 0.0419444 | − | 0.999120i | \(-0.486645\pi\) | ||||
0.0419444 | + | 0.999120i | \(0.486645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.8866 | −1.68801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.9086 | −1.03896 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.5135 | −1.16552 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.4362 | 1.01051 | 0.505254 | − | 0.862971i | \(-0.331399\pi\) | ||||
0.505254 | + | 0.862971i | \(0.331399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.70411 | −0.133384 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.5166 | −1.15439 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.2198 | 0.941196 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.2285 | −1.08594 | −0.542968 | − | 0.839754i | \(-0.682699\pi\) | ||||
−0.542968 | + | 0.839754i | \(0.682699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.27042 | −0.354338 | −0.177169 | − | 0.984180i | \(-0.556694\pi\) | ||||
−0.177169 | + | 0.984180i | \(0.556694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.716675 | 0.0348459 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.81737 | −0.136663 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −49.5081 | −2.39027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.78849 | 0.471495 | 0.235747 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235747 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.7236 | −1.33231 | −0.666156 | − | 0.745812i | \(-0.732061\pi\) | ||||
−0.666156 | + | 0.745812i | \(0.732061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.702070 | 0.0336617 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.70110 | 0.368394 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.9337 | −1.47639 | −0.738193 | − | 0.674590i | \(-0.764321\pi\) | ||||
−0.738193 | + | 0.674590i | \(0.764321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0736 | 1.19128 | 0.595642 | − | 0.803250i | \(-0.296898\pi\) | ||||
0.595642 | + | 0.803250i | \(0.296898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.9120 | 1.22835 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.75287 | 0.461295 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.5576 | 1.25333 | 0.626665 | − | 0.779289i | \(-0.284420\pi\) | ||||
0.626665 | + | 0.779289i | \(0.284420\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.8290 | −1.54586 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.302639 | −0.0142192 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.97324 | 0.279416 | 0.139708 | − | 0.990193i | \(-0.455384\pi\) | ||||
0.139708 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.11842 | −0.238907 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7132 | 0.498961 | 0.249481 | − | 0.968380i | \(-0.419740\pi\) | ||||
0.249481 | + | 0.968380i | \(0.419740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.5686 | −1.79243 | −0.896217 | − | 0.443616i | \(-0.853695\pi\) | ||||
−0.896217 | + | 0.443616i | \(0.853695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.9362 | 1.29551 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.8471 | −1.01096 | −0.505482 | − | 0.862837i | \(-0.668685\pi\) | ||||
−0.505482 | + | 0.862837i | \(0.668685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.99288 | 0.368293 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.8069 | −2.24414 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.3933 | −1.07336 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64578 | 0.0753551 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.1702 | −1.83542 | −0.917711 | − | 0.397248i | \(-0.869965\pi\) | ||||
−0.917711 | + | 0.397248i | \(0.869965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.6234 | −1.03154 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.96245 | −0.406964 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.8525 | −1.53400 | −0.767002 | − | 0.641645i | \(-0.778252\pi\) | ||||
−0.767002 | + | 0.641645i | \(0.778252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.7145 | −0.846301 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6167 | 1.38171 | 0.690856 | − | 0.722992i | \(-0.257234\pi\) | ||||
0.690856 | + | 0.722992i | \(0.257234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.144355 | 0.00650143 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.55370 | −0.339514 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.58820 | 0.205396 | 0.102698 | − | 0.994713i | \(-0.467252\pi\) | ||||
0.102698 | + | 0.994713i | \(0.467252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.1623 | −1.61561 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4041 | 1.08813 | 0.544063 | − | 0.839044i | \(-0.316885\pi\) | ||||
0.544063 | + | 0.839044i | \(0.316885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6565 | 1.14170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.9501 | −1.19690 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0047 | 0.842367 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −42.4995 | −1.87640 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −48.4081 | −2.13312 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.69911 | −0.382586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.61356 | 0.114723 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.0560 | −1.36059 | −0.680293 | − | 0.732940i | \(-0.738147\pi\) | ||||
−0.680293 | + | 0.732940i | \(0.738147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.6108 | −1.55715 | −0.778576 | − | 0.627551i | \(-0.784058\pi\) | ||||
−0.778576 | + | 0.627551i | \(0.784058\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.74405 | 0.250215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0209164 | −0.000907694 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.5863 | −1.36815 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.9905 | −1.55601 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35.1199 | −1.51553 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.53695 | 0.0660788 | 0.0330394 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330394 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.13656 | −0.263345 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1614 | 0.606609 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.7557 | −1.14399 | −0.571995 | − | 0.820257i | \(-0.693830\pi\) | ||||
−0.571995 | + | 0.820257i | \(0.693830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.22544 | 0.180337 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.19862 | 0.0510628 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.6507 | 0.791679 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.305154 | 0.0129298 | 0.00646490 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646490 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.9593 | −1.98617 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.39201 | 0.354311 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.3537 | 1.44784 | 0.723918 | − | 0.689886i | \(-0.242339\pi\) | ||||
0.723918 | + | 0.689886i | \(0.242339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.5780 | 1.53885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 47.3530 | 1.98514 | 0.992571 | − | 0.121666i | \(-0.0388236\pi\) | ||||
0.992571 | + | 0.121666i | \(0.0388236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.15337 | 0.341208 | 0.170604 | − | 0.985340i | \(-0.445428\pi\) | ||||
0.170604 | + | 0.985340i | \(0.445428\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9163 | −0.456037 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.03766 | −0.126679 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.74738 | 0.280897 | 0.140449 | − | 0.990088i | \(-0.455146\pi\) | ||||
0.140449 | + | 0.990088i | \(0.455146\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8355 | −0.450308 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.9767 | −0.827351 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.26776 | −0.300485 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.9654 | 0.493863 | 0.246932 | − | 0.969033i | \(-0.420578\pi\) | ||||
0.246932 | + | 0.969033i | \(0.420578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.6943 | 1.96521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.9420 | −0.738037 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0872 | −0.578493 | −0.289247 | − | 0.957255i | \(-0.593405\pi\) | ||||
−0.289247 | + | 0.957255i | \(0.593405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.3806 | 1.52988 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.80253 | −0.155367 | −0.0776835 | − | 0.996978i | \(-0.524752\pi\) | ||||
−0.0776835 | + | 0.996978i | \(0.524752\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3123 | 0.624602 | 0.312301 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312301 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.38143 | 0.259872 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 60.5021 | 2.45976 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8863 | −0.604217 | −0.302108 | − | 0.953274i | \(-0.597690\pi\) | ||||
−0.302108 | + | 0.953274i | \(0.597690\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.36980 | −0.338606 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3843 | −1.14643 | −0.573216 | − | 0.819404i | \(-0.694304\pi\) | ||||
−0.573216 | + | 0.819404i | \(0.694304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.0398 | 1.05002 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.3540 | 1.14149 | 0.570745 | − | 0.821127i | \(-0.306654\pi\) | ||||
0.570745 | + | 0.821127i | \(0.306654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.1169 | 1.97417 | 0.987087 | − | 0.160184i | \(-0.0512089\pi\) | ||||
0.987087 | + | 0.160184i | \(0.0512089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.51863 | −0.221455 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9609 | −1.23844 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 69.6810 | 2.78279 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.83484 | 0.152905 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.85076 | 0.272725 | 0.136362 | − | 0.990659i | \(-0.456459\pi\) | ||||
0.136362 | + | 0.990659i | \(0.456459\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.32727 | 0.171994 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.1699 | 1.55441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.650022 | 0.0257145 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.2455 | −1.70809 | −0.854046 | − | 0.520197i | \(-0.825859\pi\) | ||||
−0.854046 | + | 0.520197i | \(0.825859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.48698 | 0.216385 | 0.108193 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108193 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.7133 | 1.52433 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.3140 | 1.54559 | 0.772796 | − | 0.634655i | \(-0.218858\pi\) | ||||
0.772796 | + | 0.634655i | \(0.218858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.253886 | 0.00996591 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.5433 | −1.58658 | −0.793290 | − | 0.608843i | \(-0.791634\pi\) | ||||
−0.793290 | + | 0.608843i | \(0.791634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.3281 | −1.22409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.53212 | 0.254842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.3289 | −0.558173 | −0.279087 | − | 0.960266i | \(-0.590032\pi\) | ||||
−0.279087 | + | 0.960266i | \(0.590032\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8444 | −0.849649 | −0.424824 | − | 0.905276i | \(-0.639664\pi\) | ||||
−0.424824 | + | 0.905276i | \(0.639664\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.07434 | 0.313581 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.155642 | 0.00602650 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.3977 | 1.09792 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −51.2890 | −1.97999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.3350 | 1.47770 | 0.738852 | − | 0.673867i | \(-0.235368\pi\) | ||||
0.738852 | + | 0.673867i | \(0.235368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.7637 | 0.645236 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.3871 | −1.05257 | −0.526286 | − | 0.850308i | \(-0.676416\pi\) | ||||
−0.526286 | + | 0.850308i | \(0.676416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7294 | 0.832673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7233 | −0.601634 | −0.300817 | − | 0.953682i | \(-0.597259\pi\) | ||||
−0.300817 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.81839 | 0.184101 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.79513 | 0.106641 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.2205 | −0.732243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2850 | 0.695596 | 0.347798 | − | 0.937570i | \(-0.386930\pi\) | ||||
0.347798 | + | 0.937570i | \(0.386930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.2472 | −1.29907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.35413 | 0.202802 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.2558 | −1.56044 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.9195 | 1.35666 | 0.678330 | − | 0.734757i | \(-0.262704\pi\) | ||||
0.678330 | + | 0.734757i | \(0.262704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.8417 | 1.20093 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.90007 | 0.259872 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.7979 | −1.15664 | −0.578320 | − | 0.815810i | \(-0.696291\pi\) | ||||
−0.578320 | + | 0.815810i | \(0.696291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.45609 | 0.167116 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.19318 | 0.231936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 88.2172 | 3.29913 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.7476 | 0.476069 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.05369 | −0.0392959 | −0.0196480 | − | 0.999807i | \(-0.506255\pi\) | ||||
−0.0196480 | + | 0.999807i | \(0.506255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.09512 | 0.226680 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.472789 | −0.0175589 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.0566 | −1.85650 | −0.928248 | − | 0.371961i | \(-0.878685\pi\) | ||||
−0.928248 | + | 0.371961i | \(0.878685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7967 | 1.10358 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.95997 | 0.294410 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.4632 | −1.19905 | −0.599527 | − | 0.800354i | \(-0.704645\pi\) | ||||
−0.599527 | + | 0.800354i | \(0.704645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −77.4588 | −2.85323 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.1789 | −0.521581 | −0.260790 | − | 0.965395i | \(-0.583983\pi\) | ||||
−0.260790 | + | 0.965395i | \(0.583983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 67.0433 | 2.46290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4829 | 1.08162 | 0.540811 | − | 0.841144i | \(-0.318117\pi\) | ||||
0.540811 | + | 0.841144i | \(0.318117\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.3784 | −0.636695 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.88625 | 0.142191 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3614 | −1.29036 | −0.645178 | − | 0.764032i | \(-0.723217\pi\) | ||||
−0.645178 | + | 0.764032i | \(0.723217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.42918 | −0.124966 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.539265 | 0.0196258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9396 | −0.579333 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.04819 | 0.328428 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9947 | 0.833558 | 0.416779 | − | 0.909008i | \(-0.363159\pi\) | ||||
0.416779 | + | 0.909008i | \(0.363159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.23194 | 0.0445410 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.244275 | 0.00882027 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7874 | −1.03810 | −0.519050 | − | 0.854744i | \(-0.673714\pi\) | ||||
−0.519050 | + | 0.854744i | \(0.673714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.89261 | −0.212217 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.6826 | −0.743901 | −0.371951 | − | 0.928253i | \(-0.621311\pi\) | ||||
−0.371951 | + | 0.928253i | \(0.621311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.8128 | −0.675775 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.4567 | 1.59283 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.89006 | −0.282329 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.858933 | −0.0306957 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.2423 | −0.508330 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.1515 | 1.46689 | 0.733446 | − | 0.679748i | \(-0.237911\pi\) | ||||
0.733446 | + | 0.679748i | \(0.237911\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.6985 | 0.416477 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.3475 | −1.75238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.8454 | 0.561979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6780 | 1.51173 | 0.755865 | − | 0.654727i | \(-0.227216\pi\) | ||||
0.755865 | + | 0.654727i | \(0.227216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.41875 | 0.0501917 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.28210 | −0.151301 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −79.2878 | −2.79801 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.9502 | 0.807885 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.11666 | 0.144734 | 0.0723671 | − | 0.997378i | \(-0.476945\pi\) | ||||
0.0723671 | + | 0.997378i | \(0.476945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.1729 | 1.27020 | 0.635102 | − | 0.772428i | \(-0.280958\pi\) | ||||
0.635102 | + | 0.772428i | \(0.280958\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.5876 | −1.17797 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.3469 | 1.16809 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.0937 | 2.31233 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8245 | 1.28518 | 0.642591 | − | 0.766209i | \(-0.277859\pi\) | ||||
0.642591 | + | 0.766209i | \(0.277859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.0251 | −1.63919 | −0.819595 | − | 0.572943i | \(-0.805802\pi\) | ||||
−0.819595 | + | 0.572943i | \(0.805802\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.4853 | −0.956917 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.1850 | −1.88420 | −0.942098 | − | 0.335337i | \(-0.891150\pi\) | ||||
−0.942098 | + | 0.335337i | \(0.891150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.7420 | 0.859326 | 0.429663 | − | 0.902989i | \(-0.358632\pi\) | ||||
0.429663 | + | 0.902989i | \(0.358632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6885 | −0.509539 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.4366 | 2.22992 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.1779 | −1.18136 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.6449 | −1.12703 | −0.563514 | − | 0.826107i | \(-0.690551\pi\) | ||||
−0.563514 | + | 0.826107i | \(0.690551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9758 | −0.999165 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.80644 | −0.303310 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.0217 | 1.65200 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.1475 | 0.485541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.13469 | 0.141735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.7319 | 0.709847 | 0.354923 | − | 0.934895i | \(-0.384507\pi\) | ||||
0.354923 | + | 0.934895i | \(0.384507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.2291 | 0.349829 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.5163 | −0.495867 | −0.247934 | − | 0.968777i | \(-0.579752\pi\) | ||||
−0.247934 | + | 0.968777i | \(0.579752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.61394 | 0.157426 | 0.0787128 | − | 0.996897i | \(-0.474919\pi\) | ||||
0.0787128 | + | 0.996897i | \(0.474919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.7672 | 0.570761 | 0.285380 | − | 0.958414i | \(-0.407880\pi\) | ||||
0.285380 | + | 0.958414i | \(0.407880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.65704 | −0.158344 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.6794 | 0.872119 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54.0887 | −1.83483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.5266 | −2.52524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.48110 | 0.0501275 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.26696 | −0.211620 | −0.105810 | − | 0.994386i | \(-0.533744\pi\) | ||||
−0.105810 | + | 0.994386i | \(0.533744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.5411 | 1.19877 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.4770 | −1.36370 | −0.681852 | − | 0.731490i | \(-0.738825\pi\) | ||||
−0.681852 | + | 0.731490i | \(0.738825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.3919 | −0.551632 | −0.275816 | − | 0.961210i | \(-0.588948\pi\) | ||||
−0.275816 | + | 0.961210i | \(0.588948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.201381 | −0.00676934 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7063 | 0.493788 | 0.246894 | − | 0.969043i | \(-0.420590\pi\) | ||||
0.246894 | + | 0.969043i | \(0.420590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.9405 | −1.40506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7802 | 0.394210 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.5792 | 2.09179 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.70567 | 0.290674 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.963922 | 0.0321486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.25803 | 0.108541 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9346 | 0.363478 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7404 | 0.622263 | 0.311132 | − | 0.950367i | \(-0.399292\pi\) | ||||
0.311132 | + | 0.950367i | \(0.399292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.23988 | −0.140628 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.806797 | −0.0267304 | −0.0133652 | − | 0.999911i | \(-0.504254\pi\) | ||||
−0.0133652 | + | 0.999911i | \(0.504254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.1719 | −1.56116 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.6821 | 1.34491 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.8606 | 1.28189 | 0.640946 | − | 0.767586i | \(-0.278542\pi\) | ||||
0.640946 | + | 0.767586i | \(0.278542\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.9026 | −1.28189 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.59138 | −0.249873 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5598 | −0.412963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.99971 | 0.262745 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.72990 | −0.0567562 | −0.0283781 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283781 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.3678 | −0.928719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.9535 | −0.489032 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5789 | 0.541610 | 0.270805 | − | 0.962634i | \(-0.412710\pi\) | ||||
0.270805 | + | 0.962634i | \(0.412710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.2725 | −0.987904 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9020 | −1.07257 | −0.536287 | − | 0.844036i | \(-0.680174\pi\) | ||||
−0.536287 | + | 0.844036i | \(0.680174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.77277 | 0.187987 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.7189 | −0.998230 | −0.499115 | − | 0.866536i | \(-0.666341\pi\) | ||||
−0.499115 | + | 0.866536i | \(0.666341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.2864 | −2.47636 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.6844 | −1.28686 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.6042 | −1.25051 | −0.625256 | − | 0.780420i | \(-0.715006\pi\) | ||||
−0.625256 | + | 0.780420i | \(0.715006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.4515 | 0.629437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.40828 | 0.0455233 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.35550 | 0.237274 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.94764 | 0.191660 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3075 | 0.621530 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.3349 | 1.74729 | 0.873646 | − | 0.486563i | \(-0.161750\pi\) | ||||
0.873646 | + | 0.486563i | \(0.161750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3644 | −0.365076 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0981 | 0.388247 | 0.194123 | − | 0.980977i | \(-0.437814\pi\) | ||||
0.194123 | + | 0.980977i | \(0.437814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.4449 | −0.846914 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.4277 | 0.493574 | 0.246787 | − | 0.969070i | \(-0.420625\pi\) | ||||
0.246787 | + | 0.969070i | \(0.420625\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.9768 | 1.66119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.34025 | −0.0747186 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.00301 | 0.0638862 | 0.0319431 | − | 0.999490i | \(-0.489830\pi\) | ||||
0.0319431 | + | 0.999490i | \(0.489830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.9704 | 1.01866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.58237 | 0.272903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.4943 | −1.22281 | −0.611406 | − | 0.791317i | \(-0.709396\pi\) | ||||
−0.611406 | + | 0.791317i | \(0.709396\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.0968 | −1.08203 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −66.6075 | −2.11160 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0730 | 0.889081 | 0.444541 | − | 0.895759i | \(-0.353367\pi\) | ||||
0.444541 | + | 0.895759i | \(0.353367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.8178 | −0.721924 |
(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 | 9016.2.a.bk.1.5 | 11 | ||
7.2 | even | 3 | 1288.2.q.d.921.7 | yes | 22 | ||
7.4 | even | 3 | 1288.2.q.d.737.7 | ✓ | 22 | ||
7.6 | odd | 2 | 9016.2.a.br.1.7 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1288.2.q.d.737.7 | ✓ | 22 | 7.4 | even | 3 | ||
1288.2.q.d.921.7 | yes | 22 | 7.2 | even | 3 | ||
9016.2.a.bk.1.5 | 11 | 1.1 | even | 1 | trivial | ||
9016.2.a.br.1.7 | 11 | 7.6 | odd | 2 |