Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.44419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 1.44419 | 0.833803 | 0.416901 | − | 0.908952i | \(-0.363116\pi\) | ||||
0.416901 | + | 0.908952i | \(0.363116\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.20437 | −1.43304 | −0.716520 | − | 0.697567i | \(-0.754266\pi\) | ||||
−0.716520 | + | 0.697567i | \(0.754266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.914318 | −0.304773 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.62772 | −1.19487 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.31952 | −0.562565 | −0.281283 | − | 0.959625i | \(-0.590760\pi\) | ||||
−0.281283 | + | 0.959625i | \(0.590760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.29372 | 1.44388 | 0.721940 | − | 0.691956i | \(-0.243251\pi\) | ||||
0.721940 | + | 0.691956i | \(0.243251\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44419 | 0.315148 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.44251 | −0.717812 | −0.358906 | − | 0.933374i | \(-0.616850\pi\) | ||||
−0.358906 | + | 0.933374i | \(0.616850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.26801 | 1.05360 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65302 | −1.08792 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.75096 | 1.43932 | 0.719659 | − | 0.694328i | \(-0.244298\pi\) | ||||
0.719659 | + | 0.694328i | \(0.244298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.59336 | 1.36381 | 0.681904 | − | 0.731441i | \(-0.261152\pi\) | ||||
0.681904 | + | 0.731441i | \(0.261152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.44419 | −0.251401 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.20437 | −0.541638 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.91871 | 0.808632 | 0.404316 | − | 0.914619i | \(-0.367510\pi\) | ||||
0.404316 | + | 0.914619i | \(0.367510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.44419 | −0.231255 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.73003 | −1.05105 | −0.525527 | − | 0.850777i | \(-0.676132\pi\) | ||||
−0.525527 | + | 0.850777i | \(0.676132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.09518 | 1.38700 | 0.693501 | − | 0.720456i | \(-0.256067\pi\) | ||||
0.693501 | + | 0.720456i | \(0.256067\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.92982 | 0.436751 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.34640 | 0.196392 | 0.0981961 | − | 0.995167i | \(-0.468693\pi\) | ||||
0.0981961 | + | 0.995167i | \(0.468693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.34982 | −0.469068 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.22970 | −0.993076 | −0.496538 | − | 0.868015i | \(-0.665396\pi\) | ||||
−0.496538 | + | 0.868015i | \(0.665396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.20437 | 0.432078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.08933 | 1.20391 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.77419 | −0.621547 | −0.310773 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310773 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.83923 | −0.235490 | −0.117745 | − | 0.993044i | \(-0.537566\pi\) | ||||
−0.117745 | + | 0.993044i | \(0.537566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.914318 | −0.115193 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.20437 | 0.397454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8247 | 1.32245 | 0.661226 | − | 0.750187i | \(-0.270036\pi\) | ||||
0.661226 | + | 0.750187i | \(0.270036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.97163 | −0.598514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.88452 | −0.461008 | −0.230504 | − | 0.973071i | \(-0.574038\pi\) | ||||
−0.230504 | + | 0.973071i | \(0.574038\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1855 | −1.30916 | −0.654579 | − | 0.755993i | \(-0.727154\pi\) | ||||
−0.654579 | + | 0.755993i | \(0.727154\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.60800 | 0.878496 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.193203 | −0.0217370 | −0.0108685 | − | 0.999941i | \(-0.503460\pi\) | ||||
−0.0108685 | + | 0.999941i | \(0.503460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.42107 | −0.602341 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.916052 | −0.100550 | −0.0502749 | − | 0.998735i | \(-0.516010\pi\) | ||||
−0.0502749 | + | 0.998735i | \(0.516010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.43259 | 0.806178 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.1939 | 1.20011 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.66381 | −1.02436 | −0.512181 | − | 0.858878i | \(-0.671162\pi\) | ||||
−0.512181 | + | 0.858878i | \(0.671162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9663 | 1.13715 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.1674 | −2.06914 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9476 | −1.61924 | −0.809618 | − | 0.586957i | \(-0.800326\pi\) | ||||
−0.809618 | + | 0.586957i | \(0.800326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.914318 | 0.0918924 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.0368 | −1.89423 | −0.947117 | − | 0.320890i | \(-0.896018\pi\) | ||||
−0.947117 | + | 0.320890i | \(0.896018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.07416 | 0.795570 | 0.397785 | − | 0.917479i | \(-0.369779\pi\) | ||||
0.397785 | + | 0.917479i | \(0.369779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.62772 | −0.451619 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5277 | −1.11443 | −0.557214 | − | 0.830369i | \(-0.688130\pi\) | ||||
−0.557214 | + | 0.830369i | \(0.688130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6152 | −1.20831 | −0.604157 | − | 0.796865i | \(-0.706490\pi\) | ||||
−0.604157 | + | 0.796865i | \(0.706490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.10355 | 0.674239 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.36869 | 0.128756 | 0.0643778 | − | 0.997926i | \(-0.479494\pi\) | ||||
0.0643778 | + | 0.997926i | \(0.479494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0311 | 1.02865 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.914318 | 0.0845287 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.31952 | −0.212630 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.71944 | −0.876372 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.858794 | −0.0768129 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.79620 | −0.514330 | −0.257165 | − | 0.966368i | \(-0.582788\pi\) | ||||
−0.257165 | + | 0.966368i | \(0.582788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.1352 | 1.15649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.40661 | −0.472378 | −0.236189 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236189 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.29372 | 0.545735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.1144 | 1.55904 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.40955 | −0.291298 | −0.145649 | − | 0.989336i | \(-0.546527\pi\) | ||||
−0.145649 | + | 0.989336i | \(0.546527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4035 | 1.22169 | 0.610843 | − | 0.791752i | \(-0.290831\pi\) | ||||
0.610843 | + | 0.791752i | \(0.290831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.94445 | 0.163752 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.8370 | −2.06260 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.44419 | 0.119115 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.7281 | −1.69811 | −0.849057 | − | 0.528301i | \(-0.822829\pi\) | ||||
−0.849057 | + | 0.528301i | \(0.822829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.57387 | −0.290838 | −0.145419 | − | 0.989370i | \(-0.546453\pi\) | ||||
−0.145419 | + | 0.989370i | \(0.546453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.12077 | 0.171454 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.3320 | −1.95439 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.9355 | −1.99007 | −0.995035 | − | 0.0995229i | \(-0.968268\pi\) | ||||
−0.995035 | + | 0.0995229i | \(0.968268\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4411 | −0.828030 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.44251 | −0.271307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.63735 | −0.676529 | −0.338265 | − | 0.941051i | \(-0.609840\pi\) | ||||
−0.338265 | + | 0.941051i | \(0.609840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.62772 | 0.360268 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.69294 | 0.363150 | 0.181575 | − | 0.983377i | \(-0.441880\pi\) | ||||
0.181575 | + | 0.983377i | \(0.441880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.75447 | −0.440055 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.64279 | 0.429013 | 0.214507 | − | 0.976723i | \(-0.431186\pi\) | ||||
0.214507 | + | 0.976723i | \(0.431186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.26801 | 0.398224 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.89484 | −0.518248 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9075 | 1.18898 | 0.594491 | − | 0.804103i | \(-0.297354\pi\) | ||||
0.594491 | + | 0.804103i | \(0.297354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.03636 | −0.225691 | −0.112845 | − | 0.993613i | \(-0.535996\pi\) | ||||
−0.112845 | + | 0.993613i | \(0.535996\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.65620 | −0.196352 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.7614 | −1.15880 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.31952 | 0.169620 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.65302 | −0.411196 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.02901 | 0.146814 | 0.0734071 | − | 0.997302i | \(-0.476613\pi\) | ||||
0.0734071 | + | 0.997302i | \(0.476613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.6853 | −1.34500 | −0.672499 | − | 0.740098i | \(-0.734779\pi\) | ||||
−0.672499 | + | 0.740098i | \(0.734779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.62772 | 0.331398 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.29290 | −0.163362 | −0.0816811 | − | 0.996659i | \(-0.526029\pi\) | ||||
−0.0816811 | + | 0.996659i | \(0.526029\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8927 | −1.41015 | −0.705077 | − | 0.709131i | \(-0.749088\pi\) | ||||
−0.705077 | + | 0.709131i | \(0.749088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.6330 | 1.10266 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.75096 | 0.544011 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.5655 | 1.50620 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.14754 | 0.218769 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.29372 | −0.435346 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.4066 | −0.854106 | −0.427053 | − | 0.904227i | \(-0.640448\pi\) | ||||
−0.427053 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.60999 | −0.384390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.1443 | −1.98763 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.59336 | 0.515471 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.1539 | −1.09158 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.31952 | 0.156027 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.84264 | 0.257322 | 0.128661 | − | 0.991689i | \(-0.458932\pi\) | ||||
0.128661 | + | 0.991689i | \(0.458932\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.81663 | −0.321109 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.2631 | −0.946675 | −0.473337 | − | 0.880881i | \(-0.656951\pi\) | ||||
−0.473337 | + | 0.880881i | \(0.656951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2055 | 1.40130 | 0.700648 | − | 0.713507i | \(-0.252894\pi\) | ||||
0.700648 | + | 0.713507i | \(0.252894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.44419 | −0.0950207 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2038 | −0.996037 | −0.498019 | − | 0.867166i | \(-0.665939\pi\) | ||||
−0.498019 | + | 0.867166i | \(0.665939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.31436 | −0.281438 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.279021 | −0.0181244 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.1442 | 1.82050 | 0.910248 | − | 0.414063i | \(-0.135891\pi\) | ||||
0.910248 | + | 0.414063i | \(0.135891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.48559 | −0.224527 | −0.112263 | − | 0.993678i | \(-0.535810\pi\) | ||||
−0.112263 | + | 0.993678i | \(0.535810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.13000 | 0.585690 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.20437 | −0.204720 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.29372 | −0.400460 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.32295 | −0.0838387 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.01109 | 0.190058 | 0.0950291 | − | 0.995474i | \(-0.469706\pi\) | ||||
0.0950291 | + | 0.995474i | \(0.469706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.44251 | 0.216428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.7341 | 0.672193 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.4961 | 1.52803 | 0.764014 | − | 0.645200i | \(-0.223226\pi\) | ||||
0.764014 | + | 0.645200i | \(0.223226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.91871 | 0.305634 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.08685 | −0.438665 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.3192 | 1.12961 | 0.564804 | − | 0.825225i | \(-0.308952\pi\) | ||||
0.564804 | + | 0.825225i | \(0.308952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.1667 | 1.42312 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.9564 | −0.854115 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8621 | 0.845189 | 0.422594 | − | 0.906319i | \(-0.361119\pi\) | ||||
0.422594 | + | 0.906319i | \(0.361119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2214 | 1.28911 | 0.644555 | − | 0.764558i | \(-0.277042\pi\) | ||||
0.644555 | + | 0.764558i | \(0.277042\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.44419 | −0.0874063 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.26801 | −0.317673 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3438 | −0.621497 | −0.310749 | − | 0.950492i | \(-0.600580\pi\) | ||||
−0.310749 | + | 0.950492i | \(0.600580\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.94275 | −0.415652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.5867 | −1.82465 | −0.912324 | − | 0.409469i | \(-0.865714\pi\) | ||||
−0.912324 | + | 0.409469i | \(0.865714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.97881 | −0.355404 | −0.177702 | − | 0.984084i | \(-0.556866\pi\) | ||||
−0.177702 | + | 0.984084i | \(0.556866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.1256 | −1.72525 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.73003 | −0.397261 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.6198 | −0.683520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.0314 | −1.35012 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.92545 | −0.112486 | −0.0562430 | − | 0.998417i | \(-0.517912\pi\) | ||||
−0.0562430 | + | 0.998417i | \(0.517912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2983 | 0.890701 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65302 | 0.328021 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.44251 | 0.199085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.09518 | 0.524237 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.4927 | −1.57942 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.89359 | 0.337466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.64519 | −0.150969 | −0.0754845 | − | 0.997147i | \(-0.524050\pi\) | ||||
−0.0754845 | + | 0.997147i | \(0.524050\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6606 | 0.663349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4111 | 1.10070 | 0.550352 | − | 0.834932i | \(-0.314493\pi\) | ||||
0.550352 | + | 0.834932i | \(0.314493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.05781 | 0.172838 | 0.0864188 | − | 0.996259i | \(-0.472458\pi\) | ||||
0.0864188 | + | 0.996259i | \(0.472458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.92982 | 0.165076 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2197 | −0.742491 | −0.371245 | − | 0.928535i | \(-0.621069\pi\) | ||||
−0.371245 | + | 0.928535i | \(0.621069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.75096 | −0.433971 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.6482 | −0.929214 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5984 | −0.812276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.26801 | −0.292216 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.2187 | −1.00750 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.34640 | 0.0742293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.6991 | −1.90723 | −0.953617 | − | 0.301021i | \(-0.902673\pi\) | ||||
−0.953617 | + | 0.301021i | \(0.902673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.49727 | −0.246449 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.6865 | −1.89513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.19120 | 0.0648890 | 0.0324445 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324445 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.97665 | 0.107357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.59336 | −0.411204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.9310 | 0.857694 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.36302 | −0.0731705 | −0.0365852 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365852 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7802 | 1.59410 | 0.797050 | − | 0.603913i | \(-0.206393\pi\) | ||||
0.797050 | + | 0.603913i | \(0.206393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.65302 | 0.301736 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.1209 | −1.33705 | −0.668526 | − | 0.743689i | \(-0.733074\pi\) | ||||
−0.668526 | + | 0.743689i | \(0.733074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4475 | 0.660643 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.34982 | −0.177291 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6694 | 1.40756 | 0.703779 | − | 0.710419i | \(-0.251495\pi\) | ||||
0.703779 | + | 0.710419i | \(0.251495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.6110 | 1.08479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.44419 | 0.0758003 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.8424 | 1.87608 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.86807 | 0.410710 | 0.205355 | − | 0.978688i | \(-0.434165\pi\) | ||||
0.205355 | + | 0.978688i | \(0.434165\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.15339 | 0.320333 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.22970 | −0.375348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.9264 | 1.13530 | 0.567652 | − | 0.823269i | \(-0.307852\pi\) | ||||
0.567652 | + | 0.823269i | \(0.307852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.24026 | −0.0640468 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.75096 | −0.399195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4705 | −0.794667 | −0.397333 | − | 0.917674i | \(-0.630064\pi\) | ||||
−0.397333 | + | 0.917674i | \(0.630064\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.37081 | −0.428850 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.2393 | −0.983080 | −0.491540 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491540 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.20437 | 0.163310 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.31588 | −0.422720 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.09352 | 0.106145 | 0.0530727 | − | 0.998591i | \(-0.483098\pi\) | ||||
0.0530727 | + | 0.998591i | \(0.483098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.98494 | 0.403816 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.80817 | −0.393870 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.619093 | 0.0311500 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.42903 | −0.121910 | −0.0609549 | − | 0.998141i | \(-0.519415\pi\) | ||||
−0.0609549 | + | 0.998141i | \(0.519415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.08933 | 0.455036 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1875 | 1.85706 | 0.928528 | − | 0.371262i | \(-0.121075\pi\) | ||||
0.928528 | + | 0.371262i | \(0.121075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.59336 | −0.378252 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.3711 | 0.863178 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.91871 | −0.243812 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9890 | −0.741159 | −0.370579 | − | 0.928801i | \(-0.620841\pi\) | ||||
−0.370579 | + | 0.928801i | \(0.620841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.92404 | −0.242885 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.77419 | −0.234923 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.93537 | 0.144092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8013 | 1.01865 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0522 | 0.539933 | 0.269967 | − | 0.962870i | \(-0.412987\pi\) | ||||
0.269967 | + | 0.962870i | \(0.412987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3196 | −0.795368 | −0.397684 | − | 0.917522i | \(-0.630186\pi\) | ||||
−0.397684 | + | 0.917522i | \(0.630186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.23104 | −0.0598550 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.2192 | −0.592719 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.83923 | −0.0890067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.44419 | 0.0697261 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.8849 | 0.861485 | 0.430742 | − | 0.902475i | \(-0.358252\pi\) | ||||
0.430742 | + | 0.902475i | \(0.358252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6237 | −0.846939 | −0.423469 | − | 0.905910i | \(-0.639188\pi\) | ||||
−0.423469 | + | 0.905910i | \(0.639188\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −35.8693 | −1.71980 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.6662 | −1.03643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.0473 | −1.48181 | −0.740903 | − | 0.671612i | \(-0.765602\pi\) | ||||
−0.740903 | + | 0.671612i | \(0.765602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.914318 | −0.0435390 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.1022 | −0.907575 | −0.453787 | − | 0.891110i | \(-0.649927\pi\) | ||||
−0.453787 | + | 0.891110i | \(0.649927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.9664 | 1.46795 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.9353 | −1.41589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0218 | −0.472960 | −0.236480 | − | 0.971636i | \(-0.575994\pi\) | ||||
−0.236480 | + | 0.971636i | \(0.575994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.73003 | 0.316905 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.16135 | −0.242501 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.20437 | 0.150223 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.7473 | −1.39152 | −0.695760 | − | 0.718274i | \(-0.744932\pi\) | ||||
−0.695760 | + | 0.718274i | \(0.744932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.1123 | 0.612028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.5306 | −1.60825 | −0.804125 | − | 0.594460i | \(-0.797366\pi\) | ||||
−0.804125 | + | 0.594460i | \(0.797366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2120 | 0.939332 | 0.469666 | − | 0.882844i | \(-0.344374\pi\) | ||||
0.469666 | + | 0.882844i | \(0.344374\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −35.1400 | −1.62958 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.6012 | −0.999585 | −0.499792 | − | 0.866145i | \(-0.666590\pi\) | ||||
−0.499792 | + | 0.866145i | \(0.666590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8247 | 0.499840 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.0116 | −1.65933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.09518 | −0.418197 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.1554 | 1.52127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.61025 | 0.302663 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.51296 | −0.160511 | −0.0802556 | − | 0.996774i | \(-0.525574\pi\) | ||||
−0.0802556 | + | 0.996774i | \(0.525574\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91871 | −0.224274 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.97163 | −0.226217 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 51.1022 | 2.32043 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5414 | 0.568307 | 0.284154 | − | 0.958779i | \(-0.408287\pi\) | ||||
0.284154 | + | 0.958779i | \(0.408287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.4740 | −0.564092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.99406 | 0.180250 | 0.0901248 | − | 0.995930i | \(-0.471273\pi\) | ||||
0.0901248 | + | 0.995930i | \(0.471273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.9785 | −0.809710 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.92982 | −0.131685 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.88452 | −0.174245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.4341 | −1.49672 | −0.748358 | − | 0.663295i | \(-0.769157\pi\) | ||||
−0.748358 | + | 0.663295i | \(0.769157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.77749 | 0.302796 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2391 | 1.34830 | 0.674148 | − | 0.738596i | \(-0.264511\pi\) | ||||
0.674148 | + | 0.738596i | \(0.264511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 61.0010 | 2.71451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.44419 | 0.0641387 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.11821 | −0.359833 | −0.179917 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179917 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1855 | −0.494816 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.5785 | −1.57083 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.8726 | −1.14008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.34640 | −0.0592145 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.14925 | 0.357713 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.43863 | −0.0630277 | −0.0315139 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315139 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.7573 | −1.30119 | −0.650597 | − | 0.759423i | \(-0.725481\pi\) | ||||
−0.650597 | + | 0.759423i | \(0.725481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.60800 | 0.332040 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.6129 | −0.767231 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1492 | −0.484746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.36513 | 0.189431 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.73003 | 0.291510 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.9392 | 1.59702 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.9734 | 0.991376 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4480 | 0.879128 | 0.439564 | − | 0.898211i | \(-0.355133\pi\) | ||||
0.439564 | + | 0.898211i | \(0.355133\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.38508 | −0.188182 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.4237 | 1.73156 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.2759 | 1.42278 | 0.711388 | − | 0.702799i | \(-0.248067\pi\) | ||||
0.711388 | + | 0.702799i | \(0.248067\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.68164 | 0.0717708 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.7824 | 2.07820 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.193203 | −0.00821581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.7624 | −0.966211 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.87173 | 0.164050 | 0.0820252 | − | 0.996630i | \(-0.473861\pi\) | ||||
0.0820252 | + | 0.996630i | \(0.473861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.09518 | −0.384685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.34982 | 0.141429 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.8940 | −0.627708 | −0.313854 | − | 0.949471i | \(-0.601620\pi\) | ||||
−0.313854 | + | 0.949471i | \(0.601620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.38580 | −0.184512 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.42107 | −0.227663 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.9316 | −1.25480 | −0.627399 | − | 0.778698i | \(-0.715880\pi\) | ||||
−0.627399 | + | 0.778698i | \(0.715880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1058 | −0.464762 | −0.232381 | − | 0.972625i | \(-0.574652\pi\) | ||||
−0.232381 | + | 0.972625i | \(0.574652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.93028 | 0.122414 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.1351 | −0.756288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5890 | −1.39833 | −0.699165 | − | 0.714961i | \(-0.746445\pi\) | ||||
−0.699165 | + | 0.714961i | \(0.746445\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.9851 | −1.12146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.916052 | −0.0380042 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.22970 | 0.299424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.92982 | −0.121133 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.92290 | 0.327013 | 0.163507 | − | 0.986542i | \(-0.447719\pi\) | ||||
0.163507 | + | 0.986542i | \(0.447719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.7905 | 1.96917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.31138 | −0.136212 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.3912 | 0.755235 | 0.377618 | − | 0.925962i | \(-0.376743\pi\) | ||||
0.377618 | + | 0.925962i | \(0.376743\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.43259 | 0.304707 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.7288 | −1.17579 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5765 | 1.20846 | 0.604232 | − | 0.796808i | \(-0.293480\pi\) | ||||
0.604232 | + | 0.796808i | \(0.293480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3041 | 0.501895 | 0.250948 | − | 0.968001i | \(-0.419258\pi\) | ||||
0.250948 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.89725 | −0.403047 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.20437 | −0.130276 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.0101 | −1.25866 | −0.629331 | − | 0.777137i | \(-0.716671\pi\) | ||||
−0.629331 | + | 0.777137i | \(0.716671\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.1939 | 0.453598 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34640 | −0.0544694 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.2716 | −1.78811 | −0.894056 | − | 0.447955i | \(-0.852152\pi\) | ||||
−0.894056 | + | 0.447955i | \(0.852152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.1447 | 1.25588 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.0672 | 1.65330 | 0.826651 | − | 0.562715i | \(-0.190243\pi\) | ||||
0.826651 | + | 0.562715i | \(0.190243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9283 | −1.04214 | −0.521072 | − | 0.853513i | \(-0.674468\pi\) | ||||
−0.521072 | + | 0.853513i | \(0.674468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.4605 | 0.780924 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.66381 | −0.387172 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5881 | −0.943525 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.08933 | −0.362993 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.4090 | −0.454908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.3034 | 1.40541 | 0.702704 | − | 0.711483i | \(-0.251976\pi\) | ||||
0.702704 | + | 0.711483i | \(0.251976\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.9175 | −0.712156 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.5732 | 0.737055 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.55169 | 0.140503 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.0440 | 1.73963 | 0.869816 | − | 0.493376i | \(-0.164237\pi\) | ||||
0.869816 | + | 0.493376i | \(0.164237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.3413 | −0.683875 | −0.341937 | − | 0.939723i | \(-0.611083\pi\) | ||||
−0.341937 | + | 0.939723i | \(0.611083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.0899 | −1.65729 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.57704 | −0.337198 | −0.168599 | − | 0.985685i | \(-0.553924\pi\) | ||||
−0.168599 | + | 0.985685i | \(0.553924\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.77419 | 0.187403 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9663 | 0.429801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.46090 | 0.174569 | 0.0872843 | − | 0.996183i | \(-0.472181\pi\) | ||||
0.0872843 | + | 0.996183i | \(0.472181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3248 | 0.676936 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2271 | 0.398996 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.4968 | −0.486805 | −0.243402 | − | 0.969925i | \(-0.578264\pi\) | ||||
−0.243402 | + | 0.969925i | \(0.578264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.91620 | −0.307905 | −0.153952 | − | 0.988078i | \(-0.549200\pi\) | ||||
−0.153952 | + | 0.988078i | \(0.549200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.34982 | 0.130096 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.1674 | −0.782060 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.6827 | −1.03316 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.54949 | 0.214556 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.83923 | 0.0710028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.8822 | 1.92282 | 0.961408 | − | 0.275126i | \(-0.0887195\pi\) | ||||
0.961408 | + | 0.275126i | \(0.0887195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −29.7801 | −1.14624 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7608 | 0.528870 | 0.264435 | − | 0.964404i | \(-0.414815\pi\) | ||||
0.264435 | + | 0.964404i | \(0.414815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.9476 | −0.612014 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.5986 | −0.789340 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.42960 | −0.360814 | −0.180407 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180407 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.9255 | 0.417441 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.6247 | 1.16841 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.22970 | 0.275430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.3993 | 1.04232 | 0.521159 | − | 0.853460i | \(-0.325500\pi\) | ||||
0.521159 | + | 0.853460i | \(0.325500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.914318 | 0.0347321 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.1541 | −1.75072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6104 | 0.591286 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.9572 | −0.830499 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4288 | −0.771587 | −0.385793 | − | 0.922585i | \(-0.626072\pi\) | ||||
−0.385793 | + | 0.922585i | \(0.626072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.9570 | 1.16757 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.23075 | −0.234664 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.0368 | −0.715953 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7380 | 1.34217 | 0.671085 | − | 0.741380i | \(-0.265828\pi\) | ||||
0.671085 | + | 0.741380i | \(0.265828\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.176649 | 0.00662484 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.1402 | −0.978958 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.20437 | −0.119837 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.6455 | 1.51793 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.2923 | 1.35347 | 0.676737 | − | 0.736225i | \(-0.263393\pi\) | ||||
0.676737 | + | 0.736225i | \(0.263393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.07416 | 0.300697 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.03385 | −0.187211 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.8321 | 1.51647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4117 | −0.460326 | −0.230163 | − | 0.973152i | \(-0.573926\pi\) | ||||
−0.230163 | + | 0.973152i | \(0.573926\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4486 | 1.09069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.0964 | −0.780279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −53.4904 | −1.97571 | −0.987856 | − | 0.155372i | \(-0.950342\pi\) | ||||
−0.987856 | + | 0.155372i | \(0.950342\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.62772 | −0.170696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8247 | −0.398734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.7385 | −0.689306 | −0.344653 | − | 0.938730i | \(-0.612003\pi\) | ||||
−0.344653 | + | 0.938730i | \(0.612003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.08933 | −0.333905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1809 | −0.446875 | −0.223438 | − | 0.974718i | \(-0.571728\pi\) | ||||
−0.223438 | + | 0.974718i | \(0.571728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 66.4207 | 2.43346 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.837563 | 0.0306448 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.5277 | −0.421215 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.39702 | −0.0509781 | −0.0254891 | − | 0.999675i | \(-0.508114\pi\) | ||||
−0.0254891 | + | 0.999675i | \(0.508114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.34858 | 0.158471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4520 | 0.416782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5775 | 1.03867 | 0.519333 | − | 0.854572i | \(-0.326180\pi\) | ||||
0.519333 | + | 0.854572i | \(0.326180\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.97163 | 0.180459 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.46884 | −0.270745 | −0.135373 | − | 0.990795i | \(-0.543223\pi\) | ||||
−0.135373 | + | 0.990795i | \(0.543223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6152 | −0.456700 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.79575 | −0.245701 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.77419 | 0.172386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.26487 | −0.225917 | −0.112958 | − | 0.993600i | \(-0.536033\pi\) | ||||
−0.112958 | + | 0.993600i | \(0.536033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.3771 | 1.27407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.328063 | 0.0117996 | 0.00589980 | − | 0.999983i | \(-0.498122\pi\) | ||||
0.00589980 | + | 0.999983i | \(0.498122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.0019 | 1.43691 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.10355 | 0.254839 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.3570 | −1.51760 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.88452 | 0.138999 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.8163 | −1.56587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 79.9027 | 2.85185 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.7572 | −1.41719 | −0.708596 | − | 0.705614i | \(-0.750671\pi\) | ||||
−0.708596 | + | 0.705614i | \(0.750671\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.4563 | 0.941871 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.36869 | 0.0486650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.83923 | 0.0653131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.4571 | 1.18660 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.10621 | −0.145450 | −0.0727248 | − | 0.997352i | \(-0.523169\pi\) | ||||
−0.0727248 | + | 0.997352i | \(0.523169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.12299 | −0.110483 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.83579 | 0.312197 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.1855 | 0.394726 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0311 | 0.388794 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0195 | 0.704721 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.6278 | 1.28776 | 0.643882 | − | 0.765125i | \(-0.277323\pi\) | ||||
0.643882 | + | 0.765125i | \(0.277323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.01553 | −0.0356602 | −0.0178301 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178301 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.6478 | 1.07486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.6773 | 0.969493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.2425 | 2.00266 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.914318 | 0.0319489 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.9550 | −0.975636 | −0.487818 | − | 0.872945i | \(-0.662207\pi\) | ||||
−0.487818 | + | 0.872945i | \(0.662207\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8816 | 0.553597 | 0.276798 | − | 0.960928i | \(-0.410727\pi\) | ||||
0.276798 | + | 0.960928i | \(0.410727\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.60800 | −0.264876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.4062 | 0.813915 | 0.406957 | − | 0.913447i | \(-0.366590\pi\) | ||||
0.406957 | + | 0.913447i | \(0.366590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.62109 | −0.0910341 | −0.0455171 | − | 0.998964i | \(-0.514494\pi\) | ||||
−0.0455171 | + | 0.998964i | \(0.514494\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9384 | −0.518206 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.31952 | −0.0803664 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0379 | −0.520409 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.9254 | −1.48372 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.9194 | −1.20555 | −0.602776 | − | 0.797910i | \(-0.705939\pi\) | ||||
−0.602776 | + | 0.797910i | \(0.705939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.0775 | 1.07164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.1729 | −1.52140 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.20437 | −0.110234 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.63454 | −0.296336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.9327 | −0.580445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.9813 | −0.649907 | −0.324954 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324954 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.4395 | 0.630616 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.9430 | −1.09115 | −0.545577 | − | 0.838061i | \(-0.683689\pi\) | ||||
−0.545577 | + | 0.838061i | \(0.683689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8276 | −1.42714 | −0.713570 | − | 0.700584i | \(-0.752923\pi\) | ||||
−0.713570 | + | 0.700584i | \(0.752923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.71944 | −0.331237 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.1376 | −1.53650 | −0.768250 | − | 0.640149i | \(-0.778872\pi\) | ||||
−0.768250 | + | 0.640149i | \(0.778872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0816 | −0.614793 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7813 | −0.569921 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.193203 | 0.00655395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8247 | −0.366782 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.5812 | 0.493499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.858794 | −0.0290325 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.8694 | 1.95411 | 0.977055 | − | 0.212985i | \(-0.0683186\pi\) | ||||
0.977055 | + | 0.212985i | \(0.0683186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.78071 | −0.0937912 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.5819 | 1.40093 | 0.700465 | − | 0.713687i | \(-0.252976\pi\) | ||||
0.700465 | + | 0.713687i | \(0.252976\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5021 | 0.723604 | 0.361802 | − | 0.932255i | \(-0.382162\pi\) | ||||
0.361802 | + | 0.932255i | \(0.382162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.0936 | 0.742669 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.9618 | −0.401638 | −0.200819 | − | 0.979628i | \(-0.564360\pi\) | ||||
−0.200819 | + | 0.979628i | \(0.564360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.79620 | −0.194398 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.42107 | 0.181613 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.47385 | 0.283567 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.9735 | −1.70386 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.97163 | 0.165998 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.8559 | 1.96295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7694 | 0.558670 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.1352 | 0.437111 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.72962 | 0.323424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1790 | 0.470805 | 0.235402 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.4057 | 0.577311 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5401 | 0.415472 | 0.207736 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207736 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.916052 | 0.0303169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.51145 | 0.281380 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.40661 | −0.178542 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.3897 | 1.46428 | 0.732141 | − | 0.681153i | \(-0.238521\pi\) | ||||
0.732141 | + | 0.681153i | \(0.238521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.82015 | −0.125878 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.88452 | 0.127861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9118 | 0.851975 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.38235 | −0.242468 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.8764 | −0.455269 | −0.227634 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227634 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.29372 | 0.206268 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.0334 | 0.917771 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.43259 | −0.243072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7319 | 1.69001 | 0.845003 | − | 0.534761i | \(-0.179598\pi\) | ||||
0.845003 | + | 0.534761i | \(0.179598\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.41605 | 0.144112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.8613 | 1.20164 | 0.600821 | − | 0.799383i | \(-0.294840\pi\) | ||||
0.600821 | + | 0.799383i | \(0.294840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1682 | 0.754459 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.1144 | 0.589260 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.5413 | 0.570014 | 0.285007 | − | 0.958525i | \(-0.408004\pi\) | ||||
0.285007 | + | 0.958525i | \(0.408004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1855 | 0.363095 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.0917 | −0.619091 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5672 | −0.698630 | −0.349315 | − | 0.937005i | \(-0.613586\pi\) | ||||
−0.349315 | + | 0.937005i | \(0.613586\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.50172 | −0.210391 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1939 | −0.361846 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.40955 | −0.110100 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.6592 | 0.859973 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5400 | 0.339648 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 59.8747 | 1.92743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.8799 | −0.960874 | −0.480437 | − | 0.877029i | \(-0.659522\pi\) | ||||
−0.480437 | + | 0.877029i | \(0.659522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.0828 | −0.677278 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.3515 | −0.524744 | −0.262372 | − | 0.964967i | \(-0.584505\pi\) | ||||
−0.262372 | + | 0.964967i | \(0.584505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4035 | 0.461754 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.60800 | −0.243651 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9649 | −1.08663 | −0.543317 | − | 0.839527i | \(-0.682832\pi\) | ||||
−0.543317 | + | 0.839527i | \(0.682832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.66381 | 0.308857 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5343 | 0.368261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.2905 | −1.41265 | −0.706324 | − | 0.707889i | \(-0.749648\pi\) | ||||
−0.706324 | + | 0.707889i | \(0.749648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.34730 | 0.234104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.94445 | 0.0618926 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.3102 | −0.995606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.59295 | 0.114134 | 0.0570669 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570669 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.1121 | −1.59026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.7435 | 2.02081 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.16274 | 0.163506 | 0.0817528 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817528 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.8056 | −0.879729 |
(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 | 8008.2.a.y.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.10 | ✓ | 14 | 1.1 | even | 1 | trivial |