Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1183) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.136454 | −0.0964874 | −0.0482437 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482437 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(3\) | −2.96681 | −1.71289 | −0.856445 | − | 0.516238i | \(-0.827332\pi\) | ||||
−0.856445 | + | 0.516238i | \(0.827332\pi\) | |||||||
\(4\) | −1.98138 | −0.990690 | ||||||||
\(5\) | −3.29030 | −1.47147 | −0.735733 | − | 0.677272i | \(-0.763162\pi\) | ||||
−0.735733 | + | 0.677272i | \(0.763162\pi\) | |||||||
\(6\) | 0.404833 | 0.165272 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.543274 | 0.192076 | ||||||||
\(9\) | 5.80198 | 1.93399 | ||||||||
\(10\) | 0.448974 | 0.141978 | ||||||||
\(11\) | −0.874918 | −0.263798 | −0.131899 | − | 0.991263i | \(-0.542107\pi\) | ||||
−0.131899 | + | 0.991263i | \(0.542107\pi\) | |||||||
\(12\) | 5.87839 | 1.69694 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.76170 | 2.52046 | ||||||||
\(16\) | 3.88863 | 0.972157 | ||||||||
\(17\) | −5.43856 | −1.31905 | −0.659523 | − | 0.751685i | \(-0.729242\pi\) | ||||
−0.659523 | + | 0.751685i | \(0.729242\pi\) | |||||||
\(18\) | −0.791703 | −0.186606 | ||||||||
\(19\) | −1.86947 | −0.428885 | −0.214442 | − | 0.976737i | \(-0.568793\pi\) | ||||
−0.214442 | + | 0.976737i | \(0.568793\pi\) | |||||||
\(20\) | 6.51933 | 1.45777 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.119386 | 0.0254531 | ||||||||
\(23\) | −6.86854 | −1.43219 | −0.716095 | − | 0.698003i | \(-0.754072\pi\) | ||||
−0.716095 | + | 0.698003i | \(0.754072\pi\) | |||||||
\(24\) | −1.61179 | −0.329006 | ||||||||
\(25\) | 5.82606 | 1.16521 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.31297 | −1.59983 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.15579 | −0.771711 | −0.385856 | − | 0.922559i | \(-0.626094\pi\) | ||||
−0.385856 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(30\) | −1.33202 | −0.243193 | ||||||||
\(31\) | −9.04712 | −1.62491 | −0.812455 | − | 0.583023i | \(-0.801870\pi\) | ||||
−0.812455 | + | 0.583023i | \(0.801870\pi\) | |||||||
\(32\) | −1.61717 | −0.285877 | ||||||||
\(33\) | 2.59572 | 0.451857 | ||||||||
\(34\) | 0.742113 | 0.127271 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.4959 | −1.91599 | ||||||||
\(37\) | −0.719941 | −0.118358 | −0.0591788 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591788 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(38\) | 0.255096 | 0.0413820 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.78753 | −0.282634 | ||||||||
\(41\) | 0.916940 | 0.143202 | 0.0716010 | − | 0.997433i | \(-0.477189\pi\) | ||||
0.0716010 | + | 0.997433i | \(0.477189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.76897 | 0.879760 | 0.439880 | − | 0.898057i | \(-0.355021\pi\) | ||||
0.439880 | + | 0.898057i | \(0.355021\pi\) | |||||||
\(44\) | 1.73354 | 0.261342 | ||||||||
\(45\) | −19.0903 | −2.84581 | ||||||||
\(46\) | 0.937238 | 0.138188 | ||||||||
\(47\) | 3.51803 | 0.513157 | 0.256579 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256579 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(48\) | −11.5368 | −1.66520 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.794988 | −0.112428 | ||||||||
\(51\) | 16.1352 | 2.25938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.82004 | 0.662083 | 0.331041 | − | 0.943616i | \(-0.392600\pi\) | ||||
0.331041 | + | 0.943616i | \(0.392600\pi\) | |||||||
\(54\) | 1.13434 | 0.154364 | ||||||||
\(55\) | 2.87874 | 0.388169 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.54636 | 0.734633 | ||||||||
\(58\) | 0.567074 | 0.0744604 | ||||||||
\(59\) | −4.84944 | −0.631343 | −0.315671 | − | 0.948869i | \(-0.602230\pi\) | ||||
−0.315671 | + | 0.948869i | \(0.602230\pi\) | |||||||
\(60\) | −19.3416 | −2.49700 | ||||||||
\(61\) | 0.968366 | 0.123987 | 0.0619933 | − | 0.998077i | \(-0.480254\pi\) | ||||
0.0619933 | + | 0.998077i | \(0.480254\pi\) | |||||||
\(62\) | 1.23451 | 0.156783 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.55659 | −0.944574 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.354196 | −0.0435985 | ||||||||
\(67\) | −6.84691 | −0.836483 | −0.418242 | − | 0.908336i | \(-0.637353\pi\) | ||||
−0.418242 | + | 0.908336i | \(0.637353\pi\) | |||||||
\(68\) | 10.7759 | 1.30677 | ||||||||
\(69\) | 20.3777 | 2.45318 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.91393 | 0.820532 | 0.410266 | − | 0.911966i | \(-0.365436\pi\) | ||||
0.410266 | + | 0.911966i | \(0.365436\pi\) | |||||||
\(72\) | 3.15207 | 0.371475 | ||||||||
\(73\) | 3.29618 | 0.385789 | 0.192894 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192894 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(74\) | 0.0982387 | 0.0114200 | ||||||||
\(75\) | −17.2848 | −1.99588 | ||||||||
\(76\) | 3.70412 | 0.424892 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.00190 | 1.01279 | 0.506397 | − | 0.862301i | \(-0.330977\pi\) | ||||
0.506397 | + | 0.862301i | \(0.330977\pi\) | |||||||
\(80\) | −12.7947 | −1.43050 | ||||||||
\(81\) | 7.25707 | 0.806341 | ||||||||
\(82\) | −0.125120 | −0.0138172 | ||||||||
\(83\) | −10.1044 | −1.10910 | −0.554549 | − | 0.832151i | \(-0.687109\pi\) | ||||
−0.554549 | + | 0.832151i | \(0.687109\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.8945 | 1.94093 | ||||||||
\(86\) | −0.787198 | −0.0848857 | ||||||||
\(87\) | 12.3295 | 1.32186 | ||||||||
\(88\) | −0.475320 | −0.0506693 | ||||||||
\(89\) | −9.67789 | −1.02585 | −0.512927 | − | 0.858432i | \(-0.671439\pi\) | ||||
−0.512927 | + | 0.858432i | \(0.671439\pi\) | |||||||
\(90\) | 2.60494 | 0.274585 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.6092 | 1.41886 | ||||||||
\(93\) | 26.8411 | 2.78329 | ||||||||
\(94\) | −0.480048 | −0.0495132 | ||||||||
\(95\) | 6.15110 | 0.631089 | ||||||||
\(96\) | 4.79783 | 0.489677 | ||||||||
\(97\) | 15.9432 | 1.61879 | 0.809395 | − | 0.587265i | \(-0.199795\pi\) | ||||
0.809395 | + | 0.587265i | \(0.199795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.07626 | −0.510183 | ||||||||
\(100\) | −11.5436 | −1.15436 | ||||||||
\(101\) | −2.37023 | −0.235846 | −0.117923 | − | 0.993023i | \(-0.537624\pi\) | ||||
−0.117923 | + | 0.993023i | \(0.537624\pi\) | |||||||
\(102\) | −2.20171 | −0.218002 | ||||||||
\(103\) | −2.17665 | −0.214472 | −0.107236 | − | 0.994234i | \(-0.534200\pi\) | ||||
−0.107236 | + | 0.994234i | \(0.534200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.657712 | −0.0638826 | ||||||||
\(107\) | 9.09356 | 0.879107 | 0.439554 | − | 0.898216i | \(-0.355137\pi\) | ||||
0.439554 | + | 0.898216i | \(0.355137\pi\) | |||||||
\(108\) | 16.4711 | 1.58494 | ||||||||
\(109\) | 12.0207 | 1.15137 | 0.575685 | − | 0.817672i | \(-0.304736\pi\) | ||||
0.575685 | + | 0.817672i | \(0.304736\pi\) | |||||||
\(110\) | −0.392815 | −0.0374534 | ||||||||
\(111\) | 2.13593 | 0.202734 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.638453 | −0.0600606 | −0.0300303 | − | 0.999549i | \(-0.509560\pi\) | ||||
−0.0300303 | + | 0.999549i | \(0.509560\pi\) | |||||||
\(114\) | −0.756821 | −0.0708828 | ||||||||
\(115\) | 22.5995 | 2.10742 | ||||||||
\(116\) | 8.23421 | 0.764527 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.661724 | 0.0609166 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.30328 | 0.484121 | ||||||||
\(121\) | −10.2345 | −0.930411 | ||||||||
\(122\) | −0.132137 | −0.0119631 | ||||||||
\(123\) | −2.72039 | −0.245289 | ||||||||
\(124\) | 17.9258 | 1.60978 | ||||||||
\(125\) | −2.71798 | −0.243103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9130 | −1.67826 | −0.839128 | − | 0.543933i | \(-0.816934\pi\) | ||||
−0.839128 | + | 0.543933i | \(0.816934\pi\) | |||||||
\(128\) | 4.26546 | 0.377017 | ||||||||
\(129\) | −17.1155 | −1.50693 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1156 | 1.05855 | 0.529274 | − | 0.848451i | \(-0.322464\pi\) | ||||
0.529274 | + | 0.848451i | \(0.322464\pi\) | |||||||
\(132\) | −5.14311 | −0.447650 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.934287 | 0.0807101 | ||||||||
\(135\) | 27.3521 | 2.35410 | ||||||||
\(136\) | −2.95463 | −0.253358 | ||||||||
\(137\) | 9.52030 | 0.813374 | 0.406687 | − | 0.913568i | \(-0.366684\pi\) | ||||
0.406687 | + | 0.913568i | \(0.366684\pi\) | |||||||
\(138\) | −2.78061 | −0.236701 | ||||||||
\(139\) | 19.2876 | 1.63596 | 0.817978 | − | 0.575250i | \(-0.195095\pi\) | ||||
0.817978 | + | 0.575250i | \(0.195095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4373 | −0.878982 | ||||||||
\(142\) | −0.943431 | −0.0791710 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 22.5618 | 1.88015 | ||||||||
\(145\) | 13.6738 | 1.13555 | ||||||||
\(146\) | −0.449776 | −0.0372237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.42648 | 0.117256 | ||||||||
\(149\) | 3.71001 | 0.303935 | 0.151968 | − | 0.988385i | \(-0.451439\pi\) | ||||
0.151968 | + | 0.988385i | \(0.451439\pi\) | |||||||
\(150\) | 2.35858 | 0.192577 | ||||||||
\(151\) | 16.5840 | 1.34959 | 0.674795 | − | 0.738005i | \(-0.264232\pi\) | ||||
0.674795 | + | 0.738005i | \(0.264232\pi\) | |||||||
\(152\) | −1.01563 | −0.0823787 | ||||||||
\(153\) | −31.5545 | −2.55103 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.7677 | 2.39100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.66389 | 0.452028 | 0.226014 | − | 0.974124i | \(-0.427430\pi\) | ||||
0.226014 | + | 0.974124i | \(0.427430\pi\) | |||||||
\(158\) | −1.22834 | −0.0977218 | ||||||||
\(159\) | −14.3001 | −1.13408 | ||||||||
\(160\) | 5.32096 | 0.420659 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.990255 | −0.0778017 | ||||||||
\(163\) | 12.2573 | 0.960068 | 0.480034 | − | 0.877250i | \(-0.340624\pi\) | ||||
0.480034 | + | 0.877250i | \(0.340624\pi\) | |||||||
\(164\) | −1.81681 | −0.141869 | ||||||||
\(165\) | −8.54069 | −0.664891 | ||||||||
\(166\) | 1.37878 | 0.107014 | ||||||||
\(167\) | −4.44819 | −0.344212 | −0.172106 | − | 0.985078i | \(-0.555057\pi\) | ||||
−0.172106 | + | 0.985078i | \(0.555057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.44177 | −0.187275 | ||||||||
\(171\) | −10.8466 | −0.829461 | ||||||||
\(172\) | −11.4305 | −0.871569 | ||||||||
\(173\) | 24.1401 | 1.83534 | 0.917670 | − | 0.397344i | \(-0.130068\pi\) | ||||
0.917670 | + | 0.397344i | \(0.130068\pi\) | |||||||
\(174\) | −1.68240 | −0.127543 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.40223 | −0.256453 | ||||||||
\(177\) | 14.3874 | 1.08142 | ||||||||
\(178\) | 1.32058 | 0.0989820 | ||||||||
\(179\) | −5.68045 | −0.424577 | −0.212288 | − | 0.977207i | \(-0.568092\pi\) | ||||
−0.212288 | + | 0.977207i | \(0.568092\pi\) | |||||||
\(180\) | 37.8251 | 2.81931 | ||||||||
\(181\) | −8.39175 | −0.623754 | −0.311877 | − | 0.950122i | \(-0.600958\pi\) | ||||
−0.311877 | + | 0.950122i | \(0.600958\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.87296 | −0.212375 | ||||||||
\(184\) | −3.73150 | −0.275090 | ||||||||
\(185\) | 2.36882 | 0.174159 | ||||||||
\(186\) | −3.66257 | −0.268553 | ||||||||
\(187\) | 4.75830 | 0.347961 | ||||||||
\(188\) | −6.97055 | −0.508380 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.839341 | −0.0608922 | ||||||||
\(191\) | 9.18700 | 0.664748 | 0.332374 | − | 0.943148i | \(-0.392150\pi\) | ||||
0.332374 | + | 0.943148i | \(0.392150\pi\) | |||||||
\(192\) | 22.4190 | 1.61795 | ||||||||
\(193\) | 5.14507 | 0.370350 | 0.185175 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185175 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(194\) | −2.17551 | −0.156193 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.26605 | 0.660178 | 0.330089 | − | 0.943950i | \(-0.392921\pi\) | ||||
0.330089 | + | 0.943950i | \(0.392921\pi\) | |||||||
\(198\) | 0.692675 | 0.0492263 | ||||||||
\(199\) | 15.0967 | 1.07018 | 0.535090 | − | 0.844795i | \(-0.320278\pi\) | ||||
0.535090 | + | 0.844795i | \(0.320278\pi\) | |||||||
\(200\) | 3.16515 | 0.223810 | ||||||||
\(201\) | 20.3135 | 1.43280 | ||||||||
\(202\) | 0.323426 | 0.0227562 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −31.9700 | −2.23835 | ||||||||
\(205\) | −3.01701 | −0.210717 | ||||||||
\(206\) | 0.297012 | 0.0206938 | ||||||||
\(207\) | −39.8511 | −2.76985 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.63563 | 0.113139 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.34760 | 0.574673 | 0.287336 | − | 0.957830i | \(-0.407230\pi\) | ||||
0.287336 | + | 0.957830i | \(0.407230\pi\) | |||||||
\(212\) | −9.55032 | −0.655919 | ||||||||
\(213\) | −20.5123 | −1.40548 | ||||||||
\(214\) | −1.24085 | −0.0848228 | ||||||||
\(215\) | −18.9816 | −1.29454 | ||||||||
\(216\) | −4.51622 | −0.307290 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.64026 | −0.111093 | ||||||||
\(219\) | −9.77915 | −0.660814 | ||||||||
\(220\) | −5.70388 | −0.384555 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.291456 | −0.0195612 | ||||||||
\(223\) | 19.1988 | 1.28565 | 0.642823 | − | 0.766015i | \(-0.277763\pi\) | ||||
0.642823 | + | 0.766015i | \(0.277763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33.8027 | 2.25351 | ||||||||
\(226\) | 0.0871193 | 0.00579509 | ||||||||
\(227\) | −20.4239 | −1.35558 | −0.677792 | − | 0.735254i | \(-0.737063\pi\) | ||||
−0.677792 | + | 0.735254i | \(0.737063\pi\) | |||||||
\(228\) | −10.9894 | −0.727794 | ||||||||
\(229\) | −18.2761 | −1.20772 | −0.603859 | − | 0.797091i | \(-0.706371\pi\) | ||||
−0.603859 | + | 0.797091i | \(0.706371\pi\) | |||||||
\(230\) | −3.08379 | −0.203339 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.25774 | −0.148228 | ||||||||
\(233\) | −7.95222 | −0.520967 | −0.260484 | − | 0.965478i | \(-0.583882\pi\) | ||||
−0.260484 | + | 0.965478i | \(0.583882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5754 | −0.755093 | ||||||||
\(236\) | 9.60858 | 0.625465 | ||||||||
\(237\) | −26.7070 | −1.73480 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.7653 | −1.86067 | −0.930335 | − | 0.366711i | \(-0.880484\pi\) | ||||
−0.930335 | + | 0.366711i | \(0.880484\pi\) | |||||||
\(240\) | 37.9596 | 2.45028 | ||||||||
\(241\) | 0.159407 | 0.0102683 | 0.00513414 | − | 0.999987i | \(-0.498366\pi\) | ||||
0.00513414 | + | 0.999987i | \(0.498366\pi\) | |||||||
\(242\) | 1.39654 | 0.0897729 | ||||||||
\(243\) | 3.40852 | 0.218657 | ||||||||
\(244\) | −1.91870 | −0.122832 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.371208 | 0.0236673 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.91507 | −0.312107 | ||||||||
\(249\) | 29.9778 | 1.89976 | ||||||||
\(250\) | 0.370878 | 0.0234564 | ||||||||
\(251\) | −10.3711 | −0.654621 | −0.327310 | − | 0.944917i | \(-0.606142\pi\) | ||||
−0.327310 | + | 0.944917i | \(0.606142\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00941 | 0.377808 | ||||||||
\(254\) | 2.58075 | 0.161931 | ||||||||
\(255\) | −53.0896 | −3.32460 | ||||||||
\(256\) | 14.5311 | 0.908196 | ||||||||
\(257\) | 22.5730 | 1.40807 | 0.704033 | − | 0.710167i | \(-0.251381\pi\) | ||||
0.704033 | + | 0.710167i | \(0.251381\pi\) | |||||||
\(258\) | 2.33547 | 0.145400 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.1118 | −1.49249 | ||||||||
\(262\) | −1.65322 | −0.102137 | ||||||||
\(263\) | −21.1607 | −1.30483 | −0.652414 | − | 0.757863i | \(-0.726243\pi\) | ||||
−0.652414 | + | 0.757863i | \(0.726243\pi\) | |||||||
\(264\) | 1.41019 | 0.0867910 | ||||||||
\(265\) | −15.8594 | −0.974232 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.7125 | 1.75718 | ||||||||
\(268\) | 13.5663 | 0.828696 | ||||||||
\(269\) | −21.0444 | −1.28310 | −0.641549 | − | 0.767082i | \(-0.721708\pi\) | ||||
−0.641549 | + | 0.767082i | \(0.721708\pi\) | |||||||
\(270\) | −3.73230 | −0.227141 | ||||||||
\(271\) | −28.0520 | −1.70404 | −0.852019 | − | 0.523510i | \(-0.824622\pi\) | ||||
−0.852019 | + | 0.523510i | \(0.824622\pi\) | |||||||
\(272\) | −21.1486 | −1.28232 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.29908 | −0.0784803 | ||||||||
\(275\) | −5.09732 | −0.307380 | ||||||||
\(276\) | −40.3759 | −2.43034 | ||||||||
\(277\) | 28.0308 | 1.68421 | 0.842104 | − | 0.539315i | \(-0.181317\pi\) | ||||
0.842104 | + | 0.539315i | \(0.181317\pi\) | |||||||
\(278\) | −2.63187 | −0.157849 | ||||||||
\(279\) | −52.4912 | −3.14257 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.73990 | −0.223104 | −0.111552 | − | 0.993759i | \(-0.535582\pi\) | ||||
−0.111552 | + | 0.993759i | \(0.535582\pi\) | |||||||
\(282\) | 1.42421 | 0.0848107 | ||||||||
\(283\) | 2.59894 | 0.154491 | 0.0772455 | − | 0.997012i | \(-0.475387\pi\) | ||||
0.0772455 | + | 0.997012i | \(0.475387\pi\) | |||||||
\(284\) | −13.6991 | −0.812893 | ||||||||
\(285\) | −18.2492 | −1.08099 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.38278 | −0.552885 | ||||||||
\(289\) | 12.5780 | 0.739881 | ||||||||
\(290\) | −1.86584 | −0.109566 | ||||||||
\(291\) | −47.3006 | −2.77281 | ||||||||
\(292\) | −6.53099 | −0.382197 | ||||||||
\(293\) | 21.1964 | 1.23831 | 0.619154 | − | 0.785270i | \(-0.287476\pi\) | ||||
0.619154 | + | 0.785270i | \(0.287476\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.9561 | 0.928999 | ||||||||
\(296\) | −0.391126 | −0.0227337 | ||||||||
\(297\) | 7.27316 | 0.422032 | ||||||||
\(298\) | −0.506244 | −0.0293259 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 34.2478 | 1.97730 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.26295 | −0.130218 | ||||||||
\(303\) | 7.03202 | 0.403979 | ||||||||
\(304\) | −7.26966 | −0.416944 | ||||||||
\(305\) | −3.18621 | −0.182442 | ||||||||
\(306\) | 4.30573 | 0.246142 | ||||||||
\(307\) | −5.82988 | −0.332729 | −0.166364 | − | 0.986064i | \(-0.553203\pi\) | ||||
−0.166364 | + | 0.986064i | \(0.553203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.45771 | 0.367366 | ||||||||
\(310\) | −4.06192 | −0.230701 | ||||||||
\(311\) | −0.938430 | −0.0532135 | −0.0266067 | − | 0.999646i | \(-0.508470\pi\) | ||||
−0.0266067 | + | 0.999646i | \(0.508470\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3375 | −0.923450 | −0.461725 | − | 0.887023i | \(-0.652769\pi\) | ||||
−0.461725 | + | 0.887023i | \(0.652769\pi\) | |||||||
\(314\) | −0.772860 | −0.0436150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.8362 | −1.00336 | ||||||||
\(317\) | −2.68669 | −0.150900 | −0.0754498 | − | 0.997150i | \(-0.524039\pi\) | ||||
−0.0754498 | + | 0.997150i | \(0.524039\pi\) | |||||||
\(318\) | 1.95131 | 0.109424 | ||||||||
\(319\) | 3.63598 | 0.203576 | ||||||||
\(320\) | 24.8634 | 1.38991 | ||||||||
\(321\) | −26.9789 | −1.50581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1672 | 0.565719 | ||||||||
\(324\) | −14.3790 | −0.798834 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.67256 | −0.0926344 | ||||||||
\(327\) | −35.6630 | −1.97217 | ||||||||
\(328\) | 0.498150 | 0.0275057 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.16541 | 0.0641536 | ||||||||
\(331\) | 17.1409 | 0.942151 | 0.471076 | − | 0.882093i | \(-0.343866\pi\) | ||||
0.471076 | + | 0.882093i | \(0.343866\pi\) | |||||||
\(332\) | 20.0206 | 1.09877 | ||||||||
\(333\) | −4.17709 | −0.228903 | ||||||||
\(334\) | 0.606973 | 0.0332121 | ||||||||
\(335\) | 22.5284 | 1.23086 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2932 | −0.560704 | −0.280352 | − | 0.959897i | \(-0.590451\pi\) | ||||
−0.280352 | + | 0.959897i | \(0.590451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.89417 | 0.102877 | ||||||||
\(340\) | −35.4558 | −1.92286 | ||||||||
\(341\) | 7.91549 | 0.428648 | ||||||||
\(342\) | 1.48006 | 0.0800325 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.13413 | 0.168981 | ||||||||
\(345\) | −67.0486 | −3.60978 | ||||||||
\(346\) | −3.29401 | −0.177087 | ||||||||
\(347\) | −16.0255 | −0.860295 | −0.430148 | − | 0.902759i | \(-0.641539\pi\) | ||||
−0.430148 | + | 0.902759i | \(0.641539\pi\) | |||||||
\(348\) | −24.4294 | −1.30955 | ||||||||
\(349\) | 7.61273 | 0.407500 | 0.203750 | − | 0.979023i | \(-0.434687\pi\) | ||||
0.203750 | + | 0.979023i | \(0.434687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.41489 | 0.0754138 | ||||||||
\(353\) | −1.15411 | −0.0614269 | −0.0307134 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307134 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(354\) | −1.96321 | −0.104343 | ||||||||
\(355\) | −22.7489 | −1.20738 | ||||||||
\(356\) | 19.1756 | 1.01630 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.775119 | 0.0409663 | ||||||||
\(359\) | 4.42310 | 0.233442 | 0.116721 | − | 0.993165i | \(-0.462762\pi\) | ||||
0.116721 | + | 0.993165i | \(0.462762\pi\) | |||||||
\(360\) | −10.3712 | −0.546613 | ||||||||
\(361\) | −15.5051 | −0.816058 | ||||||||
\(362\) | 1.14509 | 0.0601844 | ||||||||
\(363\) | 30.3639 | 1.59369 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8454 | −0.567675 | ||||||||
\(366\) | 0.392026 | 0.0204916 | ||||||||
\(367\) | 15.1442 | 0.790523 | 0.395261 | − | 0.918569i | \(-0.370654\pi\) | ||||
0.395261 | + | 0.918569i | \(0.370654\pi\) | |||||||
\(368\) | −26.7092 | −1.39231 | ||||||||
\(369\) | 5.32007 | 0.276952 | ||||||||
\(370\) | −0.323235 | −0.0168042 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −53.1825 | −2.75738 | ||||||||
\(373\) | 2.47652 | 0.128229 | 0.0641147 | − | 0.997943i | \(-0.479578\pi\) | ||||
0.0641147 | + | 0.997943i | \(0.479578\pi\) | |||||||
\(374\) | −0.649287 | −0.0335739 | ||||||||
\(375\) | 8.06374 | 0.416410 | ||||||||
\(376\) | 1.91126 | 0.0985655 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7790 | −1.47828 | −0.739140 | − | 0.673552i | \(-0.764768\pi\) | ||||
−0.739140 | + | 0.673552i | \(0.764768\pi\) | |||||||
\(380\) | −12.1877 | −0.625214 | ||||||||
\(381\) | 56.1113 | 2.87467 | ||||||||
\(382\) | −1.25360 | −0.0641398 | ||||||||
\(383\) | −24.1588 | −1.23446 | −0.617228 | − | 0.786785i | \(-0.711744\pi\) | ||||
−0.617228 | + | 0.786785i | \(0.711744\pi\) | |||||||
\(384\) | −12.6548 | −0.645789 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.702064 | −0.0357341 | ||||||||
\(387\) | 33.4715 | 1.70145 | ||||||||
\(388\) | −31.5896 | −1.60372 | ||||||||
\(389\) | 26.5443 | 1.34585 | 0.672924 | − | 0.739711i | \(-0.265038\pi\) | ||||
0.672924 | + | 0.739711i | \(0.265038\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.3550 | 1.88912 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.9449 | −1.81318 | ||||||||
\(394\) | −1.26439 | −0.0636989 | ||||||||
\(395\) | −29.6189 | −1.49029 | ||||||||
\(396\) | 10.0580 | 0.505434 | ||||||||
\(397\) | −3.61620 | −0.181492 | −0.0907458 | − | 0.995874i | \(-0.528925\pi\) | ||||
−0.0907458 | + | 0.995874i | \(0.528925\pi\) | |||||||
\(398\) | −2.06001 | −0.103259 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.6554 | 1.13277 | ||||||||
\(401\) | −26.5061 | −1.32365 | −0.661825 | − | 0.749659i | \(-0.730218\pi\) | ||||
−0.661825 | + | 0.749659i | \(0.730218\pi\) | |||||||
\(402\) | −2.77186 | −0.138248 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.69632 | 0.233651 | ||||||||
\(405\) | −23.8779 | −1.18650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.629889 | 0.0312225 | ||||||||
\(408\) | 8.76584 | 0.433974 | ||||||||
\(409\) | 23.6953 | 1.17166 | 0.585828 | − | 0.810435i | \(-0.300769\pi\) | ||||
0.585828 | + | 0.810435i | \(0.300769\pi\) | |||||||
\(410\) | 0.411682 | 0.0203315 | ||||||||
\(411\) | −28.2450 | −1.39322 | ||||||||
\(412\) | 4.31277 | 0.212475 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.43784 | 0.267255 | ||||||||
\(415\) | 33.2464 | 1.63200 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −57.2228 | −2.80221 | ||||||||
\(418\) | −0.223188 | −0.0109165 | ||||||||
\(419\) | 13.0737 | 0.638693 | 0.319347 | − | 0.947638i | \(-0.396537\pi\) | ||||
0.319347 | + | 0.947638i | \(0.396537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2855 | 0.939920 | 0.469960 | − | 0.882688i | \(-0.344268\pi\) | ||||
0.469960 | + | 0.882688i | \(0.344268\pi\) | |||||||
\(422\) | −1.13906 | −0.0554487 | ||||||||
\(423\) | 20.4116 | 0.992444 | ||||||||
\(424\) | 2.61860 | 0.127171 | ||||||||
\(425\) | −31.6854 | −1.53697 | ||||||||
\(426\) | 2.79899 | 0.135611 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.0178 | −0.870923 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.59012 | 0.124906 | ||||||||
\(431\) | 6.08723 | 0.293212 | 0.146606 | − | 0.989195i | \(-0.453165\pi\) | ||||
0.146606 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(432\) | −32.3260 | −1.55529 | ||||||||
\(433\) | 27.8249 | 1.33718 | 0.668589 | − | 0.743633i | \(-0.266899\pi\) | ||||
0.668589 | + | 0.743633i | \(0.266899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.5676 | −1.94507 | ||||||||
\(436\) | −23.8175 | −1.14065 | ||||||||
\(437\) | 12.8405 | 0.614244 | ||||||||
\(438\) | 1.33440 | 0.0637602 | ||||||||
\(439\) | 1.40848 | 0.0672230 | 0.0336115 | − | 0.999435i | \(-0.489299\pi\) | ||||
0.0336115 | + | 0.999435i | \(0.489299\pi\) | |||||||
\(440\) | 1.56395 | 0.0745582 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5545 | −1.07160 | −0.535799 | − | 0.844346i | \(-0.679989\pi\) | ||||
−0.535799 | + | 0.844346i | \(0.679989\pi\) | |||||||
\(444\) | −4.23209 | −0.200846 | ||||||||
\(445\) | 31.8431 | 1.50951 | ||||||||
\(446\) | −2.61975 | −0.124049 | ||||||||
\(447\) | −11.0069 | −0.520608 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.1488 | −1.61158 | −0.805791 | − | 0.592200i | \(-0.798260\pi\) | ||||
−0.805791 | + | 0.592200i | \(0.798260\pi\) | |||||||
\(450\) | −4.61251 | −0.217436 | ||||||||
\(451\) | −0.802247 | −0.0377763 | ||||||||
\(452\) | 1.26502 | 0.0595015 | ||||||||
\(453\) | −49.2017 | −2.31170 | ||||||||
\(454\) | 2.78692 | 0.130797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.01319 | 0.141106 | ||||||||
\(457\) | −22.4990 | −1.05246 | −0.526228 | − | 0.850343i | \(-0.676394\pi\) | ||||
−0.526228 | + | 0.850343i | \(0.676394\pi\) | |||||||
\(458\) | 2.49384 | 0.116530 | ||||||||
\(459\) | 45.2106 | 2.11025 | ||||||||
\(460\) | −44.7783 | −2.08780 | ||||||||
\(461\) | −12.9804 | −0.604558 | −0.302279 | − | 0.953219i | \(-0.597747\pi\) | ||||
−0.302279 | + | 0.953219i | \(0.597747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3212 | 1.40915 | 0.704574 | − | 0.709631i | \(-0.251138\pi\) | ||||
0.704574 | + | 0.709631i | \(0.251138\pi\) | |||||||
\(464\) | −16.1603 | −0.750225 | ||||||||
\(465\) | −88.3153 | −4.09552 | ||||||||
\(466\) | 1.08511 | 0.0502668 | ||||||||
\(467\) | 16.5353 | 0.765164 | 0.382582 | − | 0.923922i | \(-0.375035\pi\) | ||||
0.382582 | + | 0.923922i | \(0.375035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.57950 | 0.0728570 | ||||||||
\(471\) | −16.8037 | −0.774275 | ||||||||
\(472\) | −2.63457 | −0.121266 | ||||||||
\(473\) | −5.04738 | −0.232079 | ||||||||
\(474\) | 3.64427 | 0.167387 | ||||||||
\(475\) | −10.8916 | −0.499742 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.9658 | 1.28046 | ||||||||
\(478\) | 3.92513 | 0.179531 | ||||||||
\(479\) | −9.44551 | −0.431576 | −0.215788 | − | 0.976440i | \(-0.569232\pi\) | ||||
−0.215788 | + | 0.976440i | \(0.569232\pi\) | |||||||
\(480\) | −15.7863 | −0.720543 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.0217516 | −0.000990760 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.2785 | 0.921749 | ||||||||
\(485\) | −52.4580 | −2.38199 | ||||||||
\(486\) | −0.465106 | −0.0210976 | ||||||||
\(487\) | 2.82874 | 0.128182 | 0.0640912 | − | 0.997944i | \(-0.479585\pi\) | ||||
0.0640912 | + | 0.997944i | \(0.479585\pi\) | |||||||
\(488\) | 0.526088 | 0.0238149 | ||||||||
\(489\) | −36.3652 | −1.64449 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.2871 | 1.68274 | 0.841371 | − | 0.540457i | \(-0.181749\pi\) | ||||
0.841371 | + | 0.540457i | \(0.181749\pi\) | |||||||
\(492\) | 5.39013 | 0.243006 | ||||||||
\(493\) | 22.6015 | 1.01792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.7024 | 0.750717 | ||||||||
\(496\) | −35.1809 | −1.57967 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.09058 | −0.183303 | ||||||||
\(499\) | −18.2471 | −0.816851 | −0.408426 | − | 0.912792i | \(-0.633922\pi\) | ||||
−0.408426 | + | 0.912792i | \(0.633922\pi\) | |||||||
\(500\) | 5.38535 | 0.240840 | ||||||||
\(501\) | 13.1970 | 0.589597 | ||||||||
\(502\) | 1.41518 | 0.0631627 | ||||||||
\(503\) | 39.6222 | 1.76667 | 0.883334 | − | 0.468745i | \(-0.155294\pi\) | ||||
0.883334 | + | 0.468745i | \(0.155294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.79875 | 0.347040 | ||||||||
\(506\) | −0.820006 | −0.0364537 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.4738 | 1.66263 | ||||||||
\(509\) | −42.4787 | −1.88283 | −0.941417 | − | 0.337244i | \(-0.890505\pi\) | ||||
−0.941417 | + | 0.337244i | \(0.890505\pi\) | |||||||
\(510\) | 7.24428 | 0.320782 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.5137 | −0.464646 | ||||||||
\(513\) | 15.5408 | 0.686143 | ||||||||
\(514\) | −3.08017 | −0.135861 | ||||||||
\(515\) | 7.16182 | 0.315588 | ||||||||
\(516\) | 33.9122 | 1.49290 | ||||||||
\(517\) | −3.07799 | −0.135370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −71.6193 | −3.14374 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7345 | 0.908393 | 0.454197 | − | 0.890901i | \(-0.349926\pi\) | ||||
0.454197 | + | 0.890901i | \(0.349926\pi\) | |||||||
\(522\) | 3.29015 | 0.144006 | ||||||||
\(523\) | 12.4110 | 0.542694 | 0.271347 | − | 0.962482i | \(-0.412531\pi\) | ||||
0.271347 | + | 0.962482i | \(0.412531\pi\) | |||||||
\(524\) | −24.0057 | −1.04869 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.88746 | 0.125899 | ||||||||
\(527\) | 49.2033 | 2.14333 | ||||||||
\(528\) | 10.0938 | 0.439276 | ||||||||
\(529\) | 24.1768 | 1.05117 | ||||||||
\(530\) | 2.16407 | 0.0940011 | ||||||||
\(531\) | −28.1363 | −1.22101 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.91793 | −0.169545 | ||||||||
\(535\) | −29.9205 | −1.29358 | ||||||||
\(536\) | −3.71975 | −0.160669 | ||||||||
\(537\) | 16.8528 | 0.727253 | ||||||||
\(538\) | 2.87158 | 0.123803 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −54.1950 | −2.33218 | ||||||||
\(541\) | 23.1917 | 0.997087 | 0.498544 | − | 0.866865i | \(-0.333868\pi\) | ||||
0.498544 | + | 0.866865i | \(0.333868\pi\) | |||||||
\(542\) | 3.82780 | 0.164418 | ||||||||
\(543\) | 24.8968 | 1.06842 | ||||||||
\(544\) | 8.79506 | 0.377085 | ||||||||
\(545\) | −39.5515 | −1.69420 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3740 | 0.999401 | 0.499700 | − | 0.866198i | \(-0.333443\pi\) | ||||
0.499700 | + | 0.866198i | \(0.333443\pi\) | |||||||
\(548\) | −18.8633 | −0.805802 | ||||||||
\(549\) | 5.61845 | 0.239789 | ||||||||
\(550\) | 0.695549 | 0.0296583 | ||||||||
\(551\) | 7.76911 | 0.330975 | ||||||||
\(552\) | 11.0707 | 0.471199 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.82491 | −0.162505 | ||||||||
\(555\) | −7.02785 | −0.298316 | ||||||||
\(556\) | −38.2161 | −1.62073 | ||||||||
\(557\) | 24.1355 | 1.02265 | 0.511327 | − | 0.859386i | \(-0.329154\pi\) | ||||
0.511327 | + | 0.859386i | \(0.329154\pi\) | |||||||
\(558\) | 7.16263 | 0.303218 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1170 | −0.596019 | ||||||||
\(562\) | 0.510323 | 0.0215267 | ||||||||
\(563\) | 14.5788 | 0.614421 | 0.307211 | − | 0.951642i | \(-0.400604\pi\) | ||||
0.307211 | + | 0.951642i | \(0.400604\pi\) | |||||||
\(564\) | 20.6803 | 0.870799 | ||||||||
\(565\) | 2.10070 | 0.0883771 | ||||||||
\(566\) | −0.354635 | −0.0149064 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.75616 | 0.157605 | ||||||||
\(569\) | 44.7162 | 1.87460 | 0.937300 | − | 0.348523i | \(-0.113317\pi\) | ||||
0.937300 | + | 0.348523i | \(0.113317\pi\) | |||||||
\(570\) | 2.49017 | 0.104302 | ||||||||
\(571\) | 5.72926 | 0.239762 | 0.119881 | − | 0.992788i | \(-0.461749\pi\) | ||||
0.119881 | + | 0.992788i | \(0.461749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.2561 | −1.13864 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.0165 | −1.66880 | ||||||||
\(576\) | −43.8432 | −1.82680 | ||||||||
\(577\) | 22.5788 | 0.939969 | 0.469985 | − | 0.882675i | \(-0.344259\pi\) | ||||
0.469985 | + | 0.882675i | \(0.344259\pi\) | |||||||
\(578\) | −1.71631 | −0.0713892 | ||||||||
\(579\) | −15.2645 | −0.634370 | ||||||||
\(580\) | −27.0930 | −1.12498 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.45435 | 0.267541 | ||||||||
\(583\) | −4.21714 | −0.174656 | ||||||||
\(584\) | 1.79073 | 0.0741009 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.89233 | −0.119481 | ||||||||
\(587\) | −34.4761 | −1.42298 | −0.711491 | − | 0.702695i | \(-0.751980\pi\) | ||||
−0.711491 | + | 0.702695i | \(0.751980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9133 | 0.696900 | ||||||||
\(590\) | −2.17727 | −0.0896367 | ||||||||
\(591\) | −27.4906 | −1.13081 | ||||||||
\(592\) | −2.79958 | −0.115062 | ||||||||
\(593\) | 23.1502 | 0.950666 | 0.475333 | − | 0.879806i | \(-0.342328\pi\) | ||||
0.475333 | + | 0.879806i | \(0.342328\pi\) | |||||||
\(594\) | −0.992450 | −0.0407207 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.35093 | −0.301106 | ||||||||
\(597\) | −44.7892 | −1.83310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.5535 | −0.676357 | −0.338179 | − | 0.941082i | \(-0.609811\pi\) | ||||
−0.338179 | + | 0.941082i | \(0.609811\pi\) | |||||||
\(600\) | −9.39041 | −0.383362 | ||||||||
\(601\) | −7.89385 | −0.321997 | −0.160999 | − | 0.986955i | \(-0.551471\pi\) | ||||
−0.160999 | + | 0.986955i | \(0.551471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −39.7257 | −1.61775 | ||||||||
\(604\) | −32.8593 | −1.33703 | ||||||||
\(605\) | 33.6746 | 1.36907 | ||||||||
\(606\) | −0.959545 | −0.0389789 | ||||||||
\(607\) | −38.3412 | −1.55622 | −0.778110 | − | 0.628128i | \(-0.783821\pi\) | ||||
−0.778110 | + | 0.628128i | \(0.783821\pi\) | |||||||
\(608\) | 3.02324 | 0.122608 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.434771 | 0.0176034 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 62.5214 | 2.52728 | ||||||||
\(613\) | −45.1692 | −1.82437 | −0.912184 | − | 0.409781i | \(-0.865605\pi\) | ||||
−0.912184 | + | 0.409781i | \(0.865605\pi\) | |||||||
\(614\) | 0.795509 | 0.0321041 | ||||||||
\(615\) | 8.95090 | 0.360935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.1763 | −1.61744 | −0.808718 | − | 0.588196i | \(-0.799838\pi\) | ||||
−0.808718 | + | 0.588196i | \(0.799838\pi\) | |||||||
\(618\) | −0.881179 | −0.0354462 | ||||||||
\(619\) | 8.14489 | 0.327371 | 0.163685 | − | 0.986513i | \(-0.447662\pi\) | ||||
0.163685 | + | 0.986513i | \(0.447662\pi\) | |||||||
\(620\) | −58.9812 | −2.36874 | ||||||||
\(621\) | 57.0979 | 2.29126 | ||||||||
\(622\) | 0.128052 | 0.00513443 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1873 | −0.807493 | ||||||||
\(626\) | 2.22931 | 0.0891013 | ||||||||
\(627\) | −4.85261 | −0.193794 | ||||||||
\(628\) | −11.2223 | −0.447820 | ||||||||
\(629\) | 3.91545 | 0.156119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6934 | −0.545124 | −0.272562 | − | 0.962138i | \(-0.587871\pi\) | ||||
−0.272562 | + | 0.962138i | \(0.587871\pi\) | |||||||
\(632\) | 4.89050 | 0.194534 | ||||||||
\(633\) | −24.7658 | −0.984352 | ||||||||
\(634\) | 0.366609 | 0.0145599 | ||||||||
\(635\) | 62.2294 | 2.46950 | ||||||||
\(636\) | 28.3340 | 1.12352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.496143 | −0.0196425 | ||||||||
\(639\) | 40.1145 | 1.58690 | ||||||||
\(640\) | −14.0346 | −0.554767 | ||||||||
\(641\) | −3.32843 | −0.131465 | −0.0657326 | − | 0.997837i | \(-0.520938\pi\) | ||||
−0.0657326 | + | 0.997837i | \(0.520938\pi\) | |||||||
\(642\) | 3.68137 | 0.145292 | ||||||||
\(643\) | −0.362106 | −0.0142801 | −0.00714003 | − | 0.999975i | \(-0.502273\pi\) | ||||
−0.00714003 | + | 0.999975i | \(0.502273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 56.3150 | 2.21740 | ||||||||
\(646\) | −1.38735 | −0.0545847 | ||||||||
\(647\) | 16.4860 | 0.648131 | 0.324066 | − | 0.946035i | \(-0.394950\pi\) | ||||
0.324066 | + | 0.946035i | \(0.394950\pi\) | |||||||
\(648\) | 3.94258 | 0.154879 | ||||||||
\(649\) | 4.24286 | 0.166547 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.2864 | −0.951130 | ||||||||
\(653\) | 30.0950 | 1.17771 | 0.588853 | − | 0.808240i | \(-0.299580\pi\) | ||||
0.588853 | + | 0.808240i | \(0.299580\pi\) | |||||||
\(654\) | 4.86636 | 0.190290 | ||||||||
\(655\) | −39.8641 | −1.55762 | ||||||||
\(656\) | 3.56564 | 0.139215 | ||||||||
\(657\) | 19.1244 | 0.746113 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.13142 | 0.316755 | 0.158378 | − | 0.987379i | \(-0.449374\pi\) | ||||
0.158378 | + | 0.987379i | \(0.449374\pi\) | |||||||
\(660\) | 16.9223 | 0.658701 | ||||||||
\(661\) | −23.9240 | −0.930534 | −0.465267 | − | 0.885170i | \(-0.654042\pi\) | ||||
−0.465267 | + | 0.885170i | \(0.654042\pi\) | |||||||
\(662\) | −2.33895 | −0.0909057 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.48944 | −0.213032 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.569979 | 0.0220863 | ||||||||
\(667\) | 28.5442 | 1.10524 | ||||||||
\(668\) | 8.81357 | 0.341007 | ||||||||
\(669\) | −56.9592 | −2.20217 | ||||||||
\(670\) | −3.07408 | −0.118762 | ||||||||
\(671\) | −0.847241 | −0.0327074 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.3113 | −0.744395 | −0.372197 | − | 0.928154i | \(-0.621396\pi\) | ||||
−0.372197 | + | 0.928154i | \(0.621396\pi\) | |||||||
\(674\) | 1.40454 | 0.0541008 | ||||||||
\(675\) | −48.4318 | −1.86414 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.1767 | 0.890752 | 0.445376 | − | 0.895344i | \(-0.353070\pi\) | ||||
0.445376 | + | 0.895344i | \(0.353070\pi\) | |||||||
\(678\) | −0.258467 | −0.00992636 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.72162 | 0.372807 | ||||||||
\(681\) | 60.5940 | 2.32197 | ||||||||
\(682\) | −1.08010 | −0.0413591 | ||||||||
\(683\) | 35.9572 | 1.37586 | 0.687932 | − | 0.725775i | \(-0.258519\pi\) | ||||
0.687932 | + | 0.725775i | \(0.258519\pi\) | |||||||
\(684\) | 21.4913 | 0.821739 | ||||||||
\(685\) | −31.3246 | −1.19685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.2218 | 2.06869 | ||||||||
\(688\) | 22.4334 | 0.855265 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 9.14904 | 0.348298 | ||||||||
\(691\) | 19.2587 | 0.732636 | 0.366318 | − | 0.930490i | \(-0.380618\pi\) | ||||
0.366318 | + | 0.930490i | \(0.380618\pi\) | |||||||
\(692\) | −47.8308 | −1.81825 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.18674 | 0.0830076 | ||||||||
\(695\) | −63.4621 | −2.40725 | ||||||||
\(696\) | 6.69828 | 0.253898 | ||||||||
\(697\) | −4.98684 | −0.188890 | ||||||||
\(698\) | −1.03879 | −0.0393186 | ||||||||
\(699\) | 23.5928 | 0.892360 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.0603 | 1.09759 | 0.548797 | − | 0.835956i | \(-0.315086\pi\) | ||||
0.548797 | + | 0.835956i | \(0.315086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.34591 | 0.0507618 | ||||||||
\(704\) | 6.61139 | 0.249176 | ||||||||
\(705\) | 34.3420 | 1.29339 | ||||||||
\(706\) | 0.157482 | 0.00592692 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.5069 | −1.07135 | ||||||||
\(709\) | −31.0355 | −1.16556 | −0.582781 | − | 0.812629i | \(-0.698036\pi\) | ||||
−0.582781 | + | 0.812629i | \(0.698036\pi\) | |||||||
\(710\) | 3.10417 | 0.116497 | ||||||||
\(711\) | 52.2289 | 1.95874 | ||||||||
\(712\) | −5.25775 | −0.197042 | ||||||||
\(713\) | 62.1405 | 2.32718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.2551 | 0.420624 | ||||||||
\(717\) | 85.3412 | 3.18712 | ||||||||
\(718\) | −0.603549 | −0.0225243 | ||||||||
\(719\) | −9.26681 | −0.345594 | −0.172797 | − | 0.984957i | \(-0.555280\pi\) | ||||
−0.172797 | + | 0.984957i | \(0.555280\pi\) | |||||||
\(720\) | −74.2349 | −2.76657 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.11573 | 0.0787393 | ||||||||
\(723\) | −0.472930 | −0.0175884 | ||||||||
\(724\) | 16.6273 | 0.617947 | ||||||||
\(725\) | −24.2119 | −0.899207 | ||||||||
\(726\) | −4.14327 | −0.153771 | ||||||||
\(727\) | −13.0885 | −0.485426 | −0.242713 | − | 0.970098i | \(-0.578037\pi\) | ||||
−0.242713 | + | 0.970098i | \(0.578037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.8837 | −1.18088 | ||||||||
\(730\) | 1.47990 | 0.0547735 | ||||||||
\(731\) | −31.3749 | −1.16044 | ||||||||
\(732\) | 5.69243 | 0.210398 | ||||||||
\(733\) | 8.28796 | 0.306123 | 0.153061 | − | 0.988217i | \(-0.451087\pi\) | ||||
0.153061 | + | 0.988217i | \(0.451087\pi\) | |||||||
\(734\) | −2.06649 | −0.0762755 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.1076 | 0.409431 | ||||||||
\(737\) | 5.99048 | 0.220662 | ||||||||
\(738\) | −0.725944 | −0.0267224 | ||||||||
\(739\) | 9.11800 | 0.335411 | 0.167705 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167705 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(740\) | −4.69353 | −0.172538 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.607766 | −0.0222968 | −0.0111484 | − | 0.999938i | \(-0.503549\pi\) | ||||
−0.0111484 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(744\) | 14.5821 | 0.534605 | ||||||||
\(745\) | −12.2070 | −0.447231 | ||||||||
\(746\) | −0.337930 | −0.0123725 | ||||||||
\(747\) | −58.6254 | −2.14499 | ||||||||
\(748\) | −9.42800 | −0.344722 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.10033 | −0.0401783 | ||||||||
\(751\) | −18.1861 | −0.663622 | −0.331811 | − | 0.943346i | \(-0.607660\pi\) | ||||
−0.331811 | + | 0.943346i | \(0.607660\pi\) | |||||||
\(752\) | 13.6803 | 0.498870 | ||||||||
\(753\) | 30.7693 | 1.12129 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.5664 | −1.98588 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8225 | −0.466041 | −0.233021 | − | 0.972472i | \(-0.574861\pi\) | ||||
−0.233021 | + | 0.972472i | \(0.574861\pi\) | |||||||
\(758\) | 3.92701 | 0.142635 | ||||||||
\(759\) | −17.8288 | −0.647144 | ||||||||
\(760\) | 3.34173 | 0.121217 | ||||||||
\(761\) | −15.8260 | −0.573691 | −0.286845 | − | 0.957977i | \(-0.592607\pi\) | ||||
−0.286845 | + | 0.957977i | \(0.592607\pi\) | |||||||
\(762\) | −7.65660 | −0.277369 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.2029 | −0.658560 | ||||||||
\(765\) | 103.824 | 3.75375 | ||||||||
\(766\) | 3.29655 | 0.119109 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −43.1112 | −1.55564 | ||||||||
\(769\) | 24.6606 | 0.889284 | 0.444642 | − | 0.895708i | \(-0.353331\pi\) | ||||
0.444642 | + | 0.895708i | \(0.353331\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −66.9699 | −2.41186 | ||||||||
\(772\) | −10.1943 | −0.366902 | ||||||||
\(773\) | 0.0738456 | 0.00265604 | 0.00132802 | − | 0.999999i | \(-0.499577\pi\) | ||||
0.00132802 | + | 0.999999i | \(0.499577\pi\) | |||||||
\(774\) | −4.56731 | −0.164169 | ||||||||
\(775\) | −52.7090 | −1.89336 | ||||||||
\(776\) | 8.66155 | 0.310932 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.62207 | −0.129857 | ||||||||
\(779\) | −1.71419 | −0.0614172 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.04912 | −0.216454 | ||||||||
\(782\) | −5.09723 | −0.182277 | ||||||||
\(783\) | 34.5470 | 1.23461 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.6359 | −0.665144 | ||||||||
\(786\) | 4.90481 | 0.174949 | ||||||||
\(787\) | −0.329950 | −0.0117614 | −0.00588072 | − | 0.999983i | \(-0.501872\pi\) | ||||
−0.00588072 | + | 0.999983i | \(0.501872\pi\) | |||||||
\(788\) | −18.3596 | −0.654032 | ||||||||
\(789\) | 62.7800 | 2.23503 | ||||||||
\(790\) | 4.04162 | 0.143794 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.75780 | −0.0979942 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.493443 | 0.0175117 | ||||||||
\(795\) | 47.0517 | 1.66875 | ||||||||
\(796\) | −29.9124 | −1.06022 | ||||||||
\(797\) | 30.4986 | 1.08032 | 0.540158 | − | 0.841563i | \(-0.318364\pi\) | ||||
0.540158 | + | 0.841563i | \(0.318364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.1330 | −0.676878 | ||||||||
\(800\) | −9.42171 | −0.333108 | ||||||||
\(801\) | −56.1510 | −1.98400 | ||||||||
\(802\) | 3.61685 | 0.127715 | ||||||||
\(803\) | −2.88389 | −0.101770 | ||||||||
\(804\) | −40.2488 | −1.41947 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 62.4347 | 2.19781 | ||||||||
\(808\) | −1.28768 | −0.0453005 | ||||||||
\(809\) | 29.6860 | 1.04370 | 0.521852 | − | 0.853036i | \(-0.325241\pi\) | ||||
0.521852 | + | 0.853036i | \(0.325241\pi\) | |||||||
\(810\) | 3.25823 | 0.114483 | ||||||||
\(811\) | 38.5645 | 1.35418 | 0.677091 | − | 0.735899i | \(-0.263240\pi\) | ||||
0.677091 | + | 0.735899i | \(0.263240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 83.2251 | 2.91883 | ||||||||
\(814\) | −0.0859508 | −0.00301257 | ||||||||
\(815\) | −40.3302 | −1.41271 | ||||||||
\(816\) | 62.7438 | 2.19647 | ||||||||
\(817\) | −10.7849 | −0.377316 | ||||||||
\(818\) | −3.23331 | −0.113050 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.97784 | 0.208755 | ||||||||
\(821\) | −46.9737 | −1.63939 | −0.819697 | − | 0.572797i | \(-0.805858\pi\) | ||||
−0.819697 | + | 0.572797i | \(0.805858\pi\) | |||||||
\(822\) | 3.85413 | 0.134428 | ||||||||
\(823\) | −22.0488 | −0.768574 | −0.384287 | − | 0.923214i | \(-0.625553\pi\) | ||||
−0.384287 | + | 0.923214i | \(0.625553\pi\) | |||||||
\(824\) | −1.18252 | −0.0411949 | ||||||||
\(825\) | 15.1228 | 0.526509 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.6514 | −1.13540 | −0.567700 | − | 0.823235i | \(-0.692167\pi\) | ||||
−0.567700 | + | 0.823235i | \(0.692167\pi\) | |||||||
\(828\) | 78.9603 | 2.74406 | ||||||||
\(829\) | 4.38573 | 0.152323 | 0.0761613 | − | 0.997096i | \(-0.475734\pi\) | ||||
0.0761613 | + | 0.997096i | \(0.475734\pi\) | |||||||
\(830\) | −4.53659 | −0.157467 | ||||||||
\(831\) | −83.1622 | −2.88486 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.80827 | 0.270378 | ||||||||
\(835\) | 14.6359 | 0.506496 | ||||||||
\(836\) | −3.24080 | −0.112086 | ||||||||
\(837\) | 75.2084 | 2.59958 | ||||||||
\(838\) | −1.78396 | −0.0616259 | ||||||||
\(839\) | −29.9207 | −1.03298 | −0.516488 | − | 0.856294i | \(-0.672761\pi\) | ||||
−0.516488 | + | 0.856294i | \(0.672761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.7294 | −0.404461 | ||||||||
\(842\) | −2.63158 | −0.0906904 | ||||||||
\(843\) | 11.0956 | 0.382152 | ||||||||
\(844\) | −16.5398 | −0.569323 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.78523 | −0.0957583 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 18.7433 | 0.643649 | ||||||||
\(849\) | −7.71058 | −0.264626 | ||||||||
\(850\) | 4.32359 | 0.148298 | ||||||||
\(851\) | 4.94494 | 0.169510 | ||||||||
\(852\) | 40.6427 | 1.39240 | ||||||||
\(853\) | 44.3926 | 1.51997 | 0.759987 | − | 0.649938i | \(-0.225205\pi\) | ||||
0.759987 | + | 0.649938i | \(0.225205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35.6886 | 1.22052 | ||||||||
\(856\) | 4.94030 | 0.168856 | ||||||||
\(857\) | 8.92234 | 0.304781 | 0.152391 | − | 0.988320i | \(-0.451303\pi\) | ||||
0.152391 | + | 0.988320i | \(0.451303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3911 | −0.525138 | −0.262569 | − | 0.964913i | \(-0.584570\pi\) | ||||
−0.262569 | + | 0.964913i | \(0.584570\pi\) | |||||||
\(860\) | 37.6098 | 1.28248 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.830626 | −0.0282912 | ||||||||
\(863\) | −20.5667 | −0.700100 | −0.350050 | − | 0.936731i | \(-0.613835\pi\) | ||||
−0.350050 | + | 0.936731i | \(0.613835\pi\) | |||||||
\(864\) | 13.4435 | 0.457356 | ||||||||
\(865\) | −79.4282 | −2.70064 | ||||||||
\(866\) | −3.79681 | −0.129021 | ||||||||
\(867\) | −37.3165 | −1.26734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.87593 | −0.267172 | ||||||||
\(870\) | 5.53560 | 0.187675 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.53051 | 0.221151 | ||||||||
\(873\) | 92.5024 | 3.13073 | ||||||||
\(874\) | −1.75213 | −0.0592668 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.3762 | 0.654662 | ||||||||
\(877\) | 8.61874 | 0.291034 | 0.145517 | − | 0.989356i | \(-0.453515\pi\) | ||||
0.145517 | + | 0.989356i | \(0.453515\pi\) | |||||||
\(878\) | −0.192192 | −0.00648617 | ||||||||
\(879\) | −62.8858 | −2.12109 | ||||||||
\(880\) | 11.1944 | 0.377362 | ||||||||
\(881\) | 16.6027 | 0.559358 | 0.279679 | − | 0.960094i | \(-0.409772\pi\) | ||||
0.279679 | + | 0.960094i | \(0.409772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0699 | 1.34846 | 0.674231 | − | 0.738521i | \(-0.264475\pi\) | ||||
0.674231 | + | 0.738521i | \(0.264475\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −47.3387 | −1.59127 | ||||||||
\(886\) | 3.07765 | 0.103396 | ||||||||
\(887\) | −14.6818 | −0.492965 | −0.246483 | − | 0.969147i | \(-0.579275\pi\) | ||||
−0.246483 | + | 0.969147i | \(0.579275\pi\) | |||||||
\(888\) | 1.16040 | 0.0389404 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.34512 | −0.145649 | ||||||||
\(891\) | −6.34934 | −0.212711 | ||||||||
\(892\) | −38.0401 | −1.27368 | ||||||||
\(893\) | −6.57684 | −0.220085 | ||||||||
\(894\) | 1.50193 | 0.0502321 | ||||||||
\(895\) | 18.6904 | 0.624750 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.65973 | 0.155497 | ||||||||
\(899\) | 37.5980 | 1.25396 | ||||||||
\(900\) | −66.9760 | −2.23253 | ||||||||
\(901\) | −26.2141 | −0.873317 | ||||||||
\(902\) | 0.109470 | 0.00364494 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.346855 | −0.0115362 | ||||||||
\(905\) | 27.6114 | 0.917833 | ||||||||
\(906\) | 6.71376 | 0.223050 | ||||||||
\(907\) | −2.62676 | −0.0872201 | −0.0436100 | − | 0.999049i | \(-0.513886\pi\) | ||||
−0.0436100 | + | 0.999049i | \(0.513886\pi\) | |||||||
\(908\) | 40.4676 | 1.34296 | ||||||||
\(909\) | −13.7520 | −0.456125 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.3583 | −1.10521 | −0.552605 | − | 0.833443i | \(-0.686366\pi\) | ||||
−0.552605 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(912\) | 21.5677 | 0.714179 | ||||||||
\(913\) | 8.84049 | 0.292578 | ||||||||
\(914\) | 3.07007 | 0.101549 | ||||||||
\(915\) | 9.45290 | 0.312503 | ||||||||
\(916\) | 36.2119 | 1.19647 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.16916 | −0.203612 | ||||||||
\(919\) | 30.3581 | 1.00142 | 0.500710 | − | 0.865615i | \(-0.333072\pi\) | ||||
0.500710 | + | 0.865615i | \(0.333072\pi\) | |||||||
\(920\) | 12.2777 | 0.404785 | ||||||||
\(921\) | 17.2962 | 0.569928 | ||||||||
\(922\) | 1.77123 | 0.0583322 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19442 | −0.137912 | ||||||||
\(926\) | −4.13745 | −0.135965 | ||||||||
\(927\) | −12.6289 | −0.414787 | ||||||||
\(928\) | 6.72061 | 0.220615 | ||||||||
\(929\) | −30.0306 | −0.985272 | −0.492636 | − | 0.870235i | \(-0.663967\pi\) | ||||
−0.492636 | + | 0.870235i | \(0.663967\pi\) | |||||||
\(930\) | 12.0510 | 0.395166 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.7564 | 0.516117 | ||||||||
\(933\) | 2.78415 | 0.0911489 | ||||||||
\(934\) | −2.25631 | −0.0738287 | ||||||||
\(935\) | −15.6562 | −0.512013 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4444 | 0.961908 | 0.480954 | − | 0.876746i | \(-0.340290\pi\) | ||||
0.480954 | + | 0.876746i | \(0.340290\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.4703 | 1.58177 | ||||||||
\(940\) | 22.9352 | 0.748064 | ||||||||
\(941\) | 54.0312 | 1.76137 | 0.880683 | − | 0.473706i | \(-0.157084\pi\) | ||||
0.880683 | + | 0.473706i | \(0.157084\pi\) | |||||||
\(942\) | 2.29293 | 0.0747077 | ||||||||
\(943\) | −6.29804 | −0.205092 | ||||||||
\(944\) | −18.8577 | −0.613764 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.688733 | 0.0223927 | ||||||||
\(947\) | −43.0267 | −1.39818 | −0.699090 | − | 0.715034i | \(-0.746411\pi\) | ||||
−0.699090 | + | 0.715034i | \(0.746411\pi\) | |||||||
\(948\) | 52.9167 | 1.71865 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.48620 | 0.0482188 | ||||||||
\(951\) | 7.97091 | 0.258475 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.1236 | −0.878618 | −0.439309 | − | 0.898336i | \(-0.644777\pi\) | ||||
−0.439309 | + | 0.898336i | \(0.644777\pi\) | |||||||
\(954\) | −3.81603 | −0.123549 | ||||||||
\(955\) | −30.2280 | −0.978154 | ||||||||
\(956\) | 56.9949 | 1.84335 | ||||||||
\(957\) | −10.7873 | −0.348703 | ||||||||
\(958\) | 1.28888 | 0.0416417 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −73.7652 | −2.38076 | ||||||||
\(961\) | 50.8504 | 1.64033 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.7607 | 1.70019 | ||||||||
\(964\) | −0.315845 | −0.0101727 | ||||||||
\(965\) | −16.9288 | −0.544958 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.4007 | −0.848990 | −0.424495 | − | 0.905430i | \(-0.639548\pi\) | ||||
−0.424495 | + | 0.905430i | \(0.639548\pi\) | |||||||
\(968\) | −5.56015 | −0.178710 | ||||||||
\(969\) | −30.1642 | −0.969014 | ||||||||
\(970\) | 7.15809 | 0.229832 | ||||||||
\(971\) | −5.38602 | −0.172846 | −0.0864228 | − | 0.996259i | \(-0.527544\pi\) | ||||
−0.0864228 | + | 0.996259i | \(0.527544\pi\) | |||||||
\(972\) | −6.75358 | −0.216621 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.385992 | −0.0123680 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.76562 | 0.120534 | ||||||||
\(977\) | 30.5139 | 0.976226 | 0.488113 | − | 0.872781i | \(-0.337685\pi\) | ||||
0.488113 | + | 0.872781i | \(0.337685\pi\) | |||||||
\(978\) | 4.96217 | 0.158673 | ||||||||
\(979\) | 8.46736 | 0.270618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 69.7436 | 2.22674 | ||||||||
\(982\) | −5.08796 | −0.162363 | ||||||||
\(983\) | 36.0083 | 1.14849 | 0.574243 | − | 0.818685i | \(-0.305297\pi\) | ||||
0.574243 | + | 0.818685i | \(0.305297\pi\) | |||||||
\(984\) | −1.47792 | −0.0471143 | ||||||||
\(985\) | −30.4880 | −0.971430 | ||||||||
\(986\) | −3.08407 | −0.0982167 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.6244 | −1.25998 | ||||||||
\(990\) | −2.27911 | −0.0724347 | ||||||||
\(991\) | 50.2430 | 1.59602 | 0.798011 | − | 0.602643i | \(-0.205886\pi\) | ||||
0.798011 | + | 0.602643i | \(0.205886\pi\) | |||||||
\(992\) | 14.6307 | 0.464525 | ||||||||
\(993\) | −50.8540 | −1.61380 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.6728 | −1.57473 | ||||||||
\(996\) | −59.3974 | −1.88208 | ||||||||
\(997\) | 28.0968 | 0.889836 | 0.444918 | − | 0.895571i | \(-0.353233\pi\) | ||||
0.444918 | + | 0.895571i | \(0.353233\pi\) | |||||||
\(998\) | 2.48988 | 0.0788159 | ||||||||
\(999\) | 5.98485 | 0.189352 |
(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 | 8281.2.a.ct.1.13 | 24 | ||
7.3 | odd | 6 | 1183.2.e.l.170.12 | yes | 48 | ||
7.5 | odd | 6 | 1183.2.e.l.508.12 | yes | 48 | ||
7.6 | odd | 2 | 8281.2.a.cu.1.13 | 24 | |||
13.12 | even | 2 | 8281.2.a.cw.1.12 | 24 | |||
91.12 | odd | 6 | 1183.2.e.k.508.13 | yes | 48 | ||
91.38 | odd | 6 | 1183.2.e.k.170.13 | ✓ | 48 | ||
91.90 | odd | 2 | 8281.2.a.cv.1.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.e.k.170.13 | ✓ | 48 | 91.38 | odd | 6 | ||
1183.2.e.k.508.13 | yes | 48 | 91.12 | odd | 6 | ||
1183.2.e.l.170.12 | yes | 48 | 7.3 | odd | 6 | ||
1183.2.e.l.508.12 | yes | 48 | 7.5 | odd | 6 | ||
8281.2.a.ct.1.13 | 24 | 1.1 | even | 1 | trivial | ||
8281.2.a.cu.1.13 | 24 | 7.6 | odd | 2 | |||
8281.2.a.cv.1.12 | 24 | 91.90 | odd | 2 | |||
8281.2.a.cw.1.12 | 24 | 13.12 | even | 2 |