Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, 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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.46980000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 80x^{4} - 180x^{2} + 145 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.63148\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63148 | −1.15363 | −0.576817 | − | 0.816874i | \(-0.695705\pi\) | ||||
−0.576817 | + | 0.816874i | \(0.695705\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.661739 | 0.330869 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44512 | −0.546206 | −0.273103 | − | 0.961985i | \(-0.588050\pi\) | ||||
−0.273103 | + | 0.961985i | \(0.588050\pi\) | |||||||
\(8\) | 2.18335 | 0.771931 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.797518 | −0.240461 | −0.120230 | − | 0.992746i | \(-0.538363\pi\) | ||||
−0.120230 | + | 0.992746i | \(0.538363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02701 | 0.839542 | 0.419771 | − | 0.907630i | \(-0.362110\pi\) | ||||
0.419771 | + | 0.907630i | \(0.362110\pi\) | |||||||
\(14\) | 2.35770 | 0.630121 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88558 | −1.22139 | ||||||||
\(17\) | −0.282098 | −0.0684189 | −0.0342094 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342094 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.88558 | 0.661997 | 0.330999 | − | 0.943631i | \(-0.392614\pi\) | ||||
0.330999 | + | 0.943631i | \(0.392614\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.30114 | 0.277403 | ||||||||
\(23\) | 3.47376 | 0.724329 | 0.362165 | − | 0.932114i | \(-0.382038\pi\) | ||||
0.362165 | + | 0.932114i | \(0.382038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.93852 | −0.968523 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.956295 | −0.180723 | ||||||||
\(29\) | 7.73271 | 1.43593 | 0.717964 | − | 0.696080i | \(-0.245074\pi\) | ||||
0.717964 | + | 0.696080i | \(0.245074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.38761 | 0.428828 | 0.214414 | − | 0.976743i | \(-0.431216\pi\) | ||||
0.214414 | + | 0.976743i | \(0.431216\pi\) | |||||||
\(32\) | 3.60404 | 0.637110 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.460239 | 0.0789303 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.64195 | 0.763133 | 0.381566 | − | 0.924341i | \(-0.375385\pi\) | ||||
0.381566 | + | 0.924341i | \(0.375385\pi\) | |||||||
\(38\) | −4.70778 | −0.763702 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.42719 | −1.31611 | −0.658053 | − | 0.752972i | \(-0.728620\pi\) | ||||
−0.658053 | + | 0.752972i | \(0.728620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.07985 | 0.927169 | 0.463584 | − | 0.886053i | \(-0.346563\pi\) | ||||
0.463584 | + | 0.886053i | \(0.346563\pi\) | |||||||
\(44\) | −0.527748 | −0.0795611 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.66739 | −0.835610 | ||||||||
\(47\) | 1.16013 | 0.169223 | 0.0846114 | − | 0.996414i | \(-0.473035\pi\) | ||||
0.0846114 | + | 0.996414i | \(0.473035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.91161 | −0.701659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00309 | 0.277779 | ||||||||
\(53\) | −11.7932 | −1.61992 | −0.809960 | − | 0.586485i | \(-0.800511\pi\) | ||||
−0.809960 | + | 0.586485i | \(0.800511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.15522 | −0.421633 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.6158 | −1.65653 | ||||||||
\(59\) | −12.2420 | −1.59378 | −0.796888 | − | 0.604127i | \(-0.793522\pi\) | ||||
−0.796888 | + | 0.604127i | \(0.793522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.868886 | −0.111249 | −0.0556247 | − | 0.998452i | \(-0.517715\pi\) | ||||
−0.0556247 | + | 0.998452i | \(0.517715\pi\) | |||||||
\(62\) | −3.89535 | −0.494710 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.89123 | 0.486403 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3892 | 1.39141 | 0.695706 | − | 0.718327i | \(-0.255092\pi\) | ||||
0.695706 | + | 0.718327i | \(0.255092\pi\) | |||||||
\(68\) | −0.186675 | −0.0226377 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.63389 | −0.549942 | −0.274971 | − | 0.961453i | \(-0.588668\pi\) | ||||
−0.274971 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8327 | 1.26788 | 0.633938 | − | 0.773384i | \(-0.281437\pi\) | ||||
0.633938 | + | 0.773384i | \(0.281437\pi\) | |||||||
\(74\) | −7.57327 | −0.880375 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.90950 | 0.219035 | ||||||||
\(77\) | 1.15251 | 0.131341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.73501 | −0.532730 | −0.266365 | − | 0.963872i | \(-0.585823\pi\) | ||||
−0.266365 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.7488 | 1.51830 | ||||||||
\(83\) | 16.6753 | 1.83035 | 0.915177 | − | 0.403052i | \(-0.132051\pi\) | ||||
0.915177 | + | 0.403052i | \(0.132051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.91918 | −1.06961 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.74126 | −0.185619 | ||||||||
\(89\) | 16.2163 | 1.71892 | 0.859462 | − | 0.511200i | \(-0.170799\pi\) | ||||
0.859462 | + | 0.511200i | \(0.170799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.37441 | −0.458563 | ||||||||
\(92\) | 2.29872 | 0.239658 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.89274 | −0.195221 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8409 | 1.10073 | 0.550363 | − | 0.834925i | \(-0.314489\pi\) | ||||
0.550363 | + | 0.834925i | \(0.314489\pi\) | |||||||
\(98\) | 8.01322 | 0.809457 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.97095 | −0.594132 | −0.297066 | − | 0.954857i | \(-0.596008\pi\) | ||||
−0.297066 | + | 0.954857i | \(0.596008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.38631 | −0.826327 | −0.413164 | − | 0.910657i | \(-0.635576\pi\) | ||||
−0.413164 | + | 0.910657i | \(0.635576\pi\) | |||||||
\(104\) | 6.60903 | 0.648069 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.2404 | 1.86879 | ||||||||
\(107\) | −10.0314 | −0.969775 | −0.484888 | − | 0.874576i | \(-0.661140\pi\) | ||||
−0.484888 | + | 0.874576i | \(0.661140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.57433 | −0.342359 | −0.171179 | − | 0.985240i | \(-0.554758\pi\) | ||||
−0.171179 | + | 0.985240i | \(0.554758\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.06027 | 0.667133 | ||||||||
\(113\) | −10.3012 | −0.969056 | −0.484528 | − | 0.874776i | \(-0.661009\pi\) | ||||
−0.484528 | + | 0.874776i | \(0.661009\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.11704 | 0.475105 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.9727 | 1.83863 | ||||||||
\(119\) | 0.407667 | 0.0373708 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3640 | −0.942179 | ||||||||
\(122\) | 1.41757 | 0.128341 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.57998 | 0.141886 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.78181 | 0.601788 | 0.300894 | − | 0.953658i | \(-0.402715\pi\) | ||||
0.300894 | + | 0.953658i | \(0.402715\pi\) | |||||||
\(128\) | −13.5566 | −1.19824 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.1690 | −1.76218 | −0.881088 | − | 0.472952i | \(-0.843188\pi\) | ||||
−0.881088 | + | 0.472952i | \(0.843188\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.17002 | −0.361587 | ||||||||
\(134\) | −18.5813 | −1.60518 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.615920 | −0.0528147 | ||||||||
\(137\) | 11.2562 | 0.961685 | 0.480843 | − | 0.876807i | \(-0.340331\pi\) | ||||
0.480843 | + | 0.876807i | \(0.340331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.73034 | −0.655679 | −0.327839 | − | 0.944733i | \(-0.606321\pi\) | ||||
−0.327839 | + | 0.944733i | \(0.606321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.56012 | 0.634431 | ||||||||
\(143\) | −2.41409 | −0.201877 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.6734 | −1.46266 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.07176 | 0.252497 | ||||||||
\(149\) | −7.96312 | −0.652364 | −0.326182 | − | 0.945307i | \(-0.605762\pi\) | ||||
−0.326182 | + | 0.945307i | \(0.605762\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0043 | 1.62793 | 0.813965 | − | 0.580914i | \(-0.197305\pi\) | ||||
0.813965 | + | 0.580914i | \(0.197305\pi\) | |||||||
\(152\) | 6.30023 | 0.511016 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.88031 | −0.151519 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.40707 | −0.431531 | −0.215765 | − | 0.976445i | \(-0.569225\pi\) | ||||
−0.215765 | + | 0.976445i | \(0.569225\pi\) | |||||||
\(158\) | 7.72509 | 0.614575 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.02002 | −0.395633 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.96446 | 0.467172 | 0.233586 | − | 0.972336i | \(-0.424954\pi\) | ||||
0.233586 | + | 0.972336i | \(0.424954\pi\) | |||||||
\(164\) | −5.57660 | −0.435459 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −27.2055 | −2.11156 | ||||||||
\(167\) | −8.52261 | −0.659499 | −0.329750 | − | 0.944068i | \(-0.606964\pi\) | ||||
−0.329750 | + | 0.944068i | \(0.606964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.83720 | −0.295170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.02327 | 0.306772 | ||||||||
\(173\) | 7.42809 | 0.564747 | 0.282374 | − | 0.959305i | \(-0.408878\pi\) | ||||
0.282374 | + | 0.959305i | \(0.408878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.89634 | 0.293697 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.4566 | −1.98301 | ||||||||
\(179\) | 20.7650 | 1.55205 | 0.776023 | − | 0.630704i | \(-0.217234\pi\) | ||||
0.776023 | + | 0.630704i | \(0.217234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.7654 | 1.46915 | 0.734575 | − | 0.678528i | \(-0.237382\pi\) | ||||
0.734575 | + | 0.678528i | \(0.237382\pi\) | |||||||
\(182\) | 7.13678 | 0.529013 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.58444 | 0.559133 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.224978 | 0.0164521 | ||||||||
\(188\) | 0.767705 | 0.0559906 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8195 | −1.21702 | −0.608509 | − | 0.793547i | \(-0.708232\pi\) | ||||
−0.608509 | + | 0.793547i | \(0.708232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1885 | 1.45320 | 0.726602 | − | 0.687059i | \(-0.241099\pi\) | ||||
0.726602 | + | 0.687059i | \(0.241099\pi\) | |||||||
\(194\) | −17.6867 | −1.26983 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.25021 | −0.232158 | ||||||||
\(197\) | −12.3010 | −0.876410 | −0.438205 | − | 0.898875i | \(-0.644386\pi\) | ||||
−0.438205 | + | 0.898875i | \(0.644386\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6340 | 1.39182 | 0.695909 | − | 0.718130i | \(-0.255002\pi\) | ||||
0.695909 | + | 0.718130i | \(0.255002\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.74151 | 0.685410 | ||||||||
\(203\) | −11.1747 | −0.784313 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.6821 | 0.953279 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.7887 | −1.02541 | ||||||||
\(209\) | −2.30130 | −0.159184 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.55552 | 0.520144 | 0.260072 | − | 0.965589i | \(-0.416254\pi\) | ||||
0.260072 | + | 0.965589i | \(0.416254\pi\) | |||||||
\(212\) | −7.80402 | −0.535982 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.3661 | 1.11877 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.45040 | −0.234228 | ||||||||
\(218\) | 5.83146 | 0.394956 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.853915 | −0.0574405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.60772 | 0.107661 | 0.0538303 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538303 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(224\) | −5.20829 | −0.347993 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.8062 | 1.11793 | ||||||||
\(227\) | 5.53703 | 0.367506 | 0.183753 | − | 0.982972i | \(-0.441175\pi\) | ||||
0.183753 | + | 0.982972i | \(0.441175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3562 | 0.816521 | 0.408260 | − | 0.912865i | \(-0.366136\pi\) | ||||
0.408260 | + | 0.912865i | \(0.366136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.8832 | 1.10844 | ||||||||
\(233\) | 6.66543 | 0.436667 | 0.218333 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218333 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.10102 | −0.527332 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.665103 | −0.0431122 | ||||||||
\(239\) | 5.71449 | 0.369640 | 0.184820 | − | 0.982772i | \(-0.440830\pi\) | ||||
0.184820 | + | 0.982772i | \(0.440830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.1134 | −1.36003 | −0.680016 | − | 0.733198i | \(-0.738027\pi\) | ||||
−0.680016 | + | 0.733198i | \(0.738027\pi\) | |||||||
\(242\) | 16.9086 | 1.08693 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.574975 | −0.0368090 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.73468 | 0.555774 | ||||||||
\(248\) | 5.21300 | 0.331026 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.39926 | −0.467037 | −0.233519 | − | 0.972352i | \(-0.575024\pi\) | ||||
−0.233519 | + | 0.972352i | \(0.575024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.77039 | −0.174173 | ||||||||
\(254\) | −11.0644 | −0.694243 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.3348 | 0.895928 | ||||||||
\(257\) | −7.27627 | −0.453881 | −0.226941 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226941 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.70820 | −0.416828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 32.9054 | 2.03290 | ||||||||
\(263\) | −8.62308 | −0.531722 | −0.265861 | − | 0.964011i | \(-0.585656\pi\) | ||||
−0.265861 | + | 0.964011i | \(0.585656\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.80332 | 0.417139 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.53667 | 0.460375 | ||||||||
\(269\) | 11.3763 | 0.693626 | 0.346813 | − | 0.937934i | \(-0.387264\pi\) | ||||
0.346813 | + | 0.937934i | \(0.387264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6887 | −0.831532 | −0.415766 | − | 0.909472i | \(-0.636487\pi\) | ||||
−0.415766 | + | 0.909472i | \(0.636487\pi\) | |||||||
\(272\) | 1.37821 | 0.0835665 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.3644 | −1.10943 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4969 | 1.59204 | 0.796022 | − | 0.605267i | \(-0.206934\pi\) | ||||
0.796022 | + | 0.605267i | \(0.206934\pi\) | |||||||
\(278\) | 12.6119 | 0.756413 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1577 | −0.665612 | −0.332806 | − | 0.942995i | \(-0.607995\pi\) | ||||
−0.332806 | + | 0.942995i | \(0.607995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7714 | −1.41306 | −0.706532 | − | 0.707681i | \(-0.749742\pi\) | ||||
−0.706532 | + | 0.707681i | \(0.749742\pi\) | |||||||
\(284\) | −3.06643 | −0.181959 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.93856 | 0.232892 | ||||||||
\(287\) | 12.1783 | 0.718865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9204 | −0.995319 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.16844 | 0.419501 | ||||||||
\(293\) | 0.0928455 | 0.00542409 | 0.00271204 | − | 0.999996i | \(-0.499137\pi\) | ||||
0.00271204 | + | 0.999996i | \(0.499137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.1350 | 0.589086 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.9917 | 0.752589 | ||||||||
\(299\) | 10.5151 | 0.608105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.78615 | −0.506425 | ||||||||
\(302\) | −32.6368 | −1.87803 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.0977 | −0.808560 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5168 | 0.714372 | 0.357186 | − | 0.934033i | \(-0.383736\pi\) | ||||
0.357186 | + | 0.934033i | \(0.383736\pi\) | |||||||
\(308\) | 0.762662 | 0.0434567 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5365 | 1.73157 | 0.865783 | − | 0.500420i | \(-0.166821\pi\) | ||||
0.865783 | + | 0.500420i | \(0.166821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4428 | −0.759833 | −0.379916 | − | 0.925021i | \(-0.624047\pi\) | ||||
−0.379916 | + | 0.925021i | \(0.624047\pi\) | |||||||
\(314\) | 8.82154 | 0.497828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.13334 | −0.176264 | ||||||||
\(317\) | −12.4363 | −0.698493 | −0.349247 | − | 0.937031i | \(-0.613562\pi\) | ||||
−0.349247 | + | 0.937031i | \(0.613562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.16697 | −0.345284 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.19008 | 0.456415 | ||||||||
\(323\) | −0.814017 | −0.0452931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.73091 | −0.538945 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.3995 | −1.01594 | ||||||||
\(329\) | −1.67654 | −0.0924304 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.86199 | 0.102344 | 0.0511721 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511721 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(332\) | 11.0347 | 0.605608 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.9045 | 0.760820 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3165 | −0.616450 | −0.308225 | − | 0.951313i | \(-0.599735\pi\) | ||||
−0.308225 | + | 0.951313i | \(0.599735\pi\) | |||||||
\(338\) | 6.26034 | 0.340517 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90416 | −0.103116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2138 | 0.929456 | ||||||||
\(344\) | 13.2745 | 0.715711 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.1188 | −0.651511 | ||||||||
\(347\) | 25.4682 | 1.36721 | 0.683603 | − | 0.729854i | \(-0.260412\pi\) | ||||
0.683603 | + | 0.729854i | \(0.260412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2236 | 0.600787 | 0.300394 | − | 0.953815i | \(-0.402882\pi\) | ||||
0.300394 | + | 0.953815i | \(0.402882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.87429 | −0.153200 | ||||||||
\(353\) | 13.0338 | 0.693722 | 0.346861 | − | 0.937917i | \(-0.387248\pi\) | ||||
0.346861 | + | 0.937917i | \(0.387248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.7310 | 0.568739 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −33.8777 | −1.79049 | ||||||||
\(359\) | 29.5123 | 1.55760 | 0.778800 | − | 0.627273i | \(-0.215829\pi\) | ||||
0.778800 | + | 0.627273i | \(0.215829\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.6734 | −0.561760 | ||||||||
\(362\) | −32.2469 | −1.69486 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.89472 | −0.151724 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2070 | 0.898199 | 0.449100 | − | 0.893482i | \(-0.351745\pi\) | ||||
0.449100 | + | 0.893482i | \(0.351745\pi\) | |||||||
\(368\) | −16.9713 | −0.884692 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0426 | 0.884810 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2030 | 0.838957 | 0.419479 | − | 0.907765i | \(-0.362213\pi\) | ||||
0.419479 | + | 0.907765i | \(0.362213\pi\) | |||||||
\(374\) | −0.367049 | −0.0189796 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.53298 | 0.130628 | ||||||||
\(377\) | 23.4070 | 1.20552 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5047 | 1.46419 | 0.732095 | − | 0.681203i | \(-0.238543\pi\) | ||||
0.732095 | + | 0.681203i | \(0.238543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 27.4408 | 1.40399 | ||||||||
\(383\) | −26.9679 | −1.37800 | −0.688998 | − | 0.724763i | \(-0.741949\pi\) | ||||
−0.688998 | + | 0.724763i | \(0.741949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.9373 | −1.67646 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.17384 | 0.364197 | ||||||||
\(389\) | −6.02735 | −0.305599 | −0.152799 | − | 0.988257i | \(-0.548829\pi\) | ||||
−0.152799 | + | 0.988257i | \(0.548829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.979942 | −0.0495578 | ||||||||
\(392\) | −10.7238 | −0.541633 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.0689 | 1.01106 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4231 | 0.924627 | 0.462313 | − | 0.886717i | \(-0.347020\pi\) | ||||
0.462313 | + | 0.886717i | \(0.347020\pi\) | |||||||
\(398\) | −32.0325 | −1.60565 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.4430 | 0.871063 | 0.435532 | − | 0.900173i | \(-0.356560\pi\) | ||||
0.435532 | + | 0.900173i | \(0.356560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.22733 | 0.360019 | ||||||||
\(404\) | −3.95121 | −0.196580 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.2314 | 0.904809 | ||||||||
\(407\) | −3.70204 | −0.183503 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9024 | −1.08300 | −0.541501 | − | 0.840700i | \(-0.682144\pi\) | ||||
−0.541501 | + | 0.840700i | \(0.682144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.54954 | −0.273406 | ||||||||
\(413\) | 17.6913 | 0.870530 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.9095 | 0.534881 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.75453 | 0.183640 | ||||||||
\(419\) | 8.29532 | 0.405253 | 0.202626 | − | 0.979256i | \(-0.435052\pi\) | ||||
0.202626 | + | 0.979256i | \(0.435052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0805 | −0.540028 | −0.270014 | − | 0.962856i | \(-0.587028\pi\) | ||||
−0.270014 | + | 0.962856i | \(0.587028\pi\) | |||||||
\(422\) | −12.3267 | −0.600055 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.7487 | −1.25047 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.25565 | 0.0607651 | ||||||||
\(428\) | −6.63819 | −0.320869 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.2816 | 1.21777 | 0.608885 | − | 0.793259i | \(-0.291617\pi\) | ||||
0.608885 | + | 0.793259i | \(0.291617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.04358 | 0.290436 | 0.145218 | − | 0.989400i | \(-0.453612\pi\) | ||||
0.145218 | + | 0.989400i | \(0.453612\pi\) | |||||||
\(434\) | 5.62927 | 0.270214 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.36527 | −0.113276 | ||||||||
\(437\) | 10.0238 | 0.479504 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0624 | −0.862073 | −0.431036 | − | 0.902335i | \(-0.641852\pi\) | ||||
−0.431036 | + | 0.902335i | \(0.641852\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.39315 | 0.0662653 | ||||||||
\(443\) | 12.8138 | 0.608804 | 0.304402 | − | 0.952544i | \(-0.401543\pi\) | ||||
0.304402 | + | 0.952544i | \(0.401543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.62296 | −0.124201 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.62331 | −0.265676 | ||||||||
\(449\) | 34.9139 | 1.64769 | 0.823845 | − | 0.566815i | \(-0.191825\pi\) | ||||
0.823845 | + | 0.566815i | \(0.191825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.72083 | 0.316472 | ||||||||
\(452\) | −6.81671 | −0.320631 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.03358 | −0.423967 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6673 | −0.919999 | −0.459999 | − | 0.887919i | \(-0.652150\pi\) | ||||
−0.459999 | + | 0.887919i | \(0.652150\pi\) | |||||||
\(458\) | −20.1589 | −0.941966 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0991 | 1.44843 | 0.724215 | − | 0.689575i | \(-0.242202\pi\) | ||||
0.724215 | + | 0.689575i | \(0.242202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.9301 | 1.80924 | 0.904618 | − | 0.426222i | \(-0.140156\pi\) | ||||
0.904618 | + | 0.426222i | \(0.140156\pi\) | |||||||
\(464\) | −37.7788 | −1.75384 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.8745 | −0.503753 | ||||||||
\(467\) | 11.3805 | 0.526626 | 0.263313 | − | 0.964710i | \(-0.415185\pi\) | ||||
0.263313 | + | 0.964710i | \(0.415185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4588 | −0.759997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −26.7286 | −1.23029 | ||||||||
\(473\) | −4.84879 | −0.222948 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.269769 | 0.0123649 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.32310 | −0.426429 | ||||||||
\(479\) | −24.6901 | −1.12812 | −0.564060 | − | 0.825734i | \(-0.690762\pi\) | ||||
−0.564060 | + | 0.825734i | \(0.690762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0512 | 0.640682 | ||||||||
\(482\) | 34.4461 | 1.56898 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.85824 | −0.311738 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.83392 | −0.173731 | −0.0868657 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868657 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(488\) | −1.89708 | −0.0858769 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.57778 | −0.341980 | −0.170990 | − | 0.985273i | \(-0.554697\pi\) | ||||
−0.170990 | + | 0.985273i | \(0.554697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.18139 | −0.0982447 | ||||||||
\(494\) | −14.2505 | −0.641160 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.6649 | −0.523768 | ||||||||
\(497\) | 6.69656 | 0.300382 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9554 | 1.02763 | 0.513813 | − | 0.857902i | \(-0.328232\pi\) | ||||
0.513813 | + | 0.857902i | \(0.328232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0718 | 0.538789 | ||||||||
\(503\) | 31.2801 | 1.39471 | 0.697355 | − | 0.716726i | \(-0.254360\pi\) | ||||
0.697355 | + | 0.716726i | \(0.254360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.51984 | 0.200931 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.48778 | 0.199113 | ||||||||
\(509\) | 23.1936 | 1.02804 | 0.514020 | − | 0.857778i | \(-0.328156\pi\) | ||||
0.514020 | + | 0.857778i | \(0.328156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.6547 | −0.692521 | ||||||||
\(512\) | 3.72605 | 0.164670 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.8711 | 0.523612 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.925226 | −0.0406914 | ||||||||
\(518\) | 10.9443 | 0.480866 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0116 | 1.35864 | 0.679321 | − | 0.733841i | \(-0.262274\pi\) | ||||
0.679321 | + | 0.733841i | \(0.262274\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3537 | −0.496462 | −0.248231 | − | 0.968701i | \(-0.579849\pi\) | ||||
−0.248231 | + | 0.968701i | \(0.579849\pi\) | |||||||
\(524\) | −13.3466 | −0.583050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0684 | 0.613412 | ||||||||
\(527\) | −0.673542 | −0.0293399 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9330 | −0.475347 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.75947 | −0.119638 | ||||||||
\(533\) | −25.5092 | −1.10493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.8666 | 1.07407 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.5603 | −0.800190 | ||||||||
\(539\) | 3.91710 | 0.168721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.8120 | −1.15274 | −0.576368 | − | 0.817190i | \(-0.695531\pi\) | ||||
−0.576368 | + | 0.817190i | \(0.695531\pi\) | |||||||
\(542\) | 22.3330 | 0.959283 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.01669 | −0.0435904 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.2250 | 1.67714 | 0.838570 | − | 0.544793i | \(-0.183392\pi\) | ||||
0.838570 | + | 0.544793i | \(0.183392\pi\) | |||||||
\(548\) | 7.44869 | 0.318192 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3134 | 0.950581 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.84268 | 0.290980 | ||||||||
\(554\) | −43.2293 | −1.83664 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.11547 | −0.216944 | ||||||||
\(557\) | −44.3906 | −1.88089 | −0.940445 | − | 0.339946i | \(-0.889591\pi\) | ||||
−0.940445 | + | 0.339946i | \(0.889591\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.4038 | 0.778397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.2036 | 0.767873 | ||||||||
\(563\) | 33.4717 | 1.41066 | 0.705332 | − | 0.708877i | \(-0.250798\pi\) | ||||
0.705332 | + | 0.708877i | \(0.250798\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.7827 | 1.63016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1174 | −0.424517 | ||||||||
\(569\) | −0.968748 | −0.0406120 | −0.0203060 | − | 0.999794i | \(-0.506464\pi\) | ||||
−0.0203060 | + | 0.999794i | \(0.506464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5141 | 1.06773 | 0.533867 | − | 0.845569i | \(-0.320738\pi\) | ||||
0.533867 | + | 0.845569i | \(0.320738\pi\) | |||||||
\(572\) | −1.59750 | −0.0667948 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.8688 | −0.829306 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.3026 | −1.42804 | −0.714019 | − | 0.700127i | \(-0.753127\pi\) | ||||
−0.714019 | + | 0.700127i | \(0.753127\pi\) | |||||||
\(578\) | 27.6054 | 1.14823 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0979 | −0.999750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.40528 | 0.389527 | ||||||||
\(584\) | 23.6517 | 0.978713 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.151476 | −0.00625741 | ||||||||
\(587\) | 25.3199 | 1.04507 | 0.522533 | − | 0.852619i | \(-0.324987\pi\) | ||||
0.522533 | + | 0.852619i | \(0.324987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.88965 | 0.283883 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.6786 | −0.932086 | ||||||||
\(593\) | −0.909773 | −0.0373599 | −0.0186800 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186800 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.26951 | −0.215847 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.1552 | −0.701530 | ||||||||
\(599\) | −2.86390 | −0.117016 | −0.0585080 | − | 0.998287i | \(-0.518634\pi\) | ||||
−0.0585080 | + | 0.998287i | \(0.518634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.46431 | −0.141312 | −0.0706560 | − | 0.997501i | \(-0.522509\pi\) | ||||
−0.0706560 | + | 0.997501i | \(0.522509\pi\) | |||||||
\(602\) | 14.3345 | 0.584229 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.2376 | 0.538632 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.9220 | −0.565075 | −0.282538 | − | 0.959256i | \(-0.591176\pi\) | ||||
−0.282538 | + | 0.959256i | \(0.591176\pi\) | |||||||
\(608\) | 10.3997 | 0.421765 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.51173 | 0.142070 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.86475 | 0.196485 | 0.0982427 | − | 0.995162i | \(-0.468678\pi\) | ||||
0.0982427 | + | 0.995162i | \(0.468678\pi\) | |||||||
\(614\) | −20.4210 | −0.824124 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.51634 | 0.101386 | ||||||||
\(617\) | −20.0261 | −0.806220 | −0.403110 | − | 0.915152i | \(-0.632071\pi\) | ||||
−0.403110 | + | 0.915152i | \(0.632071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.7672 | 1.51799 | 0.758996 | − | 0.651095i | \(-0.225690\pi\) | ||||
0.758996 | + | 0.651095i | \(0.225690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −49.8198 | −1.99759 | ||||||||
\(623\) | −23.4346 | −0.938886 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.9317 | 0.876568 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.57807 | −0.142780 | ||||||||
\(629\) | −1.30949 | −0.0522127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0097 | −0.995622 | −0.497811 | − | 0.867286i | \(-0.665863\pi\) | ||||
−0.497811 | + | 0.867286i | \(0.665863\pi\) | |||||||
\(632\) | −10.3382 | −0.411231 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.2896 | 0.805805 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8675 | −0.589072 | ||||||||
\(638\) | 10.0613 | 0.398331 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.8546 | 0.428731 | 0.214365 | − | 0.976754i | \(-0.431232\pi\) | ||||
0.214365 | + | 0.976754i | \(0.431232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.0302 | 1.22371 | 0.611856 | − | 0.790969i | \(-0.290423\pi\) | ||||
0.611856 | + | 0.790969i | \(0.290423\pi\) | |||||||
\(644\) | −3.32194 | −0.130903 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.32806 | 0.0522516 | ||||||||
\(647\) | −49.2351 | −1.93563 | −0.967815 | − | 0.251662i | \(-0.919023\pi\) | ||||
−0.967815 | + | 0.251662i | \(0.919023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.76323 | 0.383240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.94691 | 0.154573 | ||||||||
\(653\) | 42.5573 | 1.66540 | 0.832698 | − | 0.553727i | \(-0.186795\pi\) | ||||
0.832698 | + | 0.553727i | \(0.186795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.1717 | 1.60748 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.73524 | 0.106631 | ||||||||
\(659\) | 32.0671 | 1.24916 | 0.624578 | − | 0.780963i | \(-0.285271\pi\) | ||||
0.624578 | + | 0.780963i | \(0.285271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0549 | 1.48016 | 0.740082 | − | 0.672517i | \(-0.234787\pi\) | ||||
0.740082 | + | 0.672517i | \(0.234787\pi\) | |||||||
\(662\) | −3.03780 | −0.118068 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 36.4081 | 1.41291 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8616 | 1.04009 | ||||||||
\(668\) | −5.63974 | −0.218208 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.692952 | 0.0267511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8508 | 0.919381 | 0.459691 | − | 0.888079i | \(-0.347960\pi\) | ||||
0.459691 | + | 0.888079i | \(0.347960\pi\) | |||||||
\(674\) | 18.4627 | 0.711158 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.53923 | −0.0976626 | ||||||||
\(677\) | −10.5516 | −0.405530 | −0.202765 | − | 0.979227i | \(-0.564993\pi\) | ||||
−0.202765 | + | 0.979227i | \(0.564993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6665 | −0.601223 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.10661 | 0.118958 | ||||||||
\(683\) | −19.9516 | −0.763427 | −0.381713 | − | 0.924281i | \(-0.624666\pi\) | ||||
−0.381713 | + | 0.924281i | \(0.624666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −28.0840 | −1.07225 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −29.7036 | −1.13244 | ||||||||
\(689\) | −35.6981 | −1.35999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.7907 | 1.24742 | 0.623708 | − | 0.781657i | \(-0.285625\pi\) | ||||
0.623708 | + | 0.781657i | \(0.285625\pi\) | |||||||
\(692\) | 4.91545 | 0.186858 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −41.5510 | −1.57725 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.37730 | 0.0900465 | ||||||||
\(698\) | −18.3112 | −0.693088 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.70090 | 0.102012 | 0.0510058 | − | 0.998698i | \(-0.483757\pi\) | ||||
0.0510058 | + | 0.998698i | \(0.483757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3947 | 0.505192 | ||||||||
\(704\) | −3.10332 | −0.116961 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.2645 | −0.800300 | ||||||||
\(707\) | 8.62877 | 0.324518 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.2828 | −1.13729 | −0.568647 | − | 0.822582i | \(-0.692533\pi\) | ||||
−0.568647 | + | 0.822582i | \(0.692533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35.4059 | 1.32689 | ||||||||
\(713\) | 8.29400 | 0.310613 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.7410 | 0.513525 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −48.1488 | −1.79690 | ||||||||
\(719\) | 20.3313 | 0.758228 | 0.379114 | − | 0.925350i | \(-0.376229\pi\) | ||||
0.379114 | + | 0.925350i | \(0.376229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1193 | 0.451345 | ||||||||
\(722\) | 17.4135 | 0.648064 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.0795 | 0.486097 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6351 | 0.802400 | 0.401200 | − | 0.915991i | \(-0.368593\pi\) | ||||
0.401200 | + | 0.915991i | \(0.368593\pi\) | |||||||
\(728\) | −9.55087 | −0.353979 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.71512 | −0.0634359 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.5223 | 1.57060 | 0.785299 | − | 0.619116i | \(-0.212509\pi\) | ||||
0.785299 | + | 0.619116i | \(0.212509\pi\) | |||||||
\(734\) | −28.0730 | −1.03619 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.5196 | 0.461478 | ||||||||
\(737\) | −9.08308 | −0.334580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.7281 | −0.431425 | −0.215713 | − | 0.976457i | \(-0.569207\pi\) | ||||
−0.215713 | + | 0.976457i | \(0.569207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.8048 | −1.02075 | ||||||||
\(743\) | −27.4555 | −1.00724 | −0.503622 | − | 0.863924i | \(-0.668000\pi\) | ||||
−0.503622 | + | 0.863924i | \(0.668000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.4349 | −0.967849 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.148877 | 0.00544348 | ||||||||
\(749\) | 14.4967 | 0.529697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8528 | −0.943383 | −0.471692 | − | 0.881764i | \(-0.656356\pi\) | ||||
−0.471692 | + | 0.881764i | \(0.656356\pi\) | |||||||
\(752\) | −5.66792 | −0.206688 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.1881 | −1.39073 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.8785 | −1.04961 | −0.524803 | − | 0.851224i | \(-0.675861\pi\) | ||||
−0.524803 | + | 0.851224i | \(0.675861\pi\) | |||||||
\(758\) | −46.5050 | −1.68914 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.6966 | 1.47525 | 0.737626 | − | 0.675210i | \(-0.235947\pi\) | ||||
0.737626 | + | 0.675210i | \(0.235947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.16535 | 0.186998 | ||||||||
\(764\) | −11.1301 | −0.402674 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.9977 | 1.58970 | ||||||||
\(767\) | −37.0567 | −1.33804 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8126 | 0.462033 | 0.231017 | − | 0.972950i | \(-0.425795\pi\) | ||||
0.231017 | + | 0.972950i | \(0.425795\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.3595 | 0.480820 | ||||||||
\(773\) | −29.1725 | −1.04926 | −0.524632 | − | 0.851329i | \(-0.675797\pi\) | ||||
−0.524632 | + | 0.851329i | \(0.675797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.6695 | 0.849685 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.83352 | 0.352549 | ||||||||
\(779\) | −24.3173 | −0.871258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.69561 | 0.132239 | ||||||||
\(782\) | 1.59876 | 0.0571715 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.9961 | 0.857003 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5839 | −0.412921 | −0.206460 | − | 0.978455i | \(-0.566194\pi\) | ||||
−0.206460 | + | 0.978455i | \(0.566194\pi\) | |||||||
\(788\) | −8.14005 | −0.289977 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.8865 | 0.529304 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.63013 | −0.0933985 | ||||||||
\(794\) | −30.0569 | −1.06668 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.9926 | 0.460510 | ||||||||
\(797\) | 38.8479 | 1.37606 | 0.688031 | − | 0.725681i | \(-0.258475\pi\) | ||||
0.688031 | + | 0.725681i | \(0.258475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.327271 | −0.0115780 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.4580 | −1.00489 | ||||||||
\(803\) | −8.63930 | −0.304874 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7913 | −0.415330 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.0367 | −0.458629 | ||||||||
\(809\) | 32.9255 | 1.15760 | 0.578799 | − | 0.815470i | \(-0.303521\pi\) | ||||
0.578799 | + | 0.815470i | \(0.303521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.59127 | −0.196336 | −0.0981680 | − | 0.995170i | \(-0.531298\pi\) | ||||
−0.0981680 | + | 0.995170i | \(0.531298\pi\) | |||||||
\(812\) | −7.39476 | −0.259505 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.03982 | 0.211696 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.5439 | 0.613783 | ||||||||
\(818\) | 35.7333 | 1.24939 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.8837 | 0.484545 | 0.242272 | − | 0.970208i | \(-0.422107\pi\) | ||||
0.242272 | + | 0.970208i | \(0.422107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.1074 | 0.805473 | 0.402736 | − | 0.915316i | \(-0.368059\pi\) | ||||
0.402736 | + | 0.915316i | \(0.368059\pi\) | |||||||
\(824\) | −18.3103 | −0.637868 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.8630 | −1.00427 | ||||||||
\(827\) | 49.3260 | 1.71523 | 0.857616 | − | 0.514290i | \(-0.171944\pi\) | ||||
0.857616 | + | 0.514290i | \(0.171944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.0813 | 1.42681 | 0.713406 | − | 0.700751i | \(-0.247152\pi\) | ||||
0.713406 | + | 0.700751i | \(0.247152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.7788 | 0.408356 | ||||||||
\(833\) | 1.38556 | 0.0480067 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.52286 | −0.0526692 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.5337 | −0.467513 | ||||||||
\(839\) | 6.97734 | 0.240884 | 0.120442 | − | 0.992720i | \(-0.461569\pi\) | ||||
0.120442 | + | 0.992720i | \(0.461569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.7948 | 1.06189 | ||||||||
\(842\) | 18.0776 | 0.622995 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.99978 | 0.172100 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.9772 | 0.514624 | ||||||||
\(848\) | 57.6166 | 1.97856 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.1250 | 0.552759 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0382 | 0.994249 | 0.497125 | − | 0.867679i | \(-0.334389\pi\) | ||||
0.497125 | + | 0.867679i | \(0.334389\pi\) | |||||||
\(854\) | −2.04857 | −0.0701006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.9021 | −0.748600 | ||||||||
\(857\) | 4.63176 | 0.158218 | 0.0791090 | − | 0.996866i | \(-0.474792\pi\) | ||||
0.0791090 | + | 0.996866i | \(0.474792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.8416 | −0.369912 | −0.184956 | − | 0.982747i | \(-0.559214\pi\) | ||||
−0.184956 | + | 0.982747i | \(0.559214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.2465 | −1.40486 | ||||||||
\(863\) | −26.1400 | −0.889815 | −0.444908 | − | 0.895576i | \(-0.646763\pi\) | ||||
−0.444908 | + | 0.895576i | \(0.646763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.86000 | −0.335056 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.28326 | −0.0774990 | ||||||||
\(869\) | 3.77625 | 0.128101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.4752 | 1.16815 | ||||||||
\(872\) | −7.80402 | −0.264277 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.3537 | −0.553172 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.1008 | −1.35411 | −0.677054 | − | 0.735933i | \(-0.736744\pi\) | ||||
−0.677054 | + | 0.735933i | \(0.736744\pi\) | |||||||
\(878\) | 29.4686 | 0.994516 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.4321 | 1.16005 | 0.580023 | − | 0.814600i | \(-0.303044\pi\) | ||||
0.580023 | + | 0.814600i | \(0.303044\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3034 | 1.72650 | 0.863249 | − | 0.504778i | \(-0.168426\pi\) | ||||
0.863249 | + | 0.504778i | \(0.168426\pi\) | |||||||
\(884\) | −0.565069 | −0.0190053 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.9056 | −0.702336 | ||||||||
\(887\) | 11.5446 | 0.387631 | 0.193815 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193815 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.80056 | −0.328700 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.06389 | 0.0356216 | ||||||||
\(893\) | 3.34765 | 0.112025 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.5909 | 0.654486 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −56.9615 | −1.90083 | ||||||||
\(899\) | 18.4627 | 0.615766 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.32684 | 0.110833 | ||||||||
\(902\) | −10.9649 | −0.365092 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.4911 | −0.748044 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.4860 | −0.979067 | −0.489533 | − | 0.871985i | \(-0.662833\pi\) | ||||
−0.489533 | + | 0.871985i | \(0.662833\pi\) | |||||||
\(908\) | 3.66407 | 0.121596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.96402 | 0.230728 | 0.115364 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115364 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2989 | −0.440128 | ||||||||
\(914\) | 32.0869 | 1.06134 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.17658 | 0.270162 | ||||||||
\(917\) | 29.1468 | 0.962511 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0012 | −0.692767 | −0.346384 | − | 0.938093i | \(-0.612590\pi\) | ||||
−0.346384 | + | 0.938093i | \(0.612590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −50.7377 | −1.67096 | ||||||||
\(923\) | −14.0268 | −0.461699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −63.5139 | −2.08720 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 27.8690 | 0.914845 | ||||||||
\(929\) | −9.22471 | −0.302653 | −0.151326 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151326 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1729 | −0.464496 | ||||||||
\(932\) | 4.41077 | 0.144480 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.5671 | −0.607533 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.5933 | −1.16278 | −0.581392 | − | 0.813624i | \(-0.697492\pi\) | ||||
−0.581392 | + | 0.813624i | \(0.697492\pi\) | |||||||
\(938\) | 26.8523 | 0.876758 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.0875 | −1.73060 | −0.865302 | − | 0.501250i | \(-0.832874\pi\) | ||||
−0.865302 | + | 0.501250i | \(0.832874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.2740 | −0.953294 | ||||||||
\(944\) | 59.8094 | 1.94663 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.91072 | 0.257200 | ||||||||
\(947\) | −20.8873 | −0.678746 | −0.339373 | − | 0.940652i | \(-0.610215\pi\) | ||||
−0.339373 | + | 0.940652i | \(0.610215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7908 | 1.06443 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.890081 | 0.0288477 | ||||||||
\(953\) | −35.0040 | −1.13389 | −0.566945 | − | 0.823755i | \(-0.691875\pi\) | ||||
−0.566945 | + | 0.823755i | \(0.691875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.78150 | 0.122303 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.2815 | 1.30144 | ||||||||
\(959\) | −16.2667 | −0.525278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.2993 | −0.816107 | ||||||||
\(962\) | −22.9244 | −0.739112 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.9715 | −0.449993 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.32372 | −0.267673 | −0.133836 | − | 0.991003i | \(-0.542730\pi\) | ||||
−0.133836 | + | 0.991003i | \(0.542730\pi\) | |||||||
\(968\) | −22.6282 | −0.727297 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0277 | 0.418080 | 0.209040 | − | 0.977907i | \(-0.432966\pi\) | ||||
0.209040 | + | 0.977907i | \(0.432966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1713 | 0.358136 | ||||||||
\(974\) | 6.25497 | 0.200422 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.24501 | 0.135879 | ||||||||
\(977\) | −48.0089 | −1.53594 | −0.767970 | − | 0.640486i | \(-0.778733\pi\) | ||||
−0.767970 | + | 0.640486i | \(0.778733\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9328 | −0.413334 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.3630 | 0.394520 | ||||||||
\(983\) | 30.3257 | 0.967240 | 0.483620 | − | 0.875278i | \(-0.339322\pi\) | ||||
0.483620 | + | 0.875278i | \(0.339322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.55889 | 0.113338 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.78008 | 0.183889 | ||||||||
\(989\) | 21.1200 | 0.671576 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8408 | 0.344368 | 0.172184 | − | 0.985065i | \(-0.444918\pi\) | ||||
0.172184 | + | 0.985065i | \(0.444918\pi\) | |||||||
\(992\) | 8.60505 | 0.273211 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.9253 | −0.346530 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.33544 | 0.0422939 | 0.0211470 | − | 0.999776i | \(-0.493268\pi\) | ||||
0.0211470 | + | 0.999776i | \(0.493268\pi\) | |||||||
\(998\) | −37.4514 | −1.18550 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.ba.1.3 | yes | 8 | |
3.2 | odd | 2 | inner | 5625.2.a.ba.1.6 | yes | 8 | |
5.4 | even | 2 | 5625.2.a.y.1.6 | yes | 8 | ||
15.14 | odd | 2 | 5625.2.a.y.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5625.2.a.y.1.3 | ✓ | 8 | 15.14 | odd | 2 | ||
5625.2.a.y.1.6 | yes | 8 | 5.4 | even | 2 | ||
5625.2.a.ba.1.3 | yes | 8 | 1.1 | even | 1 | trivial | |
5625.2.a.ba.1.6 | yes | 8 | 3.2 | odd | 2 | inner |