Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1536) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.02734 | 1.80108 | 0.900540 | − | 0.434772i | \(-0.143171\pi\) | ||||
0.900540 | + | 0.434772i | \(0.143171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.61313 | 1.74360 | 0.871799 | − | 0.489864i | \(-0.162954\pi\) | ||||
0.871799 | + | 0.489864i | \(0.162954\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53073 | 0.461534 | 0.230767 | − | 0.973009i | \(-0.425877\pi\) | ||||
0.230767 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.57900 | −1.54734 | −0.773668 | − | 0.633591i | \(-0.781580\pi\) | ||||
−0.773668 | + | 0.633591i | \(0.781580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.02734 | −1.03985 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.29769 | −0.314737 | −0.157368 | − | 0.987540i | \(-0.550301\pi\) | ||||
−0.157368 | + | 0.987540i | \(0.550301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35916 | 1.00006 | 0.500030 | − | 0.866008i | \(-0.333322\pi\) | ||||
0.500030 | + | 0.866008i | \(0.333322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.61313 | −1.00667 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.2195 | 2.24389 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.86256 | −0.345868 | −0.172934 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172934 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.77791 | −0.498927 | −0.249464 | − | 0.968384i | \(-0.580254\pi\) | ||||
−0.249464 | + | 0.968384i | \(0.580254\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.53073 | −0.266467 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.5786 | 3.14036 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.97682 | 0.653786 | 0.326893 | − | 0.945061i | \(-0.393998\pi\) | ||||
0.326893 | + | 0.945061i | \(0.393998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.57900 | 0.893355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.03188 | −0.473499 | −0.236750 | − | 0.971571i | \(-0.576082\pi\) | ||||
−0.236750 | + | 0.971571i | \(0.576082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03188 | 0.462357 | 0.231178 | − | 0.972911i | \(-0.425742\pi\) | ||||
0.231178 | + | 0.972911i | \(0.425742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.02734 | 0.600360 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.65685 | 1.40860 | 0.704298 | − | 0.709904i | \(-0.251262\pi\) | ||||
0.704298 | + | 0.709904i | \(0.251262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.2809 | 2.04013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.29769 | 0.181713 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.58995 | −1.17992 | −0.589960 | − | 0.807432i | \(-0.700857\pi\) | ||||
−0.589960 | + | 0.807432i | \(0.700857\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.16478 | 0.831259 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.35916 | −0.577385 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.73418 | 0.746527 | 0.373263 | − | 0.927725i | \(-0.378239\pi\) | ||||
0.373263 | + | 0.927725i | \(0.378239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.64725 | −0.979131 | −0.489565 | − | 0.871967i | \(-0.662845\pi\) | ||||
−0.489565 | + | 0.871967i | \(0.662845\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.61313 | 0.581199 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.4685 | −2.78688 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.79565 | −1.07456 | −0.537280 | − | 0.843404i | \(-0.680548\pi\) | ||||
−0.537280 | + | 0.843404i | \(0.680548\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.88311 | −0.816874 | −0.408437 | − | 0.912786i | \(-0.633926\pi\) | ||||
−0.408437 | + | 0.912786i | \(0.633926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50114 | −0.409778 | −0.204889 | − | 0.978785i | \(-0.565683\pi\) | ||||
−0.204889 | + | 0.978785i | \(0.565683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.2195 | −1.29551 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.06147 | 0.804729 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.18252 | 0.920606 | 0.460303 | − | 0.887762i | \(-0.347741\pi\) | ||||
0.460303 | + | 0.887762i | \(0.347741\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.12612 | 0.452901 | 0.226450 | − | 0.974023i | \(-0.427288\pi\) | ||||
0.226450 | + | 0.974023i | \(0.427288\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.22625 | −0.566867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.86256 | 0.199687 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.98642 | 0.846559 | 0.423280 | − | 0.905999i | \(-0.360879\pi\) | ||||
0.423280 | + | 0.905999i | \(0.360879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.7366 | −2.69793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.77791 | 0.288056 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.5558 | 1.80119 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.40461 | −0.142617 | −0.0713084 | − | 0.997454i | \(-0.522717\pi\) | ||||
−0.0713084 | + | 0.997454i | \(0.522717\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.53073 | 0.153845 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.457942 | −0.0455669 | −0.0227835 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227835 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.77563 | 0.766155 | 0.383078 | − | 0.923716i | \(-0.374864\pi\) | ||||
0.383078 | + | 0.923716i | \(0.374864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.5786 | −1.81309 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7047 | −1.42156 | −0.710781 | − | 0.703414i | \(-0.751658\pi\) | ||||
−0.710781 | + | 0.703414i | \(0.751658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.09372 | −0.104759 | −0.0523795 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523795 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.97682 | −0.377463 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.1094 | 1.50221 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.57900 | −0.515779 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.98642 | −0.548775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.65685 | −0.786987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.03188 | 0.273375 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.0479 | 2.24035 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.900845 | −0.0799371 | −0.0399685 | − | 0.999201i | \(-0.512726\pi\) | ||||
−0.0399685 | + | 0.999201i | \(0.512726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.03188 | −0.266942 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.7206 | −1.37352 | −0.686758 | − | 0.726886i | \(-0.740967\pi\) | ||||
−0.686758 | + | 0.726886i | \(0.740967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.1094 | 1.74370 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.02734 | −0.346618 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.76377 | −0.150689 | −0.0753447 | − | 0.997158i | \(-0.524006\pi\) | ||||
−0.0753447 | + | 0.997158i | \(0.524006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.3752 | −1.55856 | −0.779281 | − | 0.626675i | \(-0.784416\pi\) | ||||
−0.779281 | + | 0.626675i | \(0.784416\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.65685 | −0.813254 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.53996 | −0.714147 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.50114 | −0.622936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2809 | −1.17787 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.68419 | −0.137975 | −0.0689873 | − | 0.997618i | \(-0.521977\pi\) | ||||
−0.0689873 | + | 0.997618i | \(0.521977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3118 | 0.839165 | 0.419582 | − | 0.907717i | \(-0.362177\pi\) | ||||
0.419582 | + | 0.907717i | \(0.362177\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.29769 | −0.104912 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.1876 | −0.898609 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6337 | −1.08809 | −0.544043 | − | 0.839057i | \(-0.683107\pi\) | ||||
−0.544043 | + | 0.839057i | \(0.683107\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.58995 | 0.681227 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.4525 | 1.45426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.17476 | 0.248666 | 0.124333 | − | 0.992241i | \(-0.460321\pi\) | ||||
0.124333 | + | 0.992241i | \(0.460321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.16478 | −0.479928 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.4170 | 1.42515 | 0.712576 | − | 0.701595i | \(-0.247528\pi\) | ||||
0.712576 | + | 0.701595i | \(0.247528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.1252 | 1.39425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.35916 | 0.333353 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0341 | 0.838909 | 0.419455 | − | 0.907776i | \(-0.362221\pi\) | ||||
0.419455 | + | 0.907776i | \(0.362221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.7568 | 3.91245 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.73418 | −0.431008 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.795649 | −0.0594696 | −0.0297348 | − | 0.999558i | \(-0.509466\pi\) | ||||
−0.0297348 | + | 0.999558i | \(0.509466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.24943 | −0.390187 | −0.195093 | − | 0.980785i | \(-0.562501\pi\) | ||||
−0.195093 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.64725 | 0.565301 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.0160 | 1.17752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.98642 | −0.145262 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.61313 | −0.335556 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.0060 | 1.80937 | 0.904687 | − | 0.426077i | \(-0.140105\pi\) | ||||
0.904687 | + | 0.426077i | \(0.140105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9378 | 1.65110 | 0.825549 | − | 0.564331i | \(-0.190866\pi\) | ||||
0.825549 | + | 0.564331i | \(0.190866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.4685 | 1.60900 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0533 | 1.07251 | 0.536253 | − | 0.844058i | \(-0.319839\pi\) | ||||
0.536253 | + | 0.844058i | \(0.319839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.7485 | −1.39993 | −0.699966 | − | 0.714176i | \(-0.746802\pi\) | ||||
−0.699966 | + | 0.714176i | \(0.746802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.79565 | 0.620397 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.59220 | −0.603054 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.2104 | −0.852811 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.67271 | 0.461561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.938533 | −0.0646112 | −0.0323056 | − | 0.999478i | \(-0.510285\pi\) | ||||
−0.0323056 | + | 0.999478i | \(0.510285\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.88311 | 0.471623 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.2104 | 0.832742 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.8149 | −0.869929 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.50114 | 0.236585 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.23983 | 0.487004 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.2783 | −1.75973 | −0.879863 | − | 0.475228i | \(-0.842366\pi\) | ||||
−0.879863 | + | 0.475228i | \(0.842366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2195 | 0.747964 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9082 | 0.724002 | 0.362001 | − | 0.932178i | \(-0.382094\pi\) | ||||
0.362001 | + | 0.932178i | \(0.382094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8599 | −1.24630 | −0.623150 | − | 0.782103i | \(-0.714147\pi\) | ||||
−0.623150 | + | 0.782103i | \(0.714147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.06147 | −0.464610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7662 | 1.29493 | 0.647464 | − | 0.762096i | \(-0.275830\pi\) | ||||
0.647464 | + | 0.762096i | \(0.275830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.8914 | 2.53700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.18252 | −0.531512 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.3515 | −0.928319 | −0.464160 | − | 0.885752i | \(-0.653644\pi\) | ||||
−0.464160 | + | 0.885752i | \(0.653644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7534 | 1.40126 | 0.700629 | − | 0.713525i | \(-0.252903\pi\) | ||||
0.700629 | + | 0.713525i | \(0.252903\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 57.5142 | 3.67444 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.3197 | −1.54743 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.12612 | −0.261482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.53073 | −0.601575 | −0.300787 | − | 0.953691i | \(-0.597249\pi\) | ||||
−0.300787 | + | 0.953691i | \(0.597249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.12293 | 0.384946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.22625 | 0.327281 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.20435 | −0.0751253 | −0.0375627 | − | 0.999294i | \(-0.511959\pi\) | ||||
−0.0375627 | + | 0.999294i | \(0.511959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3456 | 1.13994 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.86256 | −0.115289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.5777 | 1.70052 | 0.850258 | − | 0.526367i | \(-0.176446\pi\) | ||||
0.850258 | + | 0.526367i | \(0.176446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.5946 | −2.12513 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.98642 | −0.488761 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.6646 | 0.894115 | 0.447057 | − | 0.894505i | \(-0.352472\pi\) | ||||
0.447057 | + | 0.894505i | \(0.352472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3574 | −1.23663 | −0.618313 | − | 0.785932i | \(-0.712184\pi\) | ||||
−0.618313 | + | 0.785932i | \(0.712184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.7366 | 1.55765 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.1740 | 1.03563 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.8113 | 1.43068 | 0.715341 | − | 0.698776i | \(-0.246271\pi\) | ||||
0.715341 | + | 0.698776i | \(0.246271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.77791 | −0.166309 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.1116 | −1.02079 | −0.510397 | − | 0.859939i | \(-0.670502\pi\) | ||||
−0.510397 | + | 0.859939i | \(0.670502\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.26582 | 0.134689 | 0.0673444 | − | 0.997730i | \(-0.478547\pi\) | ||||
0.0673444 | + | 0.997730i | \(0.478547\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.5558 | −1.03992 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.9864 | −0.825592 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3160 | −0.900941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.40461 | 0.0823399 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.90366 | −0.228054 | −0.114027 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114027 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.0935 | 1.34456 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.53073 | −0.0888222 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.3160 | −1.29057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.9864 | 0.806164 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.457942 | 0.0263081 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.7981 | −1.76349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2323 | 1.49716 | 0.748578 | − | 0.663047i | \(-0.230737\pi\) | ||||
0.748578 | + | 0.663047i | \(0.230737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.77563 | −0.442340 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.12522 | 0.517444 | 0.258722 | − | 0.965952i | \(-0.416699\pi\) | ||||
0.258722 | + | 0.965952i | \(0.416699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.28093 | −0.524589 | −0.262295 | − | 0.964988i | \(-0.584479\pi\) | ||||
−0.262295 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.5786 | 1.04679 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.3652 | −1.81781 | −0.908906 | − | 0.417000i | \(-0.863081\pi\) | ||||
−0.908906 | + | 0.417000i | \(0.863081\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.85108 | −0.159630 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.7047 | 0.820739 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.65685 | −0.314756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −62.5934 | −3.47206 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.09372 | 0.0604827 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.5483 | 2.45603 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8435 | 1.20063 | 0.600315 | − | 0.799764i | \(-0.295042\pi\) | ||||
0.600315 | + | 0.799764i | \(0.295042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.97682 | 0.217929 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −35.4231 | −1.93537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.8722 | −1.57277 | −0.786385 | − | 0.617736i | \(-0.788050\pi\) | ||||
−0.786385 | + | 0.617736i | \(0.788050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.65685 | 0.415863 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.25224 | −0.230272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 33.5879 | 1.81357 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.1094 | −0.867299 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.9697 | 1.17939 | 0.589697 | − | 0.807625i | \(-0.299247\pi\) | ||||
0.589697 | + | 0.807625i | \(0.299247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0862 | 1.07519 | 0.537594 | − | 0.843204i | \(-0.319333\pi\) | ||||
0.537594 | + | 0.843204i | \(0.319333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.57900 | 0.297785 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.9570 | −1.96702 | −0.983511 | − | 0.180849i | \(-0.942116\pi\) | ||||
−0.983511 | + | 0.180849i | \(0.942116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.7206 | −1.47126 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.98642 | 0.316835 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.5264 | 1.18890 | 0.594449 | − | 0.804134i | \(-0.297370\pi\) | ||||
0.594449 | + | 0.804134i | \(0.297370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.00228335 | 0.000120176 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.65685 | 0.454367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.1003 | −0.738043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.535798 | 0.0279684 | 0.0139842 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139842 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.03188 | −0.157833 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −39.6265 | −2.05731 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.83803 | −0.457616 | −0.228808 | − | 0.973472i | \(-0.573483\pi\) | ||||
−0.228808 | + | 0.973472i | \(0.573483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.0479 | −1.29347 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3912 | 0.535174 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.6887 | −1.26817 | −0.634087 | − | 0.773261i | \(-0.718624\pi\) | ||||
−0.634087 | + | 0.773261i | \(0.718624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.900845 | 0.0461517 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.1290 | −1.59062 | −0.795308 | − | 0.606205i | \(-0.792691\pi\) | ||||
−0.795308 | + | 0.606205i | \(0.792691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.4389 | 1.44938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.03188 | 0.154119 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.3614 | 1.03236 | 0.516182 | − | 0.856479i | \(-0.327353\pi\) | ||||
0.516182 | + | 0.856479i | \(0.327353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.19077 | −0.262509 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.7206 | 0.793000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.9538 | 1.65809 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.60090 | 0.180724 | 0.0903620 | − | 0.995909i | \(-0.471198\pi\) | ||||
0.0903620 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.1094 | −1.00673 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0160 | −0.899677 | −0.449838 | − | 0.893110i | \(-0.648518\pi\) | ||||
−0.449838 | + | 0.893110i | \(0.648518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4980 | 0.772008 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.02734 | 0.200120 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.08746 | 0.301744 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.1572 | −1.24395 | −0.621973 | − | 0.783039i | \(-0.713669\pi\) | ||||
−0.621973 | + | 0.783039i | \(0.713669\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.76377 | 0.0870006 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.4525 | 1.30164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6173 | 0.815711 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.3752 | 0.899836 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.52845 | 0.318936 | 0.159468 | − | 0.987203i | \(-0.449022\pi\) | ||||
0.159468 | + | 0.987203i | \(0.449022\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8758 | −0.968687 | −0.484343 | − | 0.874878i | \(-0.660941\pi\) | ||||
−0.484343 | + | 0.874878i | \(0.660941\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.65685 | 0.469532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.5594 | −0.706236 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.2777 | −1.70721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.53996 | 0.412313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.7368 | 1.67321 | 0.836606 | − | 0.547805i | \(-0.184537\pi\) | ||||
0.836606 | + | 0.547805i | \(0.184537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.0935 | −1.30203 | −0.651015 | − | 0.759065i | \(-0.725657\pi\) | ||||
−0.651015 | + | 0.759065i | \(0.725657\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.50114 | 0.359652 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.4366 | 0.834108 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.52976 | −0.168466 | −0.0842331 | − | 0.996446i | \(-0.526844\pi\) | ||||
−0.0842331 | + | 0.996446i | \(0.526844\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.2809 | 0.680044 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.71742 | −0.271643 | −0.135821 | − | 0.990733i | \(-0.543367\pi\) | ||||
−0.135821 | + | 0.990733i | \(0.543367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.1640 | 1.52472 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.68419 | 0.0796596 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9346 | 1.36551 | 0.682754 | − | 0.730648i | \(-0.260782\pi\) | ||||
0.682754 | + | 0.730648i | \(0.260782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.64099 | −0.218536 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.3118 | −0.484492 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −103.650 | −4.85919 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.6233 | −1.57283 | −0.786416 | − | 0.617697i | \(-0.788066\pi\) | ||||
−0.786416 | + | 0.617697i | \(0.788066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.29769 | 0.0605711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.27730 | 0.245788 | 0.122894 | − | 0.992420i | \(-0.460782\pi\) | ||||
0.122894 | + | 0.992420i | \(0.460782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1430 | 0.517857 | 0.258929 | − | 0.965896i | \(-0.416631\pi\) | ||||
0.258929 | + | 0.965896i | \(0.416631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.1876 | 0.518812 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.5013 | −1.22633 | −0.613167 | − | 0.789953i | \(-0.710105\pi\) | ||||
−0.613167 | + | 0.789953i | \(0.710105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.5754 | −1.87360 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.6337 | 0.628207 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.64099 | 0.213393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.9074 | 2.24403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.58995 | −0.393307 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.4170 | −1.02426 | −0.512130 | − | 0.858908i | \(-0.671143\pi\) | ||||
−0.512130 | + | 0.858908i | \(0.671143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1867 | −1.01163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.4525 | −0.839618 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.65685 | −0.256865 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.42235 | −0.336339 | −0.168169 | − | 0.985758i | \(-0.553786\pi\) | ||||
−0.168169 | + | 0.985758i | \(0.553786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.17476 | −0.143568 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3711 | −0.783946 | −0.391973 | − | 0.919977i | \(-0.628207\pi\) | ||||
−0.391973 | + | 0.919977i | \(0.628207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.41703 | 0.108857 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.16478 | 0.277086 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.7526 | −1.42430 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.2938 | −1.66950 | −0.834749 | − | 0.550631i | \(-0.814387\pi\) | ||||
−0.834749 | + | 0.550631i | \(0.814387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.4170 | −0.822812 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8672 | −0.618310 | −0.309155 | − | 0.951012i | \(-0.600046\pi\) | ||||
−0.309155 | + | 0.951012i | \(0.600046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.84429 | −0.0820697 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.1252 | −0.804969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.6311 | 1.53499 | 0.767497 | − | 0.641052i | \(-0.221502\pi\) | ||||
0.767497 | + | 0.641052i | \(0.221502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1512 | −0.714487 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.35916 | −0.192462 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.3151 | 1.37991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7821 | 0.650115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.0341 | −0.484344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.8437 | 1.52653 | 0.763265 | − | 0.646086i | \(-0.223595\pi\) | ||||
0.763265 | + | 0.646086i | \(0.223595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5499 | 1.11722 | 0.558610 | − | 0.829430i | \(-0.311335\pi\) | ||||
0.558610 | + | 0.829430i | \(0.311335\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −51.7568 | −2.25885 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.60488 | 0.157031 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.73418 | 0.248842 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.9148 | 0.732662 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −59.2210 | −2.56035 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.795649 | 0.0343348 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.8603 | 0.941590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.8735 | −1.41334 | −0.706671 | − | 0.707542i | \(-0.749804\pi\) | ||||
−0.706671 | + | 0.707542i | \(0.749804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24943 | 0.225275 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.40477 | −0.188680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.4414 | −1.38709 | −0.693546 | − | 0.720412i | \(-0.743953\pi\) | ||||
−0.693546 | + | 0.720412i | \(0.743953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.64725 | −0.326377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.11918 | −0.345889 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.7470 | 1.60517 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.0160 | −0.679842 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.25025 | 0.0953462 | 0.0476731 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476731 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.9148 | −0.715421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.98642 | 0.0838668 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.37608 | −0.0579948 | −0.0289974 | − | 0.999579i | \(-0.509231\pi\) | ||||
−0.0289974 | + | 0.999579i | \(0.509231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.8368 | −1.29731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.61313 | 0.193733 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5043 | 0.649975 | 0.324988 | − | 0.945718i | \(-0.394640\pi\) | ||||
0.324988 | + | 0.945718i | \(0.394640\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.45659 | 0.312049 | 0.156024 | − | 0.987753i | \(-0.450132\pi\) | ||||
0.156024 | + | 0.987753i | \(0.450132\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0060 | −1.04464 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.8779 | 1.87154 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9355 | −1.07971 | −0.539855 | − | 0.841758i | \(-0.681521\pi\) | ||||
−0.539855 | + | 0.841758i | \(0.681521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.9378 | −0.953262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.0343 | 0.789676 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1489 | −0.544573 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.4685 | −0.928959 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.6233 | 1.38778 | 0.693892 | − | 0.720079i | \(-0.255895\pi\) | ||||
0.693892 | + | 0.720079i | \(0.255895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.1094 | −0.498957 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.0533 | −0.619211 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.0302 | 1.80810 | 0.904052 | − | 0.427422i | \(-0.140578\pi\) | ||||
0.904052 | + | 0.427422i | \(0.140578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.1094 | −0.988387 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.7485 | 0.808251 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.09578 | 0.249067 | 0.124533 | − | 0.992215i | \(-0.460257\pi\) | ||||
0.124533 | + | 0.992215i | \(0.460257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8126 | −0.481845 | −0.240922 | − | 0.970544i | \(-0.577450\pi\) | ||||
−0.240922 | + | 0.970544i | \(0.577450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.79565 | −0.358187 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −34.8641 | −1.41743 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.66330 | 0.189277 | 0.0946387 | − | 0.995512i | \(-0.469830\pi\) | ||||
0.0946387 | + | 0.995512i | \(0.469830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.59220 | 0.348174 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.8756 | −2.17957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.5715 | 1.15399 | 0.576995 | − | 0.816748i | \(-0.304225\pi\) | ||||
0.576995 | + | 0.816748i | \(0.304225\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.2104 | 0.492371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2482 | −0.855418 | −0.427709 | − | 0.903916i | \(-0.640679\pi\) | ||||
−0.427709 | + | 0.903916i | \(0.640679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4412 | −0.459861 | −0.229931 | − | 0.973207i | \(-0.573850\pi\) | ||||
−0.229931 | + | 0.973207i | \(0.573850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.8424 | 1.47606 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.7790 | 1.79116 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.67271 | −0.266483 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.16070 | −0.205770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.9427 | −0.674478 | −0.337239 | − | 0.941419i | \(-0.609493\pi\) | ||||
−0.337239 | + | 0.941419i | \(0.609493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.938533 | 0.0373033 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.62801 | −0.143973 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −79.6733 | −3.15677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.88311 | −0.272291 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.8596 | −1.10039 | −0.550193 | − | 0.835037i | \(-0.685446\pi\) | ||||
−0.550193 | + | 0.835037i | \(0.685446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.6114 | −0.812834 | −0.406417 | − | 0.913688i | \(-0.633222\pi\) | ||||
−0.406417 | + | 0.913688i | \(0.633222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.2104 | −0.480784 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.7142 | 0.460534 | 0.230267 | − | 0.973127i | \(-0.426040\pi\) | ||||
0.230267 | + | 0.973127i | \(0.426040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.77751 | 0.344547 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8149 | 0.502254 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 51.0435 | 1.99749 | 0.998743 | − | 0.0501153i | \(-0.0159589\pi\) | ||||
0.998743 | + | 0.0501153i | \(0.0159589\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −63.3122 | −2.47381 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.50114 | −0.136593 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.68401 | 0.221418 | 0.110709 | − | 0.993853i | \(-0.464688\pi\) | ||||
0.110709 | + | 0.993853i | \(0.464688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.2611 | 1.41039 | 0.705197 | − | 0.709012i | \(-0.250859\pi\) | ||||
0.705197 | + | 0.709012i | \(0.250859\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.23983 | −0.281172 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 80.9872 | 3.14055 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.45022 | −0.288474 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.2783 | 1.01598 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7059 | −0.451902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6569 | 0.680622 | 0.340311 | − | 0.940313i | \(-0.389468\pi\) | ||||
0.340311 | + | 0.940313i | \(0.389468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.2195 | −0.431837 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0866 | 0.695124 | 0.347562 | − | 0.937657i | \(-0.387010\pi\) | ||||
0.347562 | + | 0.937657i | \(0.387010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.47966 | −0.248666 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.9082 | −0.418003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.3448 | 0.778474 | 0.389237 | − | 0.921138i | \(-0.372739\pi\) | ||||
0.389237 | + | 0.921138i | \(0.372739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.10332 | −0.271404 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.8599 | 0.719551 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47.9233 | 1.82573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.1118 | −0.765089 | −0.382544 | − | 0.923937i | \(-0.624952\pi\) | ||||
−0.382544 | + | 0.923937i | \(0.624952\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.06147 | 0.268243 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −74.0031 | −2.80710 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.93444 | 0.149028 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.7662 | −0.747627 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9263 | 0.752606 | 0.376303 | − | 0.926497i | \(-0.377195\pi\) | ||||
0.376303 | + | 0.926497i | \(0.377195\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3356 | 0.653825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.8914 | −1.46474 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.11254 | −0.0794504 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.30141 | −0.123987 | −0.0619935 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619935 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.18252 | 0.306869 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.1116 | −0.416134 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.3933 | −1.28624 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.3515 | 0.535965 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.2104 | −1.49959 | −0.749797 | − | 0.661668i | \(-0.769849\pi\) | ||||
−0.749797 | + | 0.661668i | \(0.769849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.8699 | 1.33587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.7534 | −0.809017 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.8969 | −0.776090 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4272 | 1.46227 | 0.731137 | − | 0.682230i | \(-0.238990\pi\) | ||||
0.731137 | + | 0.682230i | \(0.238990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.93444 | −0.145521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7370 | 0.765938 | 0.382969 | − | 0.923761i | \(-0.374902\pi\) | ||||
0.382969 | + | 0.923761i | \(0.374902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −57.5142 | −2.12144 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4638 | −0.495945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.9529 | 0.513266 | 0.256633 | − | 0.966509i | \(-0.417387\pi\) | ||||
0.256633 | + | 0.966509i | \(0.417387\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.3197 | 0.893408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.02418 | −0.184319 | −0.0921597 | − | 0.995744i | \(-0.529377\pi\) | ||||
−0.0921597 | + | 0.995744i | \(0.529377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.78282 | −0.248503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.12612 | 0.150967 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.8348 | −2.47863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.44425 | −0.198664 | −0.0993318 | − | 0.995054i | \(-0.531671\pi\) | ||||
−0.0993318 | + | 0.995054i | \(0.531671\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.53073 | 0.347319 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.5292 | 1.51140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.7698 | −0.536816 | −0.268408 | − | 0.963305i | \(-0.586498\pi\) | ||||
−0.268408 | + | 0.963305i | \(0.586498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.12293 | −0.222248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.96584 | −0.0712617 | −0.0356308 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356308 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.04545 | −0.182658 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.22625 | −0.188956 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.9910 | −1.15513 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.09244 | −0.255760 | −0.127880 | − | 0.991790i | \(-0.540817\pi\) | ||||
−0.127880 | + | 0.991790i | \(0.540817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.20435 | 0.0433736 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.5696 | −0.991609 | −0.495804 | − | 0.868434i | \(-0.665127\pi\) | ||||
−0.495804 | + | 0.868434i | \(0.665127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.1667 | −1.11954 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.3456 | −0.658144 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.2164 | −0.473528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5362 | −0.377015 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.86256 | 0.0665623 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.9074 | −1.95973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.6529 | −1.05701 | −0.528506 | − | 0.848929i | \(-0.677248\pi\) | ||||
−0.528506 | + | 0.848929i | \(0.677248\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.5777 | −0.981793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.3220 | −1.25591 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.6640 | 1.51504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.5946 | 1.22695 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.43832 | 0.192635 | 0.0963177 | − | 0.995351i | \(-0.469294\pi\) | ||||
0.0963177 | + | 0.995351i | \(0.469294\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5316 | −0.443337 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.98642 | 0.282186 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.35932 | −0.189126 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 74.3145 | 2.61924 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.6646 | −0.516218 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.1548 | 0.603131 | 0.301566 | − | 0.953445i | \(-0.402491\pi\) | ||||
0.301566 | + | 0.953445i | \(0.402491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.46624 | 0.332404 | 0.166202 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166202 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.3574 | 0.713966 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7858 | 0.447868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2164 | 0.462384 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.7366 | −0.899310 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1198 | −0.667285 | −0.333642 | − | 0.942700i | \(-0.608278\pi\) | ||||
−0.333642 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5257 | 0.366902 | 0.183451 | − | 0.983029i | \(-0.441273\pi\) | ||||
0.183451 | + | 0.983029i | \(0.441273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.1740 | −0.597922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.9841 | 0.938330 | 0.469165 | − | 0.883110i | \(-0.344555\pi\) | ||||
0.469165 | + | 0.883110i | \(0.344555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.4704 | 0.433116 | 0.216558 | − | 0.976270i | \(-0.430517\pi\) | ||||
0.216558 | + | 0.976270i | \(0.430517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.8113 | −0.826005 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.5323 | −0.642105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.1716 | 2.56681 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.77791 | 0.0960186 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.4631 | 1.01718 | 0.508590 | − | 0.861009i | \(-0.330167\pi\) | ||||
0.508590 | + | 0.861009i | \(0.330167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5309 | −0.880375 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.1116 | 0.589356 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.9964 | 2.51115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.9352 | −1.37219 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.26582 | −0.0777627 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.9073 | 0.545295 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.1955 | −0.554525 | −0.277262 | − | 0.960794i | \(-0.589427\pi\) | ||||
−0.277262 | + | 0.960794i | \(0.589427\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.5558 | 0.600396 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.3592 | −0.968730 | −0.484365 | − | 0.874866i | \(-0.660949\pi\) | ||||
−0.484365 | + | 0.874866i | \(0.660949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.51562 | −0.0858319 | −0.0429159 | − | 0.999079i | \(-0.513665\pi\) | ||||
−0.0429159 | + | 0.999079i | \(0.513665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.9864 | 0.476656 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.8944 | 0.472971 | 0.236485 | − | 0.971635i | \(-0.424004\pi\) | ||||
0.236485 | + | 0.971635i | \(0.424004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.4382 | 1.51094 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3160 | 0.520158 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5253 | 0.424891 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.0709 | 1.66270 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.40461 | −0.0475390 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 115.549 | 3.90627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7216 | 0.902323 | 0.451161 | − | 0.892442i | \(-0.351010\pi\) | ||||
0.451161 | + | 0.892442i | \(0.351010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.90366 | 0.131667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5460 | 0.388995 | 0.194497 | − | 0.980903i | \(-0.437692\pi\) | ||||
0.194497 | + | 0.980903i | \(0.437692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.1868 | −1.78988 | −0.894940 | − | 0.446187i | \(-0.852782\pi\) | ||||
−0.894940 | + | 0.446187i | \(0.852782\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.0935 | −0.776279 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.8123 | 1.50465 | 0.752325 | − | 0.658792i | \(-0.228932\pi\) | ||||
0.752325 | + | 0.658792i | \(0.228932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.15571 | −0.139378 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.53073 | 0.0512815 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0958 | 1.40868 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.20435 | −0.107110 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.3160 | 0.745109 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.17401 | 0.172563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.1471 | 0.371364 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.9864 | −0.465439 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.1412 | −0.702758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.3297 | 0.973877 | 0.486939 | − | 0.873436i | \(-0.338113\pi\) | ||||
0.486939 | + | 0.873436i | \(0.338113\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.457942 | −0.0151890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.91483 | 0.162835 | 0.0814177 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814177 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.31599 | 0.209029 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.7981 | 1.01815 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −72.5211 | −2.39486 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9465 | 0.624986 | 0.312493 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312493 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.2323 | −0.864383 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.4008 | 1.26398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.6178 | 1.46702 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.77563 | 0.255385 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.40296 | −0.275692 | −0.137846 | − | 0.990454i | \(-0.544018\pi\) | ||||
−0.137846 | + | 0.990454i | \(0.544018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 62.2529 | 2.04026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.12522 | −0.298746 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.8100 | −1.43121 | −0.715605 | − | 0.698505i | \(-0.753849\pi\) | ||||
−0.715605 | + | 0.698505i | \(0.753849\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.28093 | 0.302872 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5363 | −0.539069 | −0.269534 | − | 0.962991i | \(-0.586870\pi\) | ||||
−0.269534 | + | 0.962991i | \(0.586870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.1275 | −0.394926 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.5786 | −0.604363 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7639 | 1.51962 | 0.759812 | − | 0.650143i | \(-0.225291\pi\) | ||||
0.759812 | + | 0.650143i | \(0.225291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5329 | 0.634064 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.3652 | 1.04951 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.4436 | −1.40728 | −0.703639 | − | 0.710558i | \(-0.748443\pi\) | ||||
−0.703639 | + | 0.710558i | \(0.748443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 100.708 | 3.25883 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.85108 | 0.0921622 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.13651 | −0.262742 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2832 | −0.751071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7047 | −0.473854 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 92.3782 | 2.97376 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.3718 | −1.33043 | −0.665214 | − | 0.746653i | \(-0.731660\pi\) | ||||
−0.665214 | + | 0.746653i | \(0.731660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.65685 | 0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.1541 | −1.76998 | −0.884989 | − | 0.465612i | \(-0.845834\pi\) | ||||
−0.884989 | + | 0.465612i | \(0.845834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −84.7670 | −2.71751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 62.5934 | 2.00459 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.9120 | −1.50085 | −0.750424 | − | 0.660957i | \(-0.770151\pi\) | ||||
−0.750424 | + | 0.660957i | \(0.770151\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.2251 | 0.390715 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.09372 | −0.0349197 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.71195 | −0.150288 | −0.0751439 | − | 0.997173i | \(-0.523942\pi\) | ||||
−0.0751439 | + | 0.997173i | \(0.523942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60.6249 | 1.93167 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.5483 | −1.41799 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1275 | 0.385632 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3733 | −0.424817 | −0.212408 | − | 0.977181i | \(-0.568131\pi\) | ||||
−0.212408 | + | 0.977181i | \(0.568131\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.8435 | −0.693184 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −79.5338 | −2.52139 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8445 | −0.786833 | −0.393416 | − | 0.919360i | \(-0.628707\pi\) | ||||
−0.393416 | + | 0.919360i | \(0.628707\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.97682 | −0.125821 |
(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 | 3072.2.a.m.1.4 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bl.1.1 | 4 | |||
4.3 | odd | 2 | 3072.2.a.p.1.4 | 4 | |||
8.3 | odd | 2 | 3072.2.a.j.1.1 | 4 | |||
8.5 | even | 2 | 3072.2.a.s.1.1 | 4 | |||
12.11 | even | 2 | 9216.2.a.z.1.1 | 4 | |||
16.3 | odd | 4 | 3072.2.d.j.1537.5 | 8 | |||
16.5 | even | 4 | 3072.2.d.e.1537.8 | 8 | |||
16.11 | odd | 4 | 3072.2.d.j.1537.4 | 8 | |||
16.13 | even | 4 | 3072.2.d.e.1537.1 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bm.1.4 | 4 | |||
24.11 | even | 2 | 9216.2.a.ba.1.4 | 4 | |||
32.3 | odd | 8 | 1536.2.j.f.1153.3 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.j.385.4 | yes | 8 | ||
32.11 | odd | 8 | 1536.2.j.f.385.3 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.j.1153.4 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.i.1153.2 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.e.385.1 | ✓ | 8 | ||
32.27 | odd | 8 | 1536.2.j.i.385.2 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.e.1153.1 | yes | 8 | ||
96.5 | odd | 8 | 4608.2.k.be.3457.1 | 8 | |||
96.11 | even | 8 | 4608.2.k.bj.3457.4 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bh.1153.4 | 8 | |||
96.35 | even | 8 | 4608.2.k.bj.1153.4 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bh.3457.4 | 8 | |||
96.59 | even | 8 | 4608.2.k.bc.3457.1 | 8 | |||
96.77 | odd | 8 | 4608.2.k.be.1153.1 | 8 | |||
96.83 | even | 8 | 4608.2.k.bc.1153.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.e.385.1 | ✓ | 8 | 32.21 | even | 8 | ||
1536.2.j.e.1153.1 | yes | 8 | 32.29 | even | 8 | ||
1536.2.j.f.385.3 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.f.1153.3 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.i.385.2 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.i.1153.2 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.j.385.4 | yes | 8 | 32.5 | even | 8 | ||
1536.2.j.j.1153.4 | yes | 8 | 32.13 | even | 8 | ||
3072.2.a.j.1.1 | 4 | 8.3 | odd | 2 | |||
3072.2.a.m.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.p.1.4 | 4 | 4.3 | odd | 2 | |||
3072.2.a.s.1.1 | 4 | 8.5 | even | 2 | |||
3072.2.d.e.1537.1 | 8 | 16.13 | even | 4 | |||
3072.2.d.e.1537.8 | 8 | 16.5 | even | 4 | |||
3072.2.d.j.1537.4 | 8 | 16.11 | odd | 4 | |||
3072.2.d.j.1537.5 | 8 | 16.3 | odd | 4 | |||
4608.2.k.bc.1153.1 | 8 | 96.83 | even | 8 | |||
4608.2.k.bc.3457.1 | 8 | 96.59 | even | 8 | |||
4608.2.k.be.1153.1 | 8 | 96.77 | odd | 8 | |||
4608.2.k.be.3457.1 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bh.1153.4 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bh.3457.4 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bj.1153.4 | 8 | 96.35 | even | 8 | |||
4608.2.k.bj.3457.4 | 8 | 96.11 | even | 8 | |||
9216.2.a.z.1.1 | 4 | 12.11 | even | 2 | |||
9216.2.a.ba.1.4 | 4 | 24.11 | even | 2 | |||
9216.2.a.bl.1.1 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bm.1.4 | 4 | 24.5 | odd | 2 |