Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.69353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.819031 | −0.309565 | −0.154782 | − | 0.987949i | \(-0.549468\pi\) | ||||
−0.154782 | + | 0.987949i | \(0.549468\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.08298 | −0.326530 | −0.163265 | − | 0.986582i | \(-0.552202\pi\) | ||||
−0.163265 | + | 0.986582i | \(0.552202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.18097 | 0.286427 | 0.143213 | − | 0.989692i | \(-0.454256\pi\) | ||||
0.143213 | + | 0.989692i | \(0.454256\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.51016 | 1.49353 | 0.746766 | − | 0.665087i | \(-0.231605\pi\) | ||||
0.746766 | + | 0.665087i | \(0.231605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.819031 | 0.178727 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.819031 | −0.170780 | −0.0853899 | − | 0.996348i | \(-0.527214\pi\) | ||||
−0.0853899 | + | 0.996348i | \(0.527214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.51016 | 1.58030 | 0.790148 | − | 0.612916i | \(-0.210004\pi\) | ||||
0.790148 | + | 0.612916i | \(0.210004\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.08298 | 0.188522 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.819031 | −0.138442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.917024 | 0.150758 | 0.0753789 | − | 0.997155i | \(-0.475983\pi\) | ||||
0.0753789 | + | 0.997155i | \(0.475983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.08298 | 0.481480 | 0.240740 | − | 0.970590i | \(-0.422610\pi\) | ||||
0.240740 | + | 0.970590i | \(0.422610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.41216 | −1.28284 | −0.641421 | − | 0.767189i | \(-0.721655\pi\) | ||||
−0.641421 | + | 0.767189i | \(0.721655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.32919 | −0.904170 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18097 | −0.165369 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.49514 | −1.02954 | −0.514768 | − | 0.857329i | \(-0.672122\pi\) | ||||
−0.514768 | + | 0.857329i | \(0.672122\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.08298 | −0.146028 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.51016 | −0.862291 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.195985 | −0.0255150 | −0.0127575 | − | 0.999919i | \(-0.504061\pi\) | ||||
−0.0127575 | + | 0.999919i | \(0.504061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.55509 | 0.327145 | 0.163573 | − | 0.986531i | \(-0.447698\pi\) | ||||
0.163573 | + | 0.986531i | \(0.447698\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.819031 | −0.103188 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2462 | −1.25177 | −0.625887 | − | 0.779914i | \(-0.715263\pi\) | ||||
−0.625887 | + | 0.779914i | \(0.715263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.819031 | 0.0985998 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.85708 | −0.932463 | −0.466232 | − | 0.884663i | \(-0.654389\pi\) | ||||
−0.466232 | + | 0.884663i | \(0.654389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.09799 | 0.479634 | 0.239817 | − | 0.970818i | \(-0.422913\pi\) | ||||
0.239817 | + | 0.970818i | \(0.422913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.886992 | 0.101082 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.69112 | 1.09034 | 0.545168 | − | 0.838327i | \(-0.316466\pi\) | ||||
0.545168 | + | 0.838327i | \(0.316466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18097 | 0.128094 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.51016 | −0.912384 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6911 | 1.23926 | 0.619628 | − | 0.784895i | \(-0.287283\pi\) | ||||
0.619628 | + | 0.784895i | \(0.287283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.819031 | −0.0858578 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.51016 | 0.667928 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2013 | 1.44192 | 0.720961 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720961 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08298 | −0.108843 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.03805 | 0.899319 | 0.449660 | − | 0.893200i | \(-0.351545\pi\) | ||||
0.449660 | + | 0.893200i | \(0.351545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5781 | 1.04229 | 0.521146 | − | 0.853467i | \(-0.325505\pi\) | ||||
0.521146 | + | 0.853467i | \(0.325505\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.819031 | 0.0799293 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1033 | 1.36342 | 0.681708 | − | 0.731624i | \(-0.261237\pi\) | ||||
0.681708 | + | 0.731624i | \(0.261237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73606 | 0.166284 | 0.0831420 | − | 0.996538i | \(-0.473505\pi\) | ||||
0.0831420 | + | 0.996538i | \(0.473505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.917024 | −0.0870400 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6462 | 1.66001 | 0.830007 | − | 0.557753i | \(-0.188336\pi\) | ||||
0.830007 | + | 0.557753i | \(0.188336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.819031 | −0.0763751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.967250 | −0.0886677 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.82716 | −0.893378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.08298 | −0.277983 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9701 | −0.973438 | −0.486719 | − | 0.873559i | \(-0.661806\pi\) | ||||
−0.486719 | + | 0.873559i | \(0.661806\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.41216 | 0.740650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.90201 | 0.166179 | 0.0830896 | − | 0.996542i | \(-0.473521\pi\) | ||||
0.0830896 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.33202 | −0.462345 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.77410 | −0.407879 | −0.203939 | − | 0.978983i | \(-0.565375\pi\) | ||||
−0.203939 | + | 0.978983i | \(0.565375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4652 | −1.73584 | −0.867919 | − | 0.496706i | \(-0.834543\pi\) | ||||
−0.867919 | + | 0.496706i | \(0.834543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.08298 | −0.0905630 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.51016 | 0.706730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.32919 | 0.522023 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.9073 | −1.30318 | −0.651589 | − | 0.758573i | \(-0.725897\pi\) | ||||
−0.651589 | + | 0.758573i | \(0.725897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.27613 | 0.266607 | 0.133304 | − | 0.991075i | \(-0.457441\pi\) | ||||
0.133304 | + | 0.991075i | \(0.457441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.18097 | 0.0954756 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0502 | 0.961713 | 0.480856 | − | 0.876799i | \(-0.340326\pi\) | ||||
0.480856 | + | 0.876799i | \(0.340326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.49514 | 0.594403 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.670813 | 0.0528674 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.05306 | 0.317460 | 0.158730 | − | 0.987322i | \(-0.449260\pi\) | ||||
0.158730 | + | 0.987322i | \(0.449260\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.08298 | 0.0843096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.6283 | 1.59627 | 0.798135 | − | 0.602479i | \(-0.205820\pi\) | ||||
0.798135 | + | 0.602479i | \(0.205820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.51016 | 0.497844 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0502 | −0.916162 | −0.458081 | − | 0.888911i | \(-0.651463\pi\) | ||||
−0.458081 | + | 0.888911i | \(0.651463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.819031 | −0.0619130 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.195985 | 0.0147311 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.4802 | 1.30653 | 0.653267 | − | 0.757127i | \(-0.273398\pi\) | ||||
0.653267 | + | 0.757127i | \(0.273398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.47495 | 0.258291 | 0.129145 | − | 0.991626i | \(-0.458777\pi\) | ||||
0.129145 | + | 0.991626i | \(0.458777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.55509 | −0.188877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.917024 | 0.0674209 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.27896 | −0.0935269 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.819031 | 0.0595758 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.11017 | 0.0803293 | 0.0401647 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401647 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.34692 | 0.240917 | 0.120458 | − | 0.992718i | \(-0.461564\pi\) | ||||
0.120458 | + | 0.992718i | \(0.461564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.05023 | −0.573555 | −0.286777 | − | 0.957997i | \(-0.592584\pi\) | ||||
−0.286777 | + | 0.957997i | \(0.592584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5223 | 1.24213 | 0.621063 | − | 0.783761i | \(-0.286701\pi\) | ||||
0.621063 | + | 0.783761i | \(0.286701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2462 | 0.722712 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.97009 | −0.489204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.08298 | 0.215324 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.819031 | −0.0569266 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.05034 | −0.487683 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.33190 | −0.573592 | −0.286796 | − | 0.957992i | \(-0.592590\pi\) | ||||
−0.286796 | + | 0.957992i | \(0.592590\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.85708 | 0.538358 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.41216 | −0.573705 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.09799 | −0.276917 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18097 | 0.0794405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7263 | −0.986148 | −0.493074 | − | 0.869987i | \(-0.664127\pi\) | ||||
−0.493074 | + | 0.869987i | \(0.664127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3822 | −1.02096 | −0.510478 | − | 0.859891i | \(-0.670531\pi\) | ||||
−0.510478 | + | 0.859891i | \(0.670531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7918 | 0.713144 | 0.356572 | − | 0.934268i | \(-0.383945\pi\) | ||||
0.356572 | + | 0.934268i | \(0.383945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.886992 | −0.0583598 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.29114 | 0.150098 | 0.0750488 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750488 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.69112 | −0.629506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.10329 | −0.136050 | −0.0680252 | − | 0.997684i | \(-0.521670\pi\) | ||||
−0.0680252 | + | 0.997684i | \(0.521670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6584 | 1.58839 | 0.794193 | − | 0.607666i | \(-0.207894\pi\) | ||||
0.794193 | + | 0.607666i | \(0.207894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.32919 | −0.404357 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.51016 | 0.414231 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.24621 | 0.395838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37412 | 0.0867336 | 0.0433668 | − | 0.999059i | \(-0.486192\pi\) | ||||
0.0433668 | + | 0.999059i | \(0.486192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.886992 | 0.0557647 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.18097 | −0.0739551 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.7263 | −0.793847 | −0.396923 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396923 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.751071 | −0.0466693 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51016 | 0.526765 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.82187 | 0.420654 | 0.210327 | − | 0.977631i | \(-0.432547\pi\) | ||||
0.210327 | + | 0.977631i | \(0.432547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.49514 | −0.460423 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.6911 | −0.715485 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.59030 | 0.462789 | 0.231394 | − | 0.972860i | \(-0.425671\pi\) | ||||
0.231394 | + | 0.972860i | \(0.425671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44208 | 0.330583 | 0.165291 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165291 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.819031 | 0.0495700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.08298 | −0.0653059 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.4325 | 1.40792 | 0.703961 | − | 0.710239i | \(-0.251413\pi\) | ||||
0.703961 | + | 0.710239i | \(0.251413\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9701 | 1.72821 | 0.864105 | − | 0.503311i | \(-0.167885\pi\) | ||||
0.864105 | + | 0.503311i | \(0.167885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5183 | 1.45746 | 0.728730 | − | 0.684801i | \(-0.240111\pi\) | ||||
0.728730 | + | 0.684801i | \(0.240111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.51016 | −0.385628 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52505 | −0.149049 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6053 | −0.917960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2013 | −0.832494 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4325 | 1.36894 | 0.684470 | − | 0.729041i | \(-0.260034\pi\) | ||||
0.684470 | + | 0.729041i | \(0.260034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.195985 | −0.0114107 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.08298 | 0.0628407 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.819031 | −0.0473658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.88983 | 0.397123 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.03805 | −0.519222 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.55509 | 0.146304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.19870 | −0.0684135 | −0.0342068 | − | 0.999415i | \(-0.510890\pi\) | ||||
−0.0342068 | + | 0.999415i | \(0.510890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.5781 | −0.601768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3822 | 1.55270 | 0.776352 | − | 0.630299i | \(-0.217068\pi\) | ||||
0.776352 | + | 0.630299i | \(0.217068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.2964 | 1.48636 | 0.743181 | − | 0.669090i | \(-0.233316\pi\) | ||||
0.743181 | + | 0.669090i | \(0.233316\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.819031 | −0.0461472 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8243 | 0.832617 | 0.416309 | − | 0.909223i | \(-0.363324\pi\) | ||||
0.416309 | + | 0.909223i | \(0.363324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.21630 | −0.516014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.1033 | −0.787169 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.68829 | 0.427788 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.73606 | −0.0960041 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.78628 | 0.0981829 | 0.0490915 | − | 0.998794i | \(-0.484367\pi\) | ||||
0.0490915 | + | 0.998794i | \(0.484367\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.917024 | 0.0502526 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2462 | −0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.3522 | −1.70786 | −0.853932 | − | 0.520385i | \(-0.825789\pi\) | ||||
−0.853932 | + | 0.520385i | \(0.825789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.6462 | −0.958410 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9170 | 0.589464 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.819031 | 0.0440952 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0733 | −0.648126 | −0.324063 | − | 0.946035i | \(-0.605049\pi\) | ||||
−0.324063 | + | 0.946035i | \(0.605049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.29398 | 0.229851 | 0.114926 | − | 0.993374i | \(-0.463337\pi\) | ||||
0.114926 | + | 0.993374i | \(0.463337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.4325 | −1.03429 | −0.517143 | − | 0.855899i | \(-0.673005\pi\) | ||||
−0.517143 | + | 0.855899i | \(0.673005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.85708 | −0.417010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.967250 | 0.0511923 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7538 | 0.725897 | 0.362949 | − | 0.931809i | \(-0.381770\pi\) | ||||
0.362949 | + | 0.931809i | \(0.381770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.3821 | 1.23064 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.82716 | 0.515792 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.09799 | 0.214499 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.804133 | 0.0419754 | 0.0209877 | − | 0.999780i | \(-0.493319\pi\) | ||||
0.0209877 | + | 0.999780i | \(0.493319\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.08298 | 0.160493 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.13876 | 0.318708 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5984 | −0.704100 | −0.352050 | − | 0.935981i | \(-0.614515\pi\) | ||||
−0.352050 | + | 0.935981i | \(0.614515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.51016 | 0.438295 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4447 | −1.66657 | −0.833285 | − | 0.552844i | \(-0.813543\pi\) | ||||
−0.833285 | + | 0.552844i | \(0.813543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9701 | 0.562015 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.4026 | 1.65569 | 0.827847 | − | 0.560954i | \(-0.189566\pi\) | ||||
0.827847 | + | 0.560954i | \(0.189566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.886992 | 0.0452053 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.41216 | −0.427614 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3142 | 0.624353 | 0.312177 | − | 0.950024i | \(-0.398942\pi\) | ||||
0.312177 | + | 0.950024i | \(0.398942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.967250 | −0.0489160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.90201 | −0.0959436 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.69112 | 0.487613 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.0678 | −1.60944 | −0.804719 | − | 0.593656i | \(-0.797684\pi\) | ||||
−0.804719 | + | 0.593656i | \(0.797684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.33202 | 0.266935 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0801 | 0.653191 | 0.326596 | − | 0.945164i | \(-0.394099\pi\) | ||||
0.326596 | + | 0.945164i | \(0.394099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.993115 | −0.0492269 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8544 | −0.833394 | −0.416697 | − | 0.909045i | \(-0.636812\pi\) | ||||
−0.416697 | + | 0.909045i | \(0.636812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.77410 | 0.235489 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.160518 | 0.00789855 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.24621 | −0.306614 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.4652 | 1.00219 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.81215 | −0.283942 | −0.141971 | − | 0.989871i | \(-0.545344\pi\) | ||||
−0.141971 | + | 0.989871i | \(0.545344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2639 | 0.890130 | 0.445065 | − | 0.895498i | \(-0.353181\pi\) | ||||
0.445065 | + | 0.895498i | \(0.353181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.18097 | 0.0572854 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.09270 | −0.101273 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.08298 | 0.0522866 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.1562 | 1.40441 | 0.702203 | − | 0.711977i | \(-0.252200\pi\) | ||||
0.702203 | + | 0.711977i | \(0.252200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.19598 | −0.105532 | −0.0527661 | − | 0.998607i | \(-0.516804\pi\) | ||||
−0.0527661 | + | 0.998607i | \(0.516804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.51016 | −0.408031 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.33202 | −0.255065 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4953 | 1.07364 | 0.536820 | − | 0.843697i | \(-0.319625\pi\) | ||||
0.536820 | + | 0.843697i | \(0.319625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.32919 | −0.301390 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.47495 | 0.0700768 | 0.0350384 | − | 0.999386i | \(-0.488845\pi\) | ||||
0.0350384 | + | 0.999386i | \(0.488845\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6911 | 0.554212 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.9073 | 0.752390 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.2937 | 1.19368 | 0.596842 | − | 0.802359i | \(-0.296422\pi\) | ||||
0.596842 | + | 0.802359i | \(0.296422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.33879 | −0.157217 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.27613 | −0.153926 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.819031 | −0.0383968 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.47741 | 0.443334 | 0.221667 | − | 0.975122i | \(-0.428850\pi\) | ||||
0.221667 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.18097 | −0.0551229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.88156 | −0.413655 | −0.206828 | − | 0.978377i | \(-0.566314\pi\) | ||||
−0.206828 | + | 0.978377i | \(0.566314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9850 | 0.510515 | 0.255258 | − | 0.966873i | \(-0.417840\pi\) | ||||
0.255258 | + | 0.966873i | \(0.417840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.6054 | −0.722133 | −0.361067 | − | 0.932540i | \(-0.617587\pi\) | ||||
−0.361067 | + | 0.932540i | \(0.617587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.39197 | 0.387505 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0502 | −0.555245 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.11017 | 0.418886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.51016 | 0.298706 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.49514 | −0.343179 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.2790 | 0.789496 | 0.394748 | − | 0.918789i | \(-0.370832\pi\) | ||||
0.394748 | + | 0.918789i | \(0.370832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.917024 | 0.0418127 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.670813 | −0.0305230 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.2013 | 0.644847 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.8093 | −0.897646 | −0.448823 | − | 0.893621i | \(-0.648157\pi\) | ||||
−0.448823 | + | 0.893621i | \(0.648157\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.05306 | −0.183286 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.7564 | −0.575687 | −0.287843 | − | 0.957677i | \(-0.592938\pi\) | ||||
−0.287843 | + | 0.957677i | \(0.592938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0502 | 0.452639 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.08298 | −0.0486762 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.43519 | 0.288658 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2543 | 0.727644 | 0.363822 | − | 0.931468i | \(-0.381472\pi\) | ||||
0.363822 | + | 0.931468i | \(0.381472\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.6283 | −0.921606 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.42990 | 0.286695 | 0.143347 | − | 0.989672i | \(-0.454213\pi\) | ||||
0.143347 | + | 0.989672i | \(0.454213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.03805 | 0.402188 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.61087 | −0.337346 | −0.168673 | − | 0.985672i | \(-0.553948\pi\) | ||||
−0.168673 | + | 0.985672i | \(0.553948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.35638 | −0.148478 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.51016 | −0.287430 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.5781 | 0.466127 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0502 | 0.528946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.9797 | 0.568650 | 0.284325 | − | 0.958728i | \(-0.408230\pi\) | ||||
0.284325 | + | 0.958728i | \(0.408230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.3265 | −0.976268 | −0.488134 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488134 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.819031 | 0.0357455 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3292 | −0.970834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.195985 | −0.00850501 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.08298 | 0.133539 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1033 | 0.609738 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.4802 | −0.754328 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.85436 | 0.295238 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4299 | 0.878350 | 0.439175 | − | 0.898402i | \(-0.355271\pi\) | ||||
0.439175 | + | 0.898402i | \(0.355271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.47495 | −0.149124 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.73606 | 0.0743644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2721 | 0.610230 | 0.305115 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305115 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.55509 | 0.109048 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.4024 | 2.36022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.93734 | −0.337530 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.917024 | −0.0389255 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.7142 | −1.08954 | −0.544772 | − | 0.838584i | \(-0.683384\pi\) | ||||
−0.544772 | + | 0.838584i | \(0.683384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.41216 | −0.355797 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.27896 | 0.0539978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.8515 | 1.04737 | 0.523683 | − | 0.851913i | \(-0.324557\pi\) | ||||
0.523683 | + | 0.851913i | \(0.324557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.6462 | 0.742381 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.819031 | −0.0343961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5685 | 1.19765 | 0.598827 | − | 0.800878i | \(-0.295634\pi\) | ||||
0.598827 | + | 0.800878i | \(0.295634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.1236 | −1.46988 | −0.734938 | − | 0.678134i | \(-0.762789\pi\) | ||||
−0.734938 | + | 0.678134i | \(0.762789\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.11017 | −0.0463782 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.819031 | −0.0341560 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0952 | −0.420267 | −0.210133 | − | 0.977673i | \(-0.567390\pi\) | ||||
−0.210133 | + | 0.977673i | \(0.567390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.34692 | −0.139093 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.11584 | 0.212241 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.11706 | 0.336174 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5985 | 1.34549 | 0.672743 | − | 0.739876i | \(-0.265116\pi\) | ||||
0.672743 | + | 0.739876i | \(0.265116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.05023 | 0.331142 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.58784 | 0.0652046 | 0.0326023 | − | 0.999468i | \(-0.489621\pi\) | ||||
0.0326023 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.967250 | −0.0396534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.5223 | −0.717142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.3319 | 0.830739 | 0.415370 | − | 0.909653i | \(-0.363652\pi\) | ||||
0.415370 | + | 0.909653i | \(0.363652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.38497 | −0.260448 | −0.130224 | − | 0.991485i | \(-0.541570\pi\) | ||||
−0.130224 | + | 0.991485i | \(0.541570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2462 | −0.417258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.82716 | −0.399531 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.1360 | −1.50731 | −0.753653 | − | 0.657273i | \(-0.771710\pi\) | ||||
−0.753653 | + | 0.657273i | \(0.771710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.97009 | 0.282442 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.91702 | −0.198597 | −0.0992984 | − | 0.995058i | \(-0.531660\pi\) | ||||
−0.0992984 | + | 0.995058i | \(0.531660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.08298 | −0.124318 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.22590 | −0.290904 | −0.145452 | − | 0.989365i | \(-0.546464\pi\) | ||||
−0.145452 | + | 0.989365i | \(0.546464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.57566 | −0.183911 | −0.0919556 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919556 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.819031 | 0.0328666 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.57540 | −0.383630 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.05034 | 0.281564 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.08298 | 0.0431811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0761 | 0.560360 | 0.280180 | − | 0.959947i | \(-0.409606\pi\) | ||||
0.280180 | + | 0.959947i | \(0.409606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.33190 | 0.331163 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.9701 | −0.435335 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.32919 | −0.250772 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.85708 | −0.310821 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.3725 | 1.59462 | 0.797310 | − | 0.603571i | \(-0.206256\pi\) | ||||
0.797310 | + | 0.603571i | \(0.206256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0230 | −0.395270 | −0.197635 | − | 0.980276i | \(-0.563326\pi\) | ||||
−0.197635 | + | 0.980276i | \(0.563326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.41216 | 0.331229 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.87481 | 0.388219 | 0.194109 | − | 0.980980i | \(-0.437818\pi\) | ||||
0.194109 | + | 0.980980i | \(0.437818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.212247 | 0.00833141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.5781 | −0.805284 | −0.402642 | − | 0.915358i | \(-0.631908\pi\) | ||||
−0.402642 | + | 0.915358i | \(0.631908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.90201 | 0.0743176 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.09799 | 0.159878 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.4502 | 0.601855 | 0.300927 | − | 0.953647i | \(-0.402704\pi\) | ||||
0.300927 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6502 | 0.569828 | 0.284914 | − | 0.958553i | \(-0.408035\pi\) | ||||
0.284914 | + | 0.958553i | \(0.408035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.18097 | −0.0458650 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.33202 | −0.206767 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.97009 | −0.269883 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7263 | 0.569353 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.76710 | −0.106823 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0503 | −0.811431 | −0.405716 | − | 0.913999i | \(-0.632978\pi\) | ||||
−0.405716 | + | 0.913999i | \(0.632978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.1332 | 0.812215 | 0.406107 | − | 0.913825i | \(-0.366886\pi\) | ||||
0.406107 | + | 0.913825i | \(0.366886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6313 | −0.446368 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3822 | 0.589449 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.9604 | −1.45251 | −0.726257 | − | 0.687424i | \(-0.758742\pi\) | ||||
−0.726257 | + | 0.687424i | \(0.758742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.77410 | −0.182409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7918 | −0.411734 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.49514 | −0.285542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7061 | −0.711615 | −0.355808 | − | 0.934559i | \(-0.615794\pi\) | ||||
−0.355808 | + | 0.934559i | \(0.615794\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.886992 | 0.0336940 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.4652 | −0.776290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.64090 | 0.137909 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.29114 | −0.0866589 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.95790 | −0.225027 | −0.112513 | − | 0.993650i | \(-0.535890\pi\) | ||||
−0.112513 | + | 0.993650i | \(0.535890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.96997 | 0.225162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.40244 | −0.278398 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7918 | 0.405296 | 0.202648 | − | 0.979252i | \(-0.435045\pi\) | ||||
0.202648 | + | 0.979252i | \(0.435045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.69112 | 0.363446 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.08298 | −0.0405010 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.10329 | 0.0785487 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.7482 | 0.997541 | 0.498770 | − | 0.866734i | \(-0.333785\pi\) | ||||
0.498770 | + | 0.866734i | \(0.333785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.66381 | −0.322657 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.6584 | −0.917055 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.51016 | 0.316059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9401 | −0.628272 | −0.314136 | − | 0.949378i | \(-0.601715\pi\) | ||||
−0.314136 | + | 0.949378i | \(0.601715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.93450 | −0.367441 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.8014 | 0.805254 | 0.402627 | − | 0.915364i | \(-0.368097\pi\) | ||||
0.402627 | + | 0.915364i | \(0.368097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.32919 | 0.233456 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0964 | 0.408741 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.2787 | −1.40810 | −0.704052 | − | 0.710148i | \(-0.748628\pi\) | ||||
−0.704052 | + | 0.710148i | \(0.748628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.51016 | −0.239157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.813735 | 0.0298531 | 0.0149265 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149265 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9073 | −0.582799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.24621 | −0.228537 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.5510 | −0.422066 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.9972 | −0.510764 | −0.255382 | − | 0.966840i | \(-0.582201\pi\) | ||||
−0.255382 | + | 0.966840i | \(0.582201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.37412 | −0.0500756 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.27613 | 0.119230 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1508 | 0.914121 | 0.457061 | − | 0.889436i | \(-0.348902\pi\) | ||||
0.457061 | + | 0.889436i | \(0.348902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.886992 | −0.0321958 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.0801 | 1.05415 | 0.527077 | − | 0.849817i | \(-0.323288\pi\) | ||||
0.527077 | + | 0.849817i | \(0.323288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42188 | −0.0514757 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.18097 | 0.0426980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.195985 | −0.00707660 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.2163 | −1.70266 | −0.851332 | − | 0.524628i | \(-0.824204\pi\) | ||||
−0.851332 | + | 0.524628i | \(0.824204\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7263 | 0.458328 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.3767 | −0.948704 | −0.474352 | − | 0.880335i | \(-0.657318\pi\) | ||||
−0.474352 | + | 0.880335i | \(0.657318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.751071 | 0.0269445 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0707 | 0.719106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.50903 | 0.304477 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.51016 | −0.304128 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0502 | 0.430091 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.94977 | −0.354671 | −0.177336 | − | 0.984150i | \(-0.556748\pi\) | ||||
−0.177336 | + | 0.984150i | \(0.556748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.82187 | −0.242865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4528 | −0.513882 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55509 | 0.0907338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.49514 | 0.265825 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.6053 | −1.15494 | −0.577470 | − | 0.816412i | \(-0.695960\pi\) | ||||
−0.577470 | + | 0.816412i | \(0.695960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6911 | 0.413086 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.43803 | −0.156615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.670813 | 0.0236430 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.59030 | −0.267191 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.9848 | −1.65190 | −0.825950 | − | 0.563744i | \(-0.809360\pi\) | ||||
−0.825950 | + | 0.563744i | \(0.809360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.6106 | 0.372589 | 0.186294 | − | 0.982494i | \(-0.440352\pi\) | ||||
0.186294 | + | 0.982494i | \(0.440352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.44208 | −0.190862 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.05306 | 0.141973 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.7645 | −1.91597 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.819031 | −0.0286193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.3648 | −0.501334 | −0.250667 | − | 0.968073i | \(-0.580650\pi\) | ||||
−0.250667 | + | 0.968073i | \(0.580650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.7386 | 1.21091 | 0.605456 | − | 0.795879i | \(-0.292991\pi\) | ||||
0.605456 | + | 0.795879i | \(0.292991\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.08298 | 0.0377044 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.4625 | 0.815871 | 0.407936 | − | 0.913011i | \(-0.366249\pi\) | ||||
0.407936 | + | 0.913011i | \(0.366249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.82433 | 0.237019 | 0.118509 | − | 0.992953i | \(-0.462188\pi\) | ||||
0.118509 | + | 0.992953i | \(0.462188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.4325 | −0.812864 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.47457 | −0.258979 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.6283 | 0.713873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.3139 | 1.90965 | 0.954824 | − | 0.297171i | \(-0.0960432\pi\) | ||||
0.954824 | + | 0.297171i | \(0.0960432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.4228 | 1.49734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9701 | −0.997783 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.04876 | 0.276558 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.5183 | −0.841465 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.751071 | −0.0257464 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4596 | 0.905958 | 0.452979 | − | 0.891521i | \(-0.350361\pi\) | ||||
0.452979 | + | 0.891521i | \(0.350361\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.51016 | 0.222643 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.6734 | −1.15026 | −0.575131 | − | 0.818062i | \(-0.695049\pi\) | ||||
−0.575131 | + | 0.818062i | \(0.695049\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.95249 | −0.100738 | −0.0503688 | − | 0.998731i | \(-0.516040\pi\) | ||||
−0.0503688 | + | 0.998731i | \(0.516040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.52505 | 0.0860536 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.4066 | 1.13717 | 0.568587 | − | 0.822623i | \(-0.307490\pi\) | ||||
0.568587 | + | 0.822623i | \(0.307490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0502 | −0.409720 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6053 | 0.529984 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4953 | −0.356027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2462 | −0.347180 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2013 | 0.480641 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.819031 | −0.0276883 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.3725 | −1.63342 | −0.816712 | − | 0.577045i | \(-0.804206\pi\) | ||||
−0.816712 | + | 0.577045i | \(0.804206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4325 | −0.790358 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.36599 | 0.315548 | 0.157774 | − | 0.987475i | \(-0.449568\pi\) | ||||
0.157774 | + | 0.987475i | \(0.449568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.27208 | −0.211072 | −0.105536 | − | 0.994415i | \(-0.533656\pi\) | ||||
−0.105536 | + | 0.994415i | \(0.533656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.195985 | 0.00658795 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.8393 | 0.733293 | 0.366647 | − | 0.930360i | \(-0.380506\pi\) | ||||
0.366647 | + | 0.930360i | \(0.380506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.98485 | 0.301342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.08298 | −0.0362811 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.4802 | 0.584300 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.819031 | 0.0273467 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.85152 | −0.294887 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.88983 | −0.229279 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.47495 | 0.115511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.2771 | −1.17136 | −0.585679 | − | 0.810543i | \(-0.699172\pi\) | ||||
−0.585679 | + | 0.810543i | \(0.699172\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.03805 | 0.299773 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.8544 | 0.359621 | 0.179810 | − | 0.983701i | \(-0.442452\pi\) | ||||
0.179810 | + | 0.983701i | \(0.442452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.76450 | 0.223872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.55509 | −0.0844686 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.55780 | −0.0514432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.0979 | 0.926863 | 0.463431 | − | 0.886133i | \(-0.346618\pi\) | ||||
0.463431 | + | 0.886133i | \(0.346618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19870 | 0.0394986 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.85708 | −0.258619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.917024 | 0.0301516 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5781 | 0.347431 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.6814 | −1.40033 | −0.700166 | − | 0.713980i | \(-0.746891\pi\) | ||||
−0.700166 | + | 0.713980i | \(0.746891\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.2040 | −1.35041 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.3822 | −0.896455 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.27896 | −0.0418265 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.4827 | −1.48586 | −0.742928 | − | 0.669372i | \(-0.766563\pi\) | ||||
−0.742928 | + | 0.669372i | \(0.766563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.2964 | −0.858152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.5210 | 0.766763 | 0.383381 | − | 0.923590i | \(-0.374759\pi\) | ||||
0.383381 | + | 0.923590i | \(0.374759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.52505 | −0.0822271 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.819031 | 0.0266431 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.91002 | −0.224546 | −0.112273 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112273 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.09799 | 0.133026 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.8243 | −0.480712 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.39727 | 0.0776550 | 0.0388275 | − | 0.999246i | \(-0.487638\pi\) | ||||
0.0388275 | + | 0.999246i | \(0.487638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.11017 | 0.0359244 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.21630 | 0.297921 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.91014 | 0.126265 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.1033 | 0.454472 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.34692 | 0.107741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.0228 | −1.25489 | −0.627444 | − | 0.778662i | \(-0.715899\pi\) | ||||
−0.627444 | + | 0.778662i | \(0.715899\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.68829 | −0.246983 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.92799 | 0.0939637 | 0.0469818 | − | 0.998896i | \(-0.485040\pi\) | ||||
0.0469818 | + | 0.998896i | \(0.485040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.7617 | 0.537354 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3020 | −0.937454 | −0.468727 | − | 0.883343i | \(-0.655287\pi\) | ||||
−0.468727 | + | 0.883343i | \(0.655287\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.6612 | −0.404654 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.73606 | 0.0554280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.5084 | 1.73855 | 0.869275 | − | 0.494329i | \(-0.164586\pi\) | ||||
0.869275 | + | 0.494329i | \(0.164586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.05023 | −0.256502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.88983 | 0.219084 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.41905 | −0.235674 | −0.117837 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117837 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.78628 | −0.0566859 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.5223 | 0.555495 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.38780 | −0.265644 | −0.132822 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132822 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.917024 | −0.0290133 |
(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 | 6240.2.a.ce.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 6240.2.a.cf.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.ce.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6240.2.a.cf.1.2 | yes | 4 | 4.3 | odd | 2 |