Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8450,2,Mod(1,8450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8450.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: | \(67.4735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 650) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.10548\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.10548 | −1.79295 | −0.896476 | − | 0.443093i | \(-0.853881\pi\) | ||||
−0.896476 | + | 0.443093i | \(0.853881\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.10548 | 1.26781 | ||||||||
\(7\) | −4.10548 | −1.55173 | −0.775863 | − | 0.630901i | \(-0.782685\pi\) | ||||
−0.775863 | + | 0.630901i | \(0.782685\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.64402 | 2.21467 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53854 | 0.463887 | 0.231944 | − | 0.972729i | \(-0.425492\pi\) | ||||
0.231944 | + | 0.972729i | \(0.425492\pi\) | |||||||
\(12\) | −3.10548 | −0.896476 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.10548 | 1.09724 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | −6.64402 | −1.56601 | ||||||||
\(19\) | −1.10548 | −0.253615 | −0.126808 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126808 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.7495 | 2.78217 | ||||||||
\(22\) | −1.53854 | −0.328018 | ||||||||
\(23\) | 6.74950 | 1.40737 | 0.703685 | − | 0.710513i | \(-0.251537\pi\) | ||||
0.703685 | + | 0.710513i | \(0.251537\pi\) | |||||||
\(24\) | 3.10548 | 0.633904 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.3164 | −2.17785 | ||||||||
\(28\) | −4.10548 | −0.775863 | ||||||||
\(29\) | −5.56694 | −1.03376 | −0.516878 | − | 0.856059i | \(-0.672906\pi\) | ||||
−0.516878 | + | 0.856059i | \(0.672906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.64402 | 1.55251 | 0.776256 | − | 0.630418i | \(-0.217116\pi\) | ||||
0.776256 | + | 0.630418i | \(0.217116\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.77791 | −0.831727 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.64402 | 1.10734 | ||||||||
\(37\) | 4.53854 | 0.746131 | 0.373066 | − | 0.927805i | \(-0.378307\pi\) | ||||
0.373066 | + | 0.927805i | \(0.378307\pi\) | |||||||
\(38\) | 1.10548 | 0.179333 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.85499 | −1.22674 | −0.613371 | − | 0.789795i | \(-0.710187\pi\) | ||||
−0.613371 | + | 0.789795i | \(0.710187\pi\) | |||||||
\(42\) | −12.7495 | −1.96729 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 1.53854 | 0.231944 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.74950 | −0.995160 | ||||||||
\(47\) | 10.8550 | 1.58336 | 0.791681 | − | 0.610934i | \(-0.209206\pi\) | ||||
0.791681 | + | 0.610934i | \(0.209206\pi\) | |||||||
\(48\) | −3.10548 | −0.448238 | ||||||||
\(49\) | 9.85499 | 1.40786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.31645 | 1.30456 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.433057 | −0.0594850 | −0.0297425 | − | 0.999558i | \(-0.509469\pi\) | ||||
−0.0297425 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(54\) | 11.3164 | 1.53997 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.10548 | 0.548618 | ||||||||
\(57\) | 3.43306 | 0.454720 | ||||||||
\(58\) | 5.56694 | 0.730975 | ||||||||
\(59\) | 13.7779 | 1.79373 | 0.896865 | − | 0.442304i | \(-0.145839\pi\) | ||||
0.896865 | + | 0.442304i | \(0.145839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3164 | −1.83303 | −0.916517 | − | 0.399997i | \(-0.869011\pi\) | ||||
−0.916517 | + | 0.399997i | \(0.869011\pi\) | |||||||
\(62\) | −8.64402 | −1.09779 | ||||||||
\(63\) | −27.2769 | −3.43657 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.77791 | 0.588120 | ||||||||
\(67\) | −3.74950 | −0.458075 | −0.229037 | − | 0.973418i | \(-0.573558\pi\) | ||||
−0.229037 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(68\) | −3.00000 | −0.363803 | ||||||||
\(69\) | −20.9605 | −2.52334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −6.64402 | −0.783006 | ||||||||
\(73\) | 10.7779 | 1.26146 | 0.630729 | − | 0.776003i | \(-0.282756\pi\) | ||||
0.630729 | + | 0.776003i | \(0.282756\pi\) | |||||||
\(74\) | −4.53854 | −0.527595 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.10548 | −0.126808 | ||||||||
\(77\) | −6.31645 | −0.719826 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.53854 | −0.735643 | −0.367822 | − | 0.929896i | \(-0.619896\pi\) | ||||
−0.367822 | + | 0.929896i | \(0.619896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.2110 | 1.69011 | ||||||||
\(82\) | 7.85499 | 0.867438 | ||||||||
\(83\) | −4.46146 | −0.489709 | −0.244854 | − | 0.969560i | \(-0.578740\pi\) | ||||
−0.244854 | + | 0.969560i | \(0.578740\pi\) | |||||||
\(84\) | 12.7495 | 1.39109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 17.2880 | 1.85347 | ||||||||
\(88\) | −1.53854 | −0.164009 | ||||||||
\(89\) | 1.85499 | 0.196628 | 0.0983141 | − | 0.995155i | \(-0.468655\pi\) | ||||
0.0983141 | + | 0.995155i | \(0.468655\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.74950 | 0.703685 | ||||||||
\(93\) | −26.8439 | −2.78358 | ||||||||
\(94\) | −10.8550 | −1.11961 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.10548 | 0.316952 | ||||||||
\(97\) | −3.78903 | −0.384718 | −0.192359 | − | 0.981325i | \(-0.561614\pi\) | ||||
−0.192359 | + | 0.981325i | \(0.561614\pi\) | |||||||
\(98\) | −9.85499 | −0.995504 | ||||||||
\(99\) | 10.2221 | 1.02736 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.18256 | −0.714692 | −0.357346 | − | 0.933972i | \(-0.616318\pi\) | ||||
−0.357346 | + | 0.933972i | \(0.616318\pi\) | |||||||
\(102\) | −9.31645 | −0.922466 | ||||||||
\(103\) | 12.5385 | 1.23546 | 0.617730 | − | 0.786391i | \(-0.288053\pi\) | ||||
0.617730 | + | 0.786391i | \(0.288053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.433057 | 0.0420622 | ||||||||
\(107\) | −1.81744 | −0.175698 | −0.0878492 | − | 0.996134i | \(-0.527999\pi\) | ||||
−0.0878492 | + | 0.996134i | \(0.527999\pi\) | |||||||
\(108\) | −11.3164 | −1.08893 | ||||||||
\(109\) | 3.67243 | 0.351755 | 0.175877 | − | 0.984412i | \(-0.443724\pi\) | ||||
0.175877 | + | 0.984412i | \(0.443724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.0944 | −1.33778 | ||||||||
\(112\) | −4.10548 | −0.387932 | ||||||||
\(113\) | 16.0660 | 1.51136 | 0.755679 | − | 0.654942i | \(-0.227307\pi\) | ||||
0.755679 | + | 0.654942i | \(0.227307\pi\) | |||||||
\(114\) | −3.43306 | −0.321535 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.56694 | −0.516878 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7779 | −1.26836 | ||||||||
\(119\) | 12.3164 | 1.12905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.63290 | −0.784809 | ||||||||
\(122\) | 14.3164 | 1.29615 | ||||||||
\(123\) | 24.3935 | 2.19949 | ||||||||
\(124\) | 8.64402 | 0.776256 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 27.2769 | 2.43002 | ||||||||
\(127\) | −4.92292 | −0.436839 | −0.218419 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218419 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.4219 | 1.09369 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.866114 | 0.0756727 | 0.0378364 | − | 0.999284i | \(-0.487953\pi\) | ||||
0.0378364 | + | 0.999284i | \(0.487953\pi\) | |||||||
\(132\) | −4.77791 | −0.415864 | ||||||||
\(133\) | 4.53854 | 0.393541 | ||||||||
\(134\) | 3.74950 | 0.323908 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −16.7779 | −1.43343 | −0.716717 | − | 0.697364i | \(-0.754356\pi\) | ||||
−0.716717 | + | 0.697364i | \(0.754356\pi\) | |||||||
\(138\) | 20.9605 | 1.78427 | ||||||||
\(139\) | −4.39353 | −0.372654 | −0.186327 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186327 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.7100 | −2.83889 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.64402 | 0.553669 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.7779 | −0.891986 | ||||||||
\(147\) | −30.6045 | −2.52422 | ||||||||
\(148\) | 4.53854 | 0.373066 | ||||||||
\(149\) | −9.70998 | −0.795472 | −0.397736 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397736 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.48986 | 0.202622 | 0.101311 | − | 0.994855i | \(-0.467696\pi\) | ||||
0.101311 | + | 0.994855i | \(0.467696\pi\) | |||||||
\(152\) | 1.10548 | 0.0896665 | ||||||||
\(153\) | −19.9321 | −1.61141 | ||||||||
\(154\) | 6.31645 | 0.508994 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3935 | −0.909302 | −0.454651 | − | 0.890670i | \(-0.650236\pi\) | ||||
−0.454651 | + | 0.890670i | \(0.650236\pi\) | |||||||
\(158\) | 6.53854 | 0.520178 | ||||||||
\(159\) | 1.34485 | 0.106654 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.7100 | −2.18385 | ||||||||
\(162\) | −15.2110 | −1.19509 | ||||||||
\(163\) | −16.8155 | −1.31709 | −0.658544 | − | 0.752542i | \(-0.728827\pi\) | ||||
−0.658544 | + | 0.752542i | \(0.728827\pi\) | |||||||
\(164\) | −7.85499 | −0.613371 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.46146 | 0.346276 | ||||||||
\(167\) | −1.61562 | −0.125020 | −0.0625102 | − | 0.998044i | \(-0.519911\pi\) | ||||
−0.0625102 | + | 0.998044i | \(0.519911\pi\) | |||||||
\(168\) | −12.7495 | −0.983646 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.34485 | −0.561675 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 12.3164 | 0.936402 | 0.468201 | − | 0.883622i | \(-0.344902\pi\) | ||||
0.468201 | + | 0.883622i | \(0.344902\pi\) | |||||||
\(174\) | −17.2880 | −1.31060 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.53854 | 0.115972 | ||||||||
\(177\) | −42.7871 | −3.21607 | ||||||||
\(178\) | −1.85499 | −0.139037 | ||||||||
\(179\) | −10.1826 | −0.761080 | −0.380540 | − | 0.924764i | \(-0.624262\pi\) | ||||
−0.380540 | + | 0.924764i | \(0.624262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3935 | −0.846874 | −0.423437 | − | 0.905926i | \(-0.639177\pi\) | ||||
−0.423437 | + | 0.905926i | \(0.639177\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 44.4595 | 3.28654 | ||||||||
\(184\) | −6.74950 | −0.497580 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 26.8439 | 1.96829 | ||||||||
\(187\) | −4.61562 | −0.337527 | ||||||||
\(188\) | 10.8550 | 0.791681 | ||||||||
\(189\) | 46.4595 | 3.37943 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4990 | −1.41090 | −0.705449 | − | 0.708760i | \(-0.749255\pi\) | ||||
−0.705449 | + | 0.708760i | \(0.749255\pi\) | |||||||
\(192\) | −3.10548 | −0.224119 | ||||||||
\(193\) | 2.72110 | 0.195869 | 0.0979346 | − | 0.995193i | \(-0.468776\pi\) | ||||
0.0979346 | + | 0.995193i | \(0.468776\pi\) | |||||||
\(194\) | 3.78903 | 0.272037 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.85499 | 0.703928 | ||||||||
\(197\) | 1.61562 | 0.115108 | 0.0575540 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575540 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(198\) | −10.2221 | −0.726452 | ||||||||
\(199\) | 22.2485 | 1.57716 | 0.788578 | − | 0.614935i | \(-0.210818\pi\) | ||||
0.788578 | + | 0.614935i | \(0.210818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6440 | 0.821306 | ||||||||
\(202\) | 7.18256 | 0.505363 | ||||||||
\(203\) | 22.8550 | 1.60411 | ||||||||
\(204\) | 9.31645 | 0.652282 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.5385 | −0.873601 | ||||||||
\(207\) | 44.8439 | 3.11686 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.70083 | −0.117649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2394 | 0.704907 | 0.352454 | − | 0.935829i | \(-0.385347\pi\) | ||||
0.352454 | + | 0.935829i | \(0.385347\pi\) | |||||||
\(212\) | −0.433057 | −0.0297425 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.81744 | 0.124238 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.3164 | 0.769987 | ||||||||
\(217\) | −35.4879 | −2.40907 | ||||||||
\(218\) | −3.67243 | −0.248728 | ||||||||
\(219\) | −33.4706 | −2.26173 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 14.0944 | 0.945951 | ||||||||
\(223\) | −20.9605 | −1.40362 | −0.701808 | − | 0.712366i | \(-0.747624\pi\) | ||||
−0.701808 | + | 0.712366i | \(0.747624\pi\) | |||||||
\(224\) | 4.10548 | 0.274309 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0660 | −1.06869 | ||||||||
\(227\) | 4.85499 | 0.322237 | 0.161118 | − | 0.986935i | \(-0.448490\pi\) | ||||
0.161118 | + | 0.986935i | \(0.448490\pi\) | |||||||
\(228\) | 3.43306 | 0.227360 | ||||||||
\(229\) | 6.71196 | 0.443538 | 0.221769 | − | 0.975099i | \(-0.428817\pi\) | ||||
0.221769 | + | 0.975099i | \(0.428817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.6156 | 1.29061 | ||||||||
\(232\) | 5.56694 | 0.365488 | ||||||||
\(233\) | −14.3651 | −0.941091 | −0.470545 | − | 0.882376i | \(-0.655943\pi\) | ||||
−0.470545 | + | 0.882376i | \(0.655943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.7779 | 0.896865 | ||||||||
\(237\) | 20.3053 | 1.31897 | ||||||||
\(238\) | −12.3164 | −0.798357 | ||||||||
\(239\) | −1.14501 | −0.0740647 | −0.0370324 | − | 0.999314i | \(-0.511790\pi\) | ||||
−0.0370324 | + | 0.999314i | \(0.511790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.5669 | 1.32483 | 0.662417 | − | 0.749136i | \(-0.269531\pi\) | ||||
0.662417 | + | 0.749136i | \(0.269531\pi\) | |||||||
\(242\) | 8.63290 | 0.554944 | ||||||||
\(243\) | −13.2880 | −0.852428 | ||||||||
\(244\) | −14.3164 | −0.916517 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.3935 | −1.55527 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.64402 | −0.548896 | ||||||||
\(249\) | 13.8550 | 0.878024 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.31645 | −0.209332 | −0.104666 | − | 0.994507i | \(-0.533377\pi\) | ||||
−0.104666 | + | 0.994507i | \(0.533377\pi\) | |||||||
\(252\) | −27.2769 | −1.71828 | ||||||||
\(253\) | 10.3844 | 0.652860 | ||||||||
\(254\) | 4.92292 | 0.308892 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.4331 | −0.775553 | −0.387776 | − | 0.921753i | \(-0.626757\pi\) | ||||
−0.387776 | + | 0.921753i | \(0.626757\pi\) | |||||||
\(258\) | −12.4219 | −0.773356 | ||||||||
\(259\) | −18.6329 | −1.15779 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −36.9869 | −2.28943 | ||||||||
\(262\) | −0.866114 | −0.0535087 | ||||||||
\(263\) | 4.38438 | 0.270353 | 0.135176 | − | 0.990822i | \(-0.456840\pi\) | ||||
0.135176 | + | 0.990822i | \(0.456840\pi\) | |||||||
\(264\) | 4.77791 | 0.294060 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.53854 | −0.278276 | ||||||||
\(267\) | −5.76063 | −0.352545 | ||||||||
\(268\) | −3.74950 | −0.229037 | ||||||||
\(269\) | −5.56694 | −0.339423 | −0.169711 | − | 0.985494i | \(-0.554284\pi\) | ||||
−0.169711 | + | 0.985494i | \(0.554284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.39353 | −0.570616 | −0.285308 | − | 0.958436i | \(-0.592096\pi\) | ||||
−0.285308 | + | 0.958436i | \(0.592096\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.7779 | 1.01359 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.9605 | −1.26167 | ||||||||
\(277\) | −8.38438 | −0.503769 | −0.251884 | − | 0.967757i | \(-0.581050\pi\) | ||||
−0.251884 | + | 0.967757i | \(0.581050\pi\) | |||||||
\(278\) | 4.39353 | 0.263506 | ||||||||
\(279\) | 57.4311 | 3.43831 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6329 | −0.753615 | −0.376808 | − | 0.926292i | \(-0.622978\pi\) | ||||
−0.376808 | + | 0.926292i | \(0.622978\pi\) | |||||||
\(282\) | 33.7100 | 2.00740 | ||||||||
\(283\) | 13.4706 | 0.800744 | 0.400372 | − | 0.916353i | \(-0.368881\pi\) | ||||
0.400372 | + | 0.916353i | \(0.368881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.2485 | 1.90357 | ||||||||
\(288\) | −6.64402 | −0.391503 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.7668 | 0.689781 | ||||||||
\(292\) | 10.7779 | 0.630729 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 30.6045 | 1.78489 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.53854 | −0.263797 | ||||||||
\(297\) | −17.4108 | −1.01028 | ||||||||
\(298\) | 9.70998 | 0.562484 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4219 | 0.946544 | ||||||||
\(302\) | −2.48986 | −0.143276 | ||||||||
\(303\) | 22.3053 | 1.28141 | ||||||||
\(304\) | −1.10548 | −0.0634038 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 19.9321 | 1.13944 | ||||||||
\(307\) | 13.8925 | 0.792889 | 0.396444 | − | 0.918059i | \(-0.370244\pi\) | ||||
0.396444 | + | 0.918059i | \(0.370244\pi\) | |||||||
\(308\) | −6.31645 | −0.359913 | ||||||||
\(309\) | −38.9382 | −2.21512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.51827 | −0.199503 | −0.0997513 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997513 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.5650 | −1.38849 | −0.694247 | − | 0.719737i | \(-0.744262\pi\) | ||||
−0.694247 | + | 0.719737i | \(0.744262\pi\) | |||||||
\(314\) | 11.3935 | 0.642974 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.53854 | −0.367822 | ||||||||
\(317\) | −1.46146 | −0.0820838 | −0.0410419 | − | 0.999157i | \(-0.513068\pi\) | ||||
−0.0410419 | + | 0.999157i | \(0.513068\pi\) | |||||||
\(318\) | −1.34485 | −0.0754155 | ||||||||
\(319\) | −8.56496 | −0.479546 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.64402 | 0.315019 | ||||||||
\(322\) | 27.7100 | 1.54422 | ||||||||
\(323\) | 3.31645 | 0.184532 | ||||||||
\(324\) | 15.2110 | 0.845054 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.8155 | 0.931322 | ||||||||
\(327\) | −11.4047 | −0.630679 | ||||||||
\(328\) | 7.85499 | 0.433719 | ||||||||
\(329\) | −44.5650 | −2.45695 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2394 | 1.00253 | 0.501263 | − | 0.865295i | \(-0.332869\pi\) | ||||
0.501263 | + | 0.865295i | \(0.332869\pi\) | |||||||
\(332\) | −4.46146 | −0.244854 | ||||||||
\(333\) | 30.1542 | 1.65244 | ||||||||
\(334\) | 1.61562 | 0.0884027 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.7495 | 0.695543 | ||||||||
\(337\) | 19.6329 | 1.06947 | 0.534736 | − | 0.845019i | \(-0.320411\pi\) | ||||
0.534736 | + | 0.845019i | \(0.320411\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −49.8925 | −2.70979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.2992 | 0.720190 | ||||||||
\(342\) | 7.34485 | 0.397164 | ||||||||
\(343\) | −11.7211 | −0.632880 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3164 | −0.662136 | ||||||||
\(347\) | −23.6816 | −1.27129 | −0.635647 | − | 0.771980i | \(-0.719266\pi\) | ||||
−0.635647 | + | 0.771980i | \(0.719266\pi\) | |||||||
\(348\) | 17.2880 | 0.926736 | ||||||||
\(349\) | 0.154159 | 0.00825192 | 0.00412596 | − | 0.999991i | \(-0.498687\pi\) | ||||
0.00412596 | + | 0.999991i | \(0.498687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.53854 | −0.0820044 | ||||||||
\(353\) | 36.6329 | 1.94977 | 0.974886 | − | 0.222704i | \(-0.0714883\pi\) | ||||
0.974886 | + | 0.222704i | \(0.0714883\pi\) | |||||||
\(354\) | 42.7871 | 2.27411 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.85499 | 0.0983141 | ||||||||
\(357\) | −38.2485 | −2.02433 | ||||||||
\(358\) | 10.1826 | 0.538165 | ||||||||
\(359\) | 27.2394 | 1.43764 | 0.718819 | − | 0.695197i | \(-0.244683\pi\) | ||||
0.718819 | + | 0.695197i | \(0.244683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7779 | −0.935679 | ||||||||
\(362\) | 11.3935 | 0.598830 | ||||||||
\(363\) | 26.8093 | 1.40712 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −44.4595 | −2.32393 | ||||||||
\(367\) | −23.8641 | −1.24570 | −0.622849 | − | 0.782342i | \(-0.714025\pi\) | ||||
−0.622849 | + | 0.782342i | \(0.714025\pi\) | |||||||
\(368\) | 6.74950 | 0.351842 | ||||||||
\(369\) | −52.1887 | −2.71684 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.77791 | 0.0923044 | ||||||||
\(372\) | −26.8439 | −1.39179 | ||||||||
\(373\) | −22.3164 | −1.15550 | −0.577751 | − | 0.816213i | \(-0.696070\pi\) | ||||
−0.577751 | + | 0.816213i | \(0.696070\pi\) | |||||||
\(374\) | 4.61562 | 0.238668 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8550 | −0.559803 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −46.4595 | −2.38962 | ||||||||
\(379\) | −9.74950 | −0.500798 | −0.250399 | − | 0.968143i | \(-0.580562\pi\) | ||||
−0.250399 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.2880 | 0.783230 | ||||||||
\(382\) | 19.4990 | 0.997656 | ||||||||
\(383\) | −24.7871 | −1.26656 | −0.633280 | − | 0.773923i | \(-0.718292\pi\) | ||||
−0.633280 | + | 0.773923i | \(0.718292\pi\) | |||||||
\(384\) | 3.10548 | 0.158476 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.72110 | −0.138500 | ||||||||
\(387\) | −26.5761 | −1.35094 | ||||||||
\(388\) | −3.78903 | −0.192359 | ||||||||
\(389\) | 0.749505 | 0.0380014 | 0.0190007 | − | 0.999819i | \(-0.493952\pi\) | ||||
0.0190007 | + | 0.999819i | \(0.493952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2485 | −1.02401 | ||||||||
\(392\) | −9.85499 | −0.497752 | ||||||||
\(393\) | −2.68970 | −0.135678 | ||||||||
\(394\) | −1.61562 | −0.0813937 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.2221 | 0.513679 | ||||||||
\(397\) | −9.67243 | −0.485445 | −0.242723 | − | 0.970096i | \(-0.578040\pi\) | ||||
−0.242723 | + | 0.970096i | \(0.578040\pi\) | |||||||
\(398\) | −22.2485 | −1.11522 | ||||||||
\(399\) | −14.0944 | −0.705600 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9321 | 0.545921 | 0.272961 | − | 0.962025i | \(-0.411997\pi\) | ||||
0.272961 | + | 0.962025i | \(0.411997\pi\) | |||||||
\(402\) | −11.6440 | −0.580751 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.18256 | −0.357346 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.8550 | −1.13427 | ||||||||
\(407\) | 6.98272 | 0.346121 | ||||||||
\(408\) | −9.31645 | −0.461233 | ||||||||
\(409\) | 26.5669 | 1.31365 | 0.656825 | − | 0.754043i | \(-0.271899\pi\) | ||||
0.656825 | + | 0.754043i | \(0.271899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 52.1035 | 2.57008 | ||||||||
\(412\) | 12.5385 | 0.617730 | ||||||||
\(413\) | −56.5650 | −2.78338 | ||||||||
\(414\) | −44.8439 | −2.20396 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6440 | 0.668151 | ||||||||
\(418\) | 1.70083 | 0.0831903 | ||||||||
\(419\) | 24.3145 | 1.18784 | 0.593920 | − | 0.804524i | \(-0.297580\pi\) | ||||
0.593920 | + | 0.804524i | \(0.297580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.15416 | 0.299935 | 0.149968 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149968 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(422\) | −10.2394 | −0.498445 | ||||||||
\(423\) | 72.1208 | 3.50663 | ||||||||
\(424\) | 0.433057 | 0.0210311 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 58.7759 | 2.84437 | ||||||||
\(428\) | −1.81744 | −0.0878492 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.828565 | −0.0399106 | −0.0199553 | − | 0.999801i | \(-0.506352\pi\) | ||||
−0.0199553 | + | 0.999801i | \(0.506352\pi\) | |||||||
\(432\) | −11.3164 | −0.544463 | ||||||||
\(433\) | −15.7008 | −0.754534 | −0.377267 | − | 0.926105i | \(-0.623136\pi\) | ||||
−0.377267 | + | 0.926105i | \(0.623136\pi\) | |||||||
\(434\) | 35.4879 | 1.70347 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.67243 | 0.175877 | ||||||||
\(437\) | −7.46146 | −0.356930 | ||||||||
\(438\) | 33.4706 | 1.59929 | ||||||||
\(439\) | 9.17144 | 0.437729 | 0.218864 | − | 0.975755i | \(-0.429765\pi\) | ||||
0.218864 | + | 0.975755i | \(0.429765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 65.4768 | 3.11794 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.3164 | 0.727706 | 0.363853 | − | 0.931456i | \(-0.381461\pi\) | ||||
0.363853 | + | 0.931456i | \(0.381461\pi\) | |||||||
\(444\) | −14.0944 | −0.668889 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.9605 | 0.992507 | ||||||||
\(447\) | 30.1542 | 1.42624 | ||||||||
\(448\) | −4.10548 | −0.193966 | ||||||||
\(449\) | −23.4108 | −1.10482 | −0.552412 | − | 0.833571i | \(-0.686292\pi\) | ||||
−0.552412 | + | 0.833571i | \(0.686292\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0852 | −0.569070 | ||||||||
\(452\) | 16.0660 | 0.755679 | ||||||||
\(453\) | −7.73223 | −0.363292 | ||||||||
\(454\) | −4.85499 | −0.227856 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.43306 | −0.160768 | ||||||||
\(457\) | 22.9321 | 1.07272 | 0.536358 | − | 0.843990i | \(-0.319800\pi\) | ||||
0.536358 | + | 0.843990i | \(0.319800\pi\) | |||||||
\(458\) | −6.71196 | −0.313629 | ||||||||
\(459\) | 33.9493 | 1.58462 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4615 | 0.626963 | 0.313481 | − | 0.949594i | \(-0.398505\pi\) | ||||
0.313481 | + | 0.949594i | \(0.398505\pi\) | |||||||
\(462\) | −19.6156 | −0.912601 | ||||||||
\(463\) | −16.0264 | −0.744811 | −0.372406 | − | 0.928070i | \(-0.621467\pi\) | ||||
−0.372406 | + | 0.928070i | \(0.621467\pi\) | |||||||
\(464\) | −5.56694 | −0.258439 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.3651 | 0.665452 | ||||||||
\(467\) | 0.866114 | 0.0400790 | 0.0200395 | − | 0.999799i | \(-0.493621\pi\) | ||||
0.0200395 | + | 0.999799i | \(0.493621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.3935 | 0.710807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.3824 | 1.63033 | ||||||||
\(472\) | −13.7779 | −0.634180 | ||||||||
\(473\) | −6.15416 | −0.282969 | ||||||||
\(474\) | −20.3053 | −0.932654 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.3164 | 0.564523 | ||||||||
\(477\) | −2.87724 | −0.131740 | ||||||||
\(478\) | 1.14501 | 0.0523717 | ||||||||
\(479\) | 29.4879 | 1.34734 | 0.673668 | − | 0.739034i | \(-0.264718\pi\) | ||||
0.673668 | + | 0.739034i | \(0.264718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −20.5669 | −0.936799 | ||||||||
\(483\) | 86.0528 | 3.91554 | ||||||||
\(484\) | −8.63290 | −0.392404 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.2880 | 0.602758 | ||||||||
\(487\) | −35.4503 | −1.60641 | −0.803204 | − | 0.595704i | \(-0.796873\pi\) | ||||
−0.803204 | + | 0.595704i | \(0.796873\pi\) | |||||||
\(488\) | 14.3164 | 0.648075 | ||||||||
\(489\) | 52.2201 | 2.36148 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1319 | 1.45009 | 0.725046 | − | 0.688700i | \(-0.241818\pi\) | ||||
0.725046 | + | 0.688700i | \(0.241818\pi\) | |||||||
\(492\) | 24.3935 | 1.09975 | ||||||||
\(493\) | 16.7008 | 0.752168 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.64402 | 0.388128 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.8550 | −0.620857 | ||||||||
\(499\) | 27.2769 | 1.22108 | 0.610541 | − | 0.791984i | \(-0.290952\pi\) | ||||
0.610541 | + | 0.791984i | \(0.290952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.01728 | 0.224155 | ||||||||
\(502\) | 3.31645 | 0.148020 | ||||||||
\(503\) | 26.9980 | 1.20378 | 0.601891 | − | 0.798578i | \(-0.294414\pi\) | ||||
0.601891 | + | 0.798578i | \(0.294414\pi\) | |||||||
\(504\) | 27.2769 | 1.21501 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.3844 | −0.461642 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.92292 | −0.218419 | ||||||||
\(509\) | −38.8814 | −1.72339 | −0.861694 | − | 0.507428i | \(-0.830596\pi\) | ||||
−0.861694 | + | 0.507428i | \(0.830596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.2485 | −1.95744 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.5101 | 0.552336 | ||||||||
\(514\) | 12.4331 | 0.548399 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.4219 | 0.546845 | ||||||||
\(517\) | 16.7008 | 0.734502 | ||||||||
\(518\) | 18.6329 | 0.818682 | ||||||||
\(519\) | −38.2485 | −1.67892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.06595 | 0.178133 | 0.0890663 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890663 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(522\) | 36.9869 | 1.61887 | ||||||||
\(523\) | 34.8723 | 1.52486 | 0.762429 | − | 0.647072i | \(-0.224007\pi\) | ||||
0.762429 | + | 0.647072i | \(0.224007\pi\) | |||||||
\(524\) | 0.866114 | 0.0378364 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.38438 | −0.191168 | ||||||||
\(527\) | −25.9321 | −1.12962 | ||||||||
\(528\) | −4.77791 | −0.207932 | ||||||||
\(529\) | 22.5558 | 0.980688 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 91.5407 | 3.97253 | ||||||||
\(532\) | 4.53854 | 0.196771 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.76063 | 0.249287 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.74950 | 0.161954 | ||||||||
\(537\) | 31.6218 | 1.36458 | ||||||||
\(538\) | 5.56694 | 0.240008 | ||||||||
\(539\) | 15.1623 | 0.653086 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.2282 | −1.60057 | −0.800284 | − | 0.599622i | \(-0.795318\pi\) | ||||
−0.800284 | + | 0.599622i | \(0.795318\pi\) | |||||||
\(542\) | 9.39353 | 0.403487 | ||||||||
\(543\) | 35.3824 | 1.51840 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.9493 | −1.53708 | −0.768541 | − | 0.639800i | \(-0.779017\pi\) | ||||
−0.768541 | + | 0.639800i | \(0.779017\pi\) | |||||||
\(548\) | −16.7779 | −0.716717 | ||||||||
\(549\) | −95.1188 | −4.05957 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.15416 | 0.262176 | ||||||||
\(552\) | 20.9605 | 0.892137 | ||||||||
\(553\) | 26.8439 | 1.14152 | ||||||||
\(554\) | 8.38438 | 0.356218 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.39353 | −0.186327 | ||||||||
\(557\) | 14.0944 | 0.597197 | 0.298599 | − | 0.954379i | \(-0.403481\pi\) | ||||
0.298599 | + | 0.954379i | \(0.403481\pi\) | |||||||
\(558\) | −57.4311 | −2.43125 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.3337 | 0.605170 | ||||||||
\(562\) | 12.6329 | 0.532887 | ||||||||
\(563\) | 28.2678 | 1.19134 | 0.595672 | − | 0.803228i | \(-0.296886\pi\) | ||||
0.595672 | + | 0.803228i | \(0.296886\pi\) | |||||||
\(564\) | −33.7100 | −1.41945 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.4706 | −0.566212 | ||||||||
\(567\) | −62.4484 | −2.62258 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.1339 | 1.09559 | 0.547795 | − | 0.836613i | \(-0.315467\pi\) | ||||
0.547795 | + | 0.836613i | \(0.315467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7871 | −0.451424 | −0.225712 | − | 0.974194i | \(-0.572471\pi\) | ||||
−0.225712 | + | 0.974194i | \(0.572471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.5538 | 2.52967 | ||||||||
\(574\) | −32.2485 | −1.34603 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.64402 | 0.276834 | ||||||||
\(577\) | 12.1228 | 0.504677 | 0.252339 | − | 0.967639i | \(-0.418800\pi\) | ||||
0.252339 | + | 0.967639i | \(0.418800\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | −8.45033 | −0.351184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.3164 | 0.759894 | ||||||||
\(582\) | −11.7668 | −0.487749 | ||||||||
\(583\) | −0.666275 | −0.0275943 | ||||||||
\(584\) | −10.7779 | −0.445993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −35.2485 | −1.45486 | −0.727431 | − | 0.686181i | \(-0.759286\pi\) | ||||
−0.727431 | + | 0.686181i | \(0.759286\pi\) | |||||||
\(588\) | −30.6045 | −1.26211 | ||||||||
\(589\) | −9.55582 | −0.393741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.01728 | −0.206383 | ||||||||
\(592\) | 4.53854 | 0.186533 | ||||||||
\(593\) | −11.0862 | −0.455257 | −0.227628 | − | 0.973748i | \(-0.573097\pi\) | ||||
−0.227628 | + | 0.973748i | \(0.573097\pi\) | |||||||
\(594\) | 17.4108 | 0.714374 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.70998 | −0.397736 | ||||||||
\(597\) | −69.0924 | −2.82776 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.4990 | 1.28701 | 0.643507 | − | 0.765440i | \(-0.277479\pi\) | ||||
0.643507 | + | 0.765440i | \(0.277479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6329 | 0.800843 | 0.400421 | − | 0.916331i | \(-0.368864\pi\) | ||||
0.400421 | + | 0.916331i | \(0.368864\pi\) | |||||||
\(602\) | −16.4219 | −0.669308 | ||||||||
\(603\) | −24.9118 | −1.01449 | ||||||||
\(604\) | 2.48986 | 0.101311 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.3053 | −0.906092 | ||||||||
\(607\) | 17.6156 | 0.714996 | 0.357498 | − | 0.933914i | \(-0.383630\pi\) | ||||
0.357498 | + | 0.933914i | \(0.383630\pi\) | |||||||
\(608\) | 1.10548 | 0.0448332 | ||||||||
\(609\) | −70.9758 | −2.87608 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −19.9321 | −0.805706 | ||||||||
\(613\) | 25.4200 | 1.02670 | 0.513351 | − | 0.858179i | \(-0.328404\pi\) | ||||
0.513351 | + | 0.858179i | \(0.328404\pi\) | |||||||
\(614\) | −13.8925 | −0.560657 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.31645 | 0.254497 | ||||||||
\(617\) | 27.7100 | 1.11556 | 0.557781 | − | 0.829988i | \(-0.311653\pi\) | ||||
0.557781 | + | 0.829988i | \(0.311653\pi\) | |||||||
\(618\) | 38.9382 | 1.56632 | ||||||||
\(619\) | 20.8439 | 0.837786 | 0.418893 | − | 0.908036i | \(-0.362418\pi\) | ||||
0.418893 | + | 0.908036i | \(0.362418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −76.3804 | −3.06504 | ||||||||
\(622\) | 3.51827 | 0.141070 | ||||||||
\(623\) | −7.61562 | −0.305113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.5650 | 0.981813 | ||||||||
\(627\) | 5.28189 | 0.210939 | ||||||||
\(628\) | −11.3935 | −0.454651 | ||||||||
\(629\) | −13.6156 | −0.542890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.7495 | 1.22412 | 0.612059 | − | 0.790812i | \(-0.290341\pi\) | ||||
0.612059 | + | 0.790812i | \(0.290341\pi\) | |||||||
\(632\) | 6.53854 | 0.260089 | ||||||||
\(633\) | −31.7982 | −1.26386 | ||||||||
\(634\) | 1.46146 | 0.0580420 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.34485 | 0.0533268 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.56496 | 0.339090 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0660 | −0.753060 | −0.376530 | − | 0.926404i | \(-0.622883\pi\) | ||||
−0.376530 | + | 0.926404i | \(0.622883\pi\) | |||||||
\(642\) | −5.64402 | −0.222752 | ||||||||
\(643\) | 45.8641 | 1.80870 | 0.904352 | − | 0.426786i | \(-0.140354\pi\) | ||||
0.904352 | + | 0.426786i | \(0.140354\pi\) | |||||||
\(644\) | −27.7100 | −1.09193 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.31645 | −0.130484 | ||||||||
\(647\) | −11.0173 | −0.433134 | −0.216567 | − | 0.976268i | \(-0.569486\pi\) | ||||
−0.216567 | + | 0.976268i | \(0.569486\pi\) | |||||||
\(648\) | −15.2110 | −0.597543 | ||||||||
\(649\) | 21.1979 | 0.832089 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 110.207 | 4.31935 | ||||||||
\(652\) | −16.8155 | −0.658544 | ||||||||
\(653\) | −14.5650 | −0.569971 | −0.284986 | − | 0.958532i | \(-0.591989\pi\) | ||||
−0.284986 | + | 0.958532i | \(0.591989\pi\) | |||||||
\(654\) | 11.4047 | 0.445957 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.85499 | −0.306686 | ||||||||
\(657\) | 71.6087 | 2.79372 | ||||||||
\(658\) | 44.5650 | 1.73732 | ||||||||
\(659\) | 19.8174 | 0.771978 | 0.385989 | − | 0.922503i | \(-0.373860\pi\) | ||||
0.385989 | + | 0.922503i | \(0.373860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4615 | 0.523590 | 0.261795 | − | 0.965123i | \(-0.415686\pi\) | ||||
0.261795 | + | 0.965123i | \(0.415686\pi\) | |||||||
\(662\) | −18.2394 | −0.708893 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.46146 | 0.173138 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −30.1542 | −1.16845 | ||||||||
\(667\) | −37.5741 | −1.45488 | ||||||||
\(668\) | −1.61562 | −0.0625102 | ||||||||
\(669\) | 65.0924 | 2.51662 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.0264 | −0.850321 | ||||||||
\(672\) | −12.7495 | −0.491823 | ||||||||
\(673\) | 0.0679332 | 0.00261863 | 0.00130932 | − | 0.999999i | \(-0.499583\pi\) | ||||
0.00130932 | + | 0.999999i | \(0.499583\pi\) | |||||||
\(674\) | −19.6329 | −0.756231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.1319 | −1.00433 | −0.502165 | − | 0.864772i | \(-0.667463\pi\) | ||||
−0.502165 | + | 0.864772i | \(0.667463\pi\) | |||||||
\(678\) | 49.8925 | 1.91611 | ||||||||
\(679\) | 15.5558 | 0.596977 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.0771 | −0.577755 | ||||||||
\(682\) | −13.2992 | −0.509252 | ||||||||
\(683\) | 17.0944 | 0.654097 | 0.327049 | − | 0.945007i | \(-0.393946\pi\) | ||||
0.327049 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(684\) | −7.34485 | −0.280837 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.7211 | 0.447514 | ||||||||
\(687\) | −20.8439 | −0.795243 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.3844 | 0.965667 | 0.482834 | − | 0.875712i | \(-0.339608\pi\) | ||||
0.482834 | + | 0.875712i | \(0.339608\pi\) | |||||||
\(692\) | 12.3164 | 0.468201 | ||||||||
\(693\) | −41.9666 | −1.59418 | ||||||||
\(694\) | 23.6816 | 0.898940 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.2880 | −0.655302 | ||||||||
\(697\) | 23.5650 | 0.892587 | ||||||||
\(698\) | −0.154159 | −0.00583499 | ||||||||
\(699\) | 44.6106 | 1.68733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.43108 | −0.356207 | −0.178103 | − | 0.984012i | \(-0.556996\pi\) | ||||
−0.178103 | + | 0.984012i | \(0.556996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.01728 | −0.189230 | ||||||||
\(704\) | 1.53854 | 0.0579859 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.6329 | −1.37870 | ||||||||
\(707\) | 29.4879 | 1.10901 | ||||||||
\(708\) | −42.7871 | −1.60804 | ||||||||
\(709\) | 20.1734 | 0.757629 | 0.378814 | − | 0.925473i | \(-0.376332\pi\) | ||||
0.378814 | + | 0.925473i | \(0.376332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.4422 | −1.62921 | ||||||||
\(712\) | −1.85499 | −0.0695186 | ||||||||
\(713\) | 58.3429 | 2.18496 | ||||||||
\(714\) | 38.2485 | 1.43141 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.1826 | −0.380540 | ||||||||
\(717\) | 3.55582 | 0.132794 | ||||||||
\(718\) | −27.2394 | −1.01656 | ||||||||
\(719\) | 31.4990 | 1.17471 | 0.587357 | − | 0.809328i | \(-0.300168\pi\) | ||||
0.587357 | + | 0.809328i | \(0.300168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.4768 | −1.91709 | ||||||||
\(722\) | 17.7779 | 0.661625 | ||||||||
\(723\) | −63.8703 | −2.37536 | ||||||||
\(724\) | −11.3935 | −0.423437 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.8093 | −0.994987 | ||||||||
\(727\) | −22.8814 | −0.848625 | −0.424312 | − | 0.905516i | \(-0.639484\pi\) | ||||
−0.424312 | + | 0.905516i | \(0.639484\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.36710 | −0.161745 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | 0.443836 | ||||||||
\(732\) | 44.4595 | 1.64327 | ||||||||
\(733\) | 48.1126 | 1.77708 | 0.888541 | − | 0.458798i | \(-0.151720\pi\) | ||||
0.888541 | + | 0.458798i | \(0.151720\pi\) | |||||||
\(734\) | 23.8641 | 0.880841 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.74950 | −0.248790 | ||||||||
\(737\) | −5.76876 | −0.212495 | ||||||||
\(738\) | 52.1887 | 1.92109 | ||||||||
\(739\) | 19.9321 | 0.733213 | 0.366606 | − | 0.930376i | \(-0.380520\pi\) | ||||
0.366606 | + | 0.930376i | \(0.380520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.77791 | −0.0652691 | ||||||||
\(743\) | −24.6248 | −0.903395 | −0.451698 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451698 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(744\) | 26.8439 | 0.984144 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.3164 | 0.817063 | ||||||||
\(747\) | −29.6420 | −1.08455 | ||||||||
\(748\) | −4.61562 | −0.168764 | ||||||||
\(749\) | 7.46146 | 0.272636 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.7273 | 1.34020 | 0.670098 | − | 0.742272i | \(-0.266252\pi\) | ||||
0.670098 | + | 0.742272i | \(0.266252\pi\) | |||||||
\(752\) | 10.8550 | 0.395841 | ||||||||
\(753\) | 10.2992 | 0.375323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 46.4595 | 1.68971 | ||||||||
\(757\) | 37.0091 | 1.34512 | 0.672560 | − | 0.740042i | \(-0.265195\pi\) | ||||
0.672560 | + | 0.740042i | \(0.265195\pi\) | |||||||
\(758\) | 9.74950 | 0.354118 | ||||||||
\(759\) | −32.2485 | −1.17055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.6420 | 0.965773 | 0.482887 | − | 0.875683i | \(-0.339588\pi\) | ||||
0.482887 | + | 0.875683i | \(0.339588\pi\) | |||||||
\(762\) | −15.2880 | −0.553827 | ||||||||
\(763\) | −15.0771 | −0.545827 | ||||||||
\(764\) | −19.4990 | −0.705449 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.7871 | 0.895593 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.10548 | −0.112059 | ||||||||
\(769\) | 37.2972 | 1.34497 | 0.672486 | − | 0.740110i | \(-0.265227\pi\) | ||||
0.672486 | + | 0.740110i | \(0.265227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.6106 | 1.39053 | ||||||||
\(772\) | 2.72110 | 0.0979346 | ||||||||
\(773\) | 10.5385 | 0.379045 | 0.189522 | − | 0.981876i | \(-0.439306\pi\) | ||||
0.189522 | + | 0.981876i | \(0.439306\pi\) | |||||||
\(774\) | 26.5761 | 0.955258 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.78903 | 0.136018 | ||||||||
\(777\) | 57.8641 | 2.07586 | ||||||||
\(778\) | −0.749505 | −0.0268711 | ||||||||
\(779\) | 8.68355 | 0.311121 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 20.2485 | 0.724085 | ||||||||
\(783\) | 62.9980 | 2.25137 | ||||||||
\(784\) | 9.85499 | 0.351964 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.68970 | 0.0959385 | ||||||||
\(787\) | −0.278898 | −0.00994165 | −0.00497083 | − | 0.999988i | \(-0.501582\pi\) | ||||
−0.00497083 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(788\) | 1.61562 | 0.0575540 | ||||||||
\(789\) | −13.6156 | −0.484729 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.9585 | −2.34521 | ||||||||
\(792\) | −10.2221 | −0.363226 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.67243 | 0.343262 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.2485 | 0.788578 | ||||||||
\(797\) | 42.0832 | 1.49066 | 0.745332 | − | 0.666693i | \(-0.232291\pi\) | ||||
0.745332 | + | 0.666693i | \(0.232291\pi\) | |||||||
\(798\) | 14.0944 | 0.498935 | ||||||||
\(799\) | −32.5650 | −1.15207 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.3246 | 0.435468 | ||||||||
\(802\) | −10.9321 | −0.386025 | ||||||||
\(803\) | 16.5822 | 0.585175 | ||||||||
\(804\) | 11.6440 | 0.410653 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.2880 | 0.608568 | ||||||||
\(808\) | 7.18256 | 0.252682 | ||||||||
\(809\) | −12.6329 | −0.444149 | −0.222074 | − | 0.975030i | \(-0.571283\pi\) | ||||
−0.222074 | + | 0.975030i | \(0.571283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1411 | −1.51489 | −0.757444 | − | 0.652901i | \(-0.773552\pi\) | ||||
−0.757444 | + | 0.652901i | \(0.773552\pi\) | |||||||
\(812\) | 22.8550 | 0.802053 | ||||||||
\(813\) | 29.1714 | 1.02309 | ||||||||
\(814\) | −6.98272 | −0.244744 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.31645 | 0.326141 | ||||||||
\(817\) | 4.42193 | 0.154704 | ||||||||
\(818\) | −26.5669 | −0.928891 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0173 | −0.803308 | −0.401654 | − | 0.915791i | \(-0.631565\pi\) | ||||
−0.401654 | + | 0.915791i | \(0.631565\pi\) | |||||||
\(822\) | −52.1035 | −1.81732 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | −12.5385 | −0.436801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 56.5650 | 1.96815 | ||||||||
\(827\) | −35.4027 | −1.23107 | −0.615536 | − | 0.788109i | \(-0.711060\pi\) | ||||
−0.615536 | + | 0.788109i | \(0.711060\pi\) | |||||||
\(828\) | 44.8439 | 1.55843 | ||||||||
\(829\) | 10.6065 | 0.368378 | 0.184189 | − | 0.982891i | \(-0.441034\pi\) | ||||
0.184189 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.0375 | 0.903233 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.5650 | −1.02437 | ||||||||
\(834\) | −13.6440 | −0.472454 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.70083 | −0.0588244 | ||||||||
\(837\) | −97.8196 | −3.38114 | ||||||||
\(838\) | −24.3145 | −0.839929 | ||||||||
\(839\) | −19.4615 | −0.671884 | −0.335942 | − | 0.941883i | \(-0.609055\pi\) | ||||
−0.335942 | + | 0.941883i | \(0.609055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.99085 | 0.0686501 | ||||||||
\(842\) | −6.15416 | −0.212086 | ||||||||
\(843\) | 39.2312 | 1.35120 | ||||||||
\(844\) | 10.2394 | 0.352454 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −72.1208 | −2.47956 | ||||||||
\(847\) | 35.4422 | 1.21781 | ||||||||
\(848\) | −0.433057 | −0.0148712 | ||||||||
\(849\) | −41.8327 | −1.43570 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.6329 | 1.05008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9807 | 0.547170 | 0.273585 | − | 0.961848i | \(-0.411790\pi\) | ||||
0.273585 | + | 0.961848i | \(0.411790\pi\) | |||||||
\(854\) | −58.7759 | −2.01127 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.81744 | 0.0621188 | ||||||||
\(857\) | −38.5669 | −1.31742 | −0.658711 | − | 0.752396i | \(-0.728898\pi\) | ||||
−0.658711 | + | 0.752396i | \(0.728898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.6836 | −0.978670 | −0.489335 | − | 0.872096i | \(-0.662760\pi\) | ||||
−0.489335 | + | 0.872096i | \(0.662760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −100.147 | −3.41301 | ||||||||
\(862\) | 0.828565 | 0.0282210 | ||||||||
\(863\) | 36.4706 | 1.24147 | 0.620737 | − | 0.784019i | \(-0.286834\pi\) | ||||
0.620737 | + | 0.784019i | \(0.286834\pi\) | |||||||
\(864\) | 11.3164 | 0.384993 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.7008 | 0.533536 | ||||||||
\(867\) | 24.8439 | 0.843742 | ||||||||
\(868\) | −35.4879 | −1.20454 | ||||||||
\(869\) | −10.0598 | −0.341255 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.67243 | −0.124364 | ||||||||
\(873\) | −25.1744 | −0.852025 | ||||||||
\(874\) | 7.46146 | 0.252388 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.4706 | −1.13087 | ||||||||
\(877\) | 7.02027 | 0.237058 | 0.118529 | − | 0.992951i | \(-0.462182\pi\) | ||||
0.118529 | + | 0.992951i | \(0.462182\pi\) | |||||||
\(878\) | −9.17144 | −0.309521 | ||||||||
\(879\) | −18.6329 | −0.628472 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.93405 | −0.166232 | −0.0831161 | − | 0.996540i | \(-0.526487\pi\) | ||||
−0.0831161 | + | 0.996540i | \(0.526487\pi\) | |||||||
\(882\) | −65.4768 | −2.20472 | ||||||||
\(883\) | 49.9493 | 1.68093 | 0.840465 | − | 0.541866i | \(-0.182282\pi\) | ||||
0.840465 | + | 0.541866i | \(0.182282\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.3164 | −0.514566 | ||||||||
\(887\) | −3.86413 | −0.129745 | −0.0648725 | − | 0.997894i | \(-0.520664\pi\) | ||||
−0.0648725 | + | 0.997894i | \(0.520664\pi\) | |||||||
\(888\) | 14.0944 | 0.472976 | ||||||||
\(889\) | 20.2110 | 0.677854 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.4027 | 0.784019 | ||||||||
\(892\) | −20.9605 | −0.701808 | ||||||||
\(893\) | −12.0000 | −0.401565 | ||||||||
\(894\) | −30.1542 | −1.00851 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.10548 | 0.137155 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.4108 | 0.781229 | ||||||||
\(899\) | −48.1208 | −1.60492 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29917 | 0.0432817 | ||||||||
\(902\) | 12.0852 | 0.402393 | ||||||||
\(903\) | −50.9980 | −1.69711 | ||||||||
\(904\) | −16.0660 | −0.534346 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.73223 | 0.256886 | ||||||||
\(907\) | −17.5558 | −0.582931 | −0.291466 | − | 0.956581i | \(-0.594143\pi\) | ||||
−0.291466 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(908\) | 4.85499 | 0.161118 | ||||||||
\(909\) | −47.7211 | −1.58281 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9807 | −0.927043 | −0.463522 | − | 0.886086i | \(-0.653414\pi\) | ||||
−0.463522 | + | 0.886086i | \(0.653414\pi\) | |||||||
\(912\) | 3.43306 | 0.113680 | ||||||||
\(913\) | −6.86413 | −0.227170 | ||||||||
\(914\) | −22.9321 | −0.758525 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.71196 | 0.221769 | ||||||||
\(917\) | −3.55582 | −0.117423 | ||||||||
\(918\) | −33.9493 | −1.12050 | ||||||||
\(919\) | 31.0356 | 1.02377 | 0.511884 | − | 0.859054i | \(-0.328948\pi\) | ||||
0.511884 | + | 0.859054i | \(0.328948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.1430 | −1.42161 | ||||||||
\(922\) | −13.4615 | −0.443330 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 19.6156 | 0.645306 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.0264 | 0.526661 | ||||||||
\(927\) | 83.3063 | 2.73614 | ||||||||
\(928\) | 5.56694 | 0.182744 | ||||||||
\(929\) | −24.0000 | −0.787414 | −0.393707 | − | 0.919236i | \(-0.628808\pi\) | ||||
−0.393707 | + | 0.919236i | \(0.628808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.8945 | −0.357053 | ||||||||
\(932\) | −14.3651 | −0.470545 | ||||||||
\(933\) | 10.9259 | 0.357698 | ||||||||
\(934\) | −0.866114 | −0.0283401 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.8987 | 1.98947 | 0.994737 | − | 0.102464i | \(-0.0326727\pi\) | ||||
0.994737 | + | 0.102464i | \(0.0326727\pi\) | |||||||
\(938\) | −15.3935 | −0.502616 | ||||||||
\(939\) | 76.2861 | 2.48950 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.2485 | −1.05127 | −0.525636 | − | 0.850710i | \(-0.676173\pi\) | ||||
−0.525636 | + | 0.850710i | \(0.676173\pi\) | |||||||
\(942\) | −35.3824 | −1.15282 | ||||||||
\(943\) | −53.0173 | −1.72648 | ||||||||
\(944\) | 13.7779 | 0.448433 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.15416 | 0.200089 | ||||||||
\(947\) | 20.4108 | 0.663262 | 0.331631 | − | 0.943409i | \(-0.392401\pi\) | ||||
0.331631 | + | 0.943409i | \(0.392401\pi\) | |||||||
\(948\) | 20.3053 | 0.659486 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.53854 | 0.147172 | ||||||||
\(952\) | −12.3164 | −0.399178 | ||||||||
\(953\) | 8.36710 | 0.271037 | 0.135519 | − | 0.990775i | \(-0.456730\pi\) | ||||
0.135519 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(954\) | 2.87724 | 0.0931541 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.14501 | −0.0370324 | ||||||||
\(957\) | 26.5983 | 0.859802 | ||||||||
\(958\) | −29.4879 | −0.952710 | ||||||||
\(959\) | 68.8814 | 2.22430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.7191 | 1.41029 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0751 | −0.389115 | ||||||||
\(964\) | 20.5669 | 0.662417 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −86.0528 | −2.76870 | ||||||||
\(967\) | 14.4108 | 0.463420 | 0.231710 | − | 0.972785i | \(-0.425568\pi\) | ||||
0.231710 | + | 0.972785i | \(0.425568\pi\) | |||||||
\(968\) | 8.63290 | 0.277472 | ||||||||
\(969\) | −10.2992 | −0.330857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.1806 | 0.808083 | 0.404042 | − | 0.914741i | \(-0.367605\pi\) | ||||
0.404042 | + | 0.914741i | \(0.367605\pi\) | |||||||
\(972\) | −13.2880 | −0.426214 | ||||||||
\(973\) | 18.0375 | 0.578257 | ||||||||
\(974\) | 35.4503 | 1.13590 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.3164 | −0.458258 | ||||||||
\(977\) | −38.1633 | −1.22095 | −0.610476 | − | 0.792035i | \(-0.709022\pi\) | ||||
−0.610476 | + | 0.792035i | \(0.709022\pi\) | |||||||
\(978\) | −52.2201 | −1.66982 | ||||||||
\(979\) | 2.85397 | 0.0912133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.3997 | 0.779022 | ||||||||
\(982\) | −32.1319 | −1.02537 | ||||||||
\(983\) | 49.8906 | 1.59126 | 0.795631 | − | 0.605782i | \(-0.207140\pi\) | ||||
0.795631 | + | 0.605782i | \(0.207140\pi\) | |||||||
\(984\) | −24.3935 | −0.777637 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.7008 | −0.531863 | ||||||||
\(987\) | 138.396 | 4.40518 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.9980 | −0.858487 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.6329 | −0.337765 | −0.168883 | − | 0.985636i | \(-0.554016\pi\) | ||||
−0.168883 | + | 0.985636i | \(0.554016\pi\) | |||||||
\(992\) | −8.64402 | −0.274448 | ||||||||
\(993\) | −56.6420 | −1.79748 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.8550 | 0.439012 | ||||||||
\(997\) | −2.99085 | −0.0947213 | −0.0473606 | − | 0.998878i | \(-0.515081\pi\) | ||||
−0.0473606 | + | 0.998878i | \(0.515081\pi\) | |||||||
\(998\) | −27.2769 | −0.863436 | ||||||||
\(999\) | −51.3601 | −1.62496 |
(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 | 8450.2.a.br.1.1 | 3 | ||
5.4 | even | 2 | 8450.2.a.ce.1.3 | 3 | |||
13.5 | odd | 4 | 650.2.d.c.51.4 | yes | 6 | ||
13.8 | odd | 4 | 650.2.d.c.51.1 | ✓ | 6 | ||
13.12 | even | 2 | 8450.2.a.cd.1.1 | 3 | |||
65.8 | even | 4 | 650.2.c.e.649.1 | 6 | |||
65.18 | even | 4 | 650.2.c.f.649.1 | 6 | |||
65.34 | odd | 4 | 650.2.d.d.51.6 | yes | 6 | ||
65.44 | odd | 4 | 650.2.d.d.51.3 | yes | 6 | ||
65.47 | even | 4 | 650.2.c.f.649.6 | 6 | |||
65.57 | even | 4 | 650.2.c.e.649.6 | 6 | |||
65.64 | even | 2 | 8450.2.a.bq.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
650.2.c.e.649.1 | 6 | 65.8 | even | 4 | |||
650.2.c.e.649.6 | 6 | 65.57 | even | 4 | |||
650.2.c.f.649.1 | 6 | 65.18 | even | 4 | |||
650.2.c.f.649.6 | 6 | 65.47 | even | 4 | |||
650.2.d.c.51.1 | ✓ | 6 | 13.8 | odd | 4 | ||
650.2.d.c.51.4 | yes | 6 | 13.5 | odd | 4 | ||
650.2.d.d.51.3 | yes | 6 | 65.44 | odd | 4 | ||
650.2.d.d.51.6 | yes | 6 | 65.34 | odd | 4 | ||
8450.2.a.bq.1.3 | 3 | 65.64 | even | 2 | |||
8450.2.a.br.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8450.2.a.cd.1.1 | 3 | 13.12 | even | 2 | |||
8450.2.a.ce.1.3 | 3 | 5.4 | even | 2 |