Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, 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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.345065.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 14x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.04534\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 | ||||||||
\(3\) | 1.04534 | 0.603528 | 0.301764 | − | 0.953383i | \(-0.402425\pi\) | ||||
0.301764 | + | 0.953383i | \(0.402425\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.635591 | 0.284245 | 0.142123 | − | 0.989849i | \(-0.454607\pi\) | ||||
0.142123 | + | 0.989849i | \(0.454607\pi\) | |||||||
\(6\) | 1.04534 | 0.426759 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.90726 | −0.635754 | ||||||||
\(10\) | 0.635591 | 0.200992 | ||||||||
\(11\) | −6.16435 | −1.85862 | −0.929311 | − | 0.369297i | \(-0.879599\pi\) | ||||
−0.929311 | + | 0.369297i | \(0.879599\pi\) | |||||||
\(12\) | 1.04534 | 0.301764 | ||||||||
\(13\) | −3.50826 | −0.973017 | −0.486508 | − | 0.873676i | \(-0.661730\pi\) | ||||
−0.486508 | + | 0.873676i | \(0.661730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.664410 | 0.171550 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.49417 | −1.09000 | −0.544998 | − | 0.838437i | \(-0.683470\pi\) | ||||
−0.544998 | + | 0.838437i | \(0.683470\pi\) | |||||||
\(18\) | −1.90726 | −0.449546 | ||||||||
\(19\) | 2.66684 | 0.611816 | 0.305908 | − | 0.952061i | \(-0.401040\pi\) | ||||
0.305908 | + | 0.952061i | \(0.401040\pi\) | |||||||
\(20\) | 0.635591 | 0.142123 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.16435 | −1.31424 | ||||||||
\(23\) | 0.452171 | 0.0942841 | 0.0471421 | − | 0.998888i | \(-0.484989\pi\) | ||||
0.0471421 | + | 0.998888i | \(0.484989\pi\) | |||||||
\(24\) | 1.04534 | 0.213379 | ||||||||
\(25\) | −4.59602 | −0.919205 | ||||||||
\(26\) | −3.50826 | −0.688027 | ||||||||
\(27\) | −5.12976 | −0.987223 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0.664410 | 0.121304 | ||||||||
\(31\) | −8.57744 | −1.54055 | −0.770277 | − | 0.637709i | \(-0.779882\pi\) | ||||
−0.770277 | + | 0.637709i | \(0.779882\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.44385 | −1.12173 | ||||||||
\(34\) | −4.49417 | −0.770744 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.90726 | −0.317877 | ||||||||
\(37\) | 3.80826 | 0.626075 | 0.313037 | − | 0.949741i | \(-0.398654\pi\) | ||||
0.313037 | + | 0.949741i | \(0.398654\pi\) | |||||||
\(38\) | 2.66684 | 0.432619 | ||||||||
\(39\) | −3.66733 | −0.587243 | ||||||||
\(40\) | 0.635591 | 0.100496 | ||||||||
\(41\) | −7.48968 | −1.16969 | −0.584846 | − | 0.811144i | \(-0.698845\pi\) | ||||
−0.584846 | + | 0.811144i | \(0.698845\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90726 | 0.443353 | 0.221677 | − | 0.975120i | \(-0.428847\pi\) | ||||
0.221677 | + | 0.975120i | \(0.428847\pi\) | |||||||
\(44\) | −6.16435 | −0.929311 | ||||||||
\(45\) | −1.21224 | −0.180710 | ||||||||
\(46\) | 0.452171 | 0.0666689 | ||||||||
\(47\) | 5.21018 | 0.759983 | 0.379992 | − | 0.924990i | \(-0.375927\pi\) | ||||
0.379992 | + | 0.924990i | \(0.375927\pi\) | |||||||
\(48\) | 1.04534 | 0.150882 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.59602 | −0.649976 | ||||||||
\(51\) | −4.69794 | −0.657844 | ||||||||
\(52\) | −3.50826 | −0.486508 | ||||||||
\(53\) | 14.4482 | 1.98461 | 0.992307 | − | 0.123800i | \(-0.0395082\pi\) | ||||
0.992307 | + | 0.123800i | \(0.0395082\pi\) | |||||||
\(54\) | −5.12976 | −0.698072 | ||||||||
\(55\) | −3.91801 | −0.528305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.78776 | 0.369248 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −5.00626 | −0.651760 | −0.325880 | − | 0.945411i | \(-0.605660\pi\) | ||||
−0.325880 | + | 0.945411i | \(0.605660\pi\) | |||||||
\(60\) | 0.664410 | 0.0857750 | ||||||||
\(61\) | −2.07416 | −0.265569 | −0.132784 | − | 0.991145i | \(-0.542392\pi\) | ||||
−0.132784 | + | 0.991145i | \(0.542392\pi\) | |||||||
\(62\) | −8.57744 | −1.08934 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.22982 | −0.276575 | ||||||||
\(66\) | −6.44385 | −0.793184 | ||||||||
\(67\) | −4.11658 | −0.502920 | −0.251460 | − | 0.967868i | \(-0.580911\pi\) | ||||
−0.251460 | + | 0.967868i | \(0.580911\pi\) | |||||||
\(68\) | −4.49417 | −0.544998 | ||||||||
\(69\) | 0.472673 | 0.0569031 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.69502 | 0.319840 | 0.159920 | − | 0.987130i | \(-0.448876\pi\) | ||||
0.159920 | + | 0.987130i | \(0.448876\pi\) | |||||||
\(72\) | −1.90726 | −0.224773 | ||||||||
\(73\) | 8.43154 | 0.986837 | 0.493418 | − | 0.869792i | \(-0.335747\pi\) | ||||
0.493418 | + | 0.869792i | \(0.335747\pi\) | |||||||
\(74\) | 3.80826 | 0.442702 | ||||||||
\(75\) | −4.80441 | −0.554766 | ||||||||
\(76\) | 2.66684 | 0.305908 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.66733 | −0.415243 | ||||||||
\(79\) | −0.108600 | −0.0122185 | −0.00610923 | − | 0.999981i | \(-0.501945\pi\) | ||||
−0.00610923 | + | 0.999981i | \(0.501945\pi\) | |||||||
\(80\) | 0.635591 | 0.0710613 | ||||||||
\(81\) | 0.359432 | 0.0399369 | ||||||||
\(82\) | −7.48968 | −0.827097 | ||||||||
\(83\) | −0.985249 | −0.108145 | −0.0540726 | − | 0.998537i | \(-0.517220\pi\) | ||||
−0.0540726 | + | 0.998537i | \(0.517220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.85646 | −0.309826 | ||||||||
\(86\) | 2.90726 | 0.313498 | ||||||||
\(87\) | 1.04534 | 0.112072 | ||||||||
\(88\) | −6.16435 | −0.657122 | ||||||||
\(89\) | −17.7911 | −1.88586 | −0.942929 | − | 0.332995i | \(-0.891941\pi\) | ||||
−0.942929 | + | 0.332995i | \(0.891941\pi\) | |||||||
\(90\) | −1.21224 | −0.127781 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.452171 | 0.0471421 | ||||||||
\(93\) | −8.96636 | −0.929768 | ||||||||
\(94\) | 5.21018 | 0.537389 | ||||||||
\(95\) | 1.69502 | 0.173906 | ||||||||
\(96\) | 1.04534 | 0.106690 | ||||||||
\(97\) | 2.64094 | 0.268147 | 0.134074 | − | 0.990971i | \(-0.457194\pi\) | ||||
0.134074 | + | 0.990971i | \(0.457194\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7570 | 1.18163 | ||||||||
\(100\) | −4.59602 | −0.459602 | ||||||||
\(101\) | −1.78442 | −0.177556 | −0.0887782 | − | 0.996051i | \(-0.528296\pi\) | ||||
−0.0887782 | + | 0.996051i | \(0.528296\pi\) | |||||||
\(102\) | −4.69794 | −0.465166 | ||||||||
\(103\) | 11.6741 | 1.15028 | 0.575139 | − | 0.818056i | \(-0.304948\pi\) | ||||
0.575139 | + | 0.818056i | \(0.304948\pi\) | |||||||
\(104\) | −3.50826 | −0.344013 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.4482 | 1.40333 | ||||||||
\(107\) | −10.8464 | −1.04856 | −0.524282 | − | 0.851545i | \(-0.675666\pi\) | ||||
−0.524282 | + | 0.851545i | \(0.675666\pi\) | |||||||
\(108\) | −5.12976 | −0.493612 | ||||||||
\(109\) | −12.0238 | −1.15168 | −0.575838 | − | 0.817564i | \(-0.695324\pi\) | ||||
−0.575838 | + | 0.817564i | \(0.695324\pi\) | |||||||
\(110\) | −3.91801 | −0.373568 | ||||||||
\(111\) | 3.98093 | 0.377854 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.4936 | 1.92787 | 0.963937 | − | 0.266132i | \(-0.0857457\pi\) | ||||
0.963937 | + | 0.266132i | \(0.0857457\pi\) | |||||||
\(114\) | 2.78776 | 0.261098 | ||||||||
\(115\) | 0.287396 | 0.0267998 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 6.69117 | 0.618599 | ||||||||
\(118\) | −5.00626 | −0.460864 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.664410 | 0.0606521 | ||||||||
\(121\) | 26.9993 | 2.45448 | ||||||||
\(122\) | −2.07416 | −0.187786 | ||||||||
\(123\) | −7.82927 | −0.705942 | ||||||||
\(124\) | −8.57744 | −0.770277 | ||||||||
\(125\) | −6.09915 | −0.545525 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.47893 | 0.752384 | 0.376192 | − | 0.926542i | \(-0.377233\pi\) | ||||
0.376192 | + | 0.926542i | \(0.377233\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.03908 | 0.267576 | ||||||||
\(130\) | −2.22982 | −0.195568 | ||||||||
\(131\) | 0.635591 | 0.0555319 | 0.0277659 | − | 0.999614i | \(-0.491161\pi\) | ||||
0.0277659 | + | 0.999614i | \(0.491161\pi\) | |||||||
\(132\) | −6.44385 | −0.560866 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.11658 | −0.355618 | ||||||||
\(135\) | −3.26043 | −0.280613 | ||||||||
\(136\) | −4.49417 | −0.385372 | ||||||||
\(137\) | 2.85938 | 0.244293 | 0.122147 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122147 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(138\) | 0.472673 | 0.0402366 | ||||||||
\(139\) | −21.2565 | −1.80295 | −0.901476 | − | 0.432829i | \(-0.857516\pi\) | ||||
−0.901476 | + | 0.432829i | \(0.857516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.44642 | 0.458671 | ||||||||
\(142\) | 2.69502 | 0.226161 | ||||||||
\(143\) | 21.6262 | 1.80847 | ||||||||
\(144\) | −1.90726 | −0.158938 | ||||||||
\(145\) | 0.635591 | 0.0527830 | ||||||||
\(146\) | 8.43154 | 0.697799 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.80826 | 0.313037 | ||||||||
\(149\) | 8.48185 | 0.694861 | 0.347430 | − | 0.937706i | \(-0.387054\pi\) | ||||
0.347430 | + | 0.937706i | \(0.387054\pi\) | |||||||
\(150\) | −4.80441 | −0.392279 | ||||||||
\(151\) | 11.4003 | 0.927745 | 0.463873 | − | 0.885902i | \(-0.346460\pi\) | ||||
0.463873 | + | 0.885902i | \(0.346460\pi\) | |||||||
\(152\) | 2.66684 | 0.216310 | ||||||||
\(153\) | 8.57156 | 0.692970 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.45175 | −0.437895 | ||||||||
\(156\) | −3.66733 | −0.293621 | ||||||||
\(157\) | 15.3723 | 1.22684 | 0.613421 | − | 0.789756i | \(-0.289793\pi\) | ||||
0.613421 | + | 0.789756i | \(0.289793\pi\) | |||||||
\(158\) | −0.108600 | −0.00863976 | ||||||||
\(159\) | 15.1033 | 1.19777 | ||||||||
\(160\) | 0.635591 | 0.0502479 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.359432 | 0.0282397 | ||||||||
\(163\) | 14.9818 | 1.17347 | 0.586733 | − | 0.809781i | \(-0.300414\pi\) | ||||
0.586733 | + | 0.809781i | \(0.300414\pi\) | |||||||
\(164\) | −7.48968 | −0.584846 | ||||||||
\(165\) | −4.09566 | −0.318847 | ||||||||
\(166\) | −0.985249 | −0.0764702 | ||||||||
\(167\) | −10.8187 | −0.837174 | −0.418587 | − | 0.908177i | \(-0.637475\pi\) | ||||
−0.418587 | + | 0.908177i | \(0.637475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.692102 | −0.0532386 | ||||||||
\(170\) | −2.85646 | −0.219080 | ||||||||
\(171\) | −5.08637 | −0.388964 | ||||||||
\(172\) | 2.90726 | 0.221677 | ||||||||
\(173\) | −8.59512 | −0.653475 | −0.326737 | − | 0.945115i | \(-0.605949\pi\) | ||||
−0.326737 | + | 0.945115i | \(0.605949\pi\) | |||||||
\(174\) | 1.04534 | 0.0792471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.16435 | −0.464656 | ||||||||
\(177\) | −5.23325 | −0.393355 | ||||||||
\(178\) | −17.7911 | −1.33350 | ||||||||
\(179\) | −10.4823 | −0.783482 | −0.391741 | − | 0.920076i | \(-0.628127\pi\) | ||||
−0.391741 | + | 0.920076i | \(0.628127\pi\) | |||||||
\(180\) | −1.21224 | −0.0903550 | ||||||||
\(181\) | 8.98480 | 0.667835 | 0.333918 | − | 0.942602i | \(-0.391629\pi\) | ||||
0.333918 | + | 0.942602i | \(0.391629\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.16820 | −0.160278 | ||||||||
\(184\) | 0.452171 | 0.0333345 | ||||||||
\(185\) | 2.42050 | 0.177959 | ||||||||
\(186\) | −8.96636 | −0.657445 | ||||||||
\(187\) | 27.7037 | 2.02589 | ||||||||
\(188\) | 5.21018 | 0.379992 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.69502 | 0.122970 | ||||||||
\(191\) | −4.17699 | −0.302236 | −0.151118 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151118 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(192\) | 1.04534 | 0.0754410 | ||||||||
\(193\) | −22.9970 | −1.65536 | −0.827679 | − | 0.561202i | \(-0.810339\pi\) | ||||
−0.827679 | + | 0.561202i | \(0.810339\pi\) | |||||||
\(194\) | 2.64094 | 0.189609 | ||||||||
\(195\) | −2.33092 | −0.166921 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.1448 | −1.86274 | −0.931371 | − | 0.364070i | \(-0.881387\pi\) | ||||
−0.931371 | + | 0.364070i | \(0.881387\pi\) | |||||||
\(198\) | 11.7570 | 0.835536 | ||||||||
\(199\) | 14.5540 | 1.03171 | 0.515854 | − | 0.856677i | \(-0.327475\pi\) | ||||
0.515854 | + | 0.856677i | \(0.327475\pi\) | |||||||
\(200\) | −4.59602 | −0.324988 | ||||||||
\(201\) | −4.30323 | −0.303527 | ||||||||
\(202\) | −1.78442 | −0.125551 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.69794 | −0.328922 | ||||||||
\(205\) | −4.76038 | −0.332479 | ||||||||
\(206\) | 11.6741 | 0.813370 | ||||||||
\(207\) | −0.862408 | −0.0599415 | ||||||||
\(208\) | −3.50826 | −0.243254 | ||||||||
\(209\) | −16.4394 | −1.13713 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7774 | −1.01732 | −0.508660 | − | 0.860967i | \(-0.669859\pi\) | ||||
−0.508660 | + | 0.860967i | \(0.669859\pi\) | |||||||
\(212\) | 14.4482 | 0.992307 | ||||||||
\(213\) | 2.81722 | 0.193033 | ||||||||
\(214\) | −10.8464 | −0.741447 | ||||||||
\(215\) | 1.84783 | 0.126021 | ||||||||
\(216\) | −5.12976 | −0.349036 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.0238 | −0.814357 | ||||||||
\(219\) | 8.81383 | 0.595584 | ||||||||
\(220\) | −3.91801 | −0.264152 | ||||||||
\(221\) | 15.7667 | 1.06058 | ||||||||
\(222\) | 3.98093 | 0.267183 | ||||||||
\(223\) | 12.1276 | 0.812127 | 0.406063 | − | 0.913845i | \(-0.366901\pi\) | ||||
0.406063 | + | 0.913845i | \(0.366901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.76582 | 0.584388 | ||||||||
\(226\) | 20.4936 | 1.36321 | ||||||||
\(227\) | −25.7246 | −1.70740 | −0.853701 | − | 0.520764i | \(-0.825647\pi\) | ||||
−0.853701 | + | 0.520764i | \(0.825647\pi\) | |||||||
\(228\) | 2.78776 | 0.184624 | ||||||||
\(229\) | −7.39225 | −0.488494 | −0.244247 | − | 0.969713i | \(-0.578541\pi\) | ||||
−0.244247 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(230\) | 0.287396 | 0.0189503 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 1.24860 | 0.0817987 | 0.0408994 | − | 0.999163i | \(-0.486978\pi\) | ||||
0.0408994 | + | 0.999163i | \(0.486978\pi\) | |||||||
\(234\) | 6.69117 | 0.437416 | ||||||||
\(235\) | 3.31155 | 0.216022 | ||||||||
\(236\) | −5.00626 | −0.325880 | ||||||||
\(237\) | −0.113524 | −0.00737418 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6217 | 1.46328 | 0.731640 | − | 0.681692i | \(-0.238755\pi\) | ||||
0.731640 | + | 0.681692i | \(0.238755\pi\) | |||||||
\(240\) | 0.664410 | 0.0428875 | ||||||||
\(241\) | −29.9759 | −1.93092 | −0.965458 | − | 0.260560i | \(-0.916093\pi\) | ||||
−0.965458 | + | 0.260560i | \(0.916093\pi\) | |||||||
\(242\) | 26.9993 | 1.73558 | ||||||||
\(243\) | 15.7650 | 1.01133 | ||||||||
\(244\) | −2.07416 | −0.132784 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.82927 | −0.499176 | ||||||||
\(247\) | −9.35598 | −0.595307 | ||||||||
\(248\) | −8.57744 | −0.544668 | ||||||||
\(249\) | −1.02992 | −0.0652686 | ||||||||
\(250\) | −6.09915 | −0.385744 | ||||||||
\(251\) | 6.13268 | 0.387092 | 0.193546 | − | 0.981091i | \(-0.438001\pi\) | ||||
0.193546 | + | 0.981091i | \(0.438001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.78734 | −0.175239 | ||||||||
\(254\) | 8.47893 | 0.532016 | ||||||||
\(255\) | −2.98597 | −0.186989 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.8072 | −1.79694 | −0.898472 | − | 0.439031i | \(-0.855322\pi\) | ||||
−0.898472 | + | 0.439031i | \(0.855322\pi\) | |||||||
\(258\) | 3.03908 | 0.189205 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.22982 | −0.138288 | ||||||||
\(261\) | −1.90726 | −0.118057 | ||||||||
\(262\) | 0.635591 | 0.0392670 | ||||||||
\(263\) | −12.6525 | −0.780185 | −0.390092 | − | 0.920776i | \(-0.627557\pi\) | ||||
−0.390092 | + | 0.920776i | \(0.627557\pi\) | |||||||
\(264\) | −6.44385 | −0.396592 | ||||||||
\(265\) | 9.18316 | 0.564117 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.5978 | −1.13817 | ||||||||
\(268\) | −4.11658 | −0.251460 | ||||||||
\(269\) | −25.5822 | −1.55977 | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(270\) | −3.26043 | −0.198424 | ||||||||
\(271\) | −9.13120 | −0.554681 | −0.277340 | − | 0.960772i | \(-0.589453\pi\) | ||||
−0.277340 | + | 0.960772i | \(0.589453\pi\) | |||||||
\(272\) | −4.49417 | −0.272499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.85938 | 0.172741 | ||||||||
\(275\) | 28.3315 | 1.70845 | ||||||||
\(276\) | 0.472673 | 0.0284516 | ||||||||
\(277\) | −7.53642 | −0.452820 | −0.226410 | − | 0.974032i | \(-0.572699\pi\) | ||||
−0.226410 | + | 0.974032i | \(0.572699\pi\) | |||||||
\(278\) | −21.2565 | −1.27488 | ||||||||
\(279\) | 16.3594 | 0.979414 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.16607 | 0.248527 | 0.124264 | − | 0.992249i | \(-0.460343\pi\) | ||||
0.124264 | + | 0.992249i | \(0.460343\pi\) | |||||||
\(282\) | 5.44642 | 0.324330 | ||||||||
\(283\) | −2.62137 | −0.155824 | −0.0779121 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779121 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(284\) | 2.69502 | 0.159920 | ||||||||
\(285\) | 1.77188 | 0.104957 | ||||||||
\(286\) | 21.6262 | 1.27878 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.90726 | −0.112386 | ||||||||
\(289\) | 3.19758 | 0.188093 | ||||||||
\(290\) | 0.635591 | 0.0373232 | ||||||||
\(291\) | 2.76069 | 0.161834 | ||||||||
\(292\) | 8.43154 | 0.493418 | ||||||||
\(293\) | −15.0423 | −0.878780 | −0.439390 | − | 0.898296i | \(-0.644805\pi\) | ||||
−0.439390 | + | 0.898296i | \(0.644805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.18194 | −0.185260 | ||||||||
\(296\) | 3.80826 | 0.221351 | ||||||||
\(297\) | 31.6217 | 1.83488 | ||||||||
\(298\) | 8.48185 | 0.491341 | ||||||||
\(299\) | −1.58633 | −0.0917400 | ||||||||
\(300\) | −4.80441 | −0.277383 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.4003 | 0.656015 | ||||||||
\(303\) | −1.86533 | −0.107160 | ||||||||
\(304\) | 2.66684 | 0.152954 | ||||||||
\(305\) | −1.31832 | −0.0754867 | ||||||||
\(306\) | 8.57156 | 0.490004 | ||||||||
\(307\) | 2.56941 | 0.146644 | 0.0733221 | − | 0.997308i | \(-0.476640\pi\) | ||||
0.0733221 | + | 0.997308i | \(0.476640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.2034 | 0.694225 | ||||||||
\(310\) | −5.45175 | −0.309639 | ||||||||
\(311\) | 8.70307 | 0.493506 | 0.246753 | − | 0.969078i | \(-0.420636\pi\) | ||||
0.246753 | + | 0.969078i | \(0.420636\pi\) | |||||||
\(312\) | −3.66733 | −0.207622 | ||||||||
\(313\) | −17.5432 | −0.991601 | −0.495800 | − | 0.868437i | \(-0.665125\pi\) | ||||
−0.495800 | + | 0.868437i | \(0.665125\pi\) | |||||||
\(314\) | 15.3723 | 0.867508 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.108600 | −0.00610923 | ||||||||
\(317\) | −13.6648 | −0.767492 | −0.383746 | − | 0.923439i | \(-0.625366\pi\) | ||||
−0.383746 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(318\) | 15.1033 | 0.846952 | ||||||||
\(319\) | −6.16435 | −0.345138 | ||||||||
\(320\) | 0.635591 | 0.0355306 | ||||||||
\(321\) | −11.3382 | −0.632838 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.9852 | −0.666877 | ||||||||
\(324\) | 0.359432 | 0.0199685 | ||||||||
\(325\) | 16.1241 | 0.894401 | ||||||||
\(326\) | 14.9818 | 0.829765 | ||||||||
\(327\) | −12.5690 | −0.695068 | ||||||||
\(328\) | −7.48968 | −0.413549 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.09566 | −0.225459 | ||||||||
\(331\) | −30.2232 | −1.66122 | −0.830609 | − | 0.556855i | \(-0.812008\pi\) | ||||
−0.830609 | + | 0.556855i | \(0.812008\pi\) | |||||||
\(332\) | −0.985249 | −0.0540726 | ||||||||
\(333\) | −7.26335 | −0.398029 | ||||||||
\(334\) | −10.8187 | −0.591972 | ||||||||
\(335\) | −2.61646 | −0.142953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4947 | 1.38878 | 0.694392 | − | 0.719597i | \(-0.255673\pi\) | ||||
0.694392 | + | 0.719597i | \(0.255673\pi\) | |||||||
\(338\) | −0.692102 | −0.0376454 | ||||||||
\(339\) | 21.4228 | 1.16353 | ||||||||
\(340\) | −2.85646 | −0.154913 | ||||||||
\(341\) | 52.8744 | 2.86331 | ||||||||
\(342\) | −5.08637 | −0.275039 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.90726 | 0.156749 | ||||||||
\(345\) | 0.300427 | 0.0161744 | ||||||||
\(346\) | −8.59512 | −0.462076 | ||||||||
\(347\) | 13.5955 | 0.729845 | 0.364923 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364923 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(348\) | 1.04534 | 0.0560362 | ||||||||
\(349\) | 10.7077 | 0.573171 | 0.286585 | − | 0.958055i | \(-0.407480\pi\) | ||||
0.286585 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.9965 | 0.960585 | ||||||||
\(352\) | −6.16435 | −0.328561 | ||||||||
\(353\) | 2.57148 | 0.136866 | 0.0684330 | − | 0.997656i | \(-0.478200\pi\) | ||||
0.0684330 | + | 0.997656i | \(0.478200\pi\) | |||||||
\(354\) | −5.23325 | −0.278144 | ||||||||
\(355\) | 1.71293 | 0.0909131 | ||||||||
\(356\) | −17.7911 | −0.942929 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.4823 | −0.554005 | ||||||||
\(359\) | 3.91909 | 0.206842 | 0.103421 | − | 0.994638i | \(-0.467021\pi\) | ||||
0.103421 | + | 0.994638i | \(0.467021\pi\) | |||||||
\(360\) | −1.21224 | −0.0638906 | ||||||||
\(361\) | −11.8879 | −0.625682 | ||||||||
\(362\) | 8.98480 | 0.472231 | ||||||||
\(363\) | 28.2234 | 1.48135 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.35901 | 0.280504 | ||||||||
\(366\) | −2.16820 | −0.113334 | ||||||||
\(367\) | 3.16192 | 0.165051 | 0.0825255 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825255 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(368\) | 0.452171 | 0.0235710 | ||||||||
\(369\) | 14.2848 | 0.743636 | ||||||||
\(370\) | 2.42050 | 0.125836 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.96636 | −0.464884 | ||||||||
\(373\) | 1.74384 | 0.0902924 | 0.0451462 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451462 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(374\) | 27.7037 | 1.43252 | ||||||||
\(375\) | −6.37569 | −0.329239 | ||||||||
\(376\) | 5.21018 | 0.268695 | ||||||||
\(377\) | −3.50826 | −0.180685 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.9277 | 0.869515 | 0.434758 | − | 0.900548i | \(-0.356834\pi\) | ||||
0.434758 | + | 0.900548i | \(0.356834\pi\) | |||||||
\(380\) | 1.69502 | 0.0869528 | ||||||||
\(381\) | 8.86338 | 0.454085 | ||||||||
\(382\) | −4.17699 | −0.213713 | ||||||||
\(383\) | −35.6648 | −1.82239 | −0.911194 | − | 0.411978i | \(-0.864838\pi\) | ||||
−0.911194 | + | 0.411978i | \(0.864838\pi\) | |||||||
\(384\) | 1.04534 | 0.0533448 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.9970 | −1.17051 | ||||||||
\(387\) | −5.54491 | −0.281864 | ||||||||
\(388\) | 2.64094 | 0.134074 | ||||||||
\(389\) | 7.20134 | 0.365122 | 0.182561 | − | 0.983194i | \(-0.441561\pi\) | ||||
0.182561 | + | 0.983194i | \(0.441561\pi\) | |||||||
\(390\) | −2.33092 | −0.118031 | ||||||||
\(391\) | −2.03213 | −0.102769 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.664410 | 0.0335150 | ||||||||
\(394\) | −26.1448 | −1.31716 | ||||||||
\(395\) | −0.0690253 | −0.00347304 | ||||||||
\(396\) | 11.7570 | 0.590813 | ||||||||
\(397\) | 29.7904 | 1.49514 | 0.747568 | − | 0.664185i | \(-0.231221\pi\) | ||||
0.747568 | + | 0.664185i | \(0.231221\pi\) | |||||||
\(398\) | 14.5540 | 0.729527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.59602 | −0.229801 | ||||||||
\(401\) | −33.3827 | −1.66705 | −0.833525 | − | 0.552482i | \(-0.813681\pi\) | ||||
−0.833525 | + | 0.552482i | \(0.813681\pi\) | |||||||
\(402\) | −4.30323 | −0.214626 | ||||||||
\(403\) | 30.0919 | 1.49899 | ||||||||
\(404\) | −1.78442 | −0.0887782 | ||||||||
\(405\) | 0.228452 | 0.0113519 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4755 | −1.16364 | ||||||||
\(408\) | −4.69794 | −0.232583 | ||||||||
\(409\) | 10.8266 | 0.535342 | 0.267671 | − | 0.963510i | \(-0.413746\pi\) | ||||
0.267671 | + | 0.963510i | \(0.413746\pi\) | |||||||
\(410\) | −4.76038 | −0.235098 | ||||||||
\(411\) | 2.98902 | 0.147438 | ||||||||
\(412\) | 11.6741 | 0.575139 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.862408 | −0.0423850 | ||||||||
\(415\) | −0.626216 | −0.0307397 | ||||||||
\(416\) | −3.50826 | −0.172007 | ||||||||
\(417\) | −22.2203 | −1.08813 | ||||||||
\(418\) | −16.4394 | −0.804076 | ||||||||
\(419\) | 14.9526 | 0.730485 | 0.365242 | − | 0.930912i | \(-0.380986\pi\) | ||||
0.365242 | + | 0.930912i | \(0.380986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2610 | −1.23115 | −0.615573 | − | 0.788080i | \(-0.711075\pi\) | ||||
−0.615573 | + | 0.788080i | \(0.711075\pi\) | |||||||
\(422\) | −14.7774 | −0.719354 | ||||||||
\(423\) | −9.93718 | −0.483162 | ||||||||
\(424\) | 14.4482 | 0.701667 | ||||||||
\(425\) | 20.6553 | 1.00193 | ||||||||
\(426\) | 2.81722 | 0.136495 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.8464 | −0.524282 | ||||||||
\(429\) | 22.6067 | 1.09146 | ||||||||
\(430\) | 1.84783 | 0.0891103 | ||||||||
\(431\) | 19.1672 | 0.923251 | 0.461625 | − | 0.887075i | \(-0.347266\pi\) | ||||
0.461625 | + | 0.887075i | \(0.347266\pi\) | |||||||
\(432\) | −5.12976 | −0.246806 | ||||||||
\(433\) | 3.89446 | 0.187156 | 0.0935778 | − | 0.995612i | \(-0.470170\pi\) | ||||
0.0935778 | + | 0.995612i | \(0.470170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.664410 | 0.0318560 | ||||||||
\(436\) | −12.0238 | −0.575838 | ||||||||
\(437\) | 1.20587 | 0.0576845 | ||||||||
\(438\) | 8.81383 | 0.421141 | ||||||||
\(439\) | −29.6761 | −1.41637 | −0.708183 | − | 0.706029i | \(-0.750485\pi\) | ||||
−0.708183 | + | 0.706029i | \(0.750485\pi\) | |||||||
\(440\) | −3.91801 | −0.186784 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.7667 | 0.749947 | ||||||||
\(443\) | −16.1588 | −0.767727 | −0.383864 | − | 0.923390i | \(-0.625407\pi\) | ||||
−0.383864 | + | 0.923390i | \(0.625407\pi\) | |||||||
\(444\) | 3.98093 | 0.188927 | ||||||||
\(445\) | −11.3079 | −0.536046 | ||||||||
\(446\) | 12.1276 | 0.574260 | ||||||||
\(447\) | 8.86643 | 0.419368 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.30425 | 0.344709 | 0.172354 | − | 0.985035i | \(-0.444863\pi\) | ||||
0.172354 | + | 0.985035i | \(0.444863\pi\) | |||||||
\(450\) | 8.76582 | 0.413225 | ||||||||
\(451\) | 46.1691 | 2.17402 | ||||||||
\(452\) | 20.4936 | 0.963937 | ||||||||
\(453\) | 11.9172 | 0.559920 | ||||||||
\(454\) | −25.7246 | −1.20732 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.78776 | 0.130549 | ||||||||
\(457\) | 30.1311 | 1.40947 | 0.704737 | − | 0.709469i | \(-0.251065\pi\) | ||||
0.704737 | + | 0.709469i | \(0.251065\pi\) | |||||||
\(458\) | −7.39225 | −0.345417 | ||||||||
\(459\) | 23.0540 | 1.07607 | ||||||||
\(460\) | 0.287396 | 0.0133999 | ||||||||
\(461\) | 41.2596 | 1.92165 | 0.960825 | − | 0.277156i | \(-0.0893919\pi\) | ||||
0.960825 | + | 0.277156i | \(0.0893919\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.3019 | −0.525246 | −0.262623 | − | 0.964899i | \(-0.584588\pi\) | ||||
−0.262623 | + | 0.964899i | \(0.584588\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −5.69894 | −0.264282 | ||||||||
\(466\) | 1.24860 | 0.0578404 | ||||||||
\(467\) | 17.3358 | 0.802205 | 0.401102 | − | 0.916033i | \(-0.368627\pi\) | ||||
0.401102 | + | 0.916033i | \(0.368627\pi\) | |||||||
\(468\) | 6.69117 | 0.309300 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.31155 | 0.152750 | ||||||||
\(471\) | 16.0693 | 0.740433 | ||||||||
\(472\) | −5.00626 | −0.230432 | ||||||||
\(473\) | −17.9214 | −0.824027 | ||||||||
\(474\) | −0.113524 | −0.00521434 | ||||||||
\(475\) | −12.2569 | −0.562384 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.5565 | −1.26173 | ||||||||
\(478\) | 22.6217 | 1.03469 | ||||||||
\(479\) | −0.254037 | −0.0116072 | −0.00580361 | − | 0.999983i | \(-0.501847\pi\) | ||||
−0.00580361 | + | 0.999983i | \(0.501847\pi\) | |||||||
\(480\) | 0.664410 | 0.0303260 | ||||||||
\(481\) | −13.3604 | −0.609181 | ||||||||
\(482\) | −29.9759 | −1.36536 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.9993 | 1.22724 | ||||||||
\(485\) | 1.67856 | 0.0762196 | ||||||||
\(486\) | 15.7650 | 0.715116 | ||||||||
\(487\) | −22.7370 | −1.03031 | −0.515157 | − | 0.857096i | \(-0.672266\pi\) | ||||
−0.515157 | + | 0.857096i | \(0.672266\pi\) | |||||||
\(488\) | −2.07416 | −0.0938928 | ||||||||
\(489\) | 15.6611 | 0.708219 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.39496 | −0.423988 | −0.211994 | − | 0.977271i | \(-0.567996\pi\) | ||||
−0.211994 | + | 0.977271i | \(0.567996\pi\) | |||||||
\(492\) | −7.82927 | −0.352971 | ||||||||
\(493\) | −4.49417 | −0.202407 | ||||||||
\(494\) | −9.35598 | −0.420946 | ||||||||
\(495\) | 7.47267 | 0.335872 | ||||||||
\(496\) | −8.57744 | −0.385139 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.02992 | −0.0461519 | ||||||||
\(499\) | 15.1235 | 0.677022 | 0.338511 | − | 0.940962i | \(-0.390077\pi\) | ||||
0.338511 | + | 0.940962i | \(0.390077\pi\) | |||||||
\(500\) | −6.09915 | −0.272762 | ||||||||
\(501\) | −11.3092 | −0.505258 | ||||||||
\(502\) | 6.13268 | 0.273715 | ||||||||
\(503\) | 25.8775 | 1.15382 | 0.576910 | − | 0.816808i | \(-0.304258\pi\) | ||||
0.576910 | + | 0.816808i | \(0.304258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.13416 | −0.0504696 | ||||||||
\(506\) | −2.78734 | −0.123912 | ||||||||
\(507\) | −0.723483 | −0.0321310 | ||||||||
\(508\) | 8.47893 | 0.376192 | ||||||||
\(509\) | −13.1819 | −0.584278 | −0.292139 | − | 0.956376i | \(-0.594367\pi\) | ||||
−0.292139 | + | 0.956376i | \(0.594367\pi\) | |||||||
\(510\) | −2.98597 | −0.132221 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.6803 | −0.603999 | ||||||||
\(514\) | −28.8072 | −1.27063 | ||||||||
\(515\) | 7.41993 | 0.326961 | ||||||||
\(516\) | 3.03908 | 0.133788 | ||||||||
\(517\) | −32.1174 | −1.41252 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.98483 | −0.394390 | ||||||||
\(520\) | −2.22982 | −0.0977841 | ||||||||
\(521\) | −27.9223 | −1.22330 | −0.611648 | − | 0.791130i | \(-0.709493\pi\) | ||||
−0.611648 | + | 0.791130i | \(0.709493\pi\) | |||||||
\(522\) | −1.90726 | −0.0834786 | ||||||||
\(523\) | 30.4241 | 1.33035 | 0.665177 | − | 0.746686i | \(-0.268356\pi\) | ||||
0.665177 | + | 0.746686i | \(0.268356\pi\) | |||||||
\(524\) | 0.635591 | 0.0277659 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6525 | −0.551674 | ||||||||
\(527\) | 38.5485 | 1.67920 | ||||||||
\(528\) | −6.44385 | −0.280433 | ||||||||
\(529\) | −22.7955 | −0.991111 | ||||||||
\(530\) | 9.18316 | 0.398891 | ||||||||
\(531\) | 9.54825 | 0.414359 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.2758 | 1.13813 | ||||||||
\(534\) | −18.5978 | −0.804806 | ||||||||
\(535\) | −6.89390 | −0.298049 | ||||||||
\(536\) | −4.11658 | −0.177809 | ||||||||
\(537\) | −10.9576 | −0.472853 | ||||||||
\(538\) | −25.5822 | −1.10293 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.26043 | −0.140307 | ||||||||
\(541\) | −17.9943 | −0.773636 | −0.386818 | − | 0.922156i | \(-0.626426\pi\) | ||||
−0.386818 | + | 0.922156i | \(0.626426\pi\) | |||||||
\(542\) | −9.13120 | −0.392219 | ||||||||
\(543\) | 9.39218 | 0.403057 | ||||||||
\(544\) | −4.49417 | −0.192686 | ||||||||
\(545\) | −7.64225 | −0.327358 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.298717 | 0.0127722 | 0.00638610 | − | 0.999980i | \(-0.497967\pi\) | ||||
0.00638610 | + | 0.999980i | \(0.497967\pi\) | |||||||
\(548\) | 2.85938 | 0.122147 | ||||||||
\(549\) | 3.95597 | 0.168836 | ||||||||
\(550\) | 28.3315 | 1.20806 | ||||||||
\(551\) | 2.66684 | 0.113611 | ||||||||
\(552\) | 0.472673 | 0.0201183 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.53642 | −0.320192 | ||||||||
\(555\) | 2.53025 | 0.107403 | ||||||||
\(556\) | −21.2565 | −0.901476 | ||||||||
\(557\) | 6.32568 | 0.268028 | 0.134014 | − | 0.990979i | \(-0.457213\pi\) | ||||
0.134014 | + | 0.990979i | \(0.457213\pi\) | |||||||
\(558\) | 16.3594 | 0.692550 | ||||||||
\(559\) | −10.1994 | −0.431390 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.9598 | 1.22268 | ||||||||
\(562\) | 4.16607 | 0.175735 | ||||||||
\(563\) | 32.1866 | 1.35650 | 0.678251 | − | 0.734830i | \(-0.262738\pi\) | ||||
0.678251 | + | 0.734830i | \(0.262738\pi\) | |||||||
\(564\) | 5.44642 | 0.229336 | ||||||||
\(565\) | 13.0255 | 0.547989 | ||||||||
\(566\) | −2.62137 | −0.110184 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.69502 | 0.113081 | ||||||||
\(569\) | −5.75826 | −0.241399 | −0.120699 | − | 0.992689i | \(-0.538514\pi\) | ||||
−0.120699 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(570\) | 1.77188 | 0.0742158 | ||||||||
\(571\) | 10.5601 | 0.441926 | 0.220963 | − | 0.975282i | \(-0.429080\pi\) | ||||
0.220963 | + | 0.975282i | \(0.429080\pi\) | |||||||
\(572\) | 21.6262 | 0.904235 | ||||||||
\(573\) | −4.36638 | −0.182408 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.07819 | −0.0866664 | ||||||||
\(576\) | −1.90726 | −0.0794692 | ||||||||
\(577\) | 7.50762 | 0.312546 | 0.156273 | − | 0.987714i | \(-0.450052\pi\) | ||||
0.156273 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(578\) | 3.19758 | 0.133002 | ||||||||
\(579\) | −24.0397 | −0.999055 | ||||||||
\(580\) | 0.635591 | 0.0263915 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.76069 | 0.114434 | ||||||||
\(583\) | −89.0639 | −3.68865 | ||||||||
\(584\) | 8.43154 | 0.348899 | ||||||||
\(585\) | 4.25285 | 0.175834 | ||||||||
\(586\) | −15.0423 | −0.621391 | ||||||||
\(587\) | 39.3707 | 1.62500 | 0.812502 | − | 0.582958i | \(-0.198105\pi\) | ||||
0.812502 | + | 0.582958i | \(0.198105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8747 | −0.942535 | ||||||||
\(590\) | −3.18194 | −0.130998 | ||||||||
\(591\) | −27.3303 | −1.12422 | ||||||||
\(592\) | 3.80826 | 0.156519 | ||||||||
\(593\) | −6.32018 | −0.259539 | −0.129769 | − | 0.991544i | \(-0.541424\pi\) | ||||
−0.129769 | + | 0.991544i | \(0.541424\pi\) | |||||||
\(594\) | 31.6217 | 1.29745 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.48185 | 0.347430 | ||||||||
\(597\) | 15.2139 | 0.622664 | ||||||||
\(598\) | −1.58633 | −0.0648700 | ||||||||
\(599\) | 8.59138 | 0.351034 | 0.175517 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175517 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(600\) | −4.80441 | −0.196139 | ||||||||
\(601\) | 8.77356 | 0.357881 | 0.178941 | − | 0.983860i | \(-0.442733\pi\) | ||||
0.178941 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.85140 | 0.319734 | ||||||||
\(604\) | 11.4003 | 0.463873 | ||||||||
\(605\) | 17.1605 | 0.697674 | ||||||||
\(606\) | −1.86533 | −0.0757738 | ||||||||
\(607\) | 41.5762 | 1.68753 | 0.843763 | − | 0.536716i | \(-0.180336\pi\) | ||||
0.843763 | + | 0.536716i | \(0.180336\pi\) | |||||||
\(608\) | 2.66684 | 0.108155 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.31832 | −0.0533771 | ||||||||
\(611\) | −18.2787 | −0.739476 | ||||||||
\(612\) | 8.57156 | 0.346485 | ||||||||
\(613\) | 32.3946 | 1.30841 | 0.654204 | − | 0.756318i | \(-0.273004\pi\) | ||||
0.654204 | + | 0.756318i | \(0.273004\pi\) | |||||||
\(614\) | 2.56941 | 0.103693 | ||||||||
\(615\) | −4.97622 | −0.200661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8684 | −0.638840 | −0.319420 | − | 0.947613i | \(-0.603488\pi\) | ||||
−0.319420 | + | 0.947613i | \(0.603488\pi\) | |||||||
\(618\) | 12.2034 | 0.490891 | ||||||||
\(619\) | −33.3284 | −1.33958 | −0.669790 | − | 0.742551i | \(-0.733616\pi\) | ||||
−0.669790 | + | 0.742551i | \(0.733616\pi\) | |||||||
\(620\) | −5.45175 | −0.218948 | ||||||||
\(621\) | −2.31953 | −0.0930795 | ||||||||
\(622\) | 8.70307 | 0.348961 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.66733 | −0.146811 | ||||||||
\(625\) | 19.1035 | 0.764142 | ||||||||
\(626\) | −17.5432 | −0.701168 | ||||||||
\(627\) | −17.1847 | −0.686293 | ||||||||
\(628\) | 15.3723 | 0.613421 | ||||||||
\(629\) | −17.1150 | −0.682419 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0390 | 0.558884 | 0.279442 | − | 0.960163i | \(-0.409850\pi\) | ||||
0.279442 | + | 0.960163i | \(0.409850\pi\) | |||||||
\(632\) | −0.108600 | −0.00431988 | ||||||||
\(633\) | −15.4475 | −0.613981 | ||||||||
\(634\) | −13.6648 | −0.542699 | ||||||||
\(635\) | 5.38914 | 0.213861 | ||||||||
\(636\) | 15.1033 | 0.598885 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.16435 | −0.244049 | ||||||||
\(639\) | −5.14011 | −0.203340 | ||||||||
\(640\) | 0.635591 | 0.0251240 | ||||||||
\(641\) | 27.5077 | 1.08649 | 0.543245 | − | 0.839574i | \(-0.317196\pi\) | ||||
0.543245 | + | 0.839574i | \(0.317196\pi\) | |||||||
\(642\) | −11.3382 | −0.447484 | ||||||||
\(643\) | −9.62486 | −0.379568 | −0.189784 | − | 0.981826i | \(-0.560779\pi\) | ||||
−0.189784 | + | 0.981826i | \(0.560779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.93161 | 0.0760572 | ||||||||
\(646\) | −11.9852 | −0.471553 | ||||||||
\(647\) | 6.83452 | 0.268693 | 0.134346 | − | 0.990934i | \(-0.457107\pi\) | ||||
0.134346 | + | 0.990934i | \(0.457107\pi\) | |||||||
\(648\) | 0.359432 | 0.0141198 | ||||||||
\(649\) | 30.8604 | 1.21138 | ||||||||
\(650\) | 16.1241 | 0.632437 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.9818 | 0.586733 | ||||||||
\(653\) | −10.6600 | −0.417159 | −0.208580 | − | 0.978005i | \(-0.566884\pi\) | ||||
−0.208580 | + | 0.978005i | \(0.566884\pi\) | |||||||
\(654\) | −12.5690 | −0.491488 | ||||||||
\(655\) | 0.403976 | 0.0157847 | ||||||||
\(656\) | −7.48968 | −0.292423 | ||||||||
\(657\) | −16.0811 | −0.627385 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.7780 | −1.39371 | −0.696857 | − | 0.717210i | \(-0.745419\pi\) | ||||
−0.696857 | + | 0.717210i | \(0.745419\pi\) | |||||||
\(660\) | −4.09566 | −0.159423 | ||||||||
\(661\) | −20.8487 | −0.810920 | −0.405460 | − | 0.914113i | \(-0.632889\pi\) | ||||
−0.405460 | + | 0.914113i | \(0.632889\pi\) | |||||||
\(662\) | −30.2232 | −1.17466 | ||||||||
\(663\) | 16.4816 | 0.640093 | ||||||||
\(664\) | −0.985249 | −0.0382351 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.26335 | −0.281449 | ||||||||
\(667\) | 0.452171 | 0.0175081 | ||||||||
\(668\) | −10.8187 | −0.418587 | ||||||||
\(669\) | 12.6775 | 0.490141 | ||||||||
\(670\) | −2.61646 | −0.101083 | ||||||||
\(671\) | 12.7859 | 0.493593 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.7639 | 1.34005 | 0.670024 | − | 0.742339i | \(-0.266284\pi\) | ||||
0.670024 | + | 0.742339i | \(0.266284\pi\) | |||||||
\(674\) | 25.4947 | 0.982019 | ||||||||
\(675\) | 23.5765 | 0.907460 | ||||||||
\(676\) | −0.692102 | −0.0266193 | ||||||||
\(677\) | 2.27679 | 0.0875043 | 0.0437521 | − | 0.999042i | \(-0.486069\pi\) | ||||
0.0437521 | + | 0.999042i | \(0.486069\pi\) | |||||||
\(678\) | 21.4228 | 0.822737 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.85646 | −0.109540 | ||||||||
\(681\) | −26.8910 | −1.03046 | ||||||||
\(682\) | 52.8744 | 2.02467 | ||||||||
\(683\) | −17.2288 | −0.659240 | −0.329620 | − | 0.944114i | \(-0.606921\pi\) | ||||
−0.329620 | + | 0.944114i | \(0.606921\pi\) | |||||||
\(684\) | −5.08637 | −0.194482 | ||||||||
\(685\) | 1.81740 | 0.0694391 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.72743 | −0.294820 | ||||||||
\(688\) | 2.90726 | 0.110838 | ||||||||
\(689\) | −50.6881 | −1.93106 | ||||||||
\(690\) | 0.300427 | 0.0114370 | ||||||||
\(691\) | −30.8224 | −1.17254 | −0.586269 | − | 0.810116i | \(-0.699404\pi\) | ||||
−0.586269 | + | 0.810116i | \(0.699404\pi\) | |||||||
\(692\) | −8.59512 | −0.326737 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.5955 | 0.516079 | ||||||||
\(695\) | −13.5104 | −0.512480 | ||||||||
\(696\) | 1.04534 | 0.0396236 | ||||||||
\(697\) | 33.6599 | 1.27496 | ||||||||
\(698\) | 10.7077 | 0.405293 | ||||||||
\(699\) | 1.30522 | 0.0493678 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.7823 | −1.54033 | −0.770163 | − | 0.637848i | \(-0.779825\pi\) | ||||
−0.770163 | + | 0.637848i | \(0.779825\pi\) | |||||||
\(702\) | 17.9965 | 0.679236 | ||||||||
\(703\) | 10.1560 | 0.383042 | ||||||||
\(704\) | −6.16435 | −0.232328 | ||||||||
\(705\) | 3.46170 | 0.130375 | ||||||||
\(706\) | 2.57148 | 0.0967788 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.23325 | −0.196678 | ||||||||
\(709\) | 26.9991 | 1.01397 | 0.506986 | − | 0.861954i | \(-0.330760\pi\) | ||||
0.506986 | + | 0.861954i | \(0.330760\pi\) | |||||||
\(710\) | 1.71293 | 0.0642852 | ||||||||
\(711\) | 0.207129 | 0.00776793 | ||||||||
\(712\) | −17.7911 | −0.666751 | ||||||||
\(713\) | −3.87847 | −0.145250 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7454 | 0.514049 | ||||||||
\(716\) | −10.4823 | −0.391741 | ||||||||
\(717\) | 23.6474 | 0.883130 | ||||||||
\(718\) | 3.91909 | 0.146259 | ||||||||
\(719\) | 35.4494 | 1.32204 | 0.661020 | − | 0.750368i | \(-0.270124\pi\) | ||||
0.661020 | + | 0.750368i | \(0.270124\pi\) | |||||||
\(720\) | −1.21224 | −0.0451775 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.8879 | −0.442424 | ||||||||
\(723\) | −31.3350 | −1.16536 | ||||||||
\(724\) | 8.98480 | 0.333918 | ||||||||
\(725\) | −4.59602 | −0.170692 | ||||||||
\(726\) | 28.2234 | 1.04747 | ||||||||
\(727\) | −22.5096 | −0.834834 | −0.417417 | − | 0.908715i | \(-0.637064\pi\) | ||||
−0.417417 | + | 0.908715i | \(0.637064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4015 | 0.570427 | ||||||||
\(730\) | 5.35901 | 0.198346 | ||||||||
\(731\) | −13.0657 | −0.483254 | ||||||||
\(732\) | −2.16820 | −0.0801392 | ||||||||
\(733\) | 7.77593 | 0.287211 | 0.143605 | − | 0.989635i | \(-0.454130\pi\) | ||||
0.143605 | + | 0.989635i | \(0.454130\pi\) | |||||||
\(734\) | 3.16192 | 0.116709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.452171 | 0.0166672 | ||||||||
\(737\) | 25.3761 | 0.934739 | ||||||||
\(738\) | 14.2848 | 0.525830 | ||||||||
\(739\) | 36.7027 | 1.35013 | 0.675065 | − | 0.737758i | \(-0.264116\pi\) | ||||
0.675065 | + | 0.737758i | \(0.264116\pi\) | |||||||
\(740\) | 2.42050 | 0.0889793 | ||||||||
\(741\) | −9.78019 | −0.359284 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3936 | 0.417992 | 0.208996 | − | 0.977916i | \(-0.432980\pi\) | ||||
0.208996 | + | 0.977916i | \(0.432980\pi\) | |||||||
\(744\) | −8.96636 | −0.328723 | ||||||||
\(745\) | 5.39099 | 0.197511 | ||||||||
\(746\) | 1.74384 | 0.0638464 | ||||||||
\(747\) | 1.87913 | 0.0687537 | ||||||||
\(748\) | 27.7037 | 1.01295 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.37569 | −0.232807 | ||||||||
\(751\) | −50.6364 | −1.84775 | −0.923874 | − | 0.382697i | \(-0.874995\pi\) | ||||
−0.923874 | + | 0.382697i | \(0.874995\pi\) | |||||||
\(752\) | 5.21018 | 0.189996 | ||||||||
\(753\) | 6.41075 | 0.233621 | ||||||||
\(754\) | −3.50826 | −0.127763 | ||||||||
\(755\) | 7.24595 | 0.263707 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8232 | 1.37471 | 0.687354 | − | 0.726323i | \(-0.258772\pi\) | ||||
0.687354 | + | 0.726323i | \(0.258772\pi\) | |||||||
\(758\) | 16.9277 | 0.614840 | ||||||||
\(759\) | −2.91372 | −0.105761 | ||||||||
\(760\) | 1.69502 | 0.0614849 | ||||||||
\(761\) | −16.1435 | −0.585200 | −0.292600 | − | 0.956235i | \(-0.594521\pi\) | ||||
−0.292600 | + | 0.956235i | \(0.594521\pi\) | |||||||
\(762\) | 8.86338 | 0.321086 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.17699 | −0.151118 | ||||||||
\(765\) | 5.44801 | 0.196973 | ||||||||
\(766\) | −35.6648 | −1.28862 | ||||||||
\(767\) | 17.5633 | 0.634173 | ||||||||
\(768\) | 1.04534 | 0.0377205 | ||||||||
\(769\) | −14.3761 | −0.518414 | −0.259207 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259207 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.1134 | −1.08451 | ||||||||
\(772\) | −22.9970 | −0.827679 | ||||||||
\(773\) | −26.5183 | −0.953799 | −0.476899 | − | 0.878958i | \(-0.658239\pi\) | ||||
−0.476899 | + | 0.878958i | \(0.658239\pi\) | |||||||
\(774\) | −5.54491 | −0.199308 | ||||||||
\(775\) | 39.4221 | 1.41609 | ||||||||
\(776\) | 2.64094 | 0.0948044 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.20134 | 0.258180 | ||||||||
\(779\) | −19.9738 | −0.715636 | ||||||||
\(780\) | −2.33092 | −0.0834605 | ||||||||
\(781\) | −16.6131 | −0.594463 | ||||||||
\(782\) | −2.03213 | −0.0726689 | ||||||||
\(783\) | −5.12976 | −0.183323 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.77049 | 0.348724 | ||||||||
\(786\) | 0.664410 | 0.0236987 | ||||||||
\(787\) | 21.1678 | 0.754550 | 0.377275 | − | 0.926101i | \(-0.376861\pi\) | ||||
0.377275 | + | 0.926101i | \(0.376861\pi\) | |||||||
\(788\) | −26.1448 | −0.931371 | ||||||||
\(789\) | −13.2261 | −0.470863 | ||||||||
\(790\) | −0.0690253 | −0.00245581 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.7570 | 0.417768 | ||||||||
\(793\) | 7.27669 | 0.258403 | ||||||||
\(794\) | 29.7904 | 1.05722 | ||||||||
\(795\) | 9.59953 | 0.340460 | ||||||||
\(796\) | 14.5540 | 0.515854 | ||||||||
\(797\) | 16.3454 | 0.578983 | 0.289491 | − | 0.957181i | \(-0.406514\pi\) | ||||
0.289491 | + | 0.957181i | \(0.406514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4155 | −0.828379 | ||||||||
\(800\) | −4.59602 | −0.162494 | ||||||||
\(801\) | 33.9324 | 1.19894 | ||||||||
\(802\) | −33.3827 | −1.17878 | ||||||||
\(803\) | −51.9750 | −1.83416 | ||||||||
\(804\) | −4.30323 | −0.151763 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.0919 | 1.05994 | ||||||||
\(807\) | −26.7421 | −0.941367 | ||||||||
\(808\) | −1.78442 | −0.0627757 | ||||||||
\(809\) | 1.26689 | 0.0445416 | 0.0222708 | − | 0.999752i | \(-0.492910\pi\) | ||||
0.0222708 | + | 0.999752i | \(0.492910\pi\) | |||||||
\(810\) | 0.228452 | 0.00802699 | ||||||||
\(811\) | 8.85737 | 0.311024 | 0.155512 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155512 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.54522 | −0.334765 | ||||||||
\(814\) | −23.4755 | −0.822815 | ||||||||
\(815\) | 9.52230 | 0.333552 | ||||||||
\(816\) | −4.69794 | −0.164461 | ||||||||
\(817\) | 7.75321 | 0.271250 | ||||||||
\(818\) | 10.8266 | 0.378544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.76038 | −0.166240 | ||||||||
\(821\) | 18.6382 | 0.650476 | 0.325238 | − | 0.945632i | \(-0.394556\pi\) | ||||
0.325238 | + | 0.945632i | \(0.394556\pi\) | |||||||
\(822\) | 2.98902 | 0.104254 | ||||||||
\(823\) | 34.2281 | 1.19312 | 0.596559 | − | 0.802569i | \(-0.296534\pi\) | ||||
0.596559 | + | 0.802569i | \(0.296534\pi\) | |||||||
\(824\) | 11.6741 | 0.406685 | ||||||||
\(825\) | 29.6161 | 1.03110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0340 | 0.800971 | 0.400486 | − | 0.916303i | \(-0.368841\pi\) | ||||
0.400486 | + | 0.916303i | \(0.368841\pi\) | |||||||
\(828\) | −0.862408 | −0.0299707 | ||||||||
\(829\) | −9.14291 | −0.317546 | −0.158773 | − | 0.987315i | \(-0.550754\pi\) | ||||
−0.158773 | + | 0.987315i | \(0.550754\pi\) | |||||||
\(830\) | −0.626216 | −0.0217363 | ||||||||
\(831\) | −7.87813 | −0.273289 | ||||||||
\(832\) | −3.50826 | −0.121627 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −22.2203 | −0.769426 | ||||||||
\(835\) | −6.87626 | −0.237963 | ||||||||
\(836\) | −16.4394 | −0.568567 | ||||||||
\(837\) | 44.0003 | 1.52087 | ||||||||
\(838\) | 14.9526 | 0.516531 | ||||||||
\(839\) | 38.9599 | 1.34505 | 0.672523 | − | 0.740076i | \(-0.265211\pi\) | ||||
0.672523 | + | 0.740076i | \(0.265211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −25.2610 | −0.870552 | ||||||||
\(843\) | 4.35497 | 0.149993 | ||||||||
\(844\) | −14.7774 | −0.508660 | ||||||||
\(845\) | −0.439894 | −0.0151328 | ||||||||
\(846\) | −9.93718 | −0.341647 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.4482 | 0.496154 | ||||||||
\(849\) | −2.74023 | −0.0940443 | ||||||||
\(850\) | 20.6553 | 0.708472 | ||||||||
\(851\) | 1.72198 | 0.0590289 | ||||||||
\(852\) | 2.81722 | 0.0965163 | ||||||||
\(853\) | 2.41528 | 0.0826975 | 0.0413487 | − | 0.999145i | \(-0.486835\pi\) | ||||
0.0413487 | + | 0.999145i | \(0.486835\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.23285 | −0.110561 | ||||||||
\(856\) | −10.8464 | −0.370724 | ||||||||
\(857\) | −52.7601 | −1.80225 | −0.901125 | − | 0.433560i | \(-0.857257\pi\) | ||||
−0.901125 | + | 0.433560i | \(0.857257\pi\) | |||||||
\(858\) | 22.6067 | 0.771781 | ||||||||
\(859\) | 35.0323 | 1.19529 | 0.597643 | − | 0.801762i | \(-0.296104\pi\) | ||||
0.597643 | + | 0.801762i | \(0.296104\pi\) | |||||||
\(860\) | 1.84783 | 0.0630105 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.1672 | 0.652837 | ||||||||
\(863\) | −0.337360 | −0.0114839 | −0.00574193 | − | 0.999984i | \(-0.501828\pi\) | ||||
−0.00574193 | + | 0.999984i | \(0.501828\pi\) | |||||||
\(864\) | −5.12976 | −0.174518 | ||||||||
\(865\) | −5.46298 | −0.185747 | ||||||||
\(866\) | 3.89446 | 0.132339 | ||||||||
\(867\) | 3.34256 | 0.113519 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.669449 | 0.0227095 | ||||||||
\(870\) | 0.664410 | 0.0225256 | ||||||||
\(871\) | 14.4420 | 0.489350 | ||||||||
\(872\) | −12.0238 | −0.407179 | ||||||||
\(873\) | −5.03697 | −0.170476 | ||||||||
\(874\) | 1.20587 | 0.0407891 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.81383 | 0.297792 | ||||||||
\(877\) | 20.1477 | 0.680340 | 0.340170 | − | 0.940364i | \(-0.389515\pi\) | ||||
0.340170 | + | 0.940364i | \(0.389515\pi\) | |||||||
\(878\) | −29.6761 | −1.00152 | ||||||||
\(879\) | −15.7243 | −0.530368 | ||||||||
\(880\) | −3.91801 | −0.132076 | ||||||||
\(881\) | −43.0268 | −1.44961 | −0.724805 | − | 0.688954i | \(-0.758070\pi\) | ||||
−0.724805 | + | 0.688954i | \(0.758070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.9078 | 0.602647 | 0.301323 | − | 0.953522i | \(-0.402572\pi\) | ||||
0.301323 | + | 0.953522i | \(0.402572\pi\) | |||||||
\(884\) | 15.7667 | 0.530292 | ||||||||
\(885\) | −3.32621 | −0.111809 | ||||||||
\(886\) | −16.1588 | −0.542865 | ||||||||
\(887\) | −1.24843 | −0.0419183 | −0.0209591 | − | 0.999780i | \(-0.506672\pi\) | ||||
−0.0209591 | + | 0.999780i | \(0.506672\pi\) | |||||||
\(888\) | 3.98093 | 0.133591 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.3079 | −0.379042 | ||||||||
\(891\) | −2.21567 | −0.0742277 | ||||||||
\(892\) | 12.1276 | 0.406063 | ||||||||
\(893\) | 13.8947 | 0.464970 | ||||||||
\(894\) | 8.86643 | 0.296538 | ||||||||
\(895\) | −6.66244 | −0.222701 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.65826 | −0.0553677 | ||||||||
\(898\) | 7.30425 | 0.243746 | ||||||||
\(899\) | −8.57744 | −0.286074 | ||||||||
\(900\) | 8.76582 | 0.292194 | ||||||||
\(901\) | −64.9327 | −2.16322 | ||||||||
\(902\) | 46.1691 | 1.53726 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.4936 | 0.681606 | ||||||||
\(905\) | 5.71066 | 0.189829 | ||||||||
\(906\) | 11.9172 | 0.395923 | ||||||||
\(907\) | 20.6827 | 0.686757 | 0.343379 | − | 0.939197i | \(-0.388429\pi\) | ||||
0.343379 | + | 0.939197i | \(0.388429\pi\) | |||||||
\(908\) | −25.7246 | −0.853701 | ||||||||
\(909\) | 3.40336 | 0.112882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.2033 | −1.13320 | −0.566602 | − | 0.823991i | \(-0.691742\pi\) | ||||
−0.566602 | + | 0.823991i | \(0.691742\pi\) | |||||||
\(912\) | 2.78776 | 0.0923120 | ||||||||
\(913\) | 6.07343 | 0.201001 | ||||||||
\(914\) | 30.1311 | 0.996649 | ||||||||
\(915\) | −1.37809 | −0.0455583 | ||||||||
\(916\) | −7.39225 | −0.244247 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 23.0540 | 0.760897 | ||||||||
\(919\) | 23.5515 | 0.776892 | 0.388446 | − | 0.921472i | \(-0.373012\pi\) | ||||
0.388446 | + | 0.921472i | \(0.373012\pi\) | |||||||
\(920\) | 0.287396 | 0.00947516 | ||||||||
\(921\) | 2.68591 | 0.0885038 | ||||||||
\(922\) | 41.2596 | 1.35881 | ||||||||
\(923\) | −9.45484 | −0.311210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.5029 | −0.575491 | ||||||||
\(926\) | −11.3019 | −0.371405 | ||||||||
\(927\) | −22.2655 | −0.731294 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −40.4148 | −1.32597 | −0.662983 | − | 0.748635i | \(-0.730710\pi\) | ||||
−0.662983 | + | 0.748635i | \(0.730710\pi\) | |||||||
\(930\) | −5.69894 | −0.186876 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.24860 | 0.0408994 | ||||||||
\(933\) | 9.09768 | 0.297845 | ||||||||
\(934\) | 17.3358 | 0.567244 | ||||||||
\(935\) | 17.6082 | 0.575850 | ||||||||
\(936\) | 6.69117 | 0.218708 | ||||||||
\(937\) | −8.61562 | −0.281460 | −0.140730 | − | 0.990048i | \(-0.544945\pi\) | ||||
−0.140730 | + | 0.990048i | \(0.544945\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.3386 | −0.598459 | ||||||||
\(940\) | 3.31155 | 0.108011 | ||||||||
\(941\) | −14.4716 | −0.471761 | −0.235880 | − | 0.971782i | \(-0.575797\pi\) | ||||
−0.235880 | + | 0.971782i | \(0.575797\pi\) | |||||||
\(942\) | 16.0693 | 0.523565 | ||||||||
\(943\) | −3.38662 | −0.110283 | ||||||||
\(944\) | −5.00626 | −0.162940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.9214 | −0.582675 | ||||||||
\(947\) | 17.9649 | 0.583782 | 0.291891 | − | 0.956452i | \(-0.405715\pi\) | ||||
0.291891 | + | 0.956452i | \(0.405715\pi\) | |||||||
\(948\) | −0.113524 | −0.00368709 | ||||||||
\(949\) | −29.5800 | −0.960209 | ||||||||
\(950\) | −12.2569 | −0.397665 | ||||||||
\(951\) | −14.2844 | −0.463203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.4336 | −0.532336 | −0.266168 | − | 0.963927i | \(-0.585758\pi\) | ||||
−0.266168 | + | 0.963927i | \(0.585758\pi\) | |||||||
\(954\) | −27.5565 | −0.892175 | ||||||||
\(955\) | −2.65486 | −0.0859092 | ||||||||
\(956\) | 22.6217 | 0.731640 | ||||||||
\(957\) | −6.44385 | −0.208300 | ||||||||
\(958\) | −0.254037 | −0.00820755 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.664410 | 0.0214437 | ||||||||
\(961\) | 42.5726 | 1.37331 | ||||||||
\(962\) | −13.3604 | −0.430756 | ||||||||
\(963\) | 20.6870 | 0.666629 | ||||||||
\(964\) | −29.9759 | −0.965458 | ||||||||
\(965\) | −14.6167 | −0.470527 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2292 | −0.972105 | −0.486052 | − | 0.873930i | \(-0.661564\pi\) | ||||
−0.486052 | + | 0.873930i | \(0.661564\pi\) | |||||||
\(968\) | 26.9993 | 0.867789 | ||||||||
\(969\) | −12.5287 | −0.402479 | ||||||||
\(970\) | 1.67856 | 0.0538954 | ||||||||
\(971\) | −46.4281 | −1.48995 | −0.744974 | − | 0.667093i | \(-0.767538\pi\) | ||||
−0.744974 | + | 0.667093i | \(0.767538\pi\) | |||||||
\(972\) | 15.7650 | 0.505663 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.7370 | −0.728541 | ||||||||
\(975\) | 16.8551 | 0.539796 | ||||||||
\(976\) | −2.07416 | −0.0663922 | ||||||||
\(977\) | 9.28266 | 0.296978 | 0.148489 | − | 0.988914i | \(-0.452559\pi\) | ||||
0.148489 | + | 0.988914i | \(0.452559\pi\) | |||||||
\(978\) | 15.6611 | 0.500786 | ||||||||
\(979\) | 109.671 | 3.50510 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.9326 | 0.732182 | ||||||||
\(982\) | −9.39496 | −0.299805 | ||||||||
\(983\) | −27.4369 | −0.875100 | −0.437550 | − | 0.899194i | \(-0.644154\pi\) | ||||
−0.437550 | + | 0.899194i | \(0.644154\pi\) | |||||||
\(984\) | −7.82927 | −0.249588 | ||||||||
\(985\) | −16.6174 | −0.529476 | ||||||||
\(986\) | −4.49417 | −0.143124 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.35598 | −0.297653 | ||||||||
\(989\) | 1.31458 | 0.0418012 | ||||||||
\(990\) | 7.47267 | 0.237497 | ||||||||
\(991\) | 2.03251 | 0.0645649 | 0.0322825 | − | 0.999479i | \(-0.489722\pi\) | ||||
0.0322825 | + | 0.999479i | \(0.489722\pi\) | |||||||
\(992\) | −8.57744 | −0.272334 | ||||||||
\(993\) | −31.5936 | −1.00259 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.25041 | 0.293258 | ||||||||
\(996\) | −1.02992 | −0.0326343 | ||||||||
\(997\) | 6.56303 | 0.207853 | 0.103927 | − | 0.994585i | \(-0.466859\pi\) | ||||
0.103927 | + | 0.994585i | \(0.466859\pi\) | |||||||
\(998\) | 15.1235 | 0.478727 | ||||||||
\(999\) | −19.5355 | −0.618075 |
(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 | 2842.2.a.w.1.4 | 5 | ||
7.2 | even | 3 | 406.2.e.b.291.2 | yes | 10 | ||
7.4 | even | 3 | 406.2.e.b.233.2 | ✓ | 10 | ||
7.6 | odd | 2 | 2842.2.a.y.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.b.233.2 | ✓ | 10 | 7.4 | even | 3 | ||
406.2.e.b.291.2 | yes | 10 | 7.2 | even | 3 | ||
2842.2.a.w.1.4 | 5 | 1.1 | even | 1 | trivial | ||
2842.2.a.y.1.2 | 5 | 7.6 | odd | 2 |