Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.42048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 8x + 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.18558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.82843 | 0.817697 | 0.408849 | − | 0.912602i | \(-0.365930\pi\) | ||||
0.408849 | + | 0.912602i | \(0.365930\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.82843 | 0.578199 | ||||||||
\(11\) | 1.68049 | 0.506686 | 0.253343 | − | 0.967376i | \(-0.418470\pi\) | ||||
0.253343 | + | 0.967376i | \(0.418470\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.77137 | 1.04599 | 0.522995 | − | 0.852336i | \(-0.324815\pi\) | ||||
0.522995 | + | 0.852336i | \(0.324815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.82843 | 0.472098 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.59980 | 0.630543 | 0.315272 | − | 0.949001i | \(-0.397904\pi\) | ||||
0.315272 | + | 0.949001i | \(0.397904\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.09088 | 0.250265 | 0.125133 | − | 0.992140i | \(-0.460064\pi\) | ||||
0.125133 | + | 0.992140i | \(0.460064\pi\) | |||||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.68049 | 0.358281 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.65685 | −0.331371 | ||||||||
\(26\) | 3.77137 | 0.739626 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.771369 | −0.143240 | −0.0716199 | − | 0.997432i | \(-0.522817\pi\) | ||||
−0.0716199 | + | 0.997432i | \(0.522817\pi\) | |||||||
\(30\) | 1.82843 | 0.333824 | ||||||||
\(31\) | −3.86225 | −0.693681 | −0.346840 | − | 0.937924i | \(-0.612745\pi\) | ||||
−0.346840 | + | 0.937924i | \(0.612745\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.68049 | 0.292535 | ||||||||
\(34\) | 2.59980 | 0.445861 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.45186 | 0.403083 | 0.201541 | − | 0.979480i | \(-0.435405\pi\) | ||||
0.201541 | + | 0.979480i | \(0.435405\pi\) | |||||||
\(38\) | 1.09088 | 0.176964 | ||||||||
\(39\) | 3.77137 | 0.603902 | ||||||||
\(40\) | 1.82843 | 0.289100 | ||||||||
\(41\) | −1.09088 | −0.170367 | −0.0851835 | − | 0.996365i | \(-0.527148\pi\) | ||||
−0.0851835 | + | 0.996365i | \(0.527148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2959 | 1.57011 | 0.785053 | − | 0.619428i | \(-0.212636\pi\) | ||||
0.785053 | + | 0.619428i | \(0.212636\pi\) | |||||||
\(44\) | 1.68049 | 0.253343 | ||||||||
\(45\) | 1.82843 | 0.272566 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −2.22323 | −0.324291 | −0.162146 | − | 0.986767i | \(-0.551841\pi\) | ||||
−0.162146 | + | 0.986767i | \(0.551841\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.65685 | −0.234315 | ||||||||
\(51\) | 2.59980 | 0.364044 | ||||||||
\(52\) | 3.77137 | 0.522995 | ||||||||
\(53\) | −7.37117 | −1.01251 | −0.506254 | − | 0.862385i | \(-0.668970\pi\) | ||||
−0.506254 | + | 0.862385i | \(0.668970\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.07265 | 0.414316 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.09088 | 0.144491 | ||||||||
\(58\) | −0.771369 | −0.101286 | ||||||||
\(59\) | −6.42822 | −0.836883 | −0.418442 | − | 0.908244i | \(-0.637424\pi\) | ||||
−0.418442 | + | 0.908244i | \(0.637424\pi\) | |||||||
\(60\) | 1.82843 | 0.236049 | ||||||||
\(61\) | 9.08548 | 1.16328 | 0.581638 | − | 0.813448i | \(-0.302412\pi\) | ||||
0.581638 | + | 0.813448i | \(0.302412\pi\) | |||||||
\(62\) | −3.86225 | −0.490506 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.89567 | 0.855303 | ||||||||
\(66\) | 1.68049 | 0.206854 | ||||||||
\(67\) | −12.8903 | −1.57480 | −0.787399 | − | 0.616444i | \(-0.788573\pi\) | ||||
−0.787399 | + | 0.616444i | \(0.788573\pi\) | |||||||
\(68\) | 2.59980 | 0.315272 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.22863 | 0.976559 | 0.488279 | − | 0.872687i | \(-0.337625\pi\) | ||||
0.488279 | + | 0.872687i | \(0.337625\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.86225 | −0.335001 | −0.167501 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167501 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(74\) | 2.45186 | 0.285023 | ||||||||
\(75\) | −1.65685 | −0.191317 | ||||||||
\(76\) | 1.09088 | 0.125133 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.77137 | 0.427023 | ||||||||
\(79\) | 0.771369 | 0.0867858 | 0.0433929 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433929 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(80\) | 1.82843 | 0.204424 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.09088 | −0.120468 | ||||||||
\(83\) | 3.33734 | 0.366321 | 0.183160 | − | 0.983083i | \(-0.441367\pi\) | ||||
0.183160 | + | 0.983083i | \(0.441367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.75354 | 0.515594 | ||||||||
\(86\) | 10.2959 | 1.11023 | ||||||||
\(87\) | −0.771369 | −0.0826995 | ||||||||
\(88\) | 1.68049 | 0.179141 | ||||||||
\(89\) | 3.20500 | 0.339729 | 0.169864 | − | 0.985467i | \(-0.445667\pi\) | ||||
0.169864 | + | 0.985467i | \(0.445667\pi\) | |||||||
\(90\) | 1.82843 | 0.192733 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.86225 | −0.400497 | ||||||||
\(94\) | −2.22323 | −0.229308 | ||||||||
\(95\) | 1.99460 | 0.204641 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.4282 | −1.05883 | −0.529413 | − | 0.848364i | \(-0.677588\pi\) | ||||
−0.529413 | + | 0.848364i | \(0.677588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.68049 | 0.168895 | ||||||||
\(100\) | −1.65685 | −0.165685 | ||||||||
\(101\) | −6.47764 | −0.644549 | −0.322275 | − | 0.946646i | \(-0.604447\pi\) | ||||
−0.322275 | + | 0.946646i | \(0.604447\pi\) | |||||||
\(102\) | 2.59980 | 0.257418 | ||||||||
\(103\) | −18.8903 | −1.86131 | −0.930657 | − | 0.365893i | \(-0.880764\pi\) | ||||
−0.930657 | + | 0.365893i | \(0.880764\pi\) | |||||||
\(104\) | 3.77137 | 0.369813 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.37117 | −0.715951 | ||||||||
\(107\) | 13.8150 | 1.33554 | 0.667772 | − | 0.744366i | \(-0.267248\pi\) | ||||
0.667772 | + | 0.744366i | \(0.267248\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.0676 | 0.964306 | 0.482153 | − | 0.876087i | \(-0.339855\pi\) | ||||
0.482153 | + | 0.876087i | \(0.339855\pi\) | |||||||
\(110\) | 3.07265 | 0.292966 | ||||||||
\(111\) | 2.45186 | 0.232720 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.30392 | 0.593023 | 0.296511 | − | 0.955029i | \(-0.404177\pi\) | ||||
0.296511 | + | 0.955029i | \(0.404177\pi\) | |||||||
\(114\) | 1.09088 | 0.102170 | ||||||||
\(115\) | 1.82843 | 0.170502 | ||||||||
\(116\) | −0.771369 | −0.0716199 | ||||||||
\(117\) | 3.77137 | 0.348663 | ||||||||
\(118\) | −6.42822 | −0.591766 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.82843 | 0.166912 | ||||||||
\(121\) | −8.17596 | −0.743269 | ||||||||
\(122\) | 9.08548 | 0.822560 | ||||||||
\(123\) | −1.09088 | −0.0983614 | ||||||||
\(124\) | −3.86225 | −0.346840 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.02363 | 0.357040 | 0.178520 | − | 0.983936i | \(-0.442869\pi\) | ||||
0.178520 | + | 0.983936i | \(0.442869\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.2959 | 0.906501 | ||||||||
\(130\) | 6.89567 | 0.604791 | ||||||||
\(131\) | 10.9946 | 0.960602 | 0.480301 | − | 0.877104i | \(-0.340527\pi\) | ||||
0.480301 | + | 0.877104i | \(0.340527\pi\) | |||||||
\(132\) | 1.68049 | 0.146268 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.8903 | −1.11355 | ||||||||
\(135\) | 1.82843 | 0.157366 | ||||||||
\(136\) | 2.59980 | 0.222931 | ||||||||
\(137\) | 4.14794 | 0.354382 | 0.177191 | − | 0.984176i | \(-0.443299\pi\) | ||||
0.177191 | + | 0.984176i | \(0.443299\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −13.3137 | −1.12925 | −0.564627 | − | 0.825346i | \(-0.690980\pi\) | ||||
−0.564627 | + | 0.825346i | \(0.690980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.22323 | −0.187229 | ||||||||
\(142\) | 8.22863 | 0.690531 | ||||||||
\(143\) | 6.33774 | 0.529989 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.41039 | −0.117127 | ||||||||
\(146\) | −2.86225 | −0.236882 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.45186 | 0.201541 | ||||||||
\(149\) | −11.8724 | −0.972628 | −0.486314 | − | 0.873784i | \(-0.661659\pi\) | ||||
−0.486314 | + | 0.873784i | \(0.661659\pi\) | |||||||
\(150\) | −1.65685 | −0.135282 | ||||||||
\(151\) | 1.07265 | 0.0872911 | 0.0436455 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436455 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(152\) | 1.09088 | 0.0884821 | ||||||||
\(153\) | 2.59980 | 0.210181 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.06184 | −0.567221 | ||||||||
\(156\) | 3.77137 | 0.301951 | ||||||||
\(157\) | 21.3760 | 1.70599 | 0.852993 | − | 0.521922i | \(-0.174785\pi\) | ||||
0.852993 | + | 0.521922i | \(0.174785\pi\) | |||||||
\(158\) | 0.771369 | 0.0613669 | ||||||||
\(159\) | −7.37117 | −0.584571 | ||||||||
\(160\) | 1.82843 | 0.144550 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.88048 | 0.147291 | 0.0736453 | − | 0.997284i | \(-0.476537\pi\) | ||||
0.0736453 | + | 0.997284i | \(0.476537\pi\) | |||||||
\(164\) | −1.09088 | −0.0851835 | ||||||||
\(165\) | 3.07265 | 0.239206 | ||||||||
\(166\) | 3.33734 | 0.259028 | ||||||||
\(167\) | −19.6511 | −1.52064 | −0.760322 | − | 0.649546i | \(-0.774959\pi\) | ||||
−0.760322 | + | 0.649546i | \(0.774959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.22323 | 0.0940944 | ||||||||
\(170\) | 4.75354 | 0.364580 | ||||||||
\(171\) | 1.09088 | 0.0834218 | ||||||||
\(172\) | 10.2959 | 0.785053 | ||||||||
\(173\) | −1.77097 | −0.134644 | −0.0673222 | − | 0.997731i | \(-0.521446\pi\) | ||||
−0.0673222 | + | 0.997731i | \(0.521446\pi\) | |||||||
\(174\) | −0.771369 | −0.0584774 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.68049 | 0.126672 | ||||||||
\(177\) | −6.42822 | −0.483175 | ||||||||
\(178\) | 3.20500 | 0.240225 | ||||||||
\(179\) | −12.2232 | −0.913607 | −0.456803 | − | 0.889568i | \(-0.651006\pi\) | ||||
−0.456803 | + | 0.889568i | \(0.651006\pi\) | |||||||
\(180\) | 1.82843 | 0.136283 | ||||||||
\(181\) | 0.820785 | 0.0610085 | 0.0305043 | − | 0.999535i | \(-0.490289\pi\) | ||||
0.0305043 | + | 0.999535i | \(0.490289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.08548 | 0.671618 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 4.48304 | 0.329600 | ||||||||
\(186\) | −3.86225 | −0.283194 | ||||||||
\(187\) | 4.36893 | 0.319488 | ||||||||
\(188\) | −2.22323 | −0.162146 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.99460 | 0.144703 | ||||||||
\(191\) | −12.4519 | −0.900985 | −0.450492 | − | 0.892780i | \(-0.648752\pi\) | ||||
−0.450492 | + | 0.892780i | \(0.648752\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.70412 | 0.482573 | 0.241287 | − | 0.970454i | \(-0.422431\pi\) | ||||
0.241287 | + | 0.970454i | \(0.422431\pi\) | |||||||
\(194\) | −10.4282 | −0.748703 | ||||||||
\(195\) | 6.89567 | 0.493809 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5606 | 1.17989 | 0.589946 | − | 0.807443i | \(-0.299149\pi\) | ||||
0.589946 | + | 0.807443i | \(0.299149\pi\) | |||||||
\(198\) | 1.68049 | 0.119427 | ||||||||
\(199\) | −5.01783 | −0.355705 | −0.177852 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177852 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(200\) | −1.65685 | −0.117157 | ||||||||
\(201\) | −12.8903 | −0.909210 | ||||||||
\(202\) | −6.47764 | −0.455765 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.59980 | 0.182022 | ||||||||
\(205\) | −1.99460 | −0.139309 | ||||||||
\(206\) | −18.8903 | −1.31615 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 3.77137 | 0.261497 | ||||||||
\(209\) | 1.83321 | 0.126806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1523 | 1.18081 | 0.590407 | − | 0.807105i | \(-0.298967\pi\) | ||||
0.590407 | + | 0.807105i | \(0.298967\pi\) | |||||||
\(212\) | −7.37117 | −0.506254 | ||||||||
\(213\) | 8.22863 | 0.563816 | ||||||||
\(214\) | 13.8150 | 0.944373 | ||||||||
\(215\) | 18.8253 | 1.28387 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0676 | 0.681867 | ||||||||
\(219\) | −2.86225 | −0.193413 | ||||||||
\(220\) | 3.07265 | 0.207158 | ||||||||
\(221\) | 9.80479 | 0.659542 | ||||||||
\(222\) | 2.45186 | 0.164558 | ||||||||
\(223\) | 4.42282 | 0.296174 | 0.148087 | − | 0.988974i | \(-0.452688\pi\) | ||||
0.148087 | + | 0.988974i | \(0.452688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.65685 | −0.110457 | ||||||||
\(226\) | 6.30392 | 0.419330 | ||||||||
\(227\) | −12.0905 | −0.802473 | −0.401237 | − | 0.915974i | \(-0.631420\pi\) | ||||
−0.401237 | + | 0.915974i | \(0.631420\pi\) | |||||||
\(228\) | 1.09088 | 0.0722454 | ||||||||
\(229\) | −9.09088 | −0.600742 | −0.300371 | − | 0.953822i | \(-0.597111\pi\) | ||||
−0.300371 | + | 0.953822i | \(0.597111\pi\) | |||||||
\(230\) | 1.82843 | 0.120563 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.771369 | −0.0506429 | ||||||||
\(233\) | 6.74774 | 0.442059 | 0.221029 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221029 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(234\) | 3.77137 | 0.246542 | ||||||||
\(235\) | −4.06501 | −0.265172 | ||||||||
\(236\) | −6.42822 | −0.418442 | ||||||||
\(237\) | 0.771369 | 0.0501058 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5918 | 1.33197 | 0.665985 | − | 0.745965i | \(-0.268011\pi\) | ||||
0.665985 | + | 0.745965i | \(0.268011\pi\) | |||||||
\(240\) | 1.82843 | 0.118024 | ||||||||
\(241\) | 17.1814 | 1.10675 | 0.553374 | − | 0.832933i | \(-0.313340\pi\) | ||||
0.553374 | + | 0.832933i | \(0.313340\pi\) | |||||||
\(242\) | −8.17596 | −0.525571 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.08548 | 0.581638 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.09088 | −0.0695520 | ||||||||
\(247\) | 4.11412 | 0.261775 | ||||||||
\(248\) | −3.86225 | −0.245253 | ||||||||
\(249\) | 3.33734 | 0.211495 | ||||||||
\(250\) | −12.1716 | −0.769798 | ||||||||
\(251\) | −15.1760 | −0.957898 | −0.478949 | − | 0.877843i | \(-0.658982\pi\) | ||||
−0.478949 | + | 0.877843i | \(0.658982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.68049 | 0.105651 | ||||||||
\(254\) | 4.02363 | 0.252465 | ||||||||
\(255\) | 4.75354 | 0.297678 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.9946 | −0.997716 | −0.498858 | − | 0.866684i | \(-0.666247\pi\) | ||||
−0.498858 | + | 0.866684i | \(0.666247\pi\) | |||||||
\(258\) | 10.2959 | 0.640993 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.89567 | 0.427652 | ||||||||
\(261\) | −0.771369 | −0.0477466 | ||||||||
\(262\) | 10.9946 | 0.679248 | ||||||||
\(263\) | 21.7602 | 1.34179 | 0.670895 | − | 0.741553i | \(-0.265910\pi\) | ||||
0.670895 | + | 0.741553i | \(0.265910\pi\) | |||||||
\(264\) | 1.68049 | 0.103427 | ||||||||
\(265\) | −13.4776 | −0.827925 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.20500 | 0.196143 | ||||||||
\(268\) | −12.8903 | −0.787399 | ||||||||
\(269\) | 20.5627 | 1.25373 | 0.626866 | − | 0.779127i | \(-0.284338\pi\) | ||||
0.626866 | + | 0.779127i | \(0.284338\pi\) | |||||||
\(270\) | 1.82843 | 0.111275 | ||||||||
\(271\) | 3.86225 | 0.234615 | 0.117308 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117308 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(272\) | 2.59980 | 0.157636 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.14794 | 0.250586 | ||||||||
\(275\) | −2.78432 | −0.167901 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 24.1295 | 1.44980 | 0.724900 | − | 0.688854i | \(-0.241886\pi\) | ||||
0.724900 | + | 0.688854i | \(0.241886\pi\) | |||||||
\(278\) | −13.3137 | −0.798503 | ||||||||
\(279\) | −3.86225 | −0.231227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6853 | 1.65156 | 0.825782 | − | 0.563989i | \(-0.190734\pi\) | ||||
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(282\) | −2.22323 | −0.132391 | ||||||||
\(283\) | 5.96618 | 0.354652 | 0.177326 | − | 0.984152i | \(-0.443255\pi\) | ||||
0.177326 | + | 0.984152i | \(0.443255\pi\) | |||||||
\(284\) | 8.22863 | 0.488279 | ||||||||
\(285\) | 1.99460 | 0.118150 | ||||||||
\(286\) | 6.33774 | 0.374759 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.2411 | −0.602415 | ||||||||
\(290\) | −1.41039 | −0.0828211 | ||||||||
\(291\) | −10.4282 | −0.611313 | ||||||||
\(292\) | −2.86225 | −0.167501 | ||||||||
\(293\) | −31.4853 | −1.83939 | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||||
−0.919695 | + | 0.392634i | \(0.871564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7535 | −0.684317 | ||||||||
\(296\) | 2.45186 | 0.142511 | ||||||||
\(297\) | 1.68049 | 0.0975118 | ||||||||
\(298\) | −11.8724 | −0.687752 | ||||||||
\(299\) | 3.77137 | 0.218104 | ||||||||
\(300\) | −1.65685 | −0.0956585 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.07265 | 0.0617241 | ||||||||
\(303\) | −6.47764 | −0.372131 | ||||||||
\(304\) | 1.09088 | 0.0625663 | ||||||||
\(305\) | 16.6121 | 0.951208 | ||||||||
\(306\) | 2.59980 | 0.148620 | ||||||||
\(307\) | 5.13815 | 0.293250 | 0.146625 | − | 0.989192i | \(-0.453159\pi\) | ||||
0.146625 | + | 0.989192i | \(0.453159\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.8903 | −1.07463 | ||||||||
\(310\) | −7.06184 | −0.401086 | ||||||||
\(311\) | −15.5627 | −0.882481 | −0.441240 | − | 0.897389i | \(-0.645461\pi\) | ||||
−0.441240 | + | 0.897389i | \(0.645461\pi\) | |||||||
\(312\) | 3.77137 | 0.213512 | ||||||||
\(313\) | −22.1527 | −1.25215 | −0.626073 | − | 0.779764i | \(-0.715339\pi\) | ||||
−0.626073 | + | 0.779764i | \(0.715339\pi\) | |||||||
\(314\) | 21.3760 | 1.20631 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.771369 | 0.0433929 | ||||||||
\(317\) | 18.5627 | 1.04259 | 0.521293 | − | 0.853378i | \(-0.325450\pi\) | ||||
0.521293 | + | 0.853378i | \(0.325450\pi\) | |||||||
\(318\) | −7.37117 | −0.413354 | ||||||||
\(319\) | −1.29628 | −0.0725776 | ||||||||
\(320\) | 1.82843 | 0.102212 | ||||||||
\(321\) | 13.8150 | 0.771077 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.83607 | 0.157803 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.24861 | −0.346610 | ||||||||
\(326\) | 1.88048 | 0.104150 | ||||||||
\(327\) | 10.0676 | 0.556742 | ||||||||
\(328\) | −1.09088 | −0.0602338 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.07265 | 0.169144 | ||||||||
\(331\) | 2.86265 | 0.157345 | 0.0786727 | − | 0.996900i | \(-0.474932\pi\) | ||||
0.0786727 | + | 0.996900i | \(0.474932\pi\) | |||||||
\(332\) | 3.33734 | 0.183160 | ||||||||
\(333\) | 2.45186 | 0.134361 | ||||||||
\(334\) | −19.6511 | −1.07526 | ||||||||
\(335\) | −23.5689 | −1.28771 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.70627 | −0.419787 | −0.209894 | − | 0.977724i | \(-0.567312\pi\) | ||||
−0.209894 | + | 0.977724i | \(0.567312\pi\) | |||||||
\(338\) | 1.22323 | 0.0665348 | ||||||||
\(339\) | 6.30392 | 0.342382 | ||||||||
\(340\) | 4.75354 | 0.257797 | ||||||||
\(341\) | −6.49047 | −0.351478 | ||||||||
\(342\) | 1.09088 | 0.0589881 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.2959 | 0.555117 | ||||||||
\(345\) | 1.82843 | 0.0984392 | ||||||||
\(346\) | −1.77097 | −0.0952079 | ||||||||
\(347\) | −9.94773 | −0.534022 | −0.267011 | − | 0.963693i | \(-0.586036\pi\) | ||||
−0.267011 | + | 0.963693i | \(0.586036\pi\) | |||||||
\(348\) | −0.771369 | −0.0413497 | ||||||||
\(349\) | −8.54489 | −0.457397 | −0.228699 | − | 0.973497i | \(-0.573447\pi\) | ||||
−0.228699 | + | 0.973497i | \(0.573447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.77137 | 0.201301 | ||||||||
\(352\) | 1.68049 | 0.0895703 | ||||||||
\(353\) | −1.99460 | −0.106162 | −0.0530808 | − | 0.998590i | \(-0.516904\pi\) | ||||
−0.0530808 | + | 0.998590i | \(0.516904\pi\) | |||||||
\(354\) | −6.42822 | −0.341656 | ||||||||
\(355\) | 15.0455 | 0.798530 | ||||||||
\(356\) | 3.20500 | 0.169864 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.2232 | −0.646018 | ||||||||
\(359\) | −27.7129 | −1.46263 | −0.731315 | − | 0.682040i | \(-0.761093\pi\) | ||||
−0.731315 | + | 0.682040i | \(0.761093\pi\) | |||||||
\(360\) | 1.82843 | 0.0963666 | ||||||||
\(361\) | −17.8100 | −0.937367 | ||||||||
\(362\) | 0.820785 | 0.0431395 | ||||||||
\(363\) | −8.17596 | −0.429127 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.23342 | −0.273930 | ||||||||
\(366\) | 9.08548 | 0.474906 | ||||||||
\(367\) | −21.7758 | −1.13669 | −0.568343 | − | 0.822792i | \(-0.692415\pi\) | ||||
−0.568343 | + | 0.822792i | \(0.692415\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.09088 | −0.0567890 | ||||||||
\(370\) | 4.48304 | 0.233062 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.86225 | −0.200248 | ||||||||
\(373\) | 13.3610 | 0.691805 | 0.345903 | − | 0.938270i | \(-0.387573\pi\) | ||||
0.345903 | + | 0.938270i | \(0.387573\pi\) | |||||||
\(374\) | 4.36893 | 0.225912 | ||||||||
\(375\) | −12.1716 | −0.628537 | ||||||||
\(376\) | −2.22323 | −0.114654 | ||||||||
\(377\) | −2.90912 | −0.149827 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.50892 | −0.180241 | −0.0901204 | − | 0.995931i | \(-0.528725\pi\) | ||||
−0.0901204 | + | 0.995931i | \(0.528725\pi\) | |||||||
\(380\) | 1.99460 | 0.102321 | ||||||||
\(381\) | 4.02363 | 0.206137 | ||||||||
\(382\) | −12.4519 | −0.637092 | ||||||||
\(383\) | 0.483043 | 0.0246824 | 0.0123412 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123412 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.70412 | 0.341231 | ||||||||
\(387\) | 10.2959 | 0.523369 | ||||||||
\(388\) | −10.4282 | −0.529413 | ||||||||
\(389\) | 18.6282 | 0.944488 | 0.472244 | − | 0.881468i | \(-0.343444\pi\) | ||||
0.472244 | + | 0.881468i | \(0.343444\pi\) | |||||||
\(390\) | 6.89567 | 0.349176 | ||||||||
\(391\) | 2.59980 | 0.131477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9946 | 0.554604 | ||||||||
\(394\) | 16.5606 | 0.834309 | ||||||||
\(395\) | 1.41039 | 0.0709646 | ||||||||
\(396\) | 1.68049 | 0.0844477 | ||||||||
\(397\) | 31.7445 | 1.59321 | 0.796605 | − | 0.604500i | \(-0.206627\pi\) | ||||
0.796605 | + | 0.604500i | \(0.206627\pi\) | |||||||
\(398\) | −5.01783 | −0.251521 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.65685 | −0.0828427 | ||||||||
\(401\) | −20.7762 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(402\) | −12.8903 | −0.642908 | ||||||||
\(403\) | −14.5660 | −0.725583 | ||||||||
\(404\) | −6.47764 | −0.322275 | ||||||||
\(405\) | 1.82843 | 0.0908553 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.12032 | 0.204237 | ||||||||
\(408\) | 2.59980 | 0.128709 | ||||||||
\(409\) | 19.6951 | 0.973858 | 0.486929 | − | 0.873441i | \(-0.338117\pi\) | ||||
0.486929 | + | 0.873441i | \(0.338117\pi\) | |||||||
\(410\) | −1.99460 | −0.0985061 | ||||||||
\(411\) | 4.14794 | 0.204603 | ||||||||
\(412\) | −18.8903 | −0.930657 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 6.10209 | 0.299540 | ||||||||
\(416\) | 3.77137 | 0.184907 | ||||||||
\(417\) | −13.3137 | −0.651975 | ||||||||
\(418\) | 1.83321 | 0.0896654 | ||||||||
\(419\) | −1.70412 | −0.0832518 | −0.0416259 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416259 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8564 | −0.626585 | −0.313292 | − | 0.949657i | \(-0.601432\pi\) | ||||
−0.313292 | + | 0.949657i | \(0.601432\pi\) | |||||||
\(422\) | 17.1523 | 0.834962 | ||||||||
\(423\) | −2.22323 | −0.108097 | ||||||||
\(424\) | −7.37117 | −0.357975 | ||||||||
\(425\) | −4.30748 | −0.208944 | ||||||||
\(426\) | 8.22863 | 0.398678 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.8150 | 0.667772 | ||||||||
\(429\) | 6.33774 | 0.305989 | ||||||||
\(430\) | 18.8253 | 0.907835 | ||||||||
\(431\) | −11.5419 | −0.555956 | −0.277978 | − | 0.960587i | \(-0.589664\pi\) | ||||
−0.277978 | + | 0.960587i | \(0.589664\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −24.7627 | −1.19002 | −0.595010 | − | 0.803718i | \(-0.702852\pi\) | ||||
−0.595010 | + | 0.803718i | \(0.702852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41039 | −0.0676232 | ||||||||
\(436\) | 10.0676 | 0.482153 | ||||||||
\(437\) | 1.09088 | 0.0521839 | ||||||||
\(438\) | −2.86225 | −0.136764 | ||||||||
\(439\) | −7.82579 | −0.373505 | −0.186752 | − | 0.982407i | \(-0.559796\pi\) | ||||
−0.186752 | + | 0.982407i | \(0.559796\pi\) | |||||||
\(440\) | 3.07265 | 0.146483 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.80479 | 0.466366 | ||||||||
\(443\) | −0.994597 | −0.0472547 | −0.0236274 | − | 0.999721i | \(-0.507522\pi\) | ||||
−0.0236274 | + | 0.999721i | \(0.507522\pi\) | |||||||
\(444\) | 2.45186 | 0.116360 | ||||||||
\(445\) | 5.86010 | 0.277796 | ||||||||
\(446\) | 4.42282 | 0.209427 | ||||||||
\(447\) | −11.8724 | −0.561547 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.1291 | 1.23311 | 0.616554 | − | 0.787313i | \(-0.288528\pi\) | ||||
0.616554 | + | 0.787313i | \(0.288528\pi\) | |||||||
\(450\) | −1.65685 | −0.0781049 | ||||||||
\(451\) | −1.83321 | −0.0863226 | ||||||||
\(452\) | 6.30392 | 0.296511 | ||||||||
\(453\) | 1.07265 | 0.0503975 | ||||||||
\(454\) | −12.0905 | −0.567434 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.09088 | 0.0510852 | ||||||||
\(457\) | 18.7445 | 0.876830 | 0.438415 | − | 0.898773i | \(-0.355540\pi\) | ||||
0.438415 | + | 0.898773i | \(0.355540\pi\) | |||||||
\(458\) | −9.09088 | −0.424789 | ||||||||
\(459\) | 2.59980 | 0.121348 | ||||||||
\(460\) | 1.82843 | 0.0852509 | ||||||||
\(461\) | −5.63648 | −0.262517 | −0.131258 | − | 0.991348i | \(-0.541902\pi\) | ||||
−0.131258 | + | 0.991348i | \(0.541902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5337 | −0.954281 | −0.477141 | − | 0.878827i | \(-0.658327\pi\) | ||||
−0.477141 | + | 0.878827i | \(0.658327\pi\) | |||||||
\(464\) | −0.771369 | −0.0358099 | ||||||||
\(465\) | −7.06184 | −0.327485 | ||||||||
\(466\) | 6.74774 | 0.312583 | ||||||||
\(467\) | −1.17921 | −0.0545675 | −0.0272838 | − | 0.999628i | \(-0.508686\pi\) | ||||
−0.0272838 | + | 0.999628i | \(0.508686\pi\) | |||||||
\(468\) | 3.77137 | 0.174332 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.06501 | −0.187505 | ||||||||
\(471\) | 21.3760 | 0.984952 | ||||||||
\(472\) | −6.42822 | −0.295883 | ||||||||
\(473\) | 17.3021 | 0.795552 | ||||||||
\(474\) | 0.771369 | 0.0354302 | ||||||||
\(475\) | −1.80743 | −0.0829306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.37117 | −0.337503 | ||||||||
\(478\) | 20.5918 | 0.941845 | ||||||||
\(479\) | 1.68264 | 0.0768816 | 0.0384408 | − | 0.999261i | \(-0.487761\pi\) | ||||
0.0384408 | + | 0.999261i | \(0.487761\pi\) | |||||||
\(480\) | 1.82843 | 0.0834559 | ||||||||
\(481\) | 9.24686 | 0.421621 | ||||||||
\(482\) | 17.1814 | 0.782590 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.17596 | −0.371634 | ||||||||
\(485\) | −19.0672 | −0.865799 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −17.2901 | −0.783488 | −0.391744 | − | 0.920074i | \(-0.628128\pi\) | ||||
−0.391744 | + | 0.920074i | \(0.628128\pi\) | |||||||
\(488\) | 9.08548 | 0.411280 | ||||||||
\(489\) | 1.88048 | 0.0850383 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.7361 | 1.16146 | 0.580728 | − | 0.814098i | \(-0.302768\pi\) | ||||
0.580728 | + | 0.814098i | \(0.302768\pi\) | |||||||
\(492\) | −1.09088 | −0.0491807 | ||||||||
\(493\) | −2.00540 | −0.0903188 | ||||||||
\(494\) | 4.11412 | 0.185103 | ||||||||
\(495\) | 3.07265 | 0.138105 | ||||||||
\(496\) | −3.86225 | −0.173420 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.33734 | 0.149550 | ||||||||
\(499\) | −23.1996 | −1.03856 | −0.519278 | − | 0.854605i | \(-0.673799\pi\) | ||||
−0.519278 | + | 0.854605i | \(0.673799\pi\) | |||||||
\(500\) | −12.1716 | −0.544329 | ||||||||
\(501\) | −19.6511 | −0.877944 | ||||||||
\(502\) | −15.1760 | −0.677336 | ||||||||
\(503\) | −42.3054 | −1.88631 | −0.943153 | − | 0.332358i | \(-0.892156\pi\) | ||||
−0.943153 | + | 0.332358i | \(0.892156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.8439 | −0.527046 | ||||||||
\(506\) | 1.68049 | 0.0747068 | ||||||||
\(507\) | 1.22323 | 0.0543254 | ||||||||
\(508\) | 4.02363 | 0.178520 | ||||||||
\(509\) | −27.9033 | −1.23679 | −0.618396 | − | 0.785866i | \(-0.712217\pi\) | ||||
−0.618396 | + | 0.785866i | \(0.712217\pi\) | |||||||
\(510\) | 4.75354 | 0.210490 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.09088 | 0.0481636 | ||||||||
\(514\) | −15.9946 | −0.705491 | ||||||||
\(515\) | −34.5395 | −1.52199 | ||||||||
\(516\) | 10.2959 | 0.453251 | ||||||||
\(517\) | −3.73611 | −0.164314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.77097 | −0.0777369 | ||||||||
\(520\) | 6.89567 | 0.302395 | ||||||||
\(521\) | 17.9554 | 0.786639 | 0.393320 | − | 0.919402i | \(-0.371327\pi\) | ||||
0.393320 | + | 0.919402i | \(0.371327\pi\) | |||||||
\(522\) | −0.771369 | −0.0337619 | ||||||||
\(523\) | −12.9375 | −0.565719 | −0.282860 | − | 0.959161i | \(-0.591283\pi\) | ||||
−0.282860 | + | 0.959161i | \(0.591283\pi\) | |||||||
\(524\) | 10.9946 | 0.480301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.7602 | 0.948788 | ||||||||
\(527\) | −10.0411 | −0.437396 | ||||||||
\(528\) | 1.68049 | 0.0731339 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −13.4776 | −0.585431 | ||||||||
\(531\) | −6.42822 | −0.278961 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.11412 | −0.178202 | ||||||||
\(534\) | 3.20500 | 0.138694 | ||||||||
\(535\) | 25.2597 | 1.09207 | ||||||||
\(536\) | −12.8903 | −0.556775 | ||||||||
\(537\) | −12.2232 | −0.527471 | ||||||||
\(538\) | 20.5627 | 0.886522 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.82843 | 0.0786830 | ||||||||
\(541\) | 40.9797 | 1.76186 | 0.880928 | − | 0.473250i | \(-0.156919\pi\) | ||||
0.880928 | + | 0.473250i | \(0.156919\pi\) | |||||||
\(542\) | 3.86225 | 0.165898 | ||||||||
\(543\) | 0.820785 | 0.0352233 | ||||||||
\(544\) | 2.59980 | 0.111465 | ||||||||
\(545\) | 18.4080 | 0.788510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.6515 | −1.78089 | −0.890444 | − | 0.455093i | \(-0.849606\pi\) | ||||
−0.890444 | + | 0.455093i | \(0.849606\pi\) | |||||||
\(548\) | 4.14794 | 0.177191 | ||||||||
\(549\) | 9.08548 | 0.387759 | ||||||||
\(550\) | −2.78432 | −0.118724 | ||||||||
\(551\) | −0.841472 | −0.0358479 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.1295 | 1.02516 | ||||||||
\(555\) | 4.48304 | 0.190295 | ||||||||
\(556\) | −13.3137 | −0.564627 | ||||||||
\(557\) | −17.8158 | −0.754879 | −0.377439 | − | 0.926034i | \(-0.623195\pi\) | ||||
−0.377439 | + | 0.926034i | \(0.623195\pi\) | |||||||
\(558\) | −3.86225 | −0.163502 | ||||||||
\(559\) | 38.8296 | 1.64232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.36893 | 0.184456 | ||||||||
\(562\) | 27.6853 | 1.16783 | ||||||||
\(563\) | −0.891688 | −0.0375802 | −0.0187901 | − | 0.999823i | \(-0.505981\pi\) | ||||
−0.0187901 | + | 0.999823i | \(0.505981\pi\) | |||||||
\(564\) | −2.22323 | −0.0936147 | ||||||||
\(565\) | 11.5263 | 0.484913 | ||||||||
\(566\) | 5.96618 | 0.250777 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.22863 | 0.345266 | ||||||||
\(569\) | −7.29149 | −0.305675 | −0.152838 | − | 0.988251i | \(-0.548841\pi\) | ||||
−0.152838 | + | 0.988251i | \(0.548841\pi\) | |||||||
\(570\) | 1.99460 | 0.0835445 | ||||||||
\(571\) | 32.3803 | 1.35507 | 0.677537 | − | 0.735488i | \(-0.263047\pi\) | ||||
0.677537 | + | 0.735488i | \(0.263047\pi\) | |||||||
\(572\) | 6.33774 | 0.264994 | ||||||||
\(573\) | −12.4519 | −0.520184 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.65685 | −0.0690956 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.45401 | −0.185423 | −0.0927113 | − | 0.995693i | \(-0.529553\pi\) | ||||
−0.0927113 | + | 0.995693i | \(0.529553\pi\) | |||||||
\(578\) | −10.2411 | −0.425972 | ||||||||
\(579\) | 6.70412 | 0.278614 | ||||||||
\(580\) | −1.41039 | −0.0585634 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.4282 | −0.432264 | ||||||||
\(583\) | −12.3872 | −0.513024 | ||||||||
\(584\) | −2.86225 | −0.118441 | ||||||||
\(585\) | 6.89567 | 0.285101 | ||||||||
\(586\) | −31.4853 | −1.30064 | ||||||||
\(587\) | −13.6693 | −0.564192 | −0.282096 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282096 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.21326 | −0.173604 | ||||||||
\(590\) | −11.7535 | −0.483886 | ||||||||
\(591\) | 16.5606 | 0.681211 | ||||||||
\(592\) | 2.45186 | 0.100771 | ||||||||
\(593\) | −13.2104 | −0.542486 | −0.271243 | − | 0.962511i | \(-0.587435\pi\) | ||||
−0.271243 | + | 0.962511i | \(0.587435\pi\) | |||||||
\(594\) | 1.68049 | 0.0689513 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.8724 | −0.486314 | ||||||||
\(597\) | −5.01783 | −0.205366 | ||||||||
\(598\) | 3.77137 | 0.154223 | ||||||||
\(599\) | 27.3133 | 1.11599 | 0.557996 | − | 0.829844i | \(-0.311571\pi\) | ||||
0.557996 | + | 0.829844i | \(0.311571\pi\) | |||||||
\(600\) | −1.65685 | −0.0676408 | ||||||||
\(601\) | 39.7677 | 1.62216 | 0.811079 | − | 0.584936i | \(-0.198880\pi\) | ||||
0.811079 | + | 0.584936i | \(0.198880\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.8903 | −0.524932 | ||||||||
\(604\) | 1.07265 | 0.0436455 | ||||||||
\(605\) | −14.9491 | −0.607769 | ||||||||
\(606\) | −6.47764 | −0.263136 | ||||||||
\(607\) | −9.51910 | −0.386369 | −0.193184 | − | 0.981162i | \(-0.561882\pi\) | ||||
−0.193184 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(608\) | 1.09088 | 0.0442411 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.6121 | 0.672606 | ||||||||
\(611\) | −8.38461 | −0.339205 | ||||||||
\(612\) | 2.59980 | 0.105091 | ||||||||
\(613\) | −45.7805 | −1.84906 | −0.924529 | − | 0.381111i | \(-0.875542\pi\) | ||||
−0.924529 | + | 0.381111i | \(0.875542\pi\) | |||||||
\(614\) | 5.13815 | 0.207359 | ||||||||
\(615\) | −1.99460 | −0.0804299 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.5293 | −0.947254 | −0.473627 | − | 0.880726i | \(-0.657055\pi\) | ||||
−0.473627 | + | 0.880726i | \(0.657055\pi\) | |||||||
\(618\) | −18.8903 | −0.759878 | ||||||||
\(619\) | −4.86449 | −0.195520 | −0.0977602 | − | 0.995210i | \(-0.531168\pi\) | ||||
−0.0977602 | + | 0.995210i | \(0.531168\pi\) | |||||||
\(620\) | −7.06184 | −0.283610 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −15.5627 | −0.624008 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.77137 | 0.150976 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | −22.1527 | −0.885401 | ||||||||
\(627\) | 1.83321 | 0.0732115 | ||||||||
\(628\) | 21.3760 | 0.852993 | ||||||||
\(629\) | 6.37433 | 0.254161 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.5940 | −1.01888 | −0.509440 | − | 0.860506i | \(-0.670148\pi\) | ||||
−0.509440 | + | 0.860506i | \(0.670148\pi\) | |||||||
\(632\) | 0.771369 | 0.0306834 | ||||||||
\(633\) | 17.1523 | 0.681744 | ||||||||
\(634\) | 18.5627 | 0.737220 | ||||||||
\(635\) | 7.35692 | 0.291951 | ||||||||
\(636\) | −7.37117 | −0.292286 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.29628 | −0.0513201 | ||||||||
\(639\) | 8.22863 | 0.325520 | ||||||||
\(640\) | 1.82843 | 0.0722749 | ||||||||
\(641\) | −14.6355 | −0.578066 | −0.289033 | − | 0.957319i | \(-0.593334\pi\) | ||||
−0.289033 | + | 0.957319i | \(0.593334\pi\) | |||||||
\(642\) | 13.8150 | 0.545234 | ||||||||
\(643\) | 41.6246 | 1.64151 | 0.820756 | − | 0.571279i | \(-0.193552\pi\) | ||||
0.820756 | + | 0.571279i | \(0.193552\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.8253 | 0.741244 | ||||||||
\(646\) | 2.83607 | 0.111584 | ||||||||
\(647\) | −31.6192 | −1.24308 | −0.621539 | − | 0.783383i | \(-0.713492\pi\) | ||||
−0.621539 | + | 0.783383i | \(0.713492\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −10.8026 | −0.424037 | ||||||||
\(650\) | −6.24861 | −0.245091 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.88048 | 0.0736453 | ||||||||
\(653\) | −3.29628 | −0.128993 | −0.0644966 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644966 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(654\) | 10.0676 | 0.393676 | ||||||||
\(655\) | 20.1028 | 0.785482 | ||||||||
\(656\) | −1.09088 | −0.0425917 | ||||||||
\(657\) | −2.86225 | −0.111667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0203785 | 0.000793834 0 | 0.000396917 | − | 1.00000i | \(-0.499874\pi\) | ||||
0.000396917 | 1.00000i | \(0.499874\pi\) | ||||||||
\(660\) | 3.07265 | 0.119603 | ||||||||
\(661\) | 42.2013 | 1.64144 | 0.820721 | − | 0.571329i | \(-0.193572\pi\) | ||||
0.820721 | + | 0.571329i | \(0.193572\pi\) | |||||||
\(662\) | 2.86265 | 0.111260 | ||||||||
\(663\) | 9.80479 | 0.380787 | ||||||||
\(664\) | 3.33734 | 0.129514 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.45186 | 0.0950076 | ||||||||
\(667\) | −0.771369 | −0.0298675 | ||||||||
\(668\) | −19.6511 | −0.760322 | ||||||||
\(669\) | 4.42282 | 0.170996 | ||||||||
\(670\) | −23.5689 | −0.910547 | ||||||||
\(671\) | 15.2680 | 0.589416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4540 | −0.634255 | −0.317128 | − | 0.948383i | \(-0.602718\pi\) | ||||
−0.317128 | + | 0.948383i | \(0.602718\pi\) | |||||||
\(674\) | −7.70627 | −0.296834 | ||||||||
\(675\) | −1.65685 | −0.0637723 | ||||||||
\(676\) | 1.22323 | 0.0470472 | ||||||||
\(677\) | −23.8845 | −0.917955 | −0.458977 | − | 0.888448i | \(-0.651784\pi\) | ||||
−0.458977 | + | 0.888448i | \(0.651784\pi\) | |||||||
\(678\) | 6.30392 | 0.242101 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.75354 | 0.182290 | ||||||||
\(681\) | −12.0905 | −0.463308 | ||||||||
\(682\) | −6.49047 | −0.248533 | ||||||||
\(683\) | 11.0934 | 0.424478 | 0.212239 | − | 0.977218i | \(-0.431924\pi\) | ||||
0.212239 | + | 0.977218i | \(0.431924\pi\) | |||||||
\(684\) | 1.09088 | 0.0417109 | ||||||||
\(685\) | 7.58420 | 0.289778 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.09088 | −0.346839 | ||||||||
\(688\) | 10.2959 | 0.392527 | ||||||||
\(689\) | −27.7994 | −1.05907 | ||||||||
\(690\) | 1.82843 | 0.0696070 | ||||||||
\(691\) | −6.63282 | −0.252324 | −0.126162 | − | 0.992010i | \(-0.540266\pi\) | ||||
−0.126162 | + | 0.992010i | \(0.540266\pi\) | |||||||
\(692\) | −1.77097 | −0.0673222 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.94773 | −0.377611 | ||||||||
\(695\) | −24.3431 | −0.923388 | ||||||||
\(696\) | −0.771369 | −0.0292387 | ||||||||
\(697\) | −2.83607 | −0.107424 | ||||||||
\(698\) | −8.54489 | −0.323429 | ||||||||
\(699\) | 6.74774 | 0.255223 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.07784 | −0.305096 | −0.152548 | − | 0.988296i | \(-0.548748\pi\) | ||||
−0.152548 | + | 0.988296i | \(0.548748\pi\) | |||||||
\(702\) | 3.77137 | 0.142341 | ||||||||
\(703\) | 2.67469 | 0.100878 | ||||||||
\(704\) | 1.68049 | 0.0633358 | ||||||||
\(705\) | −4.06501 | −0.153097 | ||||||||
\(706\) | −1.99460 | −0.0750676 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.42822 | −0.241587 | ||||||||
\(709\) | 37.4893 | 1.40794 | 0.703970 | − | 0.710230i | \(-0.251409\pi\) | ||||
0.703970 | + | 0.710230i | \(0.251409\pi\) | |||||||
\(710\) | 15.0455 | 0.564646 | ||||||||
\(711\) | 0.771369 | 0.0289286 | ||||||||
\(712\) | 3.20500 | 0.120112 | ||||||||
\(713\) | −3.86225 | −0.144642 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.5881 | 0.433370 | ||||||||
\(716\) | −12.2232 | −0.456803 | ||||||||
\(717\) | 20.5918 | 0.769013 | ||||||||
\(718\) | −27.7129 | −1.03424 | ||||||||
\(719\) | 5.40244 | 0.201477 | 0.100739 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100739 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(720\) | 1.82843 | 0.0681415 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.8100 | −0.662819 | ||||||||
\(723\) | 17.1814 | 0.638982 | ||||||||
\(724\) | 0.820785 | 0.0305043 | ||||||||
\(725\) | 1.27805 | 0.0474655 | ||||||||
\(726\) | −8.17596 | −0.303438 | ||||||||
\(727\) | 15.4461 | 0.572862 | 0.286431 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286431 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.23342 | −0.193697 | ||||||||
\(731\) | 26.7672 | 0.990020 | ||||||||
\(732\) | 9.08548 | 0.335809 | ||||||||
\(733\) | 5.50167 | 0.203209 | 0.101604 | − | 0.994825i | \(-0.467602\pi\) | ||||
0.101604 | + | 0.994825i | \(0.467602\pi\) | |||||||
\(734\) | −21.7758 | −0.803758 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −21.6619 | −0.797928 | ||||||||
\(738\) | −1.09088 | −0.0401559 | ||||||||
\(739\) | −39.9419 | −1.46929 | −0.734644 | − | 0.678453i | \(-0.762651\pi\) | ||||
−0.734644 | + | 0.678453i | \(0.762651\pi\) | |||||||
\(740\) | 4.48304 | 0.164800 | ||||||||
\(741\) | 4.11412 | 0.151136 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5889 | 0.792020 | 0.396010 | − | 0.918246i | \(-0.370395\pi\) | ||||
0.396010 | + | 0.918246i | \(0.370395\pi\) | |||||||
\(744\) | −3.86225 | −0.141597 | ||||||||
\(745\) | −21.7079 | −0.795316 | ||||||||
\(746\) | 13.3610 | 0.489180 | ||||||||
\(747\) | 3.33734 | 0.122107 | ||||||||
\(748\) | 4.36893 | 0.159744 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −12.1716 | −0.444443 | ||||||||
\(751\) | −16.2312 | −0.592284 | −0.296142 | − | 0.955144i | \(-0.595700\pi\) | ||||
−0.296142 | + | 0.955144i | \(0.595700\pi\) | |||||||
\(752\) | −2.22323 | −0.0810728 | ||||||||
\(753\) | −15.1760 | −0.553043 | ||||||||
\(754\) | −2.90912 | −0.105944 | ||||||||
\(755\) | 1.96126 | 0.0713777 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.4632 | −0.925475 | −0.462737 | − | 0.886495i | \(-0.653133\pi\) | ||||
−0.462737 | + | 0.886495i | \(0.653133\pi\) | |||||||
\(758\) | −3.50892 | −0.127450 | ||||||||
\(759\) | 1.68049 | 0.0609979 | ||||||||
\(760\) | 1.99460 | 0.0723516 | ||||||||
\(761\) | −53.1985 | −1.92844 | −0.964222 | − | 0.265097i | \(-0.914596\pi\) | ||||
−0.964222 | + | 0.265097i | \(0.914596\pi\) | |||||||
\(762\) | 4.02363 | 0.145761 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.4519 | −0.450492 | ||||||||
\(765\) | 4.75354 | 0.171865 | ||||||||
\(766\) | 0.483043 | 0.0174531 | ||||||||
\(767\) | −24.2432 | −0.875371 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 1.70627 | 0.0615297 | 0.0307648 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307648 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.9946 | −0.576031 | ||||||||
\(772\) | 6.70412 | 0.241287 | ||||||||
\(773\) | 27.0517 | 0.972980 | 0.486490 | − | 0.873686i | \(-0.338277\pi\) | ||||
0.486490 | + | 0.873686i | \(0.338277\pi\) | |||||||
\(774\) | 10.2959 | 0.370078 | ||||||||
\(775\) | 6.39919 | 0.229866 | ||||||||
\(776\) | −10.4282 | −0.374351 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.6282 | 0.667854 | ||||||||
\(779\) | −1.19002 | −0.0426369 | ||||||||
\(780\) | 6.89567 | 0.246905 | ||||||||
\(781\) | 13.8281 | 0.494809 | ||||||||
\(782\) | 2.59980 | 0.0929685 | ||||||||
\(783\) | −0.771369 | −0.0275665 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.0844 | 1.39498 | ||||||||
\(786\) | 10.9946 | 0.392164 | ||||||||
\(787\) | 34.3857 | 1.22572 | 0.612860 | − | 0.790192i | \(-0.290019\pi\) | ||||
0.612860 | + | 0.790192i | \(0.290019\pi\) | |||||||
\(788\) | 16.5606 | 0.589946 | ||||||||
\(789\) | 21.7602 | 0.774682 | ||||||||
\(790\) | 1.41039 | 0.0501795 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.68049 | 0.0597136 | ||||||||
\(793\) | 34.2647 | 1.21677 | ||||||||
\(794\) | 31.7445 | 1.12657 | ||||||||
\(795\) | −13.4776 | −0.478003 | ||||||||
\(796\) | −5.01783 | −0.177852 | ||||||||
\(797\) | −7.25705 | −0.257058 | −0.128529 | − | 0.991706i | \(-0.541026\pi\) | ||||
−0.128529 | + | 0.991706i | \(0.541026\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.77994 | −0.204480 | ||||||||
\(800\) | −1.65685 | −0.0585786 | ||||||||
\(801\) | 3.20500 | 0.113243 | ||||||||
\(802\) | −20.7762 | −0.733632 | ||||||||
\(803\) | −4.80998 | −0.169740 | ||||||||
\(804\) | −12.8903 | −0.454605 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5660 | −0.513065 | ||||||||
\(807\) | 20.5627 | 0.723842 | ||||||||
\(808\) | −6.47764 | −0.227883 | ||||||||
\(809\) | −6.44105 | −0.226455 | −0.113228 | − | 0.993569i | \(-0.536119\pi\) | ||||
−0.113228 | + | 0.993569i | \(0.536119\pi\) | |||||||
\(810\) | 1.82843 | 0.0642444 | ||||||||
\(811\) | 21.6925 | 0.761727 | 0.380864 | − | 0.924631i | \(-0.375627\pi\) | ||||
0.380864 | + | 0.924631i | \(0.375627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.86225 | 0.135455 | ||||||||
\(814\) | 4.12032 | 0.144417 | ||||||||
\(815\) | 3.43832 | 0.120439 | ||||||||
\(816\) | 2.59980 | 0.0910111 | ||||||||
\(817\) | 11.2316 | 0.392943 | ||||||||
\(818\) | 19.6951 | 0.688622 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.99460 | −0.0696543 | ||||||||
\(821\) | −5.07805 | −0.177225 | −0.0886127 | − | 0.996066i | \(-0.528243\pi\) | ||||
−0.0886127 | + | 0.996066i | \(0.528243\pi\) | |||||||
\(822\) | 4.14794 | 0.144676 | ||||||||
\(823\) | 54.3723 | 1.89530 | 0.947650 | − | 0.319312i | \(-0.103452\pi\) | ||||
0.947650 | + | 0.319312i | \(0.103452\pi\) | |||||||
\(824\) | −18.8903 | −0.658074 | ||||||||
\(825\) | −2.78432 | −0.0969377 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.8979 | −0.831012 | −0.415506 | − | 0.909590i | \(-0.636395\pi\) | ||||
−0.415506 | + | 0.909590i | \(0.636395\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −9.33989 | −0.324388 | −0.162194 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162194 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(830\) | 6.10209 | 0.211807 | ||||||||
\(831\) | 24.1295 | 0.837043 | ||||||||
\(832\) | 3.77137 | 0.130749 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.3137 | −0.461016 | ||||||||
\(835\) | −35.9305 | −1.24343 | ||||||||
\(836\) | 1.83321 | 0.0634030 | ||||||||
\(837\) | −3.86225 | −0.133499 | ||||||||
\(838\) | −1.70412 | −0.0588679 | ||||||||
\(839\) | 56.1851 | 1.93973 | 0.969863 | − | 0.243651i | \(-0.0783450\pi\) | ||||
0.969863 | + | 0.243651i | \(0.0783450\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4050 | −0.979482 | ||||||||
\(842\) | −12.8564 | −0.443062 | ||||||||
\(843\) | 27.6853 | 0.953531 | ||||||||
\(844\) | 17.1523 | 0.590407 | ||||||||
\(845\) | 2.23658 | 0.0769407 | ||||||||
\(846\) | −2.22323 | −0.0764361 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.37117 | −0.253127 | ||||||||
\(849\) | 5.96618 | 0.204759 | ||||||||
\(850\) | −4.30748 | −0.147745 | ||||||||
\(851\) | 2.45186 | 0.0840486 | ||||||||
\(852\) | 8.22863 | 0.281908 | ||||||||
\(853\) | 32.1818 | 1.10188 | 0.550941 | − | 0.834544i | \(-0.314269\pi\) | ||||
0.550941 | + | 0.834544i | \(0.314269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.99460 | 0.0682138 | ||||||||
\(856\) | 13.8150 | 0.472186 | ||||||||
\(857\) | 14.3893 | 0.491529 | 0.245765 | − | 0.969330i | \(-0.420961\pi\) | ||||
0.245765 | + | 0.969330i | \(0.420961\pi\) | |||||||
\(858\) | 6.33774 | 0.216367 | ||||||||
\(859\) | −28.8242 | −0.983467 | −0.491734 | − | 0.870746i | \(-0.663637\pi\) | ||||
−0.491734 | + | 0.870746i | \(0.663637\pi\) | |||||||
\(860\) | 18.8253 | 0.641936 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.5419 | −0.393120 | ||||||||
\(863\) | −39.3593 | −1.33981 | −0.669904 | − | 0.742448i | \(-0.733665\pi\) | ||||
−0.669904 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.23809 | −0.110098 | ||||||||
\(866\) | −24.7627 | −0.841471 | ||||||||
\(867\) | −10.2411 | −0.347805 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.29628 | 0.0439732 | ||||||||
\(870\) | −1.41039 | −0.0478168 | ||||||||
\(871\) | −48.6140 | −1.64722 | ||||||||
\(872\) | 10.0676 | 0.340934 | ||||||||
\(873\) | −10.4282 | −0.352942 | ||||||||
\(874\) | 1.09088 | 0.0368996 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.86225 | −0.0967065 | ||||||||
\(877\) | 31.8382 | 1.07510 | 0.537550 | − | 0.843232i | \(-0.319350\pi\) | ||||
0.537550 | + | 0.843232i | \(0.319350\pi\) | |||||||
\(878\) | −7.82579 | −0.264108 | ||||||||
\(879\) | −31.4853 | −1.06197 | ||||||||
\(880\) | 3.07265 | 0.103579 | ||||||||
\(881\) | −3.69068 | −0.124342 | −0.0621710 | − | 0.998066i | \(-0.519802\pi\) | ||||
−0.0621710 | + | 0.998066i | \(0.519802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.0034 | 1.68275 | 0.841374 | − | 0.540454i | \(-0.181747\pi\) | ||||
0.841374 | + | 0.540454i | \(0.181747\pi\) | |||||||
\(884\) | 9.80479 | 0.329771 | ||||||||
\(885\) | −11.7535 | −0.395091 | ||||||||
\(886\) | −0.994597 | −0.0334141 | ||||||||
\(887\) | 40.1337 | 1.34756 | 0.673779 | − | 0.738933i | \(-0.264670\pi\) | ||||
0.673779 | + | 0.738933i | \(0.264670\pi\) | |||||||
\(888\) | 2.45186 | 0.0822790 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.86010 | 0.196431 | ||||||||
\(891\) | 1.68049 | 0.0562985 | ||||||||
\(892\) | 4.42282 | 0.148087 | ||||||||
\(893\) | −2.42528 | −0.0811588 | ||||||||
\(894\) | −11.8724 | −0.397074 | ||||||||
\(895\) | −22.3493 | −0.747054 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.77137 | 0.125922 | ||||||||
\(898\) | 26.1291 | 0.871939 | ||||||||
\(899\) | 2.97922 | 0.0993626 | ||||||||
\(900\) | −1.65685 | −0.0552285 | ||||||||
\(901\) | −19.1635 | −0.638430 | ||||||||
\(902\) | −1.83321 | −0.0610393 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.30392 | 0.209665 | ||||||||
\(905\) | 1.50075 | 0.0498865 | ||||||||
\(906\) | 1.07265 | 0.0356364 | ||||||||
\(907\) | 16.6558 | 0.553048 | 0.276524 | − | 0.961007i | \(-0.410817\pi\) | ||||
0.276524 | + | 0.961007i | \(0.410817\pi\) | |||||||
\(908\) | −12.0905 | −0.401237 | ||||||||
\(909\) | −6.47764 | −0.214850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.6860 | −1.97749 | −0.988743 | − | 0.149625i | \(-0.952193\pi\) | ||||
−0.988743 | + | 0.149625i | \(0.952193\pi\) | |||||||
\(912\) | 1.09088 | 0.0361227 | ||||||||
\(913\) | 5.60837 | 0.185610 | ||||||||
\(914\) | 18.7445 | 0.620012 | ||||||||
\(915\) | 16.6121 | 0.549180 | ||||||||
\(916\) | −9.09088 | −0.300371 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.59980 | 0.0858061 | ||||||||
\(919\) | −37.6122 | −1.24071 | −0.620356 | − | 0.784320i | \(-0.713012\pi\) | ||||
−0.620356 | + | 0.784320i | \(0.713012\pi\) | |||||||
\(920\) | 1.82843 | 0.0602815 | ||||||||
\(921\) | 5.13815 | 0.169308 | ||||||||
\(922\) | −5.63648 | −0.185627 | ||||||||
\(923\) | 31.0332 | 1.02147 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.06237 | −0.133570 | ||||||||
\(926\) | −20.5337 | −0.674779 | ||||||||
\(927\) | −18.8903 | −0.620438 | ||||||||
\(928\) | −0.771369 | −0.0253214 | ||||||||
\(929\) | −15.7095 | −0.515413 | −0.257706 | − | 0.966223i | \(-0.582967\pi\) | ||||
−0.257706 | + | 0.966223i | \(0.582967\pi\) | |||||||
\(930\) | −7.06184 | −0.231567 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.74774 | 0.221029 | ||||||||
\(933\) | −15.5627 | −0.509501 | ||||||||
\(934\) | −1.17921 | −0.0385851 | ||||||||
\(935\) | 7.98827 | 0.261244 | ||||||||
\(936\) | 3.77137 | 0.123271 | ||||||||
\(937\) | −42.2196 | −1.37925 | −0.689627 | − | 0.724165i | \(-0.742225\pi\) | ||||
−0.689627 | + | 0.724165i | \(0.742225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.1527 | −0.722927 | ||||||||
\(940\) | −4.06501 | −0.132586 | ||||||||
\(941\) | 26.6722 | 0.869490 | 0.434745 | − | 0.900554i | \(-0.356839\pi\) | ||||
0.434745 | + | 0.900554i | \(0.356839\pi\) | |||||||
\(942\) | 21.3760 | 0.696466 | ||||||||
\(943\) | −1.09088 | −0.0355240 | ||||||||
\(944\) | −6.42822 | −0.209221 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.3021 | 0.562540 | ||||||||
\(947\) | −41.0789 | −1.33488 | −0.667442 | − | 0.744662i | \(-0.732611\pi\) | ||||
−0.667442 | + | 0.744662i | \(0.732611\pi\) | |||||||
\(948\) | 0.771369 | 0.0250529 | ||||||||
\(949\) | −10.7946 | −0.350408 | ||||||||
\(950\) | −1.80743 | −0.0586408 | ||||||||
\(951\) | 18.5627 | 0.601937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0374 | −1.13497 | −0.567487 | − | 0.823383i | \(-0.692084\pi\) | ||||
−0.567487 | + | 0.823383i | \(0.692084\pi\) | |||||||
\(954\) | −7.37117 | −0.238650 | ||||||||
\(955\) | −22.7673 | −0.736733 | ||||||||
\(956\) | 20.5918 | 0.665985 | ||||||||
\(957\) | −1.29628 | −0.0419027 | ||||||||
\(958\) | 1.68264 | 0.0543635 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.82843 | 0.0590122 | ||||||||
\(961\) | −16.0830 | −0.518807 | ||||||||
\(962\) | 9.24686 | 0.298131 | ||||||||
\(963\) | 13.8150 | 0.445182 | ||||||||
\(964\) | 17.1814 | 0.553374 | ||||||||
\(965\) | 12.2580 | 0.394599 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.28833 | 0.202219 | 0.101109 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101109 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(968\) | −8.17596 | −0.262785 | ||||||||
\(969\) | 2.83607 | 0.0911077 | ||||||||
\(970\) | −19.0672 | −0.612212 | ||||||||
\(971\) | 34.9942 | 1.12302 | 0.561509 | − | 0.827471i | \(-0.310221\pi\) | ||||
0.561509 | + | 0.827471i | \(0.310221\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.2901 | −0.554010 | ||||||||
\(975\) | −6.24861 | −0.200116 | ||||||||
\(976\) | 9.08548 | 0.290819 | ||||||||
\(977\) | 12.1632 | 0.389136 | 0.194568 | − | 0.980889i | \(-0.437670\pi\) | ||||
0.194568 | + | 0.980889i | \(0.437670\pi\) | |||||||
\(978\) | 1.88048 | 0.0601312 | ||||||||
\(979\) | 5.38596 | 0.172136 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0676 | 0.321435 | ||||||||
\(982\) | 25.7361 | 0.821273 | ||||||||
\(983\) | −31.3083 | −0.998580 | −0.499290 | − | 0.866435i | \(-0.666406\pi\) | ||||
−0.499290 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(984\) | −1.09088 | −0.0347760 | ||||||||
\(985\) | 30.2798 | 0.964794 | ||||||||
\(986\) | −2.00540 | −0.0638651 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.11412 | 0.130887 | ||||||||
\(989\) | 10.2959 | 0.327390 | ||||||||
\(990\) | 3.07265 | 0.0976552 | ||||||||
\(991\) | −44.3959 | −1.41028 | −0.705142 | − | 0.709067i | \(-0.749117\pi\) | ||||
−0.705142 | + | 0.709067i | \(0.749117\pi\) | |||||||
\(992\) | −3.86225 | −0.122627 | ||||||||
\(993\) | 2.86265 | 0.0908435 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.17474 | −0.290859 | ||||||||
\(996\) | 3.33734 | 0.105748 | ||||||||
\(997\) | 45.2814 | 1.43408 | 0.717038 | − | 0.697034i | \(-0.245497\pi\) | ||||
0.717038 | + | 0.697034i | \(0.245497\pi\) | |||||||
\(998\) | −23.1996 | −0.734370 | ||||||||
\(999\) | 2.45186 | 0.0775733 |
(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 | 6762.2.a.cp.1.3 | 4 | ||
7.2 | even | 3 | 966.2.i.l.277.2 | ✓ | 8 | ||
7.4 | even | 3 | 966.2.i.l.415.2 | yes | 8 | ||
7.6 | odd | 2 | 6762.2.a.cm.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.l.277.2 | ✓ | 8 | 7.2 | even | 3 | ||
966.2.i.l.415.2 | yes | 8 | 7.4 | even | 3 | ||
6762.2.a.cm.1.1 | 4 | 7.6 | odd | 2 | |||
6762.2.a.cp.1.3 | 4 | 1.1 | even | 1 | trivial |