Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21700 | −1.56766 | −0.783829 | − | 0.620977i | \(-0.786736\pi\) | ||||
−0.783829 | + | 0.620977i | \(0.786736\pi\) | |||||||
\(3\) | 0.365824 | 0.211209 | 0.105604 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105604 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(4\) | 2.91510 | 1.45755 | ||||||||
\(5\) | 2.81066 | 1.25697 | 0.628483 | − | 0.777823i | \(-0.283676\pi\) | ||||
0.628483 | + | 0.777823i | \(0.283676\pi\) | |||||||
\(6\) | −0.811033 | −0.331103 | ||||||||
\(7\) | −0.497651 | −0.188094 | −0.0940471 | − | 0.995568i | \(-0.529980\pi\) | ||||
−0.0940471 | + | 0.995568i | \(0.529980\pi\) | |||||||
\(8\) | −2.02878 | −0.717281 | ||||||||
\(9\) | −2.86617 | −0.955391 | ||||||||
\(10\) | −6.23125 | −1.97049 | ||||||||
\(11\) | 4.45060 | 1.34191 | 0.670953 | − | 0.741500i | \(-0.265885\pi\) | ||||
0.670953 | + | 0.741500i | \(0.265885\pi\) | |||||||
\(12\) | 1.06641 | 0.307847 | ||||||||
\(13\) | −2.00286 | −0.555492 | −0.277746 | − | 0.960654i | \(-0.589587\pi\) | ||||
−0.277746 | + | 0.960654i | \(0.589587\pi\) | |||||||
\(14\) | 1.10329 | 0.294867 | ||||||||
\(15\) | 1.02821 | 0.265482 | ||||||||
\(16\) | −1.33240 | −0.333099 | ||||||||
\(17\) | 5.19461 | 1.25988 | 0.629938 | − | 0.776645i | \(-0.283080\pi\) | ||||
0.629938 | + | 0.776645i | \(0.283080\pi\) | |||||||
\(18\) | 6.35431 | 1.49773 | ||||||||
\(19\) | −5.56713 | −1.27719 | −0.638594 | − | 0.769544i | \(-0.720484\pi\) | ||||
−0.638594 | + | 0.769544i | \(0.720484\pi\) | |||||||
\(20\) | 8.19336 | 1.83209 | ||||||||
\(21\) | −0.182053 | −0.0397271 | ||||||||
\(22\) | −9.86699 | −2.10365 | ||||||||
\(23\) | 4.82647 | 1.00639 | 0.503195 | − | 0.864173i | \(-0.332158\pi\) | ||||
0.503195 | + | 0.864173i | \(0.332158\pi\) | |||||||
\(24\) | −0.742175 | −0.151496 | ||||||||
\(25\) | 2.89983 | 0.579965 | ||||||||
\(26\) | 4.44034 | 0.870822 | ||||||||
\(27\) | −2.14599 | −0.412995 | ||||||||
\(28\) | −1.45070 | −0.274157 | ||||||||
\(29\) | −3.04267 | −0.565010 | −0.282505 | − | 0.959266i | \(-0.591165\pi\) | ||||
−0.282505 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(30\) | −2.27954 | −0.416185 | ||||||||
\(31\) | −2.64110 | −0.474356 | −0.237178 | − | 0.971466i | \(-0.576222\pi\) | ||||
−0.237178 | + | 0.971466i | \(0.576222\pi\) | |||||||
\(32\) | 7.01148 | 1.23947 | ||||||||
\(33\) | 1.62814 | 0.283422 | ||||||||
\(34\) | −11.5165 | −1.97506 | ||||||||
\(35\) | −1.39873 | −0.236428 | ||||||||
\(36\) | −8.35518 | −1.39253 | ||||||||
\(37\) | 1.70848 | 0.280872 | 0.140436 | − | 0.990090i | \(-0.455150\pi\) | ||||
0.140436 | + | 0.990090i | \(0.455150\pi\) | |||||||
\(38\) | 12.3423 | 2.00219 | ||||||||
\(39\) | −0.732693 | −0.117325 | ||||||||
\(40\) | −5.70220 | −0.901598 | ||||||||
\(41\) | 9.42310 | 1.47164 | 0.735820 | − | 0.677177i | \(-0.236797\pi\) | ||||
0.735820 | + | 0.677177i | \(0.236797\pi\) | |||||||
\(42\) | 0.403611 | 0.0622785 | ||||||||
\(43\) | 4.27362 | 0.651721 | 0.325861 | − | 0.945418i | \(-0.394346\pi\) | ||||
0.325861 | + | 0.945418i | \(0.394346\pi\) | |||||||
\(44\) | 12.9739 | 1.95589 | ||||||||
\(45\) | −8.05585 | −1.20089 | ||||||||
\(46\) | −10.7003 | −1.57767 | ||||||||
\(47\) | 1.23819 | 0.180609 | 0.0903043 | − | 0.995914i | \(-0.471216\pi\) | ||||
0.0903043 | + | 0.995914i | \(0.471216\pi\) | |||||||
\(48\) | −0.487423 | −0.0703534 | ||||||||
\(49\) | −6.75234 | −0.964621 | ||||||||
\(50\) | −6.42892 | −0.909187 | ||||||||
\(51\) | 1.90031 | 0.266097 | ||||||||
\(52\) | −5.83852 | −0.809658 | ||||||||
\(53\) | −11.4657 | −1.57493 | −0.787467 | − | 0.616356i | \(-0.788608\pi\) | ||||
−0.787467 | + | 0.616356i | \(0.788608\pi\) | |||||||
\(54\) | 4.75766 | 0.647435 | ||||||||
\(55\) | 12.5091 | 1.68673 | ||||||||
\(56\) | 1.00962 | 0.134916 | ||||||||
\(57\) | −2.03659 | −0.269753 | ||||||||
\(58\) | 6.74561 | 0.885742 | ||||||||
\(59\) | 10.1871 | 1.32625 | 0.663125 | − | 0.748509i | \(-0.269230\pi\) | ||||
0.663125 | + | 0.748509i | \(0.269230\pi\) | |||||||
\(60\) | 2.99733 | 0.386953 | ||||||||
\(61\) | 3.77568 | 0.483426 | 0.241713 | − | 0.970348i | \(-0.422291\pi\) | ||||
0.241713 | + | 0.970348i | \(0.422291\pi\) | |||||||
\(62\) | 5.85533 | 0.743627 | ||||||||
\(63\) | 1.42635 | 0.179704 | ||||||||
\(64\) | −12.8797 | −1.60996 | ||||||||
\(65\) | −5.62935 | −0.698235 | ||||||||
\(66\) | −3.60958 | −0.444309 | ||||||||
\(67\) | −5.13248 | −0.627032 | −0.313516 | − | 0.949583i | \(-0.601507\pi\) | ||||
−0.313516 | + | 0.949583i | \(0.601507\pi\) | |||||||
\(68\) | 15.1428 | 1.83633 | ||||||||
\(69\) | 1.76564 | 0.212558 | ||||||||
\(70\) | 3.10098 | 0.370638 | ||||||||
\(71\) | 16.0868 | 1.90916 | 0.954579 | − | 0.297960i | \(-0.0963060\pi\) | ||||
0.954579 | + | 0.297960i | \(0.0963060\pi\) | |||||||
\(72\) | 5.81482 | 0.685283 | ||||||||
\(73\) | 2.84487 | 0.332967 | 0.166484 | − | 0.986044i | \(-0.446759\pi\) | ||||
0.166484 | + | 0.986044i | \(0.446759\pi\) | |||||||
\(74\) | −3.78770 | −0.440312 | ||||||||
\(75\) | 1.06083 | 0.122494 | ||||||||
\(76\) | −16.2287 | −1.86156 | ||||||||
\(77\) | −2.21484 | −0.252405 | ||||||||
\(78\) | 1.62438 | 0.183925 | ||||||||
\(79\) | −12.0950 | −1.36079 | −0.680396 | − | 0.732845i | \(-0.738192\pi\) | ||||
−0.680396 | + | 0.732845i | \(0.738192\pi\) | |||||||
\(80\) | −3.74492 | −0.418695 | ||||||||
\(81\) | 7.81346 | 0.868163 | ||||||||
\(82\) | −20.8910 | −2.30703 | ||||||||
\(83\) | −5.14999 | −0.565285 | −0.282642 | − | 0.959225i | \(-0.591211\pi\) | ||||
−0.282642 | + | 0.959225i | \(0.591211\pi\) | |||||||
\(84\) | −0.530701 | −0.0579042 | ||||||||
\(85\) | 14.6003 | 1.58362 | ||||||||
\(86\) | −9.47463 | −1.02168 | ||||||||
\(87\) | −1.11308 | −0.119335 | ||||||||
\(88\) | −9.02927 | −0.962523 | ||||||||
\(89\) | 8.87946 | 0.941221 | 0.470610 | − | 0.882341i | \(-0.344034\pi\) | ||||
0.470610 | + | 0.882341i | \(0.344034\pi\) | |||||||
\(90\) | 17.8598 | 1.88259 | ||||||||
\(91\) | 0.996723 | 0.104485 | ||||||||
\(92\) | 14.0696 | 1.46686 | ||||||||
\(93\) | −0.966178 | −0.100188 | ||||||||
\(94\) | −2.74507 | −0.283132 | ||||||||
\(95\) | −15.6473 | −1.60538 | ||||||||
\(96\) | 2.56497 | 0.261786 | ||||||||
\(97\) | 9.95199 | 1.01047 | 0.505236 | − | 0.862982i | \(-0.331406\pi\) | ||||
0.505236 | + | 0.862982i | \(0.331406\pi\) | |||||||
\(98\) | 14.9700 | 1.51219 | ||||||||
\(99\) | −12.7562 | −1.28205 | ||||||||
\(100\) | 8.45328 | 0.845328 | ||||||||
\(101\) | 10.7383 | 1.06850 | 0.534252 | − | 0.845326i | \(-0.320594\pi\) | ||||
0.534252 | + | 0.845326i | \(0.320594\pi\) | |||||||
\(102\) | −4.21299 | −0.417149 | ||||||||
\(103\) | 12.0097 | 1.18335 | 0.591674 | − | 0.806177i | \(-0.298467\pi\) | ||||
0.591674 | + | 0.806177i | \(0.298467\pi\) | |||||||
\(104\) | 4.06335 | 0.398444 | ||||||||
\(105\) | −0.511688 | −0.0499357 | ||||||||
\(106\) | 25.4195 | 2.46896 | ||||||||
\(107\) | 11.3375 | 1.09604 | 0.548020 | − | 0.836466i | \(-0.315382\pi\) | ||||
0.548020 | + | 0.836466i | \(0.315382\pi\) | |||||||
\(108\) | −6.25576 | −0.601961 | ||||||||
\(109\) | 17.2438 | 1.65166 | 0.825828 | − | 0.563922i | \(-0.190708\pi\) | ||||
0.825828 | + | 0.563922i | \(0.190708\pi\) | |||||||
\(110\) | −27.7328 | −2.64422 | ||||||||
\(111\) | 0.625003 | 0.0593227 | ||||||||
\(112\) | 0.663068 | 0.0626541 | ||||||||
\(113\) | 14.9172 | 1.40329 | 0.701644 | − | 0.712528i | \(-0.252450\pi\) | ||||
0.701644 | + | 0.712528i | \(0.252450\pi\) | |||||||
\(114\) | 4.51512 | 0.422880 | ||||||||
\(115\) | 13.5656 | 1.26500 | ||||||||
\(116\) | −8.86969 | −0.823530 | ||||||||
\(117\) | 5.74053 | 0.530712 | ||||||||
\(118\) | −22.5849 | −2.07910 | ||||||||
\(119\) | −2.58510 | −0.236976 | ||||||||
\(120\) | −2.08600 | −0.190425 | ||||||||
\(121\) | 8.80784 | 0.800713 | ||||||||
\(122\) | −8.37068 | −0.757846 | ||||||||
\(123\) | 3.44720 | 0.310823 | ||||||||
\(124\) | −7.69907 | −0.691397 | ||||||||
\(125\) | −5.90288 | −0.527970 | ||||||||
\(126\) | −3.16223 | −0.281714 | ||||||||
\(127\) | 8.39595 | 0.745020 | 0.372510 | − | 0.928028i | \(-0.378497\pi\) | ||||
0.372510 | + | 0.928028i | \(0.378497\pi\) | |||||||
\(128\) | 14.5313 | 1.28440 | ||||||||
\(129\) | 1.56339 | 0.137649 | ||||||||
\(130\) | 12.4803 | 1.09459 | ||||||||
\(131\) | −9.40775 | −0.821959 | −0.410980 | − | 0.911645i | \(-0.634813\pi\) | ||||
−0.410980 | + | 0.911645i | \(0.634813\pi\) | |||||||
\(132\) | 4.74618 | 0.413102 | ||||||||
\(133\) | 2.77049 | 0.240232 | ||||||||
\(134\) | 11.3787 | 0.982971 | ||||||||
\(135\) | −6.03165 | −0.519121 | ||||||||
\(136\) | −10.5387 | −0.903685 | ||||||||
\(137\) | 8.43309 | 0.720487 | 0.360244 | − | 0.932858i | \(-0.382694\pi\) | ||||
0.360244 | + | 0.932858i | \(0.382694\pi\) | |||||||
\(138\) | −3.91443 | −0.333218 | ||||||||
\(139\) | −6.95296 | −0.589742 | −0.294871 | − | 0.955537i | \(-0.595277\pi\) | ||||
−0.294871 | + | 0.955537i | \(0.595277\pi\) | |||||||
\(140\) | −4.07743 | −0.344606 | ||||||||
\(141\) | 0.452959 | 0.0381461 | ||||||||
\(142\) | −35.6646 | −2.99290 | ||||||||
\(143\) | −8.91391 | −0.745419 | ||||||||
\(144\) | 3.81888 | 0.318240 | ||||||||
\(145\) | −8.55193 | −0.710199 | ||||||||
\(146\) | −6.30709 | −0.521979 | ||||||||
\(147\) | −2.47017 | −0.203736 | ||||||||
\(148\) | 4.98039 | 0.409385 | ||||||||
\(149\) | −5.62980 | −0.461211 | −0.230606 | − | 0.973047i | \(-0.574071\pi\) | ||||
−0.230606 | + | 0.973047i | \(0.574071\pi\) | |||||||
\(150\) | −2.35185 | −0.192028 | ||||||||
\(151\) | −13.0527 | −1.06222 | −0.531108 | − | 0.847304i | \(-0.678224\pi\) | ||||
−0.531108 | + | 0.847304i | \(0.678224\pi\) | |||||||
\(152\) | 11.2945 | 0.916102 | ||||||||
\(153\) | −14.8886 | −1.20368 | ||||||||
\(154\) | 4.91031 | 0.395684 | ||||||||
\(155\) | −7.42325 | −0.596250 | ||||||||
\(156\) | −2.13587 | −0.171007 | ||||||||
\(157\) | −12.8484 | −1.02541 | −0.512706 | − | 0.858564i | \(-0.671357\pi\) | ||||
−0.512706 | + | 0.858564i | \(0.671357\pi\) | |||||||
\(158\) | 26.8146 | 2.13325 | ||||||||
\(159\) | −4.19443 | −0.332640 | ||||||||
\(160\) | 19.7069 | 1.55797 | ||||||||
\(161\) | −2.40190 | −0.189296 | ||||||||
\(162\) | −17.3225 | −1.36098 | ||||||||
\(163\) | −5.25420 | −0.411541 | −0.205770 | − | 0.978600i | \(-0.565970\pi\) | ||||
−0.205770 | + | 0.978600i | \(0.565970\pi\) | |||||||
\(164\) | 27.4693 | 2.14499 | ||||||||
\(165\) | 4.57614 | 0.356252 | ||||||||
\(166\) | 11.4175 | 0.886173 | ||||||||
\(167\) | 5.68137 | 0.439637 | 0.219819 | − | 0.975541i | \(-0.429453\pi\) | ||||
0.219819 | + | 0.975541i | \(0.429453\pi\) | |||||||
\(168\) | 0.369344 | 0.0284955 | ||||||||
\(169\) | −8.98857 | −0.691428 | ||||||||
\(170\) | −32.3689 | −2.48258 | ||||||||
\(171\) | 15.9564 | 1.22021 | ||||||||
\(172\) | 12.4580 | 0.949916 | ||||||||
\(173\) | 14.1023 | 1.07218 | 0.536090 | − | 0.844161i | \(-0.319901\pi\) | ||||
0.536090 | + | 0.844161i | \(0.319901\pi\) | |||||||
\(174\) | 2.46771 | 0.187076 | ||||||||
\(175\) | −1.44310 | −0.109088 | ||||||||
\(176\) | −5.92997 | −0.446988 | ||||||||
\(177\) | 3.72669 | 0.280115 | ||||||||
\(178\) | −19.6858 | −1.47551 | ||||||||
\(179\) | −24.2263 | −1.81076 | −0.905381 | − | 0.424600i | \(-0.860415\pi\) | ||||
−0.905381 | + | 0.424600i | \(0.860415\pi\) | |||||||
\(180\) | −23.4836 | −1.75036 | ||||||||
\(181\) | −13.5637 | −1.00818 | −0.504089 | − | 0.863652i | \(-0.668172\pi\) | ||||
−0.504089 | + | 0.863652i | \(0.668172\pi\) | |||||||
\(182\) | −2.20974 | −0.163797 | ||||||||
\(183\) | 1.38123 | 0.102104 | ||||||||
\(184\) | −9.79183 | −0.721863 | ||||||||
\(185\) | 4.80196 | 0.353047 | ||||||||
\(186\) | 2.14202 | 0.157061 | ||||||||
\(187\) | 23.1191 | 1.69064 | ||||||||
\(188\) | 3.60944 | 0.263246 | ||||||||
\(189\) | 1.06795 | 0.0776821 | ||||||||
\(190\) | 34.6902 | 2.51669 | ||||||||
\(191\) | 22.9796 | 1.66275 | 0.831373 | − | 0.555715i | \(-0.187555\pi\) | ||||
0.831373 | + | 0.555715i | \(0.187555\pi\) | |||||||
\(192\) | −4.71169 | −0.340037 | ||||||||
\(193\) | −1.23120 | −0.0886235 | −0.0443118 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443118 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(194\) | −22.0636 | −1.58407 | ||||||||
\(195\) | −2.05935 | −0.147473 | ||||||||
\(196\) | −19.6837 | −1.40598 | ||||||||
\(197\) | −7.68849 | −0.547783 | −0.273891 | − | 0.961761i | \(-0.588311\pi\) | ||||
−0.273891 | + | 0.961761i | \(0.588311\pi\) | |||||||
\(198\) | 28.2805 | 2.00981 | ||||||||
\(199\) | 19.0580 | 1.35099 | 0.675494 | − | 0.737366i | \(-0.263930\pi\) | ||||
0.675494 | + | 0.737366i | \(0.263930\pi\) | |||||||
\(200\) | −5.88310 | −0.415998 | ||||||||
\(201\) | −1.87758 | −0.132435 | ||||||||
\(202\) | −23.8069 | −1.67505 | ||||||||
\(203\) | 1.51419 | 0.106275 | ||||||||
\(204\) | 5.53960 | 0.387849 | ||||||||
\(205\) | 26.4852 | 1.84980 | ||||||||
\(206\) | −26.6255 | −1.85509 | ||||||||
\(207\) | −13.8335 | −0.961495 | ||||||||
\(208\) | 2.66860 | 0.185034 | ||||||||
\(209\) | −24.7771 | −1.71387 | ||||||||
\(210\) | 1.13441 | 0.0782820 | ||||||||
\(211\) | 4.40958 | 0.303568 | 0.151784 | − | 0.988414i | \(-0.451498\pi\) | ||||
0.151784 | + | 0.988414i | \(0.451498\pi\) | |||||||
\(212\) | −33.4236 | −2.29554 | ||||||||
\(213\) | 5.88495 | 0.403230 | ||||||||
\(214\) | −25.1353 | −1.71821 | ||||||||
\(215\) | 12.0117 | 0.819192 | ||||||||
\(216\) | 4.35373 | 0.296234 | ||||||||
\(217\) | 1.31435 | 0.0892236 | ||||||||
\(218\) | −38.2295 | −2.58923 | ||||||||
\(219\) | 1.04072 | 0.0703256 | ||||||||
\(220\) | 36.4654 | 2.45849 | ||||||||
\(221\) | −10.4040 | −0.699852 | ||||||||
\(222\) | −1.38563 | −0.0929976 | ||||||||
\(223\) | −2.38168 | −0.159489 | −0.0797447 | − | 0.996815i | \(-0.525410\pi\) | ||||
−0.0797447 | + | 0.996815i | \(0.525410\pi\) | |||||||
\(224\) | −3.48927 | −0.233136 | ||||||||
\(225\) | −8.31140 | −0.554094 | ||||||||
\(226\) | −33.0714 | −2.19987 | ||||||||
\(227\) | −9.35137 | −0.620672 | −0.310336 | − | 0.950627i | \(-0.600442\pi\) | ||||
−0.310336 | + | 0.950627i | \(0.600442\pi\) | |||||||
\(228\) | −5.93686 | −0.393178 | ||||||||
\(229\) | 18.4579 | 1.21973 | 0.609865 | − | 0.792505i | \(-0.291224\pi\) | ||||
0.609865 | + | 0.792505i | \(0.291224\pi\) | |||||||
\(230\) | −30.0749 | −1.98308 | ||||||||
\(231\) | −0.810243 | −0.0533101 | ||||||||
\(232\) | 6.17290 | 0.405271 | ||||||||
\(233\) | −9.61225 | −0.629719 | −0.314860 | − | 0.949138i | \(-0.601957\pi\) | ||||
−0.314860 | + | 0.949138i | \(0.601957\pi\) | |||||||
\(234\) | −12.7268 | −0.831975 | ||||||||
\(235\) | 3.48013 | 0.227019 | ||||||||
\(236\) | 29.6964 | 1.93307 | ||||||||
\(237\) | −4.42463 | −0.287411 | ||||||||
\(238\) | 5.73117 | 0.371497 | ||||||||
\(239\) | 8.92695 | 0.577436 | 0.288718 | − | 0.957414i | \(-0.406771\pi\) | ||||
0.288718 | + | 0.957414i | \(0.406771\pi\) | |||||||
\(240\) | −1.36998 | −0.0884319 | ||||||||
\(241\) | −3.90210 | −0.251357 | −0.125678 | − | 0.992071i | \(-0.540111\pi\) | ||||
−0.125678 | + | 0.992071i | \(0.540111\pi\) | |||||||
\(242\) | −19.5270 | −1.25524 | ||||||||
\(243\) | 9.29631 | 0.596359 | ||||||||
\(244\) | 11.0065 | 0.704617 | ||||||||
\(245\) | −18.9786 | −1.21250 | ||||||||
\(246\) | −7.64244 | −0.487264 | ||||||||
\(247\) | 11.1502 | 0.709468 | ||||||||
\(248\) | 5.35820 | 0.340246 | ||||||||
\(249\) | −1.88399 | −0.119393 | ||||||||
\(250\) | 13.0867 | 0.827675 | ||||||||
\(251\) | −15.4281 | −0.973814 | −0.486907 | − | 0.873454i | \(-0.661875\pi\) | ||||
−0.486907 | + | 0.873454i | \(0.661875\pi\) | |||||||
\(252\) | 4.15796 | 0.261927 | ||||||||
\(253\) | 21.4807 | 1.35048 | ||||||||
\(254\) | −18.6138 | −1.16794 | ||||||||
\(255\) | 5.34114 | 0.334475 | ||||||||
\(256\) | −6.45658 | −0.403536 | ||||||||
\(257\) | −22.4270 | −1.39896 | −0.699478 | − | 0.714654i | \(-0.746584\pi\) | ||||
−0.699478 | + | 0.714654i | \(0.746584\pi\) | |||||||
\(258\) | −3.46605 | −0.215787 | ||||||||
\(259\) | −0.850226 | −0.0528305 | ||||||||
\(260\) | −16.4101 | −1.01771 | ||||||||
\(261\) | 8.72083 | 0.539806 | ||||||||
\(262\) | 20.8570 | 1.28855 | ||||||||
\(263\) | −0.840588 | −0.0518328 | −0.0259164 | − | 0.999664i | \(-0.508250\pi\) | ||||
−0.0259164 | + | 0.999664i | \(0.508250\pi\) | |||||||
\(264\) | −3.30312 | −0.203293 | ||||||||
\(265\) | −32.2262 | −1.97964 | ||||||||
\(266\) | −6.14217 | −0.376601 | ||||||||
\(267\) | 3.24832 | 0.198794 | ||||||||
\(268\) | −14.9617 | −0.913930 | ||||||||
\(269\) | −23.7175 | −1.44608 | −0.723040 | − | 0.690806i | \(-0.757256\pi\) | ||||
−0.723040 | + | 0.690806i | \(0.757256\pi\) | |||||||
\(270\) | 13.3722 | 0.813804 | ||||||||
\(271\) | 26.1155 | 1.58640 | 0.793202 | − | 0.608959i | \(-0.208413\pi\) | ||||
0.793202 | + | 0.608959i | \(0.208413\pi\) | |||||||
\(272\) | −6.92128 | −0.419664 | ||||||||
\(273\) | 0.364625 | 0.0220681 | ||||||||
\(274\) | −18.6962 | −1.12948 | ||||||||
\(275\) | 12.9060 | 0.778259 | ||||||||
\(276\) | 5.14701 | 0.309814 | ||||||||
\(277\) | −25.3763 | −1.52471 | −0.762357 | − | 0.647156i | \(-0.775958\pi\) | ||||
−0.762357 | + | 0.647156i | \(0.775958\pi\) | |||||||
\(278\) | 15.4147 | 0.924514 | ||||||||
\(279\) | 7.56985 | 0.453195 | ||||||||
\(280\) | 2.83771 | 0.169585 | ||||||||
\(281\) | 30.5131 | 1.82026 | 0.910131 | − | 0.414322i | \(-0.135981\pi\) | ||||
0.910131 | + | 0.414322i | \(0.135981\pi\) | |||||||
\(282\) | −1.00421 | −0.0598000 | ||||||||
\(283\) | −15.6512 | −0.930365 | −0.465183 | − | 0.885215i | \(-0.654011\pi\) | ||||
−0.465183 | + | 0.885215i | \(0.654011\pi\) | |||||||
\(284\) | 46.8947 | 2.78269 | ||||||||
\(285\) | −5.72417 | −0.339070 | ||||||||
\(286\) | 19.7622 | 1.16856 | ||||||||
\(287\) | −4.68941 | −0.276807 | ||||||||
\(288\) | −20.0961 | −1.18417 | ||||||||
\(289\) | 9.98393 | 0.587290 | ||||||||
\(290\) | 18.9596 | 1.11335 | ||||||||
\(291\) | 3.64068 | 0.213420 | ||||||||
\(292\) | 8.29309 | 0.485316 | ||||||||
\(293\) | −19.5960 | −1.14481 | −0.572406 | − | 0.819970i | \(-0.693990\pi\) | ||||
−0.572406 | + | 0.819970i | \(0.693990\pi\) | |||||||
\(294\) | 5.47637 | 0.319388 | ||||||||
\(295\) | 28.6325 | 1.66705 | ||||||||
\(296\) | −3.46612 | −0.201464 | ||||||||
\(297\) | −9.55093 | −0.554201 | ||||||||
\(298\) | 12.4813 | 0.723021 | ||||||||
\(299\) | −9.66673 | −0.559042 | ||||||||
\(300\) | 3.09241 | 0.178541 | ||||||||
\(301\) | −2.12677 | −0.122585 | ||||||||
\(302\) | 28.9379 | 1.66519 | ||||||||
\(303\) | 3.92834 | 0.225677 | ||||||||
\(304\) | 7.41763 | 0.425430 | ||||||||
\(305\) | 10.6122 | 0.607650 | ||||||||
\(306\) | 33.0081 | 1.88695 | ||||||||
\(307\) | 21.1550 | 1.20738 | 0.603689 | − | 0.797220i | \(-0.293697\pi\) | ||||
0.603689 | + | 0.797220i | \(0.293697\pi\) | |||||||
\(308\) | −6.45649 | −0.367893 | ||||||||
\(309\) | 4.39343 | 0.249933 | ||||||||
\(310\) | 16.4574 | 0.934715 | ||||||||
\(311\) | 32.8451 | 1.86248 | 0.931239 | − | 0.364410i | \(-0.118729\pi\) | ||||
0.931239 | + | 0.364410i | \(0.118729\pi\) | |||||||
\(312\) | 1.48647 | 0.0841548 | ||||||||
\(313\) | 5.25756 | 0.297175 | 0.148588 | − | 0.988899i | \(-0.452527\pi\) | ||||
0.148588 | + | 0.988899i | \(0.452527\pi\) | |||||||
\(314\) | 28.4849 | 1.60749 | ||||||||
\(315\) | 4.00900 | 0.225881 | ||||||||
\(316\) | −35.2581 | −1.98342 | ||||||||
\(317\) | 31.6990 | 1.78039 | 0.890197 | − | 0.455576i | \(-0.150567\pi\) | ||||
0.890197 | + | 0.455576i | \(0.150567\pi\) | |||||||
\(318\) | 9.29905 | 0.521465 | ||||||||
\(319\) | −13.5417 | −0.758191 | ||||||||
\(320\) | −36.2004 | −2.02366 | ||||||||
\(321\) | 4.14754 | 0.231493 | ||||||||
\(322\) | 5.32501 | 0.296751 | ||||||||
\(323\) | −28.9190 | −1.60910 | ||||||||
\(324\) | 22.7770 | 1.26539 | ||||||||
\(325\) | −5.80794 | −0.322166 | ||||||||
\(326\) | 11.6486 | 0.645155 | ||||||||
\(327\) | 6.30819 | 0.348844 | ||||||||
\(328\) | −19.1174 | −1.05558 | ||||||||
\(329\) | −0.616186 | −0.0339714 | ||||||||
\(330\) | −10.1453 | −0.558481 | ||||||||
\(331\) | −16.5764 | −0.911120 | −0.455560 | − | 0.890205i | \(-0.650561\pi\) | ||||
−0.455560 | + | 0.890205i | \(0.650561\pi\) | |||||||
\(332\) | −15.0127 | −0.823931 | ||||||||
\(333\) | −4.89680 | −0.268343 | ||||||||
\(334\) | −12.5956 | −0.689201 | ||||||||
\(335\) | −14.4257 | −0.788158 | ||||||||
\(336\) | 0.242566 | 0.0132331 | ||||||||
\(337\) | 36.0895 | 1.96592 | 0.982959 | − | 0.183825i | \(-0.0588479\pi\) | ||||
0.982959 | + | 0.183825i | \(0.0588479\pi\) | |||||||
\(338\) | 19.9277 | 1.08392 | ||||||||
\(339\) | 5.45705 | 0.296386 | ||||||||
\(340\) | 42.5613 | 2.30821 | ||||||||
\(341\) | −11.7545 | −0.636541 | ||||||||
\(342\) | −35.3753 | −1.91288 | ||||||||
\(343\) | 6.84386 | 0.369534 | ||||||||
\(344\) | −8.67022 | −0.467467 | ||||||||
\(345\) | 4.96262 | 0.267178 | ||||||||
\(346\) | −31.2649 | −1.68081 | ||||||||
\(347\) | −30.1062 | −1.61619 | −0.808093 | − | 0.589054i | \(-0.799500\pi\) | ||||
−0.808093 | + | 0.589054i | \(0.799500\pi\) | |||||||
\(348\) | −3.24475 | −0.173937 | ||||||||
\(349\) | −34.4658 | −1.84491 | −0.922455 | − | 0.386104i | \(-0.873821\pi\) | ||||
−0.922455 | + | 0.386104i | \(0.873821\pi\) | |||||||
\(350\) | 3.19936 | 0.171013 | ||||||||
\(351\) | 4.29810 | 0.229416 | ||||||||
\(352\) | 31.2053 | 1.66325 | ||||||||
\(353\) | 19.0134 | 1.01198 | 0.505990 | − | 0.862539i | \(-0.331127\pi\) | ||||
0.505990 | + | 0.862539i | \(0.331127\pi\) | |||||||
\(354\) | −8.26208 | −0.439125 | ||||||||
\(355\) | 45.2147 | 2.39975 | ||||||||
\(356\) | 25.8845 | 1.37188 | ||||||||
\(357\) | −0.945691 | −0.0500513 | ||||||||
\(358\) | 53.7099 | 2.83865 | ||||||||
\(359\) | 37.4606 | 1.97709 | 0.988547 | − | 0.150913i | \(-0.0482213\pi\) | ||||
0.988547 | + | 0.150913i | \(0.0482213\pi\) | |||||||
\(360\) | 16.3435 | 0.861378 | ||||||||
\(361\) | 11.9929 | 0.631207 | ||||||||
\(362\) | 30.0707 | 1.58048 | ||||||||
\(363\) | 3.22212 | 0.169117 | ||||||||
\(364\) | 2.90554 | 0.152292 | ||||||||
\(365\) | 7.99598 | 0.418529 | ||||||||
\(366\) | −3.06220 | −0.160064 | ||||||||
\(367\) | 8.83409 | 0.461136 | 0.230568 | − | 0.973056i | \(-0.425942\pi\) | ||||
0.230568 | + | 0.973056i | \(0.425942\pi\) | |||||||
\(368\) | −6.43078 | −0.335228 | ||||||||
\(369\) | −27.0082 | −1.40599 | ||||||||
\(370\) | −10.6460 | −0.553457 | ||||||||
\(371\) | 5.70591 | 0.296236 | ||||||||
\(372\) | −2.81651 | −0.146029 | ||||||||
\(373\) | −18.5727 | −0.961656 | −0.480828 | − | 0.876815i | \(-0.659664\pi\) | ||||
−0.480828 | + | 0.876815i | \(0.659664\pi\) | |||||||
\(374\) | −51.2551 | −2.65034 | ||||||||
\(375\) | −2.15942 | −0.111512 | ||||||||
\(376\) | −2.51201 | −0.129547 | ||||||||
\(377\) | 6.09404 | 0.313859 | ||||||||
\(378\) | −2.36765 | −0.121779 | ||||||||
\(379\) | 10.8376 | 0.556691 | 0.278345 | − | 0.960481i | \(-0.410214\pi\) | ||||
0.278345 | + | 0.960481i | \(0.410214\pi\) | |||||||
\(380\) | −45.6135 | −2.33992 | ||||||||
\(381\) | 3.07144 | 0.157355 | ||||||||
\(382\) | −50.9458 | −2.60662 | ||||||||
\(383\) | 24.6609 | 1.26011 | 0.630056 | − | 0.776549i | \(-0.283032\pi\) | ||||
0.630056 | + | 0.776549i | \(0.283032\pi\) | |||||||
\(384\) | 5.31590 | 0.271276 | ||||||||
\(385\) | −6.22518 | −0.317265 | ||||||||
\(386\) | 2.72957 | 0.138931 | ||||||||
\(387\) | −12.2489 | −0.622649 | ||||||||
\(388\) | 29.0110 | 1.47281 | ||||||||
\(389\) | 23.6603 | 1.19963 | 0.599813 | − | 0.800140i | \(-0.295241\pi\) | ||||
0.599813 | + | 0.800140i | \(0.295241\pi\) | |||||||
\(390\) | 4.56559 | 0.231188 | ||||||||
\(391\) | 25.0716 | 1.26793 | ||||||||
\(392\) | 13.6990 | 0.691904 | ||||||||
\(393\) | −3.44158 | −0.173605 | ||||||||
\(394\) | 17.0454 | 0.858735 | ||||||||
\(395\) | −33.9949 | −1.71047 | ||||||||
\(396\) | −37.1855 | −1.86864 | ||||||||
\(397\) | 2.36371 | 0.118631 | 0.0593157 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593157 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(398\) | −42.2517 | −2.11789 | ||||||||
\(399\) | 1.01351 | 0.0507390 | ||||||||
\(400\) | −3.86372 | −0.193186 | ||||||||
\(401\) | 30.8622 | 1.54119 | 0.770593 | − | 0.637328i | \(-0.219960\pi\) | ||||
0.770593 | + | 0.637328i | \(0.219960\pi\) | |||||||
\(402\) | 4.16261 | 0.207612 | ||||||||
\(403\) | 5.28975 | 0.263501 | ||||||||
\(404\) | 31.3033 | 1.55740 | ||||||||
\(405\) | 21.9610 | 1.09125 | ||||||||
\(406\) | −3.35696 | −0.166603 | ||||||||
\(407\) | 7.60376 | 0.376904 | ||||||||
\(408\) | −3.85531 | −0.190866 | ||||||||
\(409\) | −20.4684 | −1.01210 | −0.506049 | − | 0.862505i | \(-0.668894\pi\) | ||||
−0.506049 | + | 0.862505i | \(0.668894\pi\) | |||||||
\(410\) | −58.7177 | −2.89986 | ||||||||
\(411\) | 3.08503 | 0.152173 | ||||||||
\(412\) | 35.0094 | 1.72479 | ||||||||
\(413\) | −5.06962 | −0.249460 | ||||||||
\(414\) | 30.6689 | 1.50729 | ||||||||
\(415\) | −14.4749 | −0.710544 | ||||||||
\(416\) | −14.0430 | −0.688514 | ||||||||
\(417\) | −2.54356 | −0.124559 | ||||||||
\(418\) | 54.9308 | 2.68675 | ||||||||
\(419\) | 35.1238 | 1.71591 | 0.857956 | − | 0.513724i | \(-0.171734\pi\) | ||||
0.857956 | + | 0.513724i | \(0.171734\pi\) | |||||||
\(420\) | −1.49162 | −0.0727837 | ||||||||
\(421\) | 14.7872 | 0.720683 | 0.360342 | − | 0.932820i | \(-0.382660\pi\) | ||||
0.360342 | + | 0.932820i | \(0.382660\pi\) | |||||||
\(422\) | −9.77604 | −0.475890 | ||||||||
\(423\) | −3.54887 | −0.172552 | ||||||||
\(424\) | 23.2613 | 1.12967 | ||||||||
\(425\) | 15.0635 | 0.730685 | ||||||||
\(426\) | −13.0470 | −0.632127 | ||||||||
\(427\) | −1.87897 | −0.0909296 | ||||||||
\(428\) | 33.0500 | 1.59753 | ||||||||
\(429\) | −3.26092 | −0.157439 | ||||||||
\(430\) | −26.6300 | −1.28421 | ||||||||
\(431\) | 6.98802 | 0.336601 | 0.168301 | − | 0.985736i | \(-0.446172\pi\) | ||||
0.168301 | + | 0.985736i | \(0.446172\pi\) | |||||||
\(432\) | 2.85931 | 0.137568 | ||||||||
\(433\) | 2.83323 | 0.136156 | 0.0680782 | − | 0.997680i | \(-0.478313\pi\) | ||||
0.0680782 | + | 0.997680i | \(0.478313\pi\) | |||||||
\(434\) | −2.91391 | −0.139872 | ||||||||
\(435\) | −3.12850 | −0.150000 | ||||||||
\(436\) | 50.2674 | 2.40737 | ||||||||
\(437\) | −26.8696 | −1.28535 | ||||||||
\(438\) | −2.30729 | −0.110246 | ||||||||
\(439\) | 37.7169 | 1.80013 | 0.900066 | − | 0.435755i | \(-0.143518\pi\) | ||||
0.900066 | + | 0.435755i | \(0.143518\pi\) | |||||||
\(440\) | −25.3782 | −1.20986 | ||||||||
\(441\) | 19.3534 | 0.921590 | ||||||||
\(442\) | 23.0658 | 1.09713 | ||||||||
\(443\) | 25.8786 | 1.22953 | 0.614766 | − | 0.788710i | \(-0.289251\pi\) | ||||
0.614766 | + | 0.788710i | \(0.289251\pi\) | |||||||
\(444\) | 1.82195 | 0.0864657 | ||||||||
\(445\) | 24.9572 | 1.18308 | ||||||||
\(446\) | 5.28020 | 0.250025 | ||||||||
\(447\) | −2.05952 | −0.0974117 | ||||||||
\(448\) | 6.40958 | 0.302824 | ||||||||
\(449\) | 39.7352 | 1.87522 | 0.937610 | − | 0.347689i | \(-0.113034\pi\) | ||||
0.937610 | + | 0.347689i | \(0.113034\pi\) | |||||||
\(450\) | 18.4264 | 0.868629 | ||||||||
\(451\) | 41.9384 | 1.97480 | ||||||||
\(452\) | 43.4850 | 2.04536 | ||||||||
\(453\) | −4.77500 | −0.224349 | ||||||||
\(454\) | 20.7320 | 0.973001 | ||||||||
\(455\) | 2.80145 | 0.131334 | ||||||||
\(456\) | 4.13178 | 0.193489 | ||||||||
\(457\) | 5.09670 | 0.238414 | 0.119207 | − | 0.992869i | \(-0.461965\pi\) | ||||
0.119207 | + | 0.992869i | \(0.461965\pi\) | |||||||
\(458\) | −40.9211 | −1.91212 | ||||||||
\(459\) | −11.1476 | −0.520323 | ||||||||
\(460\) | 39.5450 | 1.84380 | ||||||||
\(461\) | −24.4950 | −1.14085 | −0.570423 | − | 0.821351i | \(-0.693221\pi\) | ||||
−0.570423 | + | 0.821351i | \(0.693221\pi\) | |||||||
\(462\) | 1.79631 | 0.0835719 | ||||||||
\(463\) | −37.0768 | −1.72310 | −0.861552 | − | 0.507670i | \(-0.830507\pi\) | ||||
−0.861552 | + | 0.507670i | \(0.830507\pi\) | |||||||
\(464\) | 4.05405 | 0.188204 | ||||||||
\(465\) | −2.71560 | −0.125933 | ||||||||
\(466\) | 21.3104 | 0.987184 | ||||||||
\(467\) | −34.9945 | −1.61935 | −0.809677 | − | 0.586876i | \(-0.800358\pi\) | ||||
−0.809677 | + | 0.586876i | \(0.800358\pi\) | |||||||
\(468\) | 16.7342 | 0.773539 | ||||||||
\(469\) | 2.55418 | 0.117941 | ||||||||
\(470\) | −7.71546 | −0.355888 | ||||||||
\(471\) | −4.70024 | −0.216576 | ||||||||
\(472\) | −20.6674 | −0.951293 | ||||||||
\(473\) | 19.0202 | 0.874549 | ||||||||
\(474\) | 9.80942 | 0.450562 | ||||||||
\(475\) | −16.1437 | −0.740724 | ||||||||
\(476\) | −7.53582 | −0.345404 | ||||||||
\(477\) | 32.8627 | 1.50468 | ||||||||
\(478\) | −19.7911 | −0.905222 | ||||||||
\(479\) | −26.3152 | −1.20237 | −0.601185 | − | 0.799110i | \(-0.705305\pi\) | ||||
−0.601185 | + | 0.799110i | \(0.705305\pi\) | |||||||
\(480\) | 7.20926 | 0.329056 | ||||||||
\(481\) | −3.42184 | −0.156022 | ||||||||
\(482\) | 8.65097 | 0.394041 | ||||||||
\(483\) | −0.878672 | −0.0399809 | ||||||||
\(484\) | 25.6757 | 1.16708 | ||||||||
\(485\) | 27.9717 | 1.27013 | ||||||||
\(486\) | −20.6099 | −0.934886 | ||||||||
\(487\) | −2.81618 | −0.127613 | −0.0638066 | − | 0.997962i | \(-0.520324\pi\) | ||||
−0.0638066 | + | 0.997962i | \(0.520324\pi\) | |||||||
\(488\) | −7.66000 | −0.346752 | ||||||||
\(489\) | −1.92211 | −0.0869209 | ||||||||
\(490\) | 42.0755 | 1.90078 | ||||||||
\(491\) | −38.7046 | −1.74671 | −0.873356 | − | 0.487082i | \(-0.838061\pi\) | ||||
−0.873356 | + | 0.487082i | \(0.838061\pi\) | |||||||
\(492\) | 10.0489 | 0.453040 | ||||||||
\(493\) | −15.8055 | −0.711843 | ||||||||
\(494\) | −24.7199 | −1.11220 | ||||||||
\(495\) | −35.8533 | −1.61149 | ||||||||
\(496\) | 3.51900 | 0.158008 | ||||||||
\(497\) | −8.00563 | −0.359101 | ||||||||
\(498\) | 4.17681 | 0.187167 | ||||||||
\(499\) | 40.6016 | 1.81758 | 0.908790 | − | 0.417254i | \(-0.137008\pi\) | ||||
0.908790 | + | 0.417254i | \(0.137008\pi\) | |||||||
\(500\) | −17.2075 | −0.769542 | ||||||||
\(501\) | 2.07838 | 0.0928552 | ||||||||
\(502\) | 34.2042 | 1.52661 | ||||||||
\(503\) | −18.3406 | −0.817767 | −0.408884 | − | 0.912587i | \(-0.634082\pi\) | ||||
−0.408884 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(504\) | −2.89375 | −0.128898 | ||||||||
\(505\) | 30.1818 | 1.34307 | ||||||||
\(506\) | −47.6228 | −2.11709 | ||||||||
\(507\) | −3.28823 | −0.146036 | ||||||||
\(508\) | 24.4750 | 1.08590 | ||||||||
\(509\) | 11.4105 | 0.505760 | 0.252880 | − | 0.967498i | \(-0.418622\pi\) | ||||
0.252880 | + | 0.967498i | \(0.418622\pi\) | |||||||
\(510\) | −11.8413 | −0.524342 | ||||||||
\(511\) | −1.41575 | −0.0626292 | ||||||||
\(512\) | −14.7483 | −0.651791 | ||||||||
\(513\) | 11.9470 | 0.527472 | ||||||||
\(514\) | 49.7206 | 2.19308 | ||||||||
\(515\) | 33.7552 | 1.48743 | ||||||||
\(516\) | 4.55745 | 0.200630 | ||||||||
\(517\) | 5.51069 | 0.242360 | ||||||||
\(518\) | 1.88495 | 0.0828201 | ||||||||
\(519\) | 5.15897 | 0.226454 | ||||||||
\(520\) | 11.4207 | 0.500831 | ||||||||
\(521\) | −6.92978 | −0.303599 | −0.151799 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151799 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(522\) | −19.3341 | −0.846230 | ||||||||
\(523\) | −11.1293 | −0.486650 | −0.243325 | − | 0.969945i | \(-0.578238\pi\) | ||||
−0.243325 | + | 0.969945i | \(0.578238\pi\) | |||||||
\(524\) | −27.4245 | −1.19805 | ||||||||
\(525\) | −0.527921 | −0.0230404 | ||||||||
\(526\) | 1.86358 | 0.0812561 | ||||||||
\(527\) | −13.7195 | −0.597630 | ||||||||
\(528\) | −2.16932 | −0.0944077 | ||||||||
\(529\) | 0.294842 | 0.0128192 | ||||||||
\(530\) | 71.4456 | 3.10340 | ||||||||
\(531\) | −29.1980 | −1.26709 | ||||||||
\(532\) | 8.07624 | 0.350149 | ||||||||
\(533\) | −18.8731 | −0.817485 | ||||||||
\(534\) | −7.20153 | −0.311641 | ||||||||
\(535\) | 31.8659 | 1.37768 | ||||||||
\(536\) | 10.4126 | 0.449758 | ||||||||
\(537\) | −8.86258 | −0.382448 | ||||||||
\(538\) | 52.5817 | 2.26696 | ||||||||
\(539\) | −30.0520 | −1.29443 | ||||||||
\(540\) | −17.5828 | −0.756645 | ||||||||
\(541\) | −9.44965 | −0.406272 | −0.203136 | − | 0.979150i | \(-0.565113\pi\) | ||||
−0.203136 | + | 0.979150i | \(0.565113\pi\) | |||||||
\(542\) | −57.8981 | −2.48694 | ||||||||
\(543\) | −4.96191 | −0.212936 | ||||||||
\(544\) | 36.4219 | 1.56157 | ||||||||
\(545\) | 48.4665 | 2.07608 | ||||||||
\(546\) | −0.808375 | −0.0345952 | ||||||||
\(547\) | 20.3596 | 0.870514 | 0.435257 | − | 0.900306i | \(-0.356658\pi\) | ||||
0.435257 | + | 0.900306i | \(0.356658\pi\) | |||||||
\(548\) | 24.5833 | 1.05015 | ||||||||
\(549\) | −10.8217 | −0.461861 | ||||||||
\(550\) | −28.6126 | −1.22004 | ||||||||
\(551\) | 16.9390 | 0.721624 | ||||||||
\(552\) | −3.58209 | −0.152464 | ||||||||
\(553\) | 6.01907 | 0.255957 | ||||||||
\(554\) | 56.2593 | 2.39023 | ||||||||
\(555\) | 1.75667 | 0.0745666 | ||||||||
\(556\) | −20.2686 | −0.859578 | ||||||||
\(557\) | −23.6312 | −1.00129 | −0.500644 | − | 0.865653i | \(-0.666903\pi\) | ||||
−0.500644 | + | 0.865653i | \(0.666903\pi\) | |||||||
\(558\) | −16.7824 | −0.710455 | ||||||||
\(559\) | −8.55945 | −0.362026 | ||||||||
\(560\) | 1.86366 | 0.0787541 | ||||||||
\(561\) | 8.45753 | 0.357077 | ||||||||
\(562\) | −67.6477 | −2.85355 | ||||||||
\(563\) | −14.6097 | −0.615728 | −0.307864 | − | 0.951430i | \(-0.599614\pi\) | ||||
−0.307864 | + | 0.951430i | \(0.599614\pi\) | |||||||
\(564\) | 1.32042 | 0.0555998 | ||||||||
\(565\) | 41.9271 | 1.76389 | ||||||||
\(566\) | 34.6987 | 1.45849 | ||||||||
\(567\) | −3.88838 | −0.163296 | ||||||||
\(568\) | −32.6366 | −1.36940 | ||||||||
\(569\) | 3.08716 | 0.129420 | 0.0647102 | − | 0.997904i | \(-0.479388\pi\) | ||||
0.0647102 | + | 0.997904i | \(0.479388\pi\) | |||||||
\(570\) | 12.6905 | 0.531546 | ||||||||
\(571\) | 24.0448 | 1.00624 | 0.503121 | − | 0.864216i | \(-0.332185\pi\) | ||||
0.503121 | + | 0.864216i | \(0.332185\pi\) | |||||||
\(572\) | −25.9849 | −1.08648 | ||||||||
\(573\) | 8.40649 | 0.351186 | ||||||||
\(574\) | 10.3964 | 0.433939 | ||||||||
\(575\) | 13.9959 | 0.583671 | ||||||||
\(576\) | 36.9154 | 1.53814 | ||||||||
\(577\) | −34.0354 | −1.41691 | −0.708455 | − | 0.705756i | \(-0.750608\pi\) | ||||
−0.708455 | + | 0.705756i | \(0.750608\pi\) | |||||||
\(578\) | −22.1344 | −0.920669 | ||||||||
\(579\) | −0.450402 | −0.0187180 | ||||||||
\(580\) | −24.9297 | −1.03515 | ||||||||
\(581\) | 2.56290 | 0.106327 | ||||||||
\(582\) | −8.07138 | −0.334570 | ||||||||
\(583\) | −51.0292 | −2.11341 | ||||||||
\(584\) | −5.77161 | −0.238831 | ||||||||
\(585\) | 16.1347 | 0.667088 | ||||||||
\(586\) | 43.4444 | 1.79467 | ||||||||
\(587\) | 13.9403 | 0.575379 | 0.287689 | − | 0.957724i | \(-0.407113\pi\) | ||||
0.287689 | + | 0.957724i | \(0.407113\pi\) | |||||||
\(588\) | −7.20079 | −0.296955 | ||||||||
\(589\) | 14.7034 | 0.605841 | ||||||||
\(590\) | −63.4784 | −2.61336 | ||||||||
\(591\) | −2.81264 | −0.115696 | ||||||||
\(592\) | −2.27637 | −0.0935584 | ||||||||
\(593\) | −45.0631 | −1.85052 | −0.925259 | − | 0.379335i | \(-0.876153\pi\) | ||||
−0.925259 | + | 0.379335i | \(0.876153\pi\) | |||||||
\(594\) | 21.1744 | 0.868797 | ||||||||
\(595\) | −7.26584 | −0.297870 | ||||||||
\(596\) | −16.4114 | −0.672238 | ||||||||
\(597\) | 6.97188 | 0.285340 | ||||||||
\(598\) | 21.4312 | 0.876386 | ||||||||
\(599\) | 18.8110 | 0.768597 | 0.384298 | − | 0.923209i | \(-0.374443\pi\) | ||||
0.384298 | + | 0.923209i | \(0.374443\pi\) | |||||||
\(600\) | −2.15218 | −0.0878623 | ||||||||
\(601\) | 31.1413 | 1.27028 | 0.635139 | − | 0.772398i | \(-0.280943\pi\) | ||||
0.635139 | + | 0.772398i | \(0.280943\pi\) | |||||||
\(602\) | 4.71506 | 0.192171 | ||||||||
\(603\) | 14.7106 | 0.599061 | ||||||||
\(604\) | −38.0500 | −1.54823 | ||||||||
\(605\) | 24.7559 | 1.00647 | ||||||||
\(606\) | −8.70913 | −0.353784 | ||||||||
\(607\) | 5.69455 | 0.231135 | 0.115567 | − | 0.993300i | \(-0.463131\pi\) | ||||
0.115567 | + | 0.993300i | \(0.463131\pi\) | |||||||
\(608\) | −39.0338 | −1.58303 | ||||||||
\(609\) | 0.553926 | 0.0224462 | ||||||||
\(610\) | −23.5272 | −0.952587 | ||||||||
\(611\) | −2.47992 | −0.100327 | ||||||||
\(612\) | −43.4018 | −1.75442 | ||||||||
\(613\) | −45.3709 | −1.83251 | −0.916257 | − | 0.400592i | \(-0.868805\pi\) | ||||
−0.916257 | + | 0.400592i | \(0.868805\pi\) | |||||||
\(614\) | −46.9006 | −1.89276 | ||||||||
\(615\) | 9.68891 | 0.390694 | ||||||||
\(616\) | 4.49342 | 0.181045 | ||||||||
\(617\) | 6.79248 | 0.273455 | 0.136727 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136727 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(618\) | −9.74024 | −0.391810 | ||||||||
\(619\) | 10.9342 | 0.439481 | 0.219741 | − | 0.975558i | \(-0.429479\pi\) | ||||
0.219741 | + | 0.975558i | \(0.429479\pi\) | |||||||
\(620\) | −21.6395 | −0.869063 | ||||||||
\(621\) | −10.3575 | −0.415634 | ||||||||
\(622\) | −72.8177 | −2.91973 | ||||||||
\(623\) | −4.41887 | −0.177038 | ||||||||
\(624\) | 0.976238 | 0.0390808 | ||||||||
\(625\) | −31.0901 | −1.24361 | ||||||||
\(626\) | −11.6560 | −0.465869 | ||||||||
\(627\) | −9.06405 | −0.361983 | ||||||||
\(628\) | −37.4543 | −1.49459 | ||||||||
\(629\) | 8.87488 | 0.353865 | ||||||||
\(630\) | −8.88795 | −0.354105 | ||||||||
\(631\) | −19.2251 | −0.765341 | −0.382670 | − | 0.923885i | \(-0.624995\pi\) | ||||
−0.382670 | + | 0.923885i | \(0.624995\pi\) | |||||||
\(632\) | 24.5380 | 0.976069 | ||||||||
\(633\) | 1.61313 | 0.0641161 | ||||||||
\(634\) | −70.2768 | −2.79105 | ||||||||
\(635\) | 23.5982 | 0.936465 | ||||||||
\(636\) | −12.2272 | −0.484839 | ||||||||
\(637\) | 13.5240 | 0.535839 | ||||||||
\(638\) | 30.0220 | 1.18858 | ||||||||
\(639\) | −46.1077 | −1.82399 | ||||||||
\(640\) | 40.8426 | 1.61444 | ||||||||
\(641\) | 12.2946 | 0.485608 | 0.242804 | − | 0.970075i | \(-0.421933\pi\) | ||||
0.242804 | + | 0.970075i | \(0.421933\pi\) | |||||||
\(642\) | −9.19509 | −0.362901 | ||||||||
\(643\) | −14.5822 | −0.575066 | −0.287533 | − | 0.957771i | \(-0.592835\pi\) | ||||
−0.287533 | + | 0.957771i | \(0.592835\pi\) | |||||||
\(644\) | −7.00177 | −0.275908 | ||||||||
\(645\) | 4.39417 | 0.173020 | ||||||||
\(646\) | 64.1136 | 2.52252 | ||||||||
\(647\) | 20.9376 | 0.823142 | 0.411571 | − | 0.911378i | \(-0.364980\pi\) | ||||
0.411571 | + | 0.911378i | \(0.364980\pi\) | |||||||
\(648\) | −15.8518 | −0.622716 | ||||||||
\(649\) | 45.3388 | 1.77970 | ||||||||
\(650\) | 12.8762 | 0.505046 | ||||||||
\(651\) | 0.480819 | 0.0188448 | ||||||||
\(652\) | −15.3165 | −0.599841 | ||||||||
\(653\) | 27.5327 | 1.07744 | 0.538719 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538719 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(654\) | −13.9853 | −0.546868 | ||||||||
\(655\) | −26.4420 | −1.03318 | ||||||||
\(656\) | −12.5553 | −0.490203 | ||||||||
\(657\) | −8.15390 | −0.318114 | ||||||||
\(658\) | 1.36609 | 0.0532555 | ||||||||
\(659\) | 12.4193 | 0.483785 | 0.241893 | − | 0.970303i | \(-0.422232\pi\) | ||||
0.241893 | + | 0.970303i | \(0.422232\pi\) | |||||||
\(660\) | 13.3399 | 0.519255 | ||||||||
\(661\) | −2.22396 | −0.0865021 | −0.0432511 | − | 0.999064i | \(-0.513772\pi\) | ||||
−0.0432511 | + | 0.999064i | \(0.513772\pi\) | |||||||
\(662\) | 36.7499 | 1.42832 | ||||||||
\(663\) | −3.80605 | −0.147815 | ||||||||
\(664\) | 10.4482 | 0.405468 | ||||||||
\(665\) | 7.78690 | 0.301963 | ||||||||
\(666\) | 10.8562 | 0.420670 | ||||||||
\(667\) | −14.6854 | −0.568620 | ||||||||
\(668\) | 16.5617 | 0.640793 | ||||||||
\(669\) | −0.871277 | −0.0336855 | ||||||||
\(670\) | 31.9817 | 1.23556 | ||||||||
\(671\) | 16.8040 | 0.648712 | ||||||||
\(672\) | −1.27646 | −0.0492404 | ||||||||
\(673\) | −32.3718 | −1.24784 | −0.623920 | − | 0.781488i | \(-0.714461\pi\) | ||||
−0.623920 | + | 0.781488i | \(0.714461\pi\) | |||||||
\(674\) | −80.0104 | −3.08189 | ||||||||
\(675\) | −6.22299 | −0.239523 | ||||||||
\(676\) | −26.2026 | −1.00779 | ||||||||
\(677\) | 30.3272 | 1.16557 | 0.582784 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582784 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(678\) | −12.0983 | −0.464632 | ||||||||
\(679\) | −4.95261 | −0.190064 | ||||||||
\(680\) | −29.6207 | −1.13590 | ||||||||
\(681\) | −3.42096 | −0.131091 | ||||||||
\(682\) | 26.0597 | 0.997879 | ||||||||
\(683\) | 25.3359 | 0.969452 | 0.484726 | − | 0.874666i | \(-0.338919\pi\) | ||||
0.484726 | + | 0.874666i | \(0.338919\pi\) | |||||||
\(684\) | 46.5144 | 1.77852 | ||||||||
\(685\) | 23.7026 | 0.905629 | ||||||||
\(686\) | −15.1729 | −0.579302 | ||||||||
\(687\) | 6.75233 | 0.257617 | ||||||||
\(688\) | −5.69416 | −0.217088 | ||||||||
\(689\) | 22.9641 | 0.874864 | ||||||||
\(690\) | −11.0021 | −0.418844 | ||||||||
\(691\) | 22.9999 | 0.874958 | 0.437479 | − | 0.899229i | \(-0.355872\pi\) | ||||
0.437479 | + | 0.899229i | \(0.355872\pi\) | |||||||
\(692\) | 41.1097 | 1.56275 | ||||||||
\(693\) | 6.34813 | 0.241145 | ||||||||
\(694\) | 66.7456 | 2.53363 | ||||||||
\(695\) | −19.5424 | −0.741286 | ||||||||
\(696\) | 2.25820 | 0.0855967 | ||||||||
\(697\) | 48.9493 | 1.85409 | ||||||||
\(698\) | 76.4107 | 2.89219 | ||||||||
\(699\) | −3.51639 | −0.133002 | ||||||||
\(700\) | −4.20678 | −0.159001 | ||||||||
\(701\) | −13.0035 | −0.491134 | −0.245567 | − | 0.969380i | \(-0.578974\pi\) | ||||
−0.245567 | + | 0.969380i | \(0.578974\pi\) | |||||||
\(702\) | −9.52890 | −0.359645 | ||||||||
\(703\) | −9.51133 | −0.358727 | ||||||||
\(704\) | −57.3223 | −2.16041 | ||||||||
\(705\) | 1.27312 | 0.0479483 | ||||||||
\(706\) | −42.1527 | −1.58644 | ||||||||
\(707\) | −5.34393 | −0.200979 | ||||||||
\(708\) | 10.8637 | 0.408282 | ||||||||
\(709\) | −10.9808 | −0.412392 | −0.206196 | − | 0.978511i | \(-0.566109\pi\) | ||||
−0.206196 | + | 0.978511i | \(0.566109\pi\) | |||||||
\(710\) | −100.241 | −3.76198 | ||||||||
\(711\) | 34.6663 | 1.30009 | ||||||||
\(712\) | −18.0144 | −0.675119 | ||||||||
\(713\) | −12.7472 | −0.477387 | ||||||||
\(714\) | 2.09660 | 0.0784633 | ||||||||
\(715\) | −25.0540 | −0.936967 | ||||||||
\(716\) | −70.6222 | −2.63927 | ||||||||
\(717\) | 3.26569 | 0.121959 | ||||||||
\(718\) | −83.0502 | −3.09941 | ||||||||
\(719\) | 20.8023 | 0.775794 | 0.387897 | − | 0.921703i | \(-0.373202\pi\) | ||||
0.387897 | + | 0.921703i | \(0.373202\pi\) | |||||||
\(720\) | 10.7336 | 0.400017 | ||||||||
\(721\) | −5.97663 | −0.222581 | ||||||||
\(722\) | −26.5884 | −0.989517 | ||||||||
\(723\) | −1.42748 | −0.0530887 | ||||||||
\(724\) | −39.5394 | −1.46947 | ||||||||
\(725\) | −8.82322 | −0.327686 | ||||||||
\(726\) | −7.14345 | −0.265118 | ||||||||
\(727\) | 23.9110 | 0.886811 | 0.443405 | − | 0.896321i | \(-0.353770\pi\) | ||||
0.443405 | + | 0.896321i | \(0.353770\pi\) | |||||||
\(728\) | −2.02213 | −0.0749450 | ||||||||
\(729\) | −20.0396 | −0.742207 | ||||||||
\(730\) | −17.7271 | −0.656110 | ||||||||
\(731\) | 22.1998 | 0.821089 | ||||||||
\(732\) | 4.02643 | 0.148821 | ||||||||
\(733\) | 18.2961 | 0.675783 | 0.337891 | − | 0.941185i | \(-0.390286\pi\) | ||||
0.337891 | + | 0.941185i | \(0.390286\pi\) | |||||||
\(734\) | −19.5852 | −0.722903 | ||||||||
\(735\) | −6.94281 | −0.256090 | ||||||||
\(736\) | 33.8407 | 1.24739 | ||||||||
\(737\) | −22.8426 | −0.841418 | ||||||||
\(738\) | 59.8773 | 2.20411 | ||||||||
\(739\) | 5.28788 | 0.194518 | 0.0972590 | − | 0.995259i | \(-0.468992\pi\) | ||||
0.0972590 | + | 0.995259i | \(0.468992\pi\) | |||||||
\(740\) | 13.9982 | 0.514584 | ||||||||
\(741\) | 4.07900 | 0.149846 | ||||||||
\(742\) | −12.6500 | −0.464397 | ||||||||
\(743\) | 5.39567 | 0.197948 | 0.0989740 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989740 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(744\) | 1.96016 | 0.0718629 | ||||||||
\(745\) | −15.8235 | −0.579727 | ||||||||
\(746\) | 41.1756 | 1.50755 | ||||||||
\(747\) | 14.7608 | 0.540068 | ||||||||
\(748\) | 67.3945 | 2.46419 | ||||||||
\(749\) | −5.64212 | −0.206159 | ||||||||
\(750\) | 4.78743 | 0.174812 | ||||||||
\(751\) | −19.3478 | −0.706010 | −0.353005 | − | 0.935622i | \(-0.614840\pi\) | ||||
−0.353005 | + | 0.935622i | \(0.614840\pi\) | |||||||
\(752\) | −1.64976 | −0.0601606 | ||||||||
\(753\) | −5.64398 | −0.205678 | ||||||||
\(754\) | −13.5105 | −0.492023 | ||||||||
\(755\) | −36.6868 | −1.33517 | ||||||||
\(756\) | 3.11318 | 0.113225 | ||||||||
\(757\) | −43.5090 | −1.58136 | −0.790680 | − | 0.612230i | \(-0.790273\pi\) | ||||
−0.790680 | + | 0.612230i | \(0.790273\pi\) | |||||||
\(758\) | −24.0270 | −0.872700 | ||||||||
\(759\) | 7.85816 | 0.285233 | ||||||||
\(760\) | 31.7449 | 1.15151 | ||||||||
\(761\) | 7.18963 | 0.260624 | 0.130312 | − | 0.991473i | \(-0.458402\pi\) | ||||
0.130312 | + | 0.991473i | \(0.458402\pi\) | |||||||
\(762\) | −6.80939 | −0.246678 | ||||||||
\(763\) | −8.58139 | −0.310667 | ||||||||
\(764\) | 66.9878 | 2.42353 | ||||||||
\(765\) | −41.8469 | −1.51298 | ||||||||
\(766\) | −54.6733 | −1.97543 | ||||||||
\(767\) | −20.4033 | −0.736721 | ||||||||
\(768\) | −2.36197 | −0.0852303 | ||||||||
\(769\) | 19.3679 | 0.698426 | 0.349213 | − | 0.937043i | \(-0.386449\pi\) | ||||
0.349213 | + | 0.937043i | \(0.386449\pi\) | |||||||
\(770\) | 13.8012 | 0.497362 | ||||||||
\(771\) | −8.20432 | −0.295471 | ||||||||
\(772\) | −3.58906 | −0.129173 | ||||||||
\(773\) | 42.9751 | 1.54571 | 0.772854 | − | 0.634584i | \(-0.218828\pi\) | ||||
0.772854 | + | 0.634584i | \(0.218828\pi\) | |||||||
\(774\) | 27.1559 | 0.976100 | ||||||||
\(775\) | −7.65874 | −0.275110 | ||||||||
\(776\) | −20.1903 | −0.724791 | ||||||||
\(777\) | −0.311033 | −0.0111583 | ||||||||
\(778\) | −52.4550 | −1.88060 | ||||||||
\(779\) | −52.4596 | −1.87956 | ||||||||
\(780\) | −6.00322 | −0.214950 | ||||||||
\(781\) | 71.5961 | 2.56191 | ||||||||
\(782\) | −55.5838 | −1.98767 | ||||||||
\(783\) | 6.52954 | 0.233347 | ||||||||
\(784\) | 8.99680 | 0.321314 | ||||||||
\(785\) | −36.1124 | −1.28891 | ||||||||
\(786\) | 7.62999 | 0.272153 | ||||||||
\(787\) | 9.52179 | 0.339415 | 0.169708 | − | 0.985494i | \(-0.445718\pi\) | ||||
0.169708 | + | 0.985494i | \(0.445718\pi\) | |||||||
\(788\) | −22.4127 | −0.798420 | ||||||||
\(789\) | −0.307507 | −0.0109475 | ||||||||
\(790\) | 75.3668 | 2.68143 | ||||||||
\(791\) | −7.42353 | −0.263950 | ||||||||
\(792\) | 25.8794 | 0.919586 | ||||||||
\(793\) | −7.56214 | −0.268539 | ||||||||
\(794\) | −5.24036 | −0.185973 | ||||||||
\(795\) | −11.7891 | −0.418117 | ||||||||
\(796\) | 55.5560 | 1.96913 | ||||||||
\(797\) | −24.9984 | −0.885489 | −0.442745 | − | 0.896648i | \(-0.645995\pi\) | ||||
−0.442745 | + | 0.896648i | \(0.645995\pi\) | |||||||
\(798\) | −2.24695 | −0.0795413 | ||||||||
\(799\) | 6.43191 | 0.227544 | ||||||||
\(800\) | 20.3321 | 0.718847 | ||||||||
\(801\) | −25.4501 | −0.899234 | ||||||||
\(802\) | −68.4216 | −2.41605 | ||||||||
\(803\) | 12.6614 | 0.446811 | ||||||||
\(804\) | −5.47334 | −0.193030 | ||||||||
\(805\) | −6.75092 | −0.237939 | ||||||||
\(806\) | −11.7274 | −0.413079 | ||||||||
\(807\) | −8.67642 | −0.305425 | ||||||||
\(808\) | −21.7857 | −0.766416 | ||||||||
\(809\) | −18.6563 | −0.655922 | −0.327961 | − | 0.944691i | \(-0.606361\pi\) | ||||
−0.327961 | + | 0.944691i | \(0.606361\pi\) | |||||||
\(810\) | −48.6876 | −1.71071 | ||||||||
\(811\) | −32.1045 | −1.12734 | −0.563671 | − | 0.826000i | \(-0.690611\pi\) | ||||
−0.563671 | + | 0.826000i | \(0.690611\pi\) | |||||||
\(812\) | 4.41401 | 0.154901 | ||||||||
\(813\) | 9.55368 | 0.335062 | ||||||||
\(814\) | −16.8576 | −0.590857 | ||||||||
\(815\) | −14.7678 | −0.517293 | ||||||||
\(816\) | −2.53197 | −0.0886367 | ||||||||
\(817\) | −23.7918 | −0.832370 | ||||||||
\(818\) | 45.3785 | 1.58662 | ||||||||
\(819\) | −2.85678 | −0.0998240 | ||||||||
\(820\) | 77.2068 | 2.69618 | ||||||||
\(821\) | 31.9294 | 1.11434 | 0.557172 | − | 0.830397i | \(-0.311886\pi\) | ||||
0.557172 | + | 0.830397i | \(0.311886\pi\) | |||||||
\(822\) | −6.83951 | −0.238555 | ||||||||
\(823\) | −17.9305 | −0.625016 | −0.312508 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312508 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(824\) | −24.3649 | −0.848793 | ||||||||
\(825\) | 4.72131 | 0.164375 | ||||||||
\(826\) | 11.2394 | 0.391068 | ||||||||
\(827\) | 5.87465 | 0.204282 | 0.102141 | − | 0.994770i | \(-0.467431\pi\) | ||||
0.102141 | + | 0.994770i | \(0.467431\pi\) | |||||||
\(828\) | −40.3260 | −1.40143 | ||||||||
\(829\) | −39.0940 | −1.35779 | −0.678895 | − | 0.734235i | \(-0.737541\pi\) | ||||
−0.678895 | + | 0.734235i | \(0.737541\pi\) | |||||||
\(830\) | 32.0909 | 1.11389 | ||||||||
\(831\) | −9.28326 | −0.322033 | ||||||||
\(832\) | 25.7961 | 0.894320 | ||||||||
\(833\) | −35.0758 | −1.21530 | ||||||||
\(834\) | 5.63908 | 0.195265 | ||||||||
\(835\) | 15.9684 | 0.552610 | ||||||||
\(836\) | −72.2276 | −2.49804 | ||||||||
\(837\) | 5.66777 | 0.195907 | ||||||||
\(838\) | −77.8696 | −2.68996 | ||||||||
\(839\) | −3.90927 | −0.134963 | −0.0674815 | − | 0.997721i | \(-0.521496\pi\) | ||||
−0.0674815 | + | 0.997721i | \(0.521496\pi\) | |||||||
\(840\) | 1.03810 | 0.0358179 | ||||||||
\(841\) | −19.7421 | −0.680764 | ||||||||
\(842\) | −32.7832 | −1.12978 | ||||||||
\(843\) | 11.1624 | 0.384455 | ||||||||
\(844\) | 12.8544 | 0.442465 | ||||||||
\(845\) | −25.2638 | −0.869102 | ||||||||
\(846\) | 7.86784 | 0.270502 | ||||||||
\(847\) | −4.38323 | −0.150610 | ||||||||
\(848\) | 15.2769 | 0.524610 | ||||||||
\(849\) | −5.72557 | −0.196501 | ||||||||
\(850\) | −33.3957 | −1.14546 | ||||||||
\(851\) | 8.24593 | 0.282667 | ||||||||
\(852\) | 17.1552 | 0.587728 | ||||||||
\(853\) | 11.1564 | 0.381988 | 0.190994 | − | 0.981591i | \(-0.438829\pi\) | ||||
0.190994 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(854\) | 4.16568 | 0.142546 | ||||||||
\(855\) | 44.8479 | 1.53377 | ||||||||
\(856\) | −23.0013 | −0.786167 | ||||||||
\(857\) | −33.1545 | −1.13253 | −0.566267 | − | 0.824222i | \(-0.691613\pi\) | ||||
−0.566267 | + | 0.824222i | \(0.691613\pi\) | |||||||
\(858\) | 7.22947 | 0.246810 | ||||||||
\(859\) | 37.6497 | 1.28459 | 0.642295 | − | 0.766457i | \(-0.277982\pi\) | ||||
0.642295 | + | 0.766457i | \(0.277982\pi\) | |||||||
\(860\) | 35.0153 | 1.19401 | ||||||||
\(861\) | −1.71550 | −0.0584641 | ||||||||
\(862\) | −15.4925 | −0.527675 | ||||||||
\(863\) | −49.9751 | −1.70117 | −0.850587 | − | 0.525835i | \(-0.823753\pi\) | ||||
−0.850587 | + | 0.525835i | \(0.823753\pi\) | |||||||
\(864\) | −15.0465 | −0.511894 | ||||||||
\(865\) | 39.6369 | 1.34769 | ||||||||
\(866\) | −6.28128 | −0.213446 | ||||||||
\(867\) | 3.65236 | 0.124041 | ||||||||
\(868\) | 3.83145 | 0.130048 | ||||||||
\(869\) | −53.8299 | −1.82605 | ||||||||
\(870\) | 6.93589 | 0.235149 | ||||||||
\(871\) | 10.2796 | 0.348311 | ||||||||
\(872\) | −34.9838 | −1.18470 | ||||||||
\(873\) | −28.5241 | −0.965395 | ||||||||
\(874\) | 59.5700 | 2.01498 | ||||||||
\(875\) | 2.93757 | 0.0993081 | ||||||||
\(876\) | 3.03381 | 0.102503 | ||||||||
\(877\) | 30.3207 | 1.02386 | 0.511929 | − | 0.859028i | \(-0.328931\pi\) | ||||
0.511929 | + | 0.859028i | \(0.328931\pi\) | |||||||
\(878\) | −83.6185 | −2.82199 | ||||||||
\(879\) | −7.16870 | −0.241794 | ||||||||
\(880\) | −16.6671 | −0.561849 | ||||||||
\(881\) | −3.49837 | −0.117863 | −0.0589315 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589315 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(882\) | −42.9065 | −1.44474 | ||||||||
\(883\) | −23.2890 | −0.783738 | −0.391869 | − | 0.920021i | \(-0.628171\pi\) | ||||
−0.391869 | + | 0.920021i | \(0.628171\pi\) | |||||||
\(884\) | −30.3288 | −1.02007 | ||||||||
\(885\) | 10.4745 | 0.352095 | ||||||||
\(886\) | −57.3730 | −1.92748 | ||||||||
\(887\) | −0.700030 | −0.0235047 | −0.0117524 | − | 0.999931i | \(-0.503741\pi\) | ||||
−0.0117524 | + | 0.999931i | \(0.503741\pi\) | |||||||
\(888\) | −1.26799 | −0.0425510 | ||||||||
\(889\) | −4.17825 | −0.140134 | ||||||||
\(890\) | −55.3301 | −1.85467 | ||||||||
\(891\) | 34.7746 | 1.16499 | ||||||||
\(892\) | −6.94284 | −0.232464 | ||||||||
\(893\) | −6.89316 | −0.230671 | ||||||||
\(894\) | 4.56595 | 0.152708 | ||||||||
\(895\) | −68.0921 | −2.27607 | ||||||||
\(896\) | −7.23151 | −0.241588 | ||||||||
\(897\) | −3.53632 | −0.118074 | ||||||||
\(898\) | −88.0930 | −2.93970 | ||||||||
\(899\) | 8.03601 | 0.268016 | ||||||||
\(900\) | −24.2286 | −0.807619 | ||||||||
\(901\) | −59.5598 | −1.98422 | ||||||||
\(902\) | −92.9776 | −3.09582 | ||||||||
\(903\) | −0.778024 | −0.0258910 | ||||||||
\(904\) | −30.2636 | −1.00655 | ||||||||
\(905\) | −38.1229 | −1.26725 | ||||||||
\(906\) | 10.5862 | 0.351703 | ||||||||
\(907\) | −31.1663 | −1.03486 | −0.517431 | − | 0.855725i | \(-0.673111\pi\) | ||||
−0.517431 | + | 0.855725i | \(0.673111\pi\) | |||||||
\(908\) | −27.2602 | −0.904660 | ||||||||
\(909\) | −30.7779 | −1.02084 | ||||||||
\(910\) | −6.21082 | −0.205887 | ||||||||
\(911\) | 44.9647 | 1.48975 | 0.744874 | − | 0.667205i | \(-0.232509\pi\) | ||||
0.744874 | + | 0.667205i | \(0.232509\pi\) | |||||||
\(912\) | 2.71355 | 0.0898545 | ||||||||
\(913\) | −22.9206 | −0.758560 | ||||||||
\(914\) | −11.2994 | −0.373751 | ||||||||
\(915\) | 3.88218 | 0.128341 | ||||||||
\(916\) | 53.8065 | 1.77782 | ||||||||
\(917\) | 4.68177 | 0.154606 | ||||||||
\(918\) | 24.7142 | 0.815689 | ||||||||
\(919\) | −22.3892 | −0.738552 | −0.369276 | − | 0.929320i | \(-0.620394\pi\) | ||||
−0.369276 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(920\) | −27.5215 | −0.907358 | ||||||||
\(921\) | 7.73900 | 0.255009 | ||||||||
\(922\) | 54.3055 | 1.78846 | ||||||||
\(923\) | −32.2196 | −1.06052 | ||||||||
\(924\) | −2.36194 | −0.0777021 | ||||||||
\(925\) | 4.95430 | 0.162896 | ||||||||
\(926\) | 82.1993 | 2.70124 | ||||||||
\(927\) | −34.4218 | −1.13056 | ||||||||
\(928\) | −21.3336 | −0.700311 | ||||||||
\(929\) | 9.50966 | 0.312002 | 0.156001 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.156001 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(930\) | 6.02050 | 0.197420 | ||||||||
\(931\) | 37.5912 | 1.23200 | ||||||||
\(932\) | −28.0206 | −0.917847 | ||||||||
\(933\) | 12.0155 | 0.393371 | ||||||||
\(934\) | 77.5830 | 2.53859 | ||||||||
\(935\) | 64.9800 | 2.12507 | ||||||||
\(936\) | −11.6463 | −0.380670 | ||||||||
\(937\) | 19.6391 | 0.641583 | 0.320791 | − | 0.947150i | \(-0.396051\pi\) | ||||
0.320791 | + | 0.947150i | \(0.396051\pi\) | |||||||
\(938\) | −5.66262 | −0.184891 | ||||||||
\(939\) | 1.92334 | 0.0627659 | ||||||||
\(940\) | 10.1449 | 0.330891 | ||||||||
\(941\) | 36.8201 | 1.20030 | 0.600151 | − | 0.799887i | \(-0.295107\pi\) | ||||
0.600151 | + | 0.799887i | \(0.295107\pi\) | |||||||
\(942\) | 10.4204 | 0.339516 | ||||||||
\(943\) | 45.4803 | 1.48104 | ||||||||
\(944\) | −13.5733 | −0.441773 | ||||||||
\(945\) | 3.00165 | 0.0976438 | ||||||||
\(946\) | −42.1678 | −1.37099 | ||||||||
\(947\) | 3.76703 | 0.122412 | 0.0612060 | − | 0.998125i | \(-0.480505\pi\) | ||||
0.0612060 | + | 0.998125i | \(0.480505\pi\) | |||||||
\(948\) | −12.8982 | −0.418915 | ||||||||
\(949\) | −5.69787 | −0.184961 | ||||||||
\(950\) | 35.7906 | 1.16120 | ||||||||
\(951\) | 11.5963 | 0.376035 | ||||||||
\(952\) | 5.24459 | 0.169978 | ||||||||
\(953\) | −4.90914 | −0.159023 | −0.0795113 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795113 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(954\) | −72.8566 | −2.35882 | ||||||||
\(955\) | 64.5879 | 2.09002 | ||||||||
\(956\) | 26.0229 | 0.841642 | ||||||||
\(957\) | −4.95389 | −0.160136 | ||||||||
\(958\) | 58.3408 | 1.88490 | ||||||||
\(959\) | −4.19673 | −0.135520 | ||||||||
\(960\) | −13.2430 | −0.427415 | ||||||||
\(961\) | −24.0246 | −0.774986 | ||||||||
\(962\) | 7.58623 | 0.244590 | ||||||||
\(963\) | −32.4953 | −1.04715 | ||||||||
\(964\) | −11.3750 | −0.366365 | ||||||||
\(965\) | −3.46048 | −0.111397 | ||||||||
\(966\) | 1.94802 | 0.0626764 | ||||||||
\(967\) | 40.5043 | 1.30253 | 0.651266 | − | 0.758850i | \(-0.274238\pi\) | ||||
0.651266 | + | 0.758850i | \(0.274238\pi\) | |||||||
\(968\) | −17.8691 | −0.574336 | ||||||||
\(969\) | −10.5793 | −0.339855 | ||||||||
\(970\) | −62.0133 | −1.99113 | ||||||||
\(971\) | 20.0468 | 0.643332 | 0.321666 | − | 0.946853i | \(-0.395757\pi\) | ||||
0.321666 | + | 0.946853i | \(0.395757\pi\) | |||||||
\(972\) | 27.0997 | 0.869222 | ||||||||
\(973\) | 3.46014 | 0.110927 | ||||||||
\(974\) | 6.24347 | 0.200054 | ||||||||
\(975\) | −2.12468 | −0.0680443 | ||||||||
\(976\) | −5.03070 | −0.161029 | ||||||||
\(977\) | −37.9158 | −1.21303 | −0.606516 | − | 0.795071i | \(-0.707433\pi\) | ||||
−0.606516 | + | 0.795071i | \(0.707433\pi\) | |||||||
\(978\) | 4.26133 | 0.136262 | ||||||||
\(979\) | 39.5189 | 1.26303 | ||||||||
\(980\) | −55.3244 | −1.76727 | ||||||||
\(981\) | −49.4237 | −1.57798 | ||||||||
\(982\) | 85.8081 | 2.73825 | ||||||||
\(983\) | 22.8675 | 0.729359 | 0.364680 | − | 0.931133i | \(-0.381178\pi\) | ||||
0.364680 | + | 0.931133i | \(0.381178\pi\) | |||||||
\(984\) | −6.99359 | −0.222947 | ||||||||
\(985\) | −21.6098 | −0.688544 | ||||||||
\(986\) | 35.0408 | 1.11593 | ||||||||
\(987\) | −0.225416 | −0.00717506 | ||||||||
\(988\) | 32.5038 | 1.03408 | ||||||||
\(989\) | 20.6265 | 0.655885 | ||||||||
\(990\) | 79.4870 | 2.52626 | ||||||||
\(991\) | 48.4051 | 1.53764 | 0.768819 | − | 0.639466i | \(-0.220844\pi\) | ||||
0.768819 | + | 0.639466i | \(0.220844\pi\) | |||||||
\(992\) | −18.5180 | −0.587948 | ||||||||
\(993\) | −6.06404 | −0.192436 | ||||||||
\(994\) | 17.7485 | 0.562948 | ||||||||
\(995\) | 53.5657 | 1.69815 | ||||||||
\(996\) | −5.49202 | −0.174021 | ||||||||
\(997\) | 1.21389 | 0.0384443 | 0.0192222 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192222 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(998\) | −90.0139 | −2.84934 | ||||||||
\(999\) | −3.66638 | −0.115999 |
(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 | 4001.2.a.b.1.29 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.29 | ✓ | 184 | 1.1 | even | 1 | trivial |