Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11517 | −1.49565 | −0.747826 | − | 0.663895i | \(-0.768902\pi\) | ||||
−0.747826 | + | 0.663895i | \(0.768902\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.47395 | 1.23697 | ||||||||
\(5\) | 2.21169 | 0.989096 | 0.494548 | − | 0.869150i | \(-0.335334\pi\) | ||||
0.494548 | + | 0.869150i | \(0.335334\pi\) | |||||||
\(6\) | 2.11517 | 0.863515 | ||||||||
\(7\) | −2.99289 | −1.13121 | −0.565603 | − | 0.824678i | \(-0.691356\pi\) | ||||
−0.565603 | + | 0.824678i | \(0.691356\pi\) | |||||||
\(8\) | −1.00248 | −0.354431 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.67809 | −1.47934 | ||||||||
\(11\) | −4.68964 | −1.41398 | −0.706990 | − | 0.707223i | \(-0.749948\pi\) | ||||
−0.706990 | + | 0.707223i | \(0.749948\pi\) | |||||||
\(12\) | −2.47395 | −0.714168 | ||||||||
\(13\) | −6.95442 | −1.92881 | −0.964405 | − | 0.264431i | \(-0.914816\pi\) | ||||
−0.964405 | + | 0.264431i | \(0.914816\pi\) | |||||||
\(14\) | 6.33047 | 1.69189 | ||||||||
\(15\) | −2.21169 | −0.571055 | ||||||||
\(16\) | −2.82747 | −0.706869 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.11517 | −0.498551 | ||||||||
\(19\) | −3.64474 | −0.836160 | −0.418080 | − | 0.908410i | \(-0.637297\pi\) | ||||
−0.418080 | + | 0.908410i | \(0.637297\pi\) | |||||||
\(20\) | 5.47160 | 1.22349 | ||||||||
\(21\) | 2.99289 | 0.653102 | ||||||||
\(22\) | 9.91940 | 2.11482 | ||||||||
\(23\) | 2.77589 | 0.578813 | 0.289407 | − | 0.957206i | \(-0.406542\pi\) | ||||
0.289407 | + | 0.957206i | \(0.406542\pi\) | |||||||
\(24\) | 1.00248 | 0.204631 | ||||||||
\(25\) | −0.108448 | −0.0216896 | ||||||||
\(26\) | 14.7098 | 2.88483 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −7.40425 | −1.39927 | ||||||||
\(29\) | −3.63506 | −0.675014 | −0.337507 | − | 0.941323i | \(-0.609584\pi\) | ||||
−0.337507 | + | 0.941323i | \(0.609584\pi\) | |||||||
\(30\) | 4.67809 | 0.854099 | ||||||||
\(31\) | 4.06933 | 0.730873 | 0.365436 | − | 0.930836i | \(-0.380920\pi\) | ||||
0.365436 | + | 0.930836i | \(0.380920\pi\) | |||||||
\(32\) | 7.98556 | 1.41166 | ||||||||
\(33\) | 4.68964 | 0.816362 | ||||||||
\(34\) | −2.11517 | −0.362749 | ||||||||
\(35\) | −6.61933 | −1.11887 | ||||||||
\(36\) | 2.47395 | 0.412325 | ||||||||
\(37\) | −8.99989 | −1.47957 | −0.739787 | − | 0.672841i | \(-0.765074\pi\) | ||||
−0.739787 | + | 0.672841i | \(0.765074\pi\) | |||||||
\(38\) | 7.70925 | 1.25061 | ||||||||
\(39\) | 6.95442 | 1.11360 | ||||||||
\(40\) | −2.21718 | −0.350567 | ||||||||
\(41\) | −10.7319 | −1.67605 | −0.838023 | − | 0.545635i | \(-0.816289\pi\) | ||||
−0.838023 | + | 0.545635i | \(0.816289\pi\) | |||||||
\(42\) | −6.33047 | −0.976813 | ||||||||
\(43\) | −5.09670 | −0.777240 | −0.388620 | − | 0.921398i | \(-0.627048\pi\) | ||||
−0.388620 | + | 0.921398i | \(0.627048\pi\) | |||||||
\(44\) | −11.6019 | −1.74906 | ||||||||
\(45\) | 2.21169 | 0.329699 | ||||||||
\(46\) | −5.87148 | −0.865703 | ||||||||
\(47\) | 12.1496 | 1.77221 | 0.886103 | − | 0.463487i | \(-0.153402\pi\) | ||||
0.886103 | + | 0.463487i | \(0.153402\pi\) | |||||||
\(48\) | 2.82747 | 0.408111 | ||||||||
\(49\) | 1.95738 | 0.279626 | ||||||||
\(50\) | 0.229386 | 0.0324401 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −17.2049 | −2.38589 | ||||||||
\(53\) | 2.12525 | 0.291926 | 0.145963 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145963 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(54\) | 2.11517 | 0.287838 | ||||||||
\(55\) | −10.3720 | −1.39856 | ||||||||
\(56\) | 3.00032 | 0.400935 | ||||||||
\(57\) | 3.64474 | 0.482757 | ||||||||
\(58\) | 7.68878 | 1.00959 | ||||||||
\(59\) | −12.0228 | −1.56524 | −0.782619 | − | 0.622502i | \(-0.786116\pi\) | ||||
−0.782619 | + | 0.622502i | \(0.786116\pi\) | |||||||
\(60\) | −5.47160 | −0.706380 | ||||||||
\(61\) | 2.48960 | 0.318761 | 0.159380 | − | 0.987217i | \(-0.449050\pi\) | ||||
0.159380 | + | 0.987217i | \(0.449050\pi\) | |||||||
\(62\) | −8.60732 | −1.09313 | ||||||||
\(63\) | −2.99289 | −0.377068 | ||||||||
\(64\) | −11.2359 | −1.40448 | ||||||||
\(65\) | −15.3810 | −1.90778 | ||||||||
\(66\) | −9.91940 | −1.22099 | ||||||||
\(67\) | −5.59912 | −0.684041 | −0.342021 | − | 0.939692i | \(-0.611111\pi\) | ||||
−0.342021 | + | 0.939692i | \(0.611111\pi\) | |||||||
\(68\) | 2.47395 | 0.300010 | ||||||||
\(69\) | −2.77589 | −0.334178 | ||||||||
\(70\) | 14.0010 | 1.67344 | ||||||||
\(71\) | −4.99860 | −0.593224 | −0.296612 | − | 0.954998i | \(-0.595857\pi\) | ||||
−0.296612 | + | 0.954998i | \(0.595857\pi\) | |||||||
\(72\) | −1.00248 | −0.118144 | ||||||||
\(73\) | −16.7937 | −1.96556 | −0.982778 | − | 0.184790i | \(-0.940839\pi\) | ||||
−0.982778 | + | 0.184790i | \(0.940839\pi\) | |||||||
\(74\) | 19.0363 | 2.21293 | ||||||||
\(75\) | 0.108448 | 0.0125225 | ||||||||
\(76\) | −9.01690 | −1.03431 | ||||||||
\(77\) | 14.0356 | 1.59950 | ||||||||
\(78\) | −14.7098 | −1.66556 | ||||||||
\(79\) | −7.56114 | −0.850695 | −0.425347 | − | 0.905030i | \(-0.639848\pi\) | ||||
−0.425347 | + | 0.905030i | \(0.639848\pi\) | |||||||
\(80\) | −6.25348 | −0.699161 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.6999 | 2.50678 | ||||||||
\(83\) | −7.89794 | −0.866912 | −0.433456 | − | 0.901175i | \(-0.642706\pi\) | ||||
−0.433456 | + | 0.901175i | \(0.642706\pi\) | |||||||
\(84\) | 7.40425 | 0.807870 | ||||||||
\(85\) | 2.21169 | 0.239891 | ||||||||
\(86\) | 10.7804 | 1.16248 | ||||||||
\(87\) | 3.63506 | 0.389720 | ||||||||
\(88\) | 4.70129 | 0.501159 | ||||||||
\(89\) | −3.95383 | −0.419105 | −0.209552 | − | 0.977797i | \(-0.567201\pi\) | ||||
−0.209552 | + | 0.977797i | \(0.567201\pi\) | |||||||
\(90\) | −4.67809 | −0.493114 | ||||||||
\(91\) | 20.8138 | 2.18188 | ||||||||
\(92\) | 6.86741 | 0.715977 | ||||||||
\(93\) | −4.06933 | −0.421969 | ||||||||
\(94\) | −25.6986 | −2.65060 | ||||||||
\(95\) | −8.06102 | −0.827043 | ||||||||
\(96\) | −7.98556 | −0.815023 | ||||||||
\(97\) | 6.85456 | 0.695975 | 0.347988 | − | 0.937499i | \(-0.386865\pi\) | ||||
0.347988 | + | 0.937499i | \(0.386865\pi\) | |||||||
\(98\) | −4.14019 | −0.418223 | ||||||||
\(99\) | −4.68964 | −0.471327 | ||||||||
\(100\) | −0.268295 | −0.0268295 | ||||||||
\(101\) | 10.2019 | 1.01512 | 0.507562 | − | 0.861615i | \(-0.330547\pi\) | ||||
0.507562 | + | 0.861615i | \(0.330547\pi\) | |||||||
\(102\) | 2.11517 | 0.209433 | ||||||||
\(103\) | −8.15582 | −0.803617 | −0.401808 | − | 0.915724i | \(-0.631618\pi\) | ||||
−0.401808 | + | 0.915724i | \(0.631618\pi\) | |||||||
\(104\) | 6.97169 | 0.683630 | ||||||||
\(105\) | 6.61933 | 0.645980 | ||||||||
\(106\) | −4.49527 | −0.436619 | ||||||||
\(107\) | −15.2536 | −1.47462 | −0.737310 | − | 0.675555i | \(-0.763904\pi\) | ||||
−0.737310 | + | 0.675555i | \(0.763904\pi\) | |||||||
\(108\) | −2.47395 | −0.238056 | ||||||||
\(109\) | 9.54476 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(110\) | 21.9386 | 2.09176 | ||||||||
\(111\) | 8.99989 | 0.854232 | ||||||||
\(112\) | 8.46231 | 0.799614 | ||||||||
\(113\) | 16.2493 | 1.52860 | 0.764300 | − | 0.644860i | \(-0.223084\pi\) | ||||
0.764300 | + | 0.644860i | \(0.223084\pi\) | |||||||
\(114\) | −7.70925 | −0.722037 | ||||||||
\(115\) | 6.13940 | 0.572502 | ||||||||
\(116\) | −8.99296 | −0.834975 | ||||||||
\(117\) | −6.95442 | −0.642936 | ||||||||
\(118\) | 25.4303 | 2.34105 | ||||||||
\(119\) | −2.99289 | −0.274358 | ||||||||
\(120\) | 2.21718 | 0.202400 | ||||||||
\(121\) | 10.9928 | 0.999341 | ||||||||
\(122\) | −5.26593 | −0.476755 | ||||||||
\(123\) | 10.7319 | 0.967666 | ||||||||
\(124\) | 10.0673 | 0.904071 | ||||||||
\(125\) | −11.2983 | −1.01055 | ||||||||
\(126\) | 6.33047 | 0.563963 | ||||||||
\(127\) | −9.93243 | −0.881361 | −0.440680 | − | 0.897664i | \(-0.645263\pi\) | ||||
−0.440680 | + | 0.897664i | \(0.645263\pi\) | |||||||
\(128\) | 7.79468 | 0.688959 | ||||||||
\(129\) | 5.09670 | 0.448740 | ||||||||
\(130\) | 32.5334 | 2.85337 | ||||||||
\(131\) | −21.7380 | −1.89926 | −0.949629 | − | 0.313376i | \(-0.898540\pi\) | ||||
−0.949629 | + | 0.313376i | \(0.898540\pi\) | |||||||
\(132\) | 11.6019 | 1.00982 | ||||||||
\(133\) | 10.9083 | 0.945869 | ||||||||
\(134\) | 11.8431 | 1.02309 | ||||||||
\(135\) | −2.21169 | −0.190352 | ||||||||
\(136\) | −1.00248 | −0.0859622 | ||||||||
\(137\) | 1.01464 | 0.0866867 | 0.0433433 | − | 0.999060i | \(-0.486199\pi\) | ||||
0.0433433 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(138\) | 5.87148 | 0.499814 | ||||||||
\(139\) | 9.47463 | 0.803628 | 0.401814 | − | 0.915721i | \(-0.368380\pi\) | ||||
0.401814 | + | 0.915721i | \(0.368380\pi\) | |||||||
\(140\) | −16.3759 | −1.38401 | ||||||||
\(141\) | −12.1496 | −1.02318 | ||||||||
\(142\) | 10.5729 | 0.887257 | ||||||||
\(143\) | 32.6137 | 2.72730 | ||||||||
\(144\) | −2.82747 | −0.235623 | ||||||||
\(145\) | −8.03962 | −0.667654 | ||||||||
\(146\) | 35.5216 | 2.93979 | ||||||||
\(147\) | −1.95738 | −0.161442 | ||||||||
\(148\) | −22.2653 | −1.83019 | ||||||||
\(149\) | −9.83733 | −0.805905 | −0.402953 | − | 0.915221i | \(-0.632016\pi\) | ||||
−0.402953 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(150\) | −0.229386 | −0.0187293 | ||||||||
\(151\) | 12.2730 | 0.998762 | 0.499381 | − | 0.866382i | \(-0.333561\pi\) | ||||
0.499381 | + | 0.866382i | \(0.333561\pi\) | |||||||
\(152\) | 3.65379 | 0.296362 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −29.6876 | −2.39230 | ||||||||
\(155\) | 9.00007 | 0.722903 | ||||||||
\(156\) | 17.2049 | 1.37749 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 15.9931 | 1.27234 | ||||||||
\(159\) | −2.12525 | −0.168543 | ||||||||
\(160\) | 17.6615 | 1.39627 | ||||||||
\(161\) | −8.30793 | −0.654757 | ||||||||
\(162\) | −2.11517 | −0.166184 | ||||||||
\(163\) | −9.37235 | −0.734099 | −0.367050 | − | 0.930201i | \(-0.619632\pi\) | ||||
−0.367050 | + | 0.930201i | \(0.619632\pi\) | |||||||
\(164\) | −26.5503 | −2.07323 | ||||||||
\(165\) | 10.3720 | 0.807460 | ||||||||
\(166\) | 16.7055 | 1.29660 | ||||||||
\(167\) | −24.8082 | −1.91972 | −0.959859 | − | 0.280484i | \(-0.909505\pi\) | ||||
−0.959859 | + | 0.280484i | \(0.909505\pi\) | |||||||
\(168\) | −3.00032 | −0.231480 | ||||||||
\(169\) | 35.3640 | 2.72030 | ||||||||
\(170\) | −4.67809 | −0.358793 | ||||||||
\(171\) | −3.64474 | −0.278720 | ||||||||
\(172\) | −12.6090 | −0.961426 | ||||||||
\(173\) | 11.7404 | 0.892603 | 0.446301 | − | 0.894883i | \(-0.352741\pi\) | ||||
0.446301 | + | 0.894883i | \(0.352741\pi\) | |||||||
\(174\) | −7.68878 | −0.582885 | ||||||||
\(175\) | 0.324573 | 0.0245354 | ||||||||
\(176\) | 13.2598 | 0.999498 | ||||||||
\(177\) | 12.0228 | 0.903690 | ||||||||
\(178\) | 8.36302 | 0.626835 | ||||||||
\(179\) | 8.94912 | 0.668888 | 0.334444 | − | 0.942416i | \(-0.391451\pi\) | ||||
0.334444 | + | 0.942416i | \(0.391451\pi\) | |||||||
\(180\) | 5.47160 | 0.407829 | ||||||||
\(181\) | 13.0507 | 0.970052 | 0.485026 | − | 0.874500i | \(-0.338810\pi\) | ||||
0.485026 | + | 0.874500i | \(0.338810\pi\) | |||||||
\(182\) | −44.0247 | −3.26333 | ||||||||
\(183\) | −2.48960 | −0.184037 | ||||||||
\(184\) | −2.78278 | −0.205150 | ||||||||
\(185\) | −19.9049 | −1.46344 | ||||||||
\(186\) | 8.60732 | 0.631119 | ||||||||
\(187\) | −4.68964 | −0.342941 | ||||||||
\(188\) | 30.0576 | 2.19217 | ||||||||
\(189\) | 2.99289 | 0.217701 | ||||||||
\(190\) | 17.0504 | 1.23697 | ||||||||
\(191\) | 19.3245 | 1.39827 | 0.699135 | − | 0.714990i | \(-0.253569\pi\) | ||||
0.699135 | + | 0.714990i | \(0.253569\pi\) | |||||||
\(192\) | 11.2359 | 0.810879 | ||||||||
\(193\) | 7.91560 | 0.569777 | 0.284889 | − | 0.958561i | \(-0.408043\pi\) | ||||
0.284889 | + | 0.958561i | \(0.408043\pi\) | |||||||
\(194\) | −14.4986 | −1.04094 | ||||||||
\(195\) | 15.3810 | 1.10146 | ||||||||
\(196\) | 4.84246 | 0.345890 | ||||||||
\(197\) | 17.5967 | 1.25371 | 0.626855 | − | 0.779136i | \(-0.284342\pi\) | ||||
0.626855 | + | 0.779136i | \(0.284342\pi\) | |||||||
\(198\) | 9.91940 | 0.704941 | ||||||||
\(199\) | −19.0361 | −1.34943 | −0.674715 | − | 0.738078i | \(-0.735734\pi\) | ||||
−0.674715 | + | 0.738078i | \(0.735734\pi\) | |||||||
\(200\) | 0.108717 | 0.00768749 | ||||||||
\(201\) | 5.59912 | 0.394931 | ||||||||
\(202\) | −21.5787 | −1.51827 | ||||||||
\(203\) | 10.8793 | 0.763580 | ||||||||
\(204\) | −2.47395 | −0.173211 | ||||||||
\(205\) | −23.7357 | −1.65777 | ||||||||
\(206\) | 17.2510 | 1.20193 | ||||||||
\(207\) | 2.77589 | 0.192938 | ||||||||
\(208\) | 19.6634 | 1.36341 | ||||||||
\(209\) | 17.0925 | 1.18231 | ||||||||
\(210\) | −14.0010 | −0.966161 | ||||||||
\(211\) | −17.4733 | −1.20291 | −0.601457 | − | 0.798905i | \(-0.705413\pi\) | ||||
−0.601457 | + | 0.798905i | \(0.705413\pi\) | |||||||
\(212\) | 5.25776 | 0.361105 | ||||||||
\(213\) | 4.99860 | 0.342498 | ||||||||
\(214\) | 32.2639 | 2.20552 | ||||||||
\(215\) | −11.2723 | −0.768765 | ||||||||
\(216\) | 1.00248 | 0.0682103 | ||||||||
\(217\) | −12.1790 | −0.826767 | ||||||||
\(218\) | −20.1888 | −1.36736 | ||||||||
\(219\) | 16.7937 | 1.13481 | ||||||||
\(220\) | −25.6598 | −1.72999 | ||||||||
\(221\) | −6.95442 | −0.467805 | ||||||||
\(222\) | −19.0363 | −1.27763 | ||||||||
\(223\) | 25.5231 | 1.70915 | 0.854576 | − | 0.519326i | \(-0.173817\pi\) | ||||
0.854576 | + | 0.519326i | \(0.173817\pi\) | |||||||
\(224\) | −23.8999 | −1.59688 | ||||||||
\(225\) | −0.108448 | −0.00722988 | ||||||||
\(226\) | −34.3699 | −2.28625 | ||||||||
\(227\) | −12.0584 | −0.800343 | −0.400172 | − | 0.916440i | \(-0.631049\pi\) | ||||
−0.400172 | + | 0.916440i | \(0.631049\pi\) | |||||||
\(228\) | 9.01690 | 0.597159 | ||||||||
\(229\) | −13.1585 | −0.869536 | −0.434768 | − | 0.900542i | \(-0.643170\pi\) | ||||
−0.434768 | + | 0.900542i | \(0.643170\pi\) | |||||||
\(230\) | −12.9859 | −0.856263 | ||||||||
\(231\) | −14.0356 | −0.923473 | ||||||||
\(232\) | 3.64409 | 0.239246 | ||||||||
\(233\) | −3.11835 | −0.204290 | −0.102145 | − | 0.994770i | \(-0.532571\pi\) | ||||
−0.102145 | + | 0.994770i | \(0.532571\pi\) | |||||||
\(234\) | 14.7098 | 0.961609 | ||||||||
\(235\) | 26.8712 | 1.75288 | ||||||||
\(236\) | −29.7438 | −1.93616 | ||||||||
\(237\) | 7.56114 | 0.491149 | ||||||||
\(238\) | 6.33047 | 0.410343 | ||||||||
\(239\) | 0.545179 | 0.0352647 | 0.0176324 | − | 0.999845i | \(-0.494387\pi\) | ||||
0.0176324 | + | 0.999845i | \(0.494387\pi\) | |||||||
\(240\) | 6.25348 | 0.403661 | ||||||||
\(241\) | −23.4255 | −1.50897 | −0.754484 | − | 0.656319i | \(-0.772113\pi\) | ||||
−0.754484 | + | 0.656319i | \(0.772113\pi\) | |||||||
\(242\) | −23.2516 | −1.49467 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.15915 | 0.394299 | ||||||||
\(245\) | 4.32911 | 0.276576 | ||||||||
\(246\) | −22.6999 | −1.44729 | ||||||||
\(247\) | 25.3470 | 1.61279 | ||||||||
\(248\) | −4.07943 | −0.259044 | ||||||||
\(249\) | 7.89794 | 0.500512 | ||||||||
\(250\) | 23.8978 | 1.51143 | ||||||||
\(251\) | 16.2359 | 1.02480 | 0.512402 | − | 0.858746i | \(-0.328756\pi\) | ||||
0.512402 | + | 0.858746i | \(0.328756\pi\) | |||||||
\(252\) | −7.40425 | −0.466424 | ||||||||
\(253\) | −13.0179 | −0.818431 | ||||||||
\(254\) | 21.0088 | 1.31821 | ||||||||
\(255\) | −2.21169 | −0.138501 | ||||||||
\(256\) | 5.98467 | 0.374042 | ||||||||
\(257\) | −31.4934 | −1.96450 | −0.982251 | − | 0.187570i | \(-0.939939\pi\) | ||||
−0.982251 | + | 0.187570i | \(0.939939\pi\) | |||||||
\(258\) | −10.7804 | −0.671158 | ||||||||
\(259\) | 26.9357 | 1.67370 | ||||||||
\(260\) | −38.0518 | −2.35987 | ||||||||
\(261\) | −3.63506 | −0.225005 | ||||||||
\(262\) | 45.9796 | 2.84063 | ||||||||
\(263\) | −12.5384 | −0.773151 | −0.386576 | − | 0.922258i | \(-0.626342\pi\) | ||||
−0.386576 | + | 0.922258i | \(0.626342\pi\) | |||||||
\(264\) | −4.70129 | −0.289344 | ||||||||
\(265\) | 4.70039 | 0.288742 | ||||||||
\(266\) | −23.0729 | −1.41469 | ||||||||
\(267\) | 3.95383 | 0.241970 | ||||||||
\(268\) | −13.8519 | −0.846142 | ||||||||
\(269\) | −27.3995 | −1.67058 | −0.835290 | − | 0.549810i | \(-0.814700\pi\) | ||||
−0.835290 | + | 0.549810i | \(0.814700\pi\) | |||||||
\(270\) | 4.67809 | 0.284700 | ||||||||
\(271\) | −24.1438 | −1.46663 | −0.733317 | − | 0.679887i | \(-0.762029\pi\) | ||||
−0.733317 | + | 0.679887i | \(0.762029\pi\) | |||||||
\(272\) | −2.82747 | −0.171441 | ||||||||
\(273\) | −20.8138 | −1.25971 | ||||||||
\(274\) | −2.14614 | −0.129653 | ||||||||
\(275\) | 0.508583 | 0.0306687 | ||||||||
\(276\) | −6.86741 | −0.413370 | ||||||||
\(277\) | 17.7425 | 1.06604 | 0.533021 | − | 0.846102i | \(-0.321057\pi\) | ||||
0.533021 | + | 0.846102i | \(0.321057\pi\) | |||||||
\(278\) | −20.0405 | −1.20195 | ||||||||
\(279\) | 4.06933 | 0.243624 | ||||||||
\(280\) | 6.63576 | 0.396563 | ||||||||
\(281\) | −15.2451 | −0.909446 | −0.454723 | − | 0.890633i | \(-0.650262\pi\) | ||||
−0.454723 | + | 0.890633i | \(0.650262\pi\) | |||||||
\(282\) | 25.6986 | 1.53033 | ||||||||
\(283\) | −0.603246 | −0.0358593 | −0.0179296 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179296 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(284\) | −12.3663 | −0.733803 | ||||||||
\(285\) | 8.06102 | 0.477493 | ||||||||
\(286\) | −68.9837 | −4.07909 | ||||||||
\(287\) | 32.1195 | 1.89595 | ||||||||
\(288\) | 7.98556 | 0.470554 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 17.0052 | 0.998578 | ||||||||
\(291\) | −6.85456 | −0.401821 | ||||||||
\(292\) | −41.5468 | −2.43134 | ||||||||
\(293\) | 12.3145 | 0.719419 | 0.359710 | − | 0.933064i | \(-0.382876\pi\) | ||||
0.359710 | + | 0.933064i | \(0.382876\pi\) | |||||||
\(294\) | 4.14019 | 0.241461 | ||||||||
\(295\) | −26.5907 | −1.54817 | ||||||||
\(296\) | 9.02224 | 0.524407 | ||||||||
\(297\) | 4.68964 | 0.272121 | ||||||||
\(298\) | 20.8076 | 1.20535 | ||||||||
\(299\) | −19.3047 | −1.11642 | ||||||||
\(300\) | 0.268295 | 0.0154900 | ||||||||
\(301\) | 15.2539 | 0.879218 | ||||||||
\(302\) | −25.9595 | −1.49380 | ||||||||
\(303\) | −10.2019 | −0.586083 | ||||||||
\(304\) | 10.3054 | 0.591056 | ||||||||
\(305\) | 5.50621 | 0.315285 | ||||||||
\(306\) | −2.11517 | −0.120916 | ||||||||
\(307\) | 6.64694 | 0.379361 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(308\) | 34.7233 | 1.97854 | ||||||||
\(309\) | 8.15582 | 0.463968 | ||||||||
\(310\) | −19.0367 | −1.08121 | ||||||||
\(311\) | 10.3816 | 0.588685 | 0.294343 | − | 0.955700i | \(-0.404899\pi\) | ||||
0.294343 | + | 0.955700i | \(0.404899\pi\) | |||||||
\(312\) | −6.97169 | −0.394694 | ||||||||
\(313\) | 13.3531 | 0.754763 | 0.377382 | − | 0.926058i | \(-0.376825\pi\) | ||||
0.377382 | + | 0.926058i | \(0.376825\pi\) | |||||||
\(314\) | 2.11517 | 0.119366 | ||||||||
\(315\) | −6.61933 | −0.372957 | ||||||||
\(316\) | −18.7059 | −1.05229 | ||||||||
\(317\) | 9.25260 | 0.519678 | 0.259839 | − | 0.965652i | \(-0.416331\pi\) | ||||
0.259839 | + | 0.965652i | \(0.416331\pi\) | |||||||
\(318\) | 4.49527 | 0.252082 | ||||||||
\(319\) | 17.0471 | 0.954457 | ||||||||
\(320\) | −24.8502 | −1.38917 | ||||||||
\(321\) | 15.2536 | 0.851372 | ||||||||
\(322\) | 17.5727 | 0.979288 | ||||||||
\(323\) | −3.64474 | −0.202799 | ||||||||
\(324\) | 2.47395 | 0.137442 | ||||||||
\(325\) | 0.754194 | 0.0418352 | ||||||||
\(326\) | 19.8241 | 1.09796 | ||||||||
\(327\) | −9.54476 | −0.527826 | ||||||||
\(328\) | 10.7586 | 0.594043 | ||||||||
\(329\) | −36.3625 | −2.00473 | ||||||||
\(330\) | −21.9386 | −1.20768 | ||||||||
\(331\) | −24.4559 | −1.34422 | −0.672109 | − | 0.740452i | \(-0.734611\pi\) | ||||
−0.672109 | + | 0.740452i | \(0.734611\pi\) | |||||||
\(332\) | −19.5391 | −1.07235 | ||||||||
\(333\) | −8.99989 | −0.493191 | ||||||||
\(334\) | 52.4736 | 2.87123 | ||||||||
\(335\) | −12.3835 | −0.676582 | ||||||||
\(336\) | −8.46231 | −0.461657 | ||||||||
\(337\) | 18.2007 | 0.991456 | 0.495728 | − | 0.868478i | \(-0.334901\pi\) | ||||
0.495728 | + | 0.868478i | \(0.334901\pi\) | |||||||
\(338\) | −74.8008 | −4.06863 | ||||||||
\(339\) | −16.2493 | −0.882538 | ||||||||
\(340\) | 5.47160 | 0.296739 | ||||||||
\(341\) | −19.0837 | −1.03344 | ||||||||
\(342\) | 7.70925 | 0.416868 | ||||||||
\(343\) | 15.0920 | 0.814891 | ||||||||
\(344\) | 5.10936 | 0.275478 | ||||||||
\(345\) | −6.13940 | −0.330534 | ||||||||
\(346\) | −24.8329 | −1.33502 | ||||||||
\(347\) | 8.80901 | 0.472892 | 0.236446 | − | 0.971645i | \(-0.424017\pi\) | ||||
0.236446 | + | 0.971645i | \(0.424017\pi\) | |||||||
\(348\) | 8.99296 | 0.482073 | ||||||||
\(349\) | 4.21599 | 0.225677 | 0.112838 | − | 0.993613i | \(-0.464006\pi\) | ||||
0.112838 | + | 0.993613i | \(0.464006\pi\) | |||||||
\(350\) | −0.686528 | −0.0366965 | ||||||||
\(351\) | 6.95442 | 0.371199 | ||||||||
\(352\) | −37.4494 | −1.99606 | ||||||||
\(353\) | −5.00317 | −0.266292 | −0.133146 | − | 0.991096i | \(-0.542508\pi\) | ||||
−0.133146 | + | 0.991096i | \(0.542508\pi\) | |||||||
\(354\) | −25.4303 | −1.35161 | ||||||||
\(355\) | −11.0553 | −0.586755 | ||||||||
\(356\) | −9.78156 | −0.518422 | ||||||||
\(357\) | 2.99289 | 0.158400 | ||||||||
\(358\) | −18.9289 | −1.00042 | ||||||||
\(359\) | −10.5320 | −0.555858 | −0.277929 | − | 0.960602i | \(-0.589648\pi\) | ||||
−0.277929 | + | 0.960602i | \(0.589648\pi\) | |||||||
\(360\) | −2.21718 | −0.116856 | ||||||||
\(361\) | −5.71588 | −0.300836 | ||||||||
\(362\) | −27.6045 | −1.45086 | ||||||||
\(363\) | −10.9928 | −0.576970 | ||||||||
\(364\) | 51.4923 | 2.69893 | ||||||||
\(365\) | −37.1424 | −1.94412 | ||||||||
\(366\) | 5.26593 | 0.275255 | ||||||||
\(367\) | 4.38556 | 0.228924 | 0.114462 | − | 0.993428i | \(-0.463486\pi\) | ||||
0.114462 | + | 0.993428i | \(0.463486\pi\) | |||||||
\(368\) | −7.84876 | −0.409145 | ||||||||
\(369\) | −10.7319 | −0.558682 | ||||||||
\(370\) | 42.1023 | 2.18880 | ||||||||
\(371\) | −6.36064 | −0.330228 | ||||||||
\(372\) | −10.0673 | −0.521965 | ||||||||
\(373\) | 10.4074 | 0.538875 | 0.269438 | − | 0.963018i | \(-0.413162\pi\) | ||||
0.269438 | + | 0.963018i | \(0.413162\pi\) | |||||||
\(374\) | 9.91940 | 0.512920 | ||||||||
\(375\) | 11.2983 | 0.583441 | ||||||||
\(376\) | −12.1798 | −0.628126 | ||||||||
\(377\) | 25.2798 | 1.30197 | ||||||||
\(378\) | −6.33047 | −0.325604 | ||||||||
\(379\) | −16.0605 | −0.824972 | −0.412486 | − | 0.910964i | \(-0.635339\pi\) | ||||
−0.412486 | + | 0.910964i | \(0.635339\pi\) | |||||||
\(380\) | −19.9425 | −1.02303 | ||||||||
\(381\) | 9.93243 | 0.508854 | ||||||||
\(382\) | −40.8746 | −2.09132 | ||||||||
\(383\) | −25.8834 | −1.32258 | −0.661290 | − | 0.750130i | \(-0.729991\pi\) | ||||
−0.661290 | + | 0.750130i | \(0.729991\pi\) | |||||||
\(384\) | −7.79468 | −0.397771 | ||||||||
\(385\) | 31.0423 | 1.58206 | ||||||||
\(386\) | −16.7428 | −0.852188 | ||||||||
\(387\) | −5.09670 | −0.259080 | ||||||||
\(388\) | 16.9578 | 0.860904 | ||||||||
\(389\) | 17.8472 | 0.904889 | 0.452444 | − | 0.891793i | \(-0.350552\pi\) | ||||
0.452444 | + | 0.891793i | \(0.350552\pi\) | |||||||
\(390\) | −32.5334 | −1.64739 | ||||||||
\(391\) | 2.77589 | 0.140383 | ||||||||
\(392\) | −1.96224 | −0.0991081 | ||||||||
\(393\) | 21.7380 | 1.09654 | ||||||||
\(394\) | −37.2200 | −1.87511 | ||||||||
\(395\) | −16.7229 | −0.841419 | ||||||||
\(396\) | −11.6019 | −0.583019 | ||||||||
\(397\) | 16.6494 | 0.835609 | 0.417805 | − | 0.908537i | \(-0.362800\pi\) | ||||
0.417805 | + | 0.908537i | \(0.362800\pi\) | |||||||
\(398\) | 40.2645 | 2.01828 | ||||||||
\(399\) | −10.9083 | −0.546098 | ||||||||
\(400\) | 0.306634 | 0.0153317 | ||||||||
\(401\) | −4.02629 | −0.201063 | −0.100532 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100532 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(402\) | −11.8431 | −0.590680 | ||||||||
\(403\) | −28.2998 | −1.40971 | ||||||||
\(404\) | 25.2389 | 1.25568 | ||||||||
\(405\) | 2.21169 | 0.109900 | ||||||||
\(406\) | −23.0117 | −1.14205 | ||||||||
\(407\) | 42.2063 | 2.09209 | ||||||||
\(408\) | 1.00248 | 0.0496303 | ||||||||
\(409\) | −12.2830 | −0.607356 | −0.303678 | − | 0.952775i | \(-0.598215\pi\) | ||||
−0.303678 | + | 0.952775i | \(0.598215\pi\) | |||||||
\(410\) | 50.2050 | 2.47945 | ||||||||
\(411\) | −1.01464 | −0.0500486 | ||||||||
\(412\) | −20.1771 | −0.994053 | ||||||||
\(413\) | 35.9829 | 1.77060 | ||||||||
\(414\) | −5.87148 | −0.288568 | ||||||||
\(415\) | −17.4678 | −0.857459 | ||||||||
\(416\) | −55.5349 | −2.72282 | ||||||||
\(417\) | −9.47463 | −0.463975 | ||||||||
\(418\) | −36.1536 | −1.76833 | ||||||||
\(419\) | 4.96217 | 0.242418 | 0.121209 | − | 0.992627i | \(-0.461323\pi\) | ||||
0.121209 | + | 0.992627i | \(0.461323\pi\) | |||||||
\(420\) | 16.3759 | 0.799061 | ||||||||
\(421\) | 5.39691 | 0.263029 | 0.131515 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131515 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(422\) | 36.9591 | 1.79914 | ||||||||
\(423\) | 12.1496 | 0.590736 | ||||||||
\(424\) | −2.13053 | −0.103468 | ||||||||
\(425\) | −0.108448 | −0.00526051 | ||||||||
\(426\) | −10.5729 | −0.512258 | ||||||||
\(427\) | −7.45110 | −0.360584 | ||||||||
\(428\) | −37.7366 | −1.82407 | ||||||||
\(429\) | −32.6137 | −1.57461 | ||||||||
\(430\) | 23.8428 | 1.14980 | ||||||||
\(431\) | −15.1582 | −0.730145 | −0.365072 | − | 0.930979i | \(-0.618956\pi\) | ||||
−0.365072 | + | 0.930979i | \(0.618956\pi\) | |||||||
\(432\) | 2.82747 | 0.136037 | ||||||||
\(433\) | 7.10789 | 0.341583 | 0.170792 | − | 0.985307i | \(-0.445368\pi\) | ||||
0.170792 | + | 0.985307i | \(0.445368\pi\) | |||||||
\(434\) | 25.7607 | 1.23656 | ||||||||
\(435\) | 8.03962 | 0.385470 | ||||||||
\(436\) | 23.6132 | 1.13087 | ||||||||
\(437\) | −10.1174 | −0.483981 | ||||||||
\(438\) | −35.5216 | −1.69729 | ||||||||
\(439\) | 13.1216 | 0.626260 | 0.313130 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313130 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(440\) | 10.3978 | 0.495694 | ||||||||
\(441\) | 1.95738 | 0.0932085 | ||||||||
\(442\) | 14.7098 | 0.699673 | ||||||||
\(443\) | −25.8189 | −1.22669 | −0.613346 | − | 0.789814i | \(-0.710177\pi\) | ||||
−0.613346 | + | 0.789814i | \(0.710177\pi\) | |||||||
\(444\) | 22.2653 | 1.05666 | ||||||||
\(445\) | −8.74462 | −0.414535 | ||||||||
\(446\) | −53.9857 | −2.55630 | ||||||||
\(447\) | 9.83733 | 0.465290 | ||||||||
\(448\) | 33.6277 | 1.58876 | ||||||||
\(449\) | −12.1983 | −0.575675 | −0.287837 | − | 0.957679i | \(-0.592936\pi\) | ||||
−0.287837 | + | 0.957679i | \(0.592936\pi\) | |||||||
\(450\) | 0.229386 | 0.0108134 | ||||||||
\(451\) | 50.3289 | 2.36990 | ||||||||
\(452\) | 40.1998 | 1.89084 | ||||||||
\(453\) | −12.2730 | −0.576636 | ||||||||
\(454\) | 25.5055 | 1.19703 | ||||||||
\(455\) | 46.0336 | 2.15809 | ||||||||
\(456\) | −3.65379 | −0.171104 | ||||||||
\(457\) | 33.8724 | 1.58449 | 0.792243 | − | 0.610206i | \(-0.208913\pi\) | ||||
0.792243 | + | 0.610206i | \(0.208913\pi\) | |||||||
\(458\) | 27.8324 | 1.30052 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 15.1886 | 0.708170 | ||||||||
\(461\) | 29.5625 | 1.37686 | 0.688430 | − | 0.725302i | \(-0.258300\pi\) | ||||
0.688430 | + | 0.725302i | \(0.258300\pi\) | |||||||
\(462\) | 29.6876 | 1.38119 | ||||||||
\(463\) | 27.5942 | 1.28241 | 0.641207 | − | 0.767368i | \(-0.278434\pi\) | ||||
0.641207 | + | 0.767368i | \(0.278434\pi\) | |||||||
\(464\) | 10.2780 | 0.477146 | ||||||||
\(465\) | −9.00007 | −0.417368 | ||||||||
\(466\) | 6.59584 | 0.305546 | ||||||||
\(467\) | −2.87292 | −0.132943 | −0.0664714 | − | 0.997788i | \(-0.521174\pi\) | ||||
−0.0664714 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(468\) | −17.2049 | −0.795296 | ||||||||
\(469\) | 16.7575 | 0.773791 | ||||||||
\(470\) | −56.8371 | −2.62170 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 12.0527 | 0.554769 | ||||||||
\(473\) | 23.9017 | 1.09900 | ||||||||
\(474\) | −15.9931 | −0.734588 | ||||||||
\(475\) | 0.395265 | 0.0181360 | ||||||||
\(476\) | −7.40425 | −0.339373 | ||||||||
\(477\) | 2.12525 | 0.0973086 | ||||||||
\(478\) | −1.15315 | −0.0527437 | ||||||||
\(479\) | −18.6693 | −0.853021 | −0.426510 | − | 0.904483i | \(-0.640257\pi\) | ||||
−0.426510 | + | 0.904483i | \(0.640257\pi\) | |||||||
\(480\) | −17.6615 | −0.806135 | ||||||||
\(481\) | 62.5890 | 2.85381 | ||||||||
\(482\) | 49.5489 | 2.25689 | ||||||||
\(483\) | 8.30793 | 0.378024 | ||||||||
\(484\) | 27.1955 | 1.23616 | ||||||||
\(485\) | 15.1601 | 0.688386 | ||||||||
\(486\) | 2.11517 | 0.0959461 | ||||||||
\(487\) | 19.4921 | 0.883273 | 0.441636 | − | 0.897194i | \(-0.354398\pi\) | ||||
0.441636 | + | 0.897194i | \(0.354398\pi\) | |||||||
\(488\) | −2.49578 | −0.112979 | ||||||||
\(489\) | 9.37235 | 0.423832 | ||||||||
\(490\) | −9.15680 | −0.413662 | ||||||||
\(491\) | −29.2036 | −1.31794 | −0.658970 | − | 0.752169i | \(-0.729008\pi\) | ||||
−0.658970 | + | 0.752169i | \(0.729008\pi\) | |||||||
\(492\) | 26.5503 | 1.19698 | ||||||||
\(493\) | −3.63506 | −0.163715 | ||||||||
\(494\) | −53.6133 | −2.41218 | ||||||||
\(495\) | −10.3720 | −0.466187 | ||||||||
\(496\) | −11.5059 | −0.516631 | ||||||||
\(497\) | 14.9602 | 0.671058 | ||||||||
\(498\) | −16.7055 | −0.748591 | ||||||||
\(499\) | −39.9318 | −1.78759 | −0.893797 | − | 0.448473i | \(-0.851968\pi\) | ||||
−0.893797 | + | 0.448473i | \(0.851968\pi\) | |||||||
\(500\) | −27.9514 | −1.25002 | ||||||||
\(501\) | 24.8082 | 1.10835 | ||||||||
\(502\) | −34.3418 | −1.53275 | ||||||||
\(503\) | 24.3591 | 1.08612 | 0.543060 | − | 0.839694i | \(-0.317266\pi\) | ||||
0.543060 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(504\) | 3.00032 | 0.133645 | ||||||||
\(505\) | 22.5633 | 1.00406 | ||||||||
\(506\) | 27.5352 | 1.22409 | ||||||||
\(507\) | −35.3640 | −1.57057 | ||||||||
\(508\) | −24.5723 | −1.09022 | ||||||||
\(509\) | −11.9945 | −0.531645 | −0.265823 | − | 0.964022i | \(-0.585644\pi\) | ||||
−0.265823 | + | 0.964022i | \(0.585644\pi\) | |||||||
\(510\) | 4.67809 | 0.207149 | ||||||||
\(511\) | 50.2617 | 2.22345 | ||||||||
\(512\) | −28.2480 | −1.24839 | ||||||||
\(513\) | 3.64474 | 0.160919 | ||||||||
\(514\) | 66.6139 | 2.93821 | ||||||||
\(515\) | −18.0381 | −0.794854 | ||||||||
\(516\) | 12.6090 | 0.555079 | ||||||||
\(517\) | −56.9775 | −2.50587 | ||||||||
\(518\) | −56.9736 | −2.50327 | ||||||||
\(519\) | −11.7404 | −0.515344 | ||||||||
\(520\) | 15.4192 | 0.676176 | ||||||||
\(521\) | −16.2521 | −0.712016 | −0.356008 | − | 0.934483i | \(-0.615862\pi\) | ||||
−0.356008 | + | 0.934483i | \(0.615862\pi\) | |||||||
\(522\) | 7.68878 | 0.336529 | ||||||||
\(523\) | 10.7979 | 0.472157 | 0.236079 | − | 0.971734i | \(-0.424138\pi\) | ||||
0.236079 | + | 0.971734i | \(0.424138\pi\) | |||||||
\(524\) | −53.7787 | −2.34933 | ||||||||
\(525\) | −0.324573 | −0.0141655 | ||||||||
\(526\) | 26.5209 | 1.15637 | ||||||||
\(527\) | 4.06933 | 0.177263 | ||||||||
\(528\) | −13.2598 | −0.577061 | ||||||||
\(529\) | −15.2944 | −0.664975 | ||||||||
\(530\) | −9.94212 | −0.431858 | ||||||||
\(531\) | −12.0228 | −0.521746 | ||||||||
\(532\) | 26.9866 | 1.17002 | ||||||||
\(533\) | 74.6344 | 3.23277 | ||||||||
\(534\) | −8.36302 | −0.361903 | ||||||||
\(535\) | −33.7361 | −1.45854 | ||||||||
\(536\) | 5.61302 | 0.242446 | ||||||||
\(537\) | −8.94912 | −0.386183 | ||||||||
\(538\) | 57.9547 | 2.49861 | ||||||||
\(539\) | −9.17941 | −0.395385 | ||||||||
\(540\) | −5.47160 | −0.235460 | ||||||||
\(541\) | 7.82090 | 0.336247 | 0.168123 | − | 0.985766i | \(-0.446229\pi\) | ||||
0.168123 | + | 0.985766i | \(0.446229\pi\) | |||||||
\(542\) | 51.0683 | 2.19357 | ||||||||
\(543\) | −13.0507 | −0.560060 | ||||||||
\(544\) | 7.98556 | 0.342378 | ||||||||
\(545\) | 21.1100 | 0.904253 | ||||||||
\(546\) | 44.0247 | 1.88409 | ||||||||
\(547\) | −19.1823 | −0.820175 | −0.410087 | − | 0.912046i | \(-0.634502\pi\) | ||||
−0.410087 | + | 0.912046i | \(0.634502\pi\) | |||||||
\(548\) | 2.51017 | 0.107229 | ||||||||
\(549\) | 2.48960 | 0.106254 | ||||||||
\(550\) | −1.07574 | −0.0458697 | ||||||||
\(551\) | 13.2489 | 0.564420 | ||||||||
\(552\) | 2.78278 | 0.118443 | ||||||||
\(553\) | 22.6296 | 0.962311 | ||||||||
\(554\) | −37.5284 | −1.59443 | ||||||||
\(555\) | 19.9049 | 0.844917 | ||||||||
\(556\) | 23.4398 | 0.994067 | ||||||||
\(557\) | −13.3471 | −0.565535 | −0.282768 | − | 0.959188i | \(-0.591252\pi\) | ||||
−0.282768 | + | 0.959188i | \(0.591252\pi\) | |||||||
\(558\) | −8.60732 | −0.364377 | ||||||||
\(559\) | 35.4446 | 1.49915 | ||||||||
\(560\) | 18.7160 | 0.790894 | ||||||||
\(561\) | 4.68964 | 0.197997 | ||||||||
\(562\) | 32.2460 | 1.36021 | ||||||||
\(563\) | −0.865035 | −0.0364569 | −0.0182284 | − | 0.999834i | \(-0.505803\pi\) | ||||
−0.0182284 | + | 0.999834i | \(0.505803\pi\) | |||||||
\(564\) | −30.0576 | −1.26565 | ||||||||
\(565\) | 35.9382 | 1.51193 | ||||||||
\(566\) | 1.27597 | 0.0536330 | ||||||||
\(567\) | −2.99289 | −0.125689 | ||||||||
\(568\) | 5.01101 | 0.210257 | ||||||||
\(569\) | 12.0048 | 0.503267 | 0.251634 | − | 0.967823i | \(-0.419032\pi\) | ||||
0.251634 | + | 0.967823i | \(0.419032\pi\) | |||||||
\(570\) | −17.0504 | −0.714164 | ||||||||
\(571\) | −25.6057 | −1.07156 | −0.535782 | − | 0.844356i | \(-0.679983\pi\) | ||||
−0.535782 | + | 0.844356i | \(0.679983\pi\) | |||||||
\(572\) | 80.6848 | 3.37360 | ||||||||
\(573\) | −19.3245 | −0.807291 | ||||||||
\(574\) | −67.9382 | −2.83568 | ||||||||
\(575\) | −0.301040 | −0.0125542 | ||||||||
\(576\) | −11.2359 | −0.468161 | ||||||||
\(577\) | 11.8436 | 0.493056 | 0.246528 | − | 0.969136i | \(-0.420710\pi\) | ||||
0.246528 | + | 0.969136i | \(0.420710\pi\) | |||||||
\(578\) | −2.11517 | −0.0879795 | ||||||||
\(579\) | −7.91560 | −0.328961 | ||||||||
\(580\) | −19.8896 | −0.825871 | ||||||||
\(581\) | 23.6377 | 0.980655 | ||||||||
\(582\) | 14.4986 | 0.600985 | ||||||||
\(583\) | −9.96667 | −0.412777 | ||||||||
\(584\) | 16.8354 | 0.696655 | ||||||||
\(585\) | −15.3810 | −0.635926 | ||||||||
\(586\) | −26.0472 | −1.07600 | ||||||||
\(587\) | 14.5040 | 0.598643 | 0.299322 | − | 0.954152i | \(-0.403240\pi\) | ||||
0.299322 | + | 0.954152i | \(0.403240\pi\) | |||||||
\(588\) | −4.84246 | −0.199700 | ||||||||
\(589\) | −14.8316 | −0.611127 | ||||||||
\(590\) | 56.2438 | 2.31552 | ||||||||
\(591\) | −17.5967 | −0.723830 | ||||||||
\(592\) | 25.4470 | 1.04586 | ||||||||
\(593\) | 1.28751 | 0.0528717 | 0.0264359 | − | 0.999651i | \(-0.491584\pi\) | ||||
0.0264359 | + | 0.999651i | \(0.491584\pi\) | |||||||
\(594\) | −9.91940 | −0.406998 | ||||||||
\(595\) | −6.61933 | −0.271366 | ||||||||
\(596\) | −24.3370 | −0.996884 | ||||||||
\(597\) | 19.0361 | 0.779094 | ||||||||
\(598\) | 40.8328 | 1.66978 | ||||||||
\(599\) | 42.3012 | 1.72838 | 0.864190 | − | 0.503166i | \(-0.167832\pi\) | ||||
0.864190 | + | 0.503166i | \(0.167832\pi\) | |||||||
\(600\) | −0.108717 | −0.00443837 | ||||||||
\(601\) | 9.10385 | 0.371354 | 0.185677 | − | 0.982611i | \(-0.440552\pi\) | ||||
0.185677 | + | 0.982611i | \(0.440552\pi\) | |||||||
\(602\) | −32.2645 | −1.31500 | ||||||||
\(603\) | −5.59912 | −0.228014 | ||||||||
\(604\) | 30.3628 | 1.23544 | ||||||||
\(605\) | 24.3125 | 0.988444 | ||||||||
\(606\) | 21.5787 | 0.876575 | ||||||||
\(607\) | 19.1639 | 0.777839 | 0.388920 | − | 0.921272i | \(-0.372848\pi\) | ||||
0.388920 | + | 0.921272i | \(0.372848\pi\) | |||||||
\(608\) | −29.1053 | −1.18037 | ||||||||
\(609\) | −10.8793 | −0.440853 | ||||||||
\(610\) | −11.6466 | −0.471557 | ||||||||
\(611\) | −84.4937 | −3.41825 | ||||||||
\(612\) | 2.47395 | 0.100003 | ||||||||
\(613\) | −1.50860 | −0.0609319 | −0.0304660 | − | 0.999536i | \(-0.509699\pi\) | ||||
−0.0304660 | + | 0.999536i | \(0.509699\pi\) | |||||||
\(614\) | −14.0594 | −0.567392 | ||||||||
\(615\) | 23.7357 | 0.957114 | ||||||||
\(616\) | −14.0704 | −0.566914 | ||||||||
\(617\) | 7.44653 | 0.299786 | 0.149893 | − | 0.988702i | \(-0.452107\pi\) | ||||
0.149893 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(618\) | −17.2510 | −0.693935 | ||||||||
\(619\) | −34.9998 | −1.40676 | −0.703380 | − | 0.710814i | \(-0.748327\pi\) | ||||
−0.703380 | + | 0.710814i | \(0.748327\pi\) | |||||||
\(620\) | 22.2657 | 0.894213 | ||||||||
\(621\) | −2.77589 | −0.111393 | ||||||||
\(622\) | −21.9588 | −0.880468 | ||||||||
\(623\) | 11.8334 | 0.474093 | ||||||||
\(624\) | −19.6634 | −0.787168 | ||||||||
\(625\) | −24.4460 | −0.977840 | ||||||||
\(626\) | −28.2441 | −1.12886 | ||||||||
\(627\) | −17.0925 | −0.682610 | ||||||||
\(628\) | −2.47395 | −0.0987213 | ||||||||
\(629\) | −8.99989 | −0.358849 | ||||||||
\(630\) | 14.0010 | 0.557814 | ||||||||
\(631\) | −4.55011 | −0.181137 | −0.0905686 | − | 0.995890i | \(-0.528868\pi\) | ||||
−0.0905686 | + | 0.995890i | \(0.528868\pi\) | |||||||
\(632\) | 7.57992 | 0.301513 | ||||||||
\(633\) | 17.4733 | 0.694502 | ||||||||
\(634\) | −19.5708 | −0.777257 | ||||||||
\(635\) | −21.9674 | −0.871750 | ||||||||
\(636\) | −5.25776 | −0.208484 | ||||||||
\(637\) | −13.6124 | −0.539344 | ||||||||
\(638\) | −36.0576 | −1.42754 | ||||||||
\(639\) | −4.99860 | −0.197741 | ||||||||
\(640\) | 17.2394 | 0.681446 | ||||||||
\(641\) | 15.7780 | 0.623193 | 0.311596 | − | 0.950215i | \(-0.399136\pi\) | ||||
0.311596 | + | 0.950215i | \(0.399136\pi\) | |||||||
\(642\) | −32.2639 | −1.27336 | ||||||||
\(643\) | 13.7775 | 0.543331 | 0.271665 | − | 0.962392i | \(-0.412426\pi\) | ||||
0.271665 | + | 0.962392i | \(0.412426\pi\) | |||||||
\(644\) | −20.5534 | −0.809917 | ||||||||
\(645\) | 11.2723 | 0.443846 | ||||||||
\(646\) | 7.70925 | 0.303316 | ||||||||
\(647\) | 17.9724 | 0.706568 | 0.353284 | − | 0.935516i | \(-0.385065\pi\) | ||||
0.353284 | + | 0.935516i | \(0.385065\pi\) | |||||||
\(648\) | −1.00248 | −0.0393813 | ||||||||
\(649\) | 56.3827 | 2.21322 | ||||||||
\(650\) | −1.59525 | −0.0625708 | ||||||||
\(651\) | 12.1790 | 0.477334 | ||||||||
\(652\) | −23.1867 | −0.908062 | ||||||||
\(653\) | 22.5831 | 0.883745 | 0.441873 | − | 0.897078i | \(-0.354314\pi\) | ||||
0.441873 | + | 0.897078i | \(0.354314\pi\) | |||||||
\(654\) | 20.1888 | 0.789444 | ||||||||
\(655\) | −48.0776 | −1.87855 | ||||||||
\(656\) | 30.3443 | 1.18474 | ||||||||
\(657\) | −16.7937 | −0.655185 | ||||||||
\(658\) | 76.9129 | 2.99838 | ||||||||
\(659\) | −47.4653 | −1.84899 | −0.924493 | − | 0.381200i | \(-0.875511\pi\) | ||||
−0.924493 | + | 0.381200i | \(0.875511\pi\) | |||||||
\(660\) | 25.6598 | 0.998808 | ||||||||
\(661\) | −34.7572 | −1.35190 | −0.675950 | − | 0.736948i | \(-0.736266\pi\) | ||||
−0.675950 | + | 0.736948i | \(0.736266\pi\) | |||||||
\(662\) | 51.7284 | 2.01048 | ||||||||
\(663\) | 6.95442 | 0.270087 | ||||||||
\(664\) | 7.91755 | 0.307261 | ||||||||
\(665\) | 24.1257 | 0.935555 | ||||||||
\(666\) | 19.0363 | 0.737642 | ||||||||
\(667\) | −10.0905 | −0.390707 | ||||||||
\(668\) | −61.3743 | −2.37464 | ||||||||
\(669\) | −25.5231 | −0.986779 | ||||||||
\(670\) | 26.1932 | 1.01193 | ||||||||
\(671\) | −11.6753 | −0.450722 | ||||||||
\(672\) | 23.8999 | 0.921958 | ||||||||
\(673\) | 3.53855 | 0.136401 | 0.0682005 | − | 0.997672i | \(-0.478274\pi\) | ||||
0.0682005 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(674\) | −38.4976 | −1.48287 | ||||||||
\(675\) | 0.108448 | 0.00417417 | ||||||||
\(676\) | 87.4886 | 3.36495 | ||||||||
\(677\) | 37.6929 | 1.44866 | 0.724328 | − | 0.689456i | \(-0.242150\pi\) | ||||
0.724328 | + | 0.689456i | \(0.242150\pi\) | |||||||
\(678\) | 34.3699 | 1.31997 | ||||||||
\(679\) | −20.5149 | −0.787291 | ||||||||
\(680\) | −2.21718 | −0.0850249 | ||||||||
\(681\) | 12.0584 | 0.462078 | ||||||||
\(682\) | 40.3653 | 1.54567 | ||||||||
\(683\) | 12.0601 | 0.461465 | 0.230733 | − | 0.973017i | \(-0.425888\pi\) | ||||
0.230733 | + | 0.973017i | \(0.425888\pi\) | |||||||
\(684\) | −9.01690 | −0.344770 | ||||||||
\(685\) | 2.24407 | 0.0857414 | ||||||||
\(686\) | −31.9222 | −1.21879 | ||||||||
\(687\) | 13.1585 | 0.502027 | ||||||||
\(688\) | 14.4108 | 0.549406 | ||||||||
\(689\) | −14.7799 | −0.563069 | ||||||||
\(690\) | 12.9859 | 0.494364 | ||||||||
\(691\) | 5.84913 | 0.222511 | 0.111256 | − | 0.993792i | \(-0.464513\pi\) | ||||
0.111256 | + | 0.993792i | \(0.464513\pi\) | |||||||
\(692\) | 29.0450 | 1.10413 | ||||||||
\(693\) | 14.0356 | 0.533167 | ||||||||
\(694\) | −18.6326 | −0.707282 | ||||||||
\(695\) | 20.9549 | 0.794865 | ||||||||
\(696\) | −3.64409 | −0.138129 | ||||||||
\(697\) | −10.7319 | −0.406501 | ||||||||
\(698\) | −8.91754 | −0.337534 | ||||||||
\(699\) | 3.11835 | 0.117947 | ||||||||
\(700\) | 0.802978 | 0.0303497 | ||||||||
\(701\) | −38.6454 | −1.45962 | −0.729808 | − | 0.683652i | \(-0.760390\pi\) | ||||
−0.729808 | + | 0.683652i | \(0.760390\pi\) | |||||||
\(702\) | −14.7098 | −0.555185 | ||||||||
\(703\) | 32.8023 | 1.23716 | ||||||||
\(704\) | 52.6922 | 1.98591 | ||||||||
\(705\) | −26.8712 | −1.01203 | ||||||||
\(706\) | 10.5826 | 0.398280 | ||||||||
\(707\) | −30.5331 | −1.14831 | ||||||||
\(708\) | 29.7438 | 1.11784 | ||||||||
\(709\) | 43.4457 | 1.63164 | 0.815819 | − | 0.578308i | \(-0.196287\pi\) | ||||
0.815819 | + | 0.578308i | \(0.196287\pi\) | |||||||
\(710\) | 23.3839 | 0.877582 | ||||||||
\(711\) | −7.56114 | −0.283565 | ||||||||
\(712\) | 3.96364 | 0.148544 | ||||||||
\(713\) | 11.2960 | 0.423039 | ||||||||
\(714\) | −6.33047 | −0.236912 | ||||||||
\(715\) | 72.1313 | 2.69756 | ||||||||
\(716\) | 22.1397 | 0.827398 | ||||||||
\(717\) | −0.545179 | −0.0203601 | ||||||||
\(718\) | 22.2770 | 0.831370 | ||||||||
\(719\) | −20.9423 | −0.781015 | −0.390507 | − | 0.920600i | \(-0.627700\pi\) | ||||
−0.390507 | + | 0.920600i | \(0.627700\pi\) | |||||||
\(720\) | −6.25348 | −0.233054 | ||||||||
\(721\) | 24.4095 | 0.909056 | ||||||||
\(722\) | 12.0901 | 0.449945 | ||||||||
\(723\) | 23.4255 | 0.871203 | ||||||||
\(724\) | 32.2868 | 1.19993 | ||||||||
\(725\) | 0.394216 | 0.0146408 | ||||||||
\(726\) | 23.2516 | 0.862946 | ||||||||
\(727\) | −21.1461 | −0.784264 | −0.392132 | − | 0.919909i | \(-0.628262\pi\) | ||||
−0.392132 | + | 0.919909i | \(0.628262\pi\) | |||||||
\(728\) | −20.8655 | −0.773326 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 78.5626 | 2.90773 | ||||||||
\(731\) | −5.09670 | −0.188508 | ||||||||
\(732\) | −6.15915 | −0.227649 | ||||||||
\(733\) | 23.2197 | 0.857638 | 0.428819 | − | 0.903390i | \(-0.358930\pi\) | ||||
0.428819 | + | 0.903390i | \(0.358930\pi\) | |||||||
\(734\) | −9.27621 | −0.342391 | ||||||||
\(735\) | −4.32911 | −0.159681 | ||||||||
\(736\) | 22.1670 | 0.817088 | ||||||||
\(737\) | 26.2579 | 0.967221 | ||||||||
\(738\) | 22.6999 | 0.835594 | ||||||||
\(739\) | 1.84687 | 0.0679381 | 0.0339690 | − | 0.999423i | \(-0.489185\pi\) | ||||
0.0339690 | + | 0.999423i | \(0.489185\pi\) | |||||||
\(740\) | −49.2438 | −1.81024 | ||||||||
\(741\) | −25.3470 | −0.931147 | ||||||||
\(742\) | 13.4538 | 0.493906 | ||||||||
\(743\) | −2.62844 | −0.0964282 | −0.0482141 | − | 0.998837i | \(-0.515353\pi\) | ||||
−0.0482141 | + | 0.998837i | \(0.515353\pi\) | |||||||
\(744\) | 4.07943 | 0.149559 | ||||||||
\(745\) | −21.7571 | −0.797118 | ||||||||
\(746\) | −22.0135 | −0.805970 | ||||||||
\(747\) | −7.89794 | −0.288971 | ||||||||
\(748\) | −11.6019 | −0.424209 | ||||||||
\(749\) | 45.6523 | 1.66810 | ||||||||
\(750\) | −23.8978 | −0.872624 | ||||||||
\(751\) | −0.923927 | −0.0337146 | −0.0168573 | − | 0.999858i | \(-0.505366\pi\) | ||||
−0.0168573 | + | 0.999858i | \(0.505366\pi\) | |||||||
\(752\) | −34.3528 | −1.25272 | ||||||||
\(753\) | −16.2359 | −0.591670 | ||||||||
\(754\) | −53.4710 | −1.94730 | ||||||||
\(755\) | 27.1440 | 0.987871 | ||||||||
\(756\) | 7.40425 | 0.269290 | ||||||||
\(757\) | 18.1811 | 0.660804 | 0.330402 | − | 0.943840i | \(-0.392816\pi\) | ||||
0.330402 | + | 0.943840i | \(0.392816\pi\) | |||||||
\(758\) | 33.9707 | 1.23387 | ||||||||
\(759\) | 13.0179 | 0.472521 | ||||||||
\(760\) | 8.08103 | 0.293130 | ||||||||
\(761\) | 13.2886 | 0.481710 | 0.240855 | − | 0.970561i | \(-0.422572\pi\) | ||||
0.240855 | + | 0.970561i | \(0.422572\pi\) | |||||||
\(762\) | −21.0088 | −0.761068 | ||||||||
\(763\) | −28.5664 | −1.03417 | ||||||||
\(764\) | 47.8077 | 1.72962 | ||||||||
\(765\) | 2.21169 | 0.0799637 | ||||||||
\(766\) | 54.7478 | 1.97812 | ||||||||
\(767\) | 83.6117 | 3.01904 | ||||||||
\(768\) | −5.98467 | −0.215953 | ||||||||
\(769\) | 15.6726 | 0.565168 | 0.282584 | − | 0.959243i | \(-0.408808\pi\) | ||||
0.282584 | + | 0.959243i | \(0.408808\pi\) | |||||||
\(770\) | −65.6597 | −2.36621 | ||||||||
\(771\) | 31.4934 | 1.13421 | ||||||||
\(772\) | 19.5828 | 0.704800 | ||||||||
\(773\) | −20.3744 | −0.732818 | −0.366409 | − | 0.930454i | \(-0.619413\pi\) | ||||
−0.366409 | + | 0.930454i | \(0.619413\pi\) | |||||||
\(774\) | 10.7804 | 0.387493 | ||||||||
\(775\) | −0.441311 | −0.0158524 | ||||||||
\(776\) | −6.87158 | −0.246675 | ||||||||
\(777\) | −26.9357 | −0.966312 | ||||||||
\(778\) | −37.7499 | −1.35340 | ||||||||
\(779\) | 39.1151 | 1.40144 | ||||||||
\(780\) | 38.0518 | 1.36247 | ||||||||
\(781\) | 23.4416 | 0.838807 | ||||||||
\(782\) | −5.87148 | −0.209964 | ||||||||
\(783\) | 3.63506 | 0.129907 | ||||||||
\(784\) | −5.53444 | −0.197659 | ||||||||
\(785\) | −2.21169 | −0.0789384 | ||||||||
\(786\) | −45.9796 | −1.64004 | ||||||||
\(787\) | −6.38489 | −0.227597 | −0.113798 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113798 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(788\) | 43.5332 | 1.55081 | ||||||||
\(789\) | 12.5384 | 0.446379 | ||||||||
\(790\) | 35.3717 | 1.25847 | ||||||||
\(791\) | −48.6322 | −1.72916 | ||||||||
\(792\) | 4.70129 | 0.167053 | ||||||||
\(793\) | −17.3137 | −0.614829 | ||||||||
\(794\) | −35.2163 | −1.24978 | ||||||||
\(795\) | −4.70039 | −0.166706 | ||||||||
\(796\) | −47.0942 | −1.66921 | ||||||||
\(797\) | −11.4414 | −0.405276 | −0.202638 | − | 0.979254i | \(-0.564951\pi\) | ||||
−0.202638 | + | 0.979254i | \(0.564951\pi\) | |||||||
\(798\) | 23.0729 | 0.816772 | ||||||||
\(799\) | 12.1496 | 0.429823 | ||||||||
\(800\) | −0.866019 | −0.0306184 | ||||||||
\(801\) | −3.95383 | −0.139702 | ||||||||
\(802\) | 8.51629 | 0.300721 | ||||||||
\(803\) | 78.7565 | 2.77926 | ||||||||
\(804\) | 13.8519 | 0.488520 | ||||||||
\(805\) | −18.3745 | −0.647617 | ||||||||
\(806\) | 59.8589 | 2.10844 | ||||||||
\(807\) | 27.3995 | 0.964510 | ||||||||
\(808\) | −10.2272 | −0.359792 | ||||||||
\(809\) | 3.89624 | 0.136985 | 0.0684923 | − | 0.997652i | \(-0.478181\pi\) | ||||
0.0684923 | + | 0.997652i | \(0.478181\pi\) | |||||||
\(810\) | −4.67809 | −0.164371 | ||||||||
\(811\) | −19.7153 | −0.692298 | −0.346149 | − | 0.938179i | \(-0.612511\pi\) | ||||
−0.346149 | + | 0.938179i | \(0.612511\pi\) | |||||||
\(812\) | 26.9149 | 0.944529 | ||||||||
\(813\) | 24.1438 | 0.846761 | ||||||||
\(814\) | −89.2735 | −3.12904 | ||||||||
\(815\) | −20.7287 | −0.726094 | ||||||||
\(816\) | 2.82747 | 0.0989814 | ||||||||
\(817\) | 18.5762 | 0.649897 | ||||||||
\(818\) | 25.9807 | 0.908393 | ||||||||
\(819\) | 20.8138 | 0.727293 | ||||||||
\(820\) | −58.7208 | −2.05062 | ||||||||
\(821\) | 2.43074 | 0.0848334 | 0.0424167 | − | 0.999100i | \(-0.486494\pi\) | ||||
0.0424167 | + | 0.999100i | \(0.486494\pi\) | |||||||
\(822\) | 2.14614 | 0.0748552 | ||||||||
\(823\) | −42.4943 | −1.48126 | −0.740630 | − | 0.671913i | \(-0.765473\pi\) | ||||
−0.740630 | + | 0.671913i | \(0.765473\pi\) | |||||||
\(824\) | 8.17607 | 0.284827 | ||||||||
\(825\) | −0.508583 | −0.0177066 | ||||||||
\(826\) | −76.1101 | −2.64821 | ||||||||
\(827\) | −18.0549 | −0.627831 | −0.313915 | − | 0.949451i | \(-0.601641\pi\) | ||||
−0.313915 | + | 0.949451i | \(0.601641\pi\) | |||||||
\(828\) | 6.86741 | 0.238659 | ||||||||
\(829\) | −22.3010 | −0.774546 | −0.387273 | − | 0.921965i | \(-0.626583\pi\) | ||||
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(830\) | 36.9473 | 1.28246 | ||||||||
\(831\) | −17.7425 | −0.615479 | ||||||||
\(832\) | 78.1390 | 2.70898 | ||||||||
\(833\) | 1.95738 | 0.0678192 | ||||||||
\(834\) | 20.0405 | 0.693945 | ||||||||
\(835\) | −54.8680 | −1.89878 | ||||||||
\(836\) | 42.2860 | 1.46249 | ||||||||
\(837\) | −4.06933 | −0.140656 | ||||||||
\(838\) | −10.4958 | −0.362573 | ||||||||
\(839\) | −46.1079 | −1.59182 | −0.795910 | − | 0.605415i | \(-0.793007\pi\) | ||||
−0.795910 | + | 0.605415i | \(0.793007\pi\) | |||||||
\(840\) | −6.63576 | −0.228956 | ||||||||
\(841\) | −15.7863 | −0.544356 | ||||||||
\(842\) | −11.4154 | −0.393400 | ||||||||
\(843\) | 15.2451 | 0.525069 | ||||||||
\(844\) | −43.2281 | −1.48797 | ||||||||
\(845\) | 78.2139 | 2.69064 | ||||||||
\(846\) | −25.6986 | −0.883535 | ||||||||
\(847\) | −32.9001 | −1.13046 | ||||||||
\(848\) | −6.00909 | −0.206353 | ||||||||
\(849\) | 0.603246 | 0.0207034 | ||||||||
\(850\) | 0.229386 | 0.00786789 | ||||||||
\(851\) | −24.9827 | −0.856397 | ||||||||
\(852\) | 12.3663 | 0.423661 | ||||||||
\(853\) | −35.6243 | −1.21975 | −0.609876 | − | 0.792497i | \(-0.708781\pi\) | ||||
−0.609876 | + | 0.792497i | \(0.708781\pi\) | |||||||
\(854\) | 15.7603 | 0.539308 | ||||||||
\(855\) | −8.06102 | −0.275681 | ||||||||
\(856\) | 15.2915 | 0.522651 | ||||||||
\(857\) | 13.0494 | 0.445758 | 0.222879 | − | 0.974846i | \(-0.428454\pi\) | ||||
0.222879 | + | 0.974846i | \(0.428454\pi\) | |||||||
\(858\) | 68.9837 | 2.35506 | ||||||||
\(859\) | 0.382639 | 0.0130555 | 0.00652773 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652773 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(860\) | −27.8871 | −0.950942 | ||||||||
\(861\) | −32.1195 | −1.09463 | ||||||||
\(862\) | 32.0622 | 1.09204 | ||||||||
\(863\) | 38.0383 | 1.29484 | 0.647419 | − | 0.762134i | \(-0.275848\pi\) | ||||
0.647419 | + | 0.762134i | \(0.275848\pi\) | |||||||
\(864\) | −7.98556 | −0.271674 | ||||||||
\(865\) | 25.9660 | 0.882870 | ||||||||
\(866\) | −15.0344 | −0.510890 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −30.1303 | −1.02269 | ||||||||
\(869\) | 35.4591 | 1.20287 | ||||||||
\(870\) | −17.0052 | −0.576529 | ||||||||
\(871\) | 38.9386 | 1.31938 | ||||||||
\(872\) | −9.56846 | −0.324029 | ||||||||
\(873\) | 6.85456 | 0.231992 | ||||||||
\(874\) | 21.4000 | 0.723867 | ||||||||
\(875\) | 33.8145 | 1.14314 | ||||||||
\(876\) | 41.5468 | 1.40374 | ||||||||
\(877\) | −7.75974 | −0.262028 | −0.131014 | − | 0.991381i | \(-0.541823\pi\) | ||||
−0.131014 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(878\) | −27.7544 | −0.936667 | ||||||||
\(879\) | −12.3145 | −0.415357 | ||||||||
\(880\) | 29.3266 | 0.988600 | ||||||||
\(881\) | −29.7293 | −1.00161 | −0.500803 | − | 0.865561i | \(-0.666962\pi\) | ||||
−0.500803 | + | 0.865561i | \(0.666962\pi\) | |||||||
\(882\) | −4.14019 | −0.139408 | ||||||||
\(883\) | −46.3870 | −1.56105 | −0.780523 | − | 0.625127i | \(-0.785047\pi\) | ||||
−0.780523 | + | 0.625127i | \(0.785047\pi\) | |||||||
\(884\) | −17.2049 | −0.578663 | ||||||||
\(885\) | 26.5907 | 0.893836 | ||||||||
\(886\) | 54.6114 | 1.83471 | ||||||||
\(887\) | 32.1160 | 1.07835 | 0.539175 | − | 0.842194i | \(-0.318736\pi\) | ||||
0.539175 | + | 0.842194i | \(0.318736\pi\) | |||||||
\(888\) | −9.02224 | −0.302767 | ||||||||
\(889\) | 29.7267 | 0.997000 | ||||||||
\(890\) | 18.4964 | 0.620000 | ||||||||
\(891\) | −4.68964 | −0.157109 | ||||||||
\(892\) | 63.1428 | 2.11418 | ||||||||
\(893\) | −44.2823 | −1.48185 | ||||||||
\(894\) | −20.8076 | −0.695911 | ||||||||
\(895\) | 19.7926 | 0.661595 | ||||||||
\(896\) | −23.3286 | −0.779354 | ||||||||
\(897\) | 19.3047 | 0.644565 | ||||||||
\(898\) | 25.8016 | 0.861009 | ||||||||
\(899\) | −14.7923 | −0.493349 | ||||||||
\(900\) | −0.268295 | −0.00894318 | ||||||||
\(901\) | 2.12525 | 0.0708024 | ||||||||
\(902\) | −106.454 | −3.54454 | ||||||||
\(903\) | −15.2539 | −0.507617 | ||||||||
\(904\) | −16.2896 | −0.541784 | ||||||||
\(905\) | 28.8641 | 0.959474 | ||||||||
\(906\) | 25.9595 | 0.862446 | ||||||||
\(907\) | 46.8974 | 1.55720 | 0.778601 | − | 0.627520i | \(-0.215930\pi\) | ||||
0.778601 | + | 0.627520i | \(0.215930\pi\) | |||||||
\(908\) | −29.8318 | −0.990004 | ||||||||
\(909\) | 10.2019 | 0.338375 | ||||||||
\(910\) | −97.3689 | −3.22775 | ||||||||
\(911\) | 40.6151 | 1.34564 | 0.672820 | − | 0.739806i | \(-0.265083\pi\) | ||||
0.672820 | + | 0.739806i | \(0.265083\pi\) | |||||||
\(912\) | −10.3054 | −0.341246 | ||||||||
\(913\) | 37.0385 | 1.22580 | ||||||||
\(914\) | −71.6460 | −2.36984 | ||||||||
\(915\) | −5.50621 | −0.182030 | ||||||||
\(916\) | −32.5534 | −1.07559 | ||||||||
\(917\) | 65.0594 | 2.14845 | ||||||||
\(918\) | 2.11517 | 0.0698111 | ||||||||
\(919\) | 52.3789 | 1.72782 | 0.863910 | − | 0.503647i | \(-0.168009\pi\) | ||||
0.863910 | + | 0.503647i | \(0.168009\pi\) | |||||||
\(920\) | −6.15464 | −0.202913 | ||||||||
\(921\) | −6.64694 | −0.219024 | ||||||||
\(922\) | −62.5296 | −2.05930 | ||||||||
\(923\) | 34.7623 | 1.14422 | ||||||||
\(924\) | −34.7233 | −1.14231 | ||||||||
\(925\) | 0.976022 | 0.0320914 | ||||||||
\(926\) | −58.3665 | −1.91804 | ||||||||
\(927\) | −8.15582 | −0.267872 | ||||||||
\(928\) | −29.0280 | −0.952891 | ||||||||
\(929\) | 25.3934 | 0.833131 | 0.416566 | − | 0.909106i | \(-0.363234\pi\) | ||||
0.416566 | + | 0.909106i | \(0.363234\pi\) | |||||||
\(930\) | 19.0367 | 0.624238 | ||||||||
\(931\) | −7.13414 | −0.233812 | ||||||||
\(932\) | −7.71463 | −0.252701 | ||||||||
\(933\) | −10.3816 | −0.339878 | ||||||||
\(934\) | 6.07671 | 0.198836 | ||||||||
\(935\) | −10.3720 | −0.339201 | ||||||||
\(936\) | 6.97169 | 0.227877 | ||||||||
\(937\) | 34.9127 | 1.14055 | 0.570274 | − | 0.821454i | \(-0.306837\pi\) | ||||
0.570274 | + | 0.821454i | \(0.306837\pi\) | |||||||
\(938\) | −35.4451 | −1.15732 | ||||||||
\(939\) | −13.3531 | −0.435763 | ||||||||
\(940\) | 66.4779 | 2.16827 | ||||||||
\(941\) | 25.4958 | 0.831138 | 0.415569 | − | 0.909562i | \(-0.363582\pi\) | ||||
0.415569 | + | 0.909562i | \(0.363582\pi\) | |||||||
\(942\) | −2.11517 | −0.0689160 | ||||||||
\(943\) | −29.7907 | −0.970118 | ||||||||
\(944\) | 33.9942 | 1.10642 | ||||||||
\(945\) | 6.61933 | 0.215327 | ||||||||
\(946\) | −50.5562 | −1.64372 | ||||||||
\(947\) | −5.90348 | −0.191837 | −0.0959187 | − | 0.995389i | \(-0.530579\pi\) | ||||
−0.0959187 | + | 0.995389i | \(0.530579\pi\) | |||||||
\(948\) | 18.7059 | 0.607539 | ||||||||
\(949\) | 116.791 | 3.79118 | ||||||||
\(950\) | −0.836054 | −0.0271252 | ||||||||
\(951\) | −9.25260 | −0.300036 | ||||||||
\(952\) | 3.00032 | 0.0972409 | ||||||||
\(953\) | 12.0090 | 0.389010 | 0.194505 | − | 0.980902i | \(-0.437690\pi\) | ||||
0.194505 | + | 0.980902i | \(0.437690\pi\) | |||||||
\(954\) | −4.49527 | −0.145540 | ||||||||
\(955\) | 42.7396 | 1.38302 | ||||||||
\(956\) | 1.34875 | 0.0436215 | ||||||||
\(957\) | −17.0471 | −0.551056 | ||||||||
\(958\) | 39.4887 | 1.27582 | ||||||||
\(959\) | −3.03671 | −0.0980604 | ||||||||
\(960\) | 24.8502 | 0.802037 | ||||||||
\(961\) | −14.4406 | −0.465825 | ||||||||
\(962\) | −132.387 | −4.26831 | ||||||||
\(963\) | −15.2536 | −0.491540 | ||||||||
\(964\) | −57.9534 | −1.86655 | ||||||||
\(965\) | 17.5068 | 0.563564 | ||||||||
\(966\) | −17.5727 | −0.565392 | ||||||||
\(967\) | 38.3175 | 1.23221 | 0.616104 | − | 0.787665i | \(-0.288710\pi\) | ||||
0.616104 | + | 0.787665i | \(0.288710\pi\) | |||||||
\(968\) | −11.0201 | −0.354198 | ||||||||
\(969\) | 3.64474 | 0.117086 | ||||||||
\(970\) | −32.0663 | −1.02959 | ||||||||
\(971\) | 2.10520 | 0.0675590 | 0.0337795 | − | 0.999429i | \(-0.489246\pi\) | ||||
0.0337795 | + | 0.999429i | \(0.489246\pi\) | |||||||
\(972\) | −2.47395 | −0.0793520 | ||||||||
\(973\) | −28.3565 | −0.909068 | ||||||||
\(974\) | −41.2292 | −1.32107 | ||||||||
\(975\) | −0.754194 | −0.0241535 | ||||||||
\(976\) | −7.03928 | −0.225322 | ||||||||
\(977\) | 2.62543 | 0.0839948 | 0.0419974 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419974 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(978\) | −19.8241 | −0.633906 | ||||||||
\(979\) | 18.5420 | 0.592606 | ||||||||
\(980\) | 10.7100 | 0.342118 | ||||||||
\(981\) | 9.54476 | 0.304741 | ||||||||
\(982\) | 61.7706 | 1.97118 | ||||||||
\(983\) | −32.0679 | −1.02281 | −0.511404 | − | 0.859340i | \(-0.670874\pi\) | ||||
−0.511404 | + | 0.859340i | \(0.670874\pi\) | |||||||
\(984\) | −10.7586 | −0.342971 | ||||||||
\(985\) | 38.9183 | 1.24004 | ||||||||
\(986\) | 7.68878 | 0.244861 | ||||||||
\(987\) | 36.3625 | 1.15743 | ||||||||
\(988\) | 62.7073 | 1.99498 | ||||||||
\(989\) | −14.1479 | −0.449877 | ||||||||
\(990\) | 21.9386 | 0.697254 | ||||||||
\(991\) | −25.0986 | −0.797283 | −0.398642 | − | 0.917107i | \(-0.630518\pi\) | ||||
−0.398642 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(992\) | 32.4958 | 1.03174 | ||||||||
\(993\) | 24.4559 | 0.776084 | ||||||||
\(994\) | −31.6435 | −1.00367 | ||||||||
\(995\) | −42.1018 | −1.33472 | ||||||||
\(996\) | 19.5391 | 0.619120 | ||||||||
\(997\) | 36.6615 | 1.16108 | 0.580540 | − | 0.814231i | \(-0.302841\pi\) | ||||
0.580540 | + | 0.814231i | \(0.302841\pi\) | |||||||
\(998\) | 84.4626 | 2.67362 | ||||||||
\(999\) | 8.99989 | 0.284744 |
(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 | 8007.2.a.j.1.11 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.11 | ✓ | 64 | 1.1 | even | 1 | trivial |