Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.692297\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.69230 | −1.20403 | −0.602016 | − | 0.798484i | \(-0.705636\pi\) | ||||
−0.602016 | + | 0.798484i | \(0.705636\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.69230 | 0.851379 | ||||||||
\(11\) | −4.49978 | −1.35673 | −0.678367 | − | 0.734723i | \(-0.737312\pi\) | ||||
−0.678367 | + | 0.734723i | \(0.737312\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.69230 | 0.695148 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.88438 | −1.91224 | −0.956121 | − | 0.292972i | \(-0.905356\pi\) | ||||
−0.956121 | + | 0.292972i | \(0.905356\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.03500 | −1.38452 | −0.692262 | − | 0.721646i | \(-0.743386\pi\) | ||||
−0.692262 | + | 0.721646i | \(0.743386\pi\) | |||||||
\(20\) | −2.69230 | −0.602016 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.49978 | 0.959356 | ||||||||
\(23\) | 2.65041 | 0.552649 | 0.276324 | − | 0.961064i | \(-0.410884\pi\) | ||||
0.276324 | + | 0.961064i | \(0.410884\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.24846 | 0.449693 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.64173 | −0.304862 | −0.152431 | − | 0.988314i | \(-0.548710\pi\) | ||||
−0.152431 | + | 0.988314i | \(0.548710\pi\) | |||||||
\(30\) | −2.69230 | −0.491544 | ||||||||
\(31\) | −1.84937 | −0.332157 | −0.166078 | − | 0.986113i | \(-0.553110\pi\) | ||||
−0.166078 | + | 0.986113i | \(0.553110\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.49978 | 0.783311 | ||||||||
\(34\) | 7.88438 | 1.35216 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.44922 | −0.895846 | −0.447923 | − | 0.894072i | \(-0.647836\pi\) | ||||
−0.447923 | + | 0.894072i | \(0.647836\pi\) | |||||||
\(38\) | 6.03500 | 0.979007 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.69230 | 0.425690 | ||||||||
\(41\) | −3.56484 | −0.556735 | −0.278367 | − | 0.960475i | \(-0.589793\pi\) | ||||
−0.278367 | + | 0.960475i | \(0.589793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.34959 | 0.205811 | 0.102905 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102905 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(44\) | −4.49978 | −0.678367 | ||||||||
\(45\) | −2.69230 | −0.401344 | ||||||||
\(46\) | −2.65041 | −0.390782 | ||||||||
\(47\) | 3.16246 | 0.461292 | 0.230646 | − | 0.973038i | \(-0.425916\pi\) | ||||
0.230646 | + | 0.973038i | \(0.425916\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.24846 | −0.317981 | ||||||||
\(51\) | 7.88438 | 1.10403 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −5.16246 | −0.709118 | −0.354559 | − | 0.935034i | \(-0.615369\pi\) | ||||
−0.354559 | + | 0.935034i | \(0.615369\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 12.1147 | 1.63355 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.03500 | 0.799356 | ||||||||
\(58\) | 1.64173 | 0.215570 | ||||||||
\(59\) | −13.4643 | −1.75291 | −0.876454 | − | 0.481486i | \(-0.840097\pi\) | ||||
−0.876454 | + | 0.481486i | \(0.840097\pi\) | |||||||
\(60\) | 2.69230 | 0.347574 | ||||||||
\(61\) | 14.6290 | 1.87306 | 0.936528 | − | 0.350594i | \(-0.114020\pi\) | ||||
0.936528 | + | 0.350594i | \(0.114020\pi\) | |||||||
\(62\) | 1.84937 | 0.234870 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.69230 | −0.333938 | ||||||||
\(66\) | −4.49978 | −0.553885 | ||||||||
\(67\) | 4.85805 | 0.593505 | 0.296752 | − | 0.954954i | \(-0.404096\pi\) | ||||
0.296752 | + | 0.954954i | \(0.404096\pi\) | |||||||
\(68\) | −7.88438 | −0.956121 | ||||||||
\(69\) | −2.65041 | −0.319072 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.80748 | 0.214509 | 0.107254 | − | 0.994232i | \(-0.465794\pi\) | ||||
0.107254 | + | 0.994232i | \(0.465794\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.9641 | −1.86846 | −0.934229 | − | 0.356673i | \(-0.883911\pi\) | ||||
−0.934229 | + | 0.356673i | \(0.883911\pi\) | |||||||
\(74\) | 5.44922 | 0.633459 | ||||||||
\(75\) | −2.24846 | −0.259630 | ||||||||
\(76\) | −6.03500 | −0.692262 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.89126 | −0.662818 | −0.331409 | − | 0.943487i | \(-0.607524\pi\) | ||||
−0.331409 | + | 0.943487i | \(0.607524\pi\) | |||||||
\(80\) | −2.69230 | −0.301008 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.56484 | 0.393671 | ||||||||
\(83\) | −3.72774 | −0.409173 | −0.204586 | − | 0.978849i | \(-0.565585\pi\) | ||||
−0.204586 | + | 0.978849i | \(0.565585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.2271 | 2.30240 | ||||||||
\(86\) | −1.34959 | −0.145530 | ||||||||
\(87\) | 1.64173 | 0.176012 | ||||||||
\(88\) | 4.49978 | 0.479678 | ||||||||
\(89\) | −12.7569 | −1.35223 | −0.676115 | − | 0.736796i | \(-0.736338\pi\) | ||||
−0.676115 | + | 0.736796i | \(0.736338\pi\) | |||||||
\(90\) | 2.69230 | 0.283793 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.65041 | 0.276324 | ||||||||
\(93\) | 1.84937 | 0.191771 | ||||||||
\(94\) | −3.16246 | −0.326183 | ||||||||
\(95\) | 16.2480 | 1.66701 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.28347 | −0.536455 | −0.268228 | − | 0.963356i | \(-0.586438\pi\) | ||||
−0.268228 | + | 0.963356i | \(0.586438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.49978 | −0.452245 | ||||||||
\(100\) | 2.24846 | 0.224846 | ||||||||
\(101\) | 2.27988 | 0.226856 | 0.113428 | − | 0.993546i | \(-0.463817\pi\) | ||||
0.113428 | + | 0.993546i | \(0.463817\pi\) | |||||||
\(102\) | −7.88438 | −0.780669 | ||||||||
\(103\) | −2.57890 | −0.254107 | −0.127053 | − | 0.991896i | \(-0.540552\pi\) | ||||
−0.127053 | + | 0.991896i | \(0.540552\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.16246 | 0.501422 | ||||||||
\(107\) | −13.7146 | −1.32584 | −0.662920 | − | 0.748690i | \(-0.730683\pi\) | ||||
−0.662920 | + | 0.748690i | \(0.730683\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.1653 | 1.45257 | 0.726287 | − | 0.687392i | \(-0.241245\pi\) | ||||
0.726287 | + | 0.687392i | \(0.241245\pi\) | |||||||
\(110\) | −12.1147 | −1.15510 | ||||||||
\(111\) | 5.44922 | 0.517217 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.71969 | 0.443991 | 0.221995 | − | 0.975048i | \(-0.428743\pi\) | ||||
0.221995 | + | 0.975048i | \(0.428743\pi\) | |||||||
\(114\) | −6.03500 | −0.565230 | ||||||||
\(115\) | −7.13569 | −0.665407 | ||||||||
\(116\) | −1.64173 | −0.152431 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 13.4643 | 1.23949 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.69230 | −0.245772 | ||||||||
\(121\) | 9.24803 | 0.840730 | ||||||||
\(122\) | −14.6290 | −1.32445 | ||||||||
\(123\) | 3.56484 | 0.321431 | ||||||||
\(124\) | −1.84937 | −0.166078 | ||||||||
\(125\) | 7.40795 | 0.662587 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.67736 | −0.858727 | −0.429363 | − | 0.903132i | \(-0.641262\pi\) | ||||
−0.429363 | + | 0.903132i | \(0.641262\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.34959 | −0.118825 | ||||||||
\(130\) | 2.69230 | 0.236130 | ||||||||
\(131\) | −9.90173 | −0.865118 | −0.432559 | − | 0.901606i | \(-0.642389\pi\) | ||||
−0.432559 | + | 0.901606i | \(0.642389\pi\) | |||||||
\(132\) | 4.49978 | 0.391656 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.85805 | −0.419671 | ||||||||
\(135\) | 2.69230 | 0.231716 | ||||||||
\(136\) | 7.88438 | 0.676080 | ||||||||
\(137\) | 13.5702 | 1.15938 | 0.579691 | − | 0.814836i | \(-0.303173\pi\) | ||||
0.579691 | + | 0.814836i | \(0.303173\pi\) | |||||||
\(138\) | 2.65041 | 0.225618 | ||||||||
\(139\) | −1.08780 | −0.0922658 | −0.0461329 | − | 0.998935i | \(-0.514690\pi\) | ||||
−0.0461329 | + | 0.998935i | \(0.514690\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.16246 | −0.266327 | ||||||||
\(142\) | −1.80748 | −0.151681 | ||||||||
\(143\) | −4.49978 | −0.376291 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.42004 | 0.367064 | ||||||||
\(146\) | 15.9641 | 1.32120 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.44922 | −0.447923 | ||||||||
\(149\) | −4.55617 | −0.373256 | −0.186628 | − | 0.982431i | \(-0.559756\pi\) | ||||
−0.186628 | + | 0.982431i | \(0.559756\pi\) | |||||||
\(150\) | 2.24846 | 0.183586 | ||||||||
\(151\) | −2.78369 | −0.226533 | −0.113267 | − | 0.993565i | \(-0.536131\pi\) | ||||
−0.113267 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(152\) | 6.03500 | 0.489503 | ||||||||
\(153\) | −7.88438 | −0.637414 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.97906 | 0.399927 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 1.22796 | 0.0980019 | 0.0490009 | − | 0.998799i | \(-0.484396\pi\) | ||||
0.0490009 | + | 0.998799i | \(0.484396\pi\) | |||||||
\(158\) | 5.89126 | 0.468683 | ||||||||
\(159\) | 5.16246 | 0.409410 | ||||||||
\(160\) | 2.69230 | 0.212845 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −19.5047 | −1.52773 | −0.763864 | − | 0.645377i | \(-0.776700\pi\) | ||||
−0.763864 | + | 0.645377i | \(0.776700\pi\) | |||||||
\(164\) | −3.56484 | −0.278367 | ||||||||
\(165\) | −12.1147 | −0.943132 | ||||||||
\(166\) | 3.72774 | 0.289329 | ||||||||
\(167\) | 25.3686 | 1.96308 | 0.981541 | − | 0.191254i | \(-0.0612555\pi\) | ||||
0.981541 | + | 0.191254i | \(0.0612555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −21.2271 | −1.62804 | ||||||||
\(171\) | −6.03500 | −0.461508 | ||||||||
\(172\) | 1.34959 | 0.102905 | ||||||||
\(173\) | −17.6355 | −1.34080 | −0.670400 | − | 0.742000i | \(-0.733877\pi\) | ||||
−0.670400 | + | 0.742000i | \(0.733877\pi\) | |||||||
\(174\) | −1.64173 | −0.124460 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.49978 | −0.339184 | ||||||||
\(177\) | 13.4643 | 1.01204 | ||||||||
\(178\) | 12.7569 | 0.956172 | ||||||||
\(179\) | 8.41377 | 0.628875 | 0.314438 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314438 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(180\) | −2.69230 | −0.200672 | ||||||||
\(181\) | 16.1119 | 1.19759 | 0.598794 | − | 0.800903i | \(-0.295647\pi\) | ||||
0.598794 | + | 0.800903i | \(0.295647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6290 | −1.08141 | ||||||||
\(184\) | −2.65041 | −0.195391 | ||||||||
\(185\) | 14.6709 | 1.07863 | ||||||||
\(186\) | −1.84937 | −0.135602 | ||||||||
\(187\) | 35.4780 | 2.59441 | ||||||||
\(188\) | 3.16246 | 0.230646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2480 | −1.17876 | ||||||||
\(191\) | 17.2766 | 1.25009 | 0.625045 | − | 0.780589i | \(-0.285081\pi\) | ||||
0.625045 | + | 0.780589i | \(0.285081\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.2211 | 0.807711 | 0.403855 | − | 0.914823i | \(-0.367670\pi\) | ||||
0.403855 | + | 0.914823i | \(0.367670\pi\) | |||||||
\(194\) | 5.28347 | 0.379331 | ||||||||
\(195\) | 2.69230 | 0.192799 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.5940 | 1.60976 | 0.804879 | − | 0.593439i | \(-0.202230\pi\) | ||||
0.804879 | + | 0.593439i | \(0.202230\pi\) | |||||||
\(198\) | 4.49978 | 0.319785 | ||||||||
\(199\) | 19.9635 | 1.41517 | 0.707587 | − | 0.706626i | \(-0.249784\pi\) | ||||
0.707587 | + | 0.706626i | \(0.249784\pi\) | |||||||
\(200\) | −2.24846 | −0.158990 | ||||||||
\(201\) | −4.85805 | −0.342660 | ||||||||
\(202\) | −2.27988 | −0.160412 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.88438 | 0.552017 | ||||||||
\(205\) | 9.59762 | 0.670327 | ||||||||
\(206\) | 2.57890 | 0.179681 | ||||||||
\(207\) | 2.65041 | 0.184216 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 27.1562 | 1.87843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2364 | −1.25544 | −0.627722 | − | 0.778438i | \(-0.716013\pi\) | ||||
−0.627722 | + | 0.778438i | \(0.716013\pi\) | |||||||
\(212\) | −5.16246 | −0.354559 | ||||||||
\(213\) | −1.80748 | −0.123847 | ||||||||
\(214\) | 13.7146 | 0.937510 | ||||||||
\(215\) | −3.63350 | −0.247803 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.1653 | −1.02712 | ||||||||
\(219\) | 15.9641 | 1.07876 | ||||||||
\(220\) | 12.1147 | 0.816776 | ||||||||
\(221\) | −7.88438 | −0.530360 | ||||||||
\(222\) | −5.44922 | −0.365728 | ||||||||
\(223\) | −11.7442 | −0.786451 | −0.393225 | − | 0.919442i | \(-0.628641\pi\) | ||||
−0.393225 | + | 0.919442i | \(0.628641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.24846 | 0.149898 | ||||||||
\(226\) | −4.71969 | −0.313949 | ||||||||
\(227\) | 15.5170 | 1.02990 | 0.514950 | − | 0.857220i | \(-0.327811\pi\) | ||||
0.514950 | + | 0.857220i | \(0.327811\pi\) | |||||||
\(228\) | 6.03500 | 0.399678 | ||||||||
\(229\) | −5.13284 | −0.339188 | −0.169594 | − | 0.985514i | \(-0.554246\pi\) | ||||
−0.169594 | + | 0.985514i | \(0.554246\pi\) | |||||||
\(230\) | 7.13569 | 0.470514 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.64173 | 0.107785 | ||||||||
\(233\) | 27.7861 | 1.82033 | 0.910164 | − | 0.414248i | \(-0.135955\pi\) | ||||
0.910164 | + | 0.414248i | \(0.135955\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −8.51428 | −0.555410 | ||||||||
\(236\) | −13.4643 | −0.876454 | ||||||||
\(237\) | 5.89126 | 0.382678 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.54811 | 0.488247 | 0.244123 | − | 0.969744i | \(-0.421500\pi\) | ||||
0.244123 | + | 0.969744i | \(0.421500\pi\) | |||||||
\(240\) | 2.69230 | 0.173787 | ||||||||
\(241\) | −28.7857 | −1.85425 | −0.927124 | − | 0.374755i | \(-0.877727\pi\) | ||||
−0.927124 | + | 0.374755i | \(0.877727\pi\) | |||||||
\(242\) | −9.24803 | −0.594486 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.6290 | 0.936528 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.56484 | −0.227286 | ||||||||
\(247\) | −6.03500 | −0.383998 | ||||||||
\(248\) | 1.84937 | 0.117435 | ||||||||
\(249\) | 3.72774 | 0.236236 | ||||||||
\(250\) | −7.40795 | −0.468520 | ||||||||
\(251\) | −23.6112 | −1.49033 | −0.745164 | − | 0.666881i | \(-0.767629\pi\) | ||||
−0.745164 | + | 0.666881i | \(0.767629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9263 | −0.749798 | ||||||||
\(254\) | 9.67736 | 0.607212 | ||||||||
\(255\) | −21.2271 | −1.32929 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.31415 | 0.518622 | 0.259311 | − | 0.965794i | \(-0.416504\pi\) | ||||
0.259311 | + | 0.965794i | \(0.416504\pi\) | |||||||
\(258\) | 1.34959 | 0.0840218 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.69230 | −0.166969 | ||||||||
\(261\) | −1.64173 | −0.101621 | ||||||||
\(262\) | 9.90173 | 0.611731 | ||||||||
\(263\) | 10.8877 | 0.671362 | 0.335681 | − | 0.941976i | \(-0.391034\pi\) | ||||
0.335681 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(264\) | −4.49978 | −0.276942 | ||||||||
\(265\) | 13.8989 | 0.853801 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7569 | 0.780711 | ||||||||
\(268\) | 4.85805 | 0.296752 | ||||||||
\(269\) | −22.0486 | −1.34433 | −0.672164 | − | 0.740402i | \(-0.734635\pi\) | ||||
−0.672164 | + | 0.740402i | \(0.734635\pi\) | |||||||
\(270\) | −2.69230 | −0.163848 | ||||||||
\(271\) | 19.9613 | 1.21256 | 0.606280 | − | 0.795251i | \(-0.292661\pi\) | ||||
0.606280 | + | 0.795251i | \(0.292661\pi\) | |||||||
\(272\) | −7.88438 | −0.478060 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.5702 | −0.819807 | ||||||||
\(275\) | −10.1176 | −0.610114 | ||||||||
\(276\) | −2.65041 | −0.159536 | ||||||||
\(277\) | 6.76157 | 0.406264 | 0.203132 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203132 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(278\) | 1.08780 | 0.0652418 | ||||||||
\(279\) | −1.84937 | −0.110719 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.69830 | −0.518897 | −0.259449 | − | 0.965757i | \(-0.583541\pi\) | ||||
−0.259449 | + | 0.965757i | \(0.583541\pi\) | |||||||
\(282\) | 3.16246 | 0.188322 | ||||||||
\(283\) | 13.3556 | 0.793908 | 0.396954 | − | 0.917839i | \(-0.370067\pi\) | ||||
0.396954 | + | 0.917839i | \(0.370067\pi\) | |||||||
\(284\) | 1.80748 | 0.107254 | ||||||||
\(285\) | −16.2480 | −0.962450 | ||||||||
\(286\) | 4.49978 | 0.266078 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 45.1634 | 2.65667 | ||||||||
\(290\) | −4.42004 | −0.259554 | ||||||||
\(291\) | 5.28347 | 0.309722 | ||||||||
\(292\) | −15.9641 | −0.934229 | ||||||||
\(293\) | −30.5553 | −1.78506 | −0.892530 | − | 0.450989i | \(-0.851071\pi\) | ||||
−0.892530 | + | 0.450989i | \(0.851071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.2500 | 2.11056 | ||||||||
\(296\) | 5.44922 | 0.316729 | ||||||||
\(297\) | 4.49978 | 0.261104 | ||||||||
\(298\) | 4.55617 | 0.263932 | ||||||||
\(299\) | 2.65041 | 0.153277 | ||||||||
\(300\) | −2.24846 | −0.129815 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.78369 | 0.160183 | ||||||||
\(303\) | −2.27988 | −0.130975 | ||||||||
\(304\) | −6.03500 | −0.346131 | ||||||||
\(305\) | −39.3857 | −2.25522 | ||||||||
\(306\) | 7.88438 | 0.450720 | ||||||||
\(307\) | 12.6145 | 0.719949 | 0.359975 | − | 0.932962i | \(-0.382785\pi\) | ||||
0.359975 | + | 0.932962i | \(0.382785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.57890 | 0.146709 | ||||||||
\(310\) | −4.97906 | −0.282791 | ||||||||
\(311\) | 10.6746 | 0.605303 | 0.302652 | − | 0.953101i | \(-0.402128\pi\) | ||||
0.302652 | + | 0.953101i | \(0.402128\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 13.2604 | 0.749524 | 0.374762 | − | 0.927121i | \(-0.377724\pi\) | ||||
0.374762 | + | 0.927121i | \(0.377724\pi\) | |||||||
\(314\) | −1.22796 | −0.0692978 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89126 | −0.331409 | ||||||||
\(317\) | −22.1743 | −1.24543 | −0.622716 | − | 0.782448i | \(-0.713971\pi\) | ||||
−0.622716 | + | 0.782448i | \(0.713971\pi\) | |||||||
\(318\) | −5.16246 | −0.289496 | ||||||||
\(319\) | 7.38745 | 0.413618 | ||||||||
\(320\) | −2.69230 | −0.150504 | ||||||||
\(321\) | 13.7146 | 0.765474 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.5822 | 2.64755 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.24846 | 0.124722 | ||||||||
\(326\) | 19.5047 | 1.08027 | ||||||||
\(327\) | −15.1653 | −0.838644 | ||||||||
\(328\) | 3.56484 | 0.196836 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.1147 | 0.666895 | ||||||||
\(331\) | −32.1523 | −1.76725 | −0.883625 | − | 0.468196i | \(-0.844904\pi\) | ||||
−0.883625 | + | 0.468196i | \(0.844904\pi\) | |||||||
\(332\) | −3.72774 | −0.204586 | ||||||||
\(333\) | −5.44922 | −0.298615 | ||||||||
\(334\) | −25.3686 | −1.38811 | ||||||||
\(335\) | −13.0793 | −0.714599 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.13657 | 0.497701 | 0.248850 | − | 0.968542i | \(-0.419947\pi\) | ||||
0.248850 | + | 0.968542i | \(0.419947\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −4.71969 | −0.256338 | ||||||||
\(340\) | 21.2271 | 1.15120 | ||||||||
\(341\) | 8.32176 | 0.450649 | ||||||||
\(342\) | 6.03500 | 0.326336 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.34959 | −0.0727650 | ||||||||
\(345\) | 7.13569 | 0.384173 | ||||||||
\(346\) | 17.6355 | 0.948089 | ||||||||
\(347\) | −6.45566 | −0.346558 | −0.173279 | − | 0.984873i | \(-0.555436\pi\) | ||||
−0.173279 | + | 0.984873i | \(0.555436\pi\) | |||||||
\(348\) | 1.64173 | 0.0880062 | ||||||||
\(349\) | 18.0971 | 0.968715 | 0.484358 | − | 0.874870i | \(-0.339053\pi\) | ||||
0.484358 | + | 0.874870i | \(0.339053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 4.49978 | 0.239839 | ||||||||
\(353\) | 15.3091 | 0.814819 | 0.407409 | − | 0.913246i | \(-0.366432\pi\) | ||||
0.407409 | + | 0.913246i | \(0.366432\pi\) | |||||||
\(354\) | −13.4643 | −0.715621 | ||||||||
\(355\) | −4.86628 | −0.258275 | ||||||||
\(356\) | −12.7569 | −0.676115 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.41377 | −0.444682 | ||||||||
\(359\) | −5.01691 | −0.264782 | −0.132391 | − | 0.991198i | \(-0.542266\pi\) | ||||
−0.132391 | + | 0.991198i | \(0.542266\pi\) | |||||||
\(360\) | 2.69230 | 0.141897 | ||||||||
\(361\) | 17.4213 | 0.916909 | ||||||||
\(362\) | −16.1119 | −0.846822 | ||||||||
\(363\) | −9.24803 | −0.485395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.9802 | 2.24968 | ||||||||
\(366\) | 14.6290 | 0.764672 | ||||||||
\(367\) | 10.5644 | 0.551457 | 0.275729 | − | 0.961235i | \(-0.411081\pi\) | ||||
0.275729 | + | 0.961235i | \(0.411081\pi\) | |||||||
\(368\) | 2.65041 | 0.138162 | ||||||||
\(369\) | −3.56484 | −0.185578 | ||||||||
\(370\) | −14.6709 | −0.762705 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.84937 | 0.0958854 | ||||||||
\(373\) | −7.53435 | −0.390114 | −0.195057 | − | 0.980792i | \(-0.562489\pi\) | ||||
−0.195057 | + | 0.980792i | \(0.562489\pi\) | |||||||
\(374\) | −35.4780 | −1.83452 | ||||||||
\(375\) | −7.40795 | −0.382545 | ||||||||
\(376\) | −3.16246 | −0.163091 | ||||||||
\(377\) | −1.64173 | −0.0845536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3541 | −1.50782 | −0.753909 | − | 0.656978i | \(-0.771834\pi\) | ||||
−0.753909 | + | 0.656978i | \(0.771834\pi\) | |||||||
\(380\) | 16.2480 | 0.833506 | ||||||||
\(381\) | 9.67736 | 0.495786 | ||||||||
\(382\) | −17.2766 | −0.883947 | ||||||||
\(383\) | 14.4564 | 0.738687 | 0.369344 | − | 0.929293i | \(-0.379583\pi\) | ||||
0.369344 | + | 0.929293i | \(0.379583\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2211 | −0.571138 | ||||||||
\(387\) | 1.34959 | 0.0686035 | ||||||||
\(388\) | −5.28347 | −0.268228 | ||||||||
\(389\) | −20.1504 | −1.02166 | −0.510832 | − | 0.859680i | \(-0.670663\pi\) | ||||
−0.510832 | + | 0.859680i | \(0.670663\pi\) | |||||||
\(390\) | −2.69230 | −0.136330 | ||||||||
\(391\) | −20.8968 | −1.05680 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.90173 | 0.499476 | ||||||||
\(394\) | −22.5940 | −1.13827 | ||||||||
\(395\) | 15.8610 | 0.798054 | ||||||||
\(396\) | −4.49978 | −0.226122 | ||||||||
\(397\) | 19.5860 | 0.982992 | 0.491496 | − | 0.870880i | \(-0.336450\pi\) | ||||
0.491496 | + | 0.870880i | \(0.336450\pi\) | |||||||
\(398\) | −19.9635 | −1.00068 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.24846 | 0.112423 | ||||||||
\(401\) | 15.6987 | 0.783958 | 0.391979 | − | 0.919974i | \(-0.371791\pi\) | ||||
0.391979 | + | 0.919974i | \(0.371791\pi\) | |||||||
\(402\) | 4.85805 | 0.242297 | ||||||||
\(403\) | −1.84937 | −0.0921237 | ||||||||
\(404\) | 2.27988 | 0.113428 | ||||||||
\(405\) | −2.69230 | −0.133781 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.5203 | 1.21543 | ||||||||
\(408\) | −7.88438 | −0.390335 | ||||||||
\(409\) | −26.9161 | −1.33091 | −0.665457 | − | 0.746436i | \(-0.731764\pi\) | ||||
−0.665457 | + | 0.746436i | \(0.731764\pi\) | |||||||
\(410\) | −9.59762 | −0.473992 | ||||||||
\(411\) | −13.5702 | −0.669370 | ||||||||
\(412\) | −2.57890 | −0.127053 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.65041 | −0.130261 | ||||||||
\(415\) | 10.0362 | 0.492657 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 1.08780 | 0.0532697 | ||||||||
\(418\) | −27.1562 | −1.32825 | ||||||||
\(419\) | −23.1735 | −1.13210 | −0.566051 | − | 0.824370i | \(-0.691529\pi\) | ||||
−0.566051 | + | 0.824370i | \(0.691529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.04969 | −0.246107 | −0.123053 | − | 0.992400i | \(-0.539269\pi\) | ||||
−0.123053 | + | 0.992400i | \(0.539269\pi\) | |||||||
\(422\) | 18.2364 | 0.887733 | ||||||||
\(423\) | 3.16246 | 0.153764 | ||||||||
\(424\) | 5.16246 | 0.250711 | ||||||||
\(425\) | −17.7277 | −0.859922 | ||||||||
\(426\) | 1.80748 | 0.0875729 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.7146 | −0.662920 | ||||||||
\(429\) | 4.49978 | 0.217251 | ||||||||
\(430\) | 3.63350 | 0.175223 | ||||||||
\(431\) | 23.5665 | 1.13516 | 0.567579 | − | 0.823319i | \(-0.307880\pi\) | ||||
0.567579 | + | 0.823319i | \(0.307880\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 36.0319 | 1.73158 | 0.865791 | − | 0.500405i | \(-0.166816\pi\) | ||||
0.865791 | + | 0.500405i | \(0.166816\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.42004 | −0.211925 | ||||||||
\(436\) | 15.1653 | 0.726287 | ||||||||
\(437\) | −15.9952 | −0.765156 | ||||||||
\(438\) | −15.9641 | −0.762795 | ||||||||
\(439\) | 26.1939 | 1.25017 | 0.625083 | − | 0.780559i | \(-0.285065\pi\) | ||||
0.625083 | + | 0.780559i | \(0.285065\pi\) | |||||||
\(440\) | −12.1147 | −0.577548 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.88438 | 0.375021 | ||||||||
\(443\) | −13.6304 | −0.647599 | −0.323800 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323800 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(444\) | 5.44922 | 0.258608 | ||||||||
\(445\) | 34.3454 | 1.62813 | ||||||||
\(446\) | 11.7442 | 0.556105 | ||||||||
\(447\) | 4.55617 | 0.215499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.28274 | 0.249308 | 0.124654 | − | 0.992200i | \(-0.460218\pi\) | ||||
0.124654 | + | 0.992200i | \(0.460218\pi\) | |||||||
\(450\) | −2.24846 | −0.105994 | ||||||||
\(451\) | 16.0410 | 0.755342 | ||||||||
\(452\) | 4.71969 | 0.221995 | ||||||||
\(453\) | 2.78369 | 0.130789 | ||||||||
\(454\) | −15.5170 | −0.728249 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.03500 | −0.282615 | ||||||||
\(457\) | 34.4510 | 1.61155 | 0.805775 | − | 0.592222i | \(-0.201749\pi\) | ||||
0.805775 | + | 0.592222i | \(0.201749\pi\) | |||||||
\(458\) | 5.13284 | 0.239842 | ||||||||
\(459\) | 7.88438 | 0.368011 | ||||||||
\(460\) | −7.13569 | −0.332703 | ||||||||
\(461\) | 36.7860 | 1.71329 | 0.856647 | − | 0.515904i | \(-0.172544\pi\) | ||||
0.856647 | + | 0.515904i | \(0.172544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.95694 | −0.137421 | −0.0687103 | − | 0.997637i | \(-0.521888\pi\) | ||||
−0.0687103 | + | 0.997637i | \(0.521888\pi\) | |||||||
\(464\) | −1.64173 | −0.0762156 | ||||||||
\(465\) | −4.97906 | −0.230898 | ||||||||
\(466\) | −27.7861 | −1.28717 | ||||||||
\(467\) | 35.3821 | 1.63729 | 0.818644 | − | 0.574301i | \(-0.194726\pi\) | ||||
0.818644 | + | 0.574301i | \(0.194726\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.51428 | 0.392734 | ||||||||
\(471\) | −1.22796 | −0.0565814 | ||||||||
\(472\) | 13.4643 | 0.619746 | ||||||||
\(473\) | −6.07286 | −0.279230 | ||||||||
\(474\) | −5.89126 | −0.270594 | ||||||||
\(475\) | −13.5695 | −0.622611 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.16246 | −0.236373 | ||||||||
\(478\) | −7.54811 | −0.345243 | ||||||||
\(479\) | −27.9002 | −1.27479 | −0.637397 | − | 0.770536i | \(-0.719989\pi\) | ||||
−0.637397 | + | 0.770536i | \(0.719989\pi\) | |||||||
\(480\) | −2.69230 | −0.122886 | ||||||||
\(481\) | −5.44922 | −0.248463 | ||||||||
\(482\) | 28.7857 | 1.31115 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.24803 | 0.420365 | ||||||||
\(485\) | 14.2247 | 0.645909 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 9.04057 | 0.409667 | 0.204834 | − | 0.978797i | \(-0.434335\pi\) | ||||
0.204834 | + | 0.978797i | \(0.434335\pi\) | |||||||
\(488\) | −14.6290 | −0.662225 | ||||||||
\(489\) | 19.5047 | 0.882034 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.3219 | −1.41354 | −0.706770 | − | 0.707444i | \(-0.749848\pi\) | ||||
−0.706770 | + | 0.707444i | \(0.749848\pi\) | |||||||
\(492\) | 3.56484 | 0.160716 | ||||||||
\(493\) | 12.9441 | 0.582971 | ||||||||
\(494\) | 6.03500 | 0.271528 | ||||||||
\(495\) | 12.1147 | 0.544517 | ||||||||
\(496\) | −1.84937 | −0.0830392 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.72774 | −0.167044 | ||||||||
\(499\) | −2.46943 | −0.110547 | −0.0552734 | − | 0.998471i | \(-0.517603\pi\) | ||||
−0.0552734 | + | 0.998471i | \(0.517603\pi\) | |||||||
\(500\) | 7.40795 | 0.331294 | ||||||||
\(501\) | −25.3686 | −1.13339 | ||||||||
\(502\) | 23.6112 | 1.05382 | ||||||||
\(503\) | −0.193757 | −0.00863921 | −0.00431961 | − | 0.999991i | \(-0.501375\pi\) | ||||
−0.00431961 | + | 0.999991i | \(0.501375\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.13810 | −0.273142 | ||||||||
\(506\) | 11.9263 | 0.530187 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −9.67736 | −0.429363 | ||||||||
\(509\) | −37.2347 | −1.65040 | −0.825200 | − | 0.564841i | \(-0.808937\pi\) | ||||
−0.825200 | + | 0.564841i | \(0.808937\pi\) | |||||||
\(510\) | 21.2271 | 0.939951 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.03500 | 0.266452 | ||||||||
\(514\) | −8.31415 | −0.366721 | ||||||||
\(515\) | 6.94317 | 0.305953 | ||||||||
\(516\) | −1.34959 | −0.0594124 | ||||||||
\(517\) | −14.2304 | −0.625851 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6355 | 0.774111 | ||||||||
\(520\) | 2.69230 | 0.118065 | ||||||||
\(521\) | 9.79702 | 0.429215 | 0.214608 | − | 0.976700i | \(-0.431153\pi\) | ||||
0.214608 | + | 0.976700i | \(0.431153\pi\) | |||||||
\(522\) | 1.64173 | 0.0718568 | ||||||||
\(523\) | 2.80792 | 0.122782 | 0.0613909 | − | 0.998114i | \(-0.480446\pi\) | ||||
0.0613909 | + | 0.998114i | \(0.480446\pi\) | |||||||
\(524\) | −9.90173 | −0.432559 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.8877 | −0.474725 | ||||||||
\(527\) | 14.5811 | 0.635164 | ||||||||
\(528\) | 4.49978 | 0.195828 | ||||||||
\(529\) | −15.9753 | −0.694579 | ||||||||
\(530\) | −13.8989 | −0.603729 | ||||||||
\(531\) | −13.4643 | −0.584302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.56484 | −0.154410 | ||||||||
\(534\) | −12.7569 | −0.552046 | ||||||||
\(535\) | 36.9238 | 1.59635 | ||||||||
\(536\) | −4.85805 | −0.209836 | ||||||||
\(537\) | −8.41377 | −0.363081 | ||||||||
\(538\) | 22.0486 | 0.950584 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.69230 | 0.115858 | ||||||||
\(541\) | −9.04771 | −0.388992 | −0.194496 | − | 0.980903i | \(-0.562307\pi\) | ||||
−0.194496 | + | 0.980903i | \(0.562307\pi\) | |||||||
\(542\) | −19.9613 | −0.857410 | ||||||||
\(543\) | −16.1119 | −0.691428 | ||||||||
\(544\) | 7.88438 | 0.338040 | ||||||||
\(545\) | −40.8295 | −1.74894 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.9822 | −0.469565 | −0.234783 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234783 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(548\) | 13.5702 | 0.579691 | ||||||||
\(549\) | 14.6290 | 0.624352 | ||||||||
\(550\) | 10.1176 | 0.431416 | ||||||||
\(551\) | 9.90788 | 0.422090 | ||||||||
\(552\) | 2.65041 | 0.112809 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.76157 | −0.287272 | ||||||||
\(555\) | −14.6709 | −0.622746 | ||||||||
\(556\) | −1.08780 | −0.0461329 | ||||||||
\(557\) | 24.2701 | 1.02836 | 0.514179 | − | 0.857683i | \(-0.328097\pi\) | ||||
0.514179 | + | 0.857683i | \(0.328097\pi\) | |||||||
\(558\) | 1.84937 | 0.0782901 | ||||||||
\(559\) | 1.34959 | 0.0570816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.4780 | −1.49788 | ||||||||
\(562\) | 8.69830 | 0.366916 | ||||||||
\(563\) | 40.2742 | 1.69736 | 0.848678 | − | 0.528909i | \(-0.177399\pi\) | ||||
0.848678 | + | 0.528909i | \(0.177399\pi\) | |||||||
\(564\) | −3.16246 | −0.133164 | ||||||||
\(565\) | −12.7068 | −0.534579 | ||||||||
\(566\) | −13.3556 | −0.561378 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.80748 | −0.0758403 | ||||||||
\(569\) | 14.7878 | 0.619936 | 0.309968 | − | 0.950747i | \(-0.399682\pi\) | ||||
0.309968 | + | 0.950747i | \(0.399682\pi\) | |||||||
\(570\) | 16.2480 | 0.680555 | ||||||||
\(571\) | 7.58597 | 0.317463 | 0.158731 | − | 0.987322i | \(-0.449260\pi\) | ||||
0.158731 | + | 0.987322i | \(0.449260\pi\) | |||||||
\(572\) | −4.49978 | −0.188145 | ||||||||
\(573\) | −17.2766 | −0.721740 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.95935 | 0.248522 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.68673 | 0.0702195 | 0.0351097 | − | 0.999383i | \(-0.488822\pi\) | ||||
0.0351097 | + | 0.999383i | \(0.488822\pi\) | |||||||
\(578\) | −45.1634 | −1.87855 | ||||||||
\(579\) | −11.2211 | −0.466332 | ||||||||
\(580\) | 4.42004 | 0.183532 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.28347 | −0.219007 | ||||||||
\(583\) | 23.2299 | 0.962086 | ||||||||
\(584\) | 15.9641 | 0.660600 | ||||||||
\(585\) | −2.69230 | −0.111313 | ||||||||
\(586\) | 30.5553 | 1.26223 | ||||||||
\(587\) | −43.9528 | −1.81413 | −0.907063 | − | 0.420996i | \(-0.861681\pi\) | ||||
−0.907063 | + | 0.420996i | \(0.861681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1610 | 0.459879 | ||||||||
\(590\) | −36.2500 | −1.49239 | ||||||||
\(591\) | −22.5940 | −0.929394 | ||||||||
\(592\) | −5.44922 | −0.223961 | ||||||||
\(593\) | 5.78548 | 0.237581 | 0.118791 | − | 0.992919i | \(-0.462098\pi\) | ||||
0.118791 | + | 0.992919i | \(0.462098\pi\) | |||||||
\(594\) | −4.49978 | −0.184628 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.55617 | −0.186628 | ||||||||
\(597\) | −19.9635 | −0.817052 | ||||||||
\(598\) | −2.65041 | −0.108383 | ||||||||
\(599\) | −22.3189 | −0.911926 | −0.455963 | − | 0.889999i | \(-0.650705\pi\) | ||||
−0.455963 | + | 0.889999i | \(0.650705\pi\) | |||||||
\(600\) | 2.24846 | 0.0917932 | ||||||||
\(601\) | −21.4802 | −0.876195 | −0.438098 | − | 0.898927i | \(-0.644348\pi\) | ||||
−0.438098 | + | 0.898927i | \(0.644348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.85805 | 0.197835 | ||||||||
\(604\) | −2.78369 | −0.113267 | ||||||||
\(605\) | −24.8984 | −1.01227 | ||||||||
\(606\) | 2.27988 | 0.0926136 | ||||||||
\(607\) | −38.8676 | −1.57759 | −0.788794 | − | 0.614657i | \(-0.789294\pi\) | ||||
−0.788794 | + | 0.614657i | \(0.789294\pi\) | |||||||
\(608\) | 6.03500 | 0.244752 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.3857 | 1.59468 | ||||||||
\(611\) | 3.16246 | 0.127939 | ||||||||
\(612\) | −7.88438 | −0.318707 | ||||||||
\(613\) | 28.2196 | 1.13978 | 0.569890 | − | 0.821721i | \(-0.306986\pi\) | ||||
0.569890 | + | 0.821721i | \(0.306986\pi\) | |||||||
\(614\) | −12.6145 | −0.509081 | ||||||||
\(615\) | −9.59762 | −0.387013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.332231 | −0.0133751 | −0.00668755 | − | 0.999978i | \(-0.502129\pi\) | ||||
−0.00668755 | + | 0.999978i | \(0.502129\pi\) | |||||||
\(618\) | −2.57890 | −0.103739 | ||||||||
\(619\) | −21.5973 | −0.868069 | −0.434035 | − | 0.900896i | \(-0.642910\pi\) | ||||
−0.434035 | + | 0.900896i | \(0.642910\pi\) | |||||||
\(620\) | 4.97906 | 0.199964 | ||||||||
\(621\) | −2.65041 | −0.106357 | ||||||||
\(622\) | −10.6746 | −0.428014 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −31.1867 | −1.24747 | ||||||||
\(626\) | −13.2604 | −0.529993 | ||||||||
\(627\) | −27.1562 | −1.08451 | ||||||||
\(628\) | 1.22796 | 0.0490009 | ||||||||
\(629\) | 42.9637 | 1.71307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8790 | −1.58756 | −0.793780 | − | 0.608205i | \(-0.791890\pi\) | ||||
−0.793780 | + | 0.608205i | \(0.791890\pi\) | |||||||
\(632\) | 5.89126 | 0.234342 | ||||||||
\(633\) | 18.2364 | 0.724831 | ||||||||
\(634\) | 22.1743 | 0.880654 | ||||||||
\(635\) | 26.0543 | 1.03393 | ||||||||
\(636\) | 5.16246 | 0.204705 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.38745 | −0.292472 | ||||||||
\(639\) | 1.80748 | 0.0715029 | ||||||||
\(640\) | 2.69230 | 0.106422 | ||||||||
\(641\) | 3.18131 | 0.125654 | 0.0628270 | − | 0.998024i | \(-0.479988\pi\) | ||||
0.0628270 | + | 0.998024i | \(0.479988\pi\) | |||||||
\(642\) | −13.7146 | −0.541272 | ||||||||
\(643\) | −34.3447 | −1.35442 | −0.677211 | − | 0.735789i | \(-0.736812\pi\) | ||||
−0.677211 | + | 0.735789i | \(0.736812\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.63350 | 0.143069 | ||||||||
\(646\) | −47.5822 | −1.87210 | ||||||||
\(647\) | −35.3700 | −1.39054 | −0.695268 | − | 0.718750i | \(-0.744714\pi\) | ||||
−0.695268 | + | 0.718750i | \(0.744714\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 60.5866 | 2.37823 | ||||||||
\(650\) | −2.24846 | −0.0881920 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.5047 | −0.763864 | ||||||||
\(653\) | −0.192833 | −0.00754615 | −0.00377307 | − | 0.999993i | \(-0.501201\pi\) | ||||
−0.00377307 | + | 0.999993i | \(0.501201\pi\) | |||||||
\(654\) | 15.1653 | 0.593011 | ||||||||
\(655\) | 26.6584 | 1.04163 | ||||||||
\(656\) | −3.56484 | −0.139184 | ||||||||
\(657\) | −15.9641 | −0.622820 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.4811 | −0.992601 | −0.496301 | − | 0.868151i | \(-0.665309\pi\) | ||||
−0.496301 | + | 0.868151i | \(0.665309\pi\) | |||||||
\(660\) | −12.1147 | −0.471566 | ||||||||
\(661\) | 18.1400 | 0.705565 | 0.352782 | − | 0.935705i | \(-0.385236\pi\) | ||||
0.352782 | + | 0.935705i | \(0.385236\pi\) | |||||||
\(662\) | 32.1523 | 1.24963 | ||||||||
\(663\) | 7.88438 | 0.306204 | ||||||||
\(664\) | 3.72774 | 0.144664 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.44922 | 0.211153 | ||||||||
\(667\) | −4.35127 | −0.168482 | ||||||||
\(668\) | 25.3686 | 0.981541 | ||||||||
\(669\) | 11.7442 | 0.454058 | ||||||||
\(670\) | 13.0793 | 0.505298 | ||||||||
\(671\) | −65.8274 | −2.54124 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.8883 | −1.73032 | −0.865159 | − | 0.501498i | \(-0.832783\pi\) | ||||
−0.865159 | + | 0.501498i | \(0.832783\pi\) | |||||||
\(674\) | −9.13657 | −0.351927 | ||||||||
\(675\) | −2.24846 | −0.0865435 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 16.8320 | 0.646907 | 0.323453 | − | 0.946244i | \(-0.395156\pi\) | ||||
0.323453 | + | 0.946244i | \(0.395156\pi\) | |||||||
\(678\) | 4.71969 | 0.181258 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −21.2271 | −0.814021 | ||||||||
\(681\) | −15.5170 | −0.594613 | ||||||||
\(682\) | −8.32176 | −0.318657 | ||||||||
\(683\) | −35.1260 | −1.34406 | −0.672029 | − | 0.740525i | \(-0.734577\pi\) | ||||
−0.672029 | + | 0.740525i | \(0.734577\pi\) | |||||||
\(684\) | −6.03500 | −0.230754 | ||||||||
\(685\) | −36.5351 | −1.39593 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.13284 | 0.195830 | ||||||||
\(688\) | 1.34959 | 0.0514526 | ||||||||
\(689\) | −5.16246 | −0.196674 | ||||||||
\(690\) | −7.13569 | −0.271651 | ||||||||
\(691\) | −4.99956 | −0.190192 | −0.0950961 | − | 0.995468i | \(-0.530316\pi\) | ||||
−0.0950961 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(692\) | −17.6355 | −0.670400 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.45566 | 0.245054 | ||||||||
\(695\) | 2.92868 | 0.111091 | ||||||||
\(696\) | −1.64173 | −0.0622298 | ||||||||
\(697\) | 28.1066 | 1.06461 | ||||||||
\(698\) | −18.0971 | −0.684985 | ||||||||
\(699\) | −27.7861 | −1.05097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.7133 | 1.87764 | 0.938822 | − | 0.344401i | \(-0.111918\pi\) | ||||
0.938822 | + | 0.344401i | \(0.111918\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 32.8861 | 1.24032 | ||||||||
\(704\) | −4.49978 | −0.169592 | ||||||||
\(705\) | 8.51428 | 0.320666 | ||||||||
\(706\) | −15.3091 | −0.576164 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.4643 | 0.506021 | ||||||||
\(709\) | −30.2805 | −1.13721 | −0.568604 | − | 0.822611i | \(-0.692516\pi\) | ||||
−0.568604 | + | 0.822611i | \(0.692516\pi\) | |||||||
\(710\) | 4.86628 | 0.182628 | ||||||||
\(711\) | −5.89126 | −0.220939 | ||||||||
\(712\) | 12.7569 | 0.478086 | ||||||||
\(713\) | −4.90159 | −0.183566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1147 | 0.453066 | ||||||||
\(716\) | 8.41377 | 0.314438 | ||||||||
\(717\) | −7.54811 | −0.281889 | ||||||||
\(718\) | 5.01691 | 0.187229 | ||||||||
\(719\) | −8.93629 | −0.333267 | −0.166634 | − | 0.986019i | \(-0.553290\pi\) | ||||
−0.166634 | + | 0.986019i | \(0.553290\pi\) | |||||||
\(720\) | −2.69230 | −0.100336 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.4213 | −0.648353 | ||||||||
\(723\) | 28.7857 | 1.07055 | ||||||||
\(724\) | 16.1119 | 0.598794 | ||||||||
\(725\) | −3.69138 | −0.137095 | ||||||||
\(726\) | 9.24803 | 0.343226 | ||||||||
\(727\) | 15.9333 | 0.590932 | 0.295466 | − | 0.955353i | \(-0.404525\pi\) | ||||
0.295466 | + | 0.955353i | \(0.404525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −42.9802 | −1.59077 | ||||||||
\(731\) | −10.6407 | −0.393560 | ||||||||
\(732\) | −14.6290 | −0.540704 | ||||||||
\(733\) | 32.7897 | 1.21111 | 0.605557 | − | 0.795802i | \(-0.292950\pi\) | ||||
0.605557 | + | 0.795802i | \(0.292950\pi\) | |||||||
\(734\) | −10.5644 | −0.389939 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.65041 | −0.0976954 | ||||||||
\(737\) | −21.8601 | −0.805229 | ||||||||
\(738\) | 3.56484 | 0.131224 | ||||||||
\(739\) | −13.4218 | −0.493730 | −0.246865 | − | 0.969050i | \(-0.579400\pi\) | ||||
−0.246865 | + | 0.969050i | \(0.579400\pi\) | |||||||
\(740\) | 14.6709 | 0.539314 | ||||||||
\(741\) | 6.03500 | 0.221701 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.3828 | 1.66493 | 0.832467 | − | 0.554074i | \(-0.186928\pi\) | ||||
0.832467 | + | 0.554074i | \(0.186928\pi\) | |||||||
\(744\) | −1.84937 | −0.0678012 | ||||||||
\(745\) | 12.2666 | 0.449412 | ||||||||
\(746\) | 7.53435 | 0.275852 | ||||||||
\(747\) | −3.72774 | −0.136391 | ||||||||
\(748\) | 35.4780 | 1.29720 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.40795 | 0.270500 | ||||||||
\(751\) | −7.58070 | −0.276624 | −0.138312 | − | 0.990389i | \(-0.544168\pi\) | ||||
−0.138312 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(752\) | 3.16246 | 0.115323 | ||||||||
\(753\) | 23.6112 | 0.860441 | ||||||||
\(754\) | 1.64173 | 0.0597884 | ||||||||
\(755\) | 7.49452 | 0.272753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.4808 | −1.43495 | −0.717477 | − | 0.696582i | \(-0.754703\pi\) | ||||
−0.717477 | + | 0.696582i | \(0.754703\pi\) | |||||||
\(758\) | 29.3541 | 1.06619 | ||||||||
\(759\) | 11.9263 | 0.432896 | ||||||||
\(760\) | −16.2480 | −0.589378 | ||||||||
\(761\) | −5.32370 | −0.192984 | −0.0964920 | − | 0.995334i | \(-0.530762\pi\) | ||||
−0.0964920 | + | 0.995334i | \(0.530762\pi\) | |||||||
\(762\) | −9.67736 | −0.350574 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.2766 | 0.625045 | ||||||||
\(765\) | 21.2271 | 0.767467 | ||||||||
\(766\) | −14.4564 | −0.522331 | ||||||||
\(767\) | −13.4643 | −0.486169 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −10.3557 | −0.373437 | −0.186719 | − | 0.982413i | \(-0.559785\pi\) | ||||
−0.186719 | + | 0.982413i | \(0.559785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.31415 | −0.299427 | ||||||||
\(772\) | 11.2211 | 0.403855 | ||||||||
\(773\) | 7.88841 | 0.283726 | 0.141863 | − | 0.989886i | \(-0.454691\pi\) | ||||
0.141863 | + | 0.989886i | \(0.454691\pi\) | |||||||
\(774\) | −1.34959 | −0.0485100 | ||||||||
\(775\) | −4.15825 | −0.149369 | ||||||||
\(776\) | 5.28347 | 0.189665 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.1504 | 0.722426 | ||||||||
\(779\) | 21.5138 | 0.770813 | ||||||||
\(780\) | 2.69230 | 0.0963997 | ||||||||
\(781\) | −8.13328 | −0.291032 | ||||||||
\(782\) | 20.8968 | 0.747269 | ||||||||
\(783\) | 1.64173 | 0.0586708 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.30603 | −0.117997 | ||||||||
\(786\) | −9.90173 | −0.353183 | ||||||||
\(787\) | −13.7939 | −0.491698 | −0.245849 | − | 0.969308i | \(-0.579067\pi\) | ||||
−0.245849 | + | 0.969308i | \(0.579067\pi\) | |||||||
\(788\) | 22.5940 | 0.804879 | ||||||||
\(789\) | −10.8877 | −0.387611 | ||||||||
\(790\) | −15.8610 | −0.564310 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.49978 | 0.159893 | ||||||||
\(793\) | 14.6290 | 0.519492 | ||||||||
\(794\) | −19.5860 | −0.695080 | ||||||||
\(795\) | −13.8989 | −0.492942 | ||||||||
\(796\) | 19.9635 | 0.707587 | ||||||||
\(797\) | 28.5094 | 1.00985 | 0.504927 | − | 0.863162i | \(-0.331519\pi\) | ||||
0.504927 | + | 0.863162i | \(0.331519\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.9340 | −0.882102 | ||||||||
\(800\) | −2.24846 | −0.0794952 | ||||||||
\(801\) | −12.7569 | −0.450744 | ||||||||
\(802\) | −15.6987 | −0.554342 | ||||||||
\(803\) | 71.8350 | 2.53500 | ||||||||
\(804\) | −4.85805 | −0.171330 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.84937 | 0.0651413 | ||||||||
\(807\) | 22.0486 | 0.776148 | ||||||||
\(808\) | −2.27988 | −0.0802058 | ||||||||
\(809\) | 4.67568 | 0.164388 | 0.0821941 | − | 0.996616i | \(-0.473807\pi\) | ||||
0.0821941 | + | 0.996616i | \(0.473807\pi\) | |||||||
\(810\) | 2.69230 | 0.0945977 | ||||||||
\(811\) | −15.5444 | −0.545837 | −0.272919 | − | 0.962037i | \(-0.587989\pi\) | ||||
−0.272919 | + | 0.962037i | \(0.587989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9613 | −0.700072 | ||||||||
\(814\) | −24.5203 | −0.859436 | ||||||||
\(815\) | 52.5125 | 1.83943 | ||||||||
\(816\) | 7.88438 | 0.276008 | ||||||||
\(817\) | −8.14478 | −0.284950 | ||||||||
\(818\) | 26.9161 | 0.941099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.59762 | 0.335163 | ||||||||
\(821\) | −21.9617 | −0.766468 | −0.383234 | − | 0.923651i | \(-0.625190\pi\) | ||||
−0.383234 | + | 0.923651i | \(0.625190\pi\) | |||||||
\(822\) | 13.5702 | 0.473316 | ||||||||
\(823\) | 3.49965 | 0.121990 | 0.0609950 | − | 0.998138i | \(-0.480573\pi\) | ||||
0.0609950 | + | 0.998138i | \(0.480573\pi\) | |||||||
\(824\) | 2.57890 | 0.0898404 | ||||||||
\(825\) | 10.1176 | 0.352250 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.1450 | −0.700510 | −0.350255 | − | 0.936654i | \(-0.613905\pi\) | ||||
−0.350255 | + | 0.936654i | \(0.613905\pi\) | |||||||
\(828\) | 2.65041 | 0.0921081 | ||||||||
\(829\) | 4.20211 | 0.145945 | 0.0729726 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729726 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(830\) | −10.0362 | −0.348361 | ||||||||
\(831\) | −6.76157 | −0.234556 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.08780 | −0.0376674 | ||||||||
\(835\) | −68.2998 | −2.36361 | ||||||||
\(836\) | 27.1562 | 0.939217 | ||||||||
\(837\) | 1.84937 | 0.0639236 | ||||||||
\(838\) | 23.1735 | 0.800517 | ||||||||
\(839\) | 19.0605 | 0.658040 | 0.329020 | − | 0.944323i | \(-0.393282\pi\) | ||||
0.329020 | + | 0.944323i | \(0.393282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3047 | −0.907059 | ||||||||
\(842\) | 5.04969 | 0.174024 | ||||||||
\(843\) | 8.69830 | 0.299585 | ||||||||
\(844\) | −18.2364 | −0.627722 | ||||||||
\(845\) | −2.69230 | −0.0926178 | ||||||||
\(846\) | −3.16246 | −0.108728 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.16246 | −0.177280 | ||||||||
\(849\) | −13.3556 | −0.458363 | ||||||||
\(850\) | 17.7277 | 0.608056 | ||||||||
\(851\) | −14.4427 | −0.495088 | ||||||||
\(852\) | −1.80748 | −0.0619234 | ||||||||
\(853\) | −0.957674 | −0.0327901 | −0.0163951 | − | 0.999866i | \(-0.505219\pi\) | ||||
−0.0163951 | + | 0.999866i | \(0.505219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.2480 | 0.555671 | ||||||||
\(856\) | 13.7146 | 0.468755 | ||||||||
\(857\) | 3.21134 | 0.109697 | 0.0548487 | − | 0.998495i | \(-0.482532\pi\) | ||||
0.0548487 | + | 0.998495i | \(0.482532\pi\) | |||||||
\(858\) | −4.49978 | −0.153620 | ||||||||
\(859\) | 8.85209 | 0.302029 | 0.151015 | − | 0.988532i | \(-0.451746\pi\) | ||||
0.151015 | + | 0.988532i | \(0.451746\pi\) | |||||||
\(860\) | −3.63350 | −0.123901 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.5665 | −0.802678 | ||||||||
\(863\) | −56.7277 | −1.93103 | −0.965516 | − | 0.260343i | \(-0.916164\pi\) | ||||
−0.965516 | + | 0.260343i | \(0.916164\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 47.4799 | 1.61437 | ||||||||
\(866\) | −36.0319 | −1.22441 | ||||||||
\(867\) | −45.1634 | −1.53383 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.5094 | 0.899269 | ||||||||
\(870\) | 4.42004 | 0.149853 | ||||||||
\(871\) | 4.85805 | 0.164609 | ||||||||
\(872\) | −15.1653 | −0.513562 | ||||||||
\(873\) | −5.28347 | −0.178818 | ||||||||
\(874\) | 15.9952 | 0.541047 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.9641 | 0.539378 | ||||||||
\(877\) | 28.2985 | 0.955571 | 0.477785 | − | 0.878477i | \(-0.341440\pi\) | ||||
0.477785 | + | 0.878477i | \(0.341440\pi\) | |||||||
\(878\) | −26.1939 | −0.884000 | ||||||||
\(879\) | 30.5553 | 1.03060 | ||||||||
\(880\) | 12.1147 | 0.408388 | ||||||||
\(881\) | 42.7828 | 1.44139 | 0.720695 | − | 0.693253i | \(-0.243823\pi\) | ||||
0.720695 | + | 0.693253i | \(0.243823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8162 | 0.633216 | 0.316608 | − | 0.948557i | \(-0.397456\pi\) | ||||
0.316608 | + | 0.948557i | \(0.397456\pi\) | |||||||
\(884\) | −7.88438 | −0.265180 | ||||||||
\(885\) | −36.2500 | −1.21853 | ||||||||
\(886\) | 13.6304 | 0.457922 | ||||||||
\(887\) | −11.3962 | −0.382648 | −0.191324 | − | 0.981527i | \(-0.561278\pi\) | ||||
−0.191324 | + | 0.981527i | \(0.561278\pi\) | |||||||
\(888\) | −5.44922 | −0.182864 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −34.3454 | −1.15126 | ||||||||
\(891\) | −4.49978 | −0.150748 | ||||||||
\(892\) | −11.7442 | −0.393225 | ||||||||
\(893\) | −19.0855 | −0.638670 | ||||||||
\(894\) | −4.55617 | −0.152381 | ||||||||
\(895\) | −22.6524 | −0.757186 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.65041 | −0.0884946 | ||||||||
\(898\) | −5.28274 | −0.176287 | ||||||||
\(899\) | 3.03618 | 0.101262 | ||||||||
\(900\) | 2.24846 | 0.0749488 | ||||||||
\(901\) | 40.7028 | 1.35601 | ||||||||
\(902\) | −16.0410 | −0.534107 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.71969 | −0.156974 | ||||||||
\(905\) | −43.3780 | −1.44193 | ||||||||
\(906\) | −2.78369 | −0.0924819 | ||||||||
\(907\) | −0.939083 | −0.0311817 | −0.0155909 | − | 0.999878i | \(-0.504963\pi\) | ||||
−0.0155909 | + | 0.999878i | \(0.504963\pi\) | |||||||
\(908\) | 15.5170 | 0.514950 | ||||||||
\(909\) | 2.27988 | 0.0756187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.4543 | −0.578287 | −0.289143 | − | 0.957286i | \(-0.593370\pi\) | ||||
−0.289143 | + | 0.957286i | \(0.593370\pi\) | |||||||
\(912\) | 6.03500 | 0.199839 | ||||||||
\(913\) | 16.7740 | 0.555139 | ||||||||
\(914\) | −34.4510 | −1.13954 | ||||||||
\(915\) | 39.3857 | 1.30205 | ||||||||
\(916\) | −5.13284 | −0.169594 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.88438 | −0.260223 | ||||||||
\(919\) | −31.5976 | −1.04231 | −0.521155 | − | 0.853462i | \(-0.674499\pi\) | ||||
−0.521155 | + | 0.853462i | \(0.674499\pi\) | |||||||
\(920\) | 7.13569 | 0.235257 | ||||||||
\(921\) | −12.6145 | −0.415663 | ||||||||
\(922\) | −36.7860 | −1.21148 | ||||||||
\(923\) | 1.80748 | 0.0594940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.2524 | −0.402856 | ||||||||
\(926\) | 2.95694 | 0.0971711 | ||||||||
\(927\) | −2.57890 | −0.0847023 | ||||||||
\(928\) | 1.64173 | 0.0538926 | ||||||||
\(929\) | −5.25640 | −0.172457 | −0.0862284 | − | 0.996275i | \(-0.527481\pi\) | ||||
−0.0862284 | + | 0.996275i | \(0.527481\pi\) | |||||||
\(930\) | 4.97906 | 0.163270 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.7861 | 0.910164 | ||||||||
\(933\) | −10.6746 | −0.349472 | ||||||||
\(934\) | −35.3821 | −1.15774 | ||||||||
\(935\) | −95.5172 | −3.12375 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −37.5309 | −1.22608 | −0.613041 | − | 0.790051i | \(-0.710054\pi\) | ||||
−0.613041 | + | 0.790051i | \(0.710054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.2604 | −0.432738 | ||||||||
\(940\) | −8.51428 | −0.277705 | ||||||||
\(941\) | 46.7865 | 1.52520 | 0.762599 | − | 0.646872i | \(-0.223923\pi\) | ||||
0.762599 | + | 0.646872i | \(0.223923\pi\) | |||||||
\(942\) | 1.22796 | 0.0400091 | ||||||||
\(943\) | −9.44829 | −0.307679 | ||||||||
\(944\) | −13.4643 | −0.438227 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.07286 | 0.197446 | ||||||||
\(947\) | 40.1513 | 1.30474 | 0.652371 | − | 0.757900i | \(-0.273774\pi\) | ||||
0.652371 | + | 0.757900i | \(0.273774\pi\) | |||||||
\(948\) | 5.89126 | 0.191339 | ||||||||
\(949\) | −15.9641 | −0.518217 | ||||||||
\(950\) | 13.5695 | 0.440253 | ||||||||
\(951\) | 22.1743 | 0.719051 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.5428 | −0.633055 | −0.316527 | − | 0.948583i | \(-0.602517\pi\) | ||||
−0.316527 | + | 0.948583i | \(0.602517\pi\) | |||||||
\(954\) | 5.16246 | 0.167141 | ||||||||
\(955\) | −46.5137 | −1.50515 | ||||||||
\(956\) | 7.54811 | 0.244123 | ||||||||
\(957\) | −7.38745 | −0.238802 | ||||||||
\(958\) | 27.9002 | 0.901415 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.69230 | 0.0868935 | ||||||||
\(961\) | −27.5798 | −0.889672 | ||||||||
\(962\) | 5.44922 | 0.175690 | ||||||||
\(963\) | −13.7146 | −0.441947 | ||||||||
\(964\) | −28.7857 | −0.927124 | ||||||||
\(965\) | −30.2105 | −0.972510 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9146 | 0.447464 | 0.223732 | − | 0.974651i | \(-0.428176\pi\) | ||||
0.223732 | + | 0.974651i | \(0.428176\pi\) | |||||||
\(968\) | −9.24803 | −0.297243 | ||||||||
\(969\) | −47.5822 | −1.52856 | ||||||||
\(970\) | −14.2247 | −0.456727 | ||||||||
\(971\) | −44.5544 | −1.42982 | −0.714910 | − | 0.699217i | \(-0.753532\pi\) | ||||
−0.714910 | + | 0.699217i | \(0.753532\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.04057 | −0.289679 | ||||||||
\(975\) | −2.24846 | −0.0720085 | ||||||||
\(976\) | 14.6290 | 0.468264 | ||||||||
\(977\) | −50.7580 | −1.62389 | −0.811946 | − | 0.583732i | \(-0.801592\pi\) | ||||
−0.811946 | + | 0.583732i | \(0.801592\pi\) | |||||||
\(978\) | −19.5047 | −0.623692 | ||||||||
\(979\) | 57.4033 | 1.83462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1653 | 0.484191 | ||||||||
\(982\) | 31.3219 | 0.999523 | ||||||||
\(983\) | −14.8704 | −0.474293 | −0.237146 | − | 0.971474i | \(-0.576212\pi\) | ||||
−0.237146 | + | 0.971474i | \(0.576212\pi\) | |||||||
\(984\) | −3.56484 | −0.113643 | ||||||||
\(985\) | −60.8298 | −1.93820 | ||||||||
\(986\) | −12.9441 | −0.412223 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.03500 | −0.191999 | ||||||||
\(989\) | 3.57697 | 0.113741 | ||||||||
\(990\) | −12.1147 | −0.385032 | ||||||||
\(991\) | −30.6681 | −0.974203 | −0.487102 | − | 0.873345i | \(-0.661946\pi\) | ||||
−0.487102 | + | 0.873345i | \(0.661946\pi\) | |||||||
\(992\) | 1.84937 | 0.0587176 | ||||||||
\(993\) | 32.1523 | 1.02032 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.7477 | −1.70392 | ||||||||
\(996\) | 3.72774 | 0.118118 | ||||||||
\(997\) | −34.8339 | −1.10320 | −0.551600 | − | 0.834109i | \(-0.685982\pi\) | ||||
−0.551600 | + | 0.834109i | \(0.685982\pi\) | |||||||
\(998\) | 2.46943 | 0.0781684 | ||||||||
\(999\) | 5.44922 | 0.172406 |
(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 | 3822.2.a.bx.1.2 | ✓ | 4 | |
7.6 | odd | 2 | 3822.2.a.by.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bx.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3822.2.a.by.1.3 | yes | 4 | 7.6 | odd | 2 |