Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,2,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1104.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(8.81548438315\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.47214 | −1.69031 | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.763932 | 0.230334 | 0.115167 | − | 0.993346i | \(-0.463260\pi\) | ||||
0.115167 | + | 0.993346i | \(0.463260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.23607 | 0.835549 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.70820 | 1.76838 | 0.884192 | − | 0.467124i | \(-0.154710\pi\) | ||||
0.884192 | + | 0.467124i | \(0.154710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.47214 | 0.975900 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.763932 | −0.132983 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.4721 | 2.44624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.76393 | 1.11198 | 0.555992 | − | 0.831188i | \(-0.312339\pi\) | ||||
0.555992 | + | 0.831188i | \(0.312339\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.47214 | 0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.23607 | 1.40849 | 0.704244 | − | 0.709958i | \(-0.251286\pi\) | ||||
0.704244 | + | 0.709958i | \(0.251286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.23607 | −0.482405 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0000 | 1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.763932 | 0.104934 | 0.0524671 | − | 0.998623i | \(-0.483292\pi\) | ||||
0.0524671 | + | 0.998623i | \(0.483292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.47214 | −0.333343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.70820 | −1.02098 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.23607 | 0.670410 | 0.335205 | − | 0.942145i | \(-0.391194\pi\) | ||||
0.335205 | + | 0.942145i | \(0.391194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.47214 | −0.563436 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70820 | 0.453029 | 0.226515 | − | 0.974008i | \(-0.427267\pi\) | ||||
0.226515 | + | 0.974008i | \(0.427267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.47214 | 0.523424 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.47214 | −0.631868 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.41641 | −0.389336 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.47214 | 0.503155 | 0.251577 | − | 0.967837i | \(-0.419051\pi\) | ||||
0.251577 | + | 0.967837i | \(0.419051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.76393 | −0.961967 | −0.480983 | − | 0.876730i | \(-0.659720\pi\) | ||||
−0.480983 | + | 0.876730i | \(0.659720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9443 | 1.40400 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.47214 | −0.479463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.52786 | −0.161953 | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809766 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.0000 | 2.09657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47214 | 0.671129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.9443 | −2.55923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.763932 | 0.0767781 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47214 | −0.444994 | −0.222497 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222497 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.4721 | −1.41234 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.6525 | −1.80320 | −0.901601 | − | 0.432568i | \(-0.857608\pi\) | ||||
−0.901601 | + | 0.432568i | \(0.857608\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.23607 | 0.884655 | 0.442327 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442327 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.76393 | −0.642004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4721 | −1.36142 | −0.680712 | − | 0.732551i | \(-0.738329\pi\) | ||||
−0.680712 | + | 0.732551i | \(0.738329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.23607 | 0.301765 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.8885 | 1.63984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.23607 | −0.813190 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4721 | 1.61392 | 0.806959 | − | 0.590607i | \(-0.201112\pi\) | ||||
0.806959 | + | 0.590607i | \(0.201112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −34.4721 | −2.98911 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.23607 | 0.278516 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.9443 | 1.78939 | 0.894695 | − | 0.446678i | \(-0.147393\pi\) | ||||
0.894695 | + | 0.446678i | \(0.147393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.944272 | −0.0800921 | −0.0400460 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400460 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41641 | −0.285694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4721 | −1.20185 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.0000 | −1.07222 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.70820 | 0.139942 | 0.0699708 | − | 0.997549i | \(-0.477709\pi\) | ||||
0.0699708 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.52786 | 0.449851 | 0.224926 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224926 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.9443 | 1.68228 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.6525 | 1.96748 | 0.983741 | − | 0.179594i | \(-0.0574783\pi\) | ||||
0.983741 | + | 0.179594i | \(0.0574783\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.763932 | −0.0605838 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.47214 | 0.352454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.47214 | −0.506937 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.47214 | 0.192456 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.944272 | 0.0730700 | 0.0365350 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365350 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.70820 | 0.589461 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.41641 | 0.715916 | 0.357958 | − | 0.933738i | \(-0.383473\pi\) | ||||
0.357958 | + | 0.933738i | \(0.383473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.4721 | −1.84992 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.41641 | 0.554328 | 0.277164 | − | 0.960823i | \(-0.410605\pi\) | ||||
0.277164 | + | 0.960823i | \(0.410605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.76393 | −0.502759 | −0.251380 | − | 0.967889i | \(-0.580884\pi\) | ||||
−0.251380 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.23607 | −0.387061 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.8885 | −1.60928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.05573 | −0.223457 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.47214 | 0.325300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.47214 | 0.178877 | 0.0894387 | − | 0.995992i | \(-0.471493\pi\) | ||||
0.0894387 | + | 0.995992i | \(0.471493\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8885 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.4721 | −1.03637 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9443 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.41641 | 0.667511 | 0.333756 | − | 0.942660i | \(-0.391684\pi\) | ||||
0.333756 | + | 0.942660i | \(0.391684\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.0000 | −1.40372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47214 | 0.452034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.88854 | 0.407319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.41641 | −0.235195 | −0.117598 | − | 0.993061i | \(-0.537519\pi\) | ||||
−0.117598 | + | 0.993061i | \(0.537519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.94427 | −0.612851 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.8885 | −2.03838 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.9443 | 1.96487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.47214 | −0.302199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8885 | 1.20331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.41641 | 0.496639 | 0.248320 | − | 0.968678i | \(-0.420122\pi\) | ||||
0.248320 | + | 0.968678i | \(0.420122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.47214 | 0.364809 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.76393 | 0.316193 | 0.158097 | − | 0.987424i | \(-0.449464\pi\) | ||||
0.158097 | + | 0.987424i | \(0.449464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.29180 | 0.283610 | 0.141805 | − | 0.989895i | \(-0.454709\pi\) | ||||
0.141805 | + | 0.989895i | \(0.454709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.41641 | 0.224783 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8885 | −1.04089 | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520447 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9443 | 0.844391 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.47214 | −0.290496 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9443 | −0.837295 | −0.418648 | − | 0.908149i | \(-0.637496\pi\) | ||||
−0.418648 | + | 0.908149i | \(0.637496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.52786 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42.0689 | −2.68768 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.4721 | −2.19341 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.76393 | 0.555392 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.29180 | 0.397135 | 0.198567 | − | 0.980087i | \(-0.436371\pi\) | ||||
0.198567 | + | 0.980087i | \(0.436371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.763932 | −0.0480280 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.9443 | −0.810602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.8885 | 1.49013 | 0.745063 | − | 0.666994i | \(-0.232419\pi\) | ||||
0.745063 | + | 0.666994i | \(0.232419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.2492 | −1.87960 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47214 | 0.276818 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.05573 | −0.435075 | −0.217537 | − | 0.976052i | \(-0.569802\pi\) | ||||
−0.217537 | + | 0.976052i | \(0.569802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.47214 | −0.151862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.52786 | 0.0935038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.9443 | −1.88671 | −0.943353 | − | 0.331791i | \(-0.892347\pi\) | ||||
−0.943353 | + | 0.331791i | \(0.892347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.944272 | −0.0573604 | −0.0286802 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286802 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.0000 | −1.21046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.18034 | 0.252084 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5279 | −0.692642 | −0.346321 | − | 0.938116i | \(-0.612569\pi\) | ||||
−0.346321 | + | 0.938116i | \(0.612569\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.47214 | −0.387477 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4721 | −1.34058 | −0.670288 | − | 0.742101i | \(-0.733829\pi\) | ||||
−0.670288 | + | 0.742101i | \(0.733829\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1803 | 1.55626 | 0.778130 | − | 0.628103i | \(-0.216169\pi\) | ||||
0.778130 | + | 0.628103i | \(0.216169\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.9443 | 1.47757 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94427 | 0.527964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.47214 | 0.496645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.7082 | 0.800842 | 0.400421 | − | 0.916331i | \(-0.368864\pi\) | ||||
0.400421 | + | 0.916331i | \(0.368864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.9443 | 1.68520 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.763932 | −0.0443278 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.47214 | 0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.3050 | −2.38078 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.47214 | 0.256917 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.9443 | −0.970226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4164 | 0.651569 | 0.325784 | − | 0.945444i | \(-0.394372\pi\) | ||||
0.325784 | + | 0.945444i | \(0.394372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.05573 | 0.173274 | 0.0866372 | − | 0.996240i | \(-0.472388\pi\) | ||||
0.0866372 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4721 | 1.38325 | 0.691623 | − | 0.722258i | \(-0.256896\pi\) | ||||
0.691623 | + | 0.722258i | \(0.256896\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.4721 | 0.815412 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.4721 | 1.59915 | 0.799577 | − | 0.600563i | \(-0.205057\pi\) | ||||
0.799577 | + | 0.600563i | \(0.205057\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.41641 | 0.191282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.6525 | 1.04108 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.8328 | −1.71558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.4721 | −1.35747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.23607 | −0.510756 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.8885 | 0.986227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.52786 | 0.0839790 | 0.0419895 | − | 0.999118i | \(-0.486630\pi\) | ||||
0.0419895 | + | 0.999118i | \(0.486630\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.76393 | 0.370661 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8885 | 0.865504 | 0.432752 | − | 0.901513i | \(-0.357543\pi\) | ||||
0.432752 | + | 0.901513i | \(0.357543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4721 | 0.786019 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.94427 | −0.267747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.8328 | −1.44884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.23607 | −0.174224 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.5279 | −1.15568 | −0.577838 | − | 0.816151i | \(-0.696104\pi\) | ||||
−0.577838 | + | 0.816151i | \(0.696104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.8885 | −1.70695 | −0.853477 | − | 0.521130i | \(-0.825511\pi\) | ||||
−0.853477 | + | 0.521130i | \(0.825511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8885 | 1.69726 | 0.848628 | − | 0.528990i | \(-0.177429\pi\) | ||||
0.848628 | + | 0.528990i | \(0.177429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.9443 | −1.53620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8885 | −0.946762 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.3050 | 1.75777 | 0.878884 | − | 0.477035i | \(-0.158289\pi\) | ||||
0.878884 | + | 0.477035i | \(0.158289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.4164 | 2.12718 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4164 | 0.546720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4721 | −0.757506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4164 | 0.909129 | 0.454565 | − | 0.890714i | \(-0.349795\pi\) | ||||
0.454565 | + | 0.890714i | \(0.349795\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.41641 | −0.177371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5967 | 0.704013 | 0.352006 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352006 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.52786 | 0.0788986 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.291796 | −0.0149886 | −0.00749428 | − | 0.999972i | \(-0.502386\pi\) | ||||
−0.00749428 | + | 0.999972i | \(0.502386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9443 | −1.27459 | −0.637296 | − | 0.770619i | \(-0.719947\pi\) | ||||
−0.637296 | + | 0.770619i | \(0.719947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.0557 | 0.563452 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.23607 | 0.469496 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2918 | 0.521815 | 0.260907 | − | 0.965364i | \(-0.415978\pi\) | ||||
0.260907 | + | 0.965364i | \(0.415978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4721 | −0.931796 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4721 | −0.728172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.05573 | 0.454494 | 0.227247 | − | 0.973837i | \(-0.427028\pi\) | ||||
0.227247 | + | 0.973837i | \(0.427028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 34.4721 | 1.72577 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.94427 | −0.446656 | −0.223328 | − | 0.974743i | \(-0.571692\pi\) | ||||
−0.223328 | + | 0.974743i | \(0.571692\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9443 | 1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.23607 | −0.160802 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.16718 | 0.256128 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.111456 | −0.00551115 | −0.00275558 | − | 0.999996i | \(-0.500877\pi\) | ||||
−0.00275558 | + | 0.999996i | \(0.500877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.9443 | −1.03310 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.0000 | 1.96827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.3607 | 1.39217 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.944272 | 0.0462412 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0689 | 1.46896 | 0.734481 | − | 0.678630i | \(-0.237426\pi\) | ||||
0.734481 | + | 0.678630i | \(0.237426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.23607 | −0.255190 | −0.127595 | − | 0.991826i | \(-0.540726\pi\) | ||||
−0.127595 | + | 0.991826i | \(0.540726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.00000 | −0.194487 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.8885 | −1.06175 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.4164 | −1.13320 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.41641 | 0.164946 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.41641 | −0.164563 | −0.0822813 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822813 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.41641 | 0.260296 | 0.130148 | − | 0.991495i | \(-0.458455\pi\) | ||||
0.130148 | + | 0.991495i | \(0.458455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4721 | 0.693886 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.70820 | −0.368733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.9443 | −1.76325 | −0.881627 | − | 0.471947i | \(-0.843551\pi\) | ||||
−0.881627 | + | 0.471947i | \(0.843551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | 0.619048 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.9443 | 1.56523 | 0.782615 | − | 0.622506i | \(-0.213885\pi\) | ||||
0.782615 | + | 0.622506i | \(0.213885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.94427 | 0.234381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.70820 | −0.0807953 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8885 | −0.938598 | −0.469299 | − | 0.883039i | \(-0.655493\pi\) | ||||
−0.469299 | + | 0.883039i | \(0.655493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52786 | −0.0719443 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52786 | −0.259722 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −64.7214 | −3.03418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.4721 | 1.70609 | 0.853047 | − | 0.521834i | \(-0.174752\pi\) | ||||
0.853047 | + | 0.521834i | \(0.174752\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000 | 1.02464 | 0.512321 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512321 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.9443 | −0.971267 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.1803 | 1.85932 | 0.929662 | − | 0.368413i | \(-0.120099\pi\) | ||||
0.929662 | + | 0.368413i | \(0.120099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.5836 | −0.765759 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.6525 | −1.13593 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.05573 | 0.324423 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.1803 | 1.93537 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.763932 | 0.0349780 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0557 | 0.505149 | 0.252575 | − | 0.967577i | \(-0.418723\pi\) | ||||
0.252575 | + | 0.967577i | \(0.418723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.2492 | −1.37925 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.47214 | −0.203489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.4164 | 1.24491 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8885 | 1.17312 | 0.586561 | − | 0.809905i | \(-0.300481\pi\) | ||||
0.586561 | + | 0.809905i | \(0.300481\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.47214 | 0.292680 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.3050 | 1.50303 | 0.751516 | − | 0.659715i | \(-0.229323\pi\) | ||||
0.751516 | + | 0.659715i | \(0.229323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.8885 | −0.805659 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.47214 | −0.111114 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.0000 | −1.79425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.4164 | −1.22733 | −0.613663 | − | 0.789568i | \(-0.710305\pi\) | ||||
−0.613663 | + | 0.789568i | \(0.710305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.944272 | −0.0421870 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.52786 | −0.0681241 | −0.0340620 | − | 0.999420i | \(-0.510844\pi\) | ||||
−0.0340620 | + | 0.999420i | \(0.510844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4721 | 0.644002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.58359 | −0.291813 | −0.145906 | − | 0.989298i | \(-0.546610\pi\) | ||||
−0.145906 | + | 0.989298i | \(0.546610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0000 | −0.884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.70820 | −0.340326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.4164 | −0.855589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.05573 | −0.134391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.41641 | −0.413334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0000 | 0.700973 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2918 | −0.537483 | −0.268741 | − | 0.963212i | \(-0.586608\pi\) | ||||
−0.268741 | + | 0.963212i | \(0.586608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.4721 | 1.06805 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.8885 | 1.12772 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 60.3607 | 2.60962 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.41641 | −0.320042 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.93112 | 0.427763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.8885 | 1.88692 | 0.943458 | − | 0.331492i | \(-0.107552\pi\) | ||||
0.943458 | + | 0.331492i | \(0.107552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.76393 | 0.290268 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.8885 | −1.28028 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3050 | 0.910934 | 0.455467 | − | 0.890253i | \(-0.349472\pi\) | ||||
0.455467 | + | 0.890253i | \(0.349472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.23607 | 0.223470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4721 | 1.46856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | −0.850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.8885 | 0.929117 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.1246 | 1.06456 | 0.532282 | − | 0.846567i | \(-0.321335\pi\) | ||||
0.532282 | + | 0.846567i | \(0.321335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.3050 | −1.74701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.05573 | 0.129013 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.65248 | 0.280368 | 0.140184 | − | 0.990125i | \(-0.455231\pi\) | ||||
0.140184 | + | 0.990125i | \(0.455231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.8328 | 1.97027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.47214 | −0.187812 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0000 | 0.838444 | 0.419222 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419222 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7082 | 1.15955 | 0.579776 | − | 0.814776i | \(-0.303140\pi\) | ||||
0.579776 | + | 0.814776i | \(0.303140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.47214 | −0.103275 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.47214 | −0.228204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3607 | 0.431321 | 0.215660 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215660 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8885 | 0.494071 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.1935 | 1.62602 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.583592 | 0.0241699 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.4721 | 0.598349 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.47214 | 0.102036 | 0.0510180 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510180 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.8885 | −2.05562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.9443 | 0.614725 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.7771 | −1.55132 | −0.775660 | − | 0.631152i | \(-0.782583\pi\) | ||||
−0.775660 | + | 0.631152i | \(0.782583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −57.8885 | −2.37320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.41641 | −0.385388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.88854 | 0.0771638 | 0.0385819 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385819 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.3607 | 1.40160 | 0.700801 | − | 0.713357i | \(-0.252826\pi\) | ||||
0.700801 | + | 0.713357i | \(0.252826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.70820 | 0.151010 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.7082 | 1.37043 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4721 | 1.07447 | 0.537235 | − | 0.843432i | \(-0.319469\pi\) | ||||
0.537235 | + | 0.843432i | \(0.319469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0000 | 0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.8885 | 0.723693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1246 | 0.610877 | 0.305439 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305439 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47214 | −0.260982 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.3607 | −0.980724 | −0.490362 | − | 0.871519i | \(-0.663135\pi\) | ||||
−0.490362 | + | 0.871519i | \(0.663135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7082 | −1.27446 | −0.637230 | − | 0.770674i | \(-0.719920\pi\) | ||||
−0.637230 | + | 0.770674i | \(0.719920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.83282 | 0.273751 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.88854 | −0.235166 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.0557 | −1.07878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.00000 | 0.238856 | 0.119428 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119428 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.41641 | 0.135790 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.9443 | −0.513678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −58.1378 | −2.30350 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.94427 | 0.353830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.00000 | 0.157991 | 0.0789953 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789953 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.5410 | −1.36216 | −0.681082 | − | 0.732207i | \(-0.738490\pi\) | ||||
−0.681082 | + | 0.732207i | \(0.738490\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.8885 | 1.17686 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.94427 | 0.194379 | 0.0971897 | − | 0.995266i | \(-0.469015\pi\) | ||||
0.0971897 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.83282 | −0.268211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.9443 | −1.13442 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.4164 | −0.681557 | −0.340778 | − | 0.940144i | \(-0.610691\pi\) | ||||
−0.340778 | + | 0.940144i | \(0.610691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59.7771 | −2.33568 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.47214 | 0.174475 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.34752 | 0.0524921 | 0.0262460 | − | 0.999656i | \(-0.491645\pi\) | ||||
0.0262460 | + | 0.999656i | \(0.491645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1803 | 1.01830 | 0.509149 | − | 0.860679i | \(-0.329960\pi\) | ||||
0.509149 | + | 0.860679i | \(0.329960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8885 | −0.694733 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 111.554 | 4.32589 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.47214 | −0.173162 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.41641 | −0.286735 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.47214 | −0.172388 | −0.0861941 | − | 0.996278i | \(-0.527471\pi\) | ||||
−0.0861941 | + | 0.996278i | \(0.527471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.47214 | −0.210623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1246 | −0.811885 | −0.405942 | − | 0.913899i | \(-0.633057\pi\) | ||||
−0.405942 | + | 0.913899i | \(0.633057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.8885 | 1.45403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.76393 | −0.182554 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.52786 | −0.211518 | −0.105759 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105759 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −67.7771 | −2.58963 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.29180 | −0.163742 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.41641 | −0.130155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.4164 | −1.65164 | −0.825819 | − | 0.563935i | \(-0.809287\pi\) | ||||
−0.825819 | + | 0.563935i | \(0.809287\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.41641 | −0.129779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.05573 | 0.115910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.8885 | 0.600960 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.1246 | 1.40218 | 0.701089 | − | 0.713074i | \(-0.252698\pi\) | ||||
0.701089 | + | 0.713074i | \(0.252698\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.1378 | 1.96641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9443 | −0.487509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0000 | 0.752177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.0132 | −1.54028 | −0.770141 | − | 0.637874i | \(-0.779814\pi\) | ||||
−0.770141 | + | 0.637874i | \(0.779814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.47214 | 0.167718 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.47214 | 0.242383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0557 | 0.413461 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9443 | 0.483413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9443 | 0.781090 | 0.390545 | − | 0.920584i | \(-0.372287\pi\) | ||||
0.390545 | + | 0.920584i | \(0.372287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.8328 | −0.999306 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.52786 | 0.131203 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.4721 | 0.908872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.3050 | −1.60609 | −0.803046 | − | 0.595917i | \(-0.796789\pi\) | ||||
−0.803046 | + | 0.595917i | \(0.796789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.9443 | −1.36643 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.29180 | −0.306264 | −0.153132 | − | 0.988206i | \(-0.548936\pi\) | ||||
−0.153132 | + | 0.988206i | \(0.548936\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 42.0689 | 1.55173 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.83282 | 0.104348 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0557 | 0.553834 | 0.276917 | − | 0.960894i | \(-0.410687\pi\) | ||||
0.276917 | + | 0.960894i | \(0.410687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.4721 | 1.26637 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.52786 | −0.202525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.76393 | −0.320656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 83.4164 | 3.04797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0000 | 0.656829 | 0.328415 | − | 0.944534i | \(-0.393486\pi\) | ||||
0.328415 | + | 0.944534i | \(0.393486\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.29180 | −0.229286 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.6525 | −1.18677 | −0.593387 | − | 0.804917i | \(-0.702210\pi\) | ||||
−0.593387 | + | 0.804917i | \(0.702210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.763932 | 0.0277290 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9443 | −0.831729 | −0.415865 | − | 0.909427i | \(-0.636521\pi\) | ||||
−0.415865 | + | 0.909427i | \(0.636521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.3050 | −1.49534 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.9443 | 0.468001 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.0000 | 1.44432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.52786 | 0.127218 | 0.0636090 | − | 0.997975i | \(-0.479739\pi\) | ||||
0.0636090 | + | 0.997975i | \(0.479739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8885 | −0.860325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8197 | −0.568994 | −0.284497 | − | 0.958677i | \(-0.591827\pi\) | ||||
−0.284497 | + | 0.958677i | \(0.591827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.4164 | −1.27219 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.2492 | 1.08518 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4164 | −0.552350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.83282 | 0.244497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.47214 | −0.159821 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −79.7771 | −2.84737 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.7639 | −1.09662 | −0.548308 | − | 0.836277i | \(-0.684728\pi\) | ||||
−0.548308 | + | 0.836277i | \(0.684728\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.05573 | 0.251191 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 64.7214 | 2.30123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.4164 | −0.831541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.47214 | 0.0876776 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.59675 | −0.269091 | −0.134545 | − | 0.990907i | \(-0.542957\pi\) | ||||
−0.134545 | + | 0.990907i | \(0.542957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.52786 | −0.0539844 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.41641 | 0.120562 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.4721 | −0.510076 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9443 | 1.08929 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.0557 | 0.880912 | 0.440456 | − | 0.897774i | \(-0.354817\pi\) | ||||
0.440456 | + | 0.897774i | \(0.354817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.3050 | 0.748118 | 0.374059 | − | 0.927405i | \(-0.377966\pi\) | ||||
0.374059 | + | 0.927405i | \(0.377966\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.944272 | 0.0331171 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.9443 | 0.733646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.1935 | 2.49075 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.0000 | 0.698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.4721 | 1.69169 | 0.845845 | − | 0.533429i | \(-0.179097\pi\) | ||||
0.845845 | + | 0.533429i | \(0.179097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.63932 | 0.266290 | 0.133145 | − | 0.991097i | \(-0.457492\pi\) | ||||
0.133145 | + | 0.991097i | \(0.457492\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.18034 | −0.145541 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5967 | −0.959633 | −0.479816 | − | 0.877369i | \(-0.659297\pi\) | ||||
−0.479816 | + | 0.877369i | \(0.659297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.5279 | 0.399897 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −52.0000 | −1.80169 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.05573 | −0.105748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.47214 | 0.223710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.1115 | 0.349086 | 0.174543 | − | 0.984650i | \(-0.444155\pi\) | ||||
0.174543 | + | 0.984650i | \(0.444155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.4721 | 0.773981 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.6525 | −0.779269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.5836 | 1.60063 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.1803 | −0.898507 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.76393 | −0.231865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.9443 | −0.853076 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0000 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.94427 | −0.304820 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.8328 | 1.32188 | 0.660942 | − | 0.750437i | \(-0.270157\pi\) | ||||
0.660942 | + | 0.750437i | \(0.270157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.4721 | −1.03608 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.41641 | 0.115894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.5836 | −0.561914 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.47214 | −0.286738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.83282 | 0.230991 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.2492 | 1.08898 | 0.544489 | − | 0.838768i | \(-0.316723\pi\) | ||||
0.544489 | + | 0.838768i | \(0.316723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.7082 | −0.462366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5836 | 0.423952 | 0.211976 | − | 0.977275i | \(-0.432010\pi\) | ||||
0.211976 | + | 0.977275i | \(0.432010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4721 | −0.756248 | −0.378124 | − | 0.925755i | \(-0.623431\pi\) | ||||
−0.378124 | + | 0.925755i | \(0.623431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.9443 | −0.972951 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.944272 | −0.0317055 | −0.0158528 | − | 0.999874i | \(-0.505046\pi\) | ||||
−0.0158528 | + | 0.999874i | \(0.505046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.8885 | −0.599963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.763932 | 0.0255927 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.8328 | −1.03178 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | −0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.47214 | −0.149320 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.9443 | −0.965346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.05573 | −0.101801 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.3050 | 1.37454 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.8885 | 0.727600 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1803 | 0.603668 | 0.301834 | − | 0.953360i | \(-0.402401\pi\) | ||||
0.301834 | + | 0.953360i | \(0.402401\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.47214 | −0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.4164 | −1.43845 | −0.719225 | − | 0.694777i | \(-0.755503\pi\) | ||||
−0.719225 | + | 0.694777i | \(0.755503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.69505 | −0.221574 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.9443 | 0.560160 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −82.6099 | −2.72802 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.52786 | 0.248321 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4164 | −0.376183 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.0000 | −1.31662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.0132 | 1.21699 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.8328 | 0.945974 | 0.472987 | − | 0.881069i | \(-0.343176\pi\) | ||||
0.472987 | + | 0.881069i | \(0.343176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 100.207 | 3.28414 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.05573 | −0.100040 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.88854 | 0.323390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.4721 | −0.798618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8197 | 0.515706 | 0.257853 | − | 0.966184i | \(-0.416985\pi\) | ||||
0.257853 | + | 0.966184i | \(0.416985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000 | 0.0651290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.4721 | −0.470779 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.1935 | −1.66357 | −0.831783 | − | 0.555102i | \(-0.812679\pi\) | ||||
−0.831783 | + | 0.555102i | \(0.812679\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.4721 | −0.923272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7771 | 0.770215 | 0.385108 | − | 0.922872i | \(-0.374164\pi\) | ||||
0.385108 | + | 0.922872i | \(0.374164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.41641 | −0.110437 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −93.6656 | −3.02462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.6525 | −0.601068 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.4721 | 1.23846 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.4164 | 0.367127 | 0.183563 | − | 0.983008i | \(-0.441237\pi\) | ||||
0.183563 | + | 0.983008i | \(0.441237\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.8328 | 0.990493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1246 | −0.677921 | −0.338961 | − | 0.940801i | \(-0.610075\pi\) | ||||
−0.338961 | + | 0.940801i | \(0.610075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.22291 | 0.135380 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.4721 | 0.783736 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.8328 | 1.75426 | 0.877129 | − | 0.480256i | \(-0.159456\pi\) | ||||
0.877129 | + | 0.480256i | \(0.159456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.16718 | −0.0373034 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.23607 | 0.294885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.4164 | −0.874448 | −0.437224 | − | 0.899353i | \(-0.644038\pi\) | ||||
−0.437224 | + | 0.899353i | \(0.644038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.3607 | 1.54090 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.8885 | −0.569399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.23607 | −0.293690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.52786 | 0.0485342 | 0.0242671 | − | 0.999706i | \(-0.492275\pi\) | ||||
0.0242671 | + | 0.999706i | \(0.492275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.52786 | −0.0484853 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.4721 | −0.966032 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9443 | 0.726652 | 0.363326 | − | 0.931662i | \(-0.381641\pi\) | ||||
0.363326 | + | 0.931662i | \(0.381641\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.76393 | −0.214001 |
(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 | 1104.2.a.j.1.1 | 2 | ||
3.2 | odd | 2 | 3312.2.a.bc.1.2 | 2 | |||
4.3 | odd | 2 | 138.2.a.d.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 4416.2.a.bh.1.2 | 2 | |||
8.5 | even | 2 | 4416.2.a.bl.1.2 | 2 | |||
12.11 | even | 2 | 414.2.a.f.1.2 | 2 | |||
20.3 | even | 4 | 3450.2.d.x.2899.1 | 4 | |||
20.7 | even | 4 | 3450.2.d.x.2899.4 | 4 | |||
20.19 | odd | 2 | 3450.2.a.be.1.1 | 2 | |||
28.27 | even | 2 | 6762.2.a.cb.1.2 | 2 | |||
92.91 | even | 2 | 3174.2.a.s.1.2 | 2 | |||
276.275 | odd | 2 | 9522.2.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
414.2.a.f.1.2 | 2 | 12.11 | even | 2 | |||
1104.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3174.2.a.s.1.2 | 2 | 92.91 | even | 2 | |||
3312.2.a.bc.1.2 | 2 | 3.2 | odd | 2 | |||
3450.2.a.be.1.1 | 2 | 20.19 | odd | 2 | |||
3450.2.d.x.2899.1 | 4 | 20.3 | even | 4 | |||
3450.2.d.x.2899.4 | 4 | 20.7 | even | 4 | |||
4416.2.a.bh.1.2 | 2 | 8.3 | odd | 2 | |||
4416.2.a.bl.1.2 | 2 | 8.5 | even | 2 | |||
6762.2.a.cb.1.2 | 2 | 28.27 | even | 2 | |||
9522.2.a.q.1.1 | 2 | 276.275 | odd | 2 |