Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3249,2,Mod(1,3249)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3249, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3249.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3249 = 3^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3249.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: | \(25.9433956167\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 361) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3249.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.23607 | −1.65579 | ||||||||
\(11\) | 1.61803 | 0.487856 | 0.243928 | − | 0.969793i | \(-0.421564\pi\) | ||||
0.243928 | + | 0.969793i | \(0.421564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 4.85410 | 1.29731 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.61803 | 0.558167 | ||||||||
\(23\) | −5.38197 | −1.12222 | −0.561109 | − | 0.827742i | \(-0.689625\pi\) | ||||
−0.561109 | + | 0.827742i | \(0.689625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 1.61803 | 0.317323 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | −3.61803 | −0.671852 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.85410 | 1.59024 | 0.795122 | − | 0.606450i | \(-0.207407\pi\) | ||||
0.795122 | + | 0.606450i | \(0.207407\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.23607 | −0.211984 | ||||||||
\(35\) | −9.70820 | −1.64099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.85410 | −1.45561 | −0.727803 | − | 0.685787i | \(-0.759458\pi\) | ||||
−0.727803 | + | 0.685787i | \(0.759458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.23607 | 1.14412 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.145898 | −0.0222492 | −0.0111246 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111246 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.70820 | −1.28395 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 8.85410 | 1.25216 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.618034 | 0.0857059 | ||||||||
\(53\) | −6.32624 | −0.868976 | −0.434488 | − | 0.900678i | \(-0.643071\pi\) | ||||
−0.434488 | + | 0.900678i | \(0.643071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.23607 | −0.706031 | ||||||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | 0.326238 | 0.0424726 | 0.0212363 | − | 0.999774i | \(-0.493240\pi\) | ||||
0.0212363 | + | 0.999774i | \(0.493240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2361 | −1.31059 | −0.655297 | − | 0.755371i | \(-0.727457\pi\) | ||||
−0.655297 | + | 0.755371i | \(0.727457\pi\) | |||||||
\(62\) | 14.3262 | 1.81943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −3.23607 | −0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | −0.472136 | −0.0572549 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −15.7082 | −1.87749 | ||||||||
\(71\) | −7.47214 | −0.886779 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.70820 | −0.316971 | −0.158486 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158486 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(74\) | −14.3262 | −1.66539 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.85410 | 0.553176 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4164 | −1.50946 | −0.754732 | − | 0.656033i | \(-0.772233\pi\) | ||||
−0.754732 | + | 0.656033i | \(0.772233\pi\) | |||||||
\(80\) | 15.7082 | 1.75623 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.85410 | −0.536046 | ||||||||
\(83\) | −8.47214 | −0.929938 | −0.464969 | − | 0.885327i | \(-0.653934\pi\) | ||||
−0.464969 | + | 0.885327i | \(0.653934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.47214 | 0.268141 | ||||||||
\(86\) | −0.236068 | −0.0254559 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.61803 | −0.385684 | ||||||||
\(89\) | −7.76393 | −0.822975 | −0.411488 | − | 0.911415i | \(-0.634991\pi\) | ||||
−0.411488 | + | 0.911415i | \(0.634991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | 0.314485 | ||||||||
\(92\) | −3.32624 | −0.346784 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.85410 | −0.500662 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8541 | −1.40667 | −0.703335 | − | 0.710858i | \(-0.748307\pi\) | ||||
−0.703335 | + | 0.710858i | \(0.748307\pi\) | |||||||
\(98\) | 3.23607 | 0.326892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.38197 | 0.338197 | ||||||||
\(101\) | 9.18034 | 0.913478 | 0.456739 | − | 0.889601i | \(-0.349017\pi\) | ||||
0.456739 | + | 0.889601i | \(0.349017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3262 | −1.41161 | −0.705803 | − | 0.708408i | \(-0.749414\pi\) | ||||
−0.705803 | + | 0.708408i | \(0.749414\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2361 | −0.994215 | ||||||||
\(107\) | 16.4164 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.29180 | 0.315297 | 0.157648 | − | 0.987495i | \(-0.449609\pi\) | ||||
0.157648 | + | 0.987495i | \(0.449609\pi\) | |||||||
\(110\) | −8.47214 | −0.807786 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.5623 | −1.37601 | ||||||||
\(113\) | 6.76393 | 0.636297 | 0.318149 | − | 0.948041i | \(-0.396939\pi\) | ||||
0.318149 | + | 0.948041i | \(0.396939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4164 | 1.62409 | ||||||||
\(116\) | −2.23607 | −0.207614 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.527864 | 0.0485938 | ||||||||
\(119\) | −2.29180 | −0.210089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.38197 | −0.761997 | ||||||||
\(122\) | −16.5623 | −1.49948 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.47214 | 0.491412 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76393 | −0.511466 | −0.255733 | − | 0.966747i | \(-0.582317\pi\) | ||||
−0.255733 | + | 0.966747i | \(0.582317\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.23607 | −0.459234 | ||||||||
\(131\) | −15.0902 | −1.31843 | −0.659217 | − | 0.751953i | \(-0.729112\pi\) | ||||
−0.659217 | + | 0.751953i | \(0.729112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.3262 | 0.978438 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.70820 | 0.146477 | ||||||||
\(137\) | −7.47214 | −0.638388 | −0.319194 | − | 0.947689i | \(-0.603412\pi\) | ||||
−0.319194 | + | 0.947689i | \(0.603412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7984 | 1.25518 | 0.627591 | − | 0.778543i | \(-0.284041\pi\) | ||||
0.627591 | + | 0.778543i | \(0.284041\pi\) | |||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0902 | −1.01458 | ||||||||
\(143\) | 1.61803 | 0.135307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7082 | 0.972313 | ||||||||
\(146\) | −4.38197 | −0.362654 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.47214 | −0.449807 | ||||||||
\(149\) | 1.90983 | 0.156459 | 0.0782297 | − | 0.996935i | \(-0.475073\pi\) | ||||
0.0782297 | + | 0.996935i | \(0.475073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.0902 | 1.71629 | 0.858147 | − | 0.513404i | \(-0.171616\pi\) | ||||
0.858147 | + | 0.513404i | \(0.171616\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.85410 | 0.632902 | ||||||||
\(155\) | −28.6525 | −2.30142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.8541 | −1.42491 | −0.712456 | − | 0.701717i | \(-0.752417\pi\) | ||||
−0.712456 | + | 0.701717i | \(0.752417\pi\) | |||||||
\(158\) | −21.7082 | −1.72701 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.9443 | 0.865221 | ||||||||
\(161\) | −16.1459 | −1.27248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.76393 | 0.138162 | 0.0690809 | − | 0.997611i | \(-0.477993\pi\) | ||||
0.0690809 | + | 0.997611i | \(0.477993\pi\) | |||||||
\(164\) | −1.85410 | −0.144781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.7082 | −1.06396 | ||||||||
\(167\) | 20.2361 | 1.56591 | 0.782957 | − | 0.622076i | \(-0.213710\pi\) | ||||
0.782957 | + | 0.622076i | \(0.213710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0901699 | −0.00687539 | ||||||||
\(173\) | −0.472136 | −0.0358958 | −0.0179479 | − | 0.999839i | \(-0.505713\pi\) | ||||
−0.0179479 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.4164 | 1.24096 | ||||||||
\(176\) | −7.85410 | −0.592025 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.5623 | −0.941585 | ||||||||
\(179\) | 12.2361 | 0.914567 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0000 | −0.891953 | −0.445976 | − | 0.895045i | \(-0.647144\pi\) | ||||
−0.445976 | + | 0.895045i | \(0.647144\pi\) | |||||||
\(182\) | 4.85410 | 0.359810 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0344 | 0.887191 | ||||||||
\(185\) | 28.6525 | 2.10657 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23607 | −0.0903902 | ||||||||
\(188\) | −1.85410 | −0.135224 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2361 | −1.03009 | −0.515043 | − | 0.857164i | \(-0.672224\pi\) | ||||
−0.515043 | + | 0.857164i | \(0.672224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.05573 | −0.363919 | −0.181960 | − | 0.983306i | \(-0.558244\pi\) | ||||
−0.181960 | + | 0.983306i | \(0.558244\pi\) | |||||||
\(194\) | −22.4164 | −1.60940 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23607 | 0.0882906 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4164 | −0.951064 | −0.475532 | − | 0.879698i | \(-0.657744\pi\) | ||||
−0.475532 | + | 0.879698i | \(0.657744\pi\) | |||||||
\(200\) | −12.2361 | −0.865221 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.8541 | 1.04513 | ||||||||
\(203\) | −10.8541 | −0.761809 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.70820 | 0.678050 | ||||||||
\(206\) | −23.1803 | −1.61505 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.85410 | 0.265327 | 0.132664 | − | 0.991161i | \(-0.457647\pi\) | ||||
0.132664 | + | 0.991161i | \(0.457647\pi\) | |||||||
\(212\) | −3.90983 | −0.268528 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.5623 | 1.81576 | ||||||||
\(215\) | 0.472136 | 0.0321994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.5623 | 1.80317 | ||||||||
\(218\) | 5.32624 | 0.360738 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.23607 | −0.218176 | ||||||||
\(221\) | −0.763932 | −0.0513876 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6525 | 0.780307 | 0.390154 | − | 0.920750i | \(-0.372422\pi\) | ||||
0.390154 | + | 0.920750i | \(0.372422\pi\) | |||||||
\(224\) | −10.1459 | −0.677901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.9443 | 0.728002 | ||||||||
\(227\) | 16.4164 | 1.08960 | 0.544798 | − | 0.838568i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838568i | \(0.316606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6180 | −0.899905 | −0.449953 | − | 0.893052i | \(-0.648559\pi\) | ||||
−0.449953 | + | 0.893052i | \(0.648559\pi\) | |||||||
\(230\) | 28.1803 | 1.85816 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.09017 | 0.531146 | ||||||||
\(233\) | −4.52786 | −0.296630 | −0.148315 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148315 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.70820 | 0.633293 | ||||||||
\(236\) | 0.201626 | 0.0131247 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.70820 | −0.240367 | ||||||||
\(239\) | 0.326238 | 0.0211026 | 0.0105513 | − | 0.999944i | \(-0.496641\pi\) | ||||
0.0105513 | + | 0.999944i | \(0.496641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.18034 | −0.204864 | −0.102432 | − | 0.994740i | \(-0.532662\pi\) | ||||
−0.102432 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(242\) | −13.5623 | −0.871818 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.32624 | −0.404996 | ||||||||
\(245\) | −6.47214 | −0.413490 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −19.7984 | −1.25720 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.47214 | −0.156352 | ||||||||
\(251\) | 25.3607 | 1.60075 | 0.800376 | − | 0.599498i | \(-0.204633\pi\) | ||||
0.800376 | + | 0.599498i | \(0.204633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.70820 | −0.547480 | ||||||||
\(254\) | −9.32624 | −0.585180 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 20.3607 | 1.27006 | 0.635032 | − | 0.772486i | \(-0.280987\pi\) | ||||
0.635032 | + | 0.772486i | \(0.280987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.5623 | −1.65050 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.4164 | −1.50845 | ||||||||
\(263\) | 14.9443 | 0.921503 | 0.460752 | − | 0.887529i | \(-0.347580\pi\) | ||||
0.460752 | + | 0.887529i | \(0.347580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.4721 | 1.25759 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.32624 | 0.264267 | ||||||||
\(269\) | 30.3262 | 1.84902 | 0.924512 | − | 0.381154i | \(-0.124473\pi\) | ||||
0.924512 | + | 0.381154i | \(0.124473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14590 | 0.0696083 | 0.0348042 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348042 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(272\) | 3.70820 | 0.224843 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0902 | −0.730394 | ||||||||
\(275\) | 8.85410 | 0.533922 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4164 | 0.685945 | 0.342973 | − | 0.939345i | \(-0.388566\pi\) | ||||
0.342973 | + | 0.939345i | \(0.388566\pi\) | |||||||
\(278\) | 23.9443 | 1.43608 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 21.7082 | 1.29731 | ||||||||
\(281\) | −29.5066 | −1.76021 | −0.880107 | − | 0.474775i | \(-0.842530\pi\) | ||||
−0.880107 | + | 0.474775i | \(0.842530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.0344 | 1.54759 | 0.773793 | − | 0.633438i | \(-0.218357\pi\) | ||||
0.773793 | + | 0.633438i | \(0.218357\pi\) | |||||||
\(284\) | −4.61803 | −0.274030 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.61803 | 0.154808 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 18.9443 | 1.11245 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.67376 | −0.0979495 | ||||||||
\(293\) | −10.1459 | −0.592730 | −0.296365 | − | 0.955075i | \(-0.595774\pi\) | ||||
−0.296365 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.05573 | −0.0614669 | ||||||||
\(296\) | 19.7984 | 1.15076 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.09017 | 0.179009 | ||||||||
\(299\) | −5.38197 | −0.311247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.437694 | −0.0252283 | ||||||||
\(302\) | 34.1246 | 1.96365 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.1246 | 1.89671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3262 | 0.988861 | 0.494430 | − | 0.869217i | \(-0.335377\pi\) | ||||
0.494430 | + | 0.869217i | \(0.335377\pi\) | |||||||
\(308\) | 3.00000 | 0.170941 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −46.3607 | −2.63311 | ||||||||
\(311\) | −12.6525 | −0.717456 | −0.358728 | − | 0.933442i | \(-0.616789\pi\) | ||||
−0.358728 | + | 0.933442i | \(0.616789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3262 | −0.640197 | −0.320098 | − | 0.947384i | \(-0.603716\pi\) | ||||
−0.320098 | + | 0.947384i | \(0.603716\pi\) | |||||||
\(314\) | −28.8885 | −1.63027 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.29180 | −0.466450 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.85410 | −0.327767 | ||||||||
\(320\) | −13.7082 | −0.766312 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −26.1246 | −1.45587 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.47214 | 0.303539 | ||||||||
\(326\) | 2.85410 | 0.158074 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.70820 | 0.370399 | ||||||||
\(329\) | −9.00000 | −0.496186 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9443 | −0.601552 | −0.300776 | − | 0.953695i | \(-0.597246\pi\) | ||||
−0.300776 | + | 0.953695i | \(0.597246\pi\) | |||||||
\(332\) | −5.23607 | −0.287367 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.7426 | 1.79160 | ||||||||
\(335\) | −22.6525 | −1.23764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1246 | 0.932837 | 0.466419 | − | 0.884564i | \(-0.345544\pi\) | ||||
0.466419 | + | 0.884564i | \(0.345544\pi\) | |||||||
\(338\) | −19.4164 | −1.05611 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.52786 | 0.0828601 | ||||||||
\(341\) | 14.3262 | 0.775809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0.326238 | 0.0175896 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.763932 | −0.0410692 | ||||||||
\(347\) | 25.4164 | 1.36442 | 0.682212 | − | 0.731154i | \(-0.261018\pi\) | ||||
0.682212 | + | 0.731154i | \(0.261018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.9787 | −1.12296 | −0.561482 | − | 0.827489i | \(-0.689769\pi\) | ||||
−0.561482 | + | 0.827489i | \(0.689769\pi\) | |||||||
\(350\) | 26.5623 | 1.41981 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.47214 | −0.291666 | ||||||||
\(353\) | −24.4508 | −1.30139 | −0.650694 | − | 0.759340i | \(-0.725522\pi\) | ||||
−0.650694 | + | 0.759340i | \(0.725522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.1803 | 1.28336 | ||||||||
\(356\) | −4.79837 | −0.254313 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.7984 | 1.04638 | ||||||||
\(359\) | −7.03444 | −0.371264 | −0.185632 | − | 0.982619i | \(-0.559433\pi\) | ||||
−0.185632 | + | 0.982619i | \(0.559433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −19.4164 | −1.02050 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.85410 | 0.0971813 | ||||||||
\(365\) | 8.76393 | 0.458725 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.9443 | −0.832284 | −0.416142 | − | 0.909300i | \(-0.636618\pi\) | ||||
−0.416142 | + | 0.909300i | \(0.636618\pi\) | |||||||
\(368\) | 26.1246 | 1.36184 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 46.3607 | 2.41018 | ||||||||
\(371\) | −18.9787 | −0.985326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.47214 | 0.283336 | 0.141668 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141668 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(374\) | −2.00000 | −0.103418 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.70820 | 0.345949 | ||||||||
\(377\) | −3.61803 | −0.186338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1246 | 0.776899 | 0.388450 | − | 0.921470i | \(-0.373011\pi\) | ||||
0.388450 | + | 0.921470i | \(0.373011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.0344 | −1.17854 | ||||||||
\(383\) | 0.381966 | 0.0195176 | 0.00975878 | − | 0.999952i | \(-0.496894\pi\) | ||||
0.00975878 | + | 0.999952i | \(0.496894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.7082 | −0.800564 | ||||||||
\(386\) | −8.18034 | −0.416368 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.56231 | −0.434685 | ||||||||
\(389\) | −9.27051 | −0.470034 | −0.235017 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235017 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.11146 | 0.207925 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.85410 | −0.244546 | ||||||||
\(395\) | 43.4164 | 2.18452 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4721 | −0.575770 | −0.287885 | − | 0.957665i | \(-0.592952\pi\) | ||||
−0.287885 | + | 0.957665i | \(0.592952\pi\) | |||||||
\(398\) | −21.7082 | −1.08813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | −35.8885 | −1.79219 | −0.896094 | − | 0.443864i | \(-0.853607\pi\) | ||||
−0.896094 | + | 0.443864i | \(0.853607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.85410 | 0.441054 | ||||||||
\(404\) | 5.67376 | 0.282280 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5623 | −0.871603 | ||||||||
\(407\) | −14.3262 | −0.710125 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.29180 | 0.410003 | 0.205001 | − | 0.978762i | \(-0.434280\pi\) | ||||
0.205001 | + | 0.978762i | \(0.434280\pi\) | |||||||
\(410\) | 15.7082 | 0.775773 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.85410 | −0.436210 | ||||||||
\(413\) | 0.978714 | 0.0481594 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.4164 | 1.34582 | ||||||||
\(416\) | −3.38197 | −0.165815 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.94427 | 0.436956 | 0.218478 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218478 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4721 | 1.33891 | 0.669455 | − | 0.742853i | \(-0.266528\pi\) | ||||
0.669455 | + | 0.742853i | \(0.266528\pi\) | |||||||
\(422\) | 6.23607 | 0.303567 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.1459 | 0.686986 | ||||||||
\(425\) | −4.18034 | −0.202776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.7082 | −1.48607 | ||||||||
\(428\) | 10.1459 | 0.490420 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.763932 | 0.0368401 | ||||||||
\(431\) | 27.6525 | 1.33197 | 0.665986 | − | 0.745964i | \(-0.268011\pi\) | ||||
0.665986 | + | 0.745964i | \(0.268011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.43769 | 0.165205 | 0.0826025 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826025 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(434\) | 42.9787 | 2.06304 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.03444 | 0.0974321 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5967 | 1.65121 | 0.825606 | − | 0.564247i | \(-0.190833\pi\) | ||||
0.825606 | + | 0.564247i | \(0.190833\pi\) | |||||||
\(440\) | 11.7082 | 0.558167 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.23607 | −0.0587938 | ||||||||
\(443\) | 7.58359 | 0.360307 | 0.180154 | − | 0.983638i | \(-0.442340\pi\) | ||||
0.180154 | + | 0.983638i | \(0.442340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.1246 | 1.19102 | ||||||||
\(446\) | 18.8541 | 0.892768 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.7082 | 0.600406 | ||||||||
\(449\) | 2.88854 | 0.136319 | 0.0681594 | − | 0.997674i | \(-0.478287\pi\) | ||||
0.0681594 | + | 0.997674i | \(0.478287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.85410 | −0.228571 | ||||||||
\(452\) | 4.18034 | 0.196627 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.5623 | 1.24663 | ||||||||
\(455\) | −9.70820 | −0.455128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7082 | 0.921911 | 0.460955 | − | 0.887423i | \(-0.347507\pi\) | ||||
0.460955 | + | 0.887423i | \(0.347507\pi\) | |||||||
\(458\) | −22.0344 | −1.02960 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.7639 | 0.501871 | ||||||||
\(461\) | −20.9443 | −0.975472 | −0.487736 | − | 0.872991i | \(-0.662177\pi\) | ||||
−0.487736 | + | 0.872991i | \(0.662177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.2705 | 1.31384 | 0.656921 | − | 0.753959i | \(-0.271858\pi\) | ||||
0.656921 | + | 0.753959i | \(0.271858\pi\) | |||||||
\(464\) | 17.5623 | 0.815310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.32624 | −0.339381 | ||||||||
\(467\) | 15.9443 | 0.737813 | 0.368906 | − | 0.929467i | \(-0.379732\pi\) | ||||
0.368906 | + | 0.929467i | \(0.379732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 15.7082 | 0.724565 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.729490 | −0.0335775 | ||||||||
\(473\) | −0.236068 | −0.0108544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.41641 | −0.0649209 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.527864 | 0.0241439 | ||||||||
\(479\) | −23.0902 | −1.05502 | −0.527508 | − | 0.849550i | \(-0.676874\pi\) | ||||
−0.527508 | + | 0.849550i | \(0.676874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.85410 | −0.403712 | ||||||||
\(482\) | −5.14590 | −0.234389 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.18034 | −0.235470 | ||||||||
\(485\) | 44.8328 | 2.03575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.18034 | −0.189429 | −0.0947146 | − | 0.995504i | \(-0.530194\pi\) | ||||
−0.0947146 | + | 0.995504i | \(0.530194\pi\) | |||||||
\(488\) | 22.8885 | 1.03612 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.4721 | −0.473083 | ||||||||
\(491\) | 21.2148 | 0.957410 | 0.478705 | − | 0.877976i | \(-0.341106\pi\) | ||||
0.478705 | + | 0.877976i | \(0.341106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.76393 | 0.124481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42.9787 | −1.92980 | ||||||||
\(497\) | −22.4164 | −1.00551 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.1246 | 1.12473 | 0.562366 | − | 0.826888i | \(-0.309891\pi\) | ||||
0.562366 | + | 0.826888i | \(0.309891\pi\) | |||||||
\(500\) | −0.944272 | −0.0422291 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.0344 | 1.83146 | ||||||||
\(503\) | −35.8328 | −1.59771 | −0.798853 | − | 0.601526i | \(-0.794560\pi\) | ||||
−0.798853 | + | 0.601526i | \(0.794560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.7082 | −1.32200 | ||||||||
\(506\) | −14.0902 | −0.626384 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.56231 | −0.158052 | ||||||||
\(509\) | 2.03444 | 0.0901750 | 0.0450875 | − | 0.998983i | \(-0.485643\pi\) | ||||
0.0450875 | + | 0.998983i | \(0.485643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.12461 | −0.359412 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.9443 | 1.45311 | ||||||||
\(515\) | 46.3607 | 2.04290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.85410 | −0.213483 | ||||||||
\(518\) | −42.9787 | −1.88838 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.23607 | 0.317323 | ||||||||
\(521\) | 6.27051 | 0.274716 | 0.137358 | − | 0.990521i | \(-0.456139\pi\) | ||||
0.137358 | + | 0.990521i | \(0.456139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.41641 | 0.193116 | 0.0965580 | − | 0.995327i | \(-0.469217\pi\) | ||||
0.0965580 | + | 0.995327i | \(0.469217\pi\) | |||||||
\(524\) | −9.32624 | −0.407419 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1803 | 1.05431 | ||||||||
\(527\) | −6.76393 | −0.294642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.96556 | 0.259372 | ||||||||
\(530\) | 33.1246 | 1.43884 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.00000 | −0.129944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.1246 | −2.29678 | ||||||||
\(536\) | −15.6525 | −0.676084 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 49.0689 | 2.11551 | ||||||||
\(539\) | 3.23607 | 0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.8328 | −1.28261 | −0.641306 | − | 0.767285i | \(-0.721607\pi\) | ||||
−0.641306 | + | 0.767285i | \(0.721607\pi\) | |||||||
\(542\) | 1.85410 | 0.0796405 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.58359 | 0.110771 | ||||||||
\(545\) | −10.6525 | −0.456302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.9230 | 1.15114 | 0.575572 | − | 0.817751i | \(-0.304779\pi\) | ||||
0.575572 | + | 0.817751i | \(0.304779\pi\) | |||||||
\(548\) | −4.61803 | −0.197273 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.3262 | 0.610873 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.2492 | −1.71157 | ||||||||
\(554\) | 18.4721 | 0.784806 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.14590 | 0.387872 | ||||||||
\(557\) | 0.819660 | 0.0347301 | 0.0173651 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173651 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.145898 | −0.00617083 | ||||||||
\(560\) | 47.1246 | 1.99138 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −47.7426 | −2.01390 | ||||||||
\(563\) | −32.8328 | −1.38374 | −0.691869 | − | 0.722023i | \(-0.743212\pi\) | ||||
−0.691869 | + | 0.722023i | \(0.743212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.8885 | −0.920858 | ||||||||
\(566\) | 42.1246 | 1.77063 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.7082 | 0.701061 | ||||||||
\(569\) | 16.9098 | 0.708897 | 0.354448 | − | 0.935076i | \(-0.384669\pi\) | ||||
0.354448 | + | 0.935076i | \(0.384669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67376 | 0.279288 | 0.139644 | − | 0.990202i | \(-0.455404\pi\) | ||||
0.139644 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(572\) | 1.00000 | 0.0418121 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.5623 | −0.607819 | ||||||||
\(575\) | −29.4508 | −1.22819 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.1246 | −0.504754 | −0.252377 | − | 0.967629i | \(-0.581212\pi\) | ||||
−0.252377 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(578\) | −26.5623 | −1.10485 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.23607 | 0.300461 | ||||||||
\(581\) | −25.4164 | −1.05445 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.2361 | −0.423935 | ||||||||
\(584\) | 6.05573 | 0.250588 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.4164 | −0.678156 | ||||||||
\(587\) | 2.12461 | 0.0876921 | 0.0438461 | − | 0.999038i | \(-0.486039\pi\) | ||||
0.0438461 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.70820 | −0.0703256 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 42.9787 | 1.76641 | ||||||||
\(593\) | −0.708204 | −0.0290824 | −0.0145412 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145412 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.41641 | 0.304043 | ||||||||
\(596\) | 1.18034 | 0.0483486 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.70820 | −0.356105 | ||||||||
\(599\) | 28.4164 | 1.16106 | 0.580531 | − | 0.814238i | \(-0.302845\pi\) | ||||
0.580531 | + | 0.814238i | \(0.302845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2918 | −0.827720 | −0.413860 | − | 0.910341i | \(-0.635820\pi\) | ||||
−0.413860 | + | 0.910341i | \(0.635820\pi\) | |||||||
\(602\) | −0.708204 | −0.0288642 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.0344 | 0.530364 | ||||||||
\(605\) | 27.1246 | 1.10277 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.27051 | 0.254512 | 0.127256 | − | 0.991870i | \(-0.459383\pi\) | ||||
0.127256 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 53.5967 | 2.17007 | ||||||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.9443 | −0.805542 | −0.402771 | − | 0.915301i | \(-0.631953\pi\) | ||||
−0.402771 | + | 0.915301i | \(0.631953\pi\) | |||||||
\(614\) | 28.0344 | 1.13138 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.8541 | −0.437324 | ||||||||
\(617\) | −7.67376 | −0.308934 | −0.154467 | − | 0.987998i | \(-0.549366\pi\) | ||||
−0.154467 | + | 0.987998i | \(0.549366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1246 | 0.406943 | 0.203471 | − | 0.979081i | \(-0.434778\pi\) | ||||
0.203471 | + | 0.979081i | \(0.434778\pi\) | |||||||
\(620\) | −17.7082 | −0.711179 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.4721 | −0.820858 | ||||||||
\(623\) | −23.2918 | −0.933166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −18.3262 | −0.732464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0344 | −0.440322 | ||||||||
\(629\) | 6.76393 | 0.269696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3607 | 1.16883 | 0.584415 | − | 0.811455i | \(-0.301324\pi\) | ||||
0.584415 | + | 0.811455i | \(0.301324\pi\) | |||||||
\(632\) | 30.0000 | 1.19334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.1246 | 1.15669 | ||||||||
\(635\) | 18.6525 | 0.740201 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | −9.47214 | −0.375005 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −44.0689 | −1.74198 | ||||||||
\(641\) | −39.5066 | −1.56042 | −0.780208 | − | 0.625520i | \(-0.784887\pi\) | ||||
−0.780208 | + | 0.625520i | \(0.784887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2918 | −0.957975 | −0.478987 | − | 0.877822i | \(-0.658996\pi\) | ||||
−0.478987 | + | 0.877822i | \(0.658996\pi\) | |||||||
\(644\) | −9.97871 | −0.393216 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.47214 | −0.293760 | −0.146880 | − | 0.989154i | \(-0.546923\pi\) | ||||
−0.146880 | + | 0.989154i | \(0.546923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.527864 | 0.0207205 | ||||||||
\(650\) | 8.85410 | 0.347286 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.09017 | 0.0426944 | ||||||||
\(653\) | 23.5623 | 0.922064 | 0.461032 | − | 0.887383i | \(-0.347479\pi\) | ||||
0.461032 | + | 0.887383i | \(0.347479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.8328 | 1.90806 | ||||||||
\(656\) | 14.5623 | 0.568563 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.5623 | −0.567698 | ||||||||
\(659\) | −25.7771 | −1.00413 | −0.502066 | − | 0.864829i | \(-0.667427\pi\) | ||||
−0.502066 | + | 0.864829i | \(0.667427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.41641 | −0.210674 | −0.105337 | − | 0.994437i | \(-0.533592\pi\) | ||||
−0.105337 | + | 0.994437i | \(0.533592\pi\) | |||||||
\(662\) | −17.7082 | −0.688249 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.9443 | 0.735180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.4721 | 0.753964 | ||||||||
\(668\) | 12.5066 | 0.483894 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36.6525 | −1.41601 | ||||||||
\(671\) | −16.5623 | −0.639381 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.1246 | −1.31541 | −0.657704 | − | 0.753277i | \(-0.728472\pi\) | ||||
−0.657704 | + | 0.753277i | \(0.728472\pi\) | |||||||
\(674\) | 27.7082 | 1.06728 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.41641 | −0.285246 | ||||||||
\(677\) | −30.7426 | −1.18154 | −0.590768 | − | 0.806842i | \(-0.701175\pi\) | ||||
−0.590768 | + | 0.806842i | \(0.701175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.5623 | −1.59501 | ||||||||
\(680\) | −5.52786 | −0.211984 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.1803 | 0.887621 | ||||||||
\(683\) | 9.65248 | 0.369342 | 0.184671 | − | 0.982800i | \(-0.440878\pi\) | ||||
0.184671 | + | 0.982800i | \(0.440878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1803 | 0.923883 | ||||||||
\(686\) | −24.2705 | −0.926652 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.708204 | 0.0270000 | ||||||||
\(689\) | −6.32624 | −0.241010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.1803 | −1.49049 | −0.745245 | − | 0.666791i | \(-0.767668\pi\) | ||||
−0.745245 | + | 0.666791i | \(0.767668\pi\) | |||||||
\(692\) | −0.291796 | −0.0110924 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.1246 | 1.56107 | ||||||||
\(695\) | −47.8885 | −1.81652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.29180 | 0.0868080 | ||||||||
\(698\) | −33.9443 | −1.28481 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.1459 | 0.383479 | ||||||||
\(701\) | 39.6312 | 1.49685 | 0.748425 | − | 0.663220i | \(-0.230811\pi\) | ||||
0.748425 | + | 0.663220i | \(0.230811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 6.85410 | 0.258324 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.5623 | −1.48895 | ||||||||
\(707\) | 27.5410 | 1.03579 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5836 | 0.622810 | 0.311405 | − | 0.950277i | \(-0.399200\pi\) | ||||
0.311405 | + | 0.950277i | \(0.399200\pi\) | |||||||
\(710\) | 39.1246 | 1.46832 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.3607 | 0.650619 | ||||||||
\(713\) | −47.6525 | −1.78460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.23607 | −0.195818 | ||||||||
\(716\) | 7.56231 | 0.282617 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.3820 | −0.424771 | ||||||||
\(719\) | −47.0344 | −1.75409 | −0.877044 | − | 0.480409i | \(-0.840488\pi\) | ||||
−0.877044 | + | 0.480409i | \(0.840488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.9787 | −1.60061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.41641 | −0.275629 | ||||||||
\(725\) | −19.7984 | −0.735293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0689 | −0.595962 | −0.297981 | − | 0.954572i | \(-0.596313\pi\) | ||||
−0.297981 | + | 0.954572i | \(0.596313\pi\) | |||||||
\(728\) | −6.70820 | −0.248623 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.1803 | 0.524838 | ||||||||
\(731\) | 0.111456 | 0.00412236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.9574 | −1.95603 | −0.978014 | − | 0.208541i | \(-0.933129\pi\) | ||||
−0.978014 | + | 0.208541i | \(0.933129\pi\) | |||||||
\(734\) | −25.7984 | −0.952235 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.2016 | 0.670921 | ||||||||
\(737\) | 11.3262 | 0.417207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0000 | −0.919640 | −0.459820 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459820 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(740\) | 17.7082 | 0.650967 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.7082 | −1.12733 | ||||||||
\(743\) | −3.36068 | −0.123291 | −0.0616457 | − | 0.998098i | \(-0.519635\pi\) | ||||
−0.0616457 | + | 0.998098i | \(0.519635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.18034 | −0.226430 | ||||||||
\(746\) | 8.85410 | 0.324172 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.763932 | −0.0279321 | ||||||||
\(749\) | 49.2492 | 1.79953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.1459 | 0.625663 | 0.312831 | − | 0.949809i | \(-0.398723\pi\) | ||||
0.312831 | + | 0.949809i | \(0.398723\pi\) | |||||||
\(752\) | 14.5623 | 0.531033 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.85410 | −0.213194 | ||||||||
\(755\) | −68.2492 | −2.48384 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7426 | 0.971978 | 0.485989 | − | 0.873965i | \(-0.338460\pi\) | ||||
0.485989 | + | 0.873965i | \(0.338460\pi\) | |||||||
\(758\) | 24.4721 | 0.888868 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.88854 | −0.177210 | −0.0886048 | − | 0.996067i | \(-0.528241\pi\) | ||||
−0.0886048 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.87539 | 0.357513 | ||||||||
\(764\) | −8.79837 | −0.318314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.618034 | 0.0223305 | ||||||||
\(767\) | 0.326238 | 0.0117798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.6312 | 1.32095 | 0.660477 | − | 0.750846i | \(-0.270354\pi\) | ||||
0.660477 | + | 0.750846i | \(0.270354\pi\) | |||||||
\(770\) | −25.4164 | −0.915944 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.12461 | −0.112457 | ||||||||
\(773\) | −35.9230 | −1.29206 | −0.646030 | − | 0.763312i | \(-0.723572\pi\) | ||||
−0.646030 | + | 0.763312i | \(0.723572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.4508 | 1.74041 | ||||||||
\(776\) | 30.9787 | 1.11207 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0000 | −0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0902 | −0.432620 | ||||||||
\(782\) | 6.65248 | 0.237892 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.70820 | −0.346722 | ||||||||
\(785\) | 57.7771 | 2.06215 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.0000 | −1.35455 | −0.677277 | − | 0.735728i | \(-0.736840\pi\) | ||||
−0.677277 | + | 0.735728i | \(0.736840\pi\) | |||||||
\(788\) | −1.85410 | −0.0660496 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 70.2492 | 2.49936 | ||||||||
\(791\) | 20.2918 | 0.721493 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2361 | −0.363493 | ||||||||
\(794\) | −18.5623 | −0.658752 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.29180 | −0.293895 | ||||||||
\(797\) | −20.2918 | −0.718772 | −0.359386 | − | 0.933189i | \(-0.617014\pi\) | ||||
−0.359386 | + | 0.933189i | \(0.617014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.29180 | 0.0810779 | ||||||||
\(800\) | −18.5066 | −0.654306 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −58.0689 | −2.05048 | ||||||||
\(803\) | −4.38197 | −0.154636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 52.2492 | 1.84154 | ||||||||
\(806\) | 14.3262 | 0.504620 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.5279 | −0.722168 | ||||||||
\(809\) | 24.7984 | 0.871864 | 0.435932 | − | 0.899980i | \(-0.356419\pi\) | ||||
0.435932 | + | 0.899980i | \(0.356419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9787 | −0.806892 | −0.403446 | − | 0.915004i | \(-0.632188\pi\) | ||||
−0.403446 | + | 0.915004i | \(0.632188\pi\) | |||||||
\(812\) | −6.70820 | −0.235412 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.1803 | −0.812470 | ||||||||
\(815\) | −5.70820 | −0.199950 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13.4164 | 0.469094 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −52.0476 | −1.81647 | −0.908237 | − | 0.418457i | \(-0.862571\pi\) | ||||
−0.908237 | + | 0.418457i | \(0.862571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5967 | −0.892247 | −0.446123 | − | 0.894972i | \(-0.647196\pi\) | ||||
−0.446123 | + | 0.894972i | \(0.647196\pi\) | |||||||
\(824\) | 32.0344 | 1.11597 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.58359 | 0.0551002 | ||||||||
\(827\) | 32.5967 | 1.13350 | 0.566750 | − | 0.823890i | \(-0.308201\pi\) | ||||
0.566750 | + | 0.823890i | \(0.308201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.67376 | −0.162326 | −0.0811632 | − | 0.996701i | \(-0.525864\pi\) | ||||
−0.0811632 | + | 0.996701i | \(0.525864\pi\) | |||||||
\(830\) | 44.3607 | 1.53978 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.23607 | 0.146859 | ||||||||
\(833\) | −1.52786 | −0.0529374 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.4853 | −2.26621 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.4721 | 0.499932 | ||||||||
\(839\) | 15.2016 | 0.524818 | 0.262409 | − | 0.964957i | \(-0.415483\pi\) | ||||
0.262409 | + | 0.964957i | \(0.415483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 44.4508 | 1.53188 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.38197 | 0.0819907 | ||||||||
\(845\) | 38.8328 | 1.33589 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.1459 | −0.864023 | ||||||||
\(848\) | 30.7082 | 1.05452 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.76393 | −0.232001 | ||||||||
\(851\) | 47.6525 | 1.63351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.7082 | 1.05143 | 0.525714 | − | 0.850661i | \(-0.323798\pi\) | ||||
0.525714 | + | 0.850661i | \(0.323798\pi\) | |||||||
\(854\) | −49.6869 | −1.70025 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | −10.6180 | −0.362705 | −0.181353 | − | 0.983418i | \(-0.558048\pi\) | ||||
−0.181353 | + | 0.983418i | \(0.558048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.5410 | −1.65620 | −0.828099 | − | 0.560582i | \(-0.810578\pi\) | ||||
−0.828099 | + | 0.560582i | \(0.810578\pi\) | |||||||
\(860\) | 0.291796 | 0.00995016 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.7426 | 1.52394 | ||||||||
\(863\) | −27.0557 | −0.920988 | −0.460494 | − | 0.887663i | \(-0.652328\pi\) | ||||
−0.460494 | + | 0.887663i | \(0.652328\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.52786 | 0.0519489 | ||||||||
\(866\) | 5.56231 | 0.189015 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.4164 | 0.557209 | ||||||||
\(869\) | −21.7082 | −0.736400 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | 0.237186 | ||||||||
\(872\) | −7.36068 | −0.249264 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.58359 | −0.154954 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.8197 | −0.399122 | −0.199561 | − | 0.979885i | \(-0.563952\pi\) | ||||
−0.199561 | + | 0.979885i | \(0.563952\pi\) | |||||||
\(878\) | 55.9787 | 1.88919 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25.4164 | 0.856787 | ||||||||
\(881\) | −32.4508 | −1.09330 | −0.546648 | − | 0.837362i | \(-0.684097\pi\) | ||||
−0.546648 | + | 0.837362i | \(0.684097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.9230 | −1.71369 | −0.856847 | − | 0.515570i | \(-0.827580\pi\) | ||||
−0.856847 | + | 0.515570i | \(0.827580\pi\) | |||||||
\(884\) | −0.472136 | −0.0158797 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.2705 | 0.412236 | ||||||||
\(887\) | 27.3475 | 0.918240 | 0.459120 | − | 0.888374i | \(-0.348165\pi\) | ||||
0.459120 | + | 0.888374i | \(0.348165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.2918 | −0.579948 | ||||||||
\(890\) | 40.6525 | 1.36267 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.20163 | 0.241128 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.5967 | −1.32357 | ||||||||
\(896\) | 40.8541 | 1.36484 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.67376 | 0.155965 | ||||||||
\(899\) | −32.0344 | −1.06841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.83282 | 0.161004 | ||||||||
\(902\) | −7.85410 | −0.261513 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.1246 | −0.503037 | ||||||||
\(905\) | 38.8328 | 1.29085 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.4721 | 0.878993 | 0.439496 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439496 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(908\) | 10.1459 | 0.336703 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.7082 | −0.520722 | ||||||||
\(911\) | 3.38197 | 0.112050 | 0.0560248 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560248 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7082 | −0.453675 | ||||||||
\(914\) | 31.8885 | 1.05478 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.41641 | −0.278086 | ||||||||
\(917\) | −45.2705 | −1.49496 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2918 | 0.768325 | 0.384163 | − | 0.923265i | \(-0.374490\pi\) | ||||
0.384163 | + | 0.923265i | \(0.374490\pi\) | |||||||
\(920\) | −38.9443 | −1.28395 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.8885 | −1.11606 | ||||||||
\(923\) | −7.47214 | −0.245948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.4508 | −1.59305 | ||||||||
\(926\) | 45.7426 | 1.50320 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.2361 | 0.401669 | ||||||||
\(929\) | −16.3820 | −0.537475 | −0.268737 | − | 0.963213i | \(-0.586606\pi\) | ||||
−0.268737 | + | 0.963213i | \(0.586606\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.79837 | −0.0916638 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.7984 | 0.844149 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.5623 | 1.32511 | 0.662556 | − | 0.749012i | \(-0.269471\pi\) | ||||
0.662556 | + | 0.749012i | \(0.269471\pi\) | |||||||
\(938\) | 33.9787 | 1.10944 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | 0.195698 | ||||||||
\(941\) | −10.6869 | −0.348384 | −0.174192 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174192 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.1459 | 0.525783 | ||||||||
\(944\) | −1.58359 | −0.0515415 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.381966 | −0.0124188 | ||||||||
\(947\) | 32.6525 | 1.06106 | 0.530531 | − | 0.847665i | \(-0.321992\pi\) | ||||
0.530531 | + | 0.847665i | \(0.321992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.70820 | −0.0879120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.12461 | 0.166090 | ||||||||
\(953\) | 17.2918 | 0.560136 | 0.280068 | − | 0.959980i | \(-0.409643\pi\) | ||||
0.280068 | + | 0.959980i | \(0.409643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.0689 | 1.49075 | ||||||||
\(956\) | 0.201626 | 0.00652105 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.3607 | −1.20707 | ||||||||
\(959\) | −22.4164 | −0.723864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.3951 | 1.52887 | ||||||||
\(962\) | −14.3262 | −0.461896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.96556 | −0.0633064 | ||||||||
\(965\) | 16.3607 | 0.526669 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.54102 | 0.210345 | 0.105173 | − | 0.994454i | \(-0.466461\pi\) | ||||
0.105173 | + | 0.994454i | \(0.466461\pi\) | |||||||
\(968\) | 18.7426 | 0.602411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.5410 | 2.32915 | ||||||||
\(971\) | 23.5066 | 0.754362 | 0.377181 | − | 0.926140i | \(-0.376893\pi\) | ||||
0.377181 | + | 0.926140i | \(0.376893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.3951 | 1.42324 | ||||||||
\(974\) | −6.76393 | −0.216730 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49.6869 | 1.59044 | ||||||||
\(977\) | 10.6393 | 0.340382 | 0.170191 | − | 0.985411i | \(-0.445562\pi\) | ||||
0.170191 | + | 0.985411i | \(0.445562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5623 | −0.401493 | ||||||||
\(980\) | −4.00000 | −0.127775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.3262 | 1.09539 | ||||||||
\(983\) | 32.6180 | 1.04035 | 0.520177 | − | 0.854059i | \(-0.325866\pi\) | ||||
0.520177 | + | 0.854059i | \(0.325866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.70820 | 0.309329 | ||||||||
\(986\) | 4.47214 | 0.142422 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.785218 | 0.0249685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.45085 | −0.236684 | −0.118342 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118342 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(992\) | −29.9443 | −0.950732 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.2705 | −1.15043 | ||||||||
\(995\) | 43.4164 | 1.37639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7082 | 1.25757 | 0.628786 | − | 0.777579i | \(-0.283552\pi\) | ||||
0.628786 | + | 0.777579i | \(0.283552\pi\) | |||||||
\(998\) | 40.6525 | 1.28683 | ||||||||
\(999\) | 0 | 0 |
(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 | 3249.2.a.o.1.2 | 2 | ||
3.2 | odd | 2 | 361.2.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 5776.2.a.bg.1.1 | 2 | |||
15.14 | odd | 2 | 9025.2.a.s.1.2 | 2 | |||
19.18 | odd | 2 | 3249.2.a.i.1.1 | 2 | |||
57.2 | even | 18 | 361.2.e.j.99.1 | 12 | |||
57.5 | odd | 18 | 361.2.e.i.234.1 | 12 | |||
57.8 | even | 6 | 361.2.c.d.292.1 | 4 | |||
57.11 | odd | 6 | 361.2.c.g.292.2 | 4 | |||
57.14 | even | 18 | 361.2.e.j.234.2 | 12 | |||
57.17 | odd | 18 | 361.2.e.i.99.2 | 12 | |||
57.23 | odd | 18 | 361.2.e.i.54.1 | 12 | |||
57.26 | odd | 6 | 361.2.c.g.68.2 | 4 | |||
57.29 | even | 18 | 361.2.e.j.62.1 | 12 | |||
57.32 | even | 18 | 361.2.e.j.245.2 | 12 | |||
57.35 | odd | 18 | 361.2.e.i.28.1 | 12 | |||
57.41 | even | 18 | 361.2.e.j.28.2 | 12 | |||
57.44 | odd | 18 | 361.2.e.i.245.1 | 12 | |||
57.47 | odd | 18 | 361.2.e.i.62.2 | 12 | |||
57.50 | even | 6 | 361.2.c.d.68.1 | 4 | |||
57.53 | even | 18 | 361.2.e.j.54.2 | 12 | |||
57.56 | even | 2 | 361.2.a.f.1.2 | yes | 2 | ||
228.227 | odd | 2 | 5776.2.a.s.1.2 | 2 | |||
285.284 | even | 2 | 9025.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
361.2.a.f.1.2 | yes | 2 | 57.56 | even | 2 | ||
361.2.c.d.68.1 | 4 | 57.50 | even | 6 | |||
361.2.c.d.292.1 | 4 | 57.8 | even | 6 | |||
361.2.c.g.68.2 | 4 | 57.26 | odd | 6 | |||
361.2.c.g.292.2 | 4 | 57.11 | odd | 6 | |||
361.2.e.i.28.1 | 12 | 57.35 | odd | 18 | |||
361.2.e.i.54.1 | 12 | 57.23 | odd | 18 | |||
361.2.e.i.62.2 | 12 | 57.47 | odd | 18 | |||
361.2.e.i.99.2 | 12 | 57.17 | odd | 18 | |||
361.2.e.i.234.1 | 12 | 57.5 | odd | 18 | |||
361.2.e.i.245.1 | 12 | 57.44 | odd | 18 | |||
361.2.e.j.28.2 | 12 | 57.41 | even | 18 | |||
361.2.e.j.54.2 | 12 | 57.53 | even | 18 | |||
361.2.e.j.62.1 | 12 | 57.29 | even | 18 | |||
361.2.e.j.99.1 | 12 | 57.2 | even | 18 | |||
361.2.e.j.234.2 | 12 | 57.14 | even | 18 | |||
361.2.e.j.245.2 | 12 | 57.32 | even | 18 | |||
3249.2.a.i.1.1 | 2 | 19.18 | odd | 2 | |||
3249.2.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5776.2.a.s.1.2 | 2 | 228.227 | odd | 2 | |||
5776.2.a.bg.1.1 | 2 | 12.11 | even | 2 | |||
9025.2.a.n.1.1 | 2 | 285.284 | even | 2 | |||
9025.2.a.s.1.2 | 2 | 15.14 | odd | 2 |