Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7997584.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 7x^{4} + 5x^{3} + 12x^{2} - 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.83264\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83264 | −1.29588 | −0.647938 | − | 0.761693i | \(-0.724368\pi\) | ||||
−0.647938 | + | 0.761693i | \(0.724368\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.35859 | 0.679293 | ||||||||
\(5\) | −0.943490 | −0.421941 | −0.210971 | − | 0.977492i | \(-0.567662\pi\) | ||||
−0.210971 | + | 0.977492i | \(0.567662\pi\) | |||||||
\(6\) | 1.83264 | 0.748174 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.17548 | 0.415597 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.72908 | 0.546783 | ||||||||
\(11\) | 2.08680 | 0.629194 | 0.314597 | − | 0.949225i | \(-0.398131\pi\) | ||||
0.314597 | + | 0.949225i | \(0.398131\pi\) | |||||||
\(12\) | −1.35859 | −0.392190 | ||||||||
\(13\) | 3.64405 | 1.01068 | 0.505339 | − | 0.862921i | \(-0.331368\pi\) | ||||
0.505339 | + | 0.862921i | \(0.331368\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.943490 | 0.243608 | ||||||||
\(16\) | −4.87142 | −1.21785 | ||||||||
\(17\) | 0.299440 | 0.0726249 | 0.0363124 | − | 0.999340i | \(-0.488439\pi\) | ||||
0.0363124 | + | 0.999340i | \(0.488439\pi\) | |||||||
\(18\) | −1.83264 | −0.431958 | ||||||||
\(19\) | −0.579464 | −0.132938 | −0.0664690 | − | 0.997788i | \(-0.521173\pi\) | ||||
−0.0664690 | + | 0.997788i | \(0.521173\pi\) | |||||||
\(20\) | −1.28181 | −0.286622 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.82436 | −0.815357 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.17548 | −0.239945 | ||||||||
\(25\) | −4.10983 | −0.821965 | ||||||||
\(26\) | −6.67825 | −1.30971 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.89363 | −1.09442 | −0.547210 | − | 0.836995i | \(-0.684310\pi\) | ||||
−0.547210 | + | 0.836995i | \(0.684310\pi\) | |||||||
\(30\) | −1.72908 | −0.315686 | ||||||||
\(31\) | −6.02387 | −1.08192 | −0.540960 | − | 0.841048i | \(-0.681939\pi\) | ||||
−0.540960 | + | 0.841048i | \(0.681939\pi\) | |||||||
\(32\) | 6.57660 | 1.16259 | ||||||||
\(33\) | −2.08680 | −0.363265 | ||||||||
\(34\) | −0.548767 | −0.0941128 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.35859 | 0.226431 | ||||||||
\(37\) | −1.23744 | −0.203433 | −0.101717 | − | 0.994813i | \(-0.532433\pi\) | ||||
−0.101717 | + | 0.994813i | \(0.532433\pi\) | |||||||
\(38\) | 1.06195 | 0.172271 | ||||||||
\(39\) | −3.64405 | −0.583515 | ||||||||
\(40\) | −1.10906 | −0.175357 | ||||||||
\(41\) | 8.42024 | 1.31502 | 0.657510 | − | 0.753446i | \(-0.271610\pi\) | ||||
0.657510 | + | 0.753446i | \(0.271610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.08583 | −1.38558 | −0.692788 | − | 0.721142i | \(-0.743618\pi\) | ||||
−0.692788 | + | 0.721142i | \(0.743618\pi\) | |||||||
\(44\) | 2.83510 | 0.427407 | ||||||||
\(45\) | −0.943490 | −0.140647 | ||||||||
\(46\) | 1.83264 | 0.270209 | ||||||||
\(47\) | 5.06246 | 0.738436 | 0.369218 | − | 0.929343i | \(-0.379626\pi\) | ||||
0.369218 | + | 0.929343i | \(0.379626\pi\) | |||||||
\(48\) | 4.87142 | 0.703128 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.53185 | 1.06516 | ||||||||
\(51\) | −0.299440 | −0.0419300 | ||||||||
\(52\) | 4.95075 | 0.686546 | ||||||||
\(53\) | 2.32577 | 0.319469 | 0.159734 | − | 0.987160i | \(-0.448936\pi\) | ||||
0.159734 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(54\) | 1.83264 | 0.249391 | ||||||||
\(55\) | −1.96887 | −0.265483 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.579464 | 0.0767518 | ||||||||
\(58\) | 10.8009 | 1.41823 | ||||||||
\(59\) | 2.08015 | 0.270812 | 0.135406 | − | 0.990790i | \(-0.456766\pi\) | ||||
0.135406 | + | 0.990790i | \(0.456766\pi\) | |||||||
\(60\) | 1.28181 | 0.165481 | ||||||||
\(61\) | 12.4540 | 1.59457 | 0.797287 | − | 0.603600i | \(-0.206268\pi\) | ||||
0.797287 | + | 0.603600i | \(0.206268\pi\) | |||||||
\(62\) | 11.0396 | 1.40203 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.30974 | −0.288718 | ||||||||
\(65\) | −3.43812 | −0.426447 | ||||||||
\(66\) | 3.82436 | 0.470747 | ||||||||
\(67\) | −4.13763 | −0.505493 | −0.252746 | − | 0.967533i | \(-0.581334\pi\) | ||||
−0.252746 | + | 0.967533i | \(0.581334\pi\) | |||||||
\(68\) | 0.406815 | 0.0493335 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6439 | −1.38188 | −0.690938 | − | 0.722914i | \(-0.742802\pi\) | ||||
−0.690938 | + | 0.722914i | \(0.742802\pi\) | |||||||
\(72\) | 1.17548 | 0.138532 | ||||||||
\(73\) | −11.5700 | −1.35416 | −0.677082 | − | 0.735908i | \(-0.736756\pi\) | ||||
−0.677082 | + | 0.735908i | \(0.736756\pi\) | |||||||
\(74\) | 2.26778 | 0.263624 | ||||||||
\(75\) | 4.10983 | 0.474562 | ||||||||
\(76\) | −0.787251 | −0.0903039 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.67825 | 0.756163 | ||||||||
\(79\) | 17.1584 | 1.93047 | 0.965235 | − | 0.261382i | \(-0.0841783\pi\) | ||||
0.965235 | + | 0.261382i | \(0.0841783\pi\) | |||||||
\(80\) | 4.59613 | 0.513863 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.4313 | −1.70410 | ||||||||
\(83\) | 10.9740 | 1.20455 | 0.602274 | − | 0.798289i | \(-0.294261\pi\) | ||||
0.602274 | + | 0.798289i | \(0.294261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.282519 | −0.0306434 | ||||||||
\(86\) | 16.6511 | 1.79553 | ||||||||
\(87\) | 5.89363 | 0.631864 | ||||||||
\(88\) | 2.45300 | 0.261491 | ||||||||
\(89\) | 2.67561 | 0.283614 | 0.141807 | − | 0.989894i | \(-0.454709\pi\) | ||||
0.141807 | + | 0.989894i | \(0.454709\pi\) | |||||||
\(90\) | 1.72908 | 0.182261 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.35859 | −0.141642 | ||||||||
\(93\) | 6.02387 | 0.624647 | ||||||||
\(94\) | −9.27770 | −0.956921 | ||||||||
\(95\) | 0.546718 | 0.0560921 | ||||||||
\(96\) | −6.57660 | −0.671222 | ||||||||
\(97\) | 0.589843 | 0.0598895 | 0.0299447 | − | 0.999552i | \(-0.490467\pi\) | ||||
0.0299447 | + | 0.999552i | \(0.490467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.08680 | 0.209731 | ||||||||
\(100\) | −5.58355 | −0.558355 | ||||||||
\(101\) | 6.22834 | 0.619743 | 0.309872 | − | 0.950778i | \(-0.399714\pi\) | ||||
0.309872 | + | 0.950778i | \(0.399714\pi\) | |||||||
\(102\) | 0.548767 | 0.0543360 | ||||||||
\(103\) | −18.6455 | −1.83719 | −0.918597 | − | 0.395195i | \(-0.870677\pi\) | ||||
−0.918597 | + | 0.395195i | \(0.870677\pi\) | |||||||
\(104\) | 4.28352 | 0.420034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.26230 | −0.413992 | ||||||||
\(107\) | −0.648883 | −0.0627299 | −0.0313650 | − | 0.999508i | \(-0.509985\pi\) | ||||
−0.0313650 | + | 0.999508i | \(0.509985\pi\) | |||||||
\(108\) | −1.35859 | −0.130730 | ||||||||
\(109\) | −13.6533 | −1.30775 | −0.653876 | − | 0.756602i | \(-0.726858\pi\) | ||||
−0.653876 | + | 0.756602i | \(0.726858\pi\) | |||||||
\(110\) | 3.60825 | 0.344033 | ||||||||
\(111\) | 1.23744 | 0.117452 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.547279 | 0.0514836 | 0.0257418 | − | 0.999669i | \(-0.491805\pi\) | ||||
0.0257418 | + | 0.999669i | \(0.491805\pi\) | |||||||
\(114\) | −1.06195 | −0.0994608 | ||||||||
\(115\) | 0.943490 | 0.0879809 | ||||||||
\(116\) | −8.00700 | −0.743431 | ||||||||
\(117\) | 3.64405 | 0.336893 | ||||||||
\(118\) | −3.81217 | −0.350939 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.10906 | 0.101243 | ||||||||
\(121\) | −6.64526 | −0.604115 | ||||||||
\(122\) | −22.8238 | −2.06637 | ||||||||
\(123\) | −8.42024 | −0.759227 | ||||||||
\(124\) | −8.18395 | −0.734940 | ||||||||
\(125\) | 8.59503 | 0.768763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.01278 | −0.0898693 | −0.0449347 | − | 0.998990i | \(-0.514308\pi\) | ||||
−0.0449347 | + | 0.998990i | \(0.514308\pi\) | |||||||
\(128\) | −8.92027 | −0.788448 | ||||||||
\(129\) | 9.08583 | 0.799962 | ||||||||
\(130\) | 6.30086 | 0.552622 | ||||||||
\(131\) | −15.0311 | −1.31327 | −0.656635 | − | 0.754209i | \(-0.728021\pi\) | ||||
−0.656635 | + | 0.754209i | \(0.728021\pi\) | |||||||
\(132\) | −2.83510 | −0.246764 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.58281 | 0.655055 | ||||||||
\(135\) | 0.943490 | 0.0812027 | ||||||||
\(136\) | 0.351987 | 0.0301827 | ||||||||
\(137\) | 9.27867 | 0.792730 | 0.396365 | − | 0.918093i | \(-0.370271\pi\) | ||||
0.396365 | + | 0.918093i | \(0.370271\pi\) | |||||||
\(138\) | −1.83264 | −0.156005 | ||||||||
\(139\) | 6.58750 | 0.558744 | 0.279372 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279372 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.06246 | −0.426336 | ||||||||
\(142\) | 21.3391 | 1.79074 | ||||||||
\(143\) | 7.60440 | 0.635912 | ||||||||
\(144\) | −4.87142 | −0.405951 | ||||||||
\(145\) | 5.56058 | 0.461781 | ||||||||
\(146\) | 21.2037 | 1.75483 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.68116 | −0.138191 | ||||||||
\(149\) | −5.88903 | −0.482448 | −0.241224 | − | 0.970469i | \(-0.577549\pi\) | ||||
−0.241224 | + | 0.970469i | \(0.577549\pi\) | |||||||
\(150\) | −7.53185 | −0.614973 | ||||||||
\(151\) | 13.1539 | 1.07045 | 0.535223 | − | 0.844711i | \(-0.320228\pi\) | ||||
0.535223 | + | 0.844711i | \(0.320228\pi\) | |||||||
\(152\) | −0.681151 | −0.0552486 | ||||||||
\(153\) | 0.299440 | 0.0242083 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.68346 | 0.456507 | ||||||||
\(156\) | −4.95075 | −0.396377 | ||||||||
\(157\) | −8.42558 | −0.672434 | −0.336217 | − | 0.941784i | \(-0.609148\pi\) | ||||
−0.336217 | + | 0.941784i | \(0.609148\pi\) | |||||||
\(158\) | −31.4452 | −2.50165 | ||||||||
\(159\) | −2.32577 | −0.184445 | ||||||||
\(160\) | −6.20496 | −0.490545 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.83264 | −0.143986 | ||||||||
\(163\) | 4.15736 | 0.325630 | 0.162815 | − | 0.986657i | \(-0.447943\pi\) | ||||
0.162815 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(164\) | 11.4396 | 0.893284 | ||||||||
\(165\) | 1.96887 | 0.153277 | ||||||||
\(166\) | −20.1114 | −1.56095 | ||||||||
\(167\) | −3.04445 | −0.235587 | −0.117793 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117793 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.279097 | 0.0214690 | ||||||||
\(170\) | 0.517756 | 0.0397101 | ||||||||
\(171\) | −0.579464 | −0.0443127 | ||||||||
\(172\) | −12.3439 | −0.941211 | ||||||||
\(173\) | 16.0543 | 1.22059 | 0.610293 | − | 0.792176i | \(-0.291052\pi\) | ||||
0.610293 | + | 0.792176i | \(0.291052\pi\) | |||||||
\(174\) | −10.8009 | −0.818816 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.1657 | −0.766267 | ||||||||
\(177\) | −2.08015 | −0.156354 | ||||||||
\(178\) | −4.90345 | −0.367529 | ||||||||
\(179\) | −5.34509 | −0.399511 | −0.199755 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199755 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(180\) | −1.28181 | −0.0955406 | ||||||||
\(181\) | −11.6201 | −0.863716 | −0.431858 | − | 0.901942i | \(-0.642142\pi\) | ||||
−0.431858 | + | 0.901942i | \(0.642142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4540 | −0.920628 | ||||||||
\(184\) | −1.17548 | −0.0866579 | ||||||||
\(185\) | 1.16751 | 0.0858369 | ||||||||
\(186\) | −11.0396 | −0.809464 | ||||||||
\(187\) | 0.624872 | 0.0456951 | ||||||||
\(188\) | 6.87779 | 0.501614 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00194 | −0.0726883 | ||||||||
\(191\) | −17.0751 | −1.23551 | −0.617757 | − | 0.786369i | \(-0.711958\pi\) | ||||
−0.617757 | + | 0.786369i | \(0.711958\pi\) | |||||||
\(192\) | 2.30974 | 0.166691 | ||||||||
\(193\) | −4.65052 | −0.334752 | −0.167376 | − | 0.985893i | \(-0.553529\pi\) | ||||
−0.167376 | + | 0.985893i | \(0.553529\pi\) | |||||||
\(194\) | −1.08097 | −0.0776093 | ||||||||
\(195\) | 3.43812 | 0.246209 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.254912 | 0.0181618 | 0.00908088 | − | 0.999959i | \(-0.497109\pi\) | ||||
0.00908088 | + | 0.999959i | \(0.497109\pi\) | |||||||
\(198\) | −3.82436 | −0.271786 | ||||||||
\(199\) | 5.47597 | 0.388181 | 0.194091 | − | 0.980984i | \(-0.437824\pi\) | ||||
0.194091 | + | 0.980984i | \(0.437824\pi\) | |||||||
\(200\) | −4.83104 | −0.341606 | ||||||||
\(201\) | 4.13763 | 0.291846 | ||||||||
\(202\) | −11.4143 | −0.803110 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.406815 | −0.0284827 | ||||||||
\(205\) | −7.94441 | −0.554861 | ||||||||
\(206\) | 34.1705 | 2.38077 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −17.7517 | −1.23086 | ||||||||
\(209\) | −1.20923 | −0.0836438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.18599 | −0.219332 | −0.109666 | − | 0.993968i | \(-0.534978\pi\) | ||||
−0.109666 | + | 0.993968i | \(0.534978\pi\) | |||||||
\(212\) | 3.15975 | 0.217013 | ||||||||
\(213\) | 11.6439 | 0.797827 | ||||||||
\(214\) | 1.18917 | 0.0812902 | ||||||||
\(215\) | 8.57238 | 0.584632 | ||||||||
\(216\) | −1.17548 | −0.0799816 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.0217 | 1.69468 | ||||||||
\(219\) | 11.5700 | 0.781827 | ||||||||
\(220\) | −2.67488 | −0.180341 | ||||||||
\(221\) | 1.09117 | 0.0734003 | ||||||||
\(222\) | −2.26778 | −0.152203 | ||||||||
\(223\) | −22.7674 | −1.52462 | −0.762309 | − | 0.647213i | \(-0.775934\pi\) | ||||
−0.762309 | + | 0.647213i | \(0.775934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.10983 | −0.273988 | ||||||||
\(226\) | −1.00297 | −0.0667164 | ||||||||
\(227\) | 10.4521 | 0.693729 | 0.346864 | − | 0.937915i | \(-0.387246\pi\) | ||||
0.346864 | + | 0.937915i | \(0.387246\pi\) | |||||||
\(228\) | 0.787251 | 0.0521370 | ||||||||
\(229\) | −10.7678 | −0.711559 | −0.355779 | − | 0.934570i | \(-0.615785\pi\) | ||||
−0.355779 | + | 0.934570i | \(0.615785\pi\) | |||||||
\(230\) | −1.72908 | −0.114012 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.92787 | −0.454837 | ||||||||
\(233\) | 11.7508 | 0.769818 | 0.384909 | − | 0.922955i | \(-0.374233\pi\) | ||||
0.384909 | + | 0.922955i | \(0.374233\pi\) | |||||||
\(234\) | −6.67825 | −0.436571 | ||||||||
\(235\) | −4.77638 | −0.311577 | ||||||||
\(236\) | 2.82606 | 0.183961 | ||||||||
\(237\) | −17.1584 | −1.11456 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.5491 | −0.811734 | −0.405867 | − | 0.913932i | \(-0.633030\pi\) | ||||
−0.405867 | + | 0.913932i | \(0.633030\pi\) | |||||||
\(240\) | −4.59613 | −0.296679 | ||||||||
\(241\) | −10.6305 | −0.684768 | −0.342384 | − | 0.939560i | \(-0.611234\pi\) | ||||
−0.342384 | + | 0.939560i | \(0.611234\pi\) | |||||||
\(242\) | 12.1784 | 0.782858 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 16.9199 | 1.08318 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.4313 | 0.983864 | ||||||||
\(247\) | −2.11159 | −0.134358 | ||||||||
\(248\) | −7.08097 | −0.449642 | ||||||||
\(249\) | −10.9740 | −0.695447 | ||||||||
\(250\) | −15.7516 | −0.996220 | ||||||||
\(251\) | −17.4415 | −1.10090 | −0.550450 | − | 0.834868i | \(-0.685544\pi\) | ||||
−0.550450 | + | 0.834868i | \(0.685544\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.08680 | −0.131196 | ||||||||
\(254\) | 1.85606 | 0.116459 | ||||||||
\(255\) | 0.282519 | 0.0176920 | ||||||||
\(256\) | 20.9672 | 1.31045 | ||||||||
\(257\) | 18.7261 | 1.16810 | 0.584050 | − | 0.811718i | \(-0.301467\pi\) | ||||
0.584050 | + | 0.811718i | \(0.301467\pi\) | |||||||
\(258\) | −16.6511 | −1.03665 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.67098 | −0.289682 | ||||||||
\(261\) | −5.89363 | −0.364807 | ||||||||
\(262\) | 27.5466 | 1.70183 | ||||||||
\(263\) | 29.9086 | 1.84424 | 0.922121 | − | 0.386902i | \(-0.126455\pi\) | ||||
0.922121 | + | 0.386902i | \(0.126455\pi\) | |||||||
\(264\) | −2.45300 | −0.150972 | ||||||||
\(265\) | −2.19434 | −0.134797 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.67561 | −0.163745 | ||||||||
\(268\) | −5.62133 | −0.343377 | ||||||||
\(269\) | 22.6461 | 1.38076 | 0.690378 | − | 0.723449i | \(-0.257444\pi\) | ||||
0.690378 | + | 0.723449i | \(0.257444\pi\) | |||||||
\(270\) | −1.72908 | −0.105229 | ||||||||
\(271\) | −12.7364 | −0.773679 | −0.386839 | − | 0.922147i | \(-0.626433\pi\) | ||||
−0.386839 | + | 0.922147i | \(0.626433\pi\) | |||||||
\(272\) | −1.45870 | −0.0884465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.0045 | −1.02728 | ||||||||
\(275\) | −8.57639 | −0.517176 | ||||||||
\(276\) | 1.35859 | 0.0817772 | ||||||||
\(277\) | −29.0127 | −1.74320 | −0.871601 | − | 0.490216i | \(-0.836918\pi\) | ||||
−0.871601 | + | 0.490216i | \(0.836918\pi\) | |||||||
\(278\) | −12.0725 | −0.724063 | ||||||||
\(279\) | −6.02387 | −0.360640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4466 | −0.742504 | −0.371252 | − | 0.928532i | \(-0.621071\pi\) | ||||
−0.371252 | + | 0.928532i | \(0.621071\pi\) | |||||||
\(282\) | 9.27770 | 0.552479 | ||||||||
\(283\) | 9.36397 | 0.556630 | 0.278315 | − | 0.960490i | \(-0.410224\pi\) | ||||
0.278315 | + | 0.960490i | \(0.410224\pi\) | |||||||
\(284\) | −15.8192 | −0.938699 | ||||||||
\(285\) | −0.546718 | −0.0323848 | ||||||||
\(286\) | −13.9362 | −0.824063 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.57660 | 0.387530 | ||||||||
\(289\) | −16.9103 | −0.994726 | ||||||||
\(290\) | −10.1906 | −0.598411 | ||||||||
\(291\) | −0.589843 | −0.0345772 | ||||||||
\(292\) | −15.7188 | −0.919874 | ||||||||
\(293\) | 5.69521 | 0.332717 | 0.166359 | − | 0.986065i | \(-0.446799\pi\) | ||||
0.166359 | + | 0.986065i | \(0.446799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.96260 | −0.114267 | ||||||||
\(296\) | −1.45459 | −0.0845461 | ||||||||
\(297\) | −2.08680 | −0.121088 | ||||||||
\(298\) | 10.7925 | 0.625192 | ||||||||
\(299\) | −3.64405 | −0.210741 | ||||||||
\(300\) | 5.58355 | 0.322367 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −24.1063 | −1.38716 | ||||||||
\(303\) | −6.22834 | −0.357809 | ||||||||
\(304\) | 2.82281 | 0.161899 | ||||||||
\(305\) | −11.7502 | −0.672817 | ||||||||
\(306\) | −0.548767 | −0.0313709 | ||||||||
\(307\) | 17.0596 | 0.973642 | 0.486821 | − | 0.873502i | \(-0.338156\pi\) | ||||
0.486821 | + | 0.873502i | \(0.338156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.6455 | 1.06070 | ||||||||
\(310\) | −10.4158 | −0.591576 | ||||||||
\(311\) | −16.5243 | −0.937005 | −0.468503 | − | 0.883462i | \(-0.655206\pi\) | ||||
−0.468503 | + | 0.883462i | \(0.655206\pi\) | |||||||
\(312\) | −4.28352 | −0.242507 | ||||||||
\(313\) | −1.49388 | −0.0844389 | −0.0422195 | − | 0.999108i | \(-0.513443\pi\) | ||||
−0.0422195 | + | 0.999108i | \(0.513443\pi\) | |||||||
\(314\) | 15.4411 | 0.871391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.3112 | 1.31135 | ||||||||
\(317\) | −18.2234 | −1.02353 | −0.511765 | − | 0.859126i | \(-0.671008\pi\) | ||||
−0.511765 | + | 0.859126i | \(0.671008\pi\) | |||||||
\(318\) | 4.26230 | 0.239018 | ||||||||
\(319\) | −12.2988 | −0.688602 | ||||||||
\(320\) | 2.17922 | 0.121822 | ||||||||
\(321\) | 0.648883 | 0.0362171 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.173515 | −0.00965461 | ||||||||
\(324\) | 1.35859 | 0.0754770 | ||||||||
\(325\) | −14.9764 | −0.830742 | ||||||||
\(326\) | −7.61897 | −0.421976 | ||||||||
\(327\) | 13.6533 | 0.755031 | ||||||||
\(328\) | 9.89786 | 0.546518 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.60825 | −0.198627 | ||||||||
\(331\) | −22.9549 | −1.26171 | −0.630857 | − | 0.775899i | \(-0.717297\pi\) | ||||
−0.630857 | + | 0.775899i | \(0.717297\pi\) | |||||||
\(332\) | 14.9091 | 0.818241 | ||||||||
\(333\) | −1.23744 | −0.0678111 | ||||||||
\(334\) | 5.57939 | 0.305291 | ||||||||
\(335\) | 3.90381 | 0.213288 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2266 | 1.21076 | 0.605381 | − | 0.795936i | \(-0.293021\pi\) | ||||
0.605381 | + | 0.795936i | \(0.293021\pi\) | |||||||
\(338\) | −0.511486 | −0.0278212 | ||||||||
\(339\) | −0.547279 | −0.0297241 | ||||||||
\(340\) | −0.383826 | −0.0208159 | ||||||||
\(341\) | −12.5706 | −0.680737 | ||||||||
\(342\) | 1.06195 | 0.0574237 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.6802 | −0.575840 | ||||||||
\(345\) | −0.943490 | −0.0507958 | ||||||||
\(346\) | −29.4218 | −1.58173 | ||||||||
\(347\) | −5.40842 | −0.290339 | −0.145170 | − | 0.989407i | \(-0.546373\pi\) | ||||
−0.145170 | + | 0.989407i | \(0.546373\pi\) | |||||||
\(348\) | 8.00700 | 0.429220 | ||||||||
\(349\) | 10.3938 | 0.556369 | 0.278184 | − | 0.960528i | \(-0.410267\pi\) | ||||
0.278184 | + | 0.960528i | \(0.410267\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.64405 | −0.194505 | ||||||||
\(352\) | 13.7241 | 0.731495 | ||||||||
\(353\) | −13.0691 | −0.695596 | −0.347798 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347798 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(354\) | 3.81217 | 0.202615 | ||||||||
\(355\) | 10.9859 | 0.583071 | ||||||||
\(356\) | 3.63505 | 0.192657 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.79565 | 0.517716 | ||||||||
\(359\) | −19.2232 | −1.01456 | −0.507281 | − | 0.861781i | \(-0.669349\pi\) | ||||
−0.507281 | + | 0.861781i | \(0.669349\pi\) | |||||||
\(360\) | −1.10906 | −0.0584525 | ||||||||
\(361\) | −18.6642 | −0.982327 | ||||||||
\(362\) | 21.2955 | 1.11927 | ||||||||
\(363\) | 6.64526 | 0.348786 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.9162 | 0.571378 | ||||||||
\(366\) | 22.8238 | 1.19302 | ||||||||
\(367\) | −1.77510 | −0.0926592 | −0.0463296 | − | 0.998926i | \(-0.514752\pi\) | ||||
−0.0463296 | + | 0.998926i | \(0.514752\pi\) | |||||||
\(368\) | 4.87142 | 0.253940 | ||||||||
\(369\) | 8.42024 | 0.438340 | ||||||||
\(370\) | −2.13963 | −0.111234 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.18395 | 0.424318 | ||||||||
\(373\) | −7.44021 | −0.385240 | −0.192620 | − | 0.981273i | \(-0.561698\pi\) | ||||
−0.192620 | + | 0.981273i | \(0.561698\pi\) | |||||||
\(374\) | −1.14517 | −0.0592152 | ||||||||
\(375\) | −8.59503 | −0.443845 | ||||||||
\(376\) | 5.95085 | 0.306892 | ||||||||
\(377\) | −21.4767 | −1.10611 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.31050 | −0.221415 | −0.110708 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110708 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(380\) | 0.742763 | 0.0381029 | ||||||||
\(381\) | 1.01278 | 0.0518861 | ||||||||
\(382\) | 31.2927 | 1.60107 | ||||||||
\(383\) | 34.6915 | 1.77265 | 0.886326 | − | 0.463062i | \(-0.153249\pi\) | ||||
0.886326 | + | 0.463062i | \(0.153249\pi\) | |||||||
\(384\) | 8.92027 | 0.455211 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.52275 | 0.433796 | ||||||||
\(387\) | −9.08583 | −0.461858 | ||||||||
\(388\) | 0.801352 | 0.0406825 | ||||||||
\(389\) | 33.1439 | 1.68046 | 0.840230 | − | 0.542230i | \(-0.182420\pi\) | ||||
0.840230 | + | 0.542230i | \(0.182420\pi\) | |||||||
\(390\) | −6.30086 | −0.319056 | ||||||||
\(391\) | −0.299440 | −0.0151433 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.0311 | 0.758217 | ||||||||
\(394\) | −0.467164 | −0.0235354 | ||||||||
\(395\) | −16.1888 | −0.814545 | ||||||||
\(396\) | 2.83510 | 0.142469 | ||||||||
\(397\) | −28.4564 | −1.42818 | −0.714092 | − | 0.700052i | \(-0.753160\pi\) | ||||
−0.714092 | + | 0.700052i | \(0.753160\pi\) | |||||||
\(398\) | −10.0355 | −0.503035 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.0207 | 1.00103 | ||||||||
\(401\) | −37.8811 | −1.89169 | −0.945846 | − | 0.324615i | \(-0.894765\pi\) | ||||
−0.945846 | + | 0.324615i | \(0.894765\pi\) | |||||||
\(402\) | −7.58281 | −0.378196 | ||||||||
\(403\) | −21.9513 | −1.09347 | ||||||||
\(404\) | 8.46174 | 0.420987 | ||||||||
\(405\) | −0.943490 | −0.0468824 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.58228 | −0.127999 | ||||||||
\(408\) | −0.351987 | −0.0174260 | ||||||||
\(409\) | 0.957146 | 0.0473278 | 0.0236639 | − | 0.999720i | \(-0.492467\pi\) | ||||
0.0236639 | + | 0.999720i | \(0.492467\pi\) | |||||||
\(410\) | 14.5593 | 0.719031 | ||||||||
\(411\) | −9.27867 | −0.457683 | ||||||||
\(412\) | −25.3315 | −1.24799 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.83264 | 0.0900696 | ||||||||
\(415\) | −10.3538 | −0.508249 | ||||||||
\(416\) | 23.9655 | 1.17500 | ||||||||
\(417\) | −6.58750 | −0.322591 | ||||||||
\(418\) | 2.21608 | 0.108392 | ||||||||
\(419\) | −40.7600 | −1.99126 | −0.995628 | − | 0.0934066i | \(-0.970224\pi\) | ||||
−0.995628 | + | 0.0934066i | \(0.970224\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0184 | −1.26806 | −0.634031 | − | 0.773308i | \(-0.718601\pi\) | ||||
−0.634031 | + | 0.773308i | \(0.718601\pi\) | |||||||
\(422\) | 5.83878 | 0.284227 | ||||||||
\(423\) | 5.06246 | 0.246145 | ||||||||
\(424\) | 2.73390 | 0.132770 | ||||||||
\(425\) | −1.23065 | −0.0596951 | ||||||||
\(426\) | −21.3391 | −1.03388 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.881564 | −0.0426120 | ||||||||
\(429\) | −7.60440 | −0.367144 | ||||||||
\(430\) | −15.7101 | −0.757610 | ||||||||
\(431\) | −31.4441 | −1.51461 | −0.757305 | − | 0.653061i | \(-0.773485\pi\) | ||||
−0.757305 | + | 0.653061i | \(0.773485\pi\) | |||||||
\(432\) | 4.87142 | 0.234376 | ||||||||
\(433\) | 3.61281 | 0.173621 | 0.0868103 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868103 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.56058 | −0.266609 | ||||||||
\(436\) | −18.5492 | −0.888347 | ||||||||
\(437\) | 0.579464 | 0.0277195 | ||||||||
\(438\) | −21.2037 | −1.01315 | ||||||||
\(439\) | 18.0511 | 0.861530 | 0.430765 | − | 0.902464i | \(-0.358244\pi\) | ||||
0.430765 | + | 0.902464i | \(0.358244\pi\) | |||||||
\(440\) | −2.31438 | −0.110334 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.99973 | −0.0951177 | ||||||||
\(443\) | −35.3301 | −1.67858 | −0.839291 | − | 0.543683i | \(-0.817030\pi\) | ||||
−0.839291 | + | 0.543683i | \(0.817030\pi\) | |||||||
\(444\) | 1.68116 | 0.0797844 | ||||||||
\(445\) | −2.52441 | −0.119669 | ||||||||
\(446\) | 41.7246 | 1.97571 | ||||||||
\(447\) | 5.88903 | 0.278541 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.95593 | 0.281078 | 0.140539 | − | 0.990075i | \(-0.455116\pi\) | ||||
0.140539 | + | 0.990075i | \(0.455116\pi\) | |||||||
\(450\) | 7.53185 | 0.355055 | ||||||||
\(451\) | 17.5714 | 0.827403 | ||||||||
\(452\) | 0.743525 | 0.0349725 | ||||||||
\(453\) | −13.1539 | −0.618022 | ||||||||
\(454\) | −19.1549 | −0.898986 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.681151 | 0.0318978 | ||||||||
\(457\) | 31.9674 | 1.49537 | 0.747685 | − | 0.664053i | \(-0.231165\pi\) | ||||
0.747685 | + | 0.664053i | \(0.231165\pi\) | |||||||
\(458\) | 19.7336 | 0.922091 | ||||||||
\(459\) | −0.299440 | −0.0139767 | ||||||||
\(460\) | 1.28181 | 0.0597648 | ||||||||
\(461\) | 7.10536 | 0.330930 | 0.165465 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165465 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.0816 | −1.95570 | −0.977848 | − | 0.209314i | \(-0.932877\pi\) | ||||
−0.977848 | + | 0.209314i | \(0.932877\pi\) | |||||||
\(464\) | 28.7103 | 1.33284 | ||||||||
\(465\) | −5.68346 | −0.263564 | ||||||||
\(466\) | −21.5350 | −0.997588 | ||||||||
\(467\) | 26.4507 | 1.22399 | 0.611995 | − | 0.790861i | \(-0.290367\pi\) | ||||
0.611995 | + | 0.790861i | \(0.290367\pi\) | |||||||
\(468\) | 4.95075 | 0.228849 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.75341 | 0.403765 | ||||||||
\(471\) | 8.42558 | 0.388230 | ||||||||
\(472\) | 2.44518 | 0.112549 | ||||||||
\(473\) | −18.9603 | −0.871796 | ||||||||
\(474\) | 31.4452 | 1.44433 | ||||||||
\(475\) | 2.38150 | 0.109271 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.32577 | 0.106490 | ||||||||
\(478\) | 22.9980 | 1.05191 | ||||||||
\(479\) | −25.2828 | −1.15520 | −0.577601 | − | 0.816319i | \(-0.696011\pi\) | ||||
−0.577601 | + | 0.816319i | \(0.696011\pi\) | |||||||
\(480\) | 6.20496 | 0.283216 | ||||||||
\(481\) | −4.50928 | −0.205605 | ||||||||
\(482\) | 19.4818 | 0.887373 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.02816 | −0.410371 | ||||||||
\(485\) | −0.556511 | −0.0252698 | ||||||||
\(486\) | 1.83264 | 0.0831304 | ||||||||
\(487\) | 19.9765 | 0.905222 | 0.452611 | − | 0.891708i | \(-0.350493\pi\) | ||||
0.452611 | + | 0.891708i | \(0.350493\pi\) | |||||||
\(488\) | 14.6395 | 0.662700 | ||||||||
\(489\) | −4.15736 | −0.188002 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.0091 | −1.85072 | −0.925358 | − | 0.379095i | \(-0.876235\pi\) | ||||
−0.925358 | + | 0.379095i | \(0.876235\pi\) | |||||||
\(492\) | −11.4396 | −0.515738 | ||||||||
\(493\) | −1.76479 | −0.0794821 | ||||||||
\(494\) | 3.86980 | 0.174111 | ||||||||
\(495\) | −1.96887 | −0.0884943 | ||||||||
\(496\) | 29.3448 | 1.31762 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 20.1114 | 0.901212 | ||||||||
\(499\) | 14.0469 | 0.628825 | 0.314412 | − | 0.949286i | \(-0.398193\pi\) | ||||
0.314412 | + | 0.949286i | \(0.398193\pi\) | |||||||
\(500\) | 11.6771 | 0.522215 | ||||||||
\(501\) | 3.04445 | 0.136016 | ||||||||
\(502\) | 31.9641 | 1.42663 | ||||||||
\(503\) | 12.8463 | 0.572787 | 0.286393 | − | 0.958112i | \(-0.407544\pi\) | ||||
0.286393 | + | 0.958112i | \(0.407544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.87638 | −0.261495 | ||||||||
\(506\) | 3.82436 | 0.170014 | ||||||||
\(507\) | −0.279097 | −0.0123951 | ||||||||
\(508\) | −1.37594 | −0.0610476 | ||||||||
\(509\) | −26.7812 | −1.18706 | −0.593528 | − | 0.804813i | \(-0.702266\pi\) | ||||
−0.593528 | + | 0.804813i | \(0.702266\pi\) | |||||||
\(510\) | −0.517756 | −0.0229266 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.5848 | −0.909730 | ||||||||
\(513\) | 0.579464 | 0.0255839 | ||||||||
\(514\) | −34.3182 | −1.51371 | ||||||||
\(515\) | 17.5918 | 0.775188 | ||||||||
\(516\) | 12.3439 | 0.543409 | ||||||||
\(517\) | 10.5644 | 0.464620 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0543 | −0.704705 | ||||||||
\(520\) | −4.04146 | −0.177230 | ||||||||
\(521\) | −26.8305 | −1.17546 | −0.587732 | − | 0.809056i | \(-0.699979\pi\) | ||||
−0.587732 | + | 0.809056i | \(0.699979\pi\) | |||||||
\(522\) | 10.8009 | 0.472744 | ||||||||
\(523\) | −16.0946 | −0.703768 | −0.351884 | − | 0.936044i | \(-0.614459\pi\) | ||||
−0.351884 | + | 0.936044i | \(0.614459\pi\) | |||||||
\(524\) | −20.4210 | −0.892095 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −54.8118 | −2.38991 | ||||||||
\(527\) | −1.80379 | −0.0785743 | ||||||||
\(528\) | 10.1657 | 0.442404 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 4.02144 | 0.174680 | ||||||||
\(531\) | 2.08015 | 0.0902708 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.6838 | 1.32906 | ||||||||
\(534\) | 4.90345 | 0.212193 | ||||||||
\(535\) | 0.612215 | 0.0264683 | ||||||||
\(536\) | −4.86373 | −0.210081 | ||||||||
\(537\) | 5.34509 | 0.230658 | ||||||||
\(538\) | −41.5022 | −1.78929 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.28181 | 0.0551604 | ||||||||
\(541\) | −0.676959 | −0.0291047 | −0.0145524 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145524 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(542\) | 23.3412 | 1.00259 | ||||||||
\(543\) | 11.6201 | 0.498667 | ||||||||
\(544\) | 1.96930 | 0.0844330 | ||||||||
\(545\) | 12.8818 | 0.551795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.38777 | −0.358635 | −0.179318 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179318 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(548\) | 12.6059 | 0.538496 | ||||||||
\(549\) | 12.4540 | 0.531525 | ||||||||
\(550\) | 15.7175 | 0.670195 | ||||||||
\(551\) | 3.41515 | 0.145490 | ||||||||
\(552\) | 1.17548 | 0.0500320 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 53.1699 | 2.25897 | ||||||||
\(555\) | −1.16751 | −0.0495579 | ||||||||
\(556\) | 8.94968 | 0.379551 | ||||||||
\(557\) | −2.49888 | −0.105881 | −0.0529404 | − | 0.998598i | \(-0.516859\pi\) | ||||
−0.0529404 | + | 0.998598i | \(0.516859\pi\) | |||||||
\(558\) | 11.0396 | 0.467344 | ||||||||
\(559\) | −33.1092 | −1.40037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.624872 | −0.0263821 | ||||||||
\(562\) | 22.8103 | 0.962193 | ||||||||
\(563\) | −40.4580 | −1.70510 | −0.852551 | − | 0.522645i | \(-0.824945\pi\) | ||||
−0.852551 | + | 0.522645i | \(0.824945\pi\) | |||||||
\(564\) | −6.87779 | −0.289607 | ||||||||
\(565\) | −0.516352 | −0.0217231 | ||||||||
\(566\) | −17.1608 | −0.721323 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.6872 | −0.574303 | ||||||||
\(569\) | −12.4802 | −0.523199 | −0.261599 | − | 0.965177i | \(-0.584250\pi\) | ||||
−0.261599 | + | 0.965177i | \(0.584250\pi\) | |||||||
\(570\) | 1.00194 | 0.0419666 | ||||||||
\(571\) | −30.9927 | −1.29700 | −0.648502 | − | 0.761213i | \(-0.724604\pi\) | ||||
−0.648502 | + | 0.761213i | \(0.724604\pi\) | |||||||
\(572\) | 10.3312 | 0.431971 | ||||||||
\(573\) | 17.0751 | 0.713324 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.10983 | 0.171392 | ||||||||
\(576\) | −2.30974 | −0.0962394 | ||||||||
\(577\) | 10.5302 | 0.438379 | 0.219190 | − | 0.975682i | \(-0.429659\pi\) | ||||
0.219190 | + | 0.975682i | \(0.429659\pi\) | |||||||
\(578\) | 30.9906 | 1.28904 | ||||||||
\(579\) | 4.65052 | 0.193269 | ||||||||
\(580\) | 7.55452 | 0.313684 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.08097 | 0.0448077 | ||||||||
\(583\) | 4.85341 | 0.201008 | ||||||||
\(584\) | −13.6003 | −0.562786 | ||||||||
\(585\) | −3.43812 | −0.142149 | ||||||||
\(586\) | −10.4373 | −0.431160 | ||||||||
\(587\) | 7.06244 | 0.291498 | 0.145749 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145749 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.49062 | 0.143828 | ||||||||
\(590\) | 3.59675 | 0.148076 | ||||||||
\(591\) | −0.254912 | −0.0104857 | ||||||||
\(592\) | 6.02806 | 0.247752 | ||||||||
\(593\) | 39.8925 | 1.63819 | 0.819094 | − | 0.573660i | \(-0.194477\pi\) | ||||
0.819094 | + | 0.573660i | \(0.194477\pi\) | |||||||
\(594\) | 3.82436 | 0.156916 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.00075 | −0.327723 | ||||||||
\(597\) | −5.47597 | −0.224117 | ||||||||
\(598\) | 6.67825 | 0.273094 | ||||||||
\(599\) | 11.8646 | 0.484773 | 0.242386 | − | 0.970180i | \(-0.422070\pi\) | ||||
0.242386 | + | 0.970180i | \(0.422070\pi\) | |||||||
\(600\) | 4.83104 | 0.197226 | ||||||||
\(601\) | 15.0105 | 0.612290 | 0.306145 | − | 0.951985i | \(-0.400961\pi\) | ||||
0.306145 | + | 0.951985i | \(0.400961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.13763 | −0.168498 | ||||||||
\(604\) | 17.8706 | 0.727146 | ||||||||
\(605\) | 6.26974 | 0.254901 | ||||||||
\(606\) | 11.4143 | 0.463676 | ||||||||
\(607\) | −4.19990 | −0.170469 | −0.0852343 | − | 0.996361i | \(-0.527164\pi\) | ||||
−0.0852343 | + | 0.996361i | \(0.527164\pi\) | |||||||
\(608\) | −3.81090 | −0.154553 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.5340 | 0.871887 | ||||||||
\(611\) | 18.4479 | 0.746321 | ||||||||
\(612\) | 0.406815 | 0.0164445 | ||||||||
\(613\) | 30.9865 | 1.25153 | 0.625766 | − | 0.780011i | \(-0.284786\pi\) | ||||
0.625766 | + | 0.780011i | \(0.284786\pi\) | |||||||
\(614\) | −31.2641 | −1.26172 | ||||||||
\(615\) | 7.94441 | 0.320349 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.93041 | 0.0777153 | 0.0388577 | − | 0.999245i | \(-0.487628\pi\) | ||||
0.0388577 | + | 0.999245i | \(0.487628\pi\) | |||||||
\(618\) | −34.1705 | −1.37454 | ||||||||
\(619\) | 33.2844 | 1.33781 | 0.668907 | − | 0.743346i | \(-0.266763\pi\) | ||||
0.668907 | + | 0.743346i | \(0.266763\pi\) | |||||||
\(620\) | 7.72147 | 0.310102 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 30.2831 | 1.21424 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.7517 | 0.710636 | ||||||||
\(625\) | 12.4398 | 0.497593 | ||||||||
\(626\) | 2.73775 | 0.109422 | ||||||||
\(627\) | 1.20923 | 0.0482918 | ||||||||
\(628\) | −11.4469 | −0.456780 | ||||||||
\(629\) | −0.370538 | −0.0147743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.49815 | 0.179068 | 0.0895342 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895342 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(632\) | 20.1694 | 0.802297 | ||||||||
\(633\) | 3.18599 | 0.126632 | ||||||||
\(634\) | 33.3971 | 1.32637 | ||||||||
\(635\) | 0.955543 | 0.0379196 | ||||||||
\(636\) | −3.15975 | −0.125292 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.5394 | 0.892343 | ||||||||
\(639\) | −11.6439 | −0.460625 | ||||||||
\(640\) | 8.41618 | 0.332679 | ||||||||
\(641\) | −26.8209 | −1.05936 | −0.529681 | − | 0.848197i | \(-0.677688\pi\) | ||||
−0.529681 | + | 0.848197i | \(0.677688\pi\) | |||||||
\(642\) | −1.18917 | −0.0469329 | ||||||||
\(643\) | −21.1912 | −0.835701 | −0.417850 | − | 0.908516i | \(-0.637216\pi\) | ||||
−0.417850 | + | 0.908516i | \(0.637216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.57238 | −0.337537 | ||||||||
\(646\) | 0.317991 | 0.0125112 | ||||||||
\(647\) | 3.28238 | 0.129044 | 0.0645218 | − | 0.997916i | \(-0.479448\pi\) | ||||
0.0645218 | + | 0.997916i | \(0.479448\pi\) | |||||||
\(648\) | 1.17548 | 0.0461774 | ||||||||
\(649\) | 4.34086 | 0.170393 | ||||||||
\(650\) | 27.4464 | 1.07654 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.64813 | 0.221198 | ||||||||
\(653\) | 32.7912 | 1.28322 | 0.641610 | − | 0.767031i | \(-0.278267\pi\) | ||||
0.641610 | + | 0.767031i | \(0.278267\pi\) | |||||||
\(654\) | −25.0217 | −0.978426 | ||||||||
\(655\) | 14.1816 | 0.554123 | ||||||||
\(656\) | −41.0185 | −1.60150 | ||||||||
\(657\) | −11.5700 | −0.451388 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1625 | 0.434828 | 0.217414 | − | 0.976079i | \(-0.430238\pi\) | ||||
0.217414 | + | 0.976079i | \(0.430238\pi\) | |||||||
\(660\) | 2.67488 | 0.104120 | ||||||||
\(661\) | 8.39461 | 0.326513 | 0.163256 | − | 0.986584i | \(-0.447800\pi\) | ||||
0.163256 | + | 0.986584i | \(0.447800\pi\) | |||||||
\(662\) | 42.0681 | 1.63502 | ||||||||
\(663\) | −1.09117 | −0.0423777 | ||||||||
\(664\) | 12.8997 | 0.500606 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.26778 | 0.0878747 | ||||||||
\(667\) | 5.89363 | 0.228202 | ||||||||
\(668\) | −4.13614 | −0.160032 | ||||||||
\(669\) | 22.7674 | 0.880239 | ||||||||
\(670\) | −7.15430 | −0.276395 | ||||||||
\(671\) | 25.9891 | 1.00330 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3183 | 1.16869 | 0.584343 | − | 0.811507i | \(-0.301352\pi\) | ||||
0.584343 | + | 0.811507i | \(0.301352\pi\) | |||||||
\(674\) | −40.7335 | −1.56900 | ||||||||
\(675\) | 4.10983 | 0.158187 | ||||||||
\(676\) | 0.379177 | 0.0145837 | ||||||||
\(677\) | −10.3013 | −0.395910 | −0.197955 | − | 0.980211i | \(-0.563430\pi\) | ||||
−0.197955 | + | 0.980211i | \(0.563430\pi\) | |||||||
\(678\) | 1.00297 | 0.0385187 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.332096 | −0.0127353 | ||||||||
\(681\) | −10.4521 | −0.400524 | ||||||||
\(682\) | 23.0375 | 0.882151 | ||||||||
\(683\) | −48.1741 | −1.84333 | −0.921666 | − | 0.387984i | \(-0.873172\pi\) | ||||
−0.921666 | + | 0.387984i | \(0.873172\pi\) | |||||||
\(684\) | −0.787251 | −0.0301013 | ||||||||
\(685\) | −8.75433 | −0.334486 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7678 | 0.410819 | ||||||||
\(688\) | 44.2608 | 1.68743 | ||||||||
\(689\) | 8.47521 | 0.322880 | ||||||||
\(690\) | 1.72908 | 0.0658250 | ||||||||
\(691\) | −36.7195 | −1.39687 | −0.698437 | − | 0.715671i | \(-0.746121\pi\) | ||||
−0.698437 | + | 0.715671i | \(0.746121\pi\) | |||||||
\(692\) | 21.8111 | 0.829135 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.91171 | 0.376243 | ||||||||
\(695\) | −6.21523 | −0.235757 | ||||||||
\(696\) | 6.92787 | 0.262600 | ||||||||
\(697\) | 2.52136 | 0.0955032 | ||||||||
\(698\) | −19.0482 | −0.720985 | ||||||||
\(699\) | −11.7508 | −0.444455 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3581 | 1.33546 | 0.667728 | − | 0.744406i | \(-0.267267\pi\) | ||||
0.667728 | + | 0.744406i | \(0.267267\pi\) | |||||||
\(702\) | 6.67825 | 0.252054 | ||||||||
\(703\) | 0.717049 | 0.0270440 | ||||||||
\(704\) | −4.81998 | −0.181660 | ||||||||
\(705\) | 4.77638 | 0.179889 | ||||||||
\(706\) | 23.9509 | 0.901405 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.82606 | −0.106210 | ||||||||
\(709\) | −10.9962 | −0.412969 | −0.206485 | − | 0.978450i | \(-0.566202\pi\) | ||||
−0.206485 | + | 0.978450i | \(0.566202\pi\) | |||||||
\(710\) | −20.1332 | −0.755587 | ||||||||
\(711\) | 17.1584 | 0.643490 | ||||||||
\(712\) | 3.14514 | 0.117869 | ||||||||
\(713\) | 6.02387 | 0.225596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.17468 | −0.268318 | ||||||||
\(716\) | −7.26176 | −0.271385 | ||||||||
\(717\) | 12.5491 | 0.468655 | ||||||||
\(718\) | 35.2293 | 1.31475 | ||||||||
\(719\) | −36.5754 | −1.36403 | −0.682016 | − | 0.731337i | \(-0.738897\pi\) | ||||
−0.682016 | + | 0.731337i | \(0.738897\pi\) | |||||||
\(720\) | 4.59613 | 0.171288 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.2049 | 1.27297 | ||||||||
\(723\) | 10.6305 | 0.395351 | ||||||||
\(724\) | −15.7869 | −0.586716 | ||||||||
\(725\) | 24.2218 | 0.899575 | ||||||||
\(726\) | −12.1784 | −0.451983 | ||||||||
\(727\) | −12.9513 | −0.480337 | −0.240169 | − | 0.970731i | \(-0.577203\pi\) | ||||
−0.240169 | + | 0.970731i | \(0.577203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.0054 | −0.740434 | ||||||||
\(731\) | −2.72066 | −0.100627 | ||||||||
\(732\) | −16.9199 | −0.625376 | ||||||||
\(733\) | 6.26355 | 0.231350 | 0.115675 | − | 0.993287i | \(-0.463097\pi\) | ||||
0.115675 | + | 0.993287i | \(0.463097\pi\) | |||||||
\(734\) | 3.25312 | 0.120075 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.57660 | −0.242417 | ||||||||
\(737\) | −8.63442 | −0.318053 | ||||||||
\(738\) | −15.4313 | −0.568034 | ||||||||
\(739\) | 32.4215 | 1.19264 | 0.596322 | − | 0.802745i | \(-0.296628\pi\) | ||||
0.596322 | + | 0.802745i | \(0.296628\pi\) | |||||||
\(740\) | 1.58616 | 0.0583084 | ||||||||
\(741\) | 2.11159 | 0.0775714 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.32354 | −0.158615 | −0.0793076 | − | 0.996850i | \(-0.525271\pi\) | ||||
−0.0793076 | + | 0.996850i | \(0.525271\pi\) | |||||||
\(744\) | 7.08097 | 0.259601 | ||||||||
\(745\) | 5.55624 | 0.203565 | ||||||||
\(746\) | 13.6353 | 0.499222 | ||||||||
\(747\) | 10.9740 | 0.401516 | ||||||||
\(748\) | 0.848942 | 0.0310404 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.7516 | 0.575168 | ||||||||
\(751\) | −12.0432 | −0.439461 | −0.219730 | − | 0.975561i | \(-0.570518\pi\) | ||||
−0.219730 | + | 0.975561i | \(0.570518\pi\) | |||||||
\(752\) | −24.6614 | −0.899308 | ||||||||
\(753\) | 17.4415 | 0.635605 | ||||||||
\(754\) | 39.3591 | 1.43337 | ||||||||
\(755\) | −12.4105 | −0.451665 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8806 | 0.649880 | 0.324940 | − | 0.945735i | \(-0.394656\pi\) | ||||
0.324940 | + | 0.945735i | \(0.394656\pi\) | |||||||
\(758\) | 7.89961 | 0.286927 | ||||||||
\(759\) | 2.08680 | 0.0757461 | ||||||||
\(760\) | 0.642659 | 0.0233117 | ||||||||
\(761\) | 26.2960 | 0.953231 | 0.476615 | − | 0.879112i | \(-0.341863\pi\) | ||||
0.476615 | + | 0.879112i | \(0.341863\pi\) | |||||||
\(762\) | −1.85606 | −0.0672379 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −23.1980 | −0.839276 | ||||||||
\(765\) | −0.282519 | −0.0102145 | ||||||||
\(766\) | −63.5772 | −2.29714 | ||||||||
\(767\) | 7.58016 | 0.273704 | ||||||||
\(768\) | −20.9672 | −0.756588 | ||||||||
\(769\) | −32.2632 | −1.16344 | −0.581720 | − | 0.813389i | \(-0.697620\pi\) | ||||
−0.581720 | + | 0.813389i | \(0.697620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.7261 | −0.674403 | ||||||||
\(772\) | −6.31813 | −0.227394 | ||||||||
\(773\) | −10.5757 | −0.380380 | −0.190190 | − | 0.981747i | \(-0.560910\pi\) | ||||
−0.190190 | + | 0.981747i | \(0.560910\pi\) | |||||||
\(774\) | 16.6511 | 0.598511 | ||||||||
\(775\) | 24.7571 | 0.889301 | ||||||||
\(776\) | 0.693351 | 0.0248899 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −60.7409 | −2.17767 | ||||||||
\(779\) | −4.87922 | −0.174816 | ||||||||
\(780\) | 4.67098 | 0.167248 | ||||||||
\(781\) | −24.2985 | −0.869468 | ||||||||
\(782\) | 0.548767 | 0.0196239 | ||||||||
\(783\) | 5.89363 | 0.210621 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.94945 | 0.283728 | ||||||||
\(786\) | −27.5466 | −0.982554 | ||||||||
\(787\) | −27.5234 | −0.981103 | −0.490552 | − | 0.871412i | \(-0.663205\pi\) | ||||
−0.490552 | + | 0.871412i | \(0.663205\pi\) | |||||||
\(788\) | 0.346320 | 0.0123371 | ||||||||
\(789\) | −29.9086 | −1.06477 | ||||||||
\(790\) | 29.6683 | 1.05555 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.45300 | 0.0871636 | ||||||||
\(793\) | 45.3831 | 1.61160 | ||||||||
\(794\) | 52.1504 | 1.85075 | ||||||||
\(795\) | 2.19434 | 0.0778251 | ||||||||
\(796\) | 7.43958 | 0.263689 | ||||||||
\(797\) | −43.4629 | −1.53953 | −0.769767 | − | 0.638324i | \(-0.779628\pi\) | ||||
−0.769767 | + | 0.638324i | \(0.779628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.51590 | 0.0536288 | ||||||||
\(800\) | −27.0287 | −0.955609 | ||||||||
\(801\) | 2.67561 | 0.0945381 | ||||||||
\(802\) | 69.4226 | 2.45140 | ||||||||
\(803\) | −24.1442 | −0.852032 | ||||||||
\(804\) | 5.62133 | 0.198249 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.2289 | 1.41700 | ||||||||
\(807\) | −22.6461 | −0.797180 | ||||||||
\(808\) | 7.32132 | 0.257563 | ||||||||
\(809\) | 42.8145 | 1.50528 | 0.752639 | − | 0.658434i | \(-0.228781\pi\) | ||||
0.752639 | + | 0.658434i | \(0.228781\pi\) | |||||||
\(810\) | 1.72908 | 0.0607537 | ||||||||
\(811\) | 45.2610 | 1.58933 | 0.794664 | − | 0.607049i | \(-0.207647\pi\) | ||||
0.794664 | + | 0.607049i | \(0.207647\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.7364 | 0.446684 | ||||||||
\(814\) | 4.73240 | 0.165871 | ||||||||
\(815\) | −3.92243 | −0.137397 | ||||||||
\(816\) | 1.45870 | 0.0510646 | ||||||||
\(817\) | 5.26491 | 0.184196 | ||||||||
\(818\) | −1.75411 | −0.0613310 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.7932 | −0.376913 | ||||||||
\(821\) | −36.3213 | −1.26762 | −0.633812 | − | 0.773487i | \(-0.718511\pi\) | ||||
−0.633812 | + | 0.773487i | \(0.718511\pi\) | |||||||
\(822\) | 17.0045 | 0.593100 | ||||||||
\(823\) | 52.1001 | 1.81610 | 0.908048 | − | 0.418865i | \(-0.137572\pi\) | ||||
0.908048 | + | 0.418865i | \(0.137572\pi\) | |||||||
\(824\) | −21.9175 | −0.763532 | ||||||||
\(825\) | 8.57639 | 0.298592 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.6989 | −0.754545 | −0.377273 | − | 0.926102i | \(-0.623138\pi\) | ||||
−0.377273 | + | 0.926102i | \(0.623138\pi\) | |||||||
\(828\) | −1.35859 | −0.0472141 | ||||||||
\(829\) | −13.5755 | −0.471497 | −0.235749 | − | 0.971814i | \(-0.575754\pi\) | ||||
−0.235749 | + | 0.971814i | \(0.575754\pi\) | |||||||
\(830\) | 18.9749 | 0.658627 | ||||||||
\(831\) | 29.0127 | 1.00644 | ||||||||
\(832\) | −8.41682 | −0.291801 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.0725 | 0.418038 | ||||||||
\(835\) | 2.87241 | 0.0994037 | ||||||||
\(836\) | −1.64284 | −0.0568187 | ||||||||
\(837\) | 6.02387 | 0.208216 | ||||||||
\(838\) | 74.6986 | 2.58042 | ||||||||
\(839\) | −40.6915 | −1.40483 | −0.702413 | − | 0.711770i | \(-0.747894\pi\) | ||||
−0.702413 | + | 0.711770i | \(0.747894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.73489 | 0.197755 | ||||||||
\(842\) | 47.6826 | 1.64325 | ||||||||
\(843\) | 12.4466 | 0.428685 | ||||||||
\(844\) | −4.32843 | −0.148991 | ||||||||
\(845\) | −0.263325 | −0.00905866 | ||||||||
\(846\) | −9.27770 | −0.318974 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.3298 | −0.389066 | ||||||||
\(849\) | −9.36397 | −0.321370 | ||||||||
\(850\) | 2.25534 | 0.0773575 | ||||||||
\(851\) | 1.23744 | 0.0424187 | ||||||||
\(852\) | 15.8192 | 0.541958 | ||||||||
\(853\) | −53.5882 | −1.83482 | −0.917412 | − | 0.397938i | \(-0.869726\pi\) | ||||
−0.917412 | + | 0.397938i | \(0.869726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.546718 | 0.0186974 | ||||||||
\(856\) | −0.762752 | −0.0260703 | ||||||||
\(857\) | −15.1853 | −0.518719 | −0.259360 | − | 0.965781i | \(-0.583511\pi\) | ||||
−0.259360 | + | 0.965781i | \(0.583511\pi\) | |||||||
\(858\) | 13.9362 | 0.475773 | ||||||||
\(859\) | −37.9385 | −1.29444 | −0.647222 | − | 0.762302i | \(-0.724069\pi\) | ||||
−0.647222 | + | 0.762302i | \(0.724069\pi\) | |||||||
\(860\) | 11.6463 | 0.397136 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 57.6259 | 1.96275 | ||||||||
\(863\) | 34.9640 | 1.19019 | 0.595094 | − | 0.803656i | \(-0.297115\pi\) | ||||
0.595094 | + | 0.803656i | \(0.297115\pi\) | |||||||
\(864\) | −6.57660 | −0.223741 | ||||||||
\(865\) | −15.1471 | −0.515015 | ||||||||
\(866\) | −6.62099 | −0.224991 | ||||||||
\(867\) | 16.9103 | 0.574305 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.8062 | 1.21464 | ||||||||
\(870\) | 10.1906 | 0.345493 | ||||||||
\(871\) | −15.0777 | −0.510890 | ||||||||
\(872\) | −16.0493 | −0.543497 | ||||||||
\(873\) | 0.589843 | 0.0199632 | ||||||||
\(874\) | −1.06195 | −0.0359210 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.7188 | 0.531089 | ||||||||
\(877\) | 39.0428 | 1.31838 | 0.659191 | − | 0.751976i | \(-0.270899\pi\) | ||||
0.659191 | + | 0.751976i | \(0.270899\pi\) | |||||||
\(878\) | −33.0812 | −1.11644 | ||||||||
\(879\) | −5.69521 | −0.192095 | ||||||||
\(880\) | 9.59121 | 0.323320 | ||||||||
\(881\) | 21.5235 | 0.725145 | 0.362572 | − | 0.931956i | \(-0.381899\pi\) | ||||
0.362572 | + | 0.931956i | \(0.381899\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0630 | −0.574217 | −0.287109 | − | 0.957898i | \(-0.592694\pi\) | ||||
−0.287109 | + | 0.957898i | \(0.592694\pi\) | |||||||
\(884\) | 1.48245 | 0.0498603 | ||||||||
\(885\) | 1.96260 | 0.0659720 | ||||||||
\(886\) | 64.7474 | 2.17523 | ||||||||
\(887\) | 43.1464 | 1.44871 | 0.724357 | − | 0.689425i | \(-0.242137\pi\) | ||||
0.724357 | + | 0.689425i | \(0.242137\pi\) | |||||||
\(888\) | 1.45459 | 0.0488127 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.62635 | 0.155076 | ||||||||
\(891\) | 2.08680 | 0.0699104 | ||||||||
\(892\) | −30.9315 | −1.03566 | ||||||||
\(893\) | −2.93351 | −0.0981663 | ||||||||
\(894\) | −10.7925 | −0.360955 | ||||||||
\(895\) | 5.04304 | 0.168570 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.64405 | 0.121671 | ||||||||
\(898\) | −10.9151 | −0.364242 | ||||||||
\(899\) | 35.5025 | 1.18407 | ||||||||
\(900\) | −5.58355 | −0.186118 | ||||||||
\(901\) | 0.696428 | 0.0232014 | ||||||||
\(902\) | −32.2020 | −1.07221 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.643318 | 0.0213964 | ||||||||
\(905\) | 10.9635 | 0.364438 | ||||||||
\(906\) | 24.1063 | 0.800879 | ||||||||
\(907\) | −9.48595 | −0.314976 | −0.157488 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157488 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(908\) | 14.2000 | 0.471245 | ||||||||
\(909\) | 6.22834 | 0.206581 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7773 | 0.588988 | 0.294494 | − | 0.955653i | \(-0.404849\pi\) | ||||
0.294494 | + | 0.955653i | \(0.404849\pi\) | |||||||
\(912\) | −2.82281 | −0.0934725 | ||||||||
\(913\) | 22.9005 | 0.757895 | ||||||||
\(914\) | −58.5848 | −1.93781 | ||||||||
\(915\) | 11.7502 | 0.388451 | ||||||||
\(916\) | −14.6290 | −0.483357 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.548767 | 0.0181120 | ||||||||
\(919\) | 3.50669 | 0.115675 | 0.0578376 | − | 0.998326i | \(-0.481579\pi\) | ||||
0.0578376 | + | 0.998326i | \(0.481579\pi\) | |||||||
\(920\) | 1.10906 | 0.0365645 | ||||||||
\(921\) | −17.0596 | −0.562132 | ||||||||
\(922\) | −13.0216 | −0.428843 | ||||||||
\(923\) | −42.4309 | −1.39663 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.08565 | 0.167215 | ||||||||
\(926\) | 77.1206 | 2.53434 | ||||||||
\(927\) | −18.6455 | −0.612398 | ||||||||
\(928\) | −38.7601 | −1.27236 | ||||||||
\(929\) | 15.2444 | 0.500153 | 0.250076 | − | 0.968226i | \(-0.419544\pi\) | ||||
0.250076 | + | 0.968226i | \(0.419544\pi\) | |||||||
\(930\) | 10.4158 | 0.341546 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.9644 | 0.522932 | ||||||||
\(933\) | 16.5243 | 0.540980 | ||||||||
\(934\) | −48.4747 | −1.58614 | ||||||||
\(935\) | −0.589560 | −0.0192807 | ||||||||
\(936\) | 4.28352 | 0.140011 | ||||||||
\(937\) | −16.0219 | −0.523414 | −0.261707 | − | 0.965147i | \(-0.584285\pi\) | ||||
−0.261707 | + | 0.965147i | \(0.584285\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.49388 | 0.0487508 | ||||||||
\(940\) | −6.48912 | −0.211652 | ||||||||
\(941\) | −8.29938 | −0.270552 | −0.135276 | − | 0.990808i | \(-0.543192\pi\) | ||||
−0.135276 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(942\) | −15.4411 | −0.503098 | ||||||||
\(943\) | −8.42024 | −0.274201 | ||||||||
\(944\) | −10.1333 | −0.329810 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.7475 | 1.12974 | ||||||||
\(947\) | 48.3210 | 1.57022 | 0.785111 | − | 0.619355i | \(-0.212606\pi\) | ||||
0.785111 | + | 0.619355i | \(0.212606\pi\) | |||||||
\(948\) | −23.3112 | −0.757111 | ||||||||
\(949\) | −42.1616 | −1.36862 | ||||||||
\(950\) | −4.36443 | −0.141601 | ||||||||
\(951\) | 18.2234 | 0.590935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0181 | 0.389303 | 0.194652 | − | 0.980872i | \(-0.437642\pi\) | ||||
0.194652 | + | 0.980872i | \(0.437642\pi\) | |||||||
\(954\) | −4.26230 | −0.137997 | ||||||||
\(955\) | 16.1102 | 0.521314 | ||||||||
\(956\) | −17.0490 | −0.551405 | ||||||||
\(957\) | 12.2988 | 0.397565 | ||||||||
\(958\) | 46.3344 | 1.49700 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.17922 | −0.0703340 | ||||||||
\(961\) | 5.28706 | 0.170550 | ||||||||
\(962\) | 8.26390 | 0.266439 | ||||||||
\(963\) | −0.648883 | −0.0209100 | ||||||||
\(964\) | −14.4424 | −0.465158 | ||||||||
\(965\) | 4.38772 | 0.141246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9914 | 0.675036 | 0.337518 | − | 0.941319i | \(-0.390413\pi\) | ||||
0.337518 | + | 0.941319i | \(0.390413\pi\) | |||||||
\(968\) | −7.81141 | −0.251068 | ||||||||
\(969\) | 0.173515 | 0.00557409 | ||||||||
\(970\) | 1.01989 | 0.0327466 | ||||||||
\(971\) | −5.29526 | −0.169933 | −0.0849665 | − | 0.996384i | \(-0.527078\pi\) | ||||
−0.0849665 | + | 0.996384i | \(0.527078\pi\) | |||||||
\(972\) | −1.35859 | −0.0435767 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36.6098 | −1.17305 | ||||||||
\(975\) | 14.9764 | 0.479629 | ||||||||
\(976\) | −60.6688 | −1.94196 | ||||||||
\(977\) | −26.6768 | −0.853466 | −0.426733 | − | 0.904378i | \(-0.640336\pi\) | ||||
−0.426733 | + | 0.904378i | \(0.640336\pi\) | |||||||
\(978\) | 7.61897 | 0.243628 | ||||||||
\(979\) | 5.58347 | 0.178448 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6533 | −0.435917 | ||||||||
\(982\) | 75.1551 | 2.39830 | ||||||||
\(983\) | 6.63941 | 0.211764 | 0.105882 | − | 0.994379i | \(-0.466233\pi\) | ||||
0.105882 | + | 0.994379i | \(0.466233\pi\) | |||||||
\(984\) | −9.89786 | −0.315532 | ||||||||
\(985\) | −0.240507 | −0.00766320 | ||||||||
\(986\) | 3.23423 | 0.102999 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.86878 | −0.0912681 | ||||||||
\(989\) | 9.08583 | 0.288912 | ||||||||
\(990\) | 3.60825 | 0.114678 | ||||||||
\(991\) | 30.3443 | 0.963917 | 0.481958 | − | 0.876194i | \(-0.339926\pi\) | ||||
0.481958 | + | 0.876194i | \(0.339926\pi\) | |||||||
\(992\) | −39.6166 | −1.25783 | ||||||||
\(993\) | 22.9549 | 0.728451 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.16652 | −0.163790 | ||||||||
\(996\) | −14.9091 | −0.472412 | ||||||||
\(997\) | 46.9848 | 1.48802 | 0.744011 | − | 0.668167i | \(-0.232921\pi\) | ||||
0.744011 | + | 0.668167i | \(0.232921\pi\) | |||||||
\(998\) | −25.7429 | −0.814878 | ||||||||
\(999\) | 1.23744 | 0.0391507 |
(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 | 3381.2.a.bc.1.2 | 6 | ||
7.2 | even | 3 | 483.2.i.f.277.5 | ✓ | 12 | ||
7.4 | even | 3 | 483.2.i.f.415.5 | yes | 12 | ||
7.6 | odd | 2 | 3381.2.a.bd.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.f.277.5 | ✓ | 12 | 7.2 | even | 3 | ||
483.2.i.f.415.5 | yes | 12 | 7.4 | even | 3 | ||
3381.2.a.bc.1.2 | 6 | 1.1 | even | 1 | trivial | ||
3381.2.a.bd.1.2 | 6 | 7.6 | odd | 2 |