Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1710) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.12311 | 1.18042 | 0.590211 | − | 0.807249i | \(-0.299044\pi\) | ||||
0.590211 | + | 0.807249i | \(0.299044\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −3.12311 | −0.834685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.12311 | 0.590211 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.12311 | 1.63856 | 0.819279 | − | 0.573395i | \(-0.194374\pi\) | ||||
0.819279 | + | 0.573395i | \(0.194374\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.12311 | 0.535608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12311 | −0.800095 | −0.400047 | − | 0.916494i | \(-0.631006\pi\) | ||||
−0.400047 | + | 0.916494i | \(0.631006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2462 | −1.56253 | −0.781266 | − | 0.624198i | \(-0.785426\pi\) | ||||
−0.781266 | + | 0.624198i | \(0.785426\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2462 | −1.49456 | −0.747282 | − | 0.664507i | \(-0.768641\pi\) | ||||
−0.747282 | + | 0.664507i | \(0.768641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.75379 | 0.393398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.12311 | −0.417343 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −3.12311 | −0.406594 | −0.203297 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203297 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2462 | 1.56797 | 0.783983 | − | 0.620782i | \(-0.213185\pi\) | ||||
0.783983 | + | 0.620782i | \(0.213185\pi\) | |||||||
\(62\) | −9.12311 | −1.15864 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24621 | −0.763096 | −0.381548 | − | 0.924349i | \(-0.624609\pi\) | ||||
−0.381548 | + | 0.924349i | \(0.624609\pi\) | |||||||
\(68\) | −3.12311 | −0.378732 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.24621 | 0.741289 | 0.370644 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370644 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 6.24621 | 0.711822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.12311 | 1.02643 | 0.513215 | − | 0.858260i | \(-0.328454\pi\) | ||||
0.513215 | + | 0.858260i | \(0.328454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.12311 | 0.565752 | ||||||||
\(83\) | −6.87689 | −0.754837 | −0.377419 | − | 0.926043i | \(-0.623188\pi\) | ||||
−0.377419 | + | 0.926043i | \(0.623188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.2462 | 1.10488 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | −11.3693 | −1.20515 | −0.602573 | − | 0.798064i | \(-0.705858\pi\) | ||||
−0.602573 | + | 0.798064i | \(0.705858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4924 | −1.30956 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2462 | 1.05682 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | −2.75379 | −0.278175 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.24621 | 0.812523 | 0.406262 | − | 0.913757i | \(-0.366832\pi\) | ||||
0.406262 | + | 0.913757i | \(0.366832\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.24621 | −0.412428 | ||||||||
\(107\) | −14.2462 | −1.37723 | −0.688617 | − | 0.725126i | \(-0.741782\pi\) | ||||
−0.688617 | + | 0.725126i | \(0.741782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.87689 | 0.467122 | 0.233561 | − | 0.972342i | \(-0.424962\pi\) | ||||
0.233561 | + | 0.972342i | \(0.424962\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.12311 | 0.295106 | ||||||||
\(113\) | −4.24621 | −0.399450 | −0.199725 | − | 0.979852i | \(-0.564005\pi\) | ||||
−0.199725 | + | 0.979852i | \(0.564005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.12311 | 0.287505 | ||||||||
\(119\) | −9.75379 | −0.894128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −12.2462 | −1.10872 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.12311 | 0.819279 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.75379 | 0.333095 | 0.166547 | − | 0.986033i | \(-0.446738\pi\) | ||||
0.166547 | + | 0.986033i | \(0.446738\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.4924 | −1.96517 | −0.982586 | − | 0.185808i | \(-0.940510\pi\) | ||||
−0.982586 | + | 0.185808i | \(0.940510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12311 | −0.270808 | ||||||||
\(134\) | 6.24621 | 0.539590 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.12311 | 0.267804 | ||||||||
\(137\) | 19.1231 | 1.63380 | 0.816899 | − | 0.576781i | \(-0.195692\pi\) | ||||
0.816899 | + | 0.576781i | \(0.195692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.24621 | −0.524170 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0000 | −1.80231 | −0.901155 | − | 0.433497i | \(-0.857280\pi\) | ||||
−0.901155 | + | 0.433497i | \(0.857280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.87689 | 0.234118 | 0.117059 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117059 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.24621 | −0.503334 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12311 | 0.0896336 | 0.0448168 | − | 0.998995i | \(-0.485730\pi\) | ||||
0.0448168 | + | 0.998995i | \(0.485730\pi\) | |||||||
\(158\) | −9.12311 | −0.725795 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −5.12311 | −0.400047 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.87689 | 0.533751 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2462 | −0.781266 | ||||||||
\(173\) | −8.24621 | −0.626948 | −0.313474 | − | 0.949597i | \(-0.601493\pi\) | ||||
−0.313474 | + | 0.949597i | \(0.601493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.3693 | 0.852166 | ||||||||
\(179\) | −8.87689 | −0.663490 | −0.331745 | − | 0.943369i | \(-0.607637\pi\) | ||||
−0.331745 | + | 0.943369i | \(0.607637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.36932 | 0.696416 | 0.348208 | − | 0.937417i | \(-0.386790\pi\) | ||||
0.348208 | + | 0.937417i | \(0.386790\pi\) | |||||||
\(182\) | 12.4924 | 0.926000 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.24621 | −0.456768 | ||||||||
\(188\) | −10.2462 | −0.747282 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4924 | −1.33111 | −0.665557 | − | 0.746347i | \(-0.731806\pi\) | ||||
−0.665557 | + | 0.746347i | \(0.731806\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | 8.24621 | 0.587518 | 0.293759 | − | 0.955879i | \(-0.405094\pi\) | ||||
0.293759 | + | 0.955879i | \(0.405094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2462 | 0.726335 | 0.363167 | − | 0.931724i | \(-0.381695\pi\) | ||||
0.363167 | + | 0.931724i | \(0.381695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −6.24621 | −0.438398 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.24621 | −0.574541 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 4.24621 | 0.291631 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.2462 | 0.973851 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.4924 | 1.93419 | ||||||||
\(218\) | −4.87689 | −0.330305 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.4924 | 0.840331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | −3.12311 | −0.208671 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.24621 | 0.282454 | ||||||||
\(227\) | 20.4924 | 1.36013 | 0.680065 | − | 0.733152i | \(-0.261952\pi\) | ||||
0.680065 | + | 0.733152i | \(0.261952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4924 | 1.22201 | 0.611007 | − | 0.791625i | \(-0.290765\pi\) | ||||
0.611007 | + | 0.791625i | \(0.290765\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | 1.36932 | 0.0897069 | 0.0448535 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448535 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.12311 | −0.203297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.75379 | 0.632244 | ||||||||
\(239\) | −1.75379 | −0.113443 | −0.0567216 | − | 0.998390i | \(-0.518065\pi\) | ||||
−0.0567216 | + | 0.998390i | \(0.518065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.246211 | 0.0158599 | 0.00792993 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792993 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.2462 | 0.783983 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | −9.12311 | −0.579318 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.2462 | 1.02545 | 0.512726 | − | 0.858552i | \(-0.328636\pi\) | ||||
0.512726 | + | 0.858552i | \(0.328636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.75379 | −0.235534 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.0000 | −0.623783 | −0.311891 | − | 0.950118i | \(-0.600963\pi\) | ||||
−0.311891 | + | 0.950118i | \(0.600963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.4924 | 1.38959 | ||||||||
\(263\) | −12.4924 | −0.770316 | −0.385158 | − | 0.922851i | \(-0.625853\pi\) | ||||
−0.385158 | + | 0.922851i | \(0.625853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.12311 | 0.191490 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.24621 | −0.381548 | ||||||||
\(269\) | 20.7386 | 1.26446 | 0.632228 | − | 0.774782i | \(-0.282140\pi\) | ||||
0.632228 | + | 0.774782i | \(0.282140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24621 | 0.136448 | 0.0682238 | − | 0.997670i | \(-0.478267\pi\) | ||||
0.0682238 | + | 0.997670i | \(0.478267\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.1231 | −1.15527 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.61553 | 0.577741 | 0.288871 | − | 0.957368i | \(-0.406720\pi\) | ||||
0.288871 | + | 0.957368i | \(0.406720\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3693 | 1.15548 | 0.577738 | − | 0.816222i | \(-0.303935\pi\) | ||||
0.577738 | + | 0.816222i | \(0.303935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.49242 | −0.504822 | −0.252411 | − | 0.967620i | \(-0.581224\pi\) | ||||
−0.252411 | + | 0.967620i | \(0.581224\pi\) | |||||||
\(284\) | 6.24621 | 0.370644 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.00000 | 0.473050 | ||||||||
\(287\) | −16.0000 | −0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 18.4924 | 1.08034 | 0.540169 | − | 0.841556i | \(-0.318360\pi\) | ||||
0.540169 | + | 0.841556i | \(0.318360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.0000 | 1.27443 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.0000 | −1.84445 | ||||||||
\(302\) | −2.87689 | −0.165547 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.75379 | 0.328386 | 0.164193 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164193 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(308\) | 6.24621 | 0.355911 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699155 | − | 0.714970i | \(-0.253560\pi\) | ||||
0.699155 | + | 0.714970i | \(0.253560\pi\) | |||||||
\(314\) | −1.12311 | −0.0633805 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.12311 | 0.513215 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12311 | 0.173774 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.12311 | 0.282876 | ||||||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4924 | −1.34623 | −0.673113 | − | 0.739540i | \(-0.735043\pi\) | ||||
−0.673113 | + | 0.739540i | \(0.735043\pi\) | |||||||
\(332\) | −6.87689 | −0.377419 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 1.41631 | 0.708155 | − | 0.706057i | \(-0.249528\pi\) | ||||
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.2462 | 0.988088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2614 | −0.716046 | ||||||||
\(344\) | 10.2462 | 0.552439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.24621 | 0.443319 | ||||||||
\(347\) | −8.63068 | −0.463319 | −0.231660 | − | 0.972797i | \(-0.574416\pi\) | ||||
−0.231660 | + | 0.972797i | \(0.574416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4924 | −0.561646 | −0.280823 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280823 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −25.8617 | −1.37648 | −0.688241 | − | 0.725482i | \(-0.741617\pi\) | ||||
−0.688241 | + | 0.725482i | \(0.741617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.3693 | −0.602573 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.87689 | 0.469158 | ||||||||
\(359\) | −10.2462 | −0.540774 | −0.270387 | − | 0.962752i | \(-0.587152\pi\) | ||||
−0.270387 | + | 0.962752i | \(0.587152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.36932 | −0.492440 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.4924 | −0.654781 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.876894 | 0.0457735 | 0.0228868 | − | 0.999738i | \(-0.492714\pi\) | ||||
0.0228868 | + | 0.999738i | \(0.492714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2614 | 0.688496 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2462 | 0.737641 | 0.368820 | − | 0.929501i | \(-0.379762\pi\) | ||||
0.368820 | + | 0.929501i | \(0.379762\pi\) | |||||||
\(374\) | 6.24621 | 0.322984 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.2462 | 0.528408 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.49242 | 0.436226 | 0.218113 | − | 0.975923i | \(-0.430010\pi\) | ||||
0.218113 | + | 0.975923i | \(0.430010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | −36.4924 | −1.86468 | −0.932338 | − | 0.361588i | \(-0.882235\pi\) | ||||
−0.932338 | + | 0.361588i | \(0.882235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.4924 | 0.941240 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000 | 0.304604 | ||||||||
\(389\) | −34.4924 | −1.74884 | −0.874418 | − | 0.485174i | \(-0.838756\pi\) | ||||
−0.874418 | + | 0.485174i | \(0.838756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.75379 | −0.139087 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.24621 | −0.415438 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.1231 | −0.658630 | −0.329315 | − | 0.944220i | \(-0.606818\pi\) | ||||
−0.329315 | + | 0.944220i | \(0.606818\pi\) | |||||||
\(398\) | −10.2462 | −0.513596 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.8617 | −1.59110 | −0.795550 | − | 0.605888i | \(-0.792818\pi\) | ||||
−0.795550 | + | 0.605888i | \(0.792818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.4924 | −1.81782 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.24621 | 0.309994 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.24621 | 0.406262 | ||||||||
\(413\) | −9.75379 | −0.479953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.00000 | 0.0978232 | ||||||||
\(419\) | −12.2462 | −0.598267 | −0.299133 | − | 0.954211i | \(-0.596698\pi\) | ||||
−0.299133 | + | 0.954211i | \(0.596698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1231 | −0.737055 | −0.368528 | − | 0.929617i | \(-0.620138\pi\) | ||||
−0.368528 | + | 0.929617i | \(0.620138\pi\) | |||||||
\(422\) | 20.0000 | 0.973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.24621 | −0.206214 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.2462 | 1.85086 | ||||||||
\(428\) | −14.2462 | −0.688617 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | −28.4924 | −1.36768 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.87689 | 0.233561 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8769 | −0.519126 | −0.259563 | − | 0.965726i | \(-0.583578\pi\) | ||||
−0.259563 | + | 0.965726i | \(0.583578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.4924 | −0.594204 | ||||||||
\(443\) | 19.8617 | 0.943660 | 0.471830 | − | 0.881690i | \(-0.343594\pi\) | ||||
0.471830 | + | 0.881690i | \(0.343594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.0000 | 0.473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.12311 | 0.147553 | ||||||||
\(449\) | −4.63068 | −0.218535 | −0.109268 | − | 0.994012i | \(-0.534851\pi\) | ||||
−0.109268 | + | 0.994012i | \(0.534851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2462 | −0.482475 | ||||||||
\(452\) | −4.24621 | −0.199725 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.4924 | −0.961757 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | −18.4924 | −0.864094 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.4924 | 1.04758 | 0.523788 | − | 0.851848i | \(-0.324518\pi\) | ||||
0.523788 | + | 0.851848i | \(0.324518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1231 | 1.07462 | 0.537311 | − | 0.843384i | \(-0.319440\pi\) | ||||
0.537311 | + | 0.843384i | \(0.319440\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.36932 | −0.0634324 | ||||||||
\(467\) | −30.8769 | −1.42881 | −0.714406 | − | 0.699731i | \(-0.753303\pi\) | ||||
−0.714406 | + | 0.699731i | \(0.753303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.5076 | −0.900776 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.12311 | 0.143753 | ||||||||
\(473\) | −20.4924 | −0.942243 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.75379 | −0.447064 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.75379 | 0.0802164 | ||||||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.246211 | −0.0112146 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7538 | 0.713872 | 0.356936 | − | 0.934129i | \(-0.383821\pi\) | ||||
0.356936 | + | 0.934129i | \(0.383821\pi\) | |||||||
\(488\) | −12.2462 | −0.554360 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4924 | −1.01507 | −0.507534 | − | 0.861631i | \(-0.669443\pi\) | ||||
−0.507534 | + | 0.861631i | \(0.669443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.24621 | 0.281315 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.12311 | 0.409640 | ||||||||
\(497\) | 19.5076 | 0.875034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.2462 | −0.725104 | ||||||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.75379 | 0.166547 | ||||||||
\(509\) | 42.4924 | 1.88344 | 0.941722 | − | 0.336393i | \(-0.109207\pi\) | ||||
0.941722 | + | 0.336393i | \(0.109207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.7386 | −0.828948 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.0000 | 0.441081 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4924 | −0.901256 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6155 | 0.596507 | 0.298254 | − | 0.954487i | \(-0.403596\pi\) | ||||
0.298254 | + | 0.954487i | \(0.403596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.7386 | −1.86883 | −0.934415 | − | 0.356186i | \(-0.884077\pi\) | ||||
−0.934415 | + | 0.356186i | \(0.884077\pi\) | |||||||
\(524\) | −22.4924 | −0.982586 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.4924 | 0.544696 | ||||||||
\(527\) | −28.4924 | −1.24115 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.12311 | −0.135404 | ||||||||
\(533\) | 20.4924 | 0.887625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.24621 | 0.269795 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.7386 | −0.894106 | ||||||||
\(539\) | 5.50758 | 0.237228 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.50758 | −0.0648158 | −0.0324079 | − | 0.999475i | \(-0.510318\pi\) | ||||
−0.0324079 | + | 0.999475i | \(0.510318\pi\) | |||||||
\(542\) | −2.24621 | −0.0964830 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.12311 | 0.133902 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.24621 | −0.0960411 | −0.0480205 | − | 0.998846i | \(-0.515291\pi\) | ||||
−0.0480205 | + | 0.998846i | \(0.515291\pi\) | |||||||
\(548\) | 19.1231 | 0.816899 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.4924 | 1.21162 | ||||||||
\(554\) | −9.61553 | −0.408525 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.4924 | −0.699435 | ||||||||
\(557\) | −16.2462 | −0.688374 | −0.344187 | − | 0.938901i | \(-0.611845\pi\) | ||||
−0.344187 | + | 0.938901i | \(0.611845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.9848 | 1.73347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.3693 | −0.817045 | ||||||||
\(563\) | 43.2311 | 1.82197 | 0.910986 | − | 0.412438i | \(-0.135322\pi\) | ||||
0.910986 | + | 0.412438i | \(0.135322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.49242 | 0.356963 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.24621 | −0.262085 | ||||||||
\(569\) | −41.1231 | −1.72397 | −0.861985 | − | 0.506934i | \(-0.830779\pi\) | ||||
−0.861985 | + | 0.506934i | \(0.830779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4924 | 1.35977 | 0.679883 | − | 0.733321i | \(-0.262031\pi\) | ||||
0.679883 | + | 0.733321i | \(0.262031\pi\) | |||||||
\(572\) | −8.00000 | −0.334497 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.0000 | 0.667827 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7386 | −1.02988 | −0.514941 | − | 0.857225i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857225i | \(0.672186\pi\) | |||||||
\(578\) | 7.24621 | 0.301403 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.4773 | −0.891027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.49242 | 0.351720 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.4924 | −0.763915 | ||||||||
\(587\) | 35.3693 | 1.45985 | 0.729924 | − | 0.683528i | \(-0.239555\pi\) | ||||
0.729924 | + | 0.683528i | \(0.239555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.12311 | −0.375911 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.6155 | 0.641253 | 0.320626 | − | 0.947206i | \(-0.396107\pi\) | ||||
0.320626 | + | 0.947206i | \(0.396107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.0000 | −0.901155 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.4924 | −0.510427 | −0.255213 | − | 0.966885i | \(-0.582146\pi\) | ||||
−0.255213 | + | 0.966885i | \(0.582146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.7386 | 1.49860 | 0.749300 | − | 0.662231i | \(-0.230390\pi\) | ||||
0.749300 | + | 0.662231i | \(0.230390\pi\) | |||||||
\(602\) | 32.0000 | 1.30422 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.87689 | 0.117059 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.24621 | 0.172348 | 0.0861742 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861742 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.9848 | 1.65807 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6307 | −0.671707 | −0.335853 | − | 0.941914i | \(-0.609025\pi\) | ||||
−0.335853 | + | 0.941914i | \(0.609025\pi\) | |||||||
\(614\) | −5.75379 | −0.232204 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.24621 | −0.251667 | ||||||||
\(617\) | −0.876894 | −0.0353024 | −0.0176512 | − | 0.999844i | \(-0.505619\pi\) | ||||
−0.0176512 | + | 0.999844i | \(0.505619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0000 | 1.44696 | 0.723481 | − | 0.690344i | \(-0.242541\pi\) | ||||
0.723481 | + | 0.690344i | \(0.242541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.0000 | −0.801927 | ||||||||
\(623\) | −35.5076 | −1.42258 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24.7386 | −0.988755 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.12311 | 0.0448168 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.9848 | −1.47234 | −0.736172 | − | 0.676795i | \(-0.763368\pi\) | ||||
−0.736172 | + | 0.676795i | \(0.763368\pi\) | |||||||
\(632\) | −9.12311 | −0.362898 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0000 | −0.556011 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0152 | −0.436436 | ||||||||
\(638\) | 4.00000 | 0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.8617 | 0.468511 | 0.234255 | − | 0.972175i | \(-0.424735\pi\) | ||||
0.234255 | + | 0.972175i | \(0.424735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.4924 | 1.28138 | 0.640688 | − | 0.767801i | \(-0.278649\pi\) | ||||
0.640688 | + | 0.767801i | \(0.278649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.12311 | −0.122877 | ||||||||
\(647\) | −4.49242 | −0.176615 | −0.0883077 | − | 0.996093i | \(-0.528146\pi\) | ||||
−0.0883077 | + | 0.996093i | \(0.528146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.24621 | −0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −26.9848 | −1.05600 | −0.527999 | − | 0.849245i | \(-0.677058\pi\) | ||||
−0.527999 | + | 0.849245i | \(0.677058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.12311 | −0.200024 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.0000 | 1.24749 | ||||||||
\(659\) | −0.384472 | −0.0149769 | −0.00748845 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00748845 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.6155 | −1.22970 | −0.614851 | − | 0.788643i | \(-0.710784\pi\) | ||||
−0.614851 | + | 0.788643i | \(0.710784\pi\) | |||||||
\(662\) | 24.4924 | 0.951925 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.87689 | 0.266875 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4924 | 0.945519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | −26.0000 | −1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −34.9848 | −1.34458 | −0.672288 | − | 0.740289i | \(-0.734689\pi\) | ||||
−0.672288 | + | 0.740289i | \(0.734689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.7386 | 0.719123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.2462 | −0.698684 | ||||||||
\(683\) | −20.0000 | −0.765279 | −0.382639 | − | 0.923898i | \(-0.624985\pi\) | ||||
−0.382639 | + | 0.923898i | \(0.624985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.2614 | 0.506321 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.2462 | −0.390633 | ||||||||
\(689\) | −16.9848 | −0.647071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.492423 | 0.0187326 | 0.00936632 | − | 0.999956i | \(-0.497019\pi\) | ||||
0.00936632 | + | 0.999956i | \(0.497019\pi\) | |||||||
\(692\) | −8.24621 | −0.313474 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.63068 | 0.327616 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | 0.606043 | ||||||||
\(698\) | 10.4924 | 0.397144 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.9848 | −1.32136 | −0.660680 | − | 0.750668i | \(-0.729732\pi\) | ||||
−0.660680 | + | 0.750668i | \(0.729732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.8617 | 0.973319 | ||||||||
\(707\) | −31.2311 | −1.17456 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.3693 | 0.426083 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.87689 | −0.331745 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.2462 | 0.382385 | ||||||||
\(719\) | 10.2462 | 0.382119 | 0.191060 | − | 0.981578i | \(-0.438808\pi\) | ||||
0.191060 | + | 0.981578i | \(0.438808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.7538 | 0.959121 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.36932 | 0.348208 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.63068 | −0.245918 | −0.122959 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122959 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(728\) | 12.4924 | 0.463000 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.6155 | −1.24162 | −0.620809 | − | 0.783962i | \(-0.713196\pi\) | ||||
−0.620809 | + | 0.783962i | \(0.713196\pi\) | |||||||
\(734\) | −0.876894 | −0.0323668 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4924 | −0.460164 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4924 | −0.606684 | −0.303342 | − | 0.952882i | \(-0.598102\pi\) | ||||
−0.303342 | + | 0.952882i | \(0.598102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.2614 | −0.486840 | ||||||||
\(743\) | −24.9848 | −0.916605 | −0.458303 | − | 0.888796i | \(-0.651542\pi\) | ||||
−0.458303 | + | 0.888796i | \(0.651542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.2462 | −0.521591 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.24621 | −0.228384 | ||||||||
\(749\) | −44.4924 | −1.62572 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.86174 | −0.286879 | −0.143439 | − | 0.989659i | \(-0.545816\pi\) | ||||
−0.143439 | + | 0.989659i | \(0.545816\pi\) | |||||||
\(752\) | −10.2462 | −0.373641 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.00000 | −0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.8617 | 1.30342 | 0.651709 | − | 0.758469i | \(-0.274053\pi\) | ||||
0.651709 | + | 0.758469i | \(0.274053\pi\) | |||||||
\(758\) | −8.49242 | −0.308459 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.2462 | −1.67642 | −0.838212 | − | 0.545345i | \(-0.816399\pi\) | ||||
−0.838212 | + | 0.545345i | \(0.816399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2311 | 0.551401 | ||||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.4924 | 1.31852 | ||||||||
\(767\) | 12.4924 | 0.451075 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.7538 | −0.856584 | −0.428292 | − | 0.903641i | \(-0.640884\pi\) | ||||
−0.428292 | + | 0.903641i | \(0.640884\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.4924 | −0.665557 | ||||||||
\(773\) | −31.7538 | −1.14210 | −0.571052 | − | 0.820914i | \(-0.693465\pi\) | ||||
−0.571052 | + | 0.820914i | \(0.693465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.4924 | 1.23661 | ||||||||
\(779\) | 5.12311 | 0.183554 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4924 | 0.447014 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.75379 | 0.0983496 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.4924 | −0.873061 | −0.436530 | − | 0.899690i | \(-0.643793\pi\) | ||||
−0.436530 | + | 0.899690i | \(0.643793\pi\) | |||||||
\(788\) | 8.24621 | 0.293759 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2614 | −0.471520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.9848 | −1.73950 | ||||||||
\(794\) | 13.1231 | 0.465722 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2462 | 0.363167 | ||||||||
\(797\) | −2.49242 | −0.0882861 | −0.0441431 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441431 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.8617 | 1.12508 | ||||||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 36.4924 | 1.28539 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | −2.24621 | −0.0789726 | −0.0394863 | − | 0.999220i | \(-0.512572\pi\) | ||||
−0.0394863 | + | 0.999220i | \(0.512572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.9848 | −1.57963 | −0.789816 | − | 0.613344i | \(-0.789824\pi\) | ||||
−0.789816 | + | 0.613344i | \(0.789824\pi\) | |||||||
\(812\) | −6.24621 | −0.219199 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2462 | 0.358470 | ||||||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.0000 | 0.488603 | 0.244302 | − | 0.969699i | \(-0.421441\pi\) | ||||
0.244302 | + | 0.969699i | \(0.421441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.86174 | −0.0648962 | −0.0324481 | − | 0.999473i | \(-0.510330\pi\) | ||||
−0.0324481 | + | 0.999473i | \(0.510330\pi\) | |||||||
\(824\) | −8.24621 | −0.287270 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.75379 | 0.339378 | ||||||||
\(827\) | −13.7538 | −0.478266 | −0.239133 | − | 0.970987i | \(-0.576863\pi\) | ||||
−0.239133 | + | 0.970987i | \(0.576863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.1080 | −1.53193 | −0.765966 | − | 0.642881i | \(-0.777739\pi\) | ||||
−0.765966 | + | 0.642881i | \(0.777739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −8.60037 | −0.297985 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.00000 | −0.0691714 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.2462 | 0.423038 | ||||||||
\(839\) | −24.9848 | −0.862573 | −0.431286 | − | 0.902215i | \(-0.641940\pi\) | ||||
−0.431286 | + | 0.902215i | \(0.641940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 15.1231 | 0.521177 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.8617 | −0.751178 | ||||||||
\(848\) | 4.24621 | 0.145815 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3693 | −0.526235 | −0.263118 | − | 0.964764i | \(-0.584751\pi\) | ||||
−0.263118 | + | 0.964764i | \(0.584751\pi\) | |||||||
\(854\) | −38.2462 | −1.30876 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.2462 | 0.486925 | ||||||||
\(857\) | 55.4773 | 1.89507 | 0.947534 | − | 0.319656i | \(-0.103567\pi\) | ||||
0.947534 | + | 0.319656i | \(0.103567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.492423 | −0.0168012 | −0.00840062 | − | 0.999965i | \(-0.502674\pi\) | ||||
−0.00840062 | + | 0.999965i | \(0.502674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | 28.4924 | 0.969893 | 0.484947 | − | 0.874544i | \(-0.338839\pi\) | ||||
0.484947 | + | 0.874544i | \(0.338839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.0000 | −0.611665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.4924 | 0.967096 | ||||||||
\(869\) | 18.2462 | 0.618960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9848 | 0.846579 | ||||||||
\(872\) | −4.87689 | −0.165152 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.2462 | −1.29148 | −0.645741 | − | 0.763556i | \(-0.723452\pi\) | ||||
−0.645741 | + | 0.763556i | \(0.723452\pi\) | |||||||
\(878\) | 10.8769 | 0.367077 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.4924 | −1.09470 | −0.547349 | − | 0.836905i | \(-0.684363\pi\) | ||||
−0.547349 | + | 0.836905i | \(0.684363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.4924 | −1.36268 | −0.681339 | − | 0.731968i | \(-0.738602\pi\) | ||||
−0.681339 | + | 0.731968i | \(0.738602\pi\) | |||||||
\(884\) | 12.4924 | 0.420166 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.8617 | −0.667268 | ||||||||
\(887\) | 8.98485 | 0.301682 | 0.150841 | − | 0.988558i | \(-0.451802\pi\) | ||||
0.150841 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7235 | 0.393193 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.0000 | −0.334825 | ||||||||
\(893\) | 10.2462 | 0.342876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.12311 | −0.104336 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.63068 | 0.154528 | ||||||||
\(899\) | −18.2462 | −0.608545 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2614 | −0.441800 | ||||||||
\(902\) | 10.2462 | 0.341162 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.24621 | 0.141227 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.9848 | 0.563973 | 0.281986 | − | 0.959418i | \(-0.409007\pi\) | ||||
0.281986 | + | 0.959418i | \(0.409007\pi\) | |||||||
\(908\) | 20.4924 | 0.680065 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.98485 | −0.297681 | −0.148841 | − | 0.988861i | \(-0.547554\pi\) | ||||
−0.148841 | + | 0.988861i | \(0.547554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7538 | −0.455184 | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4924 | 0.611007 | ||||||||
\(917\) | −70.2462 | −2.31973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.4924 | 0.544035 | 0.272017 | − | 0.962292i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962292i | \(0.412309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.4924 | −0.740748 | ||||||||
\(923\) | −24.9848 | −0.822386 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.1231 | −0.759872 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 16.4924 | 0.541099 | 0.270549 | − | 0.962706i | \(-0.412795\pi\) | ||||
0.270549 | + | 0.962706i | \(0.412795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.75379 | −0.0902518 | ||||||||
\(932\) | 1.36932 | 0.0448535 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.8769 | 1.01032 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.7538 | −1.03735 | −0.518676 | − | 0.854971i | \(-0.673575\pi\) | ||||
−0.518676 | + | 0.854971i | \(0.673575\pi\) | |||||||
\(938\) | 19.5076 | 0.636945 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2311 | 1.21370 | 0.606849 | − | 0.794817i | \(-0.292433\pi\) | ||||
0.606849 | + | 0.794817i | \(0.292433\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.12311 | −0.101648 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.4924 | 0.666266 | ||||||||
\(947\) | 9.61553 | 0.312463 | 0.156231 | − | 0.987720i | \(-0.450065\pi\) | ||||
0.156231 | + | 0.987720i | \(0.450065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.75379 | 0.316122 | ||||||||
\(953\) | 59.4773 | 1.92666 | 0.963329 | − | 0.268324i | \(-0.0864696\pi\) | ||||
0.963329 | + | 0.268324i | \(0.0864696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.75379 | −0.0567216 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | −0.129234 | ||||||||
\(959\) | 59.7235 | 1.92857 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.2311 | 1.68487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.246211 | 0.00792993 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.1231 | 1.64401 | 0.822004 | − | 0.569482i | \(-0.192856\pi\) | ||||
0.822004 | + | 0.569482i | \(0.192856\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.6155 | 1.27132 | 0.635661 | − | 0.771968i | \(-0.280727\pi\) | ||||
0.635661 | + | 0.771968i | \(0.280727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.5076 | −1.65126 | ||||||||
\(974\) | −15.7538 | −0.504784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2462 | 0.391992 | ||||||||
\(977\) | 58.0000 | 1.85558 | 0.927792 | − | 0.373097i | \(-0.121704\pi\) | ||||
0.927792 | + | 0.373097i | \(0.121704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.7386 | −0.726730 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.4924 | 0.717762 | ||||||||
\(983\) | 36.4924 | 1.16393 | 0.581964 | − | 0.813215i | \(-0.302285\pi\) | ||||
0.581964 | + | 0.813215i | \(0.302285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.24621 | −0.198920 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.61553 | −0.0513189 | −0.0256595 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256595 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(992\) | −9.12311 | −0.289659 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.5076 | −0.618743 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.3693 | −1.12016 | −0.560079 | − | 0.828439i | \(-0.689229\pi\) | ||||
−0.560079 | + | 0.828439i | \(0.689229\pi\) | |||||||
\(998\) | 4.00000 | 0.126618 | ||||||||
\(999\) | 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 | 8550.2.a.bp.1.2 | 2 | ||
3.2 | odd | 2 | 8550.2.a.bx.1.2 | 2 | |||
5.4 | even | 2 | 1710.2.a.x.1.1 | yes | 2 | ||
15.14 | odd | 2 | 1710.2.a.v.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.a.v.1.1 | ✓ | 2 | 15.14 | odd | 2 | ||
1710.2.a.x.1.1 | yes | 2 | 5.4 | even | 2 | ||
8550.2.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8550.2.a.bx.1.2 | 2 | 3.2 | odd | 2 |