Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1288,2,Mod(1,1288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1288.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1288 = 2^{3} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1288.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: | \(10.2847317803\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1288.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.539189 | −0.311301 | −0.155650 | − | 0.987812i | \(-0.549747\pi\) | ||||
−0.155650 | + | 0.987812i | \(0.549747\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.87936 | −1.28769 | −0.643845 | − | 0.765156i | \(-0.722662\pi\) | ||||
−0.643845 | + | 0.765156i | \(0.722662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63090 | −0.793245 | −0.396623 | − | 0.917982i | \(-0.629818\pi\) | ||||
−0.396623 | + | 0.917982i | \(0.629818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34017 | −1.20375 | −0.601874 | − | 0.798591i | \(-0.705579\pi\) | ||||
−0.601874 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.55252 | 0.400859 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.80098 | 1.89202 | 0.946008 | − | 0.324142i | \(-0.105076\pi\) | ||||
0.946008 | + | 0.324142i | \(0.105076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.539189 | 0.117661 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.29072 | 0.658145 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.07838 | 0.592434 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.70928 | 1.06019 | 0.530093 | − | 0.847940i | \(-0.322157\pi\) | ||||
0.530093 | + | 0.847940i | \(0.322157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1412 | 1.82141 | 0.910703 | − | 0.413062i | \(-0.135541\pi\) | ||||
0.910703 | + | 0.413062i | \(0.135541\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41855 | 0.246938 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.87936 | 0.486701 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65983 | 0.601672 | 0.300836 | − | 0.953676i | \(-0.402734\pi\) | ||||
0.300836 | + | 0.953676i | \(0.402734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.34017 | 0.374728 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.83710 | −1.38012 | −0.690062 | − | 0.723751i | \(-0.742417\pi\) | ||||
−0.690062 | + | 0.723751i | \(0.742417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.49693 | −1.29577 | −0.647885 | − | 0.761738i | \(-0.724346\pi\) | ||||
−0.647885 | + | 0.761738i | \(0.724346\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.80098 | 1.16290 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.80098 | 0.554431 | 0.277215 | − | 0.960808i | \(-0.410588\pi\) | ||||
0.277215 | + | 0.960808i | \(0.410588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.20620 | −0.588986 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.83710 | 0.664427 | 0.332213 | − | 0.943204i | \(-0.392205\pi\) | ||||
0.332213 | + | 0.943204i | \(0.392205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.57531 | 1.02145 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.72261 | −1.13559 | −0.567793 | − | 0.823171i | \(-0.692203\pi\) | ||||
−0.567793 | + | 0.823171i | \(0.692203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4547 | 1.59466 | 0.797328 | − | 0.603546i | \(-0.206246\pi\) | ||||
0.797328 | + | 0.603546i | \(0.206246\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.70928 | 0.341337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.4969 | 1.55005 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3112 | −1.38189 | −0.690944 | − | 0.722908i | \(-0.742805\pi\) | ||||
−0.690944 | + | 0.722908i | \(0.742805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.539189 | −0.0649107 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.15676 | 0.255960 | 0.127980 | − | 0.991777i | \(-0.459151\pi\) | ||||
0.127980 | + | 0.991777i | \(0.459151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.23513 | 0.612726 | 0.306363 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306363 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.77432 | −0.204881 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.63090 | 0.299819 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04945 | −0.230581 | −0.115290 | − | 0.993332i | \(-0.536780\pi\) | ||||
−0.115290 | + | 0.993332i | \(0.536780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.34017 | −0.695924 | −0.347962 | − | 0.937509i | \(-0.613126\pi\) | ||||
−0.347962 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.4619 | −2.43633 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.07838 | −0.330037 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.69594 | 0.921768 | 0.460884 | − | 0.887460i | \(-0.347532\pi\) | ||||
0.460884 | + | 0.887460i | \(0.347532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.34017 | 0.454974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.46800 | −0.567005 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1929 | 1.13646 | 0.568232 | − | 0.822868i | \(-0.307628\pi\) | ||||
0.568232 | + | 0.822868i | \(0.307628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.12783 | 0.716373 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7587 | 1.17004 | 0.585018 | − | 0.811020i | \(-0.301087\pi\) | ||||
0.585018 | + | 0.811020i | \(0.301087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.68035 | −0.855300 | −0.427650 | − | 0.903944i | \(-0.640658\pi\) | ||||
−0.427650 | + | 0.903944i | \(0.640658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.55252 | −0.151510 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6537 | 1.02993 | 0.514965 | − | 0.857211i | \(-0.327805\pi\) | ||||
0.514965 | + | 0.857211i | \(0.327805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.44521 | 0.329992 | 0.164996 | − | 0.986294i | \(-0.447239\pi\) | ||||
0.164996 | + | 0.986294i | \(0.447239\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.97334 | −0.187301 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.15676 | −0.391035 | −0.195517 | − | 0.980700i | \(-0.562639\pi\) | ||||
−0.195517 | + | 0.980700i | \(0.562639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.87936 | −0.268502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.7587 | 1.08709 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.80098 | −0.715115 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.07838 | −0.370762 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.76487 | 0.429634 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.92162 | 0.440203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65983 | −0.147286 | −0.0736429 | − | 0.997285i | \(-0.523463\pi\) | ||||
−0.0736429 | + | 0.997285i | \(0.523463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.58145 | 0.403374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3763 | 1.51817 | 0.759087 | − | 0.650989i | \(-0.225646\pi\) | ||||
0.759087 | + | 0.650989i | \(0.225646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.86376 | −0.762871 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.02052 | 0.770675 | 0.385337 | − | 0.922776i | \(-0.374085\pi\) | ||||
0.385337 | + | 0.922776i | \(0.374085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.722606 | −0.0612907 | −0.0306453 | − | 0.999530i | \(-0.509756\pi\) | ||||
−0.0306453 | + | 0.999530i | \(0.509756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.04945 | −0.172595 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.4186 | 0.954867 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.4391 | −1.36519 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.539189 | −0.0444715 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.99386 | −0.572959 | −0.286480 | − | 0.958086i | \(-0.592485\pi\) | ||||
−0.286480 | + | 0.958086i | \(0.592485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8576 | −1.77875 | −0.889374 | − | 0.457180i | \(-0.848859\pi\) | ||||
−0.889374 | + | 0.457180i | \(0.848859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.1350 | −1.70866 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.2001 | −2.34541 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53919 | −0.202649 | −0.101325 | − | 0.994853i | \(-0.532308\pi\) | ||||
−0.101325 | + | 0.994853i | \(0.532308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.60811 | −0.206837 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.6225 | −1.45863 | −0.729313 | − | 0.684180i | \(-0.760160\pi\) | ||||
−0.729313 | + | 0.684180i | \(0.760160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.08452 | −0.317980 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6114 | 1.28543 | 0.642715 | − | 0.766105i | \(-0.277808\pi\) | ||||
0.642715 | + | 0.766105i | \(0.277808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.6803 | 1.72435 | 0.862177 | − | 0.506607i | \(-0.169100\pi\) | ||||
0.862177 | + | 0.506607i | \(0.169100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.29072 | −0.248755 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.70313 | 0.353509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.183417 | 0.0137093 | 0.00685463 | − | 0.999977i | \(-0.497818\pi\) | ||||
0.00685463 | + | 0.999977i | \(0.497818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8732 | −1.62582 | −0.812912 | − | 0.582387i | \(-0.802119\pi\) | ||||
−0.812912 | + | 0.582387i | \(0.802119\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.71542 | −0.496418 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5380 | −0.774767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.5236 | −1.50083 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.07838 | −0.223919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.02052 | 0.507987 | 0.253993 | − | 0.967206i | \(-0.418256\pi\) | ||||
0.253993 | + | 0.967206i | \(0.418256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6020 | 0.979091 | 0.489546 | − | 0.871978i | \(-0.337163\pi\) | ||||
0.489546 | + | 0.871978i | \(0.337163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.73820 | −0.482533 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.523590 | 0.0373043 | 0.0186521 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186521 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6803 | 0.898886 | 0.449443 | − | 0.893309i | \(-0.351623\pi\) | ||||
0.449443 | + | 0.893309i | \(0.351623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.09890 | 0.430183 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.70928 | −0.400713 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.4452 | 1.77717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.70928 | −0.188308 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.97948 | −0.342802 | −0.171401 | − | 0.985201i | \(-0.554829\pi\) | ||||
−0.171401 | + | 0.985201i | \(0.554829\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.16290 | −0.0796805 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.4657 | 1.66855 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1412 | −0.688427 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.82273 | −0.190742 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.8576 | −2.27751 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.72261 | 0.584109 | 0.292054 | − | 0.956402i | \(-0.405661\pi\) | ||||
0.292054 | + | 0.956402i | \(0.405661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.91548 | −0.594365 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2618 | 0.880216 | 0.440108 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440108 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.7370 | 1.50250 | 0.751251 | − | 0.660017i | \(-0.229451\pi\) | ||||
0.751251 | + | 0.660017i | \(0.229451\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41855 | −0.0933338 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3896 | 0.680647 | 0.340323 | − | 0.940308i | \(-0.389463\pi\) | ||||
0.340323 | + | 0.940308i | \(0.389463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9444 | −0.713934 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.10504 | 0.0717800 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.02052 | −0.454120 | −0.227060 | − | 0.973881i | \(-0.572911\pi\) | ||||
−0.227060 | + | 0.973881i | \(0.572911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.35577 | −0.151749 | −0.0758743 | − | 0.997117i | \(-0.524175\pi\) | ||||
−0.0758743 | + | 0.997117i | \(0.524175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.7226 | −0.816156 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.87936 | −0.183956 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.41855 | 0.216642 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.3545 | 1.41101 | 0.705503 | − | 0.708707i | \(-0.250721\pi\) | ||||
0.705503 | + | 0.708707i | \(0.250721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.63090 | −0.165403 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.1112 | 0.758432 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.52359 | −0.531687 | −0.265843 | − | 0.964016i | \(-0.585650\pi\) | ||||
−0.265843 | + | 0.964016i | \(0.585650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.65983 | −0.227411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.4680 | −0.957445 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.4101 | 1.93683 | 0.968416 | − | 0.249340i | \(-0.0802135\pi\) | ||||
0.968416 | + | 0.249340i | \(0.0802135\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9278 | −0.855576 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.68876 | −0.286947 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.83710 | −0.538808 | −0.269404 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269404 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7103 | −1.62254 | −0.811268 | − | 0.584674i | \(-0.801222\pi\) | ||||
−0.811268 | + | 0.584674i | \(0.801222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.34017 | −0.141634 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.65756 | −0.522070 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0761 | −0.845752 | −0.422876 | − | 0.906188i | \(-0.638979\pi\) | ||||
−0.422876 | + | 0.906188i | \(0.638979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.4752 | −1.64490 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.39189 | −0.202343 | −0.101172 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101172 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.214614 | −0.0127575 | −0.00637875 | − | 0.999980i | \(-0.502030\pi\) | ||||
−0.00637875 | + | 0.999980i | \(0.502030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.83710 | 0.521638 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.8554 | 2.57973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.03507 | −0.353782 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.53305 | 0.556926 | 0.278463 | − | 0.960447i | \(-0.410175\pi\) | ||||
0.278463 | + | 0.960447i | \(0.410175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.1155 | 1.46228 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.09890 | −0.469946 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.34017 | −0.250999 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.49693 | 0.489755 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.34017 | −0.364233 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.8615 | −2.05342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.9639 | −0.739888 | −0.369944 | − | 0.929054i | \(-0.620623\pi\) | ||||
−0.369944 | + | 0.929054i | \(0.620623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.68035 | 0.266256 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2401 | 1.14771 | 0.573854 | − | 0.818958i | \(-0.305448\pi\) | ||||
0.573854 | + | 0.818958i | \(0.305448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.6525 | −1.95867 | −0.979336 | − | 0.202238i | \(-0.935179\pi\) | ||||
−0.979336 | + | 0.202238i | \(0.935179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.80098 | −0.439536 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.5402 | −1.65914 | −0.829572 | − | 0.558399i | \(-0.811416\pi\) | ||||
−0.829572 | + | 0.558399i | \(0.811416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0205 | −0.840988 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.74435 | −0.320618 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.2823 | −0.792240 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.85762 | −0.102727 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.80098 | −0.209555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.08452 | −0.224506 | −0.112253 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112253 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.91548 | −0.543365 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.5692 | 1.77944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.9155 | 1.62960 | 0.814800 | − | 0.579742i | \(-0.196847\pi\) | ||||
0.814800 | + | 0.579742i | \(0.196847\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.24128 | 0.121729 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.6803 | −1.44482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.55252 | 0.0835849 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6947 | −0.681488 | −0.340744 | − | 0.940156i | \(-0.610679\pi\) | ||||
−0.340744 | + | 0.940156i | \(0.610679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.62249 | 0.461551 | 0.230776 | − | 0.973007i | \(-0.425874\pi\) | ||||
0.230776 | + | 0.973007i | \(0.425874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.3607 | −0.713141 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.9733 | 0.850175 | 0.425087 | − | 0.905152i | \(-0.360243\pi\) | ||||
0.425087 | + | 0.905152i | \(0.360243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.21008 | −0.329597 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.20620 | 0.222616 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.63090 | −0.349965 | −0.174983 | − | 0.984572i | \(-0.555987\pi\) | ||||
−0.174983 | + | 0.984572i | \(0.555987\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.19902 | 0.115418 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0738 | −0.789001 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3402 | 1.58374 | 0.791872 | − | 0.610687i | \(-0.209107\pi\) | ||||
0.791872 | + | 0.610687i | \(0.209107\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.9421 | 1.24638 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.83710 | −0.251130 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.0410 | 1.65902 | 0.829511 | − | 0.558490i | \(-0.188619\pi\) | ||||
0.829511 | + | 0.558490i | \(0.188619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.65368 | −0.137036 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.7792 | −1.27620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0966 | 0.569996 | 0.284998 | − | 0.958528i | \(-0.408007\pi\) | ||||
0.284998 | + | 0.958528i | \(0.408007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.894960 | 0.0458502 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5503 | 0.641288 | 0.320644 | − | 0.947200i | \(-0.396101\pi\) | ||||
0.320644 | + | 0.947200i | \(0.396101\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.57531 | −0.386073 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.0205 | 1.17020 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0722347 | −0.00366244 | −0.00183122 | − | 0.999998i | \(-0.500583\pi\) | ||||
−0.00183122 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.80098 | 0.394513 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.36910 | −0.472609 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.90110 | 0.296917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.707008 | −0.0354837 | −0.0177419 | − | 0.999843i | \(-0.505648\pi\) | ||||
−0.0177419 | + | 0.999843i | \(0.505648\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5958 | 1.12838 | 0.564191 | − | 0.825644i | \(-0.309188\pi\) | ||||
0.564191 | + | 0.825644i | \(0.309188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.0144 | −2.19251 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.6237 | −0.925420 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.62863 | −0.477273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4969 | −0.519040 | −0.259520 | − | 0.965738i | \(-0.583564\pi\) | ||||
−0.259520 | + | 0.965738i | \(0.583564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.86376 | −0.239912 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.72261 | 0.429211 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.2557 | 0.896135 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.389621 | 0.0190798 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.7152 | −1.94022 | −0.970108 | − | 0.242673i | \(-0.921976\pi\) | ||||
−0.970108 | + | 0.242673i | \(0.921976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8781 | 0.920064 | 0.460032 | − | 0.887902i | \(-0.347838\pi\) | ||||
0.460032 | + | 0.887902i | \(0.347838\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.2979 | −0.500702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.6709 | 1.24522 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.4547 | −0.602724 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.15676 | −0.297251 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2039 | −0.732348 | −0.366174 | − | 0.930546i | \(-0.619332\pi\) | ||||
−0.366174 | + | 0.930546i | \(0.619332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.17850 | −0.152749 | −0.0763744 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763744 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.86376 | 0.424985 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8937 | −0.519930 | −0.259965 | − | 0.965618i | \(-0.583711\pi\) | ||||
−0.259965 | + | 0.965618i | \(0.583711\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.70928 | −0.129013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.7792 | 1.17730 | 0.588649 | − | 0.808389i | \(-0.299660\pi\) | ||||
0.588649 | + | 0.808389i | \(0.299660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.0388 | −1.18695 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.77101 | 0.178363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8660 | −0.937536 | −0.468768 | − | 0.883321i | \(-0.655302\pi\) | ||||
−0.468768 | + | 0.883321i | \(0.655302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2495 | 1.09478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.7854 | 0.553726 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.4969 | −0.585865 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.0928 | 1.26735 | 0.633673 | − | 0.773601i | \(-0.281547\pi\) | ||||
0.633673 | + | 0.773601i | \(0.281547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.0144 | 1.12090 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.88428 | −0.274058 | −0.137029 | − | 0.990567i | \(-0.543755\pi\) | ||||
−0.137029 | + | 0.990567i | \(0.543755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.4391 | −1.60052 | −0.800260 | − | 0.599654i | \(-0.795305\pi\) | ||||
−0.800260 | + | 0.599654i | \(0.795305\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.7443 | 0.730127 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2039 | 0.703554 | 0.351777 | − | 0.936084i | \(-0.385577\pi\) | ||||
0.351777 | + | 0.936084i | \(0.385577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3112 | 0.522305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.36910 | 0.0630849 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.3545 | 1.02786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1050 | −0.600039 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.4534 | −1.20869 | −0.604344 | − | 0.796723i | \(-0.706565\pi\) | ||||
−0.604344 | + | 0.796723i | \(0.706565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8843 | −0.724261 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.539189 | 0.0245339 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.2283 | −1.46341 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.8310 | 1.62366 | 0.811828 | − | 0.583897i | \(-0.198473\pi\) | ||||
0.811828 | + | 0.583897i | \(0.198473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0410 | 0.454071 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.1978 | −1.09203 | −0.546016 | − | 0.837775i | \(-0.683856\pi\) | ||||
−0.546016 | + | 0.837775i | \(0.683856\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.5380 | 2.00589 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.5236 | −0.922467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.15676 | −0.0967437 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7526 | 1.01855 | 0.509273 | − | 0.860605i | \(-0.329914\pi\) | ||||
0.509273 | + | 0.860605i | \(0.329914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.95669 | −0.400156 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.1050 | 0.851852 | 0.425926 | − | 0.904758i | \(-0.359948\pi\) | ||||
0.425926 | + | 0.904758i | \(0.359948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.8576 | −1.50664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.14730 | −0.139777 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.58145 | −0.291718 | −0.145859 | − | 0.989305i | \(-0.546595\pi\) | ||||
−0.145859 | + | 0.989305i | \(0.546595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.23513 | −0.231589 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.9939 | 1.10136 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.2290 | −0.536793 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1990 | 0.446827 | 0.223413 | − | 0.974724i | \(-0.428280\pi\) | ||||
0.223413 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.37137 | −0.278601 | −0.139300 | − | 0.990250i | \(-0.544485\pi\) | ||||
−0.139300 | + | 0.990250i | \(0.544485\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77432 | 0.0774378 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 79.1110 | 3.44613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.6319 | 1.02554 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.3545 | 1.66132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.6758 | −1.32623 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0988967 | −0.00426771 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.63090 | −0.113321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9132 | −0.555182 | −0.277591 | − | 0.960699i | \(-0.589536\pi\) | ||||
−0.277591 | + | 0.960699i | \(0.589536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.7938 | 0.506120 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.92001 | −0.424927 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6598 | −0.584052 | −0.292026 | − | 0.956410i | \(-0.594329\pi\) | ||||
−0.292026 | + | 0.956410i | \(0.594329\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.7431 | −1.44012 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.04945 | 0.0871514 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.68195 | 0.241186 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.3545 | 1.54039 | 0.770196 | − | 0.637807i | \(-0.220158\pi\) | ||||
0.770196 | + | 0.637807i | \(0.220158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.8781 | 1.55978 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0661 | 0.467211 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.4247 | 0.776508 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9688 | 0.503531 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.46800 | −0.271630 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8576 | 1.33554 | 0.667770 | − | 0.744367i | \(-0.267249\pi\) | ||||
0.667770 | + | 0.744367i | \(0.267249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1301 | −0.675023 | −0.337512 | − | 0.941321i | \(-0.609585\pi\) | ||||
−0.337512 | + | 0.941321i | \(0.609585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.78539 | −0.158137 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.29072 | 0.137233 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.6886 | 1.48573 | 0.742867 | − | 0.669438i | \(-0.233465\pi\) | ||||
0.742867 | + | 0.669438i | \(0.233465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.33403 | −0.304792 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.34017 | 0.263035 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.7259 | −0.527054 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.8576 | −1.39984 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1206 | 0.871742 | 0.435871 | − | 0.900009i | \(-0.356440\pi\) | ||||
0.435871 | + | 0.900009i | \(0.356440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.282314 | −0.0116129 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.57531 | 0.146820 | 0.0734101 | − | 0.997302i | \(-0.476612\pi\) | ||||
0.0734101 | + | 0.997302i | \(0.476612\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4619 | 0.920846 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.83710 | −0.279824 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0144 | 1.47151 | 0.735754 | − | 0.677249i | \(-0.236828\pi\) | ||||
0.735754 | + | 0.677249i | \(0.236828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.1773 | −1.43491 | −0.717455 | − | 0.696604i | \(-0.754693\pi\) | ||||
−0.717455 | + | 0.696604i | \(0.754693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.6453 | 1.24797 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.7431 | 0.477426 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1617 | 0.858926 | 0.429463 | − | 0.903084i | \(-0.358703\pi\) | ||||
0.429463 | + | 0.903084i | \(0.358703\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.07838 | 0.124742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4969 | −0.667394 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.4863 | 1.51406 | 0.757028 | − | 0.653383i | \(-0.226651\pi\) | ||||
0.757028 | + | 0.653383i | \(0.226651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.7198 | −0.553235 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8638 | −0.437359 | −0.218679 | − | 0.975797i | \(-0.570175\pi\) | ||||
−0.218679 | + | 0.975797i | \(0.570175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0144 | 0.965219 | 0.482610 | − | 0.875836i | \(-0.339689\pi\) | ||||
0.482610 | + | 0.875836i | \(0.339689\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.07838 | 0.123531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.69594 | −0.348396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6248 | −1.22499 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.5503 | 1.13837 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2579 | 0.925883 | 0.462942 | − | 0.886389i | \(-0.346794\pi\) | ||||
0.462942 | + | 0.886389i | \(0.346794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.68488 | 0.106714 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.77924 | 0.189658 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.34017 | −0.171964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.84324 | −0.231155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9171 | 0.431199 | 0.215600 | − | 0.976482i | \(-0.430829\pi\) | ||||
0.215600 | + | 0.976482i | \(0.430829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0456 | 0.632776 | 0.316388 | − | 0.948630i | \(-0.397530\pi\) | ||||
0.316388 | + | 0.948630i | \(0.397530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.1917 | −0.519421 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.8794 | 1.60713 | 0.803567 | − | 0.595215i | \(-0.202933\pi\) | ||||
0.803567 | + | 0.595215i | \(0.202933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.9483 | 0.900799 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.46800 | 0.214308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.7152 | −1.78898 | −0.894488 | − | 0.447092i | \(-0.852460\pi\) | ||||
−0.894488 | + | 0.447092i | \(0.852460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.0326 | −1.95494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.1834 | −0.553348 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2774 | −0.438640 | −0.219320 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219320 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.2557 | 0.708991 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.70928 | 0.221064 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.70313 | −0.181834 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.7670 | −1.26495 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.2206 | 1.16492 | 0.582459 | − | 0.812860i | \(-0.302091\pi\) | ||||
0.582459 | + | 0.812860i | \(0.302091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.1301 | 0.389907 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.30406 | 0.0501189 | 0.0250595 | − | 0.999686i | \(-0.492022\pi\) | ||||
0.0250595 | + | 0.999686i | \(0.492022\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.1929 | −0.429543 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.15061 | −0.274012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.1461 | 0.503021 | 0.251510 | − | 0.967855i | \(-0.419073\pi\) | ||||
0.251510 | + | 0.967855i | \(0.419073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.9733 | −0.992390 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.2595 | −0.467730 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.9939 | −0.799802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.11450 | −0.308690 | −0.154345 | − | 0.988017i | \(-0.549327\pi\) | ||||
−0.154345 | + | 0.988017i | \(0.549327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.12783 | −0.270764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.08065 | 0.0789234 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −68.9381 | −2.61122 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.60197 | −0.211886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2306 | 0.877408 | 0.438704 | − | 0.898632i | \(-0.355438\pi\) | ||||
0.438704 | + | 0.898632i | \(0.355438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.90110 | 0.222248 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.7587 | −0.442232 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.0784 | 1.01695 | 0.508475 | − | 0.861077i | \(-0.330209\pi\) | ||||
0.508475 | + | 0.861077i | \(0.330209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.55252 | 0.208236 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1412 | 0.379789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.8781 | −1.22957 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.78539 | 0.141368 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.650372 | −0.0242548 | −0.0121274 | − | 0.999926i | \(-0.503860\pi\) | ||||
−0.0121274 | + | 0.999926i | \(0.503860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.68035 | 0.323273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.27021 | 0.0472395 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.7877 | 0.697756 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.2039 | −0.712235 | −0.356117 | − | 0.934441i | \(-0.615900\pi\) | ||||
−0.356117 | + | 0.934441i | \(0.615900\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −66.2844 | −2.45162 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.6069 | −1.05662 | −0.528310 | − | 0.849052i | \(-0.677174\pi\) | ||||
−0.528310 | + | 0.849052i | \(0.677174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.55252 | 0.0572656 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.7587 | 1.09618 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.5523 | 1.71246 | 0.856228 | − | 0.516598i | \(-0.172802\pi\) | ||||
0.856228 | + | 0.516598i | \(0.172802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.0843 | −1.36049 | −0.680246 | − | 0.732984i | \(-0.738127\pi\) | ||||
−0.680246 | + | 0.732984i | \(0.738127\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1378 | 0.737794 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1773 | 0.628484 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6537 | −0.389277 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.5152 | −1.25948 | −0.629738 | − | 0.776807i | \(-0.716838\pi\) | ||||
−0.629738 | + | 0.776807i | \(0.716838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0533 | −0.439248 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 62.9360 | 2.29048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.1240 | 1.27660 | 0.638301 | − | 0.769787i | \(-0.279638\pi\) | ||||
0.638301 | + | 0.769787i | \(0.279638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.41855 | 0.0514901 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7464 | −0.643308 | −0.321654 | − | 0.946857i | \(-0.604239\pi\) | ||||
−0.321654 | + | 0.946857i | \(0.604239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.44521 | −0.124725 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 60.8554 | 2.20023 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.8576 | 1.36696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.9122 | 0.501686 | 0.250843 | − | 0.968028i | \(-0.419292\pi\) | ||||
0.250843 | + | 0.968028i | \(0.419292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.59583 | 0.165515 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.4378 | 1.23864 | 0.619322 | − | 0.785137i | \(-0.287408\pi\) | ||||
0.619322 | + | 0.785137i | \(0.287408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.3718 | 1.19875 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.97334 | 0.0707931 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.67420 | −0.203039 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.5753 | 0.628090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.31124 | 0.260949 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.65529 | 0.130297 | 0.0651485 | − | 0.997876i | \(-0.479248\pi\) | ||||
0.0651485 | + | 0.997876i | \(0.479248\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9360 | −0.602937 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.15676 | 0.147797 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.0554 | −1.91956 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.50970 | 0.266341 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.8108 | −1.33933 | −0.669664 | − | 0.742664i | \(-0.733562\pi\) | ||||
−0.669664 | + | 0.742664i | \(0.733562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.6514 | 1.04899 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.5597 | −0.832441 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7731 | −0.486042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.87936 | 0.101484 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.76487 | 0.167731 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.7587 | −0.975945 | −0.487972 | − | 0.872859i | \(-0.662263\pi\) | ||||
−0.487972 | + | 0.872859i | \(0.662263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.2979 | −1.27459 | −0.637296 | − | 0.770619i | \(-0.719947\pi\) | ||||
−0.637296 | + | 0.770619i | \(0.719947\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.4019 | 0.505097 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.6209 | 1.87826 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.7587 | −0.410883 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.0121 | −1.57093 | −0.785467 | − | 0.618904i | \(-0.787577\pi\) | ||||
−0.785467 | + | 0.618904i | \(0.787577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.5006 | 1.51634 | 0.758168 | − | 0.652059i | \(-0.226095\pi\) | ||||
0.758168 | + | 0.652059i | \(0.226095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.66806 | 0.162521 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9315 | −1.28423 | −0.642116 | − | 0.766607i | \(-0.721943\pi\) | ||||
−0.642116 | + | 0.766607i | \(0.721943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.255652 | −0.00887917 | −0.00443958 | − | 0.999990i | \(-0.501413\pi\) | ||||
−0.00443958 | + | 0.999990i | \(0.501413\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.58968 | 0.263283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.80098 | 0.270288 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.8303 | −1.65524 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.2183 | 1.07906 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.01438 | 0.276687 | 0.138343 | − | 0.990384i | \(-0.455822\pi\) | ||||
0.138343 | + | 0.990384i | \(0.455822\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.59583 | 0.123994 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.82887 | 0.0629896 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.8071 | −0.578183 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.07838 | 0.140135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.115718 | 0.00397142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.65983 | 0.125457 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.1362 | −0.449776 | −0.224888 | − | 0.974385i | \(-0.572202\pi\) | ||||
−0.224888 | + | 0.974385i | \(0.572202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.5585 | 1.07802 | 0.539009 | − | 0.842300i | \(-0.318799\pi\) | ||||
0.539009 | + | 0.842300i | \(0.318799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.2667 | 1.71508 | 0.857539 | − | 0.514419i | \(-0.171992\pi\) | ||||
0.857539 | + | 0.514419i | \(0.171992\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.76487 | −0.162386 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.7776 | −1.35405 | −0.677023 | − | 0.735962i | \(-0.736730\pi\) | ||||
−0.677023 | + | 0.735962i | \(0.736730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.3049 | −2.22043 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.6463 | −0.803071 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.39189 | 0.182907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.0928 | 1.66344 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.3246 | −1.02633 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.92162 | −0.166381 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.3256 | −0.855185 | −0.427593 | − | 0.903972i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903972i | \(0.640638\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.14011 | −0.173372 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.01560 | −0.270052 | −0.135026 | − | 0.990842i | \(-0.543112\pi\) | ||||
−0.135026 | + | 0.990842i | \(0.543112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.81658 | −0.128438 | −0.0642191 | − | 0.997936i | \(-0.520456\pi\) | ||||
−0.0642191 | + | 0.997936i | \(0.520456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.5420 | −0.455210 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.82150 | 0.296197 | 0.148099 | − | 0.988973i | \(-0.452685\pi\) | ||||
0.148099 | + | 0.988973i | \(0.452685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.65983 | 0.0556688 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.0166 | −0.570079 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.528125 | −0.0176533 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.34017 | 0.0781361 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 57.8987 | 1.93103 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.7342 | 1.25711 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.58145 | −0.152461 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 62.9809 | 2.09356 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1629 | 0.968338 | 0.484169 | − | 0.874974i | \(-0.339122\pi\) | ||||
0.484169 | + | 0.874974i | \(0.339122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.8576 | −1.05665 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3400 | 1.03834 | 0.519170 | − | 0.854671i | \(-0.326241\pi\) | ||||
0.519170 | + | 0.854671i | \(0.326241\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.6803 | 0.552039 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.3361 | 0.639232 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3763 | −0.573816 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0950 | −0.464952 | −0.232476 | − | 0.972602i | \(-0.574683\pi\) | ||||
−0.232476 | + | 0.972602i | \(0.574683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.98998 | 0.230328 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.36069 | −0.308111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0435 | 0.395987 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.5174 | 0.772414 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.6057 | −1.85717 | −0.928586 | − | 0.371118i | \(-0.878975\pi\) | ||||
−0.928586 | + | 0.371118i | \(0.878975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9132 | −0.357283 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59.0948 | 1.93261 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.65037 | −0.282595 | −0.141298 | − | 0.989967i | \(-0.545127\pi\) | ||||
−0.141298 | + | 0.989967i | \(0.545127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.6842 | 0.609737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.9286 | 1.82322 | 0.911611 | − | 0.411055i | \(-0.134840\pi\) | ||||
0.911611 | + | 0.411055i | \(0.134840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.83710 | −0.287776 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.86376 | 0.288338 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4863 | −0.763201 | −0.381600 | − | 0.924327i | \(-0.624627\pi\) | ||||
−0.381600 | + | 0.924327i | \(0.624627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7214 | −0.737567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.9278 | 0.516493 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.5814 | −0.342767 | −0.171383 | − | 0.985204i | \(-0.554824\pi\) | ||||
−0.171383 | + | 0.985204i | \(0.554824\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2146 | −0.654130 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.09890 | 0.261800 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.02052 | −0.291288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.8431 | 2.31752 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.8638 | −0.930122 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.1650 | −1.26077 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2967 | 0.781329 | 0.390664 | − | 0.920533i | \(-0.372245\pi\) | ||||
0.390664 | + | 0.920533i | \(0.372245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.40417 | −0.109245 | −0.0546226 | − | 0.998507i | \(-0.517396\pi\) | ||||
−0.0546226 | + | 0.998507i | \(0.517396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.722606 | 0.0231657 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.70086 | 0.246625 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6081 | 0.787283 | 0.393642 | − | 0.919264i | \(-0.371215\pi\) | ||||
0.393642 | + | 0.919264i | \(0.371215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.8781 | −0.731189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.33403 | −0.298013 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.5503 | −1.16577 | −0.582886 | − | 0.812554i | \(-0.698077\pi\) | ||||
−0.582886 | + | 0.812554i | \(0.698077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.50761 | −0.0480363 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.04945 | 0.0652347 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.49693 | −0.270187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4641 | −0.618298 | −0.309149 | − | 0.951014i | \(-0.600044\pi\) | ||||
−0.309149 | + | 0.951014i | \(0.600044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.20233 | 0.0698888 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.5113 | −1.15749 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.68649 | 0.180093 | 0.0900465 | − | 0.995938i | \(-0.471298\pi\) | ||||
0.0900465 | + | 0.995938i | \(0.471298\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.2663 | 0.356451 |
(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 | 1288.2.a.l.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 2576.2.a.y.1.2 | 3 | |||
7.6 | odd | 2 | 9016.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1288.2.a.l.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2576.2.a.y.1.2 | 3 | 4.3 | odd | 2 | |||
9016.2.a.z.1.2 | 3 | 7.6 | odd | 2 |