Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.205878\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20588 | −0.852684 | −0.426342 | − | 0.904562i | \(-0.640198\pi\) | ||||
−0.426342 | + | 0.904562i | \(0.640198\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.545859 | −0.272929 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.31539 | 1.63106 | 0.815532 | − | 0.578712i | \(-0.196445\pi\) | ||||
0.815532 | + | 0.578712i | \(0.196445\pi\) | |||||||
\(8\) | 3.06999 | 1.08541 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.20588 | 0.381332 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.18245 | 1.71470 | 0.857352 | − | 0.514731i | \(-0.172108\pi\) | ||||
0.857352 | + | 0.514731i | \(0.172108\pi\) | |||||||
\(14\) | −5.20383 | −1.39078 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.61032 | −0.652580 | ||||||||
\(17\) | 0.803988 | 0.194996 | 0.0974978 | − | 0.995236i | \(-0.468916\pi\) | ||||
0.0974978 | + | 0.995236i | \(0.468916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.87389 | −0.429899 | −0.214949 | − | 0.976625i | \(-0.568959\pi\) | ||||
−0.214949 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(20\) | 0.545859 | 0.122058 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.08431 | −1.68570 | −0.842848 | − | 0.538152i | \(-0.819123\pi\) | ||||
−0.842848 | + | 0.538152i | \(0.819123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.45528 | −1.46210 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.35559 | −0.445165 | ||||||||
\(29\) | 1.05948 | 0.196741 | 0.0983703 | − | 0.995150i | \(-0.468637\pi\) | ||||
0.0983703 | + | 0.995150i | \(0.468637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.61509 | −0.290078 | −0.145039 | − | 0.989426i | \(-0.546331\pi\) | ||||
−0.145039 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(32\) | −2.99226 | −0.528962 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.969511 | −0.166270 | ||||||||
\(35\) | −4.31539 | −0.729434 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.54134 | −0.910991 | −0.455496 | − | 0.890238i | \(-0.650538\pi\) | ||||
−0.455496 | + | 0.890238i | \(0.650538\pi\) | |||||||
\(38\) | 2.25968 | 0.366568 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.06999 | −0.485409 | ||||||||
\(41\) | −5.05198 | −0.788987 | −0.394494 | − | 0.918899i | \(-0.629080\pi\) | ||||
−0.394494 | + | 0.918899i | \(0.629080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.87101 | −1.50531 | −0.752657 | − | 0.658412i | \(-0.771228\pi\) | ||||
−0.752657 | + | 0.658412i | \(0.771228\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.74869 | 1.43737 | ||||||||
\(47\) | −12.9857 | −1.89416 | −0.947079 | − | 0.321002i | \(-0.895980\pi\) | ||||
−0.947079 | + | 0.321002i | \(0.895980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.6226 | 1.66037 | ||||||||
\(50\) | −1.20588 | −0.170537 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.37475 | −0.467993 | ||||||||
\(53\) | 2.66437 | 0.365980 | 0.182990 | − | 0.983115i | \(-0.441422\pi\) | ||||
0.182990 | + | 0.983115i | \(0.441422\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.2482 | 1.77037 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.27760 | −0.167758 | ||||||||
\(59\) | −6.60968 | −0.860507 | −0.430254 | − | 0.902708i | \(-0.641576\pi\) | ||||
−0.430254 | + | 0.902708i | \(0.641576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34760 | −0.684689 | −0.342345 | − | 0.939574i | \(-0.611221\pi\) | ||||
−0.342345 | + | 0.939574i | \(0.611221\pi\) | |||||||
\(62\) | 1.94760 | 0.247345 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.82894 | 1.10362 | ||||||||
\(65\) | −6.18245 | −0.766839 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.49018 | −0.915071 | −0.457536 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457536 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(68\) | −0.438864 | −0.0532201 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.20383 | 0.621977 | ||||||||
\(71\) | 5.82947 | 0.691830 | 0.345915 | − | 0.938266i | \(-0.387568\pi\) | ||||
0.345915 | + | 0.938266i | \(0.387568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.80148 | 0.561970 | 0.280985 | − | 0.959712i | \(-0.409339\pi\) | ||||
0.280985 | + | 0.959712i | \(0.409339\pi\) | |||||||
\(74\) | 6.68218 | 0.776788 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.02288 | 0.117332 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9499 | −1.56949 | −0.784744 | − | 0.619820i | \(-0.787206\pi\) | ||||
−0.784744 | + | 0.619820i | \(0.787206\pi\) | |||||||
\(80\) | 2.61032 | 0.291843 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.09207 | 0.672757 | ||||||||
\(83\) | −12.0568 | −1.32340 | −0.661701 | − | 0.749768i | \(-0.730165\pi\) | ||||
−0.661701 | + | 0.749768i | \(0.730165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.803988 | −0.0872047 | ||||||||
\(86\) | 11.9032 | 1.28356 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7727 | −1.35390 | −0.676951 | − | 0.736028i | \(-0.736699\pi\) | ||||
−0.676951 | + | 0.736028i | \(0.736699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.6797 | 2.79679 | ||||||||
\(92\) | 4.41289 | 0.460076 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.6592 | 1.61512 | ||||||||
\(95\) | 1.87389 | 0.192257 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.34761 | 0.136829 | 0.0684145 | − | 0.997657i | \(-0.478206\pi\) | ||||
0.0684145 | + | 0.997657i | \(0.478206\pi\) | |||||||
\(98\) | −14.0154 | −1.41577 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.545859 | −0.0545859 | ||||||||
\(101\) | 8.42949 | 0.838766 | 0.419383 | − | 0.907810i | \(-0.362247\pi\) | ||||
0.419383 | + | 0.907810i | \(0.362247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.90039 | −0.975515 | −0.487757 | − | 0.872979i | \(-0.662185\pi\) | ||||
−0.487757 | + | 0.872979i | \(0.662185\pi\) | |||||||
\(104\) | 18.9801 | 1.86115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.21291 | −0.312065 | ||||||||
\(107\) | −8.16742 | −0.789574 | −0.394787 | − | 0.918773i | \(-0.629182\pi\) | ||||
−0.394787 | + | 0.918773i | \(0.629182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4997 | 1.29303 | 0.646517 | − | 0.762900i | \(-0.276225\pi\) | ||||
0.646517 | + | 0.762900i | \(0.276225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.2645 | −1.06440 | ||||||||
\(113\) | 13.5106 | 1.27097 | 0.635485 | − | 0.772114i | \(-0.280800\pi\) | ||||
0.635485 | + | 0.772114i | \(0.280800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.08431 | 0.753866 | ||||||||
\(116\) | −0.578327 | −0.0536963 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.97047 | 0.733741 | ||||||||
\(119\) | 3.46952 | 0.318050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.44855 | 0.583824 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.881610 | 0.0791709 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.12012 | −0.188130 | −0.0940652 | − | 0.995566i | \(-0.529986\pi\) | ||||
−0.0940652 | + | 0.995566i | \(0.529986\pi\) | |||||||
\(128\) | −4.66210 | −0.412075 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.45528 | 0.653871 | ||||||||
\(131\) | −8.72324 | −0.762153 | −0.381076 | − | 0.924544i | \(-0.624447\pi\) | ||||
−0.381076 | + | 0.924544i | \(0.624447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.08654 | −0.701192 | ||||||||
\(134\) | 9.03224 | 0.780267 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.46824 | 0.211650 | ||||||||
\(137\) | 1.54382 | 0.131898 | 0.0659489 | − | 0.997823i | \(-0.478993\pi\) | ||||
0.0659489 | + | 0.997823i | \(0.478993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1982 | 1.37391 | 0.686957 | − | 0.726698i | \(-0.258946\pi\) | ||||
0.686957 | + | 0.726698i | \(0.258946\pi\) | |||||||
\(140\) | 2.35559 | 0.199084 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.02962 | −0.589913 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.05948 | −0.0879851 | ||||||||
\(146\) | −5.78999 | −0.479183 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.02479 | 0.248636 | ||||||||
\(149\) | −14.0183 | −1.14842 | −0.574212 | − | 0.818707i | \(-0.694692\pi\) | ||||
−0.574212 | + | 0.818707i | \(0.694692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5852 | −1.10554 | −0.552772 | − | 0.833332i | \(-0.686430\pi\) | ||||
−0.552772 | + | 0.833332i | \(0.686430\pi\) | |||||||
\(152\) | −5.75282 | −0.466615 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.61509 | 0.129727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.38074 | −0.349621 | −0.174810 | − | 0.984602i | \(-0.555931\pi\) | ||||
−0.174810 | + | 0.984602i | \(0.555931\pi\) | |||||||
\(158\) | 16.8219 | 1.33828 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.99226 | 0.236559 | ||||||||
\(161\) | −34.8869 | −2.74948 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.68667 | −0.367089 | −0.183544 | − | 0.983011i | \(-0.558757\pi\) | ||||
−0.183544 | + | 0.983011i | \(0.558757\pi\) | |||||||
\(164\) | 2.75767 | 0.215338 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5390 | 1.12844 | ||||||||
\(167\) | −1.64917 | −0.127617 | −0.0638084 | − | 0.997962i | \(-0.520325\pi\) | ||||
−0.0638084 | + | 0.997962i | \(0.520325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.2227 | 1.94021 | ||||||||
\(170\) | 0.969511 | 0.0743581 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.38818 | 0.410845 | ||||||||
\(173\) | 16.5722 | 1.25996 | 0.629981 | − | 0.776611i | \(-0.283063\pi\) | ||||
0.629981 | + | 0.776611i | \(0.283063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.31539 | 0.326213 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.4023 | 1.15445 | ||||||||
\(179\) | −17.5995 | −1.31545 | −0.657724 | − | 0.753259i | \(-0.728481\pi\) | ||||
−0.657724 | + | 0.753259i | \(0.728481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.40672 | 0.624867 | 0.312433 | − | 0.949940i | \(-0.398856\pi\) | ||||
0.312433 | + | 0.949940i | \(0.398856\pi\) | |||||||
\(182\) | −32.1724 | −2.38478 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24.8188 | −1.82967 | ||||||||
\(185\) | 5.54134 | 0.407408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.08835 | 0.516971 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.25968 | −0.163934 | ||||||||
\(191\) | 5.31771 | 0.384776 | 0.192388 | − | 0.981319i | \(-0.438377\pi\) | ||||
0.192388 | + | 0.981319i | \(0.438377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2872 | 1.10040 | 0.550199 | − | 0.835033i | \(-0.314552\pi\) | ||||
0.550199 | + | 0.835033i | \(0.314552\pi\) | |||||||
\(194\) | −1.62505 | −0.116672 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.34429 | −0.453163 | ||||||||
\(197\) | 1.69118 | 0.120492 | 0.0602458 | − | 0.998184i | \(-0.480812\pi\) | ||||
0.0602458 | + | 0.998184i | \(0.480812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.44855 | 0.244461 | 0.122230 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122230 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(200\) | 3.06999 | 0.217081 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.1649 | −0.715202 | ||||||||
\(203\) | 4.57207 | 0.320896 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.05198 | 0.352846 | ||||||||
\(206\) | 11.9387 | 0.831806 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.1382 | −1.11898 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.394446 | −0.0271548 | −0.0135774 | − | 0.999908i | \(-0.504322\pi\) | ||||
−0.0135774 | + | 0.999908i | \(0.504322\pi\) | |||||||
\(212\) | −1.45437 | −0.0998866 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.84890 | 0.673257 | ||||||||
\(215\) | 9.87101 | 0.673197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.96973 | −0.473136 | ||||||||
\(218\) | −16.2790 | −1.10255 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.97062 | 0.334360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.77146 | −0.520416 | −0.260208 | − | 0.965553i | \(-0.583791\pi\) | ||||
−0.260208 | + | 0.965553i | \(0.583791\pi\) | |||||||
\(224\) | −12.9128 | −0.862771 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.2921 | −1.08374 | ||||||||
\(227\) | −27.3162 | −1.81304 | −0.906519 | − | 0.422164i | \(-0.861271\pi\) | ||||
−0.906519 | + | 0.422164i | \(0.861271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5822 | 1.02970 | 0.514851 | − | 0.857280i | \(-0.327847\pi\) | ||||
0.514851 | + | 0.857280i | \(0.327847\pi\) | |||||||
\(230\) | −9.74869 | −0.642810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.25260 | 0.213544 | ||||||||
\(233\) | 27.8846 | 1.82678 | 0.913390 | − | 0.407086i | \(-0.133455\pi\) | ||||
0.913390 | + | 0.407086i | \(0.133455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9857 | 0.847093 | ||||||||
\(236\) | 3.60795 | 0.234858 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.18382 | −0.271197 | ||||||||
\(239\) | −18.7458 | −1.21257 | −0.606284 | − | 0.795248i | \(-0.707340\pi\) | ||||
−0.606284 | + | 0.795248i | \(0.707340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0049 | −0.708886 | −0.354443 | − | 0.935078i | \(-0.615329\pi\) | ||||
−0.354443 | + | 0.935078i | \(0.615329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.91903 | 0.186872 | ||||||||
\(245\) | −11.6226 | −0.742539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5852 | −0.737149 | ||||||||
\(248\) | −4.95831 | −0.314853 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.20588 | 0.0762664 | ||||||||
\(251\) | 23.3136 | 1.47154 | 0.735769 | − | 0.677232i | \(-0.236821\pi\) | ||||
0.735769 | + | 0.677232i | \(0.236821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.55661 | 0.160416 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.0360 | −0.752248 | ||||||||
\(257\) | −17.4730 | −1.08994 | −0.544969 | − | 0.838456i | \(-0.683459\pi\) | ||||
−0.544969 | + | 0.838456i | \(0.683459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9130 | −1.48588 | ||||||||
\(260\) | 3.37475 | 0.209293 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.5192 | 0.649876 | ||||||||
\(263\) | −1.61187 | −0.0993921 | −0.0496961 | − | 0.998764i | \(-0.515825\pi\) | ||||
−0.0496961 | + | 0.998764i | \(0.515825\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.66437 | −0.163671 | ||||||||
\(266\) | 9.75138 | 0.597896 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.08858 | 0.249750 | ||||||||
\(269\) | −8.17266 | −0.498296 | −0.249148 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249148 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4995 | 0.637801 | 0.318900 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318900 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(272\) | −2.09867 | −0.127250 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.86166 | −0.112467 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.92222 | 0.536084 | 0.268042 | − | 0.963407i | \(-0.413623\pi\) | ||||
0.268042 | + | 0.963407i | \(0.413623\pi\) | |||||||
\(278\) | −19.5331 | −1.17151 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.2482 | −0.791732 | ||||||||
\(281\) | −4.39358 | −0.262099 | −0.131049 | − | 0.991376i | \(-0.541835\pi\) | ||||
−0.131049 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0048 | 0.773056 | 0.386528 | − | 0.922278i | \(-0.373674\pi\) | ||||
0.386528 | + | 0.922278i | \(0.373674\pi\) | |||||||
\(284\) | −3.18207 | −0.188821 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.8013 | −1.28689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3536 | −0.961977 | ||||||||
\(290\) | 1.27760 | 0.0750235 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.62093 | −0.153378 | ||||||||
\(293\) | −15.5444 | −0.908115 | −0.454058 | − | 0.890972i | \(-0.650024\pi\) | ||||
−0.454058 | + | 0.890972i | \(0.650024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.60968 | 0.384830 | ||||||||
\(296\) | −17.0119 | −0.988796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.9044 | 0.979243 | ||||||||
\(299\) | −49.9809 | −2.89047 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.5972 | −2.45526 | ||||||||
\(302\) | 16.3820 | 0.942680 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.89144 | 0.280543 | ||||||||
\(305\) | 5.34760 | 0.306202 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.76859 | 0.500450 | 0.250225 | − | 0.968188i | \(-0.419495\pi\) | ||||
0.250225 | + | 0.968188i | \(0.419495\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.94760 | −0.110616 | ||||||||
\(311\) | 1.75121 | 0.0993020 | 0.0496510 | − | 0.998767i | \(-0.484189\pi\) | ||||
0.0496510 | + | 0.998767i | \(0.484189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5272 | −0.990697 | −0.495348 | − | 0.868694i | \(-0.664960\pi\) | ||||
−0.495348 | + | 0.868694i | \(0.664960\pi\) | |||||||
\(314\) | 5.28263 | 0.298116 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.61468 | 0.428359 | ||||||||
\(317\) | 1.99187 | 0.111874 | 0.0559372 | − | 0.998434i | \(-0.482185\pi\) | ||||
0.0559372 | + | 0.998434i | \(0.482185\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.82894 | −0.493553 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.0694 | 2.34444 | ||||||||
\(323\) | −1.50658 | −0.0838284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.18245 | 0.342941 | ||||||||
\(326\) | 5.65156 | 0.313011 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.5096 | −0.856372 | ||||||||
\(329\) | −56.0383 | −3.08949 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3437 | −0.568541 | −0.284271 | − | 0.958744i | \(-0.591751\pi\) | ||||
−0.284271 | + | 0.958744i | \(0.591751\pi\) | |||||||
\(332\) | 6.58130 | 0.361196 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.98870 | 0.108817 | ||||||||
\(335\) | 7.49018 | 0.409232 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6187 | −1.12317 | −0.561587 | − | 0.827418i | \(-0.689809\pi\) | ||||
−0.561587 | + | 0.827418i | \(0.689809\pi\) | |||||||
\(338\) | −30.4155 | −1.65439 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.438864 | 0.0238007 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9482 | 1.07710 | ||||||||
\(344\) | −30.3039 | −1.63388 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.9841 | −1.07435 | ||||||||
\(347\) | −2.98375 | −0.160176 | −0.0800879 | − | 0.996788i | \(-0.525520\pi\) | ||||
−0.0800879 | + | 0.996788i | \(0.525520\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2897 | 0.604323 | 0.302161 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302161 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(350\) | −5.20383 | −0.278156 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4952 | 0.718275 | 0.359137 | − | 0.933285i | \(-0.383071\pi\) | ||||
0.359137 | + | 0.933285i | \(0.383071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.82947 | −0.309396 | ||||||||
\(356\) | 6.97209 | 0.369520 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.2228 | 1.12166 | ||||||||
\(359\) | 24.6989 | 1.30356 | 0.651778 | − | 0.758410i | \(-0.274023\pi\) | ||||
0.651778 | + | 0.758410i | \(0.274023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4886 | −0.815187 | ||||||||
\(362\) | −10.1375 | −0.532814 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.5633 | −0.763327 | ||||||||
\(365\) | −4.80148 | −0.251321 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.34491 | 0.331201 | 0.165601 | − | 0.986193i | \(-0.447044\pi\) | ||||
0.165601 | + | 0.986193i | \(0.447044\pi\) | |||||||
\(368\) | 21.1026 | 1.10005 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.68218 | −0.347390 | ||||||||
\(371\) | 11.4978 | 0.596936 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1832 | 0.682601 | 0.341301 | − | 0.939954i | \(-0.389133\pi\) | ||||
0.341301 | + | 0.939954i | \(0.389133\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −39.8660 | −2.05593 | ||||||||
\(377\) | 6.55019 | 0.337352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5363 | −0.952144 | −0.476072 | − | 0.879406i | \(-0.657940\pi\) | ||||
−0.476072 | + | 0.879406i | \(0.657940\pi\) | |||||||
\(380\) | −1.02288 | −0.0524725 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.41251 | −0.328093 | ||||||||
\(383\) | 28.3843 | 1.45037 | 0.725185 | − | 0.688554i | \(-0.241754\pi\) | ||||
0.725185 | + | 0.688554i | \(0.241754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.4345 | −0.938293 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.735604 | −0.0373446 | ||||||||
\(389\) | −19.1714 | −0.972029 | −0.486014 | − | 0.873951i | \(-0.661550\pi\) | ||||
−0.486014 | + | 0.873951i | \(0.661550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.49969 | −0.328703 | ||||||||
\(392\) | 35.6812 | 1.80217 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.03936 | −0.102741 | ||||||||
\(395\) | 13.9499 | 0.701896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2455 | 0.815339 | 0.407670 | − | 0.913130i | \(-0.366342\pi\) | ||||
0.407670 | + | 0.913130i | \(0.366342\pi\) | |||||||
\(398\) | −4.15852 | −0.208448 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.61032 | −0.130516 | ||||||||
\(401\) | 12.3247 | 0.615465 | 0.307732 | − | 0.951473i | \(-0.400430\pi\) | ||||
0.307732 | + | 0.951473i | \(0.400430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.98520 | −0.497398 | ||||||||
\(404\) | −4.60131 | −0.228924 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.51336 | −0.273623 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.95751 | −0.0967926 | −0.0483963 | − | 0.998828i | \(-0.515411\pi\) | ||||
−0.0483963 | + | 0.998828i | \(0.515411\pi\) | |||||||
\(410\) | −6.09207 | −0.300866 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.40422 | 0.266247 | ||||||||
\(413\) | −28.5233 | −1.40354 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0568 | 0.591843 | ||||||||
\(416\) | −18.4995 | −0.907013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.5776 | −1.00528 | −0.502640 | − | 0.864496i | \(-0.667638\pi\) | ||||
−0.502640 | + | 0.864496i | \(0.667638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1205 | −0.834400 | −0.417200 | − | 0.908815i | \(-0.636989\pi\) | ||||
−0.417200 | + | 0.908815i | \(0.636989\pi\) | |||||||
\(422\) | 0.475654 | 0.0231545 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.17960 | 0.397237 | ||||||||
\(425\) | 0.803988 | 0.0389991 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.0769 | −1.11677 | ||||||||
\(428\) | 4.45826 | 0.215498 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.9032 | −0.574025 | ||||||||
\(431\) | −10.6079 | −0.510963 | −0.255481 | − | 0.966814i | \(-0.582234\pi\) | ||||
−0.255481 | + | 0.966814i | \(0.582234\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.8262 | 1.19307 | 0.596536 | − | 0.802586i | \(-0.296543\pi\) | ||||
0.596536 | + | 0.802586i | \(0.296543\pi\) | |||||||
\(434\) | 8.40464 | 0.403436 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.36892 | −0.352907 | ||||||||
\(437\) | 15.1491 | 0.724678 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.78781 | 0.323965 | 0.161982 | − | 0.986794i | \(-0.448211\pi\) | ||||
0.161982 | + | 0.986794i | \(0.448211\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.99395 | −0.285103 | ||||||||
\(443\) | 15.1500 | 0.719799 | 0.359899 | − | 0.932991i | \(-0.382811\pi\) | ||||
0.359899 | + | 0.932991i | \(0.382811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7727 | 0.605484 | ||||||||
\(446\) | 9.37143 | 0.443750 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 38.1003 | 1.80007 | ||||||||
\(449\) | 17.9310 | 0.846217 | 0.423108 | − | 0.906079i | \(-0.360939\pi\) | ||||
0.423108 | + | 0.906079i | \(0.360939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.37488 | −0.346885 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32.9400 | 1.54595 | ||||||||
\(455\) | −26.6797 | −1.25076 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.1984 | −1.92718 | −0.963590 | − | 0.267385i | \(-0.913841\pi\) | ||||
−0.963590 | + | 0.267385i | \(0.913841\pi\) | |||||||
\(458\) | −18.7902 | −0.878010 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.41289 | −0.205752 | ||||||||
\(461\) | −16.8145 | −0.783128 | −0.391564 | − | 0.920151i | \(-0.628066\pi\) | ||||
−0.391564 | + | 0.920151i | \(0.628066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.7050 | −1.65935 | −0.829676 | − | 0.558245i | \(-0.811475\pi\) | ||||
−0.829676 | + | 0.558245i | \(0.811475\pi\) | |||||||
\(464\) | −2.76558 | −0.128389 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.6254 | −1.55767 | ||||||||
\(467\) | 35.9512 | 1.66362 | 0.831811 | − | 0.555059i | \(-0.187304\pi\) | ||||
0.831811 | + | 0.555059i | \(0.187304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.3230 | −1.49254 | ||||||||
\(470\) | −15.6592 | −0.722303 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.2917 | −0.934000 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.87389 | −0.0859798 | ||||||||
\(476\) | −1.89387 | −0.0868053 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.6052 | 1.03394 | ||||||||
\(479\) | 13.8915 | 0.634721 | 0.317360 | − | 0.948305i | \(-0.397204\pi\) | ||||
0.317360 | + | 0.948305i | \(0.397204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.2591 | −1.56208 | ||||||||
\(482\) | 13.2705 | 0.604456 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.34761 | −0.0611918 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0003 | −0.634413 | −0.317207 | − | 0.948356i | \(-0.602745\pi\) | ||||
−0.317207 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(488\) | −16.4171 | −0.743167 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 14.0154 | 0.633151 | ||||||||
\(491\) | 25.2477 | 1.13941 | 0.569707 | − | 0.821848i | \(-0.307057\pi\) | ||||
0.569707 | + | 0.821848i | \(0.307057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.851809 | 0.0383636 | ||||||||
\(494\) | 13.9703 | 0.628555 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.21590 | 0.189299 | ||||||||
\(497\) | 25.1564 | 1.12842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.86257 | −0.396743 | −0.198371 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198371 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(500\) | 0.545859 | 0.0244116 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.1133 | −1.25476 | ||||||||
\(503\) | −0.661184 | −0.0294807 | −0.0147404 | − | 0.999891i | \(-0.504692\pi\) | ||||
−0.0147404 | + | 0.999891i | \(0.504692\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.42949 | −0.375107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.15729 | 0.0513463 | ||||||||
\(509\) | −38.7166 | −1.71608 | −0.858042 | − | 0.513580i | \(-0.828319\pi\) | ||||
−0.858042 | + | 0.513580i | \(0.828319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.7202 | 0.916609 | ||||||||
\(512\) | 23.8381 | 1.05351 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.0704 | 0.929373 | ||||||||
\(515\) | 9.90039 | 0.436263 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 28.8362 | 1.26699 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.9801 | −0.832332 | ||||||||
\(521\) | 24.5734 | 1.07658 | 0.538290 | − | 0.842760i | \(-0.319071\pi\) | ||||
0.538290 | + | 0.842760i | \(0.319071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.6944 | 1.47335 | 0.736677 | − | 0.676245i | \(-0.236394\pi\) | ||||
0.736677 | + | 0.676245i | \(0.236394\pi\) | |||||||
\(524\) | 4.76166 | 0.208014 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.94372 | 0.0847501 | ||||||||
\(527\) | −1.29851 | −0.0565640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.3561 | 1.84157 | ||||||||
\(530\) | 3.21291 | 0.139560 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.41411 | 0.191376 | ||||||||
\(533\) | −31.2336 | −1.35288 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.16742 | 0.353108 | ||||||||
\(536\) | −22.9948 | −0.993225 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.85523 | 0.424889 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.20840 | −0.352906 | −0.176453 | − | 0.984309i | \(-0.556462\pi\) | ||||
−0.176453 | + | 0.984309i | \(0.556462\pi\) | |||||||
\(542\) | −12.6611 | −0.543843 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.40574 | −0.103145 | ||||||||
\(545\) | −13.4997 | −0.578262 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.0759 | 1.49974 | 0.749868 | − | 0.661587i | \(-0.230117\pi\) | ||||
0.749868 | + | 0.661587i | \(0.230117\pi\) | |||||||
\(548\) | −0.842711 | −0.0359988 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.98534 | −0.0845785 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −60.1993 | −2.55993 | ||||||||
\(554\) | −10.7591 | −0.457111 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.84194 | −0.374982 | ||||||||
\(557\) | −39.6130 | −1.67846 | −0.839229 | − | 0.543779i | \(-0.816993\pi\) | ||||
−0.839229 | + | 0.543779i | \(0.816993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −61.0270 | −2.58117 | ||||||||
\(560\) | 11.2645 | 0.476014 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.29812 | 0.223488 | ||||||||
\(563\) | −21.6803 | −0.913717 | −0.456858 | − | 0.889539i | \(-0.651025\pi\) | ||||
−0.456858 | + | 0.889539i | \(0.651025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5106 | −0.568395 | ||||||||
\(566\) | −15.6822 | −0.659173 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.8964 | 0.750918 | ||||||||
\(569\) | 27.4638 | 1.15134 | 0.575672 | − | 0.817681i | \(-0.304741\pi\) | ||||
0.575672 | + | 0.817681i | \(0.304741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.8306 | 0.997281 | 0.498641 | − | 0.866809i | \(-0.333833\pi\) | ||||
0.498641 | + | 0.866809i | \(0.333833\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 26.2897 | 1.09731 | ||||||||
\(575\) | −8.08431 | −0.337139 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0731 | −0.669130 | −0.334565 | − | 0.942373i | \(-0.608589\pi\) | ||||
−0.334565 | + | 0.942373i | \(0.608589\pi\) | |||||||
\(578\) | 19.7204 | 0.820262 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.578327 | 0.0240137 | ||||||||
\(581\) | −52.0296 | −2.15855 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.7405 | 0.609966 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.7447 | 0.774336 | ||||||||
\(587\) | 17.7793 | 0.733829 | 0.366915 | − | 0.930255i | \(-0.380414\pi\) | ||||
0.366915 | + | 0.930255i | \(0.380414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.02649 | 0.124704 | ||||||||
\(590\) | −7.97047 | −0.328139 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.4647 | 0.594495 | ||||||||
\(593\) | 20.2944 | 0.833389 | 0.416695 | − | 0.909046i | \(-0.363188\pi\) | ||||
0.416695 | + | 0.909046i | \(0.363188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.46952 | −0.142236 | ||||||||
\(596\) | 7.65202 | 0.313439 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 60.2708 | 2.46466 | ||||||||
\(599\) | −9.00707 | −0.368019 | −0.184009 | − | 0.982924i | \(-0.558908\pi\) | ||||
−0.184009 | + | 0.982924i | \(0.558908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.1081 | 1.67683 | 0.838417 | − | 0.545029i | \(-0.183481\pi\) | ||||
0.838417 | + | 0.545029i | \(0.183481\pi\) | |||||||
\(602\) | 51.3671 | 2.09356 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.41558 | 0.301736 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19057 | 0.0483236 | 0.0241618 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241618 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(608\) | 5.60716 | 0.227400 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.44855 | −0.261094 | ||||||||
\(611\) | −80.2834 | −3.24792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.136596 | 0.00551706 | 0.00275853 | − | 0.999996i | \(-0.499122\pi\) | ||||
0.00275853 | + | 0.999996i | \(0.499122\pi\) | |||||||
\(614\) | −10.5738 | −0.426726 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.7011 | 0.712620 | 0.356310 | − | 0.934368i | \(-0.384035\pi\) | ||||
0.356310 | + | 0.934368i | \(0.384035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.08920 | −0.284939 | −0.142470 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142470 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(620\) | −0.881610 | −0.0354063 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.11174 | −0.0846733 | ||||||||
\(623\) | −55.1191 | −2.20830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.1357 | 0.844752 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.39127 | 0.0954219 | ||||||||
\(629\) | −4.45517 | −0.177639 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1403 | 0.961010 | 0.480505 | − | 0.876992i | \(-0.340453\pi\) | ||||
0.480505 | + | 0.876992i | \(0.340453\pi\) | |||||||
\(632\) | −42.8262 | −1.70353 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.40195 | −0.0953935 | ||||||||
\(635\) | 2.12012 | 0.0841344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 71.8560 | 2.84704 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.66210 | 0.184286 | ||||||||
\(641\) | 42.8201 | 1.69129 | 0.845646 | − | 0.533745i | \(-0.179216\pi\) | ||||
0.845646 | + | 0.533745i | \(0.179216\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.2410 | −1.35033 | −0.675166 | − | 0.737666i | \(-0.735928\pi\) | ||||
−0.675166 | + | 0.737666i | \(0.735928\pi\) | |||||||
\(644\) | 19.0433 | 0.750413 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.81675 | 0.0714792 | ||||||||
\(647\) | 10.8930 | 0.428247 | 0.214124 | − | 0.976807i | \(-0.431310\pi\) | ||||
0.214124 | + | 0.976807i | \(0.431310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.45528 | −0.292420 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.55826 | 0.100189 | ||||||||
\(653\) | 42.0505 | 1.64556 | 0.822781 | − | 0.568359i | \(-0.192421\pi\) | ||||
0.822781 | + | 0.568359i | \(0.192421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.72324 | 0.340845 | ||||||||
\(656\) | 13.1873 | 0.514877 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 67.5753 | 2.63436 | ||||||||
\(659\) | −0.425249 | −0.0165654 | −0.00828268 | − | 0.999966i | \(-0.502636\pi\) | ||||
−0.00828268 | + | 0.999966i | \(0.502636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.08477 | −0.275565 | −0.137783 | − | 0.990462i | \(-0.543998\pi\) | ||||
−0.137783 | + | 0.990462i | \(0.543998\pi\) | |||||||
\(662\) | 12.4732 | 0.484786 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.0142 | −1.43643 | ||||||||
\(665\) | 8.08654 | 0.313583 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.56517 | −0.331645 | ||||||||
\(668\) | 0.900216 | 0.0348304 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.03224 | −0.348946 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2833 | −0.473487 | −0.236743 | − | 0.971572i | \(-0.576080\pi\) | ||||
−0.236743 | + | 0.971572i | \(0.576080\pi\) | |||||||
\(674\) | 24.8637 | 0.957712 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.7680 | −0.529540 | ||||||||
\(677\) | 17.2760 | 0.663972 | 0.331986 | − | 0.943284i | \(-0.392281\pi\) | ||||
0.331986 | + | 0.943284i | \(0.392281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81545 | 0.223177 | ||||||||
\(680\) | −2.46824 | −0.0946526 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.8858 | 1.02876 | 0.514379 | − | 0.857563i | \(-0.328022\pi\) | ||||
0.514379 | + | 0.857563i | \(0.328022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.54382 | −0.0589865 | ||||||||
\(686\) | −24.0551 | −0.918428 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.7665 | 0.982338 | ||||||||
\(689\) | 16.4723 | 0.627546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9330 | 0.948496 | 0.474248 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474248 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(692\) | −9.04609 | −0.343881 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.59803 | 0.136579 | ||||||||
\(695\) | −16.1982 | −0.614433 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.06173 | −0.153849 | ||||||||
\(698\) | −13.6140 | −0.515297 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.35559 | −0.0890331 | ||||||||
\(701\) | 20.0721 | 0.758112 | 0.379056 | − | 0.925374i | \(-0.376249\pi\) | ||||
0.379056 | + | 0.925374i | \(0.376249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3838 | 0.391634 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.2735 | −0.612461 | ||||||||
\(707\) | 36.3765 | 1.36808 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3356 | −0.425717 | −0.212858 | − | 0.977083i | \(-0.568277\pi\) | ||||
−0.212858 | + | 0.977083i | \(0.568277\pi\) | |||||||
\(710\) | 7.02962 | 0.263817 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.2121 | −1.46954 | ||||||||
\(713\) | 13.0569 | 0.488984 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.60684 | 0.359025 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.7838 | −1.11152 | ||||||||
\(719\) | 4.63537 | 0.172870 | 0.0864351 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864351 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.7240 | −1.59113 | ||||||||
\(722\) | 18.6773 | 0.695097 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.58889 | −0.170545 | ||||||||
\(725\) | 1.05948 | 0.0393481 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.22651 | −0.0825766 | −0.0412883 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412883 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(728\) | 81.9065 | 3.03566 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.78999 | 0.214297 | ||||||||
\(731\) | −7.93617 | −0.293530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.4780 | −1.12573 | −0.562866 | − | 0.826548i | \(-0.690301\pi\) | ||||
−0.562866 | + | 0.826548i | \(0.690301\pi\) | |||||||
\(734\) | −7.65118 | −0.282410 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.1904 | 0.891669 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.20178 | −0.338493 | −0.169246 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169246 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(740\) | −3.02479 | −0.111194 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.8649 | −0.508998 | ||||||||
\(743\) | 1.72902 | 0.0634316 | 0.0317158 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317158 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0183 | 0.513591 | ||||||||
\(746\) | −15.8974 | −0.582043 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.2456 | −1.28785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.8778 | 1.23622 | 0.618109 | − | 0.786092i | \(-0.287899\pi\) | ||||
0.618109 | + | 0.786092i | \(0.287899\pi\) | |||||||
\(752\) | 33.8968 | 1.23609 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.89872 | −0.287655 | ||||||||
\(755\) | 13.5852 | 0.494415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.8677 | −0.976522 | −0.488261 | − | 0.872698i | \(-0.662369\pi\) | ||||
−0.488261 | + | 0.872698i | \(0.662369\pi\) | |||||||
\(758\) | 22.3525 | 0.811879 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.75282 | 0.208677 | ||||||||
\(761\) | −17.4413 | −0.632247 | −0.316124 | − | 0.948718i | \(-0.602381\pi\) | ||||
−0.316124 | + | 0.948718i | \(0.602381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.2563 | 2.10902 | ||||||||
\(764\) | −2.90272 | −0.105017 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.2280 | −1.23671 | ||||||||
\(767\) | −40.8640 | −1.47551 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.6485 | −1.50188 | −0.750942 | − | 0.660368i | \(-0.770400\pi\) | ||||
−0.750942 | + | 0.660368i | \(0.770400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.34467 | −0.300331 | ||||||||
\(773\) | 22.1515 | 0.796733 | 0.398366 | − | 0.917226i | \(-0.369577\pi\) | ||||
0.398366 | + | 0.917226i | \(0.369577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.61509 | −0.0580157 | ||||||||
\(776\) | 4.13715 | 0.148515 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.1184 | 0.828834 | ||||||||
\(779\) | 9.46684 | 0.339185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 7.83783 | 0.280280 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30.3386 | −1.08352 | ||||||||
\(785\) | 4.38074 | 0.156355 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.41235 | −0.299868 | −0.149934 | − | 0.988696i | \(-0.547906\pi\) | ||||
−0.149934 | + | 0.988696i | \(0.547906\pi\) | |||||||
\(788\) | −0.923145 | −0.0328857 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.8219 | −0.598496 | ||||||||
\(791\) | 58.3034 | 2.07303 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.0612 | −1.17404 | ||||||||
\(794\) | −19.5901 | −0.695227 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.88242 | −0.0667206 | ||||||||
\(797\) | −40.9234 | −1.44958 | −0.724791 | − | 0.688969i | \(-0.758063\pi\) | ||||
−0.724791 | + | 0.688969i | \(0.758063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.4403 | −0.369352 | ||||||||
\(800\) | −2.99226 | −0.105792 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.8621 | −0.524797 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.8869 | 1.22960 | ||||||||
\(806\) | 12.0409 | 0.424124 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.8785 | 0.910402 | ||||||||
\(809\) | 21.6716 | 0.761931 | 0.380966 | − | 0.924589i | \(-0.375592\pi\) | ||||
0.380966 | + | 0.924589i | \(0.375592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.5031 | −1.91386 | −0.956931 | − | 0.290314i | \(-0.906240\pi\) | ||||
−0.956931 | + | 0.290314i | \(0.906240\pi\) | |||||||
\(812\) | −2.49571 | −0.0875821 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.68667 | 0.164167 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4971 | 0.647133 | ||||||||
\(818\) | 2.36052 | 0.0825335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.75767 | −0.0963020 | ||||||||
\(821\) | −17.9510 | −0.626495 | −0.313247 | − | 0.949672i | \(-0.601417\pi\) | ||||
−0.313247 | + | 0.949672i | \(0.601417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.2352 | 1.22822 | 0.614110 | − | 0.789220i | \(-0.289515\pi\) | ||||
0.614110 | + | 0.789220i | \(0.289515\pi\) | |||||||
\(824\) | −30.3942 | −1.05883 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.3957 | 1.19678 | ||||||||
\(827\) | −39.9373 | −1.38876 | −0.694378 | − | 0.719610i | \(-0.744320\pi\) | ||||
−0.694378 | + | 0.719610i | \(0.744320\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.5317 | −1.58138 | −0.790690 | − | 0.612216i | \(-0.790278\pi\) | ||||
−0.790690 | + | 0.612216i | \(0.790278\pi\) | |||||||
\(830\) | −14.5390 | −0.504656 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 54.5845 | 1.89238 | ||||||||
\(833\) | 9.34441 | 0.323765 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.64917 | 0.0570720 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.8140 | 0.857186 | ||||||||
\(839\) | 18.0373 | 0.622718 | 0.311359 | − | 0.950292i | \(-0.399216\pi\) | ||||
0.311359 | + | 0.950292i | \(0.399216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8775 | −0.961293 | ||||||||
\(842\) | 20.6452 | 0.711480 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.215312 | 0.00741134 | ||||||||
\(845\) | −25.2227 | −0.867688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.95486 | −0.238831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.969511 | −0.0332540 | ||||||||
\(851\) | 44.7979 | 1.53565 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.18704 | −0.0406434 | −0.0203217 | − | 0.999793i | \(-0.506469\pi\) | ||||
−0.0203217 | + | 0.999793i | \(0.506469\pi\) | |||||||
\(854\) | 27.8280 | 0.952254 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.0739 | −0.857009 | ||||||||
\(857\) | 5.59493 | 0.191119 | 0.0955597 | − | 0.995424i | \(-0.469536\pi\) | ||||
0.0955597 | + | 0.995424i | \(0.469536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.5783 | −0.633882 | −0.316941 | − | 0.948445i | \(-0.602656\pi\) | ||||
−0.316941 | + | 0.948445i | \(0.602656\pi\) | |||||||
\(860\) | −5.38818 | −0.183735 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7918 | 0.435690 | ||||||||
\(863\) | 14.2249 | 0.484220 | 0.242110 | − | 0.970249i | \(-0.422161\pi\) | ||||
0.242110 | + | 0.970249i | \(0.422161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.5722 | −0.563472 | ||||||||
\(866\) | −29.9374 | −1.01731 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.80449 | 0.129133 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.3077 | −1.56908 | ||||||||
\(872\) | 41.4439 | 1.40347 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.2679 | −0.617922 | ||||||||
\(875\) | −4.31539 | −0.145887 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.6019 | −0.628141 | −0.314070 | − | 0.949400i | \(-0.601693\pi\) | ||||
−0.314070 | + | 0.949400i | \(0.601693\pi\) | |||||||
\(878\) | −8.18527 | −0.276240 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.5201 | −1.02825 | −0.514124 | − | 0.857716i | \(-0.671883\pi\) | ||||
−0.514124 | + | 0.857716i | \(0.671883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.2877 | −0.548125 | −0.274062 | − | 0.961712i | \(-0.588367\pi\) | ||||
−0.274062 | + | 0.961712i | \(0.588367\pi\) | |||||||
\(884\) | −2.71326 | −0.0912566 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.2691 | −0.613761 | ||||||||
\(887\) | −5.29250 | −0.177705 | −0.0888524 | − | 0.996045i | \(-0.528320\pi\) | ||||
−0.0888524 | + | 0.996045i | \(0.528320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.14915 | −0.306853 | ||||||||
\(890\) | −15.4023 | −0.516286 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.24212 | 0.142037 | ||||||||
\(893\) | 24.3337 | 0.814296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.5995 | 0.588286 | ||||||||
\(896\) | −20.1188 | −0.672121 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.6226 | −0.721556 | ||||||||
\(899\) | −1.71115 | −0.0570702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.14212 | 0.0713644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.4774 | 1.37952 | ||||||||
\(905\) | −8.40672 | −0.279449 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.15084 | 0.0382132 | 0.0191066 | − | 0.999817i | \(-0.493918\pi\) | ||||
0.0191066 | + | 0.999817i | \(0.493918\pi\) | |||||||
\(908\) | 14.9108 | 0.494832 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.1724 | 1.06651 | ||||||||
\(911\) | 24.4697 | 0.810717 | 0.405359 | − | 0.914158i | \(-0.367147\pi\) | ||||
0.405359 | + | 0.914158i | \(0.367147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 49.6802 | 1.64328 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.50569 | −0.281036 | ||||||||
\(917\) | −37.6442 | −1.24312 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.1167 | −0.894499 | −0.447249 | − | 0.894409i | \(-0.647596\pi\) | ||||
−0.447249 | + | 0.894409i | \(0.647596\pi\) | |||||||
\(920\) | 24.8188 | 0.818251 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.2762 | 0.667761 | ||||||||
\(923\) | 36.0404 | 1.18628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.54134 | −0.182198 | ||||||||
\(926\) | 43.0559 | 1.41490 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.17024 | −0.104068 | ||||||||
\(929\) | 29.0648 | 0.953587 | 0.476793 | − | 0.879015i | \(-0.341799\pi\) | ||||
0.476793 | + | 0.879015i | \(0.341799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.7794 | −0.713790 | ||||||||
\(932\) | −15.2211 | −0.498582 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −43.3527 | −1.41854 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −59.8539 | −1.95534 | −0.977671 | − | 0.210143i | \(-0.932607\pi\) | ||||
−0.977671 | + | 0.210143i | \(0.932607\pi\) | |||||||
\(938\) | 38.9776 | 1.27266 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.08835 | −0.231197 | ||||||||
\(941\) | 30.2191 | 0.985115 | 0.492558 | − | 0.870280i | \(-0.336062\pi\) | ||||
0.492558 | + | 0.870280i | \(0.336062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.8418 | 1.32999 | ||||||||
\(944\) | 17.2534 | 0.561550 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.6489 | 1.25592 | 0.627960 | − | 0.778245i | \(-0.283890\pi\) | ||||
0.627960 | + | 0.778245i | \(0.283890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.6849 | 0.963612 | ||||||||
\(950\) | 2.25968 | 0.0733136 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.6514 | 0.345214 | ||||||||
\(953\) | 44.7169 | 1.44852 | 0.724261 | − | 0.689526i | \(-0.242181\pi\) | ||||
0.724261 | + | 0.689526i | \(0.242181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.31771 | −0.172077 | ||||||||
\(956\) | 10.2326 | 0.330945 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.7515 | −0.541216 | ||||||||
\(959\) | 6.66220 | 0.215134 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3915 | −0.915855 | ||||||||
\(962\) | 41.3123 | 1.33196 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.00711 | 0.193476 | ||||||||
\(965\) | −15.2872 | −0.492113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.5876 | −1.11226 | −0.556131 | − | 0.831095i | \(-0.687715\pi\) | ||||
−0.556131 | + | 0.831095i | \(0.687715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.62505 | 0.0521773 | ||||||||
\(971\) | −6.91193 | −0.221814 | −0.110907 | − | 0.993831i | \(-0.535376\pi\) | ||||
−0.110907 | + | 0.993831i | \(0.535376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.9016 | 2.24094 | ||||||||
\(974\) | 16.8826 | 0.540954 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9589 | 0.446815 | ||||||||
\(977\) | 12.2661 | 0.392427 | 0.196214 | − | 0.980561i | \(-0.437135\pi\) | ||||
0.196214 | + | 0.980561i | \(0.437135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.34429 | 0.202661 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.4457 | −0.971561 | ||||||||
\(983\) | −0.161755 | −0.00515918 | −0.00257959 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00257959 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.69118 | −0.0538855 | ||||||||
\(986\) | −1.02718 | −0.0327120 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.32389 | 0.201190 | ||||||||
\(989\) | 79.8003 | 2.53750 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.1252 | 1.36992 | 0.684958 | − | 0.728582i | \(-0.259820\pi\) | ||||
0.684958 | + | 0.728582i | \(0.259820\pi\) | |||||||
\(992\) | 4.83277 | 0.153440 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.3356 | −0.962185 | ||||||||
\(995\) | −3.44855 | −0.109326 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.47228 | −0.0466276 | −0.0233138 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233138 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(998\) | 10.6872 | 0.338296 | ||||||||
\(999\) | 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 | 5445.2.a.ca.1.4 | 8 | ||
3.2 | odd | 2 | 5445.2.a.cd.1.5 | 8 | |||
11.3 | even | 5 | 495.2.n.h.361.2 | yes | 16 | ||
11.4 | even | 5 | 495.2.n.h.181.2 | yes | 16 | ||
11.10 | odd | 2 | 5445.2.a.cc.1.5 | 8 | |||
33.14 | odd | 10 | 495.2.n.g.361.3 | yes | 16 | ||
33.26 | odd | 10 | 495.2.n.g.181.3 | ✓ | 16 | ||
33.32 | even | 2 | 5445.2.a.cb.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.181.3 | ✓ | 16 | 33.26 | odd | 10 | ||
495.2.n.g.361.3 | yes | 16 | 33.14 | odd | 10 | ||
495.2.n.h.181.2 | yes | 16 | 11.4 | even | 5 | ||
495.2.n.h.361.2 | yes | 16 | 11.3 | even | 5 | ||
5445.2.a.ca.1.4 | 8 | 1.1 | even | 1 | trivial | ||
5445.2.a.cb.1.4 | 8 | 33.32 | even | 2 | |||
5445.2.a.cc.1.5 | 8 | 11.10 | odd | 2 | |||
5445.2.a.cd.1.5 | 8 | 3.2 | odd | 2 |