Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.91631\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.35992 | 1.93985 | 0.969924 | − | 0.243407i | \(-0.0782651\pi\) | ||||
0.969924 | + | 0.243407i | \(0.0782651\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.35877 | −0.607663 | −0.303831 | − | 0.952726i | \(-0.598266\pi\) | ||||
−0.303831 | + | 0.952726i | \(0.598266\pi\) | |||||||
\(6\) | 3.35992 | 1.37168 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.28904 | 2.76301 | ||||||||
\(10\) | −1.35877 | −0.429682 | ||||||||
\(11\) | 0.672249 | 0.202691 | 0.101345 | − | 0.994851i | \(-0.467685\pi\) | ||||
0.101345 | + | 0.994851i | \(0.467685\pi\) | |||||||
\(12\) | 3.35992 | 0.969924 | ||||||||
\(13\) | −1.04304 | −0.289286 | −0.144643 | − | 0.989484i | \(-0.546203\pi\) | ||||
−0.144643 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −4.56537 | −1.17877 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.46184 | −0.597083 | −0.298542 | − | 0.954397i | \(-0.596500\pi\) | ||||
−0.298542 | + | 0.954397i | \(0.596500\pi\) | |||||||
\(18\) | 8.28904 | 1.95374 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.35877 | −0.303831 | ||||||||
\(21\) | −3.35992 | −0.733194 | ||||||||
\(22\) | 0.672249 | 0.143324 | ||||||||
\(23\) | 9.22420 | 1.92338 | 0.961689 | − | 0.274142i | \(-0.0883938\pi\) | ||||
0.961689 | + | 0.274142i | \(0.0883938\pi\) | |||||||
\(24\) | 3.35992 | 0.685840 | ||||||||
\(25\) | −3.15373 | −0.630746 | ||||||||
\(26\) | −1.04304 | −0.204556 | ||||||||
\(27\) | 17.7707 | 3.41998 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 9.26173 | 1.71986 | 0.859930 | − | 0.510411i | \(-0.170507\pi\) | ||||
0.859930 | + | 0.510411i | \(0.170507\pi\) | |||||||
\(30\) | −4.56537 | −0.833519 | ||||||||
\(31\) | 7.38217 | 1.32588 | 0.662938 | − | 0.748674i | \(-0.269309\pi\) | ||||
0.662938 | + | 0.748674i | \(0.269309\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.25870 | 0.393189 | ||||||||
\(34\) | −2.46184 | −0.422201 | ||||||||
\(35\) | 1.35877 | 0.229675 | ||||||||
\(36\) | 8.28904 | 1.38151 | ||||||||
\(37\) | −6.98489 | −1.14831 | −0.574155 | − | 0.818747i | \(-0.694669\pi\) | ||||
−0.574155 | + | 0.818747i | \(0.694669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.50451 | −0.561171 | ||||||||
\(40\) | −1.35877 | −0.214841 | ||||||||
\(41\) | 5.46835 | 0.854012 | 0.427006 | − | 0.904249i | \(-0.359568\pi\) | ||||
0.427006 | + | 0.904249i | \(0.359568\pi\) | |||||||
\(42\) | −3.35992 | −0.518446 | ||||||||
\(43\) | 0.0812913 | 0.0123968 | 0.00619841 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619841 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(44\) | 0.672249 | 0.101345 | ||||||||
\(45\) | −11.2629 | −1.67898 | ||||||||
\(46\) | 9.22420 | 1.36003 | ||||||||
\(47\) | −0.226152 | −0.0329876 | −0.0164938 | − | 0.999864i | \(-0.505250\pi\) | ||||
−0.0164938 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(48\) | 3.35992 | 0.484962 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.15373 | −0.446005 | ||||||||
\(51\) | −8.27156 | −1.15825 | ||||||||
\(52\) | −1.04304 | −0.144643 | ||||||||
\(53\) | −6.14086 | −0.843512 | −0.421756 | − | 0.906709i | \(-0.638586\pi\) | ||||
−0.421756 | + | 0.906709i | \(0.638586\pi\) | |||||||
\(54\) | 17.7707 | 2.41829 | ||||||||
\(55\) | −0.913435 | −0.123168 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.26173 | 1.21613 | ||||||||
\(59\) | −10.2103 | −1.32926 | −0.664632 | − | 0.747171i | \(-0.731412\pi\) | ||||
−0.664632 | + | 0.747171i | \(0.731412\pi\) | |||||||
\(60\) | −4.56537 | −0.589387 | ||||||||
\(61\) | −9.07391 | −1.16179 | −0.580897 | − | 0.813977i | \(-0.697298\pi\) | ||||
−0.580897 | + | 0.813977i | \(0.697298\pi\) | |||||||
\(62\) | 7.38217 | 0.937536 | ||||||||
\(63\) | −8.28904 | −1.04432 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.41725 | 0.175788 | ||||||||
\(66\) | 2.25870 | 0.278027 | ||||||||
\(67\) | −12.4558 | −1.52172 | −0.760862 | − | 0.648914i | \(-0.775224\pi\) | ||||
−0.760862 | + | 0.648914i | \(0.775224\pi\) | |||||||
\(68\) | −2.46184 | −0.298542 | ||||||||
\(69\) | 30.9925 | 3.73106 | ||||||||
\(70\) | 1.35877 | 0.162405 | ||||||||
\(71\) | 0.358308 | 0.0425234 | 0.0212617 | − | 0.999774i | \(-0.493232\pi\) | ||||
0.0212617 | + | 0.999774i | \(0.493232\pi\) | |||||||
\(72\) | 8.28904 | 0.976872 | ||||||||
\(73\) | 5.86115 | 0.685996 | 0.342998 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342998 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(74\) | −6.98489 | −0.811978 | ||||||||
\(75\) | −10.5963 | −1.22355 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.672249 | −0.0766099 | ||||||||
\(78\) | −3.50451 | −0.396808 | ||||||||
\(79\) | 10.0492 | 1.13062 | 0.565311 | − | 0.824878i | \(-0.308756\pi\) | ||||
0.565311 | + | 0.824878i | \(0.308756\pi\) | |||||||
\(80\) | −1.35877 | −0.151916 | ||||||||
\(81\) | 34.8410 | 3.87122 | ||||||||
\(82\) | 5.46835 | 0.603878 | ||||||||
\(83\) | 2.73042 | 0.299702 | 0.149851 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149851 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(84\) | −3.35992 | −0.366597 | ||||||||
\(85\) | 3.34508 | 0.362825 | ||||||||
\(86\) | 0.0812913 | 0.00876587 | ||||||||
\(87\) | 31.1186 | 3.33627 | ||||||||
\(88\) | 0.672249 | 0.0716620 | ||||||||
\(89\) | 9.58916 | 1.01645 | 0.508225 | − | 0.861225i | \(-0.330302\pi\) | ||||
0.508225 | + | 0.861225i | \(0.330302\pi\) | |||||||
\(90\) | −11.2629 | −1.18722 | ||||||||
\(91\) | 1.04304 | 0.109340 | ||||||||
\(92\) | 9.22420 | 0.961689 | ||||||||
\(93\) | 24.8035 | 2.57200 | ||||||||
\(94\) | −0.226152 | −0.0233258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.35992 | 0.342920 | ||||||||
\(97\) | 13.2610 | 1.34646 | 0.673228 | − | 0.739435i | \(-0.264907\pi\) | ||||
0.673228 | + | 0.739435i | \(0.264907\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 5.57230 | 0.560037 | ||||||||
\(100\) | −3.15373 | −0.315373 | ||||||||
\(101\) | 18.5225 | 1.84305 | 0.921527 | − | 0.388314i | \(-0.126942\pi\) | ||||
0.921527 | + | 0.388314i | \(0.126942\pi\) | |||||||
\(102\) | −8.27156 | −0.819007 | ||||||||
\(103\) | −7.88935 | −0.777361 | −0.388681 | − | 0.921373i | \(-0.627069\pi\) | ||||
−0.388681 | + | 0.921373i | \(0.627069\pi\) | |||||||
\(104\) | −1.04304 | −0.102278 | ||||||||
\(105\) | 4.56537 | 0.445534 | ||||||||
\(106\) | −6.14086 | −0.596453 | ||||||||
\(107\) | −5.44998 | −0.526869 | −0.263435 | − | 0.964677i | \(-0.584855\pi\) | ||||
−0.263435 | + | 0.964677i | \(0.584855\pi\) | |||||||
\(108\) | 17.7707 | 1.70999 | ||||||||
\(109\) | 0.525792 | 0.0503617 | 0.0251809 | − | 0.999683i | \(-0.491984\pi\) | ||||
0.0251809 | + | 0.999683i | \(0.491984\pi\) | |||||||
\(110\) | −0.913435 | −0.0870926 | ||||||||
\(111\) | −23.4687 | −2.22755 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.3578 | −1.63289 | −0.816443 | − | 0.577426i | \(-0.804057\pi\) | ||||
−0.816443 | + | 0.577426i | \(0.804057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.5336 | −1.16877 | ||||||||
\(116\) | 9.26173 | 0.859930 | ||||||||
\(117\) | −8.64576 | −0.799301 | ||||||||
\(118\) | −10.2103 | −0.939932 | ||||||||
\(119\) | 2.46184 | 0.225676 | ||||||||
\(120\) | −4.56537 | −0.416759 | ||||||||
\(121\) | −10.5481 | −0.958916 | ||||||||
\(122\) | −9.07391 | −0.821513 | ||||||||
\(123\) | 18.3732 | 1.65665 | ||||||||
\(124\) | 7.38217 | 0.662938 | ||||||||
\(125\) | 11.0791 | 0.990943 | ||||||||
\(126\) | −8.28904 | −0.738446 | ||||||||
\(127\) | −7.06798 | −0.627182 | −0.313591 | − | 0.949558i | \(-0.601532\pi\) | ||||
−0.313591 | + | 0.949558i | \(0.601532\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.273132 | 0.0240479 | ||||||||
\(130\) | 1.41725 | 0.124301 | ||||||||
\(131\) | 9.79698 | 0.855966 | 0.427983 | − | 0.903787i | \(-0.359224\pi\) | ||||
0.427983 | + | 0.903787i | \(0.359224\pi\) | |||||||
\(132\) | 2.25870 | 0.196595 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.4558 | −1.07602 | ||||||||
\(135\) | −24.1464 | −2.07819 | ||||||||
\(136\) | −2.46184 | −0.211101 | ||||||||
\(137\) | −20.2972 | −1.73411 | −0.867054 | − | 0.498214i | \(-0.833989\pi\) | ||||
−0.867054 | + | 0.498214i | \(0.833989\pi\) | |||||||
\(138\) | 30.9925 | 2.63826 | ||||||||
\(139\) | 5.15852 | 0.437540 | 0.218770 | − | 0.975776i | \(-0.429796\pi\) | ||||
0.218770 | + | 0.975776i | \(0.429796\pi\) | |||||||
\(140\) | 1.35877 | 0.114837 | ||||||||
\(141\) | −0.759851 | −0.0639910 | ||||||||
\(142\) | 0.358308 | 0.0300685 | ||||||||
\(143\) | −0.701180 | −0.0586356 | ||||||||
\(144\) | 8.28904 | 0.690753 | ||||||||
\(145\) | −12.5846 | −1.04509 | ||||||||
\(146\) | 5.86115 | 0.485073 | ||||||||
\(147\) | 3.35992 | 0.277121 | ||||||||
\(148\) | −6.98489 | −0.574155 | ||||||||
\(149\) | 9.78505 | 0.801623 | 0.400811 | − | 0.916161i | \(-0.368728\pi\) | ||||
0.400811 | + | 0.916161i | \(0.368728\pi\) | |||||||
\(150\) | −10.5963 | −0.865182 | ||||||||
\(151\) | 6.87697 | 0.559640 | 0.279820 | − | 0.960052i | \(-0.409725\pi\) | ||||
0.279820 | + | 0.960052i | \(0.409725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.4063 | −1.64975 | ||||||||
\(154\) | −0.672249 | −0.0541714 | ||||||||
\(155\) | −10.0307 | −0.805685 | ||||||||
\(156\) | −3.50451 | −0.280585 | ||||||||
\(157\) | 12.1056 | 0.966133 | 0.483066 | − | 0.875584i | \(-0.339523\pi\) | ||||
0.483066 | + | 0.875584i | \(0.339523\pi\) | |||||||
\(158\) | 10.0492 | 0.799470 | ||||||||
\(159\) | −20.6328 | −1.63629 | ||||||||
\(160\) | −1.35877 | −0.107421 | ||||||||
\(161\) | −9.22420 | −0.726969 | ||||||||
\(162\) | 34.8410 | 2.73737 | ||||||||
\(163\) | −11.3384 | −0.888089 | −0.444045 | − | 0.896005i | \(-0.646457\pi\) | ||||
−0.444045 | + | 0.896005i | \(0.646457\pi\) | |||||||
\(164\) | 5.46835 | 0.427006 | ||||||||
\(165\) | −3.06907 | −0.238926 | ||||||||
\(166\) | 2.73042 | 0.211922 | ||||||||
\(167\) | −11.8009 | −0.913184 | −0.456592 | − | 0.889676i | \(-0.650930\pi\) | ||||
−0.456592 | + | 0.889676i | \(0.650930\pi\) | |||||||
\(168\) | −3.35992 | −0.259223 | ||||||||
\(169\) | −11.9121 | −0.916314 | ||||||||
\(170\) | 3.34508 | 0.256556 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0812913 | 0.00619841 | ||||||||
\(173\) | 18.0756 | 1.37426 | 0.687132 | − | 0.726533i | \(-0.258869\pi\) | ||||
0.687132 | + | 0.726533i | \(0.258869\pi\) | |||||||
\(174\) | 31.1186 | 2.35910 | ||||||||
\(175\) | 3.15373 | 0.238400 | ||||||||
\(176\) | 0.672249 | 0.0506727 | ||||||||
\(177\) | −34.3057 | −2.57857 | ||||||||
\(178\) | 9.58916 | 0.718738 | ||||||||
\(179\) | 4.30866 | 0.322044 | 0.161022 | − | 0.986951i | \(-0.448521\pi\) | ||||
0.161022 | + | 0.986951i | \(0.448521\pi\) | |||||||
\(180\) | −11.2629 | −0.839489 | ||||||||
\(181\) | 3.51816 | 0.261503 | 0.130751 | − | 0.991415i | \(-0.458261\pi\) | ||||
0.130751 | + | 0.991415i | \(0.458261\pi\) | |||||||
\(182\) | 1.04304 | 0.0773149 | ||||||||
\(183\) | −30.4876 | −2.25371 | ||||||||
\(184\) | 9.22420 | 0.680017 | ||||||||
\(185\) | 9.49090 | 0.697785 | ||||||||
\(186\) | 24.8035 | 1.81868 | ||||||||
\(187\) | −1.65497 | −0.121023 | ||||||||
\(188\) | −0.226152 | −0.0164938 | ||||||||
\(189\) | −17.7707 | −1.29263 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7576 | 1.14018 | 0.570090 | − | 0.821582i | \(-0.306908\pi\) | ||||
0.570090 | + | 0.821582i | \(0.306908\pi\) | |||||||
\(192\) | 3.35992 | 0.242481 | ||||||||
\(193\) | −11.2836 | −0.812214 | −0.406107 | − | 0.913826i | \(-0.633114\pi\) | ||||
−0.406107 | + | 0.913826i | \(0.633114\pi\) | |||||||
\(194\) | 13.2610 | 0.952088 | ||||||||
\(195\) | 4.76184 | 0.341003 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −14.9533 | −1.06538 | −0.532691 | − | 0.846310i | \(-0.678819\pi\) | ||||
−0.532691 | + | 0.846310i | \(0.678819\pi\) | |||||||
\(198\) | 5.57230 | 0.396006 | ||||||||
\(199\) | −1.85467 | −0.131474 | −0.0657370 | − | 0.997837i | \(-0.520940\pi\) | ||||
−0.0657370 | + | 0.997837i | \(0.520940\pi\) | |||||||
\(200\) | −3.15373 | −0.223002 | ||||||||
\(201\) | −41.8506 | −2.95191 | ||||||||
\(202\) | 18.5225 | 1.30324 | ||||||||
\(203\) | −9.26173 | −0.650046 | ||||||||
\(204\) | −8.27156 | −0.579125 | ||||||||
\(205\) | −7.43025 | −0.518951 | ||||||||
\(206\) | −7.88935 | −0.549677 | ||||||||
\(207\) | 76.4597 | 5.31432 | ||||||||
\(208\) | −1.04304 | −0.0723215 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.56537 | 0.315040 | ||||||||
\(211\) | −27.3986 | −1.88620 | −0.943100 | − | 0.332510i | \(-0.892105\pi\) | ||||
−0.943100 | + | 0.332510i | \(0.892105\pi\) | |||||||
\(212\) | −6.14086 | −0.421756 | ||||||||
\(213\) | 1.20389 | 0.0824889 | ||||||||
\(214\) | −5.44998 | −0.372553 | ||||||||
\(215\) | −0.110457 | −0.00753308 | ||||||||
\(216\) | 17.7707 | 1.20914 | ||||||||
\(217\) | −7.38217 | −0.501134 | ||||||||
\(218\) | 0.525792 | 0.0356111 | ||||||||
\(219\) | 19.6930 | 1.33073 | ||||||||
\(220\) | −0.913435 | −0.0615838 | ||||||||
\(221\) | 2.56778 | 0.172728 | ||||||||
\(222\) | −23.4687 | −1.57511 | ||||||||
\(223\) | −1.56448 | −0.104766 | −0.0523828 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523828 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −26.1414 | −1.74276 | ||||||||
\(226\) | −17.3578 | −1.15463 | ||||||||
\(227\) | −24.2868 | −1.61197 | −0.805986 | − | 0.591935i | \(-0.798364\pi\) | ||||
−0.805986 | + | 0.591935i | \(0.798364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8094 | 0.846471 | 0.423236 | − | 0.906020i | \(-0.360894\pi\) | ||||
0.423236 | + | 0.906020i | \(0.360894\pi\) | |||||||
\(230\) | −12.5336 | −0.826442 | ||||||||
\(231\) | −2.25870 | −0.148612 | ||||||||
\(232\) | 9.26173 | 0.608063 | ||||||||
\(233\) | −16.1943 | −1.06092 | −0.530460 | − | 0.847710i | \(-0.677981\pi\) | ||||
−0.530460 | + | 0.847710i | \(0.677981\pi\) | |||||||
\(234\) | −8.64576 | −0.565191 | ||||||||
\(235\) | 0.307289 | 0.0200453 | ||||||||
\(236\) | −10.2103 | −0.664632 | ||||||||
\(237\) | 33.7644 | 2.19323 | ||||||||
\(238\) | 2.46184 | 0.159577 | ||||||||
\(239\) | −11.1682 | −0.722410 | −0.361205 | − | 0.932487i | \(-0.617634\pi\) | ||||
−0.361205 | + | 0.932487i | \(0.617634\pi\) | |||||||
\(240\) | −4.56537 | −0.294693 | ||||||||
\(241\) | −18.5754 | −1.19655 | −0.598274 | − | 0.801292i | \(-0.704147\pi\) | ||||
−0.598274 | + | 0.801292i | \(0.704147\pi\) | |||||||
\(242\) | −10.5481 | −0.678056 | ||||||||
\(243\) | 63.7507 | 4.08961 | ||||||||
\(244\) | −9.07391 | −0.580897 | ||||||||
\(245\) | −1.35877 | −0.0868089 | ||||||||
\(246\) | 18.3732 | 1.17143 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.38217 | 0.468768 | ||||||||
\(249\) | 9.17397 | 0.581377 | ||||||||
\(250\) | 11.0791 | 0.700703 | ||||||||
\(251\) | −6.42172 | −0.405335 | −0.202668 | − | 0.979248i | \(-0.564961\pi\) | ||||
−0.202668 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(252\) | −8.28904 | −0.522160 | ||||||||
\(253\) | 6.20096 | 0.389851 | ||||||||
\(254\) | −7.06798 | −0.443484 | ||||||||
\(255\) | 11.2392 | 0.703826 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.64329 | −0.352019 | −0.176009 | − | 0.984389i | \(-0.556319\pi\) | ||||
−0.176009 | + | 0.984389i | \(0.556319\pi\) | |||||||
\(258\) | 0.273132 | 0.0170045 | ||||||||
\(259\) | 6.98489 | 0.434020 | ||||||||
\(260\) | 1.41725 | 0.0878941 | ||||||||
\(261\) | 76.7708 | 4.75200 | ||||||||
\(262\) | 9.79698 | 0.605259 | ||||||||
\(263\) | −6.80169 | −0.419410 | −0.209705 | − | 0.977765i | \(-0.567250\pi\) | ||||
−0.209705 | + | 0.977765i | \(0.567250\pi\) | |||||||
\(264\) | 2.25870 | 0.139013 | ||||||||
\(265\) | 8.34405 | 0.512571 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.2188 | 1.97176 | ||||||||
\(268\) | −12.4558 | −0.760862 | ||||||||
\(269\) | 16.3966 | 0.999715 | 0.499858 | − | 0.866108i | \(-0.333386\pi\) | ||||
0.499858 | + | 0.866108i | \(0.333386\pi\) | |||||||
\(270\) | −24.1464 | −1.46950 | ||||||||
\(271\) | −16.7984 | −1.02043 | −0.510216 | − | 0.860046i | \(-0.670435\pi\) | ||||
−0.510216 | + | 0.860046i | \(0.670435\pi\) | |||||||
\(272\) | −2.46184 | −0.149271 | ||||||||
\(273\) | 3.50451 | 0.212103 | ||||||||
\(274\) | −20.2972 | −1.22620 | ||||||||
\(275\) | −2.12009 | −0.127846 | ||||||||
\(276\) | 30.9925 | 1.86553 | ||||||||
\(277\) | −18.1789 | −1.09227 | −0.546133 | − | 0.837699i | \(-0.683901\pi\) | ||||
−0.546133 | + | 0.837699i | \(0.683901\pi\) | |||||||
\(278\) | 5.15852 | 0.309387 | ||||||||
\(279\) | 61.1910 | 3.66341 | ||||||||
\(280\) | 1.35877 | 0.0812023 | ||||||||
\(281\) | −16.7577 | −0.999682 | −0.499841 | − | 0.866117i | \(-0.666608\pi\) | ||||
−0.499841 | + | 0.866117i | \(0.666608\pi\) | |||||||
\(282\) | −0.759851 | −0.0452485 | ||||||||
\(283\) | −3.36785 | −0.200198 | −0.100099 | − | 0.994977i | \(-0.531916\pi\) | ||||
−0.100099 | + | 0.994977i | \(0.531916\pi\) | |||||||
\(284\) | 0.358308 | 0.0212617 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.701180 | −0.0414616 | ||||||||
\(287\) | −5.46835 | −0.322786 | ||||||||
\(288\) | 8.28904 | 0.488436 | ||||||||
\(289\) | −10.9394 | −0.643492 | ||||||||
\(290\) | −12.5846 | −0.738994 | ||||||||
\(291\) | 44.5560 | 2.61192 | ||||||||
\(292\) | 5.86115 | 0.342998 | ||||||||
\(293\) | −8.95240 | −0.523005 | −0.261502 | − | 0.965203i | \(-0.584218\pi\) | ||||
−0.261502 | + | 0.965203i | \(0.584218\pi\) | |||||||
\(294\) | 3.35992 | 0.195954 | ||||||||
\(295\) | 13.8735 | 0.807744 | ||||||||
\(296\) | −6.98489 | −0.405989 | ||||||||
\(297\) | 11.9464 | 0.693198 | ||||||||
\(298\) | 9.78505 | 0.566833 | ||||||||
\(299\) | −9.62117 | −0.556406 | ||||||||
\(300\) | −10.5963 | −0.611776 | ||||||||
\(301\) | −0.0812913 | −0.00468556 | ||||||||
\(302\) | 6.87697 | 0.395725 | ||||||||
\(303\) | 62.2339 | 3.57525 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3294 | 0.705979 | ||||||||
\(306\) | −20.4063 | −1.16655 | ||||||||
\(307\) | 10.2203 | 0.583303 | 0.291651 | − | 0.956525i | \(-0.405795\pi\) | ||||
0.291651 | + | 0.956525i | \(0.405795\pi\) | |||||||
\(308\) | −0.672249 | −0.0383050 | ||||||||
\(309\) | −26.5076 | −1.50796 | ||||||||
\(310\) | −10.0307 | −0.569705 | ||||||||
\(311\) | −11.7748 | −0.667688 | −0.333844 | − | 0.942628i | \(-0.608346\pi\) | ||||
−0.333844 | + | 0.942628i | \(0.608346\pi\) | |||||||
\(312\) | −3.50451 | −0.198404 | ||||||||
\(313\) | −8.34493 | −0.471683 | −0.235842 | − | 0.971792i | \(-0.575785\pi\) | ||||
−0.235842 | + | 0.971792i | \(0.575785\pi\) | |||||||
\(314\) | 12.1056 | 0.683159 | ||||||||
\(315\) | 11.2629 | 0.634594 | ||||||||
\(316\) | 10.0492 | 0.565311 | ||||||||
\(317\) | −21.3660 | −1.20003 | −0.600016 | − | 0.799988i | \(-0.704839\pi\) | ||||
−0.600016 | + | 0.799988i | \(0.704839\pi\) | |||||||
\(318\) | −20.6328 | −1.15703 | ||||||||
\(319\) | 6.22619 | 0.348600 | ||||||||
\(320\) | −1.35877 | −0.0759578 | ||||||||
\(321\) | −18.3115 | −1.02205 | ||||||||
\(322\) | −9.22420 | −0.514045 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 34.8410 | 1.93561 | ||||||||
\(325\) | 3.28945 | 0.182466 | ||||||||
\(326\) | −11.3384 | −0.627974 | ||||||||
\(327\) | 1.76662 | 0.0976941 | ||||||||
\(328\) | 5.46835 | 0.301939 | ||||||||
\(329\) | 0.226152 | 0.0124681 | ||||||||
\(330\) | −3.06907 | −0.168947 | ||||||||
\(331\) | 12.2945 | 0.675769 | 0.337885 | − | 0.941188i | \(-0.390289\pi\) | ||||
0.337885 | + | 0.941188i | \(0.390289\pi\) | |||||||
\(332\) | 2.73042 | 0.149851 | ||||||||
\(333\) | −57.8980 | −3.17279 | ||||||||
\(334\) | −11.8009 | −0.645718 | ||||||||
\(335\) | 16.9247 | 0.924695 | ||||||||
\(336\) | −3.35992 | −0.183298 | ||||||||
\(337\) | 29.3162 | 1.59695 | 0.798477 | − | 0.602025i | \(-0.205639\pi\) | ||||
0.798477 | + | 0.602025i | \(0.205639\pi\) | |||||||
\(338\) | −11.9121 | −0.647932 | ||||||||
\(339\) | −58.3208 | −3.16755 | ||||||||
\(340\) | 3.34508 | 0.181413 | ||||||||
\(341\) | 4.96265 | 0.268743 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.0812913 | 0.00438294 | ||||||||
\(345\) | −42.1119 | −2.26723 | ||||||||
\(346\) | 18.0756 | 0.971752 | ||||||||
\(347\) | 4.66549 | 0.250457 | 0.125228 | − | 0.992128i | \(-0.460034\pi\) | ||||
0.125228 | + | 0.992128i | \(0.460034\pi\) | |||||||
\(348\) | 31.1186 | 1.66813 | ||||||||
\(349\) | 10.9979 | 0.588705 | 0.294353 | − | 0.955697i | \(-0.404896\pi\) | ||||
0.294353 | + | 0.955697i | \(0.404896\pi\) | |||||||
\(350\) | 3.15373 | 0.168574 | ||||||||
\(351\) | −18.5355 | −0.989351 | ||||||||
\(352\) | 0.672249 | 0.0358310 | ||||||||
\(353\) | −8.33356 | −0.443551 | −0.221775 | − | 0.975098i | \(-0.571185\pi\) | ||||
−0.221775 | + | 0.975098i | \(0.571185\pi\) | |||||||
\(354\) | −34.3057 | −1.82333 | ||||||||
\(355\) | −0.486860 | −0.0258398 | ||||||||
\(356\) | 9.58916 | 0.508225 | ||||||||
\(357\) | 8.27156 | 0.437778 | ||||||||
\(358\) | 4.30866 | 0.227720 | ||||||||
\(359\) | −4.47179 | −0.236012 | −0.118006 | − | 0.993013i | \(-0.537650\pi\) | ||||
−0.118006 | + | 0.993013i | \(0.537650\pi\) | |||||||
\(360\) | −11.2629 | −0.593609 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 3.51816 | 0.184910 | ||||||||
\(363\) | −35.4407 | −1.86015 | ||||||||
\(364\) | 1.04304 | 0.0546699 | ||||||||
\(365\) | −7.96399 | −0.416854 | ||||||||
\(366\) | −30.4876 | −1.59361 | ||||||||
\(367\) | −6.11166 | −0.319026 | −0.159513 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159513 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(368\) | 9.22420 | 0.480845 | ||||||||
\(369\) | 45.3273 | 2.35965 | ||||||||
\(370\) | 9.49090 | 0.493408 | ||||||||
\(371\) | 6.14086 | 0.318818 | ||||||||
\(372\) | 24.8035 | 1.28600 | ||||||||
\(373\) | 12.6405 | 0.654502 | 0.327251 | − | 0.944937i | \(-0.393878\pi\) | ||||
0.327251 | + | 0.944937i | \(0.393878\pi\) | |||||||
\(374\) | −1.65497 | −0.0855763 | ||||||||
\(375\) | 37.2248 | 1.92228 | ||||||||
\(376\) | −0.226152 | −0.0116629 | ||||||||
\(377\) | −9.66032 | −0.497532 | ||||||||
\(378\) | −17.7707 | −0.914027 | ||||||||
\(379\) | 1.93824 | 0.0995607 | 0.0497803 | − | 0.998760i | \(-0.484148\pi\) | ||||
0.0497803 | + | 0.998760i | \(0.484148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.7478 | −1.21664 | ||||||||
\(382\) | 15.7576 | 0.806229 | ||||||||
\(383\) | −24.3608 | −1.24478 | −0.622388 | − | 0.782709i | \(-0.713837\pi\) | ||||
−0.622388 | + | 0.782709i | \(0.713837\pi\) | |||||||
\(384\) | 3.35992 | 0.171460 | ||||||||
\(385\) | 0.913435 | 0.0465530 | ||||||||
\(386\) | −11.2836 | −0.574322 | ||||||||
\(387\) | 0.673827 | 0.0342525 | ||||||||
\(388\) | 13.2610 | 0.673228 | ||||||||
\(389\) | −10.0046 | −0.507252 | −0.253626 | − | 0.967302i | \(-0.581623\pi\) | ||||
−0.253626 | + | 0.967302i | \(0.581623\pi\) | |||||||
\(390\) | 4.76184 | 0.241125 | ||||||||
\(391\) | −22.7085 | −1.14842 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 32.9170 | 1.66044 | ||||||||
\(394\) | −14.9533 | −0.753339 | ||||||||
\(395\) | −13.6546 | −0.687036 | ||||||||
\(396\) | 5.57230 | 0.280019 | ||||||||
\(397\) | −31.1380 | −1.56277 | −0.781385 | − | 0.624050i | \(-0.785486\pi\) | ||||
−0.781385 | + | 0.624050i | \(0.785486\pi\) | |||||||
\(398\) | −1.85467 | −0.0929661 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.15373 | −0.157687 | ||||||||
\(401\) | 4.25458 | 0.212464 | 0.106232 | − | 0.994341i | \(-0.466121\pi\) | ||||
0.106232 | + | 0.994341i | \(0.466121\pi\) | |||||||
\(402\) | −41.8506 | −2.08732 | ||||||||
\(403\) | −7.69986 | −0.383557 | ||||||||
\(404\) | 18.5225 | 0.921527 | ||||||||
\(405\) | −47.3411 | −2.35240 | ||||||||
\(406\) | −9.26173 | −0.459652 | ||||||||
\(407\) | −4.69559 | −0.232752 | ||||||||
\(408\) | −8.27156 | −0.409503 | ||||||||
\(409\) | 35.8582 | 1.77307 | 0.886537 | − | 0.462658i | \(-0.153104\pi\) | ||||
0.886537 | + | 0.462658i | \(0.153104\pi\) | |||||||
\(410\) | −7.43025 | −0.366954 | ||||||||
\(411\) | −68.1969 | −3.36391 | ||||||||
\(412\) | −7.88935 | −0.388681 | ||||||||
\(413\) | 10.2103 | 0.502415 | ||||||||
\(414\) | 76.4597 | 3.75779 | ||||||||
\(415\) | −3.71002 | −0.182118 | ||||||||
\(416\) | −1.04304 | −0.0511390 | ||||||||
\(417\) | 17.3322 | 0.848761 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.8254 | −1.06624 | −0.533121 | − | 0.846039i | \(-0.678981\pi\) | ||||
−0.533121 | + | 0.846039i | \(0.678981\pi\) | |||||||
\(420\) | 4.56537 | 0.222767 | ||||||||
\(421\) | 27.7218 | 1.35108 | 0.675540 | − | 0.737324i | \(-0.263911\pi\) | ||||
0.675540 | + | 0.737324i | \(0.263911\pi\) | |||||||
\(422\) | −27.3986 | −1.33374 | ||||||||
\(423\) | −1.87458 | −0.0911452 | ||||||||
\(424\) | −6.14086 | −0.298227 | ||||||||
\(425\) | 7.76397 | 0.376608 | ||||||||
\(426\) | 1.20389 | 0.0583284 | ||||||||
\(427\) | 9.07391 | 0.439117 | ||||||||
\(428\) | −5.44998 | −0.263435 | ||||||||
\(429\) | −2.35591 | −0.113744 | ||||||||
\(430\) | −0.110457 | −0.00532669 | ||||||||
\(431\) | −28.6460 | −1.37983 | −0.689915 | − | 0.723890i | \(-0.742352\pi\) | ||||
−0.689915 | + | 0.723890i | \(0.742352\pi\) | |||||||
\(432\) | 17.7707 | 0.854994 | ||||||||
\(433\) | 3.35163 | 0.161069 | 0.0805345 | − | 0.996752i | \(-0.474337\pi\) | ||||
0.0805345 | + | 0.996752i | \(0.474337\pi\) | |||||||
\(434\) | −7.38217 | −0.354355 | ||||||||
\(435\) | −42.2832 | −2.02733 | ||||||||
\(436\) | 0.525792 | 0.0251809 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 19.6930 | 0.940967 | ||||||||
\(439\) | 34.8282 | 1.66226 | 0.831130 | − | 0.556078i | \(-0.187694\pi\) | ||||
0.831130 | + | 0.556078i | \(0.187694\pi\) | |||||||
\(440\) | −0.913435 | −0.0435463 | ||||||||
\(441\) | 8.28904 | 0.394716 | ||||||||
\(442\) | 2.56778 | 0.122137 | ||||||||
\(443\) | 27.7162 | 1.31683 | 0.658417 | − | 0.752653i | \(-0.271226\pi\) | ||||
0.658417 | + | 0.752653i | \(0.271226\pi\) | |||||||
\(444\) | −23.4687 | −1.11377 | ||||||||
\(445\) | −13.0295 | −0.617658 | ||||||||
\(446\) | −1.56448 | −0.0740804 | ||||||||
\(447\) | 32.8770 | 1.55503 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −2.10506 | −0.0993438 | −0.0496719 | − | 0.998766i | \(-0.515818\pi\) | ||||
−0.0496719 | + | 0.998766i | \(0.515818\pi\) | |||||||
\(450\) | −26.1414 | −1.23232 | ||||||||
\(451\) | 3.67609 | 0.173100 | ||||||||
\(452\) | −17.3578 | −0.816443 | ||||||||
\(453\) | 23.1061 | 1.08562 | ||||||||
\(454\) | −24.2868 | −1.13984 | ||||||||
\(455\) | −1.41725 | −0.0664417 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1492 | −0.615093 | −0.307547 | − | 0.951533i | \(-0.599508\pi\) | ||||
−0.307547 | + | 0.951533i | \(0.599508\pi\) | |||||||
\(458\) | 12.8094 | 0.598546 | ||||||||
\(459\) | −43.7486 | −2.04201 | ||||||||
\(460\) | −12.5336 | −0.584383 | ||||||||
\(461\) | −13.9604 | −0.650200 | −0.325100 | − | 0.945680i | \(-0.605398\pi\) | ||||
−0.325100 | + | 0.945680i | \(0.605398\pi\) | |||||||
\(462\) | −2.25870 | −0.105084 | ||||||||
\(463\) | −5.45782 | −0.253647 | −0.126823 | − | 0.991925i | \(-0.540478\pi\) | ||||
−0.126823 | + | 0.991925i | \(0.540478\pi\) | |||||||
\(464\) | 9.26173 | 0.429965 | ||||||||
\(465\) | −33.7023 | −1.56291 | ||||||||
\(466\) | −16.1943 | −0.750184 | ||||||||
\(467\) | 40.0931 | 1.85529 | 0.927643 | − | 0.373469i | \(-0.121832\pi\) | ||||
0.927643 | + | 0.373469i | \(0.121832\pi\) | |||||||
\(468\) | −8.64576 | −0.399650 | ||||||||
\(469\) | 12.4558 | 0.575158 | ||||||||
\(470\) | 0.307289 | 0.0141742 | ||||||||
\(471\) | 40.6738 | 1.87415 | ||||||||
\(472\) | −10.2103 | −0.469966 | ||||||||
\(473\) | 0.0546480 | 0.00251272 | ||||||||
\(474\) | 33.7644 | 1.55085 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.46184 | 0.112838 | ||||||||
\(477\) | −50.9018 | −2.33063 | ||||||||
\(478\) | −11.1682 | −0.510821 | ||||||||
\(479\) | −14.5050 | −0.662751 | −0.331375 | − | 0.943499i | \(-0.607513\pi\) | ||||
−0.331375 | + | 0.943499i | \(0.607513\pi\) | |||||||
\(480\) | −4.56537 | −0.208380 | ||||||||
\(481\) | 7.28549 | 0.332190 | ||||||||
\(482\) | −18.5754 | −0.846087 | ||||||||
\(483\) | −30.9925 | −1.41021 | ||||||||
\(484\) | −10.5481 | −0.479458 | ||||||||
\(485\) | −18.0188 | −0.818190 | ||||||||
\(486\) | 63.7507 | 2.89179 | ||||||||
\(487\) | −6.25818 | −0.283585 | −0.141793 | − | 0.989896i | \(-0.545287\pi\) | ||||
−0.141793 | + | 0.989896i | \(0.545287\pi\) | |||||||
\(488\) | −9.07391 | −0.410756 | ||||||||
\(489\) | −38.0959 | −1.72276 | ||||||||
\(490\) | −1.35877 | −0.0613832 | ||||||||
\(491\) | −24.5017 | −1.10575 | −0.552873 | − | 0.833266i | \(-0.686468\pi\) | ||||
−0.552873 | + | 0.833266i | \(0.686468\pi\) | |||||||
\(492\) | 18.3732 | 0.828327 | ||||||||
\(493\) | −22.8009 | −1.02690 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.57150 | −0.340314 | ||||||||
\(496\) | 7.38217 | 0.331469 | ||||||||
\(497\) | −0.358308 | −0.0160723 | ||||||||
\(498\) | 9.17397 | 0.411096 | ||||||||
\(499\) | 3.36082 | 0.150451 | 0.0752255 | − | 0.997167i | \(-0.476032\pi\) | ||||
0.0752255 | + | 0.997167i | \(0.476032\pi\) | |||||||
\(500\) | 11.0791 | 0.495472 | ||||||||
\(501\) | −39.6501 | −1.77144 | ||||||||
\(502\) | −6.42172 | −0.286615 | ||||||||
\(503\) | −17.1646 | −0.765332 | −0.382666 | − | 0.923887i | \(-0.624994\pi\) | ||||
−0.382666 | + | 0.923887i | \(0.624994\pi\) | |||||||
\(504\) | −8.28904 | −0.369223 | ||||||||
\(505\) | −25.1679 | −1.11996 | ||||||||
\(506\) | 6.20096 | 0.275666 | ||||||||
\(507\) | −40.0236 | −1.77751 | ||||||||
\(508\) | −7.06798 | −0.313591 | ||||||||
\(509\) | 34.1490 | 1.51363 | 0.756813 | − | 0.653631i | \(-0.226755\pi\) | ||||
0.756813 | + | 0.653631i | \(0.226755\pi\) | |||||||
\(510\) | 11.2392 | 0.497680 | ||||||||
\(511\) | −5.86115 | −0.259282 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.64329 | −0.248915 | ||||||||
\(515\) | 10.7199 | 0.472373 | ||||||||
\(516\) | 0.273132 | 0.0120240 | ||||||||
\(517\) | −0.152030 | −0.00668629 | ||||||||
\(518\) | 6.98489 | 0.306899 | ||||||||
\(519\) | 60.7326 | 2.66586 | ||||||||
\(520\) | 1.41725 | 0.0621505 | ||||||||
\(521\) | −5.10628 | −0.223710 | −0.111855 | − | 0.993725i | \(-0.535679\pi\) | ||||
−0.111855 | + | 0.993725i | \(0.535679\pi\) | |||||||
\(522\) | 76.7708 | 3.36017 | ||||||||
\(523\) | −9.09139 | −0.397539 | −0.198769 | − | 0.980046i | \(-0.563694\pi\) | ||||
−0.198769 | + | 0.980046i | \(0.563694\pi\) | |||||||
\(524\) | 9.79698 | 0.427983 | ||||||||
\(525\) | 10.5963 | 0.462459 | ||||||||
\(526\) | −6.80169 | −0.296568 | ||||||||
\(527\) | −18.1737 | −0.791658 | ||||||||
\(528\) | 2.25870 | 0.0982973 | ||||||||
\(529\) | 62.0858 | 2.69938 | ||||||||
\(530\) | 8.34405 | 0.362442 | ||||||||
\(531\) | −84.6333 | −3.67277 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.70368 | −0.247054 | ||||||||
\(534\) | 32.2188 | 1.39424 | ||||||||
\(535\) | 7.40529 | 0.320159 | ||||||||
\(536\) | −12.4558 | −0.538011 | ||||||||
\(537\) | 14.4767 | 0.624717 | ||||||||
\(538\) | 16.3966 | 0.706906 | ||||||||
\(539\) | 0.672249 | 0.0289558 | ||||||||
\(540\) | −24.1464 | −1.03910 | ||||||||
\(541\) | 26.4006 | 1.13505 | 0.567525 | − | 0.823356i | \(-0.307901\pi\) | ||||
0.567525 | + | 0.823356i | \(0.307901\pi\) | |||||||
\(542\) | −16.7984 | −0.721555 | ||||||||
\(543\) | 11.8207 | 0.507276 | ||||||||
\(544\) | −2.46184 | −0.105550 | ||||||||
\(545\) | −0.714433 | −0.0306029 | ||||||||
\(546\) | 3.50451 | 0.149979 | ||||||||
\(547\) | −7.01748 | −0.300046 | −0.150023 | − | 0.988683i | \(-0.547935\pi\) | ||||
−0.150023 | + | 0.988683i | \(0.547935\pi\) | |||||||
\(548\) | −20.2972 | −0.867054 | ||||||||
\(549\) | −75.2139 | −3.21005 | ||||||||
\(550\) | −2.12009 | −0.0904011 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 30.9925 | 1.31913 | ||||||||
\(553\) | −10.0492 | −0.427335 | ||||||||
\(554\) | −18.1789 | −0.772348 | ||||||||
\(555\) | 31.8886 | 1.35360 | ||||||||
\(556\) | 5.15852 | 0.218770 | ||||||||
\(557\) | 15.3486 | 0.650342 | 0.325171 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325171 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(558\) | 61.1910 | 2.59042 | ||||||||
\(559\) | −0.0847898 | −0.00358622 | ||||||||
\(560\) | 1.35877 | 0.0574187 | ||||||||
\(561\) | −5.56055 | −0.234767 | ||||||||
\(562\) | −16.7577 | −0.706882 | ||||||||
\(563\) | 5.92162 | 0.249567 | 0.124783 | − | 0.992184i | \(-0.460176\pi\) | ||||
0.124783 | + | 0.992184i | \(0.460176\pi\) | |||||||
\(564\) | −0.759851 | −0.0319955 | ||||||||
\(565\) | 23.5854 | 0.992244 | ||||||||
\(566\) | −3.36785 | −0.141561 | ||||||||
\(567\) | −34.8410 | −1.46318 | ||||||||
\(568\) | 0.358308 | 0.0150343 | ||||||||
\(569\) | −23.2519 | −0.974770 | −0.487385 | − | 0.873187i | \(-0.662049\pi\) | ||||
−0.487385 | + | 0.873187i | \(0.662049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4012 | −0.811916 | −0.405958 | − | 0.913892i | \(-0.633062\pi\) | ||||
−0.405958 | + | 0.913892i | \(0.633062\pi\) | |||||||
\(572\) | −0.701180 | −0.0293178 | ||||||||
\(573\) | 52.9442 | 2.21178 | ||||||||
\(574\) | −5.46835 | −0.228244 | ||||||||
\(575\) | −29.0906 | −1.21316 | ||||||||
\(576\) | 8.28904 | 0.345376 | ||||||||
\(577\) | −2.39813 | −0.0998353 | −0.0499177 | − | 0.998753i | \(-0.515896\pi\) | ||||
−0.0499177 | + | 0.998753i | \(0.515896\pi\) | |||||||
\(578\) | −10.9394 | −0.455017 | ||||||||
\(579\) | −37.9121 | −1.57557 | ||||||||
\(580\) | −12.5846 | −0.522547 | ||||||||
\(581\) | −2.73042 | −0.113277 | ||||||||
\(582\) | 44.5560 | 1.84691 | ||||||||
\(583\) | −4.12819 | −0.170972 | ||||||||
\(584\) | 5.86115 | 0.242536 | ||||||||
\(585\) | 11.7476 | 0.485705 | ||||||||
\(586\) | −8.95240 | −0.369820 | ||||||||
\(587\) | −2.32808 | −0.0960903 | −0.0480452 | − | 0.998845i | \(-0.515299\pi\) | ||||
−0.0480452 | + | 0.998845i | \(0.515299\pi\) | |||||||
\(588\) | 3.35992 | 0.138561 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 13.8735 | 0.571161 | ||||||||
\(591\) | −50.2420 | −2.06668 | ||||||||
\(592\) | −6.98489 | −0.287077 | ||||||||
\(593\) | 9.50805 | 0.390449 | 0.195224 | − | 0.980759i | \(-0.437457\pi\) | ||||
0.195224 | + | 0.980759i | \(0.437457\pi\) | |||||||
\(594\) | 11.9464 | 0.490165 | ||||||||
\(595\) | −3.34508 | −0.137135 | ||||||||
\(596\) | 9.78505 | 0.400811 | ||||||||
\(597\) | −6.23153 | −0.255040 | ||||||||
\(598\) | −9.62117 | −0.393439 | ||||||||
\(599\) | −11.9202 | −0.487045 | −0.243523 | − | 0.969895i | \(-0.578303\pi\) | ||||
−0.243523 | + | 0.969895i | \(0.578303\pi\) | |||||||
\(600\) | −10.5963 | −0.432591 | ||||||||
\(601\) | −35.8525 | −1.46245 | −0.731227 | − | 0.682134i | \(-0.761052\pi\) | ||||
−0.731227 | + | 0.682134i | \(0.761052\pi\) | |||||||
\(602\) | −0.0812913 | −0.00331319 | ||||||||
\(603\) | −103.247 | −4.20454 | ||||||||
\(604\) | 6.87697 | 0.279820 | ||||||||
\(605\) | 14.3325 | 0.582698 | ||||||||
\(606\) | 62.2339 | 2.52808 | ||||||||
\(607\) | 16.0032 | 0.649549 | 0.324774 | − | 0.945792i | \(-0.394712\pi\) | ||||
0.324774 | + | 0.945792i | \(0.394712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.1186 | −1.26099 | ||||||||
\(610\) | 12.3294 | 0.499203 | ||||||||
\(611\) | 0.235884 | 0.00954286 | ||||||||
\(612\) | −20.4063 | −0.824874 | ||||||||
\(613\) | 14.1692 | 0.572290 | 0.286145 | − | 0.958186i | \(-0.407626\pi\) | ||||
0.286145 | + | 0.958186i | \(0.407626\pi\) | |||||||
\(614\) | 10.2203 | 0.412457 | ||||||||
\(615\) | −24.9650 | −1.00669 | ||||||||
\(616\) | −0.672249 | −0.0270857 | ||||||||
\(617\) | −27.0031 | −1.08710 | −0.543552 | − | 0.839375i | \(-0.682921\pi\) | ||||
−0.543552 | + | 0.839375i | \(0.682921\pi\) | |||||||
\(618\) | −26.5076 | −1.06629 | ||||||||
\(619\) | −31.9044 | −1.28235 | −0.641173 | − | 0.767397i | \(-0.721552\pi\) | ||||
−0.641173 | + | 0.767397i | \(0.721552\pi\) | |||||||
\(620\) | −10.0307 | −0.402843 | ||||||||
\(621\) | 163.921 | 6.57791 | ||||||||
\(622\) | −11.7748 | −0.472126 | ||||||||
\(623\) | −9.58916 | −0.384182 | ||||||||
\(624\) | −3.50451 | −0.140293 | ||||||||
\(625\) | 0.714673 | 0.0285869 | ||||||||
\(626\) | −8.34493 | −0.333530 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.1056 | 0.483066 | ||||||||
\(629\) | 17.1957 | 0.685636 | ||||||||
\(630\) | 11.2629 | 0.448726 | ||||||||
\(631\) | −19.9626 | −0.794699 | −0.397350 | − | 0.917667i | \(-0.630070\pi\) | ||||
−0.397350 | + | 0.917667i | \(0.630070\pi\) | |||||||
\(632\) | 10.0492 | 0.399735 | ||||||||
\(633\) | −92.0571 | −3.65894 | ||||||||
\(634\) | −21.3660 | −0.848551 | ||||||||
\(635\) | 9.60379 | 0.381115 | ||||||||
\(636\) | −20.6328 | −0.818143 | ||||||||
\(637\) | −1.04304 | −0.0413266 | ||||||||
\(638\) | 6.22619 | 0.246497 | ||||||||
\(639\) | 2.97003 | 0.117493 | ||||||||
\(640\) | −1.35877 | −0.0537103 | ||||||||
\(641\) | 14.7339 | 0.581953 | 0.290976 | − | 0.956730i | \(-0.406020\pi\) | ||||
0.290976 | + | 0.956730i | \(0.406020\pi\) | |||||||
\(642\) | −18.3115 | −0.722696 | ||||||||
\(643\) | 31.6423 | 1.24785 | 0.623926 | − | 0.781484i | \(-0.285537\pi\) | ||||
0.623926 | + | 0.781484i | \(0.285537\pi\) | |||||||
\(644\) | −9.22420 | −0.363484 | ||||||||
\(645\) | −0.371125 | −0.0146130 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.39065 | 0.172614 | 0.0863072 | − | 0.996269i | \(-0.472493\pi\) | ||||
0.0863072 | + | 0.996269i | \(0.472493\pi\) | |||||||
\(648\) | 34.8410 | 1.36868 | ||||||||
\(649\) | −6.86385 | −0.269430 | ||||||||
\(650\) | 3.28945 | 0.129023 | ||||||||
\(651\) | −24.8035 | −0.972124 | ||||||||
\(652\) | −11.3384 | −0.444045 | ||||||||
\(653\) | 9.91627 | 0.388054 | 0.194027 | − | 0.980996i | \(-0.437845\pi\) | ||||
0.194027 | + | 0.980996i | \(0.437845\pi\) | |||||||
\(654\) | 1.76662 | 0.0690802 | ||||||||
\(655\) | −13.3119 | −0.520138 | ||||||||
\(656\) | 5.46835 | 0.213503 | ||||||||
\(657\) | 48.5833 | 1.89542 | ||||||||
\(658\) | 0.226152 | 0.00881631 | ||||||||
\(659\) | 19.9626 | 0.777633 | 0.388816 | − | 0.921315i | \(-0.372884\pi\) | ||||
0.388816 | + | 0.921315i | \(0.372884\pi\) | |||||||
\(660\) | −3.06907 | −0.119463 | ||||||||
\(661\) | −9.49464 | −0.369299 | −0.184649 | − | 0.982804i | \(-0.559115\pi\) | ||||
−0.184649 | + | 0.982804i | \(0.559115\pi\) | |||||||
\(662\) | 12.2945 | 0.477841 | ||||||||
\(663\) | 8.62753 | 0.335066 | ||||||||
\(664\) | 2.73042 | 0.105961 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −57.8980 | −2.24350 | ||||||||
\(667\) | 85.4321 | 3.30794 | ||||||||
\(668\) | −11.8009 | −0.456592 | ||||||||
\(669\) | −5.25653 | −0.203229 | ||||||||
\(670\) | 16.9247 | 0.653858 | ||||||||
\(671\) | −6.09993 | −0.235485 | ||||||||
\(672\) | −3.35992 | −0.129612 | ||||||||
\(673\) | 48.6884 | 1.87680 | 0.938400 | − | 0.345552i | \(-0.112308\pi\) | ||||
0.938400 | + | 0.345552i | \(0.112308\pi\) | |||||||
\(674\) | 29.3162 | 1.12922 | ||||||||
\(675\) | −56.0441 | −2.15714 | ||||||||
\(676\) | −11.9121 | −0.458157 | ||||||||
\(677\) | 35.6077 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(678\) | −58.3208 | −2.23980 | ||||||||
\(679\) | −13.2610 | −0.508912 | ||||||||
\(680\) | 3.34508 | 0.128278 | ||||||||
\(681\) | −81.6016 | −3.12698 | ||||||||
\(682\) | 4.96265 | 0.190030 | ||||||||
\(683\) | −1.59061 | −0.0608629 | −0.0304314 | − | 0.999537i | \(-0.509688\pi\) | ||||
−0.0304314 | + | 0.999537i | \(0.509688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.5793 | 1.05375 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 43.0386 | 1.64203 | ||||||||
\(688\) | 0.0812913 | 0.00309920 | ||||||||
\(689\) | 6.40514 | 0.244016 | ||||||||
\(690\) | −42.1119 | −1.60317 | ||||||||
\(691\) | 7.59300 | 0.288851 | 0.144426 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144426 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(692\) | 18.0756 | 0.687132 | ||||||||
\(693\) | −5.57230 | −0.211674 | ||||||||
\(694\) | 4.66549 | 0.177099 | ||||||||
\(695\) | −7.00926 | −0.265877 | ||||||||
\(696\) | 31.1186 | 1.17955 | ||||||||
\(697\) | −13.4622 | −0.509916 | ||||||||
\(698\) | 10.9979 | 0.416278 | ||||||||
\(699\) | −54.4113 | −2.05803 | ||||||||
\(700\) | 3.15373 | 0.119200 | ||||||||
\(701\) | 20.5770 | 0.777183 | 0.388592 | − | 0.921410i | \(-0.372962\pi\) | ||||
0.388592 | + | 0.921410i | \(0.372962\pi\) | |||||||
\(702\) | −18.5355 | −0.699577 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.672249 | 0.0253363 | ||||||||
\(705\) | 1.03247 | 0.0388849 | ||||||||
\(706\) | −8.33356 | −0.313638 | ||||||||
\(707\) | −18.5225 | −0.696609 | ||||||||
\(708\) | −34.3057 | −1.28929 | ||||||||
\(709\) | 16.2673 | 0.610931 | 0.305465 | − | 0.952203i | \(-0.401188\pi\) | ||||
0.305465 | + | 0.952203i | \(0.401188\pi\) | |||||||
\(710\) | −0.486860 | −0.0182715 | ||||||||
\(711\) | 83.2980 | 3.12392 | ||||||||
\(712\) | 9.58916 | 0.359369 | ||||||||
\(713\) | 68.0946 | 2.55016 | ||||||||
\(714\) | 8.27156 | 0.309555 | ||||||||
\(715\) | 0.952745 | 0.0356307 | ||||||||
\(716\) | 4.30866 | 0.161022 | ||||||||
\(717\) | −37.5242 | −1.40137 | ||||||||
\(718\) | −4.47179 | −0.166886 | ||||||||
\(719\) | 49.1755 | 1.83394 | 0.916969 | − | 0.398959i | \(-0.130628\pi\) | ||||
0.916969 | + | 0.398959i | \(0.130628\pi\) | |||||||
\(720\) | −11.2629 | −0.419745 | ||||||||
\(721\) | 7.88935 | 0.293815 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −62.4119 | −2.32112 | ||||||||
\(724\) | 3.51816 | 0.130751 | ||||||||
\(725\) | −29.2090 | −1.08480 | ||||||||
\(726\) | −35.4407 | −1.31533 | ||||||||
\(727\) | −37.8702 | −1.40453 | −0.702264 | − | 0.711917i | \(-0.747827\pi\) | ||||
−0.702264 | + | 0.711917i | \(0.747827\pi\) | |||||||
\(728\) | 1.04304 | 0.0386575 | ||||||||
\(729\) | 109.674 | 4.06200 | ||||||||
\(730\) | −7.96399 | −0.294760 | ||||||||
\(731\) | −0.200126 | −0.00740193 | ||||||||
\(732\) | −30.4876 | −1.12685 | ||||||||
\(733\) | −46.4071 | −1.71409 | −0.857044 | − | 0.515244i | \(-0.827701\pi\) | ||||
−0.857044 | + | 0.515244i | \(0.827701\pi\) | |||||||
\(734\) | −6.11166 | −0.225585 | ||||||||
\(735\) | −4.56537 | −0.168396 | ||||||||
\(736\) | 9.22420 | 0.340008 | ||||||||
\(737\) | −8.37343 | −0.308439 | ||||||||
\(738\) | 45.3273 | 1.66852 | ||||||||
\(739\) | 36.1093 | 1.32830 | 0.664151 | − | 0.747598i | \(-0.268793\pi\) | ||||
0.664151 | + | 0.747598i | \(0.268793\pi\) | |||||||
\(740\) | 9.49090 | 0.348892 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.14086 | 0.225438 | ||||||||
\(743\) | 21.2678 | 0.780241 | 0.390120 | − | 0.920764i | \(-0.372433\pi\) | ||||
0.390120 | + | 0.920764i | \(0.372433\pi\) | |||||||
\(744\) | 24.8035 | 0.909339 | ||||||||
\(745\) | −13.2957 | −0.487116 | ||||||||
\(746\) | 12.6405 | 0.462803 | ||||||||
\(747\) | 22.6325 | 0.828081 | ||||||||
\(748\) | −1.65497 | −0.0605116 | ||||||||
\(749\) | 5.44998 | 0.199138 | ||||||||
\(750\) | 37.2248 | 1.35926 | ||||||||
\(751\) | 7.42960 | 0.271110 | 0.135555 | − | 0.990770i | \(-0.456718\pi\) | ||||
0.135555 | + | 0.990770i | \(0.456718\pi\) | |||||||
\(752\) | −0.226152 | −0.00824690 | ||||||||
\(753\) | −21.5764 | −0.786289 | ||||||||
\(754\) | −9.66032 | −0.351808 | ||||||||
\(755\) | −9.34426 | −0.340072 | ||||||||
\(756\) | −17.7707 | −0.646315 | ||||||||
\(757\) | −30.1366 | −1.09533 | −0.547666 | − | 0.836697i | \(-0.684484\pi\) | ||||
−0.547666 | + | 0.836697i | \(0.684484\pi\) | |||||||
\(758\) | 1.93824 | 0.0704000 | ||||||||
\(759\) | 20.8347 | 0.756252 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.5985 | −1.29044 | −0.645222 | − | 0.763995i | \(-0.723235\pi\) | ||||
−0.645222 | + | 0.763995i | \(0.723235\pi\) | |||||||
\(762\) | −23.7478 | −0.860292 | ||||||||
\(763\) | −0.525792 | −0.0190349 | ||||||||
\(764\) | 15.7576 | 0.570090 | ||||||||
\(765\) | 27.7275 | 1.00249 | ||||||||
\(766\) | −24.3608 | −0.880190 | ||||||||
\(767\) | 10.6497 | 0.384537 | ||||||||
\(768\) | 3.35992 | 0.121241 | ||||||||
\(769\) | 29.7011 | 1.07105 | 0.535525 | − | 0.844519i | \(-0.320114\pi\) | ||||
0.535525 | + | 0.844519i | \(0.320114\pi\) | |||||||
\(770\) | 0.913435 | 0.0329179 | ||||||||
\(771\) | −18.9610 | −0.682863 | ||||||||
\(772\) | −11.2836 | −0.406107 | ||||||||
\(773\) | 22.7091 | 0.816790 | 0.408395 | − | 0.912805i | \(-0.366089\pi\) | ||||
0.408395 | + | 0.912805i | \(0.366089\pi\) | |||||||
\(774\) | 0.673827 | 0.0242202 | ||||||||
\(775\) | −23.2814 | −0.836291 | ||||||||
\(776\) | 13.2610 | 0.476044 | ||||||||
\(777\) | 23.4687 | 0.841933 | ||||||||
\(778\) | −10.0046 | −0.358682 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 4.76184 | 0.170501 | ||||||||
\(781\) | 0.240872 | 0.00861909 | ||||||||
\(782\) | −22.7085 | −0.812053 | ||||||||
\(783\) | 164.588 | 5.88188 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −16.4488 | −0.587083 | ||||||||
\(786\) | 32.9170 | 1.17411 | ||||||||
\(787\) | −9.88614 | −0.352403 | −0.176201 | − | 0.984354i | \(-0.556381\pi\) | ||||
−0.176201 | + | 0.984354i | \(0.556381\pi\) | |||||||
\(788\) | −14.9533 | −0.532691 | ||||||||
\(789\) | −22.8531 | −0.813592 | ||||||||
\(790\) | −13.6546 | −0.485808 | ||||||||
\(791\) | 17.3578 | 0.617173 | ||||||||
\(792\) | 5.57230 | 0.198003 | ||||||||
\(793\) | 9.46440 | 0.336091 | ||||||||
\(794\) | −31.1380 | −1.10504 | ||||||||
\(795\) | 28.0353 | 0.994310 | ||||||||
\(796\) | −1.85467 | −0.0657370 | ||||||||
\(797\) | −13.4346 | −0.475879 | −0.237939 | − | 0.971280i | \(-0.576472\pi\) | ||||
−0.237939 | + | 0.971280i | \(0.576472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.556749 | 0.0196963 | ||||||||
\(800\) | −3.15373 | −0.111501 | ||||||||
\(801\) | 79.4849 | 2.80846 | ||||||||
\(802\) | 4.25458 | 0.150234 | ||||||||
\(803\) | 3.94016 | 0.139045 | ||||||||
\(804\) | −41.8506 | −1.47596 | ||||||||
\(805\) | 12.5336 | 0.441752 | ||||||||
\(806\) | −7.69986 | −0.271216 | ||||||||
\(807\) | 55.0910 | 1.93930 | ||||||||
\(808\) | 18.5225 | 0.651618 | ||||||||
\(809\) | −29.6717 | −1.04320 | −0.521601 | − | 0.853190i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853190i | \(0.674665\pi\) | |||||||
\(810\) | −47.3411 | −1.66340 | ||||||||
\(811\) | 46.9132 | 1.64734 | 0.823672 | − | 0.567067i | \(-0.191922\pi\) | ||||
0.823672 | + | 0.567067i | \(0.191922\pi\) | |||||||
\(812\) | −9.26173 | −0.325023 | ||||||||
\(813\) | −56.4413 | −1.97948 | ||||||||
\(814\) | −4.69559 | −0.164580 | ||||||||
\(815\) | 15.4063 | 0.539658 | ||||||||
\(816\) | −8.27156 | −0.289563 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 35.8582 | 1.25375 | ||||||||
\(819\) | 8.64576 | 0.302107 | ||||||||
\(820\) | −7.43025 | −0.259476 | ||||||||
\(821\) | 8.20066 | 0.286205 | 0.143103 | − | 0.989708i | \(-0.454292\pi\) | ||||
0.143103 | + | 0.989708i | \(0.454292\pi\) | |||||||
\(822\) | −68.1969 | −2.37864 | ||||||||
\(823\) | −13.2650 | −0.462388 | −0.231194 | − | 0.972908i | \(-0.574263\pi\) | ||||
−0.231194 | + | 0.972908i | \(0.574263\pi\) | |||||||
\(824\) | −7.88935 | −0.274839 | ||||||||
\(825\) | −7.12334 | −0.248003 | ||||||||
\(826\) | 10.2103 | 0.355261 | ||||||||
\(827\) | 7.03178 | 0.244519 | 0.122260 | − | 0.992498i | \(-0.460986\pi\) | ||||
0.122260 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(828\) | 76.4597 | 2.65716 | ||||||||
\(829\) | −9.85280 | −0.342202 | −0.171101 | − | 0.985254i | \(-0.554732\pi\) | ||||
−0.171101 | + | 0.985254i | \(0.554732\pi\) | |||||||
\(830\) | −3.71002 | −0.128777 | ||||||||
\(831\) | −61.0796 | −2.11883 | ||||||||
\(832\) | −1.04304 | −0.0361607 | ||||||||
\(833\) | −2.46184 | −0.0852976 | ||||||||
\(834\) | 17.3322 | 0.600164 | ||||||||
\(835\) | 16.0348 | 0.554907 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 131.186 | 4.53446 | ||||||||
\(838\) | −21.8254 | −0.753946 | ||||||||
\(839\) | −23.8269 | −0.822595 | −0.411298 | − | 0.911501i | \(-0.634924\pi\) | ||||
−0.411298 | + | 0.911501i | \(0.634924\pi\) | |||||||
\(840\) | 4.56537 | 0.157520 | ||||||||
\(841\) | 56.7797 | 1.95792 | ||||||||
\(842\) | 27.7218 | 0.955358 | ||||||||
\(843\) | −56.3046 | −1.93923 | ||||||||
\(844\) | −27.3986 | −0.943100 | ||||||||
\(845\) | 16.1858 | 0.556809 | ||||||||
\(846\) | −1.87458 | −0.0644494 | ||||||||
\(847\) | 10.5481 | 0.362436 | ||||||||
\(848\) | −6.14086 | −0.210878 | ||||||||
\(849\) | −11.3157 | −0.388353 | ||||||||
\(850\) | 7.76397 | 0.266302 | ||||||||
\(851\) | −64.4301 | −2.20863 | ||||||||
\(852\) | 1.20389 | 0.0412444 | ||||||||
\(853\) | −16.3690 | −0.560465 | −0.280233 | − | 0.959932i | \(-0.590412\pi\) | ||||
−0.280233 | + | 0.959932i | \(0.590412\pi\) | |||||||
\(854\) | 9.07391 | 0.310503 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.44998 | −0.186276 | ||||||||
\(857\) | −14.3213 | −0.489207 | −0.244604 | − | 0.969623i | \(-0.578658\pi\) | ||||
−0.244604 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(858\) | −2.35591 | −0.0804293 | ||||||||
\(859\) | −6.06335 | −0.206879 | −0.103439 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103439 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(860\) | −0.110457 | −0.00376654 | ||||||||
\(861\) | −18.3732 | −0.626156 | ||||||||
\(862\) | −28.6460 | −0.975688 | ||||||||
\(863\) | −34.3964 | −1.17087 | −0.585434 | − | 0.810720i | \(-0.699076\pi\) | ||||
−0.585434 | + | 0.810720i | \(0.699076\pi\) | |||||||
\(864\) | 17.7707 | 0.604572 | ||||||||
\(865\) | −24.5607 | −0.835089 | ||||||||
\(866\) | 3.35163 | 0.113893 | ||||||||
\(867\) | −36.7553 | −1.24828 | ||||||||
\(868\) | −7.38217 | −0.250567 | ||||||||
\(869\) | 6.75555 | 0.229166 | ||||||||
\(870\) | −42.2832 | −1.43354 | ||||||||
\(871\) | 12.9919 | 0.440213 | ||||||||
\(872\) | 0.525792 | 0.0178056 | ||||||||
\(873\) | 109.921 | 3.72027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0791 | −0.374541 | ||||||||
\(876\) | 19.6930 | 0.665364 | ||||||||
\(877\) | 9.81095 | 0.331292 | 0.165646 | − | 0.986185i | \(-0.447029\pi\) | ||||
0.165646 | + | 0.986185i | \(0.447029\pi\) | |||||||
\(878\) | 34.8282 | 1.17540 | ||||||||
\(879\) | −30.0793 | −1.01455 | ||||||||
\(880\) | −0.913435 | −0.0307919 | ||||||||
\(881\) | −29.8319 | −1.00506 | −0.502531 | − | 0.864559i | \(-0.667598\pi\) | ||||
−0.502531 | + | 0.864559i | \(0.667598\pi\) | |||||||
\(882\) | 8.28904 | 0.279106 | ||||||||
\(883\) | −25.5339 | −0.859283 | −0.429642 | − | 0.902999i | \(-0.641360\pi\) | ||||
−0.429642 | + | 0.902999i | \(0.641360\pi\) | |||||||
\(884\) | 2.56778 | 0.0863639 | ||||||||
\(885\) | 46.6137 | 1.56690 | ||||||||
\(886\) | 27.7162 | 0.931143 | ||||||||
\(887\) | 1.66452 | 0.0558893 | 0.0279446 | − | 0.999609i | \(-0.491104\pi\) | ||||
0.0279446 | + | 0.999609i | \(0.491104\pi\) | |||||||
\(888\) | −23.4687 | −0.787557 | ||||||||
\(889\) | 7.06798 | 0.237052 | ||||||||
\(890\) | −13.0295 | −0.436750 | ||||||||
\(891\) | 23.4218 | 0.784661 | ||||||||
\(892\) | −1.56448 | −0.0523828 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 32.8770 | 1.09957 | ||||||||
\(895\) | −5.85450 | −0.195694 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −32.3263 | −1.07934 | ||||||||
\(898\) | −2.10506 | −0.0702467 | ||||||||
\(899\) | 68.3716 | 2.28032 | ||||||||
\(900\) | −26.1414 | −0.871380 | ||||||||
\(901\) | 15.1178 | 0.503647 | ||||||||
\(902\) | 3.67609 | 0.122400 | ||||||||
\(903\) | −0.273132 | −0.00908927 | ||||||||
\(904\) | −17.3578 | −0.577313 | ||||||||
\(905\) | −4.78039 | −0.158906 | ||||||||
\(906\) | 23.1061 | 0.767647 | ||||||||
\(907\) | 42.3441 | 1.40601 | 0.703007 | − | 0.711183i | \(-0.251840\pi\) | ||||
0.703007 | + | 0.711183i | \(0.251840\pi\) | |||||||
\(908\) | −24.2868 | −0.805986 | ||||||||
\(909\) | 153.533 | 5.09238 | ||||||||
\(910\) | −1.41725 | −0.0469814 | ||||||||
\(911\) | 2.81275 | 0.0931905 | 0.0465953 | − | 0.998914i | \(-0.485163\pi\) | ||||
0.0465953 | + | 0.998914i | \(0.485163\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83552 | 0.0607469 | ||||||||
\(914\) | −13.1492 | −0.434937 | ||||||||
\(915\) | 41.4257 | 1.36949 | ||||||||
\(916\) | 12.8094 | 0.423236 | ||||||||
\(917\) | −9.79698 | −0.323525 | ||||||||
\(918\) | −43.7486 | −1.44392 | ||||||||
\(919\) | 42.3008 | 1.39537 | 0.697687 | − | 0.716403i | \(-0.254213\pi\) | ||||
0.697687 | + | 0.716403i | \(0.254213\pi\) | |||||||
\(920\) | −12.5336 | −0.413221 | ||||||||
\(921\) | 34.3393 | 1.13152 | ||||||||
\(922\) | −13.9604 | −0.459761 | ||||||||
\(923\) | −0.373728 | −0.0123014 | ||||||||
\(924\) | −2.25870 | −0.0743058 | ||||||||
\(925\) | 22.0285 | 0.724292 | ||||||||
\(926\) | −5.45782 | −0.179355 | ||||||||
\(927\) | −65.3951 | −2.14786 | ||||||||
\(928\) | 9.26173 | 0.304031 | ||||||||
\(929\) | 23.2939 | 0.764247 | 0.382123 | − | 0.924111i | \(-0.375193\pi\) | ||||
0.382123 | + | 0.924111i | \(0.375193\pi\) | |||||||
\(930\) | −33.7023 | −1.10514 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.1943 | −0.530460 | ||||||||
\(933\) | −39.5623 | −1.29521 | ||||||||
\(934\) | 40.0931 | 1.31188 | ||||||||
\(935\) | 2.24873 | 0.0735413 | ||||||||
\(936\) | −8.64576 | −0.282595 | ||||||||
\(937\) | −59.3078 | −1.93750 | −0.968750 | − | 0.248038i | \(-0.920214\pi\) | ||||
−0.968750 | + | 0.248038i | \(0.920214\pi\) | |||||||
\(938\) | 12.4558 | 0.406698 | ||||||||
\(939\) | −28.0382 | −0.914994 | ||||||||
\(940\) | 0.307289 | 0.0100227 | ||||||||
\(941\) | −0.727116 | −0.0237033 | −0.0118517 | − | 0.999930i | \(-0.503773\pi\) | ||||
−0.0118517 | + | 0.999930i | \(0.503773\pi\) | |||||||
\(942\) | 40.6738 | 1.32522 | ||||||||
\(943\) | 50.4411 | 1.64259 | ||||||||
\(944\) | −10.2103 | −0.332316 | ||||||||
\(945\) | 24.1464 | 0.785483 | ||||||||
\(946\) | 0.0546480 | 0.00177676 | ||||||||
\(947\) | 22.0588 | 0.716814 | 0.358407 | − | 0.933565i | \(-0.383320\pi\) | ||||
0.358407 | + | 0.933565i | \(0.383320\pi\) | |||||||
\(948\) | 33.7644 | 1.09662 | ||||||||
\(949\) | −6.11339 | −0.198449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −71.7879 | −2.32788 | ||||||||
\(952\) | 2.46184 | 0.0797886 | ||||||||
\(953\) | 32.6219 | 1.05673 | 0.528364 | − | 0.849018i | \(-0.322806\pi\) | ||||
0.528364 | + | 0.849018i | \(0.322806\pi\) | |||||||
\(954\) | −50.9018 | −1.64801 | ||||||||
\(955\) | −21.4110 | −0.692844 | ||||||||
\(956\) | −11.1682 | −0.361205 | ||||||||
\(957\) | 20.9195 | 0.676231 | ||||||||
\(958\) | −14.5050 | −0.468636 | ||||||||
\(959\) | 20.2972 | 0.655431 | ||||||||
\(960\) | −4.56537 | −0.147347 | ||||||||
\(961\) | 23.4964 | 0.757947 | ||||||||
\(962\) | 7.28549 | 0.234894 | ||||||||
\(963\) | −45.1751 | −1.45575 | ||||||||
\(964\) | −18.5754 | −0.598274 | ||||||||
\(965\) | 15.3319 | 0.493552 | ||||||||
\(966\) | −30.9925 | −0.997168 | ||||||||
\(967\) | −34.4438 | −1.10764 | −0.553820 | − | 0.832637i | \(-0.686830\pi\) | ||||
−0.553820 | + | 0.832637i | \(0.686830\pi\) | |||||||
\(968\) | −10.5481 | −0.339028 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.0188 | −0.578548 | ||||||||
\(971\) | 10.0122 | 0.321307 | 0.160653 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160653 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(972\) | 63.7507 | 2.04481 | ||||||||
\(973\) | −5.15852 | −0.165374 | ||||||||
\(974\) | −6.25818 | −0.200525 | ||||||||
\(975\) | 11.0523 | 0.353956 | ||||||||
\(976\) | −9.07391 | −0.290449 | ||||||||
\(977\) | −0.947408 | −0.0303103 | −0.0151551 | − | 0.999885i | \(-0.504824\pi\) | ||||
−0.0151551 | + | 0.999885i | \(0.504824\pi\) | |||||||
\(978\) | −38.0959 | −1.21817 | ||||||||
\(979\) | 6.44631 | 0.206025 | ||||||||
\(980\) | −1.35877 | −0.0434045 | ||||||||
\(981\) | 4.35831 | 0.139150 | ||||||||
\(982\) | −24.5017 | −0.781880 | ||||||||
\(983\) | −19.4148 | −0.619237 | −0.309619 | − | 0.950861i | \(-0.600201\pi\) | ||||
−0.309619 | + | 0.950861i | \(0.600201\pi\) | |||||||
\(984\) | 18.3732 | 0.585716 | ||||||||
\(985\) | 20.3182 | 0.647393 | ||||||||
\(986\) | −22.8009 | −0.726128 | ||||||||
\(987\) | 0.759851 | 0.0241863 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.749848 | 0.0238438 | ||||||||
\(990\) | −7.57150 | −0.240638 | ||||||||
\(991\) | 31.2746 | 0.993471 | 0.496736 | − | 0.867902i | \(-0.334532\pi\) | ||||
0.496736 | + | 0.867902i | \(0.334532\pi\) | |||||||
\(992\) | 7.38217 | 0.234384 | ||||||||
\(993\) | 41.3086 | 1.31089 | ||||||||
\(994\) | −0.358308 | −0.0113648 | ||||||||
\(995\) | 2.52008 | 0.0798918 | ||||||||
\(996\) | 9.17397 | 0.290689 | ||||||||
\(997\) | 20.5619 | 0.651202 | 0.325601 | − | 0.945507i | \(-0.394433\pi\) | ||||
0.325601 | + | 0.945507i | \(0.394433\pi\) | |||||||
\(998\) | 3.36082 | 0.106385 | ||||||||
\(999\) | −124.127 | −3.92719 |
(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 | 5054.2.a.bi.1.8 | yes | 8 | |
19.18 | odd | 2 | 5054.2.a.bf.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bf.1.1 | ✓ | 8 | 19.18 | odd | 2 | ||
5054.2.a.bi.1.8 | yes | 8 | 1.1 | even | 1 | trivial |