Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, 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("3850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.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: | \(30.7424047782\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1 |
$q$-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 | ||||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.41421 | −0.408248 | ||||||||
\(13\) | 1.56282 | 0.433447 | 0.216724 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216724 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.210157 | 0.0509706 | 0.0254853 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254853 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.24264 | −1.43216 | −0.716080 | − | 0.698018i | \(-0.754065\pi\) | ||||
−0.716080 | + | 0.698018i | \(0.754065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 8.79073 | 1.83299 | 0.916497 | − | 0.400042i | \(-0.131004\pi\) | ||||
0.916497 | + | 0.400042i | \(0.131004\pi\) | |||||||
\(24\) | 1.41421 | 0.288675 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.56282 | −0.306494 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −9.96230 | −1.84995 | −0.924977 | − | 0.380024i | \(-0.875916\pi\) | ||||
−0.924977 | + | 0.380024i | \(0.875916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.93933 | 1.24634 | 0.623170 | − | 0.782086i | \(-0.285844\pi\) | ||||
0.623170 | + | 0.782086i | \(0.285844\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.41421 | 0.246183 | ||||||||
\(34\) | −0.210157 | −0.0360417 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.358761 | 0.0589799 | 0.0294900 | − | 0.999565i | \(-0.490612\pi\) | ||||
0.0294900 | + | 0.999565i | \(0.490612\pi\) | |||||||
\(38\) | 6.24264 | 1.01269 | ||||||||
\(39\) | −2.21016 | −0.353908 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.76687 | −0.744461 | −0.372230 | − | 0.928140i | \(-0.621407\pi\) | ||||
−0.372230 | + | 0.928140i | \(0.621407\pi\) | |||||||
\(42\) | 1.41421 | 0.218218 | ||||||||
\(43\) | 5.44670 | 0.830614 | 0.415307 | − | 0.909681i | \(-0.363674\pi\) | ||||
0.415307 | + | 0.909681i | \(0.363674\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.79073 | −1.29612 | ||||||||
\(47\) | −3.65685 | −0.533407 | −0.266704 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266704 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(48\) | −1.41421 | −0.204124 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.297207 | −0.0416173 | ||||||||
\(52\) | 1.56282 | 0.216724 | ||||||||
\(53\) | −2.76687 | −0.380059 | −0.190030 | − | 0.981778i | \(-0.560858\pi\) | ||||
−0.190030 | + | 0.981778i | \(0.560858\pi\) | |||||||
\(54\) | −5.65685 | −0.769800 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 8.82843 | 1.16935 | ||||||||
\(58\) | 9.96230 | 1.30811 | ||||||||
\(59\) | −2.11612 | −0.275495 | −0.137748 | − | 0.990467i | \(-0.543986\pi\) | ||||
−0.137748 | + | 0.990467i | \(0.543986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.71231 | 0.859423 | 0.429711 | − | 0.902966i | \(-0.358615\pi\) | ||||
0.429711 | + | 0.902966i | \(0.358615\pi\) | |||||||
\(62\) | −6.93933 | −0.881296 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.41421 | −0.174078 | ||||||||
\(67\) | −11.9779 | −1.46334 | −0.731668 | − | 0.681661i | \(-0.761258\pi\) | ||||
−0.731668 | + | 0.681661i | \(0.761258\pi\) | |||||||
\(68\) | 0.210157 | 0.0254853 | ||||||||
\(69\) | −12.4320 | −1.49663 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2751 | 1.21943 | 0.609716 | − | 0.792620i | \(-0.291283\pi\) | ||||
0.609716 | + | 0.792620i | \(0.291283\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.02386 | −0.705039 | −0.352519 | − | 0.935804i | \(-0.614675\pi\) | ||||
−0.352519 | + | 0.935804i | \(0.614675\pi\) | |||||||
\(74\) | −0.358761 | −0.0417051 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.24264 | −0.716080 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 2.21016 | 0.250251 | ||||||||
\(79\) | −9.59530 | −1.07956 | −0.539778 | − | 0.841808i | \(-0.681492\pi\) | ||||
−0.539778 | + | 0.841808i | \(0.681492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 4.76687 | 0.526413 | ||||||||
\(83\) | 1.56282 | 0.171541 | 0.0857707 | − | 0.996315i | \(-0.472665\pi\) | ||||
0.0857707 | + | 0.996315i | \(0.472665\pi\) | |||||||
\(84\) | −1.41421 | −0.154303 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.44670 | −0.587332 | ||||||||
\(87\) | 14.0888 | 1.51048 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 8.59619 | 0.911194 | 0.455597 | − | 0.890186i | \(-0.349426\pi\) | ||||
0.455597 | + | 0.890186i | \(0.349426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.56282 | 0.163828 | ||||||||
\(92\) | 8.79073 | 0.916497 | ||||||||
\(93\) | −9.81370 | −1.01763 | ||||||||
\(94\) | 3.65685 | 0.377176 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.41421 | 0.144338 | ||||||||
\(97\) | 14.1725 | 1.43900 | 0.719498 | − | 0.694495i | \(-0.244372\pi\) | ||||
0.719498 | + | 0.694495i | \(0.244372\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.92982 | −0.988054 | −0.494027 | − | 0.869447i | \(-0.664476\pi\) | ||||
−0.494027 | + | 0.869447i | \(0.664476\pi\) | |||||||
\(102\) | 0.297207 | 0.0294279 | ||||||||
\(103\) | −10.9393 | −1.07788 | −0.538942 | − | 0.842343i | \(-0.681176\pi\) | ||||
−0.538942 | + | 0.842343i | \(0.681176\pi\) | |||||||
\(104\) | −1.56282 | −0.153247 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.76687 | 0.268743 | ||||||||
\(107\) | −12.8523 | −1.24248 | −0.621239 | − | 0.783622i | \(-0.713370\pi\) | ||||
−0.621239 | + | 0.783622i | \(0.713370\pi\) | |||||||
\(108\) | 5.65685 | 0.544331 | ||||||||
\(109\) | 14.4476 | 1.38383 | 0.691914 | − | 0.721980i | \(-0.256768\pi\) | ||||
0.691914 | + | 0.721980i | \(0.256768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.507364 | −0.0481569 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 5.55760 | 0.522815 | 0.261408 | − | 0.965228i | \(-0.415813\pi\) | ||||
0.261408 | + | 0.965228i | \(0.415813\pi\) | |||||||
\(114\) | −8.82843 | −0.826858 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.96230 | −0.924977 | ||||||||
\(117\) | −1.56282 | −0.144482 | ||||||||
\(118\) | 2.11612 | 0.194805 | ||||||||
\(119\) | 0.210157 | 0.0192651 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −6.71231 | −0.607704 | ||||||||
\(123\) | 6.74138 | 0.607850 | ||||||||
\(124\) | 6.93933 | 0.623170 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −1.07232 | −0.0951531 | −0.0475766 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475766 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.70279 | −0.678193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.8700 | −1.91079 | −0.955397 | − | 0.295324i | \(-0.904572\pi\) | ||||
−0.955397 | + | 0.295324i | \(0.904572\pi\) | |||||||
\(132\) | 1.41421 | 0.123091 | ||||||||
\(133\) | −6.24264 | −0.541306 | ||||||||
\(134\) | 11.9779 | 1.03473 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.210157 | −0.0180208 | ||||||||
\(137\) | 8.22181 | 0.702437 | 0.351218 | − | 0.936294i | \(-0.385767\pi\) | ||||
0.351218 | + | 0.936294i | \(0.385767\pi\) | |||||||
\(138\) | 12.4320 | 1.05828 | ||||||||
\(139\) | 9.71319 | 0.823862 | 0.411931 | − | 0.911215i | \(-0.364854\pi\) | ||||
0.411931 | + | 0.911215i | \(0.364854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.17157 | 0.435525 | ||||||||
\(142\) | −10.2751 | −0.862269 | ||||||||
\(143\) | −1.56282 | −0.130689 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.02386 | 0.498538 | ||||||||
\(147\) | −1.41421 | −0.116642 | ||||||||
\(148\) | 0.358761 | 0.0294900 | ||||||||
\(149\) | −5.02297 | −0.411498 | −0.205749 | − | 0.978605i | \(-0.565963\pi\) | ||||
−0.205749 | + | 0.978605i | \(0.565963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56892 | 0.209056 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(152\) | 6.24264 | 0.506345 | ||||||||
\(153\) | −0.210157 | −0.0169902 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.21016 | −0.176954 | ||||||||
\(157\) | 16.8692 | 1.34630 | 0.673152 | − | 0.739504i | \(-0.264940\pi\) | ||||
0.673152 | + | 0.739504i | \(0.264940\pi\) | |||||||
\(158\) | 9.59530 | 0.763361 | ||||||||
\(159\) | 3.91295 | 0.310317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.79073 | 0.692807 | ||||||||
\(162\) | 5.00000 | 0.392837 | ||||||||
\(163\) | −12.5723 | −0.984741 | −0.492370 | − | 0.870386i | \(-0.663869\pi\) | ||||
−0.492370 | + | 0.870386i | \(0.663869\pi\) | |||||||
\(164\) | −4.76687 | −0.372230 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.56282 | −0.121298 | ||||||||
\(167\) | 13.0962 | 1.01341 | 0.506706 | − | 0.862119i | \(-0.330863\pi\) | ||||
0.506706 | + | 0.862119i | \(0.330863\pi\) | |||||||
\(168\) | 1.41421 | 0.109109 | ||||||||
\(169\) | −10.5576 | −0.812123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.24264 | 0.477387 | ||||||||
\(172\) | 5.44670 | 0.415307 | ||||||||
\(173\) | 0.461038 | 0.0350521 | 0.0175260 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175260 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(174\) | −14.0888 | −1.06807 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 2.99265 | 0.224941 | ||||||||
\(178\) | −8.59619 | −0.644311 | ||||||||
\(179\) | −4.69544 | −0.350954 | −0.175477 | − | 0.984484i | \(-0.556147\pi\) | ||||
−0.175477 | + | 0.984484i | \(0.556147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4537 | −1.14866 | −0.574332 | − | 0.818623i | \(-0.694738\pi\) | ||||
−0.574332 | + | 0.818623i | \(0.694738\pi\) | |||||||
\(182\) | −1.56282 | −0.115844 | ||||||||
\(183\) | −9.49264 | −0.701716 | ||||||||
\(184\) | −8.79073 | −0.648061 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.81370 | 0.719575 | ||||||||
\(187\) | −0.210157 | −0.0153682 | ||||||||
\(188\) | −3.65685 | −0.266704 | ||||||||
\(189\) | 5.65685 | 0.411476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6954 | −1.06332 | −0.531662 | − | 0.846956i | \(-0.678432\pi\) | ||||
−0.531662 | + | 0.846956i | \(0.678432\pi\) | |||||||
\(192\) | −1.41421 | −0.102062 | ||||||||
\(193\) | 18.2751 | 1.31547 | 0.657736 | − | 0.753248i | \(-0.271514\pi\) | ||||
0.657736 | + | 0.753248i | \(0.271514\pi\) | |||||||
\(194\) | −14.1725 | −1.01752 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −19.8787 | −1.41630 | −0.708148 | − | 0.706064i | \(-0.750469\pi\) | ||||
−0.708148 | + | 0.706064i | \(0.750469\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −22.7941 | −1.61583 | −0.807917 | − | 0.589296i | \(-0.799405\pi\) | ||||
−0.807917 | + | 0.589296i | \(0.799405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.9393 | 1.19481 | ||||||||
\(202\) | 9.92982 | 0.698660 | ||||||||
\(203\) | −9.96230 | −0.699217 | ||||||||
\(204\) | −0.297207 | −0.0208087 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.9393 | 0.762179 | ||||||||
\(207\) | −8.79073 | −0.610998 | ||||||||
\(208\) | 1.56282 | 0.108362 | ||||||||
\(209\) | 6.24264 | 0.431812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8449 | −0.953124 | −0.476562 | − | 0.879141i | \(-0.658117\pi\) | ||||
−0.476562 | + | 0.879141i | \(0.658117\pi\) | |||||||
\(212\) | −2.76687 | −0.190030 | ||||||||
\(213\) | −14.5312 | −0.995663 | ||||||||
\(214\) | 12.8523 | 0.878564 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.65685 | −0.384900 | ||||||||
\(217\) | 6.93933 | 0.471073 | ||||||||
\(218\) | −14.4476 | −0.978514 | ||||||||
\(219\) | 8.51902 | 0.575662 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.328437 | 0.0220931 | ||||||||
\(222\) | 0.507364 | 0.0340521 | ||||||||
\(223\) | −11.1274 | −0.745146 | −0.372573 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372573 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.55760 | −0.369686 | ||||||||
\(227\) | −17.0021 | −1.12847 | −0.564236 | − | 0.825614i | \(-0.690829\pi\) | ||||
−0.564236 | + | 0.825614i | \(0.690829\pi\) | |||||||
\(228\) | 8.82843 | 0.584677 | ||||||||
\(229\) | 14.7895 | 0.977316 | 0.488658 | − | 0.872475i | \(-0.337487\pi\) | ||||
0.488658 | + | 0.872475i | \(0.337487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41421 | 0.0930484 | ||||||||
\(232\) | 9.96230 | 0.654057 | ||||||||
\(233\) | −22.0888 | −1.44709 | −0.723543 | − | 0.690279i | \(-0.757488\pi\) | ||||
−0.723543 | + | 0.690279i | \(0.757488\pi\) | |||||||
\(234\) | 1.56282 | 0.102165 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.11612 | −0.137748 | ||||||||
\(237\) | 13.5698 | 0.881454 | ||||||||
\(238\) | −0.210157 | −0.0136225 | ||||||||
\(239\) | −12.3489 | −0.798783 | −0.399391 | − | 0.916781i | \(-0.630779\pi\) | ||||
−0.399391 | + | 0.916781i | \(0.630779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0659 | 0.712814 | 0.356407 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356407 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 6.71231 | 0.429711 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.74138 | −0.429815 | ||||||||
\(247\) | −9.75611 | −0.620766 | ||||||||
\(248\) | −6.93933 | −0.440648 | ||||||||
\(249\) | −2.21016 | −0.140063 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9488 | 1.38540 | 0.692699 | − | 0.721226i | \(-0.256421\pi\) | ||||
0.692699 | + | 0.721226i | \(0.256421\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −8.79073 | −0.552668 | ||||||||
\(254\) | 1.07232 | 0.0672834 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.93845 | 0.245674 | 0.122837 | − | 0.992427i | \(-0.460801\pi\) | ||||
0.122837 | + | 0.992427i | \(0.460801\pi\) | |||||||
\(258\) | 7.70279 | 0.479555 | ||||||||
\(259\) | 0.358761 | 0.0222923 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.96230 | 0.616651 | ||||||||
\(262\) | 21.8700 | 1.35114 | ||||||||
\(263\) | 1.77996 | 0.109757 | 0.0548786 | − | 0.998493i | \(-0.482523\pi\) | ||||
0.0548786 | + | 0.998493i | \(0.482523\pi\) | |||||||
\(264\) | −1.41421 | −0.0870388 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.24264 | 0.382761 | ||||||||
\(267\) | −12.1568 | −0.743987 | ||||||||
\(268\) | −11.9779 | −0.731668 | ||||||||
\(269\) | −19.0555 | −1.16183 | −0.580916 | − | 0.813964i | \(-0.697305\pi\) | ||||
−0.580916 | + | 0.813964i | \(0.697305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5190 | −0.760476 | −0.380238 | − | 0.924889i | \(-0.624158\pi\) | ||||
−0.380238 | + | 0.924889i | \(0.624158\pi\) | |||||||
\(272\) | 0.210157 | 0.0127427 | ||||||||
\(273\) | −2.21016 | −0.133765 | ||||||||
\(274\) | −8.22181 | −0.496698 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.4320 | −0.748317 | ||||||||
\(277\) | 2.75126 | 0.165307 | 0.0826535 | − | 0.996578i | \(-0.473661\pi\) | ||||
0.0826535 | + | 0.996578i | \(0.473661\pi\) | |||||||
\(278\) | −9.71319 | −0.582559 | ||||||||
\(279\) | −6.93933 | −0.415447 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.75050 | 0.581666 | 0.290833 | − | 0.956774i | \(-0.406068\pi\) | ||||
0.290833 | + | 0.956774i | \(0.406068\pi\) | |||||||
\(282\) | −5.17157 | −0.307963 | ||||||||
\(283\) | 26.1608 | 1.55510 | 0.777548 | − | 0.628823i | \(-0.216463\pi\) | ||||
0.777548 | + | 0.628823i | \(0.216463\pi\) | |||||||
\(284\) | 10.2751 | 0.609716 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.56282 | 0.0924113 | ||||||||
\(287\) | −4.76687 | −0.281380 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.9558 | −0.997402 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.0429 | −1.17493 | ||||||||
\(292\) | −6.02386 | −0.352519 | ||||||||
\(293\) | 0.814065 | 0.0475582 | 0.0237791 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237791 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(294\) | 1.41421 | 0.0824786 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.358761 | −0.0208525 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 5.02297 | 0.290973 | ||||||||
\(299\) | 13.7383 | 0.794507 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.44670 | 0.313942 | ||||||||
\(302\) | −2.56892 | −0.147825 | ||||||||
\(303\) | 14.0429 | 0.806743 | ||||||||
\(304\) | −6.24264 | −0.358040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.210157 | 0.0120139 | ||||||||
\(307\) | −24.8593 | −1.41879 | −0.709397 | − | 0.704809i | \(-0.751033\pi\) | ||||
−0.709397 | + | 0.704809i | \(0.751033\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 15.4706 | 0.880089 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6447 | −0.773717 | −0.386859 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386859 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(312\) | 2.21016 | 0.125126 | ||||||||
\(313\) | −22.3943 | −1.26580 | −0.632899 | − | 0.774234i | \(-0.718135\pi\) | ||||
−0.632899 | + | 0.774234i | \(0.718135\pi\) | |||||||
\(314\) | −16.8692 | −0.951981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.59530 | −0.539778 | ||||||||
\(317\) | −19.3753 | −1.08822 | −0.544112 | − | 0.839013i | \(-0.683133\pi\) | ||||
−0.544112 | + | 0.839013i | \(0.683133\pi\) | |||||||
\(318\) | −3.91295 | −0.219427 | ||||||||
\(319\) | 9.96230 | 0.557782 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.1759 | 1.01448 | ||||||||
\(322\) | −8.79073 | −0.489888 | ||||||||
\(323\) | −1.31194 | −0.0729981 | ||||||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.5723 | 0.696317 | ||||||||
\(327\) | −20.4320 | −1.12989 | ||||||||
\(328\) | 4.76687 | 0.263207 | ||||||||
\(329\) | −3.65685 | −0.201609 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.1391 | −1.82149 | −0.910744 | − | 0.412972i | \(-0.864491\pi\) | ||||
−0.910744 | + | 0.412972i | \(0.864491\pi\) | |||||||
\(332\) | 1.56282 | 0.0857707 | ||||||||
\(333\) | −0.358761 | −0.0196600 | ||||||||
\(334\) | −13.0962 | −0.716591 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.41421 | −0.0771517 | ||||||||
\(337\) | 9.62740 | 0.524438 | 0.262219 | − | 0.965008i | \(-0.415546\pi\) | ||||
0.262219 | + | 0.965008i | \(0.415546\pi\) | |||||||
\(338\) | 10.5576 | 0.574258 | ||||||||
\(339\) | −7.85964 | −0.426877 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.93933 | −0.375786 | ||||||||
\(342\) | −6.24264 | −0.337563 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.44670 | −0.293666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.461038 | −0.0247856 | ||||||||
\(347\) | −29.9147 | −1.60591 | −0.802953 | − | 0.596042i | \(-0.796739\pi\) | ||||
−0.802953 | + | 0.596042i | \(0.796739\pi\) | |||||||
\(348\) | 14.0888 | 0.755240 | ||||||||
\(349\) | −8.89861 | −0.476332 | −0.238166 | − | 0.971225i | \(-0.576546\pi\) | ||||
−0.238166 | + | 0.971225i | \(0.576546\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.84063 | 0.471878 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −13.6265 | −0.725267 | −0.362634 | − | 0.931932i | \(-0.618122\pi\) | ||||
−0.362634 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(354\) | −2.99265 | −0.159057 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.59619 | 0.455597 | ||||||||
\(357\) | −0.297207 | −0.0157299 | ||||||||
\(358\) | 4.69544 | 0.248162 | ||||||||
\(359\) | −23.2110 | −1.22503 | −0.612516 | − | 0.790458i | \(-0.709843\pi\) | ||||
−0.612516 | + | 0.790458i | \(0.709843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | 15.4537 | 0.812228 | ||||||||
\(363\) | −1.41421 | −0.0742270 | ||||||||
\(364\) | 1.56282 | 0.0819139 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.49264 | 0.496188 | ||||||||
\(367\) | −9.84316 | −0.513809 | −0.256904 | − | 0.966437i | \(-0.582703\pi\) | ||||
−0.256904 | + | 0.966437i | \(0.582703\pi\) | |||||||
\(368\) | 8.79073 | 0.458248 | ||||||||
\(369\) | 4.76687 | 0.248154 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.76687 | −0.143649 | ||||||||
\(372\) | −9.81370 | −0.508817 | ||||||||
\(373\) | 4.71929 | 0.244356 | 0.122178 | − | 0.992508i | \(-0.461012\pi\) | ||||
0.122178 | + | 0.992508i | \(0.461012\pi\) | |||||||
\(374\) | 0.210157 | 0.0108670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.65685 | 0.188588 | ||||||||
\(377\) | −15.5693 | −0.801857 | ||||||||
\(378\) | −5.65685 | −0.290957 | ||||||||
\(379\) | 21.6906 | 1.11417 | 0.557085 | − | 0.830455i | \(-0.311920\pi\) | ||||
0.557085 | + | 0.830455i | \(0.311920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.51649 | 0.0776922 | ||||||||
\(382\) | 14.6954 | 0.751884 | ||||||||
\(383\) | 20.1759 | 1.03094 | 0.515469 | − | 0.856908i | \(-0.327618\pi\) | ||||
0.515469 | + | 0.856908i | \(0.327618\pi\) | |||||||
\(384\) | 1.41421 | 0.0721688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.2751 | −0.930179 | ||||||||
\(387\) | −5.44670 | −0.276871 | ||||||||
\(388\) | 14.1725 | 0.719498 | ||||||||
\(389\) | −15.3769 | −0.779640 | −0.389820 | − | 0.920891i | \(-0.627463\pi\) | ||||
−0.389820 | + | 0.920891i | \(0.627463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.84744 | 0.0934288 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 30.9289 | 1.56016 | ||||||||
\(394\) | 19.8787 | 1.00147 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −1.42983 | −0.0717610 | −0.0358805 | − | 0.999356i | \(-0.511424\pi\) | ||||
−0.0358805 | + | 0.999356i | \(0.511424\pi\) | |||||||
\(398\) | 22.7941 | 1.14257 | ||||||||
\(399\) | 8.82843 | 0.441974 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.3761 | −1.61679 | −0.808394 | − | 0.588642i | \(-0.799663\pi\) | ||||
−0.808394 | + | 0.588642i | \(0.799663\pi\) | |||||||
\(402\) | −16.9393 | −0.844857 | ||||||||
\(403\) | 10.8449 | 0.540223 | ||||||||
\(404\) | −9.92982 | −0.494027 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.96230 | 0.494421 | ||||||||
\(407\) | −0.358761 | −0.0177831 | ||||||||
\(408\) | 0.297207 | 0.0147139 | ||||||||
\(409\) | −19.1100 | −0.944930 | −0.472465 | − | 0.881350i | \(-0.656636\pi\) | ||||
−0.472465 | + | 0.881350i | \(0.656636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.6274 | −0.573537 | ||||||||
\(412\) | −10.9393 | −0.538942 | ||||||||
\(413\) | −2.11612 | −0.104127 | ||||||||
\(414\) | 8.79073 | 0.432041 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.56282 | −0.0766234 | ||||||||
\(417\) | −13.7365 | −0.672681 | ||||||||
\(418\) | −6.24264 | −0.305338 | ||||||||
\(419\) | −34.7453 | −1.69742 | −0.848710 | − | 0.528859i | \(-0.822620\pi\) | ||||
−0.848710 | + | 0.528859i | \(0.822620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3787 | 1.09067 | 0.545334 | − | 0.838219i | \(-0.316403\pi\) | ||||
0.545334 | + | 0.838219i | \(0.316403\pi\) | |||||||
\(422\) | 13.8449 | 0.673961 | ||||||||
\(423\) | 3.65685 | 0.177802 | ||||||||
\(424\) | 2.76687 | 0.134371 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.5312 | 0.704040 | ||||||||
\(427\) | 6.71231 | 0.324831 | ||||||||
\(428\) | −12.8523 | −0.621239 | ||||||||
\(429\) | 2.21016 | 0.106707 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6971 | −0.611597 | −0.305798 | − | 0.952096i | \(-0.598923\pi\) | ||||
−0.305798 | + | 0.952096i | \(0.598923\pi\) | |||||||
\(432\) | 5.65685 | 0.272166 | ||||||||
\(433\) | 15.0131 | 0.721483 | 0.360741 | − | 0.932666i | \(-0.382524\pi\) | ||||
0.360741 | + | 0.932666i | \(0.382524\pi\) | |||||||
\(434\) | −6.93933 | −0.333099 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4476 | 0.691914 | ||||||||
\(437\) | −54.8774 | −2.62514 | ||||||||
\(438\) | −8.51902 | −0.407054 | ||||||||
\(439\) | 4.29721 | 0.205095 | 0.102547 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102547 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −0.328437 | −0.0156222 | ||||||||
\(443\) | −41.8228 | −1.98706 | −0.993532 | − | 0.113555i | \(-0.963776\pi\) | ||||
−0.993532 | + | 0.113555i | \(0.963776\pi\) | |||||||
\(444\) | −0.507364 | −0.0240784 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1274 | 0.526898 | ||||||||
\(447\) | 7.10355 | 0.335986 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 15.4804 | 0.730567 | 0.365283 | − | 0.930896i | \(-0.380972\pi\) | ||||
0.365283 | + | 0.930896i | \(0.380972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.76687 | 0.224463 | ||||||||
\(452\) | 5.55760 | 0.261408 | ||||||||
\(453\) | −3.63300 | −0.170693 | ||||||||
\(454\) | 17.0021 | 0.797950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.82843 | −0.413429 | ||||||||
\(457\) | 34.5980 | 1.61842 | 0.809212 | − | 0.587517i | \(-0.199894\pi\) | ||||
0.809212 | + | 0.587517i | \(0.199894\pi\) | |||||||
\(458\) | −14.7895 | −0.691067 | ||||||||
\(459\) | 1.18883 | 0.0554898 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8250 | −1.43566 | −0.717831 | − | 0.696217i | \(-0.754865\pi\) | ||||
−0.717831 | + | 0.696217i | \(0.754865\pi\) | |||||||
\(462\) | −1.41421 | −0.0657952 | ||||||||
\(463\) | −41.3648 | −1.92239 | −0.961193 | − | 0.275875i | \(-0.911032\pi\) | ||||
−0.961193 | + | 0.275875i | \(0.911032\pi\) | |||||||
\(464\) | −9.96230 | −0.462488 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.0888 | 1.02324 | ||||||||
\(467\) | 8.74440 | 0.404643 | 0.202321 | − | 0.979319i | \(-0.435151\pi\) | ||||
0.202321 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(468\) | −1.56282 | −0.0722412 | ||||||||
\(469\) | −11.9779 | −0.553089 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.8566 | −1.09925 | ||||||||
\(472\) | 2.11612 | 0.0974023 | ||||||||
\(473\) | −5.44670 | −0.250439 | ||||||||
\(474\) | −13.5698 | −0.623282 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.210157 | 0.00963254 | ||||||||
\(477\) | 2.76687 | 0.126686 | ||||||||
\(478\) | 12.3489 | 0.564825 | ||||||||
\(479\) | −4.87437 | −0.222715 | −0.111358 | − | 0.993780i | \(-0.535520\pi\) | ||||
−0.111358 | + | 0.993780i | \(0.535520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.560678 | 0.0255647 | ||||||||
\(482\) | −11.0659 | −0.504036 | ||||||||
\(483\) | −12.4320 | −0.565674 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.89949 | 0.449050 | ||||||||
\(487\) | −16.3704 | −0.741814 | −0.370907 | − | 0.928670i | \(-0.620953\pi\) | ||||
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(488\) | −6.71231 | −0.303852 | ||||||||
\(489\) | 17.7800 | 0.804038 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.39088 | 0.423804 | 0.211902 | − | 0.977291i | \(-0.432034\pi\) | ||||
0.211902 | + | 0.977291i | \(0.432034\pi\) | |||||||
\(492\) | 6.74138 | 0.303925 | ||||||||
\(493\) | −2.09365 | −0.0942932 | ||||||||
\(494\) | 9.75611 | 0.438948 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.93933 | 0.311585 | ||||||||
\(497\) | 10.2751 | 0.460902 | ||||||||
\(498\) | 2.21016 | 0.0990395 | ||||||||
\(499\) | 35.6703 | 1.59682 | 0.798411 | − | 0.602113i | \(-0.205675\pi\) | ||||
0.798411 | + | 0.602113i | \(0.205675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.5208 | −0.827448 | ||||||||
\(502\) | −21.9488 | −0.979625 | ||||||||
\(503\) | −0.313688 | −0.0139867 | −0.00699333 | − | 0.999976i | \(-0.502226\pi\) | ||||
−0.00699333 | + | 0.999976i | \(0.502226\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.79073 | 0.390796 | ||||||||
\(507\) | 14.9307 | 0.663096 | ||||||||
\(508\) | −1.07232 | −0.0475766 | ||||||||
\(509\) | 0.0922646 | 0.00408956 | 0.00204478 | − | 0.999998i | \(-0.499349\pi\) | ||||
0.00204478 | + | 0.999998i | \(0.499349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.02386 | −0.266480 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −35.3137 | −1.55914 | ||||||||
\(514\) | −3.93845 | −0.173717 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.70279 | −0.339097 | ||||||||
\(517\) | 3.65685 | 0.160828 | ||||||||
\(518\) | −0.358761 | −0.0157630 | ||||||||
\(519\) | −0.652007 | −0.0286199 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2850 | −0.538216 | −0.269108 | − | 0.963110i | \(-0.586729\pi\) | ||||
−0.269108 | + | 0.963110i | \(0.586729\pi\) | |||||||
\(522\) | −9.96230 | −0.436038 | ||||||||
\(523\) | 2.46841 | 0.107936 | 0.0539681 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539681 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(524\) | −21.8700 | −0.955397 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.77996 | −0.0776100 | ||||||||
\(527\) | 1.45835 | 0.0635268 | ||||||||
\(528\) | 1.41421 | 0.0615457 | ||||||||
\(529\) | 54.2769 | 2.35987 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.11612 | 0.0918318 | ||||||||
\(532\) | −6.24264 | −0.270653 | ||||||||
\(533\) | −7.44975 | −0.322685 | ||||||||
\(534\) | 12.1568 | 0.526078 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.9779 | 0.517367 | ||||||||
\(537\) | 6.64035 | 0.286552 | ||||||||
\(538\) | 19.0555 | 0.821539 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.8991 | −1.67240 | −0.836202 | − | 0.548421i | \(-0.815229\pi\) | ||||
−0.836202 | + | 0.548421i | \(0.815229\pi\) | |||||||
\(542\) | 12.5190 | 0.537738 | ||||||||
\(543\) | 21.8548 | 0.937880 | ||||||||
\(544\) | −0.210157 | −0.00901042 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.21016 | 0.0945860 | ||||||||
\(547\) | 34.2548 | 1.46463 | 0.732315 | − | 0.680966i | \(-0.238440\pi\) | ||||
0.732315 | + | 0.680966i | \(0.238440\pi\) | |||||||
\(548\) | 8.22181 | 0.351218 | ||||||||
\(549\) | −6.71231 | −0.286474 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 62.1911 | 2.64943 | ||||||||
\(552\) | 12.4320 | 0.529140 | ||||||||
\(553\) | −9.59530 | −0.408034 | ||||||||
\(554\) | −2.75126 | −0.116890 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.71319 | 0.411931 | ||||||||
\(557\) | −29.2383 | −1.23887 | −0.619434 | − | 0.785049i | \(-0.712638\pi\) | ||||
−0.619434 | + | 0.785049i | \(0.712638\pi\) | |||||||
\(558\) | 6.93933 | 0.293765 | ||||||||
\(559\) | 8.51219 | 0.360027 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.297207 | 0.0125481 | ||||||||
\(562\) | −9.75050 | −0.411300 | ||||||||
\(563\) | 26.8783 | 1.13279 | 0.566393 | − | 0.824136i | \(-0.308339\pi\) | ||||
0.566393 | + | 0.824136i | \(0.308339\pi\) | |||||||
\(564\) | 5.17157 | 0.217763 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.1608 | −1.09962 | ||||||||
\(567\) | −5.00000 | −0.209980 | ||||||||
\(568\) | −10.2751 | −0.431135 | ||||||||
\(569\) | 6.92945 | 0.290498 | 0.145249 | − | 0.989395i | \(-0.453602\pi\) | ||||
0.145249 | + | 0.989395i | \(0.453602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.3155 | 1.22681 | 0.613407 | − | 0.789767i | \(-0.289798\pi\) | ||||
0.613407 | + | 0.789767i | \(0.289798\pi\) | |||||||
\(572\) | −1.56282 | −0.0653447 | ||||||||
\(573\) | 20.7825 | 0.868201 | ||||||||
\(574\) | 4.76687 | 0.198965 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 4.09278 | 0.170385 | 0.0851924 | − | 0.996365i | \(-0.472850\pi\) | ||||
0.0851924 | + | 0.996365i | \(0.472850\pi\) | |||||||
\(578\) | 16.9558 | 0.705270 | ||||||||
\(579\) | −25.8449 | −1.07408 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.56282 | 0.0648366 | ||||||||
\(582\) | 20.0429 | 0.830804 | ||||||||
\(583\) | 2.76687 | 0.114592 | ||||||||
\(584\) | 6.02386 | 0.249269 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.814065 | −0.0336287 | ||||||||
\(587\) | 42.7157 | 1.76307 | 0.881533 | − | 0.472122i | \(-0.156512\pi\) | ||||
0.881533 | + | 0.472122i | \(0.156512\pi\) | |||||||
\(588\) | −1.41421 | −0.0583212 | ||||||||
\(589\) | −43.3198 | −1.78496 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.1127 | 1.15640 | ||||||||
\(592\) | 0.358761 | 0.0147450 | ||||||||
\(593\) | −1.86952 | −0.0767719 | −0.0383860 | − | 0.999263i | \(-0.512222\pi\) | ||||
−0.0383860 | + | 0.999263i | \(0.512222\pi\) | |||||||
\(594\) | 5.65685 | 0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.02297 | −0.205749 | ||||||||
\(597\) | 32.2358 | 1.31932 | ||||||||
\(598\) | −13.7383 | −0.561801 | ||||||||
\(599\) | −13.5264 | −0.552673 | −0.276336 | − | 0.961061i | \(-0.589120\pi\) | ||||
−0.276336 | + | 0.961061i | \(0.589120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.9714 | −0.488326 | −0.244163 | − | 0.969734i | \(-0.578513\pi\) | ||||
−0.244163 | + | 0.969734i | \(0.578513\pi\) | |||||||
\(602\) | −5.44670 | −0.221991 | ||||||||
\(603\) | 11.9779 | 0.487778 | ||||||||
\(604\) | 2.56892 | 0.104528 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0429 | −0.570453 | ||||||||
\(607\) | 8.99265 | 0.365000 | 0.182500 | − | 0.983206i | \(-0.441581\pi\) | ||||
0.182500 | + | 0.983206i | \(0.441581\pi\) | |||||||
\(608\) | 6.24264 | 0.253173 | ||||||||
\(609\) | 14.0888 | 0.570908 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.71499 | −0.231204 | ||||||||
\(612\) | −0.210157 | −0.00849510 | ||||||||
\(613\) | −8.56245 | −0.345834 | −0.172917 | − | 0.984936i | \(-0.555319\pi\) | ||||
−0.172917 | + | 0.984936i | \(0.555319\pi\) | |||||||
\(614\) | 24.8593 | 1.00324 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 3.97614 | 0.160074 | 0.0800368 | − | 0.996792i | \(-0.474496\pi\) | ||||
0.0800368 | + | 0.996792i | \(0.474496\pi\) | |||||||
\(618\) | −15.4706 | −0.622317 | ||||||||
\(619\) | 39.0450 | 1.56935 | 0.784676 | − | 0.619906i | \(-0.212829\pi\) | ||||
0.784676 | + | 0.619906i | \(0.212829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 49.7279 | 1.99551 | ||||||||
\(622\) | 13.6447 | 0.547101 | ||||||||
\(623\) | 8.59619 | 0.344399 | ||||||||
\(624\) | −2.21016 | −0.0884771 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.3943 | 0.895055 | ||||||||
\(627\) | −8.82843 | −0.352573 | ||||||||
\(628\) | 16.8692 | 0.673152 | ||||||||
\(629\) | 0.0753962 | 0.00300624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.2769 | −1.12569 | −0.562843 | − | 0.826564i | \(-0.690292\pi\) | ||||
−0.562843 | + | 0.826564i | \(0.690292\pi\) | |||||||
\(632\) | 9.59530 | 0.381681 | ||||||||
\(633\) | 19.5797 | 0.778223 | ||||||||
\(634\) | 19.3753 | 0.769490 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.91295 | 0.155159 | ||||||||
\(637\) | 1.56282 | 0.0619211 | ||||||||
\(638\) | −9.96230 | −0.394411 | ||||||||
\(639\) | −10.2751 | −0.406478 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.78909 | −0.268153 | −0.134076 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134076 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(642\) | −18.1759 | −0.717344 | ||||||||
\(643\) | 12.7861 | 0.504233 | 0.252117 | − | 0.967697i | \(-0.418873\pi\) | ||||
0.252117 | + | 0.967697i | \(0.418873\pi\) | |||||||
\(644\) | 8.79073 | 0.346403 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.31194 | 0.0516174 | ||||||||
\(647\) | 34.0312 | 1.33791 | 0.668953 | − | 0.743305i | \(-0.266743\pi\) | ||||
0.668953 | + | 0.743305i | \(0.266743\pi\) | |||||||
\(648\) | 5.00000 | 0.196419 | ||||||||
\(649\) | 2.11612 | 0.0830650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.81370 | −0.384629 | ||||||||
\(652\) | −12.5723 | −0.492370 | ||||||||
\(653\) | −6.01812 | −0.235507 | −0.117754 | − | 0.993043i | \(-0.537569\pi\) | ||||
−0.117754 | + | 0.993043i | \(0.537569\pi\) | |||||||
\(654\) | 20.4320 | 0.798953 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.76687 | −0.186115 | ||||||||
\(657\) | 6.02386 | 0.235013 | ||||||||
\(658\) | 3.65685 | 0.142559 | ||||||||
\(659\) | 16.9498 | 0.660269 | 0.330134 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330134 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0714 | 1.55860 | 0.779299 | − | 0.626653i | \(-0.215576\pi\) | ||||
0.779299 | + | 0.626653i | \(0.215576\pi\) | |||||||
\(662\) | 33.1391 | 1.28799 | ||||||||
\(663\) | −0.464480 | −0.0180389 | ||||||||
\(664\) | −1.56282 | −0.0606491 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.358761 | 0.0139017 | ||||||||
\(667\) | −87.5759 | −3.39095 | ||||||||
\(668\) | 13.0962 | 0.506706 | ||||||||
\(669\) | 15.7365 | 0.608409 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.71231 | −0.259126 | ||||||||
\(672\) | 1.41421 | 0.0545545 | ||||||||
\(673\) | −24.4797 | −0.943622 | −0.471811 | − | 0.881700i | \(-0.656400\pi\) | ||||
−0.471811 | + | 0.881700i | \(0.656400\pi\) | |||||||
\(674\) | −9.62740 | −0.370833 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5576 | −0.406062 | ||||||||
\(677\) | 33.0788 | 1.27132 | 0.635660 | − | 0.771969i | \(-0.280728\pi\) | ||||
0.635660 | + | 0.771969i | \(0.280728\pi\) | |||||||
\(678\) | 7.85964 | 0.301848 | ||||||||
\(679\) | 14.1725 | 0.543889 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0447 | 0.921393 | ||||||||
\(682\) | 6.93933 | 0.265721 | ||||||||
\(683\) | −33.6175 | −1.28634 | −0.643169 | − | 0.765724i | \(-0.722381\pi\) | ||||
−0.643169 | + | 0.765724i | \(0.722381\pi\) | |||||||
\(684\) | 6.24264 | 0.238693 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −20.9155 | −0.797975 | ||||||||
\(688\) | 5.44670 | 0.207653 | ||||||||
\(689\) | −4.32412 | −0.164736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.7877 | 0.638634 | 0.319317 | − | 0.947648i | \(-0.396546\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396546\pi\) | |||||||
\(692\) | 0.461038 | 0.0175260 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 29.9147 | 1.13555 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.0888 | −0.534035 | ||||||||
\(697\) | −1.00179 | −0.0379456 | ||||||||
\(698\) | 8.89861 | 0.336817 | ||||||||
\(699\) | 31.2383 | 1.18154 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.99606 | −0.188699 | −0.0943493 | − | 0.995539i | \(-0.530077\pi\) | ||||
−0.0943493 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(702\) | −8.84063 | −0.333668 | ||||||||
\(703\) | −2.23961 | −0.0844687 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.6265 | 0.512841 | ||||||||
\(707\) | −9.92982 | −0.373449 | ||||||||
\(708\) | 2.99265 | 0.112471 | ||||||||
\(709\) | −13.3310 | −0.500655 | −0.250327 | − | 0.968161i | \(-0.580538\pi\) | ||||
−0.250327 | + | 0.968161i | \(0.580538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.59530 | 0.359852 | ||||||||
\(712\) | −8.59619 | −0.322156 | ||||||||
\(713\) | 61.0018 | 2.28454 | ||||||||
\(714\) | 0.297207 | 0.0111227 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.69544 | −0.175477 | ||||||||
\(717\) | 17.4640 | 0.652203 | ||||||||
\(718\) | 23.2110 | 0.866228 | ||||||||
\(719\) | −6.39823 | −0.238614 | −0.119307 | − | 0.992857i | \(-0.538067\pi\) | ||||
−0.119307 | + | 0.992857i | \(0.538067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9393 | −0.407402 | ||||||||
\(722\) | −19.9706 | −0.743227 | ||||||||
\(723\) | −15.6495 | −0.582010 | ||||||||
\(724\) | −15.4537 | −0.574332 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.41421 | 0.0524864 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | −1.56282 | −0.0579219 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14466 | 0.0423369 | ||||||||
\(732\) | −9.49264 | −0.350858 | ||||||||
\(733\) | −22.4463 | −0.829074 | −0.414537 | − | 0.910032i | \(-0.636056\pi\) | ||||
−0.414537 | + | 0.910032i | \(0.636056\pi\) | |||||||
\(734\) | 9.84316 | 0.363318 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.79073 | −0.324031 | ||||||||
\(737\) | 11.9779 | 0.441212 | ||||||||
\(738\) | −4.76687 | −0.175471 | ||||||||
\(739\) | −37.6127 | −1.38361 | −0.691803 | − | 0.722087i | \(-0.743183\pi\) | ||||
−0.691803 | + | 0.722087i | \(0.743183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7972 | 0.506853 | ||||||||
\(742\) | 2.76687 | 0.101575 | ||||||||
\(743\) | −23.4779 | −0.861322 | −0.430661 | − | 0.902514i | \(-0.641719\pi\) | ||||
−0.430661 | + | 0.902514i | \(0.641719\pi\) | |||||||
\(744\) | 9.81370 | 0.359788 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.71929 | −0.172786 | ||||||||
\(747\) | −1.56282 | −0.0571805 | ||||||||
\(748\) | −0.210157 | −0.00768411 | ||||||||
\(749\) | −12.8523 | −0.469612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9540 | 0.399719 | 0.199859 | − | 0.979825i | \(-0.435951\pi\) | ||||
0.199859 | + | 0.979825i | \(0.435951\pi\) | |||||||
\(752\) | −3.65685 | −0.133352 | ||||||||
\(753\) | −31.0404 | −1.13117 | ||||||||
\(754\) | 15.5693 | 0.566999 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.65685 | 0.205738 | ||||||||
\(757\) | 4.62223 | 0.167998 | 0.0839989 | − | 0.996466i | \(-0.473231\pi\) | ||||
0.0839989 | + | 0.996466i | \(0.473231\pi\) | |||||||
\(758\) | −21.6906 | −0.787838 | ||||||||
\(759\) | 12.4320 | 0.451252 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.6932 | −1.54763 | −0.773815 | − | 0.633412i | \(-0.781654\pi\) | ||||
−0.773815 | + | 0.633412i | \(0.781654\pi\) | |||||||
\(762\) | −1.51649 | −0.0549367 | ||||||||
\(763\) | 14.4476 | 0.523038 | ||||||||
\(764\) | −14.6954 | −0.531662 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.1759 | −0.728984 | ||||||||
\(767\) | −3.30711 | −0.119413 | ||||||||
\(768\) | −1.41421 | −0.0510310 | ||||||||
\(769\) | 48.9133 | 1.76386 | 0.881929 | − | 0.471382i | \(-0.156245\pi\) | ||||
0.881929 | + | 0.471382i | \(0.156245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.56980 | −0.200592 | ||||||||
\(772\) | 18.2751 | 0.657736 | ||||||||
\(773\) | 48.4801 | 1.74371 | 0.871853 | − | 0.489767i | \(-0.162918\pi\) | ||||
0.871853 | + | 0.489767i | \(0.162918\pi\) | |||||||
\(774\) | 5.44670 | 0.195777 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.1725 | −0.508762 | ||||||||
\(777\) | −0.507364 | −0.0182016 | ||||||||
\(778\) | 15.3769 | 0.551289 | ||||||||
\(779\) | 29.7579 | 1.06619 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2751 | −0.367673 | ||||||||
\(782\) | −1.84744 | −0.0660641 | ||||||||
\(783\) | −56.3553 | −2.01397 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −30.9289 | −1.10320 | ||||||||
\(787\) | −10.5021 | −0.374361 | −0.187181 | − | 0.982326i | \(-0.559935\pi\) | ||||
−0.187181 | + | 0.982326i | \(0.559935\pi\) | |||||||
\(788\) | −19.8787 | −0.708148 | ||||||||
\(789\) | −2.51725 | −0.0896163 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.55760 | 0.197606 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 10.4901 | 0.372515 | ||||||||
\(794\) | 1.42983 | 0.0507427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.7941 | −0.807917 | ||||||||
\(797\) | 37.1872 | 1.31724 | 0.658618 | − | 0.752477i | \(-0.271141\pi\) | ||||
0.658618 | + | 0.752477i | \(0.271141\pi\) | |||||||
\(798\) | −8.82843 | −0.312523 | ||||||||
\(799\) | −0.768514 | −0.0271881 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.59619 | −0.303731 | ||||||||
\(802\) | 32.3761 | 1.14324 | ||||||||
\(803\) | 6.02386 | 0.212577 | ||||||||
\(804\) | 16.9393 | 0.597404 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.8449 | −0.381996 | ||||||||
\(807\) | 26.9485 | 0.948631 | ||||||||
\(808\) | 9.92982 | 0.349330 | ||||||||
\(809\) | 43.5403 | 1.53080 | 0.765399 | − | 0.643557i | \(-0.222542\pi\) | ||||
0.765399 | + | 0.643557i | \(0.222542\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.0147 | −1.65091 | −0.825455 | − | 0.564468i | \(-0.809081\pi\) | ||||
−0.825455 | + | 0.564468i | \(0.809081\pi\) | |||||||
\(812\) | −9.96230 | −0.349608 | ||||||||
\(813\) | 17.7046 | 0.620926 | ||||||||
\(814\) | 0.358761 | 0.0125746 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.297207 | −0.0104043 | ||||||||
\(817\) | −34.0018 | −1.18957 | ||||||||
\(818\) | 19.1100 | 0.668166 | ||||||||
\(819\) | −1.56282 | −0.0546093 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.5126 | −1.48370 | −0.741849 | − | 0.670567i | \(-0.766051\pi\) | ||||
−0.741849 | + | 0.670567i | \(0.766051\pi\) | |||||||
\(822\) | 11.6274 | 0.405552 | ||||||||
\(823\) | 23.9262 | 0.834016 | 0.417008 | − | 0.908903i | \(-0.363079\pi\) | ||||
0.417008 | + | 0.908903i | \(0.363079\pi\) | |||||||
\(824\) | 10.9393 | 0.381090 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.11612 | 0.0736292 | ||||||||
\(827\) | −12.5944 | −0.437951 | −0.218975 | − | 0.975730i | \(-0.570271\pi\) | ||||
−0.218975 | + | 0.975730i | \(0.570271\pi\) | |||||||
\(828\) | −8.79073 | −0.305499 | ||||||||
\(829\) | 11.6836 | 0.405788 | 0.202894 | − | 0.979201i | \(-0.434965\pi\) | ||||
0.202894 | + | 0.979201i | \(0.434965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.89087 | −0.134973 | ||||||||
\(832\) | 1.56282 | 0.0541809 | ||||||||
\(833\) | 0.210157 | 0.00728152 | ||||||||
\(834\) | 13.7365 | 0.475657 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.24264 | 0.215906 | ||||||||
\(837\) | 39.2548 | 1.35684 | ||||||||
\(838\) | 34.7453 | 1.20026 | ||||||||
\(839\) | 40.3302 | 1.39235 | 0.696177 | − | 0.717870i | \(-0.254883\pi\) | ||||
0.696177 | + | 0.717870i | \(0.254883\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 70.2475 | 2.42233 | ||||||||
\(842\) | −22.3787 | −0.771219 | ||||||||
\(843\) | −13.7893 | −0.474929 | ||||||||
\(844\) | −13.8449 | −0.476562 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.65685 | −0.125725 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −2.76687 | −0.0950148 | ||||||||
\(849\) | −36.9969 | −1.26973 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.15377 | 0.108110 | ||||||||
\(852\) | −14.5312 | −0.497831 | ||||||||
\(853\) | 30.2920 | 1.03718 | 0.518589 | − | 0.855024i | \(-0.326457\pi\) | ||||
0.518589 | + | 0.855024i | \(0.326457\pi\) | |||||||
\(854\) | −6.71231 | −0.229690 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8523 | 0.439282 | ||||||||
\(857\) | 34.0134 | 1.16188 | 0.580938 | − | 0.813948i | \(-0.302686\pi\) | ||||
0.580938 | + | 0.813948i | \(0.302686\pi\) | |||||||
\(858\) | −2.21016 | −0.0754535 | ||||||||
\(859\) | −19.3250 | −0.659360 | −0.329680 | − | 0.944093i | \(-0.606941\pi\) | ||||
−0.329680 | + | 0.944093i | \(0.606941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.74138 | 0.229746 | ||||||||
\(862\) | 12.6971 | 0.432464 | ||||||||
\(863\) | −23.2331 | −0.790865 | −0.395432 | − | 0.918495i | \(-0.629405\pi\) | ||||
−0.395432 | + | 0.918495i | \(0.629405\pi\) | |||||||
\(864\) | −5.65685 | −0.192450 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.0131 | −0.510165 | ||||||||
\(867\) | 23.9792 | 0.814375 | ||||||||
\(868\) | 6.93933 | 0.235536 | ||||||||
\(869\) | 9.59530 | 0.325498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7193 | −0.634279 | ||||||||
\(872\) | −14.4476 | −0.489257 | ||||||||
\(873\) | −14.1725 | −0.479665 | ||||||||
\(874\) | 54.8774 | 1.85625 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.51902 | 0.287831 | ||||||||
\(877\) | 2.37260 | 0.0801171 | 0.0400586 | − | 0.999197i | \(-0.487246\pi\) | ||||
0.0400586 | + | 0.999197i | \(0.487246\pi\) | |||||||
\(878\) | −4.29721 | −0.145024 | ||||||||
\(879\) | −1.15126 | −0.0388311 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.6665 | 0.359364 | 0.179682 | − | 0.983725i | \(-0.442493\pi\) | ||||
0.179682 | + | 0.983725i | \(0.442493\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −33.1018 | −1.11396 | −0.556982 | − | 0.830525i | \(-0.688041\pi\) | ||||
−0.556982 | + | 0.830525i | \(0.688041\pi\) | |||||||
\(884\) | 0.328437 | 0.0110465 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41.8228 | 1.40507 | ||||||||
\(887\) | −18.4246 | −0.618637 | −0.309319 | − | 0.950958i | \(-0.600101\pi\) | ||||
−0.309319 | + | 0.950958i | \(0.600101\pi\) | |||||||
\(888\) | 0.507364 | 0.0170260 | ||||||||
\(889\) | −1.07232 | −0.0359645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | −11.1274 | −0.372573 | ||||||||
\(893\) | 22.8284 | 0.763924 | ||||||||
\(894\) | −7.10355 | −0.237578 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −19.4289 | −0.648712 | ||||||||
\(898\) | −15.4804 | −0.516589 | ||||||||
\(899\) | −69.1317 | −2.30567 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.581478 | −0.0193719 | ||||||||
\(902\) | −4.76687 | −0.158720 | ||||||||
\(903\) | −7.70279 | −0.256333 | ||||||||
\(904\) | −5.55760 | −0.184843 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.63300 | 0.120698 | ||||||||
\(907\) | 2.13048 | 0.0707415 | 0.0353707 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353707 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(908\) | −17.0021 | −0.564236 | ||||||||
\(909\) | 9.92982 | 0.329351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0330 | −0.597460 | −0.298730 | − | 0.954338i | \(-0.596563\pi\) | ||||
−0.298730 | + | 0.954338i | \(0.596563\pi\) | |||||||
\(912\) | 8.82843 | 0.292338 | ||||||||
\(913\) | −1.56282 | −0.0517217 | ||||||||
\(914\) | −34.5980 | −1.14440 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.7895 | 0.488658 | ||||||||
\(917\) | −21.8700 | −0.722212 | ||||||||
\(918\) | −1.18883 | −0.0392372 | ||||||||
\(919\) | −31.1326 | −1.02697 | −0.513485 | − | 0.858099i | \(-0.671646\pi\) | ||||
−0.513485 | + | 0.858099i | \(0.671646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.1563 | 1.15844 | ||||||||
\(922\) | 30.8250 | 1.01517 | ||||||||
\(923\) | 16.0581 | 0.528560 | ||||||||
\(924\) | 1.41421 | 0.0465242 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 41.3648 | 1.35933 | ||||||||
\(927\) | 10.9393 | 0.359295 | ||||||||
\(928\) | 9.96230 | 0.327029 | ||||||||
\(929\) | 40.0911 | 1.31535 | 0.657674 | − | 0.753303i | \(-0.271541\pi\) | ||||
0.657674 | + | 0.753303i | \(0.271541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.24264 | −0.204594 | ||||||||
\(932\) | −22.0888 | −0.723543 | ||||||||
\(933\) | 19.2965 | 0.631737 | ||||||||
\(934\) | −8.74440 | −0.286126 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.56282 | 0.0510823 | ||||||||
\(937\) | 2.48834 | 0.0812904 | 0.0406452 | − | 0.999174i | \(-0.487059\pi\) | ||||
0.0406452 | + | 0.999174i | \(0.487059\pi\) | |||||||
\(938\) | 11.9779 | 0.391093 | ||||||||
\(939\) | 31.6703 | 1.03352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.3300 | −0.760537 | −0.380269 | − | 0.924876i | \(-0.624168\pi\) | ||||
−0.380269 | + | 0.924876i | \(0.624168\pi\) | |||||||
\(942\) | 23.8566 | 0.777289 | ||||||||
\(943\) | −41.9043 | −1.36459 | ||||||||
\(944\) | −2.11612 | −0.0688738 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.44670 | 0.177087 | ||||||||
\(947\) | −25.6556 | −0.833694 | −0.416847 | − | 0.908977i | \(-0.636865\pi\) | ||||
−0.416847 | + | 0.908977i | \(0.636865\pi\) | |||||||
\(948\) | 13.5698 | 0.440727 | ||||||||
\(949\) | −9.41418 | −0.305597 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.4008 | 0.888530 | ||||||||
\(952\) | −0.210157 | −0.00681123 | ||||||||
\(953\) | −9.07970 | −0.294120 | −0.147060 | − | 0.989128i | \(-0.546981\pi\) | ||||
−0.147060 | + | 0.989128i | \(0.546981\pi\) | |||||||
\(954\) | −2.76687 | −0.0895808 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.3489 | −0.399391 | ||||||||
\(957\) | −14.0888 | −0.455427 | ||||||||
\(958\) | 4.87437 | 0.157484 | ||||||||
\(959\) | 8.22181 | 0.265496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1543 | 0.553366 | ||||||||
\(962\) | −0.560678 | −0.0180770 | ||||||||
\(963\) | 12.8523 | 0.414159 | ||||||||
\(964\) | 11.0659 | 0.356407 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.4320 | 0.399992 | ||||||||
\(967\) | −52.3419 | −1.68320 | −0.841600 | − | 0.540101i | \(-0.818386\pi\) | ||||
−0.841600 | + | 0.540101i | \(0.818386\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 1.85536 | 0.0596027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2600 | 0.746449 | 0.373225 | − | 0.927741i | \(-0.378252\pi\) | ||||
0.373225 | + | 0.927741i | \(0.378252\pi\) | |||||||
\(972\) | −9.89949 | −0.317526 | ||||||||
\(973\) | 9.71319 | 0.311391 | ||||||||
\(974\) | 16.3704 | 0.524542 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.71231 | 0.214856 | ||||||||
\(977\) | 48.4436 | 1.54985 | 0.774924 | − | 0.632054i | \(-0.217788\pi\) | ||||
0.774924 | + | 0.632054i | \(0.217788\pi\) | |||||||
\(978\) | −17.7800 | −0.568540 | ||||||||
\(979\) | −8.59619 | −0.274735 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.4476 | −0.461276 | ||||||||
\(982\) | −9.39088 | −0.299675 | ||||||||
\(983\) | −2.25304 | −0.0718609 | −0.0359304 | − | 0.999354i | \(-0.511439\pi\) | ||||
−0.0359304 | + | 0.999354i | \(0.511439\pi\) | |||||||
\(984\) | −6.74138 | −0.214907 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.09365 | 0.0666754 | ||||||||
\(987\) | 5.17157 | 0.164613 | ||||||||
\(988\) | −9.75611 | −0.310383 | ||||||||
\(989\) | 47.8804 | 1.52251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.8254 | 0.883901 | 0.441951 | − | 0.897039i | \(-0.354287\pi\) | ||||
0.441951 | + | 0.897039i | \(0.354287\pi\) | |||||||
\(992\) | −6.93933 | −0.220324 | ||||||||
\(993\) | 46.8657 | 1.48724 | ||||||||
\(994\) | −10.2751 | −0.325907 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.21016 | −0.0700315 | ||||||||
\(997\) | 39.9966 | 1.26670 | 0.633352 | − | 0.773864i | \(-0.281679\pi\) | ||||
0.633352 | + | 0.773864i | \(0.281679\pi\) | |||||||
\(998\) | −35.6703 | −1.12912 | ||||||||
\(999\) | 2.02946 | 0.0642092 |
(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 | 3850.2.a.bx.1.1 | 4 | ||
5.2 | odd | 4 | 770.2.c.e.309.3 | ✓ | 8 | ||
5.3 | odd | 4 | 770.2.c.e.309.5 | yes | 8 | ||
5.4 | even | 2 | 3850.2.a.by.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.c.e.309.3 | ✓ | 8 | 5.2 | odd | 4 | ||
770.2.c.e.309.5 | yes | 8 | 5.3 | odd | 4 | ||
3850.2.a.bx.1.1 | 4 | 1.1 | even | 1 | trivial | ||
3850.2.a.by.1.4 | 4 | 5.4 | even | 2 |