Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 13x^{4} + 7x^{3} + 31x^{2} - 17x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.52361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.16465 | 0.520848 | 0.260424 | − | 0.965494i | \(-0.416138\pi\) | ||||
0.260424 | + | 0.965494i | \(0.416138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.56356 | −1.97899 | −0.989494 | − | 0.144571i | \(-0.953820\pi\) | ||||
−0.989494 | + | 0.144571i | \(0.953820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.77879 | −0.493347 | −0.246674 | − | 0.969099i | \(-0.579338\pi\) | ||||
−0.246674 | + | 0.969099i | \(0.579338\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.16465 | −0.300712 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.94344 | 1.19896 | 0.599480 | − | 0.800390i | \(-0.295374\pi\) | ||||
0.599480 | + | 0.800390i | \(0.295374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.64398 | −0.377155 | −0.188577 | − | 0.982058i | \(-0.560388\pi\) | ||||
−0.188577 | + | 0.982058i | \(0.560388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.64359 | −0.728717 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.671372 | −0.124671 | −0.0623353 | − | 0.998055i | \(-0.519855\pi\) | ||||
−0.0623353 | + | 0.998055i | \(0.519855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.94344 | −0.528657 | −0.264329 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264329 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.56356 | 1.14257 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.16465 | 0.196862 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.671372 | −0.110373 | −0.0551865 | − | 0.998476i | \(-0.517575\pi\) | ||||
−0.0551865 | + | 0.998476i | \(0.517575\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.77879 | 0.284834 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.91605 | 0.611584 | 0.305792 | − | 0.952098i | \(-0.401079\pi\) | ||||
0.305792 | + | 0.952098i | \(0.401079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3156 | 1.57312 | 0.786560 | − | 0.617514i | \(-0.211860\pi\) | ||||
0.786560 | + | 0.617514i | \(0.211860\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.16465 | 0.173616 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.81177 | −1.28533 | −0.642665 | − | 0.766148i | \(-0.722171\pi\) | ||||
−0.642665 | + | 0.766148i | \(0.722171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.94344 | −0.692220 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.05684 | 0.694611 | 0.347305 | − | 0.937752i | \(-0.387097\pi\) | ||||
0.347305 | + | 0.937752i | \(0.387097\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.64426 | −1.03075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64398 | 0.217751 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.05684 | 0.397967 | 0.198983 | − | 0.980003i | \(-0.436236\pi\) | ||||
0.198983 | + | 0.980003i | \(0.436236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2078 | −1.56305 | −0.781526 | − | 0.623873i | \(-0.785558\pi\) | ||||
−0.781526 | + | 0.623873i | \(0.785558\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.07167 | −0.256959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.98566 | −0.853434 | −0.426717 | − | 0.904385i | \(-0.640330\pi\) | ||||
−0.426717 | + | 0.904385i | \(0.640330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.62041 | 1.14173 | 0.570866 | − | 0.821043i | \(-0.306608\pi\) | ||||
0.570866 | + | 0.821043i | \(0.306608\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.47894 | 1.10943 | 0.554713 | − | 0.832042i | \(-0.312828\pi\) | ||||
0.554713 | + | 0.832042i | \(0.312828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.64359 | 0.420725 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.56356 | −0.747987 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.48029 | 1.06662 | 0.533308 | − | 0.845921i | \(-0.320949\pi\) | ||||
0.533308 | + | 0.845921i | \(0.320949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.614137 | 0.0674103 | 0.0337051 | − | 0.999432i | \(-0.489269\pi\) | ||||
0.0337051 | + | 0.999432i | \(0.489269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.75738 | 0.624476 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.671372 | 0.0719786 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.08356 | −0.114857 | −0.0574285 | − | 0.998350i | \(-0.518290\pi\) | ||||
−0.0574285 | + | 0.998350i | \(0.518290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.77879 | −0.186468 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.94344 | 0.305220 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.91466 | −0.196440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.463829 | 0.0470947 | 0.0235473 | − | 0.999723i | \(-0.492504\pi\) | ||||
0.0235473 | + | 0.999723i | \(0.492504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.56356 | −0.659663 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3669 | 1.13105 | 0.565524 | − | 0.824732i | \(-0.308674\pi\) | ||||
0.565524 | + | 0.824732i | \(0.308674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3486 | 1.51234 | 0.756172 | − | 0.654373i | \(-0.227067\pi\) | ||||
0.756172 | + | 0.654373i | \(0.227067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.16465 | −0.113658 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.2911 | −1.47825 | −0.739123 | − | 0.673570i | \(-0.764760\pi\) | ||||
−0.739123 | + | 0.673570i | \(0.764760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5797 | 1.68383 | 0.841917 | − | 0.539607i | \(-0.181427\pi\) | ||||
0.841917 | + | 0.539607i | \(0.181427\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.671372 | 0.0637238 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.29043 | 0.779898 | 0.389949 | − | 0.920836i | \(-0.372493\pi\) | ||||
0.389949 | + | 0.920836i | \(0.372493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.16465 | −0.108604 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.77879 | −0.164449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.94344 | 0.453164 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.0804 | 2.91640 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.91605 | −0.353098 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0668 | −0.900399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.34413 | 0.474215 | 0.237107 | − | 0.971483i | \(-0.423801\pi\) | ||||
0.237107 | + | 0.971483i | \(0.423801\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.3156 | −0.908241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.46107 | −0.739247 | −0.369623 | − | 0.929182i | \(-0.620513\pi\) | ||||
−0.369623 | + | 0.929182i | \(0.620513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.64398 | −0.142551 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.16465 | −0.100237 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.25879 | −0.449289 | −0.224644 | − | 0.974441i | \(-0.572122\pi\) | ||||
−0.224644 | + | 0.974441i | \(0.572122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.96248 | 0.505731 | 0.252865 | − | 0.967502i | \(-0.418627\pi\) | ||||
0.252865 | + | 0.967502i | \(0.418627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.81177 | 0.742085 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6752 | 0.976328 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.781914 | −0.0649345 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5397 | 0.863446 | 0.431723 | − | 0.902006i | \(-0.357906\pi\) | ||||
0.431723 | + | 0.902006i | \(0.357906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.55080 | 0.695854 | 0.347927 | − | 0.937522i | \(-0.386886\pi\) | ||||
0.347927 | + | 0.937522i | \(0.386886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.94344 | 0.399653 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.42808 | −0.275350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.41258 | 0.431971 | 0.215985 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215985 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.05684 | −0.401034 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.1426 | −1.65602 | −0.828009 | − | 0.560715i | \(-0.810527\pi\) | ||||
−0.828009 | + | 0.560715i | \(0.810527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.64426 | 0.595105 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.35602 | 0.182314 | 0.0911571 | − | 0.995837i | \(-0.470943\pi\) | ||||
0.0911571 | + | 0.995837i | \(0.470943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.83591 | −0.756609 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.64398 | −0.125718 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.85438 | 0.140986 | 0.0704931 | − | 0.997512i | \(-0.477543\pi\) | ||||
0.0704931 | + | 0.997512i | \(0.477543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.64359 | −0.275429 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.05684 | −0.229766 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.40490 | 0.478725 | 0.239362 | − | 0.970930i | \(-0.423062\pi\) | ||||
0.239362 | + | 0.970930i | \(0.423062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9354 | −0.961478 | −0.480739 | − | 0.876864i | \(-0.659632\pi\) | ||||
−0.480739 | + | 0.876864i | \(0.659632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.2078 | 0.902428 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.781914 | −0.0574875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.4466 | −2.37273 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.87403 | −0.135600 | −0.0678001 | − | 0.997699i | \(-0.521598\pi\) | ||||
−0.0678001 | + | 0.997699i | \(0.521598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9062 | 1.79279 | 0.896394 | − | 0.443259i | \(-0.146178\pi\) | ||||
0.896394 | + | 0.443259i | \(0.146178\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.07167 | 0.148355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.41396 | −0.100741 | −0.0503704 | − | 0.998731i | \(-0.516040\pi\) | ||||
−0.0503704 | + | 0.998731i | \(0.516040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.92556 | 0.207388 | 0.103694 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103694 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.98566 | 0.492730 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.671372 | −0.0471211 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.56083 | 0.318542 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.7904 | 0.746385 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.56356 | 0.451854 | 0.225927 | − | 0.974144i | \(-0.427459\pi\) | ||||
0.225927 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.62041 | −0.659179 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0141 | 0.819356 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.94344 | −0.199814 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.47894 | −0.640527 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.79333 | −0.591504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5652 | −0.975358 | −0.487679 | − | 0.873023i | \(-0.662156\pi\) | ||||
−0.487679 | + | 0.873023i | \(0.662156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.64359 | −0.242906 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.8153 | 1.24882 | 0.624408 | − | 0.781099i | \(-0.285340\pi\) | ||||
0.624408 | + | 0.781099i | \(0.285340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.18899 | 0.607226 | 0.303613 | − | 0.952796i | \(-0.401807\pi\) | ||||
0.303613 | + | 0.952796i | \(0.401807\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.56356 | 0.431851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.8388 | −1.95481 | −0.977403 | − | 0.211383i | \(-0.932203\pi\) | ||||
−0.977403 | + | 0.211383i | \(0.932203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2626 | −0.669461 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.48029 | −0.615811 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.87254 | −0.573917 | −0.286958 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286958 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.5203 | 1.90157 | 0.950786 | − | 0.309849i | \(-0.100278\pi\) | ||||
0.950786 | + | 0.309849i | \(0.100278\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.16465 | 0.0744068 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.92429 | 0.186068 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.614137 | −0.0389194 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.7833 | −0.869993 | −0.434996 | − | 0.900432i | \(-0.643250\pi\) | ||||
−0.434996 | + | 0.900432i | \(0.643250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.56356 | 0.412648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.75738 | −0.360541 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2531 | −1.07622 | −0.538109 | − | 0.842875i | \(-0.680861\pi\) | ||||
−0.538109 | + | 0.842875i | \(0.680861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.671372 | −0.0417170 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.671372 | −0.0415569 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7629 | 1.40362 | 0.701811 | − | 0.712363i | \(-0.252375\pi\) | ||||
0.701811 | + | 0.712363i | \(0.252375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.88946 | 0.361787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08356 | 0.0663128 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.80332 | −0.292864 | −0.146432 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146432 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8544 | 0.720103 | 0.360051 | − | 0.932933i | \(-0.382759\pi\) | ||||
0.360051 | + | 0.932933i | \(0.382759\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.77879 | 0.107657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.9149 | 1.44212 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.7654 | 1.42792 | 0.713962 | − | 0.700184i | \(-0.246899\pi\) | ||||
0.713962 | + | 0.700184i | \(0.246899\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.94344 | −0.176219 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5534 | 1.10680 | 0.553402 | − | 0.832914i | \(-0.313329\pi\) | ||||
0.553402 | + | 0.832914i | \(0.313329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.0913 | 1.72930 | 0.864648 | − | 0.502378i | \(-0.167541\pi\) | ||||
0.864648 | + | 0.502378i | \(0.167541\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.91466 | 0.113415 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.91605 | 0.231157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.43759 | 0.437506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.463829 | −0.0271901 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.5422 | −1.37535 | −0.687675 | − | 0.726018i | \(-0.741369\pi\) | ||||
−0.687675 | + | 0.726018i | \(0.741369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.56016 | 0.207280 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.56356 | 0.380857 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.77879 | 0.102870 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3156 | 0.594583 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.3669 | −0.653010 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.2179 | −0.814112 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.08511 | 0.518515 | 0.259257 | − | 0.965808i | \(-0.416522\pi\) | ||||
0.259257 | + | 0.965808i | \(0.416522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3486 | −0.873152 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.98628 | 0.396155 | 0.198078 | − | 0.980186i | \(-0.436530\pi\) | ||||
0.198078 | + | 0.980186i | \(0.436530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.9157 | −1.97355 | −0.986777 | − | 0.162087i | \(-0.948178\pi\) | ||||
−0.986777 | + | 0.162087i | \(0.948178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.16465 | 0.0656207 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.29043 | 0.240974 | 0.120487 | − | 0.992715i | \(-0.461554\pi\) | ||||
0.120487 | + | 0.992715i | \(0.461554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.40659 | 0.246722 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2911 | 0.853466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.12692 | −0.452194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.48117 | 0.359511 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5797 | −0.972162 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.81177 | −0.485809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0319 | 0.991122 | 0.495561 | − | 0.868573i | \(-0.334963\pi\) | ||||
0.495561 | + | 0.868573i | \(0.334963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.671372 | −0.0367910 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.13585 | −0.444509 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9618 | 1.25081 | 0.625404 | − | 0.780301i | \(-0.284934\pi\) | ||||
0.625404 | + | 0.780301i | \(0.284934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.29043 | −0.450274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.3195 | 1.04621 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16465 | 0.0627027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.7196 | −0.575461 | −0.287730 | − | 0.957711i | \(-0.592901\pi\) | ||||
−0.287730 | + | 0.957711i | \(0.592901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6235 | 1.10395 | 0.551976 | − | 0.833860i | \(-0.313874\pi\) | ||||
0.551976 | + | 0.833860i | \(0.313874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.77879 | 0.0949447 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.999325 | −0.0531887 | −0.0265944 | − | 0.999646i | \(-0.508466\pi\) | ||||
−0.0265944 | + | 0.999646i | \(0.508466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2044 | 0.594669 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.94344 | −0.261635 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7172 | −1.04063 | −0.520317 | − | 0.853973i | \(-0.674186\pi\) | ||||
−0.520317 | + | 0.853973i | \(0.674186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2973 | −0.857754 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.0804 | −1.68378 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.0397 | 0.577842 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9023 | −0.882291 | −0.441146 | − | 0.897436i | \(-0.645428\pi\) | ||||
−0.441146 | + | 0.897436i | \(0.645428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.91605 | 0.203861 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.05684 | 0.262538 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.3505 | −1.10548 | −0.552742 | − | 0.833352i | \(-0.686419\pi\) | ||||
−0.552742 | + | 0.833352i | \(0.686419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0668 | 0.519846 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.19423 | 0.0615059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.13552 | −0.0583276 | −0.0291638 | − | 0.999575i | \(-0.509284\pi\) | ||||
−0.0291638 | + | 0.999575i | \(0.509284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.34413 | −0.273788 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.201599 | 0.0103013 | 0.00515063 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515063 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.64426 | −0.389588 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.3156 | 0.524373 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.86167 | −0.398603 | −0.199301 | − | 0.979938i | \(-0.563867\pi\) | ||||
−0.199301 | + | 0.979938i | \(0.563867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94344 | −0.250000 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.46107 | 0.426804 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0412 | 0.555544 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.9506 | −0.750348 | −0.375174 | − | 0.926954i | \(-0.622417\pi\) | ||||
−0.375174 | + | 0.926954i | \(0.622417\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.64398 | 0.0823020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.9652 | 1.09689 | 0.548445 | − | 0.836187i | \(-0.315220\pi\) | ||||
0.548445 | + | 0.836187i | \(0.315220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.23576 | 0.260812 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.16465 | 0.0578720 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.40659 | 0.218427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.4334 | 0.664237 | 0.332118 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332118 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.25879 | 0.259397 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.05684 | 0.150417 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.715255 | 0.0351105 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.96248 | −0.291984 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.6348 | 0.861518 | 0.430759 | − | 0.902467i | \(-0.358246\pi\) | ||||
0.430759 | + | 0.902467i | \(0.358246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4428 | −1.04506 | −0.522528 | − | 0.852622i | \(-0.675011\pi\) | ||||
−0.522528 | + | 0.852622i | \(0.675011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.81177 | −0.428443 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0119 | −0.873703 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2078 | −0.590778 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.6752 | −0.563683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.5274 | −0.699760 | −0.349880 | − | 0.936795i | \(-0.613778\pi\) | ||||
−0.349880 | + | 0.936795i | \(0.613778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.11498 | 0.438038 | 0.219019 | − | 0.975721i | \(-0.429714\pi\) | ||||
0.219019 | + | 0.975721i | \(0.429714\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.781914 | 0.0374899 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.64398 | 0.0786422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.9574 | −1.04797 | −0.523986 | − | 0.851727i | \(-0.675556\pi\) | ||||
−0.523986 | + | 0.851727i | \(0.675556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.69523 | −0.413123 | −0.206561 | − | 0.978434i | \(-0.566227\pi\) | ||||
−0.206561 | + | 0.978434i | \(0.566227\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.26197 | −0.0598231 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.5397 | −0.498511 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.3569 | −1.05509 | −0.527543 | − | 0.849528i | \(-0.676887\pi\) | ||||
−0.527543 | + | 0.849528i | \(0.676887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.7032 | −1.21032 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.55080 | −0.401751 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.07167 | −0.0971213 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.14429 | −0.147084 | −0.0735418 | − | 0.997292i | \(-0.523430\pi\) | ||||
−0.0735418 | + | 0.997292i | \(0.523430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.94344 | −0.230740 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0935 | 1.02900 | 0.514499 | − | 0.857491i | \(-0.327978\pi\) | ||||
0.514499 | + | 0.857491i | \(0.327978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2259 | 0.939976 | 0.469988 | − | 0.882673i | \(-0.344258\pi\) | ||||
0.469988 | + | 0.882673i | \(0.344258\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.42808 | 0.158973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.3656 | 1.86790 | 0.933948 | − | 0.357410i | \(-0.116340\pi\) | ||||
0.933948 | + | 0.357410i | \(0.116340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.98566 | −0.322568 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.41258 | −0.249399 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −67.7073 | −3.11319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.98999 | 0.274839 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.05684 | 0.231537 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.9367 | 1.68768 | 0.843841 | − | 0.536594i | \(-0.180289\pi\) | ||||
0.843841 | + | 0.536594i | \(0.180289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.19423 | 0.0544522 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.540199 | 0.0245292 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0616 | 1.36222 | 0.681111 | − | 0.732180i | \(-0.261497\pi\) | ||||
0.681111 | + | 0.732180i | \(0.261497\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.1426 | 0.956103 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.88374 | 0.0850119 | 0.0425059 | − | 0.999096i | \(-0.486466\pi\) | ||||
0.0425059 | + | 0.999096i | \(0.486466\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.31889 | −0.149475 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.64426 | −0.343584 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.62041 | 0.431534 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0103 | −0.985316 | −0.492658 | − | 0.870223i | \(-0.663975\pi\) | ||||
−0.492658 | + | 0.870223i | \(0.663975\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.35602 | −0.105259 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.7473 | 1.86142 | 0.930711 | − | 0.365757i | \(-0.119190\pi\) | ||||
0.930711 | + | 0.365757i | \(0.119190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2385 | 0.589103 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.83591 | 0.436828 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.2029 | 1.42737 | 0.713684 | − | 0.700468i | \(-0.247025\pi\) | ||||
0.713684 | + | 0.700468i | \(0.247025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.47894 | 0.419323 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.64398 | 0.0725835 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8758 | 0.787701 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 57.8366 | 2.54365 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.85438 | −0.0813984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.3487 | 1.85533 | 0.927665 | − | 0.373415i | \(-0.121813\pi\) | ||||
0.927665 | + | 0.373415i | \(0.121813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1185 | 1.31699 | 0.658494 | − | 0.752586i | \(-0.271194\pi\) | ||||
0.658494 | + | 0.752586i | \(0.271194\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.64359 | 0.159019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.5507 | −0.633839 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.05684 | 0.132656 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.96582 | −0.301723 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.8088 | −0.769942 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.40490 | −0.276392 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.56356 | −0.282713 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6549 | 0.759042 | 0.379521 | − | 0.925183i | \(-0.376089\pi\) | ||||
0.379521 | + | 0.925183i | \(0.376089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.9354 | 0.555110 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.4743 | 0.877021 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.31226 | 0.398164 | 0.199082 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199082 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.2078 | −0.521017 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10372 | 0.0470202 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.48029 | 0.403143 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.781914 | 0.0331904 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.8575 | −0.799018 | −0.399509 | − | 0.916729i | \(-0.630819\pi\) | ||||
−0.399509 | + | 0.916729i | \(0.630819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.3493 | −0.776094 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.4466 | 1.36990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.5942 | −0.488636 | −0.244318 | − | 0.969695i | \(-0.578564\pi\) | ||||
−0.244318 | + | 0.969695i | \(0.578564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.65546 | 0.406208 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8808 | 1.16882 | 0.584412 | − | 0.811457i | \(-0.301325\pi\) | ||||
0.584412 | + | 0.811457i | \(0.301325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1923 | 0.761325 | 0.380663 | − | 0.924714i | \(-0.375696\pi\) | ||||
0.380663 | + | 0.924714i | \(0.375696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.87403 | 0.0782888 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.64359 | 0.151948 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.0990 | −1.21141 | −0.605704 | − | 0.795690i | \(-0.707108\pi\) | ||||
−0.605704 | + | 0.795690i | \(0.707108\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.9062 | −1.03507 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.614137 | 0.0254787 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.1909 | −1.37463 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.07167 | −0.0856529 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1911 | −0.420632 | −0.210316 | − | 0.977633i | \(-0.567449\pi\) | ||||
−0.210316 | + | 0.977633i | \(0.567449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.83896 | 0.199386 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.41396 | 0.0581627 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.4629 | 0.429660 | 0.214830 | − | 0.976651i | \(-0.431080\pi\) | ||||
0.214830 | + | 0.976651i | \(0.431080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.75738 | 0.236030 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.92556 | −0.119735 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0401 | 0.696240 | 0.348120 | − | 0.937450i | \(-0.386820\pi\) | ||||
0.348120 | + | 0.937450i | \(0.386820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0270 | 0.980082 | 0.490041 | − | 0.871699i | \(-0.336982\pi\) | ||||
0.490041 | + | 0.871699i | \(0.336982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.98566 | −0.284478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 37.3624 | 1.51900 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2171 | 0.698819 | 0.349409 | − | 0.936970i | \(-0.386382\pi\) | ||||
0.349409 | + | 0.936970i | \(0.386382\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.671372 | 0.0272054 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6743 | 0.634113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.65928 | −0.147797 | −0.0738985 | − | 0.997266i | \(-0.523544\pi\) | ||||
−0.0738985 | + | 0.997266i | \(0.523544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.56083 | −0.183910 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5059 | 0.624245 | 0.312123 | − | 0.950042i | \(-0.398960\pi\) | ||||
0.312123 | + | 0.950042i | \(0.398960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.4731 | 1.10424 | 0.552119 | − | 0.833765i | \(-0.313819\pi\) | ||||
0.552119 | + | 0.833765i | \(0.313819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.08356 | −0.0434119 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.49367 | 0.259747 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.7904 | −0.430926 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.31889 | −0.132333 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1579 | −0.643237 | −0.321618 | − | 0.946869i | \(-0.604227\pi\) | ||||
−0.321618 | + | 0.946869i | \(0.604227\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.56356 | −0.260878 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.22405 | 0.246994 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.77879 | −0.0704782 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.62041 | 0.380577 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.1536 | −0.598533 | −0.299266 | − | 0.954170i | \(-0.596742\pi\) | ||||
−0.299266 | + | 0.954170i | \(0.596742\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0551 | 0.633150 | 0.316575 | − | 0.948567i | \(-0.397467\pi\) | ||||
0.316575 | + | 0.948567i | \(0.397467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0141 | −0.473055 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.5239 | 1.39659 | 0.698293 | − | 0.715812i | \(-0.253943\pi\) | ||||
0.698293 | + | 0.715812i | \(0.253943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0638 | −0.787572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.94344 | 0.115362 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.5511 | 0.608560 | 0.304280 | − | 0.952583i | \(-0.401584\pi\) | ||||
0.304280 | + | 0.952583i | \(0.401584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.85419 | −0.385035 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.47894 | 0.369809 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.5364 | −1.30639 | −0.653197 | − | 0.757188i | \(-0.726573\pi\) | ||||
−0.653197 | + | 0.757188i | \(0.726573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.6772 | 1.19321 | 0.596603 | − | 0.802536i | \(-0.296517\pi\) | ||||
0.596603 | + | 0.802536i | \(0.296517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.79333 | 0.341505 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.91466 | −0.0742475 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.671372 | 0.0259956 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.5652 | 0.563123 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 80.1268 | 3.09326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.11360 | −0.0814734 | −0.0407367 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407367 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.64359 | 0.140242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.0481 | −1.42388 | −0.711938 | − | 0.702242i | \(-0.752182\pi\) | ||||
−0.711938 | + | 0.702242i | \(0.752182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.463829 | 0.0178001 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.8153 | −0.721004 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.12692 | −0.157912 | −0.0789561 | − | 0.996878i | \(-0.525159\pi\) | ||||
−0.0789561 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.12466 | −0.234011 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.18899 | −0.350582 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.99505 | −0.342684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4364 | 0.853520 | 0.426760 | − | 0.904365i | \(-0.359655\pi\) | ||||
0.426760 | + | 0.904365i | \(0.359655\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.56356 | −0.249329 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.94420 | 0.263409 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3587 | 0.733265 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.8388 | 1.12861 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.2272 | −1.78375 | −0.891874 | − | 0.452284i | \(-0.850609\pi\) | ||||
−0.891874 | + | 0.452284i | \(0.850609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10372 | 0.0416277 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.2626 | 0.386514 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3669 | 0.427496 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.595776 | 0.0223748 | 0.0111874 | − | 0.999937i | \(-0.496439\pi\) | ||||
0.0111874 | + | 0.999937i | \(0.496439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.48029 | 0.355538 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.94344 | 0.110233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.5975 | 0.508519 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.87254 | 0.331351 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.2121 | −0.828370 | −0.414185 | − | 0.910193i | \(-0.635933\pi\) | ||||
−0.414185 | + | 0.910193i | \(0.635933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3486 | 0.571612 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.5203 | −1.09787 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44620 | 0.0908497 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6161 | 0.801696 | 0.400848 | − | 0.916144i | \(-0.368715\pi\) | ||||
0.400848 | + | 0.916144i | \(0.368715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.9947 | 1.88611 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.8306 | −1.06488 | −0.532442 | − | 0.846467i | \(-0.678725\pi\) | ||||
−0.532442 | + | 0.846467i | \(0.678725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.16465 | −0.0429588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.8508 | 1.68894 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.5595 | 1.93343 | 0.966716 | − | 0.255853i | \(-0.0823562\pi\) | ||||
0.966716 | + | 0.255853i | \(0.0823562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.92429 | −0.107427 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.00834 | −0.183738 | −0.0918691 | − | 0.995771i | \(-0.529284\pi\) | ||||
−0.0918691 | + | 0.995771i | \(0.529284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2751 | 0.449724 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.614137 | 0.0224701 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.2911 | −0.558725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.62343 | 0.0592399 | 0.0296199 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296199 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.7833 | 0.502291 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.95870 | 0.362434 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8414 | 0.721147 | 0.360574 | − | 0.932731i | \(-0.382581\pi\) | ||||
0.360574 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.56356 | −0.238242 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9904 | −0.942152 | −0.471076 | − | 0.882093i | \(-0.656134\pi\) | ||||
−0.471076 | + | 0.882093i | \(0.656134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.5797 | 0.636429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.75738 | 0.208159 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.43748 | −0.196336 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.8662 | 1.83428 | 0.917142 | − | 0.398561i | \(-0.130490\pi\) | ||||
0.917142 | + | 0.398561i | \(0.130490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.2531 | 0.621355 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.0843 | −1.47770 | −0.738850 | − | 0.673870i | \(-0.764631\pi\) | ||||
−0.738850 | + | 0.673870i | \(0.764631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.7247 | 0.385242 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.671372 | 0.0240853 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.43791 | −0.230662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.1441 | −2.25947 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.671372 | 0.0239929 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.30377 | 0.224991 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.53400 | −0.268558 | −0.134279 | − | 0.990944i | \(-0.542872\pi\) | ||||
−0.134279 | + | 0.990944i | \(0.542872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.7629 | −0.810382 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.29043 | 0.294774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.7151 | 0.771127 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.88946 | −0.208878 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.8202 | 0.560381 | 0.280190 | − | 0.959944i | \(-0.409602\pi\) | ||||
0.280190 | + | 0.959944i | \(0.409602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.5605 | −1.54106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.08356 | −0.0382857 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62.2156 | −2.19554 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.16465 | −0.0410486 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.80332 | 0.169085 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.7335 | −0.623478 | −0.311739 | − | 0.950168i | \(-0.600911\pi\) | ||||
−0.311739 | + | 0.950168i | \(0.600911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.01688 | 0.281511 | 0.140755 | − | 0.990044i | \(-0.455047\pi\) | ||||
0.140755 | + | 0.990044i | \(0.455047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8544 | −0.415751 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.6238 | −0.862534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.9587 | −0.593310 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.77879 | −0.0621559 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.9584 | −0.731454 | −0.365727 | − | 0.930722i | \(-0.619180\pi\) | ||||
−0.365727 | + | 0.930722i | \(0.619180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.0419 | 1.57006 | 0.785032 | − | 0.619456i | \(-0.212647\pi\) | ||||
0.785032 | + | 0.619456i | \(0.212647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.9149 | −0.832611 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.1066 | 0.420987 | 0.210494 | − | 0.977595i | \(-0.432493\pi\) | ||||
0.210494 | + | 0.977595i | \(0.432493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.8045 | −0.965688 | −0.482844 | − | 0.875706i | \(-0.660396\pi\) | ||||
−0.482844 | + | 0.875706i | \(0.660396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.7654 | −0.824413 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.94344 | 0.171280 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.74394 | 0.0949580 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.94344 | 0.101740 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.3694 | 0.806802 | 0.403401 | − | 0.915023i | \(-0.367828\pi\) | ||||
0.403401 | + | 0.915023i | \(0.367828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5493 | −0.984457 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.5534 | −0.639014 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4554 | −0.394078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.0804 | 1.10229 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.0913 | −0.998410 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.671372 | 0.0230143 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7158 | −0.572339 | −0.286170 | − | 0.958179i | \(-0.592382\pi\) | ||||
−0.286170 | + | 0.958179i | \(0.592382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.91466 | −0.0654801 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.2207 | −0.622408 | −0.311204 | − | 0.950343i | \(-0.600732\pi\) | ||||
−0.311204 | + | 0.950343i | \(0.600732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.83298 | 0.335497 | 0.167748 | − | 0.985830i | \(-0.446350\pi\) | ||||
0.167748 | + | 0.985830i | \(0.446350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.91605 | −0.133459 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.648383 | 0.0220712 | 0.0110356 | − | 0.999939i | \(-0.496487\pi\) | ||||
0.0110356 | + | 0.999939i | \(0.496487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.15971 | 0.0734324 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.43759 | −0.252594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62.2245 | −2.11082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4260 | 0.421039 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.463829 | 0.0156982 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.0668 | −0.340319 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.2854 | 1.73179 | 0.865893 | − | 0.500229i | \(-0.166751\pi\) | ||||
0.865893 | + | 0.500229i | \(0.166751\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.5422 | 0.794059 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.9911 | −0.538755 | −0.269378 | − | 0.963035i | \(-0.586818\pi\) | ||||
−0.269378 | + | 0.963035i | \(0.586818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.8120 | 0.902294 | 0.451147 | − | 0.892450i | \(-0.351015\pi\) | ||||
0.451147 | + | 0.892450i | \(0.351015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.56016 | −0.119673 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.6201 | 1.76681 | 0.883404 | − | 0.468612i | \(-0.155246\pi\) | ||||
0.883404 | + | 0.468612i | \(0.155246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.34413 | 0.179236 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.56356 | −0.219888 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.4864 | 0.484768 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.45947 | 0.249343 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.77879 | −0.0593920 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.97614 | 0.0659081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.9982 | 0.832811 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3156 | −0.343283 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0652 | −0.500784 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3547 | 0.377028 | 0.188514 | − | 0.982071i | \(-0.439633\pi\) | ||||
0.188514 | + | 0.982071i | \(0.439633\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.3669 | 0.377016 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.2394 | −1.86329 | −0.931646 | − | 0.363366i | \(-0.881627\pi\) | ||||
−0.931646 | + | 0.363366i | \(0.881627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.03093 | −0.133404 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.2179 | 0.470028 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.46107 | −0.279409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.2603 | −1.49300 | −0.746500 | − | 0.665385i | \(-0.768267\pi\) | ||||
−0.746500 | + | 0.665385i | \(0.768267\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.08511 | −0.299365 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.1127 | −0.563270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.44620 | 0.0804307 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3486 | 0.504115 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.0431 | −1.64186 | −0.820930 | − | 0.571028i | \(-0.806545\pi\) | ||||
−0.820930 | + | 0.571028i | \(0.806545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.64398 | −0.0538793 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.98628 | −0.228720 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.7889 | −1.23583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4113 | 0.993493 | 0.496746 | − | 0.867896i | \(-0.334528\pi\) | ||||
0.496746 | + | 0.867896i | \(0.334528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.9157 | 1.13943 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.8445 | −0.907706 | −0.453853 | − | 0.891077i | \(-0.649951\pi\) | ||||
−0.453853 | + | 0.891077i | \(0.649951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.91605 | −0.127524 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.16465 | −0.0378861 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.96761 | −0.161426 | −0.0807129 | − | 0.996737i | \(-0.525720\pi\) | ||||
−0.0807129 | + | 0.996737i | \(0.525720\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8610 | −0.547332 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.29043 | −0.139127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.1476 | −1.20333 | −0.601664 | − | 0.798749i | \(-0.705495\pi\) | ||||
−0.601664 | + | 0.798749i | \(0.705495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.18259 | −0.0706270 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.40659 | −0.142445 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.25879 | −0.169815 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.3362 | −0.720521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.2911 | −0.492749 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.0070 | 0.933769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.9579 | −0.995538 | −0.497769 | − | 0.867310i | \(-0.665847\pi\) | ||||
−0.497769 | + | 0.867310i | \(0.665847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.12692 | 0.261074 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.6060 | −0.950103 | −0.475052 | − | 0.879958i | \(-0.657571\pi\) | ||||
−0.475052 | + | 0.879958i | \(0.657571\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.96248 | 0.191148 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.48117 | −0.207564 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.2597 | −0.616172 | −0.308086 | − | 0.951358i | \(-0.599688\pi\) | ||||
−0.308086 | + | 0.951358i | \(0.599688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.11201 | 0.227301 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.5797 | 0.561278 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.8490 | 1.52615 | 0.763073 | − | 0.646312i | \(-0.223690\pi\) | ||||
0.763073 | + | 0.646312i | \(0.223690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.64678 | −0.0524706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.81177 | 0.280482 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.3156 | −0.328018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.6629 | −0.878741 | −0.439371 | − | 0.898306i | \(-0.644798\pi\) | ||||
−0.439371 | + | 0.898306i | \(0.644798\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.0319 | −0.572224 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.40726 | 0.108017 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.7434 | −0.371917 | −0.185959 | − | 0.982558i | \(-0.559539\pi\) | ||||
−0.185959 | + | 0.982558i | \(0.559539\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.671372 | 0.0212413 |
(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 | 7728.2.a.cg.1.4 | 6 | ||
4.3 | odd | 2 | 3864.2.a.x.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.x.1.4 | ✓ | 6 | 4.3 | odd | 2 | ||
7728.2.a.cg.1.4 | 6 | 1.1 | even | 1 | trivial |