Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.521397.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 9x^{3} - 3x^{2} + 18x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.83957\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 | ||||||||
\(3\) | −1.83957 | −1.06208 | −0.531038 | − | 0.847348i | \(-0.678198\pi\) | ||||
−0.531038 | + | 0.847348i | \(0.678198\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.97272 | 1.50155 | 0.750774 | − | 0.660559i | \(-0.229681\pi\) | ||||
0.750774 | + | 0.660559i | \(0.229681\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.384010 | 0.128003 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.10339 | 0.634196 | 0.317098 | − | 0.948393i | \(-0.397292\pi\) | ||||
0.317098 | + | 0.948393i | \(0.397292\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.35673 | −1.48569 | −0.742845 | − | 0.669463i | \(-0.766524\pi\) | ||||
−0.742845 | + | 0.669463i | \(0.766524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.29567 | −0.314246 | −0.157123 | − | 0.987579i | \(-0.550222\pi\) | ||||
−0.157123 | + | 0.987579i | \(0.550222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.10339 | 0.482551 | 0.241276 | − | 0.970457i | \(-0.422434\pi\) | ||||
0.241276 | + | 0.970457i | \(0.422434\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.30809 | −1.59476 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.81229 | 0.926126 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.03130 | 1.11998 | 0.559992 | − | 0.828498i | \(-0.310804\pi\) | ||||
0.559992 | + | 0.828498i | \(0.310804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.32489 | −1.49519 | −0.747597 | − | 0.664153i | \(-0.768793\pi\) | ||||
−0.747597 | + | 0.664153i | \(0.768793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.86933 | −0.673564 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.10131 | −0.838650 | −0.419325 | − | 0.907836i | \(-0.637733\pi\) | ||||
−0.419325 | + | 0.907836i | \(0.637733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.85407 | 1.57791 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.33994 | −1.30248 | −0.651240 | − | 0.758872i | \(-0.725751\pi\) | ||||
−0.651240 | + | 0.758872i | \(0.725751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.78253 | −1.18682 | −0.593412 | − | 0.804899i | \(-0.702220\pi\) | ||||
−0.593412 | + | 0.804899i | \(0.702220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3964 | −1.66234 | −0.831171 | − | 0.556018i | \(-0.812329\pi\) | ||||
−0.831171 | + | 0.556018i | \(0.812329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.78253 | 1.25465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.38347 | 0.333752 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.573664 | 0.0787988 | 0.0393994 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393994 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.86933 | −0.512505 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.17951 | −1.19507 | −0.597535 | − | 0.801843i | \(-0.703853\pi\) | ||||
−0.597535 | + | 0.801843i | \(0.703853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5149 | 1.73040 | 0.865201 | − | 0.501425i | \(-0.167191\pi\) | ||||
0.865201 | + | 0.501425i | \(0.167191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.52557 | 0.192203 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8314 | 1.93411 | 0.967055 | − | 0.254569i | \(-0.0819337\pi\) | ||||
0.967055 | + | 0.254569i | \(0.0819337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.83957 | −0.221458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9449 | 1.77363 | 0.886817 | − | 0.462121i | \(-0.152911\pi\) | ||||
0.886817 | + | 0.462121i | \(0.152911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.36459 | −0.979002 | −0.489501 | − | 0.872003i | \(-0.662821\pi\) | ||||
−0.489501 | + | 0.872003i | \(0.662821\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.35619 | 0.952276 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.41149 | −1.05887 | −0.529437 | − | 0.848349i | \(-0.677597\pi\) | ||||
−0.529437 | + | 0.848349i | \(0.677597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0046 | −1.11162 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.51206 | −0.165970 | −0.0829849 | − | 0.996551i | \(-0.526445\pi\) | ||||
−0.0829849 | + | 0.996551i | \(0.526445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0950 | −1.18951 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5903 | 1.12256 | 0.561282 | − | 0.827624i | \(-0.310308\pi\) | ||||
0.561282 | + | 0.827624i | \(0.310308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.2808 | −2.23084 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.3142 | 1.58801 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.337451 | 0.0342630 | 0.0171315 | − | 0.999853i | \(-0.494547\pi\) | ||||
0.0171315 | + | 0.999853i | \(0.494547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.807724 | 0.0811793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.19119 | −0.616047 | −0.308023 | − | 0.951379i | \(-0.599667\pi\) | ||||
−0.308023 | + | 0.951379i | \(0.599667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6267 | −1.24414 | −0.622071 | − | 0.782961i | \(-0.713708\pi\) | ||||
−0.622071 | + | 0.782961i | \(0.713708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7940 | −1.23684 | −0.618419 | − | 0.785848i | \(-0.712227\pi\) | ||||
−0.618419 | + | 0.785848i | \(0.712227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.3165 | 1.37127 | 0.685635 | − | 0.727945i | \(-0.259524\pi\) | ||||
0.685635 | + | 0.727945i | \(0.259524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.38421 | 0.890710 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.59463 | −0.432226 | −0.216113 | − | 0.976368i | \(-0.569338\pi\) | ||||
−0.216113 | + | 0.976368i | \(0.569338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.05704 | −0.190173 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.14733 | −0.471855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.57574 | −0.597795 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.3419 | 1.38333 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6623 | −1.12360 | −0.561801 | − | 0.827273i | \(-0.689891\pi\) | ||||
−0.561801 | + | 0.827273i | \(0.689891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.3165 | 1.26050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.68370 | 0.409217 | 0.204609 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204609 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.35619 | 0.724574 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.468120 | 0.0399942 | 0.0199971 | − | 0.999800i | \(-0.493634\pi\) | ||||
0.0199971 | + | 0.999800i | \(0.493634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.739205 | 0.0626985 | 0.0313493 | − | 0.999508i | \(-0.490020\pi\) | ||||
0.0313493 | + | 0.999508i | \(0.490020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.9645 | 1.76553 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.2673 | −0.942220 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.1561 | −1.33253 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5903 | 1.19528 | 0.597640 | − | 0.801765i | \(-0.296105\pi\) | ||||
0.597640 | + | 0.801765i | \(0.296105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6885 | 1.76498 | 0.882491 | − | 0.470329i | \(-0.155865\pi\) | ||||
0.882491 | + | 0.470329i | \(0.155865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.497550 | −0.0402245 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.71253 | −0.615527 | −0.307763 | − | 0.951463i | \(-0.599580\pi\) | ||||
−0.307763 | + | 0.951463i | \(0.599580\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.05529 | −0.0836902 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.97272 | 0.313094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.69177 | 0.367488 | 0.183744 | − | 0.982974i | \(-0.441178\pi\) | ||||
0.183744 | + | 0.982974i | \(0.441178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.6738 | −0.903343 | −0.451671 | − | 0.892184i | \(-0.649172\pi\) | ||||
−0.451671 | + | 0.892184i | \(0.649172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.6946 | 1.20728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.807724 | 0.0617682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.31723 | 0.632347 | 0.316174 | − | 0.948701i | \(-0.397602\pi\) | ||||
0.316174 | + | 0.948701i | \(0.397602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.8863 | 1.26925 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.07517 | −0.304592 | −0.152296 | − | 0.988335i | \(-0.548667\pi\) | ||||
−0.152296 | + | 0.988335i | \(0.548667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.52349 | 0.187569 | 0.0937846 | − | 0.995593i | \(-0.470103\pi\) | ||||
0.0937846 | + | 0.995593i | \(0.470103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.8615 | −1.83782 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.72530 | −0.199293 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.1179 | 1.39062 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.9380 | −1.73210 | −0.866048 | − | 0.499961i | \(-0.833348\pi\) | ||||
−0.866048 | + | 0.499961i | \(0.833348\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7733 | −1.35133 | −0.675667 | − | 0.737207i | \(-0.736144\pi\) | ||||
−0.675667 | + | 0.737207i | \(0.736144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.9052 | −1.13320 | −0.566600 | − | 0.823993i | \(-0.691741\pi\) | ||||
−0.566600 | + | 0.823993i | \(0.691741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.87544 | 0.700052 | 0.350026 | − | 0.936740i | \(-0.386173\pi\) | ||||
0.350026 | + | 0.936740i | \(0.386173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.1229 | −2.05417 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.9607 | 1.68171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.384010 | 0.0266906 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.42426 | 0.306032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.06980 | −0.486705 | −0.243353 | − | 0.969938i | \(-0.578247\pi\) | ||||
−0.243353 | + | 0.969938i | \(0.578247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.4922 | −1.88373 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.0725 | −2.24511 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.3872 | 1.03977 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.94055 | 0.466872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.58817 | −0.575106 | −0.287553 | − | 0.957765i | \(-0.592842\pi\) | ||||
−0.287553 | + | 0.957765i | \(0.592842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.2068 | −0.942937 | −0.471469 | − | 0.881883i | \(-0.656276\pi\) | ||||
−0.471469 | + | 0.881883i | \(0.656276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.49721 | −0.495429 | −0.247715 | − | 0.968833i | \(-0.579680\pi\) | ||||
−0.247715 | + | 0.968833i | \(0.579680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.3718 | −1.01139 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9301 | 1.10912 | 0.554562 | − | 0.832142i | \(-0.312886\pi\) | ||||
0.554562 | + | 0.832142i | \(0.312886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.3131 | 1.12460 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7850 | −1.15042 | −0.575208 | − | 0.818007i | \(-0.695079\pi\) | ||||
−0.575208 | + | 0.818007i | \(0.695079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.55263 | −0.615339 | −0.307669 | − | 0.951493i | \(-0.599549\pi\) | ||||
−0.307669 | + | 0.951493i | \(0.599549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.96721 | 0.254497 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.2673 | −0.716922 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.78153 | 0.176272 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2075 | −0.833651 | −0.416826 | − | 0.908986i | \(-0.636857\pi\) | ||||
−0.416826 | + | 0.908986i | \(0.636857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.10339 | 0.132239 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.41506 | 0.213025 | 0.106513 | − | 0.994311i | \(-0.466032\pi\) | ||||
0.106513 | + | 0.994311i | \(0.466032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.2661 | −1.25927 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.31608 | 0.143362 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.6589 | −1.15056 | −0.575279 | − | 0.817957i | \(-0.695106\pi\) | ||||
−0.575279 | + | 0.817957i | \(0.695106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.4815 | −1.19225 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.2224 | −1.47687 | −0.738434 | − | 0.674326i | \(-0.764434\pi\) | ||||
−0.738434 | + | 0.674326i | \(0.764434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1201 | −0.614749 | −0.307375 | − | 0.951589i | \(-0.599450\pi\) | ||||
−0.307375 | + | 0.951589i | \(0.599450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.1475 | 2.36932 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5298 | 1.41377 | 0.706884 | − | 0.707329i | \(-0.250100\pi\) | ||||
0.706884 | + | 0.707329i | \(0.250100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.19684 | −0.191390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77314 | 0.105776 | 0.0528882 | − | 0.998600i | \(-0.483157\pi\) | ||||
0.0528882 | + | 0.998600i | \(0.483157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.96641 | −0.354666 | −0.177333 | − | 0.984151i | \(-0.556747\pi\) | ||||
−0.177333 | + | 0.984151i | \(0.556747\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.1323 | −1.95574 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3212 | −0.901250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.620765 | −0.0363899 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2404 | −0.715090 | −0.357545 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357545 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.1221 | 0.587346 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.35673 | −0.309788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.9178 | −1.78207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.3891 | 0.654288 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.82713 | 0.503791 | 0.251896 | − | 0.967754i | \(-0.418946\pi\) | ||||
0.251896 | + | 0.967754i | \(0.418946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.2276 | 1.32137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9202 | −0.789345 | −0.394672 | − | 0.918822i | \(-0.629142\pi\) | ||||
−0.394672 | + | 0.918822i | \(0.629142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5030 | −1.32847 | −0.664235 | − | 0.747523i | \(-0.731243\pi\) | ||||
−0.664235 | + | 0.747523i | \(0.731243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3279 | −0.748570 | −0.374285 | − | 0.927314i | \(-0.622112\pi\) | ||||
−0.374285 | + | 0.927314i | \(0.622112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.6862 | 0.710290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.5354 | 1.31362 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.72530 | −0.151640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.3362 | −1.45639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −45.2749 | −2.49609 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.270137 | −0.0148481 | −0.00742404 | − | 0.999972i | \(-0.502363\pi\) | ||||
−0.00742404 | + | 0.999972i | \(0.502363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.95896 | −0.107350 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0205 | 1.09058 | 0.545292 | − | 0.838246i | \(-0.316419\pi\) | ||||
0.545292 | + | 0.838246i | \(0.316419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.45213 | 0.459057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5105 | −0.948247 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.08149 | 0.382364 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1156 | 0.811448 | 0.405724 | − | 0.913996i | \(-0.367019\pi\) | ||||
0.405724 | + | 0.913996i | \(0.367019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5673 | −0.779771 | −0.389886 | − | 0.920863i | \(-0.627485\pi\) | ||||
−0.389886 | + | 0.920863i | \(0.627485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.7782 | −1.37594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.5376 | −0.986656 | −0.493328 | − | 0.869843i | \(-0.664220\pi\) | ||||
−0.493328 | + | 0.869843i | \(0.664220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.46886 | 0.501145 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.1834 | −1.27635 | −0.638175 | − | 0.769891i | \(-0.720311\pi\) | ||||
−0.638175 | + | 0.769891i | \(0.720311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5757 | −0.767144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.0965 | 0.634903 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.79604 | −0.302551 | −0.151275 | − | 0.988492i | \(-0.548338\pi\) | ||||
−0.151275 | + | 0.988492i | \(0.548338\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.20262 | −0.166722 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.27901 | 0.118320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5753 | 1.32424 | 0.662119 | − | 0.749399i | \(-0.269657\pi\) | ||||
0.662119 | + | 0.749399i | \(0.269657\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −32.3081 | −1.66395 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.82223 | −0.504534 | −0.252267 | − | 0.967658i | \(-0.581176\pi\) | ||||
−0.252267 | + | 0.967658i | \(0.581176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.2932 | 1.19335 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.9797 | 1.73628 | 0.868141 | − | 0.496319i | \(-0.165315\pi\) | ||||
0.868141 | + | 0.496319i | \(0.165315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.98857 | −0.151918 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.6744 | −1.25104 | −0.625521 | − | 0.780207i | \(-0.715114\pi\) | ||||
−0.625521 | + | 0.780207i | \(0.715114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.29567 | −0.0655247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.61599 | −0.434619 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.17340 | 0.159268 | 0.0796342 | − | 0.996824i | \(-0.474625\pi\) | ||||
0.0796342 | + | 0.996824i | \(0.474625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.3718 | −0.769552 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.07720 | 0.203606 | 0.101803 | − | 0.994805i | \(-0.467539\pi\) | ||||
0.101803 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.5942 | 2.22140 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.7301 | −0.531869 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5426 | 0.916871 | 0.458435 | − | 0.888728i | \(-0.348410\pi\) | ||||
0.458435 | + | 0.888728i | \(0.348410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.861138 | −0.0424768 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.4676 | −1.79445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.35982 | −0.0665906 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.22587 | −0.157594 | −0.0787970 | − | 0.996891i | \(-0.525108\pi\) | ||||
−0.0787970 | + | 0.996891i | \(0.525108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0595 | 0.880167 | 0.440084 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.37635 | −0.212785 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 53.6909 | 2.59828 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.7270 | 1.00071 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.62458 | −0.463600 | −0.231800 | − | 0.972763i | \(-0.574461\pi\) | ||||
−0.231800 | + | 0.972763i | \(0.574461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83990 | 0.0884200 | 0.0442100 | − | 0.999022i | \(-0.485923\pi\) | ||||
0.0442100 | + | 0.999022i | \(0.485923\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.10339 | 0.100619 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.73907 | 0.321638 | 0.160819 | − | 0.986984i | \(-0.448586\pi\) | ||||
0.160819 | + | 0.986984i | \(0.448586\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.37258 | 0.160599 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.4099 | −0.542103 | −0.271051 | − | 0.962565i | \(-0.587371\pi\) | ||||
−0.271051 | + | 0.962565i | \(0.587371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.8398 | −1.26948 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8081 | 1.31235 | 0.656173 | − | 0.754610i | \(-0.272174\pi\) | ||||
0.656173 | + | 0.754610i | \(0.272174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.5422 | −0.826028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.8974 | −1.87454 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.6835 | −1.24820 | −0.624102 | − | 0.781343i | \(-0.714535\pi\) | ||||
−0.624102 | + | 0.781343i | \(0.714535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.23513 | −0.291031 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0398 | −1.07307 | −0.536534 | − | 0.843879i | \(-0.680267\pi\) | ||||
−0.536534 | + | 0.843879i | \(0.680267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3998 | 1.08748 | 0.543740 | − | 0.839253i | \(-0.317008\pi\) | ||||
0.543740 | + | 0.839253i | \(0.317008\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.29380 | −0.198693 | −0.0993467 | − | 0.995053i | \(-0.531675\pi\) | ||||
−0.0993467 | + | 0.995053i | \(0.531675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62.8936 | 2.90416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1877 | 0.653735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.3697 | −0.752680 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.220293 | 0.0100865 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.6694 | −1.21856 | −0.609278 | − | 0.792957i | \(-0.708541\pi\) | ||||
−0.609278 | + | 0.792957i | \(0.708541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3264 | 1.24597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.30809 | −0.332530 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.67114 | 0.392927 | 0.196463 | − | 0.980511i | \(-0.437054\pi\) | ||||
0.196463 | + | 0.980511i | \(0.437054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.63083 | −0.390300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0900 | −1.13229 | −0.566147 | − | 0.824304i | \(-0.691566\pi\) | ||||
−0.566147 | + | 0.824304i | \(0.691566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.81456 | −0.351950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 59.3720 | 2.66320 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.9323 | −1.56379 | −0.781893 | − | 0.623412i | \(-0.785746\pi\) | ||||
−0.781893 | + | 0.623412i | \(0.785746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4747 | 0.959418 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.7782 | −1.14939 | −0.574695 | − | 0.818367i | \(-0.694879\pi\) | ||||
−0.574695 | + | 0.818367i | \(0.694879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.8713 | −1.28222 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.21667 | 0.186900 | 0.0934502 | − | 0.995624i | \(-0.470210\pi\) | ||||
0.0934502 | + | 0.995624i | \(0.470210\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.2302 | −1.47002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.1221 | 0.446903 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.9712 | −1.05425 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.3001 | −0.671600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3112 | 1.28415 | 0.642073 | − | 0.766644i | \(-0.278075\pi\) | ||||
0.642073 | + | 0.766644i | \(0.278075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1549 | 1.36231 | 0.681154 | − | 0.732140i | \(-0.261478\pi\) | ||||
0.681154 | + | 0.732140i | \(0.261478\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7863 | 0.469858 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.52502 | −0.152973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.6748 | 1.93508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.49655 | 0.323500 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.4731 | 0.795692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7393 | 0.676683 | 0.338342 | − | 0.941023i | \(-0.390134\pi\) | ||||
0.338342 | + | 0.941023i | \(0.390134\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.64212 | −0.199213 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.2935 | 1.68007 | 0.840034 | − | 0.542534i | \(-0.182535\pi\) | ||||
0.840034 | + | 0.542534i | \(0.182535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.18985 | 0.221497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6862 | 0.540450 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.3892 | −1.58995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.1005 | −1.61437 | −0.807186 | − | 0.590297i | \(-0.799010\pi\) | ||||
−0.807186 | + | 0.590297i | \(0.799010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.6889 | 1.76325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.01337 | 0.211665 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.6868 | −1.37758 | −0.688792 | − | 0.724959i | \(-0.741859\pi\) | ||||
−0.688792 | + | 0.724959i | \(0.741859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −39.7454 | −1.66915 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0256 | 0.881438 | 0.440719 | − | 0.897645i | \(-0.354724\pi\) | ||||
0.440719 | + | 0.897645i | \(0.354724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.43876 | −0.311303 | −0.155651 | − | 0.987812i | \(-0.549748\pi\) | ||||
−0.155651 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.0357 | 1.83962 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4148 | 1.26618 | 0.633091 | − | 0.774077i | \(-0.281786\pi\) | ||||
0.633091 | + | 0.774077i | \(0.281786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.5348 | 1.43522 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00698 | −0.249212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.20664 | 0.0499739 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.7544 | 1.39319 | 0.696596 | − | 0.717464i | \(-0.254697\pi\) | ||||
0.696596 | + | 0.717464i | \(0.254697\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5105 | −0.721508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.2587 | 1.20354 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.3980 | −1.12510 | −0.562550 | − | 0.826763i | \(-0.690180\pi\) | ||||
−0.562550 | + | 0.826763i | \(0.690180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1666 | −0.743507 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.2927 | 1.52374 | 0.761869 | − | 0.647731i | \(-0.224282\pi\) | ||||
0.761869 | + | 0.647731i | \(0.224282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.26039 | −0.0922032 | −0.0461016 | − | 0.998937i | \(-0.514680\pi\) | ||||
−0.0461016 | + | 0.998937i | \(0.514680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.07941 | 0.247573 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4782 | 0.952951 | 0.476476 | − | 0.879188i | \(-0.341914\pi\) | ||||
0.476476 | + | 0.879188i | \(0.341914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −44.0773 | −1.78610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.0477 | 2.46972 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.0418 | 1.01143 | 0.505714 | − | 0.862701i | \(-0.331229\pi\) | ||||
0.505714 | + | 0.862701i | \(0.331229\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2705 | 0.735541 | 0.367771 | − | 0.929916i | \(-0.380121\pi\) | ||||
0.367771 | + | 0.929916i | \(0.380121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.17743 | 0.288485 | 0.144243 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144243 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.81229 | 0.193111 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.0721 | 1.68558 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.13872 | −0.325029 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.60960 | 0.263542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7621 | −1.14500 | −0.572500 | − | 0.819904i | \(-0.694026\pi\) | ||||
−0.572500 | + | 0.819904i | \(0.694026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0054 | 0.516917 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.0457 | −1.86402 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.73900 | 0.227031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.7383 | −1.60907 | −0.804533 | − | 0.593907i | \(-0.797585\pi\) | ||||
−0.804533 | + | 0.593907i | \(0.797585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.24043 | 0.324971 | 0.162485 | − | 0.986711i | \(-0.448049\pi\) | ||||
0.162485 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.1134 | 1.30182 | 0.650911 | − | 0.759154i | \(-0.274387\pi\) | ||||
0.650911 | + | 0.759154i | \(0.274387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.3081 | −0.757909 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60.8391 | 2.38447 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5452 | −0.569199 | −0.284599 | − | 0.958647i | \(-0.591861\pi\) | ||||
−0.284599 | + | 0.958647i | \(0.591861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.21209 | −0.125316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.4498 | −0.952427 | −0.476214 | − | 0.879330i | \(-0.657991\pi\) | ||||
−0.476214 | + | 0.879330i | \(0.657991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43400 | 0.0557763 | 0.0278882 | − | 0.999611i | \(-0.491122\pi\) | ||||
0.0278882 | + | 0.999611i | \(0.491122\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.7676 | −0.495853 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.03130 | 0.233533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.7985 | 0.610806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.4271 | 1.09742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.39873 | 0.131011 | 0.0655056 | − | 0.997852i | \(-0.479134\pi\) | ||||
0.0655056 | + | 0.997852i | \(0.479134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7751 | 0.606287 | 0.303144 | − | 0.952945i | \(-0.401964\pi\) | ||||
0.303144 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34060 | 0.0514475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.1343 | 1.00147 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.99979 | 0.191312 | 0.0956559 | − | 0.995414i | \(-0.469505\pi\) | ||||
0.0956559 | + | 0.995414i | \(0.469505\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7916 | 0.526183 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.07296 | −0.117071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6864 | 1.54779 | 0.773893 | − | 0.633317i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633317i | \(0.218307\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.20886 | 0.121895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8058 | 0.409298 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.1440 | −1.17797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.30372 | −0.0492407 | −0.0246204 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246204 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7301 | −0.404692 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.5959 | −0.925024 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.5228 | 1.97253 | 0.986267 | − | 0.165157i | \(-0.0528131\pi\) | ||||
0.986267 | + | 0.165157i | \(0.0528131\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.61411 | −0.135540 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.32489 | −0.311770 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.7167 | 1.22183 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.2329 | −0.903735 | −0.451868 | − | 0.892085i | \(-0.649242\pi\) | ||||
−0.451868 | + | 0.892085i | \(0.649242\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.1622 | −1.86814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.5727 | 0.653536 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.0943 | −1.37575 | −0.687875 | − | 0.725829i | \(-0.741456\pi\) | ||||
−0.687875 | + | 0.725829i | \(0.741456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.7158 | 0.841324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0836 | 0.372954 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.3065 | −1.71037 | −0.855184 | − | 0.518325i | \(-0.826556\pi\) | ||||
−0.855184 | + | 0.518325i | \(0.826556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.2996 | 1.22660 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3516 | −1.19007 | −0.595037 | − | 0.803698i | \(-0.702863\pi\) | ||||
−0.595037 | + | 0.803698i | \(0.702863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.7270 | 0.761425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.73343 | 0.0635935 | 0.0317967 | − | 0.999494i | \(-0.489877\pi\) | ||||
0.0317967 | + | 0.999494i | \(0.489877\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.580645 | −0.0212447 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.8268 | −1.85717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9983 | 1.56903 | 0.784515 | − | 0.620110i | \(-0.212912\pi\) | ||||
0.784515 | + | 0.620110i | \(0.212912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.2961 | 0.885400 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.3219 | −1.75629 | −0.878144 | − | 0.478397i | \(-0.841218\pi\) | ||||
−0.878144 | + | 0.478397i | \(0.841218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.86933 | −0.140448 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.2528 | 0.697915 | 0.348958 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348958 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.8754 | 2.05903 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.1722 | 1.77550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.05816 | 0.326645 | 0.163323 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163323 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.28223 | −0.226249 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.1276 | −1.04765 | −0.523824 | − | 0.851827i | \(-0.675495\pi\) | ||||
−0.523824 | + | 0.851827i | \(0.675495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.2809 | 1.33744 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.5422 | −0.628513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.4350 | 1.12483 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.0244 | 1.03725 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8771 | 0.851128 | 0.425564 | − | 0.904928i | \(-0.360076\pi\) | ||||
0.425564 | + | 0.904928i | \(0.360076\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 34.3243 | 1.22198 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.2532 | −0.649008 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −72.3956 | −2.57084 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8896 | 0.704526 | 0.352263 | − | 0.935901i | \(-0.385412\pi\) | ||||
0.352263 | + | 0.935901i | \(0.385412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7660 | 0.522383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.06677 | 0.143692 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.5940 | −0.620879 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.5588 | 1.56854 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.3598 | 0.926760 | 0.463380 | − | 0.886160i | \(-0.346637\pi\) | ||||
0.463380 | + | 0.886160i | \(0.346637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2482 | −0.500323 | −0.250161 | − | 0.968204i | \(-0.580484\pi\) | ||||
−0.250161 | + | 0.968204i | \(0.580484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.6165 | 0.652910 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.3697 | −0.572703 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.17205 | −0.285555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.56520 | 0.194227 | 0.0971134 | − | 0.995273i | \(-0.469039\pi\) | ||||
0.0971134 | + | 0.995273i | \(0.469039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.1312 | 1.18974 | 0.594869 | − | 0.803823i | \(-0.297204\pi\) | ||||
0.594869 | + | 0.803823i | \(0.297204\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5085 | 0.817472 | 0.408736 | − | 0.912653i | \(-0.365970\pi\) | ||||
0.408736 | + | 0.912653i | \(0.365970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7442 | −1.10252 | −0.551260 | − | 0.834333i | \(-0.685853\pi\) | ||||
−0.551260 | + | 0.834333i | \(0.685853\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.2846 | −1.50153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.3792 | −0.394267 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.0618 | −1.38474 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.5409 | 0.847247 | 0.423623 | − | 0.905838i | \(-0.360758\pi\) | ||||
0.423623 | + | 0.905838i | \(0.360758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.37661 | 0.254366 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.26180 | −0.112343 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.1236 | −0.897618 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.9756 | 0.376682 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.10131 | −0.174871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7499 | 0.813183 | 0.406591 | − | 0.913610i | \(-0.366717\pi\) | ||||
0.406591 | + | 0.913610i | \(0.366717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0643 | 1.47105 | 0.735524 | − | 0.677499i | \(-0.236936\pi\) | ||||
0.735524 | + | 0.677499i | \(0.236936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0591 | −0.855006 | −0.427503 | − | 0.904014i | \(-0.640607\pi\) | ||||
−0.427503 | + | 0.904014i | \(0.640607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.9490 | 2.07714 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.0967 | −1.56915 | −0.784575 | − | 0.620033i | \(-0.787119\pi\) | ||||
−0.784575 | + | 0.620033i | \(0.787119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.1845 | 0.957195 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.7960 | −0.671535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −84.8044 | −2.87349 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.129585 | 0.00438578 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.1644 | 1.18742 | 0.593709 | − | 0.804680i | \(-0.297663\pi\) | ||||
0.593709 | + | 0.804680i | \(0.297663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5170 | 0.759480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8350 | −1.30838 | −0.654192 | − | 0.756329i | \(-0.726991\pi\) | ||||
−0.654192 | + | 0.756329i | \(0.726991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5954 | −0.356562 | −0.178281 | − | 0.983980i | \(-0.557054\pi\) | ||||
−0.178281 | + | 0.983980i | \(0.557054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8733 | 0.902316 | 0.451158 | − | 0.892444i | \(-0.351011\pi\) | ||||
0.451158 | + | 0.892444i | \(0.351011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.3040 | −1.68714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0435 | −0.704984 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.9712 | −0.802165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.85407 | 0.329018 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −50.2099 | −1.67459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.743278 | −0.0247622 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 56.8754 | 1.89270 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −58.3210 | −1.93652 | −0.968259 | − | 0.249949i | \(-0.919586\pi\) | ||||
−0.968259 | + | 0.249949i | \(0.919586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.37748 | −0.0788561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3287 | 1.33615 | 0.668074 | − | 0.744095i | \(-0.267119\pi\) | ||||
0.668074 | + | 0.744095i | \(0.267119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.18045 | −0.105257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.6071 | 0.614459 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.6333 | −1.24141 | −0.620704 | − | 0.784045i | \(-0.713153\pi\) | ||||
−0.620704 | + | 0.784045i | \(0.713153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2381 | −0.535064 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −80.0559 | −2.63507 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.84877 | −0.159254 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.7190 | 1.00786 | 0.503929 | − | 0.863745i | \(-0.331887\pi\) | ||||
0.503929 | + | 0.863745i | \(0.331887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4731 | 0.605431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.6072 | 0.838343 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.5843 | 1.32583 | 0.662915 | − | 0.748694i | \(-0.269319\pi\) | ||||
0.662915 | + | 0.748694i | \(0.269319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.2355 | 1.41094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.5104 | 1.19020 | 0.595102 | − | 0.803650i | \(-0.297112\pi\) | ||||
0.595102 | + | 0.803650i | \(0.297112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.33994 | −0.271586 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.9681 | −1.13631 | −0.568155 | − | 0.822921i | \(-0.692343\pi\) | ||||
−0.568155 | + | 0.822921i | \(0.692343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.8069 | 1.45449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5176 | 0.795038 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7164 | −1.15697 | −0.578484 | − | 0.815694i | \(-0.696355\pi\) | ||||
−0.578484 | + | 0.815694i | \(0.696355\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.3371 | −0.754382 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.85971 | 0.0600532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.3038 | 1.23561 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.91301 | −0.158320 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0422 | 1.38414 | 0.692072 | − | 0.721829i | \(-0.256698\pi\) | ||||
0.692072 | + | 0.721829i | \(0.256698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.01337 | 0.161053 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.76196 | −0.313276 | −0.156638 | − | 0.987656i | \(-0.550066\pi\) | ||||
−0.156638 | + | 0.987656i | \(0.550066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.93666 | 0.0941449 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.0469 | −0.769329 | −0.384665 | − | 0.923056i | \(-0.625683\pi\) | ||||
−0.384665 | + | 0.923056i | \(0.625683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2754 | 0.711926 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.49768 | 0.175527 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.2418 | 0.613717 | 0.306859 | − | 0.951755i | \(-0.400722\pi\) | ||||
0.306859 | + | 0.951755i | \(0.400722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 83.2862 | 2.65103 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.78253 | −0.247470 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1944 | −1.21328 | −0.606642 | − | 0.794975i | \(-0.707484\pi\) | ||||
−0.606642 | + | 0.794975i | \(0.707484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.496936 | 0.0157698 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.5981 | 1.31742 | 0.658712 | − | 0.752395i | \(-0.271101\pi\) | ||||
0.658712 | + | 0.752395i | \(0.271101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.5490 | −0.776696 |
(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 | 4600.2.a.bd.1.2 | ✓ | 5 | |
4.3 | odd | 2 | 9200.2.a.cv.1.4 | 5 | |||
5.2 | odd | 4 | 4600.2.e.w.4049.8 | 10 | |||
5.3 | odd | 4 | 4600.2.e.w.4049.3 | 10 | |||
5.4 | even | 2 | 4600.2.a.bf.1.4 | yes | 5 | ||
20.19 | odd | 2 | 9200.2.a.ct.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4600.2.a.bf.1.4 | yes | 5 | 5.4 | even | 2 | ||
4600.2.e.w.4049.3 | 10 | 5.3 | odd | 4 | |||
4600.2.e.w.4049.8 | 10 | 5.2 | odd | 4 | |||
9200.2.a.ct.1.2 | 5 | 20.19 | odd | 2 | |||
9200.2.a.cv.1.4 | 5 | 4.3 | odd | 2 |