Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
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: | \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.88788\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.71231 | 1.02516 | 0.512578 | − | 0.858641i | \(-0.328690\pi\) | ||||
0.512578 | + | 0.858641i | \(0.328690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.76466 | −0.833575 | −0.416787 | − | 0.909004i | \(-0.636844\pi\) | ||||
−0.416787 | + | 0.909004i | \(0.636844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.01111 | −0.280431 | −0.140215 | − | 0.990121i | \(-0.544780\pi\) | ||||
−0.140215 | + | 0.990121i | \(0.544780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.50408 | 1.09240 | 0.546199 | − | 0.837655i | \(-0.316074\pi\) | ||||
0.546199 | + | 0.837655i | \(0.316074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.76466 | 1.09309 | 0.546543 | − | 0.837431i | \(-0.315943\pi\) | ||||
0.546543 | + | 0.837431i | \(0.315943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.08400 | −1.50116 | −0.750581 | − | 0.660779i | \(-0.770226\pi\) | ||||
−0.750581 | + | 0.660779i | \(0.770226\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.49297 | −0.986566 | −0.493283 | − | 0.869869i | \(-0.664203\pi\) | ||||
−0.493283 | + | 0.869869i | \(0.664203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.71231 | −0.458464 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9865 | −1.80617 | −0.903086 | − | 0.429460i | \(-0.858704\pi\) | ||||
−0.903086 | + | 0.429460i | \(0.858704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.43515 | 0.380306 | 0.190153 | − | 0.981754i | \(-0.439102\pi\) | ||||
0.190153 | + | 0.981754i | \(0.439102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.77576 | 0.880796 | 0.440398 | − | 0.897803i | \(-0.354837\pi\) | ||||
0.440398 | + | 0.897803i | \(0.354837\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0389 | −1.61018 | −0.805092 | − | 0.593150i | \(-0.797884\pi\) | ||||
−0.805092 | + | 0.593150i | \(0.797884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.356621 | 0.0509459 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.15293 | −1.11989 | −0.559946 | − | 0.828529i | \(-0.689178\pi\) | ||||
−0.559946 | + | 0.828529i | \(0.689178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.76466 | 0.372786 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.70120 | 0.221477 | 0.110739 | − | 0.993850i | \(-0.464678\pi\) | ||||
0.110739 | + | 0.993850i | \(0.464678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.12524 | 0.400146 | 0.200073 | − | 0.979781i | \(-0.435882\pi\) | ||||
0.200073 | + | 0.979781i | \(0.435882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.01111 | 0.125413 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.56190 | 0.679494 | 0.339747 | − | 0.940517i | \(-0.389659\pi\) | ||||
0.339747 | + | 0.940517i | \(0.389659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07456 | 0.246205 | 0.123103 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123103 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.63646 | 1.12786 | 0.563931 | − | 0.825822i | \(-0.309288\pi\) | ||||
0.563931 | + | 0.825822i | \(0.309288\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.49860 | −0.854545 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.63942 | −0.409466 | −0.204733 | − | 0.978818i | \(-0.565633\pi\) | ||||
−0.204733 | + | 0.978818i | \(0.565633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.7908 | −1.29421 | −0.647106 | − | 0.762400i | \(-0.724021\pi\) | ||||
−0.647106 | + | 0.762400i | \(0.724021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50408 | −0.488536 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.13786 | −0.438612 | −0.219306 | − | 0.975656i | \(-0.570379\pi\) | ||||
−0.219306 | + | 0.975656i | \(0.570379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74244 | −0.287486 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.76466 | −0.488843 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.89141 | 1.00432 | 0.502160 | − | 0.864775i | \(-0.332539\pi\) | ||||
0.502160 | + | 0.864775i | \(0.332539\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.44068 | 0.839879 | 0.419940 | − | 0.907552i | \(-0.362051\pi\) | ||||
0.419940 | + | 0.907552i | \(0.362051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.73948 | −0.861127 | −0.430563 | − | 0.902560i | \(-0.641685\pi\) | ||||
−0.430563 | + | 0.902560i | \(0.641685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.79235 | −0.559967 | −0.279984 | − | 0.960005i | \(-0.590329\pi\) | ||||
−0.279984 | + | 0.960005i | \(0.590329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.83848 | 0.176094 | 0.0880472 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880472 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3076 | 1.53409 | 0.767045 | − | 0.641594i | \(-0.221726\pi\) | ||||
0.767045 | + | 0.641594i | \(0.221726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2164 | 1.11988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.35668 | −0.305153 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89235 | 0.877804 | 0.438902 | − | 0.898535i | \(-0.355367\pi\) | ||||
0.438902 | + | 0.898535i | \(0.355367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.90346 | 0.603158 | 0.301579 | − | 0.953441i | \(-0.402486\pi\) | ||||
0.301579 | + | 0.953441i | \(0.402486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9232 | 1.12059 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.90267 | −0.846042 | −0.423021 | − | 0.906120i | \(-0.639030\pi\) | ||||
−0.423021 | + | 0.906120i | \(0.639030\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.37884 | −0.116951 | −0.0584757 | − | 0.998289i | \(-0.518624\pi\) | ||||
−0.0584757 | + | 0.998289i | \(0.518624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.79537 | 0.233760 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.08400 | 0.671340 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2213 | −1.00121 | −0.500603 | − | 0.865677i | \(-0.666888\pi\) | ||||
−0.500603 | + | 0.865677i | \(0.666888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.69883 | 0.626522 | 0.313261 | − | 0.949667i | \(-0.398579\pi\) | ||||
0.313261 | + | 0.949667i | \(0.398579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.49297 | 0.441206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.0768 | −1.92154 | −0.960769 | − | 0.277351i | \(-0.910543\pi\) | ||||
−0.960769 | + | 0.277351i | \(0.910543\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.71231 | −0.213760 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.96372 | 0.388788 | 0.194394 | − | 0.980923i | \(-0.437726\pi\) | ||||
0.194394 | + | 0.980923i | \(0.437726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.9010 | −0.843545 | −0.421772 | − | 0.906702i | \(-0.638592\pi\) | ||||
−0.421772 | + | 0.906702i | \(0.638592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9777 | −0.921358 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.9508 | −1.97300 | −0.986502 | − | 0.163749i | \(-0.947641\pi\) | ||||
−0.986502 | + | 0.163749i | \(0.947641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.71231 | 0.205031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.8398 | 0.959692 | 0.479846 | − | 0.877353i | \(-0.340693\pi\) | ||||
0.479846 | + | 0.877353i | \(0.340693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9453 | 1.33386 | 0.666931 | − | 0.745119i | \(-0.267608\pi\) | ||||
0.666931 | + | 0.745119i | \(0.267608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9865 | 0.807745 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4522 | −0.910596 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.25756 | −0.669854 | −0.334927 | − | 0.942244i | \(-0.608712\pi\) | ||||
−0.334927 | + | 0.942244i | \(0.608712\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0109521 | −0.000788349 0 | −0.000394175 | − | 1.00000i | \(-0.500125\pi\) | ||||
−0.000394175 | 1.00000i | \(0.500125\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0906 | −0.932669 | −0.466334 | − | 0.884609i | \(-0.654426\pi\) | ||||
−0.466334 | + | 0.884609i | \(0.654426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8980 | −1.62320 | −0.811600 | − | 0.584214i | \(-0.801403\pi\) | ||||
−0.811600 | + | 0.584214i | \(0.801403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.9263 | −1.53893 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.43515 | −0.170078 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.1726 | −0.911170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.36789 | −0.231855 | −0.115927 | − | 0.993258i | \(-0.536984\pi\) | ||||
−0.115927 | + | 0.993258i | \(0.536984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.77576 | −0.393904 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.8986 | −1.01138 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.55411 | −0.306342 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5922 | −0.843235 | −0.421617 | − | 0.906774i | \(-0.638537\pi\) | ||||
−0.421617 | + | 0.906774i | \(0.638537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4192 | −1.02341 | −0.511704 | − | 0.859162i | \(-0.670986\pi\) | ||||
−0.511704 | + | 0.859162i | \(0.670986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1989 | −1.26870 | −0.634348 | − | 0.773047i | \(-0.718732\pi\) | ||||
−0.634348 | + | 0.773047i | \(0.718732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3059 | 0.937208 | 0.468604 | − | 0.883408i | \(-0.344757\pi\) | ||||
0.468604 | + | 0.883408i | \(0.344757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0389 | 0.720096 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.39449 | 0.219571 | 0.109786 | − | 0.993955i | \(-0.464984\pi\) | ||||
0.109786 | + | 0.993955i | \(0.464984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8564 | 1.40790 | 0.703949 | − | 0.710251i | \(-0.251418\pi\) | ||||
0.703949 | + | 0.710251i | \(0.251418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.356621 | −0.0227837 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.81758 | −0.306535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.97778 | −0.503553 | −0.251777 | − | 0.967785i | \(-0.581015\pi\) | ||||
−0.251777 | + | 0.967785i | \(0.581015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.76466 | 0.173812 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.06272 | −0.502938 | −0.251469 | − | 0.967865i | \(-0.580914\pi\) | ||||
−0.251469 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.7988 | −1.85161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4983 | 1.14065 | 0.570327 | − | 0.821418i | \(-0.306816\pi\) | ||||
0.570327 | + | 0.821418i | \(0.306816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.15293 | 0.500831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.59724 | −0.158356 | −0.0791781 | − | 0.996860i | \(-0.525230\pi\) | ||||
−0.0791781 | + | 0.996860i | \(0.525230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2867 | 1.17158 | 0.585792 | − | 0.810462i | \(-0.300784\pi\) | ||||
0.585792 | + | 0.810462i | \(0.300784\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.76466 | −0.166715 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.6618 | 1.42170 | 0.710849 | − | 0.703345i | \(-0.248311\pi\) | ||||
0.710849 | + | 0.703345i | \(0.248311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1611 | −1.44133 | −0.720666 | − | 0.693282i | \(-0.756164\pi\) | ||||
−0.720666 | + | 0.693282i | \(0.756164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.1229 | −1.73117 | −0.865587 | − | 0.500758i | \(-0.833055\pi\) | ||||
−0.865587 | + | 0.500758i | \(0.833055\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.60487 | 0.389873 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.28670 | 0.193335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92004 | 0.404273 | 0.202137 | − | 0.979357i | \(-0.435211\pi\) | ||||
0.202137 | + | 0.979357i | \(0.435211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.70120 | −0.0990477 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.01111 | 0.0584739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6657 | 0.902953 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.12524 | −0.178951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.85481 | −0.220006 | −0.110003 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110003 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6124 | 0.771891 | 0.385946 | − | 0.922522i | \(-0.373875\pi\) | ||||
0.385946 | + | 0.922522i | \(0.373875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1674 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.24812 | −0.182433 | −0.0912164 | − | 0.995831i | \(-0.529076\pi\) | ||||
−0.0912164 | + | 0.995831i | \(0.529076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.3495 | 1.25133 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.4604 | 1.19409 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.01111 | −0.0560862 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.9408 | −1.65069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0304 | −1.54069 | −0.770346 | − | 0.637626i | \(-0.779916\pi\) | ||||
−0.770346 | + | 0.637626i | \(0.779916\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.56190 | −0.303879 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.39686 | 0.511880 | 0.255940 | − | 0.966693i | \(-0.417615\pi\) | ||||
0.255940 | + | 0.966693i | \(0.417615\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1862 | 0.822377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0189 | −0.972929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.55153 | 0.190656 | 0.0953280 | − | 0.995446i | \(-0.469610\pi\) | ||||
0.0953280 | + | 0.995446i | \(0.469610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1614 | −0.865101 | −0.432551 | − | 0.901610i | \(-0.642386\pi\) | ||||
−0.432551 | + | 0.901610i | \(0.642386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4955 | −0.558618 | −0.279309 | − | 0.960201i | \(-0.590105\pi\) | ||||
−0.279309 | + | 0.960201i | \(0.590105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.07456 | −0.110106 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.17832 | 0.431635 | 0.215818 | − | 0.976434i | \(-0.430758\pi\) | ||||
0.215818 | + | 0.976434i | \(0.430758\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.70194 | 0.194839 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.63646 | −0.504395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.59818 | −0.135624 | −0.0678119 | − | 0.997698i | \(-0.521602\pi\) | ||||
−0.0678119 | + | 0.997698i | \(0.521602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1133 | −1.14806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6018 | −0.704277 | −0.352139 | − | 0.935948i | \(-0.614545\pi\) | ||||
−0.352139 | + | 0.935948i | \(0.614545\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.17380 | 0.420972 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3421 | −0.993539 | −0.496770 | − | 0.867882i | \(-0.665481\pi\) | ||||
−0.496770 | + | 0.867882i | \(0.665481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7947 | 1.36915 | 0.684573 | − | 0.728944i | \(-0.259989\pi\) | ||||
0.684573 | + | 0.728944i | \(0.259989\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.49860 | 0.382164 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.27292 | 0.470156 | 0.235078 | − | 0.971977i | \(-0.424465\pi\) | ||||
0.235078 | + | 0.971977i | \(0.424465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.50408 | −0.227781 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.63942 | 0.183119 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.1497 | 1.86449 | 0.932245 | − | 0.361829i | \(-0.117848\pi\) | ||||
0.932245 | + | 0.361829i | \(0.117848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.91752 | −0.295507 | −0.147754 | − | 0.989024i | \(-0.547204\pi\) | ||||
−0.147754 | + | 0.989024i | \(0.547204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.55399 | 0.276664 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.3739 | 1.50558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.7069 | 1.07334 | 0.536669 | − | 0.843793i | \(-0.319682\pi\) | ||||
0.536669 | + | 0.843793i | \(0.319682\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.61418 | 0.227049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7908 | 0.578789 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.5305 | −1.10069 | −0.550343 | − | 0.834939i | \(-0.685503\pi\) | ||||
−0.550343 | + | 0.834939i | \(0.685503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5912 | 0.662393 | 0.331197 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331197 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.50408 | 0.218480 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.47661 | 0.410212 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.9812 | −1.68498 | −0.842492 | − | 0.538709i | \(-0.818912\pi\) | ||||
−0.842492 | + | 0.538709i | \(0.818912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.3040 | 1.11992 | 0.559959 | − | 0.828520i | \(-0.310817\pi\) | ||||
0.559959 | + | 0.828520i | \(0.310817\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.76466 | −0.227924 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8907 | −0.710693 | −0.355347 | − | 0.934735i | \(-0.615637\pi\) | ||||
−0.355347 | + | 0.934735i | \(0.615637\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3841 | −1.01599 | −0.507995 | − | 0.861360i | \(-0.669613\pi\) | ||||
−0.507995 | + | 0.861360i | \(0.669613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.13786 | 0.196153 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.9378 | 1.12970 | 0.564848 | − | 0.825195i | \(-0.308935\pi\) | ||||
0.564848 | + | 0.825195i | \(0.308935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.73234 | −0.317013 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.74244 | 0.128567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9311 | 1.07267 | 0.536337 | − | 0.844004i | \(-0.319808\pi\) | ||||
0.536337 | + | 0.844004i | \(0.319808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.3016 | −1.31814 | −0.659069 | − | 0.752083i | \(-0.729049\pi\) | ||||
−0.659069 | + | 0.752083i | \(0.729049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.97483 | 0.184726 | 0.0923629 | − | 0.995725i | \(-0.470558\pi\) | ||||
0.0923629 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4994 | −1.17997 | −0.589987 | − | 0.807413i | \(-0.700867\pi\) | ||||
−0.589987 | + | 0.807413i | \(0.700867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0856 | 0.696588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.9680 | −0.734209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.76466 | 0.218617 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.37018 | −0.153987 | −0.0769936 | − | 0.997032i | \(-0.524532\pi\) | ||||
−0.0769936 | + | 0.997032i | \(0.524532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1086 | 0.506507 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.89141 | −0.449146 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.98578 | −0.271242 | −0.135621 | − | 0.990761i | \(-0.543303\pi\) | ||||
−0.135621 | + | 0.990761i | \(0.543303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.1234 | −0.547120 | −0.273560 | − | 0.961855i | \(-0.588201\pi\) | ||||
−0.273560 | + | 0.961855i | \(0.588201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.4109 | −1.63987 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.62686 | 0.252399 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.6453 | 1.23757 | 0.618786 | − | 0.785560i | \(-0.287625\pi\) | ||||
0.618786 | + | 0.785560i | \(0.287625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.4717 | −1.89372 | −0.946860 | − | 0.321647i | \(-0.895763\pi\) | ||||
−0.946860 | + | 0.321647i | \(0.895763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.44068 | −0.375605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5778 | 0.779121 | 0.389560 | − | 0.921001i | \(-0.372627\pi\) | ||||
0.389560 | + | 0.921001i | \(0.372627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.1371 | 1.15624 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.73948 | 0.385108 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.5186 | 1.34221 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.73149 | 0.382533 | 0.191267 | − | 0.981538i | \(-0.438740\pi\) | ||||
0.191267 | + | 0.981538i | \(0.438740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6153 | −0.595357 | −0.297679 | − | 0.954666i | \(-0.596212\pi\) | ||||
−0.297679 | + | 0.954666i | \(0.596212\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.7407 | −1.07772 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.46220 | −0.106650 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.79235 | 0.250425 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.985934 | −0.0424672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.983574 | 0.0422872 | 0.0211436 | − | 0.999776i | \(-0.493269\pi\) | ||||
0.0211436 | + | 0.999776i | \(0.493269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.83848 | −0.0787518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.85622 | −0.335908 | −0.167954 | − | 0.985795i | \(-0.553716\pi\) | ||||
−0.167954 | + | 0.985795i | \(0.553716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.5175 | −1.64090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.87123 | −0.419767 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.2056 | 1.32223 | 0.661113 | − | 0.750287i | \(-0.270085\pi\) | ||||
0.661113 | + | 0.750287i | \(0.270085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.83992 | −0.247002 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9061 | −1.17610 | −0.588051 | − | 0.808823i | \(-0.700105\pi\) | ||||
−0.588051 | + | 0.808823i | \(0.700105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.3076 | −0.686066 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.5055 | −0.775789 | −0.387895 | − | 0.921704i | \(-0.626798\pi\) | ||||
−0.387895 | + | 0.921704i | \(0.626798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5458 | −1.15276 | −0.576379 | − | 0.817183i | \(-0.695535\pi\) | ||||
−0.576379 | + | 0.817183i | \(0.695535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1075 | 0.462411 | 0.231205 | − | 0.972905i | \(-0.425733\pi\) | ||||
0.231205 | + | 0.972905i | \(0.425733\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.9804 | −1.32677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.5400 | 0.933513 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.28364 | 0.259354 | 0.129677 | − | 0.991556i | \(-0.458606\pi\) | ||||
0.129677 | + | 0.991556i | \(0.458606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.1721 | −1.07840 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.4385 | −0.798242 | −0.399121 | − | 0.916898i | \(-0.630685\pi\) | ||||
−0.399121 | + | 0.916898i | \(0.630685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.2164 | −0.500825 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.3511 | −1.77128 | −0.885640 | − | 0.464373i | \(-0.846280\pi\) | ||||
−0.885640 | + | 0.464373i | \(0.846280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.8988 | −1.30118 | −0.650589 | − | 0.759430i | \(-0.725478\pi\) | ||||
−0.650589 | + | 0.759430i | \(0.725478\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.35668 | 0.136469 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.1080 | −1.42499 | −0.712495 | − | 0.701677i | \(-0.752435\pi\) | ||||
−0.712495 | + | 0.701677i | \(0.752435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.1615 | 0.451545 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.7360 | 1.20103 | 0.600513 | − | 0.799615i | \(-0.294963\pi\) | ||||
0.600513 | + | 0.799615i | \(0.294963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.8604 | 0.598257 | 0.299129 | − | 0.954213i | \(-0.403304\pi\) | ||||
0.299129 | + | 0.954213i | \(0.403304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.0063 | −1.64818 | −0.824091 | − | 0.566458i | \(-0.808313\pi\) | ||||
−0.824091 | + | 0.566458i | \(0.808313\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.2232 | −0.449646 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.4841 | −1.97306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.23016 | 0.168400 | 0.0842000 | − | 0.996449i | \(-0.473167\pi\) | ||||
0.0842000 | + | 0.996449i | \(0.473167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.89235 | −0.392566 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.360583 | −0.0142868 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.54152 | −0.218877 | −0.109438 | − | 0.993994i | \(-0.534905\pi\) | ||||
−0.109438 | + | 0.993994i | \(0.534905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.2134 | −1.94079 | −0.970393 | − | 0.241532i | \(-0.922350\pi\) | ||||
−0.970393 | + | 0.241532i | \(0.922350\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.3923 | −1.03759 | −0.518794 | − | 0.854900i | \(-0.673619\pi\) | ||||
−0.518794 | + | 0.854900i | \(0.673619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.70323 | −0.184618 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.60329 | 0.375806 | 0.187903 | − | 0.982188i | \(-0.439831\pi\) | ||||
0.187903 | + | 0.982188i | \(0.439831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.90346 | −0.269740 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0918 | 0.471030 | 0.235515 | − | 0.971871i | \(-0.424322\pi\) | ||||
0.235515 | + | 0.971871i | \(0.424322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6996 | −0.571749 | −0.285874 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285874 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.9232 | −0.501141 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.08400 | 0.313014 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.64020 | −0.333551 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9292 | 1.15369 | 0.576843 | − | 0.816855i | \(-0.304285\pi\) | ||||
0.576843 | + | 0.816855i | \(0.304285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.3623 | 0.628855 | 0.314427 | − | 0.949282i | \(-0.398187\pi\) | ||||
0.314427 | + | 0.949282i | \(0.398187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.8286 | 1.02959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.2260 | −0.506080 | −0.253040 | − | 0.967456i | \(-0.581430\pi\) | ||||
−0.253040 | + | 0.967456i | \(0.581430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.90267 | 0.378362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.24350 | 0.314052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.7402 | −1.05529 | −0.527644 | − | 0.849466i | \(-0.676924\pi\) | ||||
−0.527644 | + | 0.849466i | \(0.676924\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.37884 | 0.0523023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9681 | 0.415446 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.8407 | 1.80692 | 0.903460 | − | 0.428673i | \(-0.141019\pi\) | ||||
0.903460 | + | 0.428673i | \(0.141019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.3470 | −1.97430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.8937 | 0.861008 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5861 | −0.435127 | −0.217563 | − | 0.976046i | \(-0.569811\pi\) | ||||
−0.217563 | + | 0.976046i | \(0.569811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.49297 | 0.205713 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.79537 | −0.104541 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.6703 | 0.845461 | 0.422730 | − | 0.906255i | \(-0.361072\pi\) | ||||
0.422730 | + | 0.906255i | \(0.361072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7042 | −0.882790 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.08400 | −0.300232 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.3465 | 1.94142 | 0.970712 | − | 0.240247i | \(-0.0772286\pi\) | ||||
0.970712 | + | 0.240247i | \(0.0772286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.0145 | 0.962180 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8962 | −0.476333 | −0.238167 | − | 0.971224i | \(-0.576546\pi\) | ||||
−0.238167 | + | 0.971224i | \(0.576546\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.3767 | −0.566409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.06928 | −0.333619 | −0.166809 | − | 0.985989i | \(-0.553346\pi\) | ||||
−0.166809 | + | 0.985989i | \(0.553346\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.1257 | −0.371478 | −0.185739 | − | 0.982599i | \(-0.559468\pi\) | ||||
−0.185739 | + | 0.982599i | \(0.559468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2213 | 0.447753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.7106 | −0.574054 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.9936 | 1.13097 | 0.565486 | − | 0.824758i | \(-0.308689\pi\) | ||||
0.565486 | + | 0.824758i | \(0.308689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.69883 | −0.280189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.67914 | 0.170066 | 0.0850331 | − | 0.996378i | \(-0.472900\pi\) | ||||
0.0850331 | + | 0.996378i | \(0.472900\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.3875 | 0.739045 | 0.369523 | − | 0.929222i | \(-0.379521\pi\) | ||||
0.369523 | + | 0.929222i | \(0.379521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.98653 | 0.180524 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.72010 | −0.0621092 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.9408 | 1.29606 | 0.648029 | − | 0.761615i | \(-0.275593\pi\) | ||||
0.648029 | + | 0.761615i | \(0.275593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.59644 | 0.0933873 | 0.0466936 | − | 0.998909i | \(-0.485132\pi\) | ||||
0.0466936 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.49297 | −0.197313 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6026 | 0.415707 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.73545 | −0.205231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0768 | 0.859338 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.456271 | −0.0162643 | −0.00813215 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813215 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.2312 | 1.57268 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.15995 | −0.112213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.7327 | 0.698968 | 0.349484 | − | 0.936942i | \(-0.386357\pi\) | ||||
0.349484 | + | 0.936942i | \(0.386357\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.7199 | −1.75896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.6415 | −0.940158 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.71231 | 0.0955963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.1549 | −1.30630 | −0.653148 | − | 0.757230i | \(-0.726552\pi\) | ||||
−0.653148 | + | 0.757230i | \(0.726552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.07310 | −0.248370 | −0.124185 | − | 0.992259i | \(-0.539632\pi\) | ||||
−0.124185 | + | 0.992259i | \(0.539632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.96372 | −0.173871 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.5195 | 0.962786 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.9341 | −1.67291 | −0.836456 | − | 0.548034i | \(-0.815376\pi\) | ||||
−0.836456 | + | 0.548034i | \(0.815376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.19538 | −0.111384 | −0.0556920 | − | 0.998448i | \(-0.517737\pi\) | ||||
−0.0556920 | + | 0.998448i | \(0.517737\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.8892 | −1.49140 | −0.745701 | − | 0.666280i | \(-0.767885\pi\) | ||||
−0.745701 | + | 0.666280i | \(0.767885\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0412 | 0.452938 | 0.226469 | − | 0.974018i | \(-0.427282\pi\) | ||||
0.226469 | + | 0.974018i | \(0.427282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.60625 | 0.0556532 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9010 | 0.377245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.05070 | −0.0362741 | −0.0181371 | − | 0.999836i | \(-0.505774\pi\) | ||||
−0.0181371 | + | 0.999836i | \(0.505774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.3511 | 1.25348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9777 | 0.412044 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.10436 | −0.312829 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9865 | 0.376613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.4176 | 1.04148 | 0.520739 | − | 0.853716i | \(-0.325657\pi\) | ||||
0.520739 | + | 0.853716i | \(0.325657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5276 | 0.564570 | 0.282285 | − | 0.959331i | \(-0.408908\pi\) | ||||
0.282285 | + | 0.959331i | \(0.408908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.77145 | 0.0945607 | 0.0472803 | − | 0.998882i | \(-0.484945\pi\) | ||||
0.0472803 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.4820 | 1.00358 | 0.501790 | − | 0.864990i | \(-0.332675\pi\) | ||||
0.501790 | + | 0.864990i | \(0.332675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.9508 | 0.882354 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0617 | 0.341321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.62368 | −0.190551 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.71231 | −0.0916928 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.1487 | 1.76094 | 0.880469 | − | 0.474104i | \(-0.157228\pi\) | ||||
0.880469 | + | 0.474104i | \(0.157228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.76177 | −0.160428 | −0.0802141 | − | 0.996778i | \(-0.525560\pi\) | ||||
−0.0802141 | + | 0.996778i | \(0.525560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.9756 | −1.04241 | −0.521206 | − | 0.853431i | \(-0.674518\pi\) | ||||
−0.521206 | + | 0.853431i | \(0.674518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.6405 | 0.995231 | 0.497616 | − | 0.867398i | \(-0.334209\pi\) | ||||
0.497616 | + | 0.867398i | \(0.334209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.8311 | 0.899887 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.5964 | −1.76007 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.8398 | −0.429187 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.4051 | 1.48099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.7214 | −1.22337 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.9453 | −0.596521 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6636 | 0.453691 | 0.226846 | − | 0.973931i | \(-0.427159\pi\) | ||||
0.226846 | + | 0.973931i | \(0.427159\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2035 | −0.801897 | −0.400948 | − | 0.916101i | \(-0.631319\pi\) | ||||
−0.400948 | + | 0.916101i | \(0.631319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.5976 | 1.07882 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.7243 | 0.618331 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.4984 | −0.676181 | −0.338091 | − | 0.941114i | \(-0.609781\pi\) | ||||
−0.338091 | + | 0.941114i | \(0.609781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09761 | −0.0690436 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.9865 | −0.361234 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.6058 | −0.938527 | −0.469263 | − | 0.883058i | \(-0.655480\pi\) | ||||
−0.469263 | + | 0.883058i | \(0.655480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.69918 | 0.0556883 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.4522 | 0.407231 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.79147 | 0.319873 | 0.159937 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.7249 | 1.39279 | 0.696395 | − | 0.717658i | \(-0.254786\pi\) | ||||
0.696395 | + | 0.717658i | \(0.254786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.43515 | −0.0792992 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.69250 | 0.0874945 | 0.0437473 | − | 0.999043i | \(-0.486070\pi\) | ||||
0.0437473 | + | 0.999043i | \(0.486070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.74351 | −0.316288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.2706 | −0.624235 | −0.312117 | − | 0.950044i | \(-0.601038\pi\) | ||||
−0.312117 | + | 0.950044i | \(0.601038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.25756 | 0.299568 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.8591 | −0.867326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.827311 | −0.0266874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0109521 | 0.000352561 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.3997 | −0.527378 | −0.263689 | − | 0.964608i | \(-0.584939\pi\) | ||||
−0.263689 | + | 0.964608i | \(0.584939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.1667 | 1.73829 | 0.869146 | − | 0.494555i | \(-0.164669\pi\) | ||||
0.869146 | + | 0.494555i | \(0.164669\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.73983 | −0.119894 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.2388 | 0.807462 | 0.403731 | − | 0.914878i | \(-0.367713\pi\) | ||||
0.403731 | + | 0.914878i | \(0.367713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4398 | 0.365616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.4824 | 0.940343 | 0.470172 | − | 0.882575i | \(-0.344192\pi\) | ||||
0.470172 | + | 0.882575i | \(0.344192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0906 | 0.417102 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.77576 | −0.183659 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3421 | −1.18621 | −0.593105 | − | 0.805125i | \(-0.702098\pi\) | ||||
−0.593105 | + | 0.805125i | \(0.702098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8980 | 0.725917 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.8442 | −1.32522 | −0.662609 | − | 0.748965i | \(-0.730551\pi\) | ||||
−0.662609 | + | 0.748965i | \(0.730551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.a.bt.1.5 | ✓ | 6 | |
3.2 | odd | 2 | 8280.2.a.bu.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8280.2.a.bu.1.5 | yes | 6 | 3.2 | odd | 2 |