Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(1,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, 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("880.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 110) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.1 |
$q$-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 | ||||||||
\(3\) | 3.37228 | 1.94699 | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) | ||||
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.37228 | −1.27460 | −0.637301 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637301 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.37228 | 2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.37228 | 0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.37228 | 0.332827 | 0.166414 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166414 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.627719 | −0.144009 | −0.0720043 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720043 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.3723 | −2.48164 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.74456 | −0.572281 | −0.286140 | − | 0.958188i | \(-0.592372\pi\) | ||||
−0.286140 | + | 0.958188i | \(0.592372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.1168 | 3.48659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37228 | 0.254826 | 0.127413 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127413 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37228 | −0.605680 | −0.302840 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302840 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.37228 | 0.587039 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.37228 | 1.54079 | 0.770397 | − | 0.637565i | \(-0.220058\pi\) | ||||
0.770397 | + | 0.637565i | \(0.220058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.74456 | 1.07999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4891 | −1.79430 | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.37228 | 1.24807 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.74456 | −0.400336 | −0.200168 | − | 0.979762i | \(-0.564149\pi\) | ||||
−0.200168 | + | 0.979762i | \(0.564149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.62772 | 0.648010 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.11684 | −0.565492 | −0.282746 | − | 0.959195i | \(-0.591245\pi\) | ||||
−0.282746 | + | 0.959195i | \(0.591245\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.11684 | −0.280383 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74456 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.37228 | −0.687850 | −0.343925 | − | 0.938997i | \(-0.611757\pi\) | ||||
−0.343925 | + | 0.938997i | \(0.611757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28.2337 | −3.55711 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.25544 | −1.11422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1168 | −1.20065 | −0.600324 | − | 0.799757i | \(-0.704962\pi\) | ||||
−0.600324 | + | 0.799757i | \(0.704962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.4891 | −1.81286 | −0.906432 | − | 0.422351i | \(-0.861205\pi\) | ||||
−0.906432 | + | 0.422351i | \(0.861205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.37228 | 0.389398 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.37228 | −0.384307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.25544 | 0.141248 | 0.0706239 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706239 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.74456 | 0.301255 | 0.150627 | − | 0.988591i | \(-0.451871\pi\) | ||||
0.150627 | + | 0.988591i | \(0.451871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.37228 | 0.148845 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.62772 | 0.496144 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.37228 | −0.145462 | −0.0727308 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727308 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.74456 | −0.707022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.3723 | −1.17925 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.627719 | −0.0644026 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7446 | −1.29401 | −0.647007 | − | 0.762484i | \(-0.723980\pi\) | ||||
−0.647007 | + | 0.762484i | \(0.723980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.37228 | 0.841446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.48913 | 0.934991 | 0.467496 | − | 0.883995i | \(-0.345156\pi\) | ||||
0.467496 | + | 0.883995i | \(0.345156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.3723 | −1.10982 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4891 | −1.48359 | −0.741795 | − | 0.670627i | \(-0.766025\pi\) | ||||
−0.741795 | + | 0.670627i | \(0.766025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.6060 | 2.99991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25544 | 0.306246 | 0.153123 | − | 0.988207i | \(-0.451067\pi\) | ||||
0.153123 | + | 0.988207i | \(0.451067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.74456 | −0.255932 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7446 | 1.54804 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.62772 | −0.424222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −38.7446 | −3.49348 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.4891 | 1.18765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.1168 | −1.93236 | −0.966179 | − | 0.257873i | \(-0.916978\pi\) | ||||
−0.966179 | + | 0.257873i | \(0.916978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.11684 | 0.183554 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.1168 | 1.55925 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.74456 | 0.747098 | 0.373549 | − | 0.927610i | \(-0.378141\pi\) | ||||
0.373549 | + | 0.927610i | \(0.378141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.25544 | −0.779448 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.37228 | 0.113962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.7446 | 1.21611 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.6060 | 1.77003 | 0.885015 | − | 0.465563i | \(-0.154148\pi\) | ||||
0.885015 | + | 0.465563i | \(0.154148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2337 | 0.995563 | 0.497782 | − | 0.867302i | \(-0.334148\pi\) | ||||
0.497782 | + | 0.867302i | \(0.334148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.4891 | 0.928841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.37228 | −0.270868 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.37228 | 0.747989 | 0.373995 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373995 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.8832 | −1.10101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.25544 | 0.729431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.88316 | 0.460804 | 0.230402 | − | 0.973095i | \(-0.425996\pi\) | ||||
0.230402 | + | 0.973095i | \(0.425996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.37228 | 0.262532 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.62772 | 0.358104 | 0.179052 | − | 0.983840i | \(-0.442697\pi\) | ||||
0.179052 | + | 0.983840i | \(0.442697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.25544 | −0.401893 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37228 | −0.254921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.25544 | 0.695681 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.1168 | −1.33924 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.37228 | 0.689064 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.37228 | 0.100351 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −61.0951 | −4.44401 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.48913 | 0.397179 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8614 | 1.06975 | 0.534874 | − | 0.844932i | \(-0.320359\pi\) | ||||
0.534874 | + | 0.844932i | \(0.320359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.74456 | 0.482988 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.7446 | −1.47799 | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
−0.738994 | + | 0.673712i | \(0.764699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1168 | −1.28427 | −0.642135 | − | 0.766592i | \(-0.721951\pi\) | ||||
−0.642135 | + | 0.766592i | \(0.721951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.9783 | −1.90290 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.62772 | −0.324802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4891 | −0.802435 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.9783 | −1.59710 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.627719 | −0.0434202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.11684 | −0.421101 | −0.210550 | − | 0.977583i | \(-0.567526\pi\) | ||||
−0.210550 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.1168 | −2.33765 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3723 | 0.772001 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −52.2337 | −3.52963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.74456 | 0.184619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7446 | 1.25523 | 0.627614 | − | 0.778524i | \(-0.284031\pi\) | ||||
0.627614 | + | 0.778524i | \(0.284031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.37228 | 0.558152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74456 | 0.182163 | 0.0910815 | − | 0.995843i | \(-0.470968\pi\) | ||||
0.0910815 | + | 0.995843i | \(0.470968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.3723 | −0.748241 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.37228 | 0.0899011 | 0.0449506 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449506 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.74456 | −0.179036 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.23369 | 0.275008 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.7446 | 0.953746 | 0.476873 | − | 0.878972i | \(-0.341770\pi\) | ||||
0.476873 | + | 0.878972i | \(0.341770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 66.9783 | 4.29666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.25544 | −0.0798816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.25544 | 0.586540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.74456 | −0.173235 | −0.0866176 | − | 0.996242i | \(-0.527606\pi\) | ||||
−0.0866176 | + | 0.996242i | \(0.527606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.74456 | −0.172549 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.62772 | 0.289799 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.6060 | −1.96390 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4891 | 0.711159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8614 | 1.53302 | 0.766510 | − | 0.642232i | \(-0.221992\pi\) | ||||
0.766510 | + | 0.642232i | \(0.221992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.11684 | −0.252896 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.62772 | −0.283212 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.74456 | −0.533165 | −0.266583 | − | 0.963812i | \(-0.585895\pi\) | ||||
−0.266583 | + | 0.963812i | \(0.585895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.7446 | −1.37656 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7446 | −0.765747 | −0.382873 | − | 0.923801i | \(-0.625065\pi\) | ||||
−0.382873 | + | 0.923801i | \(0.625065\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.2337 | −1.69031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.25544 | −0.312403 | −0.156202 | − | 0.987725i | \(-0.549925\pi\) | ||||
−0.156202 | + | 0.987725i | \(0.549925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.11684 | −0.125391 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.7446 | 2.28702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1168 | −0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42.9783 | −2.51943 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4891 | 1.37225 | 0.686125 | − | 0.727484i | \(-0.259310\pi\) | ||||
0.686125 | + | 0.727484i | \(0.259310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.74456 | 0.159795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.1168 | 1.05125 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.48913 | −0.317444 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4891 | −0.777500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.2337 | 1.16240 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.37228 | −0.307616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.25544 | −0.299944 | −0.149972 | − | 0.988690i | \(-0.547918\pi\) | ||||
−0.149972 | + | 0.988690i | \(0.547918\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.0000 | 1.82042 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.3723 | −1.09850 | −0.549251 | − | 0.835658i | \(-0.685087\pi\) | ||||
−0.549251 | + | 0.835658i | \(0.685087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.2337 | −1.59079 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.3505 | −1.36766 | −0.683831 | − | 0.729640i | \(-0.739687\pi\) | ||||
−0.683831 | + | 0.729640i | \(0.739687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.37228 | 0.0768330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.4674 | 2.25867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.861407 | −0.0479299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −52.2337 | −2.88853 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.25544 | 0.510269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.9783 | −1.70272 | −0.851359 | − | 0.524583i | \(-0.824221\pi\) | ||||
−0.851359 | + | 0.524583i | \(0.824221\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 78.4674 | 4.29999 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1168 | 1.31373 | 0.656864 | − | 0.754009i | \(-0.271883\pi\) | ||||
0.656864 | + | 0.754009i | \(0.271883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9783 | 0.596257 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.37228 | −0.182619 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.25544 | −0.498296 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.2337 | 1.73040 | 0.865198 | − | 0.501431i | \(-0.167193\pi\) | ||||
0.865198 | + | 0.501431i | \(0.167193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4891 | 1.04323 | 0.521614 | − | 0.853181i | \(-0.325330\pi\) | ||||
0.521614 | + | 0.853181i | \(0.325330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.2337 | 1.93401 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.510875 | −0.0271911 | −0.0135956 | − | 0.999908i | \(-0.504328\pi\) | ||||
−0.0135956 | + | 0.999908i | \(0.504328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1168 | −0.536946 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6060 | −0.825955 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.37228 | 0.176999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.4891 | −0.810738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | 0.208798 | 0.104399 | − | 0.994535i | \(-0.466708\pi\) | ||||
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −96.1902 | −5.00746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.8832 | 0.720778 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.4891 | 1.63045 | 0.815223 | − | 0.579148i | \(-0.196615\pi\) | ||||
0.815223 | + | 0.579148i | \(0.196615\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.37228 | 0.174144 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.74456 | 0.141352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.233688 | 0.0120037 | 0.00600187 | − | 0.999982i | \(-0.498090\pi\) | ||||
0.00600187 | + | 0.999982i | \(0.498090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.9783 | −1.38214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.2337 | −1.64706 | −0.823532 | − | 0.567269i | \(-0.808000\pi\) | ||||
−0.823532 | + | 0.567269i | \(0.808000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.37228 | −0.171867 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.4891 | 1.70235 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.76631 | −0.190471 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −74.5842 | −3.76228 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.25544 | 0.0631679 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9783 | 1.25362 | 0.626811 | − | 0.779171i | \(-0.284360\pi\) | ||||
0.626811 | + | 0.779171i | \(0.284360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.13859 | 0.357377 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3723 | 0.667780 | 0.333890 | − | 0.942612i | \(-0.391639\pi\) | ||||
0.333890 | + | 0.942612i | \(0.391639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.74456 | −0.335971 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.9783 | 1.78777 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.37228 | 0.464567 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.76631 | −0.0873385 | −0.0436693 | − | 0.999046i | \(-0.513905\pi\) | ||||
−0.0436693 | + | 0.999046i | \(0.513905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.4891 | 1.45459 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.25544 | −0.455430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.74456 | 0.134725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4891 | 0.660565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2337 | 0.498759 | 0.249380 | − | 0.968406i | \(-0.419773\pi\) | ||||
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.9783 | −1.11724 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.37228 | 0.0665654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1168 | 0.876736 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.74456 | 0.325631 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.9783 | 1.68484 | 0.842422 | − | 0.538819i | \(-0.181129\pi\) | ||||
0.842422 | + | 0.538819i | \(0.181129\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7228 | 1.33227 | 0.666137 | − | 0.745830i | \(-0.267947\pi\) | ||||
0.666137 | + | 0.745830i | \(0.267947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.62772 | 0.221882 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.72281 | 0.0824133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9783 | −0.905782 | −0.452891 | − | 0.891566i | \(-0.649607\pi\) | ||||
−0.452891 | + | 0.891566i | \(0.649607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.6060 | 1.74314 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.4891 | −1.40107 | −0.700535 | − | 0.713618i | \(-0.747055\pi\) | ||||
−0.700535 | + | 0.713618i | \(0.747055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.37228 | −0.0650524 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 72.8614 | 3.44623 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9783 | 1.36757 | 0.683784 | − | 0.729684i | \(-0.260333\pi\) | ||||
0.683784 | + | 0.729684i | \(0.260333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4891 | −0.541002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 41.2554 | 1.93835 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.74456 | −0.316190 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.3505 | −0.764846 | −0.382423 | − | 0.923987i | \(-0.624910\pi\) | ||||
−0.382423 | + | 0.923987i | \(0.624910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.8614 | 1.16043 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1168 | 0.750636 | 0.375318 | − | 0.926896i | \(-0.377533\pi\) | ||||
0.375318 | + | 0.926896i | \(0.377533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.233688 | 0.0108604 | 0.00543020 | − | 0.999985i | \(-0.498272\pi\) | ||||
0.00543020 | + | 0.999985i | \(0.498272\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.3723 | −0.527377 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3723 | 0.896442 | 0.448221 | − | 0.893923i | \(-0.352058\pi\) | ||||
0.448221 | + | 0.893923i | \(0.352058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.9783 | 1.24574 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.6060 | 1.45633 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | 0.183920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.627719 | −0.0288017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.4674 | −1.57815 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.48913 | −0.250805 | −0.125402 | − | 0.992106i | \(-0.540022\pi\) | ||||
−0.125402 | + | 0.992106i | \(0.540022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7446 | 0.854678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 31.2119 | 1.42019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.7446 | −0.578701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0000 | −0.906287 | −0.453143 | − | 0.891438i | \(-0.649697\pi\) | ||||
−0.453143 | + | 0.891438i | \(0.649697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8397 | 0.897180 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.37228 | 0.332706 | 0.166353 | − | 0.986066i | \(-0.446801\pi\) | ||||
0.166353 | + | 0.986066i | \(0.446801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.88316 | 0.0848131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.37228 | 0.376306 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.1168 | 1.53035 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.4891 | 1.49918 | 0.749590 | − | 0.661903i | \(-0.230251\pi\) | ||||
0.749590 | + | 0.661903i | \(0.230251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.6060 | 0.697223 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9783 | 1.55960 | 0.779802 | − | 0.626027i | \(-0.215320\pi\) | ||||
0.779802 | + | 0.626027i | \(0.215320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.3505 | −1.34791 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.76631 | 0.432884 | 0.216442 | − | 0.976295i | \(-0.430555\pi\) | ||||
0.216442 | + | 0.976295i | \(0.430555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 52.2337 | 2.31068 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.3723 | −0.502098 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.48913 | 0.418141 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.74456 | −0.120706 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.2337 | −0.888160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5109 | 0.548111 | 0.274056 | − | 0.961714i | \(-0.411635\pi\) | ||||
0.274056 | + | 0.961714i | \(0.411635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.9783 | −1.35458 | −0.677292 | − | 0.735714i | \(-0.736847\pi\) | ||||
−0.677292 | + | 0.735714i | \(0.736847\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.3723 | −0.496327 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.62772 | −0.201587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4674 | −0.672495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.9783 | 0.997171 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9783 | −0.995299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | 0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.4674 | 1.74630 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.37228 | 0.188327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1168 | −0.864891 | −0.432445 | − | 0.901660i | \(-0.642349\pi\) | ||||
−0.432445 | + | 0.901660i | \(0.642349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −33.7228 | −1.44718 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.4891 | −0.663481 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −44.9783 | −1.91962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.861407 | −0.0366972 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.23369 | −0.180035 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 31.6060 | 1.34160 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.97825 | 0.210935 | 0.105468 | − | 0.994423i | \(-0.466366\pi\) | ||||
0.105468 | + | 0.994423i | \(0.466366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.62772 | 0.195382 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.23369 | 0.347009 | 0.173504 | − | 0.984833i | \(-0.444491\pi\) | ||||
0.173504 | + | 0.984833i | \(0.444491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.25544 | 0.136957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −121.329 | −5.09533 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.2554 | −0.639541 | −0.319771 | − | 0.947495i | \(-0.603606\pi\) | ||||
−0.319771 | + | 0.947495i | \(0.603606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.3723 | −0.643310 | −0.321655 | − | 0.946857i | \(-0.604239\pi\) | ||||
−0.321655 | + | 0.946857i | \(0.604239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5109 | 0.773303 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.74456 | −0.114456 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9783 | 1.53942 | 0.769712 | − | 0.638391i | \(-0.220400\pi\) | ||||
0.769712 | + | 0.638391i | \(0.220400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.1168 | 2.08278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.25544 | −0.383980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.11684 | −0.170502 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.7446 | 0.692302 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.8614 | −1.02614 | −0.513070 | − | 0.858347i | \(-0.671492\pi\) | ||||
−0.513070 | + | 0.858347i | \(0.671492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.11684 | 0.0872230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −69.9565 | −2.87763 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5109 | −0.513760 | −0.256880 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256880 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.62772 | −0.189718 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −61.0951 | −2.50046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.6060 | 1.61826 | 0.809128 | − | 0.587632i | \(-0.199940\pi\) | ||||
0.809128 | + | 0.587632i | \(0.199940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5109 | −0.673493 | −0.336746 | − | 0.941595i | \(-0.609326\pi\) | ||||
−0.336746 | + | 0.941595i | \(0.609326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.9783 | −2.72757 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.88316 | 0.238790 | 0.119395 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119395 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.6060 | −0.632386 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.48913 | −0.222066 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5109 | 0.828426 | 0.414213 | − | 0.910180i | \(-0.364057\pi\) | ||||
0.414213 | + | 0.910180i | \(0.364057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.7446 | −1.56233 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.23369 | −0.0899249 | −0.0449624 | − | 0.998989i | \(-0.514317\pi\) | ||||
−0.0449624 | + | 0.998989i | \(0.514317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.4674 | 1.78729 | 0.893647 | − | 0.448770i | \(-0.148138\pi\) | ||||
0.893647 | + | 0.448770i | \(0.148138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7228 | −1.99531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.62772 | 0.185406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.11684 | −0.0845386 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.8614 | 0.512818 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.1168 | −1.67665 | −0.838323 | − | 0.545175i | \(-0.816463\pi\) | ||||
−0.838323 | + | 0.545175i | \(0.816463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.6277 | −0.819878 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.74456 | 0.346472 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84.7011 | −3.35072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0951 | −1.07019 | −0.535096 | − | 0.844791i | \(-0.679725\pi\) | ||||
−0.535096 | + | 0.844791i | \(0.679725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.88316 | 0.232009 | 0.116005 | − | 0.993249i | \(-0.462991\pi\) | ||||
0.116005 | + | 0.993249i | \(0.462991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.4891 | 0.531134 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.7228 | 1.48304 | 0.741518 | − | 0.670933i | \(-0.234106\pi\) | ||||
0.741518 | + | 0.670933i | \(0.234106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.74456 | 0.107734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.3505 | 1.50308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.6277 | 0.415895 | 0.207947 | − | 0.978140i | \(-0.433322\pi\) | ||||
0.207947 | + | 0.978140i | \(0.433322\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.1168 | −0.864177 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −129.679 | −5.05927 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.8614 | −0.501009 | −0.250505 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250505 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.51087 | 0.331035 | 0.165517 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165517 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.25544 | 0.359451 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.11684 | 0.0820877 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.76631 | −0.145832 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 63.2119 | 2.44391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.37228 | −0.207395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.8614 | 0.572865 | 0.286433 | − | 0.958100i | \(-0.407531\pi\) | ||||
0.286433 | + | 0.958100i | \(0.407531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.1168 | 0.697318 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.25544 | 0.125117 | 0.0625583 | − | 0.998041i | \(-0.480074\pi\) | ||||
0.0625583 | + | 0.998041i | \(0.480074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.9783 | 1.64935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.25544 | 0.354669 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.6277 | 1.09541 | 0.547705 | − | 0.836672i | \(-0.315502\pi\) | ||||
0.547705 | + | 0.836672i | \(0.315502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.74456 | 0.334113 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.7228 | −1.28661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.23369 | −0.313679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2337 | −1.53056 | −0.765281 | − | 0.643697i | \(-0.777400\pi\) | ||||
−0.765281 | + | 0.643697i | \(0.777400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −28.2337 | −1.07251 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7663 | −0.597192 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.62772 | 0.175036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3723 | −1.41153 | −0.705766 | − | 0.708445i | \(-0.749397\pi\) | ||||
−0.705766 | + | 0.708445i | \(0.749397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.88316 | −0.221887 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.25544 | −0.348580 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.2337 | −0.760966 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.5109 | 0.394189 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.25544 | 0.346619 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 49.7228 | 1.85693 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8832 | −0.517754 | −0.258877 | − | 0.965910i | \(-0.583352\pi\) | ||||
−0.258877 | + | 0.965910i | \(0.583352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | −1.19174 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −74.1902 | −2.75916 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.37228 | 0.0509652 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2337 | 0.898778 | 0.449389 | − | 0.893336i | \(-0.351642\pi\) | ||||
0.449389 | + | 0.893336i | \(0.351642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 117.935 | 4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.48913 | 0.203023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.2337 | 1.70768 | 0.853840 | − | 0.520535i | \(-0.174268\pi\) | ||||
0.853840 | + | 0.520535i | \(0.174268\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.7446 | 0.543861 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4674 | 0.752905 | 0.376452 | − | 0.926436i | \(-0.377144\pi\) | ||||
0.376452 | + | 0.926436i | \(0.377144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.23369 | −0.155528 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.62772 | 0.169775 | 0.0848873 | − | 0.996391i | \(-0.472947\pi\) | ||||
0.0848873 | + | 0.996391i | \(0.472947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.6060 | 0.791581 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.9783 | 0.840730 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.4674 | −1.47865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.86141 | −0.323357 | −0.161679 | − | 0.986843i | \(-0.551691\pi\) | ||||
−0.161679 | + | 0.986843i | \(0.551691\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.25544 | −0.337287 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2337 | 0.445229 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.9783 | −0.762467 | −0.381234 | − | 0.924479i | \(-0.624501\pi\) | ||||
−0.381234 | + | 0.924479i | \(0.624501\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.25544 | −0.335951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.97825 | 0.180461 | 0.0902307 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902307 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52.2337 | 1.89099 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.4891 | 0.415390 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.48913 | 0.198201 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.7011 | 2.18610 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.6060 | −1.20872 | −0.604361 | − | 0.796710i | \(-0.706572\pi\) | ||||
−0.604361 | + | 0.796710i | \(0.706572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.37228 | −0.121136 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −106.584 | −3.82369 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.21194 | 0.258395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1168 | −0.362009 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.8614 | 0.888474 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.37228 | 0.334511 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4674 | 1.58509 | 0.792545 | − | 0.609813i | \(-0.208755\pi\) | ||||
0.792545 | + | 0.609813i | \(0.208755\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 83.8397 | 2.98477 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7446 | −0.381551 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.8832 | −0.492385 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4891 | 0.406966 | 0.203483 | − | 0.979079i | \(-0.434774\pi\) | ||||
0.203483 | + | 0.979079i | \(0.434774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.76631 | −0.133243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4891 | −0.405948 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.4891 | −0.546599 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.25544 | 0.326211 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.4891 | −1.03807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.8614 | −1.57530 | −0.787649 | − | 0.616125i | \(-0.788702\pi\) | ||||
−0.787649 | + | 0.616125i | \(0.788702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.9565 | 1.89234 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.88316 | 0.206078 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.51087 | −0.0878444 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −56.4674 | −1.97313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4891 | 0.400973 | 0.200487 | − | 0.979696i | \(-0.435748\pi\) | ||||
0.200487 | + | 0.979696i | \(0.435748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0000 | 0.976019 | 0.488009 | − | 0.872838i | \(-0.337723\pi\) | ||||
0.488009 | + | 0.872838i | \(0.337723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.37228 | 0.117408 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.9783 | −1.63359 | −0.816797 | − | 0.576925i | \(-0.804252\pi\) | ||||
−0.816797 | + | 0.576925i | \(0.804252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.7446 | −0.859414 | −0.429707 | − | 0.902968i | \(-0.641383\pi\) | ||||
−0.429707 | + | 0.902968i | \(0.641383\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.9783 | −1.49090 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.62772 | 0.160149 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −61.0951 | −2.11176 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9783 | 0.379011 | 0.189506 | − | 0.981880i | \(-0.439311\pi\) | ||||
0.189506 | + | 0.981880i | \(0.439311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60.7011 | 2.09066 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.37228 | −0.115873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.7228 | −0.608245 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7228 | −0.881767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.4674 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.25544 | −0.179732 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.3505 | 1.24171 | 0.620855 | − | 0.783925i | \(-0.286785\pi\) | ||||
0.620855 | + | 0.783925i | \(0.286785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.7446 | 1.45843 | 0.729213 | − | 0.684287i | \(-0.239886\pi\) | ||||
0.729213 | + | 0.684287i | \(0.239886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 130.658 | 4.45280 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.2554 | −0.723544 | −0.361772 | − | 0.932267i | \(-0.617828\pi\) | ||||
−0.361772 | + | 0.932267i | \(0.617828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.9783 | −1.73131 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.25544 | 0.0425878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −106.701 | −3.61128 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.37228 | −0.114004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.9783 | 1.24867 | 0.624333 | − | 0.781158i | \(-0.285371\pi\) | ||||
0.624333 | + | 0.781158i | \(0.285371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 79.2119 | 2.67175 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.37228 | −0.113486 | −0.0567432 | − | 0.998389i | \(-0.518072\pi\) | ||||
−0.0567432 | + | 0.998389i | \(0.518072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.25544 | 0.311118 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.9783 | 0.368614 | 0.184307 | − | 0.982869i | \(-0.440996\pi\) | ||||
0.184307 | + | 0.982869i | \(0.440996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.9783 | 0.904821 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.9783 | 1.20532 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.72281 | 0.0576517 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.5109 | −0.618060 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.62772 | −0.154343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64947 | −0.188211 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.4891 | −1.51378 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | −0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.394031 | 0.0130836 | 0.00654179 | − | 0.999979i | \(-0.497918\pi\) | ||||
0.00654179 | + | 0.999979i | \(0.497918\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.2337 | 1.66615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.39403 | 0.278107 | 0.139053 | − | 0.990285i | \(-0.455594\pi\) | ||||
0.139053 | + | 0.990285i | \(0.455594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.74456 | 0.0908318 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.1168 | −0.598924 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74.5842 | 2.46299 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.9783 | −0.626035 | −0.313017 | − | 0.949747i | \(-0.601340\pi\) | ||||
−0.313017 | + | 0.949747i | \(0.601340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7228 | −0.583987 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.2337 | −0.666000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.37228 | 0.308159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 79.4456 | 2.60934 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.3505 | 0.798915 | 0.399458 | − | 0.916752i | \(-0.369199\pi\) | ||||
0.399458 | + | 0.916752i | \(0.369199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74456 | −0.0899494 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −65.3288 | −2.13877 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.37228 | 0.0448784 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5109 | −0.931410 | −0.465705 | − | 0.884940i | \(-0.654199\pi\) | ||||
−0.465705 | + | 0.884940i | \(0.654199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −74.1902 | −2.42111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0951 | −0.492086 | −0.246043 | − | 0.969259i | \(-0.579130\pi\) | ||||
−0.246043 | + | 0.969259i | \(0.579130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.5326 | 1.02684 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −61.0951 | −1.98742 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.8614 | −1.58778 | −0.793891 | − | 0.608060i | \(-0.791948\pi\) | ||||
−0.793891 | + | 0.608060i | \(0.791948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.9783 | −1.00560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82.1168 | −2.66282 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.1168 | 1.29951 | 0.649756 | − | 0.760143i | \(-0.274871\pi\) | ||||
0.649756 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.48913 | 0.177624 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.62772 | 0.149593 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.4891 | −0.952254 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 100.467 | 3.23752 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.8614 | 0.478406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.6060 | −1.53090 | −0.765452 | − | 0.643493i | \(-0.777485\pi\) | ||||
−0.765452 | + | 0.643493i | \(0.777485\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.90491 | −0.0933190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.02175 | 0.0327895 | 0.0163947 | − | 0.999866i | \(-0.494781\pi\) | ||||
0.0163947 | + | 0.999866i | \(0.494781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.4891 | −0.432442 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.74456 | 0.215999 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.2337 | 0.455376 | 0.227688 | − | 0.973734i | \(-0.426883\pi\) | ||||
0.227688 | + | 0.973734i | \(0.426883\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.37228 | −0.0438583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −129.679 | −4.14034 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.7228 | 0.437690 | 0.218845 | − | 0.975760i | \(-0.429771\pi\) | ||||
0.218845 | + | 0.975760i | \(0.429771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.7446 | −0.660977 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.2119 | 0.993487 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.9783 | −0.349088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −104.467 | −3.31517 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.1168 | −0.574343 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.2337 | 0.704148 | 0.352074 | − | 0.935972i | \(-0.385477\pi\) | ||||
0.352074 | + | 0.935972i | \(0.385477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 169.796 | 5.37211 |
(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 | 880.2.a.n.1.2 | 2 | ||
3.2 | odd | 2 | 7920.2.a.bq.1.1 | 2 | |||
4.3 | odd | 2 | 110.2.a.d.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 4400.2.b.p.4049.1 | 4 | |||
5.3 | odd | 4 | 4400.2.b.p.4049.4 | 4 | |||
5.4 | even | 2 | 4400.2.a.bl.1.1 | 2 | |||
8.3 | odd | 2 | 3520.2.a.bq.1.2 | 2 | |||
8.5 | even | 2 | 3520.2.a.bj.1.1 | 2 | |||
11.10 | odd | 2 | 9680.2.a.bt.1.2 | 2 | |||
12.11 | even | 2 | 990.2.a.m.1.2 | 2 | |||
20.3 | even | 4 | 550.2.b.f.199.3 | 4 | |||
20.7 | even | 4 | 550.2.b.f.199.2 | 4 | |||
20.19 | odd | 2 | 550.2.a.n.1.2 | 2 | |||
28.27 | even | 2 | 5390.2.a.bp.1.2 | 2 | |||
44.43 | even | 2 | 1210.2.a.r.1.1 | 2 | |||
60.23 | odd | 4 | 4950.2.c.bc.199.1 | 4 | |||
60.47 | odd | 4 | 4950.2.c.bc.199.4 | 4 | |||
60.59 | even | 2 | 4950.2.a.bw.1.1 | 2 | |||
220.219 | even | 2 | 6050.2.a.cb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
550.2.a.n.1.2 | 2 | 20.19 | odd | 2 | |||
550.2.b.f.199.2 | 4 | 20.7 | even | 4 | |||
550.2.b.f.199.3 | 4 | 20.3 | even | 4 | |||
880.2.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
990.2.a.m.1.2 | 2 | 12.11 | even | 2 | |||
1210.2.a.r.1.1 | 2 | 44.43 | even | 2 | |||
3520.2.a.bj.1.1 | 2 | 8.5 | even | 2 | |||
3520.2.a.bq.1.2 | 2 | 8.3 | odd | 2 | |||
4400.2.a.bl.1.1 | 2 | 5.4 | even | 2 | |||
4400.2.b.p.4049.1 | 4 | 5.2 | odd | 4 | |||
4400.2.b.p.4049.4 | 4 | 5.3 | odd | 4 | |||
4950.2.a.bw.1.1 | 2 | 60.59 | even | 2 | |||
4950.2.c.bc.199.1 | 4 | 60.23 | odd | 4 | |||
4950.2.c.bc.199.4 | 4 | 60.47 | odd | 4 | |||
5390.2.a.bp.1.2 | 2 | 28.27 | even | 2 | |||
6050.2.a.cb.1.2 | 2 | 220.219 | even | 2 | |||
7920.2.a.bq.1.1 | 2 | 3.2 | odd | 2 | |||
9680.2.a.bt.1.2 | 2 | 11.10 | odd | 2 |