Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.10784448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - 4x^{3} + 31x^{2} + 22x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.0816388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.34292 | −0.775337 | −0.387669 | − | 0.921799i | \(-0.626719\pi\) | ||||
−0.387669 | + | 0.921799i | \(0.626719\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.34292 | −0.548246 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.19656 | −0.398853 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.34292 | −0.387669 | ||||||||
\(13\) | −4.31157 | −1.19582 | −0.597908 | − | 0.801565i | \(-0.704001\pi\) | ||||
−0.597908 | + | 0.801565i | \(0.704001\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.34292 | −0.346741 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.63565 | −0.639240 | −0.319620 | − | 0.947546i | \(-0.603555\pi\) | ||||
−0.319620 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(18\) | −1.19656 | −0.282031 | ||||||||
\(19\) | −6.54735 | −1.50207 | −0.751033 | − | 0.660265i | \(-0.770444\pi\) | ||||
−0.751033 | + | 0.660265i | \(0.770444\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.34292 | −0.293050 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16521 | −0.659992 | −0.329996 | − | 0.943982i | \(-0.607047\pi\) | ||||
−0.329996 | + | 0.943982i | \(0.607047\pi\) | |||||||
\(24\) | −1.34292 | −0.274123 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.31157 | −0.845569 | ||||||||
\(27\) | 5.63565 | 1.08458 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.13193 | −0.210194 | −0.105097 | − | 0.994462i | \(-0.533515\pi\) | ||||
−0.105097 | + | 0.994462i | \(0.533515\pi\) | |||||||
\(30\) | −1.34292 | −0.245183 | ||||||||
\(31\) | 1.14637 | 0.205893 | 0.102947 | − | 0.994687i | \(-0.467173\pi\) | ||||
0.102947 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.63565 | −0.452011 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.19656 | −0.199426 | ||||||||
\(37\) | 3.13193 | 0.514886 | 0.257443 | − | 0.966293i | \(-0.417120\pi\) | ||||
0.257443 | + | 0.966293i | \(0.417120\pi\) | |||||||
\(38\) | −6.54735 | −1.06212 | ||||||||
\(39\) | 5.79011 | 0.927160 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.521462 | 0.0814386 | 0.0407193 | − | 0.999171i | \(-0.487035\pi\) | ||||
0.0407193 | + | 0.999171i | \(0.487035\pi\) | |||||||
\(42\) | −1.34292 | −0.207218 | ||||||||
\(43\) | −4.96783 | −0.757587 | −0.378793 | − | 0.925481i | \(-0.623661\pi\) | ||||
−0.378793 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.19656 | −0.178372 | ||||||||
\(46\) | −3.16521 | −0.466685 | ||||||||
\(47\) | 11.8090 | 1.72251 | 0.861257 | − | 0.508170i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508170i | \(0.169678\pi\) | |||||||
\(48\) | −1.34292 | −0.193834 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.53948 | 0.495626 | ||||||||
\(52\) | −4.31157 | −0.597908 | ||||||||
\(53\) | 2.59396 | 0.356308 | 0.178154 | − | 0.984003i | \(-0.442988\pi\) | ||||
0.178154 | + | 0.984003i | \(0.442988\pi\) | |||||||
\(54\) | 5.63565 | 0.766915 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 8.79259 | 1.16461 | ||||||||
\(58\) | −1.13193 | −0.148630 | ||||||||
\(59\) | 10.9472 | 1.42521 | 0.712604 | − | 0.701567i | \(-0.247516\pi\) | ||||
0.712604 | + | 0.701567i | \(0.247516\pi\) | |||||||
\(60\) | −1.34292 | −0.173371 | ||||||||
\(61\) | 5.82933 | 0.746369 | 0.373185 | − | 0.927757i | \(-0.378266\pi\) | ||||
0.373185 | + | 0.927757i | \(0.378266\pi\) | |||||||
\(62\) | 1.14637 | 0.145589 | ||||||||
\(63\) | −1.19656 | −0.150752 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.31157 | −0.534785 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.72249 | −1.18779 | −0.593895 | − | 0.804542i | \(-0.702411\pi\) | ||||
−0.593895 | + | 0.804542i | \(0.702411\pi\) | |||||||
\(68\) | −2.63565 | −0.319620 | ||||||||
\(69\) | 4.25063 | 0.511716 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −4.50169 | −0.534252 | −0.267126 | − | 0.963662i | \(-0.586074\pi\) | ||||
−0.267126 | + | 0.963662i | \(0.586074\pi\) | |||||||
\(72\) | −1.19656 | −0.141016 | ||||||||
\(73\) | 12.1269 | 1.41934 | 0.709672 | − | 0.704533i | \(-0.248843\pi\) | ||||
0.709672 | + | 0.704533i | \(0.248843\pi\) | |||||||
\(74\) | 3.13193 | 0.364079 | ||||||||
\(75\) | −1.34292 | −0.155067 | ||||||||
\(76\) | −6.54735 | −0.751033 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.79011 | 0.655601 | ||||||||
\(79\) | 17.0893 | 1.92270 | 0.961349 | − | 0.275334i | \(-0.0887885\pi\) | ||||
0.961349 | + | 0.275334i | \(0.0887885\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −3.97858 | −0.442064 | ||||||||
\(82\) | 0.521462 | 0.0575858 | ||||||||
\(83\) | 9.06142 | 0.994620 | 0.497310 | − | 0.867573i | \(-0.334321\pi\) | ||||
0.497310 | + | 0.867573i | \(0.334321\pi\) | |||||||
\(84\) | −1.34292 | −0.146525 | ||||||||
\(85\) | −2.63565 | −0.285877 | ||||||||
\(86\) | −4.96783 | −0.535695 | ||||||||
\(87\) | 1.52009 | 0.162971 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.17843 | 0.760913 | 0.380456 | − | 0.924799i | \(-0.375767\pi\) | ||||
0.380456 | + | 0.924799i | \(0.375767\pi\) | |||||||
\(90\) | −1.19656 | −0.126128 | ||||||||
\(91\) | −4.31157 | −0.451976 | ||||||||
\(92\) | −3.16521 | −0.329996 | ||||||||
\(93\) | −1.53948 | −0.159637 | ||||||||
\(94\) | 11.8090 | 1.21800 | ||||||||
\(95\) | −6.54735 | −0.671744 | ||||||||
\(96\) | −1.34292 | −0.137062 | ||||||||
\(97\) | 9.85645 | 1.00077 | 0.500385 | − | 0.865803i | \(-0.333192\pi\) | ||||
0.500385 | + | 0.865803i | \(0.333192\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.36976 | 0.434807 | 0.217404 | − | 0.976082i | \(-0.430241\pi\) | ||||
0.217404 | + | 0.976082i | \(0.430241\pi\) | |||||||
\(102\) | 3.53948 | 0.350461 | ||||||||
\(103\) | 14.2978 | 1.40881 | 0.704403 | − | 0.709800i | \(-0.251215\pi\) | ||||
0.704403 | + | 0.709800i | \(0.251215\pi\) | |||||||
\(104\) | −4.31157 | −0.422785 | ||||||||
\(105\) | −1.34292 | −0.131056 | ||||||||
\(106\) | 2.59396 | 0.251948 | ||||||||
\(107\) | −4.78019 | −0.462118 | −0.231059 | − | 0.972940i | \(-0.574219\pi\) | ||||
−0.231059 | + | 0.972940i | \(0.574219\pi\) | |||||||
\(108\) | 5.63565 | 0.542291 | ||||||||
\(109\) | 2.58240 | 0.247349 | 0.123675 | − | 0.992323i | \(-0.460532\pi\) | ||||
0.123675 | + | 0.992323i | \(0.460532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.20594 | −0.399210 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 12.9414 | 1.21743 | 0.608714 | − | 0.793390i | \(-0.291686\pi\) | ||||
0.608714 | + | 0.793390i | \(0.291686\pi\) | |||||||
\(114\) | 8.79259 | 0.823501 | ||||||||
\(115\) | −3.16521 | −0.295157 | ||||||||
\(116\) | −1.13193 | −0.105097 | ||||||||
\(117\) | 5.15905 | 0.476954 | ||||||||
\(118\) | 10.9472 | 1.00777 | ||||||||
\(119\) | −2.63565 | −0.241610 | ||||||||
\(120\) | −1.34292 | −0.122592 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.82933 | 0.527763 | ||||||||
\(123\) | −0.700283 | −0.0631424 | ||||||||
\(124\) | 1.14637 | 0.102947 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.19656 | −0.106598 | ||||||||
\(127\) | 10.9841 | 0.974680 | 0.487340 | − | 0.873212i | \(-0.337967\pi\) | ||||
0.487340 | + | 0.873212i | \(0.337967\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.67141 | 0.587385 | ||||||||
\(130\) | −4.31157 | −0.378150 | ||||||||
\(131\) | −11.9717 | −1.04597 | −0.522986 | − | 0.852341i | \(-0.675182\pi\) | ||||
−0.522986 | + | 0.852341i | \(0.675182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.54735 | −0.567727 | ||||||||
\(134\) | −9.72249 | −0.839895 | ||||||||
\(135\) | 5.63565 | 0.485040 | ||||||||
\(136\) | −2.63565 | −0.226005 | ||||||||
\(137\) | −9.37916 | −0.801315 | −0.400658 | − | 0.916228i | \(-0.631218\pi\) | ||||
−0.400658 | + | 0.916228i | \(0.631218\pi\) | |||||||
\(138\) | 4.25063 | 0.361838 | ||||||||
\(139\) | 11.1498 | 0.945714 | 0.472857 | − | 0.881139i | \(-0.343223\pi\) | ||||
0.472857 | + | 0.881139i | \(0.343223\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −15.8585 | −1.33553 | ||||||||
\(142\) | −4.50169 | −0.377773 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.19656 | −0.0997131 | ||||||||
\(145\) | −1.13193 | −0.0940016 | ||||||||
\(146\) | 12.1269 | 1.00363 | ||||||||
\(147\) | −1.34292 | −0.110762 | ||||||||
\(148\) | 3.13193 | 0.257443 | ||||||||
\(149\) | 5.51928 | 0.452157 | 0.226079 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226079 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(150\) | −1.34292 | −0.109649 | ||||||||
\(151\) | 9.66388 | 0.786435 | 0.393218 | − | 0.919445i | \(-0.371362\pi\) | ||||
0.393218 | + | 0.919445i | \(0.371362\pi\) | |||||||
\(152\) | −6.54735 | −0.531060 | ||||||||
\(153\) | 3.15371 | 0.254962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.14637 | 0.0920783 | ||||||||
\(156\) | 5.79011 | 0.463580 | ||||||||
\(157\) | 16.8181 | 1.34223 | 0.671114 | − | 0.741355i | \(-0.265816\pi\) | ||||
0.671114 | + | 0.741355i | \(0.265816\pi\) | |||||||
\(158\) | 17.0893 | 1.35955 | ||||||||
\(159\) | −3.48349 | −0.276259 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.16521 | −0.249453 | ||||||||
\(162\) | −3.97858 | −0.312587 | ||||||||
\(163\) | −22.8952 | −1.79329 | −0.896644 | − | 0.442753i | \(-0.854002\pi\) | ||||
−0.896644 | + | 0.442753i | \(0.854002\pi\) | |||||||
\(164\) | 0.521462 | 0.0407193 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.06142 | 0.703303 | ||||||||
\(167\) | −8.29513 | −0.641896 | −0.320948 | − | 0.947097i | \(-0.604002\pi\) | ||||
−0.320948 | + | 0.947097i | \(0.604002\pi\) | |||||||
\(168\) | −1.34292 | −0.103609 | ||||||||
\(169\) | 5.58967 | 0.429975 | ||||||||
\(170\) | −2.63565 | −0.202145 | ||||||||
\(171\) | 7.83428 | 0.599103 | ||||||||
\(172\) | −4.96783 | −0.378793 | ||||||||
\(173\) | −21.9024 | −1.66521 | −0.832606 | − | 0.553866i | \(-0.813152\pi\) | ||||
−0.832606 | + | 0.553866i | \(0.813152\pi\) | |||||||
\(174\) | 1.52009 | 0.115238 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.7013 | −1.10502 | ||||||||
\(178\) | 7.17843 | 0.538046 | ||||||||
\(179\) | −3.11079 | −0.232511 | −0.116256 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116256 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(180\) | −1.19656 | −0.0891861 | ||||||||
\(181\) | 4.58252 | 0.340616 | 0.170308 | − | 0.985391i | \(-0.445524\pi\) | ||||
0.170308 | + | 0.985391i | \(0.445524\pi\) | |||||||
\(182\) | −4.31157 | −0.319595 | ||||||||
\(183\) | −7.82834 | −0.578688 | ||||||||
\(184\) | −3.16521 | −0.233342 | ||||||||
\(185\) | 3.13193 | 0.230264 | ||||||||
\(186\) | −1.53948 | −0.112880 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.8090 | 0.861257 | ||||||||
\(189\) | 5.63565 | 0.409934 | ||||||||
\(190\) | −6.54735 | −0.474995 | ||||||||
\(191\) | 4.33382 | 0.313584 | 0.156792 | − | 0.987632i | \(-0.449885\pi\) | ||||
0.156792 | + | 0.987632i | \(0.449885\pi\) | |||||||
\(192\) | −1.34292 | −0.0969171 | ||||||||
\(193\) | −13.4284 | −0.966599 | −0.483300 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483300 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(194\) | 9.85645 | 0.707652 | ||||||||
\(195\) | 5.79011 | 0.414639 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.8667 | 0.845466 | 0.422733 | − | 0.906254i | \(-0.361071\pi\) | ||||
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5672 | −1.03264 | −0.516319 | − | 0.856396i | \(-0.672698\pi\) | ||||
−0.516319 | + | 0.856396i | \(0.672698\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 13.0565 | 0.920938 | ||||||||
\(202\) | 4.36976 | 0.307455 | ||||||||
\(203\) | −1.13193 | −0.0794458 | ||||||||
\(204\) | 3.53948 | 0.247813 | ||||||||
\(205\) | 0.521462 | 0.0364205 | ||||||||
\(206\) | 14.2978 | 0.996177 | ||||||||
\(207\) | 3.78735 | 0.263239 | ||||||||
\(208\) | −4.31157 | −0.298954 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.34292 | −0.0926705 | ||||||||
\(211\) | −2.79716 | −0.192565 | −0.0962823 | − | 0.995354i | \(-0.530695\pi\) | ||||
−0.0962823 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(212\) | 2.59396 | 0.178154 | ||||||||
\(213\) | 6.04542 | 0.414226 | ||||||||
\(214\) | −4.78019 | −0.326767 | ||||||||
\(215\) | −4.96783 | −0.338803 | ||||||||
\(216\) | 5.63565 | 0.383458 | ||||||||
\(217\) | 1.14637 | 0.0778204 | ||||||||
\(218\) | 2.58240 | 0.174902 | ||||||||
\(219\) | −16.2855 | −1.10047 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3638 | 0.764413 | ||||||||
\(222\) | −4.20594 | −0.282284 | ||||||||
\(223\) | 19.6450 | 1.31553 | 0.657763 | − | 0.753225i | \(-0.271503\pi\) | ||||
0.657763 | + | 0.753225i | \(0.271503\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.19656 | −0.0797705 | ||||||||
\(226\) | 12.9414 | 0.860851 | ||||||||
\(227\) | 7.63636 | 0.506843 | 0.253422 | − | 0.967356i | \(-0.418444\pi\) | ||||
0.253422 | + | 0.967356i | \(0.418444\pi\) | |||||||
\(228\) | 8.79259 | 0.582303 | ||||||||
\(229\) | −1.56937 | −0.103707 | −0.0518536 | − | 0.998655i | \(-0.516513\pi\) | ||||
−0.0518536 | + | 0.998655i | \(0.516513\pi\) | |||||||
\(230\) | −3.16521 | −0.208708 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.13193 | −0.0743148 | ||||||||
\(233\) | −22.2894 | −1.46023 | −0.730114 | − | 0.683325i | \(-0.760533\pi\) | ||||
−0.730114 | + | 0.683325i | \(0.760533\pi\) | |||||||
\(234\) | 5.15905 | 0.337257 | ||||||||
\(235\) | 11.8090 | 0.770331 | ||||||||
\(236\) | 10.9472 | 0.712604 | ||||||||
\(237\) | −22.9496 | −1.49074 | ||||||||
\(238\) | −2.63565 | −0.170844 | ||||||||
\(239\) | −5.92057 | −0.382970 | −0.191485 | − | 0.981496i | \(-0.561330\pi\) | ||||
−0.191485 | + | 0.981496i | \(0.561330\pi\) | |||||||
\(240\) | −1.34292 | −0.0866853 | ||||||||
\(241\) | −26.9422 | −1.73550 | −0.867749 | − | 0.497002i | \(-0.834434\pi\) | ||||
−0.867749 | + | 0.497002i | \(0.834434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.5640 | −0.741833 | ||||||||
\(244\) | 5.82933 | 0.373185 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −0.700283 | −0.0446484 | ||||||||
\(247\) | 28.2294 | 1.79619 | ||||||||
\(248\) | 1.14637 | 0.0727943 | ||||||||
\(249\) | −12.1688 | −0.771166 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.5437 | −0.665514 | −0.332757 | − | 0.943013i | \(-0.607979\pi\) | ||||
−0.332757 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(252\) | −1.19656 | −0.0753760 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.9841 | 0.689203 | ||||||||
\(255\) | 3.53948 | 0.221651 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.8973 | 1.24116 | 0.620581 | − | 0.784142i | \(-0.286897\pi\) | ||||
0.620581 | + | 0.784142i | \(0.286897\pi\) | |||||||
\(258\) | 6.67141 | 0.415344 | ||||||||
\(259\) | 3.13193 | 0.194609 | ||||||||
\(260\) | −4.31157 | −0.267392 | ||||||||
\(261\) | 1.35442 | 0.0838364 | ||||||||
\(262\) | −11.9717 | −0.739613 | ||||||||
\(263\) | −12.5871 | −0.776155 | −0.388077 | − | 0.921627i | \(-0.626861\pi\) | ||||
−0.388077 | + | 0.921627i | \(0.626861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.59396 | 0.159346 | ||||||||
\(266\) | −6.54735 | −0.401444 | ||||||||
\(267\) | −9.64009 | −0.589964 | ||||||||
\(268\) | −9.72249 | −0.593895 | ||||||||
\(269\) | −6.90634 | −0.421087 | −0.210544 | − | 0.977584i | \(-0.567523\pi\) | ||||
−0.210544 | + | 0.977584i | \(0.567523\pi\) | |||||||
\(270\) | 5.63565 | 0.342975 | ||||||||
\(271\) | −7.59420 | −0.461315 | −0.230657 | − | 0.973035i | \(-0.574088\pi\) | ||||
−0.230657 | + | 0.973035i | \(0.574088\pi\) | |||||||
\(272\) | −2.63565 | −0.159810 | ||||||||
\(273\) | 5.79011 | 0.350434 | ||||||||
\(274\) | −9.37916 | −0.566616 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.25063 | 0.255858 | ||||||||
\(277\) | 16.8832 | 1.01442 | 0.507208 | − | 0.861824i | \(-0.330678\pi\) | ||||
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(278\) | 11.1498 | 0.668721 | ||||||||
\(279\) | −1.37169 | −0.0821211 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 9.62695 | 0.574296 | 0.287148 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287148 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(282\) | −15.8585 | −0.944361 | ||||||||
\(283\) | 22.5755 | 1.34198 | 0.670988 | − | 0.741468i | \(-0.265870\pi\) | ||||
0.670988 | + | 0.741468i | \(0.265870\pi\) | |||||||
\(284\) | −4.50169 | −0.267126 | ||||||||
\(285\) | 8.79259 | 0.520828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.521462 | 0.0307809 | ||||||||
\(288\) | −1.19656 | −0.0705078 | ||||||||
\(289\) | −10.0533 | −0.591372 | ||||||||
\(290\) | −1.13193 | −0.0664691 | ||||||||
\(291\) | −13.2365 | −0.775935 | ||||||||
\(292\) | 12.1269 | 0.709672 | ||||||||
\(293\) | −21.6239 | −1.26328 | −0.631640 | − | 0.775262i | \(-0.717618\pi\) | ||||
−0.631640 | + | 0.775262i | \(0.717618\pi\) | |||||||
\(294\) | −1.34292 | −0.0783209 | ||||||||
\(295\) | 10.9472 | 0.637372 | ||||||||
\(296\) | 3.13193 | 0.182040 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.51928 | 0.319723 | ||||||||
\(299\) | 13.6470 | 0.789228 | ||||||||
\(300\) | −1.34292 | −0.0775337 | ||||||||
\(301\) | −4.96783 | −0.286341 | ||||||||
\(302\) | 9.66388 | 0.556094 | ||||||||
\(303\) | −5.86825 | −0.337122 | ||||||||
\(304\) | −6.54735 | −0.375516 | ||||||||
\(305\) | 5.82933 | 0.333787 | ||||||||
\(306\) | 3.15371 | 0.180286 | ||||||||
\(307\) | 9.26120 | 0.528565 | 0.264282 | − | 0.964445i | \(-0.414865\pi\) | ||||
0.264282 | + | 0.964445i | \(0.414865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.2009 | −1.09230 | ||||||||
\(310\) | 1.14637 | 0.0651092 | ||||||||
\(311\) | 6.38689 | 0.362167 | 0.181084 | − | 0.983468i | \(-0.442040\pi\) | ||||
0.181084 | + | 0.983468i | \(0.442040\pi\) | |||||||
\(312\) | 5.79011 | 0.327801 | ||||||||
\(313\) | −1.93070 | −0.109130 | −0.0545649 | − | 0.998510i | \(-0.517377\pi\) | ||||
−0.0545649 | + | 0.998510i | \(0.517377\pi\) | |||||||
\(314\) | 16.8181 | 0.949098 | ||||||||
\(315\) | −1.19656 | −0.0674184 | ||||||||
\(316\) | 17.0893 | 0.961349 | ||||||||
\(317\) | −11.8763 | −0.667039 | −0.333519 | − | 0.942743i | \(-0.608236\pi\) | ||||
−0.333519 | + | 0.942743i | \(0.608236\pi\) | |||||||
\(318\) | −3.48349 | −0.195344 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 6.41942 | 0.358297 | ||||||||
\(322\) | −3.16521 | −0.176390 | ||||||||
\(323\) | 17.2566 | 0.960180 | ||||||||
\(324\) | −3.97858 | −0.221032 | ||||||||
\(325\) | −4.31157 | −0.239163 | ||||||||
\(326\) | −22.8952 | −1.26805 | ||||||||
\(327\) | −3.46797 | −0.191779 | ||||||||
\(328\) | 0.521462 | 0.0287929 | ||||||||
\(329\) | 11.8090 | 0.651049 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5755 | −1.57065 | −0.785324 | − | 0.619084i | \(-0.787504\pi\) | ||||
−0.785324 | + | 0.619084i | \(0.787504\pi\) | |||||||
\(332\) | 9.06142 | 0.497310 | ||||||||
\(333\) | −3.74753 | −0.205364 | ||||||||
\(334\) | −8.29513 | −0.453889 | ||||||||
\(335\) | −9.72249 | −0.531196 | ||||||||
\(336\) | −1.34292 | −0.0732625 | ||||||||
\(337\) | −8.38514 | −0.456768 | −0.228384 | − | 0.973571i | \(-0.573344\pi\) | ||||
−0.228384 | + | 0.973571i | \(0.573344\pi\) | |||||||
\(338\) | 5.58967 | 0.304038 | ||||||||
\(339\) | −17.3793 | −0.943916 | ||||||||
\(340\) | −2.63565 | −0.142938 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.83428 | 0.423629 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.96783 | −0.267847 | ||||||||
\(345\) | 4.25063 | 0.228846 | ||||||||
\(346\) | −21.9024 | −1.17748 | ||||||||
\(347\) | 23.5535 | 1.26442 | 0.632210 | − | 0.774797i | \(-0.282148\pi\) | ||||
0.632210 | + | 0.774797i | \(0.282148\pi\) | |||||||
\(348\) | 1.52009 | 0.0814856 | ||||||||
\(349\) | −25.2540 | −1.35182 | −0.675909 | − | 0.736985i | \(-0.736249\pi\) | ||||
−0.675909 | + | 0.736985i | \(0.736249\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −24.2985 | −1.29696 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.9078 | 1.11281 | 0.556406 | − | 0.830911i | \(-0.312180\pi\) | ||||
0.556406 | + | 0.830911i | \(0.312180\pi\) | |||||||
\(354\) | −14.7013 | −0.781365 | ||||||||
\(355\) | −4.50169 | −0.238925 | ||||||||
\(356\) | 7.17843 | 0.380456 | ||||||||
\(357\) | 3.53948 | 0.187329 | ||||||||
\(358\) | −3.11079 | −0.164410 | ||||||||
\(359\) | 25.9084 | 1.36739 | 0.683696 | − | 0.729767i | \(-0.260372\pi\) | ||||
0.683696 | + | 0.729767i | \(0.260372\pi\) | |||||||
\(360\) | −1.19656 | −0.0630641 | ||||||||
\(361\) | 23.8678 | 1.25620 | ||||||||
\(362\) | 4.58252 | 0.240852 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.31157 | −0.225988 | ||||||||
\(365\) | 12.1269 | 0.634750 | ||||||||
\(366\) | −7.82834 | −0.409194 | ||||||||
\(367\) | −20.8650 | −1.08914 | −0.544572 | − | 0.838714i | \(-0.683308\pi\) | ||||
−0.544572 | + | 0.838714i | \(0.683308\pi\) | |||||||
\(368\) | −3.16521 | −0.164998 | ||||||||
\(369\) | −0.623959 | −0.0324820 | ||||||||
\(370\) | 3.13193 | 0.162821 | ||||||||
\(371\) | 2.59396 | 0.134672 | ||||||||
\(372\) | −1.53948 | −0.0798184 | ||||||||
\(373\) | −10.1570 | −0.525911 | −0.262956 | − | 0.964808i | \(-0.584697\pi\) | ||||
−0.262956 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34292 | −0.0693482 | ||||||||
\(376\) | 11.8090 | 0.609000 | ||||||||
\(377\) | 4.88039 | 0.251353 | ||||||||
\(378\) | 5.63565 | 0.289867 | ||||||||
\(379\) | 29.5378 | 1.51726 | 0.758628 | − | 0.651524i | \(-0.225870\pi\) | ||||
0.758628 | + | 0.651524i | \(0.225870\pi\) | |||||||
\(380\) | −6.54735 | −0.335872 | ||||||||
\(381\) | −14.7508 | −0.755706 | ||||||||
\(382\) | 4.33382 | 0.221738 | ||||||||
\(383\) | 26.2888 | 1.34330 | 0.671648 | − | 0.740871i | \(-0.265587\pi\) | ||||
0.671648 | + | 0.740871i | \(0.265587\pi\) | |||||||
\(384\) | −1.34292 | −0.0685308 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.4284 | −0.683489 | ||||||||
\(387\) | 5.94429 | 0.302165 | ||||||||
\(388\) | 9.85645 | 0.500385 | ||||||||
\(389\) | −8.64078 | −0.438105 | −0.219052 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219052 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(390\) | 5.79011 | 0.293194 | ||||||||
\(391\) | 8.34240 | 0.421893 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 16.0771 | 0.810980 | ||||||||
\(394\) | 11.8667 | 0.597835 | ||||||||
\(395\) | 17.0893 | 0.859856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.1598 | 1.76462 | 0.882309 | − | 0.470670i | \(-0.155988\pi\) | ||||
0.882309 | + | 0.470670i | \(0.155988\pi\) | |||||||
\(398\) | −14.5672 | −0.730186 | ||||||||
\(399\) | 8.79259 | 0.440180 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −7.99484 | −0.399243 | −0.199622 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199622 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(402\) | 13.0565 | 0.651202 | ||||||||
\(403\) | −4.94264 | −0.246210 | ||||||||
\(404\) | 4.36976 | 0.217404 | ||||||||
\(405\) | −3.97858 | −0.197697 | ||||||||
\(406\) | −1.13193 | −0.0561767 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.53948 | 0.175230 | ||||||||
\(409\) | 1.92553 | 0.0952114 | 0.0476057 | − | 0.998866i | \(-0.484841\pi\) | ||||
0.0476057 | + | 0.998866i | \(0.484841\pi\) | |||||||
\(410\) | 0.521462 | 0.0257532 | ||||||||
\(411\) | 12.5955 | 0.621290 | ||||||||
\(412\) | 14.2978 | 0.704403 | ||||||||
\(413\) | 10.9472 | 0.538678 | ||||||||
\(414\) | 3.78735 | 0.186138 | ||||||||
\(415\) | 9.06142 | 0.444808 | ||||||||
\(416\) | −4.31157 | −0.211392 | ||||||||
\(417\) | −14.9733 | −0.733247 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.4861 | −1.09852 | −0.549259 | − | 0.835652i | \(-0.685090\pi\) | ||||
−0.549259 | + | 0.835652i | \(0.685090\pi\) | |||||||
\(420\) | −1.34292 | −0.0655279 | ||||||||
\(421\) | −23.3112 | −1.13612 | −0.568059 | − | 0.822988i | \(-0.692306\pi\) | ||||
−0.568059 | + | 0.822988i | \(0.692306\pi\) | |||||||
\(422\) | −2.79716 | −0.136164 | ||||||||
\(423\) | −14.1301 | −0.687029 | ||||||||
\(424\) | 2.59396 | 0.125974 | ||||||||
\(425\) | −2.63565 | −0.127848 | ||||||||
\(426\) | 6.04542 | 0.292902 | ||||||||
\(427\) | 5.82933 | 0.282101 | ||||||||
\(428\) | −4.78019 | −0.231059 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.96783 | −0.239570 | ||||||||
\(431\) | 15.2591 | 0.735003 | 0.367502 | − | 0.930023i | \(-0.380213\pi\) | ||||
0.367502 | + | 0.930023i | \(0.380213\pi\) | |||||||
\(432\) | 5.63565 | 0.271146 | ||||||||
\(433\) | −0.722365 | −0.0347146 | −0.0173573 | − | 0.999849i | \(-0.505525\pi\) | ||||
−0.0173573 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(434\) | 1.14637 | 0.0550273 | ||||||||
\(435\) | 1.52009 | 0.0728829 | ||||||||
\(436\) | 2.58240 | 0.123675 | ||||||||
\(437\) | 20.7237 | 0.991350 | ||||||||
\(438\) | −16.2855 | −0.778149 | ||||||||
\(439\) | 31.7894 | 1.51722 | 0.758612 | − | 0.651543i | \(-0.225878\pi\) | ||||
0.758612 | + | 0.651543i | \(0.225878\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.19656 | −0.0569789 | ||||||||
\(442\) | 11.3638 | 0.540522 | ||||||||
\(443\) | 29.1789 | 1.38633 | 0.693166 | − | 0.720778i | \(-0.256215\pi\) | ||||
0.693166 | + | 0.720778i | \(0.256215\pi\) | |||||||
\(444\) | −4.20594 | −0.199605 | ||||||||
\(445\) | 7.17843 | 0.340290 | ||||||||
\(446\) | 19.6450 | 0.930217 | ||||||||
\(447\) | −7.41197 | −0.350574 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 18.6378 | 0.879570 | 0.439785 | − | 0.898103i | \(-0.355055\pi\) | ||||
0.439785 | + | 0.898103i | \(0.355055\pi\) | |||||||
\(450\) | −1.19656 | −0.0564063 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.9414 | 0.608714 | ||||||||
\(453\) | −12.9778 | −0.609752 | ||||||||
\(454\) | 7.63636 | 0.358392 | ||||||||
\(455\) | −4.31157 | −0.202130 | ||||||||
\(456\) | 8.79259 | 0.411751 | ||||||||
\(457\) | 3.01602 | 0.141084 | 0.0705418 | − | 0.997509i | \(-0.477527\pi\) | ||||
0.0705418 | + | 0.997509i | \(0.477527\pi\) | |||||||
\(458\) | −1.56937 | −0.0733320 | ||||||||
\(459\) | −14.8536 | −0.693308 | ||||||||
\(460\) | −3.16521 | −0.147579 | ||||||||
\(461\) | −16.8872 | −0.786513 | −0.393257 | − | 0.919429i | \(-0.628652\pi\) | ||||
−0.393257 | + | 0.919429i | \(0.628652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.180188 | 0.00837403 | 0.00418701 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418701 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(464\) | −1.13193 | −0.0525485 | ||||||||
\(465\) | −1.53948 | −0.0713917 | ||||||||
\(466\) | −22.2894 | −1.03254 | ||||||||
\(467\) | 12.4723 | 0.577147 | 0.288574 | − | 0.957458i | \(-0.406819\pi\) | ||||
0.288574 | + | 0.957458i | \(0.406819\pi\) | |||||||
\(468\) | 5.15905 | 0.238477 | ||||||||
\(469\) | −9.72249 | −0.448943 | ||||||||
\(470\) | 11.8090 | 0.544707 | ||||||||
\(471\) | −22.5854 | −1.04068 | ||||||||
\(472\) | 10.9472 | 0.503887 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −22.9496 | −1.05411 | ||||||||
\(475\) | −6.54735 | −0.300413 | ||||||||
\(476\) | −2.63565 | −0.120805 | ||||||||
\(477\) | −3.10382 | −0.142114 | ||||||||
\(478\) | −5.92057 | −0.270801 | ||||||||
\(479\) | −1.55428 | −0.0710166 | −0.0355083 | − | 0.999369i | \(-0.511305\pi\) | ||||
−0.0355083 | + | 0.999369i | \(0.511305\pi\) | |||||||
\(480\) | −1.34292 | −0.0612958 | ||||||||
\(481\) | −13.5035 | −0.615709 | ||||||||
\(482\) | −26.9422 | −1.22718 | ||||||||
\(483\) | 4.25063 | 0.193410 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.85645 | 0.447558 | ||||||||
\(486\) | −11.5640 | −0.524555 | ||||||||
\(487\) | 29.2641 | 1.32608 | 0.663042 | − | 0.748582i | \(-0.269265\pi\) | ||||
0.663042 | + | 0.748582i | \(0.269265\pi\) | |||||||
\(488\) | 5.82933 | 0.263881 | ||||||||
\(489\) | 30.7464 | 1.39040 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −2.35553 | −0.106304 | −0.0531518 | − | 0.998586i | \(-0.516927\pi\) | ||||
−0.0531518 | + | 0.998586i | \(0.516927\pi\) | |||||||
\(492\) | −0.700283 | −0.0315712 | ||||||||
\(493\) | 2.98337 | 0.134364 | ||||||||
\(494\) | 28.2294 | 1.27010 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.14637 | 0.0514733 | ||||||||
\(497\) | −4.50169 | −0.201928 | ||||||||
\(498\) | −12.1688 | −0.545297 | ||||||||
\(499\) | 25.2783 | 1.13161 | 0.565807 | − | 0.824538i | \(-0.308565\pi\) | ||||
0.565807 | + | 0.824538i | \(0.308565\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 11.1397 | 0.497686 | ||||||||
\(502\) | −10.5437 | −0.470589 | ||||||||
\(503\) | −3.23636 | −0.144302 | −0.0721510 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721510 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(504\) | −1.19656 | −0.0532989 | ||||||||
\(505\) | 4.36976 | 0.194452 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.50650 | −0.333375 | ||||||||
\(508\) | 10.9841 | 0.487340 | ||||||||
\(509\) | 39.5692 | 1.75387 | 0.876937 | − | 0.480606i | \(-0.159583\pi\) | ||||
0.876937 | + | 0.480606i | \(0.159583\pi\) | |||||||
\(510\) | 3.53948 | 0.156731 | ||||||||
\(511\) | 12.1269 | 0.536461 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −36.8986 | −1.62911 | ||||||||
\(514\) | 19.8973 | 0.877634 | ||||||||
\(515\) | 14.2978 | 0.630037 | ||||||||
\(516\) | 6.67141 | 0.293692 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.13193 | 0.137609 | ||||||||
\(519\) | 29.4133 | 1.29110 | ||||||||
\(520\) | −4.31157 | −0.189075 | ||||||||
\(521\) | −0.586854 | −0.0257105 | −0.0128553 | − | 0.999917i | \(-0.504092\pi\) | ||||
−0.0128553 | + | 0.999917i | \(0.504092\pi\) | |||||||
\(522\) | 1.35442 | 0.0592813 | ||||||||
\(523\) | −22.7742 | −0.995846 | −0.497923 | − | 0.867221i | \(-0.665904\pi\) | ||||
−0.497923 | + | 0.867221i | \(0.665904\pi\) | |||||||
\(524\) | −11.9717 | −0.522986 | ||||||||
\(525\) | −1.34292 | −0.0586100 | ||||||||
\(526\) | −12.5871 | −0.548824 | ||||||||
\(527\) | −3.02142 | −0.131615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9815 | −0.564411 | ||||||||
\(530\) | 2.59396 | 0.112674 | ||||||||
\(531\) | −13.0990 | −0.568448 | ||||||||
\(532\) | −6.54735 | −0.283864 | ||||||||
\(533\) | −2.24832 | −0.0973856 | ||||||||
\(534\) | −9.64009 | −0.417167 | ||||||||
\(535\) | −4.78019 | −0.206665 | ||||||||
\(536\) | −9.72249 | −0.419947 | ||||||||
\(537\) | 4.17755 | 0.180274 | ||||||||
\(538\) | −6.90634 | −0.297753 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.63565 | 0.242520 | ||||||||
\(541\) | 36.2359 | 1.55790 | 0.778952 | − | 0.627084i | \(-0.215752\pi\) | ||||
0.778952 | + | 0.627084i | \(0.215752\pi\) | |||||||
\(542\) | −7.59420 | −0.326199 | ||||||||
\(543\) | −6.15397 | −0.264092 | ||||||||
\(544\) | −2.63565 | −0.113003 | ||||||||
\(545\) | 2.58240 | 0.110618 | ||||||||
\(546\) | 5.79011 | 0.247794 | ||||||||
\(547\) | 17.1863 | 0.734831 | 0.367416 | − | 0.930057i | \(-0.380243\pi\) | ||||
0.367416 | + | 0.930057i | \(0.380243\pi\) | |||||||
\(548\) | −9.37916 | −0.400658 | ||||||||
\(549\) | −6.97513 | −0.297691 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.41113 | 0.315725 | ||||||||
\(552\) | 4.25063 | 0.180919 | ||||||||
\(553\) | 17.0893 | 0.726711 | ||||||||
\(554\) | 16.8832 | 0.717300 | ||||||||
\(555\) | −4.20594 | −0.178532 | ||||||||
\(556\) | 11.1498 | 0.472857 | ||||||||
\(557\) | −31.6410 | −1.34067 | −0.670335 | − | 0.742058i | \(-0.733850\pi\) | ||||
−0.670335 | + | 0.742058i | \(0.733850\pi\) | |||||||
\(558\) | −1.37169 | −0.0580684 | ||||||||
\(559\) | 21.4192 | 0.905934 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.62695 | 0.406089 | ||||||||
\(563\) | 28.5238 | 1.20213 | 0.601066 | − | 0.799199i | \(-0.294743\pi\) | ||||
0.601066 | + | 0.799199i | \(0.294743\pi\) | |||||||
\(564\) | −15.8585 | −0.667764 | ||||||||
\(565\) | 12.9414 | 0.544450 | ||||||||
\(566\) | 22.5755 | 0.948920 | ||||||||
\(567\) | −3.97858 | −0.167085 | ||||||||
\(568\) | −4.50169 | −0.188887 | ||||||||
\(569\) | −17.6880 | −0.741520 | −0.370760 | − | 0.928729i | \(-0.620903\pi\) | ||||
−0.370760 | + | 0.928729i | \(0.620903\pi\) | |||||||
\(570\) | 8.79259 | 0.368281 | ||||||||
\(571\) | 11.2551 | 0.471012 | 0.235506 | − | 0.971873i | \(-0.424325\pi\) | ||||
0.235506 | + | 0.971873i | \(0.424325\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.81999 | −0.243134 | ||||||||
\(574\) | 0.521462 | 0.0217654 | ||||||||
\(575\) | −3.16521 | −0.131998 | ||||||||
\(576\) | −1.19656 | −0.0498566 | ||||||||
\(577\) | 3.75289 | 0.156235 | 0.0781175 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781175 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(578\) | −10.0533 | −0.418163 | ||||||||
\(579\) | 18.0333 | 0.749440 | ||||||||
\(580\) | −1.13193 | −0.0470008 | ||||||||
\(581\) | 9.06142 | 0.375931 | ||||||||
\(582\) | −13.2365 | −0.548669 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.1269 | 0.501814 | ||||||||
\(585\) | 5.15905 | 0.213300 | ||||||||
\(586\) | −21.6239 | −0.893274 | ||||||||
\(587\) | −31.3692 | −1.29475 | −0.647374 | − | 0.762173i | \(-0.724133\pi\) | ||||
−0.647374 | + | 0.762173i | \(0.724133\pi\) | |||||||
\(588\) | −1.34292 | −0.0553812 | ||||||||
\(589\) | −7.50566 | −0.309265 | ||||||||
\(590\) | 10.9472 | 0.450690 | ||||||||
\(591\) | −15.9360 | −0.655521 | ||||||||
\(592\) | 3.13193 | 0.128721 | ||||||||
\(593\) | 4.02015 | 0.165088 | 0.0825439 | − | 0.996587i | \(-0.473696\pi\) | ||||
0.0825439 | + | 0.996587i | \(0.473696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.63565 | −0.108051 | ||||||||
\(596\) | 5.51928 | 0.226079 | ||||||||
\(597\) | 19.5626 | 0.800643 | ||||||||
\(598\) | 13.6470 | 0.558069 | ||||||||
\(599\) | −15.0102 | −0.613301 | −0.306651 | − | 0.951822i | \(-0.599208\pi\) | ||||
−0.306651 | + | 0.951822i | \(0.599208\pi\) | |||||||
\(600\) | −1.34292 | −0.0548246 | ||||||||
\(601\) | −20.0520 | −0.817939 | −0.408970 | − | 0.912548i | \(-0.634112\pi\) | ||||
−0.408970 | + | 0.912548i | \(0.634112\pi\) | |||||||
\(602\) | −4.96783 | −0.202474 | ||||||||
\(603\) | 11.6335 | 0.473753 | ||||||||
\(604\) | 9.66388 | 0.393218 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.86825 | −0.238381 | ||||||||
\(607\) | 17.0030 | 0.690129 | 0.345064 | − | 0.938579i | \(-0.387857\pi\) | ||||
0.345064 | + | 0.938579i | \(0.387857\pi\) | |||||||
\(608\) | −6.54735 | −0.265530 | ||||||||
\(609\) | 1.52009 | 0.0615973 | ||||||||
\(610\) | 5.82933 | 0.236023 | ||||||||
\(611\) | −50.9152 | −2.05981 | ||||||||
\(612\) | 3.15371 | 0.127481 | ||||||||
\(613\) | −17.2655 | −0.697347 | −0.348673 | − | 0.937244i | \(-0.613368\pi\) | ||||
−0.348673 | + | 0.937244i | \(0.613368\pi\) | |||||||
\(614\) | 9.26120 | 0.373752 | ||||||||
\(615\) | −0.700283 | −0.0282381 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0616 | −0.727134 | −0.363567 | − | 0.931568i | \(-0.618441\pi\) | ||||
−0.363567 | + | 0.931568i | \(0.618441\pi\) | |||||||
\(618\) | −19.2009 | −0.772373 | ||||||||
\(619\) | 32.2086 | 1.29457 | 0.647287 | − | 0.762247i | \(-0.275904\pi\) | ||||
0.647287 | + | 0.762247i | \(0.275904\pi\) | |||||||
\(620\) | 1.14637 | 0.0460391 | ||||||||
\(621\) | −17.8380 | −0.715815 | ||||||||
\(622\) | 6.38689 | 0.256091 | ||||||||
\(623\) | 7.17843 | 0.287598 | ||||||||
\(624\) | 5.79011 | 0.231790 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.93070 | −0.0771664 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.8181 | 0.671114 | ||||||||
\(629\) | −8.25468 | −0.329136 | ||||||||
\(630\) | −1.19656 | −0.0476720 | ||||||||
\(631\) | 10.0492 | 0.400052 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(632\) | 17.0893 | 0.679776 | ||||||||
\(633\) | 3.75637 | 0.149302 | ||||||||
\(634\) | −11.8763 | −0.471667 | ||||||||
\(635\) | 10.9841 | 0.435890 | ||||||||
\(636\) | −3.48349 | −0.138129 | ||||||||
\(637\) | −4.31157 | −0.170831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.38653 | 0.213088 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −22.0387 | −0.870476 | −0.435238 | − | 0.900315i | \(-0.643336\pi\) | ||||
−0.435238 | + | 0.900315i | \(0.643336\pi\) | |||||||
\(642\) | 6.41942 | 0.253354 | ||||||||
\(643\) | −18.2425 | −0.719414 | −0.359707 | − | 0.933065i | \(-0.617123\pi\) | ||||
−0.359707 | + | 0.933065i | \(0.617123\pi\) | |||||||
\(644\) | −3.16521 | −0.124727 | ||||||||
\(645\) | 6.67141 | 0.262686 | ||||||||
\(646\) | 17.2566 | 0.678950 | ||||||||
\(647\) | −10.5244 | −0.413755 | −0.206878 | − | 0.978367i | \(-0.566330\pi\) | ||||
−0.206878 | + | 0.978367i | \(0.566330\pi\) | |||||||
\(648\) | −3.97858 | −0.156293 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.31157 | −0.169114 | ||||||||
\(651\) | −1.53948 | −0.0603370 | ||||||||
\(652\) | −22.8952 | −0.896644 | ||||||||
\(653\) | 30.1567 | 1.18012 | 0.590061 | − | 0.807358i | \(-0.299104\pi\) | ||||
0.590061 | + | 0.807358i | \(0.299104\pi\) | |||||||
\(654\) | −3.46797 | −0.135608 | ||||||||
\(655\) | −11.9717 | −0.467773 | ||||||||
\(656\) | 0.521462 | 0.0203597 | ||||||||
\(657\) | −14.5105 | −0.566109 | ||||||||
\(658\) | 11.8090 | 0.460361 | ||||||||
\(659\) | −37.5753 | −1.46373 | −0.731863 | − | 0.681451i | \(-0.761349\pi\) | ||||
−0.731863 | + | 0.681451i | \(0.761349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1822 | −0.940579 | −0.470290 | − | 0.882512i | \(-0.655851\pi\) | ||||
−0.470290 | + | 0.882512i | \(0.655851\pi\) | |||||||
\(662\) | −28.5755 | −1.11062 | ||||||||
\(663\) | −15.2607 | −0.592678 | ||||||||
\(664\) | 9.06142 | 0.351651 | ||||||||
\(665\) | −6.54735 | −0.253895 | ||||||||
\(666\) | −3.74753 | −0.145214 | ||||||||
\(667\) | 3.58279 | 0.138726 | ||||||||
\(668\) | −8.29513 | −0.320948 | ||||||||
\(669\) | −26.3817 | −1.01998 | ||||||||
\(670\) | −9.72249 | −0.375612 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.34292 | −0.0518044 | ||||||||
\(673\) | −38.4279 | −1.48129 | −0.740643 | − | 0.671899i | \(-0.765479\pi\) | ||||
−0.740643 | + | 0.671899i | \(0.765479\pi\) | |||||||
\(674\) | −8.38514 | −0.322983 | ||||||||
\(675\) | 5.63565 | 0.216916 | ||||||||
\(676\) | 5.58967 | 0.214987 | ||||||||
\(677\) | 47.8223 | 1.83796 | 0.918980 | − | 0.394304i | \(-0.129014\pi\) | ||||
0.918980 | + | 0.394304i | \(0.129014\pi\) | |||||||
\(678\) | −17.3793 | −0.667450 | ||||||||
\(679\) | 9.85645 | 0.378256 | ||||||||
\(680\) | −2.63565 | −0.101073 | ||||||||
\(681\) | −10.2550 | −0.392974 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.96235 | 0.189879 | 0.0949395 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949395 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(684\) | 7.83428 | 0.299551 | ||||||||
\(685\) | −9.37916 | −0.358359 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 2.10755 | 0.0804080 | ||||||||
\(688\) | −4.96783 | −0.189397 | ||||||||
\(689\) | −11.1841 | −0.426078 | ||||||||
\(690\) | 4.25063 | 0.161819 | ||||||||
\(691\) | 28.2052 | 1.07298 | 0.536488 | − | 0.843908i | \(-0.319751\pi\) | ||||
0.536488 | + | 0.843908i | \(0.319751\pi\) | |||||||
\(692\) | −21.9024 | −0.832606 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.5535 | 0.894080 | ||||||||
\(695\) | 11.1498 | 0.422936 | ||||||||
\(696\) | 1.52009 | 0.0576190 | ||||||||
\(697\) | −1.37439 | −0.0520588 | ||||||||
\(698\) | −25.2540 | −0.955879 | ||||||||
\(699\) | 29.9330 | 1.13217 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −16.4276 | −0.620461 | −0.310230 | − | 0.950661i | \(-0.600406\pi\) | ||||
−0.310230 | + | 0.950661i | \(0.600406\pi\) | |||||||
\(702\) | −24.2985 | −0.917089 | ||||||||
\(703\) | −20.5058 | −0.773392 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.8585 | −0.597266 | ||||||||
\(706\) | 20.9078 | 0.786877 | ||||||||
\(707\) | 4.36976 | 0.164342 | ||||||||
\(708\) | −14.7013 | −0.552508 | ||||||||
\(709\) | 26.0841 | 0.979610 | 0.489805 | − | 0.871832i | \(-0.337068\pi\) | ||||
0.489805 | + | 0.871832i | \(0.337068\pi\) | |||||||
\(710\) | −4.50169 | −0.168945 | ||||||||
\(711\) | −20.4483 | −0.766873 | ||||||||
\(712\) | 7.17843 | 0.269023 | ||||||||
\(713\) | −3.62849 | −0.135888 | ||||||||
\(714\) | 3.53948 | 0.132462 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.11079 | −0.116256 | ||||||||
\(717\) | 7.95087 | 0.296931 | ||||||||
\(718\) | 25.9084 | 0.966892 | ||||||||
\(719\) | 16.7246 | 0.623723 | 0.311862 | − | 0.950128i | \(-0.399047\pi\) | ||||
0.311862 | + | 0.950128i | \(0.399047\pi\) | |||||||
\(720\) | −1.19656 | −0.0445931 | ||||||||
\(721\) | 14.2978 | 0.532479 | ||||||||
\(722\) | 23.8678 | 0.888267 | ||||||||
\(723\) | 36.1813 | 1.34560 | ||||||||
\(724\) | 4.58252 | 0.170308 | ||||||||
\(725\) | −1.13193 | −0.0420388 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.1587 | 1.11853 | 0.559263 | − | 0.828990i | \(-0.311084\pi\) | ||||
0.559263 | + | 0.828990i | \(0.311084\pi\) | |||||||
\(728\) | −4.31157 | −0.159798 | ||||||||
\(729\) | 27.4653 | 1.01724 | ||||||||
\(730\) | 12.1269 | 0.448836 | ||||||||
\(731\) | 13.0935 | 0.484280 | ||||||||
\(732\) | −7.82834 | −0.289344 | ||||||||
\(733\) | 29.3635 | 1.08456 | 0.542282 | − | 0.840197i | \(-0.317560\pi\) | ||||
0.542282 | + | 0.840197i | \(0.317560\pi\) | |||||||
\(734\) | −20.8650 | −0.770141 | ||||||||
\(735\) | −1.34292 | −0.0495345 | ||||||||
\(736\) | −3.16521 | −0.116671 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.623959 | −0.0229682 | ||||||||
\(739\) | −17.5186 | −0.644432 | −0.322216 | − | 0.946666i | \(-0.604428\pi\) | ||||
−0.322216 | + | 0.946666i | \(0.604428\pi\) | |||||||
\(740\) | 3.13193 | 0.115132 | ||||||||
\(741\) | −37.9099 | −1.39265 | ||||||||
\(742\) | 2.59396 | 0.0952273 | ||||||||
\(743\) | −21.7292 | −0.797169 | −0.398584 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398584 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(744\) | −1.53948 | −0.0564401 | ||||||||
\(745\) | 5.51928 | 0.202211 | ||||||||
\(746\) | −10.1570 | −0.371876 | ||||||||
\(747\) | −10.8425 | −0.396707 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.78019 | −0.174664 | ||||||||
\(750\) | −1.34292 | −0.0490366 | ||||||||
\(751\) | 37.8166 | 1.37995 | 0.689974 | − | 0.723835i | \(-0.257622\pi\) | ||||
0.689974 | + | 0.723835i | \(0.257622\pi\) | |||||||
\(752\) | 11.8090 | 0.430628 | ||||||||
\(753\) | 14.1594 | 0.515998 | ||||||||
\(754\) | 4.88039 | 0.177734 | ||||||||
\(755\) | 9.66388 | 0.351705 | ||||||||
\(756\) | 5.63565 | 0.204967 | ||||||||
\(757\) | 45.5840 | 1.65678 | 0.828390 | − | 0.560152i | \(-0.189257\pi\) | ||||
0.828390 | + | 0.560152i | \(0.189257\pi\) | |||||||
\(758\) | 29.5378 | 1.07286 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.54735 | −0.237497 | ||||||||
\(761\) | 36.0860 | 1.30812 | 0.654058 | − | 0.756445i | \(-0.273065\pi\) | ||||
0.654058 | + | 0.756445i | \(0.273065\pi\) | |||||||
\(762\) | −14.7508 | −0.534365 | ||||||||
\(763\) | 2.58240 | 0.0934893 | ||||||||
\(764\) | 4.33382 | 0.156792 | ||||||||
\(765\) | 3.15371 | 0.114023 | ||||||||
\(766\) | 26.2888 | 0.949853 | ||||||||
\(767\) | −47.1998 | −1.70429 | ||||||||
\(768\) | −1.34292 | −0.0484586 | ||||||||
\(769\) | −28.8806 | −1.04146 | −0.520730 | − | 0.853722i | \(-0.674340\pi\) | ||||
−0.520730 | + | 0.853722i | \(0.674340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.7206 | −0.962319 | ||||||||
\(772\) | −13.4284 | −0.483300 | ||||||||
\(773\) | 41.6626 | 1.49850 | 0.749250 | − | 0.662287i | \(-0.230414\pi\) | ||||
0.749250 | + | 0.662287i | \(0.230414\pi\) | |||||||
\(774\) | 5.94429 | 0.213663 | ||||||||
\(775\) | 1.14637 | 0.0411787 | ||||||||
\(776\) | 9.85645 | 0.353826 | ||||||||
\(777\) | −4.20594 | −0.150887 | ||||||||
\(778\) | −8.64078 | −0.309787 | ||||||||
\(779\) | −3.41419 | −0.122326 | ||||||||
\(780\) | 5.79011 | 0.207319 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.34240 | 0.298323 | ||||||||
\(783\) | −6.37916 | −0.227973 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 16.8181 | 0.600262 | ||||||||
\(786\) | 16.0771 | 0.573450 | ||||||||
\(787\) | −13.3405 | −0.475537 | −0.237768 | − | 0.971322i | \(-0.576416\pi\) | ||||
−0.237768 | + | 0.971322i | \(0.576416\pi\) | |||||||
\(788\) | 11.8667 | 0.422733 | ||||||||
\(789\) | 16.9035 | 0.601781 | ||||||||
\(790\) | 17.0893 | 0.608010 | ||||||||
\(791\) | 12.9414 | 0.460144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.1336 | −0.892520 | ||||||||
\(794\) | 35.1598 | 1.24777 | ||||||||
\(795\) | −3.48349 | −0.123547 | ||||||||
\(796\) | −14.5672 | −0.516319 | ||||||||
\(797\) | 32.9064 | 1.16560 | 0.582802 | − | 0.812614i | \(-0.301956\pi\) | ||||
0.582802 | + | 0.812614i | \(0.301956\pi\) | |||||||
\(798\) | 8.79259 | 0.311254 | ||||||||
\(799\) | −31.1243 | −1.10110 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −8.58941 | −0.303492 | ||||||||
\(802\) | −7.99484 | −0.282308 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0565 | 0.460469 | ||||||||
\(805\) | −3.16521 | −0.111559 | ||||||||
\(806\) | −4.94264 | −0.174097 | ||||||||
\(807\) | 9.27468 | 0.326484 | ||||||||
\(808\) | 4.36976 | 0.153728 | ||||||||
\(809\) | −27.0311 | −0.950363 | −0.475182 | − | 0.879888i | \(-0.657618\pi\) | ||||
−0.475182 | + | 0.879888i | \(0.657618\pi\) | |||||||
\(810\) | −3.97858 | −0.139793 | ||||||||
\(811\) | −18.8842 | −0.663112 | −0.331556 | − | 0.943435i | \(-0.607574\pi\) | ||||
−0.331556 | + | 0.943435i | \(0.607574\pi\) | |||||||
\(812\) | −1.13193 | −0.0397229 | ||||||||
\(813\) | 10.1984 | 0.357674 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.8952 | −0.801982 | ||||||||
\(816\) | 3.53948 | 0.123907 | ||||||||
\(817\) | 32.5261 | 1.13794 | ||||||||
\(818\) | 1.92553 | 0.0673247 | ||||||||
\(819\) | 5.15905 | 0.180272 | ||||||||
\(820\) | 0.521462 | 0.0182102 | ||||||||
\(821\) | −18.9968 | −0.662992 | −0.331496 | − | 0.943457i | \(-0.607553\pi\) | ||||
−0.331496 | + | 0.943457i | \(0.607553\pi\) | |||||||
\(822\) | 12.5955 | 0.439318 | ||||||||
\(823\) | 32.5539 | 1.13476 | 0.567378 | − | 0.823457i | \(-0.307958\pi\) | ||||
0.567378 | + | 0.823457i | \(0.307958\pi\) | |||||||
\(824\) | 14.2978 | 0.498088 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.9472 | 0.380903 | ||||||||
\(827\) | −10.3868 | −0.361183 | −0.180592 | − | 0.983558i | \(-0.557801\pi\) | ||||
−0.180592 | + | 0.983558i | \(0.557801\pi\) | |||||||
\(828\) | 3.78735 | 0.131620 | ||||||||
\(829\) | −13.1965 | −0.458332 | −0.229166 | − | 0.973387i | \(-0.573600\pi\) | ||||
−0.229166 | + | 0.973387i | \(0.573600\pi\) | |||||||
\(830\) | 9.06142 | 0.314527 | ||||||||
\(831\) | −22.6729 | −0.786514 | ||||||||
\(832\) | −4.31157 | −0.149477 | ||||||||
\(833\) | −2.63565 | −0.0913200 | ||||||||
\(834\) | −14.9733 | −0.518484 | ||||||||
\(835\) | −8.29513 | −0.287065 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.46052 | 0.223308 | ||||||||
\(838\) | −22.4861 | −0.776769 | ||||||||
\(839\) | −20.4534 | −0.706128 | −0.353064 | − | 0.935599i | \(-0.614860\pi\) | ||||
−0.353064 | + | 0.935599i | \(0.614860\pi\) | |||||||
\(840\) | −1.34292 | −0.0463352 | ||||||||
\(841\) | −27.7187 | −0.955819 | ||||||||
\(842\) | −23.3112 | −0.803357 | ||||||||
\(843\) | −12.9283 | −0.445273 | ||||||||
\(844\) | −2.79716 | −0.0962823 | ||||||||
\(845\) | 5.58967 | 0.192291 | ||||||||
\(846\) | −14.1301 | −0.485803 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.59396 | 0.0890770 | ||||||||
\(849\) | −30.3172 | −1.04048 | ||||||||
\(850\) | −2.63565 | −0.0904022 | ||||||||
\(851\) | −9.91321 | −0.339820 | ||||||||
\(852\) | 6.04542 | 0.207113 | ||||||||
\(853\) | −39.8363 | −1.36397 | −0.681984 | − | 0.731367i | \(-0.738883\pi\) | ||||
−0.681984 | + | 0.731367i | \(0.738883\pi\) | |||||||
\(854\) | 5.82933 | 0.199476 | ||||||||
\(855\) | 7.83428 | 0.267927 | ||||||||
\(856\) | −4.78019 | −0.163383 | ||||||||
\(857\) | 50.5306 | 1.72609 | 0.863047 | − | 0.505124i | \(-0.168553\pi\) | ||||
0.863047 | + | 0.505124i | \(0.168553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.2746 | −1.16943 | −0.584717 | − | 0.811238i | \(-0.698794\pi\) | ||||
−0.584717 | + | 0.811238i | \(0.698794\pi\) | |||||||
\(860\) | −4.96783 | −0.169401 | ||||||||
\(861\) | −0.700283 | −0.0238656 | ||||||||
\(862\) | 15.2591 | 0.519726 | ||||||||
\(863\) | 50.1602 | 1.70747 | 0.853736 | − | 0.520706i | \(-0.174331\pi\) | ||||
0.853736 | + | 0.520706i | \(0.174331\pi\) | |||||||
\(864\) | 5.63565 | 0.191729 | ||||||||
\(865\) | −21.9024 | −0.744705 | ||||||||
\(866\) | −0.722365 | −0.0245470 | ||||||||
\(867\) | 13.5008 | 0.458513 | ||||||||
\(868\) | 1.14637 | 0.0389102 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.52009 | 0.0515360 | ||||||||
\(871\) | 41.9192 | 1.42038 | ||||||||
\(872\) | 2.58240 | 0.0874512 | ||||||||
\(873\) | −11.7938 | −0.399160 | ||||||||
\(874\) | 20.7237 | 0.700991 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −16.2855 | −0.550235 | ||||||||
\(877\) | −42.9675 | −1.45091 | −0.725454 | − | 0.688270i | \(-0.758370\pi\) | ||||
−0.725454 | + | 0.688270i | \(0.758370\pi\) | |||||||
\(878\) | 31.7894 | 1.07284 | ||||||||
\(879\) | 29.0392 | 0.979468 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.10467 | 0.239362 | 0.119681 | − | 0.992812i | \(-0.461813\pi\) | ||||
0.119681 | + | 0.992812i | \(0.461813\pi\) | |||||||
\(882\) | −1.19656 | −0.0402902 | ||||||||
\(883\) | −41.1823 | −1.38589 | −0.692947 | − | 0.720989i | \(-0.743688\pi\) | ||||
−0.692947 | + | 0.720989i | \(0.743688\pi\) | |||||||
\(884\) | 11.3638 | 0.382207 | ||||||||
\(885\) | −14.7013 | −0.494178 | ||||||||
\(886\) | 29.1789 | 0.980284 | ||||||||
\(887\) | −31.0647 | −1.04305 | −0.521525 | − | 0.853236i | \(-0.674637\pi\) | ||||
−0.521525 | + | 0.853236i | \(0.674637\pi\) | |||||||
\(888\) | −4.20594 | −0.141142 | ||||||||
\(889\) | 10.9841 | 0.368395 | ||||||||
\(890\) | 7.17843 | 0.240622 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.6450 | 0.657763 | ||||||||
\(893\) | −77.3174 | −2.58733 | ||||||||
\(894\) | −7.41197 | −0.247893 | ||||||||
\(895\) | −3.11079 | −0.103982 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −18.3269 | −0.611918 | ||||||||
\(898\) | 18.6378 | 0.621950 | ||||||||
\(899\) | −1.29760 | −0.0432775 | ||||||||
\(900\) | −1.19656 | −0.0398853 | ||||||||
\(901\) | −6.83678 | −0.227766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.67141 | 0.222011 | ||||||||
\(904\) | 12.9414 | 0.430426 | ||||||||
\(905\) | 4.58252 | 0.152328 | ||||||||
\(906\) | −12.9778 | −0.431160 | ||||||||
\(907\) | 17.7502 | 0.589386 | 0.294693 | − | 0.955592i | \(-0.404783\pi\) | ||||
0.294693 | + | 0.955592i | \(0.404783\pi\) | |||||||
\(908\) | 7.63636 | 0.253422 | ||||||||
\(909\) | −5.22867 | −0.173424 | ||||||||
\(910\) | −4.31157 | −0.142927 | ||||||||
\(911\) | 27.0043 | 0.894694 | 0.447347 | − | 0.894361i | \(-0.352369\pi\) | ||||
0.447347 | + | 0.894361i | \(0.352369\pi\) | |||||||
\(912\) | 8.79259 | 0.291152 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.01602 | 0.0997611 | ||||||||
\(915\) | −7.82834 | −0.258797 | ||||||||
\(916\) | −1.56937 | −0.0518536 | ||||||||
\(917\) | −11.9717 | −0.395340 | ||||||||
\(918\) | −14.8536 | −0.490243 | ||||||||
\(919\) | 1.75332 | 0.0578368 | 0.0289184 | − | 0.999582i | \(-0.490794\pi\) | ||||
0.0289184 | + | 0.999582i | \(0.490794\pi\) | |||||||
\(920\) | −3.16521 | −0.104354 | ||||||||
\(921\) | −12.4371 | −0.409816 | ||||||||
\(922\) | −16.8872 | −0.556149 | ||||||||
\(923\) | 19.4094 | 0.638867 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.13193 | 0.102977 | ||||||||
\(926\) | 0.180188 | 0.00592133 | ||||||||
\(927\) | −17.1082 | −0.561906 | ||||||||
\(928\) | −1.13193 | −0.0371574 | ||||||||
\(929\) | 1.51606 | 0.0497403 | 0.0248702 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248702 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(930\) | −1.53948 | −0.0504816 | ||||||||
\(931\) | −6.54735 | −0.214581 | ||||||||
\(932\) | −22.2894 | −0.730114 | ||||||||
\(933\) | −8.57710 | −0.280802 | ||||||||
\(934\) | 12.4723 | 0.408105 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.15905 | 0.168629 | ||||||||
\(937\) | −31.6995 | −1.03558 | −0.517789 | − | 0.855508i | \(-0.673245\pi\) | ||||
−0.517789 | + | 0.855508i | \(0.673245\pi\) | |||||||
\(938\) | −9.72249 | −0.317450 | ||||||||
\(939\) | 2.59279 | 0.0846124 | ||||||||
\(940\) | 11.8090 | 0.385166 | ||||||||
\(941\) | 15.4489 | 0.503619 | 0.251810 | − | 0.967777i | \(-0.418974\pi\) | ||||
0.251810 | + | 0.967777i | \(0.418974\pi\) | |||||||
\(942\) | −22.5854 | −0.735871 | ||||||||
\(943\) | −1.65054 | −0.0537488 | ||||||||
\(944\) | 10.9472 | 0.356302 | ||||||||
\(945\) | 5.63565 | 0.183328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0390 | 0.326222 | 0.163111 | − | 0.986608i | \(-0.447847\pi\) | ||||
0.163111 | + | 0.986608i | \(0.447847\pi\) | |||||||
\(948\) | −22.9496 | −0.745369 | ||||||||
\(949\) | −52.2859 | −1.69727 | ||||||||
\(950\) | −6.54735 | −0.212424 | ||||||||
\(951\) | 15.9489 | 0.517180 | ||||||||
\(952\) | −2.63565 | −0.0854220 | ||||||||
\(953\) | −41.2604 | −1.33656 | −0.668278 | − | 0.743912i | \(-0.732968\pi\) | ||||
−0.668278 | + | 0.743912i | \(0.732968\pi\) | |||||||
\(954\) | −3.10382 | −0.100490 | ||||||||
\(955\) | 4.33382 | 0.140239 | ||||||||
\(956\) | −5.92057 | −0.191485 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.55428 | −0.0502164 | ||||||||
\(959\) | −9.37916 | −0.302869 | ||||||||
\(960\) | −1.34292 | −0.0433427 | ||||||||
\(961\) | −29.6858 | −0.957608 | ||||||||
\(962\) | −13.5035 | −0.435372 | ||||||||
\(963\) | 5.71977 | 0.184317 | ||||||||
\(964\) | −26.9422 | −0.867749 | ||||||||
\(965\) | −13.4284 | −0.432276 | ||||||||
\(966\) | 4.25063 | 0.136762 | ||||||||
\(967\) | −18.8930 | −0.607557 | −0.303778 | − | 0.952743i | \(-0.598248\pi\) | ||||
−0.303778 | + | 0.952743i | \(0.598248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.1742 | −0.744463 | ||||||||
\(970\) | 9.85645 | 0.316472 | ||||||||
\(971\) | 13.6882 | 0.439277 | 0.219638 | − | 0.975581i | \(-0.429512\pi\) | ||||
0.219638 | + | 0.975581i | \(0.429512\pi\) | |||||||
\(972\) | −11.5640 | −0.370917 | ||||||||
\(973\) | 11.1498 | 0.357446 | ||||||||
\(974\) | 29.2641 | 0.937683 | ||||||||
\(975\) | 5.79011 | 0.185432 | ||||||||
\(976\) | 5.82933 | 0.186592 | ||||||||
\(977\) | 34.5173 | 1.10431 | 0.552153 | − | 0.833743i | \(-0.313807\pi\) | ||||
0.552153 | + | 0.833743i | \(0.313807\pi\) | |||||||
\(978\) | 30.7464 | 0.983163 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −3.09000 | −0.0986560 | ||||||||
\(982\) | −2.35553 | −0.0751680 | ||||||||
\(983\) | −29.7951 | −0.950316 | −0.475158 | − | 0.879900i | \(-0.657609\pi\) | ||||
−0.475158 | + | 0.879900i | \(0.657609\pi\) | |||||||
\(984\) | −0.700283 | −0.0223242 | ||||||||
\(985\) | 11.8667 | 0.378104 | ||||||||
\(986\) | 2.98337 | 0.0950099 | ||||||||
\(987\) | −15.8585 | −0.504782 | ||||||||
\(988\) | 28.2294 | 0.898096 | ||||||||
\(989\) | 15.7242 | 0.500001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.5393 | 1.25601 | 0.628004 | − | 0.778210i | \(-0.283872\pi\) | ||||
0.628004 | + | 0.778210i | \(0.283872\pi\) | |||||||
\(992\) | 1.14637 | 0.0363971 | ||||||||
\(993\) | 38.3746 | 1.21778 | ||||||||
\(994\) | −4.50169 | −0.142785 | ||||||||
\(995\) | −14.5672 | −0.461810 | ||||||||
\(996\) | −12.1688 | −0.385583 | ||||||||
\(997\) | 8.24240 | 0.261040 | 0.130520 | − | 0.991446i | \(-0.458335\pi\) | ||||
0.130520 | + | 0.991446i | \(0.458335\pi\) | |||||||
\(998\) | 25.2783 | 0.800172 | ||||||||
\(999\) | 17.6505 | 0.558436 |
(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 | 8470.2.a.df.1.1 | yes | 6 | |
11.10 | odd | 2 | 8470.2.a.cz.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cz.1.2 | ✓ | 6 | 11.10 | odd | 2 | ||
8470.2.a.df.1.1 | yes | 6 | 1.1 | even | 1 | trivial |