Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [520,2,Mod(1,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, 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("520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.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: | \(4.15222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 520.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 1.30931 | 0.654654 | − | 0.755929i | \(-0.272814\pi\) | ||||
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.73205 | 0.823744 | 0.411872 | − | 0.911242i | \(-0.364875\pi\) | ||||
0.411872 | + | 0.911242i | \(0.364875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.73205 | −0.626775 | −0.313388 | − | 0.949625i | \(-0.601464\pi\) | ||||
−0.313388 | + | 0.949625i | \(0.601464\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53590 | 0.553378 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.732051 | −0.152643 | −0.0763216 | − | 0.997083i | \(-0.524318\pi\) | ||||
−0.0763216 | + | 0.997083i | \(0.524318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.46410 | 1.75744 | 0.878720 | − | 0.477338i | \(-0.158398\pi\) | ||||
0.878720 | + | 0.477338i | \(0.158398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.196152 | −0.0352300 | −0.0176150 | − | 0.999845i | \(-0.505607\pi\) | ||||
−0.0176150 | + | 0.999845i | \(0.505607\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.732051 | 0.117222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.535898 | 0.0836933 | 0.0418466 | − | 0.999124i | \(-0.486676\pi\) | ||||
0.0418466 | + | 0.999124i | \(0.486676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.26795 | −1.10835 | −0.554176 | − | 0.832400i | \(-0.686967\pi\) | ||||
−0.554176 | + | 0.832400i | \(0.686967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46410 | 0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.53590 | 0.661629 | 0.330814 | − | 0.943696i | \(-0.392677\pi\) | ||||
0.330814 | + | 0.943696i | \(0.392677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.46410 | 0.765127 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.535898 | −0.0736113 | −0.0368057 | − | 0.999322i | \(-0.511718\pi\) | ||||
−0.0368057 | + | 0.999322i | \(0.511718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.73205 | −0.368390 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.66025 | 0.736902 | 0.368451 | − | 0.929647i | \(-0.379888\pi\) | ||||
0.368451 | + | 0.929647i | \(0.379888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3923 | −1.58667 | −0.793336 | − | 0.608784i | \(-0.791658\pi\) | ||||
−0.793336 | + | 0.608784i | \(0.791658\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.53590 | −1.07542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9282 | −1.57943 | −0.789716 | − | 0.613473i | \(-0.789772\pi\) | ||||
−0.789716 | + | 0.613473i | \(0.789772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.535898 | −0.0645146 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.26795 | 1.09990 | 0.549952 | − | 0.835197i | \(-0.314646\pi\) | ||||
0.549952 | + | 0.835197i | \(0.314646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.92820 | −0.342720 | −0.171360 | − | 0.985208i | \(-0.554816\pi\) | ||||
−0.171360 | + | 0.985208i | \(0.554816\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.46410 | 1.07853 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.53590 | −0.735346 | −0.367673 | − | 0.929955i | \(-0.619845\pi\) | ||||
−0.367673 | + | 0.929955i | \(0.619845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3923 | −1.14070 | −0.570352 | − | 0.821401i | \(-0.693193\pi\) | ||||
−0.570352 | + | 0.821401i | \(0.693193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.46410 | −0.809595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.92820 | 0.742781 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9282 | −1.37039 | −0.685193 | − | 0.728361i | \(-0.740282\pi\) | ||||
−0.685193 | + | 0.728361i | \(0.740282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.46410 | 0.363137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.143594 | −0.0148900 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.73205 | 0.280302 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8564 | 1.60997 | 0.804987 | − | 0.593292i | \(-0.202172\pi\) | ||||
0.804987 | + | 0.593292i | \(0.202172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.73205 | −0.676597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.92820 | 0.490375 | 0.245187 | − | 0.969476i | \(-0.421151\pi\) | ||||
0.245187 | + | 0.969476i | \(0.421151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.19615 | −0.610525 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.53590 | −0.247478 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.0526 | −1.93855 | −0.969277 | − | 0.245972i | \(-0.920893\pi\) | ||||
−0.969277 | + | 0.245972i | \(0.920893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8564 | 1.51877 | 0.759384 | − | 0.650643i | \(-0.225500\pi\) | ||||
0.759384 | + | 0.650643i | \(0.225500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.3923 | −1.73020 | −0.865101 | − | 0.501597i | \(-0.832746\pi\) | ||||
−0.865101 | + | 0.501597i | \(0.832746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.732051 | 0.0682641 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.46410 | −0.227806 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.8564 | 2.37025 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.53590 | −0.321445 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.392305 | 0.0353729 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.80385 | −0.160066 | −0.0800328 | − | 0.996792i | \(-0.525503\pi\) | ||||
−0.0800328 | + | 0.996792i | \(0.525503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.32051 | −0.468445 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.92820 | −0.255838 | −0.127919 | − | 0.991785i | \(-0.540830\pi\) | ||||
−0.127919 | + | 0.991785i | \(0.540830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.46410 | −0.820642 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.92820 | 0.762788 | 0.381394 | − | 0.924413i | \(-0.375444\pi\) | ||||
0.381394 | + | 0.924413i | \(0.375444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4641 | −1.14201 | −0.571005 | − | 0.820947i | \(-0.693446\pi\) | ||||
−0.571005 | + | 0.820947i | \(0.693446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.32051 | 0.279637 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73205 | 0.228466 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.46410 | −0.785951 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.66025 | 0.301893 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.85641 | −0.643622 | −0.321811 | − | 0.946804i | \(-0.604292\pi\) | ||||
−0.321811 | + | 0.946804i | \(0.604292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8038 | 0.960583 | 0.480292 | − | 0.877109i | \(-0.340531\pi\) | ||||
0.480292 | + | 0.877109i | \(0.340531\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.3923 | −1.48693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.196152 | 0.0157553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.85641 | −0.627009 | −0.313505 | − | 0.949587i | \(-0.601503\pi\) | ||||
−0.313505 | + | 0.949587i | \(0.601503\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.392305 | −0.0311118 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53590 | −0.199857 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.92820 | −0.699311 | −0.349655 | − | 0.936878i | \(-0.613701\pi\) | ||||
−0.349655 | + | 0.936878i | \(0.613701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | −0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.3205 | −1.64983 | −0.824915 | − | 0.565256i | \(-0.808777\pi\) | ||||
−0.824915 | + | 0.565256i | \(0.808777\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.73205 | 0.514813 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.39230 | −0.181884 | −0.0909418 | − | 0.995856i | \(-0.528988\pi\) | ||||
−0.0909418 | + | 0.995856i | \(0.528988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | 0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.14359 | 0.311452 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.8564 | −1.63362 | −0.816812 | − | 0.576904i | \(-0.804261\pi\) | ||||
−0.816812 | + | 0.576904i | \(0.804261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.53590 | 0.485810 | 0.242905 | − | 0.970050i | \(-0.421900\pi\) | ||||
0.242905 | + | 0.970050i | \(0.421900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.07180 | −0.670607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.3923 | 1.49123 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.8564 | −1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9282 | 1.36960 | 0.684798 | − | 0.728733i | \(-0.259890\pi\) | ||||
0.684798 | + | 0.728733i | \(0.259890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.732051 | −0.0524232 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.92820 | 0.636108 | 0.318054 | − | 0.948073i | \(-0.396971\pi\) | ||||
0.318054 | + | 0.948073i | \(0.396971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.92820 | −0.491127 | −0.245564 | − | 0.969380i | \(-0.578973\pi\) | ||||
−0.245564 | + | 0.969380i | \(0.578973\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.46410 | −0.667546 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 32.7846 | 2.30103 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.535898 | −0.0374288 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.80385 | 0.125376 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.46410 | −0.516303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.92820 | 0.201586 | 0.100793 | − | 0.994907i | \(-0.467862\pi\) | ||||
0.100793 | + | 0.994907i | \(0.467862\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.78461 | 0.464874 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.26795 | 0.495670 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.679492 | −0.0461269 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.14359 | −0.144851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.46410 | 0.502090 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.3205 | 1.69559 | 0.847793 | − | 0.530327i | \(-0.177931\pi\) | ||||
0.847793 | + | 0.530327i | \(0.177931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0000 | 1.19470 | 0.597351 | − | 0.801980i | \(-0.296220\pi\) | ||||
0.597351 | + | 0.801980i | \(0.296220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4641 | 1.28622 | 0.643112 | − | 0.765772i | \(-0.277643\pi\) | ||||
0.643112 | + | 0.765772i | \(0.277643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.92820 | 0.455842 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.53590 | −0.295889 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.78461 | −0.310794 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2679 | 1.63445 | 0.817224 | − | 0.576320i | \(-0.195512\pi\) | ||||
0.817224 | + | 0.576320i | \(0.195512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2487 | 1.30433 | 0.652167 | − | 0.758075i | \(-0.273860\pi\) | ||||
0.652167 | + | 0.758075i | \(0.273860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.73205 | −0.173836 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.60770 | −0.482118 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.3205 | 1.47198 | 0.735989 | − | 0.676994i | \(-0.236718\pi\) | ||||
0.735989 | + | 0.676994i | \(0.236718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.46410 | −0.342175 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.3205 | −1.44350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.6603 | −0.719002 | −0.359501 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359501 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.535898 | 0.0329200 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.46410 | −0.579194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.143594 | −0.00875505 | −0.00437753 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437753 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.1244 | −1.40470 | −0.702352 | − | 0.711830i | \(-0.747867\pi\) | ||||
−0.702352 | + | 0.711830i | \(0.747867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.53590 | 0.153480 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.73205 | 0.164749 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.3205 | −1.28103 | −0.640513 | − | 0.767948i | \(-0.721278\pi\) | ||||
−0.640513 | + | 0.767948i | \(0.721278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.483340 | 0.0289368 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.53590 | −0.270589 | −0.135295 | − | 0.990805i | \(-0.543198\pi\) | ||||
−0.135295 | + | 0.990805i | \(0.543198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0526 | −1.42978 | −0.714888 | − | 0.699239i | \(-0.753522\pi\) | ||||
−0.714888 | + | 0.699239i | \(0.753522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.85641 | 0.109580 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6077 | 0.680455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820 | 0.404750 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.66025 | −0.329553 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9282 | −0.634119 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.732051 | −0.0423356 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.1769 | −1.45117 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.60770 | 0.207257 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3923 | 0.709581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5359 | −0.943754 | −0.471877 | − | 0.881665i | \(-0.656423\pi\) | ||||
−0.471877 | + | 0.881665i | \(0.656423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.53590 | −0.258038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.3205 | 1.77602 | 0.888012 | − | 0.459821i | \(-0.152086\pi\) | ||||
0.888012 | + | 0.459821i | \(0.152086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3923 | 0.587408 | 0.293704 | − | 0.955896i | \(-0.405112\pi\) | ||||
0.293704 | + | 0.955896i | \(0.405112\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.53590 | 0.480943 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.85641 | −0.104266 | −0.0521331 | − | 0.998640i | \(-0.516602\pi\) | ||||
−0.0521331 | + | 0.998640i | \(0.516602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.8564 | 1.44768 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6795 | −0.819329 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.3923 | −1.13466 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.6077 | 0.641907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.7128 | 0.866275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.58846 | −0.472064 | −0.236032 | − | 0.971745i | \(-0.575847\pi\) | ||||
−0.236032 | + | 0.971745i | \(0.575847\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9282 | 0.706343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3923 | 1.21979 | 0.609893 | − | 0.792484i | \(-0.291212\pi\) | ||||
0.609893 | + | 0.792484i | \(0.291212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4641 | −0.731270 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.535898 | −0.0290205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.535898 | 0.0288518 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.19615 | 0.117896 | 0.0589478 | − | 0.998261i | \(-0.481225\pi\) | ||||
0.0589478 | + | 0.998261i | \(0.481225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5359 | 0.671031 | 0.335516 | − | 0.942035i | \(-0.391089\pi\) | ||||
0.335516 | + | 0.942035i | \(0.391089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.92820 | −0.368751 | −0.184376 | − | 0.982856i | \(-0.559026\pi\) | ||||
−0.184376 | + | 0.982856i | \(0.559026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.26795 | −0.491892 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9282 | 1.00179 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.1244 | 0.587121 | 0.293561 | − | 0.955940i | \(-0.405160\pi\) | ||||
0.293561 | + | 0.955940i | \(0.405160\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5359 | −0.607153 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.58846 | −0.135859 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92820 | 0.153269 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.41154 | −0.0736819 | −0.0368410 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368410 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.32051 | −0.0687429 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.85641 | −0.0963798 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.85641 | −0.406789 | −0.203395 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203395 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.732051 | −0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.46410 | 0.487426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.1962 | −1.03741 | −0.518703 | − | 0.854954i | \(-0.673585\pi\) | ||||
−0.518703 | + | 0.854954i | \(0.673585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.32051 | −0.0676517 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.60770 | −0.0821494 | −0.0410747 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410747 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.46410 | −0.482335 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.9090 | 0.910364 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.46410 | −0.276331 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.14359 | −0.108130 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.53590 | 0.328857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.07180 | −0.254546 | −0.127273 | − | 0.991868i | \(-0.540622\pi\) | ||||
−0.127273 | + | 0.991868i | \(0.540622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | −0.346844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7846 | −0.538558 | −0.269279 | − | 0.963062i | \(-0.586785\pi\) | ||||
−0.269279 | + | 0.963062i | \(0.586785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.196152 | −0.00977105 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.46410 | −0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3205 | 1.64759 | 0.823797 | − | 0.566886i | \(-0.191852\pi\) | ||||
0.823797 | + | 0.566886i | \(0.191852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.53590 | 0.322392 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6077 | 0.964832 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3923 | 0.510138 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.85641 | −0.482670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4641 | −1.24400 | −0.622001 | − | 0.783016i | \(-0.713680\pi\) | ||||
−0.622001 | + | 0.783016i | \(0.713680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0718 | −0.929503 | −0.464751 | − | 0.885441i | \(-0.653856\pi\) | ||||
−0.464751 | + | 0.885441i | \(0.653856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.1769 | −0.543440 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.46410 | 0.362062 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.9282 | −2.07744 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.0526 | −1.06223 | −0.531117 | − | 0.847298i | \(-0.678228\pi\) | ||||
−0.531117 | + | 0.847298i | \(0.678228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0718 | 0.724304 | 0.362152 | − | 0.932119i | \(-0.382042\pi\) | ||||
0.362152 | + | 0.932119i | \(0.382042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.92820 | −0.332182 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3205 | −0.586691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.4449 | 1.35146 | 0.675728 | − | 0.737151i | \(-0.263829\pi\) | ||||
0.675728 | + | 0.737151i | \(0.263829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9282 | 0.612856 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.75129 | −0.272027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3923 | −0.679215 | −0.339607 | − | 0.940567i | \(-0.610294\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.46410 | 0.0689419 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.64102 | 0.405990 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.46410 | −0.162400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.7846 | −1.44004 | −0.720022 | − | 0.693952i | \(-0.755868\pi\) | ||||
−0.720022 | + | 0.693952i | \(0.755868\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.8564 | −1.39358 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2487 | −0.570479 | −0.285240 | − | 0.958456i | \(-0.592073\pi\) | ||||
−0.285240 | + | 0.958456i | \(0.592073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8564 | 1.29460 | 0.647298 | − | 0.762237i | \(-0.275899\pi\) | ||||
0.647298 | + | 0.762237i | \(0.275899\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.143594 | 0.00665899 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5885 | 0.860171 | 0.430086 | − | 0.902788i | \(-0.358483\pi\) | ||||
0.430086 | + | 0.902788i | \(0.358483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.7846 | −2.06796 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.75129 | −0.265005 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.8564 | −0.912999 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.73205 | −0.125355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.32051 | 0.0604619 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.1244 | 0.508285 | 0.254142 | − | 0.967167i | \(-0.418207\pi\) | ||||
0.254142 | + | 0.967167i | \(0.418207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.85641 | −0.0844694 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8564 | −0.720002 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.8564 | −1.80607 | −0.903033 | − | 0.429571i | \(-0.858665\pi\) | ||||
−0.903033 | + | 0.429571i | \(0.858665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.53590 | −0.295564 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.4641 | −1.51021 | −0.755107 | − | 0.655602i | \(-0.772415\pi\) | ||||
−0.755107 | + | 0.655602i | \(0.772415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 70.6410 | 3.18151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.73205 | 0.302583 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.1051 | 1.44011 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1962 | 1.08317 | 0.541584 | − | 0.840646i | \(-0.317825\pi\) | ||||
0.541584 | + | 0.840646i | \(0.317825\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.6077 | −0.697300 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.1244 | −1.83364 | −0.916822 | − | 0.399296i | \(-0.869255\pi\) | ||||
−0.916822 | + | 0.399296i | \(0.869255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.92820 | −0.219302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.732051 | 0.0325115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.46410 | −0.153544 | −0.0767718 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767718 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1436 | −0.448726 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.9282 | 0.482492 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.19615 | 0.273035 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3923 | 0.545013 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.75129 | −0.0768730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.39230 | 0.367674 | 0.183837 | − | 0.982957i | \(-0.441148\pi\) | ||||
0.183837 | + | 0.982957i | \(0.441148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5167 | 0.765950 | 0.382975 | − | 0.923759i | \(-0.374900\pi\) | ||||
0.382975 | + | 0.923759i | \(0.374900\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.53590 | 0.110676 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.46410 | −0.0637773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4641 | −0.976700 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.9474 | −0.605267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.535898 | 0.0232123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0526 | 0.866948 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0000 | −0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.6603 | 0.588389 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.3923 | 1.65061 | 0.825307 | − | 0.564684i | \(-0.191002\pi\) | ||||
0.825307 | + | 0.564684i | \(0.191002\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.78461 | 0.205327 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.8564 | −0.679214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.33975 | −0.356582 | −0.178291 | − | 0.983978i | \(-0.557057\pi\) | ||||
−0.178291 | + | 0.983978i | \(0.557057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.5359 | 1.30324 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8564 | −1.10152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.6410 | −0.962794 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.8564 | 0.926086 | 0.463043 | − | 0.886336i | \(-0.346758\pi\) | ||||
0.463043 | + | 0.886336i | \(0.346758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.26795 | −0.307401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.9282 | 0.630269 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.7321 | 1.71665 | 0.858326 | − | 0.513105i | \(-0.171505\pi\) | ||||
0.858326 | + | 0.513105i | \(0.171505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3923 | 0.773770 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.4641 | 0.649431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4641 | −0.732133 | −0.366067 | − | 0.930589i | \(-0.619296\pi\) | ||||
−0.366067 | + | 0.930589i | \(0.619296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3205 | −1.14333 | −0.571664 | − | 0.820488i | \(-0.693702\pi\) | ||||
−0.571664 | + | 0.820488i | \(0.693702\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.732051 | −0.0305286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.6410 | −1.27560 | −0.637801 | − | 0.770201i | \(-0.720156\pi\) | ||||
−0.637801 | + | 0.770201i | \(0.720156\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.46410 | −0.0608460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.0000 | −1.49353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46410 | −0.0606369 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46410 | 0.101878 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.21539 | 0.0501645 | 0.0250823 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250823 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.535898 | 0.0220813 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.53590 | 0.268851 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.6410 | 1.66893 | 0.834463 | − | 0.551064i | \(-0.185778\pi\) | ||||
0.834463 | + | 0.551064i | \(0.185778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.8564 | −1.06001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.07180 | −0.207575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.4641 | −1.36731 | −0.683653 | − | 0.729807i | \(-0.739610\pi\) | ||||
−0.683653 | + | 0.729807i | \(0.739610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.85641 | −0.157306 | −0.0786531 | − | 0.996902i | \(-0.525062\pi\) | ||||
−0.0786531 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.8564 | 1.29729 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.53590 | 0.143755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.5167 | −0.548624 | −0.274312 | − | 0.961641i | \(-0.588450\pi\) | ||||
−0.274312 | + | 0.961641i | \(0.588450\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0000 | 0.972529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.53590 | 0.183503 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.143594 | −0.00579969 | −0.00289984 | − | 0.999996i | \(-0.500923\pi\) | ||||
−0.00289984 | + | 0.999996i | \(0.500923\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.392305 | −0.0158193 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.7128 | −1.84033 | −0.920164 | − | 0.391533i | \(-0.871945\pi\) | ||||
−0.920164 | + | 0.391533i | \(0.871945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3397 | −0.737137 | −0.368568 | − | 0.929601i | \(-0.620152\pi\) | ||||
−0.368568 | + | 0.929601i | \(0.620152\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.92820 | 0.117505 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.7846 | −1.79426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.46410 | −0.218215 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.80385 | −0.310666 | −0.155333 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155333 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.14359 | 0.0852002 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.80385 | 0.0715835 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | 0.198107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.8372 | −0.903424 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.928203 | −0.0366618 | −0.0183309 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183309 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.60770 | −0.378891 | −0.189445 | − | 0.981891i | \(-0.560669\pi\) | ||||
−0.189445 | + | 0.981891i | \(0.560669\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.32051 | 0.209495 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.339746 | 0.0133568 | 0.00667840 | − | 0.999978i | \(-0.497874\pi\) | ||||
0.00667840 | + | 0.999978i | \(0.497874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4641 | 0.607019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.497423 | −0.0194955 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7128 | −1.31928 | −0.659642 | − | 0.751580i | \(-0.729292\pi\) | ||||
−0.659642 | + | 0.751580i | \(0.729292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.92820 | 0.114414 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.21539 | 0.281499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.3205 | 1.53171 | 0.765855 | − | 0.643014i | \(-0.222316\pi\) | ||||
0.765855 | + | 0.643014i | \(0.222316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.9282 | 0.814013 | 0.407006 | − | 0.913425i | \(-0.366573\pi\) | ||||
0.407006 | + | 0.913425i | \(0.366573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.46410 | 0.212208 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.46410 | 0.367002 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.92820 | −0.268261 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.5359 | 0.716639 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.8564 | −1.30701 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.5359 | 1.09998 | 0.549989 | − | 0.835172i | \(-0.314632\pi\) | ||||
0.549989 | + | 0.835172i | \(0.314632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.60770 | 0.369254 | 0.184627 | − | 0.982809i | \(-0.440892\pi\) | ||||
0.184627 | + | 0.982809i | \(0.440892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.9282 | 2.10795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1769 | 0.504940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.9282 | 0.953851 | 0.476926 | − | 0.878944i | \(-0.341751\pi\) | ||||
0.476926 | + | 0.878944i | \(0.341751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.92820 | −0.341129 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.2487 | 0.543622 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.535898 | −0.0204161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.9090 | 1.67038 | 0.835188 | − | 0.549965i | \(-0.185359\pi\) | ||||
0.835188 | + | 0.549965i | \(0.185359\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.3205 | −0.885873 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.4641 | 0.510722 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1769 | 0.498397 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7128 | 1.12224 | 0.561119 | − | 0.827735i | \(-0.310371\pi\) | ||||
0.561119 | + | 0.827735i | \(0.310371\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.32051 | −0.125058 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.0718 | 0.642051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.60770 | 0.210601 | 0.105301 | − | 0.994440i | \(-0.466419\pi\) | ||||
0.105301 | + | 0.994440i | \(0.466419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.1051 | 0.603989 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.143594 | 0.00537762 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.73205 | −0.102173 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.4974 | 0.690799 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.6410 | −1.29189 | −0.645946 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645946 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.4641 | −0.799365 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.8231 | 0.551276 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.46410 | 0.351488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.9808 | −1.29736 | −0.648682 | − | 0.761059i | \(-0.724680\pi\) | ||||
−0.648682 | + | 0.761059i | \(0.724680\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.2487 | −2.00646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.8564 | −0.585670 | −0.292835 | − | 0.956163i | \(-0.594599\pi\) | ||||
−0.292835 | + | 0.956163i | \(0.594599\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.66025 | −0.135011 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.3205 | −1.30105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26795 | 0.0466423 | 0.0233211 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233211 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.3205 | 0.928919 | 0.464460 | − | 0.885594i | \(-0.346249\pi\) | ||||
0.464460 | + | 0.885594i | \(0.346249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.85641 | 0.287836 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.6077 | 0.936937 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −69.4641 | −2.53816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4641 | 1.65901 | 0.829504 | − | 0.558500i | \(-0.188623\pi\) | ||||
0.829504 | + | 0.558500i | \(0.188623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.0718 | 0.622131 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.8038 | −0.429586 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.4641 | −0.852817 | −0.426409 | − | 0.904531i | \(-0.640221\pi\) | ||||
−0.426409 | + | 0.904531i | \(0.640221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.46410 | −0.0531435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.0000 | −0.507500 | −0.253750 | − | 0.967270i | \(-0.581664\pi\) | ||||
−0.253750 | + | 0.967270i | \(0.581664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 54.9282 | 1.98853 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.3923 | 0.664975 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.66025 | 0.204380 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0718 | 0.543503 | 0.271751 | − | 0.962367i | \(-0.412397\pi\) | ||||
0.271751 | + | 0.962367i | \(0.412397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.39230 | 0.158185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.07180 | 0.182420 | 0.0912099 | − | 0.995832i | \(-0.470927\pi\) | ||||
0.0912099 | + | 0.995832i | \(0.470927\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.196152 | −0.00704600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.46410 | −0.0524569 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3205 | 0.906039 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37.8564 | −1.35288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.85641 | 0.280407 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3923 | 0.655615 | 0.327807 | − | 0.944745i | \(-0.393690\pi\) | ||||
0.327807 | + | 0.944745i | \(0.393690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.53590 | −0.303886 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.7128 | −2.26537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.3923 | −0.440064 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.392305 | 0.0139136 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.7846 | 1.65720 | 0.828598 | − | 0.559844i | \(-0.189139\pi\) | ||||
0.828598 | + | 0.559844i | \(0.189139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.8564 | 1.19775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.8564 | 1.12559 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.00000 | −0.282314 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.53590 | 0.0893787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.105118 | −0.00370032 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.67949 | 0.305155 | 0.152577 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152577 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.9090 | 1.26093 | 0.630467 | − | 0.776216i | \(-0.282863\pi\) | ||||
0.630467 | + | 0.776216i | \(0.282863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.9282 | −0.593698 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.92820 | 0.312741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8564 | 0.694688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.53590 | −0.298268 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.9282 | −0.451197 | −0.225599 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225599 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5885 | 0.926815 | 0.463408 | − | 0.886145i | \(-0.346627\pi\) | ||||
0.463408 | + | 0.886145i | \(0.346627\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.46410 | 0.120459 | 0.0602293 | − | 0.998185i | \(-0.480817\pi\) | ||||
0.0602293 | + | 0.998185i | \(0.480817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.3923 | 1.54181 | 0.770904 | − | 0.636951i | \(-0.219805\pi\) | ||||
0.770904 | + | 0.636951i | \(0.219805\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.6077 | −0.541425 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.3205 | 1.29308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.3205 | 0.737827 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.784610 | 0.0271201 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.4449 | 1.18917 | 0.594584 | − | 0.804033i | \(-0.297317\pi\) | ||||
0.594584 | + | 0.804033i | \(0.297317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5692 | 2.08859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.32051 | −0.114364 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2487 | −0.420871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6077 | −0.604295 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.71281 | −0.264082 | −0.132041 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132041 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.73205 | −0.230231 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.14359 | −0.141542 | −0.0707712 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707712 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.3923 | −0.422820 | −0.211410 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211410 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.35898 | 0.0463140 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6077 | −1.14402 | −0.572010 | − | 0.820247i | \(-0.693836\pi\) | ||||
−0.572010 | + | 0.820247i | \(0.693836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.39230 | 0.0813408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.3397 | 0.962468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8564 | −0.605737 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9282 | −0.438055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.0718 | −1.32238 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.46410 | −0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.7128 | −1.40854 | −0.704271 | − | 0.709931i | \(-0.748726\pi\) | ||||
−0.704271 | + | 0.709931i | \(0.748726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.07180 | 0.171067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.46410 | 0.184090 | 0.0920451 | − | 0.995755i | \(-0.470660\pi\) | ||||
0.0920451 | + | 0.995755i | \(0.470660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5885 | 0.760162 | 0.380081 | − | 0.924953i | \(-0.375896\pi\) | ||||
0.380081 | + | 0.924953i | \(0.375896\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.14359 | −0.139285 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.4449 | 0.417858 | 0.208929 | − | 0.977931i | \(-0.433002\pi\) | ||||
0.208929 | + | 0.977931i | \(0.433002\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.24871 | −0.209575 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.1962 | 0.408586 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.3923 | −0.414693 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.8564 | 0.730579 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.535898 | −0.0178931 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.85641 | −0.0619146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.4308 | −0.613338 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.53590 | −0.217261 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.8372 | −1.22316 | −0.611579 | − | 0.791183i | \(-0.709465\pi\) | ||||
−0.611579 | + | 0.791183i | \(0.709465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.1436 | −0.402778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7846 | −0.688625 | −0.344312 | − | 0.938855i | \(-0.611888\pi\) | ||||
−0.344312 | + | 0.938855i | \(0.611888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.3923 | −0.939648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.07180 | 0.299904 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.1436 | −0.334971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3205 | 1.29706 | 0.648532 | − | 0.761187i | \(-0.275383\pi\) | ||||
0.648532 | + | 0.761187i | \(0.275383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1051 | −0.398877 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.26795 | 0.305058 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2679 | 0.501465 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.1769 | 1.41659 | 0.708294 | − | 0.705917i | \(-0.249465\pi\) | ||||
0.708294 | + | 0.705917i | \(0.249465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6603 | −0.447697 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.9282 | 0.750636 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.3923 | −0.666900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0718 | −0.884397 | −0.442199 | − | 0.896917i | \(-0.645801\pi\) | ||||
−0.442199 | + | 0.896917i | \(0.645801\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.60770 | 0.248268 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.3923 | 0.729968 | 0.364984 | − | 0.931014i | \(-0.381074\pi\) | ||||
0.364984 | + | 0.931014i | \(0.381074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.392305 | −0.0127752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.3923 | 0.727652 | 0.363826 | − | 0.931467i | \(-0.381470\pi\) | ||||
0.363826 | + | 0.931467i | \(0.381470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.92820 | −0.0950535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.35898 | −0.0440681 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.21539 | −0.0393704 | −0.0196852 | − | 0.999806i | \(-0.506266\pi\) | ||||
−0.0196852 | + | 0.999806i | \(0.506266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.9282 | −0.612502 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.9282 | 0.611862 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.9282 | 0.998724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.4115 | 1.59226 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.0000 | −0.578841 | −0.289420 | − | 0.957202i | \(-0.593463\pi\) | ||||
−0.289420 | + | 0.957202i | \(0.593463\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.9282 | −0.479563 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.7128 | 1.40281 | 0.701405 | − | 0.712762i | \(-0.252556\pi\) | ||||
0.701405 | + | 0.712762i | \(0.252556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.6410 | −1.49524 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.732051 | 0.0234444 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.92820 | −0.0936815 | −0.0468408 | − | 0.998902i | \(-0.514915\pi\) | ||||
−0.0468408 | + | 0.998902i | \(0.514915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.3205 | −1.12885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.0718 | −1.24747 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.8564 | −0.505741 | −0.252870 | − | 0.967500i | \(-0.581375\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.92820 | −0.284476 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.5026 | 0.366131 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.32051 | 0.169182 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.8564 | −1.71081 | −0.855403 | − | 0.517964i | \(-0.826690\pi\) | ||||
−0.855403 | + | 0.517964i | \(0.826690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.28719 | −0.199518 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92820 | 0.219639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.32051 | −0.295183 | −0.147592 | − | 0.989048i | \(-0.547152\pi\) | ||||
−0.147592 | + | 0.989048i | \(0.547152\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 520.2.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4680.2.a.bd.1.2 | 2 | |||
4.3 | odd | 2 | 1040.2.a.l.1.1 | 2 | |||
5.2 | odd | 4 | 2600.2.d.m.1249.2 | 4 | |||
5.3 | odd | 4 | 2600.2.d.m.1249.3 | 4 | |||
5.4 | even | 2 | 2600.2.a.v.1.1 | 2 | |||
8.3 | odd | 2 | 4160.2.a.w.1.2 | 2 | |||
8.5 | even | 2 | 4160.2.a.bk.1.1 | 2 | |||
12.11 | even | 2 | 9360.2.a.cr.1.1 | 2 | |||
13.12 | even | 2 | 6760.2.a.o.1.2 | 2 | |||
20.19 | odd | 2 | 5200.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1040.2.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
2600.2.a.v.1.1 | 2 | 5.4 | even | 2 | |||
2600.2.d.m.1249.2 | 4 | 5.2 | odd | 4 | |||
2600.2.d.m.1249.3 | 4 | 5.3 | odd | 4 | |||
4160.2.a.w.1.2 | 2 | 8.3 | odd | 2 | |||
4160.2.a.bk.1.1 | 2 | 8.5 | even | 2 | |||
4680.2.a.bd.1.2 | 2 | 3.2 | odd | 2 | |||
5200.2.a.bn.1.2 | 2 | 20.19 | odd | 2 | |||
6760.2.a.o.1.2 | 2 | 13.12 | even | 2 | |||
9360.2.a.cr.1.1 | 2 | 12.11 | even | 2 |