Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.414214 | 0.114882 | 0.0574411 | − | 0.998349i | \(-0.481706\pi\) | ||||
0.0574411 | + | 0.998349i | \(0.481706\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.41421 | −0.585533 | −0.292766 | − | 0.956184i | \(-0.594576\pi\) | ||||
−0.292766 | + | 0.956184i | \(0.594576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.24264 | −1.30168 | −0.650840 | − | 0.759215i | \(-0.725583\pi\) | ||||
−0.650840 | + | 0.759215i | \(0.725583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2426 | 1.83963 | 0.919816 | − | 0.392349i | \(-0.128338\pi\) | ||||
0.919816 | + | 0.392349i | \(0.128338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41421 | 0.420261 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8995 | −1.95626 | −0.978132 | − | 0.207983i | \(-0.933310\pi\) | ||||
−0.978132 | + | 0.207983i | \(0.933310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58579 | 0.716180 | 0.358090 | − | 0.933687i | \(-0.383428\pi\) | ||||
0.358090 | + | 0.933687i | \(0.383428\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6569 | 1.77765 | 0.888827 | − | 0.458243i | \(-0.151521\pi\) | ||||
0.888827 | + | 0.458243i | \(0.151521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.58579 | −1.10650 | −0.553250 | − | 0.833015i | \(-0.686613\pi\) | ||||
−0.553250 | + | 0.833015i | \(0.686613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.82843 | 0.816143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.58579 | −0.904627 | −0.452314 | − | 0.891859i | \(-0.649401\pi\) | ||||
−0.452314 | + | 0.891859i | \(0.649401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.82843 | −0.639541 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.75736 | 0.228789 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.82843 | −0.874291 | −0.437145 | − | 0.899391i | \(-0.644010\pi\) | ||||
−0.437145 | + | 0.899391i | \(0.644010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.41421 | 0.172774 | 0.0863868 | − | 0.996262i | \(-0.472468\pi\) | ||||
0.0863868 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.0711 | 1.81434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.48528 | −0.294949 | −0.147474 | − | 0.989066i | \(-0.547114\pi\) | ||||
−0.147474 | + | 0.989066i | \(0.547114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8284 | 1.26737 | 0.633686 | − | 0.773591i | \(-0.281541\pi\) | ||||
0.633686 | + | 0.773591i | \(0.281541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.34315 | −0.376133 | −0.188067 | − | 0.982156i | \(-0.560222\pi\) | ||||
−0.188067 | + | 0.982156i | \(0.560222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.3137 | 1.24184 | 0.620920 | − | 0.783874i | \(-0.286759\pi\) | ||||
0.620920 | + | 0.783874i | \(0.286759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41421 | −0.258831 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.65685 | 1.02362 | 0.511812 | − | 0.859097i | \(-0.328974\pi\) | ||||
0.511812 | + | 0.859097i | \(0.328974\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.7279 | −2.56417 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0711 | −1.42870 | −0.714350 | − | 0.699788i | \(-0.753278\pi\) | ||||
−0.714350 | + | 0.699788i | \(0.753278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4853 | 1.04332 | 0.521662 | − | 0.853152i | \(-0.325312\pi\) | ||||
0.521662 | + | 0.853152i | \(0.325312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.75736 | −0.665822 | −0.332911 | − | 0.942958i | \(-0.608031\pi\) | ||||
−0.332911 | + | 0.942958i | \(0.608031\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4853 | 1.40035 | 0.700173 | − | 0.713974i | \(-0.253106\pi\) | ||||
0.700173 | + | 0.713974i | \(0.253106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3137 | −1.75414 | −0.877068 | − | 0.480367i | \(-0.840503\pi\) | ||||
−0.877068 | + | 0.480367i | \(0.840503\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.7279 | 2.72673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.07107 | 0.853334 | 0.426667 | − | 0.904409i | \(-0.359688\pi\) | ||||
0.426667 | + | 0.904409i | \(0.359688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17157 | 0.108312 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.0711 | −0.998245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.75736 | −0.333412 | −0.166706 | − | 0.986007i | \(-0.553313\pi\) | ||||
−0.166706 | + | 0.986007i | \(0.553313\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.1421 | −2.47778 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2426 | 1.76861 | 0.884304 | − | 0.466912i | \(-0.154633\pi\) | ||||
0.884304 | + | 0.466912i | \(0.154633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.3137 | 1.65008 | 0.825041 | − | 0.565073i | \(-0.191152\pi\) | ||||
0.825041 | + | 0.565073i | \(0.191152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41421 | 0.119952 | 0.0599760 | − | 0.998200i | \(-0.480898\pi\) | ||||
0.0599760 | + | 0.998200i | \(0.480898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3137 | 1.54229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.414214 | −0.0346383 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.17157 | −0.751365 | −0.375682 | − | 0.926749i | \(-0.622592\pi\) | ||||
−0.375682 | + | 0.926749i | \(0.622592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.65685 | −0.541727 | −0.270864 | − | 0.962618i | \(-0.587309\pi\) | ||||
−0.270864 | + | 0.962618i | \(0.587309\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.82843 | −0.552046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4853 | −0.836817 | −0.418408 | − | 0.908259i | \(-0.637412\pi\) | ||||
−0.418408 | + | 0.908259i | \(0.637412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.8995 | 1.26091 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.92893 | −0.229412 | −0.114706 | − | 0.993400i | \(-0.536593\pi\) | ||||
−0.114706 | + | 0.993400i | \(0.536593\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.58579 | −0.587006 | −0.293503 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293503 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8284 | −0.986802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.65685 | 0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7279 | 1.04371 | 0.521857 | − | 0.853033i | \(-0.325239\pi\) | ||||
0.521857 | + | 0.853033i | \(0.325239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.24264 | −0.318896 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.14214 | 0.309598 | 0.154799 | − | 0.987946i | \(-0.450527\pi\) | ||||
0.154799 | + | 0.987946i | \(0.450527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.5563 | −1.89959 | −0.949794 | − | 0.312875i | \(-0.898708\pi\) | ||||
−0.949794 | + | 0.312875i | \(0.898708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.4853 | 1.21863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.41421 | 0.176545 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8284 | 1.00059 | 0.500295 | − | 0.865855i | \(-0.333225\pi\) | ||||
0.500295 | + | 0.865855i | \(0.333225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.686292 | −0.0494003 | −0.0247002 | − | 0.999695i | \(-0.507863\pi\) | ||||
−0.0247002 | + | 0.999695i | \(0.507863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.2426 | 0.872252 | 0.436126 | − | 0.899886i | \(-0.356350\pi\) | ||||
0.436126 | + | 0.899886i | \(0.356350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.3848 | −0.877934 | −0.438967 | − | 0.898503i | \(-0.644655\pi\) | ||||
−0.438967 | + | 0.898503i | \(0.644655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41421 | −0.240820 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.6569 | −1.22724 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1421 | 1.18011 | 0.590057 | − | 0.807362i | \(-0.299105\pi\) | ||||
0.590057 | + | 0.807362i | \(0.299105\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.1421 | −1.76652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | −0.0672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3848 | 1.16417 | 0.582085 | − | 0.813128i | \(-0.302237\pi\) | ||||
0.582085 | + | 0.813128i | \(0.302237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.58579 | −0.105252 | −0.0526262 | − | 0.998614i | \(-0.516759\pi\) | ||||
−0.0526262 | + | 0.998614i | \(0.516759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.10051 | −0.270969 | −0.135485 | − | 0.990779i | \(-0.543259\pi\) | ||||
−0.135485 | + | 0.990779i | \(0.543259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.51472 | −0.230257 | −0.115128 | − | 0.993351i | \(-0.536728\pi\) | ||||
−0.115128 | + | 0.993351i | \(0.536728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.07107 | 0.524272 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65685 | −0.301227 | −0.150613 | − | 0.988593i | \(-0.548125\pi\) | ||||
−0.150613 | + | 0.988593i | \(0.548125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3848 | 0.668942 | 0.334471 | − | 0.942406i | \(-0.391442\pi\) | ||||
0.334471 | + | 0.942406i | \(0.391442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.828427 | 0.0527116 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.3137 | −1.73094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.55635 | 0.476953 | 0.238476 | − | 0.971148i | \(-0.423352\pi\) | ||||
0.238476 | + | 0.971148i | \(0.423352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.24264 | 0.392471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4853 | −0.654054 | −0.327027 | − | 0.945015i | \(-0.606047\pi\) | ||||
−0.327027 | + | 0.945015i | \(0.606047\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.9706 | −1.16978 | −0.584888 | − | 0.811114i | \(-0.698861\pi\) | ||||
−0.584888 | + | 0.811114i | \(0.698861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.3137 | −1.42678 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.5858 | 1.13320 | 0.566598 | − | 0.823995i | \(-0.308259\pi\) | ||||
0.566598 | + | 0.823995i | \(0.308259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.34315 | 0.142336 | 0.0711680 | − | 0.997464i | \(-0.477327\pi\) | ||||
0.0711680 | + | 0.997464i | \(0.477327\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0711 | 0.785364 | 0.392682 | − | 0.919674i | \(-0.371547\pi\) | ||||
0.392682 | + | 0.919674i | \(0.371547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.9706 | 1.73442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3137 | 1.09250 | 0.546252 | − | 0.837621i | \(-0.316054\pi\) | ||||
0.546252 | + | 0.837621i | \(0.316054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.0416 | −1.48857 | −0.744285 | − | 0.667862i | \(-0.767210\pi\) | ||||
−0.744285 | + | 0.667862i | \(0.767210\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1716 | −0.657151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.9706 | 1.99139 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.4142 | 1.07577 | 0.537885 | − | 0.843018i | \(-0.319223\pi\) | ||||
0.537885 | + | 0.843018i | \(0.319223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.414214 | −0.0240351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.58579 | −0.149540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.3137 | −1.45423 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9289 | 0.680820 | 0.340410 | − | 0.940277i | \(-0.389434\pi\) | ||||
0.340410 | + | 0.940277i | \(0.389434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3137 | 0.928054 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | 0.567048 | 0.283524 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283524 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.7279 | 1.34118 | 0.670591 | − | 0.741828i | \(-0.266041\pi\) | ||||
0.670591 | + | 0.741828i | \(0.266041\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.3431 | −0.693260 | −0.346630 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346630 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00000 | −0.0559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.9706 | −1.95187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.82843 | −0.268661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 44.2132 | 2.44500 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.51472 | 0.522976 | 0.261488 | − | 0.965207i | \(-0.415787\pi\) | ||||
0.261488 | + | 0.965207i | \(0.415787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.6569 | −1.84438 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0711 | 0.712026 | 0.356013 | − | 0.934481i | \(-0.384136\pi\) | ||||
0.356013 | + | 0.934481i | \(0.384136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.8995 | −1.18942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2426 | −0.554670 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.8701 | −1.54983 | −0.774913 | − | 0.632068i | \(-0.782206\pi\) | ||||
−0.774913 | + | 0.632068i | \(0.782206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.68629 | −0.357909 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.171573 | 0.00915788 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.2132 | −1.60809 | −0.804043 | − | 0.594571i | \(-0.797322\pi\) | ||||
−0.804043 | + | 0.594571i | \(0.797322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.6569 | −1.56523 | −0.782614 | − | 0.622507i | \(-0.786114\pi\) | ||||
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.1421 | 1.26713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2426 | −0.586861 | −0.293431 | − | 0.955980i | \(-0.594797\pi\) | ||||
−0.293431 | + | 0.955980i | \(0.594797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.9706 | 0.675221 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8284 | −1.18201 | −0.591006 | − | 0.806667i | \(-0.701269\pi\) | ||||
−0.591006 | + | 0.806667i | \(0.701269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.414214 | 0.0213331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6274 | 1.47049 | 0.735246 | − | 0.677801i | \(-0.237067\pi\) | ||||
0.735246 | + | 0.677801i | \(0.237067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.07107 | 0.464725 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.8284 | −1.16648 | −0.583239 | − | 0.812301i | \(-0.698215\pi\) | ||||
−0.583239 | + | 0.812301i | \(0.698215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.9706 | 1.67599 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.7990 | 0.547531 | 0.273765 | − | 0.961797i | \(-0.411731\pi\) | ||||
0.273765 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0711 | 0.762177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.8701 | −2.46517 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.58579 | 0.280343 | 0.140171 | − | 0.990127i | \(-0.455235\pi\) | ||||
0.140171 | + | 0.990127i | \(0.455235\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4558 | −1.22127 | −0.610633 | − | 0.791913i | \(-0.709085\pi\) | ||||
−0.610633 | + | 0.791913i | \(0.709085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.24264 | 0.211341 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.8995 | 0.589836 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.1127 | −1.63732 | −0.818659 | − | 0.574280i | \(-0.805282\pi\) | ||||
−0.818659 | + | 0.574280i | \(0.805282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.6274 | −2.29996 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.41421 | −0.167195 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.5858 | −1.39651 | −0.698254 | − | 0.715851i | \(-0.746039\pi\) | ||||
−0.698254 | + | 0.715851i | \(0.746039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3137 | −1.28245 | −0.641226 | − | 0.767352i | \(-0.721574\pi\) | ||||
−0.641226 | + | 0.767352i | \(0.721574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.4558 | −1.04322 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6569 | 1.09134 | 0.545671 | − | 0.837999i | \(-0.316275\pi\) | ||||
0.545671 | + | 0.837999i | \(0.316275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.97056 | −0.334984 | −0.167492 | − | 0.985873i | \(-0.553567\pi\) | ||||
−0.167492 | + | 0.985873i | \(0.553567\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.4853 | −0.597252 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.75736 | −0.179329 | −0.0896645 | − | 0.995972i | \(-0.528579\pi\) | ||||
−0.0896645 | + | 0.995972i | \(0.528579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.7696 | 1.65195 | 0.825976 | − | 0.563706i | \(-0.190625\pi\) | ||||
0.825976 | + | 0.563706i | \(0.190625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.1421 | 1.04729 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.4853 | −1.29711 | −0.648555 | − | 0.761168i | \(-0.724626\pi\) | ||||
−0.648555 | + | 0.761168i | \(0.724626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58579 | −0.215936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0711 | 0.755085 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.92893 | −0.230566 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.2843 | −1.50363 | −0.751814 | − | 0.659375i | \(-0.770821\pi\) | ||||
−0.751814 | + | 0.659375i | \(0.770821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4558 | −1.18303 | −0.591517 | − | 0.806293i | \(-0.701471\pi\) | ||||
−0.591517 | + | 0.806293i | \(0.701471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.41421 | −0.389363 | −0.194682 | − | 0.980866i | \(-0.562367\pi\) | ||||
−0.194682 | + | 0.980866i | \(0.562367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.3137 | 1.16639 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.6569 | −0.535983 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.6274 | −0.852891 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.5269 | −1.85172 | −0.925861 | − | 0.377864i | \(-0.876659\pi\) | ||||
−0.925861 | + | 0.377864i | \(0.876659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.92893 | −0.224740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.27208 | −0.0576434 | −0.0288217 | − | 0.999585i | \(-0.509175\pi\) | ||||
−0.0288217 | + | 0.999585i | \(0.509175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.07107 | 0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4853 | −0.518323 | −0.259162 | − | 0.965834i | \(-0.583446\pi\) | ||||
−0.259162 | + | 0.965834i | \(0.583446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.41421 | −0.108731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.7990 | −1.19969 | −0.599844 | − | 0.800117i | \(-0.704771\pi\) | ||||
−0.599844 | + | 0.800117i | \(0.704771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3137 | 0.818196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0416 | 0.759849 | 0.379924 | − | 0.925018i | \(-0.375950\pi\) | ||||
0.379924 | + | 0.925018i | \(0.375950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.9706 | 1.37545 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2426 | 0.719942 | 0.359971 | − | 0.932963i | \(-0.382787\pi\) | ||||
0.359971 | + | 0.932963i | \(0.382787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.828427 | 0.0365760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.58579 | 0.333623 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.1421 | −1.45478 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5147 | 0.678411 | 0.339206 | − | 0.940712i | \(-0.389842\pi\) | ||||
0.339206 | + | 0.940712i | \(0.389842\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.7279 | −1.07717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9706 | 0.694372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.97056 | 0.215704 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.89949 | 0.0822763 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.0000 | −0.431532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3137 | −0.529408 | −0.264704 | − | 0.964330i | \(-0.585274\pi\) | ||||
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 61.6985 | 2.64774 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.1127 | −1.50131 | −0.750655 | − | 0.660694i | \(-0.770262\pi\) | ||||
−0.750655 | + | 0.660694i | \(0.770262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.3137 | −0.824289 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.14214 | −0.0907652 | −0.0453826 | − | 0.998970i | \(-0.514451\pi\) | ||||
−0.0453826 | + | 0.998970i | \(0.514451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.82843 | 0.204221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.82843 | −0.246076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9411 | −1.17758 | −0.588789 | − | 0.808287i | \(-0.700395\pi\) | ||||
−0.588789 | + | 0.808287i | \(0.700395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.1421 | −1.43131 | −0.715656 | − | 0.698453i | \(-0.753872\pi\) | ||||
−0.715656 | + | 0.698453i | \(0.753872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.4558 | −0.981597 | −0.490798 | − | 0.871273i | \(-0.663295\pi\) | ||||
−0.490798 | + | 0.871273i | \(0.663295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.3848 | −1.39467 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.4142 | 1.51594 | 0.757972 | − | 0.652287i | \(-0.226190\pi\) | ||||
0.757972 | + | 0.652287i | \(0.226190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.65685 | 0.0688565 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.58579 | 0.272755 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8579 | 0.571975 | 0.285988 | − | 0.958233i | \(-0.407678\pi\) | ||||
0.285988 | + | 0.958233i | \(0.407678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.4853 | 0.844081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.5563 | −1.21579 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.44365 | −0.387804 | −0.193902 | − | 0.981021i | \(-0.562114\pi\) | ||||
−0.193902 | + | 0.981021i | \(0.562114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.8995 | 1.22370 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.3137 | −1.48374 | −0.741869 | − | 0.670545i | \(-0.766060\pi\) | ||||
−0.741869 | + | 0.670545i | \(0.766060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2843 | −0.745831 | −0.372915 | − | 0.927865i | \(-0.621642\pi\) | ||||
−0.372915 | + | 0.927865i | \(0.621642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0711 | −0.814660 | −0.407330 | − | 0.913281i | \(-0.633540\pi\) | ||||
−0.407330 | + | 0.913281i | \(0.633540\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.14214 | −0.127117 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.3137 | −1.18397 | −0.591985 | − | 0.805949i | \(-0.701655\pi\) | ||||
−0.591985 | + | 0.805949i | \(0.701655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4142 | 0.459519 | 0.229759 | − | 0.973247i | \(-0.426206\pi\) | ||||
0.229759 | + | 0.973247i | \(0.426206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0711 | −0.605757 | −0.302879 | − | 0.953029i | \(-0.597948\pi\) | ||||
−0.302879 | + | 0.953029i | \(0.597948\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58579 | −0.103764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.82843 | 0.192829 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.7279 | 1.14546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6274 | −1.49792 | −0.748962 | − | 0.662613i | \(-0.769447\pi\) | ||||
−0.748962 | + | 0.662613i | \(0.769447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.3848 | −1.64490 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.02944 | −0.278080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.2843 | 1.27515 | 0.637576 | − | 0.770387i | \(-0.279937\pi\) | ||||
0.637576 | + | 0.770387i | \(0.279937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.2132 | 1.19149 | 0.595746 | − | 0.803173i | \(-0.296856\pi\) | ||||
0.595746 | + | 0.803173i | \(0.296856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.1421 | −0.713241 | −0.356620 | − | 0.934249i | \(-0.616071\pi\) | ||||
−0.356620 | + | 0.934249i | \(0.616071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.75736 | −0.0689824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.2843 | 0.872051 | 0.436025 | − | 0.899934i | \(-0.356386\pi\) | ||||
0.436025 | + | 0.899934i | \(0.356386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.6274 | 1.19489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4853 | 0.681130 | 0.340565 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340565 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8284 | −1.19909 | −0.599543 | − | 0.800342i | \(-0.704651\pi\) | ||||
−0.599543 | + | 0.800342i | \(0.704651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.41421 | 0.0937603 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.24264 | −0.241716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.9706 | −1.62268 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.82843 | 0.263609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.8284 | −1.95929 | −0.979646 | − | 0.200733i | \(-0.935668\pi\) | ||||
−0.979646 | + | 0.200733i | \(0.935668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0711 | −1.38632 | −0.693162 | − | 0.720782i | \(-0.743783\pi\) | ||||
−0.693162 | + | 0.720782i | \(0.743783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.82843 | 0.146706 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.1716 | 0.503996 | 0.251998 | − | 0.967728i | \(-0.418912\pi\) | ||||
0.251998 | + | 0.967728i | \(0.418912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.89949 | 0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.72792 | −0.103926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.1421 | 0.385825 | 0.192913 | − | 0.981216i | \(-0.438207\pi\) | ||||
0.192913 | + | 0.981216i | \(0.438207\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0711 | −0.419347 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.48528 | 0.320943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.1421 | −1.40284 | −0.701420 | − | 0.712749i | \(-0.747450\pi\) | ||||
−0.701420 | + | 0.712749i | \(0.747450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.7990 | −0.897596 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.3431 | −0.801559 | −0.400779 | − | 0.916175i | \(-0.631261\pi\) | ||||
−0.400779 | + | 0.916175i | \(0.631261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.45584 | −0.354622 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −63.9411 | −2.39461 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.2426 | 0.419864 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.6985 | 1.85344 | 0.926720 | − | 0.375752i | \(-0.122615\pi\) | ||||
0.926720 | + | 0.375752i | \(0.122615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.0711 | −0.932403 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.3137 | −1.53224 | −0.766120 | − | 0.642697i | \(-0.777815\pi\) | ||||
−0.766120 | + | 0.642697i | \(0.777815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.1421 | −1.04087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6985 | 0.986131 | 0.493066 | − | 0.869992i | \(-0.335876\pi\) | ||||
0.493066 | + | 0.869992i | \(0.335876\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.41421 | −0.0520932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.79899 | −0.176534 | −0.0882668 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882668 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.89949 | 0.216431 | 0.108216 | − | 0.994127i | \(-0.465486\pi\) | ||||
0.108216 | + | 0.994127i | \(0.465486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.0000 | 1.17082 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.6274 | 0.935158 | 0.467579 | − | 0.883951i | \(-0.345126\pi\) | ||||
0.467579 | + | 0.883951i | \(0.345126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.2426 | −0.664799 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.7696 | 1.33641 | 0.668206 | − | 0.743976i | \(-0.267062\pi\) | ||||
0.668206 | + | 0.743976i | \(0.267062\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.0711 | −0.547045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.44365 | 0.161082 | 0.0805411 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805411 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.727922 | 0.0262837 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.4853 | −0.666596 | −0.333298 | − | 0.942821i | \(-0.608162\pi\) | ||||
−0.333298 | + | 0.942821i | \(0.608162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.3137 | 0.911651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.3848 | 0.769157 | 0.384578 | − | 0.923092i | \(-0.374347\pi\) | ||||
0.384578 | + | 0.923092i | \(0.374347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.17157 | 0.328606 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.48528 | 0.0889304 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.414214 | 0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.8406 | 1.52710 | 0.763552 | − | 0.645747i | \(-0.223454\pi\) | ||||
0.763552 | + | 0.645747i | \(0.223454\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.7990 | 1.63049 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.82843 | −0.100440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.9289 | −1.27267 | −0.636334 | − | 0.771414i | \(-0.719550\pi\) | ||||
−0.636334 | + | 0.771414i | \(0.719550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3137 | 0.647892 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.3137 | 0.965082 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8284 | −0.382127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −44.8701 | −1.57950 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.9411 | 1.72068 | 0.860339 | − | 0.509722i | \(-0.170252\pi\) | ||||
0.860339 | + | 0.509722i | \(0.170252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5563 | −1.38901 | −0.694506 | − | 0.719487i | \(-0.744377\pi\) | ||||
−0.694506 | + | 0.719487i | \(0.744377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.65685 | −0.198395 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.3137 | 0.815643 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4853 | 0.749841 | 0.374921 | − | 0.927057i | \(-0.377670\pi\) | ||||
0.374921 | + | 0.927057i | \(0.377670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0416 | 1.25633 | 0.628166 | − | 0.778079i | \(-0.283806\pi\) | ||||
0.628166 | + | 0.778079i | \(0.283806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0416 | 1.87921 | 0.939606 | − | 0.342259i | \(-0.111192\pi\) | ||||
0.939606 | + | 0.342259i | \(0.111192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.41421 | 0.257506 | 0.128753 | − | 0.991677i | \(-0.458903\pi\) | ||||
0.128753 | + | 0.991677i | \(0.458903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.5563 | −1.09468 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.24264 | 0.146647 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.75736 | 0.267814 | 0.133907 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133907 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.2132 | −1.52278 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 60.4558 | 2.07484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 74.2843 | 2.54643 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.31371 | −0.318895 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.4853 | −1.86118 | −0.930591 | − | 0.366061i | \(-0.880706\pi\) | ||||
−0.930591 | + | 0.366061i | \(0.880706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.4558 | −1.82389 | −0.911945 | − | 0.410313i | \(-0.865420\pi\) | ||||
−0.911945 | + | 0.410313i | \(0.865420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.1838 | −0.755144 | −0.377572 | − | 0.925980i | \(-0.623241\pi\) | ||||
−0.377572 | + | 0.925980i | \(0.623241\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.9706 | 0.915968 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.34315 | 0.113408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.585786 | 0.0198486 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.7990 | −1.34699 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.9706 | −0.910731 | −0.455366 | − | 0.890305i | \(-0.650491\pi\) | ||||
−0.455366 | + | 0.890305i | \(0.650491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −44.4558 | −1.49946 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6569 | 0.594875 | 0.297437 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297437 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1127 | −1.18164 | −0.590818 | − | 0.806805i | \(-0.701195\pi\) | ||||
−0.590818 | + | 0.806805i | \(0.701195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.2843 | 0.613926 | 0.306963 | − | 0.951721i | \(-0.400687\pi\) | ||||
0.306963 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48528 | 0.317769 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.1716 | −0.507697 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.24264 | 0.208436 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.2426 | 0.341611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8995 | 0.529689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.69848 | 0.255624 | 0.127812 | − | 0.991798i | \(-0.459205\pi\) | ||||
0.127812 | + | 0.991798i | \(0.459205\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.6569 | 0.983656 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.6863 | 0.685367 | 0.342684 | − | 0.939451i | \(-0.388664\pi\) | ||||
0.342684 | + | 0.939451i | \(0.388664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3137 | −0.374429 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.5980 | 0.943360 | 0.471680 | − | 0.881770i | \(-0.343648\pi\) | ||||
0.471680 | + | 0.881770i | \(0.343648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.7990 | −0.948959 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.02944 | −0.0338843 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1127 | −0.627743 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.5269 | −1.13279 | −0.566396 | − | 0.824133i | \(-0.691663\pi\) | ||||
−0.566396 | + | 0.824133i | \(0.691663\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.1421 | −0.790378 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.2132 | −0.464325 | −0.232163 | − | 0.972677i | \(-0.574580\pi\) | ||||
−0.232163 | + | 0.972677i | \(0.574580\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.2843 | −1.86940 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0000 | 0.782378 | 0.391189 | − | 0.920310i | \(-0.372064\pi\) | ||||
0.391189 | + | 0.920310i | \(0.372064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.6274 | −0.932237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.89949 | −0.321690 | −0.160845 | − | 0.986980i | \(-0.551422\pi\) | ||||
−0.160845 | + | 0.986980i | \(0.551422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.48528 | 0.145598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7990 | 0.966298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.3848 | −1.89127 | −0.945634 | − | 0.325232i | \(-0.894558\pi\) | ||||
−0.945634 | + | 0.325232i | \(0.894558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.41421 | 0.0780404 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.9706 | 1.32026 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8284 | −0.927060 | −0.463530 | − | 0.886081i | \(-0.653417\pi\) | ||||
−0.463530 | + | 0.886081i | \(0.653417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6569 | 0.374472 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.1838 | −0.904460 | −0.452230 | − | 0.891901i | \(-0.649371\pi\) | ||||
−0.452230 | + | 0.891901i | \(0.649371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.0833 | −1.34636 | −0.673181 | − | 0.739477i | \(-0.735073\pi\) | ||||
−0.673181 | + | 0.739477i | \(0.735073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.65685 | −0.308634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.7990 | −1.65381 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.3848 | −1.06481 | −0.532404 | − | 0.846490i | \(-0.678711\pi\) | ||||
−0.532404 | + | 0.846490i | \(0.678711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −72.7696 | −2.31394 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.31371 | −0.168796 | −0.0843978 | − | 0.996432i | \(-0.526897\pi\) | ||||
−0.0843978 | + | 0.996432i | \(0.526897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.9706 | −0.728949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8995 | 0.408531 | 0.204266 | − | 0.978916i | \(-0.434519\pi\) | ||||
0.204266 | + | 0.978916i | \(0.434519\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.92893 | −0.155945 |
(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 | 9800.2.a.bs.1.1 | 2 | ||
5.4 | even | 2 | 1960.2.a.u.1.2 | yes | 2 | ||
7.6 | odd | 2 | 9800.2.a.ca.1.2 | 2 | |||
20.19 | odd | 2 | 3920.2.a.bn.1.1 | 2 | |||
35.4 | even | 6 | 1960.2.q.p.961.1 | 4 | |||
35.9 | even | 6 | 1960.2.q.p.361.1 | 4 | |||
35.19 | odd | 6 | 1960.2.q.v.361.2 | 4 | |||
35.24 | odd | 6 | 1960.2.q.v.961.2 | 4 | |||
35.34 | odd | 2 | 1960.2.a.q.1.1 | ✓ | 2 | ||
140.139 | even | 2 | 3920.2.a.by.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.q.1.1 | ✓ | 2 | 35.34 | odd | 2 | ||
1960.2.a.u.1.2 | yes | 2 | 5.4 | even | 2 | ||
1960.2.q.p.361.1 | 4 | 35.9 | even | 6 | |||
1960.2.q.p.961.1 | 4 | 35.4 | even | 6 | |||
1960.2.q.v.361.2 | 4 | 35.19 | odd | 6 | |||
1960.2.q.v.961.2 | 4 | 35.24 | odd | 6 | |||
3920.2.a.bn.1.1 | 2 | 20.19 | odd | 2 | |||
3920.2.a.by.1.2 | 2 | 140.139 | even | 2 | |||
9800.2.a.bs.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9800.2.a.ca.1.2 | 2 | 7.6 | odd | 2 |