Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(14.8202346151\) |
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 232) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.82843 | −0.817697 | −0.408849 | − | 0.912602i | \(-0.634070\pi\) | ||||
−0.408849 | + | 0.912602i | \(0.634070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.414214 | −0.124890 | −0.0624450 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.65685 | 1.84628 | 0.923140 | − | 0.384465i | \(-0.125614\pi\) | ||||
0.923140 | + | 0.384465i | \(0.125614\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.41421 | −1.13975 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.65685 | −2.10730 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.65685 | −0.331371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.58579 | −1.00324 | −0.501618 | − | 0.865089i | \(-0.667262\pi\) | ||||
−0.501618 | + | 0.865089i | \(0.667262\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.31371 | 1.23624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.65685 | −1.58758 | −0.793789 | − | 0.608194i | \(-0.791894\pi\) | ||||
−0.793789 | + | 0.608194i | \(0.791894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.0711 | 2.57343 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.65685 | 0.258757 | 0.129379 | − | 0.991595i | \(-0.458702\pi\) | ||||
0.129379 | + | 0.991595i | \(0.458702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.41421 | −0.673161 | −0.336581 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336581 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.17157 | −0.770933 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.07107 | 0.302096 | 0.151048 | − | 0.988526i | \(-0.451735\pi\) | ||||
0.151048 | + | 0.988526i | \(0.451735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.4853 | −2.58846 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | 0.961524 | 0.480762 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480762 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.757359 | 0.102122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.82843 | −0.639541 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.48528 | 0.844312 | 0.422156 | − | 0.906523i | \(-0.361273\pi\) | ||||
0.422156 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.3137 | −1.42539 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.1716 | −1.50970 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4853 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713756\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.65685 | 0.188816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7279 | −1.76953 | −0.884765 | − | 0.466038i | \(-0.845681\pi\) | ||||
−0.884765 | + | 0.466038i | \(0.845681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.17157 | 0.348125 | 0.174063 | − | 0.984735i | \(-0.444310\pi\) | ||||
0.174063 | + | 0.984735i | \(0.444310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0000 | 1.51851 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41421 | −0.258831 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.65685 | 0.175626 | 0.0878131 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878131 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.6274 | −2.79131 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4853 | −1.39836 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.65685 | 0.375185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3137 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17157 | −0.117748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1716 | −1.10077 | −0.550384 | − | 0.834912i | \(-0.685519\pi\) | ||||
−0.550384 | + | 0.834912i | \(0.685519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.6569 | 1.72313 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6569 | −1.32026 | −0.660129 | − | 0.751152i | \(-0.729498\pi\) | ||||
−0.660129 | + | 0.751152i | \(0.729498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.82843 | 0.366697 | 0.183348 | − | 0.983048i | \(-0.441306\pi\) | ||||
0.183348 | + | 0.983048i | \(0.441306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.3137 | −2.21284 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.51472 | −0.141248 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.8284 | 1.74069 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.6274 | 2.80761 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1716 | 1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315 | 0.385392 | 0.192696 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6569 | −0.938284 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.757359 | 0.0651831 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.6569 | 1.50853 | 0.754263 | − | 0.656572i | \(-0.227994\pi\) | ||||
0.754263 | + | 0.656572i | \(0.227994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17157 | −0.269009 | −0.134505 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134505 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.75736 | −0.230582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.82843 | 0.151843 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.7279 | 1.79209 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.65685 | 0.217658 | 0.108829 | − | 0.994060i | \(-0.465290\pi\) | ||||
0.108829 | + | 0.994060i | \(0.465290\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6569 | 1.43689 | 0.718447 | − | 0.695581i | \(-0.244853\pi\) | ||||
0.718447 | + | 0.695581i | \(0.244853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.6569 | −1.75085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2132 | 0.820344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3137 | −0.902932 | −0.451466 | − | 0.892288i | \(-0.649099\pi\) | ||||
−0.451466 | + | 0.892288i | \(0.649099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.8995 | 1.34022 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.31371 | −0.261157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8995 | 1.01037 | 0.505183 | − | 0.863012i | \(-0.331425\pi\) | ||||
0.505183 | + | 0.863012i | \(0.331425\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.82843 | 0.142343 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.4853 | −1.43043 | −0.715217 | − | 0.698902i | \(-0.753672\pi\) | ||||
−0.715217 | + | 0.698902i | \(0.753672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.3137 | 2.40875 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | −0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.62742 | 0.500986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.6569 | 1.17684 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.4853 | −1.68063 | −0.840314 | − | 0.542099i | \(-0.817630\pi\) | ||||
−0.840314 | + | 0.542099i | \(0.817630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4853 | 0.853694 | 0.426847 | − | 0.904324i | \(-0.359624\pi\) | ||||
0.426847 | + | 0.904324i | \(0.359624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4853 | −1.07078 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.6569 | 1.29816 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.17157 | 0.231928 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.65685 | 0.120518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.65685 | 0.554031 | 0.277015 | − | 0.960866i | \(-0.410655\pi\) | ||||
0.277015 | + | 0.960866i | \(0.410655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.65685 | −0.407189 | −0.203595 | − | 0.979055i | \(-0.565262\pi\) | ||||
−0.203595 | + | 0.979055i | \(0.565262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29.3848 | −2.10429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.31371 | 0.663574 | 0.331787 | − | 0.943354i | \(-0.392348\pi\) | ||||
0.331787 | + | 0.943354i | \(0.392348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3431 | −1.01676 | −0.508379 | − | 0.861133i | \(-0.669755\pi\) | ||||
−0.508379 | + | 0.861133i | \(0.669755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.6569 | −0.963280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.02944 | −0.211585 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.34315 | 0.162860 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.828427 | 0.0573035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.2426 | 1.87546 | 0.937730 | − | 0.347364i | \(-0.112923\pi\) | ||||
0.937730 | + | 0.347364i | \(0.112923\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.3137 | −1.73447 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.07107 | 0.550442 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.3431 | 1.51675 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.65685 | 0.652550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −50.9706 | −3.42865 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.142136 | −0.00951811 | −0.00475905 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00475905 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.68629 | −0.312419 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.8284 | 1.11694 | 0.558471 | − | 0.829524i | \(-0.311388\pi\) | ||||
0.558471 | + | 0.829524i | \(0.311388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.34315 | −0.419167 | −0.209583 | − | 0.977791i | \(-0.567211\pi\) | ||||
−0.209583 | + | 0.977791i | \(0.567211\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.65685 | −0.436105 | −0.218053 | − | 0.975937i | \(-0.569970\pi\) | ||||
−0.218053 | + | 0.975937i | \(0.569970\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.78680 | −0.247023 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −37.9706 | −2.46645 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.1421 | −1.30289 | −0.651443 | − | 0.758697i | \(-0.725836\pi\) | ||||
−0.651443 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31371 | 0.277870 | 0.138935 | − | 0.990301i | \(-0.455632\pi\) | ||||
0.138935 | + | 0.990301i | \(0.455632\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.4558 | −1.05133 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3137 | −0.847131 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.2132 | −1.52832 | −0.764162 | − | 0.645024i | \(-0.776847\pi\) | ||||
−0.764162 | + | 0.645024i | \(0.776847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.343146 | −0.0215734 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 33.7990 | 2.11657 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.17157 | −0.135459 | −0.0677295 | − | 0.997704i | \(-0.521575\pi\) | ||||
−0.0677295 | + | 0.997704i | \(0.521575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.6274 | 2.40019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3848 | 1.44197 | 0.720984 | − | 0.692952i | \(-0.243690\pi\) | ||||
0.720984 | + | 0.692952i | \(0.243690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.7990 | −0.786236 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000 | 0.244796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9706 | 0.668887 | 0.334444 | − | 0.942416i | \(-0.391452\pi\) | ||||
0.334444 | + | 0.942416i | \(0.391452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.41421 | −0.389636 | −0.194818 | − | 0.980839i | \(-0.562412\pi\) | ||||
−0.194818 | + | 0.980839i | \(0.562412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −64.2843 | −3.89066 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.686292 | 0.0413849 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6274 | −0.999045 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.7990 | −0.945861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.82843 | −0.524796 | −0.262398 | − | 0.964960i | \(-0.584513\pi\) | ||||
−0.262398 | + | 0.964960i | \(0.584513\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.82843 | 0.522951 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.62742 | −0.391204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.9706 | 2.16725 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.3137 | 1.94621 | 0.973104 | − | 0.230367i | \(-0.0739927\pi\) | ||||
0.973104 | + | 0.230367i | \(0.0739927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.8579 | −0.690392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.171573 | 0.00995567 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.51472 | 0.318924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6569 | 1.01772 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.3137 | 1.56913 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9706 | 0.628173 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.27208 | 0.243820 | 0.121910 | − | 0.992541i | \(-0.461098\pi\) | ||||
0.121910 | + | 0.992541i | \(0.461098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.9706 | −1.53430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.9706 | −0.848903 | −0.424451 | − | 0.905451i | \(-0.639533\pi\) | ||||
−0.424451 | + | 0.905451i | \(0.639533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.51472 | −0.481280 | −0.240640 | − | 0.970614i | \(-0.577357\pi\) | ||||
−0.240640 | + | 0.970614i | \(0.577357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.6863 | 1.16554 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.414214 | 0.0231915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.9706 | −1.84024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3137 | 0.852078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0294 | −0.611803 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.24264 | 0.511119 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.28427 | −0.456727 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.07107 | −0.443626 | −0.221813 | − | 0.975089i | \(-0.571197\pi\) | ||||
−0.221813 | + | 0.975089i | \(0.571197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.3137 | −1.49678 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3431 | 0.565106 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.31371 | −0.507350 | −0.253675 | − | 0.967290i | \(-0.581639\pi\) | ||||
−0.253675 | + | 0.967290i | \(0.581639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.1421 | −1.31122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.31371 | 0.125294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.65685 | −0.196878 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4853 | 0.562879 | 0.281440 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281440 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.31371 | −0.230908 | −0.115454 | − | 0.993313i | \(-0.536832\pi\) | ||||
−0.115454 | + | 0.993313i | \(0.536832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.75736 | −0.147177 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1716 | 1.01752 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 73.9411 | 3.91338 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.2721 | 0.647696 | 0.323848 | − | 0.946109i | \(-0.395023\pi\) | ||||
0.323848 | + | 0.946109i | \(0.395023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.1421 | −1.37211 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.31371 | −0.382817 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.68629 | 0.243959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0000 | −1.45369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.48528 | −0.0769050 | −0.0384525 | − | 0.999260i | \(-0.512243\pi\) | ||||
−0.0384525 | + | 0.999260i | \(0.512243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.3848 | 1.51742 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.65685 | −0.342845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.34315 | −0.428559 | −0.214279 | − | 0.976772i | \(-0.568740\pi\) | ||||
−0.214279 | + | 0.976772i | \(0.568740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4853 | 0.537177 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.02944 | −0.154394 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.4853 | −0.634663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.6569 | 0.895238 | 0.447619 | − | 0.894224i | \(-0.352272\pi\) | ||||
0.447619 | + | 0.894224i | \(0.352272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.34315 | −0.320787 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.1421 | 1.21781 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.7574 | 1.44694 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.4558 | −0.926272 | −0.463136 | − | 0.886287i | \(-0.653276\pi\) | ||||
−0.463136 | + | 0.886287i | \(0.653276\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.3137 | 0.966895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.65685 | 0.432303 | 0.216151 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216151 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.1838 | −1.85226 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.3431 | 0.861788 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.343146 | 0.0169675 | 0.00848373 | − | 0.999964i | \(-0.497300\pi\) | ||||
0.00848373 | + | 0.999964i | \(0.497300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 42.6274 | 2.10266 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.9411 | −1.27648 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.79899 | −0.284661 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.65685 | −0.374958 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.4853 | −1.29389 | −0.646945 | − | 0.762536i | \(-0.723954\pi\) | ||||
−0.646945 | + | 0.762536i | \(0.723954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.02944 | 0.0501717 | 0.0250859 | − | 0.999685i | \(-0.492014\pi\) | ||||
0.0250859 | + | 0.999685i | \(0.492014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.85786 | 0.284819 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.6863 | 0.615376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000 | 1.16144 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.65685 | −0.321396 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7990 | −0.664674 | −0.332337 | − | 0.943161i | \(-0.607837\pi\) | ||||
−0.332337 | + | 0.943161i | \(0.607837\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.00000 | −0.384455 | −0.192228 | − | 0.981350i | \(-0.561571\pi\) | ||||
−0.192228 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.41421 | 0.211645 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.65685 | −0.0792581 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1421 | −0.961332 | −0.480666 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480666 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.4558 | 1.21218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.62742 | 0.409901 | 0.204950 | − | 0.978772i | \(-0.434297\pi\) | ||||
0.204950 | + | 0.978772i | \(0.434297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.02944 | −0.143609 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.41421 | 0.303382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.6274 | 1.35101 | 0.675506 | − | 0.737355i | \(-0.263925\pi\) | ||||
0.675506 | + | 0.737355i | \(0.263925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.686292 | −0.0323162 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 42.6274 | 2.00281 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 48.6863 | 2.28245 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6274 | −1.33913 | −0.669567 | − | 0.742752i | \(-0.733520\pi\) | ||||
−0.669567 | + | 0.742752i | \(0.733520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.17157 | 0.148036 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6863 | −0.870307 | −0.435154 | − | 0.900356i | \(-0.643306\pi\) | ||||
−0.435154 | + | 0.900356i | \(0.643306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.4558 | 1.46188 | 0.730939 | − | 0.682443i | \(-0.239083\pi\) | ||||
0.730939 | + | 0.682443i | \(0.239083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.6569 | 1.14343 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.8995 | 0.689466 | 0.344733 | − | 0.938701i | \(-0.387969\pi\) | ||||
0.344733 | + | 0.938701i | \(0.387969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.6274 | 1.04484 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.3137 | −1.25855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.82843 | 0.0840712 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.31371 | 0.152043 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.7990 | 0.906533 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.75736 | −0.217369 | −0.108685 | − | 0.994076i | \(-0.534664\pi\) | ||||
−0.108685 | + | 0.994076i | \(0.534664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −64.2843 | −2.93111 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.0000 | −1.27141 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.9706 | −0.769010 | −0.384505 | − | 0.923123i | \(-0.625628\pi\) | ||||
−0.384505 | + | 0.923123i | \(0.625628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.1421 | 1.40830 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75736 | 0.124438 | 0.0622189 | − | 0.998063i | \(-0.480182\pi\) | ||||
0.0622189 | + | 0.998063i | \(0.480182\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.65685 | 0.344847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.14214 | 0.0962818 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.9411 | 1.88132 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.1421 | −1.79701 | −0.898504 | − | 0.438965i | \(-0.855345\pi\) | ||||
−0.898504 | + | 0.438965i | \(0.855345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −44.6274 | −1.99381 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.2426 | 0.501285 | 0.250642 | − | 0.968080i | \(-0.419358\pi\) | ||||
0.250642 | + | 0.968080i | \(0.419358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.6863 | −0.920528 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 75.5980 | 3.35742 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.34315 | −0.325479 | −0.162740 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162740 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.828427 | 0.0365760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.4264 | 0.900095 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.857864 | −0.0377288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.7990 | 1.48361 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.1716 | 1.67233 | 0.836163 | − | 0.548480i | \(-0.184793\pi\) | ||||
0.836163 | + | 0.548480i | \(0.184793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.6569 | −1.29680 | −0.648402 | − | 0.761298i | \(-0.724562\pi\) | ||||
−0.648402 | + | 0.761298i | \(0.724562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.0000 | 0.698297 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.7696 | 1.86307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3431 | 0.796025 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0294 | 0.477738 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9706 | 1.07957 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −54.2843 | −2.34254 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.72792 | −0.160573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.7279 | 1.18992 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.00000 | −0.299847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.3137 | −1.33888 | −0.669439 | − | 0.742867i | \(-0.733465\pi\) | ||||
−0.669439 | + | 0.742867i | \(0.733465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9706 | −0.724286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 62.9117 | 2.67528 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.6274 | 1.80943 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3137 | −0.564120 | −0.282060 | − | 0.959397i | \(-0.591018\pi\) | ||||
−0.282060 | + | 0.959397i | \(0.591018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.3848 | −1.24284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.65685 | 0.323273 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.8995 | 0.880809 | 0.440404 | − | 0.897800i | \(-0.354835\pi\) | ||||
0.440404 | + | 0.897800i | \(0.354835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.2843 | 0.769225 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.9411 | 1.59338 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.34315 | 0.349763 | 0.174881 | − | 0.984590i | \(-0.444046\pi\) | ||||
0.174881 | + | 0.984590i | \(0.444046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.97056 | 0.375406 | 0.187703 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.4853 | 0.772234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.37258 | −0.0572407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.3137 | 1.38687 | 0.693434 | − | 0.720520i | \(-0.256097\pi\) | ||||
0.693434 | + | 0.720520i | \(0.256097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.6569 | −0.567559 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.6863 | −0.526316 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.89949 | −0.120085 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −34.4264 | −1.42336 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.1127 | −1.36671 | −0.683354 | − | 0.730088i | \(-0.739479\pi\) | ||||
−0.683354 | + | 0.730088i | \(0.739479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1716 | 0.460317 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4853 | 0.924921 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.171573 | −0.00704565 | −0.00352283 | − | 0.999994i | \(-0.501121\pi\) | ||||
−0.00352283 | + | 0.999994i | \(0.501121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56.0000 | −2.29578 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.6274 | −1.41721 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.3848 | −1.20063 | −0.600315 | − | 0.799764i | \(-0.704958\pi\) | ||||
−0.600315 | + | 0.799764i | \(0.704958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0000 | −0.489490 | −0.244745 | − | 0.969587i | \(-0.578704\pi\) | ||||
−0.244745 | + | 0.969587i | \(0.578704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.0000 | −0.651570 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.7990 | 0.804943 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8701 | 1.05003 | 0.525017 | − | 0.851092i | \(-0.324059\pi\) | ||||
0.525017 | + | 0.851092i | \(0.324059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.65685 | 0.391315 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7868 | 0.557754 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7990 | −0.759284 | −0.379642 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379642 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.31371 | −0.294917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.9706 | −1.48838 | −0.744189 | − | 0.667969i | \(-0.767164\pi\) | ||||
−0.744189 | + | 0.667969i | \(0.767164\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.6985 | −1.07310 | −0.536551 | − | 0.843868i | \(-0.680273\pi\) | ||||
−0.536551 | + | 0.843868i | \(0.680273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.343146 | −0.0137700 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.62742 | −0.265522 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000 | 0.0798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 73.9411 | 2.94823 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.7696 | 1.22492 | 0.612458 | − | 0.790503i | \(-0.290181\pi\) | ||||
0.612458 | + | 0.790503i | \(0.290181\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 65.7696 | 2.61411 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.94113 | −0.315134 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 59.9117 | 2.37379 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.6569 | −1.17321 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9706 | 1.45798 | 0.728988 | − | 0.684526i | \(-0.239991\pi\) | ||||
0.728988 | + | 0.684526i | \(0.239991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.4853 | 0.767232 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.82843 | 0.189825 | 0.0949125 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949125 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.68629 | −0.105446 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 53.9411 | 2.11412 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.37258 | −0.0537133 | −0.0268567 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268567 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.2843 | −0.714426 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3137 | 0.441390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0711 | 0.470222 | 0.235111 | − | 0.971969i | \(-0.424455\pi\) | ||||
0.235111 | + | 0.971969i | \(0.424455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68629 | 0.260067 | 0.130033 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130033 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −123.054 | −4.77901 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.6274 | −0.567227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.828427 | −0.0320768 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.343146 | −0.0132668 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.48528 | 0.0959432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.2843 | −1.36011 | −0.680054 | − | 0.733162i | \(-0.738044\pi\) | ||||
−0.680054 | + | 0.733162i | \(0.738044\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.686292 | 0.0264154 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.9706 | −0.421633 | −0.210816 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210816 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −61.2548 | −2.35074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.6274 | 1.55685 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9706 | 1.10853 | 0.554264 | − | 0.832341i | \(-0.313000\pi\) | ||||
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.2843 | −1.23352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.3137 | −0.584254 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.5980 | 1.77524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3137 | 0.734728 | 0.367364 | − | 0.930077i | \(-0.380260\pi\) | ||||
0.367364 | + | 0.930077i | \(0.380260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.68629 | 0.178017 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.79899 | 0.219968 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6863 | −0.480528 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.0711 | −0.607864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.6274 | −1.42117 | −0.710584 | − | 0.703612i | \(-0.751569\pi\) | ||||
−0.710584 | + | 0.703612i | \(0.751569\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3137 | 0.728430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.14214 | −0.344313 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.2548 | −1.70198 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.9411 | −1.23713 | −0.618565 | − | 0.785734i | \(-0.712286\pi\) | ||||
−0.618565 | + | 0.785734i | \(0.712286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.4853 | −1.66833 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.62742 | −0.173298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.04163 | 0.188546 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.6274 | −1.81602 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.4853 | −1.28608 | −0.643042 | − | 0.765831i | \(-0.722328\pi\) | ||||
−0.643042 | + | 0.765831i | \(0.722328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.6863 | 1.66420 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.4142 | 0.387309 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.65685 | 0.0615340 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2843 | −0.678126 | −0.339063 | − | 0.940764i | \(-0.610110\pi\) | ||||
−0.339063 | + | 0.940764i | \(0.610110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.7990 | 1.25010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.62742 | −0.0970459 | −0.0485229 | − | 0.998822i | \(-0.515451\pi\) | ||||
−0.0485229 | + | 0.998822i | \(0.515451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −39.7279 | −1.46539 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.34315 | 0.0863109 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.75736 | 0.322145 | 0.161072 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161072 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.1421 | −1.18077 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.5980 | 1.08584 | 0.542922 | − | 0.839783i | \(-0.317318\pi\) | ||||
0.542922 | + | 0.839783i | \(0.317318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.85786 | −0.177978 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.97056 | 0.328216 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.6274 | 1.99604 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6274 | −0.460781 | −0.230390 | − | 0.973098i | \(-0.574000\pi\) | ||||
−0.230390 | + | 0.973098i | \(0.574000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.4558 | −2.13025 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.2843 | −1.17494 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.02944 | −0.328180 | −0.164090 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164090 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.828427 | −0.0300700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9411 | 0.577865 | 0.288933 | − | 0.957349i | \(-0.406700\pi\) | ||||
0.288933 | + | 0.957349i | \(0.406700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3137 | −0.554393 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 39.5980 | 1.43167 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.1716 | 1.55884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.6274 | 1.03233 | 0.516166 | − | 0.856489i | \(-0.327359\pi\) | ||||
0.516166 | + | 0.856489i | \(0.327359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.24264 | −0.188809 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3431 | −0.515887 | −0.257944 | − | 0.966160i | \(-0.583045\pi\) | ||||
−0.257944 | + | 0.966160i | \(0.583045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.25483 | 0.332443 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 93.2548 | 3.34550 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.31371 | −0.118726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34315 | 0.155410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.414214 | 0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.6863 | 0.738325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1421 | −0.717990 | −0.358995 | − | 0.933340i | \(-0.616880\pi\) | ||||
−0.358995 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 56.4558 | 2.00988 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.0000 | 1.42224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.9411 | −1.41835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.8995 | −1.09589 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8579 | −0.561011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.68629 | 0.165582 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.65685 | −0.0584691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.05887 | 0.213547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.4853 | 0.932326 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.65685 | 0.198884 | 0.0994422 | − | 0.995043i | \(-0.468294\pi\) | ||||
0.0994422 | + | 0.995043i | \(0.468294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.4853 | −0.543093 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.5858 | −0.826174 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.82843 | 0.308868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −75.3137 | −2.63167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.65685 | 0.232326 | 0.116163 | − | 0.993230i | \(-0.462941\pi\) | ||||
0.116163 | + | 0.993230i | \(0.462941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9706 | 0.382410 | 0.191205 | − | 0.981550i | \(-0.438761\pi\) | ||||
0.191205 | + | 0.981550i | \(0.438761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.65685 | 0.0576843 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.8995 | 1.42221 | 0.711107 | − | 0.703083i | \(-0.248194\pi\) | ||||
0.711107 | + | 0.703083i | \(0.248194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0000 | −0.764092 | −0.382046 | − | 0.924143i | \(-0.624780\pi\) | ||||
−0.382046 | + | 0.924143i | \(0.624780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.1421 | −1.39252 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −68.9117 | −2.38765 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.7990 | 1.16966 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.31371 | 0.0799735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.8406 | −1.68617 | −0.843083 | − | 0.537784i | \(-0.819262\pi\) | ||||
−0.843083 | + | 0.537784i | \(0.819262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41421 | −0.0831499 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −57.2548 | −1.96963 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.3137 | 1.48828 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.3137 | −0.731485 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9411 | 0.545814 | 0.272907 | − | 0.962040i | \(-0.412015\pi\) | ||||
0.272907 | + | 0.962040i | \(0.412015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3431 | 0.353728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.1421 | −0.790520 | −0.395260 | − | 0.918569i | \(-0.629346\pi\) | ||||
−0.395260 | + | 0.918569i | \(0.629346\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5858 | −0.531780 | −0.265890 | − | 0.964003i | \(-0.585666\pi\) | ||||
−0.265890 | + | 0.964003i | \(0.585666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.8284 | −0.709008 | −0.354504 | − | 0.935055i | \(-0.615350\pi\) | ||||
−0.354504 | + | 0.935055i | \(0.615350\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.5980 | −0.870357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 100.497 | 3.41307 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.51472 | 0.220997 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.6569 | −1.27595 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.3137 | 1.46595 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48.6863 | −1.64590 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.62742 | 0.190024 | 0.0950122 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950122 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 80.4264 | 2.71272 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.6569 | 0.931783 | 0.465892 | − | 0.884842i | \(-0.345734\pi\) | ||||
0.465892 | + | 0.884842i | \(0.345734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.5980 | 0.794135 | 0.397068 | − | 0.917789i | \(-0.370028\pi\) | ||||
0.397068 | + | 0.917789i | \(0.370028\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.6274 | −0.962300 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.8701 | −1.13725 | −0.568623 | − | 0.822599i | \(-0.692524\pi\) | ||||
−0.568623 | + | 0.822599i | \(0.692524\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3726 | −0.582658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.92893 | 0.131624 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.14214 | −0.138611 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.1127 | 1.37425 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.3137 | 0.444532 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.58579 | 0.186296 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.5980 | −1.78561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.6274 | 1.41855 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.0000 | −0.698064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.2548 | −1.70189 | −0.850944 | − | 0.525256i | \(-0.823970\pi\) | ||||
−0.850944 | + | 0.525256i | \(0.823970\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.0000 | 1.06137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.5269 | 1.97221 | 0.986107 | − | 0.166110i | \(-0.0531206\pi\) | ||||
0.986107 | + | 0.166110i | \(0.0531206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.31371 | −0.0434774 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.4853 | 0.875576 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.0000 | −1.32092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.4558 | 1.03763 | 0.518816 | − | 0.854886i | \(-0.326373\pi\) | ||||
0.518816 | + | 0.854886i | \(0.326373\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3137 | 0.339848 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −69.7990 | −2.29746 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | 0.526077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.5980 | −1.03781 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.9411 | −1.70413 | −0.852067 | − | 0.523434i | \(-0.824651\pi\) | ||||
−0.852067 | + | 0.523434i | \(0.824651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.1421 | −1.18324 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.79899 | −0.189647 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6274 | 0.673868 | 0.336934 | − | 0.941528i | \(-0.390610\pi\) | ||||
0.336934 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.5563 | −0.670831 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.0833 | 1.33928 | 0.669638 | − | 0.742688i | \(-0.266449\pi\) | ||||
0.669638 | + | 0.742688i | \(0.266449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37258 | 0.0446975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.02944 | −0.0985476 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.27208 | 0.268806 | 0.134403 | − | 0.990927i | \(-0.457088\pi\) | ||||
0.134403 | + | 0.990927i | \(0.457088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.6274 | 0.864363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.7990 | 1.09601 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.0000 | −1.19855 | −0.599274 | − | 0.800544i | \(-0.704544\pi\) | ||||
−0.599274 | + | 0.800544i | \(0.704544\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0000 | −0.453029 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00000 | 0.0323254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.6274 | −2.28068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.201010 | 0.00648420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.6274 | −1.24475 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3431 | 0.332958 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.5563 | −1.17557 | −0.587786 | − | 0.809016i | \(-0.700000\pi\) | ||||
−0.587786 | + | 0.809016i | \(0.700000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.9706 | 1.18767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6863 | 0.342939 | 0.171470 | − | 0.985189i | \(-0.445148\pi\) | ||||
0.171470 | + | 0.985189i | \(0.445148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.6863 | 0.406704 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.6274 | −0.852760 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.1421 | −0.996325 | −0.498163 | − | 0.867084i | \(-0.665992\pi\) | ||||
−0.498163 | + | 0.867084i | \(0.665992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.686292 | −0.0219340 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8284 | 0.345725 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.8701 | −1.65440 | −0.827199 | − | 0.561909i | \(-0.810067\pi\) | ||||
−0.827199 | + | 0.561909i | \(0.810067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.0294 | −0.542603 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.0000 | −0.636607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.65685 | −0.116281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5147 | −0.683438 | −0.341719 | − | 0.939802i | \(-0.611009\pi\) | ||||
−0.341719 | + | 0.939802i | \(0.611009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.4853 | −0.618347 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.2254 | 0.831401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.97056 | −0.284101 | −0.142050 | − | 0.989859i | \(-0.545369\pi\) | ||||
−0.142050 | + | 0.989859i | \(0.545369\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 1856.2.a.v.1.2 | 2 | ||
4.3 | odd | 2 | 1856.2.a.s.1.1 | 2 | |||
8.3 | odd | 2 | 464.2.a.i.1.2 | 2 | |||
8.5 | even | 2 | 232.2.a.c.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 2088.2.a.q.1.1 | 2 | |||
24.11 | even | 2 | 4176.2.a.br.1.1 | 2 | |||
40.29 | even | 2 | 5800.2.a.o.1.2 | 2 | |||
232.173 | even | 2 | 6728.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.a.c.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
464.2.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
1856.2.a.s.1.1 | 2 | 4.3 | odd | 2 | |||
1856.2.a.v.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2088.2.a.q.1.1 | 2 | 24.5 | odd | 2 | |||
4176.2.a.br.1.1 | 2 | 24.11 | even | 2 | |||
5800.2.a.o.1.2 | 2 | 40.29 | even | 2 | |||
6728.2.a.f.1.2 | 2 | 232.173 | even | 2 |