Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(1,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, 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("640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.23607 | −0.835549 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.23607 | 1.92585 | 0.962927 | − | 0.269763i | \(-0.0869455\pi\) | ||||
0.962927 | + | 0.269763i | \(0.0869455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.47214 | 0.444009 | 0.222004 | − | 0.975046i | \(-0.428740\pi\) | ||||
0.222004 | + | 0.975046i | \(0.428740\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.47214 | 1.12665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.23607 | −0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9443 | 1.79923 | 0.899614 | − | 0.436687i | \(-0.143848\pi\) | ||||
0.899614 | + | 0.436687i | \(0.143848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.4721 | 2.31740 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.52786 | 0.550960 | 0.275480 | − | 0.961307i | \(-0.411163\pi\) | ||||
0.275480 | + | 0.961307i | \(0.411163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70820 | 0.870493 | 0.435246 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435246 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.47214 | 1.11388 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76393 | 0.403161 | 0.201580 | − | 0.979472i | \(-0.435392\pi\) | ||||
0.201580 | + | 0.979472i | \(0.435392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.4721 | 2.02650 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.4721 | −1.91688 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.472136 | 0.0614669 | 0.0307334 | − | 0.999528i | \(-0.490216\pi\) | ||||
0.0307334 | + | 0.999528i | \(0.490216\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.23607 | −1.16364 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.70820 | −0.697368 | −0.348684 | − | 0.937240i | \(-0.613371\pi\) | ||||
−0.348684 | + | 0.937240i | \(0.613371\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −29.8885 | −3.59816 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47214 | −0.768101 | −0.384051 | − | 0.923312i | \(-0.625471\pi\) | ||||
−0.384051 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.47214 | −0.523424 | −0.261712 | − | 0.965146i | \(-0.584287\pi\) | ||||
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.23607 | −0.373669 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.47214 | 0.281726 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.70820 | 1.06561 | 0.532807 | − | 0.846237i | \(-0.321137\pi\) | ||||
0.532807 | + | 0.846237i | \(0.321137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.47214 | −0.693886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.94427 | 0.312092 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.52786 | 0.579478 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | −0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.47214 | 0.458831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.52786 | −0.764339 | −0.382169 | − | 0.924092i | \(-0.624823\pi\) | ||||
−0.382169 | + | 0.924092i | \(0.624823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.9443 | −1.50196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.23607 | 0.121793 | 0.0608967 | − | 0.998144i | \(-0.480604\pi\) | ||||
0.0608967 | + | 0.998144i | \(0.480604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7639 | −1.23394 | −0.616968 | − | 0.786988i | \(-0.711639\pi\) | ||||
−0.616968 | + | 0.786988i | \(0.711639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.4164 | −3.36158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9443 | 1.40584 | 0.702919 | − | 0.711269i | \(-0.251879\pi\) | ||||
0.702919 | + | 0.711269i | \(0.251879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.23607 | 0.861268 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −33.4164 | −3.08935 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.52786 | 0.506738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.4164 | −1.02938 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.18034 | −0.193474 | −0.0967369 | − | 0.995310i | \(-0.530841\pi\) | ||||
−0.0967369 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.4721 | −1.62638 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.94427 | −0.257242 | −0.128621 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128621 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.52786 | −0.479327 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.4721 | −1.24556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.5279 | 0.977781 | 0.488890 | − | 0.872345i | \(-0.337402\pi\) | ||||
0.488890 | + | 0.872345i | \(0.337402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.94427 | −0.753244 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427 | 0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.7082 | 1.46055 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9443 | 0.896590 | 0.448295 | − | 0.893886i | \(-0.352031\pi\) | ||||
0.448295 | + | 0.893886i | \(0.352031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.41641 | 0.278023 | 0.139012 | − | 0.990291i | \(-0.455607\pi\) | ||||
0.139012 | + | 0.990291i | \(0.455607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.4164 | −2.70156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.47214 | 0.198567 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.9443 | −1.83115 | −0.915576 | − | 0.402145i | \(-0.868265\pi\) | ||||
−0.915576 | + | 0.402145i | \(0.868265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.4164 | −2.17426 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.4164 | −0.899739 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.70820 | 0.133797 | 0.0668984 | − | 0.997760i | \(-0.478690\pi\) | ||||
0.0668984 | + | 0.997760i | \(0.478690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.47214 | 0.503855 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6525 | 1.28861 | 0.644304 | − | 0.764770i | \(-0.277147\pi\) | ||||
0.644304 | + | 0.764770i | \(0.277147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 33.4164 | 2.55542 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.94427 | −0.527963 | −0.263982 | − | 0.964528i | \(-0.585036\pi\) | ||||
−0.263982 | + | 0.964528i | \(0.585036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23607 | −0.0934380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.52786 | −0.114841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5279 | −0.861633 | −0.430817 | − | 0.902440i | \(-0.641774\pi\) | ||||
−0.430817 | + | 0.902440i | \(0.641774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.94427 | 0.516164 | 0.258082 | − | 0.966123i | \(-0.416910\pi\) | ||||
0.258082 | + | 0.966123i | \(0.416910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.4164 | −1.43530 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9443 | 0.804639 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94427 | 0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.8885 | 1.30120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4164 | 1.11549 | 0.557746 | − | 0.830012i | \(-0.311666\pi\) | ||||
0.557746 | + | 0.830012i | \(0.311666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.4721 | −1.47362 | −0.736808 | − | 0.676102i | \(-0.763668\pi\) | ||||
−0.736808 | + | 0.676102i | \(0.763668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.4721 | 1.03637 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.47214 | 0.603615 | 0.301807 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301807 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9443 | −1.20115 | −0.600574 | − | 0.799569i | \(-0.705061\pi\) | ||||
−0.600574 | + | 0.799569i | \(0.705061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.4721 | 1.30292 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.47214 | −0.173510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.52786 | 0.246397 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 69.0132 | 4.79675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.94427 | −0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.9443 | −1.30418 | −0.652089 | − | 0.758143i | \(-0.726107\pi\) | ||||
−0.652089 | + | 0.758143i | \(0.726107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.9443 | 1.43508 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.70820 | 0.389296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.05573 | −0.207436 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4721 | 0.977936 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2361 | 0.886353 | 0.443176 | − | 0.896434i | \(-0.353852\pi\) | ||||
0.443176 | + | 0.896434i | \(0.353852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.47214 | 0.498142 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1803 | 0.808438 | 0.404219 | − | 0.914662i | \(-0.367543\pi\) | ||||
0.404219 | + | 0.914662i | \(0.367543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9443 | 0.987545 | 0.493773 | − | 0.869591i | \(-0.335618\pi\) | ||||
0.493773 | + | 0.869591i | \(0.335618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4721 | 1.60322 | 0.801611 | − | 0.597845i | \(-0.203976\pi\) | ||||
0.801611 | + | 0.597845i | \(0.203976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.76393 | 0.180299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.94427 | −0.319818 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3607 | −1.18272 | −0.591358 | − | 0.806409i | \(-0.701408\pi\) | ||||
−0.591358 | + | 0.806409i | \(0.701408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.47214 | −0.349602 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.4164 | −1.99093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.4721 | −1.16133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.4721 | 0.906280 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9443 | 0.932198 | 0.466099 | − | 0.884733i | \(-0.345659\pi\) | ||||
0.466099 | + | 0.884733i | \(0.345659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5279 | −0.840581 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.9443 | 0.925027 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.29180 | 0.264643 | 0.132322 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132322 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.47214 | 0.520439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.52786 | −0.583096 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.8885 | −0.724857 | −0.362429 | − | 0.932012i | \(-0.618052\pi\) | ||||
−0.362429 | + | 0.932012i | \(0.618052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3607 | −1.23682 | −0.618412 | − | 0.785854i | \(-0.712224\pi\) | ||||
−0.618412 | + | 0.785854i | \(0.712224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.8885 | −1.08266 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.94427 | −0.417241 | −0.208620 | − | 0.977997i | \(-0.566897\pi\) | ||||
−0.208620 | + | 0.977997i | \(0.566897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.4721 | 1.10590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4721 | 0.744025 | 0.372013 | − | 0.928228i | \(-0.378668\pi\) | ||||
0.372013 | + | 0.928228i | \(0.378668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7082 | 1.29042 | 0.645209 | − | 0.764006i | \(-0.276770\pi\) | ||||
0.645209 | + | 0.764006i | \(0.276770\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.4721 | −0.857255 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.36068 | −0.257403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.3607 | 1.42805 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8885 | −0.694536 | −0.347268 | − | 0.937766i | \(-0.612891\pi\) | ||||
−0.347268 | + | 0.937766i | \(0.612891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.472136 | 0.0274888 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.9443 | 1.67952 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41.3050 | −2.38873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.05573 | −0.406685 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.3607 | −1.85907 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7082 | −0.782369 | −0.391184 | − | 0.920312i | \(-0.627934\pi\) | ||||
−0.391184 | + | 0.920312i | \(0.627934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4164 | −0.647365 | −0.323683 | − | 0.946166i | \(-0.604921\pi\) | ||||
−0.323683 | + | 0.946166i | \(0.604921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.8328 | 1.40363 | 0.701817 | − | 0.712357i | \(-0.252372\pi\) | ||||
0.701817 | + | 0.712357i | \(0.252372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.23607 | −0.520393 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5279 | 0.647469 | 0.323735 | − | 0.946148i | \(-0.395061\pi\) | ||||
0.323735 | + | 0.946148i | \(0.395061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.3050 | 2.30542 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.52786 | −0.526892 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.41641 | −0.188353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8885 | −1.09317 | −0.546587 | − | 0.837403i | \(-0.684073\pi\) | ||||
−0.546587 | + | 0.837403i | \(0.684073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 81.7771 | 4.48136 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.70820 | −0.311872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9443 | 1.24985 | 0.624927 | − | 0.780683i | \(-0.285129\pi\) | ||||
0.624927 | + | 0.780683i | \(0.285129\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −48.3607 | −2.62659 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.94427 | −0.267747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.8885 | −1.60915 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7639 | −0.685204 | −0.342602 | − | 0.939481i | \(-0.611308\pi\) | ||||
−0.342602 | + | 0.939481i | \(0.611308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94427 | −0.157603 | −0.0788016 | − | 0.996890i | \(-0.525109\pi\) | ||||
−0.0788016 | + | 0.996890i | \(0.525109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 64.7214 | 3.45457 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9443 | 1.22120 | 0.610600 | − | 0.791939i | \(-0.290928\pi\) | ||||
0.610600 | + | 0.791939i | \(0.290928\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.47214 | −0.343505 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8885 | −0.946762 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.9443 | 1.73873 | 0.869366 | − | 0.494169i | \(-0.164527\pi\) | ||||
0.869366 | + | 0.494169i | \(0.164527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.6525 | 1.18895 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.47214 | −0.234082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.7082 | 1.65515 | 0.827577 | − | 0.561352i | \(-0.189718\pi\) | ||||
0.827577 | + | 0.561352i | \(0.189718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.3607 | 1.37228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4721 | −0.543686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.9443 | −1.18801 | −0.594005 | − | 0.804462i | \(-0.702454\pi\) | ||||
−0.594005 | + | 0.804462i | \(0.702454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.23607 | −0.167110 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.4721 | 1.25705 | 0.628525 | − | 0.777790i | \(-0.283659\pi\) | ||||
0.628525 | + | 0.777790i | \(0.283659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.05573 | 0.361476 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.7082 | −1.21143 | −0.605716 | − | 0.795681i | \(-0.707113\pi\) | ||||
−0.605716 | + | 0.795681i | \(0.707113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.47214 | 0.125992 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.6525 | 2.16815 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8885 | 1.21120 | 0.605599 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605599 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.3050 | −2.08888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.52786 | 0.480617 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.94427 | 0.248773 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.52786 | 0.177058 | 0.0885292 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885292 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.8885 | 0.895547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0557 | −0.550725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.4164 | 1.21326 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.8885 | −1.08497 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.41641 | −0.465611 | −0.232806 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232806 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.47214 | −0.319247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.583592 | −0.0287167 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.70820 | 0.476557 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.3050 | −1.82683 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.47214 | 0.218478 | 0.109239 | − | 0.994016i | \(-0.465159\pi\) | ||||
0.109239 | + | 0.994016i | \(0.465159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.8328 | −1.21028 | −0.605139 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.6525 | 1.00416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.41641 | −0.358905 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.9443 | −1.39744 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.3607 | −0.980739 | −0.490370 | − | 0.871515i | \(-0.663138\pi\) | ||||
−0.490370 | + | 0.871515i | \(0.663138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.47214 | 0.407145 | 0.203572 | − | 0.979060i | \(-0.434745\pi\) | ||||
0.203572 | + | 0.979060i | \(0.434745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.47214 | −0.310315 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.3050 | 1.97588 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.9443 | −1.57234 | −0.786172 | − | 0.618008i | \(-0.787940\pi\) | ||||
−0.786172 | + | 0.618008i | \(0.787940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.8885 | −1.94707 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.6525 | 1.26630 | 0.633149 | − | 0.774030i | \(-0.281762\pi\) | ||||
0.633149 | + | 0.774030i | \(0.281762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.94427 | 0.139572 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.4164 | −1.67514 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.4164 | 1.19947 | 0.599737 | − | 0.800197i | \(-0.295272\pi\) | ||||
0.599737 | + | 0.800197i | \(0.295272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.05573 | −0.332241 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.0557 | −0.519443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.52786 | 0.259150 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.8885 | −1.49168 | −0.745842 | − | 0.666123i | \(-0.767952\pi\) | ||||
−0.745842 | + | 0.666123i | \(0.767952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 64.7214 | 3.02093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7771 | 1.38686 | 0.693429 | − | 0.720525i | \(-0.256099\pi\) | ||||
0.693429 | + | 0.720525i | \(0.256099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.1246 | 1.81827 | 0.909137 | − | 0.416496i | \(-0.136742\pi\) | ||||
0.909137 | + | 0.416496i | \(0.136742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.00000 | −0.370991 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.59675 | −0.351536 | −0.175768 | − | 0.984432i | \(-0.556241\pi\) | ||||
−0.175768 | + | 0.984432i | \(0.556241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.05573 | 0.325803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 74.2492 | 3.42122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4164 | −0.524927 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.47214 | 0.205196 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 63.3050 | 2.89853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.94427 | 0.225910 | 0.112955 | − | 0.993600i | \(-0.463968\pi\) | ||||
0.112955 | + | 0.993600i | \(0.463968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.9443 | −2.23167 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 36.9443 | 1.68102 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.52786 | −0.341823 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.2361 | −0.781041 | −0.390520 | − | 0.920594i | \(-0.627705\pi\) | ||||
−0.390520 | + | 0.920594i | \(0.627705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.52786 | −0.249979 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.9443 | −1.75753 | −0.878765 | − | 0.477254i | \(-0.841632\pi\) | ||||
−0.878765 | + | 0.477254i | \(0.841632\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94427 | −0.402830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.9443 | −0.671695 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.4164 | 1.85405 | 0.927027 | − | 0.374996i | \(-0.122356\pi\) | ||||
0.927027 | + | 0.374996i | \(0.122356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.8885 | −2.40756 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.1246 | 1.56613 | 0.783065 | − | 0.621940i | \(-0.213655\pi\) | ||||
0.783065 | + | 0.621940i | \(0.213655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.6525 | −1.00603 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.8328 | −1.63259 | −0.816293 | − | 0.577638i | \(-0.803974\pi\) | ||||
−0.816293 | + | 0.577638i | \(0.803974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.52786 | 0.244538 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −64.7214 | −2.85752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.23607 | 0.0544677 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.52786 | −0.243115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4721 | 0.986417 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8885 | 0.871333 | 0.435666 | − | 0.900108i | \(-0.356513\pi\) | ||||
0.435666 | + | 0.900108i | \(0.356513\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.0689 | −1.66464 | −0.832318 | − | 0.554298i | \(-0.812987\pi\) | ||||
−0.832318 | + | 0.554298i | \(0.812987\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.0557 | −0.481595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.3050 | 2.70891 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.52786 | 0.153096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.7771 | −0.683382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7639 | −0.551833 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.3050 | 1.60983 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9443 | 0.471403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8885 | 0.511128 | 0.255564 | − | 0.966792i | \(-0.417739\pi\) | ||||
0.255564 | + | 0.966792i | \(0.417739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.4721 | −0.964372 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.94427 | 0.126119 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6525 | −0.455467 | −0.227733 | − | 0.973724i | \(-0.573131\pi\) | ||||
−0.227733 | + | 0.973724i | \(0.573131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 44.8328 | 1.91342 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.94427 | 0.381039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.11146 | −0.259886 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.4164 | −1.50334 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.9443 | −1.31115 | −0.655575 | − | 0.755130i | \(-0.727574\pi\) | ||||
−0.655575 | + | 0.755130i | \(0.727574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5279 | −1.07971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.9443 | −1.22203 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7082 | 0.746312 | 0.373156 | − | 0.927769i | \(-0.378276\pi\) | ||||
0.373156 | + | 0.927769i | \(0.378276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9443 | 0.628710 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.1803 | −1.26746 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3607 | 0.434342 | 0.217171 | − | 0.976134i | \(-0.430317\pi\) | ||||
0.217171 | + | 0.976134i | \(0.430317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.8328 | 1.54141 | 0.770703 | − | 0.637195i | \(-0.219905\pi\) | ||||
0.770703 | + | 0.637195i | \(0.219905\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −49.8885 | −2.08412 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.23607 | 0.385171 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.8885 | −0.661449 | −0.330724 | − | 0.943727i | \(-0.607293\pi\) | ||||
−0.330724 | + | 0.943727i | \(0.607293\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 66.2492 | 2.75322 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9443 | −0.701760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.4164 | −1.38160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.6525 | −0.934968 | −0.467484 | − | 0.884002i | \(-0.654839\pi\) | ||||
−0.467484 | + | 0.884002i | \(0.654839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.0557 | 0.455543 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.4164 | −1.12776 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52786 | 0.226620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 54.8328 | 2.24416 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8885 | −0.567471 | −0.283735 | − | 0.958903i | \(-0.591574\pi\) | ||||
−0.283735 | + | 0.958903i | \(0.591574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3607 | 0.912111 | 0.456056 | − | 0.889951i | \(-0.349262\pi\) | ||||
0.456056 | + | 0.889951i | \(0.349262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.6525 | −1.73694 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −47.1246 | −1.91273 | −0.956364 | − | 0.292176i | \(-0.905621\pi\) | ||||
−0.956364 | + | 0.292176i | \(0.905621\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3607 | −0.500060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.4721 | −1.14998 | −0.574989 | − | 0.818161i | \(-0.694994\pi\) | ||||
−0.574989 | + | 0.818161i | \(0.694994\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.4164 | −0.460354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.41641 | −0.0570224 | −0.0285112 | − | 0.999593i | \(-0.509077\pi\) | ||||
−0.0285112 | + | 0.999593i | \(0.509077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5279 | 0.463344 | 0.231672 | − | 0.972794i | \(-0.425580\pi\) | ||||
0.231672 | + | 0.972794i | \(0.425580\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −133.666 | −5.36382 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.63932 | −0.145806 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.9443 | 1.15592 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.9443 | −1.95154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5279 | 1.01625 | 0.508124 | − | 0.861284i | \(-0.330339\pi\) | ||||
0.508124 | + | 0.861284i | \(0.330339\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 61.3050 | 2.43665 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.18034 | −0.0865241 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.4721 | 0.969621 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.3607 | −1.91312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.47214 | −0.334629 | −0.167315 | − | 0.985904i | \(-0.553510\pi\) | ||||
−0.167315 | + | 0.985904i | \(0.553510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.180340 | −0.00711191 | −0.00355596 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355596 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.4721 | −0.727340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2361 | −0.677620 | −0.338810 | − | 0.940855i | \(-0.610024\pi\) | ||||
−0.338810 | + | 0.940855i | \(0.610024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.944272 | −0.0370659 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.88854 | 0.387563 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5836 | 0.883764 | 0.441882 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441882 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.94427 | −0.115042 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.4164 | −1.30370 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.41641 | −0.210993 | −0.105497 | − | 0.994420i | \(-0.533643\pi\) | ||||
−0.105497 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.111456 | −0.00433514 | −0.00216757 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216757 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −64.7214 | −2.51357 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.52786 | −0.214361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.4721 | 0.715244 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.8328 | −1.65601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.3050 | 1.51509 | 0.757547 | − | 0.652780i | \(-0.226398\pi\) | ||||
0.757547 | + | 0.652780i | \(0.226398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.4721 | −0.557033 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.3607 | −0.551926 | −0.275963 | − | 0.961168i | \(-0.588997\pi\) | ||||
−0.275963 | + | 0.961168i | \(0.588997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.30495 | 0.357091 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.4164 | −1.51044 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.7082 | 1.44286 | 0.721432 | − | 0.692485i | \(-0.243484\pi\) | ||||
0.721432 | + | 0.692485i | \(0.243484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.3607 | −1.84508 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.8885 | −1.44344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0000 | −1.14125 | −0.570627 | − | 0.821209i | \(-0.693300\pi\) | ||||
−0.570627 | + | 0.821209i | \(0.693300\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.4721 | 0.701698 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.5279 | 0.437277 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7771 | −0.597600 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −79.1935 | −2.99537 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9443 | 1.01767 | 0.508836 | − | 0.860864i | \(-0.330076\pi\) | ||||
0.508836 | + | 0.860864i | \(0.330076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.9443 | 1.84597 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.94427 | −0.336861 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.3607 | −0.464871 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0000 | 0.676004 | 0.338002 | − | 0.941145i | \(-0.390249\pi\) | ||||
0.338002 | + | 0.941145i | \(0.390249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.9443 | 1.38552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.8328 | 0.855096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.94427 | 0.334497 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | 0.597531 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.8328 | 1.14987 | 0.574935 | − | 0.818199i | \(-0.305027\pi\) | ||||
0.574935 | + | 0.818199i | \(0.305027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.52786 | −0.0569006 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 59.4164 | 2.20972 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7082 | 0.434233 | 0.217117 | − | 0.976146i | \(-0.430335\pi\) | ||||
0.217117 | + | 0.976146i | \(0.430335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.5279 | −0.944182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1115 | −0.595090 | −0.297545 | − | 0.954708i | \(-0.596168\pi\) | ||||
−0.297545 | + | 0.954708i | \(0.596168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.7082 | 0.653177 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4164 | 0.420529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.1935 | −1.80961 | −0.904806 | − | 0.425824i | \(-0.859984\pi\) | ||||
−0.904806 | + | 0.425824i | \(0.859984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 64.7214 | 2.37760 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.652476 | −0.0239370 | −0.0119685 | − | 0.999928i | \(-0.503810\pi\) | ||||
−0.0119685 | + | 0.999928i | \(0.503810\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9443 | 0.400967 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 72.5410 | 2.65414 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7771 | 0.576482 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3607 | 1.03490 | 0.517448 | − | 0.855715i | \(-0.326882\pi\) | ||||
0.517448 | + | 0.855715i | \(0.326882\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.47214 | 0.235858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.41641 | 0.124336 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8885 | 0.577479 | 0.288739 | − | 0.957408i | \(-0.406764\pi\) | ||||
0.288739 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 59.7771 | 2.16977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8885 | −1.15596 | −0.577979 | − | 0.816051i | \(-0.696159\pi\) | ||||
−0.577979 | + | 0.816051i | \(0.696159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.63932 | −0.131752 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.4164 | −1.20817 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.11146 | −0.0762403 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.94427 | 0.106173 | 0.0530866 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530866 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.3607 | −1.74167 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.3607 | 0.948128 | 0.474064 | − | 0.880490i | \(-0.342787\pi\) | ||||
0.474064 | + | 0.880490i | \(0.342787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.47214 | 0.0888017 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 43.7771 | 1.57049 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.7771 | 0.565273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9443 | 0.463182 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.9443 | −1.03438 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9443 | −0.818916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0689 | 0.501502 | 0.250751 | − | 0.968052i | \(-0.419323\pi\) | ||||
0.250751 | + | 0.968052i | \(0.419323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.8885 | −0.494445 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.4721 | −0.656794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.8328 | −0.952861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.4164 | −0.972360 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.41641 | −0.0501717 | −0.0250859 | − | 0.999685i | \(-0.507986\pi\) | ||||
−0.0250859 | + | 0.999685i | \(0.507986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.3607 | −0.437289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.0000 | 0.777332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.94427 | 0.315637 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4164 | −0.402376 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.4721 | 1.35428 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.8885 | −1.68367 | −0.841836 | − | 0.539734i | \(-0.818525\pi\) | ||||
−0.841836 | + | 0.539734i | \(0.818525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.8885 | 2.31081 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.70820 | 0.0598358 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.5279 | 0.893107 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.3050 | 1.44331 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.9443 | −1.35916 | −0.679582 | − | 0.733599i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733599i | \(0.737839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.7082 | −0.408122 | −0.204061 | − | 0.978958i | \(-0.565414\pi\) | ||||
−0.204061 | + | 0.978958i | \(0.565414\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.47214 | 0.225331 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1803 | 0.562646 | 0.281323 | − | 0.959613i | \(-0.409227\pi\) | ||||
0.281323 | + | 0.959613i | \(0.409227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.4721 | 0.779550 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.4721 | 0.847909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.6525 | 0.576283 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.7771 | −1.23664 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.3607 | −1.39010 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.65248 | 0.297303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.2492 | −2.41095 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 101.082 | 3.46505 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4721 | 0.563995 | 0.281998 | − | 0.959415i | \(-0.409003\pi\) | ||||
0.281998 | + | 0.959415i | \(0.409003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.4164 | 1.14282 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.8328 | −0.984910 | −0.492455 | − | 0.870338i | \(-0.663900\pi\) | ||||
−0.492455 | + | 0.870338i | \(0.663900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5836 | 0.770542 | 0.385271 | − | 0.922803i | \(-0.374108\pi\) | ||||
0.385271 | + | 0.922803i | \(0.374108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.1115 | 0.480917 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.7082 | −1.07936 | −0.539680 | − | 0.841870i | \(-0.681455\pi\) | ||||
−0.539680 | + | 0.841870i | \(0.681455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.94427 | −0.236112 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.70820 | −0.329708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.88854 | −0.335446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5279 | 0.864979 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −56.2492 | −1.90375 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.23607 | −0.0417867 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1115 | −0.544045 | −0.272023 | − | 0.962291i | \(-0.587693\pi\) | ||||
−0.272023 | + | 0.962291i | \(0.587693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.4721 | 1.29763 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.5279 | −0.523147 | −0.261574 | − | 0.965184i | \(-0.584241\pi\) | ||||
−0.261574 | + | 0.965184i | \(0.584241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.2918 | −0.480957 | −0.240479 | − | 0.970654i | \(-0.577304\pi\) | ||||
−0.240479 | + | 0.970654i | \(0.577304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.52786 | −0.0513586 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.5967 | 1.26238 | 0.631188 | − | 0.775630i | \(-0.282568\pi\) | ||||
0.631188 | + | 0.775630i | \(0.282568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.69505 | 0.0903890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48.8328 | −1.63596 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.3607 | 0.413634 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5279 | −0.385334 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 133.666 | 4.46297 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.94427 | 0.164901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.8885 | −1.26225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.8328 | 0.759829 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.94427 | 0.230835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.76393 | −0.158184 | −0.0790919 | − | 0.996867i | \(-0.525202\pi\) | ||||
−0.0790919 | + | 0.996867i | \(0.525202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 74.7214 | 2.47835 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.30495 | −0.308287 | −0.154143 | − | 0.988048i | \(-0.549262\pi\) | ||||
−0.154143 | + | 0.988048i | \(0.549262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.4164 | −0.642589 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.4164 | −0.641887 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.63932 | 0.120181 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.8885 | −0.985932 | −0.492966 | − | 0.870049i | \(-0.664087\pi\) | ||||
−0.492966 | + | 0.870049i | \(0.664087\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.3607 | 1.46173 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.9443 | 0.952712 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9443 | 0.359845 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.23607 | 0.303352 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5279 | 0.509453 | 0.254726 | − | 0.967013i | \(-0.418015\pi\) | ||||
0.254726 | + | 0.967013i | \(0.418015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.4721 | −0.802042 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.9443 | 1.20950 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.94427 | 0.292509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4721 | −0.407447 | −0.203723 | − | 0.979028i | \(-0.565304\pi\) | ||||
−0.203723 | + | 0.979028i | \(0.565304\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.3607 | −2.62247 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.83282 | 0.287942 | 0.143971 | − | 0.989582i | \(-0.454013\pi\) | ||||
0.143971 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.5836 | 1.06107 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.8885 | 0.581914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.1803 | 1.43567 | 0.717834 | − | 0.696214i | \(-0.245134\pi\) | ||||
0.717834 | + | 0.696214i | \(0.245134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.3050 | −1.20970 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.7771 | −0.835002 | −0.417501 | − | 0.908677i | \(-0.637094\pi\) | ||||
−0.417501 | + | 0.908677i | \(0.637094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4164 | 0.498863 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.9443 | 0.418429 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.47214 | −0.0798294 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −95.3738 | −3.07338 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.4721 | −0.659021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6525 | 1.05003 | 0.525016 | − | 0.851092i | \(-0.324059\pi\) | ||||
0.525016 | + | 0.851092i | \(0.324059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 64.7214 | 2.07915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8885 | −0.381522 | −0.190761 | − | 0.981637i | \(-0.561095\pi\) | ||||
−0.190761 | + | 0.981637i | \(0.561095\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.2492 | −0.456809 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4721 | 0.463479 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.3050 | 0.745591 | 0.372796 | − | 0.927913i | \(-0.378399\pi\) | ||||
0.372796 | + | 0.927913i | \(0.378399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.88854 | −0.188199 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.0000 | 0.702406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.0132 | 1.18054 | 0.590268 | − | 0.807207i | \(-0.299022\pi\) | ||||
0.590268 | + | 0.807207i | \(0.299022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.47214 | 0.269945 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.0557 | 0.351908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.7214 | 1.67644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4721 | 0.840915 | 0.420458 | − | 0.907312i | \(-0.361870\pi\) | ||||
0.420458 | + | 0.907312i | \(0.361870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.3607 | 2.04242 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.9443 | −0.537170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.4164 | 1.94508 | 0.972539 | − | 0.232742i | \(-0.0747697\pi\) | ||||
0.972539 | + | 0.232742i | \(0.0747697\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −158.387 | −5.01114 |
(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 | 640.2.a.j.1.1 | yes | 2 | |
3.2 | odd | 2 | 5760.2.a.cd.1.1 | 2 | |||
4.3 | odd | 2 | 640.2.a.l.1.2 | yes | 2 | ||
5.2 | odd | 4 | 3200.2.c.v.2049.4 | 4 | |||
5.3 | odd | 4 | 3200.2.c.v.2049.1 | 4 | |||
5.4 | even | 2 | 3200.2.a.bk.1.2 | 2 | |||
8.3 | odd | 2 | 640.2.a.i.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 640.2.a.k.1.2 | yes | 2 | ||
12.11 | even | 2 | 5760.2.a.bw.1.2 | 2 | |||
16.3 | odd | 4 | 1280.2.d.m.641.4 | 4 | |||
16.5 | even | 4 | 1280.2.d.k.641.4 | 4 | |||
16.11 | odd | 4 | 1280.2.d.m.641.1 | 4 | |||
16.13 | even | 4 | 1280.2.d.k.641.1 | 4 | |||
20.3 | even | 4 | 3200.2.c.x.2049.4 | 4 | |||
20.7 | even | 4 | 3200.2.c.x.2049.1 | 4 | |||
20.19 | odd | 2 | 3200.2.a.bf.1.1 | 2 | |||
24.5 | odd | 2 | 5760.2.a.ci.1.1 | 2 | |||
24.11 | even | 2 | 5760.2.a.ch.1.2 | 2 | |||
40.3 | even | 4 | 3200.2.c.u.2049.1 | 4 | |||
40.13 | odd | 4 | 3200.2.c.w.2049.4 | 4 | |||
40.19 | odd | 2 | 3200.2.a.bl.1.2 | 2 | |||
40.27 | even | 4 | 3200.2.c.u.2049.4 | 4 | |||
40.29 | even | 2 | 3200.2.a.be.1.1 | 2 | |||
40.37 | odd | 4 | 3200.2.c.w.2049.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.a.i.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
640.2.a.j.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
640.2.a.k.1.2 | yes | 2 | 8.5 | even | 2 | ||
640.2.a.l.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1280.2.d.k.641.1 | 4 | 16.13 | even | 4 | |||
1280.2.d.k.641.4 | 4 | 16.5 | even | 4 | |||
1280.2.d.m.641.1 | 4 | 16.11 | odd | 4 | |||
1280.2.d.m.641.4 | 4 | 16.3 | odd | 4 | |||
3200.2.a.be.1.1 | 2 | 40.29 | even | 2 | |||
3200.2.a.bf.1.1 | 2 | 20.19 | odd | 2 | |||
3200.2.a.bk.1.2 | 2 | 5.4 | even | 2 | |||
3200.2.a.bl.1.2 | 2 | 40.19 | odd | 2 | |||
3200.2.c.u.2049.1 | 4 | 40.3 | even | 4 | |||
3200.2.c.u.2049.4 | 4 | 40.27 | even | 4 | |||
3200.2.c.v.2049.1 | 4 | 5.3 | odd | 4 | |||
3200.2.c.v.2049.4 | 4 | 5.2 | odd | 4 | |||
3200.2.c.w.2049.1 | 4 | 40.37 | odd | 4 | |||
3200.2.c.w.2049.4 | 4 | 40.13 | odd | 4 | |||
3200.2.c.x.2049.1 | 4 | 20.7 | even | 4 | |||
3200.2.c.x.2049.4 | 4 | 20.3 | even | 4 | |||
5760.2.a.bw.1.2 | 2 | 12.11 | even | 2 | |||
5760.2.a.cd.1.1 | 2 | 3.2 | odd | 2 | |||
5760.2.a.ch.1.2 | 2 | 24.11 | even | 2 | |||
5760.2.a.ci.1.1 | 2 | 24.5 | odd | 2 |