Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,2,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(0.343356728692\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −3.41421 | −1.29045 | −0.645226 | − | 0.763992i | \(-0.723237\pi\) | ||||
−0.645226 | + | 0.763992i | \(0.723237\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.82843 | −1.52688 | ||||||||
\(11\) | −3.82843 | −1.15431 | −0.577157 | − | 0.816633i | \(-0.695838\pi\) | ||||
−0.577157 | + | 0.816633i | \(0.695838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 4.82843 | 1.29045 | ||||||||
\(15\) | 4.82843 | 1.24669 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.17157 | 0.526684 | 0.263342 | − | 0.964703i | \(-0.415175\pi\) | ||||
0.263342 | + | 0.964703i | \(0.415175\pi\) | |||||||
\(18\) | 1.41421 | 0.333333 | ||||||||
\(19\) | 0.828427 | 0.190054 | 0.0950271 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950271 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.82843 | −1.05365 | ||||||||
\(22\) | 5.41421 | 1.15431 | ||||||||
\(23\) | 6.65685 | 1.38805 | 0.694025 | − | 0.719951i | \(-0.255836\pi\) | ||||
0.694025 | + | 0.719951i | \(0.255836\pi\) | |||||||
\(24\) | 4.00000 | 0.816497 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 2.58579 | 0.507114 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24264 | −0.787839 | −0.393919 | − | 0.919145i | \(-0.628881\pi\) | ||||
−0.393919 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(30\) | −6.82843 | −1.24669 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.41421 | −0.942494 | ||||||||
\(34\) | −3.07107 | −0.526684 | ||||||||
\(35\) | −11.6569 | −1.97037 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48528 | 1.39497 | 0.697486 | − | 0.716599i | \(-0.254302\pi\) | ||||
0.697486 | + | 0.716599i | \(0.254302\pi\) | |||||||
\(38\) | −1.17157 | −0.190054 | ||||||||
\(39\) | −2.58579 | −0.414057 | ||||||||
\(40\) | 9.65685 | 1.52688 | ||||||||
\(41\) | 1.82843 | 0.285552 | 0.142776 | − | 0.989755i | \(-0.454397\pi\) | ||||
0.142776 | + | 0.989755i | \(0.454397\pi\) | |||||||
\(42\) | 6.82843 | 1.05365 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.41421 | −0.508961 | ||||||||
\(46\) | −9.41421 | −1.38805 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −5.65685 | −0.816497 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | −9.41421 | −1.33137 | ||||||||
\(51\) | 3.07107 | 0.430036 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.8284 | 1.89948 | 0.949740 | − | 0.313039i | \(-0.101347\pi\) | ||||
0.949740 | + | 0.313039i | \(0.101347\pi\) | |||||||
\(54\) | 8.00000 | 1.08866 | ||||||||
\(55\) | −13.0711 | −1.76250 | ||||||||
\(56\) | −9.65685 | −1.29045 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −4.82843 | −0.628608 | −0.314304 | − | 0.949322i | \(-0.601771\pi\) | ||||
−0.314304 | + | 0.949322i | \(0.601771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.242641 | −0.0310670 | −0.0155335 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155335 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(62\) | 4.24264 | 0.538816 | ||||||||
\(63\) | 3.41421 | 0.430150 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 7.65685 | 0.942494 | ||||||||
\(67\) | −7.48528 | −0.914473 | −0.457236 | − | 0.889345i | \(-0.651161\pi\) | ||||
−0.457236 | + | 0.889345i | \(0.651161\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.41421 | 1.13334 | ||||||||
\(70\) | 16.4853 | 1.97037 | ||||||||
\(71\) | −3.17157 | −0.376396 | −0.188198 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188198 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −16.2426 | −1.90106 | −0.950529 | − | 0.310637i | \(-0.899458\pi\) | ||||
−0.950529 | + | 0.310637i | \(0.899458\pi\) | |||||||
\(74\) | −12.0000 | −1.39497 | ||||||||
\(75\) | 9.41421 | 1.08706 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.0711 | 1.48959 | ||||||||
\(78\) | 3.65685 | 0.414057 | ||||||||
\(79\) | 4.82843 | 0.543240 | 0.271620 | − | 0.962405i | \(-0.412441\pi\) | ||||
0.271620 | + | 0.962405i | \(0.412441\pi\) | |||||||
\(80\) | −13.6569 | −1.52688 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −2.58579 | −0.285552 | ||||||||
\(83\) | 3.34315 | 0.366958 | 0.183479 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183479 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.41421 | 0.804184 | ||||||||
\(86\) | −1.41421 | −0.152499 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | −10.8284 | −1.15431 | ||||||||
\(89\) | −1.75736 | −0.186280 | −0.0931399 | − | 0.995653i | \(-0.529690\pi\) | ||||
−0.0931399 | + | 0.995653i | \(0.529690\pi\) | |||||||
\(90\) | 4.82843 | 0.508961 | ||||||||
\(91\) | 6.24264 | 0.654407 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.24264 | −0.439941 | ||||||||
\(94\) | −8.48528 | −0.875190 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.82843 | 0.185649 | 0.0928243 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928243 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(98\) | −6.58579 | −0.665265 | ||||||||
\(99\) | 3.82843 | 0.384771 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.82843 | 0.579950 | 0.289975 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289975 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(102\) | −4.34315 | −0.430036 | ||||||||
\(103\) | 0.514719 | 0.0507167 | 0.0253584 | − | 0.999678i | \(-0.491927\pi\) | ||||
0.0253584 | + | 0.999678i | \(0.491927\pi\) | |||||||
\(104\) | −5.17157 | −0.507114 | ||||||||
\(105\) | −16.4853 | −1.60880 | ||||||||
\(106\) | −19.5563 | −1.89948 | ||||||||
\(107\) | −0.343146 | −0.0331732 | −0.0165866 | − | 0.999862i | \(-0.505280\pi\) | ||||
−0.0165866 | + | 0.999862i | \(0.505280\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.9706 | −1.91283 | −0.956416 | − | 0.292006i | \(-0.905677\pi\) | ||||
−0.956416 | + | 0.292006i | \(0.905677\pi\) | |||||||
\(110\) | 18.4853 | 1.76250 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 13.6569 | 1.29045 | ||||||||
\(113\) | −6.82843 | −0.642364 | −0.321182 | − | 0.947017i | \(-0.604080\pi\) | ||||
−0.321182 | + | 0.947017i | \(0.604080\pi\) | |||||||
\(114\) | −1.65685 | −0.155179 | ||||||||
\(115\) | 22.7279 | 2.11939 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.82843 | 0.169038 | ||||||||
\(118\) | 6.82843 | 0.628608 | ||||||||
\(119\) | −7.41421 | −0.679660 | ||||||||
\(120\) | 13.6569 | 1.24669 | ||||||||
\(121\) | 3.65685 | 0.332441 | ||||||||
\(122\) | 0.343146 | 0.0310670 | ||||||||
\(123\) | 2.58579 | 0.233153 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | −4.82843 | −0.430150 | ||||||||
\(127\) | 3.82843 | 0.339718 | 0.169859 | − | 0.985468i | \(-0.445669\pi\) | ||||
0.169859 | + | 0.985468i | \(0.445669\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 1.41421 | 0.124515 | ||||||||
\(130\) | 8.82843 | 0.774304 | ||||||||
\(131\) | 9.65685 | 0.843723 | 0.421862 | − | 0.906660i | \(-0.361377\pi\) | ||||
0.421862 | + | 0.906660i | \(0.361377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82843 | −0.245256 | ||||||||
\(134\) | 10.5858 | 0.914473 | ||||||||
\(135\) | −19.3137 | −1.66226 | ||||||||
\(136\) | 6.14214 | 0.526684 | ||||||||
\(137\) | −14.4853 | −1.23756 | −0.618781 | − | 0.785564i | \(-0.712373\pi\) | ||||
−0.618781 | + | 0.785564i | \(0.712373\pi\) | |||||||
\(138\) | −13.3137 | −1.13334 | ||||||||
\(139\) | 5.48528 | 0.465255 | 0.232628 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232628 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.48528 | 0.714590 | ||||||||
\(142\) | 4.48528 | 0.376396 | ||||||||
\(143\) | 7.00000 | 0.585369 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −14.4853 | −1.20294 | ||||||||
\(146\) | 22.9706 | 1.90106 | ||||||||
\(147\) | 6.58579 | 0.543187 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.48528 | 0.695141 | 0.347571 | − | 0.937654i | \(-0.387007\pi\) | ||||
0.347571 | + | 0.937654i | \(0.387007\pi\) | |||||||
\(150\) | −13.3137 | −1.08706 | ||||||||
\(151\) | 18.2426 | 1.48457 | 0.742283 | − | 0.670087i | \(-0.233743\pi\) | ||||
0.742283 | + | 0.670087i | \(0.233743\pi\) | |||||||
\(152\) | 2.34315 | 0.190054 | ||||||||
\(153\) | −2.17157 | −0.175561 | ||||||||
\(154\) | −18.4853 | −1.48959 | ||||||||
\(155\) | −10.2426 | −0.822709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | −6.82843 | −0.543240 | ||||||||
\(159\) | 19.5563 | 1.55092 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.7279 | −1.79121 | ||||||||
\(162\) | 7.07107 | 0.555556 | ||||||||
\(163\) | −11.7574 | −0.920907 | −0.460454 | − | 0.887684i | \(-0.652313\pi\) | ||||
−0.460454 | + | 0.887684i | \(0.652313\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.4853 | −1.43908 | ||||||||
\(166\) | −4.72792 | −0.366958 | ||||||||
\(167\) | −14.3137 | −1.10763 | −0.553814 | − | 0.832640i | \(-0.686828\pi\) | ||||
−0.553814 | + | 0.832640i | \(0.686828\pi\) | |||||||
\(168\) | −13.6569 | −1.05365 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | −10.4853 | −0.804184 | ||||||||
\(171\) | −0.828427 | −0.0633514 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.6569 | 1.79860 | 0.899299 | − | 0.437335i | \(-0.144078\pi\) | ||||
0.899299 | + | 0.437335i | \(0.144078\pi\) | |||||||
\(174\) | 8.48528 | 0.643268 | ||||||||
\(175\) | −22.7279 | −1.71807 | ||||||||
\(176\) | 15.3137 | 1.15431 | ||||||||
\(177\) | −6.82843 | −0.513256 | ||||||||
\(178\) | 2.48528 | 0.186280 | ||||||||
\(179\) | −4.58579 | −0.342758 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.31371 | 0.543624 | 0.271812 | − | 0.962350i | \(-0.412377\pi\) | ||||
0.271812 | + | 0.962350i | \(0.412377\pi\) | |||||||
\(182\) | −8.82843 | −0.654407 | ||||||||
\(183\) | −0.343146 | −0.0253661 | ||||||||
\(184\) | 18.8284 | 1.38805 | ||||||||
\(185\) | 28.9706 | 2.12996 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −8.31371 | −0.607959 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.3137 | 1.40487 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −6.14214 | −0.444429 | −0.222215 | − | 0.974998i | \(-0.571329\pi\) | ||||
−0.222215 | + | 0.974998i | \(0.571329\pi\) | |||||||
\(192\) | 11.3137 | 0.816497 | ||||||||
\(193\) | 15.9706 | 1.14959 | 0.574793 | − | 0.818299i | \(-0.305083\pi\) | ||||
0.574793 | + | 0.818299i | \(0.305083\pi\) | |||||||
\(194\) | −2.58579 | −0.185649 | ||||||||
\(195\) | −8.82843 | −0.632217 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1421 | −1.00759 | −0.503793 | − | 0.863825i | \(-0.668062\pi\) | ||||
−0.503793 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(198\) | −5.41421 | −0.384771 | ||||||||
\(199\) | 7.65685 | 0.542780 | 0.271390 | − | 0.962469i | \(-0.412517\pi\) | ||||
0.271390 | + | 0.962469i | \(0.412517\pi\) | |||||||
\(200\) | 18.8284 | 1.33137 | ||||||||
\(201\) | −10.5858 | −0.746664 | ||||||||
\(202\) | −8.24264 | −0.579950 | ||||||||
\(203\) | 14.4853 | 1.01667 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.24264 | 0.436005 | ||||||||
\(206\) | −0.727922 | −0.0507167 | ||||||||
\(207\) | −6.65685 | −0.462683 | ||||||||
\(208\) | 7.31371 | 0.507114 | ||||||||
\(209\) | −3.17157 | −0.219382 | ||||||||
\(210\) | 23.3137 | 1.60880 | ||||||||
\(211\) | −0.142136 | −0.00978502 | −0.00489251 | − | 0.999988i | \(-0.501557\pi\) | ||||
−0.00489251 | + | 0.999988i | \(0.501557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.48528 | −0.307326 | ||||||||
\(214\) | 0.485281 | 0.0331732 | ||||||||
\(215\) | 3.41421 | 0.232847 | ||||||||
\(216\) | −16.0000 | −1.08866 | ||||||||
\(217\) | 10.2426 | 0.695316 | ||||||||
\(218\) | 28.2426 | 1.91283 | ||||||||
\(219\) | −22.9706 | −1.55221 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.97056 | −0.267089 | ||||||||
\(222\) | −16.9706 | −1.13899 | ||||||||
\(223\) | 4.10051 | 0.274590 | 0.137295 | − | 0.990530i | \(-0.456159\pi\) | ||||
0.137295 | + | 0.990530i | \(0.456159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.65685 | −0.443790 | ||||||||
\(226\) | 9.65685 | 0.642364 | ||||||||
\(227\) | −6.34315 | −0.421009 | −0.210505 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210505 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.9706 | −1.71618 | −0.858092 | − | 0.513497i | \(-0.828350\pi\) | ||||
−0.858092 | + | 0.513497i | \(0.828350\pi\) | |||||||
\(230\) | −32.1421 | −2.11939 | ||||||||
\(231\) | 18.4853 | 1.21624 | ||||||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | 4.82843 | 0.316321 | 0.158160 | − | 0.987413i | \(-0.449444\pi\) | ||||
0.158160 | + | 0.987413i | \(0.449444\pi\) | |||||||
\(234\) | −2.58579 | −0.169038 | ||||||||
\(235\) | 20.4853 | 1.33631 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.82843 | 0.443554 | ||||||||
\(238\) | 10.4853 | 0.679660 | ||||||||
\(239\) | 14.4853 | 0.936975 | 0.468487 | − | 0.883470i | \(-0.344799\pi\) | ||||
0.468487 | + | 0.883470i | \(0.344799\pi\) | |||||||
\(240\) | −19.3137 | −1.24669 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | −5.17157 | −0.332441 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.8995 | 1.01578 | ||||||||
\(246\) | −3.65685 | −0.233153 | ||||||||
\(247\) | −1.51472 | −0.0963792 | ||||||||
\(248\) | −8.48528 | −0.538816 | ||||||||
\(249\) | 4.72792 | 0.299620 | ||||||||
\(250\) | −8.00000 | −0.505964 | ||||||||
\(251\) | 23.1421 | 1.46072 | 0.730359 | − | 0.683063i | \(-0.239353\pi\) | ||||
0.730359 | + | 0.683063i | \(0.239353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.4853 | −1.60225 | ||||||||
\(254\) | −5.41421 | −0.339718 | ||||||||
\(255\) | 10.4853 | 0.656614 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.75736 | −0.109621 | −0.0548105 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548105 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | −28.9706 | −1.80014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.24264 | 0.262613 | ||||||||
\(262\) | −13.6569 | −0.843723 | ||||||||
\(263\) | 0.142136 | 0.00876446 | 0.00438223 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438223 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(264\) | −15.3137 | −0.942494 | ||||||||
\(265\) | 47.2132 | 2.90028 | ||||||||
\(266\) | 4.00000 | 0.245256 | ||||||||
\(267\) | −2.48528 | −0.152097 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 27.3137 | 1.66226 | ||||||||
\(271\) | −25.9706 | −1.57760 | −0.788800 | − | 0.614650i | \(-0.789297\pi\) | ||||
−0.788800 | + | 0.614650i | \(0.789297\pi\) | |||||||
\(272\) | −8.68629 | −0.526684 | ||||||||
\(273\) | 8.82843 | 0.534321 | ||||||||
\(274\) | 20.4853 | 1.23756 | ||||||||
\(275\) | −25.4853 | −1.53682 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.89949 | 0.474635 | 0.237317 | − | 0.971432i | \(-0.423732\pi\) | ||||
0.237317 | + | 0.971432i | \(0.423732\pi\) | |||||||
\(278\) | −7.75736 | −0.465255 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | −32.9706 | −1.97037 | ||||||||
\(281\) | −8.65685 | −0.516425 | −0.258212 | − | 0.966088i | \(-0.583133\pi\) | ||||
−0.258212 | + | 0.966088i | \(0.583133\pi\) | |||||||
\(282\) | −12.0000 | −0.714590 | ||||||||
\(283\) | 18.3137 | 1.08864 | 0.544318 | − | 0.838879i | \(-0.316788\pi\) | ||||
0.544318 | + | 0.838879i | \(0.316788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | −9.89949 | −0.585369 | ||||||||
\(287\) | −6.24264 | −0.368491 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2843 | −0.722604 | ||||||||
\(290\) | 20.4853 | 1.20294 | ||||||||
\(291\) | 2.58579 | 0.151581 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3431 | 0.604253 | 0.302127 | − | 0.953268i | \(-0.402303\pi\) | ||||
0.302127 | + | 0.953268i | \(0.402303\pi\) | |||||||
\(294\) | −9.31371 | −0.543187 | ||||||||
\(295\) | −16.4853 | −0.959810 | ||||||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | 21.6569 | 1.25666 | ||||||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | −12.1716 | −0.703900 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.41421 | −0.196792 | ||||||||
\(302\) | −25.7990 | −1.48457 | ||||||||
\(303\) | 8.24264 | 0.473527 | ||||||||
\(304\) | −3.31371 | −0.190054 | ||||||||
\(305\) | −0.828427 | −0.0474356 | ||||||||
\(306\) | 3.07107 | 0.175561 | ||||||||
\(307\) | 26.7990 | 1.52950 | 0.764750 | − | 0.644328i | \(-0.222863\pi\) | ||||
0.764750 | + | 0.644328i | \(0.222863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.727922 | 0.0414100 | ||||||||
\(310\) | 14.4853 | 0.822709 | ||||||||
\(311\) | −13.9706 | −0.792198 | −0.396099 | − | 0.918208i | \(-0.629636\pi\) | ||||
−0.396099 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(312\) | −7.31371 | −0.414057 | ||||||||
\(313\) | −25.2132 | −1.42513 | −0.712567 | − | 0.701604i | \(-0.752468\pi\) | ||||
−0.712567 | + | 0.701604i | \(0.752468\pi\) | |||||||
\(314\) | 14.1421 | 0.798087 | ||||||||
\(315\) | 11.6569 | 0.656789 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.8284 | 1.45067 | 0.725334 | − | 0.688397i | \(-0.241685\pi\) | ||||
0.725334 | + | 0.688397i | \(0.241685\pi\) | |||||||
\(318\) | −27.6569 | −1.55092 | ||||||||
\(319\) | 16.2426 | 0.909413 | ||||||||
\(320\) | 27.3137 | 1.52688 | ||||||||
\(321\) | −0.485281 | −0.0270858 | ||||||||
\(322\) | 32.1421 | 1.79121 | ||||||||
\(323\) | 1.79899 | 0.100098 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1716 | −0.675157 | ||||||||
\(326\) | 16.6274 | 0.920907 | ||||||||
\(327\) | −28.2426 | −1.56182 | ||||||||
\(328\) | 5.17157 | 0.285552 | ||||||||
\(329\) | −20.4853 | −1.12939 | ||||||||
\(330\) | 26.1421 | 1.43908 | ||||||||
\(331\) | 21.4142 | 1.17703 | 0.588516 | − | 0.808486i | \(-0.299712\pi\) | ||||
0.588516 | + | 0.808486i | \(0.299712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.48528 | −0.464991 | ||||||||
\(334\) | 20.2426 | 1.10763 | ||||||||
\(335\) | −25.5563 | −1.39629 | ||||||||
\(336\) | 19.3137 | 1.05365 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 13.6569 | 0.742835 | ||||||||
\(339\) | −9.65685 | −0.524488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4853 | 0.621963 | ||||||||
\(342\) | 1.17157 | 0.0633514 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 2.82843 | 0.152499 | ||||||||
\(345\) | 32.1421 | 1.73047 | ||||||||
\(346\) | −33.4558 | −1.79860 | ||||||||
\(347\) | −4.58579 | −0.246178 | −0.123089 | − | 0.992396i | \(-0.539280\pi\) | ||||
−0.123089 | + | 0.992396i | \(0.539280\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2426 | −1.08356 | −0.541782 | − | 0.840519i | \(-0.682250\pi\) | ||||
−0.541782 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(350\) | 32.1421 | 1.71807 | ||||||||
\(351\) | 10.3431 | 0.552076 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.82843 | 0.310216 | 0.155108 | − | 0.987898i | \(-0.450427\pi\) | ||||
0.155108 | + | 0.987898i | \(0.450427\pi\) | |||||||
\(354\) | 9.65685 | 0.513256 | ||||||||
\(355\) | −10.8284 | −0.574713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.4853 | −0.554940 | ||||||||
\(358\) | 6.48528 | 0.342758 | ||||||||
\(359\) | −21.3431 | −1.12645 | −0.563224 | − | 0.826304i | \(-0.690439\pi\) | ||||
−0.563224 | + | 0.826304i | \(0.690439\pi\) | |||||||
\(360\) | −9.65685 | −0.508961 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | −10.3431 | −0.543624 | ||||||||
\(363\) | 5.17157 | 0.271437 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −55.4558 | −2.90269 | ||||||||
\(366\) | 0.485281 | 0.0253661 | ||||||||
\(367\) | 9.79899 | 0.511503 | 0.255752 | − | 0.966743i | \(-0.417677\pi\) | ||||
0.255752 | + | 0.966743i | \(0.417677\pi\) | |||||||
\(368\) | −26.6274 | −1.38805 | ||||||||
\(369\) | −1.82843 | −0.0951841 | ||||||||
\(370\) | −40.9706 | −2.12996 | ||||||||
\(371\) | −47.2132 | −2.45119 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.48528 | 0.439351 | 0.219676 | − | 0.975573i | \(-0.429500\pi\) | ||||
0.219676 | + | 0.975573i | \(0.429500\pi\) | |||||||
\(374\) | 11.7574 | 0.607959 | ||||||||
\(375\) | 8.00000 | 0.413118 | ||||||||
\(376\) | 16.9706 | 0.875190 | ||||||||
\(377\) | 7.75736 | 0.399524 | ||||||||
\(378\) | −27.3137 | −1.40487 | ||||||||
\(379\) | 30.3137 | 1.55711 | 0.778555 | − | 0.627576i | \(-0.215953\pi\) | ||||
0.778555 | + | 0.627576i | \(0.215953\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.41421 | 0.277379 | ||||||||
\(382\) | 8.68629 | 0.444429 | ||||||||
\(383\) | −20.4853 | −1.04675 | −0.523374 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523374 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(384\) | −16.0000 | −0.816497 | ||||||||
\(385\) | 44.6274 | 2.27442 | ||||||||
\(386\) | −22.5858 | −1.14959 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6274 | −0.843044 | −0.421522 | − | 0.906818i | \(-0.638504\pi\) | ||||
−0.421522 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(390\) | 12.4853 | 0.632217 | ||||||||
\(391\) | 14.4558 | 0.731063 | ||||||||
\(392\) | 13.1716 | 0.665265 | ||||||||
\(393\) | 13.6569 | 0.688897 | ||||||||
\(394\) | 20.0000 | 1.00759 | ||||||||
\(395\) | 16.4853 | 0.829465 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4558 | 1.47835 | 0.739173 | − | 0.673515i | \(-0.235216\pi\) | ||||
0.739173 | + | 0.673515i | \(0.235216\pi\) | |||||||
\(398\) | −10.8284 | −0.542780 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | −26.6274 | −1.33137 | ||||||||
\(401\) | −12.5147 | −0.624955 | −0.312478 | − | 0.949925i | \(-0.601159\pi\) | ||||
−0.312478 | + | 0.949925i | \(0.601159\pi\) | |||||||
\(402\) | 14.9706 | 0.746664 | ||||||||
\(403\) | 5.48528 | 0.273241 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.0711 | −0.848268 | ||||||||
\(406\) | −20.4853 | −1.01667 | ||||||||
\(407\) | −32.4853 | −1.61024 | ||||||||
\(408\) | 8.68629 | 0.430036 | ||||||||
\(409\) | −16.8701 | −0.834171 | −0.417085 | − | 0.908867i | \(-0.636948\pi\) | ||||
−0.417085 | + | 0.908867i | \(0.636948\pi\) | |||||||
\(410\) | −8.82843 | −0.436005 | ||||||||
\(411\) | −20.4853 | −1.01046 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.4853 | 0.811188 | ||||||||
\(414\) | 9.41421 | 0.462683 | ||||||||
\(415\) | 11.4142 | 0.560302 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.75736 | 0.379880 | ||||||||
\(418\) | 4.48528 | 0.219382 | ||||||||
\(419\) | −23.8995 | −1.16757 | −0.583783 | − | 0.811909i | \(-0.698428\pi\) | ||||
−0.583783 | + | 0.811909i | \(0.698428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6569 | −0.763068 | −0.381534 | − | 0.924355i | \(-0.624604\pi\) | ||||
−0.381534 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(422\) | 0.201010 | 0.00978502 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 39.1127 | 1.89948 | ||||||||
\(425\) | 14.4558 | 0.701211 | ||||||||
\(426\) | 6.34315 | 0.307326 | ||||||||
\(427\) | 0.828427 | 0.0400904 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.89949 | 0.477952 | ||||||||
\(430\) | −4.82843 | −0.232847 | ||||||||
\(431\) | 23.2843 | 1.12156 | 0.560782 | − | 0.827964i | \(-0.310501\pi\) | ||||
0.560782 | + | 0.827964i | \(0.310501\pi\) | |||||||
\(432\) | 22.6274 | 1.08866 | ||||||||
\(433\) | 21.7574 | 1.04559 | 0.522796 | − | 0.852458i | \(-0.324889\pi\) | ||||
0.522796 | + | 0.852458i | \(0.324889\pi\) | |||||||
\(434\) | −14.4853 | −0.695316 | ||||||||
\(435\) | −20.4853 | −0.982194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.51472 | 0.263805 | ||||||||
\(438\) | 32.4853 | 1.55221 | ||||||||
\(439\) | 11.4853 | 0.548163 | 0.274081 | − | 0.961707i | \(-0.411626\pi\) | ||||
0.274081 | + | 0.961707i | \(0.411626\pi\) | |||||||
\(440\) | −36.9706 | −1.76250 | ||||||||
\(441\) | −4.65685 | −0.221755 | ||||||||
\(442\) | 5.61522 | 0.267089 | ||||||||
\(443\) | 7.85786 | 0.373338 | 0.186669 | − | 0.982423i | \(-0.440231\pi\) | ||||
0.186669 | + | 0.982423i | \(0.440231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −5.79899 | −0.274590 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | −27.3137 | −1.29045 | ||||||||
\(449\) | 33.2132 | 1.56743 | 0.783714 | − | 0.621122i | \(-0.213323\pi\) | ||||
0.783714 | + | 0.621122i | \(0.213323\pi\) | |||||||
\(450\) | 9.41421 | 0.443790 | ||||||||
\(451\) | −7.00000 | −0.329617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.7990 | 1.21214 | ||||||||
\(454\) | 8.97056 | 0.421009 | ||||||||
\(455\) | 21.3137 | 0.999202 | ||||||||
\(456\) | 3.31371 | 0.155179 | ||||||||
\(457\) | 0.727922 | 0.0340508 | 0.0170254 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170254 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(458\) | 36.7279 | 1.71618 | ||||||||
\(459\) | −12.2843 | −0.573381 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.6274 | 1.98536 | 0.992678 | − | 0.120788i | \(-0.0385420\pi\) | ||||
0.992678 | + | 0.120788i | \(0.0385420\pi\) | |||||||
\(462\) | −26.1421 | −1.21624 | ||||||||
\(463\) | −30.7279 | −1.42805 | −0.714024 | − | 0.700121i | \(-0.753129\pi\) | ||||
−0.714024 | + | 0.700121i | \(0.753129\pi\) | |||||||
\(464\) | 16.9706 | 0.787839 | ||||||||
\(465\) | −14.4853 | −0.671739 | ||||||||
\(466\) | −6.82843 | −0.316321 | ||||||||
\(467\) | 23.6569 | 1.09471 | 0.547354 | − | 0.836901i | \(-0.315635\pi\) | ||||
0.547354 | + | 0.836901i | \(0.315635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.5563 | 1.18008 | ||||||||
\(470\) | −28.9706 | −1.33631 | ||||||||
\(471\) | −14.1421 | −0.651635 | ||||||||
\(472\) | −13.6569 | −0.628608 | ||||||||
\(473\) | −3.82843 | −0.176031 | ||||||||
\(474\) | −9.65685 | −0.443554 | ||||||||
\(475\) | 5.51472 | 0.253033 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.8284 | −0.633160 | ||||||||
\(478\) | −20.4853 | −0.936975 | ||||||||
\(479\) | −6.65685 | −0.304159 | −0.152080 | − | 0.988368i | \(-0.548597\pi\) | ||||
−0.152080 | + | 0.988368i | \(0.548597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.5147 | −0.707410 | ||||||||
\(482\) | −5.65685 | −0.257663 | ||||||||
\(483\) | −32.1421 | −1.46252 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.24264 | 0.283464 | ||||||||
\(486\) | −14.0000 | −0.635053 | ||||||||
\(487\) | 22.3431 | 1.01246 | 0.506232 | − | 0.862397i | \(-0.331038\pi\) | ||||
0.506232 | + | 0.862397i | \(0.331038\pi\) | |||||||
\(488\) | −0.686292 | −0.0310670 | ||||||||
\(489\) | −16.6274 | −0.751918 | ||||||||
\(490\) | −22.4853 | −1.01578 | ||||||||
\(491\) | 13.4142 | 0.605375 | 0.302687 | − | 0.953090i | \(-0.402116\pi\) | ||||
0.302687 | + | 0.953090i | \(0.402116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.21320 | −0.414942 | ||||||||
\(494\) | 2.14214 | 0.0963792 | ||||||||
\(495\) | 13.0711 | 0.587501 | ||||||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | 10.8284 | 0.485721 | ||||||||
\(498\) | −6.68629 | −0.299620 | ||||||||
\(499\) | −25.7574 | −1.15306 | −0.576529 | − | 0.817077i | \(-0.695593\pi\) | ||||
−0.576529 | + | 0.817077i | \(0.695593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.2426 | −0.904374 | ||||||||
\(502\) | −32.7279 | −1.46072 | ||||||||
\(503\) | −30.7696 | −1.37195 | −0.685973 | − | 0.727627i | \(-0.740623\pi\) | ||||
−0.685973 | + | 0.727627i | \(0.740623\pi\) | |||||||
\(504\) | 9.65685 | 0.430150 | ||||||||
\(505\) | 19.8995 | 0.885516 | ||||||||
\(506\) | 36.0416 | 1.60225 | ||||||||
\(507\) | −13.6569 | −0.606522 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.514719 | 0.0228145 | 0.0114073 | − | 0.999935i | \(-0.496369\pi\) | ||||
0.0114073 | + | 0.999935i | \(0.496369\pi\) | |||||||
\(510\) | −14.8284 | −0.656614 | ||||||||
\(511\) | 55.4558 | 2.45322 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −4.68629 | −0.206905 | ||||||||
\(514\) | 2.48528 | 0.109621 | ||||||||
\(515\) | 1.75736 | 0.0774385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.9706 | −1.01024 | ||||||||
\(518\) | 40.9706 | 1.80014 | ||||||||
\(519\) | 33.4558 | 1.46855 | ||||||||
\(520\) | −17.6569 | −0.774304 | ||||||||
\(521\) | 16.9289 | 0.741670 | 0.370835 | − | 0.928699i | \(-0.379072\pi\) | ||||
0.370835 | + | 0.928699i | \(0.379072\pi\) | |||||||
\(522\) | −6.00000 | −0.262613 | ||||||||
\(523\) | −39.2132 | −1.71467 | −0.857337 | − | 0.514756i | \(-0.827883\pi\) | ||||
−0.857337 | + | 0.514756i | \(0.827883\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −32.1421 | −1.40280 | ||||||||
\(526\) | −0.201010 | −0.00876446 | ||||||||
\(527\) | −6.51472 | −0.283786 | ||||||||
\(528\) | 21.6569 | 0.942494 | ||||||||
\(529\) | 21.3137 | 0.926683 | ||||||||
\(530\) | −66.7696 | −2.90028 | ||||||||
\(531\) | 4.82843 | 0.209536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.34315 | −0.144808 | ||||||||
\(534\) | 3.51472 | 0.152097 | ||||||||
\(535\) | −1.17157 | −0.0506515 | ||||||||
\(536\) | −21.1716 | −0.914473 | ||||||||
\(537\) | −6.48528 | −0.279861 | ||||||||
\(538\) | 4.24264 | 0.182913 | ||||||||
\(539\) | −17.8284 | −0.767925 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.79899 | 0.378298 | 0.189149 | − | 0.981948i | \(-0.439427\pi\) | ||||
0.189149 | + | 0.981948i | \(0.439427\pi\) | |||||||
\(542\) | 36.7279 | 1.57760 | ||||||||
\(543\) | 10.3431 | 0.443867 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −68.1838 | −2.92067 | ||||||||
\(546\) | −12.4853 | −0.534321 | ||||||||
\(547\) | 9.00000 | 0.384812 | 0.192406 | − | 0.981315i | \(-0.438371\pi\) | ||||
0.192406 | + | 0.981315i | \(0.438371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.242641 | 0.0103557 | ||||||||
\(550\) | 36.0416 | 1.53682 | ||||||||
\(551\) | −3.51472 | −0.149732 | ||||||||
\(552\) | 26.6274 | 1.13334 | ||||||||
\(553\) | −16.4853 | −0.701025 | ||||||||
\(554\) | −11.1716 | −0.474635 | ||||||||
\(555\) | 40.9706 | 1.73910 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | −0.381342 | −0.190671 | − | 0.981654i | \(-0.561066\pi\) | ||||
−0.190671 | + | 0.981654i | \(0.561066\pi\) | |||||||
\(558\) | −4.24264 | −0.179605 | ||||||||
\(559\) | −1.82843 | −0.0773342 | ||||||||
\(560\) | 46.6274 | 1.97037 | ||||||||
\(561\) | −11.7574 | −0.496396 | ||||||||
\(562\) | 12.2426 | 0.516425 | ||||||||
\(563\) | 39.6274 | 1.67010 | 0.835048 | − | 0.550177i | \(-0.185440\pi\) | ||||
0.835048 | + | 0.550177i | \(0.185440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.3137 | −0.980815 | ||||||||
\(566\) | −25.8995 | −1.08864 | ||||||||
\(567\) | 17.0711 | 0.716917 | ||||||||
\(568\) | −8.97056 | −0.376396 | ||||||||
\(569\) | 13.3431 | 0.559374 | 0.279687 | − | 0.960091i | \(-0.409769\pi\) | ||||
0.279687 | + | 0.960091i | \(0.409769\pi\) | |||||||
\(570\) | −5.65685 | −0.236940 | ||||||||
\(571\) | −3.07107 | −0.128520 | −0.0642601 | − | 0.997933i | \(-0.520469\pi\) | ||||
−0.0642601 | + | 0.997933i | \(0.520469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.68629 | −0.362875 | ||||||||
\(574\) | 8.82843 | 0.368491 | ||||||||
\(575\) | 44.3137 | 1.84801 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 33.0711 | 1.37677 | 0.688383 | − | 0.725347i | \(-0.258321\pi\) | ||||
0.688383 | + | 0.725347i | \(0.258321\pi\) | |||||||
\(578\) | 17.3726 | 0.722604 | ||||||||
\(579\) | 22.5858 | 0.938633 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4142 | −0.473541 | ||||||||
\(582\) | −3.65685 | −0.151581 | ||||||||
\(583\) | −52.9411 | −2.19260 | ||||||||
\(584\) | −45.9411 | −1.90106 | ||||||||
\(585\) | 6.24264 | 0.258101 | ||||||||
\(586\) | −14.6274 | −0.604253 | ||||||||
\(587\) | 33.7990 | 1.39503 | 0.697517 | − | 0.716568i | \(-0.254288\pi\) | ||||
0.697517 | + | 0.716568i | \(0.254288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.48528 | −0.102404 | ||||||||
\(590\) | 23.3137 | 0.959810 | ||||||||
\(591\) | −20.0000 | −0.822690 | ||||||||
\(592\) | −33.9411 | −1.39497 | ||||||||
\(593\) | −9.07107 | −0.372504 | −0.186252 | − | 0.982502i | \(-0.559634\pi\) | ||||
−0.186252 | + | 0.982502i | \(0.559634\pi\) | |||||||
\(594\) | −30.6274 | −1.25666 | ||||||||
\(595\) | −25.3137 | −1.03776 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8284 | 0.443178 | ||||||||
\(598\) | 17.2132 | 0.703900 | ||||||||
\(599\) | 36.6569 | 1.49776 | 0.748879 | − | 0.662706i | \(-0.230592\pi\) | ||||
0.748879 | + | 0.662706i | \(0.230592\pi\) | |||||||
\(600\) | 26.6274 | 1.08706 | ||||||||
\(601\) | −24.9706 | −1.01857 | −0.509285 | − | 0.860598i | \(-0.670090\pi\) | ||||
−0.509285 | + | 0.860598i | \(0.670090\pi\) | |||||||
\(602\) | 4.82843 | 0.196792 | ||||||||
\(603\) | 7.48528 | 0.304824 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4853 | 0.507599 | ||||||||
\(606\) | −11.6569 | −0.473527 | ||||||||
\(607\) | −32.9706 | −1.33823 | −0.669117 | − | 0.743157i | \(-0.733327\pi\) | ||||
−0.669117 | + | 0.743157i | \(0.733327\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.4853 | 0.830105 | ||||||||
\(610\) | 1.17157 | 0.0474356 | ||||||||
\(611\) | −10.9706 | −0.443821 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.82843 | 0.275798 | 0.137899 | − | 0.990446i | \(-0.455965\pi\) | ||||
0.137899 | + | 0.990446i | \(0.455965\pi\) | |||||||
\(614\) | −37.8995 | −1.52950 | ||||||||
\(615\) | 8.82843 | 0.355997 | ||||||||
\(616\) | 36.9706 | 1.48959 | ||||||||
\(617\) | 19.9706 | 0.803985 | 0.401992 | − | 0.915643i | \(-0.368318\pi\) | ||||
0.401992 | + | 0.915643i | \(0.368318\pi\) | |||||||
\(618\) | −1.02944 | −0.0414100 | ||||||||
\(619\) | 28.9706 | 1.16443 | 0.582213 | − | 0.813037i | \(-0.302187\pi\) | ||||
0.582213 | + | 0.813037i | \(0.302187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −37.6569 | −1.51112 | ||||||||
\(622\) | 19.7574 | 0.792198 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 10.3431 | 0.414057 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 35.6569 | 1.42513 | ||||||||
\(627\) | −4.48528 | −0.179125 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.4264 | 0.734709 | ||||||||
\(630\) | −16.4853 | −0.656789 | ||||||||
\(631\) | 46.7696 | 1.86187 | 0.930933 | − | 0.365189i | \(-0.118996\pi\) | ||||
0.930933 | + | 0.365189i | \(0.118996\pi\) | |||||||
\(632\) | 13.6569 | 0.543240 | ||||||||
\(633\) | −0.201010 | −0.00798944 | ||||||||
\(634\) | −36.5269 | −1.45067 | ||||||||
\(635\) | 13.0711 | 0.518710 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.51472 | −0.337365 | ||||||||
\(638\) | −22.9706 | −0.909413 | ||||||||
\(639\) | 3.17157 | 0.125465 | ||||||||
\(640\) | −38.6274 | −1.52688 | ||||||||
\(641\) | −29.5563 | −1.16741 | −0.583703 | − | 0.811967i | \(-0.698397\pi\) | ||||
−0.583703 | + | 0.811967i | \(0.698397\pi\) | |||||||
\(642\) | 0.686292 | 0.0270858 | ||||||||
\(643\) | −26.4853 | −1.04448 | −0.522239 | − | 0.852799i | \(-0.674903\pi\) | ||||
−0.522239 | + | 0.852799i | \(0.674903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.82843 | 0.190119 | ||||||||
\(646\) | −2.54416 | −0.100098 | ||||||||
\(647\) | −1.17157 | −0.0460593 | −0.0230296 | − | 0.999735i | \(-0.507331\pi\) | ||||
−0.0230296 | + | 0.999735i | \(0.507331\pi\) | |||||||
\(648\) | −14.1421 | −0.555556 | ||||||||
\(649\) | 18.4853 | 0.725611 | ||||||||
\(650\) | 17.2132 | 0.675157 | ||||||||
\(651\) | 14.4853 | 0.567723 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.1716 | 0.593710 | 0.296855 | − | 0.954923i | \(-0.404062\pi\) | ||||
0.296855 | + | 0.954923i | \(0.404062\pi\) | |||||||
\(654\) | 39.9411 | 1.56182 | ||||||||
\(655\) | 32.9706 | 1.28827 | ||||||||
\(656\) | −7.31371 | −0.285552 | ||||||||
\(657\) | 16.2426 | 0.633686 | ||||||||
\(658\) | 28.9706 | 1.12939 | ||||||||
\(659\) | 16.3137 | 0.635492 | 0.317746 | − | 0.948176i | \(-0.397074\pi\) | ||||
0.317746 | + | 0.948176i | \(0.397074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | −0.661223 | −0.330612 | − | 0.943767i | \(-0.607255\pi\) | ||||
−0.330612 | + | 0.943767i | \(0.607255\pi\) | |||||||
\(662\) | −30.2843 | −1.17703 | ||||||||
\(663\) | −5.61522 | −0.218077 | ||||||||
\(664\) | 9.45584 | 0.366958 | ||||||||
\(665\) | −9.65685 | −0.374477 | ||||||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | −28.2426 | −1.09356 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.79899 | 0.224202 | ||||||||
\(670\) | 36.1421 | 1.39629 | ||||||||
\(671\) | 0.928932 | 0.0358610 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7279 | −0.644814 | −0.322407 | − | 0.946601i | \(-0.604492\pi\) | ||||
−0.322407 | + | 0.946601i | \(0.604492\pi\) | |||||||
\(674\) | 7.07107 | 0.272367 | ||||||||
\(675\) | −37.6569 | −1.44941 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1716 | 0.429358 | 0.214679 | − | 0.976685i | \(-0.431129\pi\) | ||||
0.214679 | + | 0.976685i | \(0.431129\pi\) | |||||||
\(678\) | 13.6569 | 0.524488 | ||||||||
\(679\) | −6.24264 | −0.239571 | ||||||||
\(680\) | 20.9706 | 0.804184 | ||||||||
\(681\) | −8.97056 | −0.343753 | ||||||||
\(682\) | −16.2426 | −0.621963 | ||||||||
\(683\) | −46.4558 | −1.77758 | −0.888792 | − | 0.458311i | \(-0.848454\pi\) | ||||
−0.888792 | + | 0.458311i | \(0.848454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.4558 | −1.88961 | ||||||||
\(686\) | −11.3137 | −0.431959 | ||||||||
\(687\) | −36.7279 | −1.40126 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | −25.2843 | −0.963254 | ||||||||
\(690\) | −45.4558 | −1.73047 | ||||||||
\(691\) | −26.7279 | −1.01678 | −0.508389 | − | 0.861128i | \(-0.669759\pi\) | ||||
−0.508389 | + | 0.861128i | \(0.669759\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.0711 | −0.496529 | ||||||||
\(694\) | 6.48528 | 0.246178 | ||||||||
\(695\) | 18.7279 | 0.710391 | ||||||||
\(696\) | −16.9706 | −0.643268 | ||||||||
\(697\) | 3.97056 | 0.150396 | ||||||||
\(698\) | 28.6274 | 1.08356 | ||||||||
\(699\) | 6.82843 | 0.258275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6569 | −1.12012 | −0.560062 | − | 0.828451i | \(-0.689223\pi\) | ||||
−0.560062 | + | 0.828451i | \(0.689223\pi\) | |||||||
\(702\) | −14.6274 | −0.552076 | ||||||||
\(703\) | 7.02944 | 0.265120 | ||||||||
\(704\) | −30.6274 | −1.15431 | ||||||||
\(705\) | 28.9706 | 1.09109 | ||||||||
\(706\) | −8.24264 | −0.310216 | ||||||||
\(707\) | −19.8995 | −0.748398 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.1127 | −1.43135 | −0.715676 | − | 0.698432i | \(-0.753881\pi\) | ||||
−0.715676 | + | 0.698432i | \(0.753881\pi\) | |||||||
\(710\) | 15.3137 | 0.574713 | ||||||||
\(711\) | −4.82843 | −0.181080 | ||||||||
\(712\) | −4.97056 | −0.186280 | ||||||||
\(713\) | −19.9706 | −0.747903 | ||||||||
\(714\) | 14.8284 | 0.554940 | ||||||||
\(715\) | 23.8995 | 0.893790 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.4853 | 0.765037 | ||||||||
\(718\) | 30.1838 | 1.12645 | ||||||||
\(719\) | −22.6274 | −0.843860 | −0.421930 | − | 0.906628i | \(-0.638647\pi\) | ||||
−0.421930 | + | 0.906628i | \(0.638647\pi\) | |||||||
\(720\) | 13.6569 | 0.508961 | ||||||||
\(721\) | −1.75736 | −0.0654475 | ||||||||
\(722\) | 25.8995 | 0.963879 | ||||||||
\(723\) | 5.65685 | 0.210381 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.2426 | −1.04891 | ||||||||
\(726\) | −7.31371 | −0.271437 | ||||||||
\(727\) | −24.9706 | −0.926107 | −0.463053 | − | 0.886330i | \(-0.653246\pi\) | ||||
−0.463053 | + | 0.886330i | \(0.653246\pi\) | |||||||
\(728\) | 17.6569 | 0.654407 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 78.4264 | 2.90269 | ||||||||
\(731\) | 2.17157 | 0.0803185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9706 | 0.626822 | 0.313411 | − | 0.949618i | \(-0.398528\pi\) | ||||
0.313411 | + | 0.949618i | \(0.398528\pi\) | |||||||
\(734\) | −13.8579 | −0.511503 | ||||||||
\(735\) | 22.4853 | 0.829382 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.6569 | 1.05559 | ||||||||
\(738\) | 2.58579 | 0.0951841 | ||||||||
\(739\) | −39.4558 | −1.45141 | −0.725703 | − | 0.688008i | \(-0.758485\pi\) | ||||
−0.725703 | + | 0.688008i | \(0.758485\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.14214 | −0.0786933 | ||||||||
\(742\) | 66.7696 | 2.45119 | ||||||||
\(743\) | 15.1127 | 0.554431 | 0.277216 | − | 0.960808i | \(-0.410588\pi\) | ||||
0.277216 | + | 0.960808i | \(0.410588\pi\) | |||||||
\(744\) | −12.0000 | −0.439941 | ||||||||
\(745\) | 28.9706 | 1.06140 | ||||||||
\(746\) | −12.0000 | −0.439351 | ||||||||
\(747\) | −3.34315 | −0.122319 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.17157 | 0.0428083 | ||||||||
\(750\) | −11.3137 | −0.413118 | ||||||||
\(751\) | −11.7574 | −0.429032 | −0.214516 | − | 0.976720i | \(-0.568817\pi\) | ||||
−0.214516 | + | 0.976720i | \(0.568817\pi\) | |||||||
\(752\) | −24.0000 | −0.875190 | ||||||||
\(753\) | 32.7279 | 1.19267 | ||||||||
\(754\) | −10.9706 | −0.399524 | ||||||||
\(755\) | 62.2843 | 2.26676 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.51472 | 0.127745 | 0.0638723 | − | 0.997958i | \(-0.479655\pi\) | ||||
0.0638723 | + | 0.997958i | \(0.479655\pi\) | |||||||
\(758\) | −42.8701 | −1.55711 | ||||||||
\(759\) | −36.0416 | −1.30823 | ||||||||
\(760\) | 8.00000 | 0.290191 | ||||||||
\(761\) | 19.1127 | 0.692835 | 0.346417 | − | 0.938080i | \(-0.387398\pi\) | ||||
0.346417 | + | 0.938080i | \(0.387398\pi\) | |||||||
\(762\) | −7.65685 | −0.277379 | ||||||||
\(763\) | 68.1838 | 2.46842 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.41421 | −0.268061 | ||||||||
\(766\) | 28.9706 | 1.04675 | ||||||||
\(767\) | 8.82843 | 0.318776 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.7696 | 1.61443 | 0.807216 | − | 0.590257i | \(-0.200973\pi\) | ||||
0.807216 | + | 0.590257i | \(0.200973\pi\) | |||||||
\(770\) | −63.1127 | −2.27442 | ||||||||
\(771\) | −2.48528 | −0.0895052 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.10051 | 0.291355 | 0.145677 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145677 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(774\) | 1.41421 | 0.0508329 | ||||||||
\(775\) | −19.9706 | −0.717364 | ||||||||
\(776\) | 5.17157 | 0.185649 | ||||||||
\(777\) | −40.9706 | −1.46981 | ||||||||
\(778\) | 23.5147 | 0.843044 | ||||||||
\(779\) | 1.51472 | 0.0542704 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.1421 | 0.434480 | ||||||||
\(782\) | −20.4437 | −0.731063 | ||||||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | −18.6274 | −0.665265 | ||||||||
\(785\) | −34.1421 | −1.21859 | ||||||||
\(786\) | −19.3137 | −0.688897 | ||||||||
\(787\) | 9.79899 | 0.349296 | 0.174648 | − | 0.984631i | \(-0.444121\pi\) | ||||
0.174648 | + | 0.984631i | \(0.444121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.201010 | 0.00715615 | ||||||||
\(790\) | −23.3137 | −0.829465 | ||||||||
\(791\) | 23.3137 | 0.828940 | ||||||||
\(792\) | 10.8284 | 0.384771 | ||||||||
\(793\) | 0.443651 | 0.0157545 | ||||||||
\(794\) | −41.6569 | −1.47835 | ||||||||
\(795\) | 66.7696 | 2.36807 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3137 | 1.25088 | 0.625438 | − | 0.780274i | \(-0.284920\pi\) | ||||
0.625438 | + | 0.780274i | \(0.284920\pi\) | |||||||
\(798\) | 5.65685 | 0.200250 | ||||||||
\(799\) | 13.0294 | 0.460948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.75736 | 0.0620932 | ||||||||
\(802\) | 17.6985 | 0.624955 | ||||||||
\(803\) | 62.1838 | 2.19442 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −77.5980 | −2.73497 | ||||||||
\(806\) | −7.75736 | −0.273241 | ||||||||
\(807\) | −4.24264 | −0.149348 | ||||||||
\(808\) | 16.4853 | 0.579950 | ||||||||
\(809\) | −5.65685 | −0.198884 | −0.0994422 | − | 0.995043i | \(-0.531706\pi\) | ||||
−0.0994422 | + | 0.995043i | \(0.531706\pi\) | |||||||
\(810\) | 24.1421 | 0.848268 | ||||||||
\(811\) | 23.2721 | 0.817193 | 0.408597 | − | 0.912715i | \(-0.366018\pi\) | ||||
0.408597 | + | 0.912715i | \(0.366018\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.7279 | −1.28810 | ||||||||
\(814\) | 45.9411 | 1.61024 | ||||||||
\(815\) | −40.1421 | −1.40612 | ||||||||
\(816\) | −12.2843 | −0.430036 | ||||||||
\(817\) | 0.828427 | 0.0289830 | ||||||||
\(818\) | 23.8579 | 0.834171 | ||||||||
\(819\) | −6.24264 | −0.218136 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.1127 | −1.81875 | −0.909373 | − | 0.415982i | \(-0.863438\pi\) | ||||
−0.909373 | + | 0.415982i | \(0.863438\pi\) | |||||||
\(822\) | 28.9706 | 1.01046 | ||||||||
\(823\) | −54.6569 | −1.90522 | −0.952609 | − | 0.304197i | \(-0.901612\pi\) | ||||
−0.952609 | + | 0.304197i | \(0.901612\pi\) | |||||||
\(824\) | 1.45584 | 0.0507167 | ||||||||
\(825\) | −36.0416 | −1.25481 | ||||||||
\(826\) | −23.3137 | −0.811188 | ||||||||
\(827\) | −1.65685 | −0.0576145 | −0.0288072 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288072 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.7990 | 0.826573 | 0.413287 | − | 0.910601i | \(-0.364381\pi\) | ||||
0.413287 | + | 0.910601i | \(0.364381\pi\) | |||||||
\(830\) | −16.1421 | −0.560302 | ||||||||
\(831\) | 11.1716 | 0.387538 | ||||||||
\(832\) | −14.6274 | −0.507114 | ||||||||
\(833\) | 10.1127 | 0.350384 | ||||||||
\(834\) | −10.9706 | −0.379880 | ||||||||
\(835\) | −48.8701 | −1.69122 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.9706 | 0.586588 | ||||||||
\(838\) | 33.7990 | 1.16757 | ||||||||
\(839\) | −48.8701 | −1.68718 | −0.843591 | − | 0.536986i | \(-0.819563\pi\) | ||||
−0.843591 | + | 0.536986i | \(0.819563\pi\) | |||||||
\(840\) | −46.6274 | −1.60880 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 22.1421 | 0.763068 | ||||||||
\(843\) | −12.2426 | −0.421659 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.9706 | −1.13422 | ||||||||
\(846\) | 8.48528 | 0.291730 | ||||||||
\(847\) | −12.4853 | −0.428999 | ||||||||
\(848\) | −55.3137 | −1.89948 | ||||||||
\(849\) | 25.8995 | 0.888868 | ||||||||
\(850\) | −20.4437 | −0.701211 | ||||||||
\(851\) | 56.4853 | 1.93629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.5980 | 1.59548 | 0.797742 | − | 0.602999i | \(-0.206028\pi\) | ||||
0.797742 | + | 0.602999i | \(0.206028\pi\) | |||||||
\(854\) | −1.17157 | −0.0400904 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | −0.970563 | −0.0331732 | ||||||||
\(857\) | 7.65685 | 0.261553 | 0.130777 | − | 0.991412i | \(-0.458253\pi\) | ||||
0.130777 | + | 0.991412i | \(0.458253\pi\) | |||||||
\(858\) | −14.0000 | −0.477952 | ||||||||
\(859\) | 16.9706 | 0.579028 | 0.289514 | − | 0.957174i | \(-0.406506\pi\) | ||||
0.289514 | + | 0.957174i | \(0.406506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.82843 | −0.300872 | ||||||||
\(862\) | −32.9289 | −1.12156 | ||||||||
\(863\) | −47.2548 | −1.60857 | −0.804287 | − | 0.594242i | \(-0.797452\pi\) | ||||
−0.804287 | + | 0.594242i | \(0.797452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 80.7696 | 2.74625 | ||||||||
\(866\) | −30.7696 | −1.04559 | ||||||||
\(867\) | −17.3726 | −0.590004 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4853 | −0.627070 | ||||||||
\(870\) | 28.9706 | 0.982194 | ||||||||
\(871\) | 13.6863 | 0.463742 | ||||||||
\(872\) | −56.4853 | −1.91283 | ||||||||
\(873\) | −1.82843 | −0.0618829 | ||||||||
\(874\) | −7.79899 | −0.263805 | ||||||||
\(875\) | −19.3137 | −0.652923 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.7990 | 1.24261 | 0.621307 | − | 0.783567i | \(-0.286602\pi\) | ||||
0.621307 | + | 0.783567i | \(0.286602\pi\) | |||||||
\(878\) | −16.2426 | −0.548163 | ||||||||
\(879\) | 14.6274 | 0.493371 | ||||||||
\(880\) | 52.2843 | 1.76250 | ||||||||
\(881\) | 36.2548 | 1.22146 | 0.610728 | − | 0.791840i | \(-0.290877\pi\) | ||||
0.610728 | + | 0.791840i | \(0.290877\pi\) | |||||||
\(882\) | 6.58579 | 0.221755 | ||||||||
\(883\) | −8.02944 | −0.270212 | −0.135106 | − | 0.990831i | \(-0.543138\pi\) | ||||
−0.135106 | + | 0.990831i | \(0.543138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.3137 | −0.783682 | ||||||||
\(886\) | −11.1127 | −0.373338 | ||||||||
\(887\) | 58.9706 | 1.98004 | 0.990019 | − | 0.140935i | \(-0.0450108\pi\) | ||||
0.990019 | + | 0.140935i | \(0.0450108\pi\) | |||||||
\(888\) | 33.9411 | 1.13899 | ||||||||
\(889\) | −13.0711 | −0.438390 | ||||||||
\(890\) | 8.48528 | 0.284427 | ||||||||
\(891\) | 19.1421 | 0.641286 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.97056 | 0.166334 | ||||||||
\(894\) | −16.9706 | −0.567581 | ||||||||
\(895\) | −15.6569 | −0.523351 | ||||||||
\(896\) | 38.6274 | 1.29045 | ||||||||
\(897\) | −17.2132 | −0.574732 | ||||||||
\(898\) | −46.9706 | −1.56743 | ||||||||
\(899\) | 12.7279 | 0.424500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0294 | 1.00043 | ||||||||
\(902\) | 9.89949 | 0.329617 | ||||||||
\(903\) | −4.82843 | −0.160680 | ||||||||
\(904\) | −19.3137 | −0.642364 | ||||||||
\(905\) | 24.9706 | 0.830050 | ||||||||
\(906\) | −36.4853 | −1.21214 | ||||||||
\(907\) | −19.9706 | −0.663112 | −0.331556 | − | 0.943436i | \(-0.607574\pi\) | ||||
−0.331556 | + | 0.943436i | \(0.607574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.82843 | −0.193317 | ||||||||
\(910\) | −30.1421 | −0.999202 | ||||||||
\(911\) | −4.24264 | −0.140565 | −0.0702825 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702825 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(912\) | −4.68629 | −0.155179 | ||||||||
\(913\) | −12.7990 | −0.423585 | ||||||||
\(914\) | −1.02944 | −0.0340508 | ||||||||
\(915\) | −1.17157 | −0.0387310 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.9706 | −1.08878 | ||||||||
\(918\) | 17.3726 | 0.573381 | ||||||||
\(919\) | −12.5147 | −0.412822 | −0.206411 | − | 0.978465i | \(-0.566178\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566178\pi\) | |||||||
\(920\) | 64.2843 | 2.11939 | ||||||||
\(921\) | 37.8995 | 1.24883 | ||||||||
\(922\) | −60.2843 | −1.98536 | ||||||||
\(923\) | 5.79899 | 0.190876 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56.4853 | 1.85722 | ||||||||
\(926\) | 43.4558 | 1.42805 | ||||||||
\(927\) | −0.514719 | −0.0169056 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.1716 | 1.28518 | 0.642589 | − | 0.766211i | \(-0.277860\pi\) | ||||
0.642589 | + | 0.766211i | \(0.277860\pi\) | |||||||
\(930\) | 20.4853 | 0.671739 | ||||||||
\(931\) | 3.85786 | 0.126436 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.7574 | −0.646827 | ||||||||
\(934\) | −33.4558 | −1.09471 | ||||||||
\(935\) | −28.3848 | −0.928281 | ||||||||
\(936\) | 5.17157 | 0.169038 | ||||||||
\(937\) | −51.0122 | −1.66650 | −0.833248 | − | 0.552900i | \(-0.813521\pi\) | ||||
−0.833248 | + | 0.552900i | \(0.813521\pi\) | |||||||
\(938\) | −36.1421 | −1.18008 | ||||||||
\(939\) | −35.6569 | −1.16362 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.6274 | −1.03102 | −0.515512 | − | 0.856882i | \(-0.672398\pi\) | ||||
−0.515512 | + | 0.856882i | \(0.672398\pi\) | |||||||
\(942\) | 20.0000 | 0.651635 | ||||||||
\(943\) | 12.1716 | 0.396361 | ||||||||
\(944\) | 19.3137 | 0.628608 | ||||||||
\(945\) | 65.9411 | 2.14506 | ||||||||
\(946\) | 5.41421 | 0.176031 | ||||||||
\(947\) | −5.82843 | −0.189398 | −0.0946992 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0946992 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.6985 | 0.964054 | ||||||||
\(950\) | −7.79899 | −0.253033 | ||||||||
\(951\) | 36.5269 | 1.18447 | ||||||||
\(952\) | −20.9706 | −0.679660 | ||||||||
\(953\) | −24.0416 | −0.778785 | −0.389392 | − | 0.921072i | \(-0.627315\pi\) | ||||
−0.389392 | + | 0.921072i | \(0.627315\pi\) | |||||||
\(954\) | 19.5563 | 0.633160 | ||||||||
\(955\) | −20.9706 | −0.678591 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.9706 | 0.742533 | ||||||||
\(958\) | 9.41421 | 0.304159 | ||||||||
\(959\) | 49.4558 | 1.59701 | ||||||||
\(960\) | 38.6274 | 1.24669 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 21.9411 | 0.707410 | ||||||||
\(963\) | 0.343146 | 0.0110577 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.5269 | 1.75528 | ||||||||
\(966\) | 45.4558 | 1.46252 | ||||||||
\(967\) | −40.9411 | −1.31658 | −0.658289 | − | 0.752765i | \(-0.728719\pi\) | ||||
−0.658289 | + | 0.752765i | \(0.728719\pi\) | |||||||
\(968\) | 10.3431 | 0.332441 | ||||||||
\(969\) | 2.54416 | 0.0817301 | ||||||||
\(970\) | −8.82843 | −0.283464 | ||||||||
\(971\) | −3.14214 | −0.100836 | −0.0504180 | − | 0.998728i | \(-0.516055\pi\) | ||||
−0.0504180 | + | 0.998728i | \(0.516055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.7279 | −0.600390 | ||||||||
\(974\) | −31.5980 | −1.01246 | ||||||||
\(975\) | −17.2132 | −0.551264 | ||||||||
\(976\) | 0.970563 | 0.0310670 | ||||||||
\(977\) | −23.3137 | −0.745872 | −0.372936 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372936 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(978\) | 23.5147 | 0.751918 | ||||||||
\(979\) | 6.72792 | 0.215025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.9706 | 0.637611 | ||||||||
\(982\) | −18.9706 | −0.605375 | ||||||||
\(983\) | −62.5269 | −1.99430 | −0.997149 | − | 0.0754527i | \(-0.975960\pi\) | ||||
−0.997149 | + | 0.0754527i | \(0.975960\pi\) | |||||||
\(984\) | 7.31371 | 0.233153 | ||||||||
\(985\) | −48.2843 | −1.53846 | ||||||||
\(986\) | 13.0294 | 0.414942 | ||||||||
\(987\) | −28.9706 | −0.922143 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.65685 | 0.211676 | ||||||||
\(990\) | −18.4853 | −0.587501 | ||||||||
\(991\) | 11.5563 | 0.367100 | 0.183550 | − | 0.983010i | \(-0.441241\pi\) | ||||
0.183550 | + | 0.983010i | \(0.441241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.2843 | 0.961042 | ||||||||
\(994\) | −15.3137 | −0.485721 | ||||||||
\(995\) | 26.1421 | 0.828761 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.92893 | 0.0927602 | 0.0463801 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463801 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(998\) | 36.4264 | 1.15306 | ||||||||
\(999\) | −48.0000 | −1.51865 |
(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 | 43.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 387.2.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 688.2.a.f.1.1 | 2 | |||
5.2 | odd | 4 | 1075.2.b.f.474.1 | 4 | |||
5.3 | odd | 4 | 1075.2.b.f.474.4 | 4 | |||
5.4 | even | 2 | 1075.2.a.i.1.2 | 2 | |||
7.6 | odd | 2 | 2107.2.a.b.1.1 | 2 | |||
8.3 | odd | 2 | 2752.2.a.m.1.2 | 2 | |||
8.5 | even | 2 | 2752.2.a.l.1.1 | 2 | |||
11.10 | odd | 2 | 5203.2.a.f.1.2 | 2 | |||
12.11 | even | 2 | 6192.2.a.bd.1.1 | 2 | |||
13.12 | even | 2 | 7267.2.a.b.1.2 | 2 | |||
15.14 | odd | 2 | 9675.2.a.bf.1.1 | 2 | |||
43.42 | odd | 2 | 1849.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
387.2.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
688.2.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
1075.2.a.i.1.2 | 2 | 5.4 | even | 2 | |||
1075.2.b.f.474.1 | 4 | 5.2 | odd | 4 | |||
1075.2.b.f.474.4 | 4 | 5.3 | odd | 4 | |||
1849.2.a.f.1.2 | 2 | 43.42 | odd | 2 | |||
2107.2.a.b.1.1 | 2 | 7.6 | odd | 2 | |||
2752.2.a.l.1.1 | 2 | 8.5 | even | 2 | |||
2752.2.a.m.1.2 | 2 | 8.3 | odd | 2 | |||
5203.2.a.f.1.2 | 2 | 11.10 | odd | 2 | |||
6192.2.a.bd.1.1 | 2 | 12.11 | even | 2 | |||
7267.2.a.b.1.2 | 2 | 13.12 | even | 2 | |||
9675.2.a.bf.1.1 | 2 | 15.14 | odd | 2 |