Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.7643393337\) |
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: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 3.41421 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(8\) | −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 | \(-0.530294\pi\) | ||||
−0.0950271 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(20\) | 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 | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(30\) | 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 | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | −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 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 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 | \(-0.495055\pi\) | ||||
0.0155335 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(62\) | −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 | \(-0.439735\pi\) | ||||
0.188198 | + | 0.982131i | \(0.439735\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | 16.2426 | 1.90106 | 0.950529 | − | 0.310637i | \(-0.100542\pi\) | ||||
0.950529 | + | 0.310637i | \(0.100542\pi\) | |||||||
\(74\) | −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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 10.8284 | 1.15431 | ||||||||
\(89\) | 1.75736 | 0.186280 | 0.0931399 | − | 0.995653i | \(-0.470310\pi\) | ||||
0.0931399 | + | 0.995653i | \(0.470310\pi\) | |||||||
\(90\) | 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 | \(-0.395920\pi\) | ||||
0.321182 | + | 0.947017i | \(0.395920\pi\) | |||||||
\(114\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.82843 | 0.774304 | ||||||||
\(131\) | −9.65685 | −0.843723 | −0.421862 | − | 0.906660i | \(-0.638623\pi\) | ||||
−0.421862 | + | 0.906660i | \(0.638623\pi\) | |||||||
\(132\) | 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 | \(-0.287627\pi\) | ||||
0.618781 | + | 0.785564i | \(0.287627\pi\) | |||||||
\(138\) | −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 | \(-0.612993\pi\) | ||||
−0.347571 | + | 0.937654i | \(0.612993\pi\) | |||||||
\(150\) | −13.3137 | −1.08706 | ||||||||
\(151\) | −18.2426 | −1.48457 | −0.742283 | − | 0.670087i | \(-0.766257\pi\) | ||||
−0.742283 | + | 0.670087i | \(0.766257\pi\) | |||||||
\(152\) | 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 | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 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 | \(-0.347687\pi\) | ||||
0.460454 | + | 0.887684i | \(0.347687\pi\) | |||||||
\(164\) | 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 | \(-0.445178\pi\) | ||||
0.171379 | + | 0.985205i | \(0.445178\pi\) | |||||||
\(180\) | 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 | \(-0.428671\pi\) | ||||
0.222215 | + | 0.974998i | \(0.428671\pi\) | |||||||
\(192\) | −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 | \(-0.587483\pi\) | ||||
−0.271390 | + | 0.962469i | \(0.587483\pi\) | |||||||
\(200\) | −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 | \(-0.498443\pi\) | ||||
0.00489251 | + | 0.999988i | \(0.498443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.48528 | −0.307326 | ||||||||
\(214\) | −0.485281 | −0.0331732 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −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 | \(-0.543841\pi\) | ||||
−0.137295 | + | 0.990530i | \(0.543841\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.65685 | −0.443790 | ||||||||
\(226\) | 9.65685 | 0.642364 | ||||||||
\(227\) | 6.34315 | 0.421009 | 0.210505 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210505 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(228\) | 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 | \(-0.550556\pi\) | ||||
−0.158160 | + | 0.987413i | \(0.550556\pi\) | |||||||
\(234\) | 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 | \(-0.541123\pi\) | ||||
−0.128831 | + | 0.991667i | \(0.541123\pi\) | |||||||
\(242\) | 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 | \(-0.482545\pi\) | ||||
0.0548105 | + | 0.998497i | \(0.482545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −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 | \(-0.501395\pi\) | ||||
−0.00438223 | + | 0.999990i | \(0.501395\pi\) | |||||||
\(264\) | −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 | \(-0.576268\pi\) | ||||
−0.237317 | + | 0.971432i | \(0.576268\pi\) | |||||||
\(278\) | 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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −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 | \(-0.247532\pi\) | ||||
0.712567 | + | 0.701604i | \(0.247532\pi\) | |||||||
\(314\) | 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 | \(-0.700288\pi\) | ||||
−0.588516 | + | 0.808486i | \(0.700288\pi\) | |||||||
\(332\) | 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 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.1421 | 1.73047 | ||||||||
\(346\) | 33.4558 | 1.79860 | ||||||||
\(347\) | 4.58579 | 0.246178 | 0.123089 | − | 0.992396i | \(-0.460720\pi\) | ||||
0.123089 | + | 0.992396i | \(0.460720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2426 | 1.08356 | 0.541782 | − | 0.840519i | \(-0.317750\pi\) | ||||
0.541782 | + | 0.840519i | \(0.317750\pi\) | |||||||
\(350\) | 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 | \(-0.570500\pi\) | ||||
−0.219676 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(374\) | −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 | \(-0.324673\pi\) | ||||
0.523374 | + | 0.852103i | \(0.324673\pi\) | |||||||
\(384\) | −16.0000 | −0.816497 | ||||||||
\(385\) | 44.6274 | 2.27442 | ||||||||
\(386\) | 22.5858 | 1.14959 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6274 | 0.843044 | 0.421522 | − | 0.906818i | \(-0.361496\pi\) | ||||
0.421522 | + | 0.906818i | \(0.361496\pi\) | |||||||
\(390\) | −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 | \(-0.363052\pi\) | ||||
0.417085 | + | 0.908867i | \(0.363052\pi\) | |||||||
\(410\) | −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 | \(-0.301572\pi\) | ||||
0.583783 | + | 0.811909i | \(0.301572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6569 | 0.763068 | 0.381534 | − | 0.924355i | \(-0.375396\pi\) | ||||
0.381534 | + | 0.924355i | \(0.375396\pi\) | |||||||
\(422\) | 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 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.675111\pi\) | ||||
−0.522796 | + | 0.852458i | \(0.675111\pi\) | |||||||
\(434\) | −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 | \(-0.786677\pi\) | ||||
−0.783714 | + | 0.621122i | \(0.786677\pi\) | |||||||
\(450\) | −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 | \(-0.505420\pi\) | ||||
−0.0170254 | + | 0.999855i | \(0.505420\pi\) | |||||||
\(458\) | −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 | \(-0.246871\pi\) | ||||
0.714024 | + | 0.700121i | \(0.246871\pi\) | |||||||
\(464\) | −16.9706 | −0.787839 | ||||||||
\(465\) | −14.4853 | −0.671739 | ||||||||
\(466\) | −6.82843 | −0.316321 | ||||||||
\(467\) | −23.6569 | −1.09471 | −0.547354 | − | 0.836901i | \(-0.684365\pi\) | ||||
−0.547354 | + | 0.836901i | \(0.684365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.5563 | −1.18008 | ||||||||
\(470\) | −28.9706 | −1.33631 | ||||||||
\(471\) | −14.1421 | −0.651635 | ||||||||
\(472\) | 13.6569 | 0.628608 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −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 | \(-0.597884\pi\) | ||||
−0.302687 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(492\) | 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 | \(-0.304407\pi\) | ||||
0.576529 | + | 0.817077i | \(0.304407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.2426 | 0.904374 | ||||||||
\(502\) | 32.7279 | 1.46072 | ||||||||
\(503\) | 30.7696 | 1.37195 | 0.685973 | − | 0.727627i | \(-0.259377\pi\) | ||||
0.685973 | + | 0.727627i | \(0.259377\pi\) | |||||||
\(504\) | 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 | \(-0.620928\pi\) | ||||
−0.370835 | + | 0.928699i | \(0.620928\pi\) | |||||||
\(522\) | −6.00000 | −0.262613 | ||||||||
\(523\) | 39.2132 | 1.71467 | 0.857337 | − | 0.514756i | \(-0.172117\pi\) | ||||
0.857337 | + | 0.514756i | \(0.172117\pi\) | |||||||
\(524\) | 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 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 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 | \(-0.479531\pi\) | ||||
0.0642601 | + | 0.997933i | \(0.479531\pi\) | |||||||
\(572\) | 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 | \(-0.741679\pi\) | ||||
−0.688383 | + | 0.725347i | \(0.741679\pi\) | |||||||
\(578\) | −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 | \(-0.745712\pi\) | ||||
−0.697517 | + | 0.716568i | \(0.745712\pi\) | |||||||
\(588\) | 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 | \(-0.440366\pi\) | ||||
0.186252 | + | 0.982502i | \(0.440366\pi\) | |||||||
\(594\) | −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 | \(-0.329910\pi\) | ||||
0.509285 | + | 0.860598i | \(0.329910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | \(-0.266673\pi\) | ||||
0.669117 | + | 0.743157i | \(0.266673\pi\) | |||||||
\(608\) | 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 | \(-0.881004\pi\) | ||||
−0.930933 | + | 0.365189i | \(0.881004\pi\) | |||||||
\(632\) | −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 | \(-0.301603\pi\) | ||||
0.583703 | + | 0.811967i | \(0.301603\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.54416 | −0.100098 | ||||||||
\(647\) | 1.17157 | 0.0460593 | 0.0230296 | − | 0.999735i | \(-0.492669\pi\) | ||||
0.0230296 | + | 0.999735i | \(0.492669\pi\) | |||||||
\(648\) | 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 | \(-0.595938\pi\) | ||||
−0.296855 | + | 0.954923i | \(0.595938\pi\) | |||||||
\(654\) | 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 | \(-0.395508\pi\) | ||||
0.322407 | + | 0.946601i | \(0.395508\pi\) | |||||||
\(674\) | −7.07107 | −0.272367 | ||||||||
\(675\) | 37.6569 | 1.44941 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.1716 | −0.429358 | −0.214679 | − | 0.976685i | \(-0.568871\pi\) | ||||
−0.214679 | + | 0.976685i | \(0.568871\pi\) | |||||||
\(678\) | −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 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.2843 | −0.963254 | ||||||||
\(690\) | 45.4558 | 1.73047 | ||||||||
\(691\) | 26.7279 | 1.01678 | 0.508389 | − | 0.861128i | \(-0.330241\pi\) | ||||
0.508389 | + | 0.861128i | \(0.330241\pi\) | |||||||
\(692\) | 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 | \(-0.346754\pi\) | ||||
0.463053 | + | 0.886330i | \(0.346754\pi\) | |||||||
\(728\) | 17.6569 | 0.654407 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −78.4264 | −2.90269 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9706 | −0.626822 | −0.313411 | − | 0.949618i | \(-0.601472\pi\) | ||||
−0.313411 | + | 0.949618i | \(0.601472\pi\) | |||||||
\(734\) | 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 | \(-0.241515\pi\) | ||||
0.725703 | + | 0.688008i | \(0.241515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.14214 | −0.0786933 | ||||||||
\(742\) | 66.7696 | 2.45119 | ||||||||
\(743\) | −15.1127 | −0.554431 | −0.277216 | − | 0.960808i | \(-0.589412\pi\) | ||||
−0.277216 | + | 0.960808i | \(0.589412\pi\) | |||||||
\(744\) | −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 | \(-0.431183\pi\) | ||||
0.214516 | + | 0.976720i | \(0.431183\pi\) | |||||||
\(752\) | −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 | \(-0.520345\pi\) | ||||
−0.0638723 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(758\) | 42.8701 | 1.55711 | ||||||||
\(759\) | 36.0416 | 1.30823 | ||||||||
\(760\) | −8.00000 | −0.290191 | ||||||||
\(761\) | −19.1127 | −0.692835 | −0.346417 | − | 0.938080i | \(-0.612602\pi\) | ||||
−0.346417 | + | 0.938080i | \(0.612602\pi\) | |||||||
\(762\) | −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 | \(-0.546536\pi\) | ||||
−0.145677 | + | 0.989332i | \(0.546536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −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 | \(-0.633982\pi\) | ||||
−0.408597 | + | 0.912715i | \(0.633982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.7279 | 1.28810 | ||||||||
\(814\) | 45.9411 | 1.61024 | ||||||||
\(815\) | −40.1421 | −1.40612 | ||||||||
\(816\) | 12.2843 | 0.430036 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 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 | \(-0.635619\pi\) | ||||
−0.413287 | + | 0.910601i | \(0.635619\pi\) | |||||||
\(830\) | −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 | \(-0.180437\pi\) | ||||
0.843591 | + | 0.536986i | \(0.180437\pi\) | |||||||
\(840\) | −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 | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.82843 | −0.300872 | ||||||||
\(862\) | 32.9289 | 1.12156 | ||||||||
\(863\) | 47.2548 | 1.60857 | 0.804287 | − | 0.594242i | \(-0.202548\pi\) | ||||
0.804287 | + | 0.594242i | \(0.202548\pi\) | |||||||
\(864\) | 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 | \(-0.954989\pi\) | ||||
−0.990019 | + | 0.140935i | \(0.954989\pi\) | |||||||
\(888\) | −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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −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 | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | −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 | \(-0.722140\pi\) | ||||
−0.642589 | + | 0.766211i | \(0.722140\pi\) | |||||||
\(930\) | −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 | \(-0.186479\pi\) | ||||
0.833248 | + | 0.552900i | \(0.186479\pi\) | |||||||
\(938\) | −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 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | \(-0.372685\pi\) | ||||
0.389392 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(954\) | −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 | \(-0.0240402\pi\) | ||||
0.997149 | + | 0.0754527i | \(0.0240402\pi\) | |||||||
\(984\) | 7.31371 | 0.233153 | ||||||||
\(985\) | 48.2843 | 1.53846 | ||||||||
\(986\) | 13.0294 | 0.414942 | ||||||||
\(987\) | −28.9706 | −0.922143 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −18.4853 | −0.587501 | ||||||||
\(991\) | −11.5563 | −0.367100 | −0.183550 | − | 0.983010i | \(-0.558759\pi\) | ||||
−0.183550 | + | 0.983010i | \(0.558759\pi\) | |||||||
\(992\) | 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 | \(-0.514769\pi\) | ||||
−0.0463801 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(998\) | 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 | 1849.2.a.f.1.2 | 2 | ||
43.42 | odd | 2 | 43.2.a.b.1.1 | ✓ | 2 | ||
129.128 | even | 2 | 387.2.a.h.1.2 | 2 | |||
172.171 | even | 2 | 688.2.a.f.1.1 | 2 | |||
215.42 | even | 4 | 1075.2.b.f.474.1 | 4 | |||
215.128 | even | 4 | 1075.2.b.f.474.4 | 4 | |||
215.214 | odd | 2 | 1075.2.a.i.1.2 | 2 | |||
301.300 | even | 2 | 2107.2.a.b.1.1 | 2 | |||
344.85 | odd | 2 | 2752.2.a.l.1.1 | 2 | |||
344.171 | even | 2 | 2752.2.a.m.1.2 | 2 | |||
473.472 | even | 2 | 5203.2.a.f.1.2 | 2 | |||
516.515 | odd | 2 | 6192.2.a.bd.1.1 | 2 | |||
559.558 | odd | 2 | 7267.2.a.b.1.2 | 2 | |||
645.644 | even | 2 | 9675.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.a.b.1.1 | ✓ | 2 | 43.42 | odd | 2 | ||
387.2.a.h.1.2 | 2 | 129.128 | even | 2 | |||
688.2.a.f.1.1 | 2 | 172.171 | even | 2 | |||
1075.2.a.i.1.2 | 2 | 215.214 | odd | 2 | |||
1075.2.b.f.474.1 | 4 | 215.42 | even | 4 | |||
1075.2.b.f.474.4 | 4 | 215.128 | even | 4 | |||
1849.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2107.2.a.b.1.1 | 2 | 301.300 | even | 2 | |||
2752.2.a.l.1.1 | 2 | 344.85 | odd | 2 | |||
2752.2.a.m.1.2 | 2 | 344.171 | even | 2 | |||
5203.2.a.f.1.2 | 2 | 473.472 | even | 2 | |||
6192.2.a.bd.1.1 | 2 | 516.515 | odd | 2 | |||
7267.2.a.b.1.2 | 2 | 559.558 | odd | 2 | |||
9675.2.a.bf.1.1 | 2 | 645.644 | even | 2 |