Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.82843 | −1.06181 | −0.530907 | − | 0.847430i | \(-0.678149\pi\) | ||||
−0.530907 | + | 0.847430i | \(0.678149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.24264 | 1.30168 | 0.650840 | − | 0.759215i | \(-0.274417\pi\) | ||||
0.650840 | + | 0.759215i | \(0.274417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.65685 | 0.493365 | 0.246683 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246683 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.41421 | −0.420261 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.41421 | −1.54769 | −0.773844 | − | 0.633377i | \(-0.781668\pi\) | ||||
−0.773844 | + | 0.633377i | \(0.781668\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.24264 | −1.48001 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.41421 | −0.845558 | −0.422779 | − | 0.906233i | \(-0.638945\pi\) | ||||
−0.422779 | + | 0.906233i | \(0.638945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.65685 | −0.246989 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4853 | 1.52944 | 0.764718 | − | 0.644365i | \(-0.222878\pi\) | ||||
0.764718 | + | 0.644365i | \(0.222878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.82843 | 1.23623 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.89949 | 1.08508 | 0.542540 | − | 0.840030i | \(-0.317463\pi\) | ||||
0.542540 | + | 0.840030i | \(0.317463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41421 | 0.187317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.58579 | 0.727207 | 0.363604 | − | 0.931554i | \(-0.381546\pi\) | ||||
0.363604 | + | 0.931554i | \(0.381546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8284 | 1.51447 | 0.757237 | − | 0.653140i | \(-0.226549\pi\) | ||||
0.757237 | + | 0.653140i | \(0.226549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.75736 | −0.336865 | −0.168433 | − | 0.985713i | \(-0.553871\pi\) | ||||
−0.168433 | + | 0.985713i | \(0.553871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.0711 | 1.81434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0711 | 1.31389 | 0.656947 | − | 0.753937i | \(-0.271848\pi\) | ||||
0.656947 | + | 0.753937i | \(0.271848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.41421 | −1.10185 | −0.550925 | − | 0.834555i | \(-0.685725\pi\) | ||||
−0.550925 | + | 0.834555i | \(0.685725\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.2426 | −1.29819 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.2426 | 1.48991 | 0.744957 | − | 0.667113i | \(-0.232470\pi\) | ||||
0.744957 | + | 0.667113i | \(0.232470\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1421 | 1.33277 | 0.666386 | − | 0.745607i | \(-0.267840\pi\) | ||||
0.666386 | + | 0.745607i | \(0.267840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.14214 | −0.232347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.41421 | 0.687676 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.4853 | 1.32344 | 0.661719 | − | 0.749752i | \(-0.269827\pi\) | ||||
0.661719 | + | 0.749752i | \(0.269827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.65685 | 1.00137 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.343146 | −0.0352060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.82843 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.17157 | 0.614094 | 0.307047 | − | 0.951694i | \(-0.400659\pi\) | ||||
0.307047 | + | 0.951694i | \(0.400659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4142 | −1.32174 | −0.660871 | − | 0.750500i | \(-0.729813\pi\) | ||||
−0.660871 | + | 0.750500i | \(0.729813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.07107 | 0.296891 | 0.148446 | − | 0.988921i | \(-0.452573\pi\) | ||||
0.148446 | + | 0.988921i | \(0.452573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4853 | 1.57900 | 0.789502 | − | 0.613748i | \(-0.210339\pi\) | ||||
0.789502 | + | 0.613748i | \(0.210339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.7279 | −2.15724 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.17157 | −0.768717 | −0.384358 | − | 0.923184i | \(-0.625577\pi\) | ||||
−0.384358 | + | 0.923184i | \(0.625577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65685 | −0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.8284 | −1.00109 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.0711 | −1.17858 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7279 | −1.39563 | −0.697814 | − | 0.716279i | \(-0.745844\pi\) | ||||
−0.697814 | + | 0.716279i | \(0.745844\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.6569 | 1.20242 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.585786 | 0.0511804 | 0.0255902 | − | 0.999673i | \(-0.491853\pi\) | ||||
0.0255902 | + | 0.999673i | \(0.491853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.242641 | 0.0208832 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.6569 | −1.42309 | −0.711546 | − | 0.702640i | \(-0.752004\pi\) | ||||
−0.711546 | + | 0.702640i | \(0.752004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.3137 | 2.13180 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.82843 | 0.320149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.55635 | −0.129248 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6569 | 1.44651 | 0.723253 | − | 0.690583i | \(-0.242646\pi\) | ||||
0.723253 | + | 0.690583i | \(0.242646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7279 | 1.27992 | 0.639960 | − | 0.768408i | \(-0.278951\pi\) | ||||
0.639960 | + | 0.768408i | \(0.278951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3431 | 0.836194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.34315 | −0.188206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6569 | 1.40917 | 0.704585 | − | 0.709619i | \(-0.251133\pi\) | ||||
0.704585 | + | 0.709619i | \(0.251133\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.0711 | 1.51243 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.72792 | −0.761950 | −0.380975 | − | 0.924585i | \(-0.624412\pi\) | ||||
−0.380975 | + | 0.924585i | \(0.624412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.41421 | 0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7279 | −1.06230 | −0.531149 | − | 0.847278i | \(-0.678240\pi\) | ||||
−0.531149 | + | 0.847278i | \(0.678240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.65685 | 0.126703 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.82843 | −0.747241 | −0.373621 | − | 0.927582i | \(-0.621884\pi\) | ||||
−0.373621 | + | 0.927582i | \(0.621884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.4853 | 1.01362 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.899495 | −0.0672314 | −0.0336157 | − | 0.999435i | \(-0.510702\pi\) | ||||
−0.0336157 | + | 0.999435i | \(0.510702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.65685 | −0.569129 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.5563 | 2.11095 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.51472 | 0.405450 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.65685 | −0.267416 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.17157 | 0.518917 | 0.259458 | − | 0.965754i | \(-0.416456\pi\) | ||||
0.259458 | + | 0.965754i | \(0.416456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.8995 | 1.57636 | 0.788180 | − | 0.615445i | \(-0.211024\pi\) | ||||
0.788180 | + | 0.615445i | \(0.211024\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.41421 | 0.387720 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.514719 | −0.0366722 | −0.0183361 | − | 0.999832i | \(-0.505837\pi\) | ||||
−0.0183361 | + | 0.999832i | \(0.505837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.100505 | −0.00712462 | −0.00356231 | − | 0.999994i | \(-0.501134\pi\) | ||||
−0.00356231 | + | 0.999994i | \(0.501134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.65685 | −0.469538 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.17157 | 0.221512 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.6569 | 1.22724 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.585786 | −0.0405197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.41421 | −0.510416 | −0.255208 | − | 0.966886i | \(-0.582144\pi\) | ||||
−0.255208 | + | 0.966886i | \(0.582144\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.7279 | 1.83137 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.31371 | −0.225993 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.7279 | −1.53581 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.0000 | −0.941742 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.58579 | −0.574947 | −0.287473 | − | 0.957789i | \(-0.592815\pi\) | ||||
−0.287473 | + | 0.957789i | \(0.592815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1716 | −0.878105 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.8284 | 1.91341 | 0.956705 | − | 0.291059i | \(-0.0940078\pi\) | ||||
0.956705 | + | 0.291059i | \(0.0940078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3137 | 1.54061 | 0.770307 | − | 0.637674i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637674i | \(0.220103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.41421 | 0.0926482 | 0.0463241 | − | 0.998926i | \(-0.485249\pi\) | ||||
0.0463241 | + | 0.998926i | \(0.485249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.14214 | −0.400669 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.9706 | 2.07671 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.2132 | −1.30748 | −0.653742 | − | 0.756718i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756718i | \(0.726802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2426 | 0.788618 | 0.394309 | − | 0.918978i | \(-0.370984\pi\) | ||||
0.394309 | + | 0.918978i | \(0.370984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24264 | −0.142696 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.3137 | 1.85768 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.1421 | 1.65008 | 0.825038 | − | 0.565077i | \(-0.191153\pi\) | ||||
0.825038 | + | 0.565077i | \(0.191153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.24264 | −0.392471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.17157 | −0.323856 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.1421 | −1.56832 | −0.784162 | − | 0.620557i | \(-0.786907\pi\) | ||||
−0.784162 | + | 0.620557i | \(0.786907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.51472 | 0.465149 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.0416 | 1.05083 | 0.525416 | − | 0.850845i | \(-0.323910\pi\) | ||||
0.525416 | + | 0.850845i | \(0.323910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.62742 | −0.284260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.1421 | 1.84467 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.34315 | 0.142864 | 0.0714321 | − | 0.997445i | \(-0.477243\pi\) | ||||
0.0714321 | + | 0.997445i | \(0.477243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.55635 | −0.276779 | −0.138389 | − | 0.990378i | \(-0.544192\pi\) | ||||
−0.138389 | + | 0.990378i | \(0.544192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.65685 | 0.280819 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.82843 | 0.109860 | 0.0549298 | − | 0.998490i | \(-0.482507\pi\) | ||||
0.0549298 | + | 0.998490i | \(0.482507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3137 | 0.677334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.72792 | 0.520664 | 0.260332 | − | 0.965519i | \(-0.416168\pi\) | ||||
0.260332 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4142 | 1.39183 | 0.695915 | − | 0.718124i | \(-0.254999\pi\) | ||||
0.695915 | + | 0.718124i | \(0.254999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.828427 | −0.0490718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.24264 | −0.541813 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8284 | −0.632603 | −0.316302 | − | 0.948659i | \(-0.602441\pi\) | ||||
−0.316302 | + | 0.948659i | \(0.602441\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.27208 | −0.190508 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | 0.0240351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8995 | −1.38214 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.8995 | 0.855954 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.92893 | −0.396750 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.89949 | −0.564994 | −0.282497 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282497 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.3848 | −1.84231 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.7279 | −0.948553 | −0.474277 | − | 0.880376i | \(-0.657290\pi\) | ||||
−0.474277 | + | 0.880376i | \(0.657290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6569 | −1.16759 | −0.583797 | − | 0.811900i | \(-0.698434\pi\) | ||||
−0.583797 | + | 0.811900i | \(0.698434\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.68629 | 0.487871 | 0.243935 | − | 0.969791i | \(-0.421562\pi\) | ||||
0.243935 | + | 0.969791i | \(0.421562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.65685 | −0.148755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.41421 | 0.413821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.14214 | 0.119192 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8284 | 0.988943 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.7990 | 2.20089 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0711 | 1.32307 | 0.661533 | − | 0.749916i | \(-0.269906\pi\) | ||||
0.661533 | + | 0.749916i | \(0.269906\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.6274 | −1.45917 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.61522 | 0.0882491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.2426 | −1.53847 | −0.769237 | − | 0.638963i | \(-0.779364\pi\) | ||||
−0.769237 | + | 0.638963i | \(0.779364\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.7279 | −1.07147 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.82843 | −0.475307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4142 | −0.934844 | −0.467422 | − | 0.884034i | \(-0.654817\pi\) | ||||
−0.467422 | + | 0.884034i | \(0.654817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58579 | 0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.68629 | −0.142977 | −0.0714884 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714884 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48528 | −0.344203 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.2426 | −1.01559 | −0.507794 | − | 0.861479i | \(-0.669539\pi\) | ||||
−0.507794 | + | 0.861479i | \(0.669539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.41421 | 0.126713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.51472 | 0.288654 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7279 | 0.559993 | 0.279996 | − | 0.960001i | \(-0.409667\pi\) | ||||
0.279996 | + | 0.960001i | \(0.409667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.3137 | −0.797200 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.9706 | −1.03404 | −0.517018 | − | 0.855974i | \(-0.672958\pi\) | ||||
−0.517018 | + | 0.855974i | \(0.672958\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.6569 | 0.705237 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.1716 | −0.523863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.8701 | −1.43159 | −0.715794 | − | 0.698311i | \(-0.753935\pi\) | ||||
−0.715794 | + | 0.698311i | \(0.753935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.9706 | −1.94529 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.38478 | 0.326247 | 0.163123 | − | 0.986606i | \(-0.447843\pi\) | ||||
0.163123 | + | 0.986606i | \(0.447843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.0000 | 0.813326 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.7279 | −1.15235 | −0.576176 | − | 0.817326i | \(-0.695456\pi\) | ||||
−0.576176 | + | 0.817326i | \(0.695456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.8284 | 1.15448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.41421 | 0.0713376 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.75736 | −0.390315 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3137 | 0.914543 | 0.457271 | − | 0.889327i | \(-0.348827\pi\) | ||||
0.457271 | + | 0.889327i | \(0.348827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3137 | −0.762830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.55635 | 0.276097 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.41421 | 0.466645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.72792 | 0.134887 | 0.0674435 | − | 0.997723i | \(-0.478516\pi\) | ||||
0.0674435 | + | 0.997723i | \(0.478516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.2132 | −1.98357 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.11270 | −0.349149 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.1421 | 1.27713 | 0.638563 | − | 0.769569i | \(-0.279529\pi\) | ||||
0.638563 | + | 0.769569i | \(0.279529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.686292 | 0.0334478 | 0.0167239 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167239 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.6569 | 1.44197 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.0294 | −0.826049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.24264 | 0.446239 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5858 | 0.847078 | 0.423539 | − | 0.905878i | \(-0.360788\pi\) | ||||
0.423539 | + | 0.905878i | \(0.360788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1421 | 1.25631 | 0.628155 | − | 0.778088i | \(-0.283810\pi\) | ||||
0.628155 | + | 0.778088i | \(0.283810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.75736 | −0.180152 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.65685 | 0.174931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3848 | 1.30700 | 0.653502 | − | 0.756925i | \(-0.273299\pi\) | ||||
0.653502 | + | 0.756925i | \(0.273299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.6274 | −0.599947 | −0.299973 | − | 0.953948i | \(-0.596978\pi\) | ||||
−0.299973 | + | 0.953948i | \(0.596978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.31371 | −0.346703 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.6274 | 2.01621 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3431 | 1.05444 | 0.527219 | − | 0.849729i | \(-0.323235\pi\) | ||||
0.527219 | + | 0.849729i | \(0.323235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.41421 | 0.254945 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.9706 | 1.78401 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6569 | −0.545285 | −0.272642 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272642 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.51472 | −0.0707010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.31371 | −0.387208 | −0.193604 | − | 0.981080i | \(-0.562018\pi\) | ||||
−0.193604 | + | 0.981080i | \(0.562018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8284 | −0.596188 | −0.298094 | − | 0.954537i | \(-0.596351\pi\) | ||||
−0.298094 | + | 0.954537i | \(0.596351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.65685 | −0.262330 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.0000 | 1.57333 | 0.786666 | − | 0.617379i | \(-0.211805\pi\) | ||||
0.786666 | + | 0.617379i | \(0.211805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 42.6274 | 1.96417 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.65685 | −0.260102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.72792 | −0.125166 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.3431 | 1.02302 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9289 | 0.545047 | 0.272523 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272523 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.0416 | 1.64336 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.24264 | 0.101833 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.65685 | 0.437594 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.4853 | −1.06204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1716 | −0.865201 | −0.432600 | − | 0.901586i | \(-0.642404\pi\) | ||||
−0.432600 | + | 0.901586i | \(0.642404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.71573 | 0.437574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.1421 | −0.991218 | −0.495609 | − | 0.868546i | \(-0.665055\pi\) | ||||
−0.495609 | + | 0.868546i | \(0.665055\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.1421 | −1.48068 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.21320 | −0.187857 | −0.0939287 | − | 0.995579i | \(-0.529943\pi\) | ||||
−0.0939287 | + | 0.995579i | \(0.529943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.61522 | −0.160875 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00000 | 0.177646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.31371 | 0.412823 | 0.206411 | − | 0.978465i | \(-0.433821\pi\) | ||||
0.206411 | + | 0.978465i | \(0.433821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.242641 | −0.0107128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.85786 | 0.346259 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4853 | −0.461142 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.7279 | −1.04154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.2843 | −1.23916 | −0.619578 | − | 0.784935i | \(-0.712696\pi\) | ||||
−0.619578 | + | 0.784935i | \(0.712696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7279 | 0.556553 | 0.278277 | − | 0.960501i | \(-0.410237\pi\) | ||||
0.278277 | + | 0.960501i | \(0.410237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6274 | 0.637180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9706 | 0.694372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7990 | 0.685618 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.7279 | 0.897826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.79899 | −0.0777771 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.17157 | −0.0937103 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8579 | −0.552803 | −0.276401 | − | 0.961042i | \(-0.589142\pi\) | ||||
−0.276401 | + | 0.961042i | \(0.589142\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.4853 | −0.793279 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.65685 | −0.413654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8701 | −1.49094 | −0.745468 | − | 0.666541i | \(-0.767774\pi\) | ||||
−0.745468 | + | 0.666541i | \(0.767774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.4558 | 1.42786 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.55635 | 0.0663027 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.3137 | 0.565135 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.51472 | 0.318409 | 0.159204 | − | 0.987246i | \(-0.449107\pi\) | ||||
0.159204 | + | 0.987246i | \(0.449107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6569 | −0.915987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.82843 | −0.372736 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.07107 | −0.382300 | −0.191150 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191150 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.78680 | 0.201382 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.00000 | −0.167689 | −0.0838444 | − | 0.996479i | \(-0.526720\pi\) | ||||
−0.0838444 | + | 0.996479i | \(0.526720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3848 | −1.10417 | −0.552084 | − | 0.833788i | \(-0.686167\pi\) | ||||
−0.552084 | + | 0.833788i | \(0.686167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3137 | 0.723291 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.0711 | −1.21235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.68629 | −0.403246 | −0.201623 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201623 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 52.8701 | 2.19720 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.89949 | −0.327164 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.34315 | 0.262257 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.1005 | 1.03601 | 0.518004 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518004 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34315 | 0.0965476 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.24264 | −0.0511154 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.6985 | 0.973180 | 0.486590 | − | 0.873630i | \(-0.338241\pi\) | ||||
0.486590 | + | 0.873630i | \(0.338241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.242641 | −0.00993062 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.6274 | −1.74171 | −0.870855 | − | 0.491541i | \(-0.836434\pi\) | ||||
−0.870855 | + | 0.491541i | \(0.836434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9411 | 1.30291 | 0.651453 | − | 0.758689i | \(-0.274160\pi\) | ||||
0.651453 | + | 0.758689i | \(0.274160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.79899 | −0.317599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.585786 | −0.0238156 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.9706 | 1.74412 | 0.872061 | − | 0.489398i | \(-0.162783\pi\) | ||||
0.872061 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.1421 | −1.62398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.6274 | 1.15625 | 0.578125 | − | 0.815948i | \(-0.303785\pi\) | ||||
0.578125 | + | 0.815948i | \(0.303785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65685 | 0.308754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.9706 | −1.68967 | −0.844836 | − | 0.535026i | \(-0.820302\pi\) | ||||
−0.844836 | + | 0.535026i | \(0.820302\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.9411 | 0.881888 | 0.440944 | − | 0.897535i | \(-0.354644\pi\) | ||||
0.440944 | + | 0.897535i | \(0.354644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58579 | −0.103764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41421 | −0.0564782 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.4264 | −1.37267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2721 | −0.926447 | −0.463223 | − | 0.886242i | \(-0.653307\pi\) | ||||
−0.463223 | + | 0.886242i | \(0.653307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.8995 | −0.711441 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.21320 | 0.365615 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.3137 | 1.23875 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.2843 | 0.603692 | 0.301846 | − | 0.953357i | \(-0.402397\pi\) | ||||
0.301846 | + | 0.953357i | \(0.402397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.58579 | −0.0625373 | −0.0312687 | − | 0.999511i | \(-0.509955\pi\) | ||||
−0.0312687 | + | 0.999511i | \(0.509955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.1838 | −1.18665 | −0.593323 | − | 0.804964i | \(-0.702184\pi\) | ||||
−0.593323 | + | 0.804964i | \(0.702184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.58579 | −0.219261 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3848 | −0.719452 | −0.359726 | − | 0.933058i | \(-0.617130\pi\) | ||||
−0.359726 | + | 0.933058i | \(0.617130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.343146 | −0.0134078 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.6274 | −1.03883 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9706 | 0.737869 | 0.368935 | − | 0.929455i | \(-0.379723\pi\) | ||||
0.368935 | + | 0.929455i | \(0.379723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.7990 | −1.31264 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.5858 | 0.642204 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7279 | −0.801388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.8284 | −0.456631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.55635 | 0.214182 | 0.107091 | − | 0.994249i | \(-0.465846\pi\) | ||||
0.107091 | + | 0.994249i | \(0.465846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.92893 | 0.0742446 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.3137 | −1.35722 | −0.678608 | − | 0.734501i | \(-0.737416\pi\) | ||||
−0.678608 | + | 0.734501i | \(0.737416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 69.5980 | 2.66700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5858 | −0.519846 | −0.259923 | − | 0.965629i | \(-0.583697\pi\) | ||||
−0.259923 | + | 0.965629i | \(0.583697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.75736 | 0.372810 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 56.2843 | 2.14738 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.2426 | −1.15215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0711 | −1.06787 | −0.533937 | − | 0.845524i | \(-0.679288\pi\) | ||||
−0.533937 | + | 0.845524i | \(0.679288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.7990 | −0.749940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.41421 | 0.129137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1127 | −0.986263 | −0.493132 | − | 0.869955i | \(-0.664148\pi\) | ||||
−0.493132 | + | 0.869955i | \(0.664148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.51472 | −0.207992 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.8284 | −0.558471 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0416 | −0.452233 | −0.226116 | − | 0.974100i | \(-0.572603\pi\) | ||||
−0.226116 | + | 0.974100i | \(0.572603\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.4558 | 1.40470 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9706 | 0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.24264 | −0.0838700 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.7990 | −1.82243 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.51472 | 0.0564895 | 0.0282447 | − | 0.999601i | \(-0.491008\pi\) | ||||
0.0282447 | + | 0.999601i | \(0.491008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.5563 | 1.09921 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.3726 | −0.459506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4264 | −1.35098 | −0.675490 | − | 0.737369i | \(-0.736068\pi\) | ||||
−0.675490 | + | 0.737369i | \(0.736068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.6863 | 0.765110 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0000 | −0.480166 | −0.240083 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240083 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.75736 | 0.101569 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.4264 | 1.92854 | 0.964268 | − | 0.264928i | \(-0.0853481\pi\) | ||||
0.964268 | + | 0.264928i | \(0.0853481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.41421 | −0.198896 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.3137 | 0.488433 | 0.244216 | − | 0.969721i | \(-0.421469\pi\) | ||||
0.244216 | + | 0.969721i | \(0.421469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3431 | −0.378944 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.3431 | 1.25655 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.6569 | −1.66604 | −0.833021 | − | 0.553241i | \(-0.813391\pi\) | ||||
−0.833021 | + | 0.553241i | \(0.813391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 63.1127 | 2.29995 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.21320 | −0.335303 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.34315 | 0.303237 | 0.151618 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151618 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.0711 | −0.547045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.9706 | 1.12268 | 0.561341 | − | 0.827585i | \(-0.310286\pi\) | ||||
0.561341 | + | 0.827585i | \(0.310286\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.05887 | −0.219059 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.3848 | −0.772160 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9706 | 0.828340 | 0.414170 | − | 0.910200i | \(-0.364072\pi\) | ||||
0.414170 | + | 0.910200i | \(0.364072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −60.6985 | −2.18600 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.9411 | −0.789167 | −0.394584 | − | 0.918860i | \(-0.629111\pi\) | ||||
−0.394584 | + | 0.918860i | \(0.629111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.6274 | −0.669117 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.17157 | −0.113633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0711 | −0.396154 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.10051 | −0.0393288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.3431 | −0.369163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.5563 | −0.483232 | −0.241616 | − | 0.970372i | \(-0.577677\pi\) | ||||
−0.241616 | + | 0.970372i | \(0.577677\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.1421 | 1.46470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.2843 | −1.60809 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.1716 | −0.396215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.65685 | −0.271220 | −0.135610 | − | 0.990762i | \(-0.543299\pi\) | ||||
−0.135610 | + | 0.990762i | \(0.543299\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.3431 | 1.35648 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.3137 | 1.24775 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.41421 | 0.332220 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.65685 | 0.199131 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.6274 | −1.63933 | −0.819666 | − | 0.572841i | \(-0.805841\pi\) | ||||
−0.819666 | + | 0.572841i | \(0.805841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.2843 | 0.852736 | 0.426368 | − | 0.904550i | \(-0.359793\pi\) | ||||
0.426368 | + | 0.904550i | \(0.359793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0000 | −0.385787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.69848 | 0.199609 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.31371 | 0.115932 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.4853 | −1.02904 | −0.514522 | − | 0.857477i | \(-0.672031\pi\) | ||||
−0.514522 | + | 0.857477i | \(0.672031\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.4558 | 1.51478 | 0.757388 | − | 0.652965i | \(-0.226475\pi\) | ||||
0.757388 | + | 0.652965i | \(0.226475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.2426 | 0.391419 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.3553 | 0.742598 | 0.371299 | − | 0.928513i | \(-0.378913\pi\) | ||||
0.371299 | + | 0.928513i | \(0.378913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7574 | 0.755664 | 0.377832 | − | 0.925874i | \(-0.376670\pi\) | ||||
0.377832 | + | 0.925874i | \(0.376670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.41421 | 0.153127 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.04163 | 0.278292 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.65685 | −0.0572693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.4853 | 0.638183 | 0.319091 | − | 0.947724i | \(-0.396622\pi\) | ||||
0.319091 | + | 0.947724i | \(0.396622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9411 | −0.756591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.0711 | 0.725726 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.970563 | −0.0333884 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.5269 | 1.94000 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.7696 | −2.01459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.970563 | −0.0331925 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.6274 | −1.18285 | −0.591425 | − | 0.806360i | \(-0.701434\pi\) | ||||
−0.591425 | + | 0.806360i | \(0.701434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.72792 | 0.195434 | 0.0977171 | − | 0.995214i | \(-0.468846\pi\) | ||||
0.0977171 | + | 0.995214i | \(0.468846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.2132 | −1.19867 | −0.599336 | − | 0.800498i | \(-0.704569\pi\) | ||||
−0.599336 | + | 0.800498i | \(0.704569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.75736 | 0.195756 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.75736 | −0.297416 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.2426 | −0.449226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5563 | 0.357688 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.8284 | −0.366487 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6274 | 0.662771 | 0.331385 | − | 0.943495i | \(-0.392484\pi\) | ||||
0.331385 | + | 0.943495i | \(0.392484\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.1421 | −0.881752 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.45584 | 0.217503 | 0.108751 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108751 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7279 | −0.529287 | −0.264643 | − | 0.964346i | \(-0.585254\pi\) | ||||
−0.264643 | + | 0.964346i | \(0.585254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.89949 | −0.265539 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.10051 | 0.104105 | 0.0520524 | − | 0.998644i | \(-0.483424\pi\) | ||||
0.0520524 | + | 0.998644i | \(0.483424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48528 | 0.317769 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.14214 | 0.205539 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.526912 | 0.0176127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −57.6985 | −1.92650 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6274 | 0.354444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.8873 | 0.962376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.48528 | 0.149096 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.6863 | −0.354832 | −0.177416 | − | 0.984136i | \(-0.556774\pi\) | ||||
−0.177416 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.4558 | 0.578974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4853 | 1.01002 | 0.505011 | − | 0.863113i | \(-0.331488\pi\) | ||||
0.505011 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.1421 | −0.401846 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.7279 | −0.553008 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.1421 | −0.730402 | −0.365201 | − | 0.930929i | \(-0.619000\pi\) | ||||
−0.365201 | + | 0.930929i | \(0.619000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8995 | −0.787515 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.3848 | −1.39511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.8406 | 1.44147 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.9411 | −1.24615 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.4558 | −1.32731 | −0.663657 | − | 0.748037i | \(-0.730996\pi\) | ||||
−0.663657 | + | 0.748037i | \(0.730996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.3848 | −1.32214 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14214 | 0.0700553 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.4142 | −0.634235 | −0.317117 | − | 0.948386i | \(-0.602715\pi\) | ||||
−0.317117 | + | 0.948386i | \(0.602715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.8701 | −1.62745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.6569 | 0.803790 | 0.401895 | − | 0.915686i | \(-0.368352\pi\) | ||||
0.401895 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.7990 | −1.10065 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.8284 | −1.13177 | −0.565886 | − | 0.824484i | \(-0.691466\pi\) | ||||
−0.565886 | + | 0.824484i | \(0.691466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0416 | 1.16996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.9706 | 0.680017 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.55635 | 0.179988 | 0.0899939 | − | 0.995942i | \(-0.471315\pi\) | ||||
0.0899939 | + | 0.995942i | \(0.471315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.20101 | −0.135941 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.41421 | −0.207342 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.68629 | 0.279912 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8284 | −0.412962 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2843 | 1.16682 | 0.583412 | − | 0.812177i | \(-0.301717\pi\) | ||||
0.583412 | + | 0.812177i | \(0.301717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.17157 | 0.166135 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2721 | −0.714745 | −0.357372 | − | 0.933962i | \(-0.616327\pi\) | ||||
−0.357372 | + | 0.933962i | \(0.616327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.0416 | 1.37844 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.0000 | 1.27971 | 0.639857 | − | 0.768494i | \(-0.278994\pi\) | ||||
0.639857 | + | 0.768494i | \(0.278994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4853 | −0.399031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.6274 | 1.48870 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.4264 | −1.03424 | −0.517121 | − | 0.855912i | \(-0.672996\pi\) | ||||
−0.517121 | + | 0.855912i | \(0.672996\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.301515 | 0.00960707 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.3137 | 1.12291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.61522 | 0.0513093 | 0.0256546 | − | 0.999671i | \(-0.491833\pi\) | ||||
0.0256546 | + | 0.999671i | \(0.491833\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 58.1127 | 1.84415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0588745 | 0.00186645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1716 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.89949 | 0.123375 |
(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 | 8624.2.a.cc.1.2 | 2 | ||
4.3 | odd | 2 | 1078.2.a.t.1.1 | 2 | |||
7.2 | even | 3 | 1232.2.q.f.529.1 | 4 | |||
7.4 | even | 3 | 1232.2.q.f.177.1 | 4 | |||
7.6 | odd | 2 | 8624.2.a.bh.1.1 | 2 | |||
12.11 | even | 2 | 9702.2.a.cx.1.1 | 2 | |||
28.3 | even | 6 | 1078.2.e.m.177.1 | 4 | |||
28.11 | odd | 6 | 154.2.e.e.23.2 | ✓ | 4 | ||
28.19 | even | 6 | 1078.2.e.m.67.1 | 4 | |||
28.23 | odd | 6 | 154.2.e.e.67.2 | yes | 4 | ||
28.27 | even | 2 | 1078.2.a.x.1.2 | 2 | |||
84.11 | even | 6 | 1386.2.k.t.793.2 | 4 | |||
84.23 | even | 6 | 1386.2.k.t.991.2 | 4 | |||
84.83 | odd | 2 | 9702.2.a.ch.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.e.23.2 | ✓ | 4 | 28.11 | odd | 6 | ||
154.2.e.e.67.2 | yes | 4 | 28.23 | odd | 6 | ||
1078.2.a.t.1.1 | 2 | 4.3 | odd | 2 | |||
1078.2.a.x.1.2 | 2 | 28.27 | even | 2 | |||
1078.2.e.m.67.1 | 4 | 28.19 | even | 6 | |||
1078.2.e.m.177.1 | 4 | 28.3 | even | 6 | |||
1232.2.q.f.177.1 | 4 | 7.4 | even | 3 | |||
1232.2.q.f.529.1 | 4 | 7.2 | even | 3 | |||
1386.2.k.t.793.2 | 4 | 84.11 | even | 6 | |||
1386.2.k.t.991.2 | 4 | 84.23 | even | 6 | |||
8624.2.a.bh.1.1 | 2 | 7.6 | odd | 2 | |||
8624.2.a.cc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9702.2.a.ch.1.2 | 2 | 84.83 | odd | 2 | |||
9702.2.a.cx.1.1 | 2 | 12.11 | even | 2 |