Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(1,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.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: | \(12.2650217505\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.82843 | −1.42383 | −0.711913 | − | 0.702268i | \(-0.752171\pi\) | ||||
−0.711913 | + | 0.702268i | \(0.752171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.58579 | 0.851559 | 0.425780 | − | 0.904827i | \(-0.360000\pi\) | ||||
0.425780 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.07107 | 1.27000 | 0.635001 | − | 0.772512i | \(-0.281000\pi\) | ||||
0.635001 | + | 0.772512i | \(0.281000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.828427 | 0.144211 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.828427 | −0.140030 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.343146 | 0.0564128 | 0.0282064 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282064 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.82843 | −0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.48528 | 1.01283 | 0.506415 | − | 0.862290i | \(-0.330970\pi\) | ||||
0.506415 | + | 0.862290i | \(0.330970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.17157 | −0.178663 | −0.0893316 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893316 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.585786 | 0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.48528 | 0.654246 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.828427 | 0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.2426 | 1.40693 | 0.703467 | − | 0.710727i | \(-0.251634\pi\) | ||||
0.703467 | + | 0.710727i | \(0.251634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.485281 | −0.0654353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6569 | 1.49251 | 0.746254 | − | 0.665662i | \(-0.231851\pi\) | ||||
0.746254 | + | 0.665662i | \(0.231851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.82843 | 0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.82843 | 0.822046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | −1.00702 | −0.503509 | − | 0.863990i | \(-0.667958\pi\) | ||||
−0.503509 | + | 0.863990i | \(0.667958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3137 | 1.32417 | 0.662085 | − | 0.749429i | \(-0.269672\pi\) | ||||
0.662085 | + | 0.749429i | \(0.269672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.17157 | 0.133513 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5858 | 1.64103 | 0.820515 | − | 0.571626i | \(-0.193687\pi\) | ||||
0.820515 | + | 0.571626i | \(0.193687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.17157 | 0.348125 | 0.174063 | − | 0.984735i | \(-0.444310\pi\) | ||||
0.174063 | + | 0.984735i | \(0.444310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.485281 | −0.0526362 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.58579 | −0.491648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.3137 | −1.83525 | −0.917625 | − | 0.397448i | \(-0.869896\pi\) | ||||
−0.917625 | + | 0.397448i | \(0.869896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82843 | −0.715814 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.07107 | −0.733236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.65685 | 0.169990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.65685 | 0.371297 | 0.185649 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185649 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.828427 | −0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7279 | 1.46548 | 0.732742 | − | 0.680507i | \(-0.238240\pi\) | ||||
0.732742 | + | 0.680507i | \(0.238240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.58579 | 0.648917 | 0.324458 | − | 0.945900i | \(-0.394818\pi\) | ||||
0.324458 | + | 0.945900i | \(0.394818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.828427 | 0.0808462 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3137 | −1.48043 | −0.740216 | − | 0.672369i | \(-0.765277\pi\) | ||||
−0.740216 | + | 0.672369i | \(0.765277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8284 | 1.22874 | 0.614370 | − | 0.789018i | \(-0.289410\pi\) | ||||
0.614370 | + | 0.789018i | \(0.289410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.82843 | 0.446388 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.17157 | 0.107398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.48528 | −0.584758 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8995 | 1.58832 | 0.794162 | − | 0.607707i | \(-0.207910\pi\) | ||||
0.794162 | + | 0.607707i | \(0.207910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.17157 | 0.103151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.31371 | 0.639002 | 0.319501 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319501 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4853 | 1.23756 | 0.618781 | − | 0.785564i | \(-0.287627\pi\) | ||||
0.618781 | + | 0.785564i | \(0.287627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.48528 | −0.377729 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.68629 | 0.223084 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.585786 | 0.0479895 | 0.0239947 | − | 0.999712i | \(-0.492362\pi\) | ||||
0.0239947 | + | 0.999712i | \(0.492362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.41421 | 0.766118 | 0.383059 | − | 0.923724i | \(-0.374871\pi\) | ||||
0.383059 | + | 0.923724i | \(0.374871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.828427 | −0.0669744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.14214 | 0.332704 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.31371 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.2426 | −0.812294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.65685 | 0.761067 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.48528 | 0.351314 | 0.175657 | − | 0.984451i | \(-0.443795\pi\) | ||||
0.175657 | + | 0.984451i | \(0.443795\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.485281 | 0.0377791 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.8995 | −0.904702 | −0.452351 | − | 0.891840i | \(-0.649415\pi\) | ||||
−0.452351 | + | 0.891840i | \(0.649415\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.58579 | 0.497839 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.65685 | −0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.6569 | −1.91768 | −0.958842 | − | 0.283941i | \(-0.908358\pi\) | ||||
−0.958842 | + | 0.283941i | \(0.908358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1421 | −1.19984 | −0.599918 | − | 0.800062i | \(-0.704800\pi\) | ||||
−0.599918 | + | 0.800062i | \(0.704800\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6569 | −0.861699 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.201010 | 0.0147786 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.686292 | 0.0501866 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | 0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.31371 | −0.529201 | −0.264601 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264601 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3137 | 0.814379 | 0.407189 | − | 0.913344i | \(-0.366509\pi\) | ||||
0.407189 | + | 0.913344i | \(0.366509\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.82843 | −0.202548 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.41421 | −0.243253 | −0.121626 | − | 0.992576i | \(-0.538811\pi\) | ||||
−0.121626 | + | 0.992576i | \(0.538811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2426 | 1.43496 | 0.717481 | − | 0.696578i | \(-0.245295\pi\) | ||||
0.717481 | + | 0.696578i | \(0.245295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.65685 | 0.399004 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.48528 | −0.455178 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.79899 | 0.265333 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.82843 | −0.474608 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.34315 | −0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | 0.581402 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.686292 | −0.0468047 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | −0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.3137 | −0.764510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.55635 | −0.506011 | −0.253005 | − | 0.967465i | \(-0.581419\pi\) | ||||
−0.253005 | + | 0.967465i | \(0.581419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1421 | 1.07139 | 0.535696 | − | 0.844411i | \(-0.320049\pi\) | ||||
0.535696 | + | 0.844411i | \(0.320049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7990 | −1.44052 | −0.720259 | − | 0.693705i | \(-0.755977\pi\) | ||||
−0.720259 | + | 0.693705i | \(0.755977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.17157 | −0.0770838 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.00000 | −0.131024 | −0.0655122 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655122 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.62742 | 0.171394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.5858 | −0.947449 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.65685 | −0.622053 | −0.311026 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311026 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.92893 | −0.187123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6569 | 0.868965 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.17157 | −0.200990 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7990 | 1.37594 | 0.687970 | − | 0.725739i | \(-0.258502\pi\) | ||||
0.687970 | + | 0.725739i | \(0.258502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65685 | 0.355643 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.485281 | 0.0303895 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.34315 | −0.520431 | −0.260216 | − | 0.965551i | \(-0.583794\pi\) | ||||
−0.260216 | + | 0.965551i | \(0.583794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.485281 | −0.0301539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.58579 | 0.283853 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.97056 | 0.553149 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.3137 | 1.05958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.24264 | −0.136736 | −0.0683681 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683681 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2426 | −0.743687 | −0.371844 | − | 0.928295i | \(-0.621274\pi\) | ||||
−0.371844 | + | 0.928295i | \(0.621274\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.82843 | 0.413275 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.85786 | 0.232638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8284 | −1.25146 | −0.625729 | − | 0.780040i | \(-0.715199\pi\) | ||||
−0.625729 | + | 0.780040i | \(0.715199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.07107 | 0.423334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3431 | −0.736330 | −0.368165 | − | 0.929760i | \(-0.620014\pi\) | ||||
−0.368165 | + | 0.929760i | \(0.620014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9706 | −1.24657 | −0.623285 | − | 0.781995i | \(-0.714202\pi\) | ||||
−0.623285 | + | 0.781995i | \(0.714202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.65685 | −0.0981436 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.17157 | −0.541381 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.65685 | −0.214369 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.0711 | −0.997302 | −0.498651 | − | 0.866803i | \(-0.666171\pi\) | ||||
−0.498651 | + | 0.866803i | \(0.666171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.65685 | 0.329355 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.828427 | 0.0480702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −32.9706 | −1.90674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65685 | 0.0954995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7279 | −0.846097 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.82843 | 0.390995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.6569 | −1.69261 | −0.846303 | − | 0.532702i | \(-0.821177\pi\) | ||||
−0.846303 | + | 0.532702i | \(0.821177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.58579 | −0.374652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68629 | −0.265735 | −0.132868 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132868 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.828427 | −0.0466766 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.8995 | −1.79165 | −0.895827 | − | 0.444403i | \(-0.853416\pi\) | ||||
−0.895827 | + | 0.444403i | \(0.853416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.79899 | −0.212703 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3137 | 0.854728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.34315 | −0.130376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.4853 | −1.24726 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.8284 | −0.709414 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.34315 | −0.349709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6569 | 0.750649 | 0.375324 | − | 0.926894i | \(-0.377531\pi\) | ||||
0.375324 | + | 0.926894i | \(0.377531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.343146 | 0.0188043 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.31371 | −0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.31371 | 0.180509 | 0.0902546 | − | 0.995919i | \(-0.471232\pi\) | ||||
0.0902546 | + | 0.995919i | \(0.471232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.65685 | 0.415863 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.85786 | −0.317221 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.7990 | 0.955500 | 0.477750 | − | 0.878496i | \(-0.341453\pi\) | ||||
0.477750 | + | 0.878496i | \(0.341453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.31371 | 0.0703212 | 0.0351606 | − | 0.999382i | \(-0.488806\pi\) | ||||
0.0351606 | + | 0.999382i | \(0.488806\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.97056 | −0.263810 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.17157 | −0.0620062 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4853 | 1.29228 | 0.646142 | − | 0.763217i | \(-0.276381\pi\) | ||||
0.646142 | + | 0.763217i | \(0.276381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3137 | 0.541329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.62742 | 0.346895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0711 | 0.786703 | 0.393352 | − | 0.919388i | \(-0.371315\pi\) | ||||
0.393352 | + | 0.919388i | \(0.371315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.48528 | 0.337610 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.4853 | −0.752038 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.343146 | −0.0177674 | −0.00888371 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888371 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.1421 | 1.14038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.8284 | −0.556219 | −0.278109 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278109 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.8995 | −0.917019 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.6569 | −1.71978 | −0.859892 | − | 0.510475i | \(-0.829470\pi\) | ||||
−0.859892 | + | 0.510475i | \(0.829470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.686292 | 0.0349767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.17157 | −0.0595544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0711 | 0.662729 | 0.331365 | − | 0.943503i | \(-0.392491\pi\) | ||||
0.331365 | + | 0.943503i | \(0.392491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685 | 0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.31371 | −0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.54416 | 0.429903 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.51472 | 0.0756414 | 0.0378207 | − | 0.999285i | \(-0.487958\pi\) | ||||
0.0378207 | + | 0.999285i | \(0.487958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.1421 | 1.70074 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.284271 | −0.0140908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.3431 | 1.00590 | 0.502952 | − | 0.864314i | \(-0.332247\pi\) | ||||
0.502952 | + | 0.864314i | \(0.332247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4853 | −0.714506 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.6569 | −0.672010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.85786 | 0.0911990 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0000 | −0.783523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.82843 | 0.235884 | 0.117942 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117942 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.51472 | 0.268771 | 0.134385 | − | 0.990929i | \(-0.457094\pi\) | ||||
0.134385 | + | 0.990929i | \(0.457094\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.48528 | 0.218082 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.85786 | 0.187134 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.4853 | −0.797779 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.85786 | 0.282163 | 0.141082 | − | 0.989998i | \(-0.454942\pi\) | ||||
0.141082 | + | 0.989998i | \(0.454942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.68629 | −0.128798 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.3137 | −0.923900 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.2132 | 1.01245 | 0.506225 | − | 0.862401i | \(-0.331040\pi\) | ||||
0.506225 | + | 0.862401i | \(0.331040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.4853 | 1.44840 | 0.724200 | − | 0.689590i | \(-0.242209\pi\) | ||||
0.724200 | + | 0.689590i | \(0.242209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1421 | −0.480783 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.585786 | −0.0277067 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.7990 | −1.21753 | −0.608765 | − | 0.793351i | \(-0.708335\pi\) | ||||
−0.608765 | + | 0.793351i | \(0.708335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.37258 | −0.252985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.41421 | −0.442318 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2843 | −1.04241 | −0.521207 | − | 0.853430i | \(-0.674518\pi\) | ||||
−0.521207 | + | 0.853430i | \(0.674518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.828427 | 0.0386677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2132 | −1.08115 | −0.540573 | − | 0.841297i | \(-0.681793\pi\) | ||||
−0.540573 | + | 0.841297i | \(0.681793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.75736 | −0.174619 | −0.0873096 | − | 0.996181i | \(-0.527827\pi\) | ||||
−0.0873096 | + | 0.996181i | \(0.527827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.14214 | −0.192087 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8284 | 0.963825 | 0.481912 | − | 0.876219i | \(-0.339942\pi\) | ||||
0.481912 | + | 0.876219i | \(0.339942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.31371 | −0.244843 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.970563 | 0.0446265 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.1716 | −0.604353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.2426 | 0.468978 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.1716 | 0.967354 | 0.483677 | − | 0.875247i | \(-0.339301\pi\) | ||||
0.483677 | + | 0.875247i | \(0.339301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.65685 | 0.0755461 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.65685 | −0.439402 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.14214 | 0.0972694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.72792 | −0.214243 | −0.107121 | − | 0.994246i | \(-0.534163\pi\) | ||||
−0.107121 | + | 0.994246i | \(0.534163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.48528 | −0.202831 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.2843 | −1.81800 | −0.909002 | − | 0.416792i | \(-0.863154\pi\) | ||||
−0.909002 | + | 0.416792i | \(0.863154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.79899 | −0.171098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.485281 | −0.0218118 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2843 | 0.728984 | 0.364492 | − | 0.931207i | \(-0.381243\pi\) | ||||
0.364492 | + | 0.931207i | \(0.381243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7990 | 0.526091 | 0.263045 | − | 0.964783i | \(-0.415273\pi\) | ||||
0.263045 | + | 0.964783i | \(0.415273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62742 | 0.383915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3137 | −0.458048 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.8701 | 1.81153 | 0.905767 | − | 0.423777i | \(-0.139296\pi\) | ||||
0.905767 | + | 0.423777i | \(0.139296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.85786 | 0.169998 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.71573 | −0.163418 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8995 | 0.522330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.1421 | −0.531957 | −0.265978 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265978 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.4558 | 1.81274 | 0.906369 | − | 0.422488i | \(-0.138843\pi\) | ||||
0.906369 | + | 0.422488i | \(0.138843\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.58579 | −0.287427 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.85786 | −0.255173 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.65685 | 0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.3137 | 1.35635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.97056 | −0.387831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.6569 | 1.10717 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.14214 | 0.178414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.828427 | 0.0356169 | 0.0178084 | − | 0.999841i | \(-0.494331\pi\) | ||||
0.0178084 | + | 0.999841i | \(0.494331\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1421 | 0.692725 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.51472 | 0.321895 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1421 | −0.775702 | −0.387851 | − | 0.921722i | \(-0.626782\pi\) | ||||
−0.387851 | + | 0.921722i | \(0.626782\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6569 | 0.497502 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9706 | 0.552565 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.6274 | −0.877167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.201010 | −0.00853240 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.7279 | −0.454557 | −0.227278 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227278 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65685 | −0.239259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.686292 | −0.0289752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.8284 | −1.38355 | −0.691777 | − | 0.722112i | \(-0.743172\pi\) | ||||
−0.691777 | + | 0.722112i | \(0.743172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.48528 | −0.188697 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.41421 | −0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1127 | 1.55585 | 0.777923 | − | 0.628360i | \(-0.216274\pi\) | ||||
0.777923 | + | 0.628360i | \(0.216274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0000 | 1.50655 | 0.753277 | − | 0.657704i | \(-0.228472\pi\) | ||||
0.753277 | + | 0.657704i | \(0.228472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.31371 | 0.305535 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.7990 | 1.32611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.68629 | 0.361615 | 0.180808 | − | 0.983518i | \(-0.442129\pi\) | ||||
0.180808 | + | 0.983518i | \(0.442129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3137 | −0.470182 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.48528 | −0.186081 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.48528 | −0.351424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.82843 | 0.116941 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.9706 | −0.535352 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.41421 | 0.140442 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.6569 | −1.29999 | −0.649996 | − | 0.759938i | \(-0.725229\pi\) | ||||
−0.649996 | + | 0.759938i | \(0.725229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.686292 | 0.0281352 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.2426 | −0.828476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.51472 | −0.143608 | −0.0718038 | − | 0.997419i | \(-0.522876\pi\) | ||||
−0.0718038 | + | 0.997419i | \(0.522876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.6274 | 1.08615 | 0.543077 | − | 0.839683i | \(-0.317259\pi\) | ||||
0.543077 | + | 0.839683i | \(0.317259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.04163 | −0.245627 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.89949 | 0.401808 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.48528 | 0.262797 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.6569 | 0.876143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.6274 | 1.64093 | 0.820463 | − | 0.571700i | \(-0.193716\pi\) | ||||
0.820463 | + | 0.571700i | \(0.193716\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.79899 | −0.153190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3137 | −1.18013 | −0.590063 | − | 0.807357i | \(-0.700897\pi\) | ||||
−0.590063 | + | 0.807357i | \(0.700897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.82843 | 0.274015 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.4853 | 0.980982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.34315 | 0.0935762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.284271 | −0.0113346 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.7279 | −1.78059 | −0.890295 | − | 0.455384i | \(-0.849502\pi\) | ||||
−0.890295 | + | 0.455384i | \(0.849502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0000 | −0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.4853 | 0.416096 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1421 | −0.956546 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.48528 | −0.335673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8284 | −1.13865 | −0.569327 | − | 0.822111i | \(-0.692796\pi\) | ||||
−0.569327 | + | 0.822111i | \(0.692796\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.1127 | −0.753731 | −0.376866 | − | 0.926268i | \(-0.622998\pi\) | ||||
−0.376866 | + | 0.926268i | \(0.622998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.686292 | 0.0270227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.4264 | −1.51070 | −0.755349 | − | 0.655323i | \(-0.772533\pi\) | ||||
−0.755349 | + | 0.655323i | \(0.772533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | 0.391931 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.3848 | 1.26731 | 0.633657 | − | 0.773614i | \(-0.281553\pi\) | ||||
0.633657 | + | 0.773614i | \(0.281553\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28427 | 0.167400 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3137 | 0.441390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.3431 | 0.558730 | 0.279365 | − | 0.960185i | \(-0.409876\pi\) | ||||
0.279365 | + | 0.960185i | \(0.409876\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.34315 | −0.0908633 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3137 | −1.21247 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.55635 | 0.292145 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.65685 | −0.372799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6863 | −0.720304 | −0.360152 | − | 0.932894i | \(-0.617275\pi\) | ||||
−0.360152 | + | 0.932894i | \(0.617275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.0711 | −0.809827 | −0.404913 | − | 0.914355i | \(-0.632698\pi\) | ||||
−0.404913 | + | 0.914355i | \(0.632698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.17157 | −0.198467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.1421 | −0.618568 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.8579 | −0.606784 | −0.303392 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303392 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.48528 | 0.324206 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.7990 | 0.831683 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.4558 | 1.88412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.8284 | −1.17277 | −0.586384 | − | 0.810033i | \(-0.699449\pi\) | ||||
−0.586384 | + | 0.810033i | \(0.699449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.17157 | 0.0445044 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.37258 | 0.355522 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.37258 | −0.203501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.00000 | 0.0756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.7279 | 1.16058 | 0.580289 | − | 0.814411i | \(-0.302940\pi\) | ||||
0.580289 | + | 0.814411i | \(0.302940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.970563 | 0.0366055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.62742 | −0.0989542 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.8284 | −0.783334 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1716 | 1.32090 | 0.660448 | − | 0.750872i | \(-0.270366\pi\) | ||||
0.660448 | + | 0.750872i | \(0.270366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5858 | 0.547010 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.2843 | −1.80826 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.34315 | −0.0876287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.3137 | 0.870666 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.48528 | −0.316448 | −0.158224 | − | 0.987403i | \(-0.550577\pi\) | ||||
−0.158224 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.31371 | −0.346861 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.65685 | 0.359142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.3553 | −0.793117 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.5269 | −1.50306 | −0.751530 | − | 0.659699i | \(-0.770684\pi\) | ||||
−0.751530 | + | 0.659699i | \(0.770684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.970563 | 0.0358976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.17157 | 0.117145 | 0.0585724 | − | 0.998283i | \(-0.481345\pi\) | ||||
0.0585724 | + | 0.998283i | \(0.481345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.92893 | 0.108035 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.68629 | 0.172622 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3137 | 1.15189 | 0.575947 | − | 0.817487i | \(-0.304634\pi\) | ||||
0.575947 | + | 0.817487i | \(0.304634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.6569 | −0.501697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.2843 | −1.77138 | −0.885689 | − | 0.464279i | \(-0.846314\pi\) | ||||
−0.885689 | + | 0.464279i | \(0.846314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.343146 | 0.0125719 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.17157 | 0.116042 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.6569 | 0.791324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4142 | −0.635454 | −0.317727 | − | 0.948182i | \(-0.602919\pi\) | ||||
−0.317727 | + | 0.948182i | \(0.602919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.7990 | −0.794399 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.51472 | 0.200701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7696 | 0.972956 | 0.486478 | − | 0.873693i | \(-0.338281\pi\) | ||||
0.486478 | + | 0.873693i | \(0.338281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.65685 | −0.205331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8284 | 1.04503 | 0.522515 | − | 0.852630i | \(-0.324994\pi\) | ||||
0.522515 | + | 0.852630i | \(0.324994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.1421 | −0.656789 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.485281 | −0.0175454 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.6274 | 1.68362 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.3137 | −0.984958 | −0.492479 | − | 0.870324i | \(-0.663909\pi\) | ||||
−0.492479 | + | 0.870324i | \(0.663909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.34315 | 0.300471 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.7574 | 1.07030 | 0.535149 | − | 0.844758i | \(-0.320255\pi\) | ||||
0.535149 | + | 0.844758i | \(0.320255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.9289 | −1.18284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.485281 | 0.0174094 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.3431 | 0.657211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.02944 | 0.251533 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.58579 | −0.163883 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.11270 | 0.111097 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8284 | 0.671161 | 0.335580 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335580 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.97056 | −0.319360 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.8284 | 0.385015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.2843 | 1.99871 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.5269 | 0.939631 | 0.469816 | − | 0.882765i | \(-0.344320\pi\) | ||||
0.469816 | + | 0.882765i | \(0.344320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.71573 | −0.131453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.3137 | −0.611750 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.37258 | −0.330751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.65685 | 0.199378 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.24264 | 0.0789447 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.5147 | 0.756417 | 0.378209 | − | 0.925720i | \(-0.376540\pi\) | ||||
0.378209 | + | 0.925720i | \(0.376540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4853 | −0.578877 | −0.289438 | − | 0.957197i | \(-0.593468\pi\) | ||||
−0.289438 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2426 | 0.429368 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.62742 | 0.0920344 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31371 | −0.115932 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.82843 | −0.238605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.0122 | 1.22193 | 0.610967 | − | 0.791656i | \(-0.290781\pi\) | ||||
0.610967 | + | 0.791656i | \(0.290781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.0711 | −1.08307 | −0.541535 | − | 0.840678i | \(-0.682157\pi\) | ||||
−0.541535 | + | 0.840678i | \(0.682157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.85786 | −0.134314 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6274 | 1.20411 | 0.602057 | − | 0.798453i | \(-0.294348\pi\) | ||||
0.602057 | + | 0.798453i | \(0.294348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5147 | 0.886163 | 0.443081 | − | 0.896481i | \(-0.353885\pi\) | ||||
0.443081 | + | 0.896481i | \(0.353885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.8284 | 0.722530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.14214 | 0.143516 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.02944 | −0.243264 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.07107 | −0.244412 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.1127 | 1.90270 | 0.951351 | − | 0.308110i | \(-0.0996964\pi\) | ||||
0.951351 | + | 0.308110i | \(0.0996964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.97056 | −0.274847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.3431 | 0.425121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.04163 | 0.207838 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5858 | 0.501174 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.9706 | 0.719708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.34315 | −0.0803220 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3137 | 0.729767 | 0.364884 | − | 0.931053i | \(-0.381109\pi\) | ||||
0.364884 | + | 0.931053i | \(0.381109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.65685 | 0.0566632 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.4853 | −0.358170 | −0.179085 | − | 0.983834i | \(-0.557314\pi\) | ||||
−0.179085 | + | 0.983834i | \(0.557314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8284 | 0.505939 | 0.252970 | − | 0.967474i | \(-0.418593\pi\) | ||||
0.252970 | + | 0.967474i | \(0.418593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.17157 | 0.312566 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.00000 | −0.136162 | −0.0680808 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680808 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.97056 | −0.237006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3137 | 0.554043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0833 | −0.409897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.3137 | −0.925490 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.65685 | 0.123766 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.00000 | 0.270449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.9411 | −1.21365 | −0.606823 | − | 0.794837i | \(-0.707556\pi\) | ||||
−0.606823 | + | 0.794837i | \(0.707556\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.0711 | 0.575793 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.6569 | 0.527493 | 0.263746 | − | 0.964592i | \(-0.415042\pi\) | ||||
0.263746 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7990 | −0.531678 | −0.265839 | − | 0.964017i | \(-0.585649\pi\) | ||||
−0.265839 | + | 0.964017i | \(0.585649\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.65685 | −0.190153 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.2843 | −1.75553 | −0.877767 | − | 0.479088i | \(-0.840968\pi\) | ||||
−0.877767 | + | 0.479088i | \(0.840968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.3137 | −0.848995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.828427 | −0.0277534 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.6863 | 0.424531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0294 | −0.502379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.9706 | 1.10086 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.4264 | 1.08148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.48528 | −0.282686 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.65685 | −0.0551367 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.45584 | −0.314323 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.8284 | 1.02364 | 0.511821 | − | 0.859092i | \(-0.328971\pi\) | ||||
0.511821 | + | 0.859092i | \(0.328971\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.7279 | 0.488494 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.5980 | 1.97457 | 0.987285 | − | 0.158963i | \(-0.0508150\pi\) | ||||
0.987285 | + | 0.158963i | \(0.0508150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.62742 | −0.0869548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.82843 | −0.225741 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3431 | −0.341561 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5563 | 0.513157 | 0.256578 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256578 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6569 | 0.977227 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.9706 | −1.34856 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.59798 | −0.0525413 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.58579 | 0.216306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8579 | 0.651515 | 0.325758 | − | 0.945453i | \(-0.394381\pi\) | ||||
0.325758 | + | 0.945453i | \(0.394381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1421 | −0.463490 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.68629 | 0.153422 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.402020 | 0.0131475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.62742 | −0.281845 | −0.140923 | − | 0.990021i | \(-0.545007\pi\) | ||||
−0.140923 | + | 0.990021i | \(0.545007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0416 | 0.979329 | 0.489665 | − | 0.871911i | \(-0.337119\pi\) | ||||
0.489665 | + | 0.871911i | \(0.337119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.2843 | −1.44209 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.828427 | 0.0269487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.3431 | −1.24598 | −0.622992 | − | 0.782228i | \(-0.714083\pi\) | ||||
−0.622992 | + | 0.782228i | \(0.714083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.6274 | 1.77328 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.8995 | 1.03441 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.4853 | 1.11709 | 0.558544 | − | 0.829475i | \(-0.311360\pi\) | ||||
0.558544 | + | 0.829475i | \(0.311360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.28427 | −0.138636 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.79899 | 0.122804 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.4853 | −0.661504 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3137 | −0.493477 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.62742 | 0.213344 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.5269 | −1.56052 | −0.780260 | − | 0.625455i | \(-0.784913\pi\) | ||||
−0.780260 | + | 0.625455i | \(0.784913\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.34315 | 0.0752727 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.1716 | −0.615245 | −0.307623 | − | 0.951508i | \(-0.599533\pi\) | ||||
−0.307623 | + | 0.951508i | \(0.599533\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.6274 | −0.725402 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22.4853 | 0.720105 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.8284 | −1.30622 | −0.653109 | − | 0.757264i | \(-0.726535\pi\) | ||||
−0.653109 | + | 0.757264i | \(0.726535\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3431 | 0.458409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8284 | 0.409580 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.3431 | 0.840216 | 0.420108 | − | 0.907474i | \(-0.361992\pi\) | ||||
0.420108 | + | 0.907474i | \(0.361992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | −0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.34315 | 0.201905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.1005 | −0.702046 | −0.351023 | − | 0.936367i | \(-0.614166\pi\) | ||||
−0.351023 | + | 0.936367i | \(0.614166\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.6569 | −0.433387 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8579 | 0.375920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.97056 | 0.220760 | 0.110380 | − | 0.993889i | \(-0.464793\pi\) | ||||
0.110380 | + | 0.993889i | \(0.464793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.343146 | −0.0108567 |
(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 | 1536.2.a.f.1.1 | yes | 2 | |
3.2 | odd | 2 | 4608.2.a.b.1.2 | 2 | |||
4.3 | odd | 2 | 1536.2.a.k.1.1 | yes | 2 | ||
8.3 | odd | 2 | 1536.2.a.a.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 1536.2.a.h.1.2 | yes | 2 | ||
12.11 | even | 2 | 4608.2.a.d.1.2 | 2 | |||
16.3 | odd | 4 | 1536.2.d.e.769.4 | 4 | |||
16.5 | even | 4 | 1536.2.d.b.769.3 | 4 | |||
16.11 | odd | 4 | 1536.2.d.e.769.1 | 4 | |||
16.13 | even | 4 | 1536.2.d.b.769.2 | 4 | |||
24.5 | odd | 2 | 4608.2.a.q.1.1 | 2 | |||
24.11 | even | 2 | 4608.2.a.o.1.1 | 2 | |||
48.5 | odd | 4 | 4608.2.d.f.2305.2 | 4 | |||
48.11 | even | 4 | 4608.2.d.h.2305.2 | 4 | |||
48.29 | odd | 4 | 4608.2.d.f.2305.3 | 4 | |||
48.35 | even | 4 | 4608.2.d.h.2305.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.a.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
1536.2.a.f.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1536.2.a.h.1.2 | yes | 2 | 8.5 | even | 2 | ||
1536.2.a.k.1.1 | yes | 2 | 4.3 | odd | 2 | ||
1536.2.d.b.769.2 | 4 | 16.13 | even | 4 | |||
1536.2.d.b.769.3 | 4 | 16.5 | even | 4 | |||
1536.2.d.e.769.1 | 4 | 16.11 | odd | 4 | |||
1536.2.d.e.769.4 | 4 | 16.3 | odd | 4 | |||
4608.2.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
4608.2.a.d.1.2 | 2 | 12.11 | even | 2 | |||
4608.2.a.o.1.1 | 2 | 24.11 | even | 2 | |||
4608.2.a.q.1.1 | 2 | 24.5 | odd | 2 | |||
4608.2.d.f.2305.2 | 4 | 48.5 | odd | 4 | |||
4608.2.d.f.2305.3 | 4 | 48.29 | odd | 4 | |||
4608.2.d.h.2305.2 | 4 | 48.11 | even | 4 | |||
4608.2.d.h.2305.3 | 4 | 48.35 | even | 4 |