Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26795 | −0.479240 | −0.239620 | − | 0.970867i | \(-0.577023\pi\) | ||||
−0.239620 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.46410 | −0.441443 | −0.220722 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.46410 | 0.406069 | 0.203034 | − | 0.979172i | \(-0.434920\pi\) | ||||
0.203034 | + | 0.979172i | \(0.434920\pi\) | |||||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.46410 | 0.355097 | 0.177548 | − | 0.984112i | \(-0.443183\pi\) | ||||
0.177548 | + | 0.984112i | \(0.443183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.46410 | −0.312148 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.46410 | 0.287134 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.26795 | −0.239620 | ||||||||
\(29\) | 8.92820 | 1.65793 | 0.828963 | − | 0.559304i | \(-0.188931\pi\) | ||||
0.828963 | + | 0.559304i | \(0.188931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.73205 | −0.490691 | −0.245345 | − | 0.969436i | \(-0.578901\pi\) | ||||
−0.245345 | + | 0.969436i | \(0.578901\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.46410 | 0.251091 | ||||||||
\(35\) | 1.26795 | 0.214323 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −4.19615 | −0.680706 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.92820 | −1.05654 | −0.528271 | − | 0.849076i | \(-0.677159\pi\) | ||||
−0.528271 | + | 0.849076i | \(0.677159\pi\) | |||||||
\(44\) | −1.46410 | −0.220722 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 1.26795 | 0.184949 | 0.0924747 | − | 0.995715i | \(-0.470522\pi\) | ||||
0.0924747 | + | 0.995715i | \(0.470522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.46410 | 0.203034 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46410 | 0.197419 | ||||||||
\(56\) | −1.26795 | −0.169437 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.92820 | 1.17233 | ||||||||
\(59\) | −0.196152 | −0.0255369 | −0.0127684 | − | 0.999918i | \(-0.504064\pi\) | ||||
−0.0127684 | + | 0.999918i | \(0.504064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | −2.73205 | −0.346971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.46410 | −0.181599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6603 | 1.66887 | 0.834433 | − | 0.551110i | \(-0.185795\pi\) | ||||
0.834433 | + | 0.551110i | \(0.185795\pi\) | |||||||
\(68\) | 1.46410 | 0.177548 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.26795 | 0.151549 | ||||||||
\(71\) | 10.9282 | 1.29694 | 0.648470 | − | 0.761241i | \(-0.275409\pi\) | ||||
0.648470 | + | 0.761241i | \(0.275409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.19615 | −0.481332 | ||||||||
\(77\) | 1.85641 | 0.211557 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.26795 | 0.592691 | 0.296345 | − | 0.955081i | \(-0.404232\pi\) | ||||
0.296345 | + | 0.955081i | \(0.404232\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | 5.26795 | 0.578233 | 0.289116 | − | 0.957294i | \(-0.406639\pi\) | ||||
0.289116 | + | 0.957294i | \(0.406639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.46410 | −0.158804 | ||||||||
\(86\) | −6.92820 | −0.747087 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.46410 | −0.156074 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85641 | −0.194604 | ||||||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.26795 | 0.130779 | ||||||||
\(95\) | 4.19615 | 0.430516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −5.39230 | −0.544705 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.53590 | 0.252331 | 0.126166 | − | 0.992009i | \(-0.459733\pi\) | ||||
0.126166 | + | 0.992009i | \(0.459733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4641 | −1.32666 | −0.663329 | − | 0.748328i | \(-0.730857\pi\) | ||||
−0.663329 | + | 0.748328i | \(0.730857\pi\) | |||||||
\(104\) | 1.46410 | 0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −6.73205 | −0.650812 | −0.325406 | − | 0.945574i | \(-0.605501\pi\) | ||||
−0.325406 | + | 0.945574i | \(0.605501\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 1.46410 | 0.139597 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.26795 | −0.119810 | ||||||||
\(113\) | 17.4641 | 1.64288 | 0.821442 | − | 0.570292i | \(-0.193170\pi\) | ||||
0.821442 | + | 0.570292i | \(0.193170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | −0.746004 | ||||||||
\(116\) | 8.92820 | 0.828963 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.196152 | −0.0180573 | ||||||||
\(119\) | −1.85641 | −0.170177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 8.92820 | 0.808322 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.73205 | −0.245345 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6603 | −1.21215 | −0.606076 | − | 0.795407i | \(-0.707257\pi\) | ||||
−0.606076 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.46410 | −0.128410 | ||||||||
\(131\) | −12.5885 | −1.09986 | −0.549929 | − | 0.835211i | \(-0.685345\pi\) | ||||
−0.549929 | + | 0.835211i | \(0.685345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.32051 | 0.461347 | ||||||||
\(134\) | 13.6603 | 1.18007 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46410 | 0.125546 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 1.26795 | 0.107161 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.9282 | 0.917074 | ||||||||
\(143\) | −2.14359 | −0.179256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.92820 | −0.741447 | ||||||||
\(146\) | 12.9282 | 1.06995 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | 16.3923 | 1.34291 | 0.671455 | − | 0.741045i | \(-0.265670\pi\) | ||||
0.671455 | + | 0.741045i | \(0.265670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.39230 | 0.682956 | 0.341478 | − | 0.939890i | \(-0.389073\pi\) | ||||
0.341478 | + | 0.939890i | \(0.389073\pi\) | |||||||
\(152\) | −4.19615 | −0.340353 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.85641 | 0.149593 | ||||||||
\(155\) | 2.73205 | 0.219444 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9282 | 1.35102 | 0.675509 | − | 0.737352i | \(-0.263924\pi\) | ||||
0.675509 | + | 0.737352i | \(0.263924\pi\) | |||||||
\(158\) | 5.26795 | 0.419096 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −10.1436 | −0.799427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.3205 | 1.82660 | 0.913302 | − | 0.407284i | \(-0.133524\pi\) | ||||
0.913302 | + | 0.407284i | \(0.133524\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26795 | 0.408872 | ||||||||
\(167\) | −5.46410 | −0.422825 | −0.211412 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211412 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | −1.46410 | −0.112291 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.92820 | −0.528271 | ||||||||
\(173\) | −10.0000 | −0.760286 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26795 | −0.0958479 | ||||||||
\(176\) | −1.46410 | −0.110361 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | 0.149906 | ||||||||
\(179\) | 17.6603 | 1.31999 | 0.659995 | − | 0.751270i | \(-0.270559\pi\) | ||||
0.659995 | + | 0.751270i | \(0.270559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.46410 | −0.108826 | −0.0544129 | − | 0.998519i | \(-0.517329\pi\) | ||||
−0.0544129 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(182\) | −1.85641 | −0.137606 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.14359 | −0.156755 | ||||||||
\(188\) | 1.26795 | 0.0924747 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.19615 | 0.304421 | ||||||||
\(191\) | 5.26795 | 0.381175 | 0.190588 | − | 0.981670i | \(-0.438961\pi\) | ||||
0.190588 | + | 0.981670i | \(0.438961\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8564 | −0.853443 | −0.426721 | − | 0.904383i | \(-0.640332\pi\) | ||||
−0.426721 | + | 0.904383i | \(0.640332\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | −18.7846 | −1.33835 | −0.669174 | − | 0.743106i | \(-0.733352\pi\) | ||||
−0.669174 | + | 0.743106i | \(0.733352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0526 | 1.84682 | 0.923408 | − | 0.383819i | \(-0.125391\pi\) | ||||
0.923408 | + | 0.383819i | \(0.125391\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.53590 | 0.178425 | ||||||||
\(203\) | −11.3205 | −0.794544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | −13.4641 | −0.938088 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.46410 | 0.101517 | ||||||||
\(209\) | 6.14359 | 0.424961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.85641 | 0.678543 | 0.339272 | − | 0.940688i | \(-0.389819\pi\) | ||||
0.339272 | + | 0.940688i | \(0.389819\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.73205 | −0.460194 | ||||||||
\(215\) | 6.92820 | 0.472500 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.46410 | 0.235159 | ||||||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.46410 | 0.0987097 | ||||||||
\(221\) | 2.14359 | 0.144194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0526 | −1.47675 | −0.738374 | − | 0.674391i | \(-0.764406\pi\) | ||||
−0.738374 | + | 0.674391i | \(0.764406\pi\) | |||||||
\(224\) | −1.26795 | −0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.4641 | 1.16169 | ||||||||
\(227\) | −3.60770 | −0.239451 | −0.119726 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119726 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8564 | 1.04782 | 0.523910 | − | 0.851773i | \(-0.324473\pi\) | ||||
0.523910 | + | 0.851773i | \(0.324473\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.92820 | 0.586165 | ||||||||
\(233\) | −15.0718 | −0.987386 | −0.493693 | − | 0.869636i | \(-0.664353\pi\) | ||||
−0.493693 | + | 0.869636i | \(0.664353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.26795 | −0.0827119 | ||||||||
\(236\) | −0.196152 | −0.0127684 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.85641 | −0.120333 | ||||||||
\(239\) | 17.2679 | 1.11697 | 0.558485 | − | 0.829514i | \(-0.311383\pi\) | ||||
0.558485 | + | 0.829514i | \(0.311383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.92820 | −0.575116 | −0.287558 | − | 0.957763i | \(-0.592843\pi\) | ||||
−0.287558 | + | 0.957763i | \(0.592843\pi\) | |||||||
\(242\) | −8.85641 | −0.569311 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.92820 | 0.571570 | ||||||||
\(245\) | 5.39230 | 0.344502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.14359 | −0.390907 | ||||||||
\(248\) | −2.73205 | −0.173485 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.7321 | −1.43483 | −0.717417 | − | 0.696644i | \(-0.754676\pi\) | ||||
−0.717417 | + | 0.696644i | \(0.754676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.7128 | −0.736378 | ||||||||
\(254\) | −13.6603 | −0.857121 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.4641 | 1.58841 | 0.794204 | − | 0.607652i | \(-0.207888\pi\) | ||||
0.794204 | + | 0.607652i | \(0.207888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.26795 | −0.0787865 | ||||||||
\(260\) | −1.46410 | −0.0907997 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.5885 | −0.777717 | ||||||||
\(263\) | −30.0526 | −1.85312 | −0.926560 | − | 0.376147i | \(-0.877249\pi\) | ||||
−0.926560 | + | 0.376147i | \(0.877249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 5.32051 | 0.326221 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.6603 | 0.834433 | ||||||||
\(269\) | 0.392305 | 0.0239192 | 0.0119596 | − | 0.999928i | \(-0.496193\pi\) | ||||
0.0119596 | + | 0.999928i | \(0.496193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7846 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(272\) | 1.46410 | 0.0887742 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −1.46410 | −0.0882886 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.2487 | −1.57713 | −0.788566 | − | 0.614950i | \(-0.789176\pi\) | ||||
−0.788566 | + | 0.614950i | \(0.789176\pi\) | |||||||
\(278\) | −6.92820 | −0.415526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.26795 | 0.0757745 | ||||||||
\(281\) | −4.92820 | −0.293992 | −0.146996 | − | 0.989137i | \(-0.546960\pi\) | ||||
−0.146996 | + | 0.989137i | \(0.546960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.39230 | −0.261095 | −0.130548 | − | 0.991442i | \(-0.541674\pi\) | ||||
−0.130548 | + | 0.991442i | \(0.541674\pi\) | |||||||
\(284\) | 10.9282 | 0.648470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.14359 | −0.126753 | ||||||||
\(287\) | −2.53590 | −0.149689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8564 | −0.873906 | ||||||||
\(290\) | −8.92820 | −0.524282 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.9282 | 0.756566 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.196152 | 0.0114204 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.3923 | 0.949581 | ||||||||
\(299\) | 11.7128 | 0.677369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.78461 | 0.506336 | ||||||||
\(302\) | 8.39230 | 0.482923 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.19615 | −0.240666 | ||||||||
\(305\) | −8.92820 | −0.511227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.5885 | −0.718461 | −0.359231 | − | 0.933249i | \(-0.616961\pi\) | ||||
−0.359231 | + | 0.933249i | \(0.616961\pi\) | |||||||
\(308\) | 1.85641 | 0.105779 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.73205 | 0.155170 | ||||||||
\(311\) | −27.1244 | −1.53808 | −0.769041 | − | 0.639200i | \(-0.779266\pi\) | ||||
−0.769041 | + | 0.639200i | \(0.779266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.85641 | 0.217977 | 0.108988 | − | 0.994043i | \(-0.465239\pi\) | ||||
0.108988 | + | 0.994043i | \(0.465239\pi\) | |||||||
\(314\) | 16.9282 | 0.955314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.26795 | 0.296345 | ||||||||
\(317\) | 31.8564 | 1.78923 | 0.894617 | − | 0.446834i | \(-0.147448\pi\) | ||||
0.894617 | + | 0.446834i | \(0.147448\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.0718 | −0.731880 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.1436 | −0.565280 | ||||||||
\(323\) | −6.14359 | −0.341839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46410 | 0.0812137 | ||||||||
\(326\) | 23.3205 | 1.29160 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | −1.60770 | −0.0886351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.87564 | −0.487850 | −0.243925 | − | 0.969794i | \(-0.578435\pi\) | ||||
−0.243925 | + | 0.969794i | \(0.578435\pi\) | |||||||
\(332\) | 5.26795 | 0.289116 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.46410 | −0.298982 | ||||||||
\(335\) | −13.6603 | −0.746339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 1.41631 | 0.708155 | − | 0.706057i | \(-0.249528\pi\) | ||||
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(338\) | −10.8564 | −0.590511 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.46410 | −0.0794021 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | −6.92820 | −0.373544 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | −0.537603 | ||||||||
\(347\) | −17.0718 | −0.916462 | −0.458231 | − | 0.888833i | \(-0.651517\pi\) | ||||
−0.458231 | + | 0.888833i | \(0.651517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.3205 | 1.03420 | 0.517102 | − | 0.855924i | \(-0.327011\pi\) | ||||
0.517102 | + | 0.855924i | \(0.327011\pi\) | |||||||
\(350\) | −1.26795 | −0.0677747 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.46410 | −0.0780369 | ||||||||
\(353\) | −15.8564 | −0.843951 | −0.421976 | − | 0.906607i | \(-0.638663\pi\) | ||||
−0.421976 | + | 0.906607i | \(0.638663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.9282 | −0.580009 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.6603 | 0.933373 | ||||||||
\(359\) | −8.39230 | −0.442929 | −0.221464 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221464 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | −1.46410 | −0.0769515 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.85641 | −0.0973021 | ||||||||
\(365\) | −12.9282 | −0.676693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6603 | −1.13066 | −0.565328 | − | 0.824866i | \(-0.691250\pi\) | ||||
−0.565328 | + | 0.824866i | \(0.691250\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.00000 | −0.0519875 | ||||||||
\(371\) | −7.60770 | −0.394972 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.7846 | 1.59397 | 0.796983 | − | 0.604001i | \(-0.206428\pi\) | ||||
0.796983 | + | 0.604001i | \(0.206428\pi\) | |||||||
\(374\) | −2.14359 | −0.110843 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.26795 | 0.0653895 | ||||||||
\(377\) | 13.0718 | 0.673232 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6077 | 0.596247 | 0.298124 | − | 0.954527i | \(-0.403639\pi\) | ||||
0.298124 | + | 0.954527i | \(0.403639\pi\) | |||||||
\(380\) | 4.19615 | 0.215258 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.26795 | 0.269532 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.85641 | −0.0946112 | ||||||||
\(386\) | −11.8564 | −0.603475 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | −15.8564 | −0.803952 | −0.401976 | − | 0.915650i | \(-0.631676\pi\) | ||||
−0.401976 | + | 0.915650i | \(0.631676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7128 | 0.592342 | ||||||||
\(392\) | −5.39230 | −0.272353 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7846 | −0.946355 | ||||||||
\(395\) | −5.26795 | −0.265059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 26.0526 | 1.30590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 19.0718 | 0.952400 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 2.53590 | 0.126166 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.3205 | −0.561827 | ||||||||
\(407\) | −1.46410 | −0.0725728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9282 | 0.837046 | 0.418523 | − | 0.908206i | \(-0.362548\pi\) | ||||
0.418523 | + | 0.908206i | \(0.362548\pi\) | |||||||
\(410\) | −2.00000 | −0.0987730 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.4641 | −0.663329 | ||||||||
\(413\) | 0.248711 | 0.0122383 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.26795 | −0.258593 | ||||||||
\(416\) | 1.46410 | 0.0717835 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.14359 | 0.300493 | ||||||||
\(419\) | 34.2487 | 1.67316 | 0.836580 | − | 0.547846i | \(-0.184552\pi\) | ||||
0.836580 | + | 0.547846i | \(0.184552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.8564 | −1.35764 | −0.678819 | − | 0.734306i | \(-0.737508\pi\) | ||||
−0.678819 | + | 0.734306i | \(0.737508\pi\) | |||||||
\(422\) | 9.85641 | 0.479802 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 1.46410 | 0.0710194 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3205 | −0.547838 | ||||||||
\(428\) | −6.73205 | −0.325406 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.92820 | 0.334108 | ||||||||
\(431\) | −8.19615 | −0.394795 | −0.197397 | − | 0.980324i | \(-0.563249\pi\) | ||||
−0.197397 | + | 0.980324i | \(0.563249\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 3.46410 | 0.166282 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −33.5692 | −1.60583 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5167 | −1.50421 | −0.752104 | − | 0.659044i | \(-0.770961\pi\) | ||||
−0.752104 | + | 0.659044i | \(0.770961\pi\) | |||||||
\(440\) | 1.46410 | 0.0697983 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.14359 | 0.101960 | ||||||||
\(443\) | 39.1244 | 1.85885 | 0.929427 | − | 0.369006i | \(-0.120302\pi\) | ||||
0.929427 | + | 0.369006i | \(0.120302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | −22.0526 | −1.04422 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.26795 | −0.0599050 | ||||||||
\(449\) | −33.7128 | −1.59101 | −0.795503 | − | 0.605950i | \(-0.792793\pi\) | ||||
−0.795503 | + | 0.605950i | \(0.792793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.92820 | −0.137884 | ||||||||
\(452\) | 17.4641 | 0.821442 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.60770 | −0.169318 | ||||||||
\(455\) | 1.85641 | 0.0870297 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.14359 | −0.193829 | −0.0969146 | − | 0.995293i | \(-0.530897\pi\) | ||||
−0.0969146 | + | 0.995293i | \(0.530897\pi\) | |||||||
\(458\) | 15.8564 | 0.740921 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.00000 | −0.373002 | ||||||||
\(461\) | 26.7846 | 1.24748 | 0.623742 | − | 0.781630i | \(-0.285612\pi\) | ||||
0.623742 | + | 0.781630i | \(0.285612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.07180 | 0.235706 | 0.117853 | − | 0.993031i | \(-0.462399\pi\) | ||||
0.117853 | + | 0.993031i | \(0.462399\pi\) | |||||||
\(464\) | 8.92820 | 0.414481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0718 | −0.698188 | ||||||||
\(467\) | −37.1769 | −1.72034 | −0.860171 | − | 0.510005i | \(-0.829643\pi\) | ||||
−0.860171 | + | 0.510005i | \(0.829643\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.3205 | −0.799787 | ||||||||
\(470\) | −1.26795 | −0.0584861 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.196152 | −0.00902865 | ||||||||
\(473\) | 10.1436 | 0.466403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.19615 | −0.192533 | ||||||||
\(476\) | −1.85641 | −0.0850883 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.2679 | 0.789818 | ||||||||
\(479\) | 34.0526 | 1.55590 | 0.777951 | − | 0.628325i | \(-0.216259\pi\) | ||||
0.777951 | + | 0.628325i | \(0.216259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46410 | 0.0667573 | ||||||||
\(482\) | −8.92820 | −0.406669 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.85641 | −0.402564 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.3923 | −0.742806 | −0.371403 | − | 0.928472i | \(-0.621123\pi\) | ||||
−0.371403 | + | 0.928472i | \(0.621123\pi\) | |||||||
\(488\) | 8.92820 | 0.404161 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.39230 | 0.243600 | ||||||||
\(491\) | 1.07180 | 0.0483695 | 0.0241848 | − | 0.999708i | \(-0.492301\pi\) | ||||
0.0241848 | + | 0.999708i | \(0.492301\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0718 | 0.588724 | ||||||||
\(494\) | −6.14359 | −0.276413 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.73205 | −0.122673 | ||||||||
\(497\) | −13.8564 | −0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.5885 | 1.81699 | 0.908494 | − | 0.417897i | \(-0.137233\pi\) | ||||
0.908494 | + | 0.417897i | \(0.137233\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.7321 | −1.01458 | ||||||||
\(503\) | 5.07180 | 0.226140 | 0.113070 | − | 0.993587i | \(-0.463932\pi\) | ||||
0.113070 | + | 0.993587i | \(0.463932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53590 | −0.112846 | ||||||||
\(506\) | −11.7128 | −0.520698 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.6603 | −0.606076 | ||||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3923 | −0.725153 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.4641 | 1.12317 | ||||||||
\(515\) | 13.4641 | 0.593299 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.85641 | −0.0816447 | ||||||||
\(518\) | −1.26795 | −0.0557105 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.46410 | −0.0642051 | ||||||||
\(521\) | −33.4641 | −1.46609 | −0.733044 | − | 0.680181i | \(-0.761901\pi\) | ||||
−0.733044 | + | 0.680181i | \(0.761901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.78461 | −0.209216 | −0.104608 | − | 0.994514i | \(-0.533359\pi\) | ||||
−0.104608 | + | 0.994514i | \(0.533359\pi\) | |||||||
\(524\) | −12.5885 | −0.549929 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0526 | −1.31035 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.32051 | 0.230673 | ||||||||
\(533\) | 2.92820 | 0.126835 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.73205 | 0.291052 | ||||||||
\(536\) | 13.6603 | 0.590033 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.392305 | 0.0169135 | ||||||||
\(539\) | 7.89488 | 0.340057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 16.7846 | 0.720961 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.46410 | 0.0627728 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.46410 | −0.0624295 | ||||||||
\(551\) | −37.4641 | −1.59602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.67949 | −0.284041 | ||||||||
\(554\) | −26.2487 | −1.11520 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.92820 | −0.293821 | ||||||||
\(557\) | 32.1051 | 1.36034 | 0.680169 | − | 0.733056i | \(-0.261906\pi\) | ||||
0.680169 | + | 0.733056i | \(0.261906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1436 | −0.429028 | ||||||||
\(560\) | 1.26795 | 0.0535806 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.92820 | −0.207884 | ||||||||
\(563\) | −17.0718 | −0.719490 | −0.359745 | − | 0.933051i | \(-0.617136\pi\) | ||||
−0.359745 | + | 0.933051i | \(0.617136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.4641 | −0.734720 | ||||||||
\(566\) | −4.39230 | −0.184622 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.9282 | 0.458537 | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | −2.14359 | −0.0896281 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.53590 | −0.105846 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.60770 | −0.150190 | −0.0750952 | − | 0.997176i | \(-0.523926\pi\) | ||||
−0.0750952 | + | 0.997176i | \(0.523926\pi\) | |||||||
\(578\) | −14.8564 | −0.617945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.92820 | −0.370723 | ||||||||
\(581\) | −6.67949 | −0.277112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.78461 | −0.363821 | ||||||||
\(584\) | 12.9282 | 0.534973 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −3.21539 | −0.132713 | −0.0663567 | − | 0.997796i | \(-0.521138\pi\) | ||||
−0.0663567 | + | 0.997796i | \(0.521138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4641 | 0.472370 | ||||||||
\(590\) | 0.196152 | 0.00807547 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −6.78461 | −0.278611 | −0.139305 | − | 0.990249i | \(-0.544487\pi\) | ||||
−0.139305 | + | 0.990249i | \(0.544487\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.85641 | 0.0761052 | ||||||||
\(596\) | 16.3923 | 0.671455 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.7128 | 0.478973 | ||||||||
\(599\) | −2.53590 | −0.103614 | −0.0518070 | − | 0.998657i | \(-0.516498\pi\) | ||||
−0.0518070 | + | 0.998657i | \(0.516498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 48.3923 | 1.97396 | 0.986982 | − | 0.160833i | \(-0.0514180\pi\) | ||||
0.986982 | + | 0.160833i | \(0.0514180\pi\) | |||||||
\(602\) | 8.78461 | 0.358034 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.39230 | 0.341478 | ||||||||
\(605\) | 8.85641 | 0.360064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.7846 | −1.65540 | −0.827698 | − | 0.561174i | \(-0.810350\pi\) | ||||
−0.827698 | + | 0.561174i | \(0.810350\pi\) | |||||||
\(608\) | −4.19615 | −0.170176 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.92820 | −0.361492 | ||||||||
\(611\) | 1.85641 | 0.0751022 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.07180 | 0.124069 | 0.0620344 | − | 0.998074i | \(-0.480241\pi\) | ||||
0.0620344 | + | 0.998074i | \(0.480241\pi\) | |||||||
\(614\) | −12.5885 | −0.508029 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.85641 | 0.0747967 | ||||||||
\(617\) | −12.9282 | −0.520470 | −0.260235 | − | 0.965545i | \(-0.583800\pi\) | ||||
−0.260235 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.85641 | 0.396162 | 0.198081 | − | 0.980186i | \(-0.436529\pi\) | ||||
0.198081 | + | 0.980186i | \(0.436529\pi\) | |||||||
\(620\) | 2.73205 | 0.109722 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.1244 | −1.08759 | ||||||||
\(623\) | −2.53590 | −0.101599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.85641 | 0.154133 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.9282 | 0.675509 | ||||||||
\(629\) | 1.46410 | 0.0583776 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.9808 | −0.835231 | −0.417615 | − | 0.908624i | \(-0.637134\pi\) | ||||
−0.417615 | + | 0.908624i | \(0.637134\pi\) | |||||||
\(632\) | 5.26795 | 0.209548 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.8564 | 1.26518 | ||||||||
\(635\) | 13.6603 | 0.542091 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.89488 | −0.312807 | ||||||||
\(638\) | −13.0718 | −0.517517 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 13.4641 | 0.531800 | 0.265900 | − | 0.964001i | \(-0.414331\pi\) | ||||
0.265900 | + | 0.964001i | \(0.414331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.4641 | 1.63518 | 0.817592 | − | 0.575798i | \(-0.195308\pi\) | ||||
0.817592 | + | 0.575798i | \(0.195308\pi\) | |||||||
\(644\) | −10.1436 | −0.399714 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.14359 | −0.241716 | ||||||||
\(647\) | −19.7128 | −0.774991 | −0.387495 | − | 0.921872i | \(-0.626660\pi\) | ||||
−0.387495 | + | 0.921872i | \(0.626660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.287187 | 0.0112731 | ||||||||
\(650\) | 1.46410 | 0.0574268 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.3205 | 0.913302 | ||||||||
\(653\) | 18.0000 | 0.704394 | 0.352197 | − | 0.935926i | \(-0.385435\pi\) | ||||
0.352197 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.5885 | 0.491872 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.60770 | −0.0626745 | ||||||||
\(659\) | −6.92820 | −0.269884 | −0.134942 | − | 0.990853i | \(-0.543085\pi\) | ||||
−0.134942 | + | 0.990853i | \(0.543085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.9282 | −1.74750 | −0.873752 | − | 0.486371i | \(-0.838320\pi\) | ||||
−0.873752 | + | 0.486371i | \(0.838320\pi\) | |||||||
\(662\) | −8.87564 | −0.344962 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.26795 | 0.204436 | ||||||||
\(665\) | −5.32051 | −0.206320 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 71.4256 | 2.76561 | ||||||||
\(668\) | −5.46410 | −0.211412 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.6603 | −0.527742 | ||||||||
\(671\) | −13.0718 | −0.504631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0718 | −0.735164 | −0.367582 | − | 0.929991i | \(-0.619814\pi\) | ||||
−0.367582 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(674\) | 26.0000 | 1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | 31.8564 | 1.22434 | 0.612171 | − | 0.790726i | \(-0.290297\pi\) | ||||
0.612171 | + | 0.790726i | \(0.290297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.53590 | 0.0973188 | ||||||||
\(680\) | −1.46410 | −0.0561457 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.00000 | 0.153168 | ||||||||
\(683\) | −36.7846 | −1.40752 | −0.703762 | − | 0.710436i | \(-0.748498\pi\) | ||||
−0.703762 | + | 0.710436i | \(0.748498\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 15.7128 | 0.599918 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.92820 | −0.264135 | ||||||||
\(689\) | 8.78461 | 0.334667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3923 | 0.775760 | 0.387880 | − | 0.921710i | \(-0.373208\pi\) | ||||
0.387880 | + | 0.921710i | \(0.373208\pi\) | |||||||
\(692\) | −10.0000 | −0.380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.0718 | −0.648037 | ||||||||
\(695\) | 6.92820 | 0.262802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.92820 | 0.110914 | ||||||||
\(698\) | 19.3205 | 0.731292 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.26795 | −0.0479240 | ||||||||
\(701\) | −15.8564 | −0.598888 | −0.299444 | − | 0.954114i | \(-0.596801\pi\) | ||||
−0.299444 | + | 0.954114i | \(0.596801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.19615 | −0.158261 | ||||||||
\(704\) | −1.46410 | −0.0551804 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8564 | −0.596764 | ||||||||
\(707\) | −3.21539 | −0.120927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1436 | 0.606285 | 0.303143 | − | 0.952945i | \(-0.401964\pi\) | ||||
0.303143 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(710\) | −10.9282 | −0.410128 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.00000 | 0.0749532 | ||||||||
\(713\) | −21.8564 | −0.818529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.14359 | 0.0801659 | ||||||||
\(716\) | 17.6603 | 0.659995 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.39230 | −0.313198 | ||||||||
\(719\) | −8.39230 | −0.312980 | −0.156490 | − | 0.987680i | \(-0.550018\pi\) | ||||
−0.156490 | + | 0.987680i | \(0.550018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.0718 | 0.635787 | ||||||||
\(722\) | −1.39230 | −0.0518162 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.46410 | −0.0544129 | ||||||||
\(725\) | 8.92820 | 0.331585 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7846 | −1.21591 | −0.607957 | − | 0.793970i | \(-0.708011\pi\) | ||||
−0.607957 | + | 0.793970i | \(0.708011\pi\) | |||||||
\(728\) | −1.85641 | −0.0688030 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.9282 | −0.478494 | ||||||||
\(731\) | −10.1436 | −0.375174 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.143594 | 0.00530375 | 0.00265187 | − | 0.999996i | \(-0.499156\pi\) | ||||
0.00265187 | + | 0.999996i | \(0.499156\pi\) | |||||||
\(734\) | −21.6603 | −0.799495 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | −20.0000 | −0.736709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.92820 | −0.254858 | −0.127429 | − | 0.991848i | \(-0.540673\pi\) | ||||
−0.127429 | + | 0.991848i | \(0.540673\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.60770 | −0.279287 | ||||||||
\(743\) | 7.12436 | 0.261367 | 0.130684 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130684 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3923 | −0.600568 | ||||||||
\(746\) | 30.7846 | 1.12710 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.14359 | −0.0783775 | ||||||||
\(749\) | 8.53590 | 0.311895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.392305 | 0.0143154 | 0.00715770 | − | 0.999974i | \(-0.497722\pi\) | ||||
0.00715770 | + | 0.999974i | \(0.497722\pi\) | |||||||
\(752\) | 1.26795 | 0.0462373 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.0718 | 0.476047 | ||||||||
\(755\) | −8.39230 | −0.305427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.7128 | −1.95223 | −0.976113 | − | 0.217265i | \(-0.930286\pi\) | ||||
−0.976113 | + | 0.217265i | \(0.930286\pi\) | |||||||
\(758\) | 11.6077 | 0.421610 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.19615 | 0.152210 | ||||||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.53590 | −0.0918057 | ||||||||
\(764\) | 5.26795 | 0.190588 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | 0.289052 | ||||||||
\(767\) | −0.287187 | −0.0103697 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9282 | 0.754690 | 0.377345 | − | 0.926073i | \(-0.376837\pi\) | ||||
0.377345 | + | 0.926073i | \(0.376837\pi\) | |||||||
\(770\) | −1.85641 | −0.0669002 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.8564 | −0.426721 | ||||||||
\(773\) | 38.7846 | 1.39499 | 0.697493 | − | 0.716592i | \(-0.254299\pi\) | ||||
0.697493 | + | 0.716592i | \(0.254299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.73205 | −0.0981382 | ||||||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.8564 | −0.568480 | ||||||||
\(779\) | −8.39230 | −0.300686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 11.7128 | 0.418849 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.39230 | −0.192582 | ||||||||
\(785\) | −16.9282 | −0.604193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8038 | 0.420762 | 0.210381 | − | 0.977620i | \(-0.432530\pi\) | ||||
0.210381 | + | 0.977620i | \(0.432530\pi\) | |||||||
\(788\) | −18.7846 | −0.669174 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.26795 | −0.187425 | ||||||||
\(791\) | −22.1436 | −0.787336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0718 | 0.464193 | ||||||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.0526 | 0.923408 | ||||||||
\(797\) | −17.4641 | −0.618610 | −0.309305 | − | 0.950963i | \(-0.600096\pi\) | ||||
−0.309305 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.85641 | 0.0656749 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.0718 | 0.673449 | ||||||||
\(803\) | −18.9282 | −0.667962 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1436 | 0.357515 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.53590 | 0.0892126 | ||||||||
\(809\) | 39.5692 | 1.39118 | 0.695590 | − | 0.718439i | \(-0.255143\pi\) | ||||
0.695590 | + | 0.718439i | \(0.255143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1436 | −0.496649 | −0.248324 | − | 0.968677i | \(-0.579880\pi\) | ||||
−0.248324 | + | 0.968677i | \(0.579880\pi\) | |||||||
\(812\) | −11.3205 | −0.397272 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.46410 | −0.0513167 | ||||||||
\(815\) | −23.3205 | −0.816882 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0718 | 1.01709 | ||||||||
\(818\) | 16.9282 | 0.591881 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4449 | −0.364085 | −0.182043 | − | 0.983291i | \(-0.558271\pi\) | ||||
−0.182043 | + | 0.983291i | \(0.558271\pi\) | |||||||
\(824\) | −13.4641 | −0.469044 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.248711 | 0.00865377 | ||||||||
\(827\) | −4.39230 | −0.152735 | −0.0763677 | − | 0.997080i | \(-0.524332\pi\) | ||||
−0.0763677 | + | 0.997080i | \(0.524332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5692 | 1.09644 | 0.548222 | − | 0.836333i | \(-0.315305\pi\) | ||||
0.548222 | + | 0.836333i | \(0.315305\pi\) | |||||||
\(830\) | −5.26795 | −0.182853 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.46410 | 0.0507586 | ||||||||
\(833\) | −7.89488 | −0.273541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.46410 | 0.189093 | ||||||||
\(836\) | 6.14359 | 0.212481 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.2487 | 1.18310 | ||||||||
\(839\) | −32.7846 | −1.13185 | −0.565925 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565925 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.7128 | 1.74872 | ||||||||
\(842\) | −27.8564 | −0.959995 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.85641 | 0.339272 | ||||||||
\(845\) | 10.8564 | 0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.2295 | 0.385849 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.46410 | 0.0502183 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0000 | −1.02718 | −0.513590 | − | 0.858036i | \(-0.671685\pi\) | ||||
−0.513590 | + | 0.858036i | \(0.671685\pi\) | |||||||
\(854\) | −11.3205 | −0.387380 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.73205 | −0.230097 | ||||||||
\(857\) | 4.14359 | 0.141542 | 0.0707712 | − | 0.997493i | \(-0.477454\pi\) | ||||
0.0707712 | + | 0.997493i | \(0.477454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4449 | −0.492852 | −0.246426 | − | 0.969162i | \(-0.579256\pi\) | ||||
−0.246426 | + | 0.969162i | \(0.579256\pi\) | |||||||
\(860\) | 6.92820 | 0.236250 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.19615 | −0.279162 | ||||||||
\(863\) | −38.4449 | −1.30868 | −0.654339 | − | 0.756201i | \(-0.727053\pi\) | ||||
−0.654339 | + | 0.756201i | \(0.727053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | 0.340010 | ||||||||
\(866\) | −34.0000 | −1.15537 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.46410 | 0.117579 | ||||||||
\(869\) | −7.71281 | −0.261639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −33.5692 | −1.13550 | ||||||||
\(875\) | 1.26795 | 0.0428645 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.7846 | −1.71487 | −0.857437 | − | 0.514589i | \(-0.827945\pi\) | ||||
−0.857437 | + | 0.514589i | \(0.827945\pi\) | |||||||
\(878\) | −31.5167 | −1.06364 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.46410 | 0.0493549 | ||||||||
\(881\) | −47.3205 | −1.59427 | −0.797134 | − | 0.603802i | \(-0.793652\pi\) | ||||
−0.797134 | + | 0.603802i | \(0.793652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.2487 | −1.15256 | −0.576280 | − | 0.817252i | \(-0.695496\pi\) | ||||
−0.576280 | + | 0.817252i | \(0.695496\pi\) | |||||||
\(884\) | 2.14359 | 0.0720969 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1244 | 1.31441 | ||||||||
\(887\) | −20.1962 | −0.678120 | −0.339060 | − | 0.940765i | \(-0.610109\pi\) | ||||
−0.339060 | + | 0.940765i | \(0.610109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.3205 | 0.580911 | ||||||||
\(890\) | −2.00000 | −0.0670402 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.0526 | −0.738374 | ||||||||
\(893\) | −5.32051 | −0.178044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.6603 | −0.590317 | ||||||||
\(896\) | −1.26795 | −0.0423592 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.7128 | −1.12501 | ||||||||
\(899\) | −24.3923 | −0.813529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.78461 | 0.292658 | ||||||||
\(902\) | −2.92820 | −0.0974985 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.4641 | 0.580847 | ||||||||
\(905\) | 1.46410 | 0.0486684 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.75129 | 0.190968 | 0.0954842 | − | 0.995431i | \(-0.469560\pi\) | ||||
0.0954842 | + | 0.995431i | \(0.469560\pi\) | |||||||
\(908\) | −3.60770 | −0.119726 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.85641 | 0.0615393 | ||||||||
\(911\) | 27.9090 | 0.924665 | 0.462333 | − | 0.886707i | \(-0.347013\pi\) | ||||
0.462333 | + | 0.886707i | \(0.347013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.71281 | −0.255257 | ||||||||
\(914\) | −4.14359 | −0.137058 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.8564 | 0.523910 | ||||||||
\(917\) | 15.9615 | 0.527096 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2679 | −0.437669 | −0.218835 | − | 0.975762i | \(-0.570226\pi\) | ||||
−0.218835 | + | 0.975762i | \(0.570226\pi\) | |||||||
\(920\) | −8.00000 | −0.263752 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.7846 | 0.882104 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 5.07180 | 0.166670 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.92820 | 0.293083 | ||||||||
\(929\) | 15.8564 | 0.520232 | 0.260116 | − | 0.965577i | \(-0.416239\pi\) | ||||
0.260116 | + | 0.965577i | \(0.416239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.6269 | 0.741568 | ||||||||
\(932\) | −15.0718 | −0.493693 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37.1769 | −1.21647 | ||||||||
\(935\) | 2.14359 | 0.0701030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85641 | 0.125983 | 0.0629917 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629917 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(938\) | −17.3205 | −0.565535 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.26795 | −0.0413559 | ||||||||
\(941\) | −28.3923 | −0.925563 | −0.462781 | − | 0.886472i | \(-0.653148\pi\) | ||||
−0.462781 | + | 0.886472i | \(0.653148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | −0.196152 | −0.00638422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.1436 | 0.329797 | ||||||||
\(947\) | 45.1769 | 1.46805 | 0.734026 | − | 0.679121i | \(-0.237639\pi\) | ||||
0.734026 | + | 0.679121i | \(0.237639\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9282 | 0.614435 | ||||||||
\(950\) | −4.19615 | −0.136141 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.85641 | −0.0601665 | ||||||||
\(953\) | 11.8564 | 0.384067 | 0.192033 | − | 0.981388i | \(-0.438492\pi\) | ||||
0.192033 | + | 0.981388i | \(0.438492\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.26795 | −0.170467 | ||||||||
\(956\) | 17.2679 | 0.558485 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.0526 | 1.10019 | ||||||||
\(959\) | 2.53590 | 0.0818884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5359 | −0.759223 | ||||||||
\(962\) | 1.46410 | 0.0472045 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.92820 | −0.287558 | ||||||||
\(965\) | 11.8564 | 0.381671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.6077 | −0.759172 | −0.379586 | − | 0.925156i | \(-0.623934\pi\) | ||||
−0.379586 | + | 0.925156i | \(0.623934\pi\) | |||||||
\(968\) | −8.85641 | −0.284656 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.00000 | 0.0642161 | ||||||||
\(971\) | −14.9282 | −0.479069 | −0.239534 | − | 0.970888i | \(-0.576995\pi\) | ||||
−0.239534 | + | 0.970888i | \(0.576995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.78461 | 0.281622 | ||||||||
\(974\) | −16.3923 | −0.525243 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.92820 | 0.285785 | ||||||||
\(977\) | 34.0000 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.92820 | −0.0935858 | ||||||||
\(980\) | 5.39230 | 0.172251 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.07180 | 0.0342024 | ||||||||
\(983\) | 38.4449 | 1.22620 | 0.613100 | − | 0.790005i | \(-0.289922\pi\) | ||||
0.613100 | + | 0.790005i | \(0.289922\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7846 | 0.598527 | ||||||||
\(986\) | 13.0718 | 0.416291 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.14359 | −0.195454 | ||||||||
\(989\) | −55.4256 | −1.76243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.94744 | 0.188927 | 0.0944633 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944633 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(992\) | −2.73205 | −0.0867427 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.8564 | −0.439499 | ||||||||
\(995\) | −26.0526 | −0.825922 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14359 | −0.131229 | −0.0656145 | − | 0.997845i | \(-0.520901\pi\) | ||||
−0.0656145 | + | 0.997845i | \(0.520901\pi\) | |||||||
\(998\) | 40.5885 | 1.28481 | ||||||||
\(999\) | 0 | 0 |
(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 | 3330.2.a.bd.1.2 | 2 | ||
3.2 | odd | 2 | 370.2.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 2960.2.a.q.1.2 | 2 | |||
15.2 | even | 4 | 1850.2.b.l.149.2 | 4 | |||
15.8 | even | 4 | 1850.2.b.l.149.3 | 4 | |||
15.14 | odd | 2 | 1850.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.e.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1850.2.a.x.1.2 | 2 | 15.14 | odd | 2 | |||
1850.2.b.l.149.2 | 4 | 15.2 | even | 4 | |||
1850.2.b.l.149.3 | 4 | 15.8 | even | 4 | |||
2960.2.a.q.1.2 | 2 | 12.11 | even | 2 | |||
3330.2.a.bd.1.2 | 2 | 1.1 | even | 1 | trivial |