Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 2960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26795 | 0.479240 | 0.239620 | − | 0.970867i | \(-0.422977\pi\) | ||||
0.239620 | + | 0.970867i | \(0.422977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | \(0.434920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.46410 | −0.355097 | −0.177548 | − | 0.984112i | \(-0.556817\pi\) | ||||
−0.177548 | + | 0.984112i | \(0.556817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19615 | 0.962663 | 0.481332 | − | 0.876539i | \(-0.340153\pi\) | ||||
0.481332 | + | 0.876539i | \(0.340153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410 | 0.755929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.92820 | −1.65793 | −0.828963 | − | 0.559304i | \(-0.811069\pi\) | ||||
−0.828963 | + | 0.559304i | \(0.811069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.73205 | 0.490691 | 0.245345 | − | 0.969436i | \(-0.421099\pi\) | ||||
0.245345 | + | 0.969436i | \(0.421099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26795 | 0.214323 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.92820 | 1.05654 | 0.528271 | − | 0.849076i | \(-0.322841\pi\) | ||||
0.528271 | + | 0.849076i | \(0.322841\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46410 | 0.665469 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46410 | −0.197419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.4641 | 1.51846 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.306335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.66025 | 0.713125 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.46410 | 0.181599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6603 | −1.66887 | −0.834433 | − | 0.551110i | \(-0.814205\pi\) | ||||
−0.834433 | + | 0.551110i | \(0.814205\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.8564 | 2.63120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(0.226876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.73205 | 0.315470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.85641 | −0.211557 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.26795 | −0.592691 | −0.296345 | − | 0.955081i | \(-0.595768\pi\) | ||||
−0.296345 | + | 0.955081i | \(0.595768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.3923 | −2.61513 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.85641 | 0.194604 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.46410 | 0.773991 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.19615 | 0.430516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.53590 | −0.656883 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.53590 | −0.252331 | −0.126166 | − | 0.992009i | \(-0.540267\pi\) | ||||
−0.126166 | + | 0.992009i | \(0.540267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4641 | 1.32666 | 0.663329 | − | 0.748328i | \(-0.269143\pi\) | ||||
0.663329 | + | 0.748328i | \(0.269143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.46410 | 0.338062 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −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 | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.73205 | 0.259315 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4641 | −1.64288 | −0.821442 | − | 0.570292i | \(-0.806830\pi\) | ||||
−0.821442 | + | 0.570292i | \(0.806830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.53590 | 0.604244 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.85641 | −0.170177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.46410 | −0.492681 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6603 | 1.21215 | 0.606076 | − | 0.795407i | \(-0.292743\pi\) | ||||
0.606076 | + | 0.795407i | \(0.292743\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.9282 | 1.66654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.46410 | 0.291730 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.14359 | −0.179256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.92820 | −0.741447 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.7321 | −1.21508 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3923 | −1.34291 | −0.671455 | − | 0.741045i | \(-0.734330\pi\) | ||||
−0.671455 | + | 0.741045i | \(0.734330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.39230 | −0.682956 | −0.341478 | − | 0.939890i | \(-0.610927\pi\) | ||||
−0.341478 | + | 0.939890i | \(0.610927\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.53590 | −0.528396 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.73205 | 0.219444 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9282 | 1.35102 | 0.675509 | − | 0.737352i | \(-0.263924\pi\) | ||||
0.675509 | + | 0.737352i | \(0.263924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.3923 | −1.29999 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.1436 | 0.799427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.3205 | −1.82660 | −0.913302 | − | 0.407284i | \(-0.866476\pi\) | ||||
−0.913302 | + | 0.407284i | \(0.866476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | −0.311400 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.7321 | 1.43248 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.26795 | 0.0958479 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.535898 | −0.0402806 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.517329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.3923 | 1.80313 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14359 | 0.156755 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.07180 | 0.368919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(0.640332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.00000 | 0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7846 | 1.33835 | 0.669174 | − | 0.743106i | \(-0.266648\pi\) | ||||
0.669174 | + | 0.743106i | \(0.266648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.0526 | −1.84682 | −0.923408 | − | 0.383819i | \(-0.874609\pi\) | ||||
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.3205 | −2.63239 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3205 | −0.794544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.7128 | 2.48221 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.14359 | −0.424961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.85641 | −0.678543 | −0.339272 | − | 0.940688i | \(-0.610181\pi\) | ||||
−0.339272 | + | 0.940688i | \(0.610181\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.8564 | 2.04573 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.92820 | 0.472500 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.46410 | 0.235159 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 35.3205 | 2.38674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.14359 | −0.144194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0526 | 1.47675 | 0.738374 | − | 0.674391i | \(-0.235594\pi\) | ||||
0.738374 | + | 0.674391i | \(0.235594\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −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 | \(0.324473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.07180 | −0.333700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0718 | 0.987386 | 0.493693 | − | 0.869636i | \(-0.335647\pi\) | ||||
0.493693 | + | 0.869636i | \(0.335647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26795 | 0.0827119 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.3923 | −0.934881 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(0.592843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.39230 | −0.344502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.14359 | 0.390907 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.3923 | 0.912075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.4641 | −1.58841 | −0.794204 | − | 0.607652i | \(-0.792112\pi\) | ||||
−0.794204 | + | 0.607652i | \(0.792112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26795 | 0.0787865 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −39.8564 | −2.46705 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.46410 | −0.334398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.392305 | −0.0239192 | −0.0119596 | − | 0.999928i | \(-0.503807\pi\) | ||||
−0.0119596 | + | 0.999928i | \(0.503807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7846 | −1.01959 | −0.509796 | − | 0.860295i | \(-0.670279\pi\) | ||||
−0.509796 | + | 0.860295i | \(0.670279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.07180 | 0.306959 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.46410 | −0.0882886 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.2487 | −1.57713 | −0.788566 | − | 0.614950i | \(-0.789176\pi\) | ||||
−0.788566 | + | 0.614950i | \(0.789176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.1962 | 0.730165 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.92820 | 0.293992 | 0.146996 | − | 0.989137i | \(-0.453040\pi\) | ||||
0.146996 | + | 0.989137i | \(0.453040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.39230 | 0.261095 | 0.130548 | − | 0.991442i | \(-0.458326\pi\) | ||||
0.130548 | + | 0.991442i | \(0.458326\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.4641 | 0.679075 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.53590 | −0.149689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8564 | −0.873906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.46410 | −0.320311 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.196152 | −0.0114204 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.85641 | −0.339823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.7128 | 0.677369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.78461 | 0.506336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.92820 | −0.398015 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.92820 | 0.511227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5885 | 0.718461 | 0.359231 | − | 0.933249i | \(-0.383039\pi\) | ||||
0.359231 | + | 0.933249i | \(0.383039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.7846 | 2.09260 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(0.465239\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.66025 | 0.318919 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.8564 | −1.78923 | −0.894617 | − | 0.446834i | \(-0.852552\pi\) | ||||
−0.894617 | + | 0.446834i | \(0.852552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.0718 | 0.731880 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3923 | −1.02656 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.14359 | −0.341839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46410 | 0.0812137 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.46410 | 0.302166 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.60770 | 0.0886351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.87564 | 0.487850 | 0.243925 | − | 0.969794i | \(-0.421565\pi\) | ||||
0.243925 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.46410 | 0.244631 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.6603 | −0.746339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 1.41631 | 0.708155 | − | 0.706057i | \(-0.249528\pi\) | ||||
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −47.7128 | −2.59140 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7128 | −0.848412 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.8564 | 1.17671 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −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 | \(0.327011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.85641 | 0.312592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8564 | 0.843951 | 0.421976 | − | 0.906607i | \(-0.361337\pi\) | ||||
0.421976 | + | 0.906607i | \(0.361337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9282 | 0.580009 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.07180 | −0.268428 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.1962 | −1.26997 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.9282 | 0.676693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6603 | 1.13066 | 0.565328 | − | 0.824866i | \(-0.308750\pi\) | ||||
0.565328 | + | 0.824866i | \(0.308750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.92820 | −0.464784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.60770 | −0.394972 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.7846 | 1.59397 | 0.796983 | − | 0.604001i | \(-0.206428\pi\) | ||||
0.796983 | + | 0.604001i | \(0.206428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73205 | 0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.0718 | −0.673232 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6077 | −0.596247 | −0.298124 | − | 0.954527i | \(-0.596361\pi\) | ||||
−0.298124 | + | 0.954527i | \(0.596361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 37.3205 | 1.91199 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.9282 | 1.57217 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8564 | 0.803952 | 0.401976 | − | 0.915650i | \(-0.368324\pi\) | ||||
0.401976 | + | 0.915650i | \(0.368324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.7128 | −0.592342 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.3923 | −1.73486 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.26795 | −0.265059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.5359 | 0.727705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.0718 | −0.952400 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.46410 | −0.122442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.46410 | −0.0725728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9282 | 0.837046 | 0.418523 | − | 0.908206i | \(-0.362548\pi\) | ||||
0.418523 | + | 0.908206i | \(0.362548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.46410 | 0.269524 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.248711 | −0.0122383 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.26795 | 0.258593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.9282 | 0.926918 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.737508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.66025 | 0.275211 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.46410 | −0.0710194 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3205 | 0.547838 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.85641 | −0.282750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.3923 | −1.16952 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.5692 | 1.60583 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5167 | 1.50421 | 0.752104 | − | 0.659044i | \(-0.229039\pi\) | ||||
0.752104 | + | 0.659044i | \(0.229039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0718 | −1.14628 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.7846 | −2.11824 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7128 | 1.59101 | 0.795503 | − | 0.605950i | \(-0.207207\pi\) | ||||
0.795503 | + | 0.605950i | \(0.207207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92820 | 0.137884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.9282 | −1.07726 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.85641 | 0.0870297 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.14359 | −0.193829 | −0.0969146 | − | 0.995293i | \(-0.530897\pi\) | ||||
−0.0969146 | + | 0.995293i | \(0.530897\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.85641 | −0.273354 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.7846 | −1.24748 | −0.623742 | − | 0.781630i | \(-0.714388\pi\) | ||||
−0.623742 | + | 0.781630i | \(0.714388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.07180 | −0.235706 | −0.117853 | − | 0.993031i | \(-0.537601\pi\) | ||||
−0.117853 | + | 0.993031i | \(0.537601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.46410 | 0.346139 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.2487 | 2.13103 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.1436 | −0.466403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.19615 | 0.192533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.7846 | −1.22638 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.7128 | 1.26098 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3923 | 0.742806 | 0.371403 | − | 0.928472i | \(-0.378877\pi\) | ||||
0.371403 | + | 0.928472i | \(0.378877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −63.7128 | −2.88119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.53590 | −0.293767 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.8564 | 0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.5885 | −1.81699 | −0.908494 | − | 0.417897i | \(-0.862767\pi\) | ||||
−0.908494 | + | 0.417897i | \(0.862767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.9282 | −0.666943 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.6603 | −1.31726 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.00000 | −0.0886484 | −0.0443242 | − | 0.999017i | \(-0.514113\pi\) | ||||
−0.0443242 | + | 0.999017i | \(0.514113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3923 | 0.725153 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.7846 | 0.741059 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.4641 | 0.593299 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.85641 | −0.0816447 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.3205 | 1.19924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4641 | 1.46609 | 0.733044 | − | 0.680181i | \(-0.238099\pi\) | ||||
0.733044 | + | 0.680181i | \(0.238099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.78461 | 0.209216 | 0.104608 | − | 0.994514i | \(-0.466641\pi\) | ||||
0.104608 | + | 0.994514i | \(0.466641\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.46410 | 0.151186 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.875644 | −0.0379997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.92820 | −0.126835 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.73205 | −0.291052 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 48.2487 | 2.08209 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.89488 | 0.340057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.00000 | −0.171656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.8564 | 1.70103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −37.4641 | −1.59602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.67949 | −0.284041 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.73205 | 0.115969 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.1051 | −1.36034 | −0.680169 | − | 0.733056i | \(-0.738094\pi\) | ||||
−0.680169 | + | 0.733056i | \(0.738094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.1436 | 0.429028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.85641 | 0.247258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.12436 | −0.131211 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.3923 | 0.601247 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.60770 | −0.150190 | −0.0750952 | − | 0.997176i | \(-0.523926\pi\) | ||||
−0.0750952 | + | 0.997176i | \(0.523926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.3923 | −1.34618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.67949 | 0.277112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.78461 | 0.363821 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.53590 | 0.270226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −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 | 0 | ||||||||
\(591\) | 51.3205 | 2.11104 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.78461 | 0.278611 | 0.139305 | − | 0.990249i | \(-0.455513\pi\) | ||||
0.139305 | + | 0.990249i | \(0.455513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85641 | −0.0761052 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −71.1769 | −2.91308 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(0.0514180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −60.9808 | −2.48333 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.85641 | −0.360064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.7846 | 1.65540 | 0.827698 | − | 0.561174i | \(-0.189650\pi\) | ||||
0.827698 | + | 0.561174i | \(0.189650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.9282 | −1.25327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.85641 | 0.0751022 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.07180 | 0.124069 | 0.0620344 | − | 0.998074i | \(-0.480241\pi\) | ||||
0.0620344 | + | 0.998074i | \(0.480241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.46410 | −0.220334 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.9282 | 0.520470 | 0.260235 | − | 0.965545i | \(-0.416200\pi\) | ||||
0.260235 | + | 0.965545i | \(0.416200\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.85641 | −0.396162 | −0.198081 | − | 0.980186i | \(-0.563471\pi\) | ||||
−0.198081 | + | 0.980186i | \(0.563471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.0000 | 1.28412 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.53590 | −0.101599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.7846 | −0.670313 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.46410 | −0.0583776 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.9808 | 0.835231 | 0.417615 | − | 0.908624i | \(-0.362866\pi\) | ||||
0.417615 | + | 0.908624i | \(0.362866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.9282 | −1.07030 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.6603 | 0.542091 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.89488 | −0.312807 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48.7846 | 1.92989 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4641 | −0.531800 | −0.265900 | − | 0.964001i | \(-0.585669\pi\) | ||||
−0.265900 | + | 0.964001i | \(0.585669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.4641 | −1.63518 | −0.817592 | − | 0.575798i | \(-0.804692\pi\) | ||||
−0.817592 | + | 0.575798i | \(0.804692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.9282 | 0.745297 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.46410 | 0.370927 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5885 | −0.491872 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 57.7128 | 2.25159 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(0.838320\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.85641 | −0.227444 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.32051 | 0.206320 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −71.4256 | −2.76561 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.2487 | 2.32935 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0718 | −0.504631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0718 | −0.735164 | −0.367582 | − | 0.929991i | \(-0.619814\pi\) | ||||
−0.367582 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.8564 | −1.22434 | −0.612171 | − | 0.790726i | \(-0.709703\pi\) | ||||
−0.612171 | + | 0.790726i | \(0.709703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.53590 | −0.0973188 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.85641 | −0.377698 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 43.3205 | 1.65278 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.78461 | −0.334667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.3923 | −0.775760 | −0.387880 | − | 0.921710i | \(-0.626792\pi\) | ||||
−0.387880 | + | 0.921710i | \(0.626792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.28719 | −0.314804 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.92820 | 0.262802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.92820 | 0.110914 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.1769 | 1.55745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8564 | 0.598888 | 0.299444 | − | 0.954114i | \(-0.403199\pi\) | ||||
0.299444 | + | 0.954114i | \(0.403199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.19615 | 0.158261 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.46410 | 0.130466 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.21539 | −0.120927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1436 | 0.606285 | 0.303143 | − | 0.952945i | \(-0.401964\pi\) | ||||
0.303143 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.5167 | −0.881944 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.8564 | 0.818529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.14359 | −0.0801659 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.1769 | 1.76185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.3923 | −0.907160 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.92820 | −0.331585 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.7846 | 1.21591 | 0.607957 | − | 0.793970i | \(-0.291989\pi\) | ||||
0.607957 | + | 0.793970i | \(0.291989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.1436 | −0.375174 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.143594 | 0.00530375 | 0.00265187 | − | 0.999996i | \(-0.499156\pi\) | ||||
0.00265187 | + | 0.999996i | \(0.499156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.7321 | −0.543400 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.0000 | 0.736709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.92820 | 0.254858 | 0.127429 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127429 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.7846 | 0.616598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.5167 | 0.860430 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.53590 | −0.311895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.392305 | −0.0143154 | −0.00715770 | − | 0.999974i | \(-0.502278\pi\) | ||||
−0.00715770 | + | 0.999974i | \(0.502278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −62.1051 | −2.26324 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.39230 | −0.305427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.7128 | −1.95223 | −0.976113 | − | 0.217265i | \(-0.930286\pi\) | ||||
−0.976113 | + | 0.217265i | \(0.930286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.0000 | −1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.53590 | 0.0918057 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.53590 | −0.236306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.287187 | −0.0103697 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9282 | 0.754690 | 0.377345 | − | 0.926073i | \(-0.376837\pi\) | ||||
0.377345 | + | 0.926073i | \(0.376837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −69.5692 | −2.50547 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.7846 | −1.39499 | −0.697493 | − | 0.716592i | \(-0.745701\pi\) | ||||
−0.697493 | + | 0.716592i | \(0.745701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.73205 | 0.0981382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.46410 | 0.124274 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.39230 | −0.300686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.7128 | −1.27627 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9282 | 0.604193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8038 | −0.420762 | −0.210381 | − | 0.977620i | \(-0.567470\pi\) | ||||
−0.210381 | + | 0.977620i | \(0.567470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −82.1051 | −2.92302 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.1436 | −0.787336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0718 | 0.464193 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.3923 | −0.581375 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.4641 | 0.618610 | 0.309305 | − | 0.950963i | \(-0.399904\pi\) | ||||
0.309305 | + | 0.950963i | \(0.399904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.85641 | −0.0656749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.92820 | −0.315463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.9282 | −0.667962 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1436 | 0.357515 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.07180 | −0.0377290 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.5692 | −1.39118 | −0.695590 | − | 0.718439i | \(-0.744857\pi\) | ||||
−0.695590 | + | 0.718439i | \(0.744857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1436 | 0.496649 | 0.248324 | − | 0.968677i | \(-0.420120\pi\) | ||||
0.248324 | + | 0.968677i | \(0.420120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −45.8564 | −1.60825 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.3205 | −0.816882 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0718 | 1.01709 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.28719 | 0.289578 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4449 | 0.364085 | 0.182043 | − | 0.983291i | \(-0.441729\pi\) | ||||
0.182043 | + | 0.983291i | \(0.441729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | \(0.315305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −71.7128 | −2.48769 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.89488 | 0.273541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.46410 | −0.189093 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.9282 | 0.377734 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4641 | 0.463728 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.8564 | −0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.2295 | −0.385849 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.0000 | 0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0000 | −1.02718 | −0.513590 | − | 0.858036i | \(-0.671685\pi\) | ||||
−0.513590 | + | 0.858036i | \(0.671685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.7321 | 0.640623 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.14359 | −0.141542 | −0.0707712 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707712 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4449 | 0.492852 | 0.246426 | − | 0.969162i | \(-0.420744\pi\) | ||||
0.246426 | + | 0.969162i | \(0.420744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.92820 | −0.236113 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.5885 | −1.37846 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.71281 | 0.261639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.92820 | −0.302174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.26795 | 0.0428645 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.7846 | −1.71487 | −0.857437 | − | 0.514589i | \(-0.827945\pi\) | ||||
−0.857437 | + | 0.514589i | \(0.827945\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.3923 | 0.552899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.3205 | 1.59427 | 0.797134 | − | 0.603802i | \(-0.206348\pi\) | ||||
0.797134 | + | 0.603802i | \(0.206348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.2487 | 1.15256 | 0.576280 | − | 0.817252i | \(-0.304504\pi\) | ||||
0.576280 | + | 0.817252i | \(0.304504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.535898 | −0.0180140 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.60770 | 0.120862 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.32051 | 0.178044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6603 | 0.590317 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.0000 | 1.06845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.3923 | −0.813529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.78461 | 0.292658 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.0000 | 0.798670 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.46410 | −0.0486684 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.75129 | −0.190968 | −0.0954842 | − | 0.995431i | \(-0.530440\pi\) | ||||
−0.0954842 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.3205 | −0.375478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.3923 | 0.806385 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.9615 | −0.527096 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2679 | 0.437669 | 0.218835 | − | 0.975762i | \(-0.429774\pi\) | ||||
0.218835 | + | 0.975762i | \(0.429774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.3923 | 1.13326 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 60.1051 | 1.97411 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8564 | −0.520232 | −0.260116 | − | 0.965577i | \(-0.583761\pi\) | ||||
−0.260116 | + | 0.965577i | \(0.583761\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.6269 | −0.741568 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −74.1051 | −2.42609 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14359 | 0.0701030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85641 | 0.125983 | 0.0629917 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629917 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5359 | 0.343826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.3923 | 0.925563 | 0.462781 | − | 0.886472i | \(-0.346852\pi\) | ||||
0.462781 | + | 0.886472i | \(0.346852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.07180 | 0.164986 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −87.0333 | −2.82225 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.8564 | −0.384067 | −0.192033 | − | 0.981388i | \(-0.561508\pi\) | ||||
−0.192033 | + | 0.981388i | \(0.561508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.26795 | 0.170467 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.7128 | 1.15443 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.53590 | 0.0818884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5359 | −0.759223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.0526 | −0.968430 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.8564 | −0.381671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.6077 | 0.759172 | 0.379586 | − | 0.925156i | \(-0.376066\pi\) | ||||
0.379586 | + | 0.925156i | \(0.376066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.7846 | −0.539199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.0000 | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.92820 | 0.0935858 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.92820 | 0.285056 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.39230 | 0.139809 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.4256 | 1.76243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.94744 | −0.188927 | −0.0944633 | − | 0.995528i | \(-0.530114\pi\) | ||||
−0.0944633 | + | 0.995528i | \(0.530114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.2487 | 0.769510 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.0526 | −0.825922 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14359 | −0.131229 | −0.0656145 | − | 0.997845i | \(-0.520901\pi\) | ||||
−0.0656145 | + | 0.997845i | \(0.520901\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 2960.2.a.q.1.2 | 2 | ||
4.3 | odd | 2 | 370.2.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 3330.2.a.bd.1.2 | 2 | |||
20.3 | even | 4 | 1850.2.b.l.149.3 | 4 | |||
20.7 | even | 4 | 1850.2.b.l.149.2 | 4 | |||
20.19 | 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 | 4.3 | odd | 2 | ||
1850.2.a.x.1.2 | 2 | 20.19 | odd | 2 | |||
1850.2.b.l.149.2 | 4 | 20.7 | even | 4 | |||
1850.2.b.l.149.3 | 4 | 20.3 | even | 4 | |||
2960.2.a.q.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3330.2.a.bd.1.2 | 2 | 12.11 | even | 2 |