Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1248,2,Mod(1,1248)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1248, 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("1248.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.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: | \(9.96533017226\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1248.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.96239 | −1.32482 | −0.662410 | − | 0.749141i | \(-0.730466\pi\) | ||||
−0.662410 | + | 0.749141i | \(0.730466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35026 | 1.26628 | 0.633140 | − | 0.774037i | \(-0.281766\pi\) | ||||
0.633140 | + | 0.774037i | \(0.281766\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61213 | −0.486075 | −0.243037 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243037 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.96239 | 0.764885 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.35026 | −0.768603 | −0.384301 | − | 0.923208i | \(-0.625558\pi\) | ||||
−0.384301 | + | 0.923208i | \(0.625558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.35026 | −0.731087 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.70052 | −1.39716 | −0.698578 | − | 0.715534i | \(-0.746183\pi\) | ||||
−0.698578 | + | 0.715534i | \(0.746183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.77575 | 0.755149 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.57452 | 1.18082 | 0.590409 | − | 0.807104i | \(-0.298966\pi\) | ||||
0.590409 | + | 0.807104i | \(0.298966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61213 | 0.280635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.92478 | −1.67759 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.92478 | 1.30283 | 0.651413 | − | 0.758724i | \(-0.274177\pi\) | ||||
0.651413 | + | 0.758724i | \(0.274177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.96239 | 1.08734 | 0.543671 | − | 0.839298i | \(-0.317034\pi\) | ||||
0.543671 | + | 0.839298i | \(0.317034\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.775746 | −0.118300 | −0.0591501 | − | 0.998249i | \(-0.518839\pi\) | ||||
−0.0591501 | + | 0.998249i | \(0.518839\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.96239 | −0.441607 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.38787 | 0.348307 | 0.174154 | − | 0.984719i | \(-0.444281\pi\) | ||||
0.174154 | + | 0.984719i | \(0.444281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22425 | 0.603465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9248 | 1.63799 | 0.818997 | − | 0.573798i | \(-0.194530\pi\) | ||||
0.818997 | + | 0.573798i | \(0.194530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.77575 | 0.643961 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.35026 | 0.443753 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.312650 | 0.0407036 | 0.0203518 | − | 0.999793i | \(-0.493521\pi\) | ||||
0.0203518 | + | 0.999793i | \(0.493521\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6253 | 1.87258 | 0.936289 | − | 0.351231i | \(-0.114237\pi\) | ||||
0.936289 | + | 0.351231i | \(0.114237\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.35026 | 0.422093 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.96239 | −0.367439 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.12601 | 0.992750 | 0.496375 | − | 0.868108i | \(-0.334664\pi\) | ||||
0.496375 | + | 0.868108i | \(0.334664\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.70052 | 0.806648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.31265 | −0.511817 | −0.255909 | − | 0.966701i | \(-0.582375\pi\) | ||||
−0.255909 | + | 0.966701i | \(0.582375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0752228 | 0.00880416 | 0.00440208 | − | 0.999990i | \(-0.498599\pi\) | ||||
0.00440208 | + | 0.999990i | \(0.498599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.77575 | −0.435986 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.40105 | −0.615506 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.31265 | −0.912432 | −0.456216 | − | 0.889869i | \(-0.650796\pi\) | ||||
−0.456216 | + | 0.889869i | \(0.650796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.92478 | −0.642632 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.88717 | 0.942038 | 0.471019 | − | 0.882123i | \(-0.343886\pi\) | ||||
0.471019 | + | 0.882123i | \(0.343886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.35026 | 0.351203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.57452 | −0.681745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.92478 | 1.01826 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.92478 | −0.804639 | −0.402320 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402320 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.61213 | −0.162025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4010 | 1.53246 | 0.766231 | − | 0.642566i | \(-0.222130\pi\) | ||||
0.766231 | + | 0.642566i | \(0.222130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.62530 | −0.455744 | −0.227872 | − | 0.973691i | \(-0.573177\pi\) | ||||
−0.227872 | + | 0.973691i | \(0.573177\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.92478 | 0.968559 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5501 | 1.40661 | 0.703305 | − | 0.710889i | \(-0.251707\pi\) | ||||
0.703305 | + | 0.710889i | \(0.251707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4010 | −1.47515 | −0.737576 | − | 0.675264i | \(-0.764030\pi\) | ||||
−0.737576 | + | 0.675264i | \(0.764030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.92478 | −0.752187 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.47627 | −0.891452 | −0.445726 | − | 0.895169i | \(-0.647055\pi\) | ||||
−0.445726 | + | 0.895169i | \(0.647055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.8496 | 1.85098 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.70052 | 0.614236 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40105 | −0.763732 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.96239 | −0.627777 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.62672 | 0.324383 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.29948 | 0.470252 | 0.235126 | − | 0.971965i | \(-0.424450\pi\) | ||||
0.235126 | + | 0.971965i | \(0.424450\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.775746 | 0.0683007 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.14903 | 0.799355 | 0.399677 | − | 0.916656i | \(-0.369122\pi\) | ||||
0.399677 | + | 0.916656i | \(0.369122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.2243 | −0.973266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.96239 | 0.254962 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.513881 | 0.0439038 | 0.0219519 | − | 0.999759i | \(-0.493012\pi\) | ||||
0.0219519 | + | 0.999759i | \(0.493012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9248 | −1.18108 | −0.590542 | − | 0.807007i | \(-0.701086\pi\) | ||||
−0.590542 | + | 0.807007i | \(0.701086\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.38787 | −0.201095 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.61213 | −0.134813 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.92478 | −0.492026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.22425 | −0.348411 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8872 | −1.05576 | −0.527879 | − | 0.849320i | \(-0.677013\pi\) | ||||
−0.527879 | + | 0.849320i | \(0.677013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2750 | 1.08031 | 0.540154 | − | 0.841566i | \(-0.318366\pi\) | ||||
0.540154 | + | 0.841566i | \(0.318366\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.4763 | −1.56437 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.0738 | 1.68187 | 0.840936 | − | 0.541134i | \(-0.182005\pi\) | ||||
0.840936 | + | 0.541134i | \(0.182005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.9248 | −0.945696 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.4485 | −1.76919 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.9003 | −1.71537 | −0.857683 | − | 0.514178i | \(-0.828097\pi\) | ||||
−0.857683 | + | 0.514178i | \(0.828097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.77575 | −0.371791 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.4617 | −1.35123 | −0.675613 | − | 0.737257i | \(-0.736121\pi\) | ||||
−0.675613 | + | 0.737257i | \(0.736121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.35026 | −0.256201 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8496 | 1.66119 | 0.830595 | − | 0.556876i | \(-0.188000\pi\) | ||||
0.830595 | + | 0.556876i | \(0.188000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.6497 | 0.956230 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.312650 | −0.0235002 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9248 | −1.63873 | −0.819367 | − | 0.573269i | \(-0.805675\pi\) | ||||
−0.819367 | + | 0.573269i | \(0.805675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6253 | −1.38441 | −0.692204 | − | 0.721702i | \(-0.743360\pi\) | ||||
−0.692204 | + | 0.721702i | \(0.743360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.6253 | −1.08113 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.4763 | −1.72601 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.22425 | −0.235781 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.35026 | −0.243696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7743 | 1.57554 | 0.787768 | − | 0.615972i | \(-0.211237\pi\) | ||||
0.787768 | + | 0.615972i | \(0.211237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.2506 | 1.38569 | 0.692844 | − | 0.721087i | \(-0.256357\pi\) | ||||
0.692844 | + | 0.721087i | \(0.256357\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.96239 | 0.212141 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.51388 | −0.321601 | −0.160800 | − | 0.986987i | \(-0.551408\pi\) | ||||
−0.160800 | + | 0.986987i | \(0.551408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.14903 | −0.648558 | −0.324279 | − | 0.945962i | \(-0.605122\pi\) | ||||
−0.324279 | + | 0.945962i | \(0.605122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.12601 | −0.573164 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.70052 | 0.470285 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.6253 | −1.44053 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.70052 | −0.465719 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.40105 | 0.373598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.31265 | 0.295498 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.29806 | 0.156727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0263 | 1.49525 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0752228 | −0.00508308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.4241 | 1.23377 | 0.616883 | − | 0.787054i | \(-0.288395\pi\) | ||||
0.616883 | + | 0.787054i | \(0.288395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.77575 | 0.251716 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.61213 | 0.107001 | 0.0535003 | − | 0.998568i | \(-0.482962\pi\) | ||||
0.0535003 | + | 0.998568i | \(0.482962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.40105 | 0.355363 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0752228 | 0.00492801 | 0.00246400 | − | 0.999997i | \(-0.499216\pi\) | ||||
0.00246400 | + | 0.999997i | \(0.499216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.07381 | −0.461444 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | −0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.08840 | 0.587880 | 0.293940 | − | 0.955824i | \(-0.405033\pi\) | ||||
0.293940 | + | 0.955824i | \(0.405033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7743 | 1.01611 | 0.508057 | − | 0.861323i | \(-0.330364\pi\) | ||||
0.508057 | + | 0.861323i | \(0.330364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.5139 | −0.799483 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.35026 | −0.213172 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.31265 | 0.526793 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2243 | −0.960946 | −0.480473 | − | 0.877009i | \(-0.659535\pi\) | ||||
−0.480473 | + | 0.877009i | \(0.659535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8021 | 0.679122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.92478 | 0.371024 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.07522 | −0.254205 | −0.127103 | − | 0.991890i | \(-0.540568\pi\) | ||||
−0.127103 | + | 0.991890i | \(0.540568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.5501 | 1.64974 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7757 | −0.787786 | −0.393893 | − | 0.919156i | \(-0.628872\pi\) | ||||
−0.393893 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.3258 | −2.17005 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.88717 | −0.543886 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.8496 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.499293 | −0.0303299 | −0.0151649 | − | 0.999885i | \(-0.504827\pi\) | ||||
−0.0151649 | + | 0.999885i | \(0.504827\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.35026 | −0.202767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.08698 | −0.367059 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8496 | −0.832139 | −0.416070 | − | 0.909333i | \(-0.636593\pi\) | ||||
−0.416070 | + | 0.909333i | \(0.636593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.57452 | 0.393606 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4387 | −0.861338 | −0.430669 | − | 0.902510i | \(-0.641722\pi\) | ||||
−0.430669 | + | 0.902510i | \(0.641722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.55008 | 0.389362 | 0.194681 | − | 0.980867i | \(-0.437633\pi\) | ||||
0.194681 | + | 0.980867i | \(0.437633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.92478 | −0.587893 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.3258 | 1.37688 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.92478 | 0.464559 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4387 | −0.843515 | −0.421758 | − | 0.906709i | \(-0.638587\pi\) | ||||
−0.421758 | + | 0.906709i | \(0.638587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.926192 | −0.0539250 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.61213 | 0.0935451 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.70052 | −0.387501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.59895 | −0.149801 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.4010 | −0.884767 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −43.3258 | −2.48083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8740 | 0.905977 | 0.452988 | − | 0.891516i | \(-0.350358\pi\) | ||||
0.452988 | + | 0.891516i | \(0.350358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.62530 | 0.263124 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.25202 | 0.467929 | 0.233964 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233964 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.40105 | −0.192239 | −0.0961193 | − | 0.995370i | \(-0.530643\pi\) | ||||
−0.0961193 | + | 0.995370i | \(0.530643\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.92478 | −0.559198 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4387 | 0.586293 | 0.293147 | − | 0.956067i | \(-0.405298\pi\) | ||||
0.293147 | + | 0.956067i | \(0.405298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22425 | −0.180524 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5501 | −0.812106 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.70052 | −0.372827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.77575 | 0.209441 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.4010 | 0.851680 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.57452 | 0.361368 | 0.180684 | − | 0.983541i | \(-0.442169\pi\) | ||||
0.180684 | + | 0.983541i | \(0.442169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.92478 | 0.434275 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.0724 | −1.31522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.4010 | 1.71052 | 0.855262 | − | 0.518196i | \(-0.173396\pi\) | ||||
0.855262 | + | 0.518196i | \(0.173396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.47627 | 0.514680 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5990 | −0.573965 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.29948 | −0.502125 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.8496 | −1.06866 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.2506 | −1.14079 | −0.570396 | − | 0.821370i | \(-0.693210\pi\) | ||||
−0.570396 | + | 0.821370i | \(0.693210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9248 | −1.06655 | −0.533274 | − | 0.845942i | \(-0.679039\pi\) | ||||
−0.533274 | + | 0.845942i | \(0.679039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.43866 | −0.342695 | −0.171348 | − | 0.985211i | \(-0.554812\pi\) | ||||
−0.171348 | + | 0.985211i | \(0.554812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7757 | 0.678066 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.70052 | −0.354629 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.5647 | −1.50759 | −0.753793 | − | 0.657112i | \(-0.771778\pi\) | ||||
−0.753793 | + | 0.657112i | \(0.771778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.77575 | −0.409250 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.40105 | 0.440941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.222839 | −0.0116639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.3258 | −1.00880 | −0.504400 | − | 0.863470i | \(-0.668286\pi\) | ||||
−0.504400 | + | 0.863470i | \(0.668286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.96239 | 0.362447 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.9511 | 2.07416 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.6991 | −1.33065 | −0.665325 | − | 0.746554i | \(-0.731707\pi\) | ||||
−0.665325 | + | 0.746554i | \(0.731707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.62672 | −0.187283 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7513 | −1.27139 | −0.635695 | − | 0.771941i | \(-0.719286\pi\) | ||||
−0.635695 | + | 0.771941i | \(0.719286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.29948 | −0.271500 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6121 | 1.10433 | 0.552164 | − | 0.833735i | \(-0.313802\pi\) | ||||
0.552164 | + | 0.833735i | \(0.313802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.775746 | −0.0394334 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.3258 | 1.28407 | 0.642035 | − | 0.766675i | \(-0.278090\pi\) | ||||
0.642035 | + | 0.766675i | \(0.278090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4010 | −0.677720 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.14903 | −0.461508 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.5487 | −1.78865 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.92478 | −0.196979 | −0.0984895 | − | 0.995138i | \(-0.531401\pi\) | ||||
−0.0984895 | + | 0.995138i | \(0.531401\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.2243 | 0.561916 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.4109 | −0.869459 | −0.434729 | − | 0.900561i | \(-0.643156\pi\) | ||||
−0.434729 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.57452 | 0.327500 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.96239 | −0.147202 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7757 | −0.633270 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.9248 | −0.787430 | −0.393715 | − | 0.919233i | \(-0.628810\pi\) | ||||
−0.393715 | + | 0.919233i | \(0.628810\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.513881 | −0.0253479 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.04746 | 0.0515422 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.6253 | 1.20881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9248 | 0.681899 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.9986 | 1.80750 | 0.903750 | − | 0.428062i | \(-0.140803\pi\) | ||||
0.903750 | + | 0.428062i | \(0.140803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.4010 | −1.92029 | −0.960145 | − | 0.279503i | \(-0.909830\pi\) | ||||
−0.960145 | + | 0.279503i | \(0.909830\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.38787 | 0.116102 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.55149 | 0.366301 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.9986 | 2.37121 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.61213 | 0.0778342 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.6385 | −1.71664 | −0.858322 | − | 0.513111i | \(-0.828493\pi\) | ||||
−0.858322 | + | 0.513111i | \(0.828493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0738 | 1.58943 | 0.794713 | − | 0.606986i | \(-0.207621\pi\) | ||||
0.794713 | + | 0.606986i | \(0.207621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.92478 | 0.284071 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.4485 | 1.07386 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.4749 | 1.54994 | 0.774970 | − | 0.631998i | \(-0.217765\pi\) | ||||
0.774970 | + | 0.631998i | \(0.217765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.22425 | 0.201155 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.14903 | 0.434684 | 0.217342 | − | 0.976096i | \(-0.430261\pi\) | ||||
0.217342 | + | 0.976096i | \(0.430261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.3272 | −1.24803 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.8872 | 0.609542 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.3634 | −1.14978 | −0.574891 | − | 0.818230i | \(-0.694955\pi\) | ||||
−0.574891 | + | 0.818230i | \(0.694955\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2243 | −0.528529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.2750 | −0.623716 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.92478 | −0.465281 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4763 | 1.37884 | 0.689421 | − | 0.724361i | \(-0.257865\pi\) | ||||
0.689421 | + | 0.724361i | \(0.257865\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.11283 | −0.331278 | −0.165639 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165639 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.7974 | −1.98896 | −0.994481 | − | 0.104918i | \(-0.966542\pi\) | ||||
−0.994481 | + | 0.104918i | \(0.966542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.4763 | 0.903190 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6253 | 0.584229 | 0.292115 | − | 0.956383i | \(-0.405641\pi\) | ||||
0.292115 | + | 0.956383i | \(0.405641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.2243 | 1.25710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0738 | −0.971030 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.25060 | 0.0575027 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6497 | −0.580410 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.9248 | 0.545998 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.3390 | −1.56899 | −0.784494 | − | 0.620136i | \(-0.787077\pi\) | ||||
−0.784494 | + | 0.620136i | \(0.787077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.92478 | 0.361339 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.4485 | 1.02144 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.4763 | 1.06600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5271 | 0.975484 | 0.487742 | − | 0.872988i | \(-0.337821\pi\) | ||||
0.487742 | + | 0.872988i | \(0.337821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.9003 | 0.990368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.0263 | 1.17455 | 0.587276 | − | 0.809387i | \(-0.300200\pi\) | ||||
0.587276 | + | 0.809387i | \(0.300200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.77575 | 0.214654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.4485 | −0.648104 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.42548 | −0.0638135 | −0.0319067 | − | 0.999491i | \(-0.510158\pi\) | ||||
−0.0319067 | + | 0.999491i | \(0.510158\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.4617 | 0.780130 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.67276 | −0.0745847 | −0.0372924 | − | 0.999304i | \(-0.511873\pi\) | ||||
−0.0372924 | + | 0.999304i | \(0.511873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.6239 | −2.03024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.58910 | 0.292057 | 0.146028 | − | 0.989280i | \(-0.453351\pi\) | ||||
0.146028 | + | 0.989280i | \(0.453351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.252016 | 0.0111485 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.35026 | 0.147918 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.7019 | 0.603780 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.84955 | −0.169303 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.8496 | −0.959089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.3733 | 1.15543 | 0.577717 | − | 0.816237i | \(-0.303944\pi\) | ||||
0.577717 | + | 0.816237i | \(0.303944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.32582 | −0.145428 | −0.0727141 | − | 0.997353i | \(-0.523166\pi\) | ||||
−0.0727141 | + | 0.997353i | \(0.523166\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.6497 | −0.552080 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.1490 | 0.572781 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8970 | 0.952044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.312650 | 0.0135679 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.96239 | 0.301575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.1030 | −1.86350 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.9248 | 0.946124 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.81003 | −0.293329 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.8496 | 1.45531 | 0.727653 | − | 0.685945i | \(-0.240611\pi\) | ||||
0.727653 | + | 0.685945i | \(0.240611\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.6253 | 0.799288 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45.6239 | 1.95431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7743 | 1.10203 | 0.551015 | − | 0.834495i | \(-0.314241\pi\) | ||||
0.551015 | + | 0.834495i | \(0.314241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6253 | 0.624193 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.70052 | −0.285452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.2031 | 1.70961 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.4763 | 0.996512 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.88717 | −0.207076 | −0.103538 | − | 0.994626i | \(-0.533016\pi\) | ||||
−0.103538 | + | 0.994626i | \(0.533016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.775746 | −0.0328106 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.22425 | 0.136128 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2228 | 1.35803 | 0.679015 | − | 0.734124i | \(-0.262407\pi\) | ||||
0.679015 | + | 0.734124i | \(0.262407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.0724 | 1.18101 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.35026 | 0.140698 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.2228 | −0.763941 | −0.381971 | − | 0.924174i | \(-0.624754\pi\) | ||||
−0.381971 | + | 0.924174i | \(0.624754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9986 | −1.54834 | −0.774171 | − | 0.632976i | \(-0.781833\pi\) | ||||
−0.774171 | + | 0.632976i | \(0.781833\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.7743 | −0.909636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.2995 | −1.05506 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.10299 | −0.0459179 | −0.0229589 | − | 0.999736i | \(-0.507309\pi\) | ||||
−0.0229589 | + | 0.999736i | \(0.507309\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2506 | −0.800028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.8496 | −1.15539 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.2243 | −0.796187 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.96239 | −0.122480 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.0884 | 1.53080 | 0.765401 | − | 0.643554i | \(-0.222541\pi\) | ||||
0.765401 | + | 0.643554i | \(0.222541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.0263 | −0.907580 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.51388 | 0.185676 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.8397 | 1.63602 | 0.818010 | − | 0.575204i | \(-0.195077\pi\) | ||||
0.818010 | + | 0.575204i | \(0.195077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.8496 | −0.813752 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.14903 | 0.374445 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0263 | 0.899972 | 0.449986 | − | 0.893036i | \(-0.351429\pi\) | ||||
0.449986 | + | 0.893036i | \(0.351429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.4010 | −1.44404 | −0.722019 | − | 0.691873i | \(-0.756786\pi\) | ||||
−0.722019 | + | 0.691873i | \(0.756786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.12601 | 0.330917 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.8872 | 1.01181 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0752 | −0.408941 | −0.204470 | − | 0.978873i | \(-0.565547\pi\) | ||||
−0.204470 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.70052 | −0.271519 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.38787 | 0.0966030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3733 | 0.580532 | 0.290266 | − | 0.956946i | \(-0.406256\pi\) | ||||
0.290266 | + | 0.956946i | \(0.406256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.6253 | 0.831692 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6615 | 1.55645 | 0.778227 | − | 0.627984i | \(-0.216119\pi\) | ||||
0.778227 | + | 0.627984i | \(0.216119\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.12601 | −0.326612 | −0.163306 | − | 0.986575i | \(-0.552216\pi\) | ||||
−0.163306 | + | 0.986575i | \(0.552216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.70052 | 0.268883 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.7743 | 1.19288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6225 | −1.18490 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.40105 | −0.215697 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8496 | 0.631963 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5745 | −0.898677 | −0.449339 | − | 0.893362i | \(-0.648340\pi\) | ||||
−0.449339 | + | 0.893362i | \(0.648340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6991 | −0.623000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.22425 | 0.167371 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.31265 | −0.170606 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8496 | −0.705015 | −0.352508 | − | 0.935809i | \(-0.614671\pi\) | ||||
−0.352508 | + | 0.935809i | \(0.614671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.47295 | −0.0975234 | −0.0487617 | − | 0.998810i | \(-0.515527\pi\) | ||||
−0.0487617 | + | 0.998810i | \(0.515527\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.29806 | −0.0904861 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.9525 | −0.902357 | −0.451179 | − | 0.892434i | \(-0.648996\pi\) | ||||
−0.451179 | + | 0.892434i | \(0.648996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.504032 | −0.0197850 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.0263 | −0.863281 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4010 | −0.759222 | −0.379611 | − | 0.925146i | \(-0.623942\pi\) | ||||
−0.379611 | + | 0.925146i | \(0.623942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.1030 | −1.05900 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.0752228 | 0.00293472 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8496 | 0.617411 | 0.308705 | − | 0.951158i | \(-0.400104\pi\) | ||||
0.308705 | + | 0.951158i | \(0.400104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.8773 | 1.20099 | 0.600494 | − | 0.799629i | \(-0.294971\pi\) | ||||
0.600494 | + | 0.799629i | \(0.294971\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.2506 | 1.28940 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.4010 | −0.518891 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.4241 | −0.712316 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.5778 | −0.910212 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3272 | 0.629369 | 0.314684 | − | 0.949196i | \(-0.398101\pi\) | ||||
0.314684 | + | 0.949196i | \(0.398101\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.77575 | −0.145329 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.0752 | 1.23275 | 0.616375 | − | 0.787452i | \(-0.288600\pi\) | ||||
0.616375 | + | 0.787452i | \(0.288600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.5501 | −1.01890 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.61213 | −0.0617768 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1344 | 0.579103 | 0.289552 | − | 0.957162i | \(-0.406494\pi\) | ||||
0.289552 | + | 0.957162i | \(0.406494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52232 | −0.0581647 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.00000 | −0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.9248 | 0.454298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7235 | −0.750319 | −0.375160 | − | 0.926960i | \(-0.622412\pi\) | ||||
−0.375160 | + | 0.926960i | \(0.622412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.40105 | −0.205169 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.2506 | 1.56472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.9248 | 0.527439 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0752228 | −0.00284519 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.92478 | −0.299315 | −0.149657 | − | 0.988738i | \(-0.547817\pi\) | ||||
−0.149657 | + | 0.988738i | \(0.547817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.5501 | −1.00136 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.07381 | 0.266415 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 51.5975 | 1.94053 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5515 | 0.584049 | 0.292024 | − | 0.956411i | \(-0.405671\pi\) | ||||
0.292024 | + | 0.956411i | \(0.405671\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.0527 | −1.64979 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.77575 | 0.178603 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.08840 | −0.339412 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.5501 | 0.691801 | 0.345901 | − | 0.938271i | \(-0.387573\pi\) | ||||
0.345901 | + | 0.938271i | \(0.387573\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4960 | −0.577100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.7743 | −0.586654 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.55149 | 0.280455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9511 | −0.443243 | −0.221621 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221621 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.55149 | −0.0573840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.80209 | 0.325113 | 0.162556 | − | 0.986699i | \(-0.448026\pi\) | ||||
0.162556 | + | 0.986699i | \(0.448026\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.5139 | 0.461581 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.1002 | −0.482550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8251 | −0.876421 | −0.438211 | − | 0.898872i | \(-0.644388\pi\) | ||||
−0.438211 | + | 0.898872i | \(0.644388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.35026 | 0.123075 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.53690 | 0.276502 | 0.138251 | − | 0.990397i | \(-0.455852\pi\) | ||||
0.138251 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.1768 | 1.39869 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.31265 | −0.304144 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.7466 | 1.78116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6253 | 1.62840 | 0.814200 | − | 0.580584i | \(-0.197176\pi\) | ||||
0.814200 | + | 0.580584i | \(0.197176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.2243 | 0.554803 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.3258 | −1.43121 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6728 | −0.424254 | −0.212127 | − | 0.977242i | \(-0.568039\pi\) | ||||
−0.212127 | + | 0.977242i | \(0.568039\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8021 | −0.392091 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8397 | −0.719189 | −0.359594 | − | 0.933109i | \(-0.617085\pi\) | ||||
−0.359594 | + | 0.933109i | \(0.617085\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.5975 | −1.86796 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.92478 | −0.214211 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.312650 | 0.0112891 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1002 | −1.26574 | −0.632872 | − | 0.774256i | \(-0.718124\pi\) | ||||
−0.632872 | + | 0.774256i | \(0.718124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.07522 | 0.146766 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.2882 | −1.23326 | −0.616631 | − | 0.787253i | \(-0.711503\pi\) | ||||
−0.616631 | + | 0.787253i | \(0.711503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.8237 | 0.891694 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.5501 | −0.952479 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.3258 | −0.835734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.95254 | 0.248781 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.4288 | −2.22818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.8251 | −1.13444 | −0.567221 | − | 0.823565i | \(-0.691982\pi\) | ||||
−0.567221 | + | 0.823565i | \(0.691982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7757 | 0.454829 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.7480 | −1.12883 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.6253 | 0.519360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.3258 | 1.25288 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0752 | 0.569414 | 0.284707 | − | 0.958615i | \(-0.408104\pi\) | ||||
0.284707 | + | 0.958615i | \(0.408104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.77575 | 0.168954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.88717 | 0.314013 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.121269 | −0.00427948 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 66.5012 | 2.34386 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.8496 | −0.769141 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.32582 | 0.0466135 | 0.0233067 | − | 0.999728i | \(-0.492581\pi\) | ||||
0.0233067 | + | 0.999728i | \(0.492581\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.3488 | 0.433627 | 0.216813 | − | 0.976213i | \(-0.430434\pi\) | ||||
0.216813 | + | 0.976213i | \(0.430434\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.499293 | 0.0175110 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64.8773 | 2.27255 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.59895 | 0.0909259 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.35026 | 0.117068 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.1378 | −1.88942 | −0.944711 | − | 0.327905i | \(-0.893657\pi\) | ||||
−0.944711 | + | 0.327905i | \(0.893657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7283 | −0.548254 | −0.274127 | − | 0.961694i | \(-0.588389\pi\) | ||||
−0.274127 | + | 0.961694i | \(0.588389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.08698 | 0.211922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4880 | 0.955852 | 0.477926 | − | 0.878400i | \(-0.341389\pi\) | ||||
0.477926 | + | 0.878400i | \(0.341389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6728 | 0.544337 | 0.272169 | − | 0.962250i | \(-0.412259\pi\) | ||||
0.272169 | + | 0.962250i | \(0.412259\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8496 | 0.480436 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.44851 | 0.292723 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.7283 | 1.79013 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.57452 | −0.227248 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8641 | 1.03102 | 0.515512 | − | 0.856882i | \(-0.327602\pi\) | ||||
0.515512 | + | 0.856882i | \(0.327602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.4387 | 0.497294 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.96239 | −0.101909 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.1457 | −0.967098 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.55008 | −0.224798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.1002 | −1.82025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.2228 | 1.17177 | 0.585884 | − | 0.810395i | \(-0.300747\pi\) | ||||
0.585884 | + | 0.810395i | \(0.300747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.92478 | 0.339420 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6267 | 0.602117 | 0.301059 | − | 0.953606i | \(-0.402660\pi\) | ||||
0.301059 | + | 0.953606i | \(0.402660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.80209 | 0.232084 | 0.116042 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116042 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.3258 | −0.794942 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.4142 | 1.10339 | 0.551696 | − | 0.834045i | \(-0.313981\pi\) | ||||
0.551696 | + | 0.834045i | \(0.313981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −64.7269 | −2.20078 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.3455 | −0.656252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.12601 | 0.275339 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.92478 | −0.268213 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1504 | 0.410760 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8773 | −0.907582 | −0.453791 | − | 0.891108i | \(-0.649929\pi\) | ||||
−0.453791 | + | 0.891108i | \(0.649929\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.4387 | 0.487004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.4763 | −1.12784 | −0.563922 | − | 0.825828i | \(-0.690708\pi\) | ||||
−0.563922 | + | 0.825828i | \(0.690708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3996 | 0.888418 | 0.444209 | − | 0.895923i | \(-0.353485\pi\) | ||||
0.444209 | + | 0.895923i | \(0.353485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.926192 | 0.0311336 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7743 | 0.462497 | 0.231248 | − | 0.972895i | \(-0.425719\pi\) | ||||
0.231248 | + | 0.972895i | \(0.425719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.7546 | 0.595471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61213 | −0.0540083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.00000 | −0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.9497 | 2.17103 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.70052 | 0.223724 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.1490 | 0.438545 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.8496 | 0.794544 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.59895 | 0.0864877 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.1754 | 1.83409 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.74798 | 0.124450 | 0.0622249 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622249 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.4010 | 0.510820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.42075 | 0.0470714 | 0.0235357 | − | 0.999723i | \(-0.492508\pi\) | ||||
0.0235357 | + | 0.999723i | \(0.492508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.4010 | 0.443510 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.3258 | 1.43231 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.6516 | 1.01221 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.5487 | −1.83238 | −0.916191 | − | 0.400743i | \(-0.868752\pi\) | ||||
−0.916191 | + | 0.400743i | \(0.868752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8740 | −0.523066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.31265 | −0.141953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.9219 | 0.983828 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.62530 | −0.151915 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.4636 | 1.62285 | 0.811424 | − | 0.584458i | \(-0.198693\pi\) | ||||
0.811424 | + | 0.584458i | \(0.198693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1524 | −0.463825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.25202 | −0.270159 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.55149 | 0.312367 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.07381 | −0.165754 | −0.0828770 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828770 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.40105 | 0.110989 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8119 | 0.613252 | 0.306626 | − | 0.951830i | \(-0.400800\pi\) | ||||
0.306626 | + | 0.951830i | \(0.400800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.6516 | −1.51919 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.92478 | 0.322853 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2652 | 0.496052 | 0.248026 | − | 0.968753i | \(-0.420218\pi\) | ||||
0.248026 | + | 0.968753i | \(0.420218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0752228 | 0.00244183 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.4387 | −0.338497 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.47627 | 0.177394 | 0.0886969 | − | 0.996059i | \(-0.471730\pi\) | ||||
0.0886969 | + | 0.996059i | \(0.471730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −64.5040 | −2.08730 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.22425 | 0.104225 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.72164 | 0.0555945 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2243 | 0.394331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.5501 | 0.468870 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57.0278 | −1.83579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0216 | −1.47996 | −0.739978 | − | 0.672632i | \(-0.765164\pi\) | ||||
−0.739978 | + | 0.672632i | \(0.765164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.70052 | 0.215252 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.4485 | 0.592041 | 0.296020 | − | 0.955182i | \(-0.404340\pi\) | ||||
0.296020 | + | 0.955182i | \(0.404340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.6516 | −1.49558 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.77575 | −0.120921 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.160295 | −0.00512828 | −0.00256414 | − | 0.999997i | \(-0.500816\pi\) | ||||
−0.00256414 | + | 0.999997i | \(0.500816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3272 | −0.457901 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.4010 | −0.491718 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.8167 | 0.919109 | 0.459555 | − | 0.888149i | \(-0.348009\pi\) | ||||
0.459555 | + | 0.888149i | \(0.348009\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3719 | 0.426063 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.19791 | 0.165284 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.2228 | 1.27772 | 0.638860 | − | 0.769323i | \(-0.279406\pi\) | ||||
0.638860 | + | 0.769323i | \(0.279406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.57452 | −0.208636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.1030 | 0.859222 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.8021 | −0.405446 | −0.202723 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202723 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.92478 | −0.250729 |
(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 | 1248.2.a.o.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 3744.2.a.ba.1.3 | 3 | |||
4.3 | odd | 2 | 1248.2.a.p.1.1 | yes | 3 | ||
8.3 | odd | 2 | 2496.2.a.bk.1.3 | 3 | |||
8.5 | even | 2 | 2496.2.a.bl.1.3 | 3 | |||
12.11 | even | 2 | 3744.2.a.z.1.3 | 3 | |||
24.5 | odd | 2 | 7488.2.a.cx.1.1 | 3 | |||
24.11 | even | 2 | 7488.2.a.cy.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.o.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1248.2.a.p.1.1 | yes | 3 | 4.3 | odd | 2 | ||
2496.2.a.bk.1.3 | 3 | 8.3 | odd | 2 | |||
2496.2.a.bl.1.3 | 3 | 8.5 | even | 2 | |||
3744.2.a.z.1.3 | 3 | 12.11 | even | 2 | |||
3744.2.a.ba.1.3 | 3 | 3.2 | odd | 2 | |||
7488.2.a.cx.1.1 | 3 | 24.5 | odd | 2 | |||
7488.2.a.cy.1.1 | 3 | 24.11 | even | 2 |