Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.14884000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.30927\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30927 | 1.63290 | 0.816452 | − | 0.577414i | \(-0.195938\pi\) | ||||
0.816452 | + | 0.577414i | \(0.195938\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.33275 | 1.66637 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.03582 | −1.14743 | −0.573716 | − | 0.819055i | \(-0.694498\pi\) | ||||
−0.573716 | + | 0.819055i | \(0.694498\pi\) | |||||||
\(8\) | 3.07768 | 1.08813 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42721 | 0.395837 | 0.197918 | − | 0.980218i | \(-0.436582\pi\) | ||||
0.197918 | + | 0.980218i | \(0.436582\pi\) | |||||||
\(14\) | −7.01054 | −1.87364 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.441718 | 0.110430 | ||||||||
\(17\) | 1.86025 | 0.451176 | 0.225588 | − | 0.974223i | \(-0.427570\pi\) | ||||
0.225588 | + | 0.974223i | \(0.427570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.903319 | 0.207236 | 0.103618 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103618 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.61855 | −0.984678 | ||||||||
\(23\) | −3.32932 | −0.694212 | −0.347106 | − | 0.937826i | \(-0.612836\pi\) | ||||
−0.347106 | + | 0.937826i | \(0.612836\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.29582 | 0.646364 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.1176 | −1.91205 | ||||||||
\(29\) | −3.96307 | −0.735924 | −0.367962 | − | 0.929841i | \(-0.619944\pi\) | ||||
−0.367962 | + | 0.929841i | \(0.619944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.43997 | −1.15665 | −0.578326 | − | 0.815806i | \(-0.696294\pi\) | ||||
−0.578326 | + | 0.815806i | \(0.696294\pi\) | |||||||
\(32\) | −5.13532 | −0.907805 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.29582 | 0.736727 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.82022 | −0.628040 | −0.314020 | − | 0.949416i | \(-0.601676\pi\) | ||||
−0.314020 | + | 0.949416i | \(0.601676\pi\) | |||||||
\(38\) | 2.08601 | 0.338396 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.83422 | 0.286457 | 0.143228 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143228 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.59445 | 0.548149 | 0.274074 | − | 0.961708i | \(-0.411629\pi\) | ||||
0.274074 | + | 0.961708i | \(0.411629\pi\) | |||||||
\(44\) | −6.66550 | −1.00486 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.68832 | −1.13358 | ||||||||
\(47\) | −4.79995 | −0.700144 | −0.350072 | − | 0.936723i | \(-0.613843\pi\) | ||||
−0.350072 | + | 0.936723i | \(0.613843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.21619 | 0.316598 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.75653 | 0.659613 | ||||||||
\(53\) | −9.50473 | −1.30558 | −0.652788 | − | 0.757541i | \(-0.726401\pi\) | ||||
−0.652788 | + | 0.757541i | \(0.726401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.34328 | −1.24855 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.15182 | −1.20169 | ||||||||
\(59\) | −10.6456 | −1.38594 | −0.692971 | − | 0.720966i | \(-0.743698\pi\) | ||||
−0.692971 | + | 0.720966i | \(0.743698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.2742 | 1.82762 | 0.913811 | − | 0.406140i | \(-0.133125\pi\) | ||||
0.913811 | + | 0.406140i | \(0.133125\pi\) | |||||||
\(62\) | −14.8716 | −1.88870 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7423 | −1.59279 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6902 | 1.30601 | 0.653007 | − | 0.757352i | \(-0.273507\pi\) | ||||
0.653007 | + | 0.757352i | \(0.273507\pi\) | |||||||
\(68\) | 6.19974 | 0.751828 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4598 | −1.47871 | −0.739356 | − | 0.673315i | \(-0.764870\pi\) | ||||
−0.739356 | + | 0.673315i | \(0.764870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.267631 | −0.0313239 | −0.0156619 | − | 0.999877i | \(-0.504986\pi\) | ||||
−0.0156619 | + | 0.999877i | \(0.504986\pi\) | |||||||
\(74\) | −8.82193 | −1.02553 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.01054 | 0.345332 | ||||||||
\(77\) | 6.07163 | 0.691927 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.57176 | −0.964398 | −0.482199 | − | 0.876062i | \(-0.660162\pi\) | ||||
−0.482199 | + | 0.876062i | \(0.660162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.23572 | 0.467757 | ||||||||
\(83\) | −12.6182 | −1.38502 | −0.692512 | − | 0.721406i | \(-0.743496\pi\) | ||||
−0.692512 | + | 0.721406i | \(0.743496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.30058 | 0.895074 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.15537 | −0.656164 | ||||||||
\(89\) | 4.76796 | 0.505402 | 0.252701 | − | 0.967544i | \(-0.418681\pi\) | ||||
0.252701 | + | 0.967544i | \(0.418681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.33275 | −0.454196 | ||||||||
\(92\) | −11.0958 | −1.15682 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.0844 | −1.14327 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.95805 | 1.01109 | 0.505543 | − | 0.862801i | \(-0.331292\pi\) | ||||
0.505543 | + | 0.862801i | \(0.331292\pi\) | |||||||
\(98\) | 5.11778 | 0.516974 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.34612 | −0.929974 | −0.464987 | − | 0.885318i | \(-0.653941\pi\) | ||||
−0.464987 | + | 0.885318i | \(0.653941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.08408 | −0.895081 | −0.447540 | − | 0.894264i | \(-0.647700\pi\) | ||||
−0.447540 | + | 0.894264i | \(0.647700\pi\) | |||||||
\(104\) | 4.39250 | 0.430720 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.9490 | −2.13188 | ||||||||
\(107\) | 5.62871 | 0.544148 | 0.272074 | − | 0.962276i | \(-0.412290\pi\) | ||||
0.272074 | + | 0.962276i | \(0.412290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1130 | −0.968649 | −0.484325 | − | 0.874888i | \(-0.660935\pi\) | ||||
−0.484325 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.34098 | −0.126710 | ||||||||
\(113\) | 10.7120 | 1.00770 | 0.503851 | − | 0.863791i | \(-0.331916\pi\) | ||||
0.503851 | + | 0.863791i | \(0.331916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.2079 | −1.22632 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.5836 | −2.26311 | ||||||||
\(119\) | −5.64737 | −0.517693 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 32.9630 | 2.98433 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −21.4628 | −1.92742 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3609 | 1.00812 | 0.504060 | − | 0.863669i | \(-0.331839\pi\) | ||||
0.504060 | + | 0.863669i | \(0.331839\pi\) | |||||||
\(128\) | −19.1548 | −1.69306 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.98771 | −0.697890 | −0.348945 | − | 0.937143i | \(-0.613460\pi\) | ||||
−0.348945 | + | 0.937143i | \(0.613460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.74231 | −0.237789 | ||||||||
\(134\) | 24.6866 | 2.13259 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.72525 | 0.490936 | ||||||||
\(137\) | 9.33726 | 0.797736 | 0.398868 | − | 0.917008i | \(-0.369403\pi\) | ||||
0.398868 | + | 0.917008i | \(0.369403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9150 | 1.51953 | 0.759767 | − | 0.650195i | \(-0.225313\pi\) | ||||
0.759767 | + | 0.650195i | \(0.225313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −28.7732 | −2.41459 | ||||||||
\(143\) | −2.85442 | −0.238699 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.618034 | −0.0511489 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.7318 | −1.04655 | ||||||||
\(149\) | 6.31395 | 0.517259 | 0.258629 | − | 0.965977i | \(-0.416729\pi\) | ||||
0.258629 | + | 0.965977i | \(0.416729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71947 | 0.384065 | 0.192033 | − | 0.981389i | \(-0.438492\pi\) | ||||
0.192033 | + | 0.981389i | \(0.438492\pi\) | |||||||
\(152\) | 2.78013 | 0.225498 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.0211 | 1.12985 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.46908 | −0.117245 | −0.0586225 | − | 0.998280i | \(-0.518671\pi\) | ||||
−0.0586225 | + | 0.998280i | \(0.518671\pi\) | |||||||
\(158\) | −19.7945 | −1.57477 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.1072 | 0.796560 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.45969 | −0.349310 | −0.174655 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174655 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(164\) | 6.11299 | 0.477345 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.1388 | −2.26161 | ||||||||
\(167\) | 10.4337 | 0.807381 | 0.403691 | − | 0.914896i | \(-0.367727\pi\) | ||||
0.403691 | + | 0.914896i | \(0.367727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9631 | −0.843313 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.9794 | 0.913421 | ||||||||
\(173\) | −7.67619 | −0.583610 | −0.291805 | − | 0.956478i | \(-0.594256\pi\) | ||||
−0.291805 | + | 0.956478i | \(0.594256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.883436 | −0.0665915 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.0105 | 0.825273 | ||||||||
\(179\) | −15.5168 | −1.15978 | −0.579889 | − | 0.814696i | \(-0.696904\pi\) | ||||
−0.579889 | + | 0.814696i | \(0.696904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.59056 | −0.118225 | −0.0591126 | − | 0.998251i | \(-0.518827\pi\) | ||||
−0.0591126 | + | 0.998251i | \(0.518827\pi\) | |||||||
\(182\) | −10.0055 | −0.741658 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.2466 | −0.755390 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.72049 | −0.272069 | ||||||||
\(188\) | −15.9970 | −1.16670 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.6684 | −1.42316 | −0.711579 | − | 0.702606i | \(-0.752020\pi\) | ||||
−0.711579 | + | 0.702606i | \(0.752020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1100 | −0.943680 | −0.471840 | − | 0.881684i | \(-0.656410\pi\) | ||||
−0.471840 | + | 0.881684i | \(0.656410\pi\) | |||||||
\(194\) | 22.9959 | 1.65101 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.38599 | 0.527571 | ||||||||
\(197\) | −3.42949 | −0.244341 | −0.122170 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122170 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6959 | 1.25443 | 0.627215 | − | 0.778846i | \(-0.284195\pi\) | ||||
0.627215 | + | 0.778846i | \(0.284195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.5828 | −1.51856 | ||||||||
\(203\) | 12.0312 | 0.844422 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.9776 | −1.46158 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.630425 | 0.0437121 | ||||||||
\(209\) | −1.80664 | −0.124968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.24366 | −0.223303 | −0.111651 | − | 0.993747i | \(-0.535614\pi\) | ||||
−0.111651 | + | 0.993747i | \(0.535614\pi\) | |||||||
\(212\) | −31.6769 | −2.17558 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.9982 | 0.888542 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5506 | 1.32718 | ||||||||
\(218\) | −23.3537 | −1.58171 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.65496 | 0.178592 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.7148 | −1.92288 | −0.961441 | − | 0.275010i | \(-0.911319\pi\) | ||||
−0.961441 | + | 0.275010i | \(0.911319\pi\) | |||||||
\(224\) | 15.5899 | 1.04164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.7370 | 1.64548 | ||||||||
\(227\) | 11.7206 | 0.777926 | 0.388963 | − | 0.921253i | \(-0.372833\pi\) | ||||
0.388963 | + | 0.921253i | \(0.372833\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4013 | −1.08383 | −0.541914 | − | 0.840434i | \(-0.682300\pi\) | ||||
−0.541914 | + | 0.840434i | \(0.682300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.1971 | −0.800777 | ||||||||
\(233\) | 22.5146 | 1.47498 | 0.737490 | − | 0.675358i | \(-0.236011\pi\) | ||||
0.737490 | + | 0.675358i | \(0.236011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −35.4792 | −2.30950 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.0413 | −0.845344 | ||||||||
\(239\) | 6.63333 | 0.429074 | 0.214537 | − | 0.976716i | \(-0.431176\pi\) | ||||
0.214537 | + | 0.976716i | \(0.431176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.2261 | 1.68937 | 0.844684 | − | 0.535265i | \(-0.179788\pi\) | ||||
0.844684 | + | 0.535265i | \(0.179788\pi\) | |||||||
\(242\) | −16.1649 | −1.03912 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 47.5723 | 3.04550 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.28923 | 0.0820315 | ||||||||
\(248\) | −19.8202 | −1.25858 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9121 | 0.688766 | 0.344383 | − | 0.938829i | \(-0.388088\pi\) | ||||
0.344383 | + | 0.938829i | \(0.388088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.65865 | 0.418626 | ||||||||
\(254\) | 26.2355 | 1.64616 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −18.7492 | −1.17182 | ||||||||
\(257\) | 6.58051 | 0.410481 | 0.205240 | − | 0.978712i | \(-0.434202\pi\) | ||||
0.205240 | + | 0.978712i | \(0.434202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5975 | 0.720632 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.4458 | −1.13959 | ||||||||
\(263\) | −27.1073 | −1.67151 | −0.835753 | − | 0.549106i | \(-0.814968\pi\) | ||||
−0.835753 | + | 0.549106i | \(0.814968\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.33275 | −0.388286 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.6277 | 2.17631 | ||||||||
\(269\) | −1.00945 | −0.0615474 | −0.0307737 | − | 0.999526i | \(-0.509797\pi\) | ||||
−0.0307737 | + | 0.999526i | \(0.509797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.25203 | 0.379784 | 0.189892 | − | 0.981805i | \(-0.439186\pi\) | ||||
0.189892 | + | 0.981805i | \(0.439186\pi\) | |||||||
\(272\) | 0.821705 | 0.0498232 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.5623 | 1.30263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.6703 | 1.48230 | 0.741148 | − | 0.671342i | \(-0.234282\pi\) | ||||
0.741148 | + | 0.671342i | \(0.234282\pi\) | |||||||
\(278\) | 41.3708 | 2.48125 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.83891 | −0.109700 | −0.0548502 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548502 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.64116 | 0.513664 | 0.256832 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256832 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(284\) | −41.5255 | −2.46409 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.59164 | −0.389772 | ||||||||
\(287\) | −5.56835 | −0.328690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5395 | −0.796440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.891948 | −0.0521973 | ||||||||
\(293\) | 6.29156 | 0.367557 | 0.183779 | − | 0.982968i | \(-0.441167\pi\) | ||||
0.183779 | + | 0.982968i | \(0.441167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.7574 | −0.683386 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.5806 | 0.844634 | ||||||||
\(299\) | −4.75164 | −0.274795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9121 | −0.628963 | ||||||||
\(302\) | 10.8986 | 0.627142 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.399012 | 0.0228849 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.6661 | 1.63606 | 0.818030 | − | 0.575175i | \(-0.195066\pi\) | ||||
0.818030 | + | 0.575175i | \(0.195066\pi\) | |||||||
\(308\) | 20.2352 | 1.15301 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.83649 | 0.444367 | 0.222183 | − | 0.975005i | \(-0.428682\pi\) | ||||
0.222183 | + | 0.975005i | \(0.428682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.4093 | −1.21012 | −0.605061 | − | 0.796179i | \(-0.706851\pi\) | ||||
−0.605061 | + | 0.796179i | \(0.706851\pi\) | |||||||
\(314\) | −3.39250 | −0.191450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.5675 | −1.60705 | ||||||||
\(317\) | 4.01983 | 0.225776 | 0.112888 | − | 0.993608i | \(-0.463990\pi\) | ||||
0.112888 | + | 0.993608i | \(0.463990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.92614 | 0.443779 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 23.3403 | 1.30071 | ||||||||
\(323\) | 1.68040 | 0.0934997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.2987 | −0.570390 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.64515 | 0.311701 | ||||||||
\(329\) | 14.5718 | 0.803367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6439 | 0.640005 | 0.320002 | − | 0.947417i | \(-0.396316\pi\) | ||||
0.320002 | + | 0.947417i | \(0.396316\pi\) | |||||||
\(332\) | −42.0532 | −2.30797 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0942 | 1.31838 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5348 | 1.17307 | 0.586537 | − | 0.809922i | \(-0.300491\pi\) | ||||
0.586537 | + | 0.809922i | \(0.300491\pi\) | |||||||
\(338\) | −25.3167 | −1.37705 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.8799 | 0.697487 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5228 | 0.784157 | ||||||||
\(344\) | 11.0626 | 0.596455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.7264 | −0.952979 | ||||||||
\(347\) | 15.5972 | 0.837303 | 0.418652 | − | 0.908147i | \(-0.362503\pi\) | ||||
0.418652 | + | 0.908147i | \(0.362503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.56598 | 0.297940 | 0.148970 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148970 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.2706 | 0.547427 | ||||||||
\(353\) | 8.02216 | 0.426977 | 0.213488 | − | 0.976946i | \(-0.431517\pi\) | ||||
0.213488 | + | 0.976946i | \(0.431517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.8904 | 0.842190 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −35.8325 | −1.89380 | ||||||||
\(359\) | 12.3427 | 0.651424 | 0.325712 | − | 0.945469i | \(-0.394396\pi\) | ||||
0.325712 | + | 0.945469i | \(0.394396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1840 | −0.957053 | ||||||||
\(362\) | −3.67303 | −0.193050 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.4400 | −0.756860 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8749 | −1.40286 | −0.701430 | − | 0.712738i | \(-0.747455\pi\) | ||||
−0.701430 | + | 0.712738i | \(0.747455\pi\) | |||||||
\(368\) | −1.47062 | −0.0766615 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.8546 | 1.49806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.6389 | 1.43109 | 0.715544 | − | 0.698567i | \(-0.246179\pi\) | ||||
0.715544 | + | 0.698567i | \(0.246179\pi\) | |||||||
\(374\) | −8.59164 | −0.444263 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.7727 | −0.761845 | ||||||||
\(377\) | −5.65614 | −0.291306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.47462 | −0.178479 | −0.0892397 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892397 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −45.4198 | −2.32388 | ||||||||
\(383\) | 27.3719 | 1.39864 | 0.699319 | − | 0.714810i | \(-0.253487\pi\) | ||||
0.699319 | + | 0.714810i | \(0.253487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.2746 | −1.54094 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.1877 | 1.68485 | ||||||||
\(389\) | −10.8845 | −0.551867 | −0.275934 | − | 0.961177i | \(-0.588987\pi\) | ||||
−0.275934 | + | 0.961177i | \(0.588987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.19336 | −0.313212 | ||||||||
\(392\) | 6.82072 | 0.344498 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.91963 | −0.398985 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.2212 | −0.814120 | −0.407060 | − | 0.913401i | \(-0.633446\pi\) | ||||
−0.407060 | + | 0.913401i | \(0.633446\pi\) | |||||||
\(398\) | 40.8647 | 2.04836 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.78686 | −0.189107 | −0.0945534 | − | 0.995520i | \(-0.530142\pi\) | ||||
−0.0945534 | + | 0.995520i | \(0.530142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.19118 | −0.457845 | ||||||||
\(404\) | −31.1483 | −1.54968 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.7832 | 1.37886 | ||||||||
\(407\) | 7.64044 | 0.378722 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.85585 | 0.0917661 | 0.0458831 | − | 0.998947i | \(-0.485390\pi\) | ||||
0.0458831 | + | 0.998947i | \(0.485390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −30.2750 | −1.49154 | ||||||||
\(413\) | 32.3181 | 1.59027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.32918 | −0.359343 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.17202 | −0.204060 | ||||||||
\(419\) | −14.3472 | −0.700907 | −0.350453 | − | 0.936580i | \(-0.613972\pi\) | ||||
−0.350453 | + | 0.936580i | \(0.613972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4545 | 0.753207 | 0.376604 | − | 0.926374i | \(-0.377092\pi\) | ||||
0.376604 | + | 0.926374i | \(0.377092\pi\) | |||||||
\(422\) | −7.49051 | −0.364632 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.2525 | −1.42063 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.3338 | −2.09707 | ||||||||
\(428\) | 18.7591 | 0.906755 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.5043 | −0.602311 | −0.301156 | − | 0.953575i | \(-0.597372\pi\) | ||||
−0.301156 | + | 0.953575i | \(0.597372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.4951 | 1.08105 | 0.540524 | − | 0.841329i | \(-0.318226\pi\) | ||||
0.540524 | + | 0.841329i | \(0.318226\pi\) | |||||||
\(434\) | 45.1476 | 2.16715 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −33.7041 | −1.61413 | ||||||||
\(437\) | −3.00744 | −0.143865 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1776 | 0.581204 | 0.290602 | − | 0.956844i | \(-0.406145\pi\) | ||||
0.290602 | + | 0.956844i | \(0.406145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.13104 | 0.291624 | ||||||||
\(443\) | −20.7101 | −0.983968 | −0.491984 | − | 0.870604i | \(-0.663728\pi\) | ||||
−0.491984 | + | 0.870604i | \(0.663728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −66.3103 | −3.13988 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 38.6833 | 1.82761 | ||||||||
\(449\) | 25.9539 | 1.22484 | 0.612420 | − | 0.790533i | \(-0.290196\pi\) | ||||
0.612420 | + | 0.790533i | \(0.290196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.66844 | −0.172740 | ||||||||
\(452\) | 35.7004 | 1.67921 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.0662 | 1.27028 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50150 | 0.397684 | 0.198842 | − | 0.980032i | \(-0.436282\pi\) | ||||
0.198842 | + | 0.980032i | \(0.436282\pi\) | |||||||
\(458\) | −37.8751 | −1.76979 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.7851 | −0.688609 | −0.344305 | − | 0.938858i | \(-0.611885\pi\) | ||||
−0.344305 | + | 0.938858i | \(0.611885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1921 | 1.03135 | 0.515677 | − | 0.856783i | \(-0.327540\pi\) | ||||
0.515677 | + | 0.856783i | \(0.327540\pi\) | |||||||
\(464\) | −1.75056 | −0.0812677 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 51.9924 | 2.40850 | ||||||||
\(467\) | −28.5014 | −1.31889 | −0.659443 | − | 0.751754i | \(-0.729208\pi\) | ||||
−0.659443 | + | 0.751754i | \(0.729208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.4534 | −1.49856 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.7638 | −1.50808 | ||||||||
\(473\) | −7.18891 | −0.330546 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.8213 | −0.862671 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.3182 | 0.700637 | ||||||||
\(479\) | −25.0569 | −1.14488 | −0.572440 | − | 0.819947i | \(-0.694003\pi\) | ||||
−0.572440 | + | 0.819947i | \(0.694003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.45225 | −0.248601 | ||||||||
\(482\) | 60.5632 | 2.75858 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.3292 | −1.06042 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.46479 | 0.0663758 | 0.0331879 | − | 0.999449i | \(-0.489434\pi\) | ||||
0.0331879 | + | 0.999449i | \(0.489434\pi\) | |||||||
\(488\) | 43.9314 | 1.98868 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0686 | 0.905685 | 0.452843 | − | 0.891591i | \(-0.350410\pi\) | ||||
0.452843 | + | 0.891591i | \(0.350410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.37229 | −0.332031 | ||||||||
\(494\) | 2.97718 | 0.133950 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.84465 | −0.127729 | ||||||||
\(497\) | 37.8258 | 1.69672 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.624999 | 0.0279788 | 0.0139894 | − | 0.999902i | \(-0.495547\pi\) | ||||
0.0139894 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.1990 | 1.12469 | ||||||||
\(503\) | −19.3052 | −0.860776 | −0.430388 | − | 0.902644i | \(-0.641623\pi\) | ||||
−0.430388 | + | 0.902644i | \(0.641623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.3766 | 0.683575 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.8631 | 1.67990 | ||||||||
\(509\) | 10.5202 | 0.466298 | 0.233149 | − | 0.972441i | \(-0.425097\pi\) | ||||
0.233149 | + | 0.972441i | \(0.425097\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.812479 | 0.0359420 | ||||||||
\(512\) | −4.98730 | −0.220410 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.1962 | 0.670276 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.59989 | 0.422203 | ||||||||
\(518\) | 26.7818 | 1.17672 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0070 | 0.438413 | 0.219207 | − | 0.975678i | \(-0.429653\pi\) | ||||
0.219207 | + | 0.975678i | \(0.429653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.7830 | −0.996233 | −0.498117 | − | 0.867110i | \(-0.665975\pi\) | ||||
−0.498117 | + | 0.867110i | \(0.665975\pi\) | |||||||
\(524\) | −26.6210 | −1.16295 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −62.5981 | −2.72941 | ||||||||
\(527\) | −11.9799 | −0.521854 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.9156 | −0.518070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.13943 | −0.396245 | ||||||||
\(533\) | 2.61782 | 0.113390 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 32.9010 | 1.42111 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.33110 | −0.100501 | ||||||||
\(539\) | −4.43237 | −0.190916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.25900 | 0.140115 | 0.0700576 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700576 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(542\) | 14.4377 | 0.620150 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.55296 | −0.409580 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.5883 | 0.580993 | 0.290497 | − | 0.956876i | \(-0.406179\pi\) | ||||
0.290497 | + | 0.956876i | \(0.406179\pi\) | |||||||
\(548\) | 31.1188 | 1.32933 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.57992 | −0.152510 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.0223 | 1.10658 | ||||||||
\(554\) | 56.9706 | 2.42045 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 59.7063 | 2.53211 | ||||||||
\(557\) | −27.6399 | −1.17114 | −0.585571 | − | 0.810621i | \(-0.699130\pi\) | ||||
−0.585571 | + | 0.810621i | \(0.699130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.13004 | 0.216978 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.24656 | −0.179130 | ||||||||
\(563\) | −1.65925 | −0.0699291 | −0.0349646 | − | 0.999389i | \(-0.511132\pi\) | ||||
−0.0349646 | + | 0.999389i | \(0.511132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.9548 | 0.838763 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38.3475 | −1.60902 | ||||||||
\(569\) | −17.8828 | −0.749686 | −0.374843 | − | 0.927088i | \(-0.622303\pi\) | ||||
−0.374843 | + | 0.927088i | \(0.622303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8723 | −1.54306 | −0.771530 | − | 0.636193i | \(-0.780508\pi\) | ||||
−0.771530 | + | 0.636193i | \(0.780508\pi\) | |||||||
\(572\) | −9.51307 | −0.397761 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.8589 | −0.536718 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8137 | 0.949746 | 0.474873 | − | 0.880054i | \(-0.342494\pi\) | ||||
0.474873 | + | 0.880054i | \(0.342494\pi\) | |||||||
\(578\) | −31.2664 | −1.30051 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.3065 | 1.58922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0095 | 0.787291 | ||||||||
\(584\) | −0.823684 | −0.0340843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5289 | 0.600185 | ||||||||
\(587\) | −11.0855 | −0.457546 | −0.228773 | − | 0.973480i | \(-0.573471\pi\) | ||||
−0.228773 | + | 0.973480i | \(0.573471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.81734 | −0.239699 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.68746 | −0.0693542 | ||||||||
\(593\) | 11.1321 | 0.457139 | 0.228570 | − | 0.973528i | \(-0.426595\pi\) | ||||
0.228570 | + | 0.973528i | \(0.426595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.0428 | 0.861947 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.9729 | −0.448713 | ||||||||
\(599\) | −36.2736 | −1.48210 | −0.741049 | − | 0.671451i | \(-0.765671\pi\) | ||||
−0.741049 | + | 0.671451i | \(0.765671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1051 | −0.616150 | −0.308075 | − | 0.951362i | \(-0.599685\pi\) | ||||
−0.308075 | + | 0.951362i | \(0.599685\pi\) | |||||||
\(602\) | −25.1990 | −1.02704 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.7288 | 0.639997 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5066 | 1.35999 | 0.679996 | − | 0.733216i | \(-0.261982\pi\) | ||||
0.679996 | + | 0.733216i | \(0.261982\pi\) | |||||||
\(608\) | −4.63883 | −0.188129 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.85053 | −0.277143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.0289 | 1.13208 | 0.566038 | − | 0.824379i | \(-0.308476\pi\) | ||||
0.566038 | + | 0.824379i | \(0.308476\pi\) | |||||||
\(614\) | 66.1979 | 2.67153 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.6866 | 0.752903 | ||||||||
\(617\) | 30.5223 | 1.22878 | 0.614391 | − | 0.789002i | \(-0.289402\pi\) | ||||
0.614391 | + | 0.789002i | \(0.289402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6971 | −0.872080 | −0.436040 | − | 0.899927i | \(-0.643619\pi\) | ||||
−0.436040 | + | 0.899927i | \(0.643619\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0966 | 0.725608 | ||||||||
\(623\) | −14.4746 | −0.579914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −49.4399 | −1.97601 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.89606 | −0.195374 | ||||||||
\(629\) | −7.10655 | −0.283357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.2277 | −0.646015 | −0.323007 | − | 0.946396i | \(-0.604694\pi\) | ||||
−0.323007 | + | 0.946396i | \(0.604694\pi\) | |||||||
\(632\) | −26.3812 | −1.04939 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.28290 | 0.368671 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.16296 | 0.125321 | ||||||||
\(638\) | 18.3036 | 0.724648 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1774 | 0.875956 | 0.437978 | − | 0.898986i | \(-0.355695\pi\) | ||||
0.437978 | + | 0.898986i | \(0.355695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2767 | 0.523583 | 0.261792 | − | 0.965124i | \(-0.415687\pi\) | ||||
0.261792 | + | 0.965124i | \(0.415687\pi\) | |||||||
\(644\) | 33.6848 | 1.32737 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.88050 | 0.152676 | ||||||||
\(647\) | −11.2853 | −0.443671 | −0.221835 | − | 0.975084i | \(-0.571205\pi\) | ||||
−0.221835 | + | 0.975084i | \(0.571205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2912 | 0.835754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.8630 | −0.582082 | ||||||||
\(653\) | −35.8134 | −1.40149 | −0.700743 | − | 0.713414i | \(-0.747148\pi\) | ||||
−0.700743 | + | 0.713414i | \(0.747148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.810208 | 0.0316333 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.6502 | 1.31182 | ||||||||
\(659\) | −39.7655 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.24734 | −0.242993 | −0.121497 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121497 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(662\) | 26.8889 | 1.04507 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.8347 | −1.50708 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.1943 | 0.510887 | ||||||||
\(668\) | 34.7728 | 1.34540 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.5484 | −1.10210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.4627 | 1.59827 | 0.799135 | − | 0.601151i | \(-0.205291\pi\) | ||||
0.799135 | + | 0.601151i | \(0.205291\pi\) | |||||||
\(674\) | 49.7297 | 1.91552 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.5372 | −1.40528 | ||||||||
\(677\) | −1.43915 | −0.0553112 | −0.0276556 | − | 0.999618i | \(-0.508804\pi\) | ||||
−0.0276556 | + | 0.999618i | \(0.508804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.2308 | −1.16015 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29.7433 | 1.13893 | ||||||||
\(683\) | −8.48623 | −0.324716 | −0.162358 | − | 0.986732i | \(-0.551910\pi\) | ||||
−0.162358 | + | 0.986732i | \(0.551910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 33.5371 | 1.28045 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.58774 | 0.0605318 | ||||||||
\(689\) | −13.5652 | −0.516795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.7797 | −1.66546 | −0.832730 | − | 0.553679i | \(-0.813223\pi\) | ||||
−0.832730 | + | 0.553679i | \(0.813223\pi\) | |||||||
\(692\) | −25.5828 | −0.972513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.0183 | 1.36724 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.41210 | 0.129243 | ||||||||
\(698\) | 12.8534 | 0.486508 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.840795 | −0.0317564 | −0.0158782 | − | 0.999874i | \(-0.505054\pi\) | ||||
−0.0158782 | + | 0.999874i | \(0.505054\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.45087 | −0.130152 | ||||||||
\(704\) | 25.4846 | 0.960487 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.5254 | 0.697212 | ||||||||
\(707\) | 28.3731 | 1.06708 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.3812 | −0.502543 | −0.251271 | − | 0.967917i | \(-0.580849\pi\) | ||||
−0.251271 | + | 0.967917i | \(0.580849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.6743 | 0.549941 | ||||||||
\(713\) | 21.4407 | 0.802962 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51.7135 | −1.93262 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.5027 | 1.06371 | ||||||||
\(719\) | −43.4148 | −1.61910 | −0.809550 | − | 0.587051i | \(-0.800289\pi\) | ||||
−0.809550 | + | 0.587051i | \(0.800289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5776 | 1.02704 | ||||||||
\(722\) | −41.9919 | −1.56278 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.30093 | −0.197007 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0480 | 1.18859 | 0.594297 | − | 0.804245i | \(-0.297430\pi\) | ||||
0.594297 | + | 0.804245i | \(0.297430\pi\) | |||||||
\(728\) | −13.3348 | −0.494222 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.68657 | 0.247312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.13928 | −0.300631 | −0.150316 | − | 0.988638i | \(-0.548029\pi\) | ||||
−0.150316 | + | 0.988638i | \(0.548029\pi\) | |||||||
\(734\) | −62.0616 | −2.29074 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.0971 | 0.630209 | ||||||||
\(737\) | −21.3804 | −0.787556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.12714 | −0.262176 | −0.131088 | − | 0.991371i | \(-0.541847\pi\) | ||||
−0.131088 | + | 0.991371i | \(0.541847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 66.6332 | 2.44618 | ||||||||
\(743\) | 21.9040 | 0.803578 | 0.401789 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401789 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 63.8258 | 2.33683 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.3995 | −0.453370 | ||||||||
\(749\) | −17.0877 | −0.624373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.21909 | 0.336409 | 0.168205 | − | 0.985752i | \(-0.446203\pi\) | ||||
0.168205 | + | 0.985752i | \(0.446203\pi\) | |||||||
\(752\) | −2.12022 | −0.0773166 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.0616 | −0.475674 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.6524 | −1.65926 | −0.829632 | − | 0.558311i | \(-0.811450\pi\) | ||||
−0.829632 | + | 0.558311i | \(0.811450\pi\) | |||||||
\(758\) | −8.02386 | −0.291440 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9058 | −1.44658 | −0.723291 | − | 0.690543i | \(-0.757372\pi\) | ||||
−0.723291 | + | 0.690543i | \(0.757372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.7012 | 1.11146 | ||||||||
\(764\) | −65.5500 | −2.37151 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 63.2092 | 2.28384 | ||||||||
\(767\) | −15.1935 | −0.548607 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.3420 | −1.59901 | −0.799506 | − | 0.600658i | \(-0.794906\pi\) | ||||
−0.799506 | + | 0.600658i | \(0.794906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43.6924 | −1.57252 | ||||||||
\(773\) | −38.4944 | −1.38455 | −0.692273 | − | 0.721635i | \(-0.743391\pi\) | ||||
−0.692273 | + | 0.721635i | \(0.743391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 30.6477 | 1.10019 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.1353 | −0.901146 | ||||||||
\(779\) | 1.65689 | 0.0593641 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9197 | 0.891697 | ||||||||
\(782\) | −14.3022 | −0.511445 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.978929 | 0.0349618 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.0202 | 1.88997 | 0.944983 | − | 0.327120i | \(-0.106078\pi\) | ||||
0.944983 | + | 0.327120i | \(0.106078\pi\) | |||||||
\(788\) | −11.4296 | −0.407164 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.5197 | −1.15627 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.3723 | 0.723440 | ||||||||
\(794\) | −37.4593 | −1.32938 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 58.9760 | 2.09035 | ||||||||
\(797\) | −12.6769 | −0.449037 | −0.224519 | − | 0.974470i | \(-0.572081\pi\) | ||||
−0.224519 | + | 0.974470i | \(0.572081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.92908 | −0.315888 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.74490 | −0.308793 | ||||||||
\(803\) | 0.535262 | 0.0188890 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.2250 | −0.747618 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.7644 | −1.01193 | ||||||||
\(809\) | 41.8935 | 1.47290 | 0.736449 | − | 0.676493i | \(-0.236501\pi\) | ||||
0.736449 | + | 0.676493i | \(0.236501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5486 | −1.21317 | −0.606583 | − | 0.795020i | \(-0.707460\pi\) | ||||
−0.606583 | + | 0.795020i | \(0.707460\pi\) | |||||||
\(812\) | 40.0968 | 1.40712 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.6439 | 0.618417 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.24694 | 0.113596 | ||||||||
\(818\) | 4.28568 | 0.149845 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.1349 | 0.737612 | 0.368806 | − | 0.929506i | \(-0.379767\pi\) | ||||
0.368806 | + | 0.929506i | \(0.379767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.17714 | −0.110748 | −0.0553740 | − | 0.998466i | \(-0.517635\pi\) | ||||
−0.0553740 | + | 0.998466i | \(0.517635\pi\) | |||||||
\(824\) | −27.9579 | −0.973960 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 74.6315 | 2.59676 | ||||||||
\(827\) | 9.74482 | 0.338860 | 0.169430 | − | 0.985542i | \(-0.445807\pi\) | ||||
0.169430 | + | 0.985542i | \(0.445807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.4352 | 0.813938 | 0.406969 | − | 0.913442i | \(-0.366586\pi\) | ||||
0.406969 | + | 0.913442i | \(0.366586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18.1859 | −0.630484 | ||||||||
\(833\) | 4.12265 | 0.142841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.02107 | −0.208243 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.1316 | −1.14451 | ||||||||
\(839\) | −42.6819 | −1.47354 | −0.736771 | − | 0.676142i | \(-0.763650\pi\) | ||||
−0.736771 | + | 0.676142i | \(0.763650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2941 | −0.458416 | ||||||||
\(842\) | 35.6887 | 1.22992 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.8103 | −0.372106 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2507 | 0.730183 | ||||||||
\(848\) | −4.19841 | −0.144174 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7187 | 0.435993 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.9610 | −0.580733 | −0.290367 | − | 0.956915i | \(-0.593777\pi\) | ||||
−0.290367 | + | 0.956915i | \(0.593777\pi\) | |||||||
\(854\) | −100.070 | −3.42431 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3234 | 0.592102 | ||||||||
\(857\) | −39.3176 | −1.34306 | −0.671531 | − | 0.740976i | \(-0.734363\pi\) | ||||
−0.671531 | + | 0.740976i | \(0.734363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.707056 | 0.0241244 | 0.0120622 | − | 0.999927i | \(-0.496160\pi\) | ||||
0.0120622 | + | 0.999927i | \(0.496160\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.8759 | −0.983516 | ||||||||
\(863\) | 0.909409 | 0.0309567 | 0.0154783 | − | 0.999880i | \(-0.495073\pi\) | ||||
0.0154783 | + | 0.999880i | \(0.495073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 51.9474 | 1.76525 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 65.1571 | 2.21158 | ||||||||
\(869\) | 17.1435 | 0.581554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2571 | 0.516968 | ||||||||
\(872\) | −31.1246 | −1.05401 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.94501 | −0.234918 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.6613 | −1.13666 | −0.568331 | − | 0.822800i | \(-0.692411\pi\) | ||||
−0.568331 | + | 0.822800i | \(0.692411\pi\) | |||||||
\(878\) | 28.1213 | 0.949050 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9283 | 0.671402 | 0.335701 | − | 0.941969i | \(-0.391027\pi\) | ||||
0.335701 | + | 0.941969i | \(0.391027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6081 | −0.525255 | −0.262627 | − | 0.964897i | \(-0.584589\pi\) | ||||
−0.262627 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(884\) | 8.84833 | 0.297601 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.8254 | −1.60673 | ||||||||
\(887\) | 46.8968 | 1.57464 | 0.787320 | − | 0.616544i | \(-0.211468\pi\) | ||||
0.787320 | + | 0.616544i | \(0.211468\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.4897 | −1.15675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −95.6991 | −3.20424 | ||||||||
\(893\) | −4.33588 | −0.145095 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 58.1505 | 1.94267 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 59.9347 | 2.00005 | ||||||||
\(899\) | 25.5220 | 0.851208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6811 | −0.589044 | ||||||||
\(902\) | −8.47143 | −0.282068 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.9682 | 1.09651 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.43447 | −0.0476308 | −0.0238154 | − | 0.999716i | \(-0.507581\pi\) | ||||
−0.0238154 | + | 0.999716i | \(0.507581\pi\) | |||||||
\(908\) | 39.0619 | 1.29632 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.81129 | 0.0931422 | 0.0465711 | − | 0.998915i | \(-0.485171\pi\) | ||||
0.0465711 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.2363 | 0.835201 | ||||||||
\(914\) | 19.6323 | 0.649379 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −54.6614 | −1.80606 | ||||||||
\(917\) | 24.2492 | 0.800780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.992236 | 0.0327308 | 0.0163654 | − | 0.999866i | \(-0.494790\pi\) | ||||
0.0163654 | + | 0.999866i | \(0.494790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.1428 | −1.12443 | ||||||||
\(923\) | −17.7828 | −0.585329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.2477 | 1.68410 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.3516 | 0.668075 | ||||||||
\(929\) | −33.3227 | −1.09328 | −0.546642 | − | 0.837367i | \(-0.684094\pi\) | ||||
−0.546642 | + | 0.837367i | \(0.684094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00192 | 0.0656104 | ||||||||
\(932\) | 75.0355 | 2.45787 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −65.8175 | −2.15361 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.3675 | −0.436698 | −0.218349 | − | 0.975871i | \(-0.570067\pi\) | ||||
−0.218349 | + | 0.975871i | \(0.570067\pi\) | |||||||
\(938\) | −74.9439 | −2.44701 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.14982 | 0.0700820 | 0.0350410 | − | 0.999386i | \(-0.488844\pi\) | ||||
0.0350410 | + | 0.999386i | \(0.488844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.10671 | −0.198862 | ||||||||
\(944\) | −4.70236 | −0.153049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.6012 | −0.539750 | ||||||||
\(947\) | 34.9183 | 1.13469 | 0.567346 | − | 0.823479i | \(-0.307970\pi\) | ||||
0.567346 | + | 0.823479i | \(0.307970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.381966 | −0.0123991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.3808 | −0.563315 | ||||||||
\(953\) | −8.27883 | −0.268178 | −0.134089 | − | 0.990969i | \(-0.542811\pi\) | ||||
−0.134089 | + | 0.990969i | \(0.542811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.1072 | 0.714998 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −57.8633 | −1.86948 | ||||||||
\(959\) | −28.3462 | −0.915347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4732 | 0.337844 | ||||||||
\(962\) | −12.5908 | −0.405942 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 87.4048 | 2.81512 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.4871 | −0.948241 | −0.474121 | − | 0.880460i | \(-0.657234\pi\) | ||||
−0.474121 | + | 0.880460i | \(0.657234\pi\) | |||||||
\(968\) | −21.5438 | −0.692443 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.8666 | −0.701733 | −0.350867 | − | 0.936425i | \(-0.614113\pi\) | ||||
−0.350867 | + | 0.936425i | \(0.614113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.3868 | −1.74356 | ||||||||
\(974\) | 3.38260 | 0.108385 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.30517 | 0.201823 | ||||||||
\(977\) | 13.8482 | 0.443043 | 0.221521 | − | 0.975155i | \(-0.428898\pi\) | ||||
0.221521 | + | 0.975155i | \(0.428898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.53591 | −0.304769 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 46.3440 | 1.47890 | ||||||||
\(983\) | 2.93538 | 0.0936241 | 0.0468120 | − | 0.998904i | \(-0.485094\pi\) | ||||
0.0468120 | + | 0.998904i | \(0.485094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.0246 | −0.542175 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.29667 | 0.136695 | ||||||||
\(989\) | −11.9671 | −0.380531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.6137 | 1.00424 | 0.502122 | − | 0.864797i | \(-0.332553\pi\) | ||||
0.502122 | + | 0.864797i | \(0.332553\pi\) | |||||||
\(992\) | 33.0713 | 1.05001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 87.3502 | 2.77058 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0885 | 0.382845 | 0.191423 | − | 0.981508i | \(-0.438690\pi\) | ||||
0.191423 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(998\) | 1.44329 | 0.0456867 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.x.1.8 | 8 | ||
3.2 | odd | 2 | 625.2.a.f.1.1 | 8 | |||
5.4 | even | 2 | inner | 5625.2.a.x.1.1 | 8 | ||
12.11 | even | 2 | 10000.2.a.bj.1.5 | 8 | |||
15.2 | even | 4 | 625.2.b.c.624.1 | 8 | |||
15.8 | even | 4 | 625.2.b.c.624.8 | 8 | |||
15.14 | odd | 2 | 625.2.a.f.1.8 | 8 | |||
25.8 | odd | 20 | 225.2.m.a.64.2 | 8 | |||
25.22 | odd | 20 | 225.2.m.a.109.2 | 8 | |||
60.59 | even | 2 | 10000.2.a.bj.1.4 | 8 | |||
75.2 | even | 20 | 625.2.e.i.124.1 | 8 | |||
75.8 | even | 20 | 25.2.e.a.14.1 | yes | 8 | ||
75.11 | odd | 10 | 625.2.d.o.501.1 | 16 | |||
75.14 | odd | 10 | 625.2.d.o.501.4 | 16 | |||
75.17 | even | 20 | 125.2.e.b.74.2 | 8 | |||
75.23 | even | 20 | 625.2.e.a.124.2 | 8 | |||
75.29 | odd | 10 | 125.2.d.b.76.1 | 16 | |||
75.38 | even | 20 | 625.2.e.i.499.1 | 8 | |||
75.41 | odd | 10 | 625.2.d.o.126.1 | 16 | |||
75.44 | odd | 10 | 125.2.d.b.51.1 | 16 | |||
75.47 | even | 20 | 25.2.e.a.9.1 | ✓ | 8 | ||
75.53 | even | 20 | 125.2.e.b.49.2 | 8 | |||
75.56 | odd | 10 | 125.2.d.b.51.4 | 16 | |||
75.59 | odd | 10 | 625.2.d.o.126.4 | 16 | |||
75.62 | even | 20 | 625.2.e.a.499.2 | 8 | |||
75.71 | odd | 10 | 125.2.d.b.76.4 | 16 | |||
300.47 | odd | 20 | 400.2.y.c.209.1 | 8 | |||
300.83 | odd | 20 | 400.2.y.c.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.9.1 | ✓ | 8 | 75.47 | even | 20 | ||
25.2.e.a.14.1 | yes | 8 | 75.8 | even | 20 | ||
125.2.d.b.51.1 | 16 | 75.44 | odd | 10 | |||
125.2.d.b.51.4 | 16 | 75.56 | odd | 10 | |||
125.2.d.b.76.1 | 16 | 75.29 | odd | 10 | |||
125.2.d.b.76.4 | 16 | 75.71 | odd | 10 | |||
125.2.e.b.49.2 | 8 | 75.53 | even | 20 | |||
125.2.e.b.74.2 | 8 | 75.17 | even | 20 | |||
225.2.m.a.64.2 | 8 | 25.8 | odd | 20 | |||
225.2.m.a.109.2 | 8 | 25.22 | odd | 20 | |||
400.2.y.c.209.1 | 8 | 300.47 | odd | 20 | |||
400.2.y.c.289.1 | 8 | 300.83 | odd | 20 | |||
625.2.a.f.1.1 | 8 | 3.2 | odd | 2 | |||
625.2.a.f.1.8 | 8 | 15.14 | odd | 2 | |||
625.2.b.c.624.1 | 8 | 15.2 | even | 4 | |||
625.2.b.c.624.8 | 8 | 15.8 | even | 4 | |||
625.2.d.o.126.1 | 16 | 75.41 | odd | 10 | |||
625.2.d.o.126.4 | 16 | 75.59 | odd | 10 | |||
625.2.d.o.501.1 | 16 | 75.11 | odd | 10 | |||
625.2.d.o.501.4 | 16 | 75.14 | odd | 10 | |||
625.2.e.a.124.2 | 8 | 75.23 | even | 20 | |||
625.2.e.a.499.2 | 8 | 75.62 | even | 20 | |||
625.2.e.i.124.1 | 8 | 75.2 | even | 20 | |||
625.2.e.i.499.1 | 8 | 75.38 | even | 20 | |||
5625.2.a.x.1.1 | 8 | 5.4 | even | 2 | inner | ||
5625.2.a.x.1.8 | 8 | 1.1 | even | 1 | trivial | ||
10000.2.a.bj.1.4 | 8 | 60.59 | even | 2 | |||
10000.2.a.bj.1.5 | 8 | 12.11 | even | 2 |