Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} - 2 x^{16} + 212 x^{15} - 289 x^{14} - 2094 x^{13} + 3933 x^{12} + 11326 x^{11} - 23166 x^{10} - 36429 x^{9} + 72042 x^{8} + 69272 x^{7} - 119982 x^{6} + \cdots + 1136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-2.05229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | 3.05229 | 1.76224 | 0.881120 | − | 0.472893i | \(-0.156790\pi\) | ||||
0.881120 | + | 0.472893i | \(0.156790\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.77561 | −1.68850 | −0.844251 | − | 0.535947i | \(-0.819955\pi\) | ||||
−0.844251 | + | 0.535947i | \(0.819955\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23812 | −0.467966 | −0.233983 | − | 0.972241i | \(-0.575176\pi\) | ||||
−0.233983 | + | 0.972241i | \(0.575176\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.31647 | 2.10549 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.24004 | −1.88144 | −0.940722 | − | 0.339180i | \(-0.889850\pi\) | ||||
−0.940722 | + | 0.339180i | \(0.889850\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.40461 | 0.389568 | 0.194784 | − | 0.980846i | \(-0.437599\pi\) | ||||
0.194784 | + | 0.980846i | \(0.437599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.5242 | −2.97555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.85333 | −1.34285 | −0.671423 | − | 0.741074i | \(-0.734317\pi\) | ||||
−0.671423 | + | 0.741074i | \(0.734317\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.77911 | −0.824669 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.79049 | −0.998887 | −0.499443 | − | 0.866346i | \(-0.666462\pi\) | ||||
−0.499443 | + | 0.866346i | \(0.666462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.25521 | 1.85104 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.1228 | 1.94814 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.61882 | 0.671999 | 0.335999 | − | 0.941862i | \(-0.390926\pi\) | ||||
0.335999 | + | 0.941862i | \(0.390926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.20076 | 1.29329 | 0.646647 | − | 0.762789i | \(-0.276171\pi\) | ||||
0.646647 | + | 0.762789i | \(0.276171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19.0464 | −3.31555 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.67466 | 0.790163 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.25299 | 0.699187 | 0.349593 | − | 0.936902i | \(-0.386320\pi\) | ||||
0.349593 | + | 0.936902i | \(0.386320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.28726 | 0.686511 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.60416 | −0.250528 | −0.125264 | − | 0.992123i | \(-0.539978\pi\) | ||||
−0.125264 | + | 0.992123i | \(0.539978\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.57197 | 0.697218 | 0.348609 | − | 0.937268i | \(-0.386654\pi\) | ||||
0.348609 | + | 0.937268i | \(0.386654\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23.8485 | −3.55512 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4542 | 1.52491 | 0.762454 | − | 0.647042i | \(-0.223994\pi\) | ||||
0.762454 | + | 0.647042i | \(0.223994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.46705 | −0.781007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05229 | 0.427406 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.40906 | 0.468270 | 0.234135 | − | 0.972204i | \(-0.424774\pi\) | ||||
0.234135 | + | 0.972204i | \(0.424774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.5599 | 3.17682 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.8661 | −2.36642 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8165 | 1.38490 | 0.692452 | − | 0.721463i | \(-0.256530\pi\) | ||||
0.692452 | + | 0.721463i | \(0.256530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.82056 | −0.985298 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.30324 | −0.657786 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.16292 | −0.386412 | −0.193206 | − | 0.981158i | \(-0.561889\pi\) | ||||
−0.193206 | + | 0.981158i | \(0.561889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.6220 | −1.76028 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.51156 | 0.416745 | 0.208373 | − | 0.978049i | \(-0.433183\pi\) | ||||
0.208373 | + | 0.978049i | \(0.433183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.4110 | −1.80372 | −0.901860 | − | 0.432029i | \(-0.857798\pi\) | ||||
−0.901860 | + | 0.432029i | \(0.857798\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.2496 | 3.26198 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.72594 | 0.880452 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.98347 | 0.560684 | 0.280342 | − | 0.959900i | \(-0.409552\pi\) | ||||
0.280342 | + | 0.959900i | \(0.409552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.9483 | 1.32759 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.57429 | −0.172801 | −0.0864003 | − | 0.996261i | \(-0.527536\pi\) | ||||
−0.0864003 | + | 0.996261i | \(0.527536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.77561 | −0.409522 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.0457 | 1.18422 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4632 | −1.10910 | −0.554549 | − | 0.832151i | \(-0.687109\pi\) | ||||
−0.554549 | + | 0.832151i | \(0.687109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73907 | −0.182305 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.9788 | 2.27910 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.0999 | 2.26740 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.93468 | −0.196437 | −0.0982187 | − | 0.995165i | \(-0.531314\pi\) | ||||
−0.0982187 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39.4150 | −3.96136 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4503 | −1.33836 | −0.669179 | − | 0.743102i | \(-0.733354\pi\) | ||||
−0.669179 | + | 0.743102i | \(0.733354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.57036 | 0.450331 | 0.225166 | − | 0.974321i | \(-0.427708\pi\) | ||||
0.225166 | + | 0.974321i | \(0.427708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.2684 | 1.39246 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.8533 | 1.82262 | 0.911311 | − | 0.411719i | \(-0.135071\pi\) | ||||
0.911311 | + | 0.411719i | \(0.135071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2595 | 1.27003 | 0.635014 | − | 0.772501i | \(-0.280994\pi\) | ||||
0.635014 | + | 0.772501i | \(0.280994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9813 | 1.23213 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.54665 | 0.709929 | 0.354964 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354964 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0870 | 1.68662 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.87215 | 0.820230 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.23812 | −0.113499 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.9381 | 2.53983 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.89637 | −0.441490 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16.0660 | −1.43699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1187 | −1.25284 | −0.626418 | − | 0.779488i | \(-0.715480\pi\) | ||||
−0.626418 | + | 0.779488i | \(0.715480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.9550 | 1.22867 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4425 | 1.08711 | 0.543555 | − | 0.839374i | \(-0.317078\pi\) | ||||
0.543555 | + | 0.839374i | \(0.317078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.24714 | 0.628407 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −38.2197 | −3.28943 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.7615 | 1.51746 | 0.758732 | − | 0.651403i | \(-0.225819\pi\) | ||||
0.758732 | + | 0.651403i | \(0.225819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4733 | 1.48206 | 0.741031 | − | 0.671470i | \(-0.234337\pi\) | ||||
0.741031 | + | 0.671470i | \(0.234337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.9094 | 2.68725 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.76480 | −0.732949 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.6633 | −1.13467 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.6870 | −1.37632 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.2271 | −1.73900 | −0.869498 | − | 0.493937i | \(-0.835557\pi\) | ||||
−0.869498 | + | 0.493937i | \(0.835557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6764 | 1.76400 | 0.881999 | − | 0.471250i | \(-0.156197\pi\) | ||||
0.881999 | + | 0.471250i | \(0.156197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.31647 | 0.510656 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.1872 | −2.18373 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1659 | 1.60941 | 0.804706 | − | 0.593674i | \(-0.202323\pi\) | ||||
0.804706 | + | 0.593674i | \(0.202323\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4054 | 0.825204 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.93122 | 0.467446 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0314 | 0.864045 | 0.432022 | − | 0.901863i | \(-0.357800\pi\) | ||||
0.432022 | + | 0.901863i | \(0.357800\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 71.9117 | 5.59832 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5916 | 1.12914 | 0.564568 | − | 0.825387i | \(-0.309043\pi\) | ||||
0.564568 | + | 0.825387i | \(0.309043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0271 | −0.848237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.9724 | −2.82735 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8605 | 1.20585 | 0.602924 | − | 0.797798i | \(-0.294002\pi\) | ||||
0.602924 | + | 0.797798i | \(0.294002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4591 | −0.866225 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.05229 | −0.229424 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.6715 | 1.02186 | 0.510928 | − | 0.859623i | \(-0.329302\pi\) | ||||
0.510928 | + | 0.859623i | \(0.329302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.82274 | 0.730119 | 0.365059 | − | 0.930984i | \(-0.381049\pi\) | ||||
0.365059 | + | 0.930984i | \(0.381049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.0149 | 2.44053 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.0576 | −1.18058 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.24004 | −0.456317 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5333 | −0.911662 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0627 | −1.66876 | −0.834379 | − | 0.551192i | \(-0.814173\pi\) | ||||
−0.834379 | + | 0.551192i | \(0.814173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8172 | −0.850624 | −0.425312 | − | 0.905047i | \(-0.639836\pi\) | ||||
−0.425312 | + | 0.905047i | \(0.639836\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.1870 | −1.15918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.34408 | −0.665738 | −0.332869 | − | 0.942973i | \(-0.608017\pi\) | ||||
−0.332869 | + | 0.942973i | \(0.608017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.08700 | −0.502384 | −0.251192 | − | 0.967937i | \(-0.580823\pi\) | ||||
−0.251192 | + | 0.967937i | \(0.580823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.65414 | −0.680950 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.48055 | −0.314473 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.05669 | 0.423017 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30.2590 | −2.10314 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36.5250 | 2.52649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3465 | 1.60724 | 0.803619 | − | 0.595144i | \(-0.202905\pi\) | ||||
0.803619 | + | 0.595144i | \(0.202905\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.7183 | 0.734405 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.2619 | −1.17725 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.91542 | −0.605218 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −47.0388 | −3.17859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40461 | 0.0944840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3835 | 1.29802 | 0.649008 | − | 0.760782i | \(-0.275184\pi\) | ||||
0.649008 | + | 0.760782i | \(0.275184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 58.4602 | 3.89735 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.9845 | 1.06093 | 0.530464 | − | 0.847708i | \(-0.322018\pi\) | ||||
0.530464 | + | 0.847708i | \(0.322018\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7512 | 0.974788 | 0.487394 | − | 0.873182i | \(-0.337948\pi\) | ||||
0.487394 | + | 0.873182i | \(0.337948\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.5818 | 1.55157 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.5607 | −1.80556 | −0.902782 | − | 0.430099i | \(-0.858479\pi\) | ||||
−0.902782 | + | 0.430099i | \(0.858479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.4711 | −2.57481 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.2110 | 0.988060 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.765675 | −0.0495274 | −0.0247637 | − | 0.999693i | \(-0.507883\pi\) | ||||
−0.0247637 | + | 0.999693i | \(0.507883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.89629 | −0.315398 | −0.157699 | − | 0.987487i | \(-0.550408\pi\) | ||||
−0.157699 | + | 0.987487i | \(0.550408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.10135 | 0.391402 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.6414 | 1.31873 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.22162 | −0.523129 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.80518 | −0.304516 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.0888 | −1.64671 | −0.823354 | − | 0.567529i | \(-0.807900\pi\) | ||||
−0.823354 | + | 0.567529i | \(0.807900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.8929 | 1.87935 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.5242 | −0.721676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.2271 | −0.762703 | −0.381351 | − | 0.924430i | \(-0.624541\pi\) | ||||
−0.381351 | + | 0.924430i | \(0.624541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.26572 | −0.327196 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.8582 | 1.41489 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.91567 | 0.611426 | 0.305713 | − | 0.952124i | \(-0.401105\pi\) | ||||
0.305713 | + | 0.952124i | \(0.401105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.8713 | −0.790675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.9368 | −1.95450 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.1519 | −0.740913 | −0.370456 | − | 0.928850i | \(-0.620799\pi\) | ||||
−0.370456 | + | 0.928850i | \(0.620799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35358 | 0.0822241 | 0.0411121 | − | 0.999155i | \(-0.486910\pi\) | ||||
0.0411121 | + | 0.999155i | \(0.486910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.30816 | −0.321264 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −57.7529 | −3.48263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.757934 | 0.0455399 | 0.0227699 | − | 0.999741i | \(-0.492751\pi\) | ||||
0.0227699 | + | 0.999741i | \(0.492751\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 45.4834 | 2.72302 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.06201 | 0.480939 | 0.240470 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240470 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.20592 | 0.368903 | 0.184452 | − | 0.982842i | \(-0.440949\pi\) | ||||
0.184452 | + | 0.982842i | \(0.440949\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 67.4552 | 3.99570 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.98615 | 0.117239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.90522 | −0.346170 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1148 | −0.999857 | −0.499928 | − | 0.866067i | \(-0.666640\pi\) | ||||
−0.499928 | + | 0.866067i | \(0.666640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.77561 | 0.219824 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −63.1667 | −3.66531 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.72876 | −0.389134 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.66065 | −0.326275 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −41.0543 | −2.35851 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.8387 | −2.33842 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.64310 | 0.207923 | 0.103961 | − | 0.994581i | \(-0.466848\pi\) | ||||
0.103961 | + | 0.994581i | \(0.466848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.9501 | 0.793591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.19420 | −0.0677171 | −0.0338586 | − | 0.999427i | \(-0.510780\pi\) | ||||
−0.0338586 | + | 0.999427i | \(0.510780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.6743 | −1.84686 | −0.923431 | − | 0.383764i | \(-0.874628\pi\) | ||||
−0.923431 | + | 0.383764i | \(0.874628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.5274 | 1.66368 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.97251 | 0.391615 | 0.195808 | − | 0.980642i | \(-0.437267\pi\) | ||||
0.195808 | + | 0.980642i | \(0.437267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5816 | −1.26433 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 57.5459 | 3.21190 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.85333 | −0.325688 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.9999 | 0.721106 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 40.4718 | 2.23809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9436 | −0.713606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0038 | −0.824686 | −0.412343 | − | 0.911029i | \(-0.635289\pi\) | ||||
−0.412343 | + | 0.911029i | \(0.635289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.8638 | 1.47213 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.9419 | 0.652458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.9217 | −1.41204 | −0.706021 | − | 0.708190i | \(-0.749512\pi\) | ||||
−0.706021 | + | 0.708190i | \(0.749512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0345 | 1.25106 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.9330 | −2.43326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4357 | 0.833452 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 55.2068 | 2.97223 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3870 | 0.826020 | 0.413010 | − | 0.910727i | \(-0.364478\pi\) | ||||
0.413010 | + | 0.910727i | \(0.364478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5559 | 1.31444 | 0.657222 | − | 0.753697i | \(-0.271731\pi\) | ||||
0.657222 | + | 0.753697i | \(0.271731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.2186 | 0.758930 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9374 | −0.582139 | −0.291070 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291070 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2583 | −0.703676 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.77911 | −0.200012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.8515 | −1.20606 | −0.603028 | − | 0.797720i | \(-0.706039\pi\) | ||||
−0.603028 | + | 0.797720i | \(0.706039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2615 | 0.803235 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 85.2752 | 4.47579 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.1858 | 3.04558 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00596 | 0.209109 | 0.104555 | − | 0.994519i | \(-0.466658\pi\) | ||||
0.104555 | + | 0.994519i | \(0.466658\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1326 | −0.527484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.22083 | −0.219135 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.89796 | 0.150051 | 0.0750254 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750254 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −49.0381 | −2.53231 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.08302 | 0.261789 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.02615 | 0.258176 | 0.129088 | − | 0.991633i | \(-0.458795\pi\) | ||||
0.129088 | + | 0.991633i | \(0.458795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.0945 | −2.20780 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.7587 | −0.651941 | −0.325971 | − | 0.945380i | \(-0.605691\pi\) | ||||
−0.325971 | + | 0.945380i | \(0.605691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.1701 | −1.48665 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.8787 | 1.46798 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.18517 | 0.0600907 | 0.0300453 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300453 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.79049 | −0.242266 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.9782 | 1.91575 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.8156 | −0.946717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3590 | −0.670471 | −0.335235 | − | 0.942134i | \(-0.608816\pi\) | ||||
−0.335235 | + | 0.942134i | \(0.608816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.1204 | 1.10740 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.2766 | −1.31219 | −0.656094 | − | 0.754679i | \(-0.727793\pi\) | ||||
−0.656094 | + | 0.754679i | \(0.727793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.1142 | 0.503826 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −45.1122 | −2.24164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.5388 | −1.31548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.8658 | 1.52622 | 0.763109 | − | 0.646270i | \(-0.223672\pi\) | ||||
0.763109 | + | 0.646270i | \(0.223672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.2131 | 2.67414 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.23812 | 0.0609240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.94390 | 0.291774 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 53.3334 | 2.61175 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.5466 | 1.39459 | 0.697295 | − | 0.716784i | \(-0.254387\pi\) | ||||
0.697295 | + | 0.716784i | \(0.254387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9895 | −0.681806 | −0.340903 | − | 0.940099i | \(-0.610733\pi\) | ||||
−0.340903 | + | 0.940099i | \(0.610733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.0339 | 3.21068 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.25521 | 0.448944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3921 | −0.648089 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.7527 | −1.29163 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.67821 | −0.225341 | −0.112671 | − | 0.993632i | \(-0.535941\pi\) | ||||
−0.112671 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3370 | 1.07345 | 0.536723 | − | 0.843758i | \(-0.319662\pi\) | ||||
0.536723 | + | 0.843758i | \(0.319662\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.7042 | −1.99956 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.0403 | 1.34135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2740 | −0.538079 | −0.269039 | − | 0.963129i | \(-0.586706\pi\) | ||||
−0.269039 | + | 0.963129i | \(0.586706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.5324 | −1.64440 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8230 | 0.799283 | 0.399642 | − | 0.916671i | \(-0.369135\pi\) | ||||
0.399642 | + | 0.916671i | \(0.369135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.5050 | 1.87272 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −64.7914 | −3.06453 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.86623 | 0.371230 | 0.185615 | − | 0.982623i | \(-0.440572\pi\) | ||||
0.185615 | + | 0.982623i | \(0.440572\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0100 | 0.471354 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 66.1626 | 3.10859 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.56606 | 0.307822 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.6990 | −1.95060 | −0.975300 | − | 0.220886i | \(-0.929105\pi\) | ||||
−0.975300 | + | 0.220886i | \(0.929105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.1228 | 0.472492 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0371 | 0.467472 | 0.233736 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233736 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.58615 | −0.166662 | −0.0833312 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833312 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −82.9833 | −3.84826 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.9734 | 0.739163 | 0.369581 | − | 0.929198i | \(-0.379501\pi\) | ||||
0.369581 | + | 0.929198i | \(0.379501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.91608 | 0.180828 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 61.5520 | 2.83617 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.5293 | −1.31178 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54.1738 | −2.48566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.5332 | 0.985937 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.8787 | −1.04536 | −0.522678 | − | 0.852530i | \(-0.675067\pi\) | ||||
−0.522678 | + | 0.852530i | \(0.675067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.97377 | 0.272381 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.1038 | 0.823751 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.30461 | 0.331685 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.9081 | 1.35527 | 0.677633 | − | 0.735400i | \(-0.263006\pi\) | ||||
0.677633 | + | 0.735400i | \(0.263006\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.6710 | 1.52265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4620 | 1.32960 | 0.664800 | − | 0.747022i | \(-0.268517\pi\) | ||||
0.664800 | + | 0.747022i | \(0.268517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.61882 | 0.162984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 148.816 | 6.68876 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.34774 | −0.195023 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.9948 | 1.79041 | 0.895207 | − | 0.445650i | \(-0.147028\pi\) | ||||
0.895207 | + | 0.445650i | \(0.147028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.5379 | 1.98981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.2775 | 1.39460 | 0.697298 | − | 0.716782i | \(-0.254386\pi\) | ||||
0.697298 | + | 0.716782i | \(0.254386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.7831 | 2.25982 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.6578 | −1.49480 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.5604 | 1.08862 | 0.544311 | − | 0.838884i | \(-0.316791\pi\) | ||||
0.544311 | + | 0.838884i | \(0.316791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.0807 | 0.844080 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.2521 | −2.61605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.2559 | −0.760385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −65.2349 | −2.86903 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.4107 | 2.12499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.1909 | −0.884581 | −0.442291 | − | 0.896872i | \(-0.645834\pi\) | ||||
−0.442291 | + | 0.896872i | \(0.645834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.4985 | 0.808882 | 0.404441 | − | 0.914564i | \(-0.367466\pi\) | ||||
0.404441 | + | 0.914564i | \(0.367466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.9764 | −1.52650 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.20076 | 0.313670 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0511709 | −0.00222482 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.31647 | −0.274111 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.25322 | −0.0975976 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −71.1828 | −3.07750 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.7294 | 1.80076 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.1146 | 1.46942 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3867 | 0.489554 | 0.244777 | − | 0.969579i | \(-0.421285\pi\) | ||||
0.244777 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.9818 | 1.28664 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.0626 | −2.14445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.22381 | −0.394382 | −0.197191 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197191 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 68.3218 | 2.91590 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.1822 | −0.902391 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.17015 | −0.262381 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −49.0125 | −2.08046 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.696560 | −0.0295142 | −0.0147571 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147571 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.42181 | 0.271614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.0464 | −0.804140 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.27115 | 0.264297 | 0.132149 | − | 0.991230i | \(-0.457812\pi\) | ||||
0.132149 | + | 0.991230i | \(0.457812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.4932 | −1.19872 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.7935 | −0.621269 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.8454 | 0.664275 | 0.332138 | − | 0.943231i | \(-0.392230\pi\) | ||||
0.332138 | + | 0.943231i | \(0.392230\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0789 | −1.38431 | −0.692154 | − | 0.721750i | \(-0.743338\pi\) | ||||
−0.692154 | + | 0.721750i | \(0.743338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −70.3940 | −2.94075 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44.3370 | −1.84898 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6859 | 0.444860 | 0.222430 | − | 0.974949i | \(-0.428601\pi\) | ||||
0.222430 | + | 0.974949i | \(0.428601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.0696 | −1.49900 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.94916 | 0.0808649 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.2727 | −0.881023 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.4977 | −1.38496 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.22005 | −0.380552 | −0.190276 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190276 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.1484 | −1.73670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.5208 | −1.17319 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.7429 | −1.18033 | −0.590165 | − | 0.807283i | \(-0.700937\pi\) | ||||
−0.590165 | + | 0.807283i | \(0.700937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.67466 | 0.191643 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.6316 | −0.885321 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.8242 | −1.70889 | −0.854446 | − | 0.519540i | \(-0.826103\pi\) | ||||
−0.854446 | + | 0.519540i | \(0.826103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2501 | 1.23393 | 0.616963 | − | 0.786992i | \(-0.288363\pi\) | ||||
0.616963 | + | 0.786992i | \(0.288363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.9785 | −0.813586 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −105.483 | −4.28851 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.32219 | 0.134844 | 0.0674218 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674218 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6759 | −0.554177 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6841 | 0.594055 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5542 | 0.507061 | 0.253531 | − | 0.967327i | \(-0.418408\pi\) | ||||
0.253531 | + | 0.967327i | \(0.418408\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.4868 | 0.745458 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0224 | −0.524261 | −0.262131 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262131 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.48932 | −0.341215 | −0.170607 | − | 0.985339i | \(-0.554573\pi\) | ||||
−0.170607 | + | 0.985339i | \(0.554573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.4933 | −1.94597 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9547 | 0.519021 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3828 | 0.575314 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 111.485 | 4.45228 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.25299 | 0.169578 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7118 | −0.705096 | −0.352548 | − | 0.935794i | \(-0.614685\pi\) | ||||
−0.352548 | + | 0.935794i | \(0.614685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 71.2602 | 2.83234 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 53.3068 | 2.11542 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.67905 | −0.304255 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1806 | 0.877453 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.3703 | 0.528096 | 0.264048 | − | 0.964510i | \(-0.414942\pi\) | ||||
0.264048 | + | 0.964510i | \(0.414942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2822 | 0.563237 | 0.281618 | − | 0.959526i | \(-0.409129\pi\) | ||||
0.281618 | + | 0.959526i | \(0.409129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −52.6884 | −2.07461 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.4578 | 0.882908 | 0.441454 | − | 0.897284i | \(-0.354463\pi\) | ||||
0.441454 | + | 0.897284i | \(0.354463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.24004 | 0.244943 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.2124 | −1.06654 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.6424 | −0.416471 | −0.208236 | − | 0.978079i | \(-0.566772\pi\) | ||||
−0.208236 | + | 0.978079i | \(0.566772\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.9781 | −1.83559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −97.3429 | −3.79771 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.8459 | −1.70799 | −0.853996 | − | 0.520279i | \(-0.825828\pi\) | ||||
−0.853996 | + | 0.520279i | \(0.825828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.7057 | −0.844255 | −0.422128 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422128 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.28726 | 0.166503 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.3624 | −1.06107 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3360 | −0.671251 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 59.1640 | 2.28741 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −67.4951 | −2.60562 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.1139 | 1.19935 | 0.599676 | − | 0.800243i | \(-0.295296\pi\) | ||||
0.599676 | + | 0.800243i | \(0.295296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 93.6887 | 3.60608 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5726 | 0.521638 | 0.260819 | − | 0.965388i | \(-0.416007\pi\) | ||||
0.260819 | + | 0.965388i | \(0.416007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.39538 | 0.0919261 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.7892 | 1.86961 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.5991 | 0.749939 | 0.374970 | − | 0.927037i | \(-0.377653\pi\) | ||||
0.374970 | + | 0.927037i | \(0.377653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −67.0603 | −2.56224 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.0250 | 1.71781 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.78838 | 0.182423 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3409 | −1.04010 | −0.520049 | − | 0.854137i | \(-0.674086\pi\) | ||||
−0.520049 | + | 0.854137i | \(0.674086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 48.8006 | 1.85378 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −65.9722 | −2.50247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.60416 | −0.0607620 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −84.1233 | −3.18184 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.1033 | −1.70353 | −0.851764 | − | 0.523926i | \(-0.824467\pi\) | ||||
−0.851764 | + | 0.523926i | \(0.824467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8941 | −0.938900 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −120.477 | −4.53744 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.6531 | 0.626306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7392 | 0.703764 | 0.351882 | − | 0.936044i | \(-0.385542\pi\) | ||||
0.351882 | + | 0.936044i | \(0.385542\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.4779 | 1.18051 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.4952 | −1.29186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.0924 | 1.23759 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.33706 | −0.0872791 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.6072 | 0.917694 | 0.458847 | − | 0.888515i | \(-0.348263\pi\) | ||||
0.458847 | + | 0.888515i | \(0.348263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65867 | −0.210740 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.9449 | −0.555807 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.4930 | 1.24390 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.73767 | −0.324062 | −0.162031 | − | 0.986786i | \(-0.551805\pi\) | ||||
−0.162031 | + | 0.986786i | \(0.551805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2219 | −0.637850 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.57197 | 0.169100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.2644 | 1.89349 | 0.946746 | − | 0.321980i | \(-0.104348\pi\) | ||||
0.946746 | + | 0.321980i | \(0.104348\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 63.0036 | 2.32392 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.7367 | 0.727012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2275 | 0.413012 | 0.206506 | − | 0.978445i | \(-0.433791\pi\) | ||||
0.206506 | + | 0.978445i | \(0.433791\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.0948 | −0.921879 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.2024 | 1.10802 | 0.554009 | − | 0.832511i | \(-0.313097\pi\) | ||||
0.554009 | + | 0.832511i | \(0.313097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 80.1453 | 2.93630 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.94394 | −0.363830 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3428 | −0.852926 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.36633 | 0.305292 | 0.152646 | − | 0.988281i | \(-0.451221\pi\) | ||||
0.152646 | + | 0.988281i | \(0.451221\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −79.6304 | −2.90189 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −81.8415 | −2.97852 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9573 | 0.398249 | 0.199125 | − | 0.979974i | \(-0.436190\pi\) | ||||
0.199125 | + | 0.979974i | \(0.436190\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 91.2417 | 3.31186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.9348 | −0.396385 | −0.198192 | − | 0.980163i | \(-0.563507\pi\) | ||||
−0.198192 | + | 0.980163i | \(0.563507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4169 | −0.594331 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.8485 | −0.862244 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.40461 | −0.0507174 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.86900 | −0.0673979 | −0.0336989 | − | 0.999432i | \(-0.510729\pi\) | ||||
−0.0336989 | + | 0.999432i | \(0.510729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.3205 | −1.34407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.9374 | −0.465324 | −0.232662 | − | 0.972558i | \(-0.574744\pi\) | ||||
−0.232662 | + | 0.972558i | \(0.574744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 66.6445 | 2.39394 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0725 | −0.576598 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.38969 | 0.336421 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.9123 | −0.784083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.6327 | 1.30914 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −76.1384 | −2.71750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.7898 | 1.56094 | 0.780469 | − | 0.625195i | \(-0.214980\pi\) | ||||
0.780469 | + | 0.625195i | \(0.214980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.2655 | 1.07748 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.34367 | −0.332223 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1929 | 0.539514 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −39.2868 | −1.39336 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.281773 | −0.00998092 | −0.00499046 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499046 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4542 | 0.369845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66.0906 | −2.33519 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 96.1652 | 3.39359 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.3940 | −0.789283 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.0910 | −1.30567 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.884554 | 0.0310993 | 0.0155496 | − | 0.999879i | \(-0.495050\pi\) | ||||
0.0155496 | + | 0.999879i | \(0.495050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.5777 | 1.03862 | 0.519308 | − | 0.854587i | \(-0.326190\pi\) | ||||
0.519308 | + | 0.854587i | \(0.326190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.13152 | 0.144899 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.6502 | −1.45894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.7612 | −0.936257 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.9848 | −0.383840 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.3064 | −0.953002 | −0.476501 | − | 0.879174i | \(-0.658095\pi\) | ||||
−0.476501 | + | 0.879174i | \(0.658095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.1330 | −1.08523 | −0.542614 | − | 0.839982i | \(-0.682565\pi\) | ||||
−0.542614 | + | 0.839982i | \(0.682565\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −176.278 | −6.13723 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.37772 | 0.187002 | 0.0935008 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935008 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.5651 | 1.58254 | 0.791271 | − | 0.611466i | \(-0.209420\pi\) | ||||
0.791271 | + | 0.611466i | \(0.209420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.31343 | 0.0802521 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.46705 | −0.189422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −55.0923 | −1.90655 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 72.8919 | 2.51951 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.6725 | −0.610123 | −0.305062 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305062 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9041 | −0.548417 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.6076 | 0.847530 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.6339 | 1.43225 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.5908 | −1.18855 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.9422 | 0.650096 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.3739 | −0.698409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2776 | 0.625814 | 0.312907 | − | 0.949784i | \(-0.398697\pi\) | ||||
0.312907 | + | 0.949784i | \(0.398697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 139.593 | 4.77398 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.2976 | −0.966627 | −0.483313 | − | 0.875447i | \(-0.660567\pi\) | ||||
−0.483313 | + | 0.875447i | \(0.660567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.97217 | −0.306126 | −0.153063 | − | 0.988216i | \(-0.548914\pi\) | ||||
−0.153063 | + | 0.988216i | \(0.548914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.06230 | 0.206603 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.79476 | 0.197256 | 0.0986280 | − | 0.995124i | \(-0.468555\pi\) | ||||
0.0986280 | + | 0.995124i | \(0.468555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −59.8829 | −2.03608 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.05229 | 0.103661 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.0971 | −1.05490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.44265 | −0.150534 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.2204 | −0.413597 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.8917 | 0.672461 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.2033 | 1.79655 | 0.898274 | − | 0.439437i | \(-0.144822\pi\) | ||||
0.898274 | + | 0.439437i | \(0.144822\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.2393 | −1.76199 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.5949 | 1.67090 | 0.835448 | − | 0.549570i | \(-0.185208\pi\) | ||||
0.835448 | + | 0.549570i | \(0.185208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.78067 | 0.127230 | 0.0636149 | − | 0.997975i | \(-0.479737\pi\) | ||||
0.0636149 | + | 0.997975i | \(0.479737\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.5242 | 0.387383 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.03510 | −0.0347551 | −0.0173776 | − | 0.999849i | \(-0.505532\pi\) | ||||
−0.0173776 | + | 0.999849i | \(0.505532\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.4807 | 0.586285 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −74.5581 | −2.49779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.1921 | −2.04772 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.6183 | −1.72541 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.5381 | −0.685747 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.0583 | 0.869093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.40906 | 0.113572 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.2780 | −0.574974 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.0868 | −1.23281 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.34934 | −0.0448040 | −0.0224020 | − | 0.999749i | \(-0.507131\pi\) | ||||
−0.0224020 | + | 0.999749i | \(0.507131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −84.9585 | −2.81790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.1573 | 1.49613 | 0.748064 | − | 0.663626i | \(-0.230984\pi\) | ||||
0.748064 | + | 0.663626i | \(0.230984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.82363 | 0.325115 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −124.651 | −4.12085 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.4054 | −0.508731 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8588 | −0.556119 | −0.278060 | − | 0.960564i | \(-0.589691\pi\) | ||||
−0.278060 | + | 0.960564i | \(0.589691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.1198 | 0.366409 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.93236 | 0.162350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.3623 | 1.29422 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.8685 | 0.948167 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.9557 | −0.753152 | −0.376576 | − | 0.926386i | \(-0.622899\pi\) | ||||
−0.376576 | + | 0.926386i | \(0.622899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.0005 | 1.04877 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.64506 | −0.119334 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.5599 | 0.770493 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3147 | −1.31703 | −0.658513 | − | 0.752570i | \(-0.728814\pi\) | ||||
−0.658513 | + | 0.752570i | \(0.728814\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −99.7315 | −3.25461 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.2320 | −1.31153 | −0.655763 | − | 0.754966i | \(-0.727653\pi\) | ||||
−0.655763 | + | 0.754966i | \(0.727653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.68473 | 0.250249 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 47.3207 | 1.53934 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.0097 | 1.59260 | 0.796300 | − | 0.604902i | \(-0.206788\pi\) | ||||
0.796300 | + | 0.604902i | \(0.206788\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.6464 | −0.702671 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2821 | 0.690120 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.1255 | 0.587142 | 0.293571 | − | 0.955937i | \(-0.405156\pi\) | ||||
0.293571 | + | 0.955937i | \(0.405156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 87.0756 | 2.81770 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −68.9256 | −2.22805 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.9909 | −0.710122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.8509 | 0.672611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 119.087 | 3.83751 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.6173 | 1.43628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7068 | 1.75925 | 0.879625 | − | 0.475667i | \(-0.157793\pi\) | ||||
0.879625 | + | 0.475667i | \(0.157793\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.8661 | −0.573940 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.9133 | −1.15251 | −0.576256 | − | 0.817269i | \(-0.695487\pi\) | ||||
−0.576256 | + | 0.817269i | \(0.695487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.6340 | −0.693555 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.6795 | 1.27076 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7512 | 0.407948 | 0.203974 | − | 0.978976i | \(-0.434614\pi\) | ||||
0.203974 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65.2909 | 2.08671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 83.7531 | 2.67403 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.4439 | −1.03480 | −0.517400 | − | 0.855744i | \(-0.673100\pi\) | ||||
−0.517400 | + | 0.855744i | \(0.673100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.2796 | 1.12410 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.5077 | −1.25754 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.9020 | −0.696442 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.35920 | −0.138474 | −0.0692372 | − | 0.997600i | \(-0.522057\pi\) | ||||
−0.0692372 | + | 0.997600i | \(0.522057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −45.7961 | −1.45329 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.7577 | 0.848277 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.8139 | −0.817533 | −0.408767 | − | 0.912639i | \(-0.634041\pi\) | ||||
−0.408767 | + | 0.912639i | \(0.634041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.0522 | 1.36211 |
(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 | 8024.2.a.v.1.16 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.v.1.16 | ✓ | 18 | 1.1 | even | 1 | trivial |