Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.70664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.70664 | −1.56268 | −0.781340 | − | 0.624106i | \(-0.785463\pi\) | ||||
−0.781340 | + | 0.624106i | \(0.785463\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.469317 | −0.209885 | −0.104943 | − | 0.994478i | \(-0.533466\pi\) | ||||
−0.104943 | + | 0.994478i | \(0.533466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.32591 | 1.44197 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.72750 | 1.42540 | 0.712698 | − | 0.701471i | \(-0.247473\pi\) | ||||
0.712698 | + | 0.701471i | \(0.247473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70239 | −0.472157 | −0.236078 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236078 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27027 | 0.327983 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.62142 | 0.878323 | 0.439162 | − | 0.898408i | \(-0.355276\pi\) | ||||
0.439162 | + | 0.898408i | \(0.355276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.482699 | −0.110739 | −0.0553694 | − | 0.998466i | \(-0.517634\pi\) | ||||
−0.0553694 | + | 0.998466i | \(0.517634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0771055 | −0.0160776 | −0.00803881 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803881 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77974 | −0.955948 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.58875 | −0.690655 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.891222 | 0.165496 | 0.0827479 | − | 0.996571i | \(-0.473630\pi\) | ||||
0.0827479 | + | 0.996571i | \(0.473630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.17820 | −1.64845 | −0.824227 | − | 0.566259i | \(-0.808390\pi\) | ||||
−0.824227 | + | 0.566259i | \(0.808390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.7957 | −2.22744 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.10312 | 0.345750 | 0.172875 | − | 0.984944i | \(-0.444694\pi\) | ||||
0.172875 | + | 0.984944i | \(0.444694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.60775 | 0.737830 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.61340 | 1.00853 | 0.504267 | − | 0.863548i | \(-0.331763\pi\) | ||||
0.504267 | + | 0.863548i | \(0.331763\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.03022 | −0.302648 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.76867 | −0.695582 | −0.347791 | − | 0.937572i | \(-0.613068\pi\) | ||||
−0.347791 | + | 0.937572i | \(0.613068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.80188 | −1.37254 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1209 | −1.66493 | −0.832466 | − | 0.554076i | \(-0.813072\pi\) | ||||
−0.832466 | + | 0.554076i | \(0.813072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.21870 | −0.299169 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.30649 | 0.173049 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.46582 | −1.10216 | −0.551078 | − | 0.834454i | \(-0.685783\pi\) | ||||
−0.551078 | + | 0.834454i | \(0.685783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21796 | −0.155944 | −0.0779719 | − | 0.996956i | \(-0.524844\pi\) | ||||
−0.0779719 | + | 0.996956i | \(0.524844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.798959 | 0.0990987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96167 | −0.483995 | −0.241998 | − | 0.970277i | \(-0.577803\pi\) | ||||
−0.241998 | + | 0.970277i | \(0.577803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.208697 | 0.0251242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.12294 | 0.607981 | 0.303991 | − | 0.952675i | \(-0.401681\pi\) | ||||
0.303991 | + | 0.952675i | \(0.401681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6052 | 1.24124 | 0.620622 | − | 0.784110i | \(-0.286880\pi\) | ||||
0.620622 | + | 0.784110i | \(0.286880\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.9370 | 1.49384 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6429 | 1.64745 | 0.823725 | − | 0.566989i | \(-0.191892\pi\) | ||||
0.823725 | + | 0.566989i | \(0.191892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.26426 | −0.362695 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.02509 | −0.112519 | −0.0562594 | − | 0.998416i | \(-0.517917\pi\) | ||||
−0.0562594 | + | 0.998416i | \(0.517917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.69960 | −0.184347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41222 | −0.258617 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.74768 | 0.397253 | 0.198626 | − | 0.980075i | \(-0.436352\pi\) | ||||
0.198626 | + | 0.980075i | \(0.436352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.8421 | 2.57601 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.226539 | 0.0232424 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0675 | −1.12373 | −0.561867 | − | 0.827228i | \(-0.689917\pi\) | ||||
−0.561867 | + | 0.827228i | \(0.689917\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.4507 | 2.05538 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9512 | −1.08969 | −0.544844 | − | 0.838537i | \(-0.683411\pi\) | ||||
−0.544844 | + | 0.838537i | \(0.683411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2036 | 1.20246 | 0.601230 | − | 0.799076i | \(-0.294677\pi\) | ||||
0.601230 | + | 0.799076i | \(0.294677\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4055 | 1.10262 | 0.551308 | − | 0.834302i | \(-0.314129\pi\) | ||||
0.551308 | + | 0.834302i | \(0.314129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.49074 | 0.621700 | 0.310850 | − | 0.950459i | \(-0.399386\pi\) | ||||
0.310850 | + | 0.950459i | \(0.399386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.69238 | −0.540297 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5427 | 1.08584 | 0.542922 | − | 0.839783i | \(-0.317318\pi\) | ||||
0.542922 | + | 0.839783i | \(0.317318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0361870 | 0.00337445 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.36436 | −0.680835 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3493 | 1.03175 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.70664 | 0.244050 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.58980 | 0.410524 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91879 | −0.170265 | −0.0851326 | − | 0.996370i | \(-0.527131\pi\) | ||||
−0.0851326 | + | 0.996370i | \(0.527131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.9001 | −1.57602 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.65847 | −0.843864 | −0.421932 | − | 0.906627i | \(-0.638648\pi\) | ||||
−0.421932 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.68426 | 0.144958 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.8543 | −1.78171 | −0.890853 | − | 0.454291i | \(-0.849893\pi\) | ||||
−0.890853 | + | 0.454291i | \(0.849893\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00753 | −0.509552 | −0.254776 | − | 0.967000i | \(-0.582002\pi\) | ||||
−0.254776 | + | 0.967000i | \(0.582002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9071 | 1.08697 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.04803 | −0.673010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.418266 | −0.0347351 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.5867 | −1.52268 | −0.761342 | − | 0.648350i | \(-0.775459\pi\) | ||||
−0.761342 | + | 0.648350i | \(0.775459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.37742 | −0.193472 | −0.0967360 | − | 0.995310i | \(-0.530840\pi\) | ||||
−0.0967360 | + | 0.995310i | \(0.530840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.6659 | 1.26651 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.30749 | 0.345986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4328 | 0.912434 | 0.456217 | − | 0.889869i | \(-0.349204\pi\) | ||||
0.456217 | + | 0.889869i | \(0.349204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 32.8069 | 2.60176 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.28613 | 0.492368 | 0.246184 | − | 0.969223i | \(-0.420823\pi\) | ||||
0.246184 | + | 0.969223i | \(0.420823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00522 | 0.467506 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3925 | 0.881577 | 0.440788 | − | 0.897611i | \(-0.354699\pi\) | ||||
0.440788 | + | 0.897611i | \(0.354699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1019 | −0.777068 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.08811 | −0.159682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.5221 | 1.63629 | 0.818147 | − | 0.575009i | \(-0.195002\pi\) | ||||
0.818147 | + | 0.575009i | \(0.195002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.9139 | 1.72232 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.43044 | −0.480633 | −0.240317 | − | 0.970695i | \(-0.577251\pi\) | ||||
−0.240317 | + | 0.970695i | \(0.577251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3408 | −1.28893 | −0.644465 | − | 0.764634i | \(-0.722920\pi\) | ||||
−0.644465 | + | 0.764634i | \(0.722920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.29658 | 0.243690 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.987030 | −0.0725679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.1203 | 1.25196 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.106130 | −0.00767931 | −0.00383966 | − | 0.999993i | \(-0.501222\pi\) | ||||
−0.00383966 | + | 0.999993i | \(0.501222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.28602 | 0.164552 | 0.0822758 | − | 0.996610i | \(-0.473781\pi\) | ||||
0.0822758 | + | 0.996610i | \(0.473781\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.16250 | −0.154860 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.89180 | 0.134785 | 0.0673924 | − | 0.997727i | \(-0.478532\pi\) | ||||
0.0673924 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.291932 | 0.0206945 | 0.0103472 | − | 0.999946i | \(-0.496706\pi\) | ||||
0.0103472 | + | 0.999946i | \(0.496706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7228 | 0.756329 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.469317 | 0.0327786 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.333551 | −0.0231834 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.28196 | −0.157847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3493 | 1.60743 | 0.803717 | − | 0.595012i | \(-0.202853\pi\) | ||||
0.803717 | + | 0.595012i | \(0.202853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8660 | −0.950080 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.10378 | −0.211676 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.7044 | −1.93967 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.16505 | −0.414706 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1824 | 0.882757 | 0.441379 | − | 0.897321i | \(-0.354490\pi\) | ||||
0.441379 | + | 0.897321i | \(0.354490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.6767 | −1.37845 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7195 | −0.711479 | −0.355740 | − | 0.934585i | \(-0.615771\pi\) | ||||
−0.355740 | + | 0.934585i | \(0.615771\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8550 | 0.849482 | 0.424741 | − | 0.905315i | \(-0.360365\pi\) | ||||
0.424741 | + | 0.905315i | \(0.360365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1885 | −0.798492 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.23802 | 0.145992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −39.6330 | −2.57444 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.28190 | 0.276973 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.35442 | 0.0872456 | 0.0436228 | − | 0.999048i | \(-0.486110\pi\) | ||||
0.0436228 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6014 | 1.25743 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.821740 | 0.0522861 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.77456 | 0.175831 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0524 | −0.697620 | −0.348810 | − | 0.937193i | \(-0.613414\pi\) | ||||
−0.348810 | + | 0.937193i | \(0.613414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.364517 | −0.0229170 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.60019 | 0.288075 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7831 | −0.859766 | −0.429883 | − | 0.902884i | \(-0.641445\pi\) | ||||
−0.429883 | + | 0.902884i | \(0.641445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85534 | 0.238640 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.36247 | −0.330664 | −0.165332 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165332 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.68855 | 0.349445 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.1436 | −0.620779 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.47122 | −0.577471 | −0.288735 | − | 0.957409i | \(-0.593235\pi\) | ||||
−0.288735 | + | 0.957409i | \(0.593235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.27313 | 0.138083 | 0.0690413 | − | 0.997614i | \(-0.478006\pi\) | ||||
0.0690413 | + | 0.997614i | \(0.478006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.5962 | −1.36260 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7734 | −1.12798 | −0.563991 | − | 0.825781i | \(-0.690735\pi\) | ||||
−0.563991 | + | 0.825781i | \(0.690735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −39.7040 | −2.37702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.35062 | −0.319192 | −0.159596 | − | 0.987182i | \(-0.551019\pi\) | ||||
−0.159596 | + | 0.987182i | \(0.551019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6731 | −0.634452 | −0.317226 | − | 0.948350i | \(-0.602751\pi\) | ||||
−0.317226 | + | 0.948350i | \(0.602751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.613160 | −0.0363205 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.88533 | −0.228549 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.9557 | 1.75604 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.9925 | 0.700608 | 0.350304 | − | 0.936636i | \(-0.386078\pi\) | ||||
0.350304 | + | 0.936636i | \(0.386078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.97316 | 0.231326 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.9658 | −0.984457 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.131263 | 0.00759115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.6411 | 1.70283 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.571610 | 0.0327303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.58847 | −0.547243 | −0.273622 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273622 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.0309 | −1.87906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.06040 | 0.457063 | 0.228532 | − | 0.973536i | \(-0.426608\pi\) | ||||
0.228532 | + | 0.973536i | \(0.426608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.2940 | −0.864467 | −0.432233 | − | 0.901762i | \(-0.642274\pi\) | ||||
−0.432233 | + | 0.901762i | \(0.642274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.16644 | −0.290176 | −0.145088 | − | 0.989419i | \(-0.546347\pi\) | ||||
−0.145088 | + | 0.989419i | \(0.546347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.21325 | 0.235897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.8707 | −1.72303 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.74806 | −0.0972645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.13696 | 0.451357 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5681 | −0.971518 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.7547 | −0.646097 | −0.323049 | − | 0.946382i | \(-0.604708\pi\) | ||||
−0.323049 | + | 0.946382i | \(0.604708\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.09789 | 0.498561 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.85928 | 0.101583 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0144 | 0.708941 | 0.354471 | − | 0.935067i | \(-0.384661\pi\) | ||||
0.354471 | + | 0.935067i | \(0.384661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.2419 | −1.69683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −43.3900 | −2.34970 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0979451 | −0.00527319 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1209 | 0.865418 | 0.432709 | − | 0.901534i | \(-0.357558\pi\) | ||||
0.432709 | + | 0.901534i | \(0.357558\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.39124 | −0.502701 | −0.251351 | − | 0.967896i | \(-0.580875\pi\) | ||||
−0.251351 | + | 0.967896i | \(0.580875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.10943 | 0.326097 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.6538 | −1.36542 | −0.682708 | − | 0.730691i | \(-0.739198\pi\) | ||||
−0.682708 | + | 0.730691i | \(0.739198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.40429 | −0.127606 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6006 | −0.559476 | −0.279738 | − | 0.960076i | \(-0.590248\pi\) | ||||
−0.279738 | + | 0.960076i | \(0.590248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7670 | −0.987737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.7184 | −1.61230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.97720 | −0.260519 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0989 | 1.31015 | 0.655077 | − | 0.755562i | \(-0.272636\pi\) | ||||
0.655077 | + | 0.755562i | \(0.272636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.32591 | −0.225198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.1194 | −1.09352 | −0.546760 | − | 0.837290i | \(-0.684139\pi\) | ||||
−0.546760 | + | 0.837290i | \(0.684139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.4229 | −0.641518 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.51720 | −0.0781399 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.5309 | −1.20870 | −0.604352 | − | 0.796718i | \(-0.706568\pi\) | ||||
−0.604352 | + | 0.796718i | \(0.706568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.19348 | 0.266070 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.96252 | 0.151378 | 0.0756890 | − | 0.997131i | \(-0.475884\pi\) | ||||
0.0756890 | + | 0.997131i | \(0.475884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.6089 | 1.45427 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.62441 | −0.234467 | −0.117233 | − | 0.993104i | \(-0.537403\pi\) | ||||
−0.117233 | + | 0.993104i | \(0.537403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.279231 | −0.0141213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.1420 | 1.31869 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.87215 | −0.345775 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.06114 | 0.454766 | 0.227383 | − | 0.973805i | \(-0.426983\pi\) | ||||
0.227383 | + | 0.973805i | \(0.426983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.7406 | 0.985797 | 0.492898 | − | 0.870087i | \(-0.335937\pi\) | ||||
0.492898 | + | 0.870087i | \(0.335937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6248 | 0.778329 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.53197 | 0.0761244 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.94249 | 0.492831 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.6659 | −1.76356 | −0.881782 | − | 0.471658i | \(-0.843656\pi\) | ||||
−0.881782 | + | 0.471658i | \(0.843656\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.4452 | 2.78424 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.481095 | 0.0236160 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.2602 | 0.796267 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.8381 | −0.920303 | −0.460151 | − | 0.887840i | \(-0.652205\pi\) | ||||
−0.460151 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1778 | 0.496034 | 0.248017 | − | 0.968756i | \(-0.420221\pi\) | ||||
0.248017 | + | 0.968756i | \(0.420221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.6288 | −1.00301 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.3094 | −0.839631 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.7831 | 1.05170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1486 | 0.681515 | 0.340757 | − | 0.940151i | \(-0.389317\pi\) | ||||
0.340757 | + | 0.940151i | \(0.389317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0822900 | 0.00395461 | 0.00197730 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197730 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.13210 | 0.0542799 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0372188 | 0.00178042 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.2966 | −1.58916 | −0.794580 | − | 0.607159i | \(-0.792309\pi\) | ||||
−0.794580 | + | 0.607159i | \(0.792309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3965 | −0.684000 | −0.342000 | − | 0.939700i | \(-0.611104\pi\) | ||||
−0.342000 | + | 0.939700i | \(0.611104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.75885 | −0.0833775 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 50.3076 | 2.37947 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.30585 | −0.108820 | −0.0544100 | − | 0.998519i | \(-0.517328\pi\) | ||||
−0.0544100 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.72750 | −0.222609 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.43483 | 0.302335 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.7308 | −0.876188 | −0.438094 | − | 0.898929i | \(-0.644346\pi\) | ||||
−0.438094 | + | 0.898929i | \(0.644346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9964 | −0.606618 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.5879 | 1.00545 | 0.502725 | − | 0.864447i | \(-0.332331\pi\) | ||||
0.502725 | + | 0.864447i | \(0.332331\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5466 | 0.815458 | 0.407729 | − | 0.913103i | \(-0.366321\pi\) | ||||
0.407729 | + | 0.913103i | \(0.366321\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.6588 | −0.540665 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.70864 | −0.171615 | −0.0858076 | − | 0.996312i | \(-0.527347\pi\) | ||||
−0.0858076 | + | 0.996312i | \(0.527347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.9444 | −1.42584 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.2649 | 1.43756 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.30718 | 0.105861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −52.4338 | −2.40078 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.20086 | −0.100560 | −0.0502798 | − | 0.998735i | \(-0.516011\pi\) | ||||
−0.0502798 | + | 0.998735i | \(0.516011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.58032 | −0.163248 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.19417 | 0.235855 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.11732 | −0.231888 | −0.115944 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115944 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.0143 | −0.769413 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.26077 | −0.0568976 | −0.0284488 | − | 0.999595i | \(-0.509057\pi\) | ||||
−0.0284488 | + | 0.999595i | \(0.509057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22749 | 0.145359 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.59788 | −0.431393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.1914 | −1.12772 | −0.563862 | − | 0.825869i | \(-0.690685\pi\) | ||||
−0.563862 | + | 0.825869i | \(0.690685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.8354 | −1.37762 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.0850 | 1.29684 | 0.648418 | − | 0.761285i | \(-0.275431\pi\) | ||||
0.648418 | + | 0.761285i | \(0.275431\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.13960 | 0.228709 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.3422 | 1.21431 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5493 | 0.733535 | 0.366767 | − | 0.930313i | \(-0.380464\pi\) | ||||
0.366767 | + | 0.930313i | \(0.380464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.73229 | 0.0764823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.72738 | −0.252379 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.5439 | −0.991480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −58.2526 | −2.55700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.9342 | −1.92479 | −0.962396 | − | 0.271649i | \(-0.912431\pi\) | ||||
−0.962396 | + | 0.271649i | \(0.912431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.18798 | 0.0956736 | 0.0478368 | − | 0.998855i | \(-0.484767\pi\) | ||||
0.0478368 | + | 0.998855i | \(0.484767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.2381 | −1.44788 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9941 | −0.999742 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.6223 | −1.58927 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.70239 | 0.0737385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.35282 | −0.231423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4049 | 0.751076 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.5895 | −1.83107 | −0.915533 | − | 0.402243i | \(-0.868231\pi\) | ||||
−0.915533 | + | 0.402243i | \(0.868231\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.9353 | 2.01419 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.04622 | −0.130486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1538 | −1.07550 | −0.537749 | − | 0.843105i | \(-0.680725\pi\) | ||||
−0.537749 | + | 0.843105i | \(0.680725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.26878 | −0.224866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.430192 | −0.0183268 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.67153 | 0.113400 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.6947 | −1.72429 | −0.862145 | − | 0.506662i | \(-0.830879\pi\) | ||||
−0.862145 | + | 0.506662i | \(0.830879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2586 | −0.476186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46.3384 | −1.95641 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.8745 | −0.500452 | −0.250226 | − | 0.968187i | \(-0.580505\pi\) | ||||
−0.250226 | + | 0.968187i | \(0.580505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.41718 | −0.227902 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.3873 | −0.435458 | −0.217729 | − | 0.976009i | \(-0.569865\pi\) | ||||
−0.217729 | + | 0.976009i | \(0.569865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.4888 | 1.15037 | 0.575184 | − | 0.818024i | \(-0.304930\pi\) | ||||
0.575184 | + | 0.818024i | \(0.304930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.287256 | 0.0120003 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.368544 | 0.0153694 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.5606 | −1.31388 | −0.656942 | − | 0.753941i | \(-0.728151\pi\) | ||||
−0.656942 | + | 0.753941i | \(0.728151\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.18745 | −0.257142 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −57.3015 | −2.37319 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.45622 | 0.142897 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.0329 | −0.950670 | −0.475335 | − | 0.879805i | \(-0.657673\pi\) | ||||
−0.475335 | + | 0.879805i | \(0.657673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.43031 | 0.182548 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.12041 | −0.210626 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.97167 | 0.204162 | 0.102081 | − | 0.994776i | \(-0.467450\pi\) | ||||
0.102081 | + | 0.994776i | \(0.467450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.790154 | −0.0323389 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7974 | 1.62608 | 0.813038 | − | 0.582211i | \(-0.197812\pi\) | ||||
0.813038 | + | 0.582211i | \(0.197812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1297 | 1.51455 | 0.757276 | − | 0.653094i | \(-0.226530\pi\) | ||||
0.757276 | + | 0.653094i | \(0.226530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.1378 | −0.697906 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.32641 | −0.216549 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.52274 | 0.142984 | 0.0714918 | − | 0.997441i | \(-0.477224\pi\) | ||||
0.0714918 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.11811 | 0.328424 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7942 | −1.36493 | −0.682467 | − | 0.730916i | \(-0.739093\pi\) | ||||
−0.682467 | + | 0.730916i | \(0.739093\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.27027 | −0.0512224 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1546 | −0.569843 | −0.284922 | − | 0.958551i | \(-0.591968\pi\) | ||||
−0.284922 | + | 0.958551i | \(0.591968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0838 | 0.968011 | 0.484006 | − | 0.875065i | \(-0.339181\pi\) | ||||
0.484006 | + | 0.875065i | \(0.339181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.276712 | 0.0111041 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7446 | 0.869785 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.17645 | 0.246664 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.61627 | 0.303680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.8465 | 1.62607 | 0.813037 | − | 0.582213i | \(-0.197813\pi\) | ||||
0.813037 | + | 0.582213i | \(0.197813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −63.1983 | −2.51191 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.900522 | 0.0357361 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1614 | 0.876690 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.7190 | 1.25283 | 0.626413 | − | 0.779491i | \(-0.284522\pi\) | ||||
0.626413 | + | 0.779491i | \(0.284522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.8966 | −1.69168 | −0.845838 | − | 0.533440i | \(-0.820899\pi\) | ||||
−0.845838 | + | 0.533440i | \(0.820899\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.40083 | 0.330782 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.1500 | 1.61777 | 0.808886 | − | 0.587966i | \(-0.200071\pi\) | ||||
0.808886 | + | 0.587966i | \(0.200071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.0222 | −1.57101 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.7638 | 0.460351 | 0.230176 | − | 0.973149i | \(-0.426070\pi\) | ||||
0.230176 | + | 0.973149i | \(0.426070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.53289 | 0.177115 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 45.8770 | 1.78983 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1634 | −1.21396 | −0.606978 | − | 0.794719i | \(-0.707618\pi\) | ||||
−0.606978 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.04814 | −0.351932 | −0.175966 | − | 0.984396i | \(-0.556305\pi\) | ||||
−0.175966 | + | 0.984396i | \(0.556305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.6866 | 0.648053 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0687182 | −0.00266078 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.6800 | −1.37947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.75791 | −0.222281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4453 | −1.17358 | −0.586791 | − | 0.809739i | \(-0.699609\pi\) | ||||
−0.586791 | + | 0.809739i | \(0.699609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.1533 | 0.660231 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.7599 | 1.41280 | 0.706399 | − | 0.707814i | \(-0.250318\pi\) | ||||
0.706399 | + | 0.707814i | \(0.250318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.0139 | 1.11181 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.06099 | 0.0788615 | 0.0394308 | − | 0.999222i | \(-0.487446\pi\) | ||||
0.0394308 | + | 0.999222i | \(0.487446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.78731 | 0.373954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.7938 | −1.32747 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.6344 | 0.786109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.4256 | −0.662901 | −0.331451 | − | 0.943473i | \(-0.607538\pi\) | ||||
−0.331451 | + | 0.943473i | \(0.607538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.81944 | 0.106947 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.62142 | −0.137171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.9898 | 1.24779 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.8136 | −1.39043 | −0.695216 | − | 0.718801i | \(-0.744691\pi\) | ||||
−0.695216 | + | 0.718801i | \(0.744691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.01517 | −0.0382880 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.05752 | −0.228139 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.9160 | −0.522628 | −0.261314 | − | 0.965254i | \(-0.584156\pi\) | ||||
−0.261314 | + | 0.965254i | \(0.584156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 63.3436 | 2.37557 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.707690 | 0.0265032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.77708 | 0.141255 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.5896 | −0.432821 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9441 | 0.706497 | 0.353248 | − | 0.935530i | \(-0.385077\pi\) | ||||
0.353248 | + | 0.935530i | \(0.385077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.66592 | −0.136337 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.25981 | −0.158205 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0404 | −0.891608 | −0.445804 | − | 0.895131i | \(-0.647082\pi\) | ||||
−0.445804 | + | 0.895131i | \(0.647082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.2612 | −1.60227 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.9499 | 0.885819 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0115 | 0.960755 | 0.480378 | − | 0.877062i | \(-0.340500\pi\) | ||||
0.480378 | + | 0.877062i | \(0.340500\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7288 | −0.689884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.4689 | −1.19439 | −0.597193 | − | 0.802097i | \(-0.703718\pi\) | ||||
−0.597193 | + | 0.802097i | \(0.703718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.22416 | −0.0817064 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3797 | 1.22458 | 0.612291 | − | 0.790633i | \(-0.290248\pi\) | ||||
0.612291 | + | 0.790633i | \(0.290248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.72308 | 0.319589 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.43446 | −0.162249 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.44890 | 0.271814 | 0.135907 | − | 0.990722i | \(-0.456605\pi\) | ||||
0.135907 | + | 0.990722i | \(0.456605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.9148 | 1.09016 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.11577 | 0.0406069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.2573 | 0.845301 | 0.422650 | − | 0.906293i | \(-0.361100\pi\) | ||||
0.422650 | + | 0.906293i | \(0.361100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.986615 | 0.0358119 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0263 | 1.01595 | 0.507976 | − | 0.861371i | \(-0.330394\pi\) | ||||
0.507976 | + | 0.861371i | \(0.330394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.35229 | −0.265823 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4121 | 0.520390 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.2387 | −0.910131 | −0.455065 | − | 0.890458i | \(-0.650384\pi\) | ||||
−0.455065 | + | 0.890458i | \(0.650384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.3059 | 1.34354 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3719 | −0.444988 | −0.222494 | − | 0.974934i | \(-0.571420\pi\) | ||||
−0.222494 | + | 0.974934i | \(0.571420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.8694 | 1.57584 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.482699 | 0.0172945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.2187 | 0.866614 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.19837 | −0.114301 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.36560 | −0.191506 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7301 | 0.632012 | 0.316006 | − | 0.948757i | \(-0.397658\pi\) | ||||
0.316006 | + | 0.948757i | \(0.397658\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.5143 | 0.516722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.07344 | 0.0736299 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.3969 | −0.546070 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.8951 | 0.988095 | 0.494048 | − | 0.869435i | \(-0.335517\pi\) | ||||
0.494048 | + | 0.869435i | \(0.335517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.2694 | −0.610946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.2121 | 0.572826 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.1360 | 1.76926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.6352 | 0.902402 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.5032 | −1.35370 | −0.676850 | − | 0.736121i | \(-0.736655\pi\) | ||||
−0.676850 | + | 0.736121i | \(0.736655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3236 | −0.854118 | −0.427059 | − | 0.904224i | \(-0.640450\pi\) | ||||
−0.427059 | + | 0.904224i | \(0.640450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.15254 | −0.215779 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.95019 | −0.103341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.19228 | −0.111684 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.0376 | −1.53692 | −0.768462 | − | 0.639895i | \(-0.778978\pi\) | ||||
−0.768462 | + | 0.639895i | \(0.778978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5903 | 1.44975 | 0.724873 | − | 0.688883i | \(-0.241899\pi\) | ||||
0.724873 | + | 0.688883i | \(0.241899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 61.1599 | 2.12931 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2346 | 0.425437 | 0.212719 | − | 0.977113i | \(-0.431768\pi\) | ||||
0.212719 | + | 0.977113i | \(0.431768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.6302 | −1.16803 | −0.584013 | − | 0.811744i | \(-0.698518\pi\) | ||||
−0.584013 | + | 0.811744i | \(0.698518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.8128 | 1.76268 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.34669 | −0.185030 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.9383 | 1.13851 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.3839 | −0.427541 | −0.213771 | − | 0.976884i | \(-0.568574\pi\) | ||||
−0.213771 | + | 0.976884i | \(0.568574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2057 | −0.972611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.4822 | 0.498794 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.74099 | 0.163095 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.8883 | 0.991445 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.162162 | −0.00555884 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.8119 | −0.404432 | −0.202216 | − | 0.979341i | \(-0.564814\pi\) | ||||
−0.202216 | + | 0.979341i | \(0.564814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.979987 | 0.0335149 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.06114 | 0.0704072 | 0.0352036 | − | 0.999380i | \(-0.488792\pi\) | ||||
0.0352036 | + | 0.999380i | \(0.488792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.0418 | −1.33209 | −0.666045 | − | 0.745911i | \(-0.732014\pi\) | ||||
−0.666045 | + | 0.745911i | \(0.732014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.5583 | 0.938095 | 0.469048 | − | 0.883173i | \(-0.344597\pi\) | ||||
0.469048 | + | 0.883173i | \(0.344597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1007 | −0.343434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.5162 | 0.357148 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.2242 | 2.34827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.74429 | 0.228521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −47.8770 | −1.62039 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.7549 | −1.84894 | −0.924471 | − | 0.381253i | \(-0.875493\pi\) | ||||
−0.924471 | + | 0.381253i | \(0.875493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.4593 | −1.09483 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.4637 | −1.73386 | −0.866929 | − | 0.498432i | \(-0.833909\pi\) | ||||
−0.866929 | + | 0.498432i | \(0.833909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.5358 | −0.960305 | −0.480152 | − | 0.877185i | \(-0.659419\pi\) | ||||
−0.480152 | + | 0.877185i | \(0.659419\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.7539 | −0.361489 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.7123 | 0.729027 | 0.364514 | − | 0.931198i | \(-0.381235\pi\) | ||||
0.364514 | + | 0.931198i | \(0.381235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.4318 | −0.516984 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.30183 | 0.0770279 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.01792 | 0.100878 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.355283 | −0.0118625 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.17982 | −0.272812 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.8948 | −1.46235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.13833 | 0.270527 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.4824 | −1.37740 | −0.688700 | − | 0.725046i | \(-0.741818\pi\) | ||||
−0.688700 | + | 0.725046i | \(0.741818\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.3740 | −1.57130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7992 | 1.15295 | 0.576474 | − | 0.817115i | \(-0.304428\pi\) | ||||
0.576474 | + | 0.817115i | \(0.304428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.84614 | −0.160384 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.54714 | −0.0511469 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.9080 | 0.524755 | 0.262378 | − | 0.964965i | \(-0.415493\pi\) | ||||
0.262378 | + | 0.964965i | \(0.415493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.9526 | 0.855166 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.72122 | −0.287062 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0524 | −0.330519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.7918 | 1.73391 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.5601 | 1.79006 | 0.895029 | − | 0.446008i | \(-0.147155\pi\) | ||||
0.895029 | + | 0.446008i | \(0.147155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.8166 | −0.714243 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.03484 | −0.262767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.49463 | 0.114164 | 0.0570822 | − | 0.998369i | \(-0.481820\pi\) | ||||
0.0570822 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.3953 | 1.35088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.2788 | 0.595871 | 0.297936 | − | 0.954586i | \(-0.403702\pi\) | ||||
0.297936 | + | 0.954586i | \(0.403702\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0771055 | 0.00251090 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.6963 | −0.445069 | −0.222534 | − | 0.974925i | \(-0.571433\pi\) | ||||
−0.222534 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0541 | −0.586061 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9837 | 0.453452 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.4865 | −1.34388 | −0.671940 | − | 0.740606i | \(-0.734539\pi\) | ||||
−0.671940 | + | 0.740606i | \(0.734539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0498088 | 0.00161177 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.4038 | −0.368631 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.2394 | 1.71740 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.3393 | 1.58994 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.07287 | −0.0345369 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.55841 | −0.307378 | −0.153689 | − | 0.988119i | \(-0.549115\pi\) | ||||
−0.153689 | + | 0.988119i | \(0.549115\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.73136 | 0.151993 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.0415 | −1.22081 | −0.610405 | − | 0.792090i | \(-0.708993\pi\) | ||||
−0.610405 | + | 0.792090i | \(0.708993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.0238 | −0.705327 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.4259 | 1.67725 | 0.838626 | − | 0.544708i | \(-0.183360\pi\) | ||||
0.838626 | + | 0.544708i | \(0.183360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.7171 | 0.566242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.0783 | 0.896471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.4487 | 0.716002 | 0.358001 | − | 0.933721i | \(-0.383458\pi\) | ||||
0.358001 | + | 0.933721i | \(0.383458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.887853 | −0.0282893 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.509930 | −0.0162148 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.6350 | −1.22728 | −0.613641 | − | 0.789585i | \(-0.710296\pi\) | ||||
−0.613641 | + | 0.789585i | \(0.710296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.8158 | 1.00964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.137009 | −0.00434347 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.4862 | 1.47223 | 0.736116 | − | 0.676855i | \(-0.236658\pi\) | ||||
0.736116 | + | 0.676855i | \(0.236658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.54756 | −0.238794 |
(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 | 8036.2.a.o.1.2 | ✓ | 10 | |
7.6 | odd | 2 | 8036.2.a.p.1.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.o.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8036.2.a.p.1.9 | yes | 10 | 7.6 | odd | 2 |