Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, 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("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.18625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 14x^{2} + 9x + 41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1250) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.08634\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | 2.46831 | 1.42508 | 0.712539 | − | 0.701633i | \(-0.247545\pi\) | ||||
0.712539 | + | 0.701633i | \(0.247545\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.710571 | −0.268570 | −0.134285 | − | 0.990943i | \(-0.542874\pi\) | ||||
−0.134285 | + | 0.990943i | \(0.542874\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.09254 | 1.03085 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.37577 | −1.62086 | −0.810428 | − | 0.585839i | \(-0.800765\pi\) | ||||
−0.810428 | + | 0.585839i | \(0.800765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.61184 | 1.83379 | 0.916897 | − | 0.399124i | \(-0.130686\pi\) | ||||
0.916897 | + | 0.399124i | \(0.130686\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.22987 | −1.75350 | −0.876751 | − | 0.480945i | \(-0.840294\pi\) | ||||
−0.876751 | + | 0.480945i | \(0.840294\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.14353 | 0.491760 | 0.245880 | − | 0.969300i | \(-0.420923\pi\) | ||||
0.245880 | + | 0.969300i | \(0.420923\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.75391 | −0.382734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.32241 | 0.692770 | 0.346385 | − | 0.938092i | \(-0.387409\pi\) | ||||
0.346385 | + | 0.938092i | \(0.387409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.228409 | 0.0439573 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56084 | −0.661232 | −0.330616 | − | 0.943765i | \(-0.607256\pi\) | ||||
−0.330616 | + | 0.943765i | \(0.607256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.67522 | −1.01930 | −0.509650 | − | 0.860382i | \(-0.670225\pi\) | ||||
−0.509650 | + | 0.860382i | \(0.670225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.2690 | −2.30984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.28943 | 0.540779 | 0.270389 | − | 0.962751i | \(-0.412848\pi\) | ||||
0.270389 | + | 0.962751i | \(0.412848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.3200 | 2.61330 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.46831 | −0.229311 | −0.114655 | − | 0.993405i | \(-0.536576\pi\) | ||||
−0.114655 | + | 0.993405i | \(0.536576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.681421 | 0.103916 | 0.0519579 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519579 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.37577 | −0.784137 | −0.392068 | − | 0.919936i | \(-0.628240\pi\) | ||||
−0.392068 | + | 0.919936i | \(0.628240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.49509 | −0.927870 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.8455 | −2.49888 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.624230 | −0.0857446 | −0.0428723 | − | 0.999081i | \(-0.513651\pi\) | ||||
−0.0428723 | + | 0.999081i | \(0.513651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.29089 | 0.700796 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.90746 | −1.28984 | −0.644921 | − | 0.764249i | \(-0.723110\pi\) | ||||
−0.644921 | + | 0.764249i | \(0.723110\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.84791 | −0.748748 | −0.374374 | − | 0.927278i | \(-0.622142\pi\) | ||||
−0.374374 | + | 0.927278i | \(0.622142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.19747 | −0.276855 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00383 | −0.977823 | −0.488912 | − | 0.872333i | \(-0.662606\pi\) | ||||
−0.488912 | + | 0.872333i | \(0.662606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.20072 | 0.987251 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.07395 | −0.958201 | −0.479101 | − | 0.877760i | \(-0.659037\pi\) | ||||
−0.479101 | + | 0.877760i | \(0.659037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8771 | 1.27306 | 0.636532 | − | 0.771251i | \(-0.280369\pi\) | ||||
0.636532 | + | 0.771251i | \(0.280369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.81986 | 0.435314 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.66283 | 0.862136 | 0.431068 | − | 0.902319i | \(-0.358137\pi\) | ||||
0.431068 | + | 0.902319i | \(0.358137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.71383 | −0.968203 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.82495 | 0.310079 | 0.155039 | − | 0.987908i | \(-0.450450\pi\) | ||||
0.155039 | + | 0.987908i | \(0.450450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.78925 | −0.942307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.02915 | 0.215089 | 0.107545 | − | 0.994200i | \(-0.465701\pi\) | ||||
0.107545 | + | 0.994200i | \(0.465701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.69818 | −0.492503 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.0082 | −1.45258 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.79308 | 0.182060 | 0.0910299 | − | 0.995848i | \(-0.470984\pi\) | ||||
0.0910299 | + | 0.995848i | \(0.470984\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.6248 | −1.67085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.26905 | 0.723297 | 0.361649 | − | 0.932314i | \(-0.382214\pi\) | ||||
0.361649 | + | 0.932314i | \(0.382214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8402 | −1.16665 | −0.583327 | − | 0.812237i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812237i | \(0.698249\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.86413 | 0.276886 | 0.138443 | − | 0.990370i | \(-0.455790\pi\) | ||||
0.138443 | + | 0.990370i | \(0.455790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.73352 | −0.740737 | −0.370369 | − | 0.928885i | \(-0.620769\pi\) | ||||
−0.370369 | + | 0.928885i | \(0.620769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.11932 | 0.770652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3772 | 1.25842 | 0.629212 | − | 0.777234i | \(-0.283378\pi\) | ||||
0.629212 | + | 0.777234i | \(0.283378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.4474 | 1.89036 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.13733 | 0.470939 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8989 | 1.62717 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.62423 | −0.326786 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4621 | −1.54951 | −0.774756 | − | 0.632261i | \(-0.782127\pi\) | ||||
−0.774756 | + | 0.632261i | \(0.782127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.68196 | 0.148088 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8064 | −1.03153 | −0.515763 | − | 0.856731i | \(-0.672492\pi\) | ||||
−0.515763 | + | 0.856731i | \(0.672492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.52313 | −0.132072 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.77159 | 0.578536 | 0.289268 | − | 0.957248i | \(-0.406588\pi\) | ||||
0.289268 | + | 0.957248i | \(0.406588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.1641 | −1.62548 | −0.812740 | − | 0.582627i | \(-0.802025\pi\) | ||||
−0.812740 | + | 0.582627i | \(0.802025\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.2690 | −1.11746 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35.5437 | −2.97231 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.0319 | −1.32229 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.4497 | −1.59338 | −0.796691 | − | 0.604386i | \(-0.793418\pi\) | ||||
−0.796691 | + | 0.604386i | \(0.793418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6095 | 0.944765 | 0.472383 | − | 0.881394i | \(-0.343394\pi\) | ||||
0.472383 | + | 0.881394i | \(0.343394\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.3586 | −1.80759 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.94664 | 0.634211 | 0.317105 | − | 0.948390i | \(-0.397289\pi\) | ||||
0.317105 | + | 0.948390i | \(0.397289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.54079 | −0.122193 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.36081 | −0.186058 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.89181 | 0.148178 | 0.0740892 | − | 0.997252i | \(-0.476395\pi\) | ||||
0.0740892 | + | 0.997252i | \(0.476395\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.14736 | 0.475697 | 0.237849 | − | 0.971302i | \(-0.423558\pi\) | ||||
0.237849 | + | 0.971302i | \(0.423558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.7164 | 2.36280 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.62895 | 0.506928 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.74592 | −0.588911 | −0.294456 | − | 0.955665i | \(-0.595138\pi\) | ||||
−0.294456 | + | 0.955665i | \(0.595138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.4547 | −1.83812 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.810766 | −0.0605995 | −0.0302998 | − | 0.999541i | \(-0.509646\pi\) | ||||
−0.0302998 | + | 0.999541i | \(0.509646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6528 | 1.53511 | 0.767556 | − | 0.640982i | \(-0.221473\pi\) | ||||
0.767556 | + | 0.640982i | \(0.221473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4344 | −1.06702 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 38.8661 | 2.84217 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.162301 | −0.0118056 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.45481 | 0.467053 | 0.233527 | − | 0.972350i | \(-0.424973\pi\) | ||||
0.233527 | + | 0.972350i | \(0.424973\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.28323 | 0.308314 | 0.154157 | − | 0.988046i | \(-0.450734\pi\) | ||||
0.154157 | + | 0.988046i | \(0.450734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.7344 | −1.76225 | −0.881127 | − | 0.472880i | \(-0.843215\pi\) | ||||
−0.881127 | + | 0.472880i | \(0.843215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3044 | −1.43934 | −0.719670 | − | 0.694316i | \(-0.755707\pi\) | ||||
−0.719670 | + | 0.694316i | \(0.755707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.7559 | −1.39347 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.53023 | 0.177587 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.2747 | 0.714139 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5231 | −0.797072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.48599 | 0.515357 | 0.257678 | − | 0.966231i | \(-0.417042\pi\) | ||||
0.257678 | + | 0.966231i | \(0.417042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.9290 | −1.36551 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.03265 | 0.273754 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.8479 | 1.81421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −47.8027 | −3.21556 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.77449 | 0.654548 | 0.327274 | − | 0.944929i | \(-0.393870\pi\) | ||||
0.327274 | + | 0.944929i | \(0.393870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.37161 | 0.489271 | 0.244635 | − | 0.969615i | \(-0.421332\pi\) | ||||
0.244635 | + | 0.969615i | \(0.421332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8379 | 1.24484 | 0.622421 | − | 0.782683i | \(-0.286149\pi\) | ||||
0.622421 | + | 0.782683i | \(0.286149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.42860 | 0.620356 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.04920 | 0.0687355 | 0.0343677 | − | 0.999409i | \(-0.489058\pi\) | ||||
0.0343677 | + | 0.999409i | \(0.489058\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.9142 | 1.22861 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.39636 | −0.349061 | −0.174531 | − | 0.984652i | \(-0.555841\pi\) | ||||
−0.174531 | + | 0.984652i | \(0.555841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2481 | −1.11105 | −0.555524 | − | 0.831501i | \(-0.687482\pi\) | ||||
−0.555524 | + | 0.831501i | \(0.687482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.1936 | −1.42372 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.1727 | 0.901786 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.97285 | 0.441886 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.283233 | −0.0178775 | −0.00893875 | − | 0.999960i | \(-0.502845\pi\) | ||||
−0.00893875 | + | 0.999960i | \(0.502845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8605 | −1.12288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.05482 | −0.0657981 | −0.0328991 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0328991 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.33737 | −0.145237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.0120 | −0.681628 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.86829 | −0.608505 | −0.304252 | − | 0.952591i | \(-0.598407\pi\) | ||||
−0.304252 | + | 0.952591i | \(0.598407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00856 | 0.306519 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.6805 | −1.13897 | −0.569486 | − | 0.822001i | \(-0.692858\pi\) | ||||
−0.569486 | + | 0.822001i | \(0.692858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.1497 | −1.04177 | −0.520886 | − | 0.853626i | \(-0.674398\pi\) | ||||
−0.520886 | + | 0.853626i | \(0.674398\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.5965 | −0.701855 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.6144 | 1.53902 | 0.769510 | − | 0.638634i | \(-0.220500\pi\) | ||||
0.769510 | + | 0.638634i | \(0.220500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.5508 | −1.05074 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.53732 | −0.449639 | −0.224819 | − | 0.974400i | \(-0.572179\pi\) | ||||
−0.224819 | + | 0.974400i | \(0.572179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.89744 | −0.410010 | −0.205005 | − | 0.978761i | \(-0.565721\pi\) | ||||
−0.205005 | + | 0.978761i | \(0.565721\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04334 | 0.0615861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.2710 | 2.07477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.42587 | 0.259449 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.8455 | −0.867286 | −0.433643 | − | 0.901085i | \(-0.642772\pi\) | ||||
−0.433643 | + | 0.901085i | \(0.642772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.22787 | −0.0712485 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.9672 | 1.27040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.484198 | −0.0279087 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.9422 | 1.03075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0515679 | 0.00294314 | 0.00147157 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00147157 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.2254 | −1.66257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.0512 | −1.42052 | −0.710262 | − | 0.703938i | \(-0.751423\pi\) | ||||
−0.710262 | + | 0.703938i | \(0.751423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4659 | −1.43942 | −0.719710 | − | 0.694275i | \(-0.755725\pi\) | ||||
−0.719710 | + | 0.694275i | \(0.755725\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0683 | −0.621659 | −0.310830 | − | 0.950466i | \(-0.600607\pi\) | ||||
−0.310830 | + | 0.950466i | \(0.600607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1423 | 1.07176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.06954 | 0.394584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.4975 | −0.862302 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.0887 | −1.05561 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.81986 | 0.210596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1768 | 0.614335 | 0.307167 | − | 0.951656i | \(-0.400619\pi\) | ||||
0.307167 | + | 0.951656i | \(0.400619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1727 | 0.557459 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9510 | 0.705486 | 0.352743 | − | 0.935720i | \(-0.385249\pi\) | ||||
0.352743 | + | 0.935720i | \(0.385249\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.0191 | 1.79335 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.5087 | 1.65214 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.58922 | 0.517769 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.4889 | −1.20727 | −0.603634 | − | 0.797262i | \(-0.706281\pi\) | ||||
−0.603634 | + | 0.797262i | \(0.706281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.57413 | −0.458962 | −0.229481 | − | 0.973313i | \(-0.573703\pi\) | ||||
−0.229481 | + | 0.973313i | \(0.573703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.51020 | 0.0806087 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2710 | 1.02569 | 0.512847 | − | 0.858480i | \(-0.328591\pi\) | ||||
0.512847 | + | 0.858480i | \(0.328591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.6805 | 0.671124 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.7188 | 0.776827 | 0.388413 | − | 0.921485i | \(-0.373023\pi\) | ||||
0.388413 | + | 0.921485i | \(0.373023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4053 | −0.758172 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 44.1800 | 2.31885 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7186 | −0.559504 | −0.279752 | − | 0.960072i | \(-0.590252\pi\) | ||||
−0.279752 | + | 0.960072i | \(0.590252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.54079 | −0.236384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.443560 | 0.0230285 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6292 | −0.550357 | −0.275179 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275179 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.5437 | −1.21256 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.1335 | −1.70195 | −0.850977 | − | 0.525203i | \(-0.823989\pi\) | ||||
−0.850977 | + | 0.525203i | \(0.823989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.1018 | −2.20817 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.1780 | −1.28653 | −0.643267 | − | 0.765642i | \(-0.722422\pi\) | ||||
−0.643267 | + | 0.765642i | \(0.722422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.10732 | 0.107121 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5075 | 0.989069 | 0.494534 | − | 0.869158i | \(-0.335339\pi\) | ||||
0.494534 | + | 0.869158i | \(0.335339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0206 | −1.21477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.1417 | −1.47001 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.7206 | −0.788994 | −0.394497 | − | 0.918897i | \(-0.629081\pi\) | ||||
−0.394497 | + | 0.918897i | \(0.629081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.75955 | −0.188213 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.03918 | 0.151769 | 0.0758846 | − | 0.997117i | \(-0.475822\pi\) | ||||
0.0758846 | + | 0.997117i | \(0.475822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.5237 | −1.86919 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6832 | −0.876524 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.4623 | 1.55571 | 0.777856 | − | 0.628443i | \(-0.216307\pi\) | ||||
0.777856 | + | 0.628443i | \(0.216307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.7144 | 0.824459 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.03995 | 0.346413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −47.3029 | −2.31643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.18213 | −0.399723 | −0.199862 | − | 0.979824i | \(-0.564049\pi\) | ||||
−0.199862 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.66960 | 0.130108 | 0.0650542 | − | 0.997882i | \(-0.479278\pi\) | ||||
0.0650542 | + | 0.997882i | \(0.479278\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.6248 | −0.808324 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.15535 | 0.201092 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −87.7328 | −4.23578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7871 | 1.24212 | 0.621060 | − | 0.783763i | \(-0.286702\pi\) | ||||
0.621060 | + | 0.783763i | \(0.286702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.6283 | −1.08744 | −0.543722 | − | 0.839265i | \(-0.682986\pi\) | ||||
−0.543722 | + | 0.839265i | \(0.682986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.12169 | 0.340676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.3967 | 1.11666 | 0.558331 | − | 0.829618i | \(-0.311442\pi\) | ||||
0.558331 | + | 0.829618i | \(0.311442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.0863 | −0.956491 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.41563 | 0.304816 | 0.152408 | − | 0.988318i | \(-0.451297\pi\) | ||||
0.152408 | + | 0.988318i | \(0.451297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −48.0079 | −2.27069 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.06192 | −0.191694 | −0.0958470 | − | 0.995396i | \(-0.530556\pi\) | ||||
−0.0958470 | + | 0.995396i | \(0.530556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.89328 | 0.371680 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.6557 | 1.34636 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5022 | 1.28650 | 0.643249 | − | 0.765657i | \(-0.277586\pi\) | ||||
0.643249 | + | 0.765657i | \(0.277586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.65137 | −0.0770792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.47486 | 0.394713 | 0.197357 | − | 0.980332i | \(-0.436764\pi\) | ||||
0.197357 | + | 0.980332i | \(0.436764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.47450 | −0.347370 | −0.173685 | − | 0.984801i | \(-0.555567\pi\) | ||||
−0.173685 | + | 0.984801i | \(0.555567\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.1388 | 0.746814 | 0.373407 | − | 0.927668i | \(-0.378189\pi\) | ||||
0.373407 | + | 0.927668i | \(0.378189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.68729 | 0.262615 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.6147 | 0.903799 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.66316 | −0.168432 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.93046 | −0.0883895 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0745 | −1.37414 | −0.687069 | − | 0.726592i | \(-0.741103\pi\) | ||||
−0.687069 | + | 0.726592i | \(0.741103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.7492 | 0.991677 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.82719 | −0.265146 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1217 | 0.685229 | 0.342615 | − | 0.939476i | \(-0.388688\pi\) | ||||
0.342615 | + | 0.939476i | \(0.388688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.66958 | 0.211166 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1187 | 1.72027 | 0.860137 | − | 0.510062i | \(-0.170378\pi\) | ||||
0.860137 | + | 0.510062i | \(0.170378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.7444 | 1.15947 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.73711 | 0.257345 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.98088 | −0.312507 | −0.156253 | − | 0.987717i | \(-0.549942\pi\) | ||||
−0.156253 | + | 0.987717i | \(0.549942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.1736 | 0.677905 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.13680 | −0.0506874 | −0.0253437 | − | 0.999679i | \(-0.508068\pi\) | ||||
−0.0253437 | + | 0.999679i | \(0.508068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 75.8175 | 3.36717 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.98435 | 0.353900 | 0.176950 | − | 0.984220i | \(-0.443377\pi\) | ||||
0.176950 | + | 0.984220i | \(0.443377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.72892 | −0.341907 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.489602 | 0.0216164 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.8989 | 1.27097 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.1193 | −0.839244 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.8997 | 1.44136 | 0.720681 | − | 0.693267i | \(-0.243829\pi\) | ||||
0.720681 | + | 0.693267i | \(0.243829\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.72859 | 0.0755858 | 0.0377929 | − | 0.999286i | \(-0.487967\pi\) | ||||
0.0377929 | + | 0.999286i | \(0.487967\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.0311 | 1.78734 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.9616 | −0.520070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.6392 | −1.32963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.70820 | −0.420509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.00122 | −0.0863590 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.9161 | 1.50394 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.2902 | 1.86119 | 0.930595 | − | 0.366051i | \(-0.119290\pi\) | ||||
0.930595 | + | 0.366051i | \(0.119290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.9775 | 2.18765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5390 | 1.60505 | 0.802526 | − | 0.596618i | \(-0.203489\pi\) | ||||
0.802526 | + | 0.596618i | \(0.203489\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0849 | −0.771843 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.63278 | −0.325167 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.44498 | −0.231544 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.0519 | −1.86654 | −0.933269 | − | 0.359178i | \(-0.883057\pi\) | ||||
−0.933269 | + | 0.359178i | \(0.883057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.50545 | 0.190560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 95.9335 | 4.05032 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.5528 | −1.62481 | −0.812404 | − | 0.583095i | \(-0.801841\pi\) | ||||
−0.812404 | + | 0.583095i | \(0.801841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.19179 | 0.260031 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.51164 | 0.356827 | 0.178413 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178413 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3845 | 0.518277 | 0.259138 | − | 0.965840i | \(-0.416561\pi\) | ||||
0.259138 | + | 0.965840i | \(0.416561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.9324 | 0.665587 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.6271 | −0.650566 | −0.325283 | − | 0.945617i | \(-0.605460\pi\) | ||||
−0.325283 | + | 0.945617i | \(0.605460\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.5723 | 0.439371 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.00733 | −0.0832780 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.35572 | 0.138980 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.4271 | −1.13204 | −0.566019 | − | 0.824392i | \(-0.691517\pi\) | ||||
−0.566019 | + | 0.824392i | \(0.691517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.1650 | −0.501251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −61.0521 | −2.51135 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8754 | 0.487663 | 0.243832 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243832 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −50.1175 | −2.05117 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.75648 | −0.276062 | −0.138031 | − | 0.990428i | \(-0.544077\pi\) | ||||
−0.138031 | + | 0.990428i | \(0.544077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.4612 | −1.44649 | −0.723246 | − | 0.690590i | \(-0.757351\pi\) | ||||
−0.723246 | + | 0.690590i | \(0.757351\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.7521 | −1.00798 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5868 | 0.429707 | 0.214853 | − | 0.976646i | \(-0.431073\pi\) | ||||
0.214853 | + | 0.976646i | \(0.431073\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.24539 | 0.253076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.5437 | −1.43794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.32513 | −0.215080 | −0.107540 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107540 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.37939 | 0.216566 | 0.108283 | − | 0.994120i | \(-0.465465\pi\) | ||||
0.108283 | + | 0.994120i | \(0.465465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3512 | −0.938565 | −0.469283 | − | 0.883048i | \(-0.655487\pi\) | ||||
−0.469283 | + | 0.883048i | \(0.655487\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.758868 | 0.0304523 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.44185 | −0.0577667 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.4426 | −1.13589 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.7822 | −0.948256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0073 | −0.756669 | −0.378334 | − | 0.925669i | \(-0.623503\pi\) | ||||
−0.378334 | + | 0.925669i | \(0.623503\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.4777 | 0.734423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42.9445 | −1.70152 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9690 | −0.987758 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7751 | 0.504585 | 0.252292 | − | 0.967651i | \(-0.418816\pi\) | ||||
0.252292 | + | 0.967651i | \(0.418816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9242 | 1.37728 | 0.688638 | − | 0.725105i | \(-0.258209\pi\) | ||||
0.688638 | + | 0.725105i | \(0.258209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1090 | −0.987135 | −0.493568 | − | 0.869707i | \(-0.664307\pi\) | ||||
−0.493568 | + | 0.869707i | \(0.664307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.2602 | 2.09065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.95381 | 0.390121 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.3657 | −1.11004 | −0.555019 | − | 0.831838i | \(-0.687289\pi\) | ||||
−0.555019 | + | 0.831838i | \(0.687289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.6377 | 1.31233 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5523 | −0.527922 | −0.263961 | − | 0.964533i | \(-0.585029\pi\) | ||||
−0.263961 | + | 0.964533i | \(0.585029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.1326 | −0.899754 | −0.449877 | − | 0.893091i | \(-0.648532\pi\) | ||||
−0.449877 | + | 0.893091i | \(0.648532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −117.992 | −4.58242 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8306 | −0.458082 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.1264 | 0.932782 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.4370 | 1.21361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.0453 | −1.62073 | −0.810364 | − | 0.585926i | \(-0.800731\pi\) | ||||
−0.810364 | + | 0.585926i | \(0.800731\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8428 | −1.30069 | −0.650343 | − | 0.759641i | \(-0.725375\pi\) | ||||
−0.650343 | + | 0.759641i | \(0.725375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.27411 | −0.0488959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.1954 | 0.697249 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0853 | 1.68688 | 0.843438 | − | 0.537226i | \(-0.180528\pi\) | ||||
0.843438 | + | 0.537226i | \(0.180528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.4977 | 1.77400 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.12731 | −0.157238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.6884 | 1.05331 | 0.526657 | − | 0.850078i | \(-0.323445\pi\) | ||||
0.526657 | + | 0.850078i | \(0.323445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.8131 | 0.448741 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6157 | 0.402097 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.58975 | 0.0979533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.2086 | 1.21650 | 0.608251 | − | 0.793745i | \(-0.291872\pi\) | ||||
0.608251 | + | 0.793745i | \(0.291872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.05099 | 0.265933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.16517 | −0.194256 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.42150 | 0.0909412 | 0.0454706 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454706 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.6976 | 0.888729 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.8554 | −0.706141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.3199 | −0.497439 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.2412 | 1.61263 | 0.806313 | − | 0.591490i | \(-0.201460\pi\) | ||||
0.806313 | + | 0.591490i | \(0.201460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.41333 | 0.313329 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.5736 | −1.58333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8936 | −0.700726 | −0.350363 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350363 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.6392 | −1.06071 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.92659 | −0.182216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.0056 | −0.628117 | −0.314059 | − | 0.949404i | \(-0.601689\pi\) | ||||
−0.314059 | + | 0.949404i | \(0.601689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.0267 | 1.58491 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.4709 | 1.15767 | 0.578837 | − | 0.815443i | \(-0.303507\pi\) | ||||
0.578837 | + | 0.815443i | \(0.303507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.9825 | 1.28511 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.62477 | 0.169666 | 0.0848331 | − | 0.996395i | \(-0.472964\pi\) | ||||
0.0848331 | + | 0.996395i | \(0.472964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.73627 | 0.319643 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.03517 | −0.0743633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.7747 | 1.81630 | 0.908152 | − | 0.418640i | \(-0.137493\pi\) | ||||
0.908152 | + | 0.418640i | \(0.137493\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.699106 | −0.0254768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6657 | −0.969183 | −0.484591 | − | 0.874741i | \(-0.661032\pi\) | ||||
−0.484591 | + | 0.874741i | \(0.661032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −44.0852 | −1.60019 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0242 | −0.544627 | −0.272314 | − | 0.962209i | \(-0.587789\pi\) | ||||
−0.272314 | + | 0.962209i | \(0.587789\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.49522 | 0.198940 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.5065 | −2.36530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.5198 | 1.78573 | 0.892865 | − | 0.450323i | \(-0.148691\pi\) | ||||
0.892865 | + | 0.450323i | \(0.148691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.60363 | −0.0937674 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.5493 | −0.739108 | −0.369554 | − | 0.929209i | \(-0.620490\pi\) | ||||
−0.369554 | + | 0.929209i | \(0.620490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.76935 | −0.206974 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.14736 | −0.112766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.4037 | 1.55311 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.813328 | −0.0290660 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.9401 | 1.31677 | 0.658386 | − | 0.752681i | \(-0.271240\pi\) | ||||
0.658386 | + | 0.752681i | \(0.271240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.3580 | −0.867166 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.50547 | −0.337976 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.6654 | −1.37305 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −54.3335 | −1.92459 | −0.962296 | − | 0.272005i | \(-0.912313\pi\) | ||||
−0.962296 | + | 0.272005i | \(0.912313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.8661 | 1.37498 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.27522 | 0.221724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.4725 | −2.06345 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.1092 | −1.62312 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.5457 | 1.46067 | 0.730335 | − | 0.683089i | \(-0.239364\pi\) | ||||
0.730335 | + | 0.683089i | \(0.239364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4405 | 1.03379 | 0.516897 | − | 0.856047i | \(-0.327087\pi\) | ||||
0.516897 | + | 0.856047i | \(0.327087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.3308 | −1.48461 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.46065 | 0.0511016 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.5293 | −0.507694 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.6634 | 1.76816 | 0.884082 | − | 0.467331i | \(-0.154784\pi\) | ||||
0.884082 | + | 0.467331i | \(0.154784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.31220 | 0.185172 | 0.0925859 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925859 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.6889 | −0.928065 | −0.464033 | − | 0.885818i | \(-0.653598\pi\) | ||||
−0.464033 | + | 0.885818i | \(0.653598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.4543 | 0.745140 | 0.372570 | − | 0.928004i | \(-0.378477\pi\) | ||||
0.372570 | + | 0.928004i | \(0.378477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 63.2242 | 2.19322 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46.9587 | 1.62702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.29627 | −0.0448057 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.730418 | −0.0252168 | −0.0126084 | − | 0.999921i | \(-0.504013\pi\) | ||||
−0.0126084 | + | 0.999921i | \(0.504013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3204 | −0.562772 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.6044 | −0.640770 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7184 | −0.437011 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.0250 | −0.584296 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9288 | 0.374635 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.2457 | 0.590483 | 0.295241 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295241 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.260256 | −0.00889017 | −0.00444509 | − | 0.999990i | \(-0.501415\pi\) | ||||
−0.00444509 | + | 0.999990i | \(0.501415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0243 | 1.50209 | 0.751044 | − | 0.660252i | \(-0.229550\pi\) | ||||
0.751044 | + | 0.660252i | \(0.229550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.57527 | 0.0877650 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.0417 | 1.77152 | 0.885760 | − | 0.464143i | \(-0.153638\pi\) | ||||
0.885760 | + | 0.464143i | \(0.153638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 87.0597 | 2.95670 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.1936 | −1.39740 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.9200 | −1.79313 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.54517 | 0.187676 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0619 | 1.25149 | 0.625746 | − | 0.780027i | \(-0.284795\pi\) | ||||
0.625746 | + | 0.780027i | \(0.284795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.6433 | −1.23595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0497 | 0.877638 | 0.438819 | − | 0.898575i | \(-0.355397\pi\) | ||||
0.438819 | + | 0.898575i | \(0.355397\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.0774468 | −0.00260629 | −0.00130315 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130315 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.03771 | −0.135573 | −0.0677866 | − | 0.997700i | \(-0.521594\pi\) | ||||
−0.0677866 | + | 0.997700i | \(0.521594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4081 | 0.416153 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.8435 | 1.56932 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.5231 | −0.385607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 54.2218 | 1.81041 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.2086 | 0.673994 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.51310 | 0.150353 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.19515 | −0.0397721 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0596 | −0.466840 | −0.233420 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233420 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.4798 | 0.745608 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.8375 | 0.392195 | 0.196097 | − | 0.980584i | \(-0.437173\pi\) | ||||
0.196097 | + | 0.980584i | \(0.437173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.1863 | −0.502593 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.38926 | 0.277038 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.1661 | −1.22600 | −0.612999 | − | 0.790084i | \(-0.710037\pi\) | ||||
−0.612999 | + | 0.790084i | \(0.710037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.127285 | 0.00419420 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.3836 | −1.75714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.6164 | −1.20264 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1665 | 1.02254 | 0.511270 | − | 0.859420i | \(-0.329175\pi\) | ||||
0.511270 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.9224 | −0.456289 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −61.8340 | −2.02436 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.1725 | 1.57373 | 0.786864 | − | 0.617127i | \(-0.211703\pi\) | ||||
0.786864 | + | 0.617127i | \(0.211703\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.8577 | −2.05128 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.1763 | 0.657728 | 0.328864 | − | 0.944377i | \(-0.393334\pi\) | ||||
0.328864 | + | 0.944377i | \(0.393334\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.87831 | −0.158860 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.3323 | 1.57059 | 0.785294 | − | 0.619123i | \(-0.212512\pi\) | ||||
0.785294 | + | 0.619123i | \(0.212512\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.9173 | 2.33454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3200 | −0.885912 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.6612 | 1.05800 | 0.529001 | − | 0.848621i | \(-0.322567\pi\) | ||||
0.529001 | + | 0.848621i | \(0.322567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.2490 | 1.52734 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.81169 | −0.155378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.20818 | 0.0389734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.85742 | 0.285426 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1632 | −0.584090 | −0.292045 | − | 0.956405i | \(-0.594336\pi\) | ||||
−0.292045 | + | 0.956405i | \(0.594336\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.2525 | −1.22885 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.01643 | −0.160985 | −0.0804924 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804924 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6175 | 0.436556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.7701 | −0.440545 | −0.220273 | − | 0.975438i | \(-0.570695\pi\) | ||||
−0.220273 | + | 0.975438i | \(0.570695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9082 | −0.348629 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.9162 | −0.763586 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.853324 | −0.0272168 | −0.0136084 | − | 0.999907i | \(-0.504332\pi\) | ||||
−0.0136084 | + | 0.999907i | \(0.504332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.42860 | 0.300116 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.26396 | 0.0719897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3689 | 0.932932 | 0.466466 | − | 0.884539i | \(-0.345527\pi\) | ||||
0.466466 | + | 0.884539i | \(0.345527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.5879 | 0.875475 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.98761 | 0.189629 | 0.0948147 | − | 0.995495i | \(-0.469774\pi\) | ||||
0.0948147 | + | 0.995495i | \(0.469774\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.751335 | 0.0237712 |
(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 | 10000.2.a.v.1.3 | 4 | ||
4.3 | odd | 2 | 1250.2.a.g.1.2 | ✓ | 4 | ||
5.4 | even | 2 | 10000.2.a.u.1.2 | 4 | |||
20.3 | even | 4 | 1250.2.b.d.1249.6 | 8 | |||
20.7 | even | 4 | 1250.2.b.d.1249.3 | 8 | |||
20.19 | odd | 2 | 1250.2.a.j.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1250.2.a.g.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
1250.2.a.j.1.3 | yes | 4 | 20.19 | odd | 2 | ||
1250.2.b.d.1249.3 | 8 | 20.7 | even | 4 | |||
1250.2.b.d.1249.6 | 8 | 20.3 | even | 4 | |||
10000.2.a.u.1.2 | 4 | 5.4 | even | 2 | |||
10000.2.a.v.1.3 | 4 | 1.1 | even | 1 | trivial |