Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6272,2,Mod(1,6272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6272, 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("6272.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6272 = 2^{7} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6272.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: | \(50.0821721477\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.78165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6272.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.95594 | 1.12926 | 0.564632 | − | 0.825343i | \(-0.309018\pi\) | ||||
0.564632 | + | 0.825343i | \(0.309018\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.703158 | 0.314462 | 0.157231 | − | 0.987562i | \(-0.449743\pi\) | ||||
0.157231 | + | 0.987562i | \(0.449743\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.825711 | 0.275237 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.90421 | 0.574140 | 0.287070 | − | 0.957910i | \(-0.407319\pi\) | ||||
0.287070 | + | 0.957910i | \(0.407319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73760 | −0.759272 | −0.379636 | − | 0.925136i | \(-0.623951\pi\) | ||||
−0.379636 | + | 0.925136i | \(0.623951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.37534 | 0.355110 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.38902 | −1.30703 | −0.653514 | − | 0.756914i | \(-0.726706\pi\) | ||||
−0.653514 | + | 0.756914i | \(0.726706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.31052 | −0.759486 | −0.379743 | − | 0.925092i | \(-0.623988\pi\) | ||||
−0.379743 | + | 0.925092i | \(0.623988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.39670 | 1.33380 | 0.666902 | − | 0.745146i | \(-0.267620\pi\) | ||||
0.666902 | + | 0.745146i | \(0.267620\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50557 | −0.901114 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.25278 | −0.818449 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.23203 | −0.414477 | −0.207239 | − | 0.978290i | \(-0.566448\pi\) | ||||
−0.207239 | + | 0.978290i | \(0.566448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.78165 | −0.858810 | −0.429405 | − | 0.903112i | \(-0.641277\pi\) | ||||
−0.429405 | + | 0.903112i | \(0.641277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.72452 | 0.648355 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.819709 | −0.134759 | −0.0673797 | − | 0.997727i | \(-0.521464\pi\) | ||||
−0.0673797 | + | 0.997727i | \(0.521464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.35458 | −0.857419 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.14391 | −1.27187 | −0.635933 | − | 0.771745i | \(-0.719384\pi\) | ||||
−0.635933 | + | 0.771745i | \(0.719384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.593684 | −0.0905359 | −0.0452679 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452679 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.580605 | 0.0865516 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.56692 | −0.228559 | −0.114280 | − | 0.993449i | \(-0.536456\pi\) | ||||
−0.114280 | + | 0.993449i | \(0.536456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.5406 | −1.47598 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3223 | −1.69259 | −0.846296 | − | 0.532712i | \(-0.821173\pi\) | ||||
−0.846296 | + | 0.532712i | \(0.821173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.33896 | 0.180545 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.47519 | −0.857660 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.36226 | 0.177351 | 0.0886755 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886755 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5400 | 1.34951 | 0.674755 | − | 0.738042i | \(-0.264249\pi\) | ||||
0.674755 | + | 0.738042i | \(0.264249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.92496 | −0.238762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9256 | −1.57911 | −0.789555 | − | 0.613680i | \(-0.789688\pi\) | ||||
−0.789555 | + | 0.613680i | \(0.789688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.5116 | 1.50622 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0385 | 1.17492 | 0.587459 | − | 0.809254i | \(-0.300128\pi\) | ||||
0.587459 | + | 0.809254i | \(0.300128\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.81263 | −1.01760 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.33896 | 1.05071 | 0.525357 | − | 0.850882i | \(-0.323932\pi\) | ||||
0.525357 | + | 0.850882i | \(0.323932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7953 | −1.19948 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.6626 | −1.38990 | −0.694948 | − | 0.719060i | \(-0.744573\pi\) | ||||
−0.694948 | + | 0.719060i | \(0.744573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.78933 | −0.411011 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.36572 | −0.468054 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.75489 | −0.292018 | −0.146009 | − | 0.989283i | \(-0.546643\pi\) | ||||
−0.146009 | + | 0.989283i | \(0.546643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.35264 | −0.969823 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.32782 | −0.238829 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4044 | −1.46254 | −0.731271 | − | 0.682087i | \(-0.761073\pi\) | ||||
−0.731271 | + | 0.682087i | \(0.761073\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.57232 | 0.158025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.239103 | 0.0237917 | 0.0118958 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118958 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.89113 | −0.383404 | −0.191702 | − | 0.981453i | \(-0.561401\pi\) | ||||
−0.191702 | + | 0.981453i | \(0.561401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.72798 | −0.360397 | −0.180199 | − | 0.983630i | \(-0.557674\pi\) | ||||
−0.180199 | + | 0.983630i | \(0.557674\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.7417 | 1.89091 | 0.945454 | − | 0.325756i | \(-0.105619\pi\) | ||||
0.945454 | + | 0.325756i | \(0.105619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.60330 | −0.152179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7761 | 1.86038 | 0.930189 | − | 0.367080i | \(-0.119643\pi\) | ||||
0.930189 | + | 0.367080i | \(0.119643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.49789 | 0.419430 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.26046 | −0.208980 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.37400 | −0.670364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.9290 | −1.43627 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.68392 | −0.597828 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7780 | −1.31134 | −0.655669 | − | 0.755048i | \(-0.727613\pi\) | ||||
−0.655669 | + | 0.755048i | \(0.727613\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.16121 | −0.102239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.4585 | 1.70010 | 0.850048 | − | 0.526705i | \(-0.176573\pi\) | ||||
0.850048 | + | 0.526705i | \(0.176573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.99038 | −0.257371 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.02844 | −0.771351 | −0.385676 | − | 0.922634i | \(-0.626032\pi\) | ||||
−0.385676 | + | 0.922634i | \(0.626032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.50979 | −0.806610 | −0.403305 | − | 0.915066i | \(-0.632139\pi\) | ||||
−0.403305 | + | 0.915066i | \(0.632139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06481 | −0.258104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.21295 | −0.435929 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.56947 | −0.130337 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5501 | −1.76545 | −0.882725 | − | 0.469890i | \(-0.844294\pi\) | ||||
−0.882725 | + | 0.469890i | \(0.844294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.22647 | 0.588082 | 0.294041 | − | 0.955793i | \(-0.405000\pi\) | ||||
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.44977 | −0.359743 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.36226 | −0.270063 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3069 | 1.14182 | 0.570908 | − | 0.821014i | \(-0.306591\pi\) | ||||
0.570908 | + | 0.821014i | \(0.306591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.1016 | −1.91138 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5162 | 1.45030 | 0.725152 | − | 0.688589i | \(-0.241770\pi\) | ||||
0.725152 | + | 0.688589i | \(0.241770\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.61893 | 0.203883 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5573 | −0.816949 | −0.408474 | − | 0.912770i | \(-0.633939\pi\) | ||||
−0.408474 | + | 0.912770i | \(0.633939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50557 | −0.423505 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.73353 | −0.209039 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1379 | 0.770771 | 0.385386 | − | 0.922756i | \(-0.374068\pi\) | ||||
0.385386 | + | 0.922756i | \(0.374068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.66450 | 0.200276 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.437136 | 0.0326731 | 0.0163366 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163366 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.45983 | −0.257167 | −0.128584 | − | 0.991699i | \(-0.541043\pi\) | ||||
−0.128584 | + | 0.991699i | \(0.541043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.6156 | 1.52395 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.576385 | −0.0423767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.2618 | −0.750417 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.62044 | 0.551396 | 0.275698 | − | 0.961244i | \(-0.411091\pi\) | ||||
0.275698 | + | 0.961244i | \(0.411091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9373 | 1.00323 | 0.501615 | − | 0.865091i | \(-0.332740\pi\) | ||||
0.501615 | + | 0.865091i | \(0.332740\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.76512 | −0.269626 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.52287 | −0.535982 | −0.267991 | − | 0.963421i | \(-0.586360\pi\) | ||||
−0.267991 | + | 0.963421i | \(0.586360\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2265 | 1.50470 | 0.752352 | − | 0.658761i | \(-0.228919\pi\) | ||||
0.752352 | + | 0.658761i | \(0.228919\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.2817 | −1.78323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.72646 | −0.399953 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.28182 | 0.367112 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.30392 | −0.436051 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2878 | 1.25899 | 0.629493 | − | 0.777006i | \(-0.283263\pi\) | ||||
0.629493 | + | 0.777006i | \(0.283263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.7357 | 0.804114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.417453 | −0.0284701 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.6347 | 1.32679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.7530 | 0.992391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.1874 | −1.01702 | −0.508511 | − | 0.861056i | \(-0.669804\pi\) | ||||
−0.508511 | + | 0.861056i | \(0.669804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.72030 | −0.248020 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.0004 | −1.06199 | −0.530993 | − | 0.847376i | \(-0.678181\pi\) | ||||
−0.530993 | + | 0.847376i | \(0.678181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.85203 | 0.188467 | 0.0942336 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942336 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92918 | 0.126385 | 0.0631925 | − | 0.998001i | \(-0.479872\pi\) | ||||
0.0631925 | + | 0.998001i | \(0.479872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.10180 | −0.0718732 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.2665 | 1.18653 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.63818 | 0.429388 | 0.214694 | − | 0.976681i | \(-0.431125\pi\) | ||||
0.214694 | + | 0.976681i | \(0.431125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.24209 | 0.530920 | 0.265460 | − | 0.964122i | \(-0.414476\pi\) | ||||
0.265460 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.35670 | −0.536083 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.06287 | 0.576657 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.7672 | −1.56956 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4812 | −1.16652 | −0.583261 | − | 0.812285i | \(-0.698224\pi\) | ||||
−0.583261 | + | 0.812285i | \(0.698224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.1806 | 0.765790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.41172 | −0.464140 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.56525 | −0.0976375 | −0.0488187 | − | 0.998808i | \(-0.515546\pi\) | ||||
−0.0488187 | + | 0.998808i | \(0.515546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.84301 | −0.114079 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.2316 | −1.80250 | −0.901249 | − | 0.433302i | \(-0.857348\pi\) | ||||
−0.901249 | + | 0.433302i | \(0.857348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.66450 | −0.532256 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.38842 | −0.329766 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4681 | −0.821166 | −0.410583 | − | 0.911823i | \(-0.634675\pi\) | ||||
−0.410583 | + | 0.911823i | \(0.634675\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3432 | −1.35725 | −0.678626 | − | 0.734484i | \(-0.737424\pi\) | ||||
−0.678626 | + | 0.734484i | \(0.737424\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.57953 | −0.517365 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1926 | 0.852753 | 0.426376 | − | 0.904546i | \(-0.359790\pi\) | ||||
0.426376 | + | 0.904546i | \(0.359790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.94826 | −0.236376 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.59562 | 0.0951870 | 0.0475935 | − | 0.998867i | \(-0.484845\pi\) | ||||
0.0475935 | + | 0.998867i | \(0.484845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.3490 | −1.92295 | −0.961475 | − | 0.274893i | \(-0.911358\pi\) | ||||
−0.961475 | + | 0.274893i | \(0.911358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.55308 | −0.269701 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0415 | 0.708324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.1741 | −1.65160 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.6364 | 1.67296 | 0.836478 | − | 0.548000i | \(-0.184611\pi\) | ||||
0.836478 | + | 0.548000i | \(0.184611\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.957884 | 0.0557701 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.09818 | −0.469904 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.5116 | −1.01272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.467673 | 0.0268671 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.41129 | 0.424369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8208 | 0.617573 | 0.308787 | − | 0.951131i | \(-0.400077\pi\) | ||||
0.308787 | + | 0.951131i | \(0.400077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.61082 | −0.432965 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.45323 | 0.0824051 | 0.0412025 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412025 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.6210 | −1.10905 | −0.554524 | − | 0.832168i | \(-0.687099\pi\) | ||||
−0.554524 | + | 0.832168i | \(0.687099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.1003 | 1.29744 | 0.648721 | − | 0.761026i | \(-0.275304\pi\) | ||||
0.648721 | + | 0.761026i | \(0.275304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.25024 | −0.237968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.29171 | −0.406983 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.8405 | 0.992670 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.3344 | 0.684191 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 38.6135 | 2.13533 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.15867 | 0.503406 | 0.251703 | − | 0.967805i | \(-0.419009\pi\) | ||||
0.251703 | + | 0.967805i | \(0.419009\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.676843 | −0.0370907 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.08872 | −0.496570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0952 | −1.31255 | −0.656274 | − | 0.754523i | \(-0.727868\pi\) | ||||
−0.656274 | + | 0.754523i | \(0.727868\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 38.6809 | 2.10086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.10525 | −0.493077 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.79761 | 0.473648 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.8375 | 0.581785 | 0.290892 | − | 0.956756i | \(-0.406048\pi\) | ||||
0.290892 | + | 0.956756i | \(0.406048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5114 | 1.09795 | 0.548975 | − | 0.835839i | \(-0.315018\pi\) | ||||
0.548975 | + | 0.835839i | \(0.315018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.6424 | 0.621426 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.54601 | −0.401633 | −0.200817 | − | 0.979629i | \(-0.564360\pi\) | ||||
−0.200817 | + | 0.979629i | \(0.564360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.21895 | 0.223919 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.4100 | −1.92164 | −0.960822 | − | 0.277166i | \(-0.910605\pi\) | ||||
−0.960822 | + | 0.277166i | \(0.910605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.04044 | −0.423181 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.4231 | −0.757017 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.05865 | 0.369467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3540 | −0.749272 | −0.374636 | − | 0.927172i | \(-0.622232\pi\) | ||||
−0.374636 | + | 0.927172i | \(0.622232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.72452 | −0.350064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.2299 | 1.40991 | 0.704956 | − | 0.709251i | \(-0.250967\pi\) | ||||
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.0734 | −0.675105 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.11039 | 0.314701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.63428 | −0.186681 | −0.0933403 | − | 0.995634i | \(-0.529754\pi\) | ||||
−0.0933403 | + | 0.995634i | \(0.529754\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.9050 | −1.48085 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.54467 | 0.232222 | 0.116111 | − | 0.993236i | \(-0.462957\pi\) | ||||
0.116111 | + | 0.993236i | \(0.462957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.490211 | −0.0249188 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.7832 | 1.61147 | 0.805735 | − | 0.592276i | \(-0.201770\pi\) | ||||
0.805735 | + | 0.592276i | \(0.201770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.4719 | −1.74332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38.0597 | 1.91986 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.56677 | 0.330410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.9868 | 1.30424 | 0.652119 | − | 0.758117i | \(-0.273880\pi\) | ||||
0.652119 | + | 0.758117i | \(0.273880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.66484 | 0.482639 | 0.241319 | − | 0.970446i | \(-0.422420\pi\) | ||||
0.241319 | + | 0.970446i | \(0.422420\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0902 | 0.652071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.59083 | −0.377191 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.56089 | −0.0773707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.7803 | −1.07697 | −0.538484 | − | 0.842636i | \(-0.681003\pi\) | ||||
−0.538484 | + | 0.842636i | \(0.681003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.6591 | −0.871059 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.90378 | −0.437069 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.6006 | −0.910875 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5329 | −0.514567 | −0.257284 | − | 0.966336i | \(-0.582827\pi\) | ||||
−0.257284 | + | 0.966336i | \(0.582827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.9908 | −1.21798 | −0.608989 | − | 0.793179i | \(-0.708425\pi\) | ||||
−0.608989 | + | 0.793179i | \(0.708425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.29383 | −0.0629080 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.2806 | 1.17778 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.1962 | −0.492278 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0695 | −0.725871 | −0.362936 | − | 0.931814i | \(-0.618226\pi\) | ||||
−0.362936 | + | 0.931814i | \(0.618226\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.8338 | −1.19344 | −0.596719 | − | 0.802450i | \(-0.703529\pi\) | ||||
−0.596719 | + | 0.802450i | \(0.703529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.06979 | −0.147185 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.1764 | −1.01301 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0653 | −0.575843 | −0.287922 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287922 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.5244 | 0.927631 | 0.463816 | − | 0.885932i | \(-0.346480\pi\) | ||||
0.463816 | + | 0.885932i | \(0.346480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.93713 | −0.0918286 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.1507 | −1.99366 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7773 | 1.59405 | 0.797025 | − | 0.603947i | \(-0.206406\pi\) | ||||
0.797025 | + | 0.603947i | \(0.206406\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.5077 | −0.730229 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.1346 | 0.664099 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.1651 | 1.17717 | 0.588587 | − | 0.808434i | \(-0.299684\pi\) | ||||
0.588587 | + | 0.808434i | \(0.299684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.9183 | 1.06974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8826 | 0.879450 | 0.439725 | − | 0.898133i | \(-0.355076\pi\) | ||||
0.439725 | + | 0.898133i | \(0.355076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.6129 | −1.56213 | −0.781063 | − | 0.624452i | \(-0.785322\pi\) | ||||
−0.781063 | + | 0.624452i | \(0.785322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.57639 | −0.304973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.41698 | −0.250668 | −0.125334 | − | 0.992115i | \(-0.540000\pi\) | ||||
−0.125334 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.9835 | 1.28941 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.13050 | −0.0519803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.9158 | 0.684383 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.1746 | −0.465864 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.71791 | 0.124185 | 0.0620923 | − | 0.998070i | \(-0.480223\pi\) | ||||
0.0620923 | + | 0.998070i | \(0.480223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.24403 | 0.102319 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1286 | −0.459914 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.2662 | −1.05429 | −0.527146 | − | 0.849775i | \(-0.676738\pi\) | ||||
−0.527146 | + | 0.849775i | \(0.676738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.2167 | 1.63778 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.9678 | −0.675489 | −0.337745 | − | 0.941238i | \(-0.609664\pi\) | ||||
−0.337745 | + | 0.941238i | \(0.609664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0284 | 0.541733 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.10559 | 0.0496927 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.515029 | −0.0230559 | −0.0115279 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115279 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.6495 | −0.922551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.8400 | 1.86555 | 0.932777 | − | 0.360454i | \(-0.117378\pi\) | ||||
0.932777 | + | 0.360454i | \(0.117378\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.168128 | 0.00748158 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.7686 | −0.478249 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.01412 | 0.355220 | 0.177610 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177610 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.0789 | 0.621600 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.73608 | −0.120566 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.98375 | −0.131225 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.8292 | 0.870404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.4024 | −0.806225 | −0.403113 | − | 0.915150i | \(-0.632072\pi\) | ||||
−0.403113 | + | 0.915150i | \(0.632072\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2378 | −1.54084 | −0.770420 | − | 0.637537i | \(-0.779953\pi\) | ||||
−0.770420 | + | 0.637537i | \(0.779953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.7684 | 1.12249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.9177 | 0.779032 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.12483 | 0.0488136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2947 | 0.965692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.62136 | −0.113331 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.855014 | 0.0368966 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.251108 | −0.0107960 | −0.00539798 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539798 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.76724 | −0.290410 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.8815 | 0.594618 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7113 | 1.09933 | 0.549667 | − | 0.835384i | \(-0.314754\pi\) | ||||
0.549667 | + | 0.835384i | \(0.314754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.70300 | 0.371435 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.38918 | 0.314790 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.12738 | −0.0478544 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.301062 | 0.0127564 | 0.00637821 | − | 0.999980i | \(-0.497970\pi\) | ||||
0.00637821 | + | 0.999980i | \(0.497970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.62527 | 0.0687414 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0715 | −0.847419 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7917 | 0.749831 | 0.374916 | − | 0.927059i | \(-0.377672\pi\) | ||||
0.374916 | + | 0.927059i | \(0.377672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.9057 | 0.585018 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9777 | 1.17289 | 0.586444 | − | 0.809990i | \(-0.300527\pi\) | ||||
0.586444 | + | 0.809990i | \(0.300527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1484 | 0.466548 | 0.233274 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233274 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9051 | 0.622671 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.8208 | −1.20191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.1874 | −0.590628 | −0.295314 | − | 0.955400i | \(-0.595424\pi\) | ||||
−0.295314 | + | 0.955400i | \(0.595424\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.2606 | 1.13291 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.4641 | −0.971785 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.58946 | −0.0657162 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.2391 | 1.16555 | 0.582776 | − | 0.812633i | \(-0.301967\pi\) | ||||
0.582776 | + | 0.812633i | \(0.301967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8298 | 0.652254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.7143 | −0.605265 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.2663 | −0.791172 | −0.395586 | − | 0.918429i | \(-0.629459\pi\) | ||||
−0.395586 | + | 0.918429i | \(0.629459\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.5178 | 1.69921 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.52719 | −0.307553 | −0.153776 | − | 0.988106i | \(-0.549144\pi\) | ||||
−0.153776 | + | 0.988106i | \(0.549144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1854 | −0.497054 | −0.248527 | − | 0.968625i | \(-0.579946\pi\) | ||||
−0.248527 | + | 0.968625i | \(0.579946\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.6728 | −0.434629 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.18509 | −0.210804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.6674 | −1.24475 | −0.622375 | − | 0.782719i | \(-0.713832\pi\) | ||||
−0.622375 | + | 0.782719i | \(0.713832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.28961 | 0.173539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.45027 | 0.300914 | 0.150457 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150457 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.2006 | −0.451653 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.6076 | −0.910150 | −0.455075 | − | 0.890453i | \(-0.650387\pi\) | ||||
−0.455075 | + | 0.890453i | \(0.650387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.8790 | −0.999970 | −0.499985 | − | 0.866034i | \(-0.666661\pi\) | ||||
−0.499985 | + | 0.866034i | \(0.666661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.2038 | −1.09165 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8280 | 0.713120 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.3301 | −0.492417 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.41743 | 0.176134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0770 | 0.799253 | 0.399626 | − | 0.916678i | \(-0.369140\pi\) | ||||
0.399626 | + | 0.916678i | \(0.369140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.7699 | 1.42173 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3913 | −0.412366 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.95427 | 0.195988 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.03428 | −0.198842 | −0.0994210 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994210 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.881508 | −0.0347633 | −0.0173816 | − | 0.999849i | \(-0.505533\pi\) | ||||
−0.0173816 | + | 0.999849i | \(0.505533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.816515 | −0.0321502 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.7718 | 0.541424 | 0.270712 | − | 0.962660i | \(-0.412741\pi\) | ||||
0.270712 | + | 0.962660i | \(0.412741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.59402 | 0.101824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.82663 | 0.345413 | 0.172706 | − | 0.984973i | \(-0.444749\pi\) | ||||
0.172706 | + | 0.984973i | \(0.444749\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6824 | 0.534616 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.28890 | 0.323381 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.1835 | 0.825191 | 0.412596 | − | 0.910914i | \(-0.364622\pi\) | ||||
0.412596 | + | 0.910914i | \(0.364622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.19143 | −0.240819 | −0.120409 | − | 0.992724i | \(-0.538421\pi\) | ||||
−0.120409 | + | 0.992724i | \(0.538421\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.8559 | 1.12067 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2776 | −0.552831 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.7056 | −1.14849 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.0703 | 0.774807 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.31626 | 0.0892853 | 0.0446426 | − | 0.999003i | \(-0.485785\pi\) | ||||
0.0446426 | + | 0.999003i | \(0.485785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.1612 | 0.737515 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.0325 | 0.654612 | 0.327306 | − | 0.944918i | \(-0.393859\pi\) | ||||
0.327306 | + | 0.944918i | \(0.393859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.2959 | −1.19926 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.2110 | −0.773351 | −0.386675 | − | 0.922216i | \(-0.626377\pi\) | ||||
−0.386675 | + | 0.922216i | \(0.626377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.34842 | −0.242561 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.57840 | 0.212829 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.7334 | 1.28514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.1929 | 0.654050 | 0.327025 | − | 0.945016i | \(-0.393954\pi\) | ||||
0.327025 | + | 0.945016i | \(0.393954\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.68689 | −0.253648 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.8877 | 1.66236 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.77337 | 0.142722 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.40632 | −0.355272 | −0.177636 | − | 0.984096i | \(-0.556845\pi\) | ||||
−0.177636 | + | 0.984096i | \(0.556845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.71366 | 0.102348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.15505 | −0.0811639 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.0010 | −1.65249 | −0.826247 | − | 0.563308i | \(-0.809528\pi\) | ||||
−0.826247 | + | 0.563308i | \(0.809528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.71128 | 0.289196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.5868 | −1.14548 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.66553 | −0.137083 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9839 | 0.484893 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.0370 | −1.34395 | −0.671977 | − | 0.740572i | \(-0.734554\pi\) | ||||
−0.671977 | + | 0.740572i | \(0.734554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1211 | 0.599548 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.0566 | 0.373491 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.02401 | −0.0750663 | −0.0375332 | − | 0.999295i | \(-0.511950\pi\) | ||||
−0.0375332 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.0408 | 0.594103 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.19937 | 0.118333 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.4651 | −1.90091 | −0.950454 | − | 0.310866i | \(-0.899381\pi\) | ||||
−0.950454 | + | 0.310866i | \(0.899381\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.6129 | −0.906629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.89999 | −0.180249 | −0.0901244 | − | 0.995931i | \(-0.528726\pi\) | ||||
−0.0901244 | + | 0.995931i | \(0.528726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.7265 | 0.651198 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.94313 | 0.364778 | 0.182389 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182389 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1531 | −0.555167 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.4556 | −0.382551 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.662823 | −0.0241868 | −0.0120934 | − | 0.999927i | \(-0.503850\pi\) | ||||
−0.0120934 | + | 0.999927i | \(0.503850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.1482 | −1.31731 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.08135 | 0.184929 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.7680 | 0.791170 | 0.395585 | − | 0.918429i | \(-0.370542\pi\) | ||||
0.395585 | + | 0.918429i | \(0.370542\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.8246 | 0.864779 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.4916 | 0.960321 | 0.480160 | − | 0.877181i | \(-0.340578\pi\) | ||||
0.480160 | + | 0.877181i | \(0.340578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.12889 | −0.113125 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.72931 | −0.134658 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5156 | 0.487386 | 0.243693 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243693 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.06153 | −0.110258 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.61625 | −0.166035 | −0.0830175 | − | 0.996548i | \(-0.526456\pi\) | ||||
−0.0830175 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5441 | 0.773886 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.9606 | 0.965964 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4252 | 0.408827 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.49233 | 0.339228 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0600 | 0.359057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.76522 | −0.0985695 | −0.0492848 | − | 0.998785i | \(-0.515694\pi\) | ||||
−0.0492848 | + | 0.998785i | \(0.515694\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −57.1753 | −2.03550 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.8543 | −1.02465 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.9473 | −0.601058 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −55.1217 | −1.95251 | −0.976255 | − | 0.216626i | \(-0.930495\pi\) | ||||
−0.976255 | + | 0.216626i | \(0.930495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.44418 | 0.298734 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.27475 | −0.0803742 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1154 | 0.674567 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.3429 | −0.927313 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.2686 | 0.747764 | 0.373882 | − | 0.927476i | \(-0.378027\pi\) | ||||
0.373882 | + | 0.927476i | \(0.378027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.9239 | −1.15611 | −0.578057 | − | 0.815996i | \(-0.696189\pi\) | ||||
−0.578057 | + | 0.815996i | \(0.696189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.7020 | −1.53270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.0198 | 0.456065 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.96540 | 0.0687607 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.55342 | −0.124015 | −0.0620077 | − | 0.998076i | \(-0.519750\pi\) | ||||
−0.0620077 | + | 0.998076i | \(0.519750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2770 | 0.881101 | 0.440550 | − | 0.897728i | \(-0.354783\pi\) | ||||
0.440550 | + | 0.897728i | \(0.354783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.7811 | −0.584242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.6746 | −0.718925 | −0.359463 | − | 0.933160i | \(-0.617040\pi\) | ||||
−0.359463 | + | 0.933160i | \(0.617040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.8563 | 0.724368 | 0.362184 | − | 0.932107i | \(-0.382031\pi\) | ||||
0.362184 | + | 0.932107i | \(0.382031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.7600 | 0.962983 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.42346 | −0.256899 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.3353 | 0.702892 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5672 | −0.641011 | −0.320506 | − | 0.947247i | \(-0.603853\pi\) | ||||
−0.320506 | + | 0.947247i | \(0.603853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0181 | −0.828209 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.12095 | 0.107491 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.87129 | −0.133176 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.2728 | −2.17152 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.24343 | −0.179742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.8522 | −1.22756 | −0.613778 | − | 0.789479i | \(-0.710351\pi\) | ||||
−0.613778 | + | 0.789479i | \(0.710351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.92211 | −0.0657347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4045 | 0.389571 | 0.194785 | − | 0.980846i | \(-0.437599\pi\) | ||||
0.194785 | + | 0.980846i | \(0.437599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.8781 | 0.848829 | 0.424414 | − | 0.905468i | \(-0.360480\pi\) | ||||
0.424414 | + | 0.905468i | \(0.360480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.9455 | −1.76825 | −0.884123 | − | 0.467254i | \(-0.845243\pi\) | ||||
−0.884123 | + | 0.467254i | \(0.845243\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.12855 | 0.242378 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.5525 | 0.799885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.7833 | 0.603257 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3850 | 1.19897 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.8939 | −0.402546 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8259 | −0.669473 | −0.334736 | − | 0.942312i | \(-0.608647\pi\) | ||||
−0.334736 | + | 0.942312i | \(0.608647\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 56.0112 | 1.88921 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.5107 | 1.53329 | 0.766647 | − | 0.642069i | \(-0.221924\pi\) | ||||
0.766647 | + | 0.642069i | \(0.221924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.4490 | −0.519901 | −0.259951 | − | 0.965622i | \(-0.583706\pi\) | ||||
−0.259951 | + | 0.965622i | \(0.583706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.87357 | 0.0629792 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.38768 | −0.147324 | −0.0736619 | − | 0.997283i | \(-0.523469\pi\) | ||||
−0.0736619 | + | 0.997283i | \(0.523469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5565 | −0.688670 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.18734 | 0.173588 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.307376 | 0.0102744 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.2516 | −1.14363 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6728 | 0.355957 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.4049 | 2.21227 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.43281 | −0.0808694 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0287 | 0.598633 | 0.299317 | − | 0.954154i | \(-0.403241\pi\) | ||||
0.299317 | + | 0.954154i | \(0.403241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.197430 | 0.00654835 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.65142 | −0.187240 | −0.0936200 | − | 0.995608i | \(-0.529844\pi\) | ||||
−0.0936200 | + | 0.995608i | \(0.529844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1121 | −0.797995 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.4961 | 0.479225 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.2298 | 1.16212 | 0.581062 | − | 0.813859i | \(-0.302637\pi\) | ||||
0.581062 | + | 0.813859i | \(0.302637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1648 | 0.697403 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.4256 | −0.540654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.69325 | 0.121433 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.21295 | −0.105527 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.6403 | −0.677186 | −0.338593 | − | 0.940933i | \(-0.609951\pi\) | ||||
−0.338593 | + | 0.940933i | \(0.609951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.84243 | 0.0930571 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.21567 | −0.235978 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1498 | −0.527590 | −0.263795 | − | 0.964579i | \(-0.584974\pi\) | ||||
−0.263795 | + | 0.964579i | \(0.584974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.3776 | −1.25241 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.5448 | 0.800137 | 0.400068 | − | 0.916485i | \(-0.368986\pi\) | ||||
0.400068 | + | 0.916485i | \(0.368986\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.0941 | −1.69642 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.3006 | −1.56956 | −0.784780 | − | 0.619775i | \(-0.787224\pi\) | ||||
−0.784780 | + | 0.619775i | \(0.787224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.4814 | −0.892082 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.1829 | 1.46515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1097 | 0.359877 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.35838 | 0.173393 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.31323 | −0.268728 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.13579 | −0.262445 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.07823 | −0.0991946 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.80013 | 0.315477 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.4719 | −1.68738 | −0.843691 | − | 0.536830i | \(-0.819622\pi\) | ||||
−0.843691 | + | 0.536830i | \(0.819622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.8949 | 1.12099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.4555 | 1.36246 | 0.681231 | − | 0.732069i | \(-0.261445\pi\) | ||||
0.681231 | + | 0.732069i | \(0.261445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.1254 | 0.772632 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.3517 | −0.875060 | −0.437530 | − | 0.899204i | \(-0.644147\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.24589 | −0.167659 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.3009 | 0.520448 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.0340 | −1.21310 | −0.606548 | − | 0.795047i | \(-0.707446\pi\) | ||||
−0.606548 | + | 0.795047i | \(0.707446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.28977 | −0.168546 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.79761 | −0.120757 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.1820 | 1.11759 | 0.558796 | − | 0.829305i | \(-0.311263\pi\) | ||||
0.558796 | + | 0.829305i | \(0.311263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.9138 | 0.568478 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.9256 | 0.473172 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1418 | −0.416205 | −0.208103 | − | 0.978107i | \(-0.566729\pi\) | ||||
−0.208103 | + | 0.978107i | \(0.566729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.48604 | 0.110294 |
(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 | 6272.2.a.bd.1.4 | 4 | ||
4.3 | odd | 2 | 6272.2.a.bt.1.1 | 4 | |||
7.2 | even | 3 | 896.2.i.e.641.1 | yes | 8 | ||
7.4 | even | 3 | 896.2.i.e.513.1 | yes | 8 | ||
7.6 | odd | 2 | 6272.2.a.bq.1.1 | 4 | |||
8.3 | odd | 2 | 6272.2.a.z.1.4 | 4 | |||
8.5 | even | 2 | 6272.2.a.bp.1.1 | 4 | |||
28.11 | odd | 6 | 896.2.i.b.513.4 | ✓ | 8 | ||
28.23 | odd | 6 | 896.2.i.b.641.4 | yes | 8 | ||
28.27 | even | 2 | 6272.2.a.ba.1.4 | 4 | |||
56.11 | odd | 6 | 896.2.i.g.513.1 | yes | 8 | ||
56.13 | odd | 2 | 6272.2.a.be.1.4 | 4 | |||
56.27 | even | 2 | 6272.2.a.bu.1.1 | 4 | |||
56.37 | even | 6 | 896.2.i.d.641.4 | yes | 8 | ||
56.51 | odd | 6 | 896.2.i.g.641.1 | yes | 8 | ||
56.53 | even | 6 | 896.2.i.d.513.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.i.b.513.4 | ✓ | 8 | 28.11 | odd | 6 | ||
896.2.i.b.641.4 | yes | 8 | 28.23 | odd | 6 | ||
896.2.i.d.513.4 | yes | 8 | 56.53 | even | 6 | ||
896.2.i.d.641.4 | yes | 8 | 56.37 | even | 6 | ||
896.2.i.e.513.1 | yes | 8 | 7.4 | even | 3 | ||
896.2.i.e.641.1 | yes | 8 | 7.2 | even | 3 | ||
896.2.i.g.513.1 | yes | 8 | 56.11 | odd | 6 | ||
896.2.i.g.641.1 | yes | 8 | 56.51 | odd | 6 | ||
6272.2.a.z.1.4 | 4 | 8.3 | odd | 2 | |||
6272.2.a.ba.1.4 | 4 | 28.27 | even | 2 | |||
6272.2.a.bd.1.4 | 4 | 1.1 | even | 1 | trivial | ||
6272.2.a.be.1.4 | 4 | 56.13 | odd | 2 | |||
6272.2.a.bp.1.1 | 4 | 8.5 | even | 2 | |||
6272.2.a.bq.1.1 | 4 | 7.6 | odd | 2 | |||
6272.2.a.bt.1.1 | 4 | 4.3 | odd | 2 | |||
6272.2.a.bu.1.1 | 4 | 56.27 | even | 2 |