Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8000,2,Mod(1,8000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8000, 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("8000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8000 = 2^{6} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8000.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: | \(63.8803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.26208800000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 34x^{4} - 30x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 4000) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.53025\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8000.1 |
$q$-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 | ||||||||
\(3\) | 0.420293 | 0.242656 | 0.121328 | − | 0.992612i | \(-0.461285\pi\) | ||||
0.121328 | + | 0.992612i | \(0.461285\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.86781 | −1.08393 | −0.541965 | − | 0.840401i | \(-0.682319\pi\) | ||||
−0.541965 | + | 0.840401i | \(0.682319\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82335 | −0.941118 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.96815 | −1.19644 | −0.598221 | − | 0.801331i | \(-0.704126\pi\) | ||||
−0.598221 | + | 0.801331i | \(0.704126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36296 | 0.932718 | 0.466359 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466359 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.80435 | 1.16523 | 0.582613 | − | 0.812750i | \(-0.302030\pi\) | ||||
0.582613 | + | 0.812750i | \(0.302030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.66856 | −1.75929 | −0.879644 | − | 0.475633i | \(-0.842219\pi\) | ||||
−0.879644 | + | 0.475633i | \(0.842219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.20532 | −0.263022 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.44782 | −1.76149 | −0.880746 | − | 0.473588i | \(-0.842959\pi\) | ||||
−0.880746 | + | 0.473588i | \(0.842959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.44752 | −0.471024 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.18632 | −0.777379 | −0.388690 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388690 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.15286 | −1.10509 | −0.552543 | − | 0.833484i | \(-0.686342\pi\) | ||||
−0.552543 | + | 0.833484i | \(0.686342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.66779 | −0.290324 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.44139 | −0.236963 | −0.118481 | − | 0.992956i | \(-0.537803\pi\) | ||||
−0.118481 | + | 0.992956i | \(0.537803\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41343 | 0.226330 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.77568 | 0.277314 | 0.138657 | − | 0.990340i | \(-0.455721\pi\) | ||||
0.138657 | + | 0.990340i | \(0.455721\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.76777 | −1.18457 | −0.592287 | − | 0.805727i | \(-0.701775\pi\) | ||||
−0.592287 | + | 0.805727i | \(0.701775\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0608 | 1.61339 | 0.806693 | − | 0.590971i | \(-0.201255\pi\) | ||||
0.806693 | + | 0.590971i | \(0.201255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.22432 | 0.174903 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.01923 | 0.282749 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4721 | 1.43846 | 0.719229 | − | 0.694773i | \(-0.244495\pi\) | ||||
0.719229 | + | 0.694773i | \(0.244495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.22304 | −0.426902 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.19188 | 0.936303 | 0.468152 | − | 0.883648i | \(-0.344920\pi\) | ||||
0.468152 | + | 0.883648i | \(0.344920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.7546 | 1.88913 | 0.944566 | − | 0.328320i | \(-0.106483\pi\) | ||||
0.944566 | + | 0.328320i | \(0.106483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.09684 | 1.02011 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.39256 | 1.14748 | 0.573742 | − | 0.819036i | \(-0.305491\pi\) | ||||
0.573742 | + | 0.819036i | \(0.305491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.55056 | −0.427437 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5735 | 1.49220 | 0.746098 | − | 0.665837i | \(-0.231925\pi\) | ||||
0.746098 | + | 0.665837i | \(0.231925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.7179 | −1.95668 | −0.978340 | − | 0.207006i | \(-0.933628\pi\) | ||||
−0.978340 | + | 0.207006i | \(0.933628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3799 | 1.29686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.42060 | 0.722374 | 0.361187 | − | 0.932493i | \(-0.382372\pi\) | ||||
0.361187 | + | 0.932493i | \(0.382372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.44139 | 0.826821 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.07230 | −0.446993 | −0.223497 | − | 0.974705i | \(-0.571747\pi\) | ||||
−0.223497 | + | 0.974705i | \(0.571747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.75948 | −0.188636 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.854102 | −0.0905346 | −0.0452673 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452673 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.64433 | −1.01100 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.58600 | −0.268156 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.04768 | −0.512514 | −0.256257 | − | 0.966609i | \(-0.582489\pi\) | ||||
−0.256257 | + | 0.966609i | \(0.582489\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.2035 | 1.12599 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.39499 | 0.238311 | 0.119155 | − | 0.992876i | \(-0.461981\pi\) | ||||
0.119155 | + | 0.992876i | \(0.461981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.417242 | 0.0411121 | 0.0205561 | − | 0.999789i | \(-0.493456\pi\) | ||||
0.0205561 | + | 0.999789i | \(0.493456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.19382 | 0.308758 | 0.154379 | − | 0.988012i | \(-0.450662\pi\) | ||||
0.154379 | + | 0.988012i | \(0.450662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2647 | 1.17475 | 0.587375 | − | 0.809315i | \(-0.300162\pi\) | ||||
0.587375 | + | 0.809315i | \(0.300162\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.605805 | −0.0575005 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.7736 | −1.48386 | −0.741928 | − | 0.670480i | \(-0.766088\pi\) | ||||
−0.741928 | + | 0.670480i | \(0.766088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.49483 | −0.877798 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.7780 | −1.26302 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.74621 | 0.431474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.746305 | 0.0672920 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2202 | −0.906898 | −0.453449 | − | 0.891282i | \(-0.649807\pi\) | ||||
−0.453449 | + | 0.891282i | \(0.649807\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.26474 | −0.287444 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.10177 | 0.707855 | 0.353928 | − | 0.935273i | \(-0.384846\pi\) | ||||
0.353928 | + | 0.935273i | \(0.384846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.9919 | 1.90694 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.3937 | −1.05887 | −0.529433 | − | 0.848352i | \(-0.677595\pi\) | ||||
−0.529433 | + | 0.848352i | \(0.677595\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4910 | 0.889837 | 0.444918 | − | 0.895571i | \(-0.353233\pi\) | ||||
0.444918 | + | 0.895571i | \(0.353233\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.64878 | 0.391498 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3447 | −1.11594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.514575 | 0.0424414 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.15167 | −0.340118 | −0.170059 | − | 0.985434i | \(-0.554396\pi\) | ||||
−0.170059 | + | 0.985434i | \(0.554396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.91651 | −0.725616 | −0.362808 | − | 0.931864i | \(-0.618182\pi\) | ||||
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5644 | −1.09662 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.7486 | −1.09726 | −0.548630 | − | 0.836065i | \(-0.684850\pi\) | ||||
−0.548630 | + | 0.836065i | \(0.684850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.40137 | 0.349051 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.2267 | 1.90933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.92450 | 0.699021 | 0.349510 | − | 0.936932i | \(-0.386348\pi\) | ||||
0.349510 | + | 0.936932i | \(0.386348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.91177 | 0.302702 | 0.151351 | − | 0.988480i | \(-0.451638\pi\) | ||||
0.151351 | + | 0.988480i | \(0.451638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.69048 | −0.130037 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.6510 | 1.65570 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8658 | 0.826115 | 0.413058 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413058 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.02270 | 0.227200 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.3833 | −1.59826 | −0.799132 | − | 0.601156i | \(-0.794707\pi\) | ||||
−0.799132 | + | 0.601156i | \(0.794707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.93253 | 0.589620 | 0.294810 | − | 0.955556i | \(-0.404744\pi\) | ||||
0.294810 | + | 0.955556i | \(0.404744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.20126 | 0.458410 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.0644 | −1.39413 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.01900 | 0.510557 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4662 | 1.11910 | 0.559549 | − | 0.828797i | \(-0.310974\pi\) | ||||
0.559549 | + | 0.828797i | \(0.310974\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.37989 | 0.531216 | 0.265608 | − | 0.964081i | \(-0.414427\pi\) | ||||
0.265608 | + | 0.964081i | \(0.414427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.13992 | 0.579945 | 0.289973 | − | 0.957035i | \(-0.406354\pi\) | ||||
0.289973 | + | 0.957035i | \(0.406354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5658 | −1.03254 | −0.516272 | − | 0.856424i | \(-0.672681\pi\) | ||||
−0.516272 | + | 0.856424i | \(0.672681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.94763 | 0.278444 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0056 | 0.842625 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.8512 | 1.65777 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.4300 | 2.10489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.476677 | −0.0328158 | −0.0164079 | − | 0.999865i | \(-0.505223\pi\) | ||||
−0.0164079 | + | 0.999865i | \(0.505223\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.28454 | 0.362091 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6452 | 1.19784 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.02641 | −0.474801 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.1569 | 1.08683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1141 | 0.744258 | 0.372129 | − | 0.928181i | \(-0.378628\pi\) | ||||
0.372129 | + | 0.928181i | \(0.378628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.70233 | 0.179360 | 0.0896801 | − | 0.995971i | \(-0.471416\pi\) | ||||
0.0896801 | + | 0.995971i | \(0.471416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.80563 | −0.185401 | −0.0927007 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0927007 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.78289 | 0.314691 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.3322 | −1.46303 | −0.731516 | − | 0.681824i | \(-0.761187\pi\) | ||||
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.69853 | 0.175289 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.88567 | −0.186658 | −0.0933292 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933292 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7061 | 1.07614 | 0.538068 | − | 0.842901i | \(-0.319154\pi\) | ||||
0.538068 | + | 0.842901i | \(0.319154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.4701 | 0.671658 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.7891 | −1.64092 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.71156 | −0.108466 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1914 | −0.895755 | −0.447877 | − | 0.894095i | \(-0.647820\pi\) | ||||
−0.447877 | + | 0.894095i | \(0.647820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.5222 | 2.10752 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0808 | 0.753582 | 0.376791 | − | 0.926298i | \(-0.377028\pi\) | ||||
0.376791 | + | 0.926298i | \(0.377028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.13362 | 0.256851 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.8195 | 0.731606 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.8222 | 0.728989 | 0.364495 | − | 0.931205i | \(-0.381242\pi\) | ||||
0.364495 | + | 0.931205i | \(0.381242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.358973 | −0.0219688 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.19229 | 0.499493 | 0.249746 | − | 0.968311i | \(-0.419653\pi\) | ||||
0.249746 | + | 0.968311i | \(0.419653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.62510 | −0.463192 | −0.231596 | − | 0.972812i | \(-0.574395\pi\) | ||||
−0.231596 | + | 0.972812i | \(0.574395\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.05345 | −0.245326 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.550561 | −0.0330800 | −0.0165400 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165400 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.3717 | 1.04002 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.84107 | −0.408104 | −0.204052 | − | 0.978960i | \(-0.565411\pi\) | ||||
−0.204052 | + | 0.978960i | \(0.565411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1942 | 1.43820 | 0.719098 | − | 0.694909i | \(-0.244555\pi\) | ||||
0.719098 | + | 0.694909i | \(0.244555\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.09230 | −0.300589 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.08178 | 0.357752 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.12150 | −0.124365 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.0273913 | 0.00160022 | 0.000800109 | − | 1.00000i | \(-0.499745\pi\) | ||||
0.000800109 | 1.00000i | \(0.499745\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.71211 | 0.563554 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.4097 | −1.64298 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.2765 | 1.28400 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00660 | 0.0578276 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.1076 | 1.20467 | 0.602337 | − | 0.798242i | \(-0.294237\pi\) | ||||
0.602337 | + | 0.798242i | \(0.294237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.175364 | 0.00997611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.87305 | −0.503145 | −0.251572 | − | 0.967839i | \(-0.580948\pi\) | ||||
−0.251572 | + | 0.967839i | \(0.580948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.3346 | 1.14938 | 0.574691 | − | 0.818371i | \(-0.305122\pi\) | ||||
0.574691 | + | 0.818371i | \(0.305122\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.97502 | −0.110928 | −0.0554641 | − | 0.998461i | \(-0.517664\pi\) | ||||
−0.0554641 | + | 0.998461i | \(0.517664\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.6119 | 0.930089 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.34234 | 0.0749221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.8424 | −2.04997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.15479 | 0.285060 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.7203 | −1.74880 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.9040 | 1.09402 | 0.547010 | − | 0.837126i | \(-0.315766\pi\) | ||||
0.547010 | + | 0.837126i | \(0.315766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.06955 | 0.223010 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.2684 | −1.15857 | −0.579283 | − | 0.815127i | \(-0.696667\pi\) | ||||
−0.579283 | + | 0.815127i | \(0.696667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.62954 | −0.360067 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.4155 | 1.32217 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5635 | 0.894347 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9866 | 0.589790 | 0.294895 | − | 0.955530i | \(-0.404715\pi\) | ||||
0.294895 | + | 0.955530i | \(0.404715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.62529 | 0.354644 | 0.177322 | − | 0.984153i | \(-0.443257\pi\) | ||||
0.177322 | + | 0.984153i | \(0.443257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.23090 | −0.439333 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.4026 | −1.61817 | −0.809083 | − | 0.587694i | \(-0.800036\pi\) | ||||
−0.809083 | + | 0.587694i | \(0.800036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.79078 | −0.306480 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.68779 | 0.511302 | 0.255651 | − | 0.966769i | \(-0.417710\pi\) | ||||
0.255651 | + | 0.966769i | \(0.417710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.8068 | 2.09509 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.99480 | 0.104700 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2186 | 0.898804 | 0.449402 | − | 0.893330i | \(-0.351637\pi\) | ||||
0.449402 | + | 0.893330i | \(0.351637\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.01336 | −0.260985 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.0321 | −1.55919 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6894 | −0.553477 | −0.276738 | − | 0.960945i | \(-0.589254\pi\) | ||||
−0.276738 | + | 0.960945i | \(0.589254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.0784 | −0.725076 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.8980 | 1.74122 | 0.870611 | − | 0.491973i | \(-0.163724\pi\) | ||||
0.870611 | + | 0.491973i | \(0.163724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.29549 | −0.220065 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6524 | 1.05529 | 0.527645 | − | 0.849465i | \(-0.323075\pi\) | ||||
0.527645 | + | 0.849465i | \(0.323075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.9312 | 1.11482 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.9527 | −0.960938 | −0.480469 | − | 0.877012i | \(-0.659534\pi\) | ||||
−0.480469 | + | 0.877012i | \(0.659534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.5863 | −2.05254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.40512 | 0.171766 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6976 | 0.787839 | 0.393920 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393920 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.24306 | 0.462732 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8937 | 1.39295 | 0.696473 | − | 0.717583i | \(-0.254752\pi\) | ||||
0.696473 | + | 0.717583i | \(0.254752\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.6918 | −1.03073 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.71964 | 0.283512 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.12092 | 0.154319 | 0.0771597 | − | 0.997019i | \(-0.475415\pi\) | ||||
0.0771597 | + | 0.997019i | \(0.475415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.20899 | −0.256941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.6249 | −1.01489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.40930 | 0.215924 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.7913 | 1.65081 | 0.825406 | − | 0.564539i | \(-0.190946\pi\) | ||||
0.825406 | + | 0.564539i | \(0.190946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.675381 | −0.0329161 | −0.0164580 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164580 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.2286 | −1.51839 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.3134 | −2.04769 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.60870 | −0.270791 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.65431 | −0.0796854 | −0.0398427 | − | 0.999206i | \(-0.512686\pi\) | ||||
−0.0398427 | + | 0.999206i | \(0.512686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.6394 | −1.08798 | −0.543991 | − | 0.839091i | \(-0.683088\pi\) | ||||
−0.543991 | + | 0.839091i | \(0.683088\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 64.7826 | 3.09897 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.41343 | 0.0674593 | 0.0337297 | − | 0.999431i | \(-0.489261\pi\) | ||||
0.0337297 | + | 0.999431i | \(0.489261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.45670 | −0.164605 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.49780 | −0.118674 | −0.0593370 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593370 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.74492 | −0.0825317 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.8464 | −1.31415 | −0.657076 | − | 0.753824i | \(-0.728207\pi\) | ||||
−0.657076 | + | 0.753824i | \(0.728207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.04615 | −0.331790 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.74755 | −0.176075 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.4721 | 1.23831 | 0.619157 | − | 0.785267i | \(-0.287474\pi\) | ||||
0.619157 | + | 0.785267i | \(0.287474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.7587 | −0.548850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.5873 | 1.14514 | 0.572572 | − | 0.819854i | \(-0.305946\pi\) | ||||
0.572572 | + | 0.819854i | \(0.305946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.4409 | −1.74003 | −0.870013 | − | 0.493030i | \(-0.835889\pi\) | ||||
−0.870013 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.3442 | −1.40416 | −0.702080 | − | 0.712098i | \(-0.747745\pi\) | ||||
−0.702080 | + | 0.712098i | \(0.747745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.9361 | −1.24379 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.77845 | −0.266257 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.8237 | 1.41727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.5665 | −1.35376 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.1338 | −1.74238 | −0.871190 | − | 0.490946i | \(-0.836651\pi\) | ||||
−0.871190 | + | 0.490946i | \(0.836651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.84733 | −0.221019 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1823 | 0.463312 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.55947 | −0.342552 | −0.171276 | − | 0.985223i | \(-0.554789\pi\) | ||||
−0.171276 | + | 0.985223i | \(0.554789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.75091 | 0.169622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7896 | 0.802832 | 0.401416 | − | 0.915896i | \(-0.368518\pi\) | ||||
0.401416 | + | 0.915896i | \(0.368518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.1125 | −0.905823 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.0583 | −1.61743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.598690 | 0.0268011 | 0.0134005 | − | 0.999910i | \(-0.495734\pi\) | ||||
0.0134005 | + | 0.999910i | \(0.495734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.64409 | 0.0734524 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.41037 | 0.196649 | 0.0983243 | − | 0.995154i | \(-0.468652\pi\) | ||||
0.0983243 | + | 0.995154i | \(0.468652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.710498 | −0.0315543 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4779 | 0.686046 | 0.343023 | − | 0.939327i | \(-0.388549\pi\) | ||||
0.343023 | + | 0.939327i | \(0.388549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.9437 | 2.12090 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.7689 | 0.828668 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.8910 | −1.93032 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.56684 | 0.200462 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.1710 | 1.36563 | 0.682813 | − | 0.730593i | \(-0.260756\pi\) | ||||
0.682813 | + | 0.730593i | \(0.260756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1630 | 0.531853 | 0.265926 | − | 0.963993i | \(-0.414322\pi\) | ||||
0.265926 | + | 0.963993i | \(0.414322\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.5605 | −1.28768 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.3657 | 2.10286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.3052 | −0.881172 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.97153 | 0.258656 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.98725 | −0.387829 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.85830 | −0.209262 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9139 | −0.942150 | −0.471075 | − | 0.882093i | \(-0.656134\pi\) | ||||
−0.471075 | + | 0.882093i | \(0.656134\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.33399 | 0.143075 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0638 | −1.54198 | −0.770988 | − | 0.636849i | \(-0.780237\pi\) | ||||
−0.770988 | + | 0.636849i | \(0.780237\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.6575 | −1.77790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.1030 | 1.36763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.4131 | −0.783003 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0363 | −0.764221 | −0.382111 | − | 0.924117i | \(-0.624803\pi\) | ||||
−0.382111 | + | 0.924117i | \(0.624803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.1227 | −1.10487 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.01263 | −0.338293 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.9028 | 0.923094 | 0.461547 | − | 0.887116i | \(-0.347295\pi\) | ||||
0.461547 | + | 0.887116i | \(0.347295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.3405 | −0.896216 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.1921 | −1.22380 | −0.611898 | − | 0.790937i | \(-0.709594\pi\) | ||||
−0.611898 | + | 0.790937i | \(0.709594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.92473 | −0.122396 | −0.0611981 | − | 0.998126i | \(-0.519492\pi\) | ||||
−0.0611981 | + | 0.998126i | \(0.519492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.50035 | 0.271556 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.13656 | 0.130577 | 0.0652884 | − | 0.997866i | \(-0.479203\pi\) | ||||
0.0652884 | + | 0.997866i | \(0.479203\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.10172 | 0.128903 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6786 | 0.484509 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.5550 | −1.72103 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.9848 | 1.27888 | 0.639440 | − | 0.768841i | \(-0.279166\pi\) | ||||
0.639440 | + | 0.768841i | \(0.279166\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.1835 | 1.94416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.42115 | 0.140727 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.4868 | 1.78579 | 0.892894 | − | 0.450267i | \(-0.148671\pi\) | ||||
0.892894 | + | 0.450267i | \(0.148671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.12192 | −0.250553 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.66139 | 0.108741 | 0.0543706 | − | 0.998521i | \(-0.482685\pi\) | ||||
0.0543706 | + | 0.998521i | \(0.482685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5824 | 0.839575 | 0.419788 | − | 0.907622i | \(-0.362105\pi\) | ||||
0.419788 | + | 0.907622i | \(0.362105\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.5185 | −1.07992 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.6471 | −0.756864 | −0.378432 | − | 0.925629i | \(-0.623537\pi\) | ||||
−0.378432 | + | 0.925629i | \(0.623537\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.04585 | 0.204468 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.1971 | 1.50483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.7510 | −1.76709 | −0.883544 | − | 0.468349i | \(-0.844849\pi\) | ||||
−0.883544 | + | 0.468349i | \(0.844849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4891 | −0.583308 | −0.291654 | − | 0.956524i | \(-0.594206\pi\) | ||||
−0.291654 | + | 0.956524i | \(0.594206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.566742 | −0.0227793 | −0.0113896 | − | 0.999935i | \(-0.503626\pi\) | ||||
−0.0113896 | + | 0.999935i | \(0.503626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.6762 | 0.829706 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.44940 | 0.0981332 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.7895 | 0.510764 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.92493 | −0.276115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2178 | 0.884476 | 0.442238 | − | 0.896898i | \(-0.354185\pi\) | ||||
0.442238 | + | 0.896898i | \(0.354185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.200344 | −0.00796296 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.11735 | 0.163135 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.4993 | −1.40433 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8330 | −0.941348 | −0.470674 | − | 0.882307i | \(-0.655989\pi\) | ||||
−0.470674 | + | 0.882307i | \(0.655989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.2951 | −0.839798 | −0.419899 | − | 0.907571i | \(-0.637934\pi\) | ||||
−0.419899 | + | 0.907571i | \(0.637934\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.9099 | 0.900681 | 0.450340 | − | 0.892857i | \(-0.351303\pi\) | ||||
0.450340 | + | 0.892857i | \(0.351303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.5385 | −1.12023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.41616 | 0.290662 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.99112 | 0.0779186 | 0.0389593 | − | 0.999241i | \(-0.487596\pi\) | ||||
0.0389593 | + | 0.999241i | \(0.487596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 47.2005 | 1.84147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.78285 | −0.225268 | −0.112634 | − | 0.993637i | \(-0.535929\pi\) | ||||
−0.112634 | + | 0.993637i | \(0.535929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.3279 | 1.60747 | 0.803734 | − | 0.594989i | \(-0.202844\pi\) | ||||
0.803734 | + | 0.594989i | \(0.202844\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.79061 | 0.263726 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.3653 | 1.36935 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.67120 | 0.180599 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58.5485 | −2.26024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.4583 | 1.13553 | 0.567767 | − | 0.823189i | \(-0.307807\pi\) | ||||
0.567767 | + | 0.823189i | \(0.307807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.43828 | 0.0937107 | 0.0468553 | − | 0.998902i | \(-0.485080\pi\) | ||||
0.0468553 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4758 | 0.555529 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.13577 | 0.0435229 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.7141 | −1.36656 | −0.683280 | − | 0.730156i | \(-0.739447\pi\) | ||||
−0.683280 | + | 0.730156i | \(0.739447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.17919 | −0.0449888 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.2174 | 1.34168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.7401 | 1.20745 | 0.603725 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603725 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.1295 | −1.22050 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.53097 | 0.323134 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.38607 | −0.355014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4576 | 0.697135 | 0.348567 | − | 0.937284i | \(-0.386668\pi\) | ||||
0.348567 | + | 0.937284i | \(0.386668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0534 | 0.416886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.86838 | −0.258312 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2179 | 1.36019 | 0.680096 | − | 0.733123i | \(-0.261938\pi\) | ||||
0.680096 | + | 0.733123i | \(0.261938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.1276 | −0.679839 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.9783 | 1.94660 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.21283 | −0.0452938 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.3058 | −0.421634 | −0.210817 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210817 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.19657 | −0.0445626 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.02147 | 0.261131 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.3501 | 1.08854 | 0.544268 | − | 0.838911i | \(-0.316807\pi\) | ||||
0.544268 | + | 0.838911i | \(0.316807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.9236 | −0.663839 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.3191 | −1.38030 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.95232 | 0.109047 | 0.0545233 | − | 0.998513i | \(-0.482636\pi\) | ||||
0.0545233 | + | 0.998513i | \(0.482636\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.2711 | −1.37290 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.3954 | −0.676685 | −0.338342 | − | 0.941023i | \(-0.609866\pi\) | ||||
−0.338342 | + | 0.941023i | \(0.609866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.8390 | −0.398179 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.3718 | −0.930802 | −0.465401 | − | 0.885100i | \(-0.654090\pi\) | ||||
−0.465401 | + | 0.885100i | \(0.654090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.4976 | 0.420673 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.15926 | −0.334672 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3460 | 1.32628 | 0.663142 | − | 0.748493i | \(-0.269222\pi\) | ||||
0.663142 | + | 0.748493i | \(0.269222\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.96456 | −0.217361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.7736 | −0.864066 | −0.432033 | − | 0.901858i | \(-0.642204\pi\) | ||||
−0.432033 | + | 0.901858i | \(0.642204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.0892 | 0.511404 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.83223 | 0.211418 | 0.105709 | − | 0.994397i | \(-0.466289\pi\) | ||||
0.105709 | + | 0.994397i | \(0.466289\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.1729 | −1.27335 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.1860 | 0.873307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.7572 | 1.07307 | 0.536535 | − | 0.843878i | \(-0.319733\pi\) | ||||
0.536535 | + | 0.843878i | \(0.319733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.07749 | 0.182861 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.27984 | −0.297805 | −0.148903 | − | 0.988852i | \(-0.547574\pi\) | ||||
−0.148903 | + | 0.988852i | \(0.547574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.73733 | 0.0623265 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.6169 | −0.487875 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.8934 | −1.78533 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2461 | 0.366165 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.8995 | −1.70743 | −0.853716 | − | 0.520739i | \(-0.825656\pi\) | ||||
−0.853716 | + | 0.520739i | \(0.825656\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.96880 | 0.176894 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.2357 | 1.60840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.6192 | 1.76203 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.5313 | 0.620992 | 0.310496 | − | 0.950575i | \(-0.399505\pi\) | ||||
0.310496 | + | 0.950575i | \(0.399505\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.1400 | 1.87996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.41143 | 0.0852038 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 66.3390 | 2.34105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.44316 | 0.121205 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.5936 | −0.934981 | −0.467491 | − | 0.883998i | \(-0.654842\pi\) | ||||
−0.467491 | + | 0.883998i | \(0.654842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.1666 | −0.673032 | −0.336516 | − | 0.941678i | \(-0.609249\pi\) | ||||
−0.336516 | + | 0.941678i | \(0.609249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.20477 | −0.112396 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.5676 | 2.08401 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.2294 | 0.951471 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.2705 | −0.498044 | −0.249022 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249022 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.6319 | 0.788898 | 0.394449 | − | 0.918918i | \(-0.370935\pi\) | ||||
0.394449 | + | 0.918918i | \(0.370935\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.2844 | 0.983543 | 0.491772 | − | 0.870724i | \(-0.336349\pi\) | ||||
0.491772 | + | 0.870724i | \(0.336349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.4274 | 0.813666 | 0.406833 | − | 0.913503i | \(-0.366633\pi\) | ||||
0.406833 | + | 0.913503i | \(0.366633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.231397 | −0.00802707 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.88208 | 0.203802 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.0592 | 0.520523 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1936 | 0.800732 | 0.400366 | − | 0.916355i | \(-0.368883\pi\) | ||||
0.400366 | + | 0.916355i | \(0.368883\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4748 | −0.395681 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.87526 | −0.0990291 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6112 | −0.467687 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.1687 | 0.348987 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.1766 | 0.417408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.65086 | −0.193482 | −0.0967408 | − | 0.995310i | \(-0.530842\pi\) | ||||
−0.0967408 | + | 0.995310i | \(0.530842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.8747 | −0.713067 | −0.356534 | − | 0.934283i | \(-0.616041\pi\) | ||||
−0.356534 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1536 | −1.26767 | −0.633833 | − | 0.773470i | \(-0.718519\pi\) | ||||
−0.633833 | + | 0.773470i | \(0.718519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.14026 | −0.0729398 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.5025 | 1.78721 | 0.893603 | − | 0.448858i | \(-0.148169\pi\) | ||||
0.893603 | + | 0.448858i | \(0.148169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.55613 | 0.0868107 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.4779 | −0.864279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5868 | 1.07028 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2514 | 0.482336 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6926 | 1.23902 | 0.619511 | − | 0.784988i | \(-0.287331\pi\) | ||||
0.619511 | + | 0.784988i | \(0.287331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.0115124 | 0.000388303 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.64878 | −0.156621 | −0.0783107 | − | 0.996929i | \(-0.524953\pi\) | ||||
−0.0783107 | + | 0.996929i | \(0.524953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.3640 | −1.49297 | −0.746484 | − | 0.665404i | \(-0.768259\pi\) | ||||
−0.746484 | + | 0.665404i | \(0.768259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.4881 | 1.12442 | 0.562210 | − | 0.826995i | \(-0.309951\pi\) | ||||
0.562210 | + | 0.826995i | \(0.309951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3096 | 0.983014 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.5285 | −0.989243 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −84.8205 | −2.83841 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.9404 | −0.398678 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.7578 | 0.859071 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.3118 | 1.67613 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.36265 | 0.311570 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.9807 | −1.65958 | −0.829792 | − | 0.558073i | \(-0.811541\pi\) | ||||
−0.829792 | + | 0.558073i | \(0.811541\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.76191 | −0.224278 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.7149 | −1.61400 | −0.806999 | − | 0.590553i | \(-0.798910\pi\) | ||||
−0.806999 | + | 0.590553i | \(0.798910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.1595 | 0.534802 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.2343 | −0.767265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0578 | −0.331776 | −0.165888 | − | 0.986145i | \(-0.553049\pi\) | ||||
−0.165888 | + | 0.986145i | \(0.553049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.87137 | 0.292321 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.2841 | 1.39180 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.17802 | −0.0386913 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8662 | 0.651788 | 0.325894 | − | 0.945406i | \(-0.394335\pi\) | ||||
0.325894 | + | 0.945406i | \(0.394335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.38879 | −0.307705 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.72928 | −0.122091 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4155 | −0.405595 | −0.202798 | − | 0.979221i | \(-0.565003\pi\) | ||||
−0.202798 | + | 0.979221i | \(0.565003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.54650 | 0.278905 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.8818 | −1.62610 | −0.813051 | − | 0.582193i | \(-0.802195\pi\) | ||||
−0.813051 | + | 0.582193i | \(0.802195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0006 | −0.488487 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9361 | 0.517854 | 0.258927 | − | 0.965897i | \(-0.416631\pi\) | ||||
0.258927 | + | 0.965897i | \(0.416631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.2216 | −1.82503 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.830087 | −0.0269174 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.3904 | −0.628115 | −0.314058 | − | 0.949404i | \(-0.601689\pi\) | ||||
−0.314058 | + | 0.949404i | \(0.601689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.98188 | 0.225692 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.5428 | 1.14774 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.85767 | 0.221215 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.01728 | −0.290578 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.6503 | −1.24291 | −0.621455 | − | 0.783450i | \(-0.713458\pi\) | ||||
−0.621455 | + | 0.783450i | \(0.713458\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.4846 | −0.497438 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.27436 | 0.265537 | 0.132768 | − | 0.991147i | \(-0.457613\pi\) | ||||
0.132768 | + | 0.991147i | \(0.457613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.0862 | −0.964520 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.0832 | −1.21839 | −0.609196 | − | 0.793020i | \(-0.708508\pi\) | ||||
−0.609196 | + | 0.793020i | \(0.708508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.38920 | 0.108319 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.6277 | −1.10558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.2844 | −0.902131 | −0.451065 | − | 0.892491i | \(-0.648956\pi\) | ||||
−0.451065 | + | 0.892491i | \(0.648956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.3318 | −0.424356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 65.6208 | 2.08662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.7331 | −0.944502 | −0.472251 | − | 0.881464i | \(-0.656558\pi\) | ||||
−0.472251 | + | 0.881464i | \(0.656558\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.36549 | 0.265471 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.3219 | 0.675271 | 0.337635 | − | 0.941277i | \(-0.390373\pi\) | ||||
0.337635 | + | 0.941277i | \(0.390373\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.52782 | 0.111615 |
(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 | 8000.2.a.bz.1.5 | 8 | ||
4.3 | odd | 2 | inner | 8000.2.a.bz.1.4 | 8 | ||
5.4 | even | 2 | 8000.2.a.by.1.4 | 8 | |||
8.3 | odd | 2 | 4000.2.a.o.1.5 | yes | 8 | ||
8.5 | even | 2 | 4000.2.a.o.1.4 | ✓ | 8 | ||
20.19 | odd | 2 | 8000.2.a.by.1.5 | 8 | |||
40.3 | even | 4 | 4000.2.c.i.1249.9 | 16 | |||
40.13 | odd | 4 | 4000.2.c.i.1249.8 | 16 | |||
40.19 | odd | 2 | 4000.2.a.p.1.4 | yes | 8 | ||
40.27 | even | 4 | 4000.2.c.i.1249.7 | 16 | |||
40.29 | even | 2 | 4000.2.a.p.1.5 | yes | 8 | ||
40.37 | odd | 4 | 4000.2.c.i.1249.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4000.2.a.o.1.4 | ✓ | 8 | 8.5 | even | 2 | ||
4000.2.a.o.1.5 | yes | 8 | 8.3 | odd | 2 | ||
4000.2.a.p.1.4 | yes | 8 | 40.19 | odd | 2 | ||
4000.2.a.p.1.5 | yes | 8 | 40.29 | even | 2 | ||
4000.2.c.i.1249.7 | 16 | 40.27 | even | 4 | |||
4000.2.c.i.1249.8 | 16 | 40.13 | odd | 4 | |||
4000.2.c.i.1249.9 | 16 | 40.3 | even | 4 | |||
4000.2.c.i.1249.10 | 16 | 40.37 | odd | 4 | |||
8000.2.a.by.1.4 | 8 | 5.4 | even | 2 | |||
8000.2.a.by.1.5 | 8 | 20.19 | odd | 2 | |||
8000.2.a.bz.1.4 | 8 | 4.3 | odd | 2 | inner | ||
8000.2.a.bz.1.5 | 8 | 1.1 | even | 1 | trivial |