Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.20822 | −1.85227 | −0.926135 | − | 0.377193i | \(-0.876889\pi\) | ||||
−0.926135 | + | 0.377193i | \(0.876889\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09579 | 0.937268 | 0.468634 | − | 0.883392i | \(-0.344746\pi\) | ||||
0.468634 | + | 0.883392i | \(0.344746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61648 | −0.610971 | −0.305486 | − | 0.952197i | \(-0.598819\pi\) | ||||
−0.305486 | + | 0.952197i | \(0.598819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.29270 | 2.43090 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.47682 | −1.04830 | −0.524150 | − | 0.851626i | \(-0.675617\pi\) | ||||
−0.524150 | + | 0.851626i | \(0.675617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.62727 | −0.728673 | −0.364337 | − | 0.931267i | \(-0.618704\pi\) | ||||
−0.364337 | + | 0.931267i | \(0.618704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.72378 | −1.73607 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.87015 | −0.938650 | −0.469325 | − | 0.883025i | \(-0.655503\pi\) | ||||
−0.469325 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.93031 | −1.13109 | −0.565545 | − | 0.824717i | \(-0.691334\pi\) | ||||
−0.565545 | + | 0.824717i | \(0.691334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.18602 | 1.13168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23385 | −0.465789 | −0.232895 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232895 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.607646 | −0.121529 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.7719 | −2.65041 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.77456 | 1.62939 | 0.814697 | − | 0.579886i | \(-0.196903\pi\) | ||||
0.814697 | + | 0.579886i | \(0.196903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.42683 | 0.615477 | 0.307738 | − | 0.951471i | \(-0.400428\pi\) | ||||
0.307738 | + | 0.951471i | \(0.400428\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.1544 | 1.94173 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.38781 | −0.572644 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.38186 | 0.227177 | 0.113589 | − | 0.993528i | \(-0.463765\pi\) | ||||
0.113589 | + | 0.993528i | \(0.463765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.42886 | 1.34970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.103622 | −0.0161830 | −0.00809148 | − | 0.999967i | \(-0.502576\pi\) | ||||
−0.00809148 | + | 0.999967i | \(0.502576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.46770 | 1.13881 | 0.569407 | − | 0.822056i | \(-0.307173\pi\) | ||||
0.569407 | + | 0.822056i | \(0.307173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.2840 | 2.27840 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4671 | −1.52678 | −0.763392 | − | 0.645936i | \(-0.776467\pi\) | ||||
−0.763392 | + | 0.645936i | \(0.776467\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.38700 | −0.626714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.4163 | 1.73863 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.46619 | 0.338757 | 0.169379 | − | 0.985551i | \(-0.445824\pi\) | ||||
0.169379 | + | 0.985551i | \(0.445824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.28670 | −0.982538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.8175 | 2.09508 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.54740 | 0.722209 | 0.361105 | − | 0.932525i | \(-0.382400\pi\) | ||||
0.361105 | + | 0.932525i | \(0.382400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.5678 | −1.86522 | −0.932608 | − | 0.360891i | \(-0.882473\pi\) | ||||
−0.932608 | + | 0.360891i | \(0.882473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.7885 | −1.48521 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.50621 | −0.682962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8462 | 1.56942 | 0.784710 | − | 0.619864i | \(-0.212812\pi\) | ||||
0.784710 | + | 0.619864i | \(0.212812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.16668 | 0.862767 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.44695 | −0.883791 | −0.441895 | − | 0.897067i | \(-0.645694\pi\) | ||||
−0.441895 | + | 0.897067i | \(0.645694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8578 | −1.38785 | −0.693927 | − | 0.720045i | \(-0.744121\pi\) | ||||
−0.693927 | + | 0.720045i | \(0.744121\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.94946 | 0.225105 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.62020 | 0.640481 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1803 | 1.70791 | 0.853957 | − | 0.520343i | \(-0.174196\pi\) | ||||
0.853957 | + | 0.520343i | \(0.174196\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 22.3054 | 2.47838 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.59809 | −0.614471 | −0.307235 | − | 0.951634i | \(-0.599404\pi\) | ||||
−0.307235 | + | 0.951634i | \(0.599404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.11105 | −0.879767 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −28.1508 | −3.01808 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.398585 | −0.0422500 | −0.0211250 | − | 0.999777i | \(-0.506725\pi\) | ||||
−0.0211250 | + | 0.999777i | \(0.506725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24692 | 0.445198 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.9940 | −1.14003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.3329 | −1.06013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67735 | −0.576447 | −0.288224 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288224 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.3554 | −2.54831 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.19860 | −0.517281 | −0.258640 | − | 0.965974i | \(-0.583274\pi\) | ||||
−0.258640 | + | 0.965974i | \(0.583274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.83961 | 0.181262 | 0.0906310 | − | 0.995885i | \(-0.471112\pi\) | ||||
0.0906310 | + | 0.995885i | \(0.471112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.8688 | 1.06069 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1507 | 1.07798 | 0.538991 | − | 0.842312i | \(-0.318806\pi\) | ||||
0.538991 | + | 0.842312i | \(0.318806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3151 | 1.46692 | 0.733462 | − | 0.679731i | \(-0.237903\pi\) | ||||
0.733462 | + | 0.679731i | \(0.237903\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.43333 | −0.420793 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.47904 | −0.233208 | −0.116604 | − | 0.993178i | \(-0.537201\pi\) | ||||
−0.116604 | + | 0.993178i | \(0.537201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.68168 | −0.436569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.1599 | −1.77133 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.25602 | 0.573488 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.08826 | 0.0989329 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.332441 | 0.0299752 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7525 | −1.05117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8868 | −1.58719 | −0.793597 | − | 0.608444i | \(-0.791794\pi\) | ||||
−0.793597 | + | 0.608444i | \(0.791794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.9581 | −2.10939 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.83716 | −0.509995 | −0.254998 | − | 0.966942i | \(-0.582075\pi\) | ||||
−0.254998 | + | 0.966942i | \(0.582075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.96973 | 0.691063 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −28.8632 | −2.48415 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5744 | 1.67235 | 0.836175 | − | 0.548463i | \(-0.184787\pi\) | ||||
0.836175 | + | 0.548463i | \(0.184787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4351 | 1.30919 | 0.654593 | − | 0.755982i | \(-0.272840\pi\) | ||||
0.654593 | + | 0.755982i | \(0.272840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.5808 | 2.82801 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.13453 | 0.763868 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.3897 | 1.52718 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.0745 | 1.16084 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.9215 | 1.71396 | 0.856980 | − | 0.515350i | \(-0.172338\pi\) | ||||
0.856980 | + | 0.515350i | \(0.172338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.09501 | −0.170489 | −0.0852446 | − | 0.996360i | \(-0.527167\pi\) | ||||
−0.0852446 | + | 0.996360i | \(0.527167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28.2239 | −2.28177 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.18193 | 0.576866 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.40896 | 0.671108 | 0.335554 | − | 0.942021i | \(-0.391076\pi\) | ||||
0.335554 | + | 0.942021i | \(0.391076\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.91209 | −0.627470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.61096 | 0.284584 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3484 | −1.12385 | −0.561925 | − | 0.827188i | \(-0.689939\pi\) | ||||
−0.561925 | + | 0.827188i | \(0.689939\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.3774 | 1.81992 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.46761 | 0.190950 | 0.0954749 | − | 0.995432i | \(-0.469563\pi\) | ||||
0.0954749 | + | 0.995432i | \(0.469563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.09746 | −0.469036 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −35.9553 | −2.74957 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.1780 | −0.773816 | −0.386908 | − | 0.922118i | \(-0.626457\pi\) | ||||
−0.386908 | + | 0.922118i | \(0.626457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.982247 | 0.0742509 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.7973 | −1.33773 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.10429 | 0.232026 | 0.116013 | − | 0.993248i | \(-0.462989\pi\) | ||||
0.116013 | + | 0.993248i | \(0.462989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4282 | 1.29543 | 0.647713 | − | 0.761884i | \(-0.275726\pi\) | ||||
0.647713 | + | 0.761884i | \(0.275726\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 46.7368 | 3.45488 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.89610 | 0.212926 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4558 | 0.983987 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.2621 | 1.61933 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.42790 | −0.537464 | −0.268732 | − | 0.963215i | \(-0.586605\pi\) | ||||
−0.268732 | + | 0.963215i | \(0.586605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.27423 | 0.523611 | 0.261805 | − | 0.965121i | \(-0.415682\pi\) | ||||
0.261805 | + | 0.965121i | \(0.415682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.6652 | 1.26503 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9919 | −0.854390 | −0.427195 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427195 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.2366 | 1.78897 | 0.894487 | − | 0.447093i | \(-0.147541\pi\) | ||||
0.894487 | + | 0.447093i | \(0.147541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −41.2136 | −2.90699 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.1839 | −0.995514 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.217169 | −0.0151678 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.2908 | −1.13229 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.1418 | 1.18572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.08568 | 0.625484 | 0.312742 | − | 0.949838i | \(-0.398753\pi\) | ||||
0.312742 | + | 0.949838i | \(0.398753\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.8915 | 1.63702 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.6508 | 1.06737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.53939 | −0.376039 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 38.0426 | 2.57068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1679 | 0.683969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.97094 | −0.600738 | −0.300369 | − | 0.953823i | \(-0.597110\pi\) | ||||
−0.300369 | + | 0.953823i | \(0.597110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.43138 | −0.295425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.6988 | 1.04197 | 0.520984 | − | 0.853566i | \(-0.325565\pi\) | ||||
0.520984 | + | 0.853566i | \(0.325565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6432 | 1.43023 | 0.715113 | − | 0.699009i | \(-0.246375\pi\) | ||||
0.715113 | + | 0.699009i | \(0.246375\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0309 | −1.18634 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.18830 | 0.405409 | 0.202705 | − | 0.979240i | \(-0.435027\pi\) | ||||
0.202705 | + | 0.979240i | \(0.435027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.9369 | −1.43101 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −48.7017 | −3.16352 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0352 | 0.972546 | 0.486273 | − | 0.873807i | \(-0.338356\pi\) | ||||
0.486273 | + | 0.873807i | \(0.338356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4752 | 0.996845 | 0.498423 | − | 0.866934i | \(-0.333913\pi\) | ||||
0.498423 | + | 0.866934i | \(0.333913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −30.2449 | −1.94021 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.19425 | −0.587399 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.9532 | 0.824195 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.9599 | 1.13816 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.5171 | 0.790070 | 0.395035 | − | 0.918666i | \(-0.370732\pi\) | ||||
0.395035 | + | 0.918666i | \(0.370732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.76668 | 0.488287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.0221 | 1.62956 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0901 | 1.68984 | 0.844918 | − | 0.534896i | \(-0.179649\pi\) | ||||
0.844918 | + | 0.534896i | \(0.179649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.23375 | −0.138799 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 63.9903 | 3.96090 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0150 | 1.17251 | 0.586257 | − | 0.810125i | \(-0.300601\pi\) | ||||
0.586257 | + | 0.810125i | \(0.300601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.16863 | 0.317506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.27875 | 0.0782583 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.6523 | −1.25920 | −0.629598 | − | 0.776921i | \(-0.716780\pi\) | ||||
−0.629598 | + | 0.776921i | \(0.716780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.67779 | −0.527138 | −0.263569 | − | 0.964641i | \(-0.584900\pi\) | ||||
−0.263569 | + | 0.964641i | \(0.584900\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.6251 | −0.824627 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.11267 | 0.127399 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.17921 | 0.431357 | 0.215678 | − | 0.976464i | \(-0.430804\pi\) | ||||
0.215678 | + | 0.976464i | \(0.430804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.9908 | 1.49616 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0419627 | 0.00250328 | 0.00125164 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00125164 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4083 | 0.915927 | 0.457964 | − | 0.888971i | \(-0.348579\pi\) | ||||
0.457964 | + | 0.888971i | \(0.348579\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.1503 | 1.96365 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.167502 | 0.00988733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.02191 | −0.118936 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.2142 | 1.06774 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.84061 | −0.282792 | −0.141396 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141396 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6262 | 0.676904 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 47.8826 | 2.77843 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.86891 | 0.339408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0714 | −0.695783 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.6783 | 0.958143 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.5311 | −1.74821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1532 | 1.03606 | 0.518030 | − | 0.855363i | \(-0.326666\pi\) | ||||
0.518030 | + | 0.855363i | \(0.326666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.90188 | −0.335746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.4671 | 0.990468 | 0.495234 | − | 0.868760i | \(-0.335082\pi\) | ||||
0.495234 | + | 0.868760i | \(0.335082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6243 | −0.713568 | −0.356784 | − | 0.934187i | \(-0.616127\pi\) | ||||
−0.356784 | + | 0.934187i | \(0.616127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.7063 | −1.39204 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.7096 | −1.55633 | −0.778164 | − | 0.628061i | \(-0.783849\pi\) | ||||
−0.778164 | + | 0.628061i | \(0.783849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.5075 | −1.70809 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.7740 | −1.99671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.0810 | 1.06170 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.59645 | 0.0885551 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −49.1344 | −2.71714 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9198 | 0.932821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3622 | −0.899347 | −0.449674 | − | 0.893193i | \(-0.648460\pi\) | ||||
−0.449674 | + | 0.893193i | \(0.648460\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0775 | 0.552245 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.9231 | 1.47097 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4560 | −0.678523 | −0.339261 | − | 0.940692i | \(-0.610177\pi\) | ||||
−0.339261 | + | 0.940692i | \(0.610177\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.95330 | 0.431964 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9145 | −0.645204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4068 | 0.993876 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.0199 | 0.808643 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.6467 | −1.80625 | −0.903126 | − | 0.429376i | \(-0.858734\pi\) | ||||
−0.903126 | + | 0.429376i | \(0.858734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1391 | 0.703319 | 0.351659 | − | 0.936128i | \(-0.385618\pi\) | ||||
0.351659 | + | 0.936128i | \(0.385618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.1826 | 1.93128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.9486 | 1.86013 | 0.930063 | − | 0.367400i | \(-0.119752\pi\) | ||||
0.930063 | + | 0.367400i | \(0.119752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.6073 | −0.828349 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.0707 | −1.06225 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3635 | −0.916410 | −0.458205 | − | 0.888847i | \(-0.651507\pi\) | ||||
−0.458205 | + | 0.888847i | \(0.651507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.30792 | 0.279364 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.49139 | −0.183250 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.8516 | −1.30079 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.15685 | 0.164786 | 0.0823931 | − | 0.996600i | \(-0.473744\pi\) | ||||
0.0823931 | + | 0.996600i | \(0.473744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.755681 | −0.0393392 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.98654 | −0.206971 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.224251 | 0.0116113 | 0.00580564 | − | 0.999983i | \(-0.498152\pi\) | ||||
0.00580564 | + | 0.999983i | \(0.498152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 37.7046 | 1.94706 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.0531 | −1.18730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9179 | 1.27995 | 0.639974 | − | 0.768396i | \(-0.278945\pi\) | ||||
0.639974 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 57.3848 | 2.93991 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9691 | −1.27586 | −0.637931 | − | 0.770093i | \(-0.720210\pi\) | ||||
−0.637931 | + | 0.770093i | \(0.720210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.7788 | 0.600302 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 54.4597 | 2.76834 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.63420 | −0.184261 | −0.0921307 | − | 0.995747i | \(-0.529368\pi\) | ||||
−0.0921307 | + | 0.995747i | \(0.529368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.64533 | 0.437213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.7269 | 0.944648 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.8147 | 1.60077 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.76527 | 0.239162 | 0.119581 | − | 0.992824i | \(-0.461845\pi\) | ||||
0.119581 | + | 0.992824i | \(0.461845\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.5687 | −1.28004 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.9525 | 1.44582 | 0.722909 | − | 0.690944i | \(-0.242805\pi\) | ||||
0.722909 | + | 0.690944i | \(0.242805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00320 | −0.448481 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 46.7475 | 2.32290 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.80449 | −0.238150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.95291 | 0.492140 | 0.246070 | − | 0.969252i | \(-0.420861\pi\) | ||||
0.246070 | + | 0.969252i | \(0.420861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −62.7989 | −3.09764 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.96724 | −0.441249 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.7325 | −0.575924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −49.5192 | −2.42496 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.94987 | −0.486083 | −0.243041 | − | 0.970016i | \(-0.578145\pi\) | ||||
−0.243041 | + | 0.970016i | \(0.578145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.02506 | 0.196170 | 0.0980848 | − | 0.995178i | \(-0.468728\pi\) | ||||
0.0980848 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −76.3335 | −3.71146 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.35168 | 0.114073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.5485 | 1.13959 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −29.3056 | −1.41489 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.83643 | 0.473804 | 0.236902 | − | 0.971534i | \(-0.423868\pi\) | ||||
0.236902 | + | 0.971534i | \(0.423868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.1021 | −1.39856 | −0.699280 | − | 0.714848i | \(-0.746496\pi\) | ||||
−0.699280 | + | 0.714848i | \(0.746496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −58.9982 | −2.82875 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.0135 | 0.526849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8345 | −0.898922 | −0.449461 | − | 0.893300i | \(-0.648384\pi\) | ||||
−0.449461 | + | 0.893300i | \(0.648384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.9931 | −1.52348 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.2229 | −1.48345 | −0.741723 | − | 0.670706i | \(-0.765991\pi\) | ||||
−0.741723 | + | 0.670706i | \(0.765991\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.835353 | −0.0395995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −67.1210 | −3.17471 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.76706 | −0.366550 | −0.183275 | − | 0.983062i | \(-0.558670\pi\) | ||||
−0.183275 | + | 0.983062i | \(0.558670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.360273 | 0.0169646 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.72125 | 0.315792 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.90067 | 0.417270 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.8235 | 0.693416 | 0.346708 | − | 0.937973i | \(-0.387299\pi\) | ||||
0.346708 | + | 0.937973i | \(0.387299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 53.2996 | 2.48781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6348 | 0.728184 | 0.364092 | − | 0.931363i | \(-0.381379\pi\) | ||||
0.364092 | + | 0.931363i | \(0.381379\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1410 | −1.07545 | −0.537727 | − | 0.843119i | \(-0.680717\pi\) | ||||
−0.537727 | + | 0.843119i | \(0.680717\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.0412 | −1.06851 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.4147 | 1.08350 | 0.541751 | − | 0.840539i | \(-0.317762\pi\) | ||||
0.541751 | + | 0.840539i | \(0.317762\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.7657 | −0.958870 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.9778 | −1.24307 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.9638 | −1.19382 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.99588 | 0.137460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.9852 | 0.823485 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8541 | −0.678700 | −0.339350 | − | 0.940660i | \(-0.610207\pi\) | ||||
−0.339350 | + | 0.940660i | \(0.610207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.63053 | −0.165538 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.5848 | −0.527126 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8986 | −0.540285 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4569 | 0.700417 | 0.350209 | − | 0.936672i | \(-0.386111\pi\) | ||||
0.350209 | + | 0.936672i | \(0.386111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.0327 | 2.08167 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.8923 | 1.93570 | 0.967851 | − | 0.251526i | \(-0.0809323\pi\) | ||||
0.967851 | + | 0.251526i | \(0.0809323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.9589 | −1.52943 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −53.1397 | −2.38845 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0378 | 0.539971 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.89126 | 0.174197 | 0.0870984 | − | 0.996200i | \(-0.472241\pi\) | ||||
0.0870984 | + | 0.996200i | \(0.472241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.91666 | −0.353690 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8952 | −0.484830 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.5620 | 0.868780 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.6610 | 1.04875 | 0.524377 | − | 0.851486i | \(-0.324298\pi\) | ||||
0.524377 | + | 0.851486i | \(0.324298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.1679 | 0.847939 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 67.8999 | 2.99786 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.85544 | 0.169891 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.3922 | 1.60053 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.6532 | 1.43332 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3018 | 1.19611 | 0.598057 | − | 0.801454i | \(-0.295940\pi\) | ||||
0.598057 | + | 0.801454i | \(0.295940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.1525 | 1.18730 | 0.593648 | − | 0.804725i | \(-0.297687\pi\) | ||||
0.593648 | + | 0.804725i | \(0.297687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.15127 | −0.137533 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.2624 | −0.577717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.0099 | −0.783041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.4555 | 1.75562 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.272242 | 0.0117921 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3696 | 1.01036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.95927 | −0.429774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.2528 | 0.656984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.15273 | −0.0495597 | −0.0247798 | − | 0.999693i | \(-0.507888\pi\) | ||||
−0.0247798 | + | 0.999693i | \(0.507888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −55.9135 | −2.39948 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.0974 | 1.37490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0762 | −1.28596 | −0.642982 | − | 0.765881i | \(-0.722303\pi\) | ||||
−0.642982 | + | 0.765881i | \(0.722303\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −106.239 | −4.53415 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.2613 | −1.84299 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.5386 | −1.04349 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.29135 | −0.394396 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2479 | 0.434216 | 0.217108 | − | 0.976148i | \(-0.430338\pi\) | ||||
0.217108 | + | 0.976148i | \(0.430338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.6197 | −0.829823 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43.1693 | −1.82261 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.3886 | 1.49145 | 0.745726 | − | 0.666253i | \(-0.232103\pi\) | ||||
0.745726 | + | 0.666253i | \(0.232103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.19555 | −0.218578 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.0562 | −1.51422 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.97851 | −0.0829435 | −0.0414718 | − | 0.999140i | \(-0.513205\pi\) | ||||
−0.0414718 | + | 0.999140i | \(0.513205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0964 | 1.42689 | 0.713444 | − | 0.700712i | \(-0.247134\pi\) | ||||
0.713444 | + | 0.700712i | \(0.247134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.8304 | 0.995528 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.35739 | 0.0566070 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.83972 | −0.243111 | −0.121555 | − | 0.992585i | \(-0.538788\pi\) | ||||
−0.121555 | + | 0.992585i | \(0.538788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.3374 | −0.969868 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.04920 | 0.375424 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.57450 | −0.355119 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −40.1552 | −1.66021 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1983 | 0.420929 | 0.210464 | − | 0.977602i | \(-0.432502\pi\) | ||||
0.210464 | + | 0.977602i | \(0.432502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8953 | −0.696159 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.4728 | 1.58256 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0738 | 0.988591 | 0.494295 | − | 0.869294i | \(-0.335426\pi\) | ||||
0.494295 | + | 0.869294i | \(0.335426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1113 | 0.537512 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −80.9647 | −3.31366 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.84785 | 0.116360 | 0.0581801 | − | 0.998306i | \(-0.481470\pi\) | ||||
0.0581801 | + | 0.998306i | \(0.481470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.9345 | 1.66975 | 0.834876 | − | 0.550439i | \(-0.185539\pi\) | ||||
0.834876 | + | 0.550439i | \(0.185539\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 93.6839 | 3.81510 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.28077 | 0.0927266 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.17608 | −0.0477358 | −0.0238679 | − | 0.999715i | \(-0.507598\pi\) | ||||
−0.0238679 | + | 0.999715i | \(0.507598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.5051 | 1.84396 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.4999 | 1.11253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3582 | 1.14538 | 0.572688 | − | 0.819773i | \(-0.305901\pi\) | ||||
0.572688 | + | 0.819773i | \(0.305901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.696728 | 0.0280948 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.7927 | 0.998115 | 0.499058 | − | 0.866569i | \(-0.333680\pi\) | ||||
0.499058 | + | 0.866569i | \(0.333680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.07443 | −0.0431851 | −0.0215926 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215926 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.7644 | 1.23453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.644304 | 0.0258135 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.5925 | −0.863701 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −54.9947 | −2.19628 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.34803 | −0.213240 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2677 | 1.32437 | 0.662183 | − | 0.749342i | \(-0.269630\pi\) | ||||
0.662183 | + | 0.749342i | \(0.269630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.1489 | −1.15856 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.4870 | −1.48763 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.5258 | 0.456670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −54.3084 | −2.14841 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.3713 | 0.725622 | 0.362811 | − | 0.931863i | \(-0.381817\pi\) | ||||
0.362811 | + | 0.931863i | \(0.381817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.75300 | 0.187440 | 0.0937201 | − | 0.995599i | \(-0.470124\pi\) | ||||
0.0937201 | + | 0.995599i | \(0.470124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −50.2112 | −1.97706 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0508 | −1.26005 | −0.630024 | − | 0.776576i | \(-0.716955\pi\) | ||||
−0.630024 | + | 0.776576i | \(0.716955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2873 | −0.757092 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.7716 | 0.696525 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.3032 | 1.22499 | 0.612494 | − | 0.790475i | \(-0.290166\pi\) | ||||
0.612494 | + | 0.790475i | \(0.290166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2335 | −0.478002 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −86.4756 | −3.37373 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5190 | 0.565579 | 0.282789 | − | 0.959182i | \(-0.408740\pi\) | ||||
0.282789 | + | 0.959182i | \(0.408740\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.4437 | −1.65087 | −0.825434 | − | 0.564498i | \(-0.809070\pi\) | ||||
−0.825434 | + | 0.564498i | \(0.809070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32.6210 | −1.26689 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.7029 | 0.647711 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.6010 | −0.758954 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.7808 | 1.11273 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.6496 | 1.95531 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.425190 | 0.0163899 | 0.00819493 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819493 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.36847 | 0.322103 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.9147 | −1.18815 | −0.594074 | − | 0.804410i | \(-0.702481\pi\) | ||||
−0.594074 | + | 0.804410i | \(0.702481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.17731 | 0.352193 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −50.3654 | −1.93001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.85610 | −0.377133 | −0.188567 | − | 0.982060i | \(-0.560384\pi\) | ||||
−0.188567 | + | 0.982060i | \(0.560384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.0238 | 1.56744 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −69.4364 | −2.64916 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.47934 | −0.246843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.8382 | 1.28727 | 0.643633 | − | 0.765334i | \(-0.277426\pi\) | ||||
0.643633 | + | 0.765334i | \(0.277426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.9864 | 1.55695 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.3487 | 1.22706 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.401031 | 0.0151901 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.8535 | −0.750927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.3540 | −0.995376 | −0.497688 | − | 0.867356i | \(-0.665817\pi\) | ||||
−0.497688 | + | 0.867356i | \(0.665817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.81302 | −0.256958 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 70.3785 | 2.65061 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.40343 | 0.316044 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0631 | −0.828596 | −0.414298 | − | 0.910141i | \(-0.635973\pi\) | ||||
−0.414298 | + | 0.910141i | \(0.635973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 110.705 | 4.15177 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.65501 | −0.286682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1441 | 0.715949 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.2363 | −1.80142 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.335174 | 0.0124999 | 0.00624994 | − | 0.999980i | \(-0.498011\pi\) | ||||
0.00624994 | + | 0.999980i | \(0.498011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.97369 | −0.110746 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −49.6479 | −1.84643 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.33183 | −0.198019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3516 | −1.45947 | −0.729736 | − | 0.683729i | \(-0.760357\pi\) | ||||
−0.729736 | + | 0.683729i | \(0.760357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.1161 | 1.11541 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.9012 | −1.06895 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.3715 | −0.752437 | −0.376219 | − | 0.926531i | \(-0.622776\pi\) | ||||
−0.376219 | + | 0.926531i | \(0.622776\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.4972 | 1.08802 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −44.6641 | −1.64522 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.37625 | −0.234554 | −0.117277 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117277 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.5569 | −1.52663 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.5912 | 0.608671 | 0.304335 | − | 0.952565i | \(-0.401566\pi\) | ||||
0.304335 | + | 0.952565i | \(0.401566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.8472 | 1.60644 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.8252 | −1.49372 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0249 | −0.658615 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0477 | 0.366647 | 0.183324 | − | 0.983053i | \(-0.441314\pi\) | ||||
0.183324 | + | 0.983053i | \(0.441314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.1575 | −1.46342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.39070 | −0.159794 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2007 | 0.879588 | 0.439794 | − | 0.898099i | \(-0.355051\pi\) | ||||
0.439794 | + | 0.898099i | \(0.355051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.9172 | −0.904438 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −53.4090 | −1.93608 | −0.968038 | − | 0.250805i | \(-0.919305\pi\) | ||||
−0.968038 | + | 0.250805i | \(0.919305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.7566 | −0.896248 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −59.1515 | −2.13863 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.5745 | −0.526255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.4710 | −1.49548 | −0.747741 | − | 0.663991i | \(-0.768861\pi\) | ||||
−0.747741 | + | 0.663991i | \(0.768861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −86.9112 | −3.13003 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.112722 | 0.00405433 | 0.00202717 | − | 0.999998i | \(-0.499355\pi\) | ||||
0.00202717 | + | 0.999998i | \(0.499355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.08230 | −0.0747984 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.16638 | 0.257093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.510886 | 0.0183044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8917 | 0.926478 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −120.843 | −4.31857 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6235 | 0.629008 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.29851 | −0.331456 | −0.165728 | − | 0.986172i | \(-0.552997\pi\) | ||||
−0.165728 | + | 0.986172i | \(0.552997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −61.0044 | −2.17181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00731 | 0.142483 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.2735 | 1.35913 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.5821 | −0.588107 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.3907 | 1.39529 | 0.697645 | − | 0.716444i | \(-0.254231\pi\) | ||||
0.697645 | + | 0.716444i | \(0.254231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.5093 | 1.43312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.90676 | −0.102705 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.2275 | 1.45489 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.56784 | 0.266731 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 66.2573 | 2.33237 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.151497 | −0.00532634 | −0.00266317 | − | 0.999996i | \(-0.500848\pi\) | ||||
−0.00266317 | + | 0.999996i | \(0.500848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.359399 | −0.0126202 | −0.00631010 | − | 0.999980i | \(-0.502009\pi\) | ||||
−0.00631010 | + | 0.999980i | \(0.502009\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.8403 | 0.976402 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.0712 | −1.05335 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.8181 | −1.28810 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.9715 | 1.08223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.4715 | −0.958761 | −0.479381 | − | 0.877607i | \(-0.659139\pi\) | ||||
−0.479381 | + | 0.877607i | \(0.659139\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.90142 | 0.240568 | 0.120284 | − | 0.992740i | \(-0.461619\pi\) | ||||
0.120284 | + | 0.992740i | \(0.461619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.77793 | −0.235977 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.0396 | −1.80960 | −0.904798 | − | 0.425842i | \(-0.859978\pi\) | ||||
−0.904798 | + | 0.425842i | \(0.859978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.6045 | −0.472504 | −0.236252 | − | 0.971692i | \(-0.575919\pi\) | ||||
−0.236252 | + | 0.971692i | \(0.575919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.0325 | −0.798989 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.9784 | 0.588265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.17161 | 0.178971 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −47.1941 | −1.63127 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.3083 | 0.977310 | 0.488655 | − | 0.872477i | \(-0.337488\pi\) | ||||
0.488655 | + | 0.872477i | \(0.337488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.9929 | 1.65493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.134626 | −0.00463675 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7790 | −0.439612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.75915 | −0.0604452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −49.4332 | −1.69654 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.08687 | −0.105817 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.5592 | 1.76535 | 0.882677 | − | 0.469979i | \(-0.155739\pi\) | ||||
0.882677 | + | 0.469979i | \(0.155739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −75.3548 | −2.57708 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.94196 | −0.202974 | −0.101487 | − | 0.994837i | \(-0.532360\pi\) | ||||
−0.101487 | + | 0.994837i | \(0.532360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.3698 | −1.47976 | −0.739880 | − | 0.672739i | \(-0.765118\pi\) | ||||
−0.739880 | + | 0.672739i | \(0.765118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.537384 | −0.0183140 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.6702 | −0.363218 | −0.181609 | − | 0.983371i | \(-0.558131\pi\) | ||||
−0.181609 | + | 0.983371i | \(0.558131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3309 | −0.725273 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.48672 | 0.220301 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.7791 | −1.79041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.7505 | −1.14359 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.4032 | −1.40129 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.9976 | 0.642237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.89159 | −0.266480 | −0.133240 | − | 0.991084i | \(-0.542538\pi\) | ||||
−0.133240 | + | 0.991084i | \(0.542538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5298 | 0.523806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.45742 | 0.150174 | 0.0750871 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750871 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7520 | −1.10219 | −0.551096 | − | 0.834442i | \(-0.685790\pi\) | ||||
−0.551096 | + | 0.834442i | \(0.685790\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37.2995 | −1.25381 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.1312 | 0.541633 | 0.270816 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270816 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.9136 | 0.969730 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −77.5518 | −2.59808 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.6060 | 1.72693 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.50596 | 0.217470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.8288 | −0.628675 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0689 | 1.00285 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.54454 | −0.317975 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.7277 | 1.28878 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.5259 | 1.21416 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0929 | 0.567560 | 0.283780 | − | 0.958889i | \(-0.408412\pi\) | ||||
0.283780 | + | 0.958889i | \(0.408412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.9119 | −1.25746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.8125 | −0.358235 | −0.179117 | − | 0.983828i | \(-0.557324\pi\) | ||||
−0.179117 | + | 0.983828i | \(0.557324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.4636 | 0.644150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 97.9507 | 3.23815 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.43564 | 0.311592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −59.0595 | −1.94819 | −0.974097 | − | 0.226132i | \(-0.927392\pi\) | ||||
−0.974097 | + | 0.226132i | \(0.927392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.2396 | −1.91906 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.5651 | 0.643995 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.839685 | −0.0276087 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.4157 | 0.440630 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.9487 | −1.54034 | −0.770168 | − | 0.637841i | \(-0.779828\pi\) | ||||
−0.770168 | + | 0.637841i | \(0.779828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6292 | 0.708870 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −56.0384 | −1.83461 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.2006 | 0.922259 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.2362 | −1.34713 | −0.673564 | − | 0.739129i | \(-0.735237\pi\) | ||||
−0.673564 | + | 0.739129i | \(0.735237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.5016 | 1.32172 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.1514 | −0.526519 | −0.263259 | − | 0.964725i | \(-0.584798\pi\) | ||||
−0.263259 | + | 0.964725i | \(0.584798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.231475 | 0.00753785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 46.6567 | 1.51774 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.3126 | −1.50496 | −0.752478 | − | 0.658618i | \(-0.771142\pi\) | ||||
−0.752478 | + | 0.658618i | \(0.771142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.1537 | 1.01129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 88.8987 | 2.88274 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.4403 | 1.95785 | 0.978926 | − | 0.204214i | \(-0.0654637\pi\) | ||||
0.978926 | + | 0.204214i | \(0.0654637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5673 | −0.503748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 97.8750 | 3.16385 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.6415 | −1.02176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2568 | −0.621188 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 81.3189 | 2.62046 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.2453 | 0.490763 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.3919 | −0.494970 | −0.247485 | − | 0.968892i | \(-0.579604\pi\) | ||||
−0.247485 | + | 0.968892i | \(0.579604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −61.2163 | −1.96655 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.2488 | −0.393083 | −0.196542 | − | 0.980495i | \(-0.562971\pi\) | ||||
−0.196542 | + | 0.980495i | \(0.562971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.9505 | −0.799875 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.12177 | −0.164028 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.75271 | −0.0880669 | −0.0440335 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440335 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38581 | 0.0442906 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 111.689 | 3.56594 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47820 | 0.0471474 | 0.0235737 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235737 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.1326 | −0.800792 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −54.2826 | −1.72784 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.6817 | −0.530447 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5421 | 0.430178 | 0.215089 | − | 0.976594i | \(-0.430996\pi\) | ||||
0.215089 | + | 0.976594i | \(0.430996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.4936 | 1.66583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.8907 | 1.67675 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.2611 | 0.863368 | 0.431684 | − | 0.902025i | \(-0.357920\pi\) | ||||
0.431684 | + | 0.902025i | \(0.357920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.0310 | −0.602113 |
(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 | 4024.2.a.f.1.2 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.32 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.2 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.32 | 33 | 4.3 | odd | 2 |