Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 15x^{7} + 15x^{6} + 66x^{5} - 59x^{4} - 77x^{3} + 34x^{2} + 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.536705\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 0.536705 | 0.309867 | 0.154933 | − | 0.987925i | \(-0.450484\pi\) | ||||
0.154933 | + | 0.987925i | \(0.450484\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.30011 | −1.47585 | −0.737926 | − | 0.674881i | \(-0.764195\pi\) | ||||
−0.737926 | + | 0.674881i | \(0.764195\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71195 | −0.903983 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.77118 | −0.457317 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.13193 | 0.759605 | 0.379803 | − | 0.925068i | \(-0.375992\pi\) | ||||
0.379803 | + | 0.925068i | \(0.375992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.06031 | −0.702082 | −0.351041 | − | 0.936360i | \(-0.614172\pi\) | ||||
−0.351041 | + | 0.936360i | \(0.614172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.536705 | −0.117119 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.420528 | 0.0876862 | 0.0438431 | − | 0.999038i | \(-0.486040\pi\) | ||||
0.0438431 | + | 0.999038i | \(0.486040\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.89071 | 1.17814 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.06563 | −0.589981 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.161852 | 0.0300552 | 0.0150276 | − | 0.999887i | \(-0.495216\pi\) | ||||
0.0150276 | + | 0.999887i | \(0.495216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3651 | 1.86162 | 0.930812 | − | 0.365498i | \(-0.119101\pi\) | ||||
0.930812 | + | 0.365498i | \(0.119101\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.536705 | 0.0934283 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.30011 | 0.557820 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.54945 | 0.747924 | 0.373962 | − | 0.927444i | \(-0.377999\pi\) | ||||
0.373962 | + | 0.927444i | \(0.377999\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.536705 | 0.0859415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.30747 | −1.45358 | −0.726792 | − | 0.686858i | \(-0.758989\pi\) | ||||
−0.726792 | + | 0.686858i | \(0.758989\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24787 | 0.342797 | 0.171398 | − | 0.985202i | \(-0.445171\pi\) | ||||
0.171398 | + | 0.985202i | \(0.445171\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.94972 | 1.33415 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.05740 | 0.300102 | 0.150051 | − | 0.988678i | \(-0.452056\pi\) | ||||
0.150051 | + | 0.988678i | \(0.452056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.68092 | 0.235376 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.66441 | 1.19015 | 0.595074 | − | 0.803671i | \(-0.297123\pi\) | ||||
0.595074 | + | 0.803671i | \(0.297123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.30011 | −0.444986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.64248 | −0.217552 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24396 | 0.552517 | 0.276258 | − | 0.961083i | \(-0.410905\pi\) | ||||
0.276258 | + | 0.961083i | \(0.410905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87493 | −0.880245 | −0.440122 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440122 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.71195 | 0.341673 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.30011 | −0.409328 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.01827 | 0.979588 | 0.489794 | − | 0.871838i | \(-0.337072\pi\) | ||||
0.489794 | + | 0.871838i | \(0.337072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.225699 | 0.0271710 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.2909 | −1.93337 | −0.966686 | − | 0.255967i | \(-0.917606\pi\) | ||||
−0.966686 | + | 0.255967i | \(0.917606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.62059 | 0.540799 | 0.270399 | − | 0.962748i | \(-0.412844\pi\) | ||||
0.270399 | + | 0.962748i | \(0.412844\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.16157 | 0.365067 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.36899 | −0.716567 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.49051 | 0.721167 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.20265 | 0.351536 | 0.175768 | − | 0.984432i | \(-0.443759\pi\) | ||||
0.175768 | + | 0.984432i | \(0.443759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3357 | −1.12107 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0868669 | 0.00931311 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.49762 | 0.582747 | 0.291373 | − | 0.956609i | \(-0.405888\pi\) | ||||
0.291373 | + | 0.956609i | \(0.405888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.56299 | 0.576855 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.0993 | 1.03617 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8560 | 1.10226 | 0.551128 | − | 0.834421i | \(-0.314197\pi\) | ||||
0.551128 | + | 0.834421i | \(0.314197\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.71195 | −0.272561 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.93119 | 0.192161 | 0.0960805 | − | 0.995374i | \(-0.469369\pi\) | ||||
0.0960805 | + | 0.995374i | \(0.469369\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6122 | −1.04565 | −0.522826 | − | 0.852439i | \(-0.675122\pi\) | ||||
−0.522826 | + | 0.852439i | \(0.675122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.77118 | 0.172850 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0451 | −1.26112 | −0.630560 | − | 0.776141i | \(-0.717175\pi\) | ||||
−0.630560 | + | 0.776141i | \(0.717175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3617 | −1.85452 | −0.927258 | − | 0.374423i | \(-0.877841\pi\) | ||||
−0.927258 | + | 0.374423i | \(0.877841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.44171 | 0.231757 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5919 | −1.18454 | −0.592271 | − | 0.805739i | \(-0.701769\pi\) | ||||
−0.592271 | + | 0.805739i | \(0.701769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.38779 | −0.129412 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.71195 | −0.250720 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.13193 | −0.287104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.99536 | −0.450417 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.93943 | −0.262911 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.74259 | 0.775779 | 0.387890 | − | 0.921706i | \(-0.373204\pi\) | ||||
0.387890 | + | 0.921706i | \(0.373204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.20644 | 0.106221 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9292 | −1.30437 | −0.652184 | − | 0.758061i | \(-0.726147\pi\) | ||||
−0.652184 | + | 0.758061i | \(0.726147\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.06031 | 0.265362 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.1169 | 0.870725 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.27810 | 0.450939 | 0.225469 | − | 0.974250i | \(-0.427608\pi\) | ||||
0.225469 | + | 0.974250i | \(0.427608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.44425 | −0.207318 | −0.103659 | − | 0.994613i | \(-0.533055\pi\) | ||||
−0.103659 | + | 0.994613i | \(0.533055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.10421 | 0.0929917 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.534130 | −0.0443571 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.536705 | 0.0442667 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.12900 | 0.174415 | 0.0872073 | − | 0.996190i | \(-0.472206\pi\) | ||||
0.0872073 | + | 0.996190i | \(0.472206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4271 | −0.929921 | −0.464961 | − | 0.885331i | \(-0.653931\pi\) | ||||
−0.464961 | + | 0.885331i | \(0.653931\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.49364 | −0.686670 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −34.2059 | −2.74748 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.35410 | −0.267686 | −0.133843 | − | 0.991003i | \(-0.542732\pi\) | ||||
−0.133843 | + | 0.991003i | \(0.542732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.65023 | 0.368787 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.420528 | −0.0331423 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.25050 | 0.724555 | 0.362278 | − | 0.932070i | \(-0.381999\pi\) | ||||
0.362278 | + | 0.932070i | \(0.381999\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.77118 | −0.137886 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.03829 | 0.0803450 | 0.0401725 | − | 0.999193i | \(-0.487209\pi\) | ||||
0.0401725 | + | 0.999193i | \(0.487209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.29939 | 0.634670 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.5134 | 1.25549 | 0.627744 | − | 0.778420i | \(-0.283979\pi\) | ||||
0.627744 | + | 0.778420i | \(0.283979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.89071 | −0.445296 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.27775 | 0.171206 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.9904 | −1.19518 | −0.597589 | − | 0.801802i | \(-0.703875\pi\) | ||||
−0.597589 | + | 0.801802i | \(0.703875\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.71442 | −0.127432 | −0.0637159 | − | 0.997968i | \(-0.520295\pi\) | ||||
−0.0637159 | + | 0.997968i | \(0.520295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.68981 | −0.272758 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0137 | −1.10383 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.13193 | 0.229030 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.06563 | 0.222992 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.4362 | −1.55107 | −0.775536 | − | 0.631304i | \(-0.782520\pi\) | ||||
−0.775536 | + | 0.631304i | \(0.782520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.23599 | −0.376895 | −0.188447 | − | 0.982083i | \(-0.560346\pi\) | ||||
−0.188447 | + | 0.982083i | \(0.560346\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.77118 | −0.126837 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.58219 | 0.255221 | 0.127610 | − | 0.991824i | \(-0.459269\pi\) | ||||
0.127610 | + | 0.991824i | \(0.459269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.2294 | −0.796029 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.30345 | 0.303542 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.161852 | −0.0113598 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.7157 | 2.14528 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.14045 | −0.0792668 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.06031 | −0.211686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8551 | 1.16035 | 0.580175 | − | 0.814492i | \(-0.302984\pi\) | ||||
0.580175 | + | 0.814492i | \(0.302984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.74339 | −0.599087 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.41821 | −0.505918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.3651 | −0.703628 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.47989 | 0.167575 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.13193 | 0.210677 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7717 | −0.788291 | −0.394146 | − | 0.919048i | \(-0.628959\pi\) | ||||
−0.394146 | + | 0.919048i | \(0.628959\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.9753 | −1.06502 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.66662 | 0.508851 | 0.254426 | − | 0.967092i | \(-0.418114\pi\) | ||||
0.254426 | + | 0.967092i | \(0.418114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.20926 | 0.212074 | 0.106037 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106037 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.536705 | −0.0353126 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.51393 | 0.295717 | 0.147859 | − | 0.989008i | \(-0.452762\pi\) | ||||
0.147859 | + | 0.989008i | \(0.452762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.78963 | −0.442907 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.41827 | −0.222040 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.95772 | −0.191319 | −0.0956595 | − | 0.995414i | \(-0.530496\pi\) | ||||
−0.0956595 | + | 0.995414i | \(0.530496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.904795 | 0.0582830 | 0.0291415 | − | 0.999575i | \(-0.490723\pi\) | ||||
0.0291415 | + | 0.999575i | \(0.490723\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6804 | 0.813446 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.30011 | −0.210836 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.06031 | −0.194723 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.71887 | 0.108929 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.70496 | −0.549452 | −0.274726 | − | 0.961522i | \(-0.588587\pi\) | ||||
−0.274726 | + | 0.961522i | \(0.588587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.420528 | 0.0264384 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.54723 | −0.347381 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.4913 | −0.966324 | −0.483162 | − | 0.875531i | \(-0.660512\pi\) | ||||
−0.483162 | + | 0.875531i | \(0.660512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.54945 | −0.282689 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.438935 | −0.0271694 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0389 | −0.865674 | −0.432837 | − | 0.901472i | \(-0.642487\pi\) | ||||
−0.432837 | + | 0.901472i | \(0.642487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.5935 | −1.75648 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.95060 | 0.180574 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8948 | −0.664265 | −0.332133 | − | 0.943233i | \(-0.607768\pi\) | ||||
−0.332133 | + | 0.943233i | \(0.607768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7704 | −0.836491 | −0.418246 | − | 0.908334i | \(-0.637355\pi\) | ||||
−0.418246 | + | 0.908334i | \(0.637355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.536705 | −0.0324828 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.89071 | 0.355223 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.8078 | −1.61072 | −0.805361 | − | 0.592785i | \(-0.798029\pi\) | ||||
−0.805361 | + | 0.592785i | \(0.798029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.1096 | −1.68288 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.68324 | −0.279379 | −0.139689 | − | 0.990195i | \(-0.544610\pi\) | ||||
−0.139689 | + | 0.990195i | \(0.544610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.5920 | 1.04573 | 0.522867 | − | 0.852415i | \(-0.324863\pi\) | ||||
0.522867 | + | 0.852415i | \(0.324863\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.42036 | 0.321075 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.30747 | 0.549403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.19099 | −0.423000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.82645 | 0.341552 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2243 | −0.714151 | −0.357076 | − | 0.934075i | \(-0.616226\pi\) | ||||
−0.357076 | + | 0.934075i | \(0.616226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0055 | −0.815433 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.06563 | −0.177886 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.420528 | 0.0243198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.24787 | −0.129565 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03648 | 0.0595443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.6880 | 1.29911 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8725 | 0.677602 | 0.338801 | − | 0.940858i | \(-0.389979\pi\) | ||||
0.338801 | + | 0.940858i | \(0.389979\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.69562 | −0.324013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2113 | 0.862552 | 0.431276 | − | 0.902220i | \(-0.358064\pi\) | ||||
0.431276 | + | 0.902220i | \(0.358064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.34839 | 0.302309 | 0.151155 | − | 0.988510i | \(-0.451701\pi\) | ||||
0.151155 | + | 0.988510i | \(0.451701\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.94972 | −0.504260 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.40846 | −0.0791071 | −0.0395535 | − | 0.999217i | \(-0.512594\pi\) | ||||
−0.0395535 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.161852 | 0.00906199 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.00138 | −0.390779 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58467 | −0.533306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.89071 | 0.326758 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.3915 | −0.574653 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.05740 | −0.113428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2286 | 1.05690 | 0.528451 | − | 0.848964i | \(-0.322773\pi\) | ||||
0.528451 | + | 0.848964i | \(0.322773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.3379 | −0.676111 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.4612 | −1.44573 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.70454 | −0.0928523 | −0.0464262 | − | 0.998922i | \(-0.514783\pi\) | ||||
−0.0464262 | + | 0.998922i | \(0.514783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75811 | −0.367050 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3651 | 0.561301 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.744832 | −0.0401004 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.17222 | 0.0629282 | 0.0314641 | − | 0.999505i | \(-0.489983\pi\) | ||||
0.0314641 | + | 0.999505i | \(0.489983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.55082 | −0.243600 | −0.121800 | − | 0.992555i | \(-0.538867\pi\) | ||||
−0.121800 | + | 0.992555i | \(0.538867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.06563 | −0.163631 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.2153 | −1.12918 | −0.564589 | − | 0.825372i | \(-0.690965\pi\) | ||||
−0.564589 | + | 0.825372i | \(0.690965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 53.7616 | 2.85337 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.68092 | −0.0889639 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.225905 | −0.0119228 | −0.00596140 | − | 0.999982i | \(-0.501898\pi\) | ||||
−0.00596140 | + | 0.999982i | \(0.501898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.63453 | −0.507080 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.536705 | 0.0281697 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2484 | −0.798140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6102 | −0.553845 | −0.276923 | − | 0.960892i | \(-0.589315\pi\) | ||||
−0.276923 | + | 0.960892i | \(0.589315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.2414 | 1.31401 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.66441 | −0.449834 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.4566 | −1.57698 | −0.788492 | − | 0.615046i | \(-0.789138\pi\) | ||||
−0.788492 | + | 0.615046i | \(0.789138\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.57761 | −0.0814673 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.161852 | 0.00833582 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.665050 | 0.0341613 | 0.0170807 | − | 0.999854i | \(-0.494563\pi\) | ||||
0.0170807 | + | 0.999854i | \(0.494563\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.69219 | 0.240388 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.68444 | 0.239364 | 0.119682 | − | 0.992812i | \(-0.461813\pi\) | ||||
0.119682 | + | 0.992812i | \(0.461813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.30011 | 0.168189 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.09611 | −0.309882 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.8620 | −0.956342 | −0.478171 | − | 0.878267i | \(-0.658700\pi\) | ||||
−0.478171 | + | 0.878267i | \(0.658700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.31707 | 0.0666069 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.01256 | −0.404180 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.0183 | 1.05755 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.5673 | −1.93564 | −0.967818 | − | 0.251653i | \(-0.919026\pi\) | ||||
−0.967818 | + | 0.251653i | \(0.919026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.64248 | 0.0822269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.2031 | 1.45833 | 0.729165 | − | 0.684337i | \(-0.239908\pi\) | ||||
0.729165 | + | 0.684337i | \(0.239908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3651 | 0.516322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.4194 | −1.06434 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.54945 | 0.225508 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.5897 | −1.46312 | −0.731559 | − | 0.681778i | \(-0.761207\pi\) | ||||
−0.731559 | + | 0.681778i | \(0.761207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.83278 | 0.139731 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.24396 | −0.208832 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.5691 | −0.518815 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.31184 | −0.0642410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.03316 | 0.294739 | 0.147370 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1980 | −0.691969 | −0.345985 | − | 0.938240i | \(-0.612455\pi\) | ||||
−0.345985 | + | 0.938240i | \(0.612455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.57956 | −0.271287 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.4493 | 0.894923 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.87493 | 0.332701 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.536705 | 0.0259123 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.47227 | −0.408095 | −0.204048 | − | 0.978961i | \(-0.565410\pi\) | ||||
−0.204048 | + | 0.978961i | \(0.565410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.72017 | 0.130723 | 0.0653616 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653616 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.286670 | −0.0137448 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.28694 | −0.0615629 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.7423 | −1.18089 | −0.590444 | − | 0.807079i | \(-0.701047\pi\) | ||||
−0.590444 | + | 0.807079i | \(0.701047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.71195 | −0.129140 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.0356 | −0.904411 | −0.452205 | − | 0.891914i | \(-0.649363\pi\) | ||||
−0.452205 | + | 0.891914i | \(0.649363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.1427 | −0.860049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.14264 | 0.0540452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6411 | 0.879728 | 0.439864 | − | 0.898064i | \(-0.355027\pi\) | ||||
0.439864 | + | 0.898064i | \(0.355027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.30747 | −0.438272 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.13296 | −0.288151 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.30011 | 0.154711 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.21145 | −0.0566693 | −0.0283346 | − | 0.999598i | \(-0.509020\pi\) | ||||
−0.0283346 | + | 0.999598i | \(0.509020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.60135 | −0.448152 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9911 | −0.977651 | −0.488826 | − | 0.872381i | \(-0.662575\pi\) | ||||
−0.488826 | + | 0.872381i | \(0.662575\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4073 | 0.669563 | 0.334781 | − | 0.942296i | \(-0.391338\pi\) | ||||
0.334781 | + | 0.942296i | \(0.391338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.3585 | −0.851353 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.23478 | 0.288511 | 0.144256 | − | 0.989540i | \(-0.453921\pi\) | ||||
0.144256 | + | 0.989540i | \(0.453921\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.01827 | −0.370250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.80016 | −0.0829470 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.24787 | 0.103357 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0274 | −0.827152 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.4974 | −1.07587 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.12161 | 0.142630 | 0.0713151 | − | 0.997454i | \(-0.477280\pi\) | ||||
0.0713151 | + | 0.997454i | \(0.477280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.54945 | 0.207437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.225699 | −0.0102697 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.8259 | −1.62677 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.5739 | 1.79327 | 0.896633 | − | 0.442775i | \(-0.146006\pi\) | ||||
0.896633 | + | 0.442775i | \(0.146006\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.96479 | 0.224515 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0328 | 1.21997 | 0.609986 | − | 0.792412i | \(-0.291175\pi\) | ||||
0.609986 | + | 0.792412i | \(0.291175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.506910 | 0.0228301 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.94972 | 0.402260 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.2909 | 0.730746 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.83496 | 0.305975 | 0.152987 | − | 0.988228i | \(-0.451111\pi\) | ||||
0.152987 | + | 0.988228i | \(0.451111\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.557253 | 0.0248962 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2970 | 0.548298 | 0.274149 | − | 0.961687i | \(-0.411604\pi\) | ||||
0.274149 | + | 0.961687i | \(0.411604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.37315 | −0.283601 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.536705 | 0.0238359 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.1664 | −1.95764 | −0.978822 | − | 0.204715i | \(-0.934373\pi\) | ||||
−0.978822 | + | 0.204715i | \(0.934373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.62059 | −0.204403 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.38176 | 0.414215 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.0214 | 1.54323 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.05740 | 0.0904842 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.86280 | 0.389034 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.613678 | 0.0268857 | 0.0134429 | − | 0.999910i | \(-0.495721\pi\) | ||||
0.0134429 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.2826 | 1.41162 | 0.705809 | − | 0.708402i | \(-0.250584\pi\) | ||||
0.705809 | + | 0.708402i | \(0.250584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.16157 | −0.137982 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.4628 | 1.41410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8232 | −0.992311 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.5094 | −0.499465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.30747 | −0.403151 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.0503 | 1.86123 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.58212 | −0.370346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.1328 | 1.85443 | 0.927213 | − | 0.374536i | \(-0.122198\pi\) | ||||
0.927213 | + | 0.374536i | \(0.122198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.920136 | −0.0394868 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 63.8958 | 2.73699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.5532 | −1.39188 | −0.695938 | − | 0.718102i | \(-0.745011\pi\) | ||||
−0.695938 | + | 0.718102i | \(0.745011\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.6445 | 0.795726 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.495317 | −0.0211012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.36899 | 0.270837 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.05790 | −0.342039 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.2761 | −1.36758 | −0.683791 | − | 0.729678i | \(-0.739670\pi\) | ||||
−0.683791 | + | 0.729678i | \(0.739670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24787 | 0.0950747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.68092 | 0.0709686 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.15428 | −0.132937 | −0.0664684 | − | 0.997789i | \(-0.521173\pi\) | ||||
−0.0664684 | + | 0.997789i | \(0.521173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41.5545 | 1.74821 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.49051 | −0.272576 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.3859 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678603\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.4876 | 1.56881 | 0.784404 | − | 0.620251i | \(-0.212969\pi\) | ||||
0.784404 | + | 0.620251i | \(0.212969\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.5049 | −0.480625 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47721 | 0.103307 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.3663 | 0.639706 | 0.319853 | − | 0.947467i | \(-0.396366\pi\) | ||||
0.319853 | + | 0.947467i | \(0.396366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.81018 | −0.116787 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.20265 | −0.132868 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.66441 | 0.358843 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.94972 | 0.370025 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.9838 | 1.56776 | 0.783880 | − | 0.620912i | \(-0.213238\pi\) | ||||
0.783880 | + | 0.620912i | \(0.213238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.7203 | −1.30701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.92258 | 0.0790843 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.2380 | 0.666813 | 0.333407 | − | 0.942783i | \(-0.391802\pi\) | ||||
0.333407 | + | 0.942783i | \(0.391802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3357 | 0.423723 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.02686 | −0.246663 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.3847 | −0.832898 | −0.416449 | − | 0.909159i | \(-0.636725\pi\) | ||||
−0.416449 | + | 0.909159i | \(0.636725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9836 | 1.10068 | 0.550342 | − | 0.834939i | \(-0.314497\pi\) | ||||
0.550342 | + | 0.834939i | \(0.314497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.7451 | −0.885531 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.30011 | −0.134168 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.2528 | −1.22792 | −0.613961 | − | 0.789337i | \(-0.710425\pi\) | ||||
−0.613961 | + | 0.789337i | \(0.710425\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0868669 | −0.00352002 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.05740 | 0.0832334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.3824 | −0.944407 | −0.472203 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472203 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.4852 | 0.664749 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.5404 | −1.83339 | −0.916694 | − | 0.399590i | \(-0.869152\pi\) | ||||
−0.916694 | + | 0.399590i | \(0.869152\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6923 | 0.469953 | 0.234977 | − | 0.972001i | \(-0.424499\pi\) | ||||
0.234977 | + | 0.972001i | \(0.424499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.28918 | −0.0517331 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.49762 | −0.220258 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.7531 | −0.790124 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.64248 | −0.0655943 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2486 | 0.568127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3113 | −0.848391 | −0.424195 | − | 0.905571i | \(-0.639443\pi\) | ||||
−0.424195 | + | 0.905571i | \(0.639443\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.04619 | 0.359554 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.8515 | −1.14494 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44.1800 | 1.74773 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1727 | −0.757277 | −0.378638 | − | 0.925545i | \(-0.623608\pi\) | ||||
−0.378638 | + | 0.925545i | \(0.623608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.4479 | 0.885261 | 0.442630 | − | 0.896704i | \(-0.354045\pi\) | ||||
0.442630 | + | 0.896704i | \(0.354045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.98139 | −0.156767 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0810 | 0.632210 | 0.316105 | − | 0.948724i | \(-0.397625\pi\) | ||||
0.316105 | + | 0.948724i | \(0.397625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.24396 | 0.166590 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.56299 | −0.218031 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.8056 | 1.59685 | 0.798423 | − | 0.602097i | \(-0.205668\pi\) | ||||
0.798423 | + | 0.602097i | \(0.205668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.2679 | 1.92506 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.5308 | −0.488873 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.0702 | −1.52196 | −0.760980 | − | 0.648776i | \(-0.775281\pi\) | ||||
−0.760980 | + | 0.648776i | \(0.775281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.68059 | 0.298740 | 0.149370 | − | 0.988781i | \(-0.452275\pi\) | ||||
0.149370 | + | 0.988781i | \(0.452275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.68092 | 0.0652816 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0993 | −0.391636 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0680634 | 0.00263543 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.31792 | −0.244265 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.87493 | −0.265404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1821 | 0.700870 | 0.350435 | − | 0.936587i | \(-0.386034\pi\) | ||||
0.350435 | + | 0.936587i | \(0.386034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0587 | −0.695081 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.4832 | −0.479769 | −0.239885 | − | 0.970801i | \(-0.577110\pi\) | ||||
−0.239885 | + | 0.970801i | \(0.577110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8560 | −0.416614 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.11471 | 0.157676 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.3127 | −1.27468 | −0.637338 | − | 0.770584i | \(-0.719965\pi\) | ||||
−0.637338 | + | 0.770584i | \(0.719965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.4183 | −0.665519 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.72242 | 0.0657146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.66441 | 0.330088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4935 | 1.65457 | 0.827285 | − | 0.561782i | \(-0.189884\pi\) | ||||
0.827285 | + | 0.561782i | \(0.189884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.71195 | 0.103018 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.06628 | 0.305971 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.1504 | −1.10415 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.42265 | 0.0916330 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4772 | 1.00003 | 0.500016 | − | 0.866016i | \(-0.333328\pi\) | ||||
0.500016 | + | 0.866016i | \(0.333328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.9227 | −0.525104 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.64403 | −0.137242 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.93119 | −0.0726300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.7514 | 1.71823 | 0.859115 | − | 0.511783i | \(-0.171015\pi\) | ||||
0.859115 | + | 0.511783i | \(0.171015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.2724 | 0.647764 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.35881 | 0.163239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.30011 | −0.123417 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.58742 | −0.0592833 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5391 | −0.952449 | −0.476225 | − | 0.879324i | \(-0.657995\pi\) | ||||
−0.476225 | + | 0.879324i | \(0.657995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6122 | 0.395219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.485608 | 0.0180599 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.953425 | 0.0354093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.0729 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.6659 | −0.469108 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.04018 | 0.260390 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.4455 | 1.60469 | 0.802347 | − | 0.596857i | \(-0.203584\pi\) | ||||
0.802347 | + | 0.596857i | \(0.203584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.77118 | −0.0653311 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.01827 | 0.295357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9020 | −0.916035 | −0.458018 | − | 0.888943i | \(-0.651440\pi\) | ||||
−0.458018 | + | 0.888943i | \(0.651440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.64248 | −0.0603380 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.8381 | −1.42483 | −0.712416 | − | 0.701758i | \(-0.752399\pi\) | ||||
−0.712416 | + | 0.701758i | \(0.752399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.02593 | −0.257410 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.68541 | −0.317782 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.0451 | 0.476658 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.6813 | −1.73992 | −0.869958 | − | 0.493125i | \(-0.835854\pi\) | ||||
−0.869958 | + | 0.493125i | \(0.835854\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.67199 | −0.170257 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.7105 | 1.37243 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.19558 | 0.297873 | 0.148937 | − | 0.988847i | \(-0.452415\pi\) | ||||
0.148937 | + | 0.988847i | \(0.452415\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.225699 | 0.00819237 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5644 | −1.03546 | −0.517730 | − | 0.855544i | \(-0.673223\pi\) | ||||
−0.517730 | + | 0.855544i | \(0.673223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3617 | 0.700941 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 28.0299 | 1.01342 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.24396 | 0.153241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.21584 | 0.224149 | 0.112075 | − | 0.993700i | \(-0.464250\pi\) | ||||
0.112075 | + | 0.993700i | \(0.464250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.31428 | −0.299431 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.97637 | 0.214955 | 0.107478 | − | 0.994208i | \(-0.465723\pi\) | ||||
0.107478 | + | 0.994208i | \(0.465723\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 61.0577 | 2.19326 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.44171 | −0.0875958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.4837 | 1.02054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.2909 | −0.582933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.496179 | −0.0177320 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0689 | 0.395065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.13999 | −0.0762824 | −0.0381412 | − | 0.999272i | \(-0.512144\pi\) | ||||
−0.0381412 | + | 0.999272i | \(0.512144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.53473 | −0.268243 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.5919 | 0.447715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.87493 | −0.244136 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.3462 | −0.544275 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.3602 | −0.579509 | −0.289754 | − | 0.957101i | \(-0.593574\pi\) | ||||
−0.289754 | + | 0.957101i | \(0.593574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.44363 | 0.227959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.9093 | −0.526793 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.62059 | 0.163057 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38779 | 0.0489131 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.84727 | −0.205834 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.7563 | 1.92513 | 0.962564 | − | 0.271055i | \(-0.0873724\pi\) | ||||
0.962564 | + | 0.271055i | \(0.0873724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8235 | 1.32816 | 0.664082 | − | 0.747660i | \(-0.268823\pi\) | ||||
0.664082 | + | 0.747660i | \(0.268823\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.39063 | −0.259201 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.5277 | −1.06934 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.87917 | −0.240672 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.71195 | 0.0947631 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.7410 | −0.758767 | −0.379384 | − | 0.925239i | \(-0.623864\pi\) | ||||
−0.379384 | + | 0.925239i | \(0.623864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2535 | 0.949997 | 0.474998 | − | 0.879987i | \(-0.342449\pi\) | ||||
0.474998 | + | 0.879987i | \(0.342449\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.16157 | 0.110072 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.6586 | −0.648821 | −0.324411 | − | 0.945916i | \(-0.605166\pi\) | ||||
−0.324411 | + | 0.945916i | \(0.605166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.1758 | −1.04805 | −0.524024 | − | 0.851704i | \(-0.675570\pi\) | ||||
−0.524024 | + | 0.851704i | \(0.675570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.3878 | −0.499109 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.13193 | 0.108515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.42646 | −0.118577 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.7755 | −1.09832 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.8451 | −0.857749 | −0.428875 | − | 0.903364i | \(-0.641090\pi\) | ||||
−0.428875 | + | 0.903364i | \(0.641090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9738 | −0.999097 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.51352 | −0.0865702 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.30011 | −0.113527 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.44168 | 0.324038 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.91317 | 0.0655826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.25064 | 0.248257 | 0.124129 | − | 0.992266i | \(-0.460386\pi\) | ||||
0.124129 | + | 0.992266i | \(0.460386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.3889 | −0.936680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.30714 | −0.283767 | −0.141883 | − | 0.989883i | \(-0.545316\pi\) | ||||
−0.141883 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.2253 | −0.894797 | −0.447399 | − | 0.894335i | \(-0.647649\pi\) | ||||
−0.447399 | + | 0.894335i | \(0.647649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.99536 | 0.170242 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.44686 | −0.253494 | −0.126747 | − | 0.991935i | \(-0.540454\pi\) | ||||
−0.126747 | + | 0.991935i | \(0.540454\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −54.4959 | −1.85291 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.85944 | −0.131073 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.36899 | −0.216053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.01827 | 0.271689 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.4408 | −0.996421 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.93943 | 0.0993710 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.850256 | −0.0287111 | −0.0143556 | − | 0.999897i | \(-0.504570\pi\) | ||||
−0.0143556 | + | 0.999897i | \(0.504570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.56084 | −0.221292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.5341 | 0.354903 | 0.177451 | − | 0.984130i | \(-0.443215\pi\) | ||||
0.177451 | + | 0.984130i | \(0.443215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.16673 | −0.173874 | −0.0869372 | − | 0.996214i | \(-0.527708\pi\) | ||||
−0.0869372 | + | 0.996214i | \(0.527708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.51683 | −0.252675 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.84275 | 0.330487 | 0.165244 | − | 0.986253i | \(-0.447159\pi\) | ||||
0.165244 | + | 0.986253i | \(0.447159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.74259 | −0.293217 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.49051 | 0.217440 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.29627 | −0.210696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.7700 | 1.76391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.225699 | 0.00753588 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.67761 | 0.0559515 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.1363 | 0.904043 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.20644 | −0.0401479 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.65777 | 0.188070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.6231 | 0.518755 | 0.259377 | − | 0.965776i | \(-0.416483\pi\) | ||||
0.259377 | + | 0.965776i | \(0.416483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.23730 | −0.173710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.4772 | 0.678439 | 0.339220 | − | 0.940707i | \(-0.389837\pi\) | ||||
0.339220 | + | 0.940707i | \(0.389837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.20265 | 0.105992 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.1768 | 0.402551 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9292 | 0.493005 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.74457 | −0.123522 | −0.0617609 | − | 0.998091i | \(-0.519672\pi\) | ||||
−0.0617609 | + | 0.998091i | \(0.519672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.37205 | 0.209966 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.2909 | −0.536221 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.7995 | 0.881161 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.7798 | 0.945252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.7883 | 0.944514 | 0.472257 | − | 0.881461i | \(-0.343439\pi\) | ||||
0.472257 | + | 0.881461i | \(0.343439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.06031 | −0.100297 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.16396 | 0.267276 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3357 | −0.338014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.2426 | −1.77203 | −0.886014 | − | 0.463659i | \(-0.846536\pi\) | ||||
−0.886014 | + | 0.463659i | \(0.846536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.87051 | 0.0936755 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2047 | −0.430462 | −0.215231 | − | 0.976563i | \(-0.569050\pi\) | ||||
−0.215231 | + | 0.976563i | \(0.569050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.91405 | −0.127459 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.1169 | −0.329103 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.9688 | −1.42879 | −0.714397 | − | 0.699740i | \(-0.753299\pi\) | ||||
−0.714397 | + | 0.699740i | \(0.753299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.62059 | 0.149991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.755928 | −0.0245126 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.2086 | −1.17291 | −0.586456 | − | 0.809981i | \(-0.699477\pi\) | ||||
−0.586456 | + | 0.809981i | \(0.699477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.7419 | 2.28915 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0868669 | 0.00280801 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.27810 | −0.170439 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.4350 | 2.46565 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.3777 | 1.14003 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.2793 | 0.556241 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.31230 | 0.267306 | 0.133653 | − | 0.991028i | \(-0.457329\pi\) | ||||
0.133653 | + | 0.991028i | \(0.457329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.14414 | −0.165254 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.7323 | 1.62808 | 0.814039 | − | 0.580810i | \(-0.197264\pi\) | ||||
0.814039 | + | 0.580810i | \(0.197264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.44425 | 0.0783590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.16157 | 0.101251 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.5080 | 0.368175 | 0.184087 | − | 0.982910i | \(-0.441067\pi\) | ||||
0.184087 | + | 0.982910i | \(0.441067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.49762 | 0.175705 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52.5080 | 1.67645 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.6057 | 0.370164 | 0.185082 | − | 0.982723i | \(-0.440745\pi\) | ||||
0.185082 | + | 0.982723i | \(0.440745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.8216 | −0.376668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.10421 | −0.0351475 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.945292 | 0.0300585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9015 | 1.52164 | 0.760821 | − | 0.648962i | \(-0.224796\pi\) | ||||
0.760821 | + | 0.648962i | \(0.224796\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3201 | 0.327498 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.0581 | 1.17482 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.76268 | 0.0558246 | 0.0279123 | − | 0.999610i | \(-0.491114\pi\) | ||||
0.0279123 | + | 0.999610i | \(0.491114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.9469 | −0.441261 |
(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 | 8008.2.a.p.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.p.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |